Influence of spatial resolution on simulated streamflow in a macroscale hydrologic model

Transcription

1 WATER RESOURCES RESEARCH, VOL. 38, NO. 7, 1124, /2001WR000854, 2002 Influence of spatial resolution on simulated streamflow in a macroscale hydrologic model Ingjerd Haddeland, Bernt V. Matheussen, 1 and Dennis P. Lettenmaier Department of Civil and Environmental Engineering, University of Washington, Seattle, Washington, USA Received 10 August 2001; revised 30 January 2002; accepted 30 January 2002; published 30 July [1] The sensitivity to spatial scale of runoff produced by the variable infiltration capacity (VIC) macroscale hydrologic model is investigated by implementing the model over the Columbia and Arkansas-Red River basins at spatial resolutions from one-eighth to 2 latitude by longitude. At lower resolutions the meteorological, topographical, and land cover data at the highest spatial resolution are averaged spatially. Simulated mean annual streamflow at lower resolutions is as much as 18 and 12% lower for the Arkansas-Red and Columbia River basins, respectively, as compared to the one-eighth degree implementation. When the VIC model subgrid parameterization for spatial precipitation variability is implemented, the model s sensitivity to spatial scale decreases slightly in the Arkansas-Red River basin, where total runoff at lower resolutions decreases by up to 14% relative to the high-resolution runs. In the Columbia River basin, total runoff is only 4% lower at 2 resolution than at one-eighth degree resolution when precipitation variation with elevation is reparameterized at lower resolutions in a manner that replicates mean annual precipitation in the corresponding higher-resolution cells. INDEX TERMS: 1836 Hydrology: Hydrologic budget (1655); 1860 Hydrology: Runoff and streamflow; 3210 Mathematical Geophysics: Modeling; KEYWORDS: macroscale hydrologic modeling, scaling, streamflow 1. Introduction [2] Runoff production is a spatially distributed process, but from a practical standpoint it is only possible to measure point values of streamflow, which effectively is an integrator in space and time. Therefore, there is a fundamental difference between streamflow and the surface atmospheric variables that govern its evolution. Furthermore, spatial variability in land surface characteristics over the area contributing streamflow critically affects the nature of the streamflow signal. These surface characteristics include, for instance, vegetation, topography, and soils, as well as geologic features that affect groundwater dynamics. [3] It is well documented, via numerous field and modeling studies, that runoff is sensitive to spatial variations in soil properties [e.g., Dooge and Bruen, 1997; Merz and Plate, 1997], to the space-timescales of precipitation inputs [e.g., Shah et al., 1996; Goodrich et al., 1997], and to topography [e.g., Beven and Kirkby, 1979; Wolock and Price, 1994]. Hydrologic models must either represent explicitly or parameterize the effects of this variability in meteorological, topographical and land cover on model predictions of water and energy fluxes at the spatial scale on which the model operates. [4] With the evolution of gridded land surface models designed for use off line (prescribed surface forcings) or coupled within land-atmosphere models used for climate and weather prediction, there is a concern as to the sensitivity of parameters to the spatial scale at which they are 1 Now at Department of Hydraulic and Environmental Engineering, Norwegian University of Science and Technology, Trondheim, Norway. Copyright 2002 by the American Geophysical Union /02/2001WR estimated. This concern arises naturally because the spatial resolution at which such models are implemented changes frequently due to increases in computing capability (the dominant factor in coupled applications), as well as evolution of higher-resolution observation methods (e.g., precipitation radar) in the case of off-line implementation. [5] Wood et al. [1990], and Seyfried and Wilcox [1995] discuss the characterization of hydrological variables across scales, and suggest that at smaller scales site-specific characteristics must be included in the hydrological model, while at larger scales a statistical representation may suffice. Various statistical methods, ranging from simple averaging of model parameters to the use of more complicated fractal scaling laws, have been developed for the purpose of aggregating hydrologic model parameters [e.g., Famiglietti and Wood, 1994; Braun et al., 1997]. Model sensitivities at both spatial and temporal scales have been widely studied at the catchment scale [e.g., Wood, 1995; Schaake et al., 1996; Becker and Braun, 1999], but the effect of parameter extrapolation to macroscale hydrologic models, which typically are applied in river basins larger than 10,000 km 2, and the linkage between model parameters at different scales, is not yet fully understood [Sivapalan and Kalma, 1995]. [6] Habets et al. [1999] tested aggregation methods in a macroscale hydrologic model at two spatial resolutions for a 1-year period, and found that accounting for subgrid variability of surface processes reduced the model s sensitivity to spatial scale. Koren et al. [1999] studied changes in hydrologic model predictions caused by rainfall variability, and concluded that a probabilistic representation of rainfall can reduce the scale dependencies to spatial variability of precipitation, and that infiltration excess type models are more scale sensitive than are saturation excess 29-1

2 29-2 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION Figure 1. (a) Location of study areas, (b) basin topography, and (c) mean annual precipitation in the basins. Contour intervals correspond to the ticks on the shading bar. type models. The Koren et al. study assumed that all land surface characteristics and model parameters were constant over the entire test area. The purpose of this study is to investigate the performance of a macroscale semidistributed hydrologic model at different spatial resolutions and under varying climatic conditions, and to determine the sensitivity of model predictions of moisture fluxes to the scale and method of aggregation of meteorological data, soil and vegetation parameters over ranges of spatial resolutions from one-eighth degree up to 2 latitude by longitude. [7] To address these questions, the macroscale variable infiltration capacity (VIC) hydrologic model [Liang et al., 1994] was implemented in two large continental river basins, both with drainage areas about 600,000 km 2 :the Columbia River basin of the U.S. and Canadian Pacific Northwest, and the Arkansas-Red River basin in the U.S. Southern Great Plains. Previous VIC model studies in the Columbia River and Arkansas-Red Rivers include work by Abdulla et al. [1996], Nijssen et al. [1997], Miles et al. [2000], and Matheussen et al. [2000]. As a part of the Land Data Assimilation System [Mitchell et al., 1999], VIC is now being used to simulate the surface hydrology of the entire U.S. 2. Approach 2.1. Model Description [8] The VIC model [Liang et al., 1994, 1996a, 1996b, 1999] is a macroscale hydrologic model that solves the water and energy balance equations at the land surface. VIC typically operates on spatial scales from one-eighth to 2 latitude by longitude and at hourly to daily temporal resolution. Surface land cover variability is described by partitioning each grid cell into multiple vegetation types and bare soil, and the soil column is divided into multiple (typically three) soil layers. Topographic variations within each grid cell can be represented through any number of elevation bands, in which all vegetation types within the grid cell are included, and hence the effect of subgrid topography on precipitation, snow accumulation and melt can be represented. Spatially distributed precipitation, where the fraction of the grid cell that receives precipitation varies with storm intensity, can be included [Liang et al., 1996a]. The saturation excess mechanism, which produces direct runoff, is parameterized through a variable infiltration curve. Release of base flow from the lowest soil layer is controlled through a nonlinear recession curve. Direct runoff and base flow for each cell is routed to the basin outlet through a channel network as described by Lohmann et al. [1998a, 1998b], taking into account the fraction of each grid cell that flows into the basin being routed [Nijssen et al., 1997]. [9] The VIC model can be run in full energy balance mode, or in water balance mode. Water balance mode is the most common implementation for hydrological applications, where surface energy fluxes (other than latent heat or evapotranspiration) need not be estimated directly. In energy balance mode, the model iterates for the surface temperature that results in closure of the surface energy and water budgets at each time step. In both simulation modes, snow accumulation and ablation processes are solved via an energy balance approach. Minimum required input data to the model is daily precipitation, and maximum and minimum daily temperatures. When radiation data and vapor pressure are not supplied to the model, VIC calculates these variables based on daily precipitation and daily minimum and maximum temperature, using algorithms developed by

3 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION 29-3 Figure 2. Simulated and naturalized/observed mean monthly streamflow at (a) The Dalles (Columbia River), (b) Little Rock (Arkansas River), and (c) Shreveport (Red River). Thornton and Running [1999], and Kimball et al. [1997] as described by Nijssen et al. [2001] Study Areas [10] Figure 1 shows the location of the Columbia and Arkansas-Red River basins, along with their topography and mean annual precipitation. The two river basins have strongly contrasting climatic and hydrologic characteristics. The majority of the precipitation in the Columbia River basin falls during the winter, and snow accumulation and melt dominate the basin s hydrology. Annual precipitation is much higher in the mountains than in the lower elevation areas. The climate of the Arkansas-Red River basin is characterized by a strong gradient of decreasing annual precipitation from east to west, interrupted by a slight increase in the headwaters region along the Continental Divide. The combined Arkansas-Red River as a whole is dominated by rainfall, which is primarily summer-dominant, with snowfall playing only a minor role aside from the headwaters region Model Implementation [11] The VIC model was previously implemented at one-eighth degree spatial resolution for the Arkansas-Red River and the Columbia River as part of the LDAS (Land Data Assimilation System) project [Mitchell et al., 1999]. The meteorological (precipitation, daily minimum and maximum temperature, and wind speed), topographical and land cover (soil, vegetation) data are described by Maurer et al. [2002]. Each grid cell at one-eighth degree resolution was divided into 200-m elevation intervals. In this project VIC was run in water balance mode, meaning that the full energy balance was only calculated during periods with snow. The water balance mode was chosen primarily because of the much smaller computational requirement at the highest spatial resolution. The model was run at daily time steps at the base (one-eighth degree) spatial resolution for a 20-year period (October 1976 September 1996), after a 1-year initialization period intended to stabilize the model s initial moisture storage states. Mean monthly simulated and naturalized (effects of reservoirs, diversions, and return flows removed) streamflow values at the most downstream location in the Columbia River basin (The Dalles, Oregon) are shown in Figure 2. In general, the simulated streamflow matches the naturalized streamflow quite closely. Similar comparisons are shown for the Arkansas River at Little Rock, Arkansas, and the Red River at Shreveport, Louisiana. In the case of the Arkansas and Red Rivers, naturalized streamflow that takes into account water management effects other than reservoirs, e.g., water used for irrigation, does not exist. Although the reservoir storage capacity in the Arkansas-Red River basins is much smaller than in the Columbia River basin, the fact that the simulated flows are somewhat larger than observed is no doubt due in part to water management effects. However, the focus of this study is on the model s sensitivity to changes in spatial aggregation, and model performance in terms of ability to reproduce observed discharge should be more than adequate. The ratio of simulated runoff to precipitation of 0.40 for the Columbia River basin is almost double that of the Arkansas-Red River basin (0.21). 2.4 Aggregation Method and Model Analyses [12] To investigate the influence of spatial resolution on resulting streamflow, a series of model analyses were performed. The aggregation method and/or the parameters aggregated varied somewhat between the analyses. In the first aggregation analysis, the historical meteorological forcing data, as well as surface characteristics data originally developed for the one-eighth degree grid resolution, were aggregated by areally averaging for use at lower spatial resolutions (one-quarter, one-half, 1, and 2 ). Hence, the input parameters in each 2 cell were the average of the input parameters in the one-eighth degree cells (up to 256) comprising one 2 cell. At the basin boundaries the original grid cell s fractional area within the basin was preserved. This method ensures that average precipitation, temperature, and wind speed over the area are conserved, as well as vegetation types and soil properties. The aggregation method s influence on precipitation in the two study areas is shown in Figure 3. The 200-m elevation intervals were applied at all resolutions. For the lower resolutions, a flow network that maintains connectivity at the higher resolution was developed. The most appropriate drainage direction for each grid cell at the coarser resolution was determined based on the higherresolution drainage direction, and boundary cells were handled in the standard way in the routing model. The VIC subgrid precipitation variability parameterization [Liang et al., 1996a] was turned off in this baseline analysis (hereafter called constant precipitation).

4 29-4 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION Figure 3. Mean annual precipitation in the (a) Columbia and (b) Arkansas-Red River basins at (1) oneeighth degree, (2) one-half degree, and (3) 2 spatial resolution. [13] The effect of subgrid precipitation was later studied by performing the model simulations with the subgrid precipitation option turned on (hereafter called distributed precipitation). In the distributed precipitation simulations the fractional coverage of precipitation was assumed to vary with precipitation intensity, following Fan et al. [1996]: m ¼ 1 e bp ; where m is fractional coverage of precipitation within the grid cell, P is precipitation (mm), and the factor b > 0 (here assumed to be 0.6 for the one-eighth degree models). For resolutions lower than one-eighth degree, b was changed according to average areal precipitation coverage in the eighth-degree cells so as to keep the mean areal fraction covered by precipitation as invariant with scale as possible. Table 1 lists the number of grid cells at the different resolutions, in addition to the b factors used in the spatially distributed precipitation simulations. [14] Simulations were also performed where the precipitation gradient with elevation (hereafter called precipitation gradient) was kept as invariant with scale as possible. The precipitation gradient at lower resolutions was represented by assigning precipitation fractions within each elevation ð1þ band according to mean annual precipitation and corresponding elevation in the original one-eighth degree cells. This analysis did not utilize the VIC spatially distributed precipitation option. [15] The effect of elevation bands was studied by running the model for the Columbia River basin without elevation bands at all spatial resolutions. In these simulations, each grid cell s mean elevation was implemented in the model, meaning that topographic variations within the grid cell were not taken into account. Mean grid cell daily precipitation when running the model with or without elevation bands was equal. [16] For the Arkansas-Red River basin, some theoretical analyses were performed to study the sensitivity of the results to precipitation amounts, and how the various aggregations each contribute to the scale dependence. First, daily precipitation values were increased by a factor of 2. Second, meteorological and topographical data, vegetation and soil parameters were disaggregated from 2 spatial resolution to one-quarter degree resolution, and the model was run using various combinations of these disaggregated parameters and the parameters originally used at one-quarter degree. One-quarter degree spatial resolution was used in these simulations (instead of oneeighth degree) to keep computational time down. Finally, a Table 1. Number of Modeled Grid Cells at Different Spatial Resolutions and the b Factor Used in the Spatially Distributed Precipitation Simulations One-Eighth Degree One-Quarter Degree One-Half Degree 1 2 Cells b Cells b Cells b Cells b Cells b Columbia River Arkansas-Red River

5 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION 29-5 Figure 4. (a) Percent changes in moisture fluxes compared to the results at one-eighth degree spatial resolution and (b) mean monthly streamflow at all spatial resolutions for the (1) Columbia and (2) Arkansas-Red River basins using spatially constant grid cell precipitation. limited exploratory test using the energy balance mode was included. 3. Results 3.1. Simulations Using Spatially Constant Grid Cell Precipitation [17] Figure 4 shows the effect of aggregation on precipitation, direct runoff, base flow and total runoff, as a function of increasing spatial resolution. In addition, Figure 4 shows mean monthly streamflow values at The Dalles (Columbia River), and the combined streamflow at Little Rock (Arkansas River) and Shreveport (Red River) at different spatial resolutions. Changes in precipitation are insignificant, due to the nature of the aggregation method, which conserves the spatial average values of the meteorological forcing data. However, spatial averaging of the precipitation values results in more evenly distributed precipitation, and hence soil moisture values, at lower spatial resolutions. [18] Figure 4 indicates that runoff production in the Arkansas-Red River basin is more sensitive to spatial aggregation than in the Columbia River basin. At 2 spatial resolution total runoff is 18 and 12% lower than at oneeighth degree spatial resolution in the Arkansas-Red River basin and the Columbia River basin, respectively. In the Columbia River basin approximately 60% of the total runoff occurs during spring snowmelt [Kirschbaum and Lettenmaier, 1997], and hence the more evenly distributed precipitation at larger scales does not influence direct runoff as much as in the Arkansas-Red River basin. The average model-predicted saturated fraction in the Arkansas-Red River basin at one-eighth degree is 7.9%, while it is 10.1% in the Columbia River basin. In the Arkansas-Red River basin, the average fraction of saturated area is 6.3% lower at 2 than at one-eighth degree spatial resolution, while the difference is only 0.6% in the Columbia River basin, which explains some of the relatively larger decrease in saturation excess runoff in the Arkansas-Red River basin. [19] Base flow is also less sensitive to changes in spatial resolution in the Columbia River basin than in the Arkansas-Red River basin. Most of the base flow in the Columbia River basin occurs during snowmelt, a time of year when transpiration is limited more by energy than by soil moisture than later in the summer. Hence the decreased spatial variation in soil moisture at lower spatial resolutions does not increase evapotranspiration as much as in the Arkansas- Red River basin, where evapotranspiration is more limited by soil moisture than by energy. [20] Evapotranspiration increases with decreased spatial variability in soil moisture partly because low soil moisture variability provides better access of vegetation to soil moisture, and partly because decreased spatial variability in soil moisture may result in decreased base flow, and hence the soils stay moist somewhat longer. In VIC, base flow is calculated as a nonlinear function of lower zone soil moisture, and the average of four base flow values calculated based on four individual soil moisture values is higher than the base flow value calculated based on the average of those four soil moisture values, if the same base flow parameters are used. However, soil parameters (e.g., soil depth, and the factors included in the variable infiltration and base flow curves) change within the basins, and the aggregation of these soil parameters may lead to changes in the nonlinear functions controlling direct runoff and base flow, and hence change the runoff characteristics within an area. The aggregation may also lead to changes in the calculations of soil moisture limitation on evapotranspiration, which is also controlled through a nonlinear function. [21] Figure 4 shows that the general form of the hydrographs is similar at all resolutions. However, streamflow tends to decrease as the scale of aggregation increases. In the Columbia River, the decrease in streamflow is most noticeable in the spring and early summer (during the snowmelt period), while in the Arkansas-Red River streamflow decreases throughout the year. Over the 20-year simulation period, model-predicted basin averaged mean maximum snow water equivalent in the Columbia River basin at 2 spatial resolution is 4.5% (8.7 mm) lower than at one-eighth degree spatial resolution, which obviously influences the spring snowmelt. Precipitation and elevation, and hence temperature, are strongly correlated in this basin (see Figure 1), and the more evenly distributed precipitation at lower resolutions results in decreased precipitation at higher elevations, and increased precipitation at lower, and hence warmer, elevations. As a result, the direct runoff in the Columbia River basin in the period November through March actually is 2% higher at 2 than at one-eighth degree spatial resolution. However, the direct runoff during this 5-month period contributes only about 30% of the total streamflow at The Dalles during the same period. The difference in base flow between 2 and one-eighth degree resolution in this period is insignificant (0.2%). Hence the

6 29-6 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION Figure 5. (a) Percent changes in moisture fluxes compared to the results at one-eighth degree spatial resolution using constant precipitation (open symbols) and spatially distributed precipitation (solid symbols) and (b) mean monthly streamflow at all spatial resolutions, spatially distributed precipitation (Arkansas-Red River basin). aggregation does not influence the runoff production in the Columbia River basin much during the winter. In the Arkansas-Red River basin, mean maximum snow water equivalent (averaged over the basin area) is 6% lower at 2 than at oneeighth degree spatial resolution. However, the model-predicted mean maximum snow water equivalent at one-eighth degree spatial resolution is only 3.9 mm, and so snowmelt does not contribute significantly to the streamflow at Little Rock and Shreveport Simulations Using Spatially Distributed Precipitation or Precipitation Gradient [22] Figure 5 compares the results from the analysis using VIC s subgrid precipitation variability algorithm for the Arkansas-Red River basin to the results using spatially constant (subgrid) precipitation (Figure 4). The subgrid precipitation variability algorithm reduces the model s sensitivity to scale somewhat in the Arkansas-Red River basin; total runoff at 2 is now 14% lower than at one-eighth degree resolution, compared to 18% lower when precipitation is assumed to be constant within the grid cell. On average, the fractional area of the basins that receives precipitation will be more similar over the scales when using spatially distributed precipitation. However, the algorithm assumes that soil moisture within a grid cell is averaged between storms [Liang et al., 1996a], meaning that the spatial variability in soil moisture is less at lower than at higher resolutions, which results in less direct runoff and more evapotranspiration. In the Columbia River basin, the results using spatially distributed precipitation are almost identical to the results when precipitation is assumed to be constant within a grid cell, and these results are therefore not shown. The precipitation in this basin is winter dominant, and in VIC solid precipitation is not spatially distributed, and hence the precipitation pattern in these simulations does not differ as much from the baseline analysis (section 3.1) as in the Arkansas-Red River basin. [23] VIC s sensitivity to changes in spatial resolution was also investigated when precipitation fractions in each elevation band within a grid cell at lower resolutions were scaled based on mean annual precipitation amounts in the corresponding higher-resolution cells. While the baseline analysis conserved mean areally averaged precipitation across spatial resolutions, this method also takes into account the topographical gradient of precipitation, and hence the interactions between precipitation amounts and temperatures are more similar across the scales than in the baseline analysis. Figure 6 shows the resulting changes in precipitation, direct runoff, base flow, and total runoff, and mean monthly streamflow at all spatial resolutions for the Columbia River basin. Total runoff in the Columbia River basin at 2 spatial resolution is now only 4% lower than at one-eighth degree spatial resolution. However, the predicted mean basin averaged snow water equivalent at 2 resolution is actually 4.5% higher than at one-eighth degree resolution, meaning that the predicted decrease in total runoff values would have been somewhat higher than 4% if modelpredicted snow accumulation and melt had been identical. Even though the average topographical gradient of precipitation is similar using this method, precipitation and temperature patterns deviate somewhat from the mean patterns from year to year, and from season to season, and hence model predicted snow accumulation and melt will not be identical across the scales. In addition, the spatially averaged wind speed will cause some changes in snow accumulation and melt. The aggregation method used in this study conserves the average fractional coverage of different vegetation types, but the distribution of the vegetation types is altered, as the vegetation types occurring in higherresolution cells are assembled in the lower resolution cell. Furthermore, VIC assumes equal vegetative cover in all elevation bands within a grid cell. Hence the average temperature and precipitation amounts experienced by each vegetation type will differ somewhat at different spatial resolutions, resulting in some changes in snow accumulation, snow ablation and evapotranspiration. In the rainfall dominated Arkansas-Red River basin, the use of a precipitation gradient does not significantly influence mean Figure 6. (a) Percent changes in moisture fluxes compared to the results at one-eighth degree spatial resolution using constant precipitation (open symbols) and precipitation gradient (solid symbols) and (b) mean monthly streamflow at all spatial resolutions, precipitation gradient (Columbia River basin).

7 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION 29-7 monthly streamflow values. The results for the Arkansas- Red River basin are quite similar to the ones in Figure 4, and percent decrease in total runoff is 17%, as compared with 18% in the baseline run (VIC s model option with spatially distributed precipitation is not included in these simulations). However, in headwater areas where the dominant hydrologic processes are related to snow accumulation and melt, these results indicate that if the model can reproduce similar snow accumulation and melt patterns, the model s sensitivity to changes in spatial resolution will decrease substantially Simulations Without Elevation Bands [24] The hydrology in the Columbia River basin is dominated by snow accumulation and melt, which are highly dependent on temperature. When topographic variations within each grid cell are disregarded, the model s sensitivity to spatial scale increases, as shown in Figure 7, and total runoff at 2 is 15% lower than at one-eighth degree spatial resolution. When elevation bands are not included, the model-predicted basin averaged mean maximum snow water equivalent over the 20-year simulation period is 5.5% lower at 2 than at one-eighth degree spatial resolution, and the snow also melts more rapidly when elevation bands are not included. Averaged over the main melting season (mid March to the end of May), the melt rate (mm/d) is about 10% higher at 2 than at the oneeighth degree implementation without elevation bands, while the corresponding number is 3% for the baseline analysis. Because of the advanced snowmelt, evapotranspiration increases, and there is a shift in both the timing and the amount of runoff. Arola and Lettenmaier [1996] also demonstrated the importance of including elevation bands when simulating snowmelt in a macroscale hydrologic model in mountainous areas Simulations Using Increased Precipitation [25] In the previous sections, runoff production in the Arkansas-Red River basin is shown to be more sensitive to Figure 7. (a) Percent changes in moisture fluxes compared to the results at one-eighth degree spatial resolution, using constant precipitation (open symbols) and no elevation bands (solid symbols) and (b) mean monthly streamflow at all spatial resolutions, no elevation bands (Columbia River basin). Figure 8. Percent changes in total runoff compared to the results at one-eighth degree spatial resolution, as a function of annual (water year) precipitation (Arkansas-Red River basin). changes in spatial scale than in the Columbia River basin, partly because of the drier conditions in the Arkansas-Red River basin. Increasing the precipitation should hence lower the model s sensitivity to spatial scale, and the VIC model was therefore run for the Arkansas-Red River basin when precipitation was increased by a factor of two. All other input parameters were kept similar to the original ones (section 3.1). Figure 8 shows the relationship between modeled (baseline and increased precipitation analyses) annual (water year) precipitation and the percent changes in total runoff at lower scales, compared to the results at one-eighth degree resolution. The decreased sensitivity with increasing annual precipitation is caused by decreased sensitivity of base flow during wet years. During the wettest years, simulated base flow increases with decreasing scale. This is consistent with the theory that the less moisture stress the vegetation experiences, the less can it make use of the extra water added to the soil column because of the decrease in direct runoff. When precipitation amounts are doubled, runoff decreases by up to 9% at lower resolutions, as compared with 18% in the baseline runs Simulations Using Disaggregated Parameters [26] For this experiment, the meteorological, topographical, and land cover data for the Arkansas-Red River basin were disaggregated from the coarsest spatial resolution to one-quarter degree spatial resolution. Hence, the onequarter degree grid cells (up to 64) comprising one 2 grid cell, were given the same spatial and temporal characteristics. The model was then run using 1) all disaggregated input parameters, 2) disaggregated precipitation only, 3) disaggregated vegetation parameters only, and 4) disaggregated soil parameters only. The other input parameters were retained at the values aggregated from one-eighth degree spatial resolution, i.e., as in section 3.1. The purpose of these simulations was to quantify the relative impact of aggregated parameters on the resulting runoff. The results are presented in Figure 9, which shows simulated direct runoff, base flow and total runoff for a series of one-quarter degree simulations, as a percentage of the simulated results at the baseline 2 spatial resolution. Figure 9 shows that when all input

8 29-8 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION Figure 9. Percent simulated direct runoff, base flow, and total runoff at one-quarter degree, compared to the baseline 2 spatial resolution, for case 1, all disaggregated input parameters; case 2, disaggregated precipitation only; case 3, disaggregated precipitation only; case 4, disaggregated soil parameters only; and case 5, baseline analysis (Arkansas- Red River basin). parameters are disaggregated (case 1), runoff production over the area is nearly insensitive to spatial scale. Figure 9 also shows that aggregation of precipitation is the most important factor leading to the model s sensitivity to spatial scale, and that the aggregated soil parameters have major influence on the model s sensitivity to spatial scale. The aggregation of vegetation parameters does not seem to influence the results greatly. [27] When input precipitation is disaggregated (case 2), the sensitivity of both direct runoff and base flow decreases significantly across the scales, compared to the results from the baseline analysis (section 3.1). Disaggregation of soil parameters (case 4) also decreases the simulated changes in direct runoff, but not nearly as much as the disaggregated precipitation. However, keeping the soil parameters constant across the scales increases the model s sensitivity to changes in base flow. The changes in total runoff, given disaggregated soil parameters, are quite similar to the changes in total runoff in the baseline analysis, meaning that disaggregation of soil parameters mainly changes the partitioning of runoff into direct runoff and base flow, and not so much the total runoff production. [28] The results indicate that both the aggregation of precipitation and soil parameters contribute to the decrease in direct runoff at lower spatial scales in the baseline analysis (section 3.1), but that the aggregation of precipitation is by far the most important factor. Aggregation of soil parameters alone may have lead to an increase in base flow at lower spatial resolutions, but total runoff production apparently would not change much. The effect of aggregated soil parameters results from the spatial averaging of the parameters, and hence an averaging of nonlinear equations controlling the saturation excess mechanisms, base flow production, and soil moisture limitation on evapotranspiration. [29] Spatial differences exist within the basin, and in some areas the effects of aggregation/disaggregation of soil parameters deviate from the general patterns described above. Consider, for instance, a spatial image (Figure 10) of the differences in simulated mean annual direct runoff, base flow, and total runoff for the disaggregated precipitation analysis (case 2) and the disaggregated soil parameters analysis (case 4). The areas showing the largest differences in direct runoff and base flow coincide in general with areas where the soil parameters (e.g., soil depth, the factors included in the variable infiltration and base flow curves, and factors controlling soil moisture limitation on evapotranspiration), have large spatial gradients Energy Balance Mode Scale Sensitivity [30] Simulations were performed in energy balance mode (in which the model skin temperature is iterated at each time step to close the surface energy balance) for the Arkansas- Red River basin for a period of five years (October 1976 to September 1981). The energy balance mode analysis uses the same meteorological forcing data and model setup as the analysis using constant precipitation (section 3.1), but in energy balance mode the model is run at 3 hourly time steps. For the 5 years simulated, total runoff at 2 is 16% lower than at one-eighth degree resolution, compared to 15% lower when the model is run in water balance mode at 3 hourly time steps for the same time period (see also Figure 11). The model was not recalibrated for the energy balance runs, and the resulting hydrographs, and the parti- Figure 10. Mean annual difference (cases 2 4) in simulated (a) direct runoff, (b) base flow, and (c) total runoff in the Arkansas-Red River basin at one-quarter degree spatial resolution. Case 2: Precipitation is disaggregated from the two degrees spatial resolution. Case 4: Soil parameters are disaggregated from the two degrees spatial resolution.

9 HADDELAND ET AL.: INFLUENCE OF SPATIAL RESOLUTION 29-9 Figure 11. Percent changes in moisture fluxes compared to the results at one-eighth degree spatial resolution when running VIC in water balance mode (open symbols) and in energy balance mode (solid symbols) at 3 hourly time steps for a 5-year period (Arkansas-Red River basin). tioning of total runoff into direct runoff and base flow, are somewhat different than when the model is run at daily time steps (previous sections). The resulting monthly streamflows, when comparing the same spatial resolution, are, however, quite similar for the energy balance mode and water balance mode at 3 hourly time steps (not shown). The results indicate that VIC s sensitivity to spatial scale for the energy balance mode is similar to those for water balance mode. Snow accumulation and melt are calculated using an energy balance approach even when VIC is run in water balance mode, and it is therefore expected that the results would be even more similar in the snowmelt-dominated Columbia River basin. 4. Conclusions [31] Aggregation of meteorological data, soil and vegetation parameters for a macroscale hydrologic model shows that the lower resolution models preserve the general form of the hydrographs at the basin outlets. However, total runoff is lower at 2 spatial resolution than at one-eighth degree spatial resolution for both snowmelt (Columbia) and rainfall-dominated (Arkansas-Red) basins. Direct runoff is more sensitive to the scale changes than base flow, and is less sensitive in the snowmelt dominated Columbia River basin than in the Arkansas-Red River basin. Total runoff is also less sensitive in the Columbia River basin than in the Arkansas-Red River basin; which also is a consequence of the snowmelt dominated hydrology in the Columbia River basin. Koren et al. [1999] found that runoff production decreases as spatial scale increases, a result that is analogous to the results from this study. However, contrary to the results from this study, they predicted an increase in base flow with increasing scale. A likely reason for this difference is that Koren et al. kept model parameters constant over the scales, while in this study model parameters are averaged. Also, the models used by Koren et al. do not explicitly account for spatial variability of soil and vegetation parameters within a basin. [32] In areas where the dominant source for streamflow generation is snowmelt, the averaging of precipitation and temperature is the main factor causing decreased streamflow values at lower resolutions. In warmer and drier areas, spatially averaged precipitation values, which result in reduced spatial variability of precipitation and soil moisture, is the main factor contributing to lower runoff at lower resolutions. In areas where soil moisture is abundant, increased infiltration is to some extent compensated by increased base flow. Analyses performed for the Arkansas-Red River basin indicate that the aggregation of soil parameters is the second most important factor (after precipitation averaging) causing sensitivity of direct runoff and base flow production to changes in spatial scale, while the aggregation of vegetation does not seem to influence runoff much. Soil parameters that are averaged in the aggregation method are included in nonlinear functions controlling runoff production and soil moisture limitation on evapotranspiration, meaning that areally averaging of these parameters does not result in areally averaged functions. Hence, areas having large spatial gradients in the soil parameters in general are more affected by the aggregation of soil parameters than homogeneous areas are. The results also indicate that aggregation of soil parameters in general results in decreased direct runoff and increased base flow, but that total runoff production does not change much because of aggregated soil parameters. However, these results may be somewhat different in areas with other land cover characteristics. [33] The use of spatially distributed precipitation decreases VIC s sensitivity to scale in rainfall dominated areas, but where snow is the dominant precipitation type, this option does not change the results significantly. The importance of taking subgrid topographic variations into account in snowfall-dominated areas is illustrated. An application where precipitation is aggregated dependent on elevation in the original one-eighth degree cells shows that this reduces VIC s sensitivity to scale in areas where snow accumulation and melt dominate the hydrology. Habets et al. [1999] also concluded that a macroscale model s sensitivity to spatial scale decreases when the aggregation method accounts for subgrid interactions between precipitation and temperature, although they used a somewhat different scheme than is used in this study. [34] VIC is run in water balance mode for the majority of the analyses performed in this project. However, exploratory simulations in energy balance mode indicate that spatial scale sensitivities are similar to those for water balance mode. [35] Calibration of macroscale hydrologic models can be a time consuming task. The results from this study indicate that it might be possible to start the calibration process at a coarse resolution, for computational considerations, and thereafter disaggregate the model parameters to higher resolutions. Once the model s sensitivity to the aggregated parameters in the area studied is established, the model can be calibrated at a coarse resolution taking the model s sensitivity into account, and thus reduce the time required for each calibration run. It should not be expected that there will be no further need for calibration at higher resolutions, but a useful starting point can be obtained. [36] Acknowledgments. This research was funded by cooperative agreement number PNW CA between the U.S. Forest Service

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