HYDROLOGICAL PROCESSES Hydrol. Process. (2010) Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hyp.7886
Effects of area under-estimations of sloped mountain terrain on simulated hydrological behaviour: a case study using the ACRU model Stefan W. Kienzle* Department of Geography, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, Canada, T1K 3M4
Abstract: Sloped areas calculated from a GIS raster file, such as a digital elevation model, are smaller than the true surface area, because they are projected to a planimetric plane. In mountainous regions this sloped area under-estimation (SAUE) can have significant consequences on hydrological calculations. A sensitivity analysis is conducted, using the ACRU agro-hydrological modelling system in a small watershed in Glacier National Park, Montana, USA, to investigate the sensitivity of the SAUE on key elements of the hydrological cycle, including precipitation depth, April snow depth, August soil moisture deficit, actual evapotranspiration depth, and runoff depth. The sensitivity analysis is based on 224 unique combinations of slope, soil and land cover types, elevation with associated precipitation depths, and north and south facing radiation regimes. Results revealed an increasing influence of the SAUE on all hydrological processes with increasing slope steepness. Distinct differences and magnitudes between different land cover types, different elevations, and, in particular, different exposition were quantified. Actual evapotranspiration increases with SAUE, while runoff decreases. April soil water is simulated to decrease with an increase in SAUE. Finally, a comparison of a streamflow simulation of a small and steep alpine watershed with and without consideration of the SAUE is carried out. The sloped area of the small watershed is under-estimated by 20Ð9%, and the difference in simulated runoff is 12Ð3%. When the SAUE was not considered, runoff was simulated to be higher, the associated coefficient of determination was slightly lower, and the slope of the regression line was flatter. Copyright 2010 John Wiley & Sons, Ltd. KEY WORDS
slope; area under-estimation; sensitivity analysis; hydrological simulation; runoff
Received 8 February 2010; Accepted 2 September 2010
INTRODUCTION It is remarkable to observe that some fundamental area calculations required in hydrology appear to have been neglected in many hydrological simulations. The fact that sloped areas, when projected to a planimetric plane, have a smaller area than the true, sloped, surface area was described by Strahler (1956). He noted that the relationship between the so-called true surface area and that of the planimetric surface area can be described mathematically as follows: AreaTrue D AreaPlanimetric /COS(Slope)
1
where AreaTrue and AreaPlanimetric are denoted in any area units and Slope is in degrees. This method is discussed in more detail by Rasmussen and Ffolliott (1981). When Equation (1) is applied in a geographic information system (GIS), such as ArcGIS (ESRI, 2008), the degrees need to be converted to radians, resulting in this equation to be used in ArcGIS: AreaTrue D AreaPlanimetric /COSSlopeDegrees ð /180 2 * Correspondence to: Stefan W. Kienzle, Department of Geography, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, Canada, T1K 3M4. E-mail:
[email protected] Copyright 2010 John Wiley & Sons, Ltd.
An example of the potentially severe area underestimation is provided in Figure 1, where a mountain slope has a gradient of 75% or 37° . In the example, the selected land segment has a true slope length of 100 m, while the associated planimetric length derived from the digital elevation model (DEM) grid cell size is 80 m, resulting in a downslope length under-estimation factor of 25%. As the length following the contour line is assumed to be represented approximately correctly in a raster GIS, the downslope length under-estimation is the same as the sloped area under-estimation (SAUE). The SAUE, here expressed in percent, is calculated as follows: SAUE D 100/COSSlopeDegrees ð /180 100 3 The SAUE factor (SAUEF) used in Agricultural Catchments’ Research Unit (ACRU) to correct the sloped area is calculated as follows: SAUEF D 1 C SAUE/100
4
where SAUE is expressed in per cent. Only few researchers have reported the correction of the planimetric area of a sloped grid cell in a DEM, which is commonly the basis for both slope derivation and the area of the hydrological response unit (HRU) delineated for hydrological simulations. For example, Guzzetti et al. (1997) computed the under-estimated areas
S. W. KIENZLE
Figure 1. Example of slope area under-estimation on a mountain slope. The sloped length is always longer than the horizontal length; this example from Glacier National Park, Montana, has a slope of 75%, or about 37° , and an associated slope area under-estimation factor of 25%. The lengths labelled do not correspond to the true length on the land surface
Figure 2. Hydrological inputs are distributed over a larger area on sloped surfaces; the output area is larger than the input area
for several watersheds in the north-central Po Plain in northern Italy and reported an under-estimation of 5–9% for the steepest basins. Duarte and Marquinez (2002), as well as Wichmann and Becht (2003), applied the same principle for geomorphological analyses of rockfall in northern Spain, and the German Alps respectively, to determine the ‘actual surface area’ using GIS analyses. Failing to correct the GIS-derived areas for a slope can have fundamental consequences in hydrological computations. Very few hydrological researchers have computed the impacts of a slope-corrected ‘true area’ in hydrological analyses. For example, Hopkinson et al. (2007) have analysed glacial ablation rates using a GIS-based surface area correction factor. Jiskoot et al. (2009), another group of glaciologists, have also corrected the planimetric areas calculated from DEMs for slope under-estimation to calculate energy balances and ablation rates in glaciers. The simulated hydrological consequences can be significant, as the precipitation depth (dark arrows in Figure 2) is distributed over a larger area. Consequently, Copyright 2010 John Wiley & Sons, Ltd.
Figure 3. Relationship between slope and sloped area under-estimation
the interception capacity is increased by the same ratio as the area, resulting in increased water losses. As the vegetated area increases, plant transpiration also increases by the SAUE, resulting in higher water losses to the atmosphere. Correspondingly, non-vegetated areas have equally elevated evaporation rates. As these combined evapotranspiration losses increase (light arrows in Figure 2), the runoff decreases. The larger ‘true’ area shown in Figure 2 is also associated with an equal increase in the amount of water that can be stored in the soil, as the soil pore space and associated field capacity and wilting point volumes increase with area. Consequently, the infiltration capacity increases by the same ratio as the area is under-estimated. This results in a reduced potential for Hortonian overland flow (Horton, 1933) or soil conservation service (SCS)-derived event flow (Schmidt and Schulze, 1987; Steenhuis et al., 1995), when rainfall intensity exceeds infiltration capacity, and Hewlett and Hibbert’s (1967) variable source area of saturated soils and associated saturation access overland flow. Further, more soil water can be held against gravity before it is redistributed to deeper soil layers and can result in groundwater recharge. Subsequently, the infiltration amounts and soil moisture levels per unit area (m2 , acre, ha, etc.) are reduced, fewer groundwater recharge events occur, and the antecedent soil moisture levels are lower, resulting in fewer and smaller runoff events. The true sloped area would be simulated to have larger initial abstractions, which is the amount of precipitation that does not contribute to the generation of stormflow because of the processes of interception and the temporary surface storage in hollows, again resulting in larger evaporative losses, thus further increasing total evaporation losses and reducing surface runoff. When the precipitation falls as snow, the snowfall is distributed over the SAUE-enlarged area, resulting in an equal decrease in soil water equivalent (SWE) per unit area. With similar climatic conditions, the consequence is a shallower snowpack, increased snowmelt from the larger ‘true’ area, and an earlier time when all snow from the land unit has melted. Hydrol. Process. (2010)
SLOPE AREA UNDER-ESTIMATION EFFECTS ON MOUNTAIN HYDROLOGY
Table I. Key statistics of the sloped area under-estimation factor as a function of the grid cell size of the DEM for the test watershed in Glacier National Park, Montana Grid cell size(m)
10 20 30 50 100 200
Sloped area under-estimation factor Mean (%)
Maximum (%)
Standard deviation (%)
17Ð3 16Ð9 17Ð4 15Ð7 14Ð1 11Ð3
1050 705 554 464 178 80
31Ð9 27Ð9 25Ð4 21Ð9 17Ð2 11Ð9
All minimum values were 0%.
Hydrological models that integrate process-based hillslope hydrology, where soil water moves laterally downhill until it feeds the stream, would likely calculate these slope-dependent processes independently from the slope area under-estimation. Several slope-dependent hydro-meteorological variables, such as radiation and air temperature, are calculated independently from the SAUEF in ACRU. Therefore, the slope-dependent processes and those variables which govern evapotranspiration processes do not provide potential feedbacks or feed-forwards to the effects of the slope area under- estimation. Figure 3 shows the relationship between the slope and the SAUE. It is evident that the SAUE is quite small, and probably hydrologically insignificant, when slopes are less than 10° (about 18%). The hydrological effects become considerably larger with slopes over 25° (47%), when the SAUE is over 10%, which may then be larger than the error of many hydrological variables measured, or estimated, for that particular land unit. A 45° (100%) slope has a SAUE of 41%, and slopes over 60° (173%) have a SAUE of over 100%. With further increasing slopes, the SAUE eventually approaches infinity, such as at nearly vertical cliffs. A small watershed in Glacier National Park in Montana was chosen as the geographical location to analyse the magnitude of hydrological impacts as a function of the
SAUE. The watershed is located upstream of St. Mary Lake and is approximately 100 km2 in size. It is a typical Rocky Mountain watershed, encompassing steep valleys and sharp mountain peaks. A DEM with a 10-m-grid cell size was used to calculate the slope and the SAUE. It is important to use high-resolution DEMs, as DEMs with a grid cell size larger than 30 m can result in potentially significant under-estimation of the slope itself (Kienzle, 2004), and, subsequently, the SAUE would also be under-estimated. Kienzle (2004) reported that the slope derived from a 30-m DEM can be over 50% less than the slope derived from a 10-m DEM, thus resulting in a potentially large under-estimation of the SAUE. For example, if a slope derived from a 30-m DEM was 30%, and the slope derived from a 10-m DEM was 45%, the SAUE would be 110% larger using a 10-m DEM when compared to the 30-m DEM. Table I lists the key SAUE statistics as a function of grid cell size of the DEM. While the mean SAUE of the test watershed does not change much with grid cell size, both the maximum and standard deviation change considerably. This means that a relatively coarse DEM with a 100-m-grid cell size can be used with reasonable success to compute mean SAUEs. However, steep areas, which have the largest slope area under-estimation factors, are potentially significantly under-estimated. On the basis of the 10-m-resolution DEM, the test watershed has a mean SAUE of 17Ð3%, and almost 50% of the watershed area has a SAUE of 10% or more. Approximately 23% of the watershed area has a SAUE of 25% or higher, reaching as high as 1050% (Figure 4). OBJECTIVES This study has two objectives. The first objective is to test the sensitivity of the SAUEF on key elements of the hydrological cycle, including precipitation depth, snow pack, actual evapotranspiration depth, soil moisture deficit, and runoff depth, using the ACRU agrohydrological modelling system (Schulze, 1995). The ACRU options that are most suited for the study area and available data are chosen and kept constant for each biophysical scenario, with SAUEF being the only variable
Figure 4. Hillshade and sloped area under-estimation of the 10-m DEM for a small watershed in Glacier National Park, Montana Copyright 2010 John Wiley & Sons, Ltd.
Hydrol. Process. (2010)
S. W. KIENZLE
to be changed. The sensitivity analysis is carried out by setting up ACRU for a range of watershed characteristics found in a typical Rocky Mountain landscape, representing unique combinations of slope, soil and land cover types, elevation with associated precipitation depths, and radiation regimes for north- and south-facing slopes. The second objective is to simulate daily streamflow in a steep Rocky Mountain watershed with and without the correction for the SAUEF, and to compare the results.
METHODS The ACRU agro-hydrological modelling system The ACRU agro-hydrological modelling system (from here on referred to simply as ACRU) has been developed in the ACRU, a research group within the School of Bioresources Engineering and Environmental Hydrology (formerly the Department of Agricultural Engineering at the University of KwaZulu-Natal, Republic of South Africa) since the late 1970s (ACRU, 2007). The developers (Schulze, 1995; Smithers and Schulze, 1995) refer to the ACRU model as a multi-purpose, multi-level, integrated physical-conceptual model that can simulate total evaporation, soil water and reservoir storages, land cover and abstraction impacts on water resources, and streamflow at a daily time step. The ACRU model revolves around multi-layer soil water budgeting with specific variables governing the atmosphere–plant–soil water interfaces. Surface runoff and infiltration are simulated using a modified SCS equation (Schmidt and Schulze, 1987), where the daily runoff depth is proportional to the antecedent soil moisture content. In 2006, a snow model was incorporated by the author to extend ACRU’s limitation for applications in snow-free regions to virtually anywhere in the world. The snow model was originally developed by Herpertz (2001), using ACRU as the modelling framework. However, significant changes and additions were made to adapt the model for high mountain ranges. For example, the new snow model incorporates a novel approach to separate precipitation into snow and rain, which was developed on the basis of almost 1000 years of daily climatic records from southern Alberta (Kienzle, 2008). Subsequent snow processes, such as canopy interception, sublimation, metamorphosis, or change in albedo and density, are simulated in a physically explicit manner. The snow melt simulation is based on either predetermined monthly snowmelt factors, or a dynamic degree-day factor, which is determined by the model on a daily basis from incoming radiation and albedo estimates. ACRU is not a parameter fitting or optimizing model, as all variables are estimated from the physical characteristics of the watershed. When all the required variables are not available, they are estimated within physically meaningful ranges based either on the literature or on local expert knowledge. Spatial variation of rainfall, soils, and land cover is facilitated by operating the Copyright 2010 John Wiley & Sons, Ltd.
model in a distributed mode, in which case the catchment is sub-divided into either small sub-watersheds or HRUs, each representing a relatively homogenous area of hydrological response. ACRU has been used extensively for water resource assessments (Kienzle et al., 1997; Everson, 2001; Schulze et al., 2004; Martinez et al., 2008), flood estimation (Smithers et al., 1997, 2001), land use impacts (Kienzle and Schulze, 1991; Tarboton and Schulze, 1993), nutrient loading (Mtetwa et al., 2003), climate change impacts (New and Schulze, 1996; New, 2002; Schulze et al., 2004), or irrigation supply (Dent et al., 1988) and irrigation impact (Kienzle and Schmidt, 2008, Schmidt et al., 2009), and often requires extensive GIS pre-processing (Kienzle, 1993, 1996; Schulze et al., 1990). Comprehensive model manuals are available through the Internet on the ACRU web page (ACRU, 2007; Schulze, 1989, 1995; Smithers and Schulze, 1995). ACRU is well described by Kiker et al. (2006). However, the snow modelling manual is not yet available. Preparing ACRU variables for watersheds with a large proportion of high mountain ranges typically results in a number of challenges, such as a large number of HRUs (often exceeding 1000), radiation calculations, and spatially explicit adjustments for daily minimum and maximum temperatures, sunshine hours, and wind speed. Testing the sensitivity of SAUEF The sensitivity of the SAUEF on hydrological behaviour is tested using a series of theoretical bio-physical scenarios, typically found in the eastern Rocky Mountains, and represented by a single HRU. The climate time series are derived from a climate station with over 30 years of reliable hydro-meteorological data. The sensitivity of the SAUEF is tested for mean annual precipitation depth, mean annual interception, April snow pack, mean annual actual evapotranspiration, August soil moisture deficit, and mean annual runoff. In order to simulate the full range of conditions for mountainous regions, a total of 224 scenarios were set up. Each scenario represents a unique combination of the following variables: ž one of 14 different slopes, ranging from 0° to 75° , thus representing SAUEFs from 0% to 285%; ž one of the four most commonly found land cover types, which are bare rock, herbaceous grasses, shrubs, and coniferous forest; ž one of two elevations, namely 1500 and 2100 m, with associated mean annual rainfall depths of 800 and 1600 mm, and associated temperature regimes; and ž one of two incoming radiation regimes, representing north- and south-facing slopes. Inevitably, this type of analysis results in many unrealistic parameter combinations, such as forests on very steep slopes, or a relatively deep soil on steep slopes. To keep in line with the set objectives, which have a focus on Hydrol. Process. (2010)
SLOPE AREA UNDER-ESTIMATION EFFECTS ON MOUNTAIN HYDROLOGY
the sensitivity of the SAUEF on hydrological processes, all parameter combinations are simulated and reported, irrespective of how realistic they are.
ACRU PARAMETERIZATION ACRU was set up to simulate 224 scenarios for a theoretical hydrological unit with an area of 1 km2 . The 14 slopes range from 0° to 75° , with slopes being incremented from 15° to 75° , in 5° intervals. Slopes and associated SAUEFs are listed in Table II. The two elevation classes were 1500 and 2100 m, with associated mean annual precipitation depths of 800 and 1600 mm respectively to represent regions typically found in the Glacier National Park, Montana. Precipitation Daily precipitation and minimum and maximum temperature time series were available for the climate station in St. Mary, Montana. There were a few missing values for the observation period 1971–2000, which were in-filled from the nearby climate station at Babb, using mean monthly correlation coefficients. In order to correct the precipitation records from the St. Mary climate station, which has an elevation of 1390 m, to the two elevations chosen for the sensitivity analysis (i.e., 1500 and 2100 m), monthly precipitation correction factors were calculated. These correction factors were derived from the monthly PRISM precipitation surfaces calculated for the 1971–2000 normals (Daly et al., 1994, 2002, 2008).
surfaces (Daly et al., 1994, 2002, 2008) of minimum and maximum temperatures (Figure 5). In this version of ACRU, the lapse-rate-adjusted daily air temperatures from the base station are only used for the separation of precipitation into snow and rain. Snowmelt, sublimation, and evapotranspiration are understood to depend on near-ground temperatures, influenced by the local characteristics. In order to enable different daily air temperatures as a function of exposition, i.e., north- versus south-facing slopes, or valleys that rarely receive direct incoming radiation, the lapse-rateadjusted air temperatures are further corrected according to daily incoming radiation and land cover. A variation of an approach described by Glassy and Running (1994) and used in MTCLIM (Thornton et al., 1997) is applied. Here, the diurnal temperature range is used as a quantifier for temperature adjustments (Equations (6) and (7)). The incoming radiation is calculated for an entire year on the basis of 30-minute time increments in a GIS, based on latitude, topography, hemispherical viewshed, atmospheric transmittivity, proportion of diffuse radiation, and elevation (Figure 6). Atmospheric transmittivity and diffuse radiation are changed on a mean monthly basis, using values from the nearest climate stations that record them. In this case, the average of three climate stations that were within 150 km, and that exhibited very similar
Temperature and radiation When temperature values are required where no measurements are available, lapse rates are commonly used to adjust the minimum and maximum temperatures measured at the nearest climate stations to the location under consideration. The use of mean annual lapse rates must be avoided, as lapse rates typically fluctuate strongly during the course of a season. Mean monthly lapse rates can be estimated from surrounding climate stations. For this study, lapse rates were calculated from monthly PRISM
Figure 5. Monthly variation of lapse rates in the St. Mary watershed, Montana, estimated from PRISM monthly temperature surfaces
Table II. Slope and associated slope area under-estimation Slope (° ) 15 20 25 30 35 40 45 50 55 60 65 70 75
Slope (%)
SAUE (%)
26Ð8 36Ð4 46Ð6 57Ð7 70Ð0 83Ð9 100Ð0 119Ð2 142Ð8 173Ð2 214Ð5 274Ð8 373Ð2
3Ð5 6Ð4 10Ð3 15Ð5 22Ð1 30Ð5 41Ð4 55Ð5 74Ð2 99Ð8 136Ð3 191Ð9 285Ð4
Copyright 2010 John Wiley & Sons, Ltd.
Figure 6. Monthly variation of atmospheric transmittivity and proportion of diffuse radiation used to calculate shortwave radiation for the St. Mary watershed Hydrol. Process. (2010)
S. W. KIENZLE
step, radiation-adjusted daily minimum and maximum temperatures are further adjusted as a function of the leaf area index (LAI), as suggested by Glassy and Running (1994). As the LAI varies seasonally, the LAI is changed on a monthly basis. The source for LAI data was MODIS (2009). The result of these complex calculations is that each combination of elevation, slope, and land cover has a unique set of daily minimum and maximum temperatures.
Figure 7. Simulated mean monthly shortwave radiation along north- and south-facing slopes for four selected months
values, was used. The incoming radiation was calculated for north- and south-facing slopes, ranging from 0° to 75° (Figure 7). The maximum mean annual incoming radiation is received at a south-facing slope of approximately 25° , which is the angle between the latitude of the watershed of 48Ð5 ° N, and the tilt of earth’s rotational axis of 23Ð4° . For the calculation of the slope and exposition-adjusted daily temperature, the monthly incoming radiation was calculated in the GIS twice: once for the true, sloped topography (Figure 7), and once for the flat topography, assuming that DEM grid cells have a slope of zero, thus still adjusting incoming radiation for elevation, atmospheric transmittivity, diffuse radiation, and shading effects, but not for slope or aspect. The radiation ratio is calculated as follows: RadRatio D RadSlope RadFlat /RadFlat
5
This results in positive values, where RadSlope is greater than RadFlat , and in negative values, where RadSlope is smaller than RadFlat . In ACRU, daily minimum and maximum temperatures are then adjusted as follows: Tmaxadj D Tmax C TRange /2 ð RadRatio
6
Tminadj D Tmin C TRange /2 ð RadRatio
7
where Tminadj and Tmaxadj are the radiation-adjusted daily minimum and maximum air temperatures, and TRange is the daily temperature range (Tmax Tmin ). The inclusion of the temperature range is based on the assumption that, under overcast conditions, TRange is small and that the incoming radiation influence is small, and that, under clear sky conditions, TRange is large, and thus the incoming radiation influence is also large. It needs to be debated and further investigated whether the halving of the TRange provides realistic results over a wide range of conditions. A first verification analysis based on observed temperatures, taken at various aspects and slopes in the vicinity of the study area, showed that this approach resulted in realistic temperatures on north- and south-facing slopes (Letts, University of Lethbridge, personal communication, 2008). In a second Copyright 2010 John Wiley & Sons, Ltd.
Land cover There are four dominant land cover types present in the eastern Rocky Mountains: coniferous forest (Engelman spruce, Douglas fir, subalpine fir, limber pine and western larch), shrub land, herbaceous grassland, which make up the alpine tundra above the tree line, and exposed rock (USGS, 2000). The challenge is to apply a series of realistic hydrological variables, which is representative of these key land cover types. Tables III–VIII present hydrological variables aimed at representing the conditions found on the eastern slopes of the Rocky Mountains, and were also selected in order to provide a realistic range of hydrological sensitivity. The highest uncertainty lies in the soil depth, as this is poorly researched, and literature values are generally not available. In order to simulate land-cover-dependent hydrological variables, the following seasonally fluctuating variables were set to represent the hydrological properties associated with that land cover type: LAI (Table III), albedo (Table IV), plant transpiration coefficient (Table V), and coefficient of initial abstractions (Table VI). There are many other ACRU variables not listed here. Albedo is altered when a snow cover is present. Therefore, the winter values listed in Table V are internally overwritten with a dynamic albedo value of 0Ð8 after a snowfall event, which then declines by 1Ð5% per day until the albedo reaches 0Ð6. The albedo is further adjusted as a function of the depth of the snow pack, and the presence of forest. The plant water use coefficients (Table V) are in principle the same as crop coefficients, which express the amount of water a plant can transpire relative to the reference evaporation, which is in ACRU the A-pan evaporation, calculated for each day using the Penman equation. Values for plant transpiration coefficients were determined from observed meteorological and flux data from grassland and coniferous forest sites from Fluxnet Canada, and AmeriFlux flux towers in Alberta, Saskatchewan, and Colorado. The values were compared and slightly adjusted for seasonality to values reported by Smithers and Schulze (1995) and McWhorter and Sunada (1977). The coefficients of initial abstractions listed in Table VI are used in the SCS stormflow calculations and refer to initial amounts of precipitation that do not contribute to the generation of stormflow because of the processes of initial infiltration, interception, or temporary surface storage in hollows, before stormflow begins. Hydrol. Process. (2010)
SLOPE AREA UNDER-ESTIMATION EFFECTS ON MOUNTAIN HYDROLOGY
Table III. Monthly leaf area indices used Land cover Bare rock Herbaceous grasses Shrubs Coniferous forest
January February March April May June July August September October November December 0Ð00 0Ð10 0Ð78 1Ð00
0Ð00 0Ð10 0Ð78 1Ð00
0Ð00 0Ð30 0Ð78 1Ð00
0Ð00 0Ð55 1Ð17 1Ð50
0Ð00 0Ð85 1Ð56 2Ð00
0Ð00 1Ð40 1Ð95 2Ð50
0Ð00 2Ð05 1Ð95 2Ð50
0Ð00 1Ð40 1Ð95 2Ð50
0Ð00 1Ð30 1Ð95 2Ð50
0Ð00 0Ð70 1Ð79 2Ð30
0Ð00 0Ð45 1Ð40 1Ð80
0Ð00 0Ð20 0Ð78 1Ð00
Table IV. Monthly albedo values used Land cover Bare rock Herbaceous grasses Shrubs Coniferous forest
January February March April May June July August September October November December 0Ð10 0Ð16 0Ð22 0Ð20
0Ð10 0Ð16 0Ð22 0Ð20
0Ð10 0Ð16 0Ð22 0Ð20
0Ð10 0Ð17 0Ð22 0Ð19
0Ð10 0Ð20 0Ð22 0Ð18
0Ð10 0Ð22 0Ð22 0Ð16
0Ð10 0Ð26 0Ð22 0Ð15
0Ð10 0Ð26 0Ð22 0Ð15
0Ð10 0Ð26 0Ð22 0Ð15
0Ð10 0Ð16 0Ð22 0Ð16
0Ð10 0Ð16 0Ð22 0Ð17
0Ð10 0Ð16 0Ð22 0Ð19
Table V. Plant water use coefficients used Land Cover Bare rock Herbaceous grasses Shrubs Coniferous forest
January February March April May June July August September October November December 0Ð00 0Ð00 0Ð00 0Ð19
0Ð00 0Ð00 0Ð00 0Ð29
0Ð00 0Ð04 0Ð00 0Ð29
0Ð00 0Ð08 0Ð09 0Ð30
0Ð00 0Ð32 0Ð32 0Ð51
0Ð00 0Ð40 0Ð50 0Ð63
0Ð00 0Ð35 0Ð56 0Ð69
0Ð00 0Ð28 0Ð47 0Ð68
0Ð00 0Ð22 0Ð37 0Ð35
0Ð00 0Ð04 0Ð08 0Ð29
0Ð00 0Ð04 0Ð00 0Ð20
0Ð00 0Ð00 0Ð00 0Ð18
Table VI. Coefficients of initial abstractions Land Cover Bare rock Herbaceous grasses Shrubs Coniferous forest
January February March April May June July August September October November December 0Ð05 0Ð05 0Ð05 0Ð05
0Ð05 0Ð05 0Ð05 0Ð05
0Ð05 0Ð08 0Ð08 0Ð08
0Ð05 0Ð15 0Ð15 0Ð20
0Ð05 0Ð20 0Ð20 0Ð30
Soils For this study, each land cover type is associated with a typical soil. The following soil properties are set individually for the A- and B-horizons: soil depth, porosity, field capacity, wilting point, and soil water redistribution factors from the A-horizon to the B-horizon and from the B-horizon to the intermediate zone (Table VII). Many soils have a high rock content, high clay content, and shallow bedrock. Common soils are alluvial soils, colluvial (bedrock) soils, glacier till soils, or bedrock limestone soils. Soil hydrological properties are based on the state soil geographic (STATSGO) soil database (United States Department of Agriculture, 1995), texture information, and texture properties available in look-up tables in the ACRU manual (Smithers and Schulze, 1995). The percentage of stones listed in Table VII was determined by relating texture information provided in the STATSGO database with the ACRU look-up tables. Average rooting depths are based on Jackson et al. (1996). In ACRU, the total soil depth is set to be the same as the rooting depth. Copyright 2010 John Wiley & Sons, Ltd.
0Ð05 0Ð20 0Ð20 0Ð30
0Ð05 0Ð20 0Ð20 0Ð30
0Ð05 0Ð20 0Ð20 0Ð30
0Ð05 0Ð20 0Ð20 0Ð30
0Ð05 0Ð20 0Ð20 0Ð30
0Ð05 0Ð20 0Ð20 0Ð30
0Ð05 0Ð08 0Ð08 0Ð08
RESULTS AND DISCUSSION OF THE SAUEF SENSITIVITY ANALYSIS Each of the 224 scenarios was run for a 30-year period (1971–2000). Results are presented for mean annual precipitation depth, mean annual actual evapotranspiration, mean annual runoff, mean annual runoff coefficients, mean April snow depth (typically the month with the highest snow depth), and mean August soil water deficit (typically the month with the largest soil water deficit). The figures here are solely for the purpose of revealing the sensitivity of hydrological processes on slope steepness under the set conditions, irrespective of the fact that some scenarios are unrealistic. Each of the Figures 9–12 consists of two types of graphs. Graphs (a) and (b) present the change in the hydrological variable as a function of slope, integrating all slope-dependent hydrological effects, including the SAUEF. Graphs (a) and (b), therefore, do not show the sensitivity of the SAUEF on hydrological behaviour, but rather show the integrated impacts of all simulated slopedependent processes. In order to demonstrate the effect Hydrol. Process. (2010)
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Table VII. Soil characteristics associated with land cover types Land cover Bare rock
Texture —
PO-A PO-B FC-A FC-B WP-A WP-B Depth A Depth B 0Ð100
—
0Ð09
—
0Ð07
—
0Ð01
0Ð01
Herbaceous grasses Silty loam 0Ð347 0Ð336 0Ð193 0Ð182 0Ð087 0Ð082
0Ð14
0Ð16
Shrubs
Silty loam 0Ð408 0Ð387 0Ð227 0Ð206 0Ð101 0Ð093
0Ð20
0Ð35
Coniferous forest
Silty loam 0Ð404 0Ð378 0Ð227 0Ð206 0Ð100 0Ð093
0Ð20
0Ð30
Comment Values derived from Clapp and Hornberger (1978) Values are reduced due to 40% stones in A-horizon, and 48% stones in B-horizon Values reduced due to 20% stones in A-horizon, and 30% in B-horizon Values reduced due to 21% stones in A-horizon, and 30% in B-horizon
PO, porosity; FC, field capacity; WP, wilting point; A, A-horizon; B, B-horizon.
of the SAUEF alone on the respective variables, Graphs (c) and (d) isolate the effects of the SAUEF by presenting the percent change in the variable when SAUEF is considered relative to ignoring the SAUEF. A positive change means that the implementation of the SAUEF results in higher values when compared to neglecting the SAUEF, and vice versa. Figure 11 is an exception, as soil water deficit is expressed here as a percentage of field capacity, and the actual, not the relative, changes are presented. The x-axes in Figures 9–12 are labelled with the well-known slope rather than the unknown SAUEF. Mean annual precipitation As the true area increases with the slope steepness, the precipitation depth (expressed in mm m2 ) decreases (Figure 8). The decrease in the precipitation depth with slope follows the magnitude of the SAUEF linearly (Table II). The precipitation on the horizontal plane does not change, and the precipitation depth is also not influenced by exposition (north- vs south-facing slopes). Total evapotranspiration The total evapotranspiration, the summation of interception loss, soil evaporation, transpiration, and sublimation, gradually increases with slope steepness on
Figure 8. Precipitation depth decrease as a function of slope Copyright 2010 John Wiley & Sons, Ltd.
south-facing slopes (Figure 9). This is due to the combined effect of increased radiation, particularly during the growing season (Figure 7), and the increase in evaporation area associated with steeper slopes (Figure 3). The north-facing slopes exhibit slight decreases up to approximately 45° slopes, as the increase in SAUE is compensated by decreases in evaporation due to decreases in radiation (Figure 7). On north-facing slopes steeper than approximately 45° , the compensation effect decreases, and the effect of SAUE becomes increasingly stronger than the evaporation effects due to decreased radiation. This behaviour is, in principle, very similar at both examined elevations. It is evident that south-facing slopes always exhibit higher total evapotranspiration values than north-facing slopes with equal gradient. For example, at 1500-m elevation with a 45° slope, a shrub landscape is simulated to have a mean annual total evapotranspiration of 338 mm on south-facing and 247 mm on north-facing slopes. The equivalent values for an elevation of 2100 m are 407 and 277 mm. There is a consistent decline in the total evapotranspiration from forests to shrubs, grasses, and bare rock. At an elevation of 2100 m, the total evapotranspiration is simulated to stay very even for forests on north-facing slopes, up to a slope of about 60° . This behaviour is explained by the compensation of the increasing evapotranspiration surface with slope steepness by the corresponding decrease in radiation (Figure 7) and soil moisture (Figure 12). The difference in total evapotranspiration between the 2100-m elevation, associated with 1600 mm of mean annual precipitation, and the 1500-m elevation, associated with 800 mm of mean annual precipitation, is simulated to never be more than about 20%. This can be explained by the compensation of cooler temperatures and associated lower potential evapotranspiration at higher altitudes with much higher precipitation, resulting in wetter soils and lower soil water deficits. Forest and shrub values are likely unrealistic for very steep slopes, as forest stands would have much lower tree densities, and soil depth would also decline with increasing slope steepness. Hydrol. Process. (2010)
SLOPE AREA UNDER-ESTIMATION EFFECTS ON MOUNTAIN HYDROLOGY
Figure 9. Total evapotranspiration as a function of slope (a,b) and percent total evapotranspiration changes after implementing the SAUEF (c,d) for elevations of 1500 and 2100 m
Figure 10. Mean annual runoff and runoff coefficient as a function of slope (a,b) and percent mean annual runoff changes after implementing the SAUEF (c,d) for elevations of 1500 and 2100 m
Copyright 2010 John Wiley & Sons, Ltd.
Hydrol. Process. (2010)
S. W. KIENZLE
Figure 11. Mean August soil water deficit, expressed as a percentage of field capacity (FC), as a function of slope (a,b) and mean August soil water deficit changes after implementing the SAUEF (c,d) for elevations of 1500 and 2100 m
Figure 9c and d presents the relative change in the total evapotranspiration due to the impact of the SAUEF alone. The SAUEF strongly impacts the total evapotranspiration, particularly on slopes exceeding 45° . For all scenarios, SAUEF results in an increase in the simulated total evapotranspiration. On very steep slopes, over approximately 60° , the total evapotranspiration can increase by 100%, which represents a doubling. Compared to 1500m elevation, the effects are stronger at an elevation of 2100 m, which has overall wetter conditions, resulting in higher soil moisture availability, which leads to higher actual evapotranspiration. Runoff Runoff (Q) is dependent on the combined processes of precipitation (P) and total evapotranspiration (ET), as the water balance equation P D ET C Q
8
applies for all conditions. Accordingly, the patterns depicted in Figure 9 are reversed in Figure 10. Slopes exhibit an accelerating reduction in runoff with increase in slope gradient and an associated increase in slope. Runoff is simulated to gradually decrease with increasing south-facing slopes, and is quite stable on north-facing slopes of less than about 45° , until runoff decreases on slopes steeper than approximately 45° , due to higher evaporation losses (Figure 9). Runoff values graphed in Figure 10 are expected to be unrealistic for very steep Copyright 2010 John Wiley & Sons, Ltd.
slopes, as the lack of soil and vegetation would increase the runoff, rather than decreasing it. Runoff coefficients are consistently lower on south-facing slopes than on north-facing slopes, and are also consistently larger at higher elevations, due to larger precipitation input and higher soil moisture levels. The impact of the SAUEF on runoff is shown in Figure 10c and d. There is a gradual and eventually steep decrease in relative runoff changes with increasing slope, steepest with coniferous forest, and gradually lesser for shrubland, grassland, and bare rock. Runoff changes due to the SAUEF are modest (below 10%) with slopes up to approximately 30° , after which they become increasingly significant. Runoff changes are simulated to be more sensitive at 1500-m elevation, as the increased total evapotranspiration (Figure 9) results in more soil water deficit, thus resulting in less frequent and smaller runoff events, making the HRU more sensitive to relative changes. An unexpected pattern is evident on very steep north-facing slopes, where the impact of the SAUEF on runoff is simulated to decrease and eventually reverse the negative runoff impacts. This is potentially a peculiar behaviour by ACRU due to very extreme hydrological conditions, but can be explained by almost always saturated soils due to very low simulated evapotranspiration amounts, and subsequent increases in frequency and magnitude of runoff and groundwater recharge events. As no dense vegetation of any kind Hydrol. Process. (2010)
SLOPE AREA UNDER-ESTIMATION EFFECTS ON MOUNTAIN HYDROLOGY
Figure 12. Mean April snow water equivalent changes as a function of slope (a,b) and percent mean April snow water equivalent changes after implementing the SAUEF (c,d) for elevations of 1500 and 2100 m
would realistically grow on slopes over 60° , this is not seen as a significant simulation problem. The comparison of Figure 10a with c and b with d reveals the significance of the slope area under-estimation on runoff, where the influences on north-facing slopes are compensated by reduced evapotranspiration, while on south-facing slopes the effects of SAUE and increased evapotranspiration are additive. Soil water deficit Soil water deficit is calculated here for the A- and the B-horizons for the month with the highest mean monthly water deficit, which is August, and is the sum of both horizons’ water deficit (Figure 11). The soil water deficit is expressed as the percentage of the field capacity, as soil depth and soil properties change with land cover (Table VII). The mean August soil water deficit is always larger on south-facing slopes, due to the higher associated evapotranspiration rates. The soil water deficit is simulated to be quite consistent throughout slope gradients and slope direction for coniferous forests at 1500-m elevation. This is due to the consistently higher plant transpiration, resulting in relatively dry soils in August, and the simulated reduction in plant evaporation when the plant available water is below 50% of its maximum. Shrubs and grassland are simulated to have the highest August soil water deficit on the steepest south-facing slopes, gradually declining towards the steepest north-facing slopes, where reduced total Copyright 2010 John Wiley & Sons, Ltd.
evapotranspiration keeps the soils wetter. Owing to higher precipitation inputs, soils at 2100-m elevation are simulated to be wetter than soils at 1500-m elevation. As soils typically get thinner with slope gradient, values simulated for very steep slopes are considered to be unrealistic. The absolute changes in soil water deficit are displayed in Figure 10c and d. The higher the SAUEF, or the steeper the slope, the larger is the simulated soil water deficit. This is due to the additive impacts of a larger surface area and associated higher total evapotranspiration losses. The SAUEF has a larger relative impact on mean August soil water deficit at higher elevations, as soils are wetter, facilitating larger soil water changes. The irregular behaviour along very steep north-facing slopes is likely due to the unique combination of extreme hydrological conditions, as observed in Figure 9. Snow pack Snow pack, expressed as snow water equivalent (SWE), is sensitive to the combined slope effects (Figure 12a and b) and the SAUEF (Figure 12c and d). This is because of the combination of reduced precipitation per unit area (e.g., m2 , Figure 8), which can drastically reduce the snow depth with increasing slope steepness, and the increased snow melt with an increase in slope gradient, owing to the larger surface area (similar to Figure 9). As the snow melt factor is calculated Hydrol. Process. (2010)
S. W. KIENZLE
daily from albedo and net radiation, snow melt is simulated to be larger and thus faster on south-facing slopes than on north-facing slopes. The April SWE is simulated to gradually decline with increasing south-facing slopes, but increases with slope steepness on north-facing slopes up to approximately 45° . The increase on north-facing slopes is because the effect of the SAUEF (Figure 12c and d) is more than compensated by the declining radiation, consequently reducing snow melt and maintaining a higher SWE until April. Snow redistribution through wind or gravity was not simulated. Values shown for very steep slopes are considered to be unrealistic because snow accumulation is affected by slope gradient along steep slopes. Values for rock, grasses, and shrubs were simulated to be the same. The snow pack is simulated to be completely melted much earlier on south-facing slopes, and also with increasing slope gradient. The relative impact of SAUEF alone on mean April SWE (Figure 12c and d) is simulated to be much stronger at lower elevations, as the thinner accumulated snowpack (Figure 12a) is more sensitive to changes than the much thicker snowpack at higher elevations (Figure 12b). This principle of higher sensitivity with thinner snowpacks is also true for coniferous forests. At 2100-m elevation, the relative mean April SWE changes are very small at northfacing slopes up to approximately 45° . Magnitudes and changes simulated for very steep slopes are considered to be rather theoretical in nature, as in reality snow redistribution would have dominant impacts on SWE.
A CASE STUDY FOR IMPACT OF SAUEF ON SIMULATED WATERSHED RUNOFF A small watershed in the upper North Saskatchewan River watershed was chosen to explore the impacts of the SAUEF on simulated runoff. In order to achieve this, ACRU was set up with the appropriate implementation of the SAUEF. On the basis of the fact that the hydrology of a mountainous watershed cannot be perfectly simulated when the simulation is based on climate data collected from approximately 59 km away and located in a valley, the objective was not to simulate daily streamflow to perfectly fit the observed hydrographs, but rather to accurately simulate mean annual water yields, along with variance, the shape of the hydrographs, and the magnitude and seasonality of streamflows. Only once simulated streamflow was verified against observed time series, the effect of the SAUEF was evaluated by disregarding it, while keeping all other ACRU variables constant. The Silverhorn Creek watershed, part of the upper North Saskatchewan River watershed in central western Alberta, has an area of 21 km2 , with the elevation ranging from 1700 to 2948 m, a mean slope of 25° , and a maximum slope of 47° . The mean SAUEF is 12Ð9%, ranging within individual HRUs from 0Ð1 to 26Ð2%, with a standard deviation of 6Ð0%. The watershed consists of approximately 76% bare rock, 11% coniferous forest, 6% herbaceous grasses, and 5% glaciers. Forests reach an Copyright 2010 John Wiley & Sons, Ltd.
elevation of up to 2240 m. The mean annual precipitation is 928 mm, with a simulated mean annual maximum of 1265 mm, and a mean annual minimum of 792 mm. In order to represent the large bio-physical diversity of the watershed, it was divided into 175 HRUs. The watershed is gauged by a Canada Water Survey Station, with available continuous daily records from 1975 to 2008. As the nearest climate station with daily climate time series is at a distance of 59 km from the centre of the watershed, there have been many years where there has been an obvious mismatch between the base climate station and the observed watershed outflow. This mismatch is indicated by severe disagreements between input and output volumes as well as the timing of major runoff events in certain years (Beven, 2001), rendering these years unreliable for simulation purposes. The 12-year period 1981–1992 was selected for verification analysis, where the daily dynamics between the precipitation recorded at the base station and the observed streamflow were relatively consistent. The comparison between the simulated and the observed daily streamflow for 1985 is presented in Figure 13. The shape of the annual hydrograph and streamflow recessions have been replicated well. During the spring and summer runoff, hydrographs are simulated realistically in terms of both magnitude and duration. The timing of the simulated snow melt typically lags by up Table VIII. Comparison of statistics for streamflow simulations with and without the implementation of the SAUEF Statistic
Daily streamflow with SAUEF Daily streamflow without SAUEF Monthly streamflow with SAUEF Monthly streamflow without SAUEF
r2
Slope of regression line
Oversimulation (%)
0Ð745
0Ð982
2Ð3
0Ð718
0Ð860
9Ð7
0Ð883
1Ð019
2Ð3
0Ð865
0Ð902
9Ð7
Figure 13. Simulated and observed daily streamflow for the Silverhorn Creek watershed for the year 1985 Hydrol. Process. (2010)
SLOPE AREA UNDER-ESTIMATION EFFECTS ON MOUNTAIN HYDROLOGY
to a week of the observed snowmelt-induced hydrographs (Figure 15). Streamflows from August to November are, on average, over-simulated, which is likely the effect of complex groundwater outflows in mountain terrain, which are difficult to simulate as there are almost no groundwater observations available. Table VIII shows the simulation statistics for daily and monthly mean simulated and observed streamflow. Both daily and monthly streamflow statistics show a strong agreement in annual water yield with very small systematic errors, as shown by the slope of the regression line being close to unity. The Nash–Sutcliffe coefficient of efficiency is 0Ð695 for daily and 0Ð844 for monthly streamflow data. It is evident from Figures 13 and 14 that the timing of individual storm events observed at the climate station does not match the observed hydrographs very well. However, the principal hyrological behaviour is quite well replicated. The same simulation setup without the consideration of the SAUEF results in a 9Ð7% over-simulation of runoff (Table VIII). The difference in mean annual streamflow between simulations with (0Ð416 m3 s1 ) and without (0Ð467 m3 s1 ) implementation of the SAUEF is 12Ð3%, slightly less than the average SAUEF for the watershed of 13Ð8%. The over-estimation of streamflow without consideration of the SAUEF should be expected, as the same precipitation input is distributed over a smaller area (Figures 14 and 15). The difference between simulations with and without SAUEF is quite low for the coefficient of determination, but is more distinct for the slope of the regression line, which is an indication of a systematic error in the simulation. The seasonal changes between simulations with and without the SAUEF of streamflow, baseflow, actual evapotranspiration (AET), and SWE are presented in Figure 16. The percent changes are modest during the cold season from November to May, and are highest from July to October, when the effect of the SAUEF on total evapotranspirational losses is most significant. The changes in baseflow are quite similar to those in runoff, indicating that a large part of the streamflow changes is due to changes in baseflow. The largest effect of the SAUEF is on seasonal SWE, with halving of SWE values
Figure 14. Simulated streamflow with and without consideration of the SAUEF for the Silverhorn Creek watershed for summer 1988 Copyright 2010 John Wiley & Sons, Ltd.
Figure 15. Comparison of simulated and observed mean monthly streamflow for the Silverhorn Creek watershed for the period 1981– 1992
Figure 16. Percent changes of key hydrological variables after implementing the SAUEF in the Silverhorn Creek watershed, based on comparison with simulation without consideration of the SAUEF
during August and September, and about a quarter less SWE during the December–June period.
DISCUSSION AND CONCLUSIONS When the area of a land segment, be it a sub-watershed, a terrain unit, a HRU, or a grid cell, is calculated on the basis of the horizontal rather than the true sloped area, it is under-estimated. The magnitude of area underestimation is a function of the slope gradient. This study investigated the impacts of the SAUEF on various simulated elements of the hydrological cycle. This was achieved by carrying out hydrological simulations of 224 different theoretical land segments, representing slopes from 0° to 75° , diverse land covers with associated different soil types and depths, two different elevations with associated mean annual precipitation totals, as well as north- and south-facing slopes. Each of the 224 scenarios was simulated on a daily time step for a 30-year period (1971–2000). Results were presented for mean annual precipitation depth, mean annual actual evapotranspiration, mean annual runoff and runoff coefficients, mean April snow depth, and mean August soil water deficit, which is typically the month with the largest soil water Hydrol. Process. (2010)
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deficit. The figures and quantities presented were solely for the purpose of revealing the sensitivity of hydrological processes on the SAUEF under the set conditions, irrespective of the realism of each scenario. Generally, results presented for slopes over approximately 45° are considered to be unrealistic because soils and land cover conditions would not be representative of the steep slope conditions, severe snow redistribution would take place, and certain hydrological runoff processes, such as lateral soil water flows, would not be simulated in ACRU. The sensitivity analysis of the impacts of the SAUEF on key hydrological processes revealed an increasing influence of the SAUEF on all hydrological processes with increasing slope steepness. Distinct differences and magnitudes between different land cover types, different elevations, and, in particular, different exposition were quantified. The total evapotranspiration increases with increasing SAUEF, while runoff decreases. The soil water deficit is simulated to strongly increase with increasing SAUEF. The results from the simulation of the small alpine Silverhorn Creek watershed located on the eastern slopes of the Rocky Mountains integrate the more theoretical findings from the sensitivity analysis. The simulated difference in mean annual streamflow with and without consideration of the SAUEF is 12Ð3%, which is slightly smaller than the average SAUEF for the watershed of 12Ð9%, and is also smaller than the total area under-estimation for the watershed of 20Ð9%. The over-estimation of streamflow without consideration of the SAUEF (Figures 10, 14–16) should be expected, as the same precipitation input is distributed over a smaller area (Figures 14 and 15), resulting in a smaller precipitation depth (Figure 8), a shallower snow pack (Figure 12), higher total evapotranspiration (Figure 9), drier soils (Figure 11), and reduced groundwater recharge (Figure 16). Hydrological variables were carefully selected to represent the bio-physical characteristics of a typical Rocky Mountain eastern slope watershed. A verification analysis was carried out for a small watershed in the upper North Saskatchewan River watershed to calibrate hydrological variables with the highest uncertainty within their possible meaningful bounds for the period 1981–1992. A correlation analysis between simulated and observed daily streamflows resulted in a coefficient of determination of 0Ð74, a slope of the regression line of 0Ð98, and an under-simulation in total streamflow for the period of 2Ð3%. The Nash–Sutcliffe coefficients of efficiency of 0Ð695 for daily and 0Ð844 for monthly streamflow indicate a high predictive power of the streamflow simulation. The correlation analysis of simulated against observed streamflow for the scenario without consideration of the SAUEF revealed a slightly weaker coefficient of determination of 0Ð718 for daily and 0Ð865 for monthly streamflow, a flatter slope of the regression line of 0Ð860 (daily) and 0Ð902 (monthly), and an over-simulation of 9Ð7%. If the ACRU model set-up was calibrated Copyright 2010 John Wiley & Sons, Ltd.
for the scenario without SAUEF, some hydrological variables would have been set to mis-represent the bio-physical characteristics to compensate for the lower actual evapotranspiration, higher runoff production, and differences in soil moisture regime and snowpack developments associated with the perceived smaller surface areas. Whilst a successful calibration within realistic bio-physical ranges is possible without the consideration of the SAUEF, some of the calibrated hydrological variables would be chosen for the wrong reasons. ACRU is a numerical model that incorporates many internationally accepted equations representing specific hydrological processes, such as a wide range of potential evapotranspiration routines, the Green–Ampt equation for infiltration, the Richard’s equation for soil water redistribution, a radiation-based snowmelt equation, seasonal plant transpiration coefficients, the von Hoyningen– Huene equation for canopy interception, and the modified SCS equation for runoff generation. As such, the computed output from ACRU depends on the combination of options used, as, for example, the Penman evapotranspiration equation will result in quite different output than the ACRU embedded Thornthwaite, Linacre, Hargreaves and Samani, Blaney Criddle, or Priestley–Tailor equations (Schulze, 1995, expanded). As every hydrological model, and within each model every different combination of options, will change the computed output, the results presented in this case study are to some extent ACRU specific. Hydrological models that can simulate snow redistribution, such as CRHM, the Cold Regional Hydrological Model (Pomeroy et al., 2007), or models that can simulate lateral hillslopes, such as the TOPMODEL (Quinn et al., 1991), are expected to provide different magnitudes of change. However, the key principles of the impact of the SAUEF on watershed processes are universal, and the principal sensitivity behaviour described here is considered to be realistic up to slopes of approximately 45° . As soil depths and plant transpiration coefficients, as well as many other ACRU variables, remained static irrespective of slope steepness during the sensitivity analysis, many combinations of bio-physical characteristics will not be found in the real world. For modest slopes of up to 25° , the slope area underestimation is less than 10% and within the range of uncertainty of many hydrological measurements. Streamflow measurements are generally approximately š5% (Winter, 1981). Point measurements of annual precipitation were reported by Rodda (1985) to be under-estimated by 3 to 30%, with larger errors in areas with significant snowfall. Similarly, Groisman and Legates (1994) reported under-estimation of annual precipitation in the United States to average 9%, ranging from 6% in snowfree regions to over 14% in regions with significant snowfall. These errors are potentially increased regionally using spatial interpolation procedures, particularly when climate stations located in valleys are used to interpolate daily precipitation in complex mountain ranges. Hydrol. Process. (2010)
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Although temperature measurements have a high level of accuracy at the monitored location, spatial interpolation of daily minimum and maximum temperatures in mountainous regions and high elevations is associated with a high level of uncertainty. Errors of other critical hydrological estimations, such as LAI, plant transpiration coefficients, radiation, or soil depths have similar, if not higher, orders of magnitudes. The error introduced when simulating watershed processes in mountainous regions by neglecting the effects of the SAUE has a magnitude similar to most hydrological measurement errors. Thus, by considering the SAUE in a hydrological model, the uncertainty of the effect of under-estimating the areas can be significantly reduced. This study hopes to contribute to a more realistic set-up of hydrological variables for physically based hydrological simulation models, with the result that impact studies in steep terrain, such as the investigation of land cover or climate change on all elements of the hydrological cycle, are improved.
ACKNOWLEDGEMENTS
This research was funded by the Alberta Ingenuity Centre for Water Research (AICWR), Grant Number 42321, and the Natural Sciences and Engineering Research Council (NSERC) of Canada, Grant Number 40286. A part of the data analyses was carried out by my graduate student Michael Nemeth, and my research assistant Markus Mueller. I thank two anonymous reviewers for their constructive comments, which considerably improved this paper.
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