Impacts of input parameter spatial aggregation on an ...water.geog.buffalo.edu/mackay/pubs/pdfs/fitzhugh_mackay_joh.pdfw £ d –2ƒ where F, is the ﬂow volume (m 3/s); w, is channel

Impacts of input parameter spatial aggregation on an agriculturalnonpoint source pollution model

T.W. FitzHugha,1, D.S. Mackayb,*aEnvironmental Monitoring Program, University of Wisconsin-Madison, Madison, WI 53706, USA

bDepartment of Forest Ecology and Management and Institute for Environmental Studies University of Wisconsin-Madison, 1630 Linden Dr.,Madison, WI 53706, USA

Received 7 October 1999; revised 31 March 2000; accepted 17 May 2000

Abstract

The accuracy of agricultural nonpoint source pollution models depends in part on how well model input parameters describethe relevant characteristics of the watershed. The spatial extent of input parameter aggregation has previously been shown tohave a substantial impact on model output. This study investigates this problem using the Soil and Water Assessment Tool(SWAT), a distributed-parameter agricultural nonpoint source pollution model. The primary question addressed here is: howdoes the size or number of subwatersheds used to partition the watershed affect model output, and what are the processesresponsible for model behavior? SWAT was run on the Pheasant Branch watershed in Dane County, WI, using eight watersheddelineations, each with a different number of subwatersheds. Model runs were conducted for the period 1990–1996. Streamflowand outlet sediment predictions were not seriously affected by changes in subwatershed size. The lack of change in outletsediment is due to the transport-limited nature of the Pheasant Branch watershed and the stable transport capacity of the lowerpart of the channel network. This research identifies the importance of channel parameters in determining the behavior ofSWAT’s outlet sediment predictions. Sediment generation estimates do change substantially, dropping by 44% between thecoarsest and the finest watershed delineations. This change is primarily due to the sensitivity of the runoff term in the ModifiedUniversal Soil Loss Equation to the area of hydrologic response units (HRUs). This sensitivity likely occurs because SWATwas implemented in this study with a very detailed set of HRUs. In order to provide some insight on the scaling behavior of themodel two indexes were derived using the mathematics of the model. The indexes predicted SWAT scaling behavior from thedata inputs without a need for running the model. Such indexes could be useful for model users by providing a direct way toevaluate alternative models directly within a geographic information systems framework.q 2000 Elsevier Science B.V. Allrights reserved.

Keywords: Aggregation effects; Geographic information systems; Nonpoint sources; Models; Sediment transport; Sediment yield

1. Introduction and background

1.1. Introduction

This research examines the impact of the size ornumber of subwatersheds used to partition awatershed on the output of a distributed-parameterhydrologic model. Distributed-parameter models use

Journal of Hydrology 236 (2000) 35–53

0022-1694/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0022-1694(00)00276-6

www.elsevier.com/locate/jhydrol

* Corresponding author. Tel.:11-608-262-1669; fax:11-608-262-9922.

E-mail addresses:[email protected] (T.W. FitzHugh),[email protected] (D.S. Mackay).

1 Present address: The Nature Conservancy, 8 South MichiganAve., Suite 2301, Chicago, Illinois 60603, USA.

spatially variable input parameters to predictwatershed response, and a common method for repre-senting watersheds in these models is to aggregateinput data on the basis of subwatersheds. However,input parameter values and model output can beaffected by the spatial extent over which input dataare aggregated to produce parameters. The goal of thisstudy was to improve our understanding of the beha-vior of an agricultural nonpoint source pollutionmodel in relation to subwatershed size. The modelused in this research was the Soil and Water Assess-ment Tool (SWAT) (Arnold et al., 1998), a spatiallyexplicit long-term simulation model.

Distributed-parameter hydrologic models partitionthe watershed into spatially discrete computationalunits and solve model equations within each ofthese units. These computational units are generallylarger than the spatial resolution of the input data, andso the calculation of parameter values for eachcomputational unit usually involves some level ofaggregation. Aggregation is necessary because: (1) itis inefficient to run models at the resolution of theinput data; and (2) some relevant watershed charac-teristics can only be measured at larger scales. Thesimplest way to prepare input parameters within eachunit is to use mean values (for quantitative inputs) orthe dominant class present (for categorical inputs).Unfortunately, hydrologic responses are often nonli-nearly related to watershed characteristics, thus meanvalues may not faithfully represent the influence ofinput variables. Using only dominant categories ispotentially problematic because less common, buthydrologically important, categories will tend to beeliminated from the dataset as subunit size grows.

An alternative is to parameterize the model withprobability distributions of inputs. In theory, thisapproach should compensate somewhat for the dele-terious effects of aggregation and allow for the use oflarger subunits. One theoretical basis for such anapproach is the concept of a representative elementaryarea (Wood et al., 1988), which suggests that thereexists a scale at which runoff can be predicted fromprobability distributions of input parameters withoutregard for their actual spatial distribution. Eachsubwatershed can be parameterized for SWAT usinga series of hydrologic response units (HRUs), each ofwhich corresponds to a particular combination of soiland land-cover within the subwatershed. Mamillapalli

et al. (1996) found that increasing the number ofHRUs successfully compensated for decreasing thenumber of subwatersheds.

Research on the effects of aggregation in grid-cellhydrologic models has shown that model output issignificantly impacted by the size of the grid-cellsused to partition the watershed. Brown et al. (1993)found that output from the ANSWERS (Beasley et al.,1980) model started to change when input parameterswere aggregated to grid-cells larger than 120 m2.They found that predictions of sediment yield andthe areally weighted percent distribution of erosionand deposition changed. These changes were attribu-ted to the impacts of increasing amounts of aggrega-tion on the distribution of overland soil, land-use, andterrain parameters. Vieux and Needham (1993) foundthat output from the AGNPS model (Young et al.,1987) also varied with changes in cell size. Whencell sizes were increased from 1 to 4 ha, sedimentyield decreased due to decreasing channel erosion.Increases in cell sizes above 4 ha caused channelerosion to disappear, but sediment yield increasedbecause of increased transport capacity as the chan-nels became shorter and straighter.

While aggregation effects can be reduced by usingcomputational units defined by basin geomorphome-try instead of arbitrarily-placed grid-cells (Band,1989), they still occur for units above a certain size.Mamillapalli et al. (1996) found that the accuracy ofSWAT streamflow predictions varied depending onthe number of subwatersheds and HRUs used to repre-sent the watershed. Decreases in accuracy at coarserlevels of aggregation were apparently due to changesin the distribution of the Soil Conservation Service(SCS) Curve Number (CN) runoff parameter. Bingneret al. (1997), also using SWAT, found that whilestreamflow predictions were stable, sediment yieldvaried significantly with changes in subwatershedsize. They attributed these changes to the effects ofincreasing levels of aggregation on average subwa-tershed slopes and on the proportion of the watersheddelineated as cropland. Model output stabilized at thepoint where decreasing subwatershed size no longercaused large changes in slopes and area of cropland.

1.2. Justification

Nonpoint source pollution is a leading cause of

T.W. FitzHugh, D.S. Mackay / Journal of Hydrology 236 (2000) 35–5336

water quality problems both in the United States andworldwide, but due to its distributed nature, it cannotbe monitored directly in the same manner as pointsources. In this context, computer models such asSWAT have the potential to be used as tools forsupporting watershed management policy, becausethey can provide estimates of sediment, nutrient, andpesticide loadings for agricultural watersheds. SWATpredicts sediment and pollutant loadings leaving awatershed and the spatial distribution of soil lossand pollution contributions within a watershed. TheWisconsin Department of Natural Resources (DNR)is interested in using distributed-parameter hydrologicmodels to help design cost-effective strategies fornonpoint source pollution control. SWAT is one ofthe models currently under consideration for use asan aid in implementing the Environmental ProtectionAgency’s Total Maximum Daily Loads (TMDLs) inWisconsin (Panuska, 1998).

The TMDL process was established by section303(d) of the Clean Water Act, and provides amechanism for bringing water bodies not meetingwater quality standards into compliance. Standardsare designed to protect drinking water, aquatic life,and other water uses. A TMDL “quantifies pollutantsources and allocates allowable loads to the contribut-ing point and nonpoint sources so that the water qual-ity standards are attained for that waterbody” (USEPA, 1991). Once the necessary pollutant reductionsare identified through establishment of TMDLs,control measures such as best management practiceswill be implemented to bring water bodies intocompliance. The Wisconsin DNR plans to use simple,intermediate, and detailed levels of modeling forestablishment of TMDLs. If adopted, SWAT wouldbe used at the intermediate level of detail, whichinvolves quantification of pollutant loads using “amechanistic water quality modeling approach inconcert with estimates of barnyard and point sourceloads” (Panuska, 1999).

Proper implementation of SWAT for thesepurposes will require that decisions be made aboutthe size or number of subwatersheds used for model-ing. It is important to understand not only the degreeto which model output is affected by changes in thenumber of subwatersheds, but the exact mechanismsby which these changes occur. The types of scalinganalysis presented above can certainly provide this

information, but they do not readily lend themselvesto analysis by a broad range of users of differentmodels and applications. A more general frameworkis needed to compare alternative models within differ-ent watersheds. This paper examines the effects ofparameter aggregation, and from this analysis wedevelop two simple indexes that can predict modelscaling behavior from input data within a geographicinformation system without running SWAT.

2. Methodology

2.1. SWAT model description

SWAT is a long-term simulation model capable ofpredicting sediment, nutrient, and pesticide yieldsfrom agricultural watersheds. It is a public domainmodel supported by the US Department of Agricul-ture, Agricultural Research Service at the Grassland,Soil and Water Research Laboratory in Temple, TX,USA. SWAT uses a modified version of the SCS CNmethod for predicting runoff (USDA-SCS, 1972), anduses the Modified Universal Soil Loss Equation(MUSLE) (Williams and Berndt, 1977) to predictsediment generation. The important equations usedby SWAT are summarized below. A completedescription can be found in Arnold et al. (1998).

SWAT calculates channel sediment transport usingthe following equation:

T � a × Vb �1�

whereT, is the transport capacity (ton/m3); V, is flowvelocity (m/s); anda andb, are constants. Dependingon whether the amount of sediment being carried isabove or below transport capacity, SWAT eitherdeposits excess sediment or re-entrains sedimentthrough channel erosion. Flow velocity is computedas:

V � Fw × d

�2�

where F, is the flow volume (m3/s); w, is channelwidth (m); andd, is depth of flow (m). For flowsbelow bankfull depth, depth of flow is calculatedusing Manning’s equation, assuming that channel

T.W. FitzHugh, D.S. Mackay / Journal of Hydrology 236 (2000) 35–53 37

width is much greater than depth:

d � F × n

w × cs0:5

� �0:6

�3�

wheren, is the Manning’s roughness coefficient forthe channel; and cs, is channel slope (m/m). For flowsabove bankfull depth, depth of flow is equal to channeldepth.

The MUSLE equation used to estimate sedimentgeneration is as follows:

Y � 11:8�Q × pr�0:56K × C × P × LS �4�whereY, is the sediment generation (metric tons);Q,is volume of runoff (m3); pr, is peak runoff rate (m3/s);K, is K-factor;C, is C-factor;P, is P-factor; and LS, isLS-factor. For each day with rainfall and runoff, sedi-ment generation is estimated by applying Eq. (4) foreach HRU in the watershed.

Peak runoff rate is calculated using a modifiedversion of the Rational equation (USDA-SCS 1986):

pr� a × q × A360× tc

�5�

where pr, is the peak runoff rate (m3/s); q, is runoff(mm);A, is HRU area (ha);tc, is time to concentration(h); and a , is a dimensionless parameter thatexpresses the proportion of total rainfall that occursduring tc. The value ofa is calculated as:

a � a1 × tp6tp5

� �× tc

6

� �a2

�6�

wherea1 is the fraction of rainfall that occurs during0.5 h; tp6 and tp5 are the 10-year frequencies of a 6and 0.5 h rainfall, respectively, derived from Hersch-field (1961); anda2 is a constant equal to 0.242 forDane County, Wisconsin.

SWAT computes time to concentration bysumming channel time to concentration and overlandtime to concentration for the HRU. Channel time iscomputed as:

ct� 0:62× L × n0:75

A0:125 × cs0:375 �7�

where ct, is the channel time to concentration (h);L, ischannel length (km);n, is Manning’s roughness coef-ficient for the channel;A, is HRU area (km2); and cs,

is channel slope (m/m). Overland time is computed as:

ot� 0:0556�sl × n�0:6s0:3 �8�

where ot, is the overland time to concentration(hours); sl, is average subwatershed slope length(m); n, is Manning’s overland roughness coefficientfor the HRU; ands, is overland slope (m/m).

The version of the model used in this research wasSWAT 98.1 (Neitsch et al., 1999) for Windows NT95/4.0. The SWAT Arcview interface (DiLuzio et al.,1998), also distributed by the Agricultural ResearchService, was used to derive model parameters fromGIS data layers and create parameter files. TheTOPAZ (Topographic Parameterization) digital land-scape analysis package (Garbrecht and Martz, 1995)was used to partition the watershed into subwater-sheds and delineate the channel network. C11 codewas also written to calculate statistics of input para-meters, and to alter input parameters for purposes ofland-cover simulations and for sensitivity analyses.

2.2. Study site and data

The study site for this research is the PheasantBranch watershed in Dane County, Wisconsin (seeFig. 1). It is primarily an agricultural watershed,with flat to rolling terrain and mostly silt loam soils.The Pheasant Branch watershed is part of the largerLake Mendota watershed, which is a Wisconsin DNRpriority watershed for purposes of controllingnonpoint source pollution. Lake Mendota has under-gone heavy eutrophication because of excessiveinputs of phosphorus from commercial fertilizersand manure, a significant portion of which is carriedinto the lake by eroding soils (Wisconsin DNR, 1997).

The input data used for this research are listed inTable 1. Geographic information system (GIS) layersof terrain, soils, and land-cover data were used toprepare SWAT input parameters. Weather recordsfrom a nearby weather station were used to preparemetereological inputs. Stream gauge data were used toevaluate model accuracy and for calibration purposes.

2.3. Watershed delineation and modelparameterization

The methodology for this research consisted ofcreating a series of watershed delineations, each


with a different number of subwatersheds and HRUs,and running SWAT for each watershed delineation.Model runs were conducted using metereologicalinputs for the period of 1990–1996, using measuredprecipitation and minimum and maximum tempera-tures from the Charmany Farm weather station. Allyears during 1990–1996 had above average rainfall.

The Pheasant Branch watershed was partitionedinto 8 different watershed delineations. Table 2shows the characteristics of each delineation. Fig. 2shows maps of these delineations. Critical source area(CSA) and minimum source channel length (MSCL)are the input parameters to TOPAZ which control thenumber and size of subwatersheds and extent of thechannel network, respectively. CSA is the minimumupstream drainage area below which a source channelcan be initiated and maintained. MSCL is the mini-mum acceptable length for a source channel. CSA andMSCL values were chosen so as to produce a widerange of subwatershed sizes.

A minimum of three subwatersheds was used toretain an internal channel link. Having one internalchannel link was desirable because SWAT’s sedimentrouting equations are not used for external channellinks. The maximum number of subwatersheds usedwas 181, because more detailed watershed delineations


Table 1Data sets used for SWAT parameterization

Data set Description

Terrain Dane County digital elevationmodel, gridded at 11.5 m.Produced by Ayres Associatefrom 1:31,680 aerial photographstaken in 1995.

Soils Digital soils data digitized fromDane County soil survey (scale1:15,840).

Land-cover WISCLAND classified satelliteimagery, gridded at 30 m. Fromclassification of Landsat TMsatellite imagery from 1991–1993. (Wisconsin DNR, 1999)

Weather Daily precipitation and minimumand maximum temperature datafrom the Charmany Farm NationalWeather Service Cooperativestation (#471416), slightly southand east of the watershed.

Streamflow and sediment Daily runoff and sediment datafrom the US Geological Surveygauging station (#05427948) onPheasant Branch.

Fig. 1. Study site location.

were found to contain an increased percentage ofspurious (small or highly elongated) subwatersheds.

SWAT allows these subwatersheds to be furthersubdivided into HRUs, each of which represents aparticular combination of soil and land-cover withinthe subwatershed. HRUs are used in an aspatial manner,in the form of probability distributions of covarying soiland land-cover characteristics within each subwa-tershed. Terrain parameters are identical for all HRUswithin a given subwatershed, except for the channellength parameter used to compute time to concentra-tion, which varies depending on the size of the HRU.

The number and area of HRUs in each

subwatershed is calculated by applying user-specifiedland-cover and soil area thresholds. The thresholdsused in this research were both 10%. In practice,this means that HRUs are composed of land-covertypes that occupy at least 10% of the area in eachsubwatershed, combined with soil types that occupyat least 10% of the area of that land-cover type. Thesepercentage thresholds cause the number of HRUs toincrease as the number of subwatersheds is increased.

2.4. Model accuracy

The “goodness-of-fit” of the predicted and


Fig. 2. Watershed delineations for the Pheasant Branch watershed. The lines represent divides between subwatersheds and the main channelsegment of each subwatershed.

Table 2Key properties for the watershed delineations used in this study

Subwatersheds 3 5 11 23 47 73 97 181

HRUs 29 64 138 244 425 638 831 1384

Subwatershed average area (ha) 1593 956 435 208 102 65 49 26HRU Average area (ha) 165 75 35 20 11 7 6 3

Critical source area (ha) 300 250 200 80 50 30 20 10Minimum source channel length (m) 3000 2000 1000 400 300 210 180 140

measured data was measured by using a modifiedcoefficient of efficiency (MCOE), as recommendedby Legates and McCabe (1999). This measure is simi-lar to the traditional Nash-Sutcliffe coefficient of effi-ciency (Nash and Sutcliffe, 1970), in that it measuresthe goodness-of-fit of simulated and measured data tothe line-of-perfect-fit (the 1:1 line) (Aitken, 1973).However, the modified version inserts an absolutevalue where the original version had a squared term,thereby reducing the sensitivity of the measure tooutlying values in the dataset. The MCOE rangesfrom minus infinity to 1.0, with higher values indicat-ing better agreement. Mean absolute error (MAE) wasalso used to evaluate accuracy, again as recommendedby Legates and McCabe (1999).

2.5. Basis for evaluating sediment predictive responseto aggregation

A sensitivity analysis was made to ascertain theunderlying causes of aggregation effects on sedimentgeneration. The inputs to the MUSLE equation werefirst individually evaluated in terms of their responseto aggregation effects. This form of sensitivity analy-sis can be of limited use when there are many spatiallycovarying parameters. An aggregation effect on onevariable could be suppressed or enhanced by an aggre-gation effect on one or more other variables. Alterna-tively, a series of parameters might in combinationproduce a predictable response to aggregation. Ouranalysis proceeded towards identifying a small setof indexes derived from the input parameters. A fulldescription of these indexes is reserved for the discus-sion section where they can be more meaningfullyrelated to our analysis.

3. Results

3.1. Streamflow and runoff

Fig. 3 shows comparisons of annual and averagemonthly measured and uncalibrated simulated stream-flow. Although average annual streamflow is under-predicted, for all except the coarsest watersheddelineation it is within 20% of measured flows. Aver-age monthly values are less accurate, with streamflowbeing overpredicted for April, June and July, andbeing underpredicted for other months. The MCOEusing annual streamflow ranges from 0.117 to 0.248,and MAEs range from 0.043 to 0.037 m3/s (see Table3). MCOEs using monthly streamflow range from20.249 to20.208, and MAEs range from 0.130 to0.126 m3/s (see Table 4). Predictions are less accuratefor monthly output, and improve slightly as subwa-tershed size decreases for both monthly and annualoutputs. Because model accuracy was not found tobe greatly affected by changing the watershed delinea-tion, it is not a focus of these results and discussion.

No calibration of annual streamflow was attempted,because the model developers’ recommend calibra-tion until water yield is within 10–20% of measuredamounts. Monthly calibration was attempted in orderto get a better fit between average monthly predictedand measured data. A proper fit to the monthly datawould require a decrease in flows for April and June,and increases for most other months. However, noneof the recommended calibration methods was found toproduce such a change in model output. Recom-mended variables for calibration of temporal patternsof streamflow are channel hydraulic conductivity,baseflow alpha factor, maximum and minimum melt


Table 3Accuracy statistics for annual streamflow

Average subwatershedarea (ha)

Modified coefficientof efficiency

Mean absoluteerror (m3/s)

1593 0.117 0.043956 0.170 0.040435 0.202 0.039208 0.199 0.039102 0.216 0.03865 0.223 0.03849 0.239 0.03726 0.248 0.037

Table 4Accuracy statistics for monthly streamflow

Average subwatershedarea (ha)


Mean absoluteerror (m3/s)

1593 20.249 0.130956 20.232 0.129435 20.234 0.129208 20.237 0.129102 20.225 0.12865 20.218 0.12749 20.219 0.12726 20.208 0.126

rates for snow, and temperature lapse rate (Arnold etal., 1997). Altering the baseflow alpha factor andtemperature lapse rate had no impact on streamflow.Changing the effective hydraulic conductivity causedmonthly averages to increase or decrease by compar-able amounts for all months. Lastly, while streamflowin winter months could ideally have been increased byincreasing snow melt rates, in practice this had littleeffect because the default settings of the melt rateparameters (used in the model runs presented here)were only slightly lower than the maximum recom-mended values for those parameters.

Streamflow increases by only 12% between thecoarsest and finest watershed delineations. Thispattern of a slight increase in streamflow was evidentin annual, monthly, and daily model output. Fig. 4

shows surface runoff, transmission gains and losses,and streamflow leaving the watershed. Surfacerunoff is practically identical for all watershed deli-neations. However, as the subwatersheds becomesmaller, transmission gains (subsurface flow andgroundwater recharge) tend to increase, and transmis-sion losses tend to decrease, leading to a net increasein streamflow.

3.2. Sediment yield

Fig. 5 shows a comparison of annual and averagemonthly measured and uncalibrated simulated outletsediment. Average annual outlet sediment is severelyunderpredicted by the model, as are most of themonthly averages. MCOE for annual outlet sediment


Fig. 3. Predicted streamflow for each watershed delineation, and measured streamflow: (A) annually for 1990–1996; and (B) averaged bymonth for the same period.


Fig. 4. Runoff, streamflow, and transmission gains and losses, by average subwatershed area, 1990–1996 annual average. Transmission gainsare from subsurface flow and groundwater recharge into the channels.

Fig. 5. Annual outlet sediment. (A) Shows predicted outlet sediment for each watershed delineation, and measured outlet sediment, annually for1990–1996. (B) Shows average monthly outlet sediment, by watershed delineation (uncalibrated).

ranges from20.158 to 20.218, and MAEs rangefrom 1243 to 1306 metric tons (see Table 5). Formonthly outlet sediment the MCOE ranges from0.418 to 0.430, and MAEs range from 125.5 to122.9 metric tons (Table 6). The slight improvementof monthly MCOE over annual values is mainly dueto an improved fit in part because of the larger samplesize. It can also partly be attributed to the low sensi-tivity of MCOE to outliers. Average monthly sedi-ment outputs conform to the same pattern asaverage monthly streamflow, indicating that changesin sediment between successive months are beingdriven by changes in streamflow.

SWAT’s sediment output can be calibrated tomeasured data by increasing the coefficient,a, in thechannel transport equation (Eq. (1)). Increasingthe coefficient decreases deposition and increasesthe accuracy of average annual sediment output. Fig.6 shows sediment predictions when using a calibrationcoefficient of 0.0003 (see also Table 7), whichprovides a good fit between average annual measuredand predicted outlet sediment. The reader should notethat Eq. (1) could also be tuned by adjusting the expo-nent,b. However, because of the nonlinearity of sedi-ment transport with respect tob, doing so would yieldmarginal improvement at one level of aggregation atthe expense of a poor fit at the other levels. Becausemonthly changes in outlet sediment are being drivenby monthly changes in streamflow, and because it wasimpossible to obtain an accurate calibration of monthlystreamflow, it was also not possible to accurately cali-brate monthly sediment output to measured data. Aswith streamflow, model accuracy is not greatlyaffected by changing the watershed delineation, andso it is not a focus of these results and discussion.

Fig. 7A shows average annual outlet sediment foreach watershed delineation, uncalibrated and cali-brated with a� 0:0003: Outlet sediment decreasesby only 9% between the coarsest and finest watersheddelineations. Calibration of average annual outletsediment had no impact on the relationship betweenmodel output and subwatershed size, because increas-ing the calibration coefficient acts as a constant multi-plier on outlet sediment predictions. The pattern of aslight decrease in sediment yield was observed in theannual and monthly results. Daily model outputsgenerally conform to the same pattern, the mainexception being extremely small sediment events.Fig. 7B shows sediment generation in the subwater-sheds, and channel deposition. Sediment generationchanges substantially as the number of subwatershedsis increased, dropping by 44%. However, sediment isdeposited into the channels at the same rate as sedi-ment generation, and so outlet sediment stays almostconstant.

4. Discussion

4.1. Streamflow and runoff

Surface runoff is unchanged for different watersheddelineations because it is strongly related to the CNparameter, whose area-weighted mean value is almostidentical for all watershed delineations. Mean CNvalues range from 68.4 to 69.1. The constant stream-flow predictions are consistent with the results ofBingner et al. (1997), who used a similar sizedwatershed (2130 ha), but did not use HRUs. Theyare consistent with the results of Mamillapalli et al.


Table 5Accuracy statistics for uncalibrated annual outlet sediment

Average subwater-shed area (ha)


Mean absolute error(metric tons/year)

1593 20.158 1243956 20.145 1228435 20.198 1285208 20.198 1286102 20.226 131565 20.206 129449 20.208 129626 20.218 1306

Table 6Accuracy statistics for uncalibrated monthly outlet sediment



Mean absolute error(metric tons/month)

1593 0.418 126956 0.417 126435 0.427 124208 0.427 124102 0.428 12365 0.429 12349 0.429 12326 0.430 123

(1996) when HRUs were created using soil- and land-cover thresholds of 5% and 10%. Mamillapalli et al.(1996) found that coefficients of efficiency (COEs)varied only slightly when changing the size of subwa-tersheds while using these thresholds. When largersoil- and land-cover thresholds were used for creating

HRUs, COEs stayed fairly constant when thewatershed was divided into 14 or more subwater-sheds. Note that Mamillapalli et al. (1996) used amuch larger watershed (430,000 ha) than PheasantBranch. When Mamillapalli et al. (1996) partitionedtheir watershed into subwatersheds nearest in size tothe ones used in this study, the results were similarto those presented here.

4.2. Outlet sediment

Sediment leaving the watershed is almost constantover the range of watershed delineations. The Phea-sant Branch watershed as simulated is transport-limited, meaning that more material can be detachedthan can be carried away by transport processes(Ahnert, 1998). In a transport-limited watershedmore sediment is being generated in upland areasthan the stream channels can transport (Keller et al.,


Fig. 6. (A) Average annual outlet sediment, by watershed delineations (calibrated witha� 0:0003�: (B) Average monthly outlet sediment, bywatershed delineation (calibrated witha� 0:0003�:

Table 7Accuracy statistics for calibrated annual outlet sediment



Mean absolute error(metric tons/year)

1593 0.292 759956 0.263 791435 0.249 805208 0.250 805102 0.226 83065 0.246 81049 0.241 81426 0.223 833

1997). Changes in outlet sediment would only occur ifchanging the watershed delineation affected the trans-port capacity of the channel network. Here, outletsediment is controlled by the transport capacity ofjust the outlet channel. Outlet sediment is relativelystable because the parameters of the outlet channel areidentical for all watershed delineations.

The slight changes in transport capacity betweenaverage subwatershed sizes of 435 and 26 ha aredue to changes in the slopes of channel links nearthe outlet of the watershed. These changes occurwhen existing channel links are sub-divided duringthe process of delineating the watershed into smallerand smaller subwatersheds. Changes in slopes furtherup in the watershed do not affect outlet sediment. Anydeposition that occurs in these channels is replaced bysediment generated further down in the watershed orby channel erosion in the channel links nearest the

outlet. If changes in slopes increase the transportcapacity of upstream channel links, the additionalsediment transported from the channels is depositedfurther downstream in the channel network.

The slight increase in average outlet sediment whenaverage subwatershed size is decreased from 1593 to956 ha is caused by an increase in streamflow. Forboth delineations, more sediment enters the outletchannel than can be transported, because in eachcase at least one of the channel links draining intothe outlet channel is an external channel link.SWAT does not calculate deposition or channelerosion for external channel links as this is implicitin MUSLE. Since the parameters of the outlet channeldo not change, flow volume is the only variable inEqs. (2) and (3) that changes for this channel betweenthese two delineations. The decrease in average outletsediment when average subwatershed size is


Fig. 7. (A) Average annual sediment yield, by subwatershed area (uncalibrated and calibrated witha� 0:0003�; for period 1990–1996. (B)Sediment generation and estimated channel deposition.

decreased from 956 to 435 ha is due to the conversionof the single external channel link draining into theoutlet channel to an internal channel link. Of the twointernal channel links subsequently draining into theoutlet reach, the one with greater flow has a substan-tially lower slope than the outlet channel, so sedimententering the outlet channel is now less than its trans-port capacity. Channel erosion does not fully make upfor this difference, leading to a decrease in outletsediment.

These results differ from the results of Bingner et al.(1997), who found that SWAT’s predictions of sedi-ment leaving the watershed increased substantially asthe watershed delineation became more detailed.They attributed these changes to changes in subwa-tershed slope and land-cover parameters. The currentresearch highlights the importance of channelprocesses, rather than only subwatershed characteris-tics, in determining the behavior of SWAT outlet sedi-ment predictions. One possible reason for thesedifferent results is that SWAT’s channel transportalgorithm has changed since the research of Bingneret al. (1997). The equations in SWAT 98.1 (Neitsch etal., 1999) are different from those used in the prior

version of the model. The previous version of themodel estimated transport based on a sediment deliv-ery ratio calculated from sediment fall velocity, chan-nel travel time, and depth of flow (Arnold et al., 1997).

4.3. Sediment generation

Unlike outlet sediment, sediment generation in thesubwatersheds drops substantially as subwatershedsize decreases. This decrease is due to changes inthe statistical distribution of MUSLE input para-meters, and more importantly, to the sensitivity ofthe runoff term in the MUSLE equation to decreasesin HRU area.

Changing the watershed delineation affects themean values of the standard USLE inputs,K, C, andLS. Mean P does not change because its value isconstant for all HRUs. Figs. 8A–D show area-weighted means ofK, C, and LS individually, andthe product ofK × C × LS calculated at the HRUlevel, for each watershed delineation. Changes in thestatistical distribution of these factors combine tocause a slight decrease in sediment generation assubwatershed size is reduced.


Fig. 8. Mean MUSLE inputs (area-weighted), by average subwatershed area: (A) showsC-factor; (B) showsK-factor; (C) shows LS-factor; and(D) showsK × C × LS:

Mean K-factor declines with decreases in subwa-tershed size because the most common soil types inthe watershed haveK-factors of 0.37, and lesscommon soil types have lowerK-factors (Fig. 9).With large subwatersheds, the lowerK-factor soilsare filtered out of the parameter distribution. Assubwatershed size is reduced down to 208 ha, lowerK-factors are introduced into the distribution, causingthe mean to drop. Similarly, mean minimumC-factorstarts to decrease at about the same subwatershed sizewhere meanK-factor levels off. Fig. 10 shows therelative amounts of area represented by each ofthree groups ofC-factors. The differences betweendifferent watershed delineations are mostly due todecreases in the area of corn�C-factor� 0:2�; apredominant land-cover type in our study site, andincreases in the area of deciduous forest�C-factor�0:001�; a much less common type. Mean LS-factorincreases as subwatershed size decreases, due to theincreasing variability of overland slope values acrossthe watershed. The increase in LS is not enough tocounteract the decreases inK andC, and so the overalltrend in these factors is a slight decrease. However,this slight decrease does not explain the large drop insediment generation.

The second, more important, reason for thedecrease in sediment generation with decreases insubwatershed size is that the runoff term in theMUSLE equation decreases substantially as subwa-tershed, and hence HRU, size decreases. This occursbecause the inputs to that term, runoff volume (Q) andpeak runoff rate (pr), vary depending on the area of theHRU for which they are being calculated. Since the

runoff term is nonlinear with respect to HRU area, itsaverage contribution to sediment generation differsdepending on whether it is calculated using a smallnumber of large HRUs, or a large number of smallHRUs.

Runoff is unrelated to changes in subwatershedarea, so on average, changes in subwatershed sizewill causeQ to change in direct proportion to differ-ences in HRU area. Likewise, pr changes almostexclusively in proportion to changes in HRU area.The only two inputs to Eqs. (5) and (6) that changein response to changes in HRU area areA andtc. Timeto concentration changes much more slowly thanHRU area, and so changes in pr are almost exclusivelydetermined by changes inA.

Average time to concentration decreases slightlybetween the coarsest and finest watershed delinea-tions, from 0.81 to 0.67 h. This decrease is minorbecause, of the two components of total time toconcentration, only channel time changes in responseto changes in HRU area, mainly due to changes inL.In contrast, overland time does not change, becausenone of the inputs to Eq. (8) change in response tochanges in HRU area. In addition, for HRUs in therange of sizes being used in this research, channeltime is a much smaller portion of total time to concen-tration than is overland time. For the coarsestwatershed delineation, average channel time is 0.2 h,while average overland time is 0.61 h. For the finestwatershed delineation, the proportion of total time toconcentration due to channel time is even less, and so


Fig. 9. Soil types, byK-factor and percent area. Each point repre-sents a single soil type. Fig. 10. Areal distribution ofC-factors, by average subwatershed

area.

total time to concentration does not change at nearlythe rate that HRU area changes.

Since the area inputs toQ and pr are the only inputsto the MUSLE runoff term that change substantiallywith changes in subwatershed size, the behavior ofthat term can be approximated with:

�A × A�0:56 � A1:12 �9�Dividing the result of Eq. (9) by HRU area gives anestimate of the contribution of the runoff term to sedi-ment generation per unit area. Calculating the area-weighted mean of this estimate for all HRUs yields anindex of the average impact of MUSLE’s runoff termon sediment generation for the entire watershed. Thisindex, which can be called the MUSLE Area MeanIndex (MAMI), is computed as follows:

MAMI �Xni�1

wi × Ai1:12

Ai

!�10�

wheren, is the number of HRUs; andw, is the ratio ofHRU area to watershed area. Fig. 11 shows the MAMIfor each watershed delineation. Because Eq. (10) isnon-linear, the value of this index drops substantiallyas the average size of the subwatersheds and HRUsdecreases. The areas used in calculating the index arethe number of DEM pixels in each HRU. The arealunit used in the calculation is unimportant, becausewhile the values of the MAMI differ depending on theunits used, the percent changes between the differentwatershed delineations are identical.

Fig. 12 shows the relationship between sedimentgeneration and a second index, which can be called

the MUSLE Output Mean Index (MOMI). The MOMIis computed as follows:

MOMI �Xni�1

wi × Ai1:12

Ai× Ki × Ci × LSi

! !i

�11�

Because it accounts for all of the inputs to the MUSLEequation that change with changes in HRU area, theMOMI provides an effective linear model of SWAT’ssediment generation estimates. Separating it intomeanK × C × LS and the MAMI identifies the contri-bution of the different MUSLE inputs to changes insediment generation. MeanK × C × LS decreases by14% between the coarsest and finest watershed deli-neations (see Fig. 8). MAMI decreases by 36%between the coarsest and finest watershed delineations(see Fig. 11). This demonstrates that the decrease insediment generation as subwatershed size decreases isprimarily due to the nonlinear relationship betweenthe MUSLE runoff term and HRU area, as expressedby the MAMI, and only secondarily, to changes in thevalues ofK, C, and LS.

It is important to note that the behavior of the runoffterm would change in larger watersheds where chan-nel time is a larger proportion of total time to concen-tration. Total time, because of changes in channeltime, would then decrease more drastically withdecreases in HRU area. These decreases would offsetthe decreases inA Eq. (5), yielding a peak runoff ratethat is less sensitive to decreases in HRU area. Thiswould reduce the change in sediment generationpredictions as subwatershed size is decreased. Notethat changes in time to concentration influence peakrunoff rate not only through Eq. (5), but also through


Fig. 11. MUSLE area mean index, by average subwatershed area.

Fig. 12. Sediment generation vs. MOMI. Each point represents asingle watershed delineation.

the value ofa (as computed in Eq. 6). The influenceof tc ona is limited because the value of its exponent,a2, is only 0.242.

Channel time would likely be a greater proportionof total time in a larger watershed than the one usedhere, assuming that the subwatersheds were alsolarger. Larger subwatersheds would have longer chan-nel lengths, which would lead to increased channeltimes to concentration. A similar result might occurif HRUs were not used, i.e. if only a single soil andland-cover type were used for each subwatershed.SWAT calculates channel length for each HRU bymultiplying the channel length of the subwatershedby the ratio of HRU area to subwatershed area. Ifeach subwatershed was modeled as a lumped unit,channel lengths would be longer, and again the chan-nel time would be a much greater portion of total timeto concentration.

The version of SWAT 98.1 used in this research hasan option that allows channel time for HRUs to becalculated using the original subwatershed channellength rather than the HRU channel length describedabove. This option was used to investigate the impactson sediment generation of increasing the proportion oftotal time to concentration due to channel time. Fig.13 shows sediment generation results for model runsconducted using both options.

Using the subwatershed channel length yields aver-age times to concentration that drop from 2.51 to0.87 h between the coarsest and finest watersheddelineations, as compared with 0.81 to 0.67 h whenusing HRU channel lengths. When using the longer

subwatershed channel lengths, channel time is largerand hence is also a larger proportion of total time toconcentration. This causes total time to concentrationvalues to be larger and to change more drasticallybetween watershed delineations. Consequently, peakrunoff rates are lower than when using the HRU chan-nel length, and peak runoff rate and hence the MUSLErunoff term no longer decrease so drastically withdecreases in HRU area. This leads to sediment genera-tion estimates that are lower and that change lessdrastically with changes in subwatershed size. Theimplication is that if channel time was a greaterproportion of overall time, as would occur in a largerwatershed than the one used here, SWAT’s sedimentgeneration estimates would be less sensitive tochanges in subwatershed size.

5. Conclusions

The model results for the Pheasant Branchwatershed lead to the following conclusions:

1. Streamflow is not seriously affected by decreases insubwatershed size. This is due to a lack of changein runoff, which is due to a similar trend in themean CN parameter.

2. Sediment generation decreases substantially withdecreases in subwatershed size. This trend isprimarily due to the sensitivity of the runoff termin the MUSLE equation to HRU area, and is alsorelated to changes in the statistical distribution ofK- andC-factors throughout the watershed.

3. Outlet sediment is not seriously affected bychanges in subwatershed size. This is hypothesizedto be due to the transport-limited nature of thewatershed and the lack of changes in channel trans-port capacity.

The difference between the behavior of sedimentgeneration and outlet sediment leads to the questionof how SWAT would behave in a source-limitedwatershed. Source-limited (or weathering-limited)denudation occurs when more material can be trans-ported away than can be detached (Ahnert, 1998). In asource-limited watershed, stream channels can trans-port more sediment than is being generated in theupland areas of the watershed (Keller et al., 1997).


Fig. 13. Sediment generation using two channel length options, byaverage subwatershed area.

The practical question of what subwatershed size touse in modeling the Pheasant Branch watershedshould be discussed here. For the purpose of predict-ing the amount of streamflow and sediment leavingthe watershed, the answer would be to use the coarsestwatershed delineation. There is no reason to increasethe number of subwatersheds, because it does notsubstantially affect model output or increase the accu-racy of predictions. One of the implications of thisresearch is that for a transport-limited watershedsuch as Pheasant Branch, accurate outlet sedimentestimates require only that the transport capacity ofthe lower part of the channel network be accuratelysimulated. The precise characteristics of the uplandsediment generating areas can for the most part beignored, if only predictions of outlet sediment aredesired. The importance of the lower part of the chan-nel network has implications for the direction of futuredata collection and model evaluation activities.

If model outputs are being calibrated to measureddata, the low sensitivity of outlet sediment generationto parameter aggregation is a positive aspect of themodel’s behavior. The amount of outlet sediment canbe adjusted by changing the coefficient,a, in the sedi-ment transport equation (Eq. (1)). Changinga acts as amultiplier on outlet sediment, and the impact is thesame for all watershed delineations. The fact that allwatershed delineations can be calibrated with thesame value ofa should make calibration of themodel easier to implement.

SWAT model users need to understand that in atransport-limited watershed such as Pheasant Branchthe stability of outlet sediment predictions does notimply that sediment generation estimates are alsoconstant. Indeed, if the model is being used to producesediment generation estimates for upland areas in thewatershed, then the decision about which subwa-tershed size to use is more difficult to make. Predic-tions of sediment generation vary by 44% between thecoarsest and finest watershed delineations, and datadoes not exist to determine which of these estimatesis more accurate. Future studies in watersheds withnested gauges would likely provide useful insight onthis aspect of model behavior.

The indexes developed in this paper, MAMI andMOMI, could be incorporated directly into GIS soft-ware to be used to make predictions about sedimentgeneration estimates prior to conducting model runs.

For example, they could be used to predict sedimentgeneration for detailed watershed delineations frominput parameter values and model outputs for lessdetailed delineations. Model users could benefitfrom such a set of simple indexes incorporated intowidely available GIS software. These could assistwith the evaluation of alternative models, weighingthe costs and benefits of data collection, and matchingdata to model. The approach taken in deriving theindexes should not be limited to just SWAT and thespecific watershed studied here. It should be possibleto develop indexes for predicting the scaling behaviorof other hydrologic models. Further research isneeded to identify whether indexes such as MAMIand MOMI can become useful tools during theprocess of implementing hydrologic and other envir-onmental models.

One result presented here that has not beendiscussed in previous research on SWAT is the impor-tance of channel parameters in determining how outletsediment predictions react to changes in the size ornumber of subwatersheds. Future research is neededto ascertain whether the transport capacity of thelower part of the channel network is as stable forother transport-limited watersheds as it is for thePheasant Branch watershed. The length, slope, anddimensions of the Pheasant Branch outlet channelwere identical for all watershed delineations. Otherwatersheds may not exhibit this and may producemore drastic changes in outlet sediment predictions.Research is also needed to determine how best toaccurately simulate channel transport capacity forthe lower portion of the watershed, either throughcalibration or through modification of modelalgorithms.

Finally, previous research on SWAT has notconsidered the sensitivity of sediment generation tosubwatershed size when detailed HRUs are used. It ispossible that using SWAT with small HRUs is whatled to sediment generation estimates that varysubstantially depending on subwatershed size. Furtherresearch is needed to determine if the substantialchange in sediment generation disappears whenHRUs are much larger in size than the ones usedhere. This might occur if SWAT was applied to awatershed that is much larger, or has more homoge-neous land-cover, than the Pheasant Branchwatershed.


Acknowledgements

The authors thank John Panuska at the WisconsinDepartment of Natural Resources for his valuableinput on the direction of this research, and for hisefforts in providing funding this project. Paul Baum-gart of the Fox-Wolf Basin 2000 organizationprovided invaluable assistance in debugging andrecompiling the FORTRAN code for the SWATmodel. Assistance in using SWAT and the Arcviewinterface was also provided by Susan Neitsch andother staff at the Blackland Research Center, TexasAgricultural Experiment Station in Temple, TX.Funding for this research was provided by the USEnvironmental Protection Agency through a subcon-tract with the Wisconsin Department of NaturalResources, under the Wisconsin TMDL 104(b)(3)funding program. A portion of this study wasconducted using the computing facilities of the Inte-grated Remote Sensing Resource Center, establishedwith support from NASA (NAG5-6535). Finally, theauthors thank Dr Jeffrey Arnold and an anonymousreviewer whose suggestions have improved thismanuscript.

References

Ahnert, F., 1998. Introduction to Geomorphology, Arnold, London.Aitken, A.P., 1973. Assessing systematic errors in rainfall-runoff

models. Journal of Hydrology 20, 121–136.Arnold, J.G., Srinivasan, R., Muttiah, R.S., Williams, J.R., 1998.

Large area hydrologic modeling and assessment part I: modeldevelopment. Journal of American Water Resources Associa-tion 34 (1), 73–89.

Arnold, J.G., Williams, J.R., Srinivasan, R., King, K.W., 1997.SWAT Documentation. Temple, Tex.: Blackland ResearchCenter, Texas Agricultural Experiment Station. http://www.brc.tamus.edu/swat/swatdoc.html.

Band, L.E., 1989. Spatial aggregation of complex terrain. Geogra-phical Analysis 21 (4), 279–293.

Beasley, D.B., Huggins, L.F., Monke, E.J., 1980. ANSWERSUser’s Manual. Purdue University, West Lafayatte, IN, USA.

Bingner, R.L., Garbrecht, J., Arnold, J.G., Srinivisan, R., 1997.Effect of watershed subdivision on simulation runoff and finesediment yield. Transactions of the ASAE 40 (5), 1329–1335.

Brown, D.G., Bian, L., Walsh, S.J., 1993. Response of a distributedwatershed erosion model to variations in input data aggregationlevels. Computers and Geosciences 19 (4), 499–509.

DiLuzio, M., Srinivasan, R., Neitsch, S.L., 1998. SWAT ArcviewInterface User’s Guide For SWAT, 98.1: 1998 Beta Release.

Blackland Research Center, Texas Agricultural ExperimentStation, Temple, TX, USA.

Garbrecht, J., Martz, L.W., 1995. TOPAZ: An automated landscapeanalysis tool for topographic evaluations, drainage identifica-tion, watershed segmentation and subcatchment parameteri-zation; Overview. ARS Pub. No. NAWQL 95-1. US Dept. ofAgriculture, Agricultural Research Service, Durant, OK,USA.

Herschfield, D.M. 1961. Rainfall frequency atlas of the UnitedStates for durations from 30 minutes to 24 hours and returnperiods from 1 to 100 years. US Dept. Commerce Tech. PaperNo. 40. Washington DC: US Dept. of Commerce.

Keller, E.A., Valentine, D.W., Gibbs, D.R., 1997. Hydrologicresponse of small watersheds following the Southern CaliforniaPainted Cave Fire of June 1990. Hydrologic Processes 11 (4),401–414.

Legates, D.R., McCabe Jr., G.J., 1999. Evaluating the use of “good-ness-of-fit” measures in hydrologic and hydroclimatic modelvalidation. Water Resources Research 35 (1), 233–241.

Mamillapalli, S., Srinivasan, R., Arnold, J.G., Engel, B.A., 1996.Effect of spatial variability on basin scale modeling. Proceed-ings, Third International Conference/Workshop on IntegratingGIS and Environmental Modeling, Santa Fe, New Mexico,January 21–26, 1996. National Center for Geographic Informa-tion and Analysis, Santa Barbara, CA, USA. http://www.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/main.html.

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting throughconceptual models, 1: A discussion of principles. Journal ofHydrology 10, 282–290.

Neitsch, S.L., Arnold, J.G., Williams, J.R., 1999. Soil and WaterAssessment Tool user’s manual: version 98.1. Grassland, Soiland Water Research Laboratory, Agricultural Research Service,and Blackland Research Center, Texas Agricultural ExperimentStation, Temple, TX, USA.

Panuska, J.C., 1998. Wisconsin Department of Natural Resources,personal communication.

Panuska, J.C., 1999. Wisconsin Department of Natural Resources,personal communication.

USDA-SCS, 1972. National Engineering Handbook, HydrologySection 4, chap. 4–10. US Dept. of Agriculture, Soil Conserva-tion Service, Washington, DC, USA.

USDA-SCS, 1986. Urban hydrology for small watersheds. Tech.Release 55. US Dept. of Agriculture, Soil Conservation Service,Washington, DC, USA.

US EPA, 1991. Guidance for Water Quality-Based Decisions: TheTMDL Process. EPA 440/4-91-001. US Environmental Protec-tion Agency, Office of Water, Washington, DC, USA. http://www.epa.gov/OWOW/tmdl/decisions/.

Vieux, B.E., Needham, S., 1993. Nonpoint-pollution model sensi-tivity to grid-cell size. Journal of Water Resources Planning andManagement 119 (2), 141–157.

Williams, J.R., Berndt, H.D., 1977. Sediment yield prediction basedon watershed hydrology. Transactions of ASAE 20 (6), 1100–1104.

Wisconsin DNR, 1997. Nonpoint Source Control Plan for the LakeMendota Priority Watershed Project: Project Summary.Publication WT-481-97. Wisconsin Department of Natural


Resources, Madison, WI, USA. http://www.dnr.state.wi.us/org/water/wm/nps/plans/mensum/mendota.htm.

Wisconsin DNR, 1999. WISCLAND Land Cover (WLC) Data.Wisconsin Department of Natural Resources, Madison, WI,USA. http://www.dnr.state.wi.us/org/at/et/geo/data/wlc.htm#WISCLAND.

Wood, E.F., Sivapalan, M., Beven, K., Band, L.E., 1988. Effects of

spatial variability and scale with implications to hydrologicmodelling. Journal of Hydrology 102, 29–47.

Young, R.A., Onstad, C.A., Bosch, D.D., Anderson, W.P., 1987.AGNPS, agricultural nonpoint source pollution model: Awatershed analysis tool. Conservation Res. Report 35. USDept. of Agriculture, Agricultural Research Service, Morris,MN, USA.


Documents

Impacts of input parameter spatial aggregation on an ...water.geog.buffalo.edu/mackay/pubs/pdfs/fitzhugh_mackay_joh.pdfw £ d –2ƒ where F, is the ﬂow volume (m 3/s); w, is channel