Effect of grid size on runoff and soil moisture for a variable-source-area hydrology model

Effect of grid size on runoff and soil moisturefor a variable-source-area hydrology model

Wen-Ling Kuo,1 Tammo S. Steenhuis,1 Charles E. McCulloch,2 Charles L. Mohler,3

David A. Weinstein,4 Stephen D. DeGloria,5 and Dennis P. Swaney4

Abstract. Soil chemical and biological dynamics in mixed use landscapes are dependenton the distribution and pattern of soil moisture and water transport. In this paper weexamine the effect of different grid sizes on soil water content for a spatially explicit,variable-source-area hydrology model applied to a watershed in central New York. Dataon topography, soil type, and land use were input at grid sizes from 10 to 600 m. Outputdata consisted of runoff and spatial pattern of soil moisture. To characterize the spatialvariability at different grid sizes, information theory was used to calculate the informationcontent of the input and output variables. Simulation results showed higher average soilwater contents and higher evaporation rates for large grid sizes. During a wet year, runoffwas not affected by grid size, whereas during a dry year runoff was greatest for thesmallest grid size. While the information content (i.e., spatial variability) of soil type andland use maps was not affected by the different grid sizes, increasing grid sizes caused theinformation content of the slope gradient to decrease slightly and the Laplacian (orcurvature of the landscape) to decrease greatly. In other words, increasing grid cell sizemisrepresented the curvature of the landscape. During wet periods the decrease ininformation content of the soil moisture data was the same as for the Laplacian as gridsize increased. During dry periods, when local fluxes such as evaporation and runoffdetermine the moisture content, this relation did not exist. The Laplacian can be used toprovide a priori estimates of the moisture content deviations by aggregation. Thesedeviations will be much smaller for the slowly undulating landscapes than the landscapewith steep valleys simulated in this study.

1. Introduction

Nonpoint source and habitat degradation problems must beaddressed at the basin or watershed level for efficient manage-ment of water quality [U.S. Environmental Protection Agency,1994, 1995, 1996]. This requires spatially explicit models tosimulate ecosystem processes. Most models are lumped andare unable to describe the variation in water and nutrientfluxes in a watershed [Swaney et al., 1996; Fisher et al., 1997].This is especially true for well-vegetated watersheds in thenortheastern United States in which shallow and sloping soilspredominate and for which the hydraulic conductivity of soilsexceeds rainfall intensity by several fold. In these watersheds,runoff is generated from localized saturated areas, and evap-oration and interflow (flow parallel with the impermeablelayer) are important components in water balance calculations[Dunne, 1978; Petch, 1988; Steenhuis et al., 1995].

Simulating water dynamics in these watersheds requires fast

computers and a vast amount of spatial information, includingtopography, soil type, and land use [Beven and Kirkby, 1979;Beven, 1986, 1995] and has been feasible only during the lastdecade [Mendicino and Sole, 1997]. To efficiently integratethese data with computational routines, grid-based distributedmodels have been developed employing geographic informa-tion systems (GIS) for spatial data management [Moore et al.,1991; Burrough, 1996]. The behavior of these highly nonlineardistributed models can be characterized by the informationcontent or entropy of their input and output data [Vieux andFarajalla, 1994]. The information content is a measure of tem-poral or spatial variability. Vieux [1993] showed that bysmoothing and aggregating digital elevation data, its informa-tion content decreased, resulting in greater errors in predictedrunoff. It is obvious then that grid size in distributed modelswill have a direct effect on information content and the accu-racy of simulation output. The most common grid sizes in GISdatabases are those used by the geological surveys of theUnited States and the United Kingdom of 30 m and 50 m,respectively [Quinn et al., 1991; Moore et al., 1993], but little isknown about the effect of grid size on simulation results orinformation content.

A few studies have examined the effect of grid size on wa-tershed simulations. Using TOPMODEL, Quinn et al. [1991],Moore et al. [1993], Zhang and Montgomery [1994], Bruneau etal. [1995], and Wolock and Price [1994] looked at how grid sizeaffected the computed topographic characteristics, wetness in-dex, and outflow. In general, they found that the finer grid sizegave more accurate results. TOPMODEL assumes that thedownslope flows take place predominantly in a saturated zone

1Department of Agricultural and Biological Engineering, CornellUniversity, Ithaca, New York.

2Department of Statistical Science, Cornell University, Ithaca, NewYork.

3Section of Ecology and Systematics, Cornell University, Ithaca,New York.

4Center for the Environment, Cornell University, Ithaca, New York.5Department of Soil, Crop and Atmospheric Sciences, Cornell Uni-

versity, Ithaca, New York.

Copyright 1999 by the American Geophysical Union.

Paper number 1999WR900183.0043-1397/99/1999WR900183$09.00

WATER RESOURCES RESEARCH, VOL. 35, NO. 11, PAGES 3419–3428, NOVEMBER 1999

3419

with a transmissivity that decreases with depth [Ambroise et al.,1996]. In the northeastern United States and other areas of theworld, where thin soils overlay slowly permeable subsoils orbedrock, the soils are only saturated for a short period afterstorm events and then the remainder of the interflow takesplace as unsaturated flow [Steenhuis et al., 1988]. The assump-tion in TOPMODEL that flow takes place only through thesaturated soil is not valid for these watersheds. With the ex-ception of the few studies with TOPMODEL the effect of GISgrid size on watershed simulations has not been well investi-gated [Star and Estes, 1990; Star et al., 1997; Baveye and Boast,1999]. Thus the goal of this study is to elucidate the role of gridsize on information loss of water movement and soil moisturein the simulation of a watershed with impermeable slopingsubsoils at shallow depths.

In this study we use a GIS-based model that includes unsat-urated flow and that was specifically developed for undulatinglandscapes with a relatively thin conductive soil layer overglacial till [Zollweg et al., 1996; Kuo et al., 1996; Frankenbergeret al., 1999]. Soil water movement and dynamics were simu-lated for three watersheds in upstate New York to evaluate theeffect of scale on simulated soil water content and runoff. Thesensitivity of the model to aggregation of specific types of inputdata was studied by increasing the grid size for one type ofinput data while keeping the other input parameters at theoriginal scale. This constituted a factorial simulation experi-ment with the input parameters as treatments and the grid sizeas level within the treatment. Information loss due to aggre-gation was calculated.

2. Methods2.1. Study Site

We chose three adjacent watersheds, typical of the north-eastern United States, of 647, 2360, and 742 ha (Table 1 andPlate 1). The watersheds are part of the Fall Creek watershedand located upstream from Freeville, New York (N428329,W768179). Terrain elevation ranges from 317 to 561 m, andslope gradient ranges from 0 to 60% (Table 1). Agriculture andforest are the main land uses. Annual precipitation averages 94cm, and mean annual air temperature averages 8.38C [Owensbyand Enzell, 1992]. Precipitation is nearly evenly distributedthroughout the year. Most soils have a shallow depth to a layerthat restricts water movement [Cornell University Department ofGeology, 1959; Neeley, 1965].

Three digital maps were made for elevation, soil type, and

land use using 10-m-square grid cells. Elevation data weredigitized from the contours of 1;24,000 U.S. Geological Surveymaps. Soil maps were obtained from soil surveys at 1;20,000scale of Tompkins, Cortland, and Cayuga Counties. Land useinformation was interpreted from 1991 aerial photographs at1;24,000 scale [Poiani et al., 1996]. For the purpose of thisstudy the 10 by 10 m grid maps were considered to be a truerepresentation.

2.2. GIS-Based Hydrology Model

The analysis was performed with a GIS-based model origi-nally developed by Zollweg et al. [1996] and further improvedby Kuo et al. [1996]. The model was designed for simulation ofsoil water and nitrogen fates in mixed use landscapes withsloping and shallow soils. The model was coded in shell scriptcommands within the Geographic Resources Analysis SupportSystem [Construction Engineering Research Laboratory, 1993;Mitasova et al., 1995]. The simulations were performed using adaily time step.

Water balance equations were written to operate on a pergrid cell basis and for each soil layer. The model divides thesoil into two main layers: a potential root zone and the com-bination of several subsoil layers. The potential root zone isdivided into the actual root zone (from which evaporationoccurs) and the remaining part which the roots eventuallypenetrate during the growing season. The change of soil waterin a layer in a cell is calculated by combining Darcy’s law forthe lateral flux and perpendicular flux to the surface f with theconservation of mass equation:

u

t 5

s SK~u !hsD 2

fn , (1)

where u is the volumetric water content, h is the hydraulichead, K(u ) is the hydraulic conductivity as an exponentialfunction of moisture content, s is the coordinate along theslope, and t is time. The first term on the right-hand side is thenet lateral flux between cells, and the second term expressesthe net upward and downward fluxes between layers in a cell.The coordinate normal to the surface is n .

The flux f includes the daily precipitation, evaporation waterloss to the atmosphere, and the water flux between the layers.Water flows downward at the rate of the saturated conductivitywhen the layer is above field capacity. If the layer below is filledup with water, downward movement stops. Local runoff occurswhen the soil reaches saturation or when precipitation inten-sity is greater than local saturated conductivity. Evapotranspi-ration takes place out of the active evaporation zone and isbased on the Thornthwaite-Mather procedure [Steenhuis andvan der Molen, 1986]. For moisture contents from field capacityto saturation the evaporation is equal to the potential rate; andfor moisture contents from field capacity to wilting point,evapotranspiration decreases linearly from a potential rate tozero. During the winter, snow accumulation and snowmelt areincluded.

Equation (1) can be rewritten as

u

t 1fn 5

Ku

u

shs 1 K

2hs2 , (2)

which shows that the net lateral exchange of water betweencells (right-hand side) depends on the hydraulic conductivityand is a function of the first derivative (h/s or slope gradi-ent) and the second derivative of the elevation (2h/s2 or the

Table 1. Summary Information for Three Basins

Basin 1 Basin 2 Basin 3

Area, ha 647 2360 742Topography

Elevation range, m 317–433 335–561 317–488Slope gradient range, % 0–44 0–59 0–35

Soil type, % of basin areaWell drained 87 79 61Poorly drained 13 21 39

Land use, % of basin areaPermanent vegetation

(forest and wetland)47 41 34

Cropland 39 43 50Grass 6 10 8Urban 8 6 8

KUO ET AL.: EFFECT OF GRID SIZE ON RUNOFF AND SOIL MOISTURE3420

Plate 1. Location, soil type, and land use maps of the study area, a subcatchment of the Fall Creekwatershed in central New York.

3421KUO ET AL.: EFFECT OF GRID SIZE ON RUNOFF AND SOIL MOISTURE

Laplacian). The Laplacian is related to the curvature of alandscape surface.

2.3. Spatial Aggregation

Increasing grid size results in a change in watershed area ifthe border cells are not adjusted for the area inside the “true”boundary [Bruneau et al., 1995]. When comparing total runoffand average moisture content for different grid sizes, the wa-tershed area needs to be conserved. To do so, we calculated foreach aggregated cell the proportion of 10 by 10 m cells (ap)that was within the watershed. The fluxes of the aggregatedborder cells were then multiplied by this factor (ap) ensuringthat no water was gained through the scaling process. Figure 1shows an example of spatial aggregation on a simple catchmentfrom the small scale L 5 l to the larger scale L 5 3l . At thesmall scale, L 5 l , the catchment area, shown as shaded, isequal to 13l2. At the larger scale, L 5 3l , four coarse cells arewithin the catchment, and ap for those cells is 2/9, 2/9, 3/9, and6/9, giving a value of 13/9L2. Because L2 5 9l2, the area isagain equal to 13l2.

On the basis of above discussion, (1) can then be written infinite difference form for a layer i , with height Di, of a cell withlength L , using the appropriate volumes and cross-sectionalareas:

apDiL2Du i

Dt 5 D~lDiK~u !S! 2 D~apL2f i! , (3)

where the length of the cell boundary l is approximated by

l 5 ÎapL2 (4)

and shows, as expected, that for internal cells l 5 L . Theleft-hand side of (3) expresses the change in volumetric mois-ture content in the part of the cell that is within the watershed.On the right-hand side of (3) the term D(lDiK(u )S) is the netlateral flux of water over a cross-sectional area lDi and iscomputed as the product of the unsaturated conductivity K(u )

and slope S in the flow direction. The last term is the netvertical flux between the layers.

Another issue in aggregation was the value of the cell pa-rameters. A distinction was made between continuous data(e.g., elevation) and categorical data (e.g., soil type and landuse). For continuous data the values of the component cellswere averaged. For categorical data the most common value ofthe component cells was selected. In case of a tie one of the(equally) most common values was chosen at random. Forborder cells, only the portion inside the watershed was consid-ered.

2.4. Simulation Experiment

The 10 3 10 m maps of elevation, soil type, land use, andwatershed boundaries for the study area were aggregated toproduce 14 sets of data with grid sizes of 10, 20, 30, 50, 70, 100,120, 150, 170, 200, 300, 400, 500, and 600 m. This procedure isdifferent than those used by others [i.e., Zhang and Montgom-ery, 1994; Wolock and Price, 1994] where the digital elevationmaps were resampled for each grid size. The aggregated basemaps were used to obtain the input maps for the simulationmodel (e.g., slope gradient and Laplacian from the elevationmap, saturated conductivity from the soil map, and potentialrooting depth from the land use map). A 3-year simulation wasperformed using daily weather data from April 1, 1991, toMarch 31, 1993, obtained from the Northeast Regional Cli-mate Center at Cornell University for the Game Farm RoadStation located in the Fall Creek watershed. Year 0 (April 1,1991, to March 31, 1992) was used to set the initial moisturecontent of the cells. Year 1 consisted of the climate data for theperiod April 1, 1992, to March 31, 1993 (108 cm of precipita-tion). Year 2 consisted of the period April 1, 1991, to March31, 1992 (82 cm of precipitation) used a second time.

2.5. Determination of Dominant Parameters:Factorial Experiments

To determine the types of data for which grid size had thegreatest effects on simulation output, we conducted two-factorsimulation experiments [Neter et al., 1996]. Among input mapswe varied the grid size of the topographic (topo) map as onefactor and varied the grid size of both the land use and soil map(lu-s) as the other factor. Each factor had two spatial resolu-tions, 20 m and 200 m. Thus we ran four different simulations:20 m topo with 20 m lu-s; 20 m topo and 200 m lu-s; 200 m topoand 20 m lu-s; and 200 m topo and 200 m lu-s.

2.6. Information Content

The numerical values for each grid cell compose the infor-mation of a map. Typically, as map resolution decreases (i.e.,larger grid size), information is lost. To describe the effect ofaggregation on the simulation results, we used the information(or entropy) theory by Shannon and Weaver [1949] which wasintroduced to hydrology by Vieux [1993], Vieux and Farajalla[1994], Mendicino and Sole [1997], and Singh [1997].

For categorical data, such as land use, information contentV, which represents a measure of variability of spatial infor-mation associated with a range of outcome values, is defined as

ln V 5 2Oi51

N

Pi ln ~Pi! , (5)

where N is the number of categories (or bins) in the range intowhich the categorical values have been divided and Pi is the

Figure 1. An example of spatial aggregation of a catchmentfrom grid cell L 5 l to large grid cell L 5 3l . The area insidethe watershed at the fine scale, L 5 l , is shown shaded.Catchment size after aggregation equals (6/9 1 3/9 1 2/9 12/9) L2 5 13l2.


proportion of cells of category i . Choices of range of outcomevalues and N are critical in comparing information indices overdifferent scales.

Choice of bins for evaluating V for continuous data is moreproblematic. As the number of bins increases, V approaches2ln (M), where M is the number of distinguishable values.This is clearly meaningless from the point of view of informa-tion content. So a proper value of N has to be chosen so thatthere is a clear distinction for different grid sizes. We want Nlarge enough to reflect the fact that the data are continuous butnot so large as to be approximately equal to 2ln (M). Figure2 shows there is a middle range in which ln (V) is changingapproximately linearly with ln (N), and effective comparisonscan be made between grid sizes. Hence we chose N 5 80 forquantifying information loss for slope gradient and N 5 600for the Laplacian.

3. Results and DiscussionSimulated cumulative runoff, average monthly soil moisture,

and cumulative effective precipitation over the three catch-ments are shown in Figure 3. Because of difference in satu-rated moisture content between cells, the soil moisture contentis normalized: 0 is air dry soil and 1 is saturation. Effectiveprecipitation is defined as the difference between rainfall andevapotranspiration. Soil moisture values (Figure 3b) increasedas the grid sizes increased. Larger grid sizes resulted in higheraverage moisture contents (Table 2). As we will discuss later,the increase in moisture content is directly related to a de-crease in the variation of slope gradient and curvature. Thedifferences in moisture content established on April 1 of year1 (resulting from the initialization of the simulation with theyear 0 precipitation) were approximately maintained through-out the 2 years, although differences were greatest during thedry summer of the second year (Figures 3a and 3c). The cu-mulative effective precipitation became less over the 2-yearperiod for increasing grid sizes. This was a direct consequenceof the higher moisture content at the large grid sizes that gavehigher actual evaporation amounts and thus lower effectiveprecipitation amounts. Runoff was the same for all the gridsizes during the wet year 1 (Figure 3a) despite the difference ineffective precipitation (Figure 3c). Thus the lower effectiverainfall input for the larger grid sizes was offset by a smaller

decrease in moisture content during the summer comparedwith the smaller grid sizes (which is confirmed by Figure 3b). Asimilar argument can be made for the lower total in cumulativerunoff at large grid size (Figure 3c). Since for the 400-m gridthe moisture content at the beginning and end of the simula-tion period was approximately the same (Figure 3b), waterbalance considerations dictate that decreases in effective pre-cipitation are directly related to a decrease in outflow from thewatershed. Because the watershed becomes drier over the2-year period for the smaller grid sizes (Figure 3b), the differ-

Figure 2. Information content (V) of slope gradient andLaplacian versus number of bins at cell sizes of 50, 200, and600 m.

Figure 3. Monthly simulation results for the whole catch-ment of total area at cell sizes of 10, 30, 50, 100, and 400 m: (a)cumulative monthly runoff, (b) monthly average soil moisture,and (c) cumulated monthly effective precipitation. Legends areshown in Figure 3a.


ences in runoff are not as great as the differences in effectiveprecipitation.

The spatial distribution of soil moisture for a selected sam-ple date, March 31, 1993, at cell sizes of 10, 30, 50, 100, and400 m is revealing (Figure 4). This was the second day after arain event (0.83 cm precipitation), and there had been norainfall or snowmelt for 5 days prior to the rain. In Figure 4,darker regions represent drier soil, and open areas indicate soilnear or at saturation. In the 10 m-simulation most areas wereat field capacity, except areas near valley bottoms. The spatial

pattern of the saturated areas indicated potential locations offlow channels and wetlands (open areas in Figure 4). Thepattern of wetness also changed with grid size: The areas atfield capacity on the 10 by 10 m grid in the middle of Figure 4became completely saturated (u . 0.99 us) in the 400-m grid.

Although Figure 4a is too small to see the many saturatedindividual 10 by 10 m grid cells, the overall pattern of wet areasshows a close correspondence with the poorly drained areas inPlate 1. Poorly drained areas are defined in the soil survey asmostly wet throughout the year, but otherwise they have thesame hydraulic properties as similar soils in upland areas of thelandscape. Thus input parameters were the same for the wetand dry areas, and the simulated degree of wetness was onlydependent on terrain location.

The difference in annual runoff for the various grid sizes wasmuch smaller between the three basins than between the 2years of simulation (Figure 5a). Differences between the yearsin soil moisture averaged over all days and grid cells wererelatively small (Figure 5b). The average soil water saturationchanged rapidly with grid sizes up to 150 m but changed verylittle after that.

The relative deviation E of the moisture content was plottedagainst the grid size (Figure 6). E is defined as

E 5 U u i 2 u0

u0U , (6)

Figure 5. Simulation results of three basins in year 1 andyear 2: (a) annual runoff and (b) yearly average soil moisture.Legends are shown in Figure 5a.

Table 2. Results of a Two-Factor Experiment: TopographyVersus Soil Type and Land Use With Two Levels of 20 and200 m

Year 1 Topography Year 2 Topography

20 m 200 m 20 m 200 m

Runoff, mmSoil type, 20 m 483 481 258 189Land use, 200 m 481 491 254 201

Averaged Soil MoistureSoil type, 20 m 0.798 0.972 0.726 0.918Land use, 200 m 0.803 0.968 0.729 0.905

Effective Precipitation, mmSoil type, 20 m 500 450 233 159Land use, 200 m 498 457 229 172

Figure 4. Spatial simulation soil moisture for a selected sam-ple date, March 31, 1993, at cell sizes of 10, 30, 50, 100, and400 m.


where u i is the average yearly soil moisture content at scale iand u0 is the reference moisture content for an infinitesimallysmall cell obtained by an extrapolation to a grid size of 0 musing a linear regression of ln u versus the grid size (Figure 5b).The relative deviation in moisture content for a particular scalewas almost the same between years, and variation in relativedeviation between basins became obvious (Figure 6). The mag-nitude of the deviation for larger grid sizes was greater forbasin 1 (Plate 1) which has a relatively high percentage ofshallow, less well drained soils than basins 2 or 3. The slope ofthe lines was, initially, about 1.2 (Figure 6), indicating that therelative deviation increased by a factor of 101.2 or 16 when gridsize increased from 10 to 100 m.

The results of the two-factor factorial experiment are sum-marized in Table 2. One factor represents the map derivedfrom elevation (topography), and the other factor representsthe maps from soil type and land use. In Table 2 the effectiveprecipitation is the difference of the precipitation and theactual evaporation. Both the annual effective precipitation andyearly averaged soil moisture for the whole watershed changedlittle when the soil type and land use maps were changed from20 to 200 m, while the grid cell size of the topography remainedthe same (Table 2). For example, for the 20-m grid topographymap the average moisture content for year 1 was 0.798 whenthe grid spacing for the soil type and land use maps was 20 m,while using a 200-m grid cell size for these two maps (andretaining the topography grid size at 20 m) resulted in anaverage moisture content of 0.803. In contrast, aggregation oftopography from 20 to 200 m had a large effect on modeloutputs. The change in scale from 20 to 200 m for topographyresulted in an increase in the watershed moisture content ofnearly 20% in both years and at both the 20- and 200-m scalesof the soil type and land use maps. Because aggregation oftopography increased wetness, it increased evapotranspirationand thereby decreased the effective precipitation (Table 2).

The spatial moisture distributions on two dates (Figure 7a)and the average soil moisture contents for three monthly pe-riods (Figure 7b) were analyzed to assess the grid size effect.These were either in dry or wet periods. The “wet” day, March31, 1992, had 1.3 cm precipitation in the previous 3 days, whileevaporation was small. The “dry” day, June 19, 1992, occurredduring a drought period with no rain for the previous 12 days

under high evaporative conditions. For monthly average data,August 1991 (dry) was compared with August 1992 and Octo-ber 1992 which were both wet but with vegetation in differentgrowth stages. In all cases, aggregation caused a dramatic lossin information of moisture content distribution of the soil.During wet periods the information content V decreased 1 to2 orders of magnitude when the grid size changed from 10 to600 m (Figures 7a and 7b). The decrease in V for increasinggrid sizes was less during dry periods than during wet periodsbut was still substantial. Thus, using the typical American gridcell size of 30 m, rather than 10 m for the simulation, results ina loss of information on soil moisture distribution of 50%during the wet period. For the usual British grid size of 50 m,the information loss was 70%. Since soil moisture is a majorfactor that controls biological and chemical processes, we inferthat simulation of those dynamics at larger grid sizes mayoverestimate the rate of anaerobic soil processes and thegrowth rate of the plants. Therefore we recommend for water-shed simulations use of a grid cell size smaller than 30 m andpreferably 10 m if the data are available.

As expected, the information content V for soil type andland use showed only a weak dependence on grid size (Figure8a). Also, aggregation did not change the information contentof the distribution of grid cell elevations and resulted in onlymoderate information loss for slope gradient (Figure 8b). In

Figure 6. Relative deviation of yearly average soil moisturefor 2 years in the three basins. The dashed line is year 1 and thesolid line is year 2. Symbols indicate basins and are shown inlegend.

Figure 7. Information content (V) versus grid size d for soilmoisture distribution: (a) at two sample dates and (b) atmonthly average soil moisture distribution at eight chosenmonths over the study period. Solid lines represent wet period,and dashed lines represent the dry period.


contrast, aggregation reduced the V value of the Laplacian(calculated from the topographic information) by 2 orders ofmagnitude (Figure 8b). Note that a small V value indicates lessdifference among cells and that the hydrological behavior athigh levels of aggregation approximates that of a uniform area.Thus the information analysis provides evidence that the ag-gregation of the topographic data is the source of most aggre-gation error in the hydrologic simulation and that much of thiserror can be attributed to the behavior of the Laplacian. Inother words, increasing the grid cell size misrepresents thecurvature of the landscape which results in higher moisturecontents and decreases variation in the distribution of moisturecontent among cells (Figure 3b).

During wet periods the decrease of the V value of soilmoisture content due to aggregation (Figure 7) was of thesame order as the information loss for the Laplacian distribu-tion (Figure 8b). This occurs because the moisture contentdifferences during wet periods are caused by lateral watertransport (equations (1) and (2)), and this process is domi-nated by the Laplacian. During dry periods, evaporation is themain factor in moisture loss and lateral transport is small,causing the information loss to be less dependent on the Lapla-cian than during wet periods (Figures 7a and 7b). These find-ings are consistent with those of Grayson et al. [1997] in thetemperate regions of Australia. They showed that when the soilis dry, the soil moisture content is primarily governed by ver-tical fluxes of percolation, rainfall, and evaporation at a par-

ticular location and thus is independent of the curvature of thelandscape. For wet soils, moisture content is dominated bylateral fluxes which are a function of, primarily, the Laplacian.

Figure 8b shows that a large grid size results in a small rangeof the Laplacian spectrum. This, in turn, can be used to par-tially explain why soils become wetter for the larger grid sizes(Figure 4): For the 10-m grid, although the overall moisturecontent is lower, the wide variation in curvature (or Laplacian)causes different inflows and outflows for each cell. As a result,there are many small but saturated areas throughout the wa-tershed after a heavy rainfall. Thus water in the 10-m grid hasonly a small distance to travel via interflow to the wet areascompared to the larger grid sizes. Once in a saturated area,water flows overland to the outlet. Overland flow is the mosteffective way (i.e., the path with the least resistance to waterflow) to drain the watershed. Thus the 10-m-grid water drainsrelatively quickly because of the short travel distance, andthere is thus less resistance to water flow than for the larger cellsizes. Since the amount of water which has to be transportedout of the watershed remains approximately the same, theunsaturated conductivity must compensate for the decrease indriving force. Since conductivity depends on moisture content,the moisture content increases. In addition, for large grid sizesthe variation in curvature is decreased. We obtain, in the limit,a uniform slope. For uniform slope without rain, inflows andoutflows are equal, and the slope has a uniform water content.Thus, during a rainfall event, saturation occurs over the wholehillslope at the same time and stops at the same time too.

Our unsaturated flow model and its saturated flow counter-part, TOPMODEL, both showed the same sensitivity of scalewith respect to the topographic input data. Even more remark-able is that Zhang and Montgomery [1994] found, similarly, fortwo watersheds with TOPMODEL that the 10-m grid sizeprovided a substantial improvement over the 30- and 90-mdata. In addition, we recently found that for a single hillsidewith some simplifications the unsaturated Richards’s formula-tion is the same as the Boussinesq’s approximation for satu-rated flow [Steenhuis et al., 1999]. Thus, despite the conceptualdifferences between TOPMODEL and ours, the model struc-ture might be more similar than originally anticipated.

4. Concluding RemarksErrors introduced by aggregation of spatial input data have

important ramifications for the use of GIS-based hydrologymodels. In this study, deviations from the simulations at thesmallest grid size increased proportionally to grid size over therange of scales most commonly used in GIS simulation studies(Figure 6). This is in agreement with the argument used byBeven [1995] that the aggregation approach toward macroscalehydrological modeling, using averaged parameter values, isinadequate for representing hydrological processes at a largescale. Thus a disaggregation approach to developing scale-dependent models is advocated by Beven [1995]. However, thecomputation cost (CPU time) decreases in proportion to thesquare of the grid size. Our results, such as represented inFigure 6, can, at least in the northeastern United States, helpguide the choice of a grid size in variable-source-area distrib-uted models which is a compromise between accuracy andcomputation time in large-area simulations.

In this study we showed that among the several types ofinput information changes in the scale of topography had thegreatest effects on the simulation results. This parallels the

Figure 8. Information content (V) versus grid size d for (a)soil type and land use and (b) elevation, slope gradient, andLaplacian.


results with TOPMODEL [Braun et al., 1997; Zhang and Mont-gomery, 1994]. Aggregation had an especially large effect dur-ing wet periods. The scale of topography is critical becausehydrological behavior is driven by the first derivative (slopegradient) and the second derivative (Laplacian or slope curva-ture) of the elevation data. The information of the Laplacianhas the same response to grid size as the relative deviation inthe simulation of the moisture content (Figures 6 and 7). Thusthe Laplacian V value can provide an a priori estimate of themagnitude of the deviation in soil moisture content valuescreated by aggregation and can aid in deciding the optimumgrid scale for simulating the hydrology of large areas. Forexample, for the slowly undulating landscapes in the midwest-ern corn belt where the Laplacian changes little with scale, alarger grid size than that used for the landscape with steepvalleys simulated in this study can be used without adverselyaffecting the output.

Acknowledgments. This research was supported by the Agricul-tural Ecosystems Program at Cornell University funded by the Coop-erative Research, Education, and Extension Service (CREES) of theUnited States Department of Agriculture.

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D. P. Swaney and D. A. Weinstein, Center for the Environment,Cornell University, Ithaca, NY 14853. ([email protected])

(Received July 6, 1998; revised June 7, 1999;accepted June 7, 1999.)


Effect of grid size on runoff and soil moisture for a variable-source-area hydrology model

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