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.
T
he 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,
1996; 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 2005.
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:
701-777-5224; e-mail: [email protected].
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):
E 2005 American Society of Agricultural Engineers ISSN 0001−2351
1
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 1996 (the model calibration year)
yielded Nash-Sutcliffe coefficients (Ej 2, computed by eq. 7
below) of −0.04 and 0.19, respectively, whereas monthly
totals of the data indicated much higher Ej 2 values of 0.58 for
1995 and 0.89 for 1996. 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 (Ej 2 = 0.62) and
monthly (Ej 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 Ej 2 value of 0.86. 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
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:
SNO i = SNO i −1 + R sfi − E subi − SNO mlti
(1)
where SNOi and SNOi−1 are the water equivalents of the
snowpack on the current day (i) and previous day (i−1), respectively, Rsfi is the water equivalent of the snow precipitation on day i, Esubi is the water equivalent of the snow
sublimation on day i, and SNOmlti 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, 1976) and is defined as:
snocov i =
+ exp(cov1 − cov 2 ⋅
SNO i
⎤
)⎥
SNOCOVMX ⎦
−1
(2)
where snocovi 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
H2O), and cov1 and cov2 are the coefficients that define the
shape of the curve. The values used for cov1 and cov2 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, cov1 and cov2 will take the values of −1.2399 and
1.8482, respectively.
The value of snocovi 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 (1976) 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 Tspi and Tspi−1 are the snowpack temperatures on the
current day (i) and the previous day (i−1), respectively, and
Tai is the mean air temperature on day i. As TIMP approaches
1.0, Tai exerts an increasingly greater influence on Tspi ; conversely, as TIMP moves away from 1.0, Tspi−1 becomes more
important.
The amount of snowmelt on the current day (i), SNOmlti ,
expressed in terms of the equivalent amount of water in mm,
or melting rate, is calculated in SWAT as:
⎛ Tspi + Tmaxi
⎞
SNO mlti = bmlti ⋅ snocovi ⎢⎢
− SMTMP ⎟⎟ (4)
2
⎝
⎠
where Tmaxi is the maximum air temperature on day i (°C),
SMTMP is the base temperature above which snowmelt is allowed (°C), and bmlti is the melt factor on day i (mm H2O/°Cday), which is calculated as:
bmlti =
+
Vol. 48(4):
SNO i
SNO i
⎡
⎪
SNOCOVMX ⎣SNOCOVMX
SMFMX + SMFMN
2
SMFMX − SMFMN
⎡ 2π
⎤
⋅ sin ⎪
(i − 81)⎥
2
⎣365
⎦
(5)
3
where SMFMX and SMFMN are the maximum and minimum snowmelt factors, respectively (mm H2O/°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 PR210018
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 1974-1997 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 1997. 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 05062500 and USGS 05064000 in figure 1.
Station USGS 05062500, for which the upstream drainage
area is 241,900 ha, monitors approximately the upper half of
the watershed, and station USGS 05064000, 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 05062500
and 05064000, respectively; for the 23 years from 1975 to
1997, there were 26.1% missing values for station USGS
05062500 and 3.5% for station USGS 05064000. From 1975
to 1997, for station USGS 05062500, 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 05064000. However, station USGS 05062500 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
05064000. 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 m3/s
at station USGS 05062500, and from 7 to 290 m3/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 PR210018 and PR215012 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]
the Period
to 1997
(mm H2O)
(°C)
Period of Record
Duration
Total Days
Days %
Days
%
Total Snowfall %
Min. Max. Mean
Station[a]
PR210018
PR212142
PR212916
PR213104
PR215012
PR218191
Average
[a]
[b]
4
1 Jan. 1949 to 30 Dec. 1997
1 Jan. 1949 to 30 Dec. 1997
1 Jan. 1949 to 30 Dec. 1997
1 Nov. 1962 to 30 Dec. 1997
1 Jan. 1949 to 30 Dec. 1997
1 Jan. 1949 to 30 Dec. 1997
17896
17896
17896
12845
17896
17896
542 3.0
1432 8.0
721 4.0
930 7.2
64
0.4
7374 41.2
304
1116
670
326
4
1014
3.5
6.2
7.6
3.7
0.1
12.0
590
641
612
554
608
635
150
146
137
141
157
156
25
23
22
25
26
25
−42
−43
−47
−41
−44
−44
41
38
39
42
39
39
5.1
4.4
4.1
5.0
4.5
4.5
17054
1844 10.6
572
5.5
607
148
24
−44
40
4.6
The number in the label is the 6-digit NWS COOP ID (cooperative station identifier) for the station.
The statistics on precipitation and temperature were computed using the data available for the period of record.
TRANSACTIONS OF THE ASAE
Table 2. Record periods and summary statistics of the daily stream flows for the U.S. Geological Survey (USGS) gauging stations
05062500 and 05064000, located within and near the outlet, respectively, of the Wild Rice River watershed, Minnesota.
Missing within the Record
Across
the Period
Station
Period of Record
Days
%
Days
%
USGS
05062500
1 July 1909
to 30 Sept. 2003
2874
20.2
908
26.1
USGS
05064000
1 Apr. 1944
to 30 Sept. 2003
211
2.3
120
3.5
1543
11.3
514
14.8
Average
[a]
[b]
1975
to 1997
Water Years with
Complete Records[a]
1 Dec. 1974 to 31 Aug. 1983,
1 Dec. 1989 to 30 Nov. 1997
1 Dec. 1974 to 31 Aug. 1984,
1 Dec. 1985 to 30 Nov. 1997
Daily Peak Discharges
in Spring (m3/s)[b]
Min.
Max.
Mean
4.0
232.2
63.1
6.9
291.7
100.6
5.5
262.0
81.9
For the Wild Rice River watershed, a water year is defined as December to November.
The statistics were computed using the data of the water years with complete records.
USGS 05064000. Near the watershed outlet, the annual average daily peak discharge in spring was about 80 m3/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 (http://edc.usgs.gove/geodata), and the
STATSGO was downloaded from the USDA-NRCS website
(http://www.ncgc.nrcs.usda.gov/branch /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
Vol. 48(4):
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 1997. 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 05062500 and
05064000, 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, 1979, 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
5
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” (PVk) was developed and used for model
evaluation. PVk is defined as the weighted average of the
Nash-Sutcliffe coefficients, deviations of volume, and error
functions across all of the evaluation stations. PVk can be
computed as:
PVk =
N
∑ αj [ω j1E 2j + ω j 2(1 − D vj )+ ω j 3 (1 − E RRj ) ]
j =1
(6)
where Ej 2 is the Nash-Sutcliffe coefficient at station j (eq. 7),
Dvj is the deviation of volume at station j (eq. 8), ERRj is the
peak-flow-weighted error function at station j (eq. 9), and
wj1, wj2, and wj3 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., wj1 + wj2 + wj3 = 1.0. When the three aspects
have an equivalent modeling priority, then wj1 = wj2 = wj3 =
1/3. The weighting factor (aj ) 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 = 1.0 .
j =1
The Nash-Sutcliffe coefficient (Ej 2) is computed as:
6
nj
E 2j = 1 −
j
j
2
∑ (Q obs
i − Q simi )
i =1
nj
(7)
j
∑ (Q obs
i
i =1
j
− Q mean
)2
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 nj evaluation time
steps.
The deviation of volume (Dvj ) is computed as:
nj
D vj =
nj
j
j
∑ Q simi − ∑ Q obsi
i =1
i =1
nj
×100%
(8)
j
∑ Q obsi
i =1
The peak-flow-weighted error function (ERRj ) is computed as:
E RRj =
1
⎡⎛ jkp
jkp ⎞ 2 ⎛ jkp
jkp ⎞ 2 ⎤ 2
Tobs − Tsim
jkp ⎪⎢ Qobs − Qsim ⎟
⎢
⎟ ⎥
+
∑ Qobs ⎪⎢
jkp
⎟
⎢
⎟ ⎥
T
Qobs
c
k =1
⎠ ⎝
⎠ ⎥⎦
⎪⎣⎝
× 100%
mj
mj
(9)
jkp
∑ Qobs
k =1
jkp
where mj is the number of evaluation years at station j, Q sim
jkp
and Q obs are the simulated and observed peak discharges, rejkp
jkp
spectively, for evaluation year k at station j, Tsim and Tobs
are the timings of the simulated and observed peaks, respectively, for evaluation year k at station j, and Tc is the SWATestimated time of concentration for the watershed (Neitsch et
al., 2002a).
The value of Ej 2 can range from −∞ to 1.0, with higher
values indicating a better overall fit and 1.0 indicating a
perfect fit. A negative Ej 2 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 Dvj 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 Ej 2, ERRj
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 Ej 2,
Dvj , and ERRj , PVk can range from −∞ to 1.0. As with Ej 2, a
value of 1.0 for PVk 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 PVk 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 wj1, wj2, wj3, and aj , a model with a higher
TRANSACTIONS OF THE ASAE
PVk 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,
05062500 and 05064000, are equivalently important, resulting in w11 = w12 = w13 = w21 = w22 = w23 = 1/3 and a1 = a2 =
1/2. Based on the author’s experience, a model is judged to
have a poor performance when PVk is less than 0.6, an
acceptable performance when PVk is between 0.6 and 0.7, a
satisfactory performance when PVk is between 0.7 and 0.8,
and a good performance when PVk is greater than 0.8.
MODEL EVALUATION METHOD
The daily stream flows observed at station USGS
05062500 from 1 December 1989 to 31 November 1997 and
at station USGS 05064000 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 05062500 from 1 December 1974 to
31 August 1983 and at station USGS 05064000 from
1 December 1974 to 31 August 1984. 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 REVAPMN), 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 H2O/°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, SNOCOVMX, and SNO50COV parameters were held at values of
−0.25°C, 4.15 mm H2O/°C-day, 4.15 mm H2O/°C-day, 0.5,
20.0 mm H2O, 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 PVk 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 PVk 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.
Snowmelt-Related Parameter
SFTMP
SMTMP
SMFMX
SMFMN
TIMP
SNOCOVMX
SNO50COV
Snowfall temperature (°C)
Snowmelt temperature (°C)
Maximum snowmelt factor (mm H2O/°C-day)
Minimum snowmelt factor (mm H2O/°C-day)
Snowpack temperature gag factor
Minimum snow water content that corresponds to 100% snow cover (mm H2O)
Fraction of SNOCOVMX that corresponds to 50% snow cover
Range[a]
PVk Change
(%)
Sensitive[b]
−1.5 to 1.0
0.0 to 3.0
1.4 to 6.9
1.4 to 6.9
0.0 to 1.0
5.0 to 35.0
0.05 to 0.35
1.6
14.3
6.3
2.1
8.5
1.2
0.1
No
Yes
Yes
No
Yes
No
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 is performance virtue (eq. 6). A parameter was empirically considered sensitive if its variations resulted in a PV change of more than 5%.
k
k
Vol. 48(4):
7
easy calibration setup with an arbitrary model. PEST implements a particularly robust variant of the Gauss-MarquardtLevenberg 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
(Ej 2) and the coefficient of determination (R2) were used to
detect the model performance discrepancies between the two
stations, while the performance virtue (PVk) 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 PVk changes of
6.3%, 8.5%, and 14.3%, respectively, whereas variations in
the other four parameters resulted in PVk 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 H2O/°C-day resulted in a gradual
increase of PVk. Further increase of this parameter, however,
decreased PVk (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
⎤
(i − 81)⎥ varies from −1.0 on 1
equation 5, the term sin ⎪
365
⎦
⎣
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 0.93. 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 H2O/°C-day thus appears to be
appropriate for the Wild Rice River watershed.
Plotting PVk 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 PVk (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.
0.80
Performance Virtue (PVk)
0.75
0.70
0.65
0.60
0.55
0.50
1.4
1.9
2.4
2.9
3.4
3.9
4.4
4.9
5.4
5.9
6.4
6.9
SMFMX (mm H2O/5C-day)
Figure 2. Plot showing the performance virtue (PVk) versus increments in the maximum snowmelt factor (SMFMX).
8
TRANSACTIONS OF THE ASAE
0.80
Performance Virtue (PVk)
0.75
0.70
0.65
0.60
0.55
0.50
0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3.0
SMTMP (5C)
Figure 3. Plot showing the performance virtue (PVk) 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 05064000, were higher than at the upstream station,
USGS 05062500. 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−
0.80
Performance Virtue (PVk)
0.75
0.70
0.65
0.60
0.55
0.50
0.04
0.12
0.20
0.28
0.36
0.44
0.52
0.60
0.68
0.76
0.84
0.92
1.00
TIMP
Figure 4. Plot showing the performance virtue (PVk) versus increments in the snowpack temperature lag factor (TIMP).
Vol. 48(4):
9
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 05062500) 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.
Annual
Calib- Daily
Monthly Mean Discharge (m3/s)
Seasonal Mean Discharge (m3/s)
Mean
ration Peak
Discharge
Winter Spring Summer Fall
Year (m3/s) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
(m3/s)
1989
0.72
0.46
1990 37.00 0.47 0.58 15.85 6.12 5.19 6.99 2.74 0.05 0.00 0.20 0.04 0.44
0.55
9.05
3.26
0.08
3.23
20.59 0.49 0.64 4.67 8.70 6.42 4.90 1.68 0.32 0.15 0.29 0.56 0.45
0.51
6.58
2.27
0.33
2.42
1991 34.06 0.46 1.76 11.00 8.51 16.91 5.74 6.75 3.35 0.62 0.10 0.62 0.89
1.03 12.14
5.28
0.45
4.72
19.17 0.48 0.76 2.63 4.62 11.89 2.92 2.80 0.57 0.57 0.58 0.74 0.93
0.72
6.40
2.09
0.63
2.46
1992 41.93 0.91 1.68 15.75 3.06 3.45 1.55 14.18 12.54 17.07 5.27 2.77 2.54
1.71
7.42
9.42
8.37
6.73
21.24 1.09 1.16 8.12 4.44 5.04 1.85 8.88 5.33 5.91 1.77 2.12 2.03
1.43
5.88
5.39
3.25
3.99
1993 114.00 1.69 1.46 4.25 19.71 6.93 11.39 32.50 40.14 5.29 1.32 0.49 2.69
1.94 10.30
28.01 2.37
10.65
111.00 1.88 1.80 6.47 15.46 7.73 9.70 30.56 28.98 7.98 3.15 2.84 2.76
2.16
9.83
23.23 4.64
9.96
1994 37.54 2.17 2.01 9.72 11.23 10.95 17.05 14.86 6.83 5.31 3.12 2.46 5.69
3.29 10.63
12.91 3.63
7.62
49.55 2.59 2.57 8.23 18.11 14.13 14.64 16.30 5.47 6.74 11.19 9.53 5.70
3.66 13.44
12.11 9.18
9.60
1995 39.66 5.52 3.35 16.44 14.39 10.47 3.63 20.79 8.59 4.69 7.43 1.16 3.45
4.11
13.77
11.00 4.43
8.33
62.30 3.64 3.25 23.45 18.72 15.24 5.47 16.12 5.87 3.23 6.70 5.39 3.77
3.56 19.14
9.19
5.13
9.26
1996 95.39 2.94 3.02 0.42 39.98 29.44 9.67 1.50 0.78 0.19 0.38 4.58 2.69
2.88 23.28
3.98
1.72
7.97
104.77 3.73 3.88 3.81 46.59 32.82 8.69 2.57 1.45 0.89 1.67 6.09 2.92
3.50 27.53
4.18
2.87
9.52
1997 152.40 2.30 2.50 1.98 84.02 19.54 12.61 26.46 7.17 3.11 4.44 1.73
2.40 35.18
15.41 3.09
14.02
232.20 2.92 3.12 3.45 69.97 18.35 10.22 25.37 6.31 3.15 5.54 6.58
3.02 30.16
14.00 5.10
13.07
Avg.
69.00
77.60
2.06
2.10
2.04
2.15
9.43 23.38 12.86
7.60 23.33 13.95
8.58 14.97 9.93
7.30 13.03 6.79
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 05062500, the annual mean discharge
during the calibration period was overpredicted by only 5%
4.54
3.58
2.78
3.86
1.73
4.23
2.39
2.38
2.24
2.32
15.22
14.87
11.16
9.06
3.02
3.89
7.91
7.53
(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
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 05062500) 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.
Annual
Valid- Daily
Monthly Mean Discharge (m3/s)
Seasonal Mean Discharge (m3/s) Mean
ation Peak
Discharge
Winter Spring Summer Fall
Year (m3/s) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
(m3/s)
1974
1.54
1.86
1975 87.53 1.18 1.19 1.01 29.74 18.56 17.30 36.83 9.12 2.30 0.66 0.33 1.44
1.34 16.44 21.08 1.10
9.99
96.84 1.45 1.48 2.11 33.21 23.37 18.75 33.28 4.38 1.39 1.38 2.44 1.74
1.64 19.42 18.80 1.73
10.40
1976 21.50 1.34 2.53 7.91 8.10 2.39 1.09 0.02 0.00 0.00 0.00 0.00 0.26
1.38
6.13
0.37
0.00
1.97
35.11 1.66 1.75 8.96 16.10 4.33 1.85 0.92 0.22 0.11 0.30 0.35 0.22
1.20
9.73
0.99
0.25
3.04
1977 29.99 0.28 0.37 11.50 3.01 0.55 0.52 0.00 0.05 2.38 3.28 3.55 4.52
1.72
5.02
0.19
3.07
2.50
3.99 0.24 0.36 0.83 2.58 0.87 0.75 0.36 0.16 0.71 1.93 3.19 3.22
1.30
1.42
0.42
1.94
1.27
1978 114.90 2.18 1.21 1.85 52.71 8.43 4.54 3.10 2.87 2.36 0.13 0.40 0.95
1.44 21.00
3.50
0.96
6.73
167.07 1.94 1.34 2.12 42.72 8.72 3.72 2.14 1.94 2.83 1.38 1.21 1.05
1.45 17.58
2.59
1.80
5.85
1979 125.20 0.83 0.98 6.60 43.58 29.73 9.93 14.47 2.90 0.29 0.01 1.58 1.43
1.08 26.64
9.10
0.62
9.36
165.09 0.99 1.18 2.34 43.70 23.58 8.52 10.13 1.58 1.04 0.76 2.86 1.69
1.29 22.98
6.73
1.55
8.14
1980 48.89 1.07 1.11 0.44 20.91 2.43 0.49 0.08 0.08 1.66 0.15 0.10 0.52
0.90
7.93
0.22
0.64
2.42
26.90 1.30 1.36 2.07 14.27 3.51 0.86 0.31 0.23 0.33 0.54 0.73 0.53
1.06
6.54
0.46
0.53
2.15
1981 13.73 0.54 1.40 2.16 0.78 1.28 3.54 8.00 2.58 3.53 4.67 3.65 2.79
1.58
1.41
4.71
3.95
2.91
9.60 0.44 0.59 1.54 2.43 2.10 3.74 4.53 2.62 4.06 6.35 5.23 2.37
1.15
2.02
3.63
5.22
3.01
1982 53.64 1.46 1.19 0.67 31.11 17.27 4.61 2.93 1.53 0.12 5.57 3.55 2.19
1.61 16.35
3.02
3.08
6.02
33.98 1.53 1.42 4.89 24.79 16.29 5.66 1.73 0.70 0.42 3.93 3.45 1.41
1.45 15.22
2.66
2.62
5.49
1983 34.86 1.10 1.04 16.44 1.42 3.14 8.97 16.23 6.12
1.07
7.00
10.44
6.17
16.71 1.25 1.26 11.03 6.72 4.32 5.24 9.75 3.07
1.25
7.36
6.03
4.88
Avg.
10
58.92 1.11
61.70 1.20
1.22
1.19
5.40
3.99
21.26 9.31
20.73 9.68
5.66
5.45
9.07
7.02
2.80
1.66
1.58
1.36
1.81
2.07
1.65 1.74
2.43 1.56
1.35
1.31
11.99
11.36
5.85
4.70
1.68
1.96
5.34
4.91
TRANSACTIONS OF THE ASAE
Table 5a. 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 Hendrum (USGS 05064000) 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.
Annual
Calib- Daily
Monthly Mean Discharge (m3/s)
Seasonal Mean Discharge (m3/s) Mean
ration Peak
Discharge
Winter Spring Summer Fall
Year (m3/s) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
(m3/s)
1985
4.22
3.62
1986 61.06 2.19 3.32 7.49 37.65 31.70 13.44 7.80 0.68 1.97 1.40 1.84 1.96
2.92 25.61
7.31
1.74
9.39
107.60 3.42 2.89 17.00 67.01 45.62 13.99 5.86 2.49 3.52 5.28 5.33 3.62
3.40 42.95
7.38
4.71
14.68
1987 64.18 1.32 1.75 35.31 8.32 6.39 5.75 9.37 15.86 1.26 0.15 0.09 1.55
1.54 16.67 10.33 0.50
7.26
41.63 2.31 2.14 24.47 12.31 13.16 7.74 10.95 6.65 2.80 3.34 2.87 2.61
2.36 16.69
8.45
3.01
7.76
1988 42.52 1.36 1.26 17.02 24.69 5.69 2.69 0.88 6.57 8.42 8.87 3.34 2.31
1.65 15.80
3.38
6.88
6.92
33.41 1.87 1.68 13.23 20.31 5.85 1.55 0.46 0.63 0.87 0.90 1.46 1.42
1.66 13.05
0.87
1.08
4.28
1989 135.30 1.39 1.30 2.09 83.31 18.34 8.83 7.68 0.57 18.06 4.01 2.84 1.24
1.35 34.58
5.69
8.31
13.49
154.33 1.43 1.54 2.04 67.59 13.99 7.45 1.73 0.38 3.10 1.18 1.59 0.49
1.14 27.44
3.14
1.95
8.55
1990 60.61 0.41 0.69 26.92 14.13 5.35 7.12 4.61 0.00 0.00 0.20 0.91 0.39
0.68 15.47
3.91
0.37
4.77
30.58 0.46 0.56 3.96 13.83 8.62 7.93 2.04 0.35 0.11 0.32 0.58 0.49
0.50
8.75
3.39
0.34
3.27
1991 45.22 0.39 2.64 10.87 16.55 23.77 14.35 15.99 7.26 0.67 0.16 1.17 1.19
1.41 17.06 12.53 0.67
7.92
26.76 0.48 0.76 4.14 6.60 15.54 3.84 4.01 0.73 0.64 0.69 1.00 1.03
0.76
8.78
2.85
0.78
3.27
1992 68.07 0.88 1.88 25.20 4.83 3.88 5.66 35.03 12.25 28.12 6.61 3.94 3.79
2.18 11.30 17.65 12.89
11.01
54.09 1.04 1.11 13.94 5.82 6.41 3.19 16.93 7.40 8.71 2.51 2.91 2.17
1.45
8.76
9.24
4.69
5.95
1993 136.40 1.81 1.43 4.54 39.02 10.46 11.32 25.21 67.85 8.52 1.57 0.49 2.35
1.86 18.01 34.79 3.53
14.55
103.92 2.01 2.10 6.94 30.15 9.89 11.96 45.45 51.90 10.11 3.78 3.24 2.95
2.36 15.50 36.71 5.69
15.09
1994 51.40 2.42 1.97 10.28 30.22 13.01 14.69 25.49 9.45 6.07 6.07 3.55 6.56
3.65 17.84 16.54 5.23
10.81
73.62 2.39 2.19 9.73 31.59 19.73 20.44 23.70 6.78 11.89 18.04 13.36 6.16
3.63 20.23 16.93 14.47
13.60
1995 65.53 5.77 4.59 24.04 36.61 12.21 4.61 31.59 13.42 10.64 11.11 2.80 3.43
4.60 24.29 16.54 8.18
13.40
87.78 3.49 3.28 38.88 24.31 24.33 6.35 27.74 8.69 4.02 9.57 5.86 4.02
3.61 29.23 14.34 6.52
13.68
1996 165.60 3.02 2.99 1.20 67.66 44.77 19.31 1.98 2.10 1.22 0.60 10.81 3.68
3.23 37.88
7.80
4.21
13.28
160.84 4.21 4.23 4.09 87.42 58.30 14.35 4.02 1.81 1.19 1.82 8.25 4.15
4.20 49.53
6.64
3.73
16.08
1997 236.40 2.40 3.49 1.68 140.30 31.98 17.48 47.30 14.64 5.72 8.44 4.24
2.94 57.99 26.47 6.13
23.38
291.66 3.74 3.45 3.68 144.85 32.54 18.66 44.95 8.38 4.42 8.89 8.52
3.60 59.44 24.05 7.30
23.80
Avg.
94.36 1.95 2.28 13.89 41.94 17.29 10.44 17.74 12.55 7.56
97.19 2.24 2.16 11.84 42.65 21.17 9.79 15.65 8.02 4.28
tended to underestimate in summer but overestimate in fall
the evapotranspiration from the drainage area upstream of
station USGS 05062500. As mentioned above, there is a large
amount of forest acreage within this partial drainage area.
The evapotranspiration from the forest might be higher in
summer but lower in fall than estimated by the SWAT model.
The trees grow most actively in August (Offelen et al., 2002),
leading to the highest water demand for evapotranspiration,
which might tend to be underestimated. On the other hand,
the evapotranspiration from the forest in November, when the
trees shed their leaves and thus demand less water, might tend
to be overestimated by the model. In addition, the missing
data on precipitation and temperature in summer and fall
might not be accurately generated by the weather generator,
which might thus also affect the predictions for these two seasons.
The results for the validation period indicated a similar
performance for the model (table 4b). The annual mean
discharge was predicted fairly well, with only 9% overprediction. For spring and winter, the predicted annual average
discharges were comparable to the corresponding observed
values (11.99 m3/s versus 11.36 m3/s in spring, and 1.35 m3/s
versus 1.31 m3/s in winter). As with the calibration period,
the discharges were overpredicted by 25% for summer but
underestimated by 14% for fall. Again, these over- and
underpredictions might be either because the evapotranspiration from the forest for these two seasons was not accurately
Vol. 48(4):
4.10
4.69
3.00
4.58
2.72
2.73
2.33
2.39
24.37
25.03
13.58
11.17
4.89
4.52
11.35
10.83
estimated by the SWAT model or because of the possible
influence of inaccurately generated data for precipitation and
temperature. For both the calibration and validation periods,
the model performed moderately well on predicting the peak
discharges, which generally occurred in the spring for any
given year. Overall, the higher peak discharges were
predicted more accurately than the lower ones. On average,
the peak discharges were underpredicted by 11% for the
calibration period and by only 5% for the validation period,
as the model underpredicted most of the peak discharges with
observed values of greater than 35 m3/s (tables 4a and 4b).
For station USGS 05064000, the model had a similar
performance. The annual mean discharge during the calibration period was overpredicted by only 5% (table 5a),
indicating that the model did a very good job. The seasonal
mean discharges for spring and winter were predicted pretty
well. Unlike station USGS 05062500, the seasonal mean
discharges for both summer and fall were overestimated. For
summer, the annual average seasonal discharge was overpredicted by 22%, which is comparable with, and thus might be
inherited from, the corresponding overestimation of 23% for
station USGS 05062500. However, the overprediction of the
annual average seasonal discharge for fall by 8% might be
because the underestimation of 22% for station USGS
05062500 was offset by a possible overestimation of the
stream flows generated from the drainage area between the
two stations. As noted earlier, within this partial drainage
11
Table 5b. 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 Hendrum (USGS 05064000) 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.
Annual
Valid- Daily
Monthly Mean Discharge (m3/s)
Seasonal Mean Discharge (m3/s) Mean
ation Peak
Discharge
Winter Spring Summer Fall
Year (m3/s) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
(m3/s)
1974
1.90
1.96
1975 126.30 1.22 1.14 6.70 42.44 29.09 13.57 70.41 15.68 3.91 0.73 0.90 1.38
1.41 26.08
33.22 1.84
15.64
216.06 1.74 1.86 2.81 61.01 32.74 24.93 88.80 6.06 2.32 1.98 3.26 1.93
1.87 31.87
40.09 2.51
19.22
1976 45.29 1.32 2.42 16.24 20.83 2.37 1.99 0.43 0.00 0.00 0.00 0.00 0.17
1.30 13.15
0.81
0.00
3.81
58.90 1.81 2.09 13.27 23.51 5.53 2.33 1.17 0.23 0.02 0.22 0.29 0.03
1.29 14.00
1.23
0.18
4.35
1977 49.61 0.23 0.39 20.27 8.29 1.18 1.35 0.05 0.11 6.20 12.46 9.72 7.70
2.77
9.91
0.50
9.46
5.66
6.85 0.00 0.01 0.82 4.74 1.59 1.04 0.36 0.03 0.72 2.37 3.23 4.27
1.47
2.36
0.47
2.11
1.24
1978 161.00 3.88 1.40 2.75 91.39 15.81 6.91 6.15 4.41 8.12 0.82 0.34 0.89
2.05 36.65
5.82
3.09
11.91
261.08 2.30 1.46 4.08 92.35 11.55 4.70 2.07 1.80 2.62 1.40 1.12 0.91
1.56 35.38
2.83
1.71
10.73
1979 187.10 0.81 0.93 10.28 66.02 62.18 14.36 28.06 6.11 2.40 0.10 3.46 2.64
1.46 46.16
16.18 1.98
16.45
244.94 0.84 0.83 1.73 86.64 32.10 11.84 17.07 2.25 1.31 1.16 3.40 1.72
1.14 39.65
10.37 1.95
13.31
1980 80.62 1.19 1.08 0.65 40.71 3.90 0.06 0.04 0.43 3.64 0.83 1.17 0.64
0.97 15.09
0.18
1.88
4.53
50.12 1.32 1.37 2.01 19.06 4.36 1.32 0.34 0.17 0.35 0.76 0.83 0.44
1.03
8.36
0.60
0.64
2.78
1981 34.20 0.51 2.21 4.04 1.64 6.29 16.57 16.29 13.44 8.31 8.39 7.86 3.75
2.16
3.99
15.43 8.19
7.44
41.91 0.25 0.35 1.48 2.99 5.06 4.10 5.01 4.19 4.78 8.15 6.00 2.79
1.16
3.18
4.44
6.33
3.58
1982 69.33 2.00 1.32 5.36 51.78 23.81 8.35 7.18 6.04 0.37 13.78 8.63 14.63
5.99 26.98
7.19
7.59
11.94
92.03 1.77 1.70 6.21 46.35 17.34 6.22 3.19 1.11 0.54 7.51 4.71 1.89
1.79 23.05
3.48
4.29
8.27
1983 53.41 2.70 1.40 26.01 5.21 2.81 11.52 39.94 13.83 7.03 3.91 4.11 5.48
3.19 11.34 21.76 5.02
10.33
63.15 1.33 1.31 20.43 10.15 4.96 11.96 21.97 4.77 2.85 4.93 4.50 2.61
1.77 11.87
12.91 4.10
7.64
1984 115.40 1.55 5.46 10.43 34.72 6.79 51.30 14.11 5.70
3.50 17.31
23.70
14.84
151.50 1.82 3.51 22.40 25.05 6.98 44.01 3.36 0.65
2.64 18.07
15.70
12.17
Avg.
92.23 1.54 1.78 10.27 36.30 15.42 12.60 18.27 6.58
118.65 1.32 1.45 7.52 37.18 12.22 11.25 14.33 2.13
area, the dominant land use is agriculture. Most of the farmlands were plowed just before planting, from late May to early June, and after harvesting, from late September to October
(Severson and Rehm, 2003). The tilled lands may have a lower runoff coefficient, and thus a smaller SCS curve number
(Sommer et al., 2004). One explanation for the overprediction of the stream flows from this partial drainage area might
be that the SWAT model was unable to make downward adjustments in the curve number to take into account the effects
of large-scale tillage on predictions for summer and fall, particularly June and September. Another explanation might be
that the generated values for the missing precipitation data
were too high.
The results for the validation period are presented in
table 5b. The annual mean discharge was overpredicted by
23%, resulting from overpredictions of the seasonal mean
discharges for summer (36%), fall (58%), and winter (64%).
The overprediction for summer might be a result of the
propagation and amplification of the prediction error for
station USGS 05062500. Additionally, it may also be
partially caused by possible inaccuracies in the generated
data for precipitation and temperature and by the inability of
the SWAT model to accurately account for the effects of
large-scale tillage before planting. The inaccurately generated data and the model’s inability to account for the effects
of large-scale tillage after harvesting may be the major
reasons for the overprediction for fall. The overprediction for
winter might be a result of the extended effects of the
post-harvesting tillage. Another reason for the relatively
large prediction error for winter might be that the observed
data could include a large measurement error because of the
12
4.44
1.72
4.56
3.16
4.02
3.04
3.92
1.85
2.48
1.57
20.67
18.78
12.48
9.21
4.34
2.65
10.25
8.33
frozen conditions that make field operations difficult at that
time of year. For both the calibration and validation periods,
the model performed moderately well in predicting the peak
discharges, which also generally occurred in spring for any
given year. As with station USGS 05062500, overall the
higher peak discharges were predicted more accurately than
the lower ones. On average, the peak discharges were
underpredicted by only 3% for the calibration period and by
22% for the validation period, as the model underpredicted
most of the peak discharges with an observed value of greater
than 90 m3/s (tables 5a and 5b).
As expected, for both stations and across the evaluation
periods, the monthly mean discharges were predicted better
for some months than for others when compared with the
seasonal mean discharges for the corresponding inclusive
seasons. The monthly mean discharges were generally
predicted better for April but worse for March and May than
the inclusive season of spring, whereas they were predicted
better for June and July but worse for August than for the
inclusive season of summer (tables 4a, 4b, 5a, and 5b). For
station USGS 05062500, the monthly mean discharges
during the calibration period were predicted better for
December and January but worse for February than for the
inclusive season of winter, and the discharges during the
validation period were predicted better for February but
worse for December and January. The discharges for the fall
months during the calibration period and the months of
September and November during the validation period were
predicted worse than for the inclusive season, but the
discharge for October during the validation period was
predicted slightly better. For station USGS 05064000, the
TRANSACTIONS OF THE ASAE
monthly mean discharges during the calibration period were
predicted better for December but worse for January and
February than for the inclusive season of winter, and the
discharges during the validation period were predicted better
for January and February but worse for December. As with
station USGS 05062500, the discharges for the fall months
during the calibration period and the months of September
and October during the validation period were predicted
worse than the inclusive season, but the discharge for
November during the validation period was predicted better.
Nevertheless, the SWAT model did a fairly good job in
predicting the monthly mean discharges. Across the two
stations, the prediction errors of the annual average monthly
mean discharges had values of less than 20% for 26 of the 48
evaluation months and were under 30% for 34 of them. The
model mostly overpredicted the monthly mean discharge for
August during the validation period at station USGS
05064000, whereas the discharge for November during the
calibration period at station USGS 05062500 was mostly
underestimated. Again, this might be because the SWAT
model was unable to accurately estimate the evapotranspiration from the forest in late summer and fall. Furthermore, for
a given year, the mean discharges for up to nine months could
be predicted with an error having an absolute value of less
than 30%, and the seasonal mean discharges may be
predicted even better.
A statistical analysis, computed from the simulated
stream flows of the four seasons, is presented in table 6.
Overall, the model had a good performance (PVk > 0.8) in
simulating the monthly, seasonal, and annual mean discharges in the Wild Rice River watershed. The daily dis-
charges could be predicted with a satisfactory accuracy (PVk
> 0.7). Season-by-season analysis of the results indicated that
the model could predict the mean discharges in an acceptable
way for all of the seasons during the calibration periods, and
that during the validation periods the mean discharges could
be predicted in an acceptable way for spring and in a marginally acceptable way for summer and fall. The poor statistics
for winter might be because the observed data may include
a large measurement error. Additionally, the SWAT model
may be unable to mimic the intermittent snow melting processes that occur during the winter, when snow melting may
be triggered by a short-period warm temperature at noon, but
the melted snow then refreezes in the afternoon before it can
contribute to the stream flows. The month-by-month analysis
of the simulation results revealed that the mean discharges for
nine months during the calibration periods could be predicted
in an acceptable way. Again, the poor predictions for August,
September, and November might be a result of the model’s
inability to accurately estimate the evapotranspiration from
the forest. Similarly, during the validation periods, the
monthly mean discharges could be predicted in an acceptable/marginally acceptable way for nine months, with the exceptions being August, September, and December. The poor
predictions for August and September might be attributed to
the inaccurate estimation of the evapotranspiration from the
forest, whereas the large measurement errors that may be included in the observed data could be one of the reasons behind the poor statistics for December. The model had a
comparable performance for both the calibration and validation periods, possibly because the datasets are almost balanced for the two periods (eight calibration years versus nine
Table 6. Statistics of daily, monthly, seasonal, and annual discharges for the evaluation water years (December to November).[a]
Calibration
Validation
USGS 05062500[b]
USGS 05064000[c]
USGS 05062500[b]
Obs. Pred.
Statistics (m3/s) (m3/s) R2
Ej 2
Daily
7.54
7.92 0.73 0.64
Obs. Pred.
(m3/s) (m3/s) R2
Ej 2 PVk
10.83 11.31 0.68 0.67 0.76
Obs. Pred.
(m3/s) (m3/s) R2
4.94 5.32 0.69
Monthly
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Ej 2
0.62
USGS 05064000[c]
Obs. Pred.
(m3/s) (m3/s)
8.23 10.13
R2
0.52
Ej 2
0.50
PVk
0.68
0.85
0.57
0.61
0.27
0.86
0.81
0.40
0.88
0.92
0.60
0.56
0.55
0.25
0.83
−0.04
0.04
−0.10
0.86
0.15
0.36
0.84
0.01
−4.48
−1.15
−1.24
−12.64
0.82
0.63
0.62
0.55
0.66
0.61
0.64
0.57
0.20
0.37
0.55
0.56
0.44
7.53
2.10
2.15
7.60
23.33
13.95
7.30
13.03
6.79
3.58
3.86
4.23
2.38
7.89
2.06
2.04
9.43
23.38
12.86
8.58
14.97
9.93
4.54
2.78
1.73
2.39
0.89
0.01
0.76
0.27
0.95
0.88
0.91
0.95
0.97
0.41
0.28
0.30
0.98
0.86
0.61
0.73
−0.02
0.91
0.86
0.76
0.91
0.68
−1.16
0.14
−0.42
0.98
10.82
2.24
2.16
11.84
42.65
21.17
9.79
15.65
8.02
4.28
4.69
4.58
2.73
11.29
1.95
2.28
13.89
41.94
17.29
10.44
17.74
12.55
7.56
4.10
3.00
2.72
0.86
0.57
0.50
0.36
0.90
0.84
0.88
0.70
0.97
0.20
0.21
0.24
0.73
0.86
0.36
0.39
0.10
0.90
0.77
0.84
0.68
−8.26
−3.44
−2.88
−0.01
0.71
0.81
0.66
0.65
0.60
0.66
0.62
0.62
0.62
0.48
0.49
0.59
0.51
0.66
4.94 5.32
1.20 1.11
1.19 1.22
3.99 5.40
20.73 21.26
9.68 9.31
5.45 5.66
7.02 9.07
1.66 2.80
1.36 1.58
2.07 1.81
2.43 1.65
1.56 1.74
0.93 0.90
0.89 0.86
0.41 −0.01
0.35 −0.77
0.92 0.86
0.93 0.89
0.92 0.92
0.97 0.90
0.92 −0.99
0.58 0.52
0.74 0.66
0.76 0.46
0.87 0.59
8.24
1.32
1.45
7.52
37.18
12.22
11.25
14.33
2.13
1.72
3.16
3.04
1.85
Seasonal 7.53
Winter
2.32
Spring 14.87
Summer 9.06
Fall
3.89
7.72
2.24
15.22
11.16
3.02
0.88
0.89
0.82
0.96
0.17
0.87
0.88
0.82
0.85
−0.21
10.82 11.29
2.39 2.33
25.03 24.37
11.17 13.58
4.52 4.89
0.87
0.75
0.82
0.90
0.06
0.87
0.75
0.80
0.84
−0.52
0.86
0.89
0.66
0.59
0.61
4.78 5.17
1.31 1.35
11.36 11.99
4.70 5.85
1.96 1.68
0.95 0.92
0.13 −1.42
0.90 0.87
0.96 0.88
0.73 0.74
8.19 10.14
1.57 2.48
18.78 20.67
9.21 12.48
2.65 4.34
0.90 0.86 0.83
0.27 −10.54 −1.65
0.90 0.88 0.64
0.80 0.72 0.56
0.49 −1.42 0.53
Annual
7.91
0.82 0.80
10.83 11.35
0.73 0.72 0.89
4.91
0.93
8.33
0.82
[a]
7.53
5.34
0.90
10.12
1.54
1.78
10.27
36.30
15.42
12.60
18.27
6.58
4.44
4.56
4.02
3.92
10.25
0.68
0.82
Obs. is the observed value, Pred. is the SWAT-predicted value, R2 is the coefficient of determination, Ej 2
is the Nash-Sutcliffe coefficient (eq. 7), and PVk is
performance virtue (eq. 6).
For station USGS 05062500, the calibration period is from 1 December 1989 to 30 November 1997, and the validation period is from 1 December 1974 to
31 August 1983.
[c] For station USGS 05064000, the calibration period is from 1 December 1985 to 30 November 1997, and the validation period is from 1 December 1974 to
31 August 1984.
[b]
Vol. 48(4):
13
Table 7. Statistics of daily, monthly, and seasonal discharges for the spring months
(March, April, and May) of the evaluation water years (December to November).[a]
Daily
Monthly
Station[b]
Calibration
USGS 05062500
USGS 05064000
Observed
(m3/s)
Predicted
(m3/s)
Ej 2
14.87
25.03
15.13
24.18
0.64
0.33
11.36
18.78
11.89
20.50
0.49
0.45
Validation
USGS 05062500
USGS 05064000
[a]
[b]
PVk
0.70
Observed Predicted
(m3/s)
(m3/s)
Ej 2
14.96
25.23
15.22
24.38
0.87
0.87
11.46
18.98
11.99
20.67
0.87
0.82
0.66
PVk
0.83
Seasonal
Observed Predicted
(m3/s)
(m3/s)
Ej 2
14.87
25.07
15.13
24.20
0.82
0.79
11.36
18.78
11.89
20.50
0.87
0.88
0.84
PVk
0.90
0.88
Ej 2 is Nash-Sutcliffe coefficient (eq. 7), and PVk is performance virtue (eq. 6).
For station USGS 05062500, the calibration period is from 1 December 1989 to 30 November 1997, and the validation period is from 1 December 1974 to
31 August 1983.
For station USGS 05064000, the calibration period is from 1 December 1985 to 30 November 1997, and the validation period is from 1 December 1974 to
31 August 1984.
Performance Virtue (PVk)
validation years for station USGS 05062500, and twelve calibration years versus ten validation years for station USGS
05064000), and the average hydrologic conditions for these
two periods were broadly comparable. As indicated by the
values of R2 and Ej 2, the model had an overall better performance for station USGS 05062500 than for station
05064000. This may be because some of the prediction errors
that were incurred upstream of USGS 05062500 were propagated downstream and amplified by the additional prediction
errors incurred in the drainage area between the two stations,
thus affecting USGS 0506400 more severely.
In order to further assess the model performance in
simulating the stream flows for the season of particular
interest for this study, namely spring, statistics were computed using only the simulated and observed stream flows
during the three spring months (March, April, and May) for
the calibration and validation periods (table 7). The daily
stream flows could be predicted with an acceptable accuracy
(PVk > 0.60), whereas the model had a good performance in
simulating the monthly and seasonal mean discharges (PVk >
0.80). As with the aforementioned findings from examining
the model performance for all four seasons, the model had an
overall better performance for station USGS 05062500 than
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
−11
−12
−13
−14
−15
−16
−17
−18
−19
for USGS 05064000 in terms of higher Ej 2 values. On a yearly
basis, the model had an overall better performance for the
years with a higher daily peak discharge than for those with
a lower peak discharge. Figure 5 shows that the PVk values,
which were computed from the daily stream flows for each
spring of the 17 years from 1975 to 1983 and from 1990 to
1997 (the overlapping evaluation years for the two stations),
tend to increase with the observed daily peak discharges at
station USGS 05064000. The same trend was noticed when
plotting the PVk values versus the observed daily peak
discharges at station USGS 05062500, and thus the plot was
omitted. This may be because the SWAT model did a better
job in simulating the melting processes of a larger snowpack
than it did for a smaller one because the years with a higher
daily peak discharge generally also had a larger snowpack.
For instance, across the 17 evaluation years, the model had
its poorest performance for 1977 (PVk = −17.28) when the
daily peak discharge was lowest (6.85 m3/s), whereas its
performance was good for 1996 (PVk = 0.83) when the daily
peak discharge was high, with a value of 160.84 m3/s.
Examination of the observed precipitation data indicated that
the snowpack amount in 1977 (about 90 mm) was far less than
it was in 1996 (about 170 mm).
Y1996
Y1977
0
50
100
150
200
250
Daily Peak Discharge at Station USGS 05064000
300
350
(m3/s)
Figure 5. Plot showing the model performance virtue (PVk), when computed using the simulated and observed daily stream flows during the three
spring months (March, April, and May), tends to increasing with daily peak discharge in spring at station USGS 05064000, implying that the SWAT
model might have a better performance for a year with a larger snowpack for the Wild Rice River watershed, Minnesota.
14
TRANSACTIONS OF THE ASAE
180
Daily Stream Flow (m3/s)
160
Observed
SWAT−predicted
140
PV k = 0.83
120
100
80
60
40
20
0
1 Dec.
1995
31 Dec.
1995
30 Jan.
1996
29 Feb.
1996
30 Mar.
1996
29 Apr.
1996
29 May
1996
28 June
1996
28 July
1996
27 Aug.
1996
26 Sept.
1996
26 Oct.
1996
25 Nov.
1996
Date
Figure 6. Observed and SWAT-predicted daily stream flows at station of Wild Rice River at Hendrum (USGS 05064000) for 1996, a typical water year
that has a model performance virtue (PVk), when computed using the simulated and observed daily stream flows during the three spring months
(March, April, and May), of greater than 0.80.
Figures 6 through 10 show the simulated and observed
daily stream flows at station USGS 05064000 for the selected
years 1996, 1976, 1979, 1992, and 1977, when the SWAT
model exhibited good, satisfactory, acceptable, and poor
performances, respectively. The corresponding plots for
station USGS 05062500 were very similar, and hence have
been omitted due to space limitations. For 1977 (PVk =
−17.28; fig. 10), the model completely mispredicted the
stream flows in spring and fall. In contrast, the daily stream
flows in 1996 (PVk = 0.83; fig. 6) were generally predicted
very well, although the secondary peak discharge was
overpredicted. For 1976 (PVk = 0.74; fig. 7), the daily stream
flows were generally predicted fairly well, while the model
was unable to predict the secondary peak and overpredicted
the major peak. However, the timing of the major peak was
successfully predicted. On the other hand, the simulated daily
stream flow hydrograph for 1992 (PVk = 0.10; fig. 9) was
shifted earlier, and its largest three peaks were underpredicted. The daily stream flows for 1979 (PVk = 0.65; fig. 8)
were generally predicted moderately well, although the
model was unable to predict the tertiary peak and overpre−
dicted the major peak. In addition, in this case the timing of
the major peak was not successfully predicted. That the peaks
were overpredicted for some years but underpredicted for
others might be because the parameters TIMP, SURLAG,
MSK_CO1, and MSK_CO2, all of which are sensitive for
predicting peak magnitude and timing, may be invariant for
the evaluation years.
CONCLUSIONS
This study evaluated the performance of the SWAT
model’s snowmelt hydrology on simulating the stream flows
for the Wild Rice River watershed, located in northwestern
Minnesota. This study also developed a measure, designated
“performance virtue,” that was then used for model evaluation in addition to the Nash-Sutcliffe coefficient and
coefficient of determination. The sensitivity analysis indicated that of the seven snowmelt-related parameters, three
parameters, namely the snowmelt temperature, maximum
snowmelt factor, and snowpack temperature lag factor, were
70
Daily Stream Flow (m3/s)
60
Observed
50
SWAT−predicted
PV k = 0.74
40
30
20
10
0
1 Dec.
1975
31 Dec.
1975
30 Jan.
1976
29 Feb.
1976
30 Mar.
1976
29 Apr.
1976
29 May
1976
28 June
1976
28 July
1976
27 Aug.
1976
26 Sept.
1976
26 Oct.
1976
25 Nov.
1976
Date
Figure 7. Observed and SWAT-predicted daily stream flows at station of Wild Rice River at Hendrum (USGS 05064000) for 1976, a typical water year
that has a model performance virtue (PVk), when computed using the simulated and observed daily stream flows during the three spring months
(March, April, and May), of between 0.70 and 0.80.
Vol. 48(4):
15
Daily Stream Flow (m3/s)
300
Observed
250
SWAT−predicted
200
PV k = 0.65
150
100
50
0
1 Dec.
1978
31 Dec.
1978
30 Jan.
1979
1 Mar.
1979
31 Mar.
1979
30 Apr.
1979
30 May
1979
29 June
1979
29 July
1979
28 Aug.
1979
27 Sept.
1979
27 Oct.
1979
26 Nov.
1979
Date
Figure 8. Observed and SWAT-predicted daily stream flows at station of Wild Rice River at Hendrum (USGS 05064000) for 1979, a typical water year
that has a model performance virtue (PVk), when computed using the simulated and observed daily stream flows during the three spring months
(March, April, and May), of between 0.60 and 0.70.
sensitive for the simulation. In addition to these three param−
eters, eight other parameters, namely the 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 PEST (Parameter ESTimation) software
to minimize a composite objective function of the modelgenerated and observed daily stream flows at the two gauging
stations, USGS 05062500 and USGS 05064000. Subsequently, the PEST-determined values for these parameters were
manually adjusted to further refine the model.
The evaluation indicated that for the study watershed, the
SWAT model had a good performance in simulating the
monthly, seasonal, and annual mean discharges, and a
satisfactory performance in predicting the daily discharges.
The model had a comparable performance for both the
calibration and validation periods, but had an overall better
performance for the upstream station (USGS 05062500) than
for the downstream station (USGS 05064000). 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 monthly and
seasonal mean discharges could be predicted very well.
Further, the model had an overall better performance for
evaluation years with a larger snowpack than for those with
a smaller snowpack. It is recommended that a more accurate
method of estimating evapotranspiration from forest and an
algorithm incorporating a varying SCS curve number to take
into account the effects of large-scale tillage that is
implemented within a defined time window be incorporated
into SWAT to make the model more applicable for watersheds such as the Wild Rice River watershed in Minnesota.
80
Observed
Daily Stream Flow (m3/s)
70
SWAT−predicted
PV k = 0.10
60
50
40
30
20
10
0
1 Dec.
1991
31 Dec.
1991
30 Jan.
1992
29 Feb.
1992
30 Mar.
1992
29 Apr.
1992
29 May
1992
28 June
1992
28 July
1992
27 Aug.
1992
26 Sept.
1992
26 Oct.
1992
25 Nov.
1992
Date
Figure 9. Observed and SWAT-predicted daily stream flows at station of Wild Rice River at Hendrum (USGS 05064000) for 1992, a typical water year
that has a model performance virtue (PVk), when computed using the simulated and observed daily stream flows during the three spring months
(March, April, and May), of between 0.00 and 0.60.
16
TRANSACTIONS OF THE ASAE
Daily Stream Flow (m3/s)
60
Observed
50
SWAT−predicted
PV k = −17.28
40
30
20
10
0
1 Dec.
1976
31 Dec.
1976
30 Jan.
1977
1 Mar.
1977
31 Mar.
1977
30 Apr.
1977
30 May
1977
29 June
1977
29 July
1977
28 Aug.
1977
27 Sept.
1977
27 Oct.
1977
26 Nov.
1977
Date
Figure 10. Observed and SWAT-predicted daily stream flows at station of Wild Rice River at Hendrum (USGS 05064000) for 1977, a typical water year
that has a negative model performance virtue (PVk), when computed using the simulated and observed daily stream flows during the three spring
months (March, April, and May).
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TRANSACTIONS OF THE ASAE