Rain gauge network design for Hormozgan province-south of Iran

Rain gauge network design for Hormozgan province-south of Iran Mohammad Nekooamal Kermani1, Bahram Bakhtiari2, Mohammad hadi Bordbar3 1 M. Sc. in Met...
Author: Dwight Higgins
0 downloads 0 Views 572KB Size
Rain gauge network design for Hormozgan province-south of Iran Mohammad Nekooamal Kermani1, Bahram Bakhtiari2, Mohammad hadi Bordbar3 1

M. Sc. in Meteorology Research Center of Hormozgan Province, Hormozgan, Iran, [email protected] 2 Department of Water Engineering, College of Agriculture, ShahidBahonar University of Kerman, Kerman, Iran, [email protected] Tel: 0341-3202664, Fax:0341-3222043 3 M. Sc. of physical oceanography,Meteorology Research Center of Hormozgan Province, Hormozgan, Iran

Abstract A raingauge network is intended to serve general as well as specific purposes such as water supply, hydropower generation, flood forecasting, irrigation and flood control. The level of accuracy a network can achieve depends on the total number and locations of gauges in the network. In this study, anarrangement raingauge network has been designed for Hormozgan province-south of Iran. Monthly rainfall totals from 124 raingauge stations within the period 2000-2009 are used. Based onDe Martonnearidity index, this province can be logically divided to four basins.Kagan’s approach was used to relocate the rain gauge network and to obtain the optimal design.In this statistical method the correlations were classified based on distance. Exponential models are fitted onaverage correlations against mean distances in all basins. The number of gauges and the distance between gauges for achieving various user requirements have been computed. The results show thatHajiabad basin has minimum value for distance (125 km) and Bandarlengeh basin has maximum value for distance (588 km). Spatial variation of rainfall in Hajiabad basin is greater than others.The results indicate that a maximum of 40, 50, 20 and 55 stations are adequate to represent the rainfall correspond to 15 percent average error in four basins including Bandarlengeh, Bandarabbas, Hajiabad and Minab, respectively.

Keywords: Rainfall; Rain gauge;Hormozgan; Statistical method Introduction Rainfall data are essential in many hydrological analyses and engineering design projects, including water budget analysis, frequency analysis and storm water drainage design. Direct measurement of rainfall can only be achieved by rain gauges, and rain gauge networks are often installed to provide measurements that characterize the temporal and spatial variations of rainfall. Rain gauge network design is a problem that has received considerable attention.The relationship between precipitation and elevation has been investigated by Danard (1971), Sevruk (1974), Osborn (1984) and Puvaneswaran and Smithson (1991), among others. Several studies also have been carried out on the relationship between rainfall distribution, orographic and climatic factors (Merva et al., 1971; Peck, 1972; Corradini, 1985). It is known that the areal variability of rainfall is affected by the nature and orientation of terrain and that it is necessary to establish a greater network density in mountainous areas than in flat areas (Hutchinson, 1970). Four major factors determining rainfall distribution in mountainous areas can be identified as the speed of ascending air, water vapor supply and wind speed and direction. Wind speed is mainly related to rainfall intensity and less to its distribution. Water vapor supply can be regarded as sufficient for the occurrence of storm events. Therefore, for a qualitative discussion, rainfall distribution can be estimated from just wind direction and the area of ascending air (Oki et al., 1991). Newly developed rainfall network design techniques are discussed and compared (St-Hilaire et al.; Cheng, et al., 2007). Although recent advances in satellite remote sensing seem to have the potential to provide full spatial coverage of pixel rainfall estimates and have caused deterioration of rain-gauge networks in some cases (Ali et al., 2005), satellite images alone still cannot provide accurate rainfall estimates at the spatial resolution to match rain-gauge measurements (Cheng, et al., 2007). Many approaches to optimal design of rainfall gauges take into account the number and location of rainfall gauges to yield greater accuracy of areal rainfall estimation with minimum cost. These approaches are generally known as the variance reduction method (Bras and Rodriguez-Iturbe, 1976; Hughes and Lettenmaier, 1981; Bastin et al., 1984; Bogardi and Bardossy, 1985; Rouhani, 1985), which involves searching for the appropriate number of rainfall gauges and their locations. Rodriguez-Iturbe and Mejia (1974) applied a hypothetical analytical model of rainfall to present estimates of variance as a function of gauge

1

density, area of interest, correlation length scale and variance of the rainfall process. Their work considers both long-term and event rainfall as well as both stratified and random sampling designs. Using radar data in Florida and South Africa, Seed and Austin (1990) found that estimation error variance increases with a random rain gauge network relative to a regular one. They also found that the mean standard error is a function of both network and rainfield characteristics, i.e. gauge density, areal rain fraction and the ratio of the standard deviation to the mean of the non-zero fraction of the rainfield. Fontaine (1991) concludes that "gauge density appears to be the most influential factor in areal mean precipitation error", but that gauge arrangement is also significant. Peters-Lidard (1998) used the statistical methods to determine the number of rain gauges in an area. The use of such methods first requires criteria against which the network density can be tested. For some applications, investigation is recommended to determine whether precipitation amounts can be interpolated with sufficient accuracy. Buishand (1986) calculated the average and interpolation errors with statistical methods. Wei et al. (2010) used the ordinarykriging to generate rainfall data at the alpine area, located at Experimental Forest of National Taiwan University in central Taiwan. The result shows that only 2 and 5 candidate rain gauges can represent 62.93% and 85.21% of variance of rainfall distribution respectively. Rain gauges often are installed for a specific purpose and later some of these are not used. These networks in some basins are sparse, while the density of other basins is high. Optimization of a network consists of specifying the density of observation sites that will be sufficient for obtaining reliable data while not requiring the establishment of an excessive number of sites (Karasseff, 1986; Shaw and O'Connell, 1976). In Hormozgan province, rain gauge networks coincide with unscientific methods and configuration of stations is irregular. The purpose of this study is to propose a rain gauge network evaluation and design approach focusing on accuracy assessment of point rainfalls across the whole study area using a statistical method.

Materials and Methods Study areaand data Hormozgan province is located in the south of Iran between 25° 23', 28 57' N, and 52° 41', 59° 15' E. This region has arid and semiarid climate, and precipitation is always in form of showers. Although the average of annual rainfall is less than 250 mm, severe floods frequently occur in the province causing heavy damage. Hormozgan province is one of the 30 provinces of Iran with an area of over 68,400 km2. It is located in southern part of the country, facing Oman Kingdom. It borders the Persian Gulf & Oman Sea on the south (Fig. 1) and is bounded by the provinces of Bushehr and Fars on the west and northwest, Kerman on the east and northeast, and Sistan&Beluchestan on the northeast. Its capital is Bandarabbas.The province comprises three regions of differing geography; the coastal region in the south, a mountainous region in the north, and a rural plateau or plains region in the centre. Hormozgan province is situated in the dominantly warm and dry zone of Iran, with temperatures sometimes exceeding 49 °C in the summer. The weather along coastal line is very hot and humid in the summer and very mild in the winter. The rainfall occurs mostly during November toFebruary and the rainfall is Shower. Relative humidity is mainly very high in the coastal zones of the Persian Gulf. In this study, time series of monthly rainfall data for 10 years, from 2000 to 2009, have been analyzed. In total 124 rain gauges were used in this period. Based on the province climate, these regions can be logically divided to four basins. Table 1 shows specifications of each basin. The basins and rain gauge positions are denoted in Figure 1. For arrangement of stations, all basins should be analyzed by Kagan’s approach (Kagan, 1972). This process is accomplished separately and independently of others for all. Due to the fact that in some months the amount of precipitation is zero, the recorded null values can lead to a strong correlation between the two stations. Hence the null values have been eliminated so that the correlation between the stations is not artificially elevated. According to last observation, 60 percent of rain gauges include amount of percent last 200 mm a year, while that of those which have precipitation between 200-250 and more than 250 mm ayear are 25 and 15 percent, respectively. The peak of precipitation occurred in Bastak with a mount of 342 mm a year and the least of all were 20 mm in Bandarlengeh. The surprising point is that there were about 48 stations in Bandarlengeh while that number of installed devices in Bastak was only 4, and clearly it illustration the appropriate distribution of raingauges. As shown in Fig. 4 the distribution of rain gauges are mainly irregular, beside this, the long length of the province have made the expense of measuring and accumulating of rainfall observation data exorbitant.

2

Fig 1.The study area and raingauge locations (http://maps.google.com)

Table1. Site-specific gauge networks Basin Basin area (km2) Number of gauge Rain average (mm) Average area for each rain gauge (km2)

Bandarlengeh 15246 39 142.5

Bandarabbas 15429 27 183.5

Hajiabad 9379 16 219.9

Minab 7496 42 213.6

391

571

586

178

Spatial Correlation Technique Kagan (1972) demonstrated that a network of rain gauges can be designed to meet a specified error criterion, given that the spatial variability of rainfall can be quantified through a spatial correlation function. However, applying such approach would require conditions, such as horizontal homogeneity and isotropy, to ensure the existence of a spatial correlation function (Shaw and O'Connell, 1976).The basis of the method is that the correlation function is a function of the distance between stations, and furthermore, it depends on characteristics of the area and the type of precipitation.The correlation between measured precipitation amounts of two stations at a distance d is often described by the following two parameter exponential relation (Kagan, 1972; Stol, 1972):

 (d )   e 0

d

d0

(1)

Where  (d ) is correlation between precipitation amounts at two stations with distance d (km) .  o is the correlation corresponding to zero distance. Correlation function  (d ) at distance d o equals 0.36  o . This relation usually provides a good fit to plots of sample correlations estimated from historic data. It is often found that  o is less than 1, and thus  (d ) differs from unity at very short distances. In the literature, this property is known as the nugget effect (Journel & Huijbregts, 1978). The nugget effect can either beascribed to random errors in precipitation measurement and microclimatic irregularities over an area (James and

3

Sreedharan, 1986; Sreedharan and James, 1983; Nandagiri, 2006). The variance of these random errors at a fixed point  1 ,is given by: 2

 12  1   0   h2 (2) where  2 is variance of rainfall time series at this point. The quantities  o and d o provide the basis for assessing h

the accuracy of a rain gauge network. Error of weigh average rainfall at a given area (Ea), and error of interpolation rainfall at a given point (Ei), are main factors for designing rain gauge network (James, 1983; James and Sreedharan, 1986). The required network density often relates to Ea. The variance of error ( v ), in the average precipitation over an area, is given by Kagan's relation (Kagan, 1972):

v   h2 1  0   0.23 h2

S (3) d0

where S is basin area. In equation 5, the first term is described as the random error and is defined by equation 2. The second term is described as the spatial variation of precipitation in the basin (James, 1983; James and Sreedharan, 1986). Hence Ea is defined as:

1  0  Ea  Cv

0.23 S d0 n (4) n

where C v is the coefficient of variation and

n

is the number of stations that are required to obtain the specified

error criterion Ea. Conversely, Ea can be evaluated if n

is given. This equation denotes that, values  o and d o

are primary parameters for rain gauge network design. The triangular grid is usually more convenient if the project region has a complex configuration. In this grid, the spacing between adjacent stations is defined as:

r

2S 3n

 1.07

S (5) n

In hydrological projects often, precipitation amounts for given points are needed. For this purpose, rainfall data is estimated by interpolation from measurements at surrounding rain gauges. The error of interpolation rainfall (Ei), often considers in rain gauge network design. For instance, in most projects, in order to lower the interpolation error than given errors, sufficient rain gauges should be installed. In triangular grid, maximum interpolated error occurs at the center of triangles. This error is evaluated by following equation:

Ei  C v

1 1   0   0.52  0 3 d0

S (6) n

The calculation of Ea and Ei requires the estimation of  (d ) , from which  0 and d o are derived. The function

 (d ) is considered by following steps: a- The correlation between monthly rainfall for a selected duration at stations ith and jth,  ij , is calculated.

4

b-  ij is classified based on distance between stations. c- Distance average and correlation average are calculated in each class. d- This correlation average is plotted against distance average, and an exponential function is fitted this curve as following:

ρ  α  e  β d (7) where α is  0 and β is corresponding to reverse of d o (James, 1983; James and Sreedharan, 1986).

Results and Discussion Kagan’s point-to-area method computes errors in the estimates of the areal mean of certain climatological variables, like precipitation. According to this approach, correlations were classified based on distance. In Table 2, consequent of this classification for each basin is shown. This table gives the average distance, the number of stations within each interval, and mean correlation for different class intervals. Average correlations are plotted against mean distances in Figure 2 for all basins. These processes are evaluated in Microsoft Excel 2003 software. Also exponential functions are fitted on each curve by least square error method. The value of  0 can be read from the intercept of the ordinate. The value of the correlation radius is calculated by using equation 1. d o ,  0 and relevant errors have been determined in Table 3. These R-square are varied between 0.84 and 0.94. Hajiabad basin has minimum value for d o =125 km and Bandarlengeh basin has maximum d o =588 km. Spatial variation of rainfall in Hajiabad basin is greater than others. This induced that d o in this basin is minimum. Bandarlengeh has the aridest climate in Hormozgan province and variation of precipitation at this area is the least in comparison with other areas, which calculated d o justifies this fact. Numbers of necessary stations for attainment usage Ea and Ei errors are calculated for all basins (Table 4). For achievement a specific error, rain gage density is minimum in Minab and maximum in Bandarlengeh. Variations of Eaare plotted against number of stations for each basin. Figure 3 gives the relative error of mean areal rainfall or relative root mean square error calculated using equation 4. The relative error of spatial interpolation for regular triangular grids is given in Fig. 4. The relative error of spatial interpolation is a more stringent error criterion and forms the basis of the design (Sreedharan and James, 1983). The error of mean areal rainfall over the basin is used mainly in the design of networks where daily rainfall data are considered. Figure 4 shows that interpolation errors (Ei) are extensive for all basins, and achievement to usage errors is not possible even if number of stations is increased. The climate of Hormozgan justifies this consequence, because precipitation in this area usually is shower and interpolation is actually impossible. The reasons of this phenomenon are described as follows: Monson system is dominant on eastern regions of this province in the spring and summer, but this system is absent on the other site of this province. On the other hands, mountains of province, consists of east (Bashagard) and north (Hajiabad) mountains, influence on amount and distribution of rainfall. Meteorological researches on this province showed that dominant system is often weak Sudan system in autumn and winter seasons. Position of the rain gage networks for attainment usage average errors are calculated and located with Excel and Arc GIS ver. 9.2 software’s. Primary position for arrangement is the meteorological synoptic station in each basin. Arrangements of these networks are shown in Figure 5. According to installation and maintenance costs, criteria precision determined by meteorological organization and also arid and semiarid climate of this province, networks with 20% average errors are selected.

5

Table2. Number of stations (NOS), mean distance(MD) and corresponding mean correlation (MC) for each basin in Hormozgan province Bandarlengeh

Hajiabad

Minab

MC

MD(Km)

NOS

MC

MD(Km)

NOS

MC

MD(Km)

NOS

(Km)

MC

MD(Km)

NOS

Distance Class

Bandarabbas

0-10

12

7

0.90

2

7.1

0.75

1

6

0.83

4

6.6

0.70

10-20

32

15

0.82

20

14.8

0.79

1

19

0.88

9

16.5

0.67

20-30

21

25

0.80

25

25.1

0.71

6

25

0.85

19

24.9

0.69

30-40

30

35

0.78

27

33.8

0.68

5

33

0.73

16

34.5

0.59

40-50

30

44

0.76

29

44.0

0.6

3

45

0.69

17

46.7

0.65

50-60

40

54

0.77

38

54.2

0.60

4

56

0.61

19

55.1

0.60

60-70

28

64

0.70

23

65.2

0.57

6

63

0.62

11

65.4

0.61

70-80

24

75

0.69

34

74.9

0.49

4

86

0.51

22

75.8

0.52

80-90

26

83

0.69

13

84.8

0.51

2

92

0.49

9

84.5

0.44

90-100

18

95

0.75

20

94.6

0.51

3

107

0.58

14

94.7

0.46

100-110

21

105

0.69

13

103.5

0.51

1

110

0.28

13

104.6

0.40

110-120

20

115

0.68

11

114.0

0.48

6

125

0.38

7

114.9

0.40

120

Suggest Documents