EVALUATION OF THE SWAT MODEL S SNOWMELT HYDROLOGY IN A NORTHWESTERN MINNESOTA WATERSHED

Transcription

1 EVALUATION OF THE SWAT MODEL S SNOWMELT HYDROLOGY IN A NORTHWESTERN MINNESOTA WATERSHED X. Wang, A. M. Melesse ABSTRACT. Snowmelt hydrology is a very important component for applying SWAT (Soil and Water Assessment Tool) in watersheds where the stream flows in spring are predominantly generated from melting snow. However, there is a lack of information about the performance of this component because most published studies were conducted in rainfall-runoff dominant watersheds. The objective of this study was to evaluate the performance of the SWAT model s snowmelt hydrology by simulating stream flows for the Wild Rice River watershed, located in northwestern Minnesota. Along with the three snowmelt-related parameters determined to be sensitive for the simulation (snowmelt temperature, maximum snowmelt factor, and snowpack temperature lag factor), eight additional parameters (surface runoff lag coefficient, Muskingum translation coefficients for normal and low flows, SCS curve number, threshold depth of water in the shallow aquifer required for return flow to occur, groundwater revap coefficient, threshold depth of water in the shallow aquifer for revap or percolation to the deep aquifer to occur, and soil evaporation compensation factor) were adjusted using the PEST (Parameter ESTimation) software. Subsequently, the PEST-determined values for these parameters were manually adjusted to further refine the model. In addition to two commonly used statistics (Nash-Sutcliffe coefficient, and coefficient of determination), a measure designated performance virtue was developed and used to evaluate the model. This evaluation indicated that for the study watershed, the SWAT model had a good performance on simulating the monthly, seasonal, and annual mean discharges and a satisfactory performance on predicting the daily discharges. When analyzed alone, the daily stream flows in spring, which were predominantly generated from melting snow, could be predicted with an acceptable accuracy, and the corresponding monthly and seasonal mean discharges could be simulated very well. Further, the model had an overall better performance for evaluation years with a larger snowpack than for those with a smaller snowpack, and tended to perform relatively better for one of the stations tested than for the other. Keywords. Minnesota, Model performance virtue, PEST, Sensitivity analysis, Snowmelt hydrology, SWAT. The Soil and Water Assessment Tool (SWAT), developed by Arnold et al. (1993), has been widely used to predict impacts of land management practices on water, sediment, and agricultural chemical yields in large complex watersheds with varying soils, land use, and management conditions over long periods of time (e.g., Srinivasan and Arnold, 1994; Rosenthal et al., 1995; Bingner, ; Peterson and Hamlett, 1998; Sophocleous et al., 1999; Spruill et al., 2000; Weber et al., 2001; Gitau et al., 2002; Van Liew and Garbrecht, 2003; Chu and Shirmohammadi, 2004). SWAT is a direct outgrowth of the SWRRB (Simulator for Water Resources in Rural Basins) model (Williams et al., 1985; Arnold et al., 1990), while incorporating features of three other USDA-ARS models, including CREAMS (Chemicals, Runoff, and Erosion from Agricultural Management Systems; Knisel, 1980), GLEAMS (Groundwater Loading Effects on Agricultural Management Systems; Article was submitted for review in November 2004; approved for publication by the Soil & Water Division of ASAE in June The authors are Xixi Wang, ASAE Member Engineer, Research Scientist, Energy and Environmental Research Center, University of North Dakota, Grand Forks, North Dakota, and Assefa M. Melesse, ASAE Member Engineer, Assistant Professor, Department of Environmental Studies, Florida International University, Miami, Florida. Corresponding author: Dr. Xixi Wang, Energy and Environmental Research Center, University of North Dakota, Grand Forks, North Dakota 58202; phone: ; xixi.wang@und.nodak.edu. Leonard et al., 1987), and EPIC (Erosion-Productivity Impact Calculator; Williams et al., 1984). SWAT is composed of three major components, namely subbasin, reservoir routing, and channel routing. Each of the components includes several subcomponents. For example, the subbasin component consists of eight subcomponents, namely hydrology, weather, sedimentation, soil moisture, crop growth, nutrients, agricultural management, and pesticides. The hydrology subcomponent, in turn, includes surface runoff, lateral subsurface flow, percolation, groundwater flow, snowmelt, evapotranspiration, transmission losses, and ponds. Detailed descriptions of the methods used in modeling these components and subcomponents can be found in Arnold et al. (1998), Srinivasan et al. (1998), and Neitsch et al. (2002a). In this study, the Soil Conservation Service (SCS) runoff curve number, adjusted according to soil moisture conditions (Arnold et al., 1993), was used to estimate surface runoff, the Priestley-Taylor (Priestley and Taylor, 1972) method was used to estimate potential evapotranspiration, and the Muskingum (Chow et al., 1988) method was used for channel routing. The hydrology subcomponent within SWAT is the driving force behind other components and subcomponents, and hence has been widely evaluated by researchers at daily and/or monthly scales for watersheds with many different characteristics. Some of these evaluations have indicated that SWAT only gives an acceptable prediction of monthly stream flows, but others indicated that it can satisfactorily predict Transactions of the ASAE Vol. 48(4): 2005 American Society of Agricultural Engineers ISSN

2 both daily and monthly stream flows. For instance, Spruill et al. (2000) evaluated SWAT s performance in simulating daily and monthly stream flows in a karst-influenced watershed in central Kentucky. In this study, assessments of the measured and simulated daily stream flows from 1995 (the model validation year) and (the model calibration year) yielded Nash-Sutcliffe coefficients (E j 2, computed by eq. 7 below) of 0.04 and 0.19, respectively, whereas monthly totals of the data indicated much higher E j 2 values of 0.58 for 1995 and 0.89 for. Spruill et al. (2000) concluded that SWAT could be an effective tool for simulating monthly runoff from small watersheds in central Kentucky that have developed on karst hydrology. In another study, Chu and Shirmohammadi (2004) evaluated the SWAT model s hydrology subcomponent in predicting surface and subsurface flows in the 346 ha Warner Creek watershed located in the Piedmont physiographic region of Maryland. The results of this study indicated that because SWAT was unable to account for subsurface flows that come from outside the watershed, it significantly underestimated the subsurface, and hence total, stream flows in the watershed. As with Spruill et al. (2000), Chu and Shirmohammadi (2004) concluded that the SWAT model s hydrology subcomponent was capable of performing an acceptable prediction of a long-term (i.e., on a scale of months) simulation for management purposes, but failed to make reasonable predictions for short time intervals (i.e., on a daily scale). In contrast, Saleh and Du (2004) showed that SWAT could satisfactorily predict both daily (E j 2 = 0.62) and monthly (E j 2 = 0.83) stream flows in the Upper North Bosque River watershed in central Texas. Spruill et al. (2000) and Chu and Shirmohammadi (2004) attributed the poor performance of SWAT in predicting daily stream flows to its inability to account for the subsurface flow contribution from outside the watersheds. However, in addition to different watershed characteristics, the unbalanced data used in these studies might also be a reason for the inconsistent conclusions. These evaluations were conducted in areas where stream flows were dominantly generated from rainfall events, with negligible/limited contributions from melting snow. Although some researchers (e.g., Peterson and Hamlett, 1998; Chu and Shirmohammadi, 2004; Qi and Grunwald, 2005) have pointed out that snowmelt hydrology is an important subcomponent, there is a lack of information regarding SWAT s performance in modeling watersheds where stream flows are predominantly generated from melting snow in spring, while stream flows in summer and fall are predominantly generated from rainfall runoff. In a study designed to address this issue, Fontaine et al. (2002) reported that by using elevation bands to distribute temperature and precipitation, the SWAT model s snowmelt hydrology subcomponent could be used to predict annual stream flow with an E j 2 value of Snowmelt and rainfall runoff are two very different kinds of hydrologic processes. Compared with the rainfall runoff process, snowmelt is a slow and gradual process, and melting snow is treated as rainfall with zero energy in SWAT (Arnold et al., 1993, 1998). For watersheds where melting snow is the dominant source for stream flows in spring but rainfall runoff is the dominant source for stream flows in summer and fall, which is the situation for the study watershed of the Wild Rice River, located in northwestern Minnesota (fig. 1), it is important to set up a SWAT model to simultaneously predict stream flows from these two hydrologic processes with an acceptable accuracy. Figure 1. Map showing the location and boundary of the Wild Rice River watershed in Minnesota, along with the National Weather Service (NWS) precipitation and temperature stations and the U.S. Geological Survey (USGS) flow gauging stations, where the data used in this study were collected. The numbers in the labels of the NWS stations are the 6-digit COOP IDs (cooperative station identifiers) for these stations. 2 TRANSACTIONS OF THE ASAE

3 The watershed in this study differs from the watershed studied by Fontaine et al. (2002) due to its very low topographic relief. The Wild Rice River watershed is characterized by broad, flat alluvial floodplains, river terraces, and gently sloping uplands (Houston Engineering, 2001). Hence, neither temperature nor precipitation has a measurable variation with topographic elevation (M. M. Ziemer, Senior Hydrologic Forecaster at the National Weather Service North Central River Forecast Center, Chanhassen, Minn., personal communication, 2004). In the Wild Rice River watershed, for a given water year (December to November), the stream flows in spring (March to May) are predominately generated from melting snow, whereas the stream flows in summer (June to August) and fall (September to November) are mainly generated from rainfall runoff. In winter (December to February), the stream flows are very low due to the river being frozen, but a snowpack accumulates that melts in the following spring. The main objective of this study was to evaluate the performance of the SWAT model s snowmelt hydrology subcomponent for simulating stream flows predominantly from melting snow in the Wild Rice River watershed. Nevertheless, the SWAT model was calibrated for all four seasons because the hydrologic conditions in one season may influence the subsequent season(s). SWAT S SNOWMELT HYDROLOGY In SWAT, snowmelt hydrology is realized on an HRU (hydrologic response unit) basis. A watershed is subdivided into a number of subbasins for modeling purposes. Portions of a subbasin that possess unique land use/management/soil attributes are grouped together and defined as one HRU (Neitsch et al., 2002a, 2002b). Depending on data availability and modeling accuracy, one subbasin may have one or several HRUs defined. When the mean daily air temperature is less than the snowfall temperature, as specified by the variable SFTMP, the precipitation within an HRU is classified as snow and the liquid water equivalent of the snow precipitation is added to the snowpack. The snowpack increases with additional snowfall, but decreases with snowmelt or sublimation. The mass balance for the snowpack is computed as: SNOi = SNOi 1 + R sfi Esubi SNOmlti (1) where SNO i and SNO i 1 are the water equivalents of the snowpack on the current day (i) and previous day (i 1), respectively, R sfi is the water equivalent of the snow precipitation on day i, E subi is the water equivalent of the snow sublimation on day i, and SNO mlti is the water equivalent of the snowmelt on day i. All of these variables are reported in terms of the equivalent water depth (mm) over the total HRU area. The snowpack is rarely uniformly distributed over the total area, resulting in a fraction of the area that is bare of snow. In SWAT, the areal coverage of snow over the total HRU area is defined using an areal depletion curve, which describes the seasonal growth and recession of the snowpack (Anderson, ) and is defined as: SNOi SNOi snocovi = SNOCOVMX SNOCOVMX 1 SNOi + exp(cov1 cov2 ) SNOCOVMX (2) where sno covi is the fraction of the HRU area covered by snow on the current day (i), SNOCOVMX is the minimum snow water content that corresponds to 100% snow cover (mm H 2 O), and cov 1 and cov 2 are the coefficients that define the shape of the curve. The values used for cov 1 and cov 2 are determined by solving equation 2 using two known points: (1) 95% coverage at 95% SNOCOVMX, and (2) 50% coverage at a fraction of SNOCOVMX, specified by the variable SNO50COV. For example, assuming that SNO50COV is equal to 0.2, cov 1 and cov 2 will take the values of and , respectively. The value of sno covi is assumed to be equal to 1.0 once the water content of the snowpack exceeds SNOCOVMX, indicating an uniform depth of snow over the HRU area. The areal depletion curve affects snowmelt only when the snowpack water content is between 0.0 and SNOCOVMX. Consequently, a small value for SNOCOVMX will assume a minimal impact of the areal depletion curve on snowmelt, whereas as the value of SNOCOVMX increases, the curve will assume a more important role in approximating the snowmelt process. In addition to the areal coverage of snow, snowmelt is also controlled by the snowpack temperature and melting rate. Anderson () found that the snowpack temperature is a function of the mean daily temperature during the preceding days and varies as a dampened function of air temperature. The influence of the previous day s snowpack temperature on the current day s snowpack temperature is described by a lag factor, specified by the variable TIMP, which implicitly accounts for snowpack density, water content, and exposure. The snowpack temperature is calculated as: Tspi = Tspi 1 (1 TIMP) + Tai TIMP (3) where T spi and T spi 1 are the snowpack temperatures on the current day (i) and the previous day (i 1), respectively, and T ai is the mean air temperature on day i. As TIMP approaches 1.0, T ai exerts an increasingly greater influence on T spi ; conversely, as TIMP moves away from 1.0, T spi 1 becomes more important. The amount of snowmelt on the current day (i), SNO mlti, expressed in terms of the equivalent amount of water in mm, or melting rate, is calculated in SWAT as: Tspi + Tmaxi SNOmlti = b mlti snocovi SMTMP (4) 2 where T maxi is the maximum air temperature on day i ( C), SMTMP is the base temperature above which snowmelt is allowed ( C), and b mlti is the melt factor on day i (mm H 2 O/ Cday), which is calculated as: SMFMX + SMFMN bmlti = 2 SMFMX SMFMN 2π + sin ( i 81) (5) Vol. 48(4): 3

4 where SMFMX and SMFMN are the maximum and minimum snowmelt factors, respectively (mm H 2 O/ C-day). MATERIALS AND METHODS STUDY WATERSHED The 433,497 ha Wild Rice River watershed, located in northwestern Minnesota (fig. 1), was selected for this study. Based on land use and land cover (LULC) data from the U.S. Environmental Protection Agency (EPA), the land use within this watershed consists of 67% agriculture, 18% forest, 7% pasture, and 8% wetland and/or open water. Agriculture dominates the western part of the watershed, whereas there is a large amount of forest acreage in the eastern part. In between is distributed pasture. Wetland and/or open water is intermingled with the forest and/or pasture. While the LULC data were developed from 1970s and 1980s aerial photography surveys, combined with land use maps and surveys (EPA, 2003), they are effectively up-to-date because there have been negligible changes in the land use types for the study watershed in the past two decades (Stoner et al., 1993; Offelen et al., 2002, 2003). The soils in the western part are dominated by clay, which is very fertile for agriculture but has a very low permeability, resulting in poor internal drainage. Towards the east, the soils tend to be clay loam and/or sandy loam mixed with sands and gravels, while the eastern part is composed mostly of clay and silt, with a loamy texture, a dark to moderately dark color, and poor to good internal drainage. The watershed has a very low topographic relief (Houston Engineering, 2001); its local relief is less than 5 m and global relief is only up to 350 m, with the elevation ranging from 255 to 600 m. The precipitation and temperature within the watershed vary negligibly with topographic elevation (M. M. Ziemer, personal communication, 2004). The National Weather Service (NWS) National Climate Data Center (NCDC) collects data on daily precipitation and minimum and maximum temperatures at stations PR and PR215012, which are located within the watershed, and at four other stations, PR212142, PR212916, PR213104, and PR218191, which abut the watershed (fig. 1). The numbers in these labels signify the 6-digit NWS COOP IDs (cooperative station identifiers) for these stations. The NWS has found that the data measured at these six stations provide good information on the spatial and temporal distributions of precipitation and temperature in the study watershed (M. M. Ziemer, personal communication, 2004). The periods for which records are available and summary statistics of the observed data for these six stations are listed in table 1. Across the stations, data for 11% of the record periods (on average) were unavailable, but for the period only 5.5% of the data were missing. A close examination revealed that the values were only unavailable for 1 to 50 days (mostly in summer) for any given year from 1974 to These few missing values would exert a limited influence, if any, on long-term simulation results. The possible influence would be even less for simulated stream flows in winter and spring. The data indicated an annual average precipitation of 607 mm, 24% of which (148 mm) was in the form of snowfall. The annual average daily temperature ranged from 44 C in winter to 40 C in summer, with a mean of 4.6 C. However, for a given year, the daily temperature could vary from 47 C to 13 C in winter, from 33 C to 34 C in spring, from 0 C to 37 C in summer, and from 31 C to 35 C in fall. The U.S. Geological Survey (USGS) has been monitoring daily stream flows within the study watershed at two stations, labeled USGS and USGS in figure 1. Station USGS , for which the upstream drainage area is 241,900 ha, monitors approximately the upper half of the watershed, and station USGS , for which the upstream drainage area is 404,030 ha, is near the watershed outlet in the west. The record periods and summary statistics of the observed daily stream flows for these two stations are listed in table 2. Across the periods of record, there were 20.2% and 2.3% missing values for stations USGS and , respectively; for the 23 years from 1975 to 1997, there were 26.1% missing values for station USGS and 3.5% for station USGS From 1975 to 1997, for station USGS , the daily stream flows from 1984 to 1989 were unavailable, but only the data in the months of January to April in 1985 were missing for station USGS However, station USGS has a complete record of observed daily stream flows for the water years (December to November) from 1975 to 1983 and from 1990 to 1997, and there is an even longer complete record of from 1975 to 1984 and from 1986 to 1997 for station USGS Therefore, the data on daily stream flows for the years with a complete record at these two stations were used for model evaluation in this study. The data indicated that in spring, the daily peak discharges ranged from 4 to 230 m 3 /s at station USGS , and from 7 to 290 m 3 /s at station Table 1. Record periods and summary statistics of daily precipitation and minimum and maximum temperatures for the National Weather Service (NWS) stations used in this study. Stations PR and PR are located within the Wild Rice River watershed, Minnesota, and the remaining four stations abut the watershed. Missing within the Record Annual Average Annual Average Across 1974 Precipitation [b] Daily Temperature [b] Period of Record the Period to 1997 (mm H 2 O) ( C) Station [a] Duration Total Days Days % Days % Total Snowfall % Min. Max. Mean PR Jan to 30 Dec PR Jan to 30 Dec PR Jan to 30 Dec PR Nov to 30 Dec PR Jan to 30 Dec PR Jan to 30 Dec Average [a] The number in the label is the 6-digit NWS COOP ID (cooperative station identifier) for the station. [b] The statistics on precipitation and temperature were computed using the data available for the period of record. 4 TRANSACTIONS OF THE ASAE

5 Table 2. Record periods and summary statistics of the daily stream flows for the U.S. Geological Survey (USGS) gauging stations and , located within and near the outlet, respectively, of the Wild Rice River watershed, Minnesota. Missing within the Record Across the Period 1975 to 1997 Daily Peak Discharges in Spring (m 3 /s) [b] Water Years with Station Period of Record Days % Days % Complete Records [a] Min. Max. Mean USGS 1 July Dec to 31 Aug. 1983, to 30 Sept Dec to 30 Nov USGS 1 Apr Dec to 31 Aug. 1984, to 30 Sept Dec to 30 Nov Average [a] For the Wild Rice River watershed, a water year is defined as December to November. [b] The statistics were computed using the data of the water years with complete records. USGS Near the watershed outlet, the annual average daily peak discharge in spring was about 80 m 3 /s. MODEL INPUT DATA In this study, the basic model inputs included the 30 m USGS National Elevation Dataset (NED), the EPA 1:250,000-scale LULC, and the USDA-NRCS (Natural Resources Conservation Service) State Soil Geographic database (STATSGO). The NED was developed by merging the highest-resolution, best-quality elevation data available across the U.S. into a seamless raster format (USGS, 2001a). The LULC was developed by combining the data obtained from 1970s and 1980s aerial photography surveys with land use maps and surveys (EPA, 2003). As mentioned above, there have been negligible changes in the types of land use in the past two decades for the Wild Rice River watershed. Hence, the LULC was an appropriate choice for this study. Data for the STATSGO are collected at the USGS 1:250,000-scale in 1- by 2-degree topographic quadrangle units, and then merged and distributed as state coverages. The STATSGO has a county-level resolution and can readily be used for river-basin water resource studies (USDA-SCS, 1993). The NED and LULC were downloaded from the USGS website ( and the STATSGO was downloaded from the USDA-NRCS website ( /ssb/products). In addition to these three datasets, the USGS National Hydrography Dataset (NHD) was also used as a model input. The NHD is a comprehensive set of digital spatial data that contains information about surface water features such as lakes, ponds, streams, rivers, springs, and wells (USGS, 2001b). This study utilized the NHD stream feature as the reference surface water drainage network to delineate subbasins for the study watershed for modeling purposes. The ArcView Interface for SWAT 2000, developed by Di Luzio et al. (2002), was used to delineate the boundaries of the entire watershed and its subbasins, along with their drainage channels. The boundaries for the subbasins were determined by trial and error to ensure the delineated drainage channels closely matched the drainage network presented by the NHD. As a result, the watershed was subdivided into 485 subbasins, with sizes ranging from 0.9 to 5386 ha. Further, LULC and STATSGO were used to define multiple HRUs for each of the 485 subbasins. With the SWAT-recommended threshold levels of 20% and 10% for land use and soil, respectively (Di Luzio et al., 2002), the interface defined one to three HRUs for these subbasins, resulting in a total of 993 HRUs for the watershed. The values for the parameters used to configure the model were automatically extracted and/or estimated from these datasets by the interface. In SWAT, these parameters are grouped at the levels of watershed, subbasin, and HRU, and are described in detail by Neitsch et al. (2002a). The data on daily precipitation and minimum and maximum temperatures for the six NWS stations (fig. 1) were preprocessed into database files with the SWAT-required format for a simulation period extending from 1 October 1974 to 30 November This simulation period was selected to minimize the missing data on precipitation and temperature (table 1). As discussed above, these missing values have only a limited influence on the simulated stream flows in summer and fall, and their possible influence on simulating stream flows in other seasons (e.g., spring) is likely to be negligible. Further, during this simulation period, complete records on daily stream flows were available for 17 and 22 water years at stations USGS and , respectively (table 2), which makes the model evaluation possible. In addition, this period includes several of the largest historical snowfall events, which occurred in the winters of 1975, 1978,, and 1997 (Houston Engineering, 2001; Offelen et al., 2002). The missing values on daily precipitation and minimum and maximum temperatures, along with solar radiation, wind speed, and relative humidity, were simulated by the weather generator that is incorporated in the SWAT software package (Neitsch et al., 2002a). MEASURE OF MODEL PERFORMANCE A hydrologic model such as SWAT is said to have a good performance when the simulated flow hydrograph at a given location within a watershed is comparable with the corresponding observed hydrograph in terms of silhouette, volume, and peak. Besides visualization plots showing simulated versus observed values, researchers use various statistics as measures of model performance. These statistics include the Nash-Sutcliffe coefficient (Nash and Sutcliffe, 1970), volume deviation (Van Liew and Garbrecht, 2003), and error function (Lee et al., 1972). These statistics can be applied for daily, monthly, seasonal, and annual evaluation time steps. The Nash-Sutcliffe coefficient measures the overall fit to the silhouette of an observed flow hydrograph, but it may be an inappropriate measure for use in simulating the volume, which is computed by integrating the flow hydrograph over the evaluation period, and for predicting the peak(s) of the hydrograph. For example, Van Liew and Garbrecht (2003) reported a Nash-Sutcliffe coefficient of Vol. 48(4): 5

6 0.65 and a deviation of volume of 1.3% for subwatershed 522 in their study. However, subwatershed 526 had a higher Nash-Sutcliffe coefficient of 0.83 but also a higher deviation of volume of 17.6%. In the same study, they presented a high Nash-Sutcliffe coefficient of 0.71 for subwatershed 550, but the peaks in 1993 and 1995 were underpredicted by 30% and 50%, respectively. Therefore, in addition to the Nash-Sutcliffe coefficient, two extra statistics, namely deviation of volume and error function, are generally employed to test whether the volume and peak(s) of an observed hydrograph are appropriately predicted. When there is more than one flow gauging station or evaluation location within a study watershed, these statistics are generally computed and examined on an individual station basis (e.g., Qi and Grunwald, 2005). Hence, these statistics might simply be the indicators of model performance for an individual station rather than for the watershed as a whole. Further, it is frequently observed that the model might perform better for some of the stations than for others. For instance, Qi and Grunwald (2005) reported a moderately good model performance for the Rock station (with a Nash-Sutcliffe coefficient of 0.75) but a very poor model performance for the Bucyrus station (with a negative Nash-Sutcliffe coefficient of 0.04). Although it is the modelers goal to calibrate a SWAT model that can satisfactorily predict all three of the aspects (silhouette, volume, and peak) of observed flow hydrographs for all the gauging stations within a study watershed, the model is unlikely to be able to predict all of these three aspects for each of the stations (e.g., Van Liew and Garbrecht, 2003; Qi and Grunwald, 2005). From the watershed perspective, and depending on the aspect(s) and location(s) of interest, the model may or may not be judged to have a satisfactory performance. In this study, in addition to the Nash-Sutcliffe coefficient, a measure designated performance virtue (PV k ) was developed and used for model evaluation. PV k is defined as the weighted average of the Nash-Sutcliffe coefficients, deviations of volume, and error functions across all of the evaluation stations. PV k can be computed as: PVk = N j= 1 j [ 2 α ω E + ω ( 1 D ) + ω (1 E )] j1 j j2 vj j3 RRj where E 2 j is the Nash-Sutcliffe coefficient at station j (eq. 7), D vj is the deviation of volume at station j (eq. 8), E RRj is the peak-flow-weighted error function at station j (eq. 9), and j1, j2, and j3 are the weights reflecting the priorities of simulating the silhouette, volume, and peak of the stream flow hydrograph, respectively, observed at station j. A higher weight indicates a higher priority, and the weights must sum to unity, i.e., j1 + j2 + j3 = 1.0. When the three aspects have an equivalent modeling priority, then j1 = j2 = j3 = 1/3. The weighting factor ( j ) reflects the influence on the model of station j. A station with a higher weight will exert a greater influence on the model evaluation, and vice versa. The weights for the N stations within the watershed are also N subject to α j = j= 1 The Nash-Sutcliffe coefficient (E 2 j ) is computed as: (6) n j j j 2 (Qobs i Qsim i ) 2 i= 1 E j = 1 (7) n j j j 2 (Qobs i Qmean ) i= 1 j j where Q simi and Q obsi are the simulated and observed stream flows, respectively, on the ith time step for station j, and j j Q mean is the average of Q obsi across the n j evaluation time steps. The deviation of volume (D vj ) is computed as: n j n j j j Q Q 1 sim i 1 obs i i= i= Dv j = 100% (8) n j j Q i= 1 obs i The peak-flow-weighted error function (E RRj ) is computed as: ERRj = 2 2 m p p p p j jk jk Q Q jk jk T T jkp Q obs sim obs sim obs + jkp 1 Q T k= obs c m j jkp Qobs k= % p where m j is the number of evaluation years at station j, Q jk sim p and Q jk obs are the simulated and observed peak discharges, respectively, for evaluation year k at station j, T jk p p sim and T jk obs are the timings of the simulated and observed peaks, respectively, for evaluation year k at station j, and T c is the SWATestimated time of concentration for the watershed (Neitsch et al., 2002a). The value of E 2 j can range from to 1.0, with higher values indicating a better overall fit and 1.0 indicating a perfect fit. A negative E 2 j indicates that for station j the simulated stream flows are less reliable than if one had used the average of the observed stream flows, while a positive value indicates that they are more reliable than using this average. The value of D vj can range from very small negative to very large positive values, with values close to zero indicating a better simulation and zero indicating an exact prediction of the observed volume. In contrast with E 2 j, E RRj can range from 0.0 to +, with lower values indicating a better simulation of the observed peak and 0.0 indicating that both the magnitude and timing of the observed peak can be exactly predicted by the model. Defined by integrating E 2 j, D vj, and E RRj, PV k can range from to 1.0. As with E 2 j, a value of 1.0 for PV k indicates that the model exactly simulates all three aspects (silhouette, volume, and peak) of the observed stream flow hydrographs for all of the gauging stations within the watershed. A negative PV k indicates that the simulated stream flows are less reliable than if one had used the average values, spanning the evaluation period across the stations, of the observed stream flows. Given a combination of j1, j2, j3, and j, a model with a higher (9) 6 TRANSACTIONS OF THE ASAE

7 PV k value is said to have an overall better performance from the watershed perspective. In this study, it was assumed that in terms of model evaluation, the three aspects have an equivalent modeling priority and that the two USGS stations, and , are equivalently important, resulting in 11 = 12 = 13 = 21 = 22 = 23 = 1/3 and 1 = 2 = 1/2. Based on the author s experience, a model is judged to have a poor performance when PV k is less than 0.6, an acceptable performance when PV k is between 0.6 and 0.7, a satisfactory performance when PV k is between 0.7 and 0.8, and a good performance when PV k is greater than 0.8. MODEL EVALUATION METHOD The daily stream flows observed at station USGS from 1 December 1989 to 31 November 1997 and at station USGS from 1 December 1985 to 31 November 1997 were used to calibrate the SWAT model, which was then validated using the observed daily stream flows at station USGS from 1 December 1974 to 31 August 1983 and at station USGS from 1 December 1974 to 31 August The calibration was implemented in two steps, consisting of: (1) conducting a sensitivity analysis to identify the snowmelt-related parameters that are sensitive for the simulation, and (2) adjusting the values for the identified sensitive parameters and for additional three watershed-level parameters, namely the surface runoff lag coefficient (variable SURLAG) and the Muskingum translation coefficients for normal flow (variable MSK_CO1) and for low flow (variable MSK_CO2), and five HRU-level parameters, namely the SCS curve number (variable CN2), threshold depth of water in the shallow aquifer required for return flow to occur (variable GWQMN), groundwater revap coefficient (variable GW_REVAP), threshold depth of water in the shallow aquifer for revap or percolation to the deep aquifer to occur (variable RE- VAPMN), and soil evaporation compensation factor (variable ESCO). The seven snowmelt-related parameters (SFTMP, SMTMP, SMFMX, SMFMN, TIMP, SNOCOVMX, and SNO50COV), discussed in the section on the SWAT model s snowmelt hydrology, were varied separately in order to determine the model sensitivity in daily stream flow simulations. The ranges for these parameters are listed in table 3. Both SMFMX and SMFMN were varied from 1.4 to 6.9 mm H 2 O/ C-day. This range was based on Huber and Dickinson (1988) and Westerstrom (1984), and suggested by the SWAT developers (Neitsch et al., 2002a). The ranges for the other five parameters were based on suggestions from an expert familiar with the Wild Rice River watershed (M. M. Ziemer, personal communication, 2004). These are thought to be typical ranges for these parameters in northwestern Minnesota, where the study watershed is located. The ranges were divided into 10 to 15 increments, and each incremental value was then tested. When one parameter was varied, the others were held at the mean values of the corresponding ranges. For example, when the SMTMP was varied from 0.0 C to 3.0 C, with an incremental value of 0.3 C, the SFTMP, SMFMX, SMFMN, TIMP, SNO- COVMX, and SNO50COV parameters were held at values of 0.25 C, 4.15 mm H 2 O/ C-day, 4.15 mm H 2 O/ C-day, 0.5, 20.0 mm H 2 O, and 0.2, respectively. Because these parameters are independent of the stream flows generated from rainfall runoff, the sensitivity was examined in terms of the simulated versus observed daily stream flows in spring of the evaluation years. The values for the PV k measure (eq. 6) were computed for the increments. In this study, a parameter was empirically considered sensitive if its variation resulted in a change in PV k of more than 5%. Along with the identified sensitive snowmelt-related parameters, the parameters SURLAG, MSK_CO1, MSK_CO2, CN2, GWQMN, GW_REVAP, REVAPMN, and ESCO were adjusted using the PEST (Parameter ESTimation) software developed by Doherty (2001, 2002, 2004) to minimize an objective function comprised of three components. These were the summed weighted squared differences over the aforementioned calibration periods between: (1) model-generated and observed daily stream flows, (2) monthly volumes calculated on the basis of modeled and observed daily stream flows, and (3) exceedence times for various flow thresholds calculated on the basis of modeled and observed daily stream flows. The weights were used to differentiate the reliability and/or importance of the observed daily stream flows for the calibration (Doherty and Johnston, 2003). For instance, in order to calibrate the model for all seasons, the weights should be chosen to ensure that high flows do not dominate the parameter estimation process simply because of their large numerical values. In this study, the means of the ranges that were used in the sensitivity analysis were specified as the initial values for the snowmeltrelated parameters, while the SWAT default values were taken as the initial values for the five HRU-level parameters, which might vary from HRU to HRU, and the three watershed-level parameters of SURLAG (0.4 days), MSK_CO1 (0.35), and MSK_CO2 (0.35). PEST is a modelindependent parameter estimator with advanced predictive analysis and regularization features. Its model independence relies on the fact that it is able to communicate with a model through the latter s own input and output files, thus allowing Table 3. Summary of the sensitivity analysis on the seven snowmelt-related parameters. PV k Change Snowmelt-Related Parameter Range [a] (%) Sensitive [b] SFTMP Snowfall temperature ( C) 1.5 to No SMTMP Snowmelt temperature ( C) 0.0 to Yes SMFMX Maximum snowmelt factor (mm H 2 O/ C-day) 1.4 to Yes SMFMN Minimum snowmelt factor (mm H 2 O/ C-day) 1.4 to No TIMP Snowpack temperature gag factor 0.0 to Yes SNOCOVMX Minimum snow water content that corresponds to 100% snow cover (mm H 2 O) 5.0 to No SNO50COV Fraction of SNOCOVMX that corresponds to 50% snow cover 0.05 to No [a] The ranges for SMFMX and SMFMN were based on Huber and Dickinson (1988) and Westerstrom (1984), and were suggested by the SWAT developers (Neitsch et al., 2002a). For the remaining five parameters, the ranges were based on the suggestions from M. M. Ziemer (personal communication, 2004). [b] PV k is performance virtue (eq. 6). A parameter was empirically considered sensitive if its variations resulted in a PV k change of more than 5%. Vol. 48(4): 7

8 easy calibration setup with an arbitrary model. PEST implements a particularly robust variant of the Gauss-Marquardt- Levenberg method of parameter estimation. Subsequently, the PEST-determined values for these calibration parameters were manually adjusted to further refine the model. The calibrated SWAT model was then used to simulate the daily stream flows for both the calibration and validation periods. The simulation results were compared with the corresponding observed values at daily, monthly, seasonal, and annual time steps. Further, the Nash-Sutcliffe coefficient (E j 2 ) and the coefficient of determination (R 2 ) were used to detect the model performance discrepancies between the two stations, while the performance virtue (PV k ) was used to judge the model performance from the watershed perspective. In addition, typical plots showing the simulated versus observed daily stream flows for the year with the poorest simulation and for the years with a better simulation were used to further scrutinize the model performance. RESULTS AND DISCUSSION SENSITIVITY ANALYSIS Of the seven snowmelt-related parameters, variations in SMFMX, TIMP, and SMTMP resulted in PV k changes of 6.3%, 8.5%, and 14.3%, respectively, whereas variations in the other four parameters resulted in PV k changes of less than 2.1% (table 3). Hence, the parameters SMFMX, TIMP, and SMTMP were considered sensitive and taken as calibration parameters. Variations of SMFMX, the maximum snowmelt factor, from 1.4 to 3.4 mm H 2 O/ C-day resulted in a gradual increase of PV k. Further increase of this parameter, however, decreased PV k (fig. 2). SMFMX is related to the snow melting rate, so any increase in its value may result in a bigger melt factor (eq. 5) and thus a higher melting rate (eq. 4). In 2π equation 5, the term sin ( i 81) varies from 1.0 on January to 1.0 on 31 December. A large negative value for this term makes the influence of SMFMX on the melt factor smaller, while a large positive value makes the influence of SMFMX larger. For the study watershed, the major snowmelt occurred from late March to May, during which time this term had a value between 0.0 and Thus, the parameter SMFMX exerts a greater influence on the melt factor and is sensitive for the simulation. In contrast, the influence of SMFMN, the minimum snowmelt factor, on the melt factor tends to be offset because it has a positive sign in the first term but a negative sign in the second term on the right side of equation 5. In addition, the parameter SMFMX is an attribute of, and is thus specific to, a particular watershed. An SMFMX value of 1.4 to 3.4 mm H 2 O/ C-day thus appears to be appropriate for the Wild Rice River watershed. Plotting PV k versus SMTMP resulted in an approximately parabolic curve (fig. 3), indicating that the model performance might be improved by adjusting SMTMP to an appropriate value. SMTMP defines when a snowpack starts and/or stops melting, thus affecting the snowpack amount available for melting on a specific day. As a result, the simulated stream flow hydrograph, in terms of its silhouette and peak, is influenced by variations in SMTMP. Theoretically, the SFTMP has a close relationship with the snowpack accumulation (particularly in winter) because it is used within SWAT to classify precipitation as rain or snow. However, variations of this parameter resulted in only a small change in PV k (1.6%). A close examination of the temperature data revealed that for the study watershed, during winter and in March and early April, the mean daily air temperature was mostly below the lower bound of the variation range ( 1.5 C to 1.0 C). Regardless of the variations, the precipitation that occurred during these periods was mainly classified as snow, leading to the relative insensitivity of SFTMP for the simulation. In addition to the parameters SMFMX and SMTMP, the simulation was also expected to be sensitive to variations in TIMP, the snowpack temperature lag factor (fig. 4), which influences prediction of the snowpack temperature on a given day (eq. 3). In conjunction with SMTMP, the predicted snowpack temperature also defines when the snowpack starts and/or stops melting, and thus affects the snowpack amount available for melting on that day. As a result, varying the parameter TIMP was sensitive for the simulation Performance Virtue (PV k ) SMFMX (mm H 2 O/ C-day) Figure 2. Plot showing the performance virtue (PV k ) versus increments in the maximum snowmelt factor (SMFMX). 8 TRANSACTIONS OF THE ASAE

9 Performance Virtue (PV k ) SMTMP ( C) Figure 3. Plot showing the performance virtue (PV k ) versus increments in the snowmelt temperature (SMTMP). The snowpack within the study watershed mainly accumulated as a result of the snowfall throughout the winter and in early spring; over this period, only a small amount of the snowpack was lost to sublimation and sporadic melting. The annual average snowpack by late March, when the major snowmelt starts, was 148 mm for the study period (table 1), exceeding the upper bound of the variation range (5.0 to 35.0 mm). As mentioned above, the areal depletion curve affects snowmelt by following equation 2 only when the snowpack water content is between 0.0 and SNOCOVMX. Thus, variations of SNOCOVMX and SNO50COV were not sensitive for the simulation in this study. The range of 5.0 to 35.0 mm for SNOCOVMX reflected the watershed character of very low topographic relief. A snowpack with water content of up to 35.0 mm was sufficient to completely cover the entire area of the watershed (M. M. Ziemer, personal communication, 2004). Similarly, the watershed character was also reflected by the range of SNO50COV (0.05 to 0.35), which has an upper bound of less than 0.5. MODEL SIMULATION RESULTS As with many other watersheds, the observed stream flows at the two USGS gauging stations in the Wild Rice River watershed showed a magnitude variation in seasonal, monthly, and even daily time scales. The stream flows were generally highest in spring but lowest in winter (tables 4a, 4b, 5a, and 5b). For most of the evaluation years, in spring the flows were highest in April and/or May, whereas in winter the flows were lowest in January. Further, due to its larger drainage area, the stream flows at the downstream station, USGS , were higher than at the upstream station, USGS To ensure that high flows do not dominate the parameter estimation process simply because of their large numerical values, weights assigned to the individual daily stream flow observations were calculated using the formula suggested by Doherty and Johnston (2003). This formula gave appropriately greater weights for lower flow observations than for higher ones. As a result, all of the flow observations used to calibrate the SWAT model may play a supposed role in the aforementioned objective function that was minimized by PEST. Subsequently, the PEST-deter Performance Virtue (PV k ) TIMP Figure 4. Plot showing the performance virtue (PV k ) versus increments in the snowpack temperature lag factor (TIMP). Vol. 48(4): 9

10 Calibration Year Table 4a. Predicted and observed (in bold type) daily peak discharges, monthly mean discharges, seasonal mean discharges, and annual mean discharges at station of Wild Rice River at Twin Valley (USGS ) for the calibration water years (December to November). The seasonal months include December to February for winter, March to May for spring, June to August for summer, and September to November for fall. The blank cells indicate data that are not applicable for the tabulation. Daily Peak (m 3 /s) Monthly Mean Discharge (m 3 /s) Seasonal Mean Discharge (m 3 /s) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Winter Spring Summer Fall Annual Mean Discharge (m 3 /s) Avg mined values for the aforementioned eleven calibration pa rameters were manually adjusted to further refine the model. After calibration, the model was validated using the same set of parameters for the two gauging stations. For station USGS , the annual mean discharge during the calibration period was overpredicted by only 5% (table 4a), indicating that the model had a very good performance. The prediction errors of the seasonal mean discharges for spring and winter had absolute values of less than 4%, whereas the seasonal mean discharges were overpredicted by 23% for summer but underestimated by 22% for fall. This is probably because the SWAT model Validation Year Table 4b. Predicted and observed (in bold type) daily peak discharges, monthly mean discharges, seasonal mean discharges, and annual mean discharges at station of Wild Rice River at Twin Valley (USGS ) for the validation water years (December to November). The seasonal months include December to February for winter, March to May for spring, June to August for summer, and September to November for fall. The blank cells indicate data that are not applicable for the tabulation. Daily Peak (m 3 /s) Monthly Mean Discharge (m 3 /s) Seasonal Mean Discharge (m 3 /s) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Winter Spring Summer Fall Annual Mean Discharge (m 3 /s) Avg TRANSACTIONS OF THE ASAE