Ecological Modelling 119 (1999) 211–230

Surface water flow in landscape models: 2. Patuxentwatershed case study

Alexey A. Voinov *, Helena Voinov, Robert CostanzaInstitute for Ecological Economics (IEE), Uni6ersity of Maryland, P.O. Box 38, Solomons, MD 20688-0038, USA

Received 27 July 1998; received in revised form 8 January 1999; accepted 25 February 1999

Abstract

We developed a system for modeling regional, spatially explicit hydrology in a way that allows integration withbroader plant, nutrient, and socio-economic model components. The relatively coarse spatial and temporal resolutionof these broader components relative to existing hydrologic models requires a different approach to hydrologicmodeling. We developed a quasi-empirical model which still retains as much of the underlying process dynamics aspossible. We tested the approach in the Patuxent watershed, Maryland, USA where we needed a time step of 1 day(compared to 1 h in most hydrologic models) and a spatial resolution of 1 km2. The model was developed, calibratedand tested at several spatial and temporal scales and extensive testing shows that it performs at least as well as morecomplex hydrologic models, even using the 1 day and 1 km2 resolution. © 1999 Elsevier Science B.V. All rightsreserved.

Keywords: Landscape spatial modeling; Hydrology; Temporal and spatial resolution; DEM; Overland flow

1. Introduction

This is the second paper in the series on quasi-empirical modeling of surface runoff in complexlandscape models (see Voinov et al. (1998)). Largelandscape models are designed for analysis andmanagement over areas that are orders of magni-

tude greater than those traditionally encounteredin hydrological applications (Beven and Kirkby,1979; Beasley and Huggins, 1980; Grayson et al.,1992). Besides, hydrology plays an auxiliary rolein these applications with much further complex-ity embodied in the other modules involved. Inthis context the issues of scale and resolutionbecome especially important and certain trade-offs in hydrologic complexity are required.

Model complexity can be measured in threedimensions: temporal, spatial and structural, thelatter standing for the level of detail in describing

* Corresponding author. Tel.: +1-410-3267207; fax: +1-410-3267354.

E-mail address: voinov@cbl.umces.edu (A.A. Voinov)

0304-3800/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S 0304 -3800 (99 )00056 -3

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the processes, variables and interactions in thesystem. For the model to be feasible we need tocompromise between the three dimensions in or-der to keep the overall complexity within reason-able bounds. There are numerous examples offairly complex models (Park et al., 1979; Parton etal., 1988 etc.), which are spatially confined to onepoint or several boxes linked with simplified spa-tial fluxing. On the other hand there are examplesof models run as part of geographic informationsystems (GIS) (ESRI, 1992; Watkins et al., 1996;Ye et al., 1996) at a very high level of spatialresolution. These models are structurally sim-plifed, performing analysis of only some aspectsof landscape ecology. Their temporal resolutionalso tends to be more aggregated. This occursbecause even with the supercomputing power athand, the modeling process implies tedious analy-sis of model performance and calibration, whichis possible only up to a certain level of complex-ity. As the modeling system becomes overcompli-cated in all the three dimensions, its behavior getsas hard to predict and understand as the opera-tion of the real-life landscape.

The Patuxent watershed covers an area of2356.2 km2. It stretches for about 150 km fromthe Piedmont area of the Appalachians to theChesapeake bay (Fig. 1). The Patuxent landscapemodel (PLM) built for this watershed is an inte-grated ecological economic model and thereforeneeds to be fairly complex in order to cover avariety of issues of landuse development and lan-duse change in addition to interaction with eco-logical processes occurring at the landscape scale(Bockstael et al., 1995). Therefore it is especiallyimportant to find the right balance between thelevels of complexity in each of the model compo-nents and in its spatial and temporal resolution.

In this paper we focus on the hydrologic mod-ule of the model, because hydrology is probablyone of the most important transport mechanisms,both delivering the essential elements to the biotaand removing the constituents that are in excess.It is therefore the component that links othermodules spatially. Our previous experience withthe Everglades landscape model (ELM) (Voinovet al., 1998), turned out to be insufficient for thearea characterized by steeper hillslopes and al-most no standing water. The flow patterns in this

watershed were quite different, requiring a revi-sion of both the unit model and its spatialimplementation.

Our major goal was to build a terrestrial ana-logue to the hydrologic module previously devel-oped and calibrated for wetlands. In addition tothat we analyzed the model performance at avariety of scales to see in what way they weredifferent and what adjustments were requiredwhen switching from one resolution to another.The model has been constructed for two spatialresolutions and tested for several areas. Calibra-tion and preliminary analysis was performed for asmall subwatershed (22.5 km2) at a 200 m resolu-tion. A larger subwatershed, that covered approx-imately half of the whole watershed area was thensimulated at the same resolution. It became clearthat this resolution was too fine and too time-con-suming to suit the needs of the full integratedmodel on the whole watershed scale. Therefore weupscaled to a 1 km2 resolution and analyzed theassociated differences in model performance.

We explore an approach similar to the one usedin other landscape models (Sklar et al., 1985),ELM in particular (Voinov et al., 1998; Fitz et al.,1999). The watershed is represented as a uniformgrid of cells (Fig. 2), in each cell local verticalhydrological dynamics is modeled. The cells arethen connected by a model of lateral horizontalflows of surface and ground water. The two sub-models are updated independently and run insequence. This approach seems to be most appro-priate for the integrated type of analysis thatPLM is pursuing, when ecological and economicmodules operating at a variety of spatial andtemporal scales, need to be brought together andrun in concert.

2. Hydrologic unit model

Based on the hydrologic module of the Generalecosystem model (GEM) (Fitz et al., 1996) theunit model in PLM simulates vertical fluxes for alocality that is assumed horizontally homoge-neous. GEM takes into account a variety of hy-drologic processes and parameters including thefollowing:

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1. Transpiration associated with plant growth,physiology and relative humidity.

2. Evaporation using pan evaporation estimatesand pan coefficients.

3. Rainfall based on precipitation data interpo-lated over seven stations.

4. Seepage of water from that stored above thesediment/soil surface into that stored in sedi-

ment pore space (either in unsaturated or satu-rated storage).

5. Roughness coefficient that depends on dy-namic simulation of plant biomass, numericdensity, and plant morphology.

The traditional scheme of vertical water move-ment (Novotny and Olem, 1994), also imple-mented in GEM, assumes that water is fluxed

Fig. 1. Patuxent watershed location. The Patuxent River is one of the major tributaries of the Chesapeake Bay. Its drainage basin(approx. 2356 km2) lies between the Baltimore and Washington DC metro areas. The background map is based on 30 m cellresolution Landsat Thematic Mapper scenes for Chesapeake Bay Land Cover Classification 1988/1989.

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Fig. 2. Spatial representation of the landscape as a uniform grid of cells with local hydrological dynamics linked by horizonatalflows. A unit model that simulates vertical hydrological flows is replicated in each cell.

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Fig. 3. The unit hydrological model. The state variables are surface water, snow/ice, unsaturated water, and saturated water. Themajor processes are precipitation, evapotranspiration, infiltration and percolation.

along the following pathway: rainfall�surfacewater�water in the unsaturated layer�water inthe saturated zone. In each of the stages someportions of water are diverted due to physical(evaporation, runoff) and biological (transpira-tion) processes, but in the vertical dimension theflow is controlled by the exchange between thesefour major phases. This same conceptual model isalso the basis of more detailed descriptions ofinfiltration and percolation (Rawls et al., 1992).

However for the temporal and spatial scales ofa watershed landscape model this scheme needs tobe reconsidered. First, at a time step of a day ormore in steady state in terrestrial landscapes witha pronounced gradient, we do not observe surfacewater over unsaturated layers. During a rapidrainfall event surface water may accumulate inquantities that are not immediately infiltrated, butover the course of the day this water will eitherinfiltrate or will be removed by horizontal runoff.There is a great variability in the infiltration rates,according to estimates of Skaggs and Khaleel(1982), the infiltration can vary between 0.048–216 m day−1, depending on the soil type andrainfall pattern. For the soil types on the Patuxent

watershed infiltration varies from 0.15 to 6.2 mday−1 (Maryland Department of State Planning,1973). In most cases this can certainly accommo-date most of the water remaining from a rainfalloccurring over a daily time period.

Second, climatic data are rarely available forbetter than daily resolutions. Moreover if themodel is intended to be run over large areas formany years, the diel rainfall data become inappro-priate and impossible to project for scenario runs.Therefore in the chosen modeling scale it shouldbe realized that a certain amount of detail will belost in any case: a flash rainfall event with adownpour of several centimeters occurring over ashort time and therefore most probably flushedaway with surface runoff becomes indistinguish-able from a drizzle that delivers the same amountof water over 24 h, entirely infiltrating into theunsaturated layer.

With this in mind, we use a simplified unithydrologic model (Fig. 3) based on the followingset of hypotheses.1. It is assumed that there can be no surface

water on top of the unsaturated layer. There-fore the rainfall (or snowmelt) is channeled

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directly into the unsaturated layer. Surfacewater appears only if the unsaturated layerbecomes saturated, or when the infiltrationrate is exceeded by the rainfall amount.

2. The surface water that may be present in a cellis that in rivers, creeks and depressions. Thereis no sheet surface flow, that is graduallyinfiltrated. All surface water is removed byhorizontal runoff or by replenishing the satu-rated water in case that storage has beendrained by lateral flow.

3. The surface water variable also takes into ac-count the shallow subsurface flow that mayoccur during rainfall. Following the approachused in the CNS model (Haith et al., 1984) weassume that the surface water variable includesthe water in the upper active 10 cm of the soil.

Conceptually the choice and meaning of thesurface water and saturated water variables inPLM are close to the slow and quick flow separa-tion (Jakeman and Hornberger, 1993; Post andJakeman, 1996) assumed in empirical models ofrunoff. In this case the surface water variableaccounts for the quick runoff, while the saturatedwater storage performs as the slow runoff, defin-ing the baseflow rate between rainfall events.

We thus assume that the spatial and temporalscale of the type of a landscape model that we arebuilding, allows us to simplify the structure of theunit model assumed in GEM, eliminating twootherwise important state variables (water in riverand water in subsurface flow) and the correspond-ing processes. The precipitation (rainfall+snowmelt) (P) is now directed into theunsaturated zone at a rate that is determined bythe infiltration function. Formalization of theinfiltration process needs to match the chosenspatial and temporal resolution. This essentiallycontinuous process needs to be defined as a dis-crete event based process and the continuous dis-tribution of water in the unsaturated layer thatshould control ponding, infiltration and verticalpercolation should be aggregated into one spa-tially averaged and uniform value. As in the ELMcase study (Voinov et al., 1998) again we allow agood deal of empiricism to be included into theprocess based modeling paradigm that we employ.

We define the amount of water infiltrated as:

F=min (Fi Fs Fs Fh, P).

where Fi is the infiltration rate; Fs is the slopeparameter for the infiltration (the steeper theslope, the smaller the infiltration); Fs, the soilparameter for the infiltration; and Fh is the habi-tat parameter for the infiltration. These threeparameters are based on the slope, soil and landuse maps, respectively. Besides, for each time stepthe infiltration capacity Ic is calculated as Ic=Uhr, where Uh is the unsaturated depth and r isporosity. If F\Ic then the unsaturated zone istotally eliminated and the incoming precipitationis added directly to the saturated water. Whateverprecipitation is in excess of either the infiltrationrate (P−F) or the capacity of the unsaturatedzone (P−Ic), is added to the surface water, whichis then subject to runoff.

In addition to the spatial features of the infiltra-tion process, there are also certain temporal pat-terns that need be accommodated in the model.Inspecting the flow data measured at gaging sta-tions and comparing it to the patterns of precipi-tation, one can notice that in most cases after along dry period the runoff is considerably lowerthan when it is caused by a series of rainfallevents. This makes sense and can be explained bythe patterns of vertical distribution of water in theunsaturated layer. If we want to avoid the spa-tially heterogeneous description in the verticaldimension we have to adopt certain empiricalrules that would modify the infiltration rate ac-cording to the observed patterns.

We do this in the model with the help of acounter n]1 that is incremented by d+ everytime when PB0.001 m and decreased by d−

whenever P\0.001 m. The infiltration rate isthen adjusted: F°=nF.

By setting d+BBd− we make sure that theinfiltration gradually grows during the dry periodand then rapidly declines to the original valueonce a rainfall series starts.

Another observation that follows from the rain-fall versus runoff data analysis is that exception-ally high precipitation usually results in relativelyhigher runoff. If data were available and analyzedat a finer resolution this could probably be ex-plained by the temporal patterns of the peak

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rainfalls that are occurring in this area. Thelargest amount of rainfall tends to be delivered inshorter time periods resulting in rapid accumula-tion of water in the immediate subsurface zone,that blocks further infiltration and increasesrunoff. To account for this empirical generaliza-tion, we further modify the infiltration rate: F=fF° where f is a hyperbolic function

f=! 1, if PBPmax

(Pmax/P)4, otherwise,

Pmax is the threshold precipitation value, whichcauses higher runoff when exceeded.

By assuming these empirical extensions for theinfiltration formalization we gain the flexibility ofaccounting for spatial and temporal variations inthe infiltration process, while reducing the resolu-tion and heterogeneity in the model variables thatwould otherwise be necessary.

3. Spatial hydrologic model

In the spatial implementation the major hy-pothesis that we are testing is that overland andchannel flow can be modeled similarly. Tradition-ally, in most models of overland flow the surfacewater is moved according to two separate al-gorithms: one for the 2-dimensional flux acrossthe landscape and the other for the 1-dimensionalchannel flow. This approach we find in some ofthe classical spatial hydrologic models such asANSWERS (Beasley and Huggins, 1980) or SHE(Abbott et al., 1986). However, once again bear-ing in mind the spatial and temporal scale of thePatuxent model, as well as its overall complexity,we intend to use the same algorithm for bothtypes of overland flow.

Taking into account the temporal resolution ofthe model, we may assume that whatever surfacewater is present in a cell, is already in the creeks,streams or rivers. Taking into account the spatialresolution we may further assume that in everycell there will be a stream or river present, whereall the surface water can accumulate. Therefore itmakes sense to consider the whole area as a linkednetwork of channels, where each cell presents achannel reach which discharges into a single next

channel reach. Based on the elevation map andgiven a series of cells marking the mouth of theriver, which is the outlet for water drained fromthe watershed, we can create a link map thatspecifies into which of the eight directions (N,NW, W, SW, S, SE, E, NE) a cell drains its water(Fig. 4). This link map can be either created by anARC/INFO procedure, or it may be created by aninternal algorithm, which is a part of the SMEpackage (Spatial Modeling Environment,(Maxwell, 1995)).

After the water head in each raster cell ismodified due to vertical fluxes, the surface watermovement between the raster cells (and associatedtransport of constituents) is calculated. The hy-drology of the whole watershed is modeled as amerge of two algorithms. One of them operates inareas with a pronounced elevation gradient. It is asimplified runoff algorithm that takes a certainportion of water from a cell and adds it to thenext cell downstream, according to the link map(Fig. 5A).

The other algorithm is implemented in areaswith standing water. These areas are marked asopen water on the landuse map and they aremuch more similar to the conditions that we haveencountered in our previous exercises with theEverglades Landscape model (Voinov et al.,1998). In this case we may look at the flowbetween two adjacent cells i and i+1 as flow inan open channel and use the so called slope-areamethod (Boyer, 1964), which is a kinematic waveapproximation of St. Venant’s momentum equa-tion. The flux (m3 d−1) in this case is described bythe empirical Manning’s equation for overlandflow. The equation is further modified to ensurethat there is no flux after the two cells are equili-brated and then it is accelerated by the multi-celldispersion algorithm. This method has been elab-orated in our previous paper and we will notdiscuss it further here.

The simplified runoff algorithm that we haveapplied for the steeper areas on the watershedrequired some investigation and adjustment. Firstit became clear that the runoff operation needs tobe performed at a different time scale than the 1day time step adopted in the rest of the ecological

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components of the model. Over 1 day water couldtravel considerably further than over one cell,especially when the spatial resolution was fineenough. The simplest way to treat this inconsis-tency was to decrease the time step of this part ofthe hydrologic module by several (10–20) times.The size of the time step and the number ofiterations needed for the hydrologic module couldbe calibrated so that water was moved sufficientlyfast.

As an alternative, we have tested anothermethod which instead of reiterating the wholefluxing algorithm N times, identified the path ofthe water on the link map over N cells and thendumped the water from the current cell directlyinto that cell N steps downstream (Fig. 5B). Theresults of both algorithms were remarkably close

and we switched to the second one since it per-formed much faster. However, as we will seebelow in the calibration section, this approachwas still very much dependent on the spatial scaleof the model: as we switched to larger areas itoccurred that the delivery rate was not highenough and the number N had to be increased.

In an effort to endogenize this process andmake the model robust to rescaling we haveadopted yet another method of calculating N. Itwas assumed that the length of the pathway thatwater was to travel over one time step was afunction of the water head in the current cell (Fig.5C). A stepwise function worked best for thispurpose:

N=mW s/(K s+W s)

Fig. 4. Link map. Each cell is marked by a number that indicates the direction of the next cell along the path of surface water flow:2=NN, 3=NW, 4=WW, 5=SW, 6=SS, 7=SE, 8=EE, 9=NE.

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Fig. 5. Calculation of pathways on the Link Map. The water may flow over more than one cell in a daily time step. (A) Definingthe water transport by running the whole hydrologic model for N iterations. (B) Defining the recipient cell as the Nth cell down thelink map and fluxing the water directly there. (C) Defining the pathway as function of the water head in current donor cell.

where N is the cell distance; m is the maximumallowed cell distance; W is the water head in thecurrent cell; K is the threshold head at which thecell distance is half the maximum and s is aparameter that controls the steepness of the stepfunction.

For saturated water fluxing a modified Darcyequation was employed. For each cell ij the flux toan adjacent cell v was determined as a function ofhorizontal conductivity and the saturated waterhead difference between the current cell and theaverage of the nine cells that included the currentone and the eight neighboring ones:

fij,v= (hij ·Pv−Gv)·Cv,

where hij is the targeted head; hij=�k= ij,vPkGk/�k= ij,vPkCk ;v={i91, j91} is the set of neigh-boring cells for cell i, j; Pv is porosity in cell v ;Gv is the amount of water in the saturated storagein cell v ; C, is the horizontal conductivity in cellCv.

4. Data sets

Spatial hydrologic modeling requires extensivedata sets. In Fig. 6 we present the basic spatialcoverages that have been employed in our model-ing effort and some of the derived layers that werealso essential for the hydrologic module. Spatial

fluxes of surface water in watershed models arepredominantly driven by the elevation gradient.The best elevation data in a digital format can beobtained by direct digitizing of the topographicmaps of the area modeled. However this is a timeconsuming, tedious and expensive procedure. Asan alternative we have relied on the United StatesGeological Survey’s (USGS) Digital ElevationModel (DEM) data that are available for down-loading from the Internet (USGS, 1995).

USGS offers elevation data in 1 degree gridcoverages for the four quadrangles covering thePatuxent watershed. DEM grids are based on1:250 000 USGS maps with 3-arc second gridspacing. Grids constructed from USGS 1-degreeDEMs are not immediately suitable for the analy-sis of such topographic features as volume, slope,or accurate visibility, because they measure the x,y (planar) locations as latitude and longitude,while the z value (elevation height) is measured inmeters. Consequently, the actual distance on theground represented by one ground unit is notconstant, and the ground distance units and thesurface elevation units are not the same. To makethis surface model compatible with other layers ofinformation and suitable for analysis, the groundunits in the 1° USGS DEM have been projectedinto nonangular units of measure such as theUTM coordinates. After reprojection the grid hasbeen rescaled to the 200 m resolution, which is the

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highest resolution currently used in the PLM. Thevertical resolution of the DEM maps is 1 m. Thisresolution is not fine enough to show the actualshoreline in the estuarine part of the watershedthat lies between 0 and 1 m of elevation. Theshoreline was derived from the river network map(TIGER/LINE-US Bureau of Census (USCB,1996)) and then combined with the estuarinebathymetry data (NOAA/National Ocean Service,1997) and elevation map to make the land-waterboundary visible.

Another inconsistency is observed when theelevation layer is combined with the river networkand ‘depressions’ show along the courses ofstreams. This is caused by widely known imper-fections in DEM data and determined primarilyby the resolution (distance between samplingpoints). Another common cause of these ‘depres-sions’ is storing the elevation data as an integernumber and hence rounding off the real data. Theadditional aggregation to the 200 m and 1 kmresolutions performed for our modeling purposesadds to the problem. This prevented the properflow of water downstream in the hydrologic mod-

ule and resulted in an erroneous link map. Cor-rections may be performed using severalARC/INFO hydrologic functions that allow oneto determine and fill depressions. This was alsodirectly incorporated into the PLM hydrologicmodule, that used the river network map as areference and smoothed out all the depressionsalong the river beds.

Using a GIS the DEM data have been prepro-cessed to create several other raster maps neededfor the hydrologic model. Watershed Boundary(Studyarea map), Slopes and Aspects layers havebeen calculated by the Watershed Basin AnalysisProgram in GRASS-Geographic Resources Anal-ysis Support System (USACERL, 1993). The bestresults were achieved with a threshold of 500 cellunits used as the minimum size of an exteriorwatershed for the 200 m resolution.

The River Network coverage has been acquiredfrom the TIGER/LINE (USCB, 1996) in a vectorformat. The database contained numerous errors:streams that were not continuous, missing chan-nels (improperly digitized or missing on the origi-nal maps or photos because they may have been

Fig. 6. Spatial GIS layers and maps used in the model. There are six basic coverages. Additional maps are created duringpreprocessing and model initialization. Other spatial parameters and variables are calculated and updated during model runs.

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dried out at the time the photos/maps were inter-preted). The hydrologic analysis tools in theARC/INFO GRID module (ESRI, 1994) wereapplied to correct the digitized stream network.Using the digital elevation model as an input wedelineated the drainage system and thenquantified its characteristics. For any location inthe grid, those tools also gave us the upslope areacontributing to that point and the downslope pathwater would follow. A ‘hydrologically proper’surface, without any artificial pits or hills, wasproduced and flow directions and flow accumula-tions were determined. Water channels were iden-tified for different threshold amounts of wateraccumulation (product of the number of cellsdraining into a target cell and the size of theprecipitation event). These water channels wereused as a background coverage to manually cor-rect stream discontinuities for the digitized RiverNetwork. The corrected River Network was con-verted into a raster (cell-based) format in order tocomply with other data layers. This River Net-work map produced from the elevation dataturned out to be more consistent, than the origi-nal vector map.

The Soils layer was originally imported fromthe State Soil Geographic (STATSGO) data base(NRCS USDA, 1997) which has been compiledusing a USGS 1:250 000 scale, 1 by 2° quadrangleseries as a map base. The STATSGO Data Basewas downloaded in GRASS format and repro-jected from the Albers Conical Projection to theneeded UTM projection. Every map unit on aSTATSGO coverage contains up to 21 compo-nents (segments) for which there are attributedata. One of the disadvantages of this dataset isthat these components cannot be spatially iden-tified, which reduces the STATSGO applicationto the coarse regional scale.

After analyzing the tabular information it wasclear that aggregation criteria did not includehydrological properties, because one map unitcould contain soils from very different hydrologi-cal groups. Therefore we could use only somegeneral hydrological parameters from STATSGObut most of the spatially explicit soil data wastaken from the Patuxent Watershed CountiesSoils map available at the Maryland Office of

Planning (MOP) (Maryland Department of StatePlanning, 1973).

The Groundwater Table Map, required as aninitial condition for the model, was approximatedfrom a series of spatial and point data sets usingthe GRASS overlay and interpolation techniques.The reference points were taken from:� MOP Soils map and the unsaturated depth

data that was provided by the Maryland De-partment of State Planning;

� The elevation and river network coverages,along which the ground water table was as-sumed to reach the surface;

� 15 well measurements of the groundwater levelover the watershed area (James et al., 1990).The groundwater depth data were interpolated

over the whole watershed with these data sets asreference points. After that the model was run for100 days, the Groundwater Table Map was regen-erated, saved and then fed back into the modelfor subsequent runs as the initial condition for thedepth of the water table. This improved the per-formance of the Hydrological Module by signifi-cantly decreasing the initial adjustment period inthe model runs.

Land Use coverages have been acquired fromMaryland Office of Planning in a vector formatand then rasterized for the required cell resolu-tions. The climatic data series were taken from theEarthinfo Inc. NCDC Summary of the Day Data-base (EARTHINFO, 1993). The point time seriesfor precipitation, temperature, humidity and windwere then interpolated across the study area tocreate spatial climatic coverages. The calibrationprocedures were mostly based on USGS gagingdata also available for downloading from theWeb (USGS, 1995a). There are 13 gaging stationsin the area that have data for the time period thatmatches the one defined by the climatic dataseries, that is 1980–94.

It should be noted that the PLM hydrologicmodule was entirely based on data available eitherfrom the Web or from the State and FederalAgencies and Institutions. There were no specialdata collection efforts undertaken for the solepurpose of this project. This fact makes us some-

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what optimistic about the possibilities of applyingthe PLM methods elsewhere in other watershedsand landscapes.

5. Calibration and scaling

Calibrating and running a model of this level ofcomplexity and resolution is quite tedious andrequires careful planning and decomposition.There is little chance to get the model running asa whole immediately and a stage-by-stage ap-proach is most fruitful.

Therefore we first identified two resolutions torun the model-the 200×200 m and the 1×1 km.On the one hand, the 200 m resolution was moreappropriate to capture some of the intrinsic pro-cesses associated with landuse change. On theother hand it was certainly too detailed and re-quired too much CPU time to perform the numer-ous model runs required for calibration and torun the full model over decades which is essentialfor scenario analysis. At the 1 km resolution the58 905 cells of the 200 m version were replaced by2352 cells.

Second, we identified a hierarchy of subwater-sheds. The whole Patuxent area has been split intoa hierarchy of nested subwatersheds to performanalysis at smaller scales. Three levels have beenidentified (Fig. 7). A small subwatershed (Cattailcreek) in the North of the Patuxent drainagebasin has been chosen as a starting point for ourspatial analysis. From there we moved on to theupper portion of the Patuxent watershed, thatincluded approximately half of the area and endedat Bowie. And finally we looked at the wholePatuxent watershed. We thus started with runningthe model over 566 cells, then jumped to 23 484cells and finally moved to all the 58 905 cells inthe study area of the Patuxent watershed at the200 m resolution.

We staged a set of experiments with the smallCattail creek subwatershed to test sensitivity ofthe hydrologic module. It was established fromthis exercise that there are three crucial parame-ters that control the surface water flow in themodel. These were the infiltration rate, the hori-zontal conductivity, controlling the baseflow rate

Fig. 7. Hierarchy of subwatersheds on the Patuxent drainagebasin used to calibrate and analyze the model. (A) 22.5 km2

Cattail Creek; (B) 939.9 km2 Upper Patuxent draining atBowie; (C) Full study area.

and the number of iterations, or the path lengthof water transport in the hydrologic module. Theinfiltration rate effectively controlled the height ofpeaks in the river water flow. The conductivitydetermined the amount of flow in the low periodand by changing the number of iterations wecould modify the length of the peaks and thedelivery rate downstream.

Calibration of the hydrologic module was con-ducted against USGS data from several gagingstations over the watershed. First the model wascalibrated for the 1990 data for the small Cattailsubwatershed. Then the model was run for 5consecutive years (1986–1990). Fig. 8 displays theannual dynamics of rainfall for 1984–1992, whichshow that the 1986–1990 period gives a goodsample of various rainfall conditions that may beobserved in the watershed, 1989 being a wet yearand 1986 representing dry year conditions. Theresults displayed in Fig. 9 are in fairly goodagreement with the data and may be consideredas a partial model verification, because none ofthe parameters have been changed after the initialcalibration using 1990 data. Some of the flow

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Fig. 8. Annual rainfall (inches) data for 1984–1992 and runoff data for the 1986–1990 period over which the model was analyzed.

statistics are presented in Table 1, were we havealso included calibration results from the Hydro-logic Simulation Program-Fortran (HSPF)(Donigian et al., 1984), that has been previouslyapplied to the Patuxent watershed (AQUATERRA, 1994). Surprisingly we attained a con-siderably better fit to data with our model, thanwith HSPF. HSPF is a more complex model thatuses much more elaborate data sets for its perfor-mance (e.g. hourly rainfall data), although itsspatial resolution is not as fine as in our model(aggregated subwatersheds).

We did not have any reliable data to calibratethe spatial dynamics of ground water. Howeverwe tracked the total amount of water in saturatedand unsaturated storage to make sure that themodel is in quasi steady state with respect togroundwater. The dynamics of these integratedvalues (Fig. 10) were in good agreement with thetotal amount of rainfall received by the watershed(Fig. 7), responding with a lower level of thegroundwater table in dry years and a rising watertable during wet periods.

The fit was less accurate once we started run-ning the same model with the same parametersover the half-watershed area. One parameter thatneeded to be adjusted was the number of itera-tions N in the hydrologic module. Now that alarger watershed was involved it turned out that abetter fit could be obtained if the number ofiterations was further increased. Apparently this

Table 1Model verification for Cattail Creek subwatershed and com-parison to the HSPF model statistics

HSPF %% errorModelDataerror

8.22510.41 2527.58 0.68Total flow−0.48 4.9930.2Max 10% 925.79

1.50 −14.7587.3Min 50% 596.25−15.66282.24Total 1986 326.16

472.83 469.25 −0.76Total 1987482.01 414.22Total 1988 −16.37 −0.7−

11.72748.29660.62Total 1989 +18.1568.78 611.31 6.96Total 1990

A.A. Voino6 et al. / Ecological Modelling 119 (1999) 211–230224

Fig. 9. Calibration and verification results for Cattail Creek (1986–1990).

A.A. Voino6 et al. / Ecological Modelling 119 (1999) 211–230 225

Fig. 10. Dynamics of groundwater in the model. As the groundwater table drops during dry years (compare to Fig. 7) the amountof water in unsaturated storage increases and vice versa.

was because at this larger scale we needed tomove water further and faster to better simulatethe short-term high peaks that were observed inthe data. This was a clear illustration of the factthat different scales present new emerging behav-ior of the system, and that rescaling is always adelicate process that cannot be done mechani-cally. The best fit to data was obtained whenrunning the model with the selfadjusting methodfor N with the maximum number of iterationsm=100 (Fig. 11). Interestingly, the Cattail sub-watershed was still performing as well as beforewith this value of m. This could be expected sincethe previous analysis showed that there was nosensitivity of subwatersheds to increases in Nbeyond 20 (m=20).

The calibration statistics for the half watershedarea are summarized in Table 2. This time the fitwas not as good as for only the Cattail subwater-shed, clearly indicating that the increased spatialextent of the model presented more heterogeneitythat was not accounted for in the Cattail subwa-tershed calibration. One potential source of erroris the groundwater dynamics. Within the subwa-tershed we assumed that the groundwater dynam-ics closely follows the surface water flows andconfined the groundwater to the subwatershedarea. This is probably not accurate for the CattailCreek and at larger scales the groundwater pat-terns are apparently even more different and re-sult in added error in the simulation.

One other possible source of error was the

spatial representation of climatic data, which wehad measured at several points and then interpo-lated over the study area. The sensitivity analysisshowed that the overall annual flows are highlysensitive to particular climatic timeseries and tothe spatial patterns of climatic data. The Cattailhydrology was driven by two climatic stations.The half-watershed model incorporated data fromeight stations. In reality over this larger area thereis certainly more variability in climatic factorsthat potentially causes some of the flash runoffthat we see in the data, but which we cannotmimic with the model based on only the fewmeteorologic stations we have smoothed over thewhole area. Nevertheless the general hydrologictrends seem to be well captured by the model, andthe total flows were still better simulated thanwith the HSPF model.

Our next experiment was related to the resolu-tion of the cells in the model. Using GIS opera-tions we have rescaled the input maps, switchingfrom a 200 m to a 1 km cell resolution. Modelruns for the 1 km resolution were remarkablyclose to the results we were getting from the 200m model (Fig. 12). This finding was especiallypromising for analysis of the other modules of thefull ecological economic model. Since most of thehorizontal spatial dynamics is stipulated by thehydrologic fluxes, we can expect that the coarser 1km resolution would be sufficient for the spatialanalysis of the integrated model of the watershed.

A.A. Voino6 et al. / Ecological Modelling 119 (1999) 211–230226

Fig. 11. Calibration for Upper Patuxent at Bowie (1986–1990).

A.A. Voino6 et al. / Ecological Modelling 119 (1999) 211–230 227

The correlation between the model results attwo resolutions turned out to be even higher thanthe correlation between some of the data setsinvolved. For example in Table 3 we present thecomparison of the model correlations with thecorresponding correlations between the elevationand slope maps considered for the 200 m and 1km resolutions. Two methods of aggregation from200 m to 1 km were explored. One is the averagemethod (A), when the aggregate value in the 1 kmgrid is defined by the average of the 25 individualvalues in the 200 m cells. The other-is the majoritymethod (M), that takes the most frequently occur-ring value as the aggregate value. Both aggrega-tion methods produce certain error. The Amethod works slightly better for the Elevationcoverage, while the M method gives less error forthe Slope coverage. However for both methodsthe slope layers were very poorly correlated. Nat-urally the model performed differently on the 200m and the aggregated 1 km data sets. But for bothaggregation methods the model performance onthe aggregated 1 km maps correlated even betterto the 200 m model, than the 1 km spatial data setcorrelated to the original 200 m data.

The comparisons of flows at gaging stations is aconvenient way to look at the model output,calibrate and analyze the model performance. Itintegrates a lot of 2-dimensional spatial informa-tion in a normalized 1 dimensional picture. An-other way to view the output of a spatial model,which is especially important to localize potential

accumulations of water and other spatial inconsis-tencies, is to output the model variables as seriesof maps, which can be then compiled into graphicanimations. While the format of a Journal publi-cation is not suitable for this kind of output, itmay be well displayed on the Internet. We there-fore refer the reader to our WWW page at http://iee.umces.edu/PLM, to view further modeloutput.

6. Conclusions

Most of the traditional hydrologic models usedin ecological applications seem to borrow muchfrom engineering hydrology that usually enjoyedthe luxury of an abundance of well performed andreplicated measurements for particular locations(weirs, culverts) or relatively small areas and forquite short-termed events (rainfalls). The tempo-ral and spatial resolution in those models could bequite fine, the processes could be considered inmuch detail and, with all the data available,model calibration was still not a problem. As themodeled systems become more integrated and asmore variables and processes in addition to thehydrologic ones are to be accounted for by themodel, we can afford less detail for each of theindividual processes and formalizations, if we areto keep the model at an overall complexity levelfeasible for analysis and understanding. As a re-sult more empiricism must be added to the model

Table 2Model verification and comparison to the HSPF model statistics for the half subwatershed draining at Bowie and the Unitysubwatershed

BowieUnity

HSPF % error% Error % ErrorModelData HSPF % errorModelData

0.8 −2.1 9.73.636617.43 37978.78Total flow 3950.54 3981.31Max 10% 15.127.916546.7012497.582.341.52148.131410.15

9.0826.76 626.78 −27.5 −12.1 7917.98 6582.62 −18.4Min 50%484.52 446.30 −8.2 4752.94 4352.84 −8.8Total 1986

8.87041.226446.08Total 1987 14.3942.00816.48−14.5 −2.6−+25.3792.10 −3.4 −11.6−+8.0Total 1988 6751.99819.30 5841.62

960.30Total 1989 12.311881.8810507.98−1.1949.458.38861.238158.45−2.1851.47Total 1990 869.94

A.A. Voino6 et al. / Ecological Modelling 119 (1999) 211–230228

Fig. 12. Comparisons of model output generated at 1 km resolution and 200 m resolution.

structure, certain processes become lumped to-gether, the models become more aggregated inspace and in time, spatially distributed parametersbecome averaged over space and assumed homo-geneous. In this case direct comparisons withother model structures are hardly meaningful, be-cause of the obvious inconsistencies and differentlevels of empiricism. The only criterion that canbe still used to evaluate the model performance isthe verifications against existing measurementsand cross calibration with other models.

In the hydrologic module of PLM we wentsomewhat beyond the traditional amount of em-piricism seen in spatial hydrologic models of wa-tersheds. We have included some new empiricalfunctions to describe infiltration and the horizon-tal propagation of surface water across the land-scape. The trade-offs that we gained were lessvariables, simpler model structure, less dataneeded for calibration, and faster performance.On the other hand this added empiricism maysignificantly impede model applicability to otherwatersheds. However, this was not the case in ourapplications to the several subwatersheds on thePatuxent drainage basin. We have succeeded inusing the same model with the same set ofparameters for several watersheds, varying in spa-tial resolution and scale. In most cases the model

performance was comparable to that of HSPF—the more complex and detailed model widely usedin various EPA programs (e.g. Chesapeake BayProgram (CBP, 1998)).

The model is also limited by the data used andthe spatial, temporal and structural scales as-sumed. In our case, the error can be explained bythe following factors:� coarse 1 day temporal scale that cannot distin-

guish between the types of rainfall events; spa-tial and temporal interpolation of climaticdata;

� vertical aggregation of variables and processes;discrete rather than continuos formalization ofprocesses;

� horizontal aggregation within cells, neglect ofspatial units that are smaller than the cell size(40 000 m2 or 1 km2).Even with these assumptions we were able to

produce a fairly good fit to the available gagingstations data and managed to simulate the long-term aggregated runoff dynamics that was essen-tial for the overall Patuxent Landscape Model. Itwas somewhat unexpected that the coarser 1 kmresolution model could mimic data almost as wellas the 200 m model. Apparently the temporal (1day) and structural (4 hydrologic variables) aggre-

A.A. Voino6 et al. / Ecological Modelling 119 (1999) 211–230 229

Table 3Correlations between flows, elevation and slopes at 200 m and 1 km resolutions (M, majority method; A, average method)

Ag. Method Maps Correl.Map 1 Model Correl.Map 2

M 0.921Elevation 200m 0.922Elevation 1 km0.25MSlope 1 kmSlope 200 m

Elevation 1 km A 0.926 0.935Elevation 200 m0.23ASlope 1 kmSlope 200 m0.996Elevation 1 km (A) Elevation 1 km (M)0.725Slope 1 km (A) Slope 1 km (M)

gation in the model is better matched by the 1 kmspatial aggregation. Therefore the added detailthat comes with the 200 m fine resolution isunessential for the overall model performance.However additional studies are required to sup-port this statement and find some guidelines forthe overall balanced model scaling in space, timeand structural complexity. At this time we couldonly see that the spatial resolution was less impor-tant than the size and characteristics of the water-shed. Larger spatial extent resulted in largersimulation errors.

Acknowledgements

Funding for this research has been provided bythe US EPA/NSF Water and Watersheds Pro-gram through the US EPA Office of Research andDevelopment (Grant no. R82-4766-010). Our sin-cere thanks are due to our project collaborators:Tom Maxwell, Lisa Wainger, Ferdinando Villa,Roel Boumans, and Elena Irwin.

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