Satellite Remote Sensing for Soil Moisture Estimation: Gumara Catchment, Ethiopia

Dagnenet Fenta Mekonnen March, 2009

Satellite remote sensing for soil moisture estimation: Gumara catchment, Ethiopia By Dagnenet Fenta Mekonnen

Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation, Specialisation: (Integrated Watershed Modelling and Management)

Thesis Assessment Board Chairman External Examiner First Supervisor Second Supervisor Member

Prof. Dr. Ing. Wout Verhoef Drs. Jennifer Grant Dr. Ir. Christiaan van der Tol Dr. Ing. T.H.M. Rientjes Dr. Zoltan Vekerdy

WREM Departement, ITC, Enschede Vrije University, Amsterdam WREM Department, ITC, Enschede WREM Department, ITC, Enschede WREM Department, ITC, Enschede

INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS

Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.

Abstract Soil moisture is an important variable in hydrology: it affects the partitioning of rainfall into runoff and infiltration, and the partitioning of incoming solar radiation into latent and sensible heat. Soil moisture is however difficult to measure at the spatial scale of a catchment. The conventional point measurement based methods such as the neutron probe or gravimetric method are not appropriate for understanding of the spatial and temporal behaviour of soil moisture. Due to the heterogeneity of soil type, land use and topography, soil moisture may change considerably in space and time. Soil moisture can also be measured by microwave remote sensing under some topographic and vegetation cover conditions, but the spatial resolution for passive microwave and temporal resolution for active microwave commonly is low and the method cannot be applied in densely vegetated areas. An alternative approach based on optical and thermal remote sensing (the triangle method) has recently been proposed and tested to estimate soil moisture at a resolution high enough to serve applications such as semi or fully distributed hydrological modelling. This approach is based on correlating Normalized Difference Vegetation Index (NDVI) and land surface temperature (LST) retrieved from remote sensing to the ground measured soil moisture. In this study, the triangle method was tested for the Gumara catchment in northwest Ethiopia. Observed soil moisture was regressed with scaled NDVI and LST retrieved from atmospherically corrected MODIS images at 1km resolution by applying 2nd and 3rd order polynomial relations, and maps of soil moisture were produced for the catchment for 9 days in September 2008. A total of 49 sampling schemes using gravimetric and indirect soil moisture measurements by theta probe were carried out during a field campaign in September 2008. A field station provided continuous radiometric surface temperature data was installed in the study area during field campaign. MODIS Aqua and Terra images were collected for 9 days from September 18, 2008 to September 29, 2008. For LST, a comparison was made between values computed using the split window method and the MODIS LST product. The latter was used for further analysis, because it correlated well with the ground measurements. Both actual LST from the MODIS product as well as elevation corrected potential surface temperature were used. From the ground based measurements of soil moisture, 35 sampling points were used for calibration, and 14 sampling points for validation. Ground measured soil moisture compared well with simulated soil moisture R2 greater than 0.7 and RMSE of 0.045 is obtained. Applying the potential surface temperature could minimize the topographic effect that is induced from LST on the simulated soil moisture, especially on high elevated areas. Statistical spatio-temporal analysis was done to see the temporal as well as the spatial variability of soil moisture in the catchment. According to the statistical spatio-temporal analysis, the high elevated area resembles high mean soil moisture, low coefficient of variability and time stable condition. But after elevation correction the high elevated area resembles low soil moisture than low elevated area. Also, elevation is found to be the dominant terrain controlling factor for the simulated soil moisture simulated by the developed algorithm. The temporal variability of soil moisture among the pixels in a catchment is high, as compared to the spatial variability of the catchment during the study period. Key words: Triangle method, LST, NDVI, potential surface temperature, soil moisture. i

Acknowledgements My greatest thanks go to the Almighty God; I don’t have sufficient words to praise you. Your grace was enough for me. I would like to express my sincere and heartfelt gratitude to the Netherlands Government through the Netherlands Fellowship Programme (NFP) for granting me the opportunity to pursue this course of study without which I would not have realized my dream to further my studies. I am tremendously grateful thanks to my first supervisor Dr. Ir. Christiaan van der Tol for his earnest guidance, critical comments and timely suggestions that made this research a success. His support and advice makes me motivated and energetic all the way through this study. My special thanks also go to my second supervisor, Dr. Ing. T.H.M. Rientjes for all his kind advice and valuable comments starting from proposal writing and field work till the end of the course research. Equally important, I extend my deep gratitude to Dr. Zoltan Vekerdy for all his effort to support and comment in revising the research critically. I would like to express my gratitude to my employer the Amhara National Regional State Water Resource Development Bureau for providing the logistics for my field work and permitting me to pursue this study. I also extend my special thanks to Ato Muche, the driver of my employer for his kind assistance during field work and also for the WRD Bureau soil laboratory technicians for their valuable contribution. I earnestly thank to all those WREM staffs that have indeed contribute in my studies in the department either teaching me or contributing through providing me technical advice and study material. My heartfelt gratitude goes to my wife Yenezewud Belay for your patience, support and encouragement and, those special words especially through the hardest time gave me the courage to continue. Special thanks go to all my dear parents who have been my mentors always supportive and using me on. Last but not least, I would like to extend my earnest thanks to my classmates, friends and colleagues who put a drop of contribution in any ways in my study.

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Table of contents 1.

Introduction......................................................................................................................... 1 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7.

2.

Description of study area .................................................................................................... 5 2.1. 2.2. 2.3. 2.4. 2.5.

3.

Climate setting of the study area................................................................................. 5 Topography................................................................................................................. 7 Hydrology ................................................................................................................... 8 Soil.............................................................................................................................. 9 Land cover ................................................................................................................ 11

Field work and materials used .......................................................................................... 13 3.1. 3.2. 3.3. 3.4.

4.

Background................................................................................................................. 1 Relevance of the study................................................................................................ 2 Research problem ....................................................................................................... 2 Objective of the study................................................................................................. 3 Research questions...................................................................................................... 3 Hypothesis .................................................................................................................. 4 Thesis outlines ............................................................................................................ 4

Soil moisture measurement....................................................................................... 13 Air and surface temperature measurements.............................................................. 15 MODIS sensor .......................................................................................................... 16 Acquiring of MODIS image ..................................................................................... 17

Literature review about remote sensing and triangle method for soil moisture................ 19 4.1. Remote sensing of soil moisture............................................................................... 19 4.1.1. Gamma radiation techniques .......................................................................... 20 4.1.2. Reflected solar techniques.............................................................................. 20 4.1.3. Thermal technique.......................................................................................... 20 4.1.4. Microwave techniques.................................................................................... 21 4.2. Soil moisture quantification using the triangle method............................................ 23 4.2.1. Description of triangle method....................................................................... 23 4.2.2. Previous studies of soil moisture using the triangle method .......................... 24

5.

Methodology..................................................................................................................... 27 5.1. General approach of the triangle method.................................................................. 27 5.2. Remote sensing......................................................................................................... 30 5.2.1. NDVI (Normalized Difference Vegetation Index) ......................................... 31 5.2.2. Land Surface Temperature computation using split window techniques....... 35 5.2.3. Land surface temperature products from MODIS sensor............................... 39 5.2.4. Potential temperature...................................................................................... 41 5.3. Algorithm Development ........................................................................................... 41 5.4. Statistical analysis..................................................................................................... 43

6.

Results, analysis and discussion ....................................................................................... 45 6.1. Observed soil moisture ............................................................................................. 45 6.2. Remote sensing measurements ................................................................................. 45 iii

6.3. 6.4.

6.5. 6.6.

6.7. 6.8. 7.

6.2.1. NDVI ..............................................................................................................45 6.2.2. LST (Land Surface Temperature)...................................................................47 Scatter plots of NDVI and LST.................................................................................49 Simulated soil moisture.............................................................................................51 6.4.1. Cross correlation between simulated and observed soil moisture ..................53 6.4.2. Sensitivity Analysis ........................................................................................54 6.4.3. Comparisons of the algorithms.......................................................................56 Statistical analysis and results of spatio-temporal variation of soil moisture ...........57 Elevation correction for the simulated soil moisture ................................................61 6.6.1. Potential surface temperature .........................................................................61 6.6.2. Simulated soil moisture using 2nd order relation to NDVI and potential temperature .....................................................................................................61 Simulated soil moisture at different elevation zones before and after correction.....63 Discussion .................................................................................................................66

Conclusion and Recommendations...................................................................................68 7.1. Conclusion ................................................................................................................68 7.2. Recommendation ......................................................................................................70

References .................................................................................................................................71 Annexes.....................................................................................................................................73 Appendix-1 DEM hydro processing procedure.................................................................73 Appendix-2 Ground observed soil moisture data..............................................................74 Appendix-3 Techniques or methods used to measure soil moisture content ....................75 Appendix-4 ILWIS script to retrieve LST from MODIS ..................................................77 Appendix-5 Least square method of 2nd order polynomial relation algorithm..................79 Appendix-6 Least square method of 3rd order polynomial relation NDVI*algorithm ......81 Appendix-7 Least square method of 3rd order polynomial relation Fr algorithm..............83 Appendix-8 NDVI map .....................................................................................................85 Appendix-9 MODIS LST product and potential surface temperature...............................86 Appendix-10 Simulated soil moisture maps after elevation correction ............................88 Appendix-11 Least square method 2nd order relation with potential temperature ............89

iv

List of figures Figure 2-1 Location maps of the study area and soil moisture sample points ........................................5 Figure 2-2 Monthly average rainfall in the Gumara catchment from (2004-2007) ................................6 Figure 2-3 Average measured yearly rainfall at 3 stations and areal rainfall of Gumara catchment (2004-2007)..............................................................................................................................................6 Figure 2-4 Daily maximum temperature at three stations (2003-2007)..................................................7 Figure 2-5 Daily minimum temperatures at three stations (2003-2007) .................................................7 Figure 2-6 Daily average temperatures for three stations (2003-2007) ..................................................7 Figure 2-7 Digital Elevation Model in m.a.s.l of the study area (processed from SRTM data) .............8 Figure 2-8 Monthly average daily flow of the Gumara River and areal average rainfall of the Gumara catchment .................................................................................................................................................9 Figure 2-9 Annual average daily flow of the Gumara River...................................................................9 Figure 2-10 Major soil groups according to the FAO classification.....................................................10 Figure 2-11 Land cover map of the Gumara catchment.........................................................................12 Figure 3-1 Sampling schemes at different land covers and sites of in-situ measurements of soil moisture:.................................................................................................................................................14 Figure 3-2 Surface temperatures from infrared gun and remote sensing..............................................15 Figure 3-3 Weather station and radiometer installed during field work ................................................16 Figure 3-4 Air temperature obtained from weather station and Sonic Anemometer. ...........................16 Figure 3-5 Terra satellite-right and Aqua-left ........................................................................................17 Figure 4-1 Universal triangle: schematic relationship between soil moisture, temperature and NDVI , source (Chauhan et al., 2003).................................................................................................................23 Figure 5-1 Flow diagram of the general procedure for soil moisture estimation from remote sensing using triangle method .............................................................................................................................30 Figure 5-2 General procedures to retrieve NDVI from MODIS ............................................................34 Figure 5-3 Methodology to retrieve land surface temperature (modified after Mao et al., 2005).........36 Figure 5-4 MODIS sinusoidal grid system.............................................................................................40 Figure 6-1 Correlation of soil moisture between direct and indirect methods.......................................45 Figure 6-2 Average NDVIs of the study area before and after atmospheric correction ........................46 Figure 6-3 NDVI map from MODIS data Sep.23, 2008 before atmospheric correction .......................47 Figure 6-4 NDVI map from MODIS data Sep.23, 2008 after atmospheric correction ..........................47 Figure 6-5 LST obtained from radiometric measurements and from MODIS instrument.....................48 Figure 6-6 MODIS LST product Sep.23, 2008 ......................................................................................48 Figure 6-7 LST calculated by split window technique for MODIS image Sep.23, 2008 ......................49 Figure 6-8 Scatter plots of LST vs NDVI of Sep.24, 2008 upper and Sep.18, 2008 lower:.................50 Figure 6-9 Simulated soil moisture by (a) 2nd and (b) 3rd order polynomial relation Sep.23, 2008.......52 Figure 6-10 Simulated soil moisture by 3rdorder Fr and LST Sep.23, 2008 ..........................................52 Figure 6-11 Correlation of observed and simulated soil moisture using 2nd order polynomial relation ................................................................................................................................................................53 Figure 6-12 Correlation of observed and simulated soil moisture from 3rd order polynomial relation 53 Figure 6-13 Correlation of observed and simulated soil moisture from 3rd order relation of Fr ..........54 Figure 6-14 Sensitivity analysis of the 2nd order relation (a) R2 (b) RMSE...........................................55 Figure 6-15 Sensitivity analysis of the 3rd order polynomial relation (a) R2 (b) RMSE........................56 v

Figure 6-16 Spatial average of NDVI, the LST product and the calculated LST during study period. 56 Figure 6-17 Average of soil moisture for 3 algorithms and air temperature......................................... 57 Figure 6-18 Statistical representation of simulated soil moisture of the study area:(a) standard deviation and (b) coefficient of variation versus spatial mean soil moisture for each day................... 57 Figure 6-19 (a) Temporal mean of the simulated soil moisture (cm3cm-3) and (b) coefficient of variation, CVs, at pixel level during the study period. .......................................................................... 58 Figure 6-20 Root mean square error of the relative difference, RMSEįi, of the estimated soil moisture ............................................................................................................................................................... 58 Figure 6-21 Joint distribution of terrain attributes and simulated soil moisture................................... 60 Figure 6-22 Potential temperature map of Sep.23, 2008....................................................................... 61 Figure 6-23 simulated soil moisture by 2nd order relation with potential temperature (Sep.23, 2008). 62 Figure 6-24 Correlations of observed and simulated soil moisture by the 2nd order polynomial relation using potential temperature ................................................................................................................... 62 Figure 6-25 Elevation zone map of Gumara catchment ....................................................................... 63 Figure 6-26 Average Soil moisture for 3 elevation zones before correction ........................................ 64 Figure 6-27 Average LST for 3 elevation zones and air temperature at low elevation area................. 64 Figure 6-28 Average Soil moisture at 3 elevation zones simulated after elevation correction............. 65

vi

List of tables Table 2-1Thiesen polygon weights of the 3 rainfall stations ...................................................................6 Table 2-2 soil properties of the three major soil groups ........................................................................10 Table 3-1 MODIS visible, NIR, thermal bands and potential applications ...........................................17 Table 3-2 General descriptions of MODIS level 1 raw data..................................................................18 Table 4-1 Summary of remote sensing techniques for measuring soil moisture (Engman and Gurney, 1991) ......................................................................................................................................................19 Table 5-1 Phases and schematic processing steps for the triangle method from remote sensing.........27 Table 5-2 MODIS/Terra solar and sensor zenith angle and atmospheric parameters............................33 Table 5-3 Summery of MODIS LST products.......................................................................................39 Table 6-1 NDVI values for Gumara catchment .....................................................................................46 Table 6-2 Minimum, maximum and average LST products and LST calculated ..................................49 Table 6-3 Coefficients for 2nd order polynomial relations .....................................................................51 Table 6-4 Coefficients for 3rd order polynomial relation with N* .........................................................51 Table 6-5 Coefficients for 3rd order polynomial relation with Fr ..........................................................52 Table 6-6 Average soil moisture of Gumara catchment using three algorithms developed ..................52 Table 6-7 Coefficients for 2nd order polynomial relation for potential temperature..............................62 Table 6-8 Average soil moisture and LST of each zone simulated by 2nd order relation with LST ......63 Table 6-9 Spatial average soil moisture before and after local correction ............................................65

vii

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

1. Introduction Soil moisture is an important bio-physical parameter that is used as interface for the land surface and for the atmosphere and it is also a key hydrologic state variable linked to water availability, the processes of evapotranspiration, runoff generation from rainfall and for irrigation scheduling. The soil moisture distribution over the area can be determined by the exchange of physical processes between the land surface and the atmosphere. It also used as a control volume for storing water for the proper plant growth.

1.1.

Background

The hydrological cycle is one of the most important but also some times poorly understood Earth System processes. It involves the journey of water from the Earth's surface to the atmosphere, and back again. This gigantic system, which is responsible for the continuous exchange of moisture between our planet’s oceans, atmosphere, and a land surface, is powered by the energy from the Sun. The bulk of the Earth’s water (about 96.5%) is stored in the global oceans, about 1.7% is stored in the polar ice caps, glaciers, and permanent snow fields, and another 1.7% is stored in groundwater, lakes, rivers, streams, and soil (Peixoto and Kettani, 1973). This complex hydrological cycle and the quantity of water can be modelled through hydrological, meteorological and climatological modelling at regional and global scale which requires the information of a number of input parameters and state variables. Among the number of state variables soil moisture is found to be one of the most important and plays a significant role in hydrological modelling. Soil moisture is important to the hydrologic research for partitioning rainfall in to runoff and infiltration components as well as separating incoming solar radiation into latent and sensible heat. It determines the soil water content available for vegetation and affects the vegetation processes such as the transpiration and plant growth. However, this important bio-physical variable is difficult to measure at large scale. Soil physical and hydraulic properties are of prime interest for water and energy balance studies and simulations of land surface atmosphere interaction at various scales. Although soil properties are typically measured in the field at the point scale, such data commonly are unavailable over large areas, have limitations in accounting for regional spatial variability, the prohibitively expensive, tedious and time consuming. Methods based on remote sensing provide alternative tools to obtain quick estimates of soil properties (Mattikalli et al., 1998). Both active and passive microwave remotely-sensed data have a great potential for providing areal estimates of soil moisture. Although remote sensing of soil moisture can be accomplished to some degree or other by all regions of the electromagnetic spectrum, only the microwave region offers truly quantitative measurements (Engman and Gurney, 1991) because the primary physical property that affects the measurement is directly dependent on the amount of water present in the soil. However, microwave remote sensing is only applicable at global scale due to its 1

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

limited temporal and spatial resolution. Therefore, other approach combining optical/IR remote sensing proposed by Carlson et al. (1994) is the best option for retrieving soil moisture at reasonably high resolution which can be applied for regional scale.

1.2.

Relevance of the study

Studying spatial distribution of soil moisture at regional level is highly important for many hydrological applications such as river flow forecasting, planning and designing of irrigation as well as hydraulic structures and for soil conservation measures. The vertical and lateral movement of rainfall on the surface and inside the soil is governed by the hydraulic conductivity and intake capacity of soil during rainfall events which are partly determined by soil moisture content that will influence infiltration and runoff processes. Because of the difficulty to measure soil moisture both spatially and temporally, using the conventional point scale measurement method, many hydrological modelling uses lump some soil information not discrete soil information. The existing point based soil moisture measurement methods such as Theta probe or gravimetric method are not appropriate for complete understanding of the spatial and temporal behaviour of soil moisture. Due to heterogeneity of soil type, land use and topography, soil moisture may change considerably in space and depth during any time interval (Haider et al., 2004). Regarding the water resources development, there is increasing water utilization along the lower Nile valley Egypt and Sudan straining the limited freshwater resources of the basin. Similarly, there is an increasing demand for irrigation and hydropower development in Ethiopia the source of Blue Nile. The country Ethiopia is experiencing a number of problems such as rapid population growth, limited water resources, environmental degradation and poverty, to cope with the recurrent drought and its impacts and to increase agricultural production to cope with increasing population (Kebede et al., 2006). Therefore, to make efficient use of water resource with balanced attention for maximizing economic, social, and environmental benefits, it is necessary to have effective integrated water management. Therefore, studying soil moisture at this catchment is vital and prerequisite because soil moisture is one of the most important initial variables for modelling water balance and for the proper irrigation management of the catchment.

1.3.

Research problem

Soil moisture is highly variable biophysical parameter in time (t), depth (d) and in horizontal direction. Therefore, to describe soil moisture behaviour in a complete manner it needs frequent and multiple measurements in the three dimensional (x, y, z) space. Despite the above, our understanding of the role of the soil moisture in hydrology, ecosystem processes and biogeochemistry, has been developed from point studies where the emphasis has been on the variability of soil moisture with depth and time. The most advanced in situ soil moisture equipment describes only the temporal variability at one particular location. The large spatial and temporal variability that soil moisture exhibits in a natural environment is exactly which makes it difficult to measure and use in earth science applications. Conventional interpolation methods between points of measurement therefore often do not yield very satisfactory results because the methods do not consider variability of surface roughness, vegetation 2

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

cover, topography and other antecedent conditions. This is the main reason to explore other techniques such as remote sensing and data assimilation. Providing a soil moisture product at catchment scale for research and application remains a significant challenge and therefore the estimation of regional scale soil moisture by remote sensing measurements may lead to the improvement of earth science applications. A major focus of remote sensing research in hydrology has been on developing approaches for estimating hydro-meteorological states and fluxes in a distributed fashion. The primary set of state variables include land surface temperature, near surface soil moisture, snow cover/water equivalent, water quality, landscape roughness, land use, vegetation canopy and bare soil temperature, surface albedo and vegetation cover. The hydro-meteorological fluxes are primarily soil evaporation, rainfall rate, recharge rate, sub surface runoff and plant transpiration or evapotranspiration, and snow melt runoff (Schmugge et al., 2002). Hydrological state variables to a large extent reflect on the hydrology and related behaviour in a system. State variables commonly are assessed by collecting point data in the field, and this method is time consuming and not appropriate for understanding the spatial and temporal behaviour of the states. Therefore, the challenge in this research is to test a novel optical/IR remote sensing technique based on triangle method as proposed by Wang et al. (2007) to obtain 1km spatial and daily temporal patterns of hydrological states soil moisture in Gumara catchment.

1.4.

Objective of the study

The main objective of this study is to provide distributed soil moisture information at catchment scale with reasonable spatial and temporal resolution. This is required for improving climatic and hydrologic modelling and prediction particularly for distributed models. Also, estimation of soil moisture at various temporal and spatial scales is a key to strategic management of water resources. Specifically • To estimate and map soil moisture at 1km spatial resolution using Optical/thermal IR remote sensing and ground based measurements. • To test and possibly improve an algorithm for soil moisture estimation from the point scale measured soil moisture and remote sensing NDVI and land surface temperature. • To analyze the spatial and temporal variability of soil moisture during the study period.

1.5. • • • • •

Research questions Is it possible to estimate soil moisture using satellite remote sensing at 1km spatial resolution for a catchment which has about 1900 m altitude difference? Which surface parameters are the most relevant to derive soil moisture using optical and infrared remote sensing technique? Which surface parameters are the most sensitive for soil moisture in the method applied for this study? Which algorithm gives most optimal result for soil moisture estimation from remote sensing? How does the soil moisture content relate to terrain controlling factors in the study area?

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

1.6. •

• •

1.7.

Hypothesis Different orders of polynomial relations of observed soil moisture with remote sensing scaled NDVI and LST can give similar results at the same spatial and temporal resolution in a particular catchment. The spatial variability of soil moisture is higher than the temporal variability during the study period. Land surface temperature is the most sensitive variable for the method applied.

Thesis outlines

The thesis contains seven chapters and has the following outlines: Chapter 1 gives a general introduction with emphasis on importance and application of soil moisture, relevance and problem statement of the study. Chapter 2 gives a brief description of the study area that covers climate, hydrology, topography, soil and land cover. Chapter 3 emphasises on field work and materials used for the study. Chapter 4 presents a literature review about the triangle method and remote sensing for soil moisture. Chapter 5 discusses the methods applied for this study. Chapter 6 presents the results, analysis and discussion of the study. Finally, chapter 7 deals with conclusion and recommendation.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

2. Description of study area The Lake Tana basins chosen for soil moisture estimation using remote sensing are located in the north-western part of Ethiopian plateau. Of more than 40 rivers feeding the lake, Gilgel-Abay, Ribb, Gumara and Megech contribute more than 45-55 % of the inflow (Abeyou, 2008). This study focuses on the Gumara catchment, which covers the area of about 1768 km2 produces a mean annual flow of 1229 MCM (Abeyou, 2008). The topography of the watershed can be categorized in two main parts. The upper most part is mountainous and rugged and the lower part is relatively gentle and plain. The Gumara catchment contributes a significant amount of inflow to the Lake Tana and consequently the low land part of the catchment is severely affected by flooding.

Sampling points

Small towns

Drainage lines

Figure 2-1 Location maps of the study area and soil moisture sample points

2.1.

Climate setting of the study area

The climate of the Gumara catchment is marked by a rainy season from May to September, with monthly rainfall varying from 72 mm in May to 419 mm in July. The areal rainfall of Gumara catchment is calculated from the point rainfall of the three stations located around the study area using Thiessen polygon method. Thiessen polygon is formed by interpolating the point map produced from the coordinates of the three rainfall stations and the weights of the stations are calculated by taking the area coverage of each station to the total area of the catchment extracted from SRTM. The three rainfall stations are located at small towns of DebreTabor, Amedber and Wereta as shown in Figure 2-1. Thiessen weights of the stations are shown on Table 2-1. Mean annual precipitation is about 1,492 mm in the upper part of the catchment at Debre Tabor station and about 1,378 mm in the lower part of the catchment at Wereta station. The dry season, from October to April, has a total rainfall of about 8% of the mean annual rainfall. Based on long term 5

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

records the average temperature variations throughout the year are minor 12.6 ºC in December (Debre Tabor) to 25.2 ºC in May (Wereta), with monthly average daily maximum and minimum temperatures of 34.0 °C (Wereta) and 2.8 °C (Debre Tabor), respectively. Humidity varies between 70% in Dec. and 88% in August. Wind speed is low, which limits potential evapotranspiration to values between 95 mm/month in December and 140 mm/month in April. Sunshine duration is reduced to 6.0–6.5 hours during July and August based on Debre Tabor meteorological station records. Table 2-1Thiesen polygon weights of the 3 rainfall stations

Stations

Thiessen weights 0.34 0.32 0.34

Wereta Amed ber Debre Tabor 450 400

Rainfall (mm)

350 300 250 200 150 100 50

be r De ce m be r

er

ve m No

be

ct ob O

pt

em

gu Se

Month

r

st

ly Au

Ju

ne Ju

ay M

ril Ap

ar ch M

ua ry br

Fe

Ja

nu

ar y

0

Figure 2-2 Monthly average rainfall in the Gumara catchment from (2004-2007) 1600

R ain fall (m m )

1550 1500 1450 1400 1350 1300 1250 Wereta

A/Ber

D/Tabor Station

Gumara catchment

Figure 2-3 Average measured yearly rainfall at 3 stations and areal rainfall of Gumara catchment (2004-2007).

6

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Wereta Tmax. D/Tabor Tmax. Amed Ber Tmax

0

Temperature ( C)

40 35 30 25 20

Month-Year

Sep-06

May-06

Jan-06

Sep-05

May-05

Jan-05

Sep-04

May-04

Jan-04

Sep-03

May-03

Jan-03

15

Figure 2-4 Daily maximum temperature at three stations (2003-2007)

0

Temperature ( C)

25

Wereta Tmin. D/Tabor Tmin. Amed ber Tmin

20 15 10 5

Ju l- 0 6

Ja

n06

l- 0 5 Ju

Ja

n05

l- 0 4 Ju

Ja

n04

l- 0 3 Ju

Ja

n03

0

Month-Year

Figure 2-5 Daily minimum temperatures at three stations (2003-2007)

0

Temperature ( C)

30

Wereta Tav. D/Tabor Tav. Amed Ber Tav.

25 20 15

Sep-06

May-06

Jan-06

Sep-05

May-05

Jan-05

Sep-04

May-04

Jan-04

Sep-03

May-03

Jan-03

10

Month-Year

Figure 2-6 Daily average temperatures for three stations (2003-2007)

2.2.

Topography

Gumara catchment is located in the eastern part of Lake Tana and it is characterized by highly rugged and undulating topography on the upper part and gentle and mild slope on the lower part of the 7

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

catchment. The elevation ranges from 1780 to 3704 m.a.s.l. During field visit in September 2008, the River in the upstream part of the catchment did not carry sediment and there were no sediment depositions around the river banks. In the lower part of the catchment however the river carried high amount of suspended sediments and sediment depositions were observed around the banks of the river. This indicates that there is high soil erosion on the middle part of the catchment with consequence affects the lower part by soil deposition and floods. Considering both the topographical effect and the available water resources of the catchment the Ministry of Ethiopian Water Resources (MEWR) planned to construct a medium scale dam in the middle of the catchment. This dam is designed for the purpose of both irrigation and flood protection downstream from the catchment. In the low and middle reaches of the river, especially in the extensive alluvial plains bordering the lake, the river meanders on its way and flows slowly, causing serious river channel deposit, high water table and overflow of riverbanks during the rainy season. Consequently, major problems of flooding and water logging must be resolved in order to develop irrigated agriculture in the area. To understand the topography of the catchment and extract some features of the catchment like drainage lines, Digital Elevation Model was processed from SRTM 90m resolution data using the DEM hydro-processing functions of ILWIS, as it is presented in Figure 2-7. See Appendix-1 for the DEM processing procedure.

Figure 2-7 Digital Elevation Model in m.a.s.l of the study area (processed from SRTM data)

2.3.

Hydrology

Gumara is one of the major rivers which contributes significant amount of inflow to Lake Tana. For this reason, the Ethiopian Ministry of Water Resources installed one gauging station downstream of the river near the small town Gumara. This gauging station has a long-term daily observation series starting from 1975. Based on the data from 2000 to 2006 records it has an average annual daily flow of 35 m3/s. Figure 2.8 shows the characteristics of flow with rainfall of the catchment. While, Figure 2-9 shows the average annual daily flow of Gumara River from 2000-2006. The rainfall data before 2003 are not available for analysis.

8

300.00

Discharge

250.00

Rainfall

0 250

200.00 150.00

500

100.00

750

50.00 0.00

Rainfall (mm)

3 -1

Discharge (m s )

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Mar-06

Mar-05

Mar-04

Mar-03

Mar-02

Mar-01

Mar-00

1000

Month Figure 2-8 Monthly average daily flow of the Gumara River and areal average rainfall of the Gumara catchment

3 -1

Discharge (m s )

50 40 30 20 10 0 2000

2001

2002

2003

2004

2005

2006

Year Figure 2-9 Annual average daily flow of the Gumara River

2.4.

Soil

A soil can be defined a three dimensional conceptual unit in which numerous physical, chemical and biological processes takes place. These processes are driven by the changes in different kinds of energy. A portion of solar energy is converted in to heat energy which results in an increase of soil temperature in the soil surface during the day. The increase of soil temperature results in high evaporation of water inside the soil particle. The seasonal soil moisture pattern in the study area follows closely the rainfall patterns. In the dry season the soil moisture content is quite low and only during the rainy season the soil moisture content increases. Soil classification is done to see the effects of the soil properties in the analysis of spatio-temporal soil moisture variation of the catchment. There are various ways of soil classification a major distinction is between natural and technical approaches. • Natural soil classifications group soils by some intrinsic property, behaviour, or genesis of the soils themselves, without reference to use.

9

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

•

Technical soil classifications group soils by some properties or functions that relate directly to a proposed use or group of uses. The soils that covered the catchment are classified by five different classes of soils based on technical soil classifications following the classification of FAO. Five of the major soil classifications in this study area are Luvisols, Lithosols, Cambisols, Vertisols, and Nitosols in combination with four diagnostic horizon modifiers: chromic, eutric, haplic, and lithic collected from MEWR. Based on the FAO soil classification the catchment is dominantly covered by two soil groups the upper part of the catchment covered by Luvisols and the lower part is covered by Nitosols. The percentage area coverage of the three major soil groups are listed in Table 2-2 and their descriptions are listed below. Table 2-2 soil properties of the three major soil groups

Major Soil Groups Nitosols Luvisols Vertisols

Soil Texture Silty clay to clay Clay to silty clay Clayay

Drainage conditions well drained moderately to well drained poorly drained

% Cover 47.52 44.24 4.67

Soil group

Figure 2-10 Major soil groups according to the FAO classification Luvisols are soils that have higher clay content in the sub soil than in the top soil as a result of pedogenetic processes (especially clay migration) leading to an argic sub soil horizon. Luvisols have high activity clays throughout the argic horizon and a high base saturation at certain depths. Luvisols have a medium to high storage capacity for water and nutrients and are well aerated. Nitosols are deep, well drained, and red, tropical soils with diffuse horizon boundaries and a surface horizon with more than 30 percent clay and moderate to strong angular blocky structure elements that easily fall apart in to characteristic shiny, polyhydric elements. The good workability of Nitosols, their good internal drainage and fair water holding properties are complemented by chemical (fertility) properties that compare favourably with those of most other tropical soils. Nitosols have relatively high contents of weathering minerals, and surface soils may contain several percent of organic matter, in particular under forest or tree crops.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Cambisols: - Soils with beginning horizon differentiation through changes in color, structure and/or texture. Their parent materials are medium to fine textured materials derived from a wide range rock, mostly in colluvial, alluvial or eolian deposits. They are found under the environment of level to mountainous terrain; arctic to tropical climates; wide range of vegetation types. Vertisols: - is a soil in which there is a high content of expansive clay known as montomorillonite that forms deep cracks in drier seasons or years. Alternate shrinkage and swelling causes selfmulching, where the soil material consistently mixes itself, causing vertisols to have an extremely deep A horizon and no B horizon. Their parent materials are sediments that are finely textured and contain a high proportion of smetite clay, or products of rock weathering that have these characteristics. The soils can be found in depression and level to undulating areas, mainly in tropical, semi-arid to sub humid and Mediterranean climates with alternation of distinct wet and dry seasons. Lithosols: - Most Lithosols are found in very step, mountainous region where erodible material is so rapidly removed by erosion that a permanent covering of deep soil cannot establish itself. Such conditions occur in almost all regions of the world where steep slopes are prevalent. All descriptions are taken from FAO (2006).

2.5.

Land cover

Land cover classification is used for many applications like: conservation measure, biodiversity assessment, water quality assessment, assessing land cover change and so on. There is no one ideal classification of land use and land cover, and it is unlikely that one could ever be developed. There is no logical reason to expect that one detailed inventory should be adequate for more than a short time, since land use and land cover patterns change. Land cover classification has a great role for analyzing soil moisture at a certain catchment because it directly affects the infiltration capacity of soil and the amount of evapotranspiration takes place. During field visits land cover signatures and the corresponding coordinates were taken for the purpose of land cover classification. Based on the classification, majority of the study area is covered by crop lands while a few high lands of the study area are covered by leafy forests, bush and shrubs as shown in Figure 2-11. The statistical coverage of the classification is about 73.6% cropland, 13.2 % bushes and shrubs, 6.3% forest, 5% grass land, 1.8% bare land and about 0.1% is covered by water.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Figure 2-11 Land cover map of the Gumara catchment “Crop land1” is matured crops where as “crop land2” is crops at growing stage.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

3. Field work and materials used The field work was conducted in September 2008 to collect both primary and secondary data. The main activities that were done during the field work are: • Measuring soil moisture in the study area using both direct and indirect methods. • Measuring air and surface temperature, incoming and outgoing both short wave and long wave radiation using a radiometer installed at a weather station and an infrared gun. • Collecting both hydrological and meteorological data from MEWR, Ethiopian Mapping Agency (EMA) and other organizations.

3.1.

Soil moisture measurement

Soil moisture or soil water content is an expression of the mass or volume of water in the soil, while the soil water potential is an expression of the soil water energy status. The relation between content and potential is not universal, but depends on characteristics of the soil, such as soil density and soil texture. Soil-water content on the basis of mass is expressed in the gravimetric soil moisture content, șg, defined by:

θ g = M water

M soil

3.1

Where Mwater is the mass of water in the soil sample and Msoil is the mass of dry soil after oven dried that is contained in the sample. The unit for Mwater and Msoil is g and for θ g is gg-1. Volumetric soil water content of the soil is often more useful and it can be expressed as:

θ v = Vwater

Vsample

3.2

Where ș v is volumetric water content, Vwater is the volume of water in the soil sample and Vsample is the total volume of (dry soil + air + water) in the sample. The unit of Vwater and Vsoil is cm3 and for θ v is cm3cm-3. The relationship between gravimetric and volumetric water content is:

θ v = θ g × G = θ g × (ρ b / ρ w )

3.3

Where G is specific gravity of soil, ȡb is the dry soil bulk density (gcm-3) and ȡw is soil water bulk density (gcm-3). Methods of soil moisture measurement on the field There are two methods to measure soil moisture. These are direct or gravimetric method and indirect methods. Both techniques were applied in the field. Gravimetric or direct measurement of soil water content: This method is very straightforward. Moist soil samples taken from the field are weighted, dry it to remove the water, and reweigh it. The customary method of drying is to place the sample in an oven at 1050 C for 24 hours. This removes the inter-particle water but not the water molecules trapped between clay layers (Gardner, 1986). Soil water content can be computed using both in equation 3.1 and 3.2. 13

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Indirect soil water content methods: There are various types of indirect soil water content measurement methods. Radiological methods, soil-water dielectrics and remote sensing soil moisture are some of the indirect methods of soil water content measurement methods. Details are found in Appendix-3. During field work a Theta probe soil moisture sensor (ML2x) was used, which responds to changes in the apparent dielectric constant of the medium. From the dielectric constant the volumetric or gravimetric water content reads directly from the sensor. A factory calibration for mineral soil was used to convert dielectric constant to volumetric soil moisture directly from the sensor reading. Before taking soil water content measurement in the field three important things were considered. • The sampling site was selected as much as possible at homogeneous land cover and also relatively uniform slope: This is to minimize the variation of soil water content and to minimize on the effect of topography. • The measurements were taken at the time of the satellite overpass of MODIS instrument for both Terra and Aqua satellites. This helps to correlate ground measured soil moisture with remote sensing data. • For each sampling site many measurements were taken to consider the spatial variability of soil moisture at pixel level. The average of the measurements was taken to represent the 1km pixel resolution of the MODIS image. Considering the above a total of 49 sampling sites were visited on different land covers during the field work. For some of the sampling sites, samples were taken for gravimetric method to calibrate the Theta probe measurements. The sampling schemes and samples of measurement locations are shown in Figure 3-1. A global positioning system (GPS) was used to obtain the coordinates of each sampling site. The raw data are presented in Appendix-2.

Figure 3-1 Sampling schemes at different land covers and sites of in-situ measurements of soil moisture: 14

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

The upper and the lower figures represent sites and location of measurements respectively and the photos are taken during the field work when the measurements were taken at different land covers.

3.2.

Air and surface temperature measurements

Surface temperature measurements were recorded from measurements by a radiometer (CNRI, kipp and zonen, Delft, the Netherlands) that was installed in the Wereta with two sensors during the field work campaign, and using infrared gun measurements at different locations at different times. These measurements are used for validating remote sensing measurements. The air temperature was also measured from the weather station and Sonic Anemometer. It was applied to estimate the minimum surface temperature for scaling land surface temperature and also for the analysis of temporal variation of soil moisture. The air and surface temperatures from field measurements and from remote sensing are shown below in Figure 3-2 and Figure 3-4. As can be seen below, most of the land surface temperatures measured from the radiometer and derived from remote sensing match except for a major shift on two points. This major shift is most likely due to the cloud effect on the remote sensing image. Also, the air temperature measured by two different sensors which are about 10 m apart each other corresponds very well as shown in Figure 3-2. The two sensors used for measuring air and surface temperature are shown in Figure 3-3.

Temperature (K)

330

Measured LST Calculated LST

320

MODIS LST product

310 300 290 280

Cloud effect

22

/0 9 22 /08 9 /9 /0 :00 8 :0 22 /0 10: 0 5 9 23 /08 5:0 0 2 /0 9/ :45 :0 24 08 2: 0 /0 2 5 9/0 40 : /0 8 1 0 0 9/ :3 0: 26 08 00 1 /0 1 :2 9/ 26 08 5:0 0 /0 10 :2 9/ 5 0 27 : 8 /0 12 00 :3 9/ 5 0 27 811 :00 /0 9 :3 27 /08 0:00 1: /0 0 9 29 /08 0:0 0 /0 9/ 3:0 5 0 29 : 8 /0 11 00 :2 9/ 08 5: 12 00 :3 5: 00

270

Date/month/year/time (UTC+3:00) Figure 3-2 Surface temperatures from infrared gun and remote sensing

15

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Figure 3-3 Weather station and radiometer installed during field work 35

25

0

Temperature ( C)

30

20 15 10 Air temp. (weather stn.) 5

Air temp. (Sonic Anemometer) 9/29/08 11:42

9/28/08 21:12

9/26/08 11:30

9/25/08 6:30

9/25/08 21:00

9/24/08 1:30

9/24/08 16:00

9/23/08 11:00

9/22/08 6:00

9/22/08 20:30

9/21/08 1:00

9/21/08 15:30

9/20/08 10:30

9/19/08 5:30

9/19/08 20:00

9/18/08 0:30

9/18/08 15:00

9/17/08 10:00

9/16/08 5:00

9/16/08 19:30

9/15/08 14:30

9/15/08 12:00

0

Date /Time (UTC+3:00)

Figure 3-4 Air temperature obtained from weather station and Sonic Anemometer.

3.3.

MODIS sensor

The Moderate Resolution Imaging Spectro-radiameter (MODIS) is a 36-band Spectro-radiometer measuring visible and infrared radiation and obtaining data is being used to derive products ranging from vegetation, land surface cover, and ocean chlorophyll fluorescence to cloud and aerosol properties, fire occurrence, snow cover on the land, and sea ice cover on the oceans. The first MODIS instrument was launched on board the Terra satellite in December 1999, and the second was launched on Aqua in May 2002. Together the instruments image the Earth every 1 to 2 days. Terra’s orbit around the Earth is timed so that it passes from north to south across the equator in the morning (10:30), while Aqua passes south to north over the equator in the after noon (1:30). Figure 3-5shows the MODIS instrument platforms of both Terra and Aqua.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Figure 3-5 Terra satellite-right and Aqua-left Table 3-1 MODIS visible, NIR, thermal bands and potential applications Primary Use

Band No. Band width (µm)

Spatial Resolution at Nadir

Vegetation index

1 2

0.620 - 0.670 0.841 - 0.876

250 m

Land/Cloud Properties

3 4 5 6 7

0.459 - 0.479 0.545 - 0.565 1.230 - 1.250 1.628 - 1.652 2.105 - 2.155

500 m

Atmospheric Water Vapor

17 18 19

0.890 - 0.920 0.931 - 0.941 0.915 - 0.965

1000m

Surface Temperature

31 32

10.780 - 11.280 11.770 - 12.270

3.4.

Acquiring of MODIS image

Table 3-2 shows the general description of MODIS level 1data products, which are freely available from the MODIS Adaptive Processing System (MODAPS) through Atmosphere Archive and Distribution System (LAADS) at http://ladsweb.nascom.nasa.gov/. The images dated from Sept.18, 2008 to Sep.29, 2008 with latitude of 11.250-12.250 and longitude of 37.250-38.50 was acquired from the above website. MODIS/Terra is used for analyzing images in this study because the images acquired from Terra satellite is relatively less cloud affected than Aqua but the image from the MODIS Aqua satellite is also processed to take information of LST for pixels where the soil moisture measurement was taken at its overpass time.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Table 3-2 General descriptions of MODIS level 1 raw data

MODIS/Terra data products MOD021KM

MODIS/Aqua data products MYD021KM

MOD02QKM

MYD02QKM

MOD02HKM

MYD02HKM

MOD03

MYD03

Data Product Description This level 1B collection contains calibrated and geolocated radiances at-aperture for all 36 MODIS spectral bands at 1km resolution. This level 1B collection contains calibrated and geolocated radiances at-aperture for MODIS spectral bands 1 through 7 at 500 m resolution. This level 1B collection contains calibrated and geolocated radiances at-aperture for MODIS spectral bands 1 and 2 at 250 m resolution. Geolocation collection contains geodetic latitude and longitude, surface height above geoid, solar zenith and azimuth angles, satellite zenith and azimuth angles, a land/sea mask for each 1km sample.

The advantages of using MODIS instrument over the other instruments for this research are: • The swath width is 2330km and one image covers the entire study area. • It passes over study area in the late morning close to mid day and in the afternoon. Therefore temperature can be retrieved twice a day and in principle it is ideal for monitoring of rapidly varying soil moisture. • Because of the morning over pass, it is expected that cloud free images can be collected. • The images are cost effective, can be downloaded freely from the MODIS archives. • It has good spectral resolution, 36 bands. • The spatial resolutions are satisfactory for soil moisture studies, 250m, 500m, and 1000m resolution. • Software or tools are available to pre-process the images. • Accurate calibration in multiple thermal infrared bands has been designed for retrievals of SST, LST and atmospheric properties.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

4. Literature review about remote sensing and triangle method for soil moisture 4.1.

Remote sensing of soil moisture

Remote sensing of soil moisture can be accomplished to some degree or other by all regions of the electromagnetic spectrum. Successful measurement of soil moisture by remote sensing techniques depends on the type of reflected or emitted radiation (Table 4-1). Table 4-1 Summary of remote sensing techniques for measuring soil moisture (Engman and Gurney, 1991)

Wave length region

Property observed

Advantages

Disadvantages

Gamma radiation

Natural gamma radiation

High spatial resolution

Atmosphere and presence of water in the soil attenuates the gamma radiation

Reflected solar

Albedo; index of reflection

Data available

No unique relationship between spectral reflectance and soil moisture; thin surface layer only; cloud interference

Thermal infrared

Surface temperature (measured diurnal range of surface temperature or crop canopy temperature

Bare soil only; cloud interference; surface topography and local meteorological conditions can cause noise; surface layer only (2 -4cm)

Passive microwave

Brightness temperature(microwave emission);dielectric constant; soil temperature

High spatial resolution, large swath; relationship between temperature and soil water pressure is independent of soil type. All weather; penetrates some vegetation; large area coverage

Active microwave

Backscatter coefficient; dielectric constant

All weather; high resolution

Limited spatial resolution; soil temperature; surface roughness; vegetation; interference from communications Surface roughness; vegetation; topography; limited swath width 19

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

4.1.1.

Gamma radiation techniques

Airborne soil moisture measurement by gamma radiation is based on detecting the difference between the natural terrestrial gamma radiation flux for wet and dry soils. This technique needs calibration flight lies to determine the back ground gamma count rate, C0, and background soil moisture, M0. The current soil moisture, M can be calculated according to:

C M =

Co

(100 + 1.1Mo) − 100 1.11

4.1

Where C is the measured gamma count rate, MO is the background soil moisture unit and CO is the background gamma count rate. This approach is limited to aircraft flying at an altitude of only 100200 m above the earth’s surface. Atmosphere and presence of water in the soil attenuates the gamma radiation.

4.1.2.

Reflected solar techniques

Reflected solar radiation is not a particularly viable technique for measuring soil moisture because there are too many noise elements that confuse the interpretation of the data. Although wet soil will generally have a lower albedo than dry soil (Crist and Cicone, 1984), and this difference can be measured theoretically, confusion factors such as organic matter, roughness, texture, incidence angle, colour, plant cover and the fact that it is a transient phenomenon all make this approach impractical (Jackson et al. 1978). However, land surface parameter which has a relation with soil moisture like NDVI can be detected with this technique.

4.1.3.

Thermal technique

Thermal infrared measurements have been successfully used to measure the surface few centimetres of soil moisture. However, atmospheric effect and vegetation cover make the thermal technique limited to their application for soil moisture estimation especially when there is thin cirrus of clouds in the atmosphere and vegetation on the surface. Idso et al. (1975) found that the volumetric moisture content for soil layers between 2 and 4 cm thick was linearly related to the amplitude of diurnal soil temperature for specific soil types. But this relation can not be effectively applied to surfaces with vegetation cover and with different soil types. After meteorological inputs to the soil surface have been accounted for, surface temperature is primarily dependent on the thermal inertia of the soil. The thermal inertia, in turn, is dependent on both the thermal conductivity and the heat capacity which increases with soil moisture according to the relationship (Price, 1982).

( D)

DTs = Ts (PM ) − Ts ( AM ) = f 1

4.2

Where DTs is the diurnal temperature difference between the afternoon surface temperature (Ts (PM)) and the early morning temperature (Ts (AM)), and D is the diurnal thermal inertia given by 20

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

D = ωσ c k

4.3

Where Ȧ corresponds to the day length, ıc is the volumetric heat capacity (Jm-1k-1) and k is the thermal conductivity (W m-1 k-1). The thermal inertia D (J m-2 k-1 s1/2) describes the ability of the soil to resist temperature change. By measuring the amplitude of diurnal temperature change we can develop a relationship between temperature change and soil moisture. However, the relationship between diurnal temperature and soil moisture depends upon soil type and is largely limited to bare soil conditions.

4.1.4.

Microwave techniques

Microwave techniques for measuring soil moisture include both passive and active microwave approaches with each having distinct advantages. The theoretical basis for measuring soil moisture by microwave techniques is based on the large contrast between the dielectric properties of water and dry soil. The large dielectric constant for water is the result of water molecules alignment of the electric Ƞ dipole in response to an applied electromagnetic field. The dielectric constant of water at around 20 C is approximately 80 compared with that of dry soils which is the order of 3 to 5. Thus, as the soil moisture increases, the dielectric constant increase to a value of 20 or more (Schmugge, 1983). For passive microwave remote sensing, this change in dielectric constant would result in a decrease of emissivity from about 0.95 to 0.6 or less. For passive microwave remote sensing of soil moisture, a radiometer measures the intensity of emission from the soil surface. This emission is proportional to the product of the surface temperature and surface emissivity which is commonly referred to as the microwave brightness temperature (TB), and can be expressed as follows (Engman and Gurney, 1991):

[

]

TB = t (H ) rTsky + (1 − r )Tsoil + Tatm

4.4

Where t (H) is the atmospheric transmission, r is the surface reflectivity, and Tsky, Tsoil and Tatm are the temperature for the sky, soil and atmosphere, in K respectively. At longer microwave (greater than about 5cm), which are better for measuring soil moisture, the atmospheric effects can be neglected and the above equation can be simplified to:

TB = (1 − r )Tsoil = εTsoil

4.5

Where İ = 1-r is the emissivity. Because the measured brightness temperature and the emissivity are dependent on soil texture, surface roughness and any vegetation present, actual soil moisture is usually related to TB empirically with ground. In this equation, the reflectance r is determined from the Fresnel equations for an electromagnetic wave at a smooth boundary. These can be written for the horizontally and vertically polarized radiation as follows: rH =

rV =

K cos θ − K − sin 2 θ K cos θ + K − sin 2 θ

cos θ − K − sin 2 θ cos θ + K − sin 2 θ

4.6

4.7

21

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Where the subscripts H and V refer to the horizontal and vertical polarizations respectively, ș is the angle of incidence and K is dielectric constant. Finally, the soil moisture content can be obtained from K by using their relationship. For the active microwave approach, soil moisture can be determined from the relation of the measured radar back scatter composed of back scatter from vegetation layer and from soil surface. This radar back scatter is obviously attenuated by vegetation canopy. The relation of measured radar back scatter and soil moisture can be mathematically described as follows:

St = Sv + S s / L

4.8

Where St is measured backscatter, Sv is backscatter from vegetation, Ss is back scatter from soil and L is attenuation caused by vegetation canopy. The soil back scatter from equation 4.8 can be directly related to volumetric soil moisture as follows: S s = RαM v

4.9

Where R is surface roughness term, Į is soil moisture sensitivity term and Mv is volumetric soil moisture. Since the early 70’s there has been extensive research studying microwave approaches for remote sensing of soil moisture. The basic conclusion of this research is that it is indeed possible to determine the moisture content of the surface layer of the soil of thickness about equal to a ¼ of a wave length thick, i.e., about a 0-5 cm layer using a 21 cm wave length (Schmugge et al., 2002). Microwave remote sensing has the potential to provide a direct measure of soil moisture. It also has the advantage of all-weather observations and penetration in to the vegetation canopy for soil moisture sensing. However, there are many reasons why microwave techniques have not been applied for estimation of soil moisture at an operational level. First, the spatial resolution of passive microwave sensors from space is poor; second, the current satellite channels do not provide adequate soil moisture sensitivity for majority of vegetation covers (i.e NDVI > 0.4); and third, a priori information (like vegetation optical depth and root mean square height of the soil surface is needed for determining reflectivity) required in existing soil moisture estimation algorithms, which cannot be obtained globally after (Chauhan et al., 2003). Active microwave remote sensing of soil moisture faces the same potential and the same limitations as the passive microwave. Radar active microwave sensor has the capability to measure soil moisture at a fine resolution but two main reasons limit the applicability. First due to the narrow swath, they operate at low temporal frequency minimum revisit time is 35 days. Secondly, the back scattering coefficient is strongly affected by other factors than the soil moisture, such as soil roughness, vegetation water content and geometrical characteristics of the vegetation. These effects are incidence angle, polarization and frequency dependent. Unlike radar active microwave, it is possible to retrieve soil moisture content by using ERS wind scatterometer globally at a temporal resolution of 3-4 days on average (Wen and Su, 2003). However, the spatial resolution and effects of soil roughness and vegetation are still limitations of the approach for applicability.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

4.2. 4.2.1.

Soil moisture quantification using the triangle method Description of triangle method

Soil moisture coupling to land surface-interactions has been used in the past to quantify soil moisture signatures. NDVI and soil temperature are proven indicators of the vegetative and thermal potential of the land surface. However, the vegetation and soil temperature have a complicated dependence on soil moisture. Careful analysis based on the available data by Carlson et al. (1994) and Gillies et al. (1997) show that there can be a unique relationship among soil moisture, NDVI, and soil temperature for a given region after (Chauhan et al., 2003). The method used to mapping land surface moisture from NDVI and surface temperature is called Triangle method. If a sufficiently large number of pixels are present and when cloud and surface water and outliers are removed, the shape of the pixel envelope in the feature space plot between NDVI and land surface temperature resembles a triangle. Figure 4-1 represents a schematic description of the relationship of soil moisture, NDVI and LST some times referred to as ‘Universal triangle’. From the triangle three important properties can be observed in the context of the relations between NDVI, LST and soil moisture. The first observation is soil moisture variation from the right to the left side of the triangle. The right side of the triangle has low soil moisture and left side of the triangle has high soil moisture. The second observation is the slope towards the left, in this case surface temperature decreases as the NDVI increases. This negative relation shows that sunlit vegetation is generally cooler than bare soil. The third and the most important observation is on the apex of the triangle. In the apex of the triangle the value of NDVI is higher but the corresponding value of surface temperature is low with small variation. The small change of surface temperature with high NDVI indicates the wetness of the soil moisture in the vegetation. From this as we will postulate, the vegetation temperature do not vary in space, so variations in temperature in the triangle reflect only the soil surface dryness or wetness (Carlson, 2007). A central assumption here is that, given a large number of pixels reflecting a full range of soil surface wetness and fractional vegetation cover, sharp boundaries in the data reflect the real limit: i.e., bare soil, 100 percent vegetation cover, and lower and upper limits of the surface soil water content. The abscissa and the ordinate are appropriately scaled versions of temperature and NDVI respectively such that:

Figure 4-1 Universal triangle: schematic relationship between soil moisture, temperature and NDVI , source (Chauhan et al., 2003). 23

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

T* =

T − To Ts − To

NDVI * =

4.10

NDVI − NDVIo NDVIs − NDVIo

4.11

Where, T and NDVI are observed soil temperature and NDVI respectively, and the subscripts o and s stand for minimum and maximum values of the pixels inside the triangle. Carlson et al. (1994) found that the relationship between soil moisture M, NDVI*, and T* can be expressed through a regression formula such as: M =

i =n j =n

¦¦ aijNDVI

* (i )

T*

( j)

4.12

i =0 j = 0

The scaling of NDVI and LST reduces the sensitivity of NDVI and LST to atmospheric correction and calibration issues, helps to isolate cloud and water pixels which tend to lie outside the triangle, and allows comparison of pixel data from different days and seasons within the same framework. Chauhan et al. (2003) argued that a single polynomial such as the one above can represent a wide range of surface climate conditions and land surface types but less accurate. The second or third order polynomial gives a reasonable representation of the data with good accuracy.

4.2.2.

Previous studies of soil moisture using the triangle method

Chauhan et al. (2003) have evaluated the triangle method approach for the estimation of soil moisture at high resolution using satellite microwave and optical/infrared data. This approach can be applied to integrate data acquired by the Visible/Infrared Imager Radiometer Sensor Suit (VIIRS) and a Conical Scanning Microwave Imager/Sounder (CMIS), planned for launch in the 2009-2010 time frames under National Polar-Orbiting Operational Environmental Satellite System (NPOESS). Chauhan et al. (2003) applied a two step approach to obtain operational, reasonably accurate, high resolution soil moisture by linking microwave derived soil moisture with optical/IR parameters. First, the soil moisture was retrieved at low resolution from microwave data. The second step involves relating microwave-derived soil moisture to NDVI, LST and albedo through regression following equation 4.12. These regression relations, in conjunction with high resolution NDVI, LST and albedo are then regressed backward to obtain soil moisture at high resolution. An error budget analysis performed on the estimation procedure showed that the RMSE in the estimation of soil moisture is of the order of 5%. Predicted soil moisture results at high resolution agree reasonably well with the low resolution estimates in both magnitude and spatio-temporal patterns. Both the triangle method and a Soil Vegetation Atmosphere Transfer (SVAT) model are also applied by Quattrochi and Luvall (2004) to retrieve surface soil moisture as an index to assess the prevalence of certain diseases such as malaria and filariasis. The surface soil moisture was used as an index of 24

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

mosquito presence that carries the parasite and need standing water for breeding. A SVAT model was applied to model surface soil moisture from the measured radiant surface temperature. The triangle method is applied to link the modelled soil moisture with satellite derived scaled NDVI and scaled LST to retrieve soil moisture map. Carlson (2007) also applied the triangle method and a SVAT model for estimation of evaporative fraction and soil moisture from measured surface parameters of scaled LST and vegetation fraction (Fr). The 3rd order polynomial relation ( M 0 , EF ) =

3

3

¦¦ a i = 0 i =0

ij

T *i Fr j was proposed and the obtained

multiple correlation R2 for both parameters are close to 1.0 and RMSE between the polynomial values and raw model output is less than 2 percent. According to Carlson (2007) the triangle method is insensitive to initial atmospheric and surface conditions, net radiation and atmospheric correction, yet can yield accuracies comparable to other methods. Recently the triangle method was applied by Wang et al. (2007) for soil moisture estimation at 1 km resolution in eastern China Shandong province, by relating the ground observed soil moisture at point scale with the satellite derived surface parameters NDVI and LST. They applied a 2nd order polynomial relation algorithm to estimate soil moisture. For a total of 93 ground stations with valid data, the results obtained was a relative error approaches 0, and the standard errors were less than 0.05; the coefficient of determination for 55 stations were greater than 0.8, 71 stations greater than 0.7 and 82 stations were greater than 0.6.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

5. Methodology 5.1.

General approach of the triangle method

Triangle method follows four work phases and eight major processing steps to obtain operational, reasonably accurate, high-resolution soil moisture by linking ground measured soil moisture with optical/IR parameters as follows. Summary of the general approach of the triangle method is listed in Table 5-1 and the general flow diagram of the method is shown in Figure 5-1. Table 5-1 Phases and schematic processing steps for the triangle method from remote sensing

Phase no. One

Phase work

Processing step

Description

Field work

Measure soil moisture in the field

Soil moisture can be measured using both direct and indirect method

Two

Remote sensing

Calculate NDVI

NDVI can be calculated using equation 5.2 below. LST can be retrieved either from MODIS product or using split window technique.

Retrieve LST Plot NDVI and LST Calculate NDVI* or Fr and T* Three

Four

Developing regression

Mapping of soil moisture

Graphic visualization of the NDVI/LST triangle Scaled NDVI and LST between its bare soil and dense vegetated values.

Set up polynomial equations of N* and T* with ground measured soil moisture

The set up can be 1st, 2nd, and 3rd order polynomial function of equation 3.13

Determine the coefficients of the polynomial equation by fine tuning the equation

Coefficients can be calibrated using least square method

Spatially map soil moisture

Using GIS packages and the equations derived by coupling remote sensing with ground measurement soil moisture

i =n j =n

(i )

M = ¦¦ aijNDVI * T *

( j)

i =0 j =0

Phase one Field work: In this phase 49 sampling points were measured using both direct and indirect methods of soil moisture measurement techniques as described in section 3.1 during field campaign.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Phase two Remote sensing: The second phase includes retrieving both NDVI and LST at 1km resolution from MODIS sensor, creating LST vs NDVI feature space and computing scaled NDVI* and T*. Phase three Developing regression relation: In case of relating soil moisture measured at the field with remote sensing scaled NDVI and scaled LST, a system of equation 4.12 was set up using ground observed soil moisture and remote sensing scaled NDVI and LST for all pixels matching the site of each ground stations. The coefficients of the polynomial relations are determined using least square method by calibrating the algorithm. Phase four Mapping soil moisture: After calibrating and validating of the developed algorithm in phase three, soil moisture can be estimated or mapped from the retrieved NDVI and LST at 1km resolution of the MODIS data. The regression relations, in conjunction with high-resolution NDVI and LST are then regressed backward, to obtain soil moisture at high resolution. The summary of phases and processing steps are found in Table 5-1. In this study soil moisture simulation from remote sensing by triangle method was tested using 2nd and 3rd order polynomial function of LST with NDVI and also 3rd order polynomial function of LST with fractional vegetation. Gillies et al.(1997) and Quattrochi and Luvall (2004) used fractional vegetation (Fr) instead of NDVI. Fr is established from a transform between NDVI and Fr following equation 5.4. The major processing steps mentioned in Table 5-1 that was applied to estimate surface soil moisture using triangle method are described in detail as follows: Retrieving NDVI and LST: - These two parameters are retrieved from MODIS image using the method described under remote sensing section 5.2 for all field days (i.e. Sep.18, 2008 - Sep.29, 2008).

Plotting NDVI and LST: - This can be done by crossing the raster images of the retrieved LST to the retrieved NDVI pixel by pixel base for all images using ILWIS. From this cross, a table can be formed which contains LST and NDVI in separate columns. The table formed by crossing LST and NDVI is exported to spreadsheet and then after, the plots between the two parameters can be produced. Calculate N*, Fr and T*:- In this step the main task was to determine NDVImax, NDVImin, Tmax and Tmin from the scatter plots formed above. In principle NDVImin is the value of the pixels that resembles for bare soil while NDVImax is the value of pixels covered by vegetation. However, for LST the reverse is true (i.e. Tmax is for bare soil and Tmin is for vegetation). Generally, the maximum and minimum values for both NDVI and LST can be related simply by observing the scatter plots between the two parameters as indicated in Figure 6-8. Corrupted and water pixels in the scatter plot are removed. Scaled LST (T*) and scaled NDVI (N*) are obtained by applying equation 4.10 and 4.11 respectively after determining the corresponding maximum and minimum values from the scatter plots. Fractional vegetation cover (Fr) is obtained using equation 5.4 by simply squaring the scaled NDVI (N*). Setup polynomial relations of ground observed soil moisture with N* or Fr and T*:- Before setting the polynomial relation, soil moisture measured in the field is converted into a point map by 28

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

using the corresponding coordinate information collected in the field using ILWIS software. Once the point map is produced the information of soil moisture, NDVI and LST at the pixel level taken from the images using pixel information tools in ILWIS by overlying the point map of soil moisture and raster maps of NDVI and LST. The polynomial relation of equation 4.12 is constructed/ modelled in a spreadsheet based on the point information of ground measured soil moisture, NDVI and LST. The coefficients of equation 4.12 are determined by fine tuning of the relations using least square method by minimizing the sum of the square errors between the measured and simulated soil moisture and by changing the values of the coefficients using solver tools in excel. The spread sheets of the three polynomial equations are found on Appendix-5, Appendix-6 and Appendix-7.

Calibration and Validation of the algorithms: Calibration stands for fine-tuning of the coefficients to improve the performance of the algorithm. In order to do calibration and validation, the measured soil moisture is grouped into two data set one for calibration and the other dataset for validation. The data set from Sep.18, 2008 to Sep.26, 2008 a total of 35 measured points are used for calibration and the data set of Sep.27, 2008 and Sep.29, 2008 a total of 14 points are used for validation. To define nth order of polynomial relation the coefficients will be calibrated by comparing the simulated soil moisture with the observed soil moisture until the simulated shows acceptable level of agreement. This level of agreement is evaluated by objective functions that measure the level of agreement between the observed soil moisture and the simulated soil moisture. Two different objective functions are considered: the root mean square error and coefficient of determination R2. Root mean square error is a frequently used measure of the differences between values predicted by the algorithms and the actually observed from the ground. It is one of many ways to quantify the amount by which an estimator differs from the true value of the quantity being estimated. RMSE =

i= N

¦ i =1

( X o − X s )2 N

5.1

Where RMSE is root mean square error, Xo is observed soil moisture, Xs is simulated soil moisture and N is the number of samples. To validate the algorithm (model), the algorithm coefficients have to be tested against on independent set of field conditions; in this study validation data of Sep.27, 2008 and Sep.29, 2008 is selected for validation. If the calibrated algorithm set of coefficients fails on the validation period the algorithm is regarded as unreliable and so not usable.

Spatial map of soil moisture: - Soil moisture can be mapped both spatially and temporally using the algorithms developed with the relations of observed soil moisture and remote sensing NDVI and LST by using different GIS package software.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Phase one

Phase two

Phase three

Legend

Phase four

Figure 5-1 Flow diagram of the general procedure for soil moisture estimation from remote sensing using triangle method

5.2.

Remote sensing

Before doing regression analysis of equation 4.12 to obtain soil moisture at high resolution, land surface temperature and NDVI from remote sensing should be retrieved accurately. The extensive requirement of temperature information on a large scale for environmental studies and management activities of the earth’s sources has made the remote sensing of Land surface temperature (LST) an important issue in recent decades. However, retrieving land surface temperature from thermal bands needs a series of steps. Methods to correct radiometric surface temperature for atmospheric interference are classified in to three categories: • Direct methods or single infrared channel method: that use radiation transfer models together with atmospheric radio soundings, satellite vertical sounder and climatological data.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

• •

Indirect methods that are based on split window or in situ temperature observations (Parodi, 2002). A new physics based day/night MODIS LST method: this is designed to take advantage of the unique capability of the MODIS instrument.

Studies based on direct methods suffer from data deficiency and reliability that comes from the sparse existing radio sound station network. The second method makes corrections for the atmospheric and surface emissivity effects with surface emissivity as input based on the differential absorption in split window. The third method uses day/night pairs of TIR data in seven MODIS bands for simultaneously retrieving surface temperatures and band averaged emissivities without knowing atmospheric temperature and water vapour profiles to high accuracy. For this study both second and third methods i.e. split window and day/night MODIS LST methods are compared with the ground measured surface temperatures. LST retrieved by applying split window technique is based on the available thermal bands of the sensor channel 31 and channel 32 for MODIS sensor, emissivity and transmissivity of every pixel of the image whereas an alternative LST is retrieved using the third method directly taken from MODIS level3 LST product from MODIS data base.

5.2.1.

NDVI (Normalized Difference Vegetation Index)

To retrieve NDVI from MODIS sensors the following procedures are used. NDVI =

Ch 2 Sur − Ch1Sur Ch 2 Sur + Ch1Sur

5.2

Where, Ch1Sur and Ch2Sur are atmospherically corrected ground reflectance in Ch1 and Ch2 respectively. To retrieve NDVI from MODIS image pre-processing such as geometric, radiometric and atmospheric corrections are a prerequisite for image analysis. Figure 5-2 shows the steps that are applied to retrieve NDVI from MODIS raw images for all days in which the images are analyzed for soil moisture estimation.

Step I File format conversion The calibrated raw images of MOD021KM and MYD021KM from MODIS data are acquired in Hierarchical Data Format (HDF). HDF is the standard data storage format selected by the Earth Observing System Data and Information System. It is developed and maintained by the National Centre for Supper Computing Applications (NCSA) at the University of Illinois at Urbana-Champaign (http://nsca.uiuc.edu). Generally, HDF is designed to allow sharing of self describing files across heterogeneous platforms. However, the HDF file format is not supported by ILWIS software. Therefore, the first step for preprocessing images is converting HDF file in to GeoTIFF file that can be read by ILWIS software and can be processed by using MODIS swath tool software. Since the swath width (2030x2030) km of MODIS image is too large to process; image sub-setting to the area of interest is done simultaneously with file conversion using MODIS swath tool software (level 1B image is swath data type). Spatial subset can be done with latitude of 11.250 - 12.250 and longitude of 37.250 - 38.50 and the output pixel size is 0.010 or 1000m. During file format conversion there are 85 different Science Data Sets (SDS) 31

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

in the MODIS level 1B Earth view products. From these 85 available SDS only EV_250_Aggr 1KM_RefSB band1 and band2 are required for NDVI and EV_1KM_Emissive of band 31 and band 32 are required for LST analysis. MOD03 geolocation HDF files (surface height above geoids, solar zenith and azimuth angles, and satellite zenith and azimuth angles) can also be converted in to GeoTIFF file format in the same way as MODIS level 1B data products. The converted GeoTIFF file can be imported to ILWIS software for further processing and analyzing of images. Each band is imported separately using import options of ILWIS using file menu option under the main menu by using ‘Use GDAL’ import format options.

Step II Conversion of raw DN value to reflectance value Level 1B generates two calibrated data products for the Reflective Solar Bands (RSBs): the reflectance and the Earth-exiting radiance. Writing these two products in floating-point format to the level 1B Earth view product files would make the file sizes prohibitively large. Instead, level 1B writes a 16-bit scaled integer representation of the calibrated digital signals measured by the MODIS, from which the reflectances and radiances can be calculated from two pairs of scale and offset terms written as attributes to the reflective band SDSs. These two pairs are derived from the calibration parameters that are input to level 1B as look up tables. Level 1B corrects the raw digital signals measured at the Reflective Band Detectors, DN, for all known instrumental effects , to produce corrected digital signals, dn*. Corrections are applied for the following effects: • Electronic offsets • Non-linearities in the analogue to digital converters • Angular variations of the scan mirror reflectance • Variations in gain caused by variations in the instrument and focal plane temperatures Level 1B then adjusts the values of dn* for the effect of variations in calibration parameters from detector to detector within each band so that one pair of calibration terms applies to every detector in each band. The values of dn* adjusted in this way, called SI, are scaled to the 15-bits of the 16-bit integer representation in the reflectance solar bands SDSs. The scaled integer values, SI, can be converted to reflectance values from the reflectance bands according to MODIS Calibration Support Teams (MCSTs) linear calibration algorithm:

ȡcos(Ĭ) = reflectance_scales(S I − reflectance_offsets)

5.3

Where ȡcos(Ĭ) is reflectance values, reflectance_scales and reflectance_offsets are obtained from the meta data of level 1B product files and it can be read using HDF viewer software.

Step III Atmospheric correction Atmospheric correction methods can be grouped according to the final product required by the application. Generally the methods are grouped into two: relative and absolute atmospheric methods. Relative atmospheric methods are simple empirical methods that include invariant object, histogram matching, and dark object. 32

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Absolute atmospheric correction methods require a description of the components in the atmospheric profile. The output of these methods is an image that matches the reflectance of the ground pixels with a maximum estimated error of 10%, if atmospheric profile is adequate enough (Kerle et al., 2004). Some typical examples of radiative transfer models used for absolute atmospheric correction are: LOWTRAN, MODTRAN,6s, 5s and SMAC (Simplified Method for Atmospheric Correction) which all are described in (Kerle et al., 2004). Absolute methods produce accurate results but they need the acquisition of atmospheric parameters like aerosol properties, ozone and water vapour content. Especially LOWTRAN and MODTRAN methods require large effort to make atmospheric corrections. The Simplified Method for Atmospheric Corrections (SMAC) is a faster technique especially when the coefficient files for sensors are available and also when viewing and solar angles are less than 500 and 600 respectively. According to Rahman and Dedieu (1994) SMAC is capable of calculating atmospheric parameters for several satellite spectral bands with results that are closely similar to 5s. Since, the viewing and solar angles of the acquired images for this study are less than 500 and 600 respectively and the aerosol optical depths are less than 0.8 at 550nm as shown in Table 5-2, SMAC is applied for the reflectance bands for this study. MOD08_D3 MODIS atmospheric products are used for retrieving optical thickness, water vapour content and total ozone for SMAC atmospheric correction. This is a level-3 MODIS gridded atmosphere daily global joint product. It contains daily 1x1 degree grid average values of atmospheric parameters related to atmospheric aerosol particle properties, total ozone burden, atmospheric water vapour etc. Table 5-2 MODIS/Terra solar and sensor zenith angle and atmospheric parameters

Image Acquisition Date 18-09-08 19-09-08 20-09-08 22-09-08 23-09-08 24-09-08 25-09-08 27-09-08 29-09-08

Solar zenith angle (deg.)

Sensor zenith angle (deg.)

18.11 30.48 20.94 23.82 15.69 26.72 18.21 20.85 23.58

35.47 58.29 10.01 19.09 58.73 41.95 45.00 23.77 4.96

Optical depth (nm) 0.41 0.29 0.30 0.53 0.34 0.57 0.40 0.23 0.30

Total ozone content (atm.cm) 0.27 0.26 0.27 0.27 0.27 0.28 0.27 0.28 0.27

Water vapour (gcm-2) 2.37 2.24 2.27 2.26 1.60 2.34 2.31 2.02 1.68

Step IV Normalized Difference Vegetations Index (NDVI) computation NDVI is one of the most widely used vegetation indices to monitor the spatial and temporal distribution of vegetation presented in certain area. It is derived from remotely sensed near infrared and red bands (see equation 5.2) due to the high spectral reflectance of vegetation in the near infrared bands. The value ranges from -1.0 to 1.0, where negative values are water pixels and positive values

33

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

are land surface pixels. The typical range for land surface is 0.1 for bare soil and 0.9 for dense vegetation.

Determination of fractional vegetation cover (Fr):- Fractional vegetation cover is an important parameter that have key role in the energy exchanges at the land surface. It measures how much the land surface is covered by vegetation. Remote sensing provides a seemingly obvious data source for quantifying Fr over large areas, and several methods have been developed in the past few decades. Most of the developed methods are using NDVI to determine Fr. For this study the method developed by Gillies et al (1997) is used.

§ (NDVI − NDVI min ) · ¸¸ Fr = ¨¨ © ( NDVI max − NDVI min ) ¹

2

5.4

Where Fr is fractional Vegetation cover, NDVImax is maximum NDVI and NDVImin is minimum NDVI of the image. Unlike the case for the NDVI, this scaling reduces but does not eliminate calibration and correction issues of images.

Legend

Figure 5-2 General procedures to retrieve NDVI from MODIS

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

5.2.2.

Land Surface Temperature computation using split window techniques

The derivation of the algorithm for LST retrieval is based on thermal radiance of the ground and its transfer from the ground through the atmosphere to the remote sensor. Generally speaking, the ground is not a black body thus ground emissivity has to be considered for computing the thermal radiance emitted by the ground and also the atmosphere has important effects on the received radiance at remote sensor level. The method developed by Mao et al. (2005) is selected for this study to retrieve LST from MODIS because it considers both the effect of emissivity and atmospheric effect and also it is relatively simplified to apply. Moreover, it is possible to get transmittance from retrieval water content by near-infrared (NIR) bands of MODIS and make the computation of transmittance accurate for every pixel using this method without any atmospheric transfer model.

General approach of the algorithm The general approach of the algorithm can be described as shown in Figure 5-3. According to the character of MODIS data, the proposed method estimates the parameters (transmittance and emissivity) at pixel level. Atmospheric transmittance is an essential parameter for the accurate retrieval of LST, which influences the accuracy of the retrieval of LST. The knowledge of temperature and humidity profiles is needed in atmospheric transmittance calculation. These profiles can be estimated by use of radiosonde data. However, radiosonde measurements are performed only at upper atmosphere stations (radiosonde stations) and not at meteorological ground stations. Studies based on these data usually suffer from data deficiency and reliability that comes from the sparse density of radiosonde stations network. By the relation between NIR band sensitivity and the water content of the atmosphere, it is possible to retrieve transmittance of atmosphere from the MODIS image. Further more estimates the transmittance of every pixel of the image by the water content of the atmosphere, which overcomes the problem of only one transmittance in an image in many split window algorithms. The cloud pixels which have much lower temperatures than the land surfaces and much higher reflectance than the land surfaces are masked using cloud mask product of MODIS before using split window methods. MODIS reflectance bands (band1, band2 and band5) are acquired and pre-processed using the steps mentioned under section 5.2.1 to compute NDVI. NIR bands from MOD021KM (band17, 18 and 19) are used to retrieve water content and transmittance of the atmosphere while thermal bands (band 31 and 32) are used to retrieve LST by applying a split window technique.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Legend

Figure 5-3 Methodology to retrieve land surface temperature (modified after Mao et al., 2005) The radiance transfer equation is the base of thermal remote sensing and LST retrieval where Planck function is the essential part of the radiance transfer equation. Because of the complexity of the Planck function, a simplification of Planck function is the precondition of LST retrieval. Mao et al. (2005) proposes a method to simplify the Planck function and to simulate the relation between radiance of MODIS 31/32 and the temperature. The transmittance of the atmosphere and emissivity of the land surface are the two key parameters of LST retrieval. Transmittance is often obtained from the simulation of the atmosphere software (6s, LOWTRAN, MODTRAN, etc.). However, in this algorithm water content can be retrieved from NIR channels of MODIS image and then transmittance can be calculated from water content. The emissivity of land surface is estimated from visible and infrared (VIR) and NIR band of MODIS data.

The simplification of Planck function: The general radiance transfer equation by Ottle and Stoll (1993) for remote sensing of LST can be formulated as follows.

[

]

Bi (Ti ) = τ i (θ ) ε i Bi (Ts ) + (1 − ε i )Li ↓ + Li ↑

36

5.5

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Where Ts is the LST, Ti is the brightness temperature in channel i, IJi(ș) is the atmospheric transmittance in band i at viewing angle ș (zenith angle from nadir), and İi is the ground emissivity. Bi (Ts) is the ground radiance, and LiĻ and LiĹ are the downwelling and upwelling path radiances, respectively. Upwelling and downwelling radiances and transmittance from equation 5.5 can be obtained by applying radiative transfer model like MODTRAN. Every term of radiance transfer equation owes Planck function. Therefore, it is a must to apply radiance transfer equation to solve equation 5.5. The products of LST usually utilize the look-up table (LUT) which utilize a linear interpolation to simplify the Planck function. After getting all the necessary data from the radiative transfer model equation 5.5 can be re written as follows to get ground radiance İiBi (Ts) ª ( Bi (Ti ) − Li ↑) º » − (1 − ε i ) Li ↓ τ i (θ ) ¬ ¼

ε i Bi (Ts ) = «

5.6

Equation 5.6 can be solved by Planck function as follows

ε i Bi (Ts ) =

ε i C1

λi π [exp(C 2 / λi T ) − 1] 5

5.7

Where C1 is first radiation constant =3.74151*10-16 Wm-2, C2 is second radiation constant = 0.0143879 mK and Ȝi is wave length of channel i. Combining equation 5.5 and 5.7 and knowing the surface emissivity, it is possible to compute surface temperature by inverting equation 5.6 as follows:

Ti =

[

C2

]

λi ln ε i C1 / ε i Bi (Ts )λi π + 1 5

5.8

In MODIS there are two thermal bands so from equation 5.8 there will be two unknown emessivities and one surface temperature and implies that the equations are not solvable as it is. Basically, there are three different techniques to make the above equation determinate by applying different assumptions. These are Emissivity ration method, two temperature method and emissivity separation method (TES). However, according to (Mao et al., 2005) the above equation 5.5 is simplified as linear equation to fit MODIS band 31 and 32 as equation 5.9 and 5.10 by passing radiative transfer model and planks function . For band 31: B31 (T ) = 0.13787T31 − 31.65677

5.9

For band 32: B32 (T ) = 0.11849T32 − 26.50036

5.10

The retrieval method of water content through MODIS data: - Among the 36 bands of MODIS, five of them are NIR bands: 2 (0.865µm), 5 (1.24 µm), 17 (0.905 µm), 18 (0.936µm) and 19 (0.940 µm). Band 17, 18 and 19 are three absorption bands, but bands 2 and 5 are atmosphere window bands. Kaufman and Gao (1992), by many experiments, conclude that the retrieval of water content by ratio is available and for details reference is made to the article. Five bands in MODIS are devised to retrieve water content according to this principle. The two and three band ratio approaches to retrieve the water content of the atmosphere. The equations are as follows:

τ w (i ) = ρ (i ) / ρ (2)

5.11

τ w (i ) = ρ (i ) / [C1ρ (2) + C 2 ρ (5)]

5.12 37

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Where ȡ(i), (i=17,18,19),ȡ(2) and ȡ(5) represent the reflectance of bands 2 and 5 respectively, IJw represents the transmittance of i channel. C1 and C2 are coefficients. For band 18, C1 equals 0.8 and C2 equals 0.2 (C1 and C2 are computed according to the linear approximate between three bands reflectance at the ground). The two approaches retrieve the water content of the atmosphere by using the same principles that use the relationship between water content and the ratio of absorption band and the window band of the atmosphere. For the relationship of water content and transmittance of the atmosphere Kaufman and Gao (1992) gives the expression as equation 5.13.

(

τ w (19 / 2) = exp α − β w

)

5.13

For complex ground surface Į= 0.02, ȕ = 0.651 and w is water content. IJw (transmittance) can be found from the image of band 2 and band 19. So water content can be obtained through equation 5.14:

§ α − ln τ w w = ¨¨ β ©

· ¸¸ ¹

5.14

According to Mao et al.(2005) the transmittances of MODIS 31/32 are prominently different at the same water content. With the increase of water content of atmosphere, this difference of transmittance also increases and the transmittance is also a function of temperature, although the temperature influences little as compared to the water content. Therefore, they set an exponential equation for the transmittance of MODIS 31/32 with water content as follows: For band 31: τ 31 = 2.89798 − 1.88366e −

( w / − 21.22704 )

For band 32: τ 32 = −3.59289 + 4.60414e ( w / −32.70639)

5.15 5.16

Determination of emissivity of the ground: - emissivity of ground surface is also a critical parameter that affects the accuracy of LST using split window algorithm. The emissivity is mainly determined by the structure of ground surface and the range of the spectral band considered. Most terrestrial materials have an emissivity higher than 0.97 with small changes in the ranges of MODIS bands 31/32 (10.780-11.280µm and 11.770-12.270 µm). Generally speaking, the pixels of MODIS can be classified as water pixels and land pixels mainly composed of various fractions of vegetation and soil. However, for this study narrow band emissivities for MODIS band31 and 32 are taken from MODIS emissivity product. Split window algorithm: - Split-window algorithm is previously proposed to retrieve LST for NOAA/AVHRR4/5. The general algorithm of split-window can be depicted as follows: Ts = T4 + A(T4 + T5 ) + B

5.17

Ts represent LST, A and B are parameters. T4 and T5 are brightness temperatures of AVHRR 4/5, respectively. The unit of Ts, T4, T5 is K. The practical split window algorithm for retrieving LST from MODIS data developed by Mao et al.(2005) is used. The algorithm is simplified based on emissivity and transmittance of MODIS band 31/32 as follows. For detail derivation of split window algorithm for MODIS data refer (Mao et al., 2005). Ts = (C 32 ( B31 + D31 ) − C 31 ( D32 + B32 )) /(C 32 A31 − C 31 A32 )

38

5.18

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Where Ts is Land surface Temperature, and A31 = 0.13787ε 31τ 31 B31 = 0.13787T31 + 31.65677τ 31ε 31 − 31.65677 C 31 = (1 − τ 31 )(1 + (1 − ε 31 )τ 31 )0.13787 D31 = (1 − τ 31 )(1 + (1 − ε 31 )τ 31 )31.65677 A32 = 0.11849ε 32τ 32 B32 = 0.11849T32 + 26.50036τ 32 ε 32 − 26.50036 C 32 = (1 − τ 32 )(1 + (1 − ε 32 )τ 32 )0.11849 D32 = (1 − τ 32 )(1 + (1 − ε 32)τ 32 )26.50036

All these series of equations are coded in ILWIS using script to retrieve LST from MODIS 31/32 bands of raw calibrated level 1B images. For ILWIS script see Appendix-4.

5.2.3.

Land surface temperature products from MODIS sensor

Besides the split window technique LST was derived directly from MODIS level 3 products as an alternative. The MODIS LST and emissivity products provide per-pixel temperature and emissivity values. Averaged temperatures are extracted in degree Kelvin with a day/night LST algorithm applied to a pair of MODIS day time and night time observations. This method yields 1K accuracy for materials with known emissivities, and view angle information is included in each LST/emissivity product. The MODIS LST products are created as a sequence of products beginning with a swath (scene) and progressing, through spatial and temporal transformations, to daily, eight day and monthly global gridded products. The MODIS LST products are archived in Hierarchal Data Format- Earth Observing System (HDFEOS). LST data products are produced as a series of seven products. The sequence begins as a swath (Scene) at a nominal pixel spatial resolution of 1km at nadir and nominal swath coverage of 2030 or 2040 lines (along track, about five minutes of MODIS scans) by 1354 pixels per lines. A summarized listing of the sequence of product is given in Table 5-3. Table 5-3 Summery of MODIS LST products

Earth Science Data Type MOD11_L2 MOD11A1 MOD11B1 MOD11A2 MOD11C1

Product level L2 L3 L3 L3 L3

Spatial resolution 1Km at nadir 1Km (actual 0.927 km) 6km (actual 5.56 km) 1Km (actual 0.927 km) 0.050 by 0.050

Temporal resolution Swath (scene) daily daily Eight days daily

MOD11C2

L3

0.050 by 0.050

Eight days

MOD11C3

L3

0.050 by 0.050

monthly

Map projection None. (lat, lon.) Sinusoidal Sinusoidal Sinusoidal equal-angle geographic equal-angle geographic equal-angle geographic

39

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

MOD11A1 day time product is selected for this study because of its spatial and temporal resolution (1km and daily) respectively and it only has data values with minimal cloud influence. The other advantage of using this product is that the cloud affected pixels are already masked from the image. MOD11A1 is constructed with the results in the MOD11_L2 (generated using the MODIS sensor radiance data product MOD021km, the geolocation product MOD03, the atmospheric temperature and water profile product MOD07_L2, the cloud mask product MOD35_L2, the quarterly land cover MOD12Q1, and snow product MOD10_L2) products of a day through mapping the SDSs of all pixels in MOD11_L2 products on to grids in the sinusoidal projection and averaging the LST values of overlapping pixels in each grid with overlapping areas as weight. It is comprised of daytime and night time LSTs, quality assessment, observation time, view angles, clear sky coverage and emissivities in band 31 and 32 estimated by the classification-based emissivity method (Snyder et al., 1998) according to land cover types in the pixel. The MODIS LST products MDO11_L2, MOD11A1, MOD11A2, and MOD11B1 have been validated at stage 1 with in situ measurements in 28 clear-sky cases including 19 cases over land sites in the temperature range of 263-322 K and the column water vapour range of 0.4-4cm.

Acquirement of MODIS LST product MODIS data or products can be found and downloaded free of charge from Earth Observing System Data Gateway (http://edcimswww.cr.usgs.gov/pub/imswelcome). MODIS level 3 LST products are defined on a global 1km sinusoidal grid. Because the grids are unmanageably large in their entirely (43200X21600 pixels at 1km, and 172800X86400 pixels at 250m), they are divided into fixed tiles approximately 100x100 in size.

Study Area (h21v07)

Figure 5-4 MODIS sinusoidal grid system Tiles are 10 degrees by 10 degrees at the equator. The tile coordinate system starts at (0, 0) (horizontal tile number, vertical tile number) in the upper left corner and proceeds right (horizontal) and downward (vertical). The tile in the bottom right corner is (35, 17). Based on the tile grids above, the study area is located at (21, 7) horizontal tile number 21 and vertical tile number 7 as indicated above in Figure 5-4.

40

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Images re-projection: MODIS imagery, however, is in a new map projection called the Sinusoidal (SIN) projection, which is not supported by most existing software packages. So before those images can be used by other software packages, re-projection should be pre-processed. The MODIS Tool is software designed to help individuals work with MODIS data by re-projecting MODIS images (Level 3) data products in to more standard map projections. The software outputs MODIS data in file format that are supported by existing software packages GeoTIFF. By using this package, MODIS productions were converted to GeoTIFF file format, which can be read by ILWIS software. The reprojection parameters are shown below: Re-sampling type: Nearest Neighbour, UTM Zone: 37N Output projection Type: UTM, Output pixel size: 1000m, Datum: WGS 84 The Converting GeoTIFF file can be imported to ILWIS for further image processing. The LST product has a unit of Kelvin and the data type is 16-bit unsigned integer with a valid range of 750065535. To convert these integer values in to Kelvin multiply by a scale factor of 0.02 is applied. The scale factor can be obtained from the attributes of the image using HDF viewer software.

5.2.4.

Potential temperature

Potential temperature is the temperature that a parcel would acquire if adiabatically brought to a standard reference pressure P0, usually 1013mb. To minimize terrain effects that are due to large elevation difference (around 1900 m) from the peak to the outlet of the catchment, potential temperature is required for elevation correction against land surface temperature. Potential temperature can be calculated using equation 5.19. §P · Θ = LST ¨ 0 ¸ ©P¹

0.286

5.19

Where :Ĭ is the potential temperature in K, LST is the near surface layer air temperature or land surface temperature in K , P0 is standard reference pressure usually 1013 mb and P is the atmospheric pressure at a surface in mb. P can be computed at different elevation (Z) by equation 5.20.

§ 293 − 0.0065Z · P = 1013¨ ¸ 293 © ¹

5.26

5.20

Atmospheric pressure can be computed from the re-sampled DEM originally processed from SRTM data at 90 m resolution into 1km MODIS resolution. After computing atmospheric pressure through equation 5.20 and retrieving LST at 1km resolution from MODIS data potential temperature can be calculated using equation 5.19 with the same spatial and temporal resolution of LST.

5.3.

Algorithm Development

The algorithms that are capable of estimating soil moisture from remote sensing is developed from 2nd and 3rd order polynomial relations of ground measured soil moisture with scaled NDVI and LST, 3rd order polynomial relation of ground measured soil moisture with fractional vegetation cover and scaled LST and 2nd order polynomial relations of ground measured soil moisture with scaled NDVI and scaled potential temperature.

41

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

2nd order polynomial relation algorithm M =

i=2 j=2

¦¦ aijNDVI

* (i )

T*

( j)

:

i =0 j =0

This algorithm has a total of 9 coefficients by relating observed soil moisture with scaled NDVI and scaled LST derived from remote sensing. NDVI and LST maps are produced for each day for the study period following the steps mentioned under section 5.2. Scatter plots of NDVI and LST were formed through crossing in ILWIS. From the scatter plots the minimum and maximum NDVI and LST are determined and using these minimum and maximum values and by applying equation 4.10 and 4.11 the scaled LST and scaled NDVI are calculated for each pixel. After calculating the scaled NDVI and scaled LST the polynomial relations are formed between the observed soil moisture with scaled surface parameters at pixel level as follows.

M = a 00 + a10 N * + a 20 N * 2 + a 01T * + a 02T *2 + a11 N * T * + a12 N * T *2 + a 21 N *2 T * + a 22 N *2 T * 2 Where M is observed soil moisture, a00-a22 are coefficients and N* and T* are scaled NDVI and scaled LST respectively. The coefficients are determined using least square method.

3rd order polynomial relation algorithm M =

i =3 j =3

¦¦ aijNDVI

* (i )

T*

( j)

:

i =0 j =0

The 3rd order polynomial relation algorithm is developed following the steps mentioned above but with 17 coefficients defined as:

M = a 00 + a10 N * + a 20 N *2 + a 30 N * 3 + a 01T * + a 02T *2 +... + a 23 N * 2 T *3 + a 33 N *3 T *3 3rd order polynomial relation algorithm M =

i =3 j =3

¦¦ aijF

r

(i )

T*

( j)

: This algorithm is developed with

i =0 j =0

the relations of observed soil moisture with fractional vegetation cover and scaled LST applying 3rd order polynomial relations following the steps explained above. The fractional vegetation cover is computed by equation 5.4 from NDVI. The equation is similar to the above 3rd order polynomial algorithm with 17 coefficients except replacing scaled NDVI with fractional vegetation cover and reads:

M = a 00 + a10 Fr + a 20 Fr + a30 Fr 3 + a01T * + a 02T *2 +... + a 23 Fr T *3 + a33 Fr T *3 2

2nd order polynomial relation algorithm M =

2

i =3 j =3

¦¦ aijNDVI

* (i )

Θ*

3

( j)

:

i =0 j =0

This algorithm is developed for the purpose of minimizing the topographic effect on the simulated soil moisture by replacing the elevation correction potential surface temperature with LST. The set up of this algorithm is similar to the above 2nd order polynomial with 9 coefficients and reads:

M = a 00 + a10 N * + a 20 N * 2 + a 01Θ * + a 02 Θ *2 + a11 N * Θ * + a12 N * Θ *2 + a 21 N *2 Θ * + a 22 N *2 Θ *2

42

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

5.4.

Statistical analysis

The spatial variations in soil moisture content can be understood in the context of a combination of several hydrological processes (i.e. infiltration, vertical and lateral redistribution, and evapotranspiration) that are related to precipitation, topography and land use. Topographic attributes including land use and terrain indices like aspect, relative elevation and hill slope position largely affect the spatial distribution of soil moisture content. The spatial and temporal distribution of simulated soil moisture is characterized by: • Statistical analysis of the spatial and temporal distributions. • Identifying locations of temporal persistence. • Assessing the relation between soil moisture statistics and terrain attributes. The statistical analysis consists of both spatial and temporal mean, standard deviation and coefficient of variation of soil moisture simulated during the study period. The spatial mean of soil moisture, θ v,t , in the catchment for each sampling day is computed as: i = Ns

θ v ,t =

¦θ

v ,i

i =1

5.21

Ns

Where Ns is the number of pixels in a given date s=1, 2, 3…, Ns and θ v , i is the volumetric soil moisture value for each pixel i. The standard deviation, σ (θ v ,t ) and the coefficient of variation (CVt) can be calculated for the catchment as follows: Ns

¦θ

σ (θ v , t ) = CVt =

, −θ v ,t

v i

i =1

Ns −1

σ (θ v , t ) θ v ,t

5.22

5.23

The temporal mean of volumetric soil moisture, θ v, s , at each pixels over the study period is computed as: Nt

θ v,s =

¦θ

,

v i

i =1

Nt

5.24

Where Nt is the number of days of the study period in which the soil is simulated at a particular pixels and θ v , i is the pixel soil moisture value. Standard deviation, σ (θ v , s ) in the time dimension and the coefficient of variation, Cvs, of the volumetric soil moisture are defined in a similar fashion to equation 5.22 and 5.23 respectively.

43

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Temporal persistence of soil moisture patterns is assessed through time stability analysis based on the −

mean relative difference, δ t , see (Vachaud et al., 1985) and the root mean square error of the relative difference, RMSEįi, see (Jacobs et al., 2004). The mean relative difference captures the difference between a location and the spatial mean for all time periods and is evaluated as:

θ v , i −θ v ,s ¦ θ v ,s i =1 Nt

−

δi =

5.25

Nt −

Nt is the total number of sampling dates. In this case, δ i is computed for each pixel in the catchment. −

The pixels that have values of δ i close to zero indicate that the site has catchment averaged conditions, while positive or negative values imply relatively wetter and drier. The variance of the relative difference, σ (δ i ) 2 , is defined as:

σ (δ i

)

2

N t § θ v , i −θ v , s − · 1 ¨ − δ i ¸¸ = ¦ N t − 1 i =1 ¨© θ v , s ¹

2

5.26

Small values of σ (δ i ) 2 indicate stable sites in the time dimension where the relative wetness remains constant during the study period. The RMSEįi is a single metric used to classify time stability with respect to both bias and spread around the bias (Jacobs et al., 2004) and is computed as:

(

RMSEδ i = δ i + σ (δ i ) 2 2

)

1/ 2

5.27

Low values of RMSEįi indicate time stable locations that capture catchment averaged conditions.

Topographic effects: Topographic properties include elevation, slope and aspect that dominantly affect the estimated soil moisture by the developed algorithms. The analysis was done by crossing the temporal mean soil moisture, temporal coefficient of variation and relative difference with topographic fields. Slope and aspect are computed from the 90 m resolution DEM processed from SRTM using ILWIS software and re-sampled to 1000m pixel resolution to match the resolution of the MODIS image.

44

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

6. 6.1.

Results, analysis and discussion Observed soil moisture

The soil moisture was measured under different land covers inside and outside of the Gumara catchment at different locations both using direct and indirect methods. Soil moisture measured directly by gravimetric methods was analyzed in laboratory while soil moisture measured indirectly using theta probe is analyzed by averaging many measurements for a single sampling site as shown in Figure 3-1. The correlation of both direct and indirect soil moisture measurement is done for sampling sites of which both measurements were taken and as shown in Figure 6-1. From the correlation made between the two the correlation coefficient R2= 0.86 was obtained.

0.6

y = 1.0397x - 0.0182 2

3

-3

Theta probe-SM (cmcm )

The reason for using both direct and indirect measurements in the field is to calibrate the indirect measurement (Theta probe) by the direct one (gravimetric method) measurements. From the correlation the slope of the trend line is almost 1 and the offset is less than 0.02 with good correlation coefficient. All this tells us that the two measurements are of good agreement. Less than 14% of the variation is caused by other factors than soil moisture, so the Theta probe data can be used as reference measurements for further analysis.

R = 0.864 0.4

0.2

0 0

0.2

0.4

0.6 3

-3

Gravimetric-SM (cm cm )

Figure 6-1 Correlation of soil moisture between direct and indirect methods

6.2. 6.2.1.

Remote sensing measurements NDVI

NDVI maps are retrieved from MODIS images of all days when soil moisture was measured in the field (see section 5.2.1). Table 6-1 shows, the minimum average NDVI of the catchment is 0.53 on Sep.18, 2008 and the maximum average NDVI is 0.68 on Sep.19, 2008. The standard deviation of the average NDVI is 0.049 for 9 days. Generally, the result shows that the temporal variations of the spatial average of NDVI values are low for all days. However, the average NDVI values are high for 45

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

all days when soil moisture measurements were taken. This can be seen on the NDVI map of Sep. 23, 2008 in Figure 6-4. The NDVI maps of the other days are shown in Appendix-8. The image of Sep.26, 2008 was removed from the analysis because it was completely covered by clouds. Table 6-1 NDVI values for Gumara catchment

DAY 18-09-08 19-09-08 20-09-08 22-09-08 23-09-08 24-09-08 25-09-08 27-09-08 29-09-08

NDVI-minimum 0.101 0.125 0.104 0.117 0.12 0.129 0.143 0.100 0.101

NDVI-maximum 0.779 0.761 0.758 0.89 0.765 0.792 0.765 0.756 0.776 STDEV

NDVI-average 0.53 0.68 0.61 0.67 0.63 0.63 0.59 0.57 0.57 0.049

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

After atmospheric correction

29-09-08

27-09-08

25-09-08

24-09-08

23-09-08

22-09-08

20-09-08

19-09-08

Before atmospheric correction 18-09-08

NDVI

Change of NDVI before and after applying atmospheric correction: - atmospheric correction is particularly important in calculating the vegetation index using the reflectance in the red and nearinfrared bands, since aerosol increases by reflecting back and perceptible water decreases by absorbing, the reflectance in each spectral band. Consequently, these effects make the NDVI value smaller than their true value. From the results obtained NDVI increases after atmospheric correction is done due to the fact that the impact of water vapour (absorption) is greater for NIR channels. The average NDVI of Gumara catchment before and after is presented in Figure 6-2. Since the atmospheric conditions have major effect on NDVI image atmospherically corrected NDVI is used for to simulate soil moisture. Figure 6-3 and Figure 6-4 shows the NDVI map before and after atmospheric correction of the Gumara catchment of Sep.23, 2008.

Days

Figure 6-2 Average NDVIs of the study area before and after atmospheric correction

46

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Figure 6-3 NDVI map from MODIS data Sep.23, 2008 before atmospheric correction

Figure 6-4 NDVI map from MODIS data Sep.23, 2008 after atmospheric correction

6.2.2.

LST (Land Surface Temperature)

Remote sensing based land surface temperatures were retrieved in two ways. 1) From the MODIS products and 2) Calculated from MODIS raw images using the practical split window technique as explained in section 5.2.2. Based on the results of the two methods, the average differences obtained for the study period range from 1.88 K to 2.69 K as shown in Table 6-2. From the table it is clear that the differences between the minimum values are relatively higher than the differences between the maximum values. This indicates that high differences occur for the pixels which have lowest LST values (pixels mostly near to the cloud affected pixels). Actually, the cloud pixels were removed from the images using MODIS cloud masking products during the image pre- processing, but the values of the pixels that are near to the cloud affected pixels remains low as can be seen from the LST map produced in Figure 6-6. The results of the two remote sensing based methods were also compared with the ground measured LST using radiometer during the field work as shown in Figure 6-5. In reality it is difficult to obtain in situ LST matching the MODIS image pixels with 1km x1km resolution exactly at the overpass time of the satellite for validation of the LST products. Generally, LST varies spatially but the ground measurement with radiometer measures at the temperature of a very small surface, practically one point compared to a MODIS pixel. Furthermore, ground emissivity results in an error in the ground 47

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

measurement of LST. However, to validate the remote sensing based LST with ground truth data the radiometer was programmed to record at every 5 minutes automatically to overcome the problem of satellite overpass time differences. Additionally, different emissivities were assumed based on the land cover where the radiometer is installed using the MODIS spectral emissivity library. The comparison shows that LST obtained from the MODIS product almost matches with the ground measurements while the calculated LST values lowers § 2.0K – 2.5K than the measured values excluding the cloud affected days in Figure 6-5. Therefore, in the further analysis, the MODIS LST products were used for algorithm development for the estimation of soil moisture from remote sensing. The MODIS LST products of the remaining days are found in Appendix-9. 315 310 305

Temperature (K)

300 LST@ emissivity 0.956

295

LST @emissivity 0.984 LST @emissivity 0.992

290

MODIS Terra_calculated LST 285 280

MODIS Terra LST product

Cloud effect

MODIS Aqua calculated LST MODIS Aqua LST product

275

9/ 2

2/ 9/ 08 1 22 0 : 9/ / 08 20 A 2 3 9/ 2/ 0 : 20 M 23 8 /0 8: PM 9/ 8 1 05 23 2 PM 9/ / 08 :5 0 23 A /0 5: 3 M 9/ 8 1 5 A 23 0 : 2 M 9/ / 08 0 A 2 3 9/ 3/ 0 : 05 M 24 8 /0 7: PM 9/ 8 1 55 24 2 PM 9/ / 08 :4 0 24 A /0 5: 2 M 9/ 8 1 5 A 24 0 : M 9/ / 08 1 0 A 24 2 : 9/ / 08 55 M 25 /0 7: 4 PM 9/ 8 1 0 P 25 2 :2 M 9/ / 08 5 A 25 5: M / 9/ 0 10 28 8 /0 9: AM 9/ 8 1 55 28 2 AM / :2 9/ 08 5 P 28 5: M 1 9/ / 08 0 P 29 9: M / 0 9/ 8 55 2 2 P 9/ 9/ 08 : 40 M 29 7 / 0 : 2 AM 8 12 5 A :1 M 0 PM

270

Date/Time (UTC+2:00)

Figure 6-5 LST obtained from radiometric measurements and from MODIS instrument

Figure 6-6 MODIS LST product Sep.23, 2008

48

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Figure 6-7 LST calculated by split window technique for MODIS image Sep.23, 2008 Table 6-2 Minimum, maximum and average LST products and LST calculated

DAY 18-09-08 19-09-08 20-09-08 22-09-08 23-09-08 24-09-08 25-09-08 27-09-08 29-09-08

6.3.

LST Calculated (K) Minimum Maximum 280.68 288.78 280.30 281.70 282.40 280.10 280.50 280.00 280.60

299.60 297.80 306.50 300.60 297.50 302.00 302.20 304.70 309.10

Average

Minimum

293.78 294.83 298.72 294.18 293.83 295.72 294.31 297.60 299.49

280.48 291.04 287.22 285.72 286.12 283.26 286.46 284.44 283.12

LST product (K) Maximum Average Average Error 301.34 296.24 2.46 300.04 297.52 2.69 307.42 300.60 1.88 301.52 296.73 2.55 299.92 296.17 2.34 304.52 298.35 2.63 303.90 296.50 2.19 306.86 299.52 1.92 308.82 301.96 2.47

Scatter plots of NDVI and LST

The scatter plots for surface temperature versus NDVI for the MODIS images of the study area of Sep. 24, 2008 and Sep.18, 2008 are shown in Figure 6-8. From the scatter plot, NDVI and LST have negative relations for most pixels found inside the triangle formed. Over bare soil, variations in surface temperature are highly correlated with variations in surface water content. Thus, point A and B on Figure 6-8 represent moist soil (high NDVI, low LST) and dry bare soil (low NDVI, high LST) respectively. As the fractional vegetation cover increases, surface temperature decreases. Point C in the figure corresponds to continuous vegetation canopies with a high resistance to evapotranspiration (high NDVI, relatively high LST), e.g. due to low soil water availability. The right enveloping line of observations in the space, B-C, represents the low evapotranspiration line or dry condition. The left enveloping line A-D represents the line of potential evapotranspiration or wet conditions. The concept of NDVI-LST space is easy to understand qualitatively, however, since the boundary of polygon is highly depended on many factors like surface physical variables and atmospheric properties, it is difficult to draw clear and unique lines (wet limit and dry limit) that would be applicable to different sites.

49

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

1

C

A

NDVImax

0.8

Warm edge

0.6

NDVImin

NDVI

0.4

B

D

0.2

Tmin

Tmax

0 0

5

10

15

20

25

30

35

40

45

-0.2

Corrupted pixels -0.4 -0.6

Water pixels

-0.8

LST (0C)

1 NDVImax

0.8 Warm edge

0.6

NDVI

0.4 NDVImin

0.2

Tmin

Tmax

0 10

15

20

25

30

35

40

45

50

-0.2 Corrupted pixels

-0.4

Water pixels

-0.6 -0.8 LST (0C) Figure 6-8 Scatter plots of LST vs NDVI of Sep.24, 2008 upper and Sep.18, 2008 lower: A relatively low number of observations at temperatures higher than the warm edge and lower than the cold edge exist due to terrain effects and cloud which are not considered in the analysis.

50

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

6.4.

Simulated soil moisture

Soil moisture is estimated from remote sensing by relating the remote sensing derived NDVI and LST with ground observed soil moisture, using the proposed triangle method. A total of 35 sample points were used to calculate algorithm and 14 points were used for validation. A system of equation 4.12 was set up using ground observed soil moisture and MODIS scaled NDVI and LST for all the pixels matching the site of each observed sampling sites. To check the performance of the algorithms developed, both calibration and validation is done for this study. In this study 1st order, 2nd order and 3rd order polynomial relations of observed soil moisture with scaled NDVI (N*) and scaled LST (T*); and also 3rd order polynomial relation of soil moisture with fractional vegetation cover (Fr) and scaled LST are tested. Both from calibration and validation a strong correlation between the simulated and the observed soil moisture is obtained from 2nd and 3rd order polynomial relations whereas poor correlation is obtained from 1st order polynomial relations. The objective functions used for calibrating the coefficients aij are correlation coefficient R2 and RMSE. The coefficients aij from equation 4.12 for each algorithm obtained after calibrations are tabulated in Table 6-3, Table 6-4 and Table 6-5. The soil moisture maps of Sep.23, 2008 simulated by using the algorithms developed are shown in Figure 6-9 and Figure 6-10. The spatial mean of the simulated soil moisture for the study period by the three algorithms is indicated in Table 6-6. Table 6-3 Coefficients for 2nd order polynomial relations

aij

j=0

j=1

j=2

i=0

0.6

-3.756

15.748

i=1

-0.736

11.321

-46.84

i=2

0.948

-9.859

35.293

Table 6-4 Coefficients for 3rd order polynomial relation with N*

aij

j=0

j=1

j=2

j=3

i=0

1.386

-6.838

8.768

-6.958

i=1

-4.992

30.736

-20.909

36.528

i=2

5.321

-26.044

-33.013

-43.56

i=3

-0.599

-1.383

49.197

20.445

51

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Table 6-5 Coefficients for 3rd order polynomial relation with Fr

aij

j=0

j=1

j=2

j=3

i=0

1.162

-6.101

10.562

4.504

i=1

-12.862

91.686

-162.35

19.18

i=2

32.299

-204.43

286.33

51.089

i=3

-18.8

94.016

-31.32

-191.82

(a)

(b)

Figure 6-9 Simulated soil moisture by (a) 2nd and (b) 3rd order polynomial relation Sep.23, 2008

Figure 6-10 Simulated soil moisture by 3rdorder Fr and LST Sep.23, 2008 Table 6-6 Average soil moisture of Gumara catchment using three algorithms developed

Day 18-09-08 19-09-08 20-09-08 22-09-08 23-09-08 24-09-08 25-09-08 27-09-08 29-09-08 52

2ndorder N* Average 3rd order N*Average 3rdorder Fr Average SM (cm3cm-3) SM (cm3cm-3) SM (cm3cm-3) 0.40 0.39 0.38 0.43 0.45 0.44 0.38 0.39 0.40 0.42 0.40 0.39 0.38 0.38 0.37 0.39 0.38 0.38 0.39 0.38 0.37 0.36 0.35 0.35 0.39 0.37 0.37

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

6.4.1.

Cross correlation between simulated and observed soil moisture

The average soil moisture simulated using the three algorithms developed is indicated in Table 6-6. Soil moisture simulated by all the three algorithms has found a strong correlation with the observed soil moisture as indicated in Figure 6-11, Figure 6-12 and Figure 6-13. After calibrating the algorithms the correlation coefficient R2 obtained from three algorithms are greater than 0.71 and RMSEs are less than of 0.045 for calibration dataset and greater than 0.672 for validation datasets with maximum RMSE of 0.028. Figure 6-11 shows the correlation made between the simulated soil moisture using the algorithm developed with 2nd order polynomial relation to the observed soil moisture. Calibration (Sep.18, 2009, Sep.26, 2008)

Validation (Sep.27,2008 and Sep.29, 2008) 0.6

2

R = 0.7139

0.5

2

R = 0.7451

3

3

y = 0.8625x + 0.061

3

0.5

SM_Simulated (cm/cm )

y = 0.6966x + 0.1129

3

SM_Sim ulated (cm /cm )

0.6

0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4 3

0.5

0.4 0.3 0.2 0.1 0

0.6

0

0.1

0.2

0.3

3

SM_Measured (cm /cm )

0.4

0.5

3

0.6

3

SM Measured (cm /cm )

Figure 6-11 Correlation of observed and simulated soil moisture using 2nd order polynomial relation Figure 6-12 below shows the correlation made between the simulated and the observed soil moisture when using 3rd order polynomial relation of ground observed soil moisture with land surface parameters of scaled NDVI and scaled LST. The correlation coefficient R2 obtained from this correlation is 0.805 and 0.672 after calibration and validation respectively with the RMSE of 0.037 and 0.033 for calibration and validation datasets respectively.

0.5

3

2

y = 0.8897x + 0.05

0.5

2

R = 0.6722

3

R = 0.8056

3

0.6

SM_simulated (cm/cm )

y = 0.7601x + 0.0889

3

SM_simulated (cm/cm )

Validation (Sep.27, 2008 and Sep.29, 2008)

Calibration (Sep. 18,2008-Sep.26, 2008)

0.6

0.4 0.3 0.2 0.1 0

0.4 0.3 0.2 0.1 0

0.0

0.1

0.2

0.3

0.4 3

0.5 3

SM_measured(cm /cm )

0.6

0.0

0.1

0.2

0.3

0.4 3

0.5

0.6

3

SM meassured (cm /cm )

Figure 6-12 Correlation of observed and simulated soil moisture from 3rd order polynomial relation 53

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Like the above two algorithms a strong correlation is also obtained between the simulated soil moisture and the ground observed soil moisture when using 3rd order polynomial relation of observed soil moisture, scaled LST and fractional vegetation cover (Fr). From the correlation as shown in Figure 6-13 the correlation coefficients R2 obtained are 0.73 and 0.80 with RMSE of 0.044 and 0.029 for calibration and validation respectively. Validation (Sep.27, 2008 and Sep.29, 2008)

Calibration (Sep.18, 2008-Sep.26, 2008)

0.6 3

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y = 1.100x - 0.031

y = 0.757x + 0.094

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Figure 6-13 Correlation of observed and simulated soil moisture from 3rd order relation of Fr

6.4.2.

Sensitivity Analysis

Any calibrated model or algorithm has its own uncertainties. Therefore, in order to reduce the uncertainty, it is essential to subject the calibrated algorithm to a sensitivity analysis. The main purpose of the sensitivity analysis is to quantify how sensitive the algorithm is to certain changes in the input data and as such, a sensitivity analysis basically is to quantify on the uncertainty of the calibrated model. It defines which parameters have the most dominant effect on the calibration result. Sensitivity analysis is done by increasing and decreasing the input parameters of the algorithm (i.e. NDVI and LST) to a certain percent. Sensitivity analysis is used to ascertain how a given model depends upon the input parameters. If a small change in a parameter results in relatively large changes in the model outcomes, the model is said to be sensitive to that parameter. This may mean that the parameter has to be determined very accurately or that the model has to be redesigned for low sensitivity. It is an important method for checking the quality of a given model, as well as a powerful tool to ensure which parameters should be emphasized when running the model (Rientjes, 2007). The percentage increase and decrease is based on the expected limit of accuracies of the input parameters. In this case, the expected accuracy of the LST is ± 20K and NDVI is ± 0.03 from LST algorithm theoretical bases document version 3.3 from the SMAC accuracy respectively. Therefore sensitivity analysis is done by increasing and decreasing values of NDVI and LST by 5 % for two objective functions selected for calibration. Based on the sensitivity analysis LST was found to be most sensitive parameter for two algorithms as can be seen in Figure 6-14 and Figure 6-15.

54

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

For 1% increase and decrease of LST the R2 for 2nd order relation decreases to 0.39 and 0.12 respectively while for 1% increase and decrease of NDVI R2 for 2nd order polynomial relation decreases to 0.70 and 0.67 respectively. For 3rd order polynomial relation a 1% increase and decrease of LST results in a decrease of R2 to 0.24 and 0.03 respectively where as a 1% increase and decrease of NDVI results a decrease of R2 to 0.79 and 0.75 respectively. An increase or decrease of LST by 1 % raises RMSE to 0.21 and 0.2. Again 2% increase and decrease of LST results in an increase of RMSE to 0.72 and 0.52 from 3rd order relation. The increase and decrease of LST and NDVI also increases RMSE for 2nd order polynomial. 1% increase and decrease of LST results an increase of RMSE to 0.2 and 0.1 respectively again RMSE increases to 0.57 and 0.34 by increasing and decreasing of LST in 2nd order polynomial. In general the R2 decreases and RMSE increases either by increasing or decreasing of both NDVI and LST. However, the decreasing and increasing rate of R2 and RMSE respectively is higher for LST than for NDVI. Sensitivity Analysis (2nd order) 0.8 0.7

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Figure 6-14 Sensitivity analysis of the 2nd order relation (a) R2 (b) RMSE Sensitivity Analysis (3rd OrderN*) 0.9

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55

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

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Figure 6-15 Sensitivity analysis of the 3rd order polynomial relation (a) R2 (b) RMSE

6.4.3.

Comparisons of the algorithms

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o

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Four different algorithms are developed including the algorithms developed for local elevation corrections based on the triangle method approach to simulate soil moisture from remote sensing. Equation 4.12 represents nth order polynomial relation between the measured soil moisture, scaled NDVI and scaled LST. Based on the calibration, the 3rd order polynomial relation with 17 terms is found to be more accurate than the others but less flexible i.e. the spatial mean variations of the simulated soil moisture temporally is limited as can be seen from Figure 6-17. On the other hand, a 1st order polynomial relation with four coefficients is less accurate which is not present in this report. The 2nd order polynomial relations with 9 terms are found to be the most optimal and relatively flexible i.e. the spatial mean variation of simulated soil moisture range is relatively high and also the error associated with data accuracy is low.

0.3 LST_Calculated_Average LST_product_average NDVI_Average

292 290

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0

Days Figure 6-16 Spatial average of NDVI, the LST product and the calculated LST during study period

56

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

26

0.46

24 23

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6.5. Statistical analysis and results of spatio-temporal variation of soil moisture In mountainous catchments like Gumara catchment knowledge on the relation of the mean soil moisture and its spatial variability is very effective. Figure 6-18 (a) presents the spatial standard deviation, σ (θ v ) as a function of spatial mean soil moisture simulated by the 2nd order polynomial t

0.07

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0.16 Coefficient of variation

S ta n d a rd d e v a tio n

relation.

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Figure 6-18 Statistical representation of simulated soil moisture of the study area:(a) standard deviation and (b) coefficient of variation versus spatial mean soil moisture for each day. From the Figure 6-18 (a) the standard deviation decreases as the mean soil moisture increases, indicating the soil moisture variability increases as soils becomes dryer. This result is consistent with field observation i.e. the soil moisture increases or soils saturate when rainfall occurs in the study 57

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

area. Under such conditions some areas remain wet while the others dry quickly when rainfall has seased. Spatial variability of soil moisture for a catchment during the study period is analysed by comparing temporal statistics of the simulated soil moisture as shown in Figure 6-19.

(a)

(b)

Figure 6-19 (a) Temporal mean of the simulated soil moisture (cm3cm-3) and (b) coefficient of variation, CVs, at pixel level during the study period. The temporal mean of soil moisture Figure 6-19 (a) shows higher temporal mean exists generally at higher elevated areas. But Figure 6-19 (b) indicates that, higher elevations show lower temporal variability while lower elevation show higher temporal variability. The spatial variability of soil moisture from Figure-18 (b) during the study period is lower than the temporal variability of soil moisture among the pixels from Figure-19 (b).

Temporal persistency of simulated soil moisture patterns:- The temporal persistence of spatial soil moisture patterns can help to identify how landscape characteristics affect basin hydrology (Jacobs et al., 2004). This temporal persistency can be characterized by RMSEįi as shown in Figure 6-20. The time stable pixels that capture the catchment average (low RMSEįi) are found in the mid elevation of the catchment where as pixels with high temporal variability (high RMSEįi) are located at low elevation area as indicated in Figure 6-20.

Figure 6-20 Root mean square error of the relative difference, RMSEįi, of the estimated soil moisture These results indicate that temporal persistency can directly be related to elevations. In this study, the pixels with higher temporal variability conditions are located at low elevation area which have 58

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

relatively high LST see Figure 6-6 possibly due to the vegetation cover type, hydraulic conductivity, storativity and physical properties of soils in the study area.

Terrain controlling effects on simulated soil moisture: - Since the topography of the study area is undulated and rugged, terrain effects on the simulated soil moisture must be assessed to allow for development of algorithms to correct for soil moisture at high elevated areas. To determine the terrain effects on the simulated soil moisture, slope and aspect for the catchment was derived from DEM processed from SRTM data. The derived slope and aspect map of 90m resolution are re-sampled to 1000m resolution to match with 1km resolution of simulated soil moisture. Figure 6-21 shows the joint distribution of terrain attributes and simulated soil moisture statistics. The statistics shown are the temporal mean soil moisture, the temporal coefficient of variation and the relative difference (RMSEįi), as compared to the elevation, slope and aspect of the catchment. Elevation X Cvt

Elevation_Temporal SM mean 0.30 Elevation X Temporal mean of SM

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59

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

ASPECTD_RES_RN x Tempo_average

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Figure 6-21 Joint distribution of terrain attributes and simulated soil moisture. The first three figures from the top of Figure 6-21 highlight the control exerted by elevation on the temporal mean soil moisture and its temporal variability. High elevations in the catchment are characterized by high mean soil moisture exhibiting low temporal variability, CVt, and soil moisture values that are time stable (low RMSEįi) while also the reverse is true for low elevation areas. Considering slope, there are many pixels found in the low to intermediate slopes (5-20%) that have high mean soil moisture. The temporal variability and time stability generally decreases as the slope increases. Slope aspect does not appear to have strong relation with temporal mean soil moisture, temporal variability as well as time stability as shown in Figure 6-21. Generally, from the statistical spatio-temporal analysis high elevated areas in the catchment is characterized by high mean soil moisture, low temporal variability and time stable (low RMSEįi) as compared to low elevated areas. Also from the analysis of Figure 6-21, elevation is the dominant terrain controlling factor for the simulated soil moisture. Based on the field observations and few samples of the measured soil moisture in the field, high elevated areas had relatively low soil moisture. However, from the simulation by using the algorithms developed in the relations of the observed soil moisture with remote sensing NDVI and LST most field days have high soil moisture at high elevation area as shown in Figure 6-9 and Figure 6-10. Presumably this discrepancy is coming from topographic factors associated with the LST. The correlation coefficient and RMSE obtained from the comparison between the observed and estimated soil moisture from Figure 6-11, Figure

6-12 and Figure 6-13 indicate that soil moisture was estimated in a better accuracy at low elevated area because most of the observed soil moisture sampling was taken from low elevated area. Therefore, elevation correction is imposed to simulate relatively low soil moisture at high elevated areas than at the low elevated areas. 60

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

6.6.

Elevation correction for the simulated soil moisture

From sensitivity analysis LST was found the most sensitive parameter and based on terrain controlling factor analysis, elevation was found the dominant topographic controlling factor. In this specific study an effort is made to correct the simulated soil moisture at high elevation area in relation to the sensitivity parameter of LST and the major controlling factor of elevation. Most of the high elevated areas have low LST and have high simulated soil moisture from Figure 6-6 and Figure 6-9 respectively. From the relation of sensitive parameter and dominant topographic factor potential surface temperature is found to be the best parameter which can correct the soil moisture at high elevation areas by minimizing the large difference of LST from high to low elevation areas due to large elevation differences. Because it has a relation with the sensitive parameter LST and major controlling factor elevation from its formula in equation 5.19 and 5.20. Therefore, other algorithm is developed from the relation of the observed soil moisture with scaled NDVI and scaled potential temperature applying triangle method.

6.6.1.

Potential surface temperature

This variable is used to correct the topographic effects on the simulated soil moisture and it was computed using equation 5.19 for each day when the soil moisture measurement was taken during the field campaign. The variations of LST obtained from MODIS LST product ranges from 280 K to 310 K is higher as compared to the variation of potential temperature that ranges only from 312 K to 323 K as can be seen from Figure 6-6 and Figure 6-22. The high variation of LST between the two elevation areas is due to the effect of topography which results in high soil moisture on the elevated area. Therefore, to minimize the variation of LST in the catchment due to topographic effect, potential temperature is found the best parameter. The results of Sep.23, 2008 is shown in Figure 6-22 below while the other days are found in Appendix-9.

Figure 6-22 Potential temperature map of Sep.23, 2008

6.6.2.

nd

Simulated soil moisture using 2 temperature

order relation to NDVI and potential

Applying the same triangle methods and procedures for potential temperature, the 2nd order polynomial relation of ground observed soil moisture with scaled NDVI and scaled potential 61

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

temperature is formed. The coefficients of 2nd order polynomial relation determined after calibration are listed in Table 6-7 and the correlations between the observed with the newly simulated soil moisture are shown in Figure 6-24 for calibration and validation data sets. From the soil moisture map simulated by 2nd order polynomial relation as indicated in Figure 6-23, high elevated areas have relatively less soil moisture than the lower elevated areas. For spread sheets of the coefficients see Appendix-11.

Figure 6-23 simulated soil moisture by 2nd order relation with potential temperature (Sep.23, 2008) Table 6-7 Coefficients for 2nd order polynomial relation for potential temperature

aij

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5.063

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Figure 6-24 Correlations of observed and simulated soil moisture by the 2nd order polynomial relation using potential temperature From Figure 6-23 the high elevation areas have relatively low soil moisture as compared to low elevation areas which can be hydraulically logical moreover it corresponds very much with field observations. Also from the correlation coefficient obtained from Figure 6-24, one can conclude that 62

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

the low elevation area is well simulated by applying potential surface temperature because most of the correlated soil samples were taken from low elevated areas. Soil moisture map estimated by 2nd order polynomial relation algorithm is indicated in Appendix-10.

6.7. Simulated soil moisture at different elevation zones before and after correction To see the effect of the major controlling factor (elevation) in detail on the simulated soil moisture map, the DEM is classified in to three elevation zones based on their elevation ranges as: • Low zone elevation ranges from 1780-1900 m.a.s.l • Medium zone elevation ranges from 1900-2300 m.a.s.l. • High zone elevation ranges from 2300-3704 m.a.s.l

Figure 6-25 Elevation zone map of Gumara catchment The average soil moisture for each zone for each day is calculated by crossing both the raster maps of elevation zone after re-sampling 90 m DEM to 1km resolution with the simulated soil moisture maps using the two 2nd order polynomial algorithms (before and after correction). The result is tabulated in Table 6-8. Table 6-8 Average soil moisture and LST of each zone simulated by 2nd order relation with LST

Day 18-09-08 19-09-08 20-09-08 22-09-08 23-09-08 24-09-08 25-09-08 27-09-08 29-09-08

Elevation zones average soil moisture (cm3cm-3) Low Medium High Low 0.39 0.38 0.39 24.60 0.42 0.47 0.45 25.11 0.40 0.39 0.39 30.32 0.41 0.40 0.39 24.81 0.36 0.36 0.41 24.78 0.38 0.38 0.38 27.59 0.39 0.37 0.38 26.23 0.33 0.34 0.38 29.67 0.35 0.36 0.39 31.78

Elevation zones average LST (oC) Medium High 23.35 20.95 24.92 23.44 28.16 25.21 24.12 22.05 23.58 21.28 26.03 22.65 24.36 21.95 27.00 23.19 29.72 25.58

Air-Temp. 22.29 22.56 23.23 23.18 23.23 23.95 25.43 25.38 24.89 63

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Soil moisture simulated by using 2nd order relation algorithm with LST at three elevation zones for different days indicates that high elevation zone have relatively high soil moisture compared to the other elevation zones for the last five days in Figure 6-26. Those days are days when the air temperature increases from 23.18oC on Sep.23, 2008 to 25.38oC on Sep.27, 2008 (Table 6-8). The increasing of air temperature indicates there was no rainfall on the study area. This was confirmed during field work. However, during field work the lower elevated area was wetter than the higher elevated area. Therefore, improving the algorithm is imperative to remove the error due to terrain effects or the error coming from the insufficient number of sample points at higher elevated areas.

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Figure 6-26 Average Soil moisture for 3 elevation zones before correction

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Figure 6-27 Average LST for 3 elevation zones and air temperature at low elevation area From the results obtained by using potential temperature, it is possible to reduce on terrain effects that propagated from the algorithms developed using NDVI and LST to the simulated soil moisture as discussed above. Figure 6-28 shows that low elevation zone with relatively wet soil moisture for entire study period as compared to the other two zones and it also matches to the situation observed during the field work. During field work it was observed that flooding water was stored in the lower part of the catchment, because of the plainness of the lower part of the catchment. Therefore, from the results obtained it seems logical to use potential temperature for undulating topography to simulate surface soil moisture if there is no sufficient sample points on the high elevated areas. Most 64

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

importantly, it is interesting to see that the spatial mean of soil moisture at low elevation zone is almost equal before and after the local correction is made but the spatial mean of soil moisture at high elevation area after local correction is lower than before local correction as can be seen in Table 6-9. The similarity of low elevation soil moisture simulated before and after local elevation correction shows that the methods applied for this study gives plausible result for areas where sufficient training points or sample points are observed. An other important observations from Figure 6-28 is that in low elevation area still the spatial variability of temporal mean soil moisture is higher than the variability of high elevation area due to high vertical flow i.e high potential evapotranspiration and high drainage conditions in low elevation area.

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Figure 6-28 Average Soil moisture at 3 elevation zones simulated after elevation correction Table 6-9 Spatial average soil moisture before and after local correction

Day 18-09-08 19-09-08 20-09-08 22-09-08 23-09-08 24-09-08 25-09-08 27-09-08 29-09-08 Mean

Soil moisture (cm3cm-3) before correction Low Medium High elevation elevation elevation 0.391 0.38 0.393 0.42 0.47 0.455 0.402 0.393 0.387 0.407 0.401 0.394 0.363 0.36 0.408 0.38 0.38 0.384 0.386 0.366 0.385 0.329 0.345 0.379 0.35 0.364 0.395 0.381 0.384 0.398

Soil moisture (cm3cm-3) After correction Low Medium elevation elevation 0.393 0.334 0.435 0.41 0.412 0.379 0.39 0.333 0.405 0.393 0.326 0.318 0.381 0.3332 0.373 0.364 0.385 0.378 0.389 0.360

High elevation 0.356 0.424 0.33 0.341 0.352 0.341 0.34 0.342 0.351 0.353

In general soil moisture decreases spatially during the study period as can be seen from Figure 6-17, as the land surface temperature increases Figure 6-16. Whereas, the soil moisture increases as the land surface temperature decreases while the average NDVI is remaining almost constant during the study period in Figure 6-16. The relation of soil moisture and LST is probably linked to the absence and 65

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

presence of rainfall. Therefore, the spatial variation of soil moisture during the study period could be affected by rainfall.

6.8.

Discussion

The average volumetric soil moisture obtained from three different algorithms ranges from 0.35-0.45 cm3cm-3 for all days as shown in Table 6-6. The average NDVI is between 0.53-0.68 and the average LST obtained by using split window technique proposed for this study is between 293.78 K- 299. 46 K where as the average LST from the product ranges from 296.24 K to 301.96 K respectively as shown in Table 6-1 and Table 6-2. The high soil moisture content, high NDVI and relatively low LST indicate the study area is highly covered with vegetation and the study period is rainy season. And also, the range of spatial variability of soil moisture, NDVI and LST are relatively low. This spatial uniformity of NDVI makes the triangle (formed by the scatter plots of NDVI and LST) difficult to visualize the cold and warm edge easily for some of the field days. This poor formation of the triangle makes the approach subjective to determine the wet and warm edge of the triangle and also the determination of minimum and maximum pixel values of the parameters. To overcome problem of the full spectral coverage a large size image and also soil moisture pattern out side the study area was taken as shown in Figure 3-1. The error associated due to the accuracy of measuring soil moisture and error due to accuracy and precision of remote sensing data of land surface parameter will propagate the error in the soil moisture estimation at high resolution. To estimate these errors, a system of polynomial equation 4.12 was set up using ground observed soil moisture, NDVI and LST for the study area. The error is estimated as the RMSE between the grounds observed soil moisture and the simulated soil moisture using the algorithms developed. For this particular catchment RMSE of 0.045 is calculated for all algorithms. To estimate the second error associated with data accuracy, a sensitivity analysis is done by changing the values of NDVI and LST by 5% increasing and decreasing their value. The result shows both increase and decrease of two parameters increases RMSE to 6.5 and 2.9 in the 3rd and 2nd order polynomial relation respectively. The high difference of RMSE value with two algorithms from sensitivity analysis is presumably from the difference of number of coefficients. This means that scaling of NDVI and LST as well as reducing the number of coefficients can minimize the errors occurred due to data accuracy. According to the statistical spatio-temporal analysis the high elevated area resembles high mean soil moisture before correction, low coefficient of variability and time stable condition. However, the real situation observed during the field work is that low elevated area is wetter than the high elevated area. This discrepancy is coming from the insufficient number of sample points from the high elevated area and local factors like back flow of water from the lake that forms artificial pond of water downstream of the catchment that could not account with the algorithm. Less number of sampling points on high elevated area induces an error on the algorithms developed. Sufficient number of sample points were taken at low elevation area and based on the coefficient of determination (R2 >0.70) was obtained from the results before and after correction was made. From this, one can conclude that the triangle method with LST can simulate soil moisture with better accuracy when sufficient number of sample points are taken and when there is no large elevation difference. 66

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

An effort is made to correct soil moisture simulation at high elevation area where there was no sufficient training sample points. From the results obtained it is possible to minimize the errors occurred at high elevated area coming due to less training sample points and due to large elevation difference by applying elevation correction technique. From Figure 6-26, one can observe that the rate of decreasing soil moisture at the high elevated zone is lower than the other two zones during the period when there is no rainfall; consequently the soil moisture becomes higher than the other two zones for the last 5 days of the study period. This low decreasing rate of soil moisture is due to the effect of topography, the type of land cover and soil physical property. Obviously, if the land cover is covered by shallow rooted crops that consume less water and the texture of soil is poorly drained then the soil moisture decreasing rate will be low. From Figure 2-10 most of the high elevated areas are covered by a soil type Luvisols which is moderately drained and the low elevation area is covered by Nithosols which is well drained soils from Table 2-2. These different drainage conditions of soils will result different pattern of soil moisture variability from high elevation area to low elevation area as can be seen from Figure 6-19 (b) and Figure 6-20. This argument is supported by Grayson et al (1997), who showed that terrain attributes influence soil moisture distributions after rainfall events while drier conditions resemble soil vegetation patterns. In this study both temporal and spatial variability of soil moisture is observed in the catchment. Since the study period is the rainy season, temporal and spatial variability of soil moisture was also due to the vertical and lateral movement of water. The area near to the drainage line becomes wetter due to lateral movement of surface runoff from uphill during rainfall, whereas, the area which has high LST gets dry quicker than the area of low LST after rainy season due to high lateral movement either from evaporation or due to high hydraulic conductivity of soils. From Figure 6-19(b) high temporal coefficient of variation is observed at low elevated area probably due to high evapotranspiration and due to the soil drainage condition.

Limitation of triangle method: - There are some limitations to this soil moisture estimation approach. The time difference between the ground measurements and the Terra overpass could impact the results. For this study ground measurements were taken based on the predicted MODIS overpass time in the study area from (http://earthobservatory.nasa.gov/MissionControl/overpass.php) and this predicted overpass has little shifts from the real overpass time of the satellite. Moreover, for the cloudy worst case, it is difficult to derive soil moisture from MODIS land parameters, which operate in the optical/IR bands. The most severe limitation of the triangle method is that identification of the triangular shape in the pixel distribution requires a flat surface and a large number of pixels over an area with a wide range of soil wetness and fractional vegetation cover. Although not of high relevance, determination of the warm edge and the vegetation limits of bare soil and a full cover requires some subjectivity (Carlson, 2007). The method does not clearly indicate the effects of land cover and topography. Moreover, the method is site specific and needs sufficient ground observed soil moisture samples for setting up a polynomial relation.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

7. Conclusion and Recommendations 7.1.

Conclusion

Passive and active microwave sensors on board satellite platforms have shown the capability to retrieve soil moisture of the surface layer under some topographic and vegetation cover conditions, but the sensitivity of microwave emission and scattering to other factors than soil moisture, such as soil roughness, vegetation physical and structural properties and surface temperature and their coarser spatial and temporal resolution limits the applicability of the approach at a catchment scale. An alternative approach based on optical and thermal remote sensing “the triangle method” has recently been proposed and tested to estimate soil moisture at a resolution high enough to serve applications such as distributed hydrological modelling. This approach is based on the relation of ground measured soil moisture, Normalized Difference Vegetation Index (NDVI) and land surface temperature (LST) retrieved from remote sensing. The main advantages of this approach are • gives high spatial and temporal resolution of soil moisture • does not need a priori information of vegetation and soil • gives relatively better soil moisture estimate under high vegetation cover • it requires less number of input variables The algorithms developed in the relations of observed soil moisture with scaled NDVI and scaled LST simulates soil moisture with a good accuracy in low elevation areas where sufficient sample points were taken and where the elevation differences are minimum. However, none of them has a capability to minimize the errors of the simulated soil moisture at high elevation propagated from LST due to large elevation differences and insufficient number of sample points. Among the terrain controlling factors elevation is found to be the main terrain controlling factor that affects soil moisture variability. To reduce the error due to elevation on the simulated soil moisture using the algorithms developed, local elevation correction is made by replacing LST with potential surface temperature. Applying potential temperature can minimizes the topographic effect that is induced from LST on the simulated soil moisture; especially on high elevated areas where there were no sufficient sampling points were taken. The general conclusion of this study is that it is possible to simulate soil moisture using triangle method at reasonably good spatial resolution because of the basis of relations of soil moisture with land surface parameters of NDVI and LST, provided that the area covers a large number of pixels to determine the triangle in the scatter plots. The technique is suitable for remote sensing soil moisture estimation because it does not require a priori information about vegetation and roughness condition of the surface and also it is not limited to pixels having NDVI > 0.4 unlike of most microwave remote 68

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

sensing techniques. The results obtained from this study suggest that the soil moisture estimation by combining ground measured soil moisture and MODIS land parameters is accurate enough when it is applied on the area where there are sufficient number of ground observed soil moisture for algorithm development and less elevation differences. The two important input variables that are required for the development of the algorithms are NDVI and LST and from these two input variables LST is found the most sensitive parameter based on sensitivity analysis done. The algorithm developed using 3rd order polynomial relation is more accurate than 1st and 2nd order polynomial relation. However, due to more number of coefficients the errors coming from the input variables especially from the most sensitive parameter of LST results in larger error on the simulated soil moisture than the 2nd order polynomial relation. Therefore, 2nd order polynomial algorithm gives better result than the others by minimizing the errors associated from data accuracy. For a catchment which has large elevation difference and when there was no sufficient soil sampling points distributed over the area, the triangle method applied with LST introduce an error on high elevated areas because of large variation of LST due to elevation. Therefore, in such condition elevation correction technique should be improved or advocated. For this study, it is possible to minimize the error due to elevation by applying a technique for elevation correction using potential surface temperature. In this case, the algorithm developed by potential surface temperature could give better result than the others for such topographically different catchment. Soil moisture can be related to the terrain controlling factors like elevation, slope and aspect. High elevations in the catchment are characterized by low mean soil moisture exhibiting low temporal variability with soil moisture values that are time stable. Based on the statistical analysis temporal coefficient of variation is higher than spatial coefficient of variation during the study period. Also, the temporal variability among the pixels is more pronounced than spatial variation of the catchment for each day. This is an indication of the difference of degree of variation of soil moisture from high elevation area to low elevation area. In general, soil moisture estimation from remote sensing is a difficult task due to terrain effects and vegetation in mountainous region. Nevertheless, the spatial information afforded by remote sensing is valuable for many applications. In this study it is possible to estimate soil moisture at 1km spatial resolution and daily temporal resolution with better accuracy which can be used as an input for many distributed hydrological models.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

7.2.

Recommendation

The study was carried out during wet season with limited number of sample points due to inaccessibility of the area and short period of field campaign. Therefore, to improve the algorithms developed by relating soil moisture measured during wet season with the remote sensing retrieved NDVI and LST during the study period the following points are recommended. • •

Further study is proposed to improve the algorithm by taking long duration of soil moisture measurements both in dry and wet seasons at different locations on different land covers. Terrain controlling factors should be assessed carefully by taking a representative transects of soil moisture measurement in the catchment.

Spatial variability is expected due to lateral movement of surface water after rainfall and temporal soil moisture variability is mostly due to vertical movement of water by evapotranspiration and downward movement of water inside the soil. Therefore, detailed analysis of surface flow characteristics and evapotranspiration of the catchment is recommended for better understanding of soil moisture and physical land processes of the study area. Topography and soil physical parameters have great impact on soil moisture. Therefore, the application of elevation correction potential surface temperature and the effect of soil physical properties should be carefully assessed for such rugged and high elevation different areas for soil moisture studies.

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References Abeyou, W., 2008. Hydrological balance of Lake Tana upper Blue Nile basin, Ethiopia, ITC, Enschede, 94 pp. Carlson, T., 2007. An overview of the "triangle method" for estimating surface evapotranspiration and soil moisture from satellite imagery. Sensors, 7(8): 1612-1629. Carlson, T.N., Gillies, R.R. and Perry, E., 1994. Method to make use of thermal infrared temperature and NDVI measurements to infer surface soil water content and fractional vegetation cover. Remote Sensing Reviews, 9: 161-173. Chauhan, N.S., Miller, S. and Ardanuy, P., 2003. Spaceborne soil moisture estimation at high resolution: a microwave-optical/IR synergistic approach. International Journal of Remote Sensing, 24(22): 4599 - 4622. Crist, E.P. and Cicone, R.C., 1984. A physically-based transformation of Thematic Mapper data: The TM tasseled cap. Environmental Research Institute of Michigan, 1001: 48107. Engman, E.T. and Gurney, R.J., 1991. Remote sensing in hydrology. Remote sensing applications. Chapman and Hall, London etc., 225 pp. FAO, 2006. World reference base for soil resource 2006: A framework for international classification, correlation and communication. 103: 121. Gillies, R.R., Carlson, T.N., Cui, J., Kustas, W.P. and Humes, K.S., 1997. A verification of thetriangle’method for obtaining surface soil water content and energy fluxes from remote measurements of the Normalized Difference Vegetation Index (NDVI) and surface radiant temperature. International Journal of Remote Sensing, 18: 3145-3166. Grayson, R.B., Western, A.W., Chiew, F.H.S. and Bloschl, G., 1997. Preferred States in Spatial Soil Moisture Patterns: Local and Nonlocal Controls. Water Resour. Res., 33. Haider, S.S., Said, S., Kothyari, U.C. and Arora, M.K., 2004. Soil moisture estimation using ERS 2 SAR data: a case study in the Solani River catchment. Hydrological Sciences Journal, 49(2): 323-334. Idso, S.B., Schmugge, T.J., Jackson, R.D. and Reginato, R.J., 1975. The utility of surface temperature measurements for the remote sensing of surface soil water status. Journal of Geophysical Research, 80(C21). Jacobs, J.M., Mohanty, B.P., Hsu, E.-C. and Miller, D., 2004. SMEX02: Field scale variability, time stability and similarity of soil moisture. Remote Sensing of Environment, 92(4): 436-446. Kaufman, Y.J. and Gao, B.C., 1992. Remote-Sensing of Water-Vapor in the near Ir from Eos/Modis. Ieee Transactions on Geoscience and Remote Sensing, 30(5): 871-884. Kebede, S., Travi, Y., Alemayehu, T. and Marc, V., 2006. Water balance of Lake Tana and its sensitivity to fluctuations in rainfall, Blue Nile basin, Ethiopia. Journal of Hydrology, 316(14): 233-247. Kerle, N.e. et al., 2004. Principles of remote sensing : an introductory textbook. ITC Educational Textbook Series;2. ITC, Enschede, 250 pp. Mao, K., Qin, Z., Shi, J. and Gong, P., 2005. A practical split-window algorithm for retrieving landsurface temperature from MODIS data. International Journal of Remote Sensing, 26(15): 3181-3204. Mattikalli, N.M., Engman, E.T., Ahuja, L.R. and Jackson, T.J., 1998. Microwave remote sensing of soil moisture for estimation of profile soil property. International Journal of Remote Sensing, 19(9): 1751-1767. 71

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Ottle, C. and Stoll, M., 1993. Effect of Atmospheric Absorption and Surface Emissivity on the Determination of Land-Surface Temperature from Infrared Satellite Data. International Journal of Remote Sensing, 14(10): 2025-2037. Parodi, G.N., 2002. AHVRR hydrological analysis system : user manual version 1.3 : AHAS user guide, ITC, Enschede. Peixoto and Kettani, 1973. The control of the water cycle. Scientific American, 228: 46-61. Price, J.C., 1982. Estimation of Regional Scale Evapotranspiration Through Analysis of Satellite Thermal-infrared Data. Geoscience and Remote Sensing, IEEE Transactions on: 286-292. Quattrochi, D.A. and Luvall, J.C., 2004. Thermal remote sensing in land surface processes. CRC, Boca Raton, 440 pp. Rahman, H. and Dedieu, G., 1994. SMAC: a simplified method for the atmospheric correction of satellite measurements in the solar spectrum. International Journal of Remote Sensing, 15(1): 123 - 143. Rientjes, T.H.M., 2007. Modelling in Hydrology. ITC Enschede, the Netherlands: 231. Schmugge, T.J., 1983. Remote Sensing of Soil Moisture: Recent Advances. Geoscience and Remote Sensing, IEEE Transactions on: 336-344. Schmugge, T.J., Kustas, W.P., Ritchie, J.C., Jackson, T.J. and Rango, A., 2002. Remote sensing in hydrology. Advances in Water Resources, 25(8-12): 1367-1385. Snyder, W.C., Wan, Z., Zhang, Y. and Feng, Y.Z., 1998. Classification-based emissivity for land surface temperature measurement from space. International Journal of Remote Sensing, 19(14): 2753-2774. Vachaud, G., Passerat De Silans, A., Balabanis, P. and Vauclin, M., 1985. Temporal Stability of Spatially Measured Soil Water Probability Density Function. Soil Science Society of America Journal, 49(4): 822. Wang, L., Qu, J.J., Zhang, S., Hao, X. and Dasgupta, S., 2007. Soil moisture estimation using MODIS and ground measurements in eastern China. International Journal of Remote Sensing, 28(6): 1413-1418. Wen, J. and Su, Z., 2003. The estimation of soil moisture from ERS wind scatterometer data over the Tibetan plateau. Physics and Chemistry of the Earth, Parts A/B/C, 28(1-3): 53-61.

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Annexes Appendix-1 DEM hydro processing procedure

Legend

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Appendix-2 Ground observed soil moisture data Point Coordinates East North 351360 1309059

Elevation (m) 1803

Date 16-09-08

Local Time 5:20

ASM-Theta (cm3cm-3) 0.511

ASMGM

Land cover Harvested crop

350541

1308434

1805

16-09-08

6:00

0.503

Grass land and crop land

352153

1310231

1804

16-09-08

7:00

0.310

Rice

345654

1305637

1775

18-09-08

4:45

0.309

0.323

350545

1308438

1798

18-09-08

5:00

0.493

0.494

Grass land and Crop land

354418

1314894

1800

18-09-08

5:20

0.425

0.485

Grass land

351762

1305965

1814

19-09-08

4:25

0.437

0.417

Mixed

353028

1303372

1848

19-09-08

5:15

0.418

0.502

355749

1303337

1831

19-09-08

6:04

0.444

Mixed crops

Forest Leafy forest

354572

1303094

1874

19-09-08

7:29

0.395

352773

1304648

1830

19-09-08

7:45

0.413

Grassland

346291

1306344

1845

20-09-08

3:00

0.360

343042

1300253

1898

20-09-08

3:27

0.353

Crop land (matured)

343060

1300258

1899

20-09-08

3:37

0.266

Maize crop

370574

1287203

2420

20-09-08

5:10

0.451

0.497

378817

1288195

2259

20-09-08

5:55

0.491

0.547

362114

1287680

2290

20-09-08

8:15

0.409

Cropland

357390

1316535

1817

22-09-08

3:42

0.506

Grassland

354415

1314856

1795

22-09-08

4:00

0.316

Grassland

357313

1316356

1818

22-09-08

4:55

0.324

Forest

357387

1316425

1818

22-09-08

5:15

0.325

Grassland

0.371

Bare land

Forest Grass land

357390

1316535

1817

22-09-08

8:00

0.412

348223

1307649

1789

23-09-08

4:00

0.552

0.549

Rice

Grassland

356497

1315816

1827

23-09-08

8:40

0.494

0.435

Rice

366278

1320051

1846

24-09-08

4:45

0.253

0.225

Mixed (both Forest and Crop)

367799

1318549

1899

24-09-08

4:50

0.228

0.218

Crop

367855

1318249

1915

24-09-08

7:48

0.308

0.319

Forest

390083

1312576

2579

24-09-08

8:15

0.340

Cropland and Eucalyptus

395850

1309930

2614

24-09-08

9:25

0.397

Grassland (Grazing)

376598

1318174

2001

24-09-08

10:25

0.397

Bare land

352778

1304652

1800

25-09-08

4:10

0.424

355247

1314790

1847

25-09-08

5:25

0.248

357390

1316535

1817

25-09-08

5:50

0.412

354794

1313767

1861

25-09-08

9:30

0.202

0.182

Bush and shrubs Bare land and grass

0.389

Bare land Forest

346287

1306346

1881

26-09-08

4:28

0.359

0.303

351764

1305966

1842

26-09-08

5:30

0.511

0.528

Rice,Teff,Grassland

352771

1304652

1820

26-09-08

5:50

0.413

0.370

Bare land

353081

1303345

1889

26-09-08

6:35

0.411

0.364

Leafy forest

350666

1308760

1805

27-09-09

5:15

0.328

Grassland

348208

1307528

1810

27-09-10

5:30

0.397

Rice

345162

1301502

1992

27-09-11

5:55

0.317

Maize

350235

1293051

2076

27-09-12

6:30

0.367

Teff and Maize

356145

1287895

2445

27-09-13

7:00

0.304

Wheat

356100

1287853

2450

27-09-14

7:20

0.406

Forest

370674

1286977

2478

27-09-15

8:20

0.474

Forest

381100

1289305

2360

27-09-16

9:05

0.358

Mixed

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

354529

1314789

1795

29-09-08

5:00

0.354

Grassland

350675

1308749

1798

29-09-08

5:25

0.317

Grassland

351762

1305962

1805

29-09-08

5:50

0.445

Mixed cropland

352771

1304653

29-09-08

6:15

0.356

Bare land

353062

1303332

1843

29-09-08

6:35

0.420

Forest

348203

1307511

1805

29-09-08

7:05

0.329

Rice

Appendix-3 Techniques or methods used to measure soil moisture content

Methods A3-1 Measurement of soil water pressure head The basic instruments capable of measuring matric potential are sufficiently inexpensive and reliable to be used in field scale monitoring programmes. However, each instrument has a limited accessible water potential range. There are two widely used water potential measuring devices and they are listed below. Piezometer A piezometer is a tube of a few cm inner diameters with a filter which is installed in a soil profile .If the filter is below the groundwater table, a piezometer is partially filled with water. By determining the height of the water level in a piezometer the pressure head in the groundwater near the filter can be determined. Tensiometer Piezometers cannot be used to measure negative pressure heads in the vadose zone, because any water in the tubes will be adsorbed by the soil. Negative pressure heads can be measured with socalled tensiometers. A tensiometer consists of a liquid-filled unglazed porous ceramic cup connected to a pressure measuring device, such as a vacuum gauge, via a liquid filled tube. If the ceramic cup is embedded in soil, the soil solution can flow into or out of the tensiometer through the very small pores in the ceramic cup. Analogously to the situation discussed for piezometers, this flow continues until the pressure potential of the liquid in the cup has become equal to the pressure potential of the soil water around the cup. The vacuum gauge does not indicate the pressure in the cup when there is a difference in height between the two. The liquid in the tube between the cup and the vacuum gauge is at static equilibrium and thus the pressure in this liquid increases linearly with depth. Therefore the pressure head of the liquid in the cup is: A3.1 h= hgauge +¨Z1+¨Z2 With z = 0 at the soil surface and without osmotic head, combination with Eq. A.1 gives for the hydraulic head H: A3.2 H =hgauge+¨Z1 While there is no resistance to flow in piezometers, so that they are always instantaneously at equilibrium with the soil water at the lower, open end, this is not necessarily true for tensiometers. A3-2 Measurement of soil water content A3-2.1 Gravimetric and volumetric soil water content The quantity of water in soil is expressed in two different units, as the volumetric water content (cm3 cm-3) and the gravimetric water content w (g g-1). Figure 2 defines the volumes and masses of solids, water, air and pores in a soil. The volumetric water content is the volume of liquid water per volume soil and is calculated as = Vw / Vtotal. The gravimetric water content is the mass of water per mass of dry soil and equals w = Mw / Ms. As the density of the solid phase varies in natural soils, gravimetric water contents are more difficult to conceive than volumetric water contents. Therefore volumetric water contents are commonly used in applied soil physics and hydrology.

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Figure A-1 Definition of volumes and masses with respect to solids, water, air, pores and total.

A3-2.2 Measurement by oven drying This method is very straightforward. You weigh the moist soil sample, dry it to remove the water, and reweigh it. The customary method of drying is to place the sample in an oven at 1050 C for 24 hrs. This removes the inter particle water but not the water molecules trapped between clay layers (Gardner, 1986). To determine the volumetric water content from the weights, either the dry bulk density ȡd (g cm-3) or the volume of the soil sample should be known. Important disadvantages of this method are that it is destructive (you can only measure once at the same place) and can not be automated. This method will be applied for this case study because of its applicability, simplicity and accessibility.

Figure A-2, sampling soil moisture using the gravimetric technique. After the samples are collected in sample cans, they are weighted, oven dried, and weighted again. Photograph by A. Robock.

A3-2.3 Measurement by Time Domain Reflectometry In the past various non-destructive methods have been proposed based on nuclear radiation, e.g. the gamma ray attenuation method and the neutron attenuation method (neutron probe). With these methods a huge amount of soil water content data have been collected, but these methods had two main disadvantages: the invisible danger of nuclear radiation and the need for site specific calibration. These disadvantages were eliminated with Time Domain Reflectometry (TDR). The technique of TDR can be explained as follows. The dielectric behavior of a material is characterized by its permittivity. The relative permittivity, İ, of a non-conducting material is generally introduced as the factor by which the capacitance of a plate capacitor increases when the vacuum or air between the plates is replaced by that medium. Thus, per definition, for vacuum and air = 1. Relative permittivities are also called dielectric constants, which name is misleading as varies with frequency, temperature, water content, etc. The volumetric water content of a soil can be determined indirectly by measuring its effective permittivity, İ, if the ș (İ) relationship for the particular soil and dielectric measuring equipment is known. The relation ș (İ) was measured by Topp et al. (1980) for a number of soils (Topp equation): ș = (- 530 +292İ- 5.5İ2 +0.043 İ3) x10-4

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SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

The relative permittivity can be measured through the propagation velocity of the electromagnetic waves travelling through the medium. Soil-specific calibration is necessary for very accurate results.

Theta Probe method The Theta Probe is designed to measure volumetric soil water content (șv) using a novel technique that matches other methods, such as time-domain reflectometry (TDR) or capacitance measurement, for accuracy and ease-of-use, whilst reducing the complexity and expense. A simplified standing wave measurement is used to determine the impedance of a sensing rod array and hence the volumetric water content of the soil matrix. Installation and data capture Input requirements are 5-15V DC with a current consumption of 19 to 23 mA. The output signal is 0 to 1 V DC that approximates to 0 to 0.5 m3m-3 volumetric water content. Theta Probes can be used to make point measurements by simply inserting into the soil so that all of the rods are fully covered and taking readings from the analogue output either using a meter or logger. The probes can be permanently installed into the soil profile either by using extension tubes or by excavation and back-filling, with periodic data being collected by data logger. As for all soil water measuring devices, care should be taken to avoid air pockets, stones and channelling water directly onto the probe rods.

Figure A-3, Theta probe device installation and operation (source MLURI technical note, 2nd Ed.) This instrument will also be used in the field because of its easiness for handling and relatively accurate than the others. Appendix-4 ILWIS script to retrieve LST from MODIS EM_31F1:=iff(EM_31F=0.49,?,EM_31F) EM_32F1:=iff(EM_32F=0.49,?,EM_32F) Tr:=band19/band2 Wc:=((0.02-LN(tr))/0.651)^2 wc1:=Wc/-21.22704 exp31:=EXP(-wc1) tr31:=2.89798-(1.88366)*(exp31) wc2:=Wc/-32.70639 exp32:=EXP(wc2) tr32:=-3.59289+(4.60414)*(exp32) bt31:=(band31+31.65677)/0.13787 bt32:=(band32+26.50036)/0.11849 A31:=0.13787*EM_31F1*tr31 B31:=0.13787*bt31+31.65677*tr31*EM_31F1-31.65677 77

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

C31:=(1-tr31)*(1+(1-EM_31F1)*tr31)*0.13787 D31:=(1-tr31)*(1+(1-EM_31F1)*tr31)*31.65677 A32:=0.11849*EM_32F1*tr32 B32:=0.11849*bt32+26.50036*tr32*EM_32F1-26.50036 C32:=(1-tr32)*(1+(1-EM_32F1)*tr32)*0.11849 D32:=(1-tr32)*(1+(1-EM_32F1)*tr32)*26.50036 LST_F:=(C32*(B31+D31)-C31*(D32+B32))/(C32*A31-C31*A32) EM_31F= Emissivity map of MODIS band31 from the product EM_31F1= Emissivity map of MODIS band 31 after removing cloud affected pixels. The pixel value of 0.49 is the cloud pixels. 0.49 is due to the offsets. EM_32F= Emissivity map of MODIS band32 from the product EM_32F1= Emissivity map of MODIS band 32 after removing cloud affected pixels. The pixel value of 0.49 is the cloud pixels. 0.49 is due to the offsets. Tr= transmittance map from MODIS band 19 and band 2. Band 19 and Band 2 are absorption and atmospheric window bands. Wc= Water vapour content map obtained from transmittance map tr31= Transmittance of MODIS band 31 tr32= Transmittance of MODIS band 32 band31= radiance map at band31 pre-processed from raw images of MODIS MOD021KM using scale factor 0.002 band32= radiance map at band32 pre-processed from raw images of MODIS MOD021KM using scale factor 0.002 bt31= Brightness temperature map at band31 from the linear relation of radiance at sensor level and brightness temperature. bt32= Brightness temperature map at band32 from the linear relation of radiance at sensor level and brightness temperature. A31---D32= Coefficients for split window algorithm from equation 4.20 LST_F= Land surface temperature map from split window algorithm of MODIS band31/32.

78

25-09-08

24-09-08

23-09-08

22-09-08

20-09-08

19-09-08

18-09-08

300.1

304.3

0.397

0.397

300.4

300.3

0.340

0.248

301

0.308

295.1

301.6

0.228

0.424

303.2

0.253

302.5

0.494

298.2

0.412

298.4

298.2

0.325

0.552

298.2

0.324

301.3

0.409

298.2

300

0.491

298.2

300.9

0.451

0.316

304.5

0.266

0.506

302.5

298

0.413

0.353

297.9

0.395

305.1

298.7

0.444

0.360

297.9

0.418

296.4

0.425

297.8

298.1

0.493

0.437

295

LST

0.309

OSM

0.676

0.367

0.634

0.665

0.662

0.686

0.686

0.676

0.639

0.585

0.717

0.791

0.791

0.755

0.552

0.618

0.687

0.631

0.678

0.678

0.638

0.686

0.693

0.683

0.688

0.699

0.475

0.466

0.435

NDVI

0.514

0.173

0.654

0.346

0.360

0.409

0.458

0.576

0.759

0.445

0.307

0.307

0.307

0.304

0.307

0.296

0.219

0.272

0.490

0.369

0.526

0.385

0.384

0.439

0.382

0.375

0.260

0.360

0.170

T*

0.713

0.016

0.563

0.641

0.633

0.693

0.693

0.668

0.551

0.397

0.648

0.779

0.779

0.716

0.357

0.533

0.728

0.569

0.703

0.703

0.589

0.874

0.885

0.869

0.877

0.895

0.494

0.481

0.436

NDVI*

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

a00

-1.931

-0.648

-2.456

-1.301

-1.352

-1.537

-1.722

-2.165

-2.852

-1.673

-1.153

-1.153

-1.153

-1.143

-1.153

-1.112

-0.823

-1.022

-1.840

-1.388

-1.976

-1.447

-1.441

-1.650

-1.436

-1.408

-0.975

-1.354

-0.638

-3.757

a10

4.160

0.469

6.730

1.888

2.038

2.634

3.306

5.227

9.072

3.123

1.482

1.482

1.482

1.458

1.482

1.380

0.755

1.165

3.778

2.149

4.355

2.335

2.317

3.038

2.300

2.212

1.061

2.045

0.454

15.748

a20

Appendix-5 Least square method of 2nd order polynomial relation algorithm

-0.525

-0.012

-0.414

-0.471

-0.466

-0.510

-0.510

-0.492

-0.406

-0.292

-0.477

-0.573

-0.573

-0.527

-0.263

-0.392

-0.536

-0.419

-0.517

-0.517

-0.434

-0.643

-0.651

-0.640

-0.646

-0.658

-0.363

-0.354

-0.321

-0.736

a01

0.482

0.000

0.300

0.389

0.380

0.456

0.456

0.424

0.288

0.150

0.399

0.576

0.576

0.485

0.121

0.269

0.503

0.307

0.468

0.468

0.329

0.725

0.743

0.717

0.730

0.759

0.231

0.219

0.181

0.948

a02

4.151

0.031

4.165

2.512

2.578

3.211

3.597

4.359

4.738

2.002

2.252

2.706

2.706

2.465

1.240

1.785

1.805

1.753

3.895

2.938

3.508

3.811

3.844

4.324

3.796

3.796

1.450

1.961

0.838

11.321

a11

4.744

0.000

4.778

1.737

1.831

2.839

3.563

5.233

6.182

1.104

1.397

2.017

2.017

1.673

0.423

0.877

0.897

0.846

4.179

2.378

3.389

3.999

4.070

5.148

3.967

3.969

0.579

1.059

0.194

35.293

a22

-2.578

0.000

-2.042

-1.401

-1.422

-1.939

-2.172

-2.537

-2.275

-0.692

-1.272

-1.836

-1.836

-1.536

-0.385

-0.828

-1.144

-0.869

-2.383

-1.798

-1.800

-2.901

-2.964

-3.274

-2.900

-2.958

-0.623

-0.821

-0.319

-9.859

a12

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

-8.826

-0.022

-11.266

-3.598

-3.837

-5.432

-6.820

-10.391

-14.879

-3.689

-2.859

-3.435

-3.435

-3.103

-1.574

-2.186

-1.636

-1.973

-7.894

-4.491

-7.633

-6.072

-6.101

-7.858

-6.001

-5.887

-1.557

-2.924

-0.589

-46.840

a21

0.276

0.418

0.395

0.354

0.350

0.321

0.299

0.258

0.469

0.632

0.369

0.383

0.383

0.373

0.492

0.393

0.422

0.389

0.286

0.339

0.339

0.407

0.417

0.405

0.410

0.425

0.402

0.432

0.400

SSM

0.001

0.000

0.000

0.002

0.000

0.000

0.005

0.000

0.001

0.006

0.002

0.003

0.004

0.003

0.000

0.000

0.005

0.004

0.000

0.000

0.000

0.000

0.000

0.002

0.000

0.000

0.001

0.004

0.008

SE

79

80

29-09-08

27-09-08

26-09-08

300.9

302.7

304.3

307.3

0.420

0.329

300.5

0.358

0.356

294.4

0.474

0.445

299.7

0.406

305.6

299.7

0.304

0.317

301.8

0.367

304

302.2

0.317

0.354

298.6

301.1

0.411

0.397

297

0.413

302.7

297.2

0.511

0.328

298

302.1

0.202

0.359

296.5

0.412

0.672

0.713

0.652

0.660

0.631

0.626

0.668

0.425

0.672

0.672

0.576

0.623

0.663

0.615

0.740

0.578

0.761

0.699

0.681

0.657

0.540

0.372

0.278

0.179

0.442

0.351

0.351

0.002

0.306

0.306

0.427

0.445

0.243

0.478

0.537

0.278

0.291

0.339

0.619

0.264

0.828

0.889

0.798

0.810

0.766

0.759

0.754

0.246

0.762

0.762

0.562

0.660

0.743

0.643

0.802

0.557

0.834

0.740

0.725

0.670

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

0.600

-2.031

-1.397

-1.045

-0.673

-1.662

-1.320

-1.318

-0.009

-1.152

-1.152

-1.604

-1.672

-0.915

-1.796

-2.020

-1.046

-1.093

-1.275

-2.327

-0.992

4.600

2.176

1.219

0.505

3.083

1.942

1.937

0.000

1.479

1.479

2.869

3.118

0.934

3.596

4.550

1.219

1.333

1.813

6.040

1.097

-0.609

-0.654

-0.587

-0.596

-0.564

-0.558

-0.555

-0.181

-0.561

-0.561

-0.413

-0.485

-0.547

-0.473

-0.590

-0.410

-0.613

-0.544

-0.533

-0.493

0.649

0.749

0.603

0.621

0.557

0.546

0.539

0.058

0.551

0.551

0.299

0.413

0.524

0.392

0.610

0.294

0.659

0.519

0.498

0.426

5.064

3.741

2.512

1.641

3.837

3.016

2.993

0.006

2.644

2.644

2.713

3.323

2.049

3.479

4.879

1.754

2.746

2.841

5.080

2.003

7.061

3.855

1.738

0.741

4.055

2.505

2.466

0.000

1.925

1.925

2.027

3.041

1.156

3.332

6.555

0.847

2.076

2.223

7.107

1.105

-3.649

-2.897

-1.745

-1.157

-2.560

-1.993

-1.964

-0.001

-1.754

-1.754

-1.327

-1.909

-1.326

-1.948

-3.407

-0.850

-1.993

-1.831

-3.206

-1.170

-11.324

-5.754

-2.892

-1.215

-7.024

-4.383

-4.343

0.000

-3.352

-3.352

-4.791

-6.118

-2.064

-6.878

-10.850

-2.019

-3.306

-3.988

-13.017

-2.188

0.001 0.083

T.Sum

0.000

0.002

0.001

0.000

0.000

0.000

0.000

0.001

0.006

0.000

0.000

0.000

0.001

0.007

0.001

0.010

0.000

0.002

0.001

0.362

0.420

0.403

0.468

0.321

0.356

0.355

0.473

0.379

0.379

0.373

0.310

0.410

0.305

0.327

0.389

0.409

0.358

0.242

0.389

25-09-08

24-09-08

23-09-08

22-09-08

20-09-08

19-09-08

18-09-08

0.717

0.412 298.2

0.657

0.634

0.397 304.3

0.412 296.5

0.665

0.397 300.1

0.676

0.662

0.340 300.3

0.367

0.686

0.308 301

0.248 300.4

0.686

0.228 301.6

0.424 295.1

0.676

0.253 303.2

0.639

0.791

0.325 298.2

0.494 302.5

0.791

0.324 298.2

0.585

0.755

0.552 298.4

0.552

0.316 298.2

0.618

0.409 301.3

0.506 298.2

0.631

0.687

0.491 300

0.678

0.451 300.9

0.678

0.266 304.5

0.686

0.413 298

0.353 302.5

0.693

0.395 297.9

0.638

0.683

0.444 298.7

0.360 305.1

0.688

0.418 297.9

0.475

0.425 296.4

0.699

0.466

0.493 298.1

0.437 297.8

0.435

NDVI

0.309 295

OSM LST

0.264

0.514

0.173

0.654

0.346

0.360

0.409

0.458

0.576

0.759

0.445

0.307

0.307

0.307

0.304

0.307

0.296

0.219

0.272

0.490

0.369

0.526

0.385

0.384

0.439

0.382

0.375

0.260

0.360

0.170

T*

0.670

0.713

0.016

0.563

0.641

0.633

0.693

0.693

0.668

0.551

0.397

0.648

0.779

0.779

0.716

0.357

0.533

0.728

0.569

0.703

0.703

0.589

0.874

0.885

0.869

0.877

0.895

0.494

0.481

0.436

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

NDVI* 1.39

a00

-1.80

-3.51

-1.18

-4.47

-2.37

-2.46

-2.80

-3.13

-3.94

-5.19

-3.04

-2.10

-2.10

-2.10

-2.08

-2.10

-2.02

-1.50

-1.86

-3.35

-2.53

-3.60

-2.63

-2.62

-3.00

-2.61

-2.56

-1.77

-2.46

-1.16

-6.84

a01

a10

a20

0.61 -3.35 2.39

2.32 -3.56 2.71

0.26 -0.08 0.00

3.75 -2.81 1.69

1.05 -3.20 2.18

1.13 -3.16 2.13

1.47 -3.46 2.56

1.84 -3.46 2.56

2.91 -3.34 2.38

5.05 -2.75 1.62

1.74 -1.98 0.84

0.83 -3.24 2.24

0.83 -3.89 3.23

0.83 -3.89 3.23

0.81 -3.57 2.72

0.83 -1.78 0.68

0.77 -2.66 1.51

0.42 -3.63 2.82

0.65 -2.84 1.73

2.10 -3.51 2.63

1.20 -3.51 2.63

2.42 -2.94 1.85

1.30 -4.36 4.07

1.29 -4.42 4.17

1.69 -4.34 4.02

1.28 -4.38 4.10

1.23 -4.47 4.26

0.59 -2.46 1.30

1.14 -2.40 1.23

0.25 -2.18 1.01

8.77 -4.99 5.32

a02

a22

-0.54

-0.99

-0.18

-2.22

-3.17

-0.79

-1.03

-1.31

-1.89

-1.89

-1.56

-0.40

-0.82

-0.84

-1.62

-1.71

-2.66

-3.33

0.00 5.44

-1.03

11.27 -4.44

0.08

11.31 -4.47

6.82

7.00

8.72

9.77

11.83 -4.89

12.86 -5.78

5.44

6.11

7.35

7.35

6.69

3.37

4.85

4.90

4.76

10.58 -3.91

7.98

9.52

10.35 -3.74

10.44 -3.81

11.74 -4.82

10.31 -3.71

10.31 -3.71

3.94

5.32

2.28

30.74 -33.01

a11

a12

-3.09

-6.81

0.00

-5.39

-3.70

-3.76

-5.12

-5.74

-6.70

-6.01

-1.83

-3.36

-4.85

-4.85

-4.06

-1.02

-2.19

-3.02

-2.30

-6.30

-4.75

-4.76

-7.66

-7.83

-8.65

-7.66

-7.81

-1.65

-2.17

-0.84

-0.98

-3.94

-0.01

-5.03

-1.61

-1.71

-2.43

-3.04

-4.64

-6.64

-1.65

-1.28

-1.53

-1.53

-1.39

-0.70

-0.98

-0.73

-0.88

-3.52

-2.00

-3.41

-2.71

-2.72

-3.51

-2.68

-2.63

-0.70

-1.31

-0.26

-26.04 -20.91

a21

Appendix-6 Least square method of 3rd order polynomial relation NDVI*algorithm

-0.13

-0.94

-0.04

-1.94

-0.29

-0.32

-0.48

-0.67

-1.33

-3.04

-0.61

-0.20

-0.20

-0.20

-0.20

-0.20

-0.18

-0.07

-0.14

-0.82

-0.35

-1.01

-0.40

-0.39

-0.59

-0.39

-0.37

-0.12

-0.33

-0.03

-6.96

a30

a23

a30

0.45

3.54

0.00

5.74

0.97

1.08

1.73

2.44

4.67

8.81

1.28

0.68

0.82

0.82

0.74

0.38

0.50

0.28

0.42

3.01

1.29

3.13

1.82

1.83

2.69

1.79

1.72

0.32

0.82

0.08

-0.36

-3.01

0.00

-3.85

-0.74

-0.81

-1.43

-2.02

-3.72

-5.79

-0.61

-0.53

-0.76

-0.76

-0.63

-0.16

-0.32

-0.24

-0.28

-2.53

-1.08

-2.20

-1.90

-1.93

-2.79

-1.87

-1.84

-0.19

-0.47

-0.04

-0.18

-0.22

0.00

-0.11

-0.16

-0.15

-0.20

-0.20

-0.18

-0.10

-0.04

-0.16

-0.28

-0.28

-0.22

-0.03

-0.09

-0.23

-0.11

-0.21

-0.21

-0.12

-0.40

-0.42

-0.39

-0.40

-0.43

-0.07

-0.07

-0.05

36.53 -43.56 -0.60

a13

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

a31

-0.11

-0.26

0.00

-0.16

-0.13

-0.13

-0.19

-0.21

-0.24

-0.18

-0.04

-0.12

-0.20

-0.20

-0.15

-0.02

-0.06

-0.12

-0.07

-0.23

-0.18

-0.15

-0.36

-0.37

-0.40

-0.36

-0.37

-0.04

-0.06

-0.02

-1.38

a33

SSM

1.03

4.72

0.00

3.75

1.55

1.62

2.74

3.44

4.87

4.75

0.61

1.26

2.19

2.19

1.67

0.21

0.65

0.91

0.67

4.09

2.33

2.78

4.87

5.02

6.24

4.85

4.95

0.40

0.71

0.12

0.11

1.01

0.00

1.02

0.22

0.24

0.47

0.66

1.17

1.50

0.11

0.16

0.28

0.28

0.21

0.03

0.08

0.08

0.08

0.83

0.36

0.61

0.78

0.80

1.14

0.77

0.77

0.04

0.11

0.01

0.39

0.25

0.43

0.40

0.37

0.37

0.31

0.28

0.24

0.49

0.57

0.38

0.37

0.37

0.37

0.47

0.43

0.41

0.41

0.26

0.34

0.35

0.41

0.43

0.42

0.41

0.44

0.42

0.47

0.36

49.20 20.45 0.00

a32

0.000

0.000

0.000

0.000

0.001

0.001

0.000

0.003

0.000

0.000

0.000

0.001

0.002

0.003

0.003

0.002

0.000

0.006

0.002

0.000

0.000

0.000

0.000

0.001

0.001

0.000

0.000

0.000

0.001

0.003

SE

81

82

29-09-08

27-09-08

26-09-08

0.652

0.713

0.672

0.420 304.3

0.329 307.3

0.668

0.358 300.5

0.66

0.425

0.474 294.4

0.356 302.7

0.672

0.406 299.7

0.445 300.9

0.672

0.304 299.7

0.631

0.576

0.367 301.8

0.626

0.623

0.317 302.2

0.317 305.6

0.663

0.354 304

0.615

0.74

0.411 301.1

0.397 298.6

0.578

0.413 297

0.328 302.7

0.761

0.511 297.2

0.681

0.699

0.202 302.1

0.359 298

0.619

0.540

0.372

0.278

0.179

0.442

0.351

0.351

0.002

0.306

0.306

0.427

0.445

0.243

0.478

0.537

0.278

0.291

0.339

0.725

0.828

0.889

0.798

0.810

0.766

0.759

0.754

0.246

0.762

0.762

0.562

0.660

0.743

0.643

0.802

0.557

0.834

0.740

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

1.386

-4.23

-3.70

-2.54

-1.90

-1.22

-3.03

-2.40

-2.40

-0.02

-2.10

-2.10

-2.92

-3.04

-1.66

-3.27

-3.68

-1.90

-1.99

-2.32

3.36 -3.62 2.79

2.56 -4.13 3.64

1.21 -4.44 4.21

0.68 -3.98 3.38

0.28 -4.04 3.49

1.72 -3.82 3.12

1.08 -3.79 3.06

1.08 -3.76 3.02

0.00 -1.23 0.32

0.82 -3.80 3.09

0.82 -3.80 3.09

1.60 -2.80 1.68

1.74 -3.29 2.32

0.52 -3.71 2.94

2.00 -3.21 2.20

2.53 -4.00 3.42

0.68 -2.78 1.65

0.74 -4.16 3.70

1.01 -3.69 2.91 -0.79

-1.94

-2.08

-2.34

-2.31

0.00

-1.80

-1.80

-1.90

-2.84

-1.08

-3.12

-1.63

-0.69

13.75 -6.61

10.16 -3.61

6.82

4.45

10.42 -3.79

8.19

8.12

0.02

7.18

7.18

7.37

9.02

5.56

9.44

13.25 -6.13

4.76

7.46

7.71

13.79 -6.65

-9.64

-7.65

-4.61

-3.06

-6.76

-5.26

-5.19

0.00

-4.63

-4.63

-3.51

-5.04

-3.50

-5.15

-9.00

-2.25

-5.27

-4.84

-8.47

-5.05

-2.57

-1.29

-0.54

-3.14

-1.96

-1.94

0.00

-1.50

-1.50

-2.14

-2.73

-0.92

-3.07

-4.84

-0.90

-1.48

-1.78

-5.81

-1.65

-1.10

-0.36

-0.15

-0.04

-0.60

-0.30

-0.30

0.00

-0.20

-0.20

-0.54

-0.61

-0.10

-0.76

-1.08

-0.15

-0.17

-0.27

4.77

1.67

0.63

0.17

2.42

1.20

1.19

0.00

0.80

0.80

1.59

2.12

0.39

2.56

4.55

0.44

0.75

1.06

6.29

-4.71

-1.77

-0.60

-0.16

-2.21

-1.09

-1.07

0.00

-0.73

-0.73

-1.07

-1.67

-0.35

-1.97

-4.35

-0.29

-0.75

-0.93

-5.43

-0.34

-0.42

-0.30

-0.32

-0.27

-0.26

-0.26

-0.01

-0.26

-0.26

-0.11

-0.17

-0.25

-0.16

-0.31

-0.10

-0.35

-0.24

-0.23

-0.42

-0.36

-0.20

-0.13

-0.28

-0.21

-0.21

0.00

-0.19

-0.19

-0.10

-0.18

-0.14

-0.18

-0.38

-0.07

-0.23

-0.19

-0.33

8.15

4.78

1.93

0.84

4.33

2.65

2.59

0.00

2.04

2.04

1.59

2.80

1.20

2.99

7.33

0.66

2.41

2.29

7.18

1.83

0.74

0.22

0.06

0.80

0.39

0.38

0.00

0.26

0.26

0.28

0.52

0.12

0.59

1.64

0.08

0.29

0.32

1.85

0.004 0.065

sum

0.000

0.002

0.001

0.001

0.000

0.000

0.000

0.001

0.005

0.002

0.000

0.000

0.000

0.008

0.000

0.011

0.000

0.001

0.39

0.43

0.40

0.47

0.29

0.34

0.34

0.47

0.37

0.37

0.41

0.31

0.41

0.31

0.32

0.41

0.40

0.35

0.23

24-09-08

23-09-08

22-09-08

20-09-08

19-09-08

18-09-08

0.676

0.686

0.686

0.662

0.665

0.634

0.253 303.22

0.228 301.64

0.308 300.98

0.340 300.32

0.397 300.14

0.397 304.26

0.585

0.717

0.412 298.2

0.639

0.791

0.325 298.2

0.494 302.46

0.791

0.324 298.2

0.552 298.36

0.755

0.618

0.409 301.28

0.316 298.16

0.687

0.491 300

0.552

0.631

0.451 300.88

0.506 298.2

0.678

0.266 304.5

0.686

0.413 297.96

0.678

0.693

0.395 297.94

0.353 302.5

0.683

0.444 298.7

0.638

0.688

0.418 297.92

0.360 305.1

0.699

0.475

0.425 296.44

0.437 297.82

0.466

0.493 298.08

NDVI

0.435

LST

0.309 294.98

SM

0.654 0.330

0.346 0.376

0.360 0.372

0.409 0.407

0.458 0.407

0.576 0.392

0.759 0.290

0.445 0.209

0.307 0.467

0.307 0.561

0.307 0.561

0.304 0.515

0.307 0.257

0.264 0.288

0.195 0.394

0.243 0.308

0.437 0.380

0.330 0.380

0.469 0.319

0.385 0.874

0.384 0.885

0.439 0.869

0.382 0.877

0.375 0.895

0.260 0.494

0.360 0.481

a00

a01

a02

a10

a20

a11

a22

a21

0.109 0.82 -2.50 4.51

0.141 0.82 -1.32 1.27

0.138 0.82 -1.38 1.37

0.166 0.82 -1.56 1.77

0.166 0.82 -1.75 2.22

0.154 0.82 -2.20 3.50

0.084 0.82 -2.90 6.08

0.044 0.82 -1.70 2.09

0.218 0.82 -1.17 0.99

0.315 0.82 -1.17 0.99

0.315 0.82 -1.17 0.99

0.266 0.82 -1.16 0.98

0.066 0.82 -1.17 0.99

0.083 0.82 -1.01 0.74

0.155 0.82 -0.75 0.40

0.095 0.82 -0.93 0.62

0.144 0.82 -1.67 2.02

0.144 0.82 -1.26 1.15

0.101 0.82 -1.80 2.33

0.764 0.82 -1.47 1.57

0.784 0.82 -1.47 1.55

0.756 0.82 -1.68 2.04

0.770 0.82 -1.46 1.54

0.800 0.82 -1.43 1.48

0.244 0.82 -0.99 0.71

0.231 0.82 -1.38 1.37 1.01

1.75

0.26

-0.67 0.08 4.45

-0.87 0.13 3.05

-0.85 0.12 3.10

-1.02 0.17 4.22

-1.02 0.17 4.73

-0.95 0.15 5.52

-0.52 0.04 3.97

-0.27 0.01 1.21

-1.34 0.30 4.17

-1.94 0.63 6.02

-1.94 0.63 6.02

-1.64 0.45 5.03

-0.41 0.03 1.26

-0.51 0.04 1.36

-0.96 0.15 1.89

-0.58 0.06 1.43

-0.89 0.13 3.93

-0.89 0.13 2.96

-0.63 0.07 2.97

1.28

0.60

0.62

1.16

1.45

1.98

1.02

0.09

1.13

2.35

2.35

1.64

0.10

0.12

0.23

0.13

1.00

0.57

0.57

-4.71 3.72 18.33 21.80

-4.83 3.91 18.73 22.74

-4.66 3.64 20.69 27.75

-4.75 3.77 18.33 21.78

-4.94 4.08 18.69 22.65

-1.50 0.38 3.94

-1.43 0.34 5.19

-1.17 0.23 2.01

-0.72

-0.64

-0.63

-1.04

-1.16

-1.26

-0.49

-0.08

-1.35

-2.80

-2.80

-1.98

-0.12

-0.17

-0.43

-0.20

-0.84

-0.63

-0.45

-20.75

-21.73

-23.16

-20.89

-22.15

-1.42

-1.77

-0.57

0.82 -3.83 10.56 -6.17 6.37 62.30 251.68 -92.25

0.190 0.82 -0.65 0.30

NDV* Fr

0.170 0.436

T*

Appendix-7 Least square method of 3rd order polynomial relation Fr algorithm a03

a13

a23

-8.09

-2.94

-3.10

-4.81

-6.04

-8.86

-8.39

-1.50

-3.56

-5.14

-5.14

-4.26

-1.08

-1.00

-1.03

-0.97

-4.78

-2.72

-3.88

-19.66

-20.00

-25.30

-19.50

-19.51

-2.85

-5.21

-0.95

-1.87 3.40

-0.28 0.65

-0.31 0.72

-0.46 1.26

-0.64 1.78

-1.28 3.28

-2.92 4.09

-0.59 0.43

-0.19 0.70

-0.19 1.01

-0.19 1.01

-0.19 0.83

-0.19 0.21

-0.12 0.17

-0.05 0.13

-0.10 0.15

-0.56 1.34

-0.24 0.58

-0.69 1.17

-0.38 4.86

-0.38 4.93

-0.57 7.13

-0.37 4.78

-0.35 4.69

-0.12 0.47

-0.31 1.20

-0.03 0.10

-0.29

-0.07

-0.08

-0.16

-0.23

-0.39

-0.26

-0.01

-0.12

-0.25

-0.25

-0.17

-0.01

-0.01

-0.02

-0.01

-0.15

-0.06

-0.09

-2.86

-2.97

-4.15

-2.84

-2.89

-0.09

-0.21

-0.02

-173.47 -6.69 111.35 -85.75

a12

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

a31

a32

a33

0.01 0.00 0.00

0.01 0.00 0.00

0.01 0.00 0.00

0.02 0.00 0.00

0.02 0.00 0.00

0.02 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0.04 0.00 0.00

0.13 0.01 0.00

0.13 0.01 0.00

0.08 0.01 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0.02 0.00 0.00

0.00 0.00 0.00

0.01 0.00 0.00

0.01 0.00 0.00

0.00 0.00 0.00

1.90 0.26 0.00

2.05 0.28 0.00

1.84 0.29 0.00

1.94 0.27 0.00

2.18 0.29 0.00

0.06 0.01 0.00

0.05 0.01 0.00

0.03 0.00 0.00

-0.04

-0.01

-0.01

-0.04

-0.05

-0.08

-0.03

0.00

-0.04

-0.11

-0.11

-0.06

0.00

0.00

0.00

0.00

-0.03

-0.01

-0.01

-3.00

-3.20

-4.31

-3.00

-3.18

-0.03

-0.07

0.00

4.26 1.53 -0.04 -117.75

a30

0.36

0.40

0.39

0.34

0.30

0.25

0.51

0.51

0.39

0.37

0.37

0.38

0.44

0.43

0.41

0.43

0.34

0.40

0.38

0.42

0.42

0.36

0.42

0.44

0.40

0.35

0.37

0.00

SSM

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.01

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.02

0.00

SE

83

84

29-09-08

27-09-08

26-09-08

25-09-08

0.668

0.358 300.5

0.652

0.713

0.672

0.356 302.68

0.420 304.32

0.329 307.28

0.66

0.425

0.474 294.36

0.445 300.94

0.672

0.406 299.72

0.631

0.672

0.304 299.72

0.626

0.576

0.367 301.84

0.317 305.56

0.623

0.317 302.16

0.354 303.96

0.663

0.397 298.61

0.74

0.411 301.08

0.615

0.578

0.413 297

0.328 302.74

0.761

0.681

0.202 302.1

0.511 297.2

0.657

0.412 296.5

0.699

0.676

0.248 300.44

0.359 297.96

0.367

0.424 295.06

0.540 0.828

0.372 0.889

0.278 0.798

0.179 0.810

0.442 0.766

0.351 0.759

0.351 0.754

0.002 0.246

0.306 0.762

0.306 0.762

0.427 0.562

0.445 0.660

0.243 0.743

0.478 0.643

0.537 0.802

0.278 0.557

0.291 0.834

0.339 0.740

0.619 0.477

0.264 0.441

0.514 0.470

0.173 0.010

0.685 0.82 -2.07 3.08

0.790 0.82 -1.42 1.46

0.636 0.82 -1.06 0.82

0.655 0.82 -0.68 0.34

0.587 0.82 -1.69 2.07

0.576 0.82 -1.34 1.30

0.568 0.82 -1.34 1.30

0.061 0.82 -0.01 0.00

0.581 0.82 -1.17 0.99

0.581 0.82 -1.17 0.99

0.315 0.82 -1.63 1.92

0.435 0.82 -1.70 2.09

0.552 0.82 -0.93 0.63

0.413 0.82 -1.83 2.41

0.643 0.82 -2.06 3.05

0.310 0.82 -1.06 0.82

0.695 0.82 -1.11 0.89

0.547 0.82 -1.30 1.22

0.227 0.82 -2.37 4.05

0.195 0.82 -1.01 0.74

0.220 0.82 -1.97 2.79

0.000 0.82 -0.66 0.31

0.00 0.00

5.00

0.67

3.23

0.00

1.87

4.55 4.56

0.00

3.47

-4.22 2.99 23.06 34.49

-4.88 3.98 18.30 21.73

-3.92 2.58 11.03 7.88

-4.04 2.74 7.31

-3.62 2.19 16.18 16.97

-3.55 2.11 12.59 10.28

-3.50 2.05 12.41 9.99

-0.37 0.02 0.01

-3.58 2.15 11.09 7.97

-3.58 2.15 11.09 7.97

-1.95 0.63 8.39

-2.68 1.21 12.06 9.44

-3.41 1.94 8.38

-2.55 1.09 12.31 9.82

-3.97 2.63 21.53 30.05

-1.91 0.61 5.37

-4.29 3.07 12.60 10.29

-3.38 1.91 11.57 8.68

-1.40 0.33 8.78

-1.20 0.24 3.20

-1.36 0.31 7.06

0.00

-23.39

-21.42

-10.39

-7.09

-14.06

-10.73

-10.44

0.00

-9.53

-9.53

-3.92

-7.77

-6.85

-7.54

-20.49

-2.47

-12.96

-9.37

-2.96

-0.92

-2.30

0.00

-34.71

-18.95

-8.54

-3.64

-19.93

-12.31

-12.12

0.00

-9.46

-9.46

-9.97

-14.95

-5.68

-16.38

-32.22

-4.16

-10.21

-10.93

-15.14

-2.35

-10.10

0.00

0.00

-1.06 12.04

-0.34 4.52

-0.14 1.53

-0.04 0.42

-0.58 5.66

-0.29 2.78

-0.29 2.73

0.00

-0.19 1.86

-0.19 1.86

-0.52 2.73

-0.59 4.27

-0.10 0.89

-0.73 5.02

-1.04 11.12

-0.14 0.74

-0.16 1.91

-0.26 2.38

-1.59 6.02

-0.12 0.40

-0.91 3.33

-0.03 0.00

-6.35

-2.75

-0.75

-0.21

-2.56

-1.23

-1.19

0.00

-0.83

-0.83

-0.66

-1.43

-0.38

-1.60

-5.50

-0.18

-1.02

-1.00

-1.05

-0.06

-0.57

0.00

1.37 0.27 0.00

2.10 0.28 0.00

1.10 0.11 0.00

1.20 0.08 0.00

0.86 0.14 0.00

0.81 0.10 0.00

0.78 0.10 0.00

0.00 0.00 0.00

0.83 0.09 0.00

0.83 0.09 0.00

0.13 0.02 0.00

0.35 0.06 0.00

0.72 0.06 0.00

0.30 0.05 0.00

1.13 0.22 0.00

0.13 0.01 0.00

1.43 0.15 0.00

0.70 0.09 0.00

0.05 0.01 0.00

0.03 0.00 0.00

0.05 0.01 0.00

0.00 0.00 0.00

-5.97

-2.99

-0.65

-0.19

-2.06

-0.97

-0.93

0.00

-0.66

-0.66

-0.29

-0.86

-0.29

-0.91

-4.86

-0.08

-0.97

-0.75

-0.33

-0.02

-0.17

0.00

0.00 0.11

Sum

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.00

0.34

0.44

0.40

0.46

0.38

0.37

0.36

0.47

0.37

0.37

0.28

0.31

0.36

0.30

0.41

0.38

0.43

0.36

0.21

0.41

0.22

0.44

SATELITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Appendix-8 NDVI map

85

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Appendix-9 MODIS LST product and potential surface temperature

86

SATELITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

87

SATELLITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

Appendix-10 Simulated soil moisture maps after elevation correction

88

25-09-08

24-09-08

23-09-08

22-09-08

20-09-08

319.92

318.97

0.397

0.397

316.48

323.34

0.340

0.412

319.59

0.308

318.16

319.59

0.228

0.248

321.45

314.53

0.253

315.91

316.83

0.412

0.494

316.83

0.325

0.552

315.85

0.324

323.21

0.409

315.71

321.16

0.491

0.316

324.69

0.451

315.85

324.09

0.266

0.506

324.09

315.66

0.413

0.353

315.63

0.395

323.85

314.7

0.444

0.360

315.61

0.418

0.425

315.39

313.89

0.493

0.437

315.65

0.309

18-09-08

19-09-08

312.98

OSM

Date

Ĭ

0.392

0.292

0.292

0.494

0.310

0.259

0.280

0.184

0.686

0.686

0.662

0.665

0.634

0.676

0.657

0.252

0.791

0.676

0.247

0.755

0.078

0.252

0.552

0.159

0.299

0.618

0.639

0.188

0.687

0.585

0.379

0.631

0.289

0.347

0.678

0.717

0.347

0.678

0.289

0.334

0.638

0.791

0.148

0.145

0.688

0.686

0.135

0.699

0.146

0.116

0.475

0.693

0.198

0.466

0.102

0.073

0.435

0.683

Ĭ*

NDVI

0.760

0.792

0.694

0.745

0.740

0.780

0.780

0.763

0.616

0.487

0.717

0.809

0.809

0.764

0.512

0.578

0.742

0.609

0.721

0.721

0.625

0.711

0.736

0.700

0.718

0.758

0.497

0.484

0.439

NDVI*

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

a00

1.537

2.337

2.155

2.581

4.113

2.433

2.433

3.266

0.652

1.324

2.411

2.411

2.103

2.059

2.103

2.492

1.567

3.160

2.889

2.889

2.781

1.232

1.220

0.854

1.212

1.126

0.965

1.649

0.611

8.334

a10

-0.372

-0.859

-0.730

-1.047

-2.660

-0.931

-0.931

-1.678

-0.067

-0.276

-0.914

-0.914

-0.695

-0.667

-0.695

-0.976

-0.386

-1.570

-1.313

-1.313

-1.216

-0.239

-0.234

-0.115

-0.231

-0.199

-0.146

-0.428

-0.059

-10.92

a20

3.850

4.012

3.514

3.772

3.748

3.947

3.947

3.864

3.118

2.465

3.629

4.095

4.095

3.868

2.591

2.924

3.758

3.081

3.649

3.649

3.166

3.601

3.729

3.546

3.638

3.839

2.517

2.451

2.225

5.063

a01

Appendix-11 Least square method 2nd order relation with potential temperature

-1.826

-1.983

-1.521

-1.753

-1.730

-1.920

-1.920

-1.839

-1.197

-0.749

-1.623

-2.065

-2.065

-1.843

-0.827

-1.054

-1.740

-1.170

-1.641

-1.641

-1.235

-1.597

-1.713

-1.549

-1.630

-1.815

-0.780

-0.740

-0.610

-3.158

a02

-2.169

-3.435

-2.775

-3.567

-5.647

-3.519

-3.519

-4.624

-0.745

-1.196

-3.205

-3.616

-3.155

-2.918

-1.997

-2.670

-2.157

-3.568

-3.863

-3.863

-3.226

-1.625

-1.667

-1.109

-1.616

-1.583

-0.890

-1.481

-0.498

-15.46

a11

0.116

0.291

0.190

0.314

0.788

0.306

0.306

0.528

0.014

0.035

0.254

0.323

0.246

0.210

0.099

0.176

0.115

0.315

0.369

0.369

0.257

0.065

0.069

0.030

0.064

0.062

0.020

0.054

0.006

5.905

a22

0.336

0.554

0.392

0.542

0.852

0.559

0.559

0.719

0.093

0.119

0.468

0.596

0.520

0.454

0.208

0.314

0.326

0.442

0.567

0.567

0.411

0.236

0.250

0.158

0.237

0.245

0.090

0.146

0.045

3.150

a12

0.330

0.795

0.592

0.912

2.301

0.848

0.848

1.496

0.048

0.157

0.765

0.863

0.657

0.595

0.416

0.659

0.335

1.117

1.106

1.106

0.888

0.198

0.201

0.094

0.194

0.176

0.085

0.242

0.030

12.761

a21

SATELITE REMOTE SENSING FOR SOIL MOISTURE ESTIMATION: GUMARA CATCHMENT, ETHIOPIA

0.377

0.288

0.392

0.327

0.337

0.298

0.298

0.307

0.490

0.454

0.360

0.266

0.279

0.333

0.472

0.440

0.392

0.381

0.338

0.338

0.401

0.445

0.429

0.483

0.442

0.424

0.434

0.468

0.324

0

SSM

0.001

0.002

0.000

0.005

0.000

0.000

0.005

0.003

0.000

0.010

0.003

0.003

0.002

0.000

0.001

0.001

0.010

0.005

0.005

0.000

0.002

0.001

0.001

0.002

0.001

0.000

0.000

0.001

0.000

0

SDE

89

90

29-09-08

27-09-08

322.61

320.37

325.46

0.356

0.420

0.329

322.522

0.358

320.84

317.64

0.474

0.445

325.85

0.406

323.56

323.85

0.304

0.317

322.96

0.367

324.85

321.85

0.317

0.354

323.09

0.397

319.95

321.64

0.202

0.328

0.106

0.344

0.713

0.672

0.370

0.668

0.210

0.109

0.425

0.652

0.548

0.672

0.128

0.441

0.672

0.66

0.393

0.576

0.255

0.334

0.623

0.631

0.400

0.663

0.315

0.323

0.615

0.626

0.383

0.681

0.687

0.757

0.353

0.764

0.764

0.604

0.230

0.753

0.753

0.550

0.649

0.734

0.632

0.772

0.801

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

-1.426

2.864

0.881

1.753

1.064

2.123

2.626

3.083

0.909

4.565

3.675

3.278

2.784

3.336

2.690

3.189

-1.289

-0.122

-0.483

-0.178

-0.709

-1.084

-1.495

-0.130

-3.277

-2.123

-1.690

-1.219

-1.750

-1.138

-1.599

3.479

3.833

1.786

3.867

3.867

3.058

1.167

3.811

3.811

2.783

3.286

3.715

3.201

3.907

4.054

-1.491

-1.810

-0.393

-1.842

-1.842

-1.152

-0.168

-1.789

-1.789

-0.954

-1.330

-1.700

-1.262

-1.881

-2.025

-3.650

-1.237

-1.147

-1.507

-3.008

-2.942

-1.318

-1.269

-6.374

-3.747

-3.947

-3.789

-3.912

-3.851

-4.736

0.329

0.038

0.033

0.056

0.224

0.214

0.043

0.040

1.004

0.347

0.385

0.355

0.378

0.366

0.554

0.511

0.191

0.082

0.235

0.468

0.362

0.062

0.195

0.978

0.420

0.522

0.566

0.504

0.606

0.773

1.035

0.108

0.199

0.159

0.633

0.765

0.402

0.114

2.882

1.364

1.282

1.045

1.293

1.026

1.496

0.001 0.084

Sum

0.001

0.002

0.000

0.000

0.004

0.000

0.000

0.001

0.001

0.000

0.000

0.001

0.001

0.006

0.362

0.455

0.404

0.427

0.329

0.421

0.351

0.454

0.373

0.338

0.360

0.331

0.361

0.300

0.280