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  • View in gallery

    Gray area represents the study domain. Watersheds included within the study domain: (a) St. Croix River at St. Croix Falls, WI; (b) St. Louis River at Scanlon, MN; (c) Mississippi River at Anoka, MN; (d) Chippewa River at Durand, WI; (e) Wisconsin River at Muscoda, WI; (f) Menominee River at Koss, MI; (g) Au Sable River at Luzerne, MI; (h) Muskegon River at Evart, MI; (i) Tittabawassee River at Midland, MI; and (j) Grand River at Grand Rapids, MI.

  • View in gallery

    (a) Distribution of open water area in the study domain as estimated from NLCD (2001); (b) distribution of wetland area in the study domain as estimated from NLCD (2001); (c) distribution of lake depth in the study domain; and (d) estimated wetland depth using DEM and land-cover data.

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    (a) Distribution of Very Small lakes in various depth ranges, (b) distribution of Small lakes in various depth ranges, (c) distribution of Medium lakes in various depth ranges, and (d) distribution of Large lakes in various depth ranges.

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    (a) Depth–area relationship described by second-order fitted polynomial on observed bathymetry data for Very Small lakes, (b) for Small lakes, (c) for Medium lakes, and (d) for Large lakes in Michigan.

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    (a) Sensitivity of runoff, baseflow, and inundation area toward fraction of vegetative surface draining into lake (R), (b) Sensitivity of runoff, baseflow, and inundation area toward width fraction ( f ), and (c) sensitivity of runoff, baseflow, and inundation area toward elevation of lake outlet (Zmin).

  • View in gallery

    (a) Sensitivity of runoff, baseflow, and inundation area toward wetland depth (Zwetland), (b) sensitivity of runoff, baseflow, and inundation area toward lake depth (Zlake), and (c) sensitivity of runoff, baseflow, and inundation area toward lake area (A).

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    Pareto plots for sensitivity analysis obtained using FF2 designs. Both main effect and interactions are explicitly extracted in this analysis. Black bars show negative effect while gray bars show positive effect. Description of parameters given in the Table 4 and X:Y represents the interaction between parameter X and parameter Y.

  • View in gallery

    Results of model calibration (1985–95) for the selected watersheds: (a) St. Croix River at St. Croix Falls, WI; (b) St. Louis River at Scanlon, MN; (c) Mississippi River at Anoka, MN; (d) Chippewa River at Durand, WI; (e) Wisconsin River at Muscoda, WI; (g) Au Sable River at Luzerne, MI; (h) Muskegon River at Evart, MI; (i) Tittabawassee River at Midland, MI; and (j) Grand River at Grand Rapids, MI.

  • View in gallery

    Same as Fig. 8 but for model evaluation (1996–2005) for the selected watersheds.

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    Model performance to simulate daily latent and sensible heat fluxes at Lost Creek, WI, and Sylvania Wilderness, WI.

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    (a) Comparison of the VIC model simulated fractional inundation area for a 1° × 1° area in northern Wisconsin, (b) seasonal variation in minimum, mean, and maximum domain-averaged inundation area fraction, (c) mean inundation area fraction in April for the period of 1985–2005, and (d) mean inundation area fraction in August for the period of 1985–2005.

  • View in gallery

    Mean (LAKE scenario) and difference (LAKE − NO-LAKE scenarios) of water balance for the period of 1985–2005: (a) mean annual precipitation (mm), (b) mean annual ET with lakes and wetlands, (c) difference in mean annual ET (Delta ET), (d) mean annual total runoff with lakes and wetlands, and (e) difference in total runoff (Delta TR).

  • View in gallery

    Mean (LAKE scenario) and difference (LAKE − NO-LAKE scenarios) of energy balance for the period of 1985–2005: (a) RNET—mean annual net radiation (W m−2) with lakes and wetlands, (b) Delta RNET—difference in mean annual RNET, (c) LH—mean annual latent heat flux (W m−2) with lakes and wetlands, (d) Delta LH—difference in mean annual LH, (e) SH—mean annual sensible heat flux (W m−2) with lakes and wetlands, and (f) Delta SH—difference in mean annual SH.

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    Seasonal cycle of changes (LAKE − NOLAKE) associated with (a) water fluxes and (b) energy fluxes.

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    Partition of water and energy fluxes in LAKE and NO-LAKE scenarios: (a) ET/P, (b) TR/P, (c) LH/RNET, (d) SH/RNET, (e) GH/RNET, and (f) SH/LH (Bowen ratio). Gray line is 1:1 line and solid black line is regression line.

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Parameterization of Lakes and Wetlands for Energy and Water Balance Studies in the Great Lakes Region

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  • 1 Agricultural and Biological Engineering, and Purdue Climate Change Research Center, Purdue University, West Lafayette, Indiana
  • | 2 Department of Agronomy, and Purdue Climate Change Research Center, Purdue University, West Lafayette, Indiana
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Abstract

Lakes and wetlands are prevalent around the Great Lakes and play an important role in the regional water and energy cycle. However, simulating their impacts on regional-scale hydrology is still a major challenge and not widely attempted. In the present study, the Variable Infiltration Capacity (VIC) model is applied and evaluated with a physically based lake and wetland algorithm, which can simulate the effect of lakes and wetlands on the grid cell energy and water balance. The VIC model was calibrated at 10 U.S. Geological Survey (USGS) stream gauging stations against daily streamflow records for the period of 1985–95, and successfully evaluated for the period of 1996–2005. Single-grid sensitivity experiments showed that runoff, baseflow, and inundation area were sensitive to the lake model parameters. Simulations were also conducted to analyze the spatial and temporal variability of inundation area for the period of 1985–2005. Results indicated that water and energy fluxes were substantially affected when lakes and wetlands were included in model simulations. Domain-averaged annual mean evapotranspiration (ET) was increased by 5% while annual mean total runoff was decreased by 12% with lakes and wetlands. Latent heat flux increased while sensible heat flux decreased because of the inclusion of lakes and wetlands.

Corresponding author address: Vimal Mishra, 225 South University Street, West Lafayette, IN 47907. Email: vmishra@purdue.edu

Abstract

Lakes and wetlands are prevalent around the Great Lakes and play an important role in the regional water and energy cycle. However, simulating their impacts on regional-scale hydrology is still a major challenge and not widely attempted. In the present study, the Variable Infiltration Capacity (VIC) model is applied and evaluated with a physically based lake and wetland algorithm, which can simulate the effect of lakes and wetlands on the grid cell energy and water balance. The VIC model was calibrated at 10 U.S. Geological Survey (USGS) stream gauging stations against daily streamflow records for the period of 1985–95, and successfully evaluated for the period of 1996–2005. Single-grid sensitivity experiments showed that runoff, baseflow, and inundation area were sensitive to the lake model parameters. Simulations were also conducted to analyze the spatial and temporal variability of inundation area for the period of 1985–2005. Results indicated that water and energy fluxes were substantially affected when lakes and wetlands were included in model simulations. Domain-averaged annual mean evapotranspiration (ET) was increased by 5% while annual mean total runoff was decreased by 12% with lakes and wetlands. Latent heat flux increased while sensible heat flux decreased because of the inclusion of lakes and wetlands.

Corresponding author address: Vimal Mishra, 225 South University Street, West Lafayette, IN 47907. Email: vmishra@purdue.edu

1. Introduction

Lakes and wetlands are important components of the global land surface. Estimates suggest that there are more than 8 million lakes larger than 1 ha globally (Meybeck 1995) and more than 10 million km2 of wetlands (Finlayson et al. 1999). Approximately 3% of the global land surface is open water (Downing et al. 2006), while an additional 5% is wetlands (Matthews and Fung 1987; Gosselink and Mitsch 2000). Downing et al. (2006) determined that the global extent of natural lakes is twice as large as previously estimated and dominated by millions of water bodies smaller than 1 km2. Therefore, the extensive presence of lakes and wetlands may play an even more important role in water and energy cycles, regional climate, and biogeochemical cycles than previously believed (Prigent et al. 2007).

Lakes play an important role in local and regional climate (Carpenter 1984; Benson and Thompson 1987; Pitman 1991; Hostetler et al. 1993; Delire et al. 2004) because of the large differences in albedo, heat capacity, roughness, and energy exchange in comparison to the land surface (Bonan 1995). Water stored in lakes and wetlands helps to control land surface temperature and energy fluxes (Prigent et al. 2007; Rouse et al. 2003; Lofgren 1997; Eaton et al. 2001; Bonan 1995; Coe and Bonan 1997). Specifically, lakes and wetlands decrease summer temperatures, increase winter temperatures (Bonan 1995), and reduce daily air temperature variability (Hostetler et al. 1993). The presence of lakes also results in phase shifts to the annual cycle of latent and sensible heat fluxes, increases in local precipitation and evaporation, and an altered atmospheric temperature gradient (Lofgren 1997; Bonan, 1995).

The inundation dynamics of lakes and wetlands respond to natural variability in the hydrologic cycle and are important to the regional-scale hydrologic cycle because of the impact of surface water storage (Hostetler et al. 1993; Small et al. 1999; Bowling and Lettenmaier 2010; Coe 1998; Coe et al. 2002). Lake water level may change seasonally and interannually in response to variations in the water balance over the lake and its watershed (Street-Perrott and Harrison 1985). These variations are important for controlling surface runoff affected by lakes and wetlands (Cardille et al. 2004). Wu and Johnston (2008) also indentified in a study conducted in a lake/wetland-dominated watershed in Michigan that the presence of lakes and wetlands delayed the timing of peak streamflow.

Previous efforts have studied the impacts of lakes and wetlands on water fluxes (Cardille et al. 2004, 2007; Vano et al. 2006) and energy fluxes (Lenters et al. 2005) in the Great Lakes region. Most of these studies were, however, limited to a few lakes or to a single watershed, leaving the larger regional role of lakes and wetlands poorly quantified. Large-scale/regional-scale models may be useful for simulating the hydroclimatic impacts of lakes and wetland at river basin scales. Despite the significance of lakes and wetlands in regional climate, biogeochemical cycles and in regional hydrology, however, they are either underrepresented or not represented in most of the land surface schemes (LSSs) used in general circulation models (GCMs) because scale issues or other complexities related to the availability of observational data for model parameterization. For instance, various LSSs were compared in the Project for Intercomparison of Land Surface Parameterization Schemes (PILPS, phase 2e), and it was concluded that the effect of lakes and wetlands on surface storage and timing of runoff was largely neglected in most of the participating LSSs (Bowling et al. 2003a; Nijssen et al. 2003). One exception to this is the Variable Infiltration Capacity (VIC) LSS, which was updated by Bowling and Lettenmaier (2010) to include a lake/wetland algorithm that simulates the contribution of surface water storage to the water and energy balance. Thus far, the VIC model lake and wetland algorithm has been mostly applied in the Arctic and sub-Arctic (Bowling et al. 2003b; Su et al. 2005; Bowling and Lettenmaier 2010).

Lakes and wetlands continue to be added to other LSSs; however, the process of integrating these algorithms into simulations is still under development. For example, only two [Community Land Model (CLM) and National Aeronautics and Space Administration (NASA) Goddard Institute for Space Studies Model E-H (GISS-EH)] of the many LSSs that participated in the fourth assessment report (AR4) of the Intergovernmental Panel on Climate Change (IPCC) included the representation of lakes. In part, this is because of a need to collect and process observed data related to lakes and wetlands in a consistent fashion that can be applied relatively easily to large regions with variable levels of data availability (e.g., Downing et al. 2006).

We identify three major challenges that need to be addressed in order to assess the role of lakes and wetlands in regional-scale water and energy cycles: (i) identify and collect observational data related to lakes’ and wetlands’ characteristics; (ii) parameterize a physically based lake and wetland algorithm using the observational data; and (iii) evaluate the parameterization using calibration and evaluation at a regional scale. By addressing these challenges, we aim to answer the overarching question: To what degree do lakes and wetlands affect the regional-scale water and energy fluxes? Considering the potential importance of lakes and wetlands and the need to parameterize them for regional-scale application, the specific objectives of the present study are to: (i) develop parameters for the VIC model lake and wetland algorithm for the Great Lakes region; (ii) quantify the sensitivity of key hydrologic variables (surface runoff, baseflow, and inundation area) to lake model parameters and lake characteristics; and (iii) implement the parameterized lake and wetland algorithm to study the regional water and energy cycle.

2. Methods and data

a. Study region

The abundance of lakes and wetlands in the Great Lakes region provides a good basis to understand their potential impacts on regional water and energy cycles. The study region includes parts of the Upper Mississippi River and Great Lakes drainage basins (Fig. 1). Evergreen and deciduous forests dominate in the northern part of the study domain, and cropland in the south. Lakes are present in almost every part of the study domain, while wetlands are located mostly to the north. Wetlands in the southern part of the study domain were drained for agriculture in the past. Lakes and wetlands are still a dominant land-cover type (20%) within the area (Table 1) according to the 2001 National Land Cover Dataset (NLCD-2001).

For the study period (1985–2005) average air temperature of the domain ranged between −6°C in the winter [December–February (DJF)], and 17°C in the summer [June–August (JJA)] with a high degree of spatial and temporal variability within the study region. The northern latitudes of the domain experienced earlier onset of winter freeze and later onset of spring thaw. The study region received around 729 mm of precipitation, annually. Winter precipitation averages around 84 mm mostly in the form of snow, which is a significant input to the wetlands when it melts. Snowmelt generally occurs in late February and early March to the south and in late April and early May to the north. The presence of significant frozen soil in the study domain (Sinha et al. 2010) often restricts the infiltration capacity, providing favorable conditions for inflow to lakes and wetlands. The spring season receives 184 mm of precipitation while summer, the wettest season, receives 270 mm of precipitation.

b. The Variable Infiltration Capacity model

The Variable Infiltration Capacity model was developed as an alternative to the earlier bucket-model-type representation with the addition of the variable infiltration capacity curve (Liang et al. 1994, 1996; Wood et al. 1992). Several modifications and updates have been made to make the VIC model more physically based, particularly with respect to cold season processes, including snow, canopy interception of snow, and soil frost (Cherkauer and Lettenmaier 1999; Cherkauer et al. 2003). The VIC model is a semidistributed model that has parameters for each grid cell; however, there is no horizontal interaction between model grid cells (Mitchell et al. 2004). It must therefore be applied at scales where the subsurface flow of water between grid cells is negligible. Vegetation is represented using a mosaic scheme, where multiple vegetation types can coexist in a single grid cell. Vegetation types are specified using the leaf area index (LAI), root-fraction, canopy resistance, and other related parameters. Runoff and baseflow generated from each grid cell is routed using a standalone routing model to the basin outlet (Lohmann et al. 1998).

For this application, the VIC model (version 4.1.2) was run at a three-hourly time step in full water and energy balance mode and included the formation of soil ice. It used 3 soil moisture layers, and 12 soil thermal nodes that were solved using the method of Cherkauer and Lettenmaier (1999) and a constant bottom boundary temperature at a damping depth of 10 m. Though the VIC model has been applied in various regions—for example, globally (e.g., Nijssen et al. 2001), to the United States (e.g., Maurer et al. 2002) and to large watersheds such as the Uruguay River basin (e.g., Saurral et al. 2008)—to date its application to study the effects of lakes and wetlands has been limited to the Arctic and sub-Arctic regions (Bowling et al. 2003b; Su et al. 2005).

c. Simulation of inundation extent

The VIC model lake and wetland algorithm was developed for use within the framework of the VIC model and includes the interaction of simulated permanent water bodies and seasonally flooded ground with the VIC model grid cell (Bowling and Lettenmaier 2010). This algorithm represents temporally varying wetland size and the one-way interaction of the VIC model grid cell with the simulated lake at various time steps. All potential open water areas (wetlands, lakes, and ponds) in a VIC model grid cell are considered as an effective gridcell water body, whose maximum extent is defined by their combined fractions. This fraction is included as a separate tile in the land-cover mosaic for each grid cell in addition to the vegetative surface and bare soils. The Great Lakes region is dominated by smaller (1–10 km2) inland lakes, and only a few lakes are present in the study domain, which have areas larger than a VIC model grid cell. These large lakes were split between multiple grid cells and no horizontal redistributions within these lakes were considered.

The depth–area relationship of the lake and wetland tile is a user-defined input to the VIC model that allows the prediction of variable inundated area with surface volume storage. The depth–area relationship can either be identified from observed bathymetry data or established empirically. As the lake area decreases, the area that is not flooded is considered exposed wetland area, and the energy balance is solved using the method of Cherkauer and Lettenmaier (1999), similar to other land-cover tiles. The energy balance of open water is solved using the method of Hostetler and Bartlein (1990) and Hostetler (1991), while lake ice is developed on the surface using the method of Patterson and Hamblin (1988).

All runoff and baseflow generated from the exposed wetland area is assumed to enter into the lake. Runoff generated from other land surface tiles within the VIC model gridcell flow into the lake according to a user-defined fraction, R, which can be adjusted during the calibration. This represents the storage retardation effect of lakes and wetlands on the streamflow.

After the estimation of a new water level for the lake/wetland class, runoff is released as function of simulated lake depth, Z, based on the equation for flow over a broad-crested weir, as follows (Bowling and Lettenmaier 2010):
i1525-7541-11-5-1057-e1
where dt is the time step length in seconds, A(Z) is the lake surface area (m2) at depth, Z, Zmin is the elevation of the lake outlet, and f is the fraction of the lake circumference through which outflow occurs. Runoff stops when the water level falls below Zmin and further decreases in lake extent happen via evaporation and subsurface drainage alone. Thus, the specified water area at a depth of Zmin, acts as a flexible lower boundary on simulated inundated area. Baseflow is calculated from below the lake as a function of the liquid water content of the wetland soils.

d. Data

1) Observed meteorology

Meteorological data included observed daily precipitation, air temperature extremes and wind speeds. Daily precipitation and temperature observations were obtained from the National Climatic Data Center (NCDC) for the period of 1915 to 2008 and used to generate a long-term gridded meteorological dataset based on methodology described in Hamlet and Lettenmaier (2005). This study used meteorological data for 1985–2005 from the long-term dataset. Daily wind velocities were obtained from the National Center for Atmospheric Research–National Centers for Environmental Prediction (NCAR–NCEP) Reanalysis Project (Kalnay et al. 1996). All daily data were gridded for the study region at a spatial resolution of ⅛° (approximately 10 km × 14 km at the center of the domain). To run the VIC model at a subdaily time step, the daily precipitation and temperature data were disaggregated to subdaily using the methods of Thornton and Running (1999) to estimate air temperature and radiation, and by uniformly distributing precipitation.

2) Soil and land-cover data

Most soil parameters were obtained from the Land Data Assimilation System (LDAS) project (Maurer et al. 2002) at a resolution of ⅛°. The soil frost algorithm was not used in the LDAS project, thus, additional parameters (e.g., bubbling pressure) were obtained from the CONUS-SOIL database (Miller and White 1998) or set to default values based on Mao and Cherkauer (2009).

Land-cover data were obtained from the NLCD-2001, which identified nine major land use classes within the study region (Table 1), when all types of wetland have been combined into a single wetland class. Wetland and open water cover about 20% of the study domain (Figs. 2a,b), forests cover about 35% of the study domain, cropland covers about 40%, while shrubland (composed of grassland and shrubland) cover about 5% of the study domain.

Each of these land-cover classes was then mapped into standard VIC model vegetation classes using a remapping strategy (Table 1). Urban area was found to be only 2%–3% of the study domain, therefore, it was not represented in this study. Land-cover classes other than urban were rescaled proportionally to make their fractional sum equal to one for each of the VIC model grid cells, effectively removing urban area. There was no change in urban fraction between simulations with and without lakes so this method does not significantly influence estimates of the impacts of lakes and wetlands. Deciduous forest, coniferous forest, and mixed forest were represented by deciduous broadleaf, evergreen needleleaf, and mixed cover, respectively. Fractions of the open water and wetland class were estimated from the NLCD maps and aggregated for each of the VIC model grid cells. Most of the wetlands in the study domain have woody and herbaceous vegetation, thus wooded grassland was considered as the representative vegetation for the wetlands. The leaf area index for each vegetation class in each grid cell was estimated from the dataset of Myneni et al. (1997). Rooting depths were obtained from Maurer et al. (2002), while other vegetation parameters were taken from the newly developed vegetation library for the Midwest (Mao and Cherkauer 2009).

3) Lake bathymetry data

Lake bathymetry data were obtained from the State Department of Natural Resources (DNR) of Michigan, Wisconsin, and Minnesota. The type of data available varied by state, but included information for major lakes. For Michigan lakes, bathymetry data came in the form of depth contours at intervals of 5 feet (more information available online at http://www.mcgi.state.mi.us/mgdl/). Minnesota provided lake shape, maximum area, and maximum depth through the Minnesota DNR Data Deli (more information available online at http://deli.dnr.state.mn.us/data_catalog.html). Maximum area and depth data were also obtained for lakes in Wisconsin (more information available online at http://dnr.wi.gov/). These data were used for the parameterization of the lake/wetland algorithm, as described in section 4 and summarized in Table 2.

Lake depths were available for about 8100 lakes in the study domain (Fig. 2c), and the distribution of deeper lakes generally corresponds to areas with higher open water fractions. The minimum size of lakes mapped by Wisconsin, Michigan, and Minnesota is 0.004, 0.0056, and 0.005 km2, respectively. The Wisconsin DNR lake data included smaller lakes than the other two states, which was reflected in the greater variety of lake depths and the larger number of very small lakes. The majority of wetlands were found in northern Minnesota, the north-central part of Wisconsin, and the Upper Peninsula of Michigan (Fig. 2b).

4) Streamflow data

Observed daily and monthly streamflow data were obtained for 10 selected gauging stations (Fig. 1) operated by the United States Geological Survey (USGS). These data were used to calibrate and evaluate the VIC model estimates of streamflow.

e. Sensitivity experiments

To understand how the VIC model responds to changes in key parameters related to the lake/wetland algorithm, a sensitivity analysis was performed for a single grid cell centered at 46.5625°N, 85.9375°W. This grid cell was selected because it is central to the domain and contains both lakes and wetlands, as summarized in Table 3. For the sensitivity analysis, two approaches were considered; first a one-way sensitivity analysis [or one-at-time (OAT) approach] was performed to understand how changes in the lake model parameters affect water fluxes (runoff and baseflow) and inundation area. Then a Full Factorial Two Level (FF2) sensitivity analysis was performed to understand the interactions among parameters along with their direct effects (e.g., Niyogi et al. 1999), as such interactions cannot be identified through the OAT approach (Stein and Alpert 1993; Niyogi et al. 1999). Both sensitivity analyses were conducted using six lake and wetland parameters: (i) the fraction of the vegetative surface draining into lake (R), (ii) the outlet width fraction ( f ), (iii) elevation of the lake outlet (Zmin), (iv) wetland depth (Zwetland), (v) lake depth (Zlake), and (vi) lake area (A). Using these six parameters, the two level full factorial design for the FF2 analysis required 26 (64) model runs. The ranges of parameters used in sensitivity analysis are presented in Table 4.

3. Lake and wetland algorithm parameterization

The VIC model lake and wetland algorithm requires parameters (see the appendix) describing the lake depth–area relationship, lake depth, lake area, wetland depth, fraction of vegetative surface draining into lake, width fraction, and elevation of the lake outlet. These were established for the Great Lakes region as follows.

a. Estimation of lake depth–area relationships

As detailed depth–area relationships for lakes were only available for Michigan, a methodology was required to develop depth–area relationships for regional lakes where only maximum area and maximum depth were available. Because of the variability in the characteristics of lakes within the study domain, attempts to fit a single maximum depth–area relationship for lakes in Michigan resulted in very low values of R2 (0.08) even after applying a log transformation. To reduce that variability, lake bathymetric data were divided into four area classes; lakes in each area class were then further divided into four subclasses based on their depth (Fig. 3). This resulted in 16 (4 × 4) classes. About 28% of lakes were classified as Very Small (<0.5 km2), with the majority of them less than 10 m deep (Fig. 3a). The largest number of lakes fall in the Small (0.5–2.0 km2) lake class (64%), in the shallowest subclass (Fig. 3b). About 8% of the lakes in the study domain were classified as Medium (2–10 km2; Fig. 3c), while only about 2% of lakes were classified as Large (>10 km2; Fig. 3d). Mean lake depth and mean lake area were 7.35 m and 1.31 km2, respectively, while the associated standard deviations are 6.54 m and 12.52 km2, respectively (Table 2).

A polynomial relationship between fractional depth and fractional area was developed for each class. Fractional depth and fractional area are lake depth and lake area divided by maximum lake depth/area for each elevation contour in the Michigan bathymetric dataset. Four relationships (linear, polynomial, exponential, and power) were tested using the observed data and the second-order polynomial was found to best describe the depth–area relationship. Figure 4 shows the fitted polynomial relationships for each nondimensional lake area and depth group for lakes in Michigan. For Very Small lakes, the polynomial relationship describing depth–area fractions worked well with R2 greater than 0.82 (Fig. 4a). Similarly, for Small lakes, four different second-order polynomials can describe the depth–area relationship with R2 greater than 0.80 (Fig. 4b). Medium and Large lakes were not represented as well, with slightly lower but generally acceptable coefficients of determination (R2 more than 0.65; Figs. 4c,d).

These polynomial relationships were used to derive the depth–area relationship for lakes in Wisconsin and Minnesota, which did not have observed bathymetry information. The appropriate polynomial equation (out of 16) was identified on the basis of the maximum depth and area of the lake. Each lake was divided into equal fractional area elements (AI), for which a fractional depth was calculated in order to obtain a set of depth–area values to define the lake depth profile. The number of fractional area elements used (n) was dependant on the depth of the lake, with a minimum of 10 elements assigned to lakes with depths of 10 m or less, and a maximum of 25 elements assigned to lakes deeper than 30 m. Fractional depth (ZFI) and depth (ZI) at each element were calculated using:
i1525-7541-11-5-1057-e2
i1525-7541-11-5-1057-e3
where a, b, and c are the coefficients of the second-order polynomials provided in Fig. 4. Here, Zlake is the maximum lake depth at maximum extent (A0 = 1). This methodology can potentially be transferred beyond the study domain where detailed bathymetry information is unavailable and the underlying geomorphic processes resulting in lake and wetland topography are similar. However, it is always helpful to have some bathymetry information for lakes in a specific region to estimate coefficients more accurately.

b. Assigning gridcell-specific depth–area relationships

A depth–area profile was generated for each lake in the study domain listed in the state DNR databases as described above. The fractional area of open water and wetland in each VIC model grid cell was estimated from the NLCD-2001. Then a method was developed that assigns an observed depth–area profile to the fractional area covered by open water and wetland. If a VIC model grid cell has more than 1% open water than a depth–area profile was assigned and a lake was simulated. If an observed lake falls in a grid cell, then the depth–area profile of that lake was used for the open water. Because of the prevalence of smaller lakes in the study area, many grid cells contained multiple lakes, in which case the depth–area profile of the largest lake was used. If a grid cell contained an open water fraction but no observed lake parameters, the depth–area profile of the deepest lake in a neighboring cell was used.

c. Estimation of wetland fractional area and wetland depth

The fractional area covered by wetlands in a grid cell was estimated from the NLCD-2001 land-cover map, as described earlier. If lakes and wetlands were present in the same grid cell then the wetlands were assumed to be located surrounding the effective grid cell lake. Therefore, an additional layer was added to the top of the lake to incorporate the additional extent of the potential open water surface because of the wetland. This new maximum extent was obtained by adding the fractional area of wetlands to that of open water within a grid cell.

Observational data of wetland depth were unavailable for the study domain, something that has been a major limitation for studying lakes and wetlands at regional or global scales. Bowling and Lettenmaier (2010) proposed a method to derive the wetland depth using a digital elevation model (DEM) and land-cover data, which was applied here. The DEM and land-cover maps were obtained from the USGS National Elevation Dataset (NED) and from the NLCD-2001, respectively. DEM data obtained from NED were at a 90-m resolution and were resampled using the nearest neighbor method to 100 m to match the resolution of the land-cover map. Wetland pixels were extracted for the study area and a zonal thickness, Thkzonal (m) (radius of the largest circle that can be drawn in each zone), map was developed in Environmental Systems Research Institute’s (ESRI’s) Geographic Information System (ArcGIS) 9.2 software using the spatial analyst tool. Wetlands in each VIC model grid cell were assigned to a different zone to obtain the average wetland depth for each VIC model grid cell. The high-resolution DEM was used to develop a map of average slope of wetland class in each VIC model grid cell, and a wetland depth map was derived using the relationship:
i1525-7541-11-5-1057-e4
where Zwetland is wetland depth (m) and β is slope (degrees). The wetland depth map was then aggregated to ⅛° in order to estimate the gridcell average maximum wetland depth for input to the lake and wetland algorithm. Wetlands up to 1.5 m deep were identified using the DEM and land-cover map with deeper wetlands located in the northern part of the study domain (Fig. 2d). The wetland bathymetric profile was assumed to be linearly generated from the wetland depth (Zwetland) and its maximum extent. The maximum gridcell water depth Zmax is then calculated as the sum of Zwetland and Zlake.

d. Fraction of land surface draining into lake (R)

The surface area of each VIC model grid cell is divided between open water and wetland, vegetated, and nonvegetated (i.e., bare soil) tiles. As there is no horizontal transport between grid cells within the VIC model, the only surface water that can drain into the lake and wetland tile must come from the current grid cell. The fraction of the surrounding grid cell that drains to the lake and wetland tile must therefore be parameterized. Bowling and Lettenmaier (2010) considered this fraction to be a calibration parameter, but kept the value fixed at 1.0 for their simulations in Alaska. Krinner (2003) suggested the fraction of vegetative surface draining into the lake be equal to the fraction of lake in the grid cell. They found, however, that this formulation underestimated the fraction of vegetative surface draining into the lake in semiarid regions. Despite this limitation, we used the approach suggested by Krinner (2003) where the fraction of the vegetative surface draining into the lake was set equal to the fraction of lake and wetland present in the grid cell.

e. Width fraction (f) and elevation of the lake outlet (Zmin)

Surface outflow from the lake is calculated as a function of total depth of the lake above the lake outlet (ZZmin) at the end of each time step, and is based on the equation for flow over a broad-crested weir assuming negligible velocity head [Eq. (1)]. The elevation of the lake outlet, Zmin, was assumed to be a function of maximum lake depth, Zlake, as follows:
i1525-7541-11-5-1057-e5
where F is the fraction of Zlake and was allowed to vary from 0.97 to 0.99, with the final value of Zmin set through sensitivity analysis and calibration. The possible range of the width fraction, f, as suggested in Bowling and Lettenmaier (2010) was 0–0.5, but for this analysis, the final value was achieved through sensitivity analysis and calibration.

4. Model calibration and evaluation

After sensitivity analysis, the VIC model was calibrated and evaluated manually against observed daily streamflow for selected watersheds (Fig. 1). Eight parameters (six soil parameters and two lake model parameters) were adjusted during calibration (Table 5). Only two ( f and Zmin) of the six lake parameters used for the sensitivity analysis were considered in model calibration, with the others from observations or through empirical relationships. Initial parameters for the soil were obtained from Sinha et al. (2010), while those for the lake algorithm were taken from Bowling and Lettenmaier (2010). For the watersheds not included in Sinha et al. (2010), initial soil parameters were obtained from the nearest watershed.

Calibration was conducted using the lake and wetland algorithm and involved the manual adjustment of parameters to improve the simulation of daily streamflow. Simulated daily streamflow values were obtained by routing runoff and baseflow from each grid cell to locations representing the USGS gauging stations using the method of Lohmann et al. (1998). The effectiveness of model calibration was checked using both a visual comparison of observed and simulated hydrographs and through maximizing three statistical performance measures described in Mishra et al. (2010): the Nash–Sutcliffe efficiency (NE; Nash and Sutcliffe 1970), the correlation coefficient (r), and the ratio of simulated mean flow to observed mean flow (MFratio).

The model calibration period was selected to be 1985–95, while the model evaluation period was selected to be 1996–2005 for all the watersheds except for the Menominee River at Koss, Michigan. Daily flow data were not available for the Menominee River at Koss, Michigan, between 1985 and 1998 so 1970–80 was used for the calibration period and 1999–2005 was used for evaluation. These periods were selected to be as close as possible to the time when data was collected for the NLCD (2001) land-cover product, thus minimizing the effect of land-cover change on streamflow. The three VIC model parameters that affect baseflow (ds, dsmax, and Ws) and two lake model parameters ( f and Zmin) were adjusted to calibrate low flows, while the infiltration parameter b-infilt and the lake model parameters were used to fit peak flows. The depths of the two soil layers were adjusted to produce the correct volume of mean daily streamflow.

Each of the 10 watersheds was calibrated to obtain its best individual set of parameters. Parameters were then transferred to the uncalibrated grid cells in the study domain using an approach similar to Nijssen et al. (2001), who used Köppen climate zones in their global-scale simulations. It was not possible to obtain distinct Köppen climate zones in the relatively small study domain, thus we used clustering of the annual average precipitation and temperature datasets to create our own climate zones. An approach based on the distribution of soil and vegetation was also considered; however, calibration parameters (Table 5) had a consistently stronger relationship with climate (e.g., precipitation and air temperature) than soil or vegetation metrics at the watershed scale. Therefore, clustering based on climate variables (e.g., precipitation and air temperature) was used. The clustering analysis was performed using the spatial analyst tool in ESRI ArcGIS 9.3, and it identified nine climatic zones. Parameters were then assigned to the uncalibrated grid cells using the nearest calibrated cells within the same climatic zone.

Several researchers (Beven 2006; Beven and Freer 2001) have documented the limitations of equifinality or nonunique solutions in hydrologic modeling. Regardless of the calibration approach (i.e., manual or automatic), calibration of a complex model such as the VIC model involves a high degree of nonlinearity, resulting in many local minima in the objective function surface (Troy et al. 2008). The possible solutions achieved through calibration may therefore not be unique and several combinations of parameter values may yield the same calibration performance. The choice of prior parameters will influence which local minima is selected. The eight parameters adjusted during calibration suggest a relatively high degree of freedom and associated uncertainty. However, the prior parameters were in ranges that have been suggested by many previous applications (see Sinha et al. 2010; Bowling and Lettenmaier 2010; Troy et al. 2008), which should aid in the selection of appropriate solutions. Verifying the location of a true global optima would require advanced computational techniques to seek the parameter values, which is beyond the scope of the work presented here and will be addressed in future efforts. However, it should be noted that autocalibration might improve the model performance (e.g., NE) in simulating daily streamflow, but that will not alter the overall conclusions of the study and our scientific understanding about the processes.

5. Regional application

After model calibration and evaluation and parameter transfer to the uncalibrated grid cells, the VIC model was applied regionally for the period of 1985–2005. To quantify the impacts of open water storage on the regional water and energy budget, model simulations were conducted for two scenarios: (i) with lake and wetland represented (LAKE), and (ii) without lake and wetland represented (NO-LAKE). For the NO-LAKE scenario, the soil parameters and meteorological forcings were kept the same as for the LAKE scenario, while the lake and wetland fractions were considered drained so that wooded grassland (the exposed wetland vegetation class) occupied the entire fractional area of the lake and wetland class. Separate calibration for the NO-LAKE scenarios was not performed because with the manual calibration it is rare to get optimal parameters (with similar calibration statistics) for both of the scenarios.

6. Preliminary results

a. Sensitivity experiment

1) One at a time approach

The sensitivity of hydrologic variables to lake and wetland parameters was first tested using a one-at-a-time approach (Figs. 5 and 6). As values of R increased from 0.15 to 0.75, the water volume entering the gridcell lake also increased, which affected the partitioning of surface runoff and baseflow, resulting in higher runoff (150% increase) and lower baseflow (24% decrease) out of the grid cell (Fig. 5a; Table 6). Inundation area was found to be sensitive to R and increased 43.8% on increasing R from 0.15 to 0.75, because of the increase in inflow as the area draining into it increased. As more water enters the lake, its depth and area must increase, which will force more water through the outlet and reduce the area of the grid cell contributing to baseflow generation (if R = 1, then only baseflow from the lake fraction exits the grid cell). If R is large and the lake and wetland area are small, then the incoming flow can overwhelm the simulated hydrologic system so that the presence of lakes actually increases the ratio of surface runoff to baseflow rather than decreasing it, as expected. This means that the selection of R is very significant to the functionality of the lake and wetland algorithm and that using an empirical relationship to set the value instead of calibrating it will reduce the potential for it to contribute to nonunique solutions during calibration.

Smaller values of the width fraction ( f ) constricted lake runoff, which led to increased water residence time in the lake (Fig. 5b). Runoff was increased dramatically by 230.4% when f was increased from 0.0001 to 0.05 (Fig. 5b; Table 6), while inundation area increased from 39.3% to 45%. Baseflow depends primarily on the spatial extent of the lake and wetland, and thus indirectly on the time in which water stays in the lake.

The difference in elevation between the lake and wetland depth (Zwetland) and the elevation of the lake outlet (Zmin) controls the rate of outflow from the lake by adjusting the depth of water above the outlet. The range of the value was set to vary from 0.97 to 0.99 of Zlake during the sensitivity analysis. Runoff was decreased by 24.6%, baseflow by 21.8% and inundation area by 28.4% with increasing Zmin (Fig. 5c; Table 6).

The OAT sensitivity analysis for (Zwetland) is summarized in Fig. 6a. Results indicate that runoff increased by 33.8% while baseflow was decreased by 14.1% with increasing the Zwetland from 0.2 to 1.0 m (Table 6). Inundation area was also decreased by 18.2%. For this analysis, Zwetland was increased while the wetland fractional area was kept constant. Hence, the volumetric capacity of the wetland to store the water was increased, but the same stored volume consumes a smaller area at a deeper depth resulting in reduced inundation area and baseflow.

Figure 6b shows the results of the sensitivity experiment conducted on lake depth (Zlake). Runoff was increased by 88% when Zlake was increased from 3 to 15 m keeping the lake area constant, in large part because Zmin was left unchanged at 0.99 of Zlake allowing the lake level to rise to a greater depth above the outlet before spreading out in the wetland fraction (Fig. 6b; Table 6). Baseflow and inundation area decreased by 23.2% and 26.5%, respectively (Table 6).

Runoff was decreased by 53.5% when lake area (A) was increased from 1% to 5% of the grid cell, while baseflow and inundation area were increased by 47.3% and 77.8%, respectively (Fig. 6c; Table 6). Runoff was found to be very sensitive to lake area as only a 1% increase in area results in a significant decrease in runoff. Inundation area was increased with the lake area, which was expected (Fig. 6c).

Analysis of daily surface runoff and inundation extent suggested that three lake model parameters (R, f, and Zmin) played unique and significant roles in controlling lake performance, suggesting that they should be used in model calibration. Increasing the value of R resulted in increased mean surface runoff and inundation extent, while reducing the surface runoff peak. Higher values of f resulted in increased mean and peak surface runoff, while decreasing inundation extent. Both inundation extent and peak surface runoff were increased and mean surface runoff decreased when Zmin was increased.

2) Full factorial two level sensitivity analysis

Full factorial two level sensitivity analysis was conducted for six parameters: R, f, Zmin, Zwetland, Zlake, and A, with 64 assigned combinations of low/high parameter values (Table 4). The resulting Pareto plots (Fig. 7) show both the main effect of a parameter and the interaction effect of parameter pairs for the same six variables analyzed in the single factor analysis. Runoff was found to be most sensitive to lake area (A) with a negative effect where increasing A decreased surface runoff (Fig. 7a). In fact, baseflow sensitivity was identical but opposite to that of runoff, highlighting the effect of lakes and wetlands on the distribution of outflows from the grid cell between runoff and baseflow (Fig. 7b). The interaction between f and A ( f:A) was found to be the second most influential on runoff and baseflow, which was expected as they are two of the three parameters most responsible for controlling the outflow rate from the lake. The other parameter controlling outflow rate, Zmin, proved to be far less influential, probably because its impact on outflow is a function of lake depth, which was influenced by the amount of runoff entering the lake.

For the inundation area, the interaction effect between f and A was higher than the main effect of any parameter (Fig. 7c). The inundation area was also positively related to the main effects of A and R. Results from the FF2 sensitivity analysis follow the same trend, which was obtained in the OAT approach; however, these give additional information about the interaction of parameters. Here, we also find that in most of the cases the interaction between f and A showed a greater effect than R, f, Zmin, Zwetland, and Zlake alone. However, as the values of A, Zlake, and Zwetland were set from observations, the sensitivity of the other lake algorithm parameters is more important for calibration.

3) Model calibration and evaluation

Using the results from the sensitivity analysis, three lake and wetland parameters were identified for adjustment during calibration at a regional scale. As discussed previously, one of those parameters, the land surface fraction draining into the lake (R), was set equal to the fractional area of lakes and wetlands in the grid cell as suggested by Krinner (2003). This left two parameters, the values of the width fraction ( f ) and elevation of the lake outlet (Zmin), for use in calibration to improve daily streamflow simulations. Based on the sensitivity analysis the calibrated parameters values for f and Zmin were obtained as 0.0001 and 0.99 of lake depth (Zlake), respectively.

Calibrated daily streamflow was in a good agreement with the observed streamflow as the variability, timing of peak, and total streamflow volume was well captured (Fig. 8). However, model results indicated a nonsystematic bias in the magnitude of predicted daily streamflow peaks where some of the peaks were underpredicted while some were overpredicted. In general, model performance was good at all 10 gauge stations with the ranges of 0.87–1.01, 0.77–0.88, and 0.47–0.76 for MFratio, r, and NE, respectively (Table 7).

At 5 out of 10 gauging stations model simulated streamflow showed a positive bias during the evaluation (Table 7), which can be attributed to the relatively large interannual variability in streamflow during the calibration period (1985–95). During the calibration period, the study region experienced two extreme events: drought in 1988, and flood in 1993. Visual comparison (Fig. 9) of model simulated and observed daily streamflow with the statistical performance measures (Table 7) indicated the reasonableness of the model performance during the evaluation period (1996–2005). The daily NE values were higher than 0.5 for 7 out of 10 gauge stations while the monthly NE values were higher than 0.6 at all gauging stations (Table 7).

The calibrated model was also evaluated against daily observed latent and sensible heat fluxes for the period of 2002–05 (Fig. 10). Two Ameriflux network sites (Lost Creek and Sylvania Wilderness, Wisconsin) were selected for the comparisons. These comparisons were made without adjusting vegetation, soil, or climate to specifically represent the Ameriflux sites, instead using the general VIC model setup for the grid cell containing the Ameriflux site. This is likely to introduce additional uncertainty into the modeled results, but serves as a test of the calibrated model used for regional analysis. For both latent and sensible heat fluxes, the model captured the seasonal cycle in a satisfactory manner (Fig. 10). The correlation coefficients were 0.78 and 0.52 at the Lost Creek site and 0.70 and 0.50 at the Sylvania Wilderness site for latent and sensible heat fluxes, respectively. Twine et al. (2000) indicated that the flux towers in northern Wisconsin are assumed to have an observational error of about ±20%. Additionally, Vano et al. (2006) have found that the Interactions between Soil, Biosphere, and Atmosphere (ISBA) model was better at simulating latent heat flux than sensible heat flux, which is consistent with the findings of this study.

Simulated monthly fractional inundated area from the VIC model was compared against the Global Inundation Dynamics Dataset (GIDD; Prigent et al. 2007) for the period of 1993 to 2000 (Fig. 11a) for a 1° × 1° area in northern Wisconsin. This area was selected for the comparison as it is dominated by small lakes and wetlands and does not include substantial river flood plains that would not be represented by the VIC model, but would be included in the GIDD. The GIDD data use satellite imagery to estimate inundation fractions for 0.25° × 0.25° grid cells. For this comparison, the mean fractional inundated area was estimated for the selected 1° × 1° box using the inundation fraction for all grid cells from both products (the VIC model and GIDD grid cells) within the box. The GIDD data do not provide inundation estimates in winter and early spring because of snow and ice cover. For the summer months, the VIC model simulated fractional inundation area captures the seasonal variability (Fig. 11a) in a satisfactory manner, but seems overpredicting maximum inundation extent in the spring. This may reflect a limitation of the GIDD product to measure the peak inundation area for mixed snow and ice conditions (Fig. 11b). Both products tend to reach a minimum in August reflecting the effect of higher summer evapotranspiration (ET) rates. During April the predicted domain-averaged fractional inundation area went as high as 0.22, while in August it reached as low as 0.08. Spatial maps of fractional inundated area show that higher inundation fractions occur in the northern part of the study domain, which is dominated by the presence of wetlands (Figs. 11c,d).

4) Effects of lakes and wetlands on regional hydroclimatology

Annual average precipitation varied from 560 to 920 mm in the study domain (Fig. 12a). The spatial variability of precipitation was quite distinct, with northwestern Minnesota drier relative to southern Wisconsin and Michigan. Average annual ET varied from 300 to 660 mm while annual average total runoff (surface runoff + baseflow; TR) varied from 100 to 480 mm when the effects of lakes and wetlands were included (LAKE scenario; Figs. 12b,d). Annual average ET was decreased by 28 mm (5%) while annual average total runoff was increased by the same amount (11.7%) under the drained lakes and wetland (NO-LAKE) scenario. A large spatial variability was associated with changes in ET and total runoff (Figs. 12c,e) in the northern part of the study domain, which is dominated by wetlands. Both annual average ET and total runoff were changed in the range of 5–350 mm (Figs. 12c,e) reflecting the substantial impacts of lakes of lakes and wetlands on the regional water balance. When lakes and wetlands were represented, annual average ranges for energy balance variables were: 50–80 W m−2 (mean = 66 W m−2), 30–60 W m−2 (mean = 40 W m−2), and 10–30 W m−2 (mean = 25 W m−2), for net radiation (RNET), latent heat (LH), and sensible heat (SH), respectively (Figs. 13a,c,e). The annual average ground heat flux was about −1 W m−2. When the lakes were drained LH was decreased, SH was increased, and minimal change was identified in RNET (Figs. 13b,d,e). Similar to the water fluxes, the largest changes in energy fluxes were found in the wetland-dominated regions. The changes in annual average LH and SH were in the range of 1–20 W m−2 (Figs. 13d,e).

Among water and energy fluxes, ET was higher because of the presence of lakes and wetlands during the April–June period (Fig. 14a) while total runoff was consistently decreased throughout the year with a significant decrease in March–April period (Fig. 14a). Under the LAKE scenario, RNET was substantially higher in May and October because of the presence of lakes and wetlands (Fig. 14b). As described above for ET, LH was largely increased during the April–June period when evaporative demand was high (Fig. 14b) while SH was decreased in the same period under the LAKE scenario. Ground heat flux was highest during April and lowest in winter and early spring under the LAKE scenario (Fig. 14b). These results were consistent with the findings based on model simulations of Bonan (1995).

The ratio of annual average ET to precipitation (ET/P) and total runoff to precipitation (TR/P) was also evaluated for each grid cell in the study domain (Fig. 15). ET/P in the LAKE scenario was about 1.06 (R2 = 0.61) that of the NO-LAKE scenario (Fig. 15a), while the total runoff ratio (TR/P) was about 0.91 times that of the NO-LAKE scenario (Fig. 15b). Thus, lakes and wetlands significantly changed the partitioning of precipitation to ET and total runoff within the study domain. Similar results were identified by Bowling and Lettenmaier (2010) and Rouse et al. (2008) for modeling and observations based studies, respectively.

For all the grid cells present in the study domain, latent heat (LH/RNET) was increased with respect to net radiation by a factor of 1.06 (R2 = 0.17) when lakes were represented [Fig. 15c]. The ratio of sensible heat to net radiation (SH/RNET) with lakes was 0.94 (R2 = 0.61) times that of the NO-LAKE scenario (Fig. 15d). Partitioning of net radiation into ground heat flux (GH/RNET) was only slightly affected (Fig. 15e). Larger changes were observed in Bowen ratio (SH/LH), where it was reduced by a factor of 0.87 (R2 = 0.39) in the LAKE scenario.

Changes in water and energy fluxes due to the presence of lakes and wetlands on watershed basis revealed a greater amount of variability (Table 8). Fractional area covered by lakes and wetlands varied from 0.17 for the Grand River watershed to 0.36 for the Menominee River watershed. Annual average total runoff was decreased by 4%–13% with the representation of lakes, while annual average ET increased in the range of 4%–15%. The Bowen ratio was decreased in the range of 5%–22% with the representation of lakes and wetlands (Table 8). Changes observed at the scale of each watershed were not directly related to their size or the fractional area covered by lakes and wetlands, but rather to their geographical location. For instance, the watersheds located in Michigan experienced larger changes in water and energy fluxes than those located in Minnesota, which suggests that these changes are driven by climate (precipitation and temperature). However, conclusions that are more concrete can only be made after detailed exploration of climatic impacts.

7. Discussion

Accurate modeling of the spatial and temporal dynamics of the inundation area related to lakes and wetlands is problematic in the light of data scarcity and the complexities of water and energy exchange in lake systems (Prigent et al. 2007). However, the estimation of inundation area of lakes and wetlands is of great interest in regional-scale hydrology, biogeochemical cycles, and hydroclimatology. For example, fluctuations in wetland inundation are strongly correlated with interannual variability of methane emission (Bousquet et al. 2006). About 60% of global wetlands are inundated only during part of the year, displaying large variability in their seasonal extent (Papa et al. 2007). Based on these simulation results, large spatial and temporal variations exist in lake/wetland inundation in the study domain, with an average seasonal increase in inundated extent of about 200%. Minimum inundation usually occurred during dry or frozen states when the soil was less saturated and had little potential to satisfy evaporative demand (e.g., Yang et al. 2003). Maximum inundation mainly occurred in spring, which was attributed to spring snowmelt generated runoff (Fig. 11b). Bowling et al. (2003b) and Papa et al. (2007) also found similar results in the snow dominated arctic regions. Under these conditions, water availability generally exceeds evaporative demand, contributing to increased recharge (i.e., baseflow). Capturing the spatial and temporal variability of inundation area and its response to climatic conditions demonstrated the efficacy of model at simulating seasonal processes.

Annual average ET was increased regionally from 65%–69% of annual precipitation when lakes were represented, with more substantial changes in the northern part of the study domain that is dominated by lakes and wetlands. The increase in water vapor supplied to the atmosphere because of the presence of lakes and wetlands might have implications for precipitation recycling in coupled models (e.g., Lofgren 1997). As ET increased, annual average total runoff decreased from 35%–31% with the inclusion of lakes and wetlands. Rouse et al. (2008) reported similar characteristics (i.e., more ET and less total runoff) for lake/wetland dominated regions in the central Mackenzie River basin, relative to upland areas. During the summer, the water balance deficit in the lake-dominated region was increased twofold during the dry years (Rouse et al. 2008) compared to average conditions. This suggests that effects of lakes and wetlands on the surface water balance could be more substantial (depending on season) under changing climatic conditions.

Lakes and wetlands altered the simulated partitioning of energy balance components with 6% higher LH and 5% lower SH with lakes represented. Rouse et al. (2008) observed a 59% increase in LH and 61% decrease in SH for lake surfaces relative to land surfaces in central Canada. The simulated results for a domain with maximum water extent on the order of 20% seem comparable. Energy partitioning over lakes and wetlands was also affected by the presence of snow and lake ice. Lakes of the study domain remained frozen from late autumn until late spring. During the snow-and-ice-free season, lakes and wetlands have greater RNET due to lower albedo, but during the ice-on conditions, RNET is negative because lakes absorb less solar radiation and experience large net longwave radiation loss (Fig. 14b; Rouse et al. 2008).

8. Conclusions

This study presents the first regional scale application of the VIC lake and wetland algorithm to simulate the hydrologic impacts of lakes and wetlands in midlatitude regions. Lakes and wetlands are an integral part of the landscape of the Great Lakes region with about 20% of the study domain covered by lakes and wetlands. Considering their significance in the hydrologic cycle, biogeochemical cycle, and land–atmosphere interactions, an evaluation of their influence on regional hydroclimatology is essential. In this work, a model parameterization approach based on commonly available data related to lakes and wetlands, a model sensitivity analysis, and an evaluation of the regional water and energy balance impacts of lakes and wetlands were presented. Data for approximately 8100 lakes were collected and processed in order to derive regional lake bathymetric curves. The VIC model with the lake and wetland algorithm was calibrated and evaluated at 10 selected gauge stations. Both a one-at-a-time (OAT) and two-way factorial (FF2) single-grid sensitivity analysis was conducted for six lake model parameters. Finally, the annual change in several water and energy balance variables was evaluated based on the inclusion of lakes and wetlands into the simulation. From this study, the following conclusions were made:

  • Runoff from grid cells with lakes and wetlands was most sensitive to the width fraction ( f ) of the lake outlet followed by the land surface fraction draining into the lake (R). Runoff was increased by 230% on increasing the width fraction from 0.0001 to 0.05 and was increased by 150% when R was increased from 0.15 to 0.75. Baseflow and inundation area were increased by 47.3% and 77.8%, respectively, when open water fraction was increased from 1%–5% of a grid cell. Runoff was decreased by 53.5% when open water fraction was increased by 1%–5%. The model simulated inundation area showed large interannual variability in lake and wetland extent suggesting their linkage with the regional hydroclimatology.
  • The presence of lakes and wetlands affected the regional water balance significantly. Domain-averaged annual mean ET was increased by 28 mm (5%) while annual average total runoff was reduced by the same amount (11.7%) when lakes and wetlands were included in model simulations. Changes in total runoff were significant during the spring when snowmelt is stored in lakes and wetlands rather than becoming streamflow directly. Similarly, changes in evapotranspiration were substantial during April–June period.
  • The simulated regional energy balance was significantly affected because of the presence of lakes and wetlands. The domain-averaged mean annual LH was 6% higher and the mean annual SH 5% lower because of the present extent of lakes and wetlands in the domain, relative to an artificial case with lakes and wetlands drained. As a result, the current Bowen ratio was 0.87 times that of the Bowen ratio with no open water.
This research, as well as other previous studies, suggests that the role of lakes and wetlands may be more pronounced during extreme climatic conditions (i.e., drought and flood), which will be considered in future work. More sophisticated approaches related to model calibration (e.g., autocalibration using multiobjective criteria) and parameter transfer to uncalibrated regions (e.g., based on combinations of soil, vegetation, and climate) within the study domain could potentially improve simulation performance, and will be investigated in the future.

Acknowledgments

The support from the NASA Land Cover/Land Use program (Grant NNG06GC40G) was greatly appreciated. Comments from the three anonymous reviewers were very insightful and helped to improve the present work. Support from the Purdue Climate Change Research Center’s (PCCRC) fellowship to the first author is also acknowledged.

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  • Yang, D., , Robinson D. , , Zhao Y. , , Estilow T. , , and Ye B. , 2003: Streamflow response to seasonal snow cover extent changes in large Siberian watersheds. J. Geophys. Res., 108 , 4578. doi:10.1029/2002JD003149.

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APPENDIX

List of Symbols Used in Model Parameterization

i1525-7541-11-5-1057-ta01

Fig. 1.
Fig. 1.

Gray area represents the study domain. Watersheds included within the study domain: (a) St. Croix River at St. Croix Falls, WI; (b) St. Louis River at Scanlon, MN; (c) Mississippi River at Anoka, MN; (d) Chippewa River at Durand, WI; (e) Wisconsin River at Muscoda, WI; (f) Menominee River at Koss, MI; (g) Au Sable River at Luzerne, MI; (h) Muskegon River at Evart, MI; (i) Tittabawassee River at Midland, MI; and (j) Grand River at Grand Rapids, MI.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 2.
Fig. 2.

(a) Distribution of open water area in the study domain as estimated from NLCD (2001); (b) distribution of wetland area in the study domain as estimated from NLCD (2001); (c) distribution of lake depth in the study domain; and (d) estimated wetland depth using DEM and land-cover data.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 3.
Fig. 3.

(a) Distribution of Very Small lakes in various depth ranges, (b) distribution of Small lakes in various depth ranges, (c) distribution of Medium lakes in various depth ranges, and (d) distribution of Large lakes in various depth ranges.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 4.
Fig. 4.

(a) Depth–area relationship described by second-order fitted polynomial on observed bathymetry data for Very Small lakes, (b) for Small lakes, (c) for Medium lakes, and (d) for Large lakes in Michigan.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 5.
Fig. 5.

(a) Sensitivity of runoff, baseflow, and inundation area toward fraction of vegetative surface draining into lake (R), (b) Sensitivity of runoff, baseflow, and inundation area toward width fraction ( f ), and (c) sensitivity of runoff, baseflow, and inundation area toward elevation of lake outlet (Zmin).

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 6.
Fig. 6.

(a) Sensitivity of runoff, baseflow, and inundation area toward wetland depth (Zwetland), (b) sensitivity of runoff, baseflow, and inundation area toward lake depth (Zlake), and (c) sensitivity of runoff, baseflow, and inundation area toward lake area (A).

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 7.
Fig. 7.

Pareto plots for sensitivity analysis obtained using FF2 designs. Both main effect and interactions are explicitly extracted in this analysis. Black bars show negative effect while gray bars show positive effect. Description of parameters given in the Table 4 and X:Y represents the interaction between parameter X and parameter Y.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 8.
Fig. 8.

Results of model calibration (1985–95) for the selected watersheds: (a) St. Croix River at St. Croix Falls, WI; (b) St. Louis River at Scanlon, MN; (c) Mississippi River at Anoka, MN; (d) Chippewa River at Durand, WI; (e) Wisconsin River at Muscoda, WI; (g) Au Sable River at Luzerne, MI; (h) Muskegon River at Evart, MI; (i) Tittabawassee River at Midland, MI; and (j) Grand River at Grand Rapids, MI.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 9.
Fig. 9.

Same as Fig. 8 but for model evaluation (1996–2005) for the selected watersheds.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 10.
Fig. 10.

Model performance to simulate daily latent and sensible heat fluxes at Lost Creek, WI, and Sylvania Wilderness, WI.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 11.
Fig. 11.

(a) Comparison of the VIC model simulated fractional inundation area for a 1° × 1° area in northern Wisconsin, (b) seasonal variation in minimum, mean, and maximum domain-averaged inundation area fraction, (c) mean inundation area fraction in April for the period of 1985–2005, and (d) mean inundation area fraction in August for the period of 1985–2005.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 12.
Fig. 12.

Mean (LAKE scenario) and difference (LAKE − NO-LAKE scenarios) of water balance for the period of 1985–2005: (a) mean annual precipitation (mm), (b) mean annual ET with lakes and wetlands, (c) difference in mean annual ET (Delta ET), (d) mean annual total runoff with lakes and wetlands, and (e) difference in total runoff (Delta TR).

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 13.
Fig. 13.

Mean (LAKE scenario) and difference (LAKE − NO-LAKE scenarios) of energy balance for the period of 1985–2005: (a) RNET—mean annual net radiation (W m−2) with lakes and wetlands, (b) Delta RNET—difference in mean annual RNET, (c) LH—mean annual latent heat flux (W m−2) with lakes and wetlands, (d) Delta LH—difference in mean annual LH, (e) SH—mean annual sensible heat flux (W m−2) with lakes and wetlands, and (f) Delta SH—difference in mean annual SH.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 14.
Fig. 14.

Seasonal cycle of changes (LAKE − NOLAKE) associated with (a) water fluxes and (b) energy fluxes.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Fig. 15.
Fig. 15.

Partition of water and energy fluxes in LAKE and NO-LAKE scenarios: (a) ET/P, (b) TR/P, (c) LH/RNET, (d) SH/RNET, (e) GH/RNET, and (f) SH/LH (Bowen ratio). Gray line is 1:1 line and solid black line is regression line.

Citation: Journal of Hydrometeorology 11, 5; 10.1175/2010JHM1207.1

Table 1.

Land-cover distribution in the study domain and remapping of NLCD land cover to representative vegetation cover for the VIC model.

Table 1.
Table 2.

Summary statistics of observed lake data.

Table 2.
Table 3.

Details of grid cell considered for a single-grid sensitivity analysis.

Table 3.
Table 4.

Parameter range used in sensitivity analysis.

Table 4.
Table 5.

Description of calibration parameters.

Table 5.
Table 6.

Percent change obtained using the lowest and the highest values of lake model parameters (Table 4). Percentage change is estimated using the average value obtained from the highest parameter value and average value obtained from the lowest parameter value.

Table 6.
Table 7.

Statistical performance measures for daily and monthly streamflow at the selected USGS gauge stations in the study domain.

Table 7.
Table 8.

Ratio (LAKE/NO-LAKE) of LAKE and NOLAKE scenarios in total runoff, ET, and Bowen ratio for the selected watersheds.

Table 8.

* Purdue Climate Change Research Center Contribution Number 1015.

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