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Keywords:

  • Fully integrated;
  • modeling;
  • surface-subsurface

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[1] Results are presented in which a physically-based, three-dimensional model that fully integrates surface and variably-saturated subsurface flow processes is applied to the 75 km2 Laurel Creek Watershed within the Grand River basin in Southern Ontario, Canada. The primary objective of this study is to gauge the model's ability to reproduce surface and subsurface hydrodynamic processes at the watershed scale. Our objective was first accomplished by calibrating the steady-state subsurface portion of the system to 50 observation wells where hydraulic head data were available, while simultaneously matching the stream baseflow discharge. The level of agreement between the observed and computed subsurface hydraulic head values, baseflow discharge and the spatial pattern of the surface drainage network indicates that the model captures the essence of the surface-subsurface hydraulic characteristics of the watershed. The calibrated model is then subjected to two time series of input rainfall data and the calculated discharge hydrographs are compared to the observed rainfall-runoff responses. The calculated and observed rainfall-runoff responses were shown to agree moderately well for both rainfall data series that were utilized. Additionally, the spatial and temporal responses of the watershed with respect to the overland flow areas contributing to streamflow and the surface-subsurface exchange fluxes across the land surface during rainfall inundation and subsequent drainage phases demonstrate the dynamic nature of the interaction occurring between the surface and subsurface hydrologic regimes. Overall, it is concluded that it is feasible to apply a fully-integrated, surface/variably-saturated subsurface flow model at the watershed scale and possibly larger scales.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[2] The advantages and disadvantages of using physically based surface/variably saturated subsurface models to analyze flow systems have been the subject of a number of discussions in the literature [e.g., Beven, 1989, 1993, 1996a, 1996b, 2000, 2001a, 2001b, 2002a, 2002b, 2006; Beven and Binley, 1992; Ebel and Loague, 2006; Grayson et al., 1992; Loague and VanderKwaak, 2004; Loague et al., 2006; Refsgaard et al., 1996; Smith et al., 1994]. However, it is only in the last few years that models such as InHM [VanderKwaak, 1999], MODHMS [Hydrogeologic, 2000; Panday and Huyakorn, 2004] and HydroGeoSphere [Therrien et al., 2005], which meet or exceed the original Freeze and Harlan [1969] blueprint, have been made available to the hydrological community for testing. Most of the initial applications of these ‘new generation’ surface-subsurface models have, to date, been limited to experimental plots or relatively small subcatchments [e.g., Di Iorio, 2003; Heppner et al., 2006; Jones et al., 2006; Loague and VanderKwaak, 2002; Loague et al., 2005; Pebesma et al., 2005; VanderKwaak and Loague, 2001]. In order for these data-intensive models to realize their full potential and to gain acceptance in the hydrological community, it needs to be demonstrated that they are capable of simulating hydrodynamic processes at larger scales.

[3] In this study, the physically based, surface/variably saturated subsurface flow model InHM [VanderKwaak, 1999] is applied to a hydrologically complex but reasonably well characterized 75 km2 watershed located in Southern Ontario, Canada. The primary objective of this study is to assess InHM's ability to simulate transient flow processes at a scale larger than has been previously attempted. This objective is accomplished by first calibrating the steady state subsurface of the system to hydraulic head data obtained from 50 observation wells while simultaneously matching the observed stream base flow discharge. The calibrated system is then subjected to two rainfall data series and the resulting discharge hydrographs are compared with the measured rainfall-runoff response. The computed hydrodynamic response of the system is next analyzed in terms of temporal variations in the contributing areas and surface-subsurface exchange fluxes occurring across the land surface during rainfall inundation and subsequent drainage phases. A secondary objective of this study is to demonstrate the advantages of using the fully integrated approach to investigate watershed-scale hydrodynamic processes. Traditionally, modeling studies at the watershed scale either treat the surface and subsurface systems as separate entities or employ a loosely coupled approach to link the two systems.

[4] InHM was originally developed at the University of Waterloo [VanderKwaak, 1999] and is capable of simulating water flow and solute transport over the two-dimensional land surface and in the three-dimensional dual continua subsurface (i.e., porous medium-macropore interactions) under variably saturated conditions. The two-dimensional form of the nonlinear diffusion-wave equation, together with Manning's equation to compute overland flow velocities, is employed on the surface while Richards' equation and Darcy's law are assumed to hold in the subsurface. Full coupling of the surface and subsurface flow regimes is accomplished by simultaneously solving one system of non-linear discrete equations arising from the control-volume finite element method to describe flow and solute transport in both flow regimes, as well as the water and solute fluxes between continua. Details concerning the theory, numerical solution techniques and example applications of InHM are given by VanderKwaak [1999] as well as VanderKwaak and Loague [2001].

2. Site Description

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[5] The candidate site for this study is the Laurel Creek Watershed, which covers approximately 75 km2 within the Grand River basin in Southern Ontario, Canada (Figure 1). The climate of the watershed is sub-humid with an average annual precipitation of 908 mm during the years 1971–2000 [Environment Canada, 2003]. The surface of the watershed is composed of sandy hills, some of which are ridges of sandy till while others consist of kames or kame moraines with outwash sands occupying the intervening hollows [Pawley et al., 1976]. Local relief in this region ranges up to 35 m. Neighboring the hilly region is an extensive area of alluvial terraces from the Grand River floodplain containing sandy and gravelly materials [Pawley et al., 1976]. Surface elevations in the study area range from about 410 m above sea level (masl) in the hilly region to 300 masl where the watershed discharges into the Grand River.

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Figure 1. Location of the Laurel Creek Watershed.

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[6] The overburden geology of the watershed is highly complex and has been altered by the advance and retreat of several glacial ice sheets that deposited a number of till units. Silty and clayey tills form the major aquitards and the aquifers consist primarily of reworked tills, glacio-fluvial sands, and gravels [Karrow, 1989]. The overburden, which ranges in thickness from 20 to over 100 meters, is bounded below by the Silurian Salina Formation which consists of shale, mudstone, dolostone, gypsum and halite [Karrow et al., 1978] and whose top few meters of bedrock are fractured [Gautry, 1996].

3. Physical System

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[7] A 25-m Digital Elevation Model (DEM) provided by the Grand River Conservation Authority of Ontario, Canada was used to identify the lateral extents of the watershed as well as define a two-dimensional triangular-element mesh representing the top of the model domain (ground surface). Elevations from the DEM were mapped onto an unstructured finite element mesh generated for InHM. A watercourse overlay was used to generate control points in order to locate nodes along the stream channels in the two-dimensional mesh. The mesh was designed such that regions near the streams have smaller finite elements (∼10 m in plan view), while finite elements further away from the drainage network are larger (∼75 m in plan view). This discretization strategy allows a more accurate rendering of the near-stream hydrodynamic processes, while reducing overall computational effort in less active areas. The major stream channels of the drainage network were then incised into the surface mesh by lowering the stream nodes 1.0 m, thereby decreasing the fluid-filled channel widths generated with the 25-m DEM to widths more commiserate to those observed in the watershed.

[8] A digital land usage map provided by the Ministry of the Environment of Ontario, Canada was interpolated onto the surface mesh and five distinct land-use categories were identified. This interpolation process was then further refined by using a watercourse overlay to incorporate the finer details of the watershed's drainage network (i.e., 2nd- and 3rd-order streams) which were not part of the digital map. The resulting land usage distribution is shown in Figure 2. As can be seen in Figure 2, the Laurel Creek Watershed is predominantly rural, although there are substantial urbanized, wetland, and forested portions. It should be noted that the land usage configuration presented in Figure 2 is specific to the time periods being simulated in this study (i.e., the late 1990s) and that a significant degree of urbanization has subsequently occurred in the lower two-thirds of the watershed [Morgan et al., 2004]. The value of the Manning's surface roughness coefficient assigned to each land-use category was determined from tables provided by McCuen [1989]. The drainage network has a Manning's coefficient value of 0.040 s/m1/3, while the rural, urban, forest and wetland categories were assigned values of 0.200 s/m1/3, 0.012 s/m1/3, 0.600 s/m1/3 and 0.050 s/m1/3, respectively. Note that the Manning's coefficient units need to be multiplied by a factor of 1.49 when converted over to English system units.

image

Figure 2. Land-use distribution and locations of the water-supply wells in the Laurel Creek Watershed.

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[9] In InHM, the two-dimensional surface flow mesh is draped over the three-dimensional triangular prism mesh used to simulate subsurface flow (Figure 3). The top of the three-dimensional mesh is coincident with the two-dimensional mesh such that dual surface-subsurface interaction nodes exist at the land surface. Twenty layers separate the surface and the base of the three-dimensional subsurface mesh, which is defined by the bedrock surface. Vertical discretization in the subsurface mesh is on the order of 0.5 meters for the two layers adjacent to the land surface and increases to a maximum of approximately 8.5 meters at depth. Ten- and thirty-layer vertical discretization schemes were also attempted in the early stages of this study and it was determined that a subsurface mesh containing twenty layers was sufficient to capture surface water-groundwater interactions occurring near the land surface interface while maintaining a reasonable computational effort.

image

Figure 3. The configuration of the numerical mesh used in this study. The mesh has 20 layers, each with 29,638 nodes. Note: the discharge point to the Grand River coincides with the location of the nonlinear critical-depth boundary condition applied to the surface mesh.

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[10] The subsurface hydraulic conductivity distribution within the Laurel Creek Watershed was mapped onto the subsurface mesh from the calibrated results of previous saturated-zone modeling studies conducted in the Waterloo Moraine [Martin, 1994; Martin and Frind, 1998; Radcliffe, 2000]. In these previous studies, a borehole log database provided by the Ministry of the Environment of Ontario, Canada was used to construct over 300 vertical cross sections of the Waterloo Moraine (which includes the Laurel Creek Watershed). These cross sections were then used to build a three-dimensional conceptual model of the Waterloo Moraine, including the configuration of the subsurface hydraulic conductivity patterns. The subsurface hydraulic conductivity field mapped onto the subsurface mesh representing the Laurel Creek Watershed is shown in Figure 4. The field contains thirteen distinct sediment types and clearly highlights the complex spatial interconnectivity between the shallow and deep flow regimes of the system. The hydraulic conductivity values assigned to each of the sediment types shown in Figure 4 were taken from Radcliffe [2000] and the corresponding porosity and specific storage values were estimated from tables by Freeze and Cherry [1979] and Mercer et al. [1982]. The wetting and drying characteristics of the watershed's coarse sands were drawn from Mace et al. [1998], while the wetting and drying characteristics of the other sediments were estimated using pedotransfer functions [Schaap et al., 1999].

image

Figure 4. Distribution of subsurface hydraulic conductivity in the Laurel Creek Watershed. Note the discontinuous nature of the individual layers.

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[11] The bottom and lateral boundaries of the domain are assumed to be impermeable with respect to both surface and subsurface flow and as such zero-flux conditions were assigned to these boundaries. Five active water-supply wells are also incorporated into the subsurface mesh at positions corresponding to their individual screen locations (shown in Figure 2). The pumping effect of each well is represented in the system as a sink term and each well was assigned a long-term average pumping rate. The names of the water-supply wells and their corresponding long-term average pumping rates are provided in Table 1.

Table 1. Water-Supply Well Names and Assigned Long-Term Average Pumping Rates
Well NameLong-term Average Pumping Rate (m3/s)
W2 & W1B4.96 × 10−3
W102.89 × 10−3
W43.33 × 10−3
W1C2.57 × 10−3

[12] Stream discharge exits the watershed through six surface nodes in the two-dimensional surface mesh, which coincide with the segment of the surficial domain where the Laurel Creek discharges into the Grand River (Figure 3). A nonlinear critical-depth boundary condition is applied at these outflow nodes which constrains neither the flow rate nor the surface water depth. Instead, discharge leaving the domain is allowed to vary naturally throughout a given simulation period depending on the calculated depth of water at the outlet.

4. Steady State Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[13] The model was initially applied to the Laurel Creek Watershed in a steady state mode. The steady state system was then, in turn, used as the initial condition for the transient flow simulations presented in the next section. Ideally, the initial condition would be defined at each grid node using stream discharge and subsurface hydraulic head data collected in the field immediately before the time period being simulated. However, in a fully integrated model such as InHM, the initial condition for a transient flow simulation must be estimated by “spinning up” the model from an arbitrary initial condition to a steady state starting condition because the true initial conditions are typically unknown. In the remainder of this section, the method used to determine a steady state initial condition is described and the surface and subsurface portions of the results are presented.

[14] As was discussed by VanderKwaak and Loague [2001], InHM requires that the water content distribution in the subsurface and the streamflow rates on the surface be defined (i.e., the initial condition) prior to simulating transient flow. While the necessary streamflow data may be available, the corresponding subsurface data are usually lacking. Therefore the initial condition for a transient flow simulation will often have to be estimated by some other means. In the work of VanderKwaak and Loague [2001], the initial condition was estimated by setting the initial water table position coincident with the ground surface and allowing the system to drain until an acceptable match was found between the computed and observed streamflows. Alternatively, the initial condition can also be determined by applying a uniform net rainfall rate to the surface of the initially saturated system that, after the system has reached steady state equilibrium, produces matching computed and observed streamflows. This latter approach is used here for a transient period whose observed initial conditions are reasonably representative of base flow conditions. The streamflow rate measured at the Erbsville gauge station (location shown in Figure 1) on 7 April 1998 was 0.186 m3/s. However, there is only limited hydraulic head data available in the subsurface, the data of which were collected at different points in time. Therefore in order to compute the initial condition, the surface of the initially saturated system was subjected to a net uniform rainfall rate of 42 cm/a, expressed as a long-term average. Note that this net rainfall input represents the actual mean rainfall rate minus evapotranspiration that, at steady state, produces an InHM-calculated streamflow rate that matches the observed rate and, additionally, the distribution of hydraulic head in the subsurface.

[15] The simulated subsurface hydraulic head distribution determined using the above procedure was then further refined by manually calibrating the hydraulic conductivity field and comparing the resulting simulated hydraulic heads to water levels measured in 50 observation wells located in the watershed. While calibrating, the model's performance with respect to subsurface processes was assessed quantitatively by statistical parameters based on the calibration residual. The expressions which describe these statistics are

  • equation image
  • equation image
  • equation image
  • equation image
  • equation image

where N is the total number of observations, C is the calculated hydraulic head, equation image is the mean of the calculated data, O is the observed hydraulic head and equation image is the mean of the observed data. The quantity Max E is the maximum residual error, MRE is the mean residual error, MARE is the mean absolute residual error, RMSE is the root mean squared residual error and R2 is the goodness-of-fit. The ideal value for the goodness-of-fit statistic is 1 and for the other statistical parameters is 0.

[16] The results of the subsurface calibration process are shown in Figure 5 and the model performance statistics are shown in Table 2. As can be seen in Figure 5, there is moderately good agreement between the simulated and observed hydraulic head data, recalling that the measured heads were obtained during different seasons over a span of many years and thus likely contain transient effects. A value of 0.79 for the goodness-of-fit presented in Table 2 indicates that the distribution of calculated heads reasonably matches the observed data. Similarly, the 7.1 m mean absolute residual error produced by the steady state model is acceptable for a watershed-scale simulation, especially in light of the potential calibration issues discussed below. However, a maximum residual error value of over 20 m is an indication that the calibration could be improved. Moreover the 5.7 m mean residual error indicates that the residuals are positively biased in that the simulated hydraulic head data are, on average, larger than the corresponding observed values.

image

Figure 5. InHM-calculated and observed hydraulic heads at 50 locations throughout the Laurel Creek Watershed.

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Table 2. Model Performance Statistics for the Steady-State Flow Simulationa
Statistic
  • a

    Note: Abbreviations are as follows: Max E (maximum absolute error), MRE (mean residual error), MARE (mean absolute residual error), RMSE (root mean square error) and R2 (goodness of fit).

Max E [m]2.1 × 101
MRE [m]5.7 × 100
MARE [m]7.1 × 100
RMSE [m]8.9 × 100
R2 [-]7.9 × 10−1

[17] The zero-flux conditions assigned to the lateral subsurface boundaries of the system domain are the likely cause of the inflation of the simulated subsurface heads. The use of this type of boundary condition means that water can only exit the system at the segment of the surficial domain where the Laurel Creek discharges into the Grand River. For the purposes of this study, it was assumed that the surface and subsurface flow catchments coincide. Previous studies have, however, indicated that surface water domain boundaries and groundwater divides often do not coincide [e.g., Tiedeman et al., 1998]. The inflation of the computed subsurface hydraulic heads implies that the simulated subsurface flow regime is, on average, over pressurized and that there may be a component of regional subsurface flow not being accounted for in the simulation. Because zero-flux conditions were assigned to the lateral subsurface boundaries any groundwater leaving the system as a component of regional subsurface flow would cause a build up of internal pressure in order to exit the system at the discharge point on the surface. To alleviate this problem in future studies, zero-flux conditions assigned to lateral boundaries of the subsurface mesh should be replaced with prescribed, perhaps transient, flux boundaries that account for regional subsurface flow. Additional field data would be required in order to quantify the distribution and magnitude of these boundary fluxes.

[18] A second source of potential error is the uncertainty in the interpretation of the spatial interconnectivity of the identified stratigraphic units. The aquitards present in the subsurface of the watershed are known to be highly discontinuous and contain numerous hydraulic connections between the shallow and deep subsurface flow systems [Martin and Frind, 1998]. Given the complex nature of the stratigraphy in this watershed, it is unlikely that all of the hydraulic windows that provide conduits between the shallow and deep flow aquifers are represented in the model.

[19] Another possible source of model mismatch pertains to the calibration data itself. The observed head data used here is a subset of the calibration data utilized in the previous study of Radcliffe [2000]. In the study by Radcliffe [2000], the data used to calibrate the groundwater model were extracted from the Waterloo Moraine borehole log database. The reason why the use of this data is problematic is because, for a given borehole log in the database, the water level data at each location consists of a single measurement made during installation of the borehole. Although water level data obtained during installation of a borehole may be somewhat affected by the disturbance to the flow system, a more troublesome issue is that the boreholes were installed at different times. Therefore the subsurface data aren't correlated to each other temporally. Ideally, the steady state results presented here should be calibrated against subsurface head data that correspond to the time period being simulated or, alternatively, hydraulic head data whose individual well hydrographs have been temporally averaged. If an extended period of monitoring data existed for each monitoring well, a transient calibration would provide an even more rigorous metric of model performance. Additionally, there are currently no transient, spatially distributed unsaturated moisture data available to calibrate the unsaturated zone properties of the sediments in the shallow subsurface. Such data are highly relevant for resolving the details of the spatial and temporal variability of the infiltration and recharge characteristics of the watershed.

[20] Figure 6 contrasts the InHM-calculated stream drainage network with the actual drainage network. As Figure 6 illustrates, the steady state system reproduces the actual drainage network quite well with respect to the location and extent of the calculated stream network except for the sizes and depths of the Laurel Creek Reservoir and Columbia Lake. This discrepancy is due to an inadequate representation of each reservoir's bathymetry as represented in the numerical mesh and the influence of the control structures that affect the discharge from them. These data were unavailable. Therefore to incise each reservoir into the mesh, the corresponding surface nodes were lowered an arbitrary value of 1.0 meter.

image

Figure 6. InHM-calculated (A) and actual (B) drainage networks.

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5. Transient Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[21] Once a steady state initial condition was achieved, 900 h of rainfall data were input in the model to assess the ability of InHM to compute transient rainfall-runoff responses due to individual, discrete rainfall events. The rainfall data used in this simulation was recorded at the University of Waterloo weather station (shown in Figure 1), which is located near Columbia Lake. Note that, because InHM cannot currently account for processes such as snowmelt and soil freeze/thaw processes, the transient rainfall-runoff simulations presented here are constrained to time periods where the effects of soil freezing and thawing and snowmelt are not a factor. It should also be noted that the version of InHM used in this study does not explicitly incorporate evapotranspiration as a mechanistic sink term into its governing equations. Therefore to approximate the effects of evapotranspiration during the transient flow simulations, the intensities of the individual, discrete rainfall events were reduced until the computed rainfall-runoff responses provided the best match to the observed rainfall-runoff responses. For this simulation, the rainfall intensity rates needed to be decreased by 45 percent. This 45 percent reduction in the rainfall intensity rates is of the same order as the long-term average evapotranspiration rate of 56 percent calculated for an earlier study conducted in a subcatchment of the watershed [Di Iorio, 2003]. Internal hydrograph nodes placed across the simulated stream channel at the Erbsville gauge station (see Figure 1) were used to compute discharge hydrographs. The discharge hydrographs were then compared to rainfall-runoff responses observed at the Erbsville gauge station, where continuous monitoring data exists. Data at two other gauge stations in the watershed were also available; however, these gauge stations have discharge responses that are severely impacted by artificial structures in the urbanized portion of the watershed about which limited information is available. Therefore these gauge stations were deemed unsuitable for calibration purposes. In a similar manner to that used for the steady state subsurface calibration, the model performance under transient conditions was assessed visually by comparing the match between calculated and observed discharge hydrographs and also quantitatively by statistical analyses. The expression used for the statistical parameters are

  • equation image
  • equation image

where Csurf is the calculated discharge, Osurf is the observed discharge, equation image surf is the mean observed discharge, EF is the modeling efficiency and PEP is the percentage error in peak discharge. As was discussed by Pebesma et al. [2005] the modeling efficiency statistic is similar to the goodness-of-fit parameter defined in equation (5). For the purposes of this study, the modeling efficiency measures model performance relative to the mean observed discharge rate. A modeling efficiency value of unity indicates perfect model prediction while a negative value indicates that model predictions are worse than simply employing the observed mean discharge value.

[22] The InHM-calculated and observed rainfall-runoff responses for the simulation are shown in Figure 7 and the corresponding model performance are presented in Table 3. As can be seen in Figure 7, the computed discharge hydrograph reasonably matches with the observed data. The calculated and observed peak discharges also match quite well as indicated by the percent error peak discharge value of 0.61 % shown in Table 3. However, the modeling efficiency calculated for the simulation period is only 0.6 (Table 3), which indicates that the results could be improved upon. Also, the calculated and observed cumulative discharges over the simulation period are approximately 6.0 × 105 m3 and 7.0 × 105 m3, respectively, yielding a cumulative discharge error of approximately 15 percent. This trend of the model to underpredict the discharge is also indicated by the value of the mean residual error in Table 3. The trend is believed to be primarily due to the simplistic way in which the effects of evapotranspiration are being represented. Li et al. [2006], for example, found that inclusion of a dynamical, soil-moisture, land-cover-type evapotranspiration model in the fully integrated HydroGeoSphere model [Therrien et al., 2005] greatly improved the match between computed and observed rainfall-runoff responses. Because the rainfall intensity rates were uniformly lowered by a sizable amount, direct overland runoff during and immediately following an intense rainfall event will be reduced. This reduction in direct overland runoff is believed to take place due to an increased amount of infiltration occurring in the near-channel contributing areas thereby causing the model to underestimate the extent of the contributing areas and the direct runoff originating from these contributing areas. Another possible source of model mismatch is the rainfall data used in the simulation. The rainfall data used to drive the model was obtained from one discrete point in the watershed (i.e., the University of Waterloo weather station) and applied in a spatially uniform manner over the entire surface, although the model can handle spatially- and temporally variable rainfall input. However, rainfall is often observed to be highly spatially variable at the watershed scale [e.g., Ogden and Julien, 1993].

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Figure 7. InHM-calculated and observed rainfall-runoff responses for the 900-h transient-flow simulation at the Erbsville gauge station.

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Table 3. Model Performance Statistics for the Transient-Flow Simulationsa
Statistic
SimulationMax E [m3/s]MRE [m3/s]MARE [m3/s]RMSE [m3/s]EF [-]PEP [-]
  • a

    Note: Abbreviations are as follows: Max E (maximum absolute error), MRE (mean residual error), MARE (mean absolute residual error), RMSE (root mean square error), EF (modeling efficiency) and PEP (percent error in peak discharge).

900-hour3.4 × 10−1−3.3 × 10−24.1 × 10−26.5 × 10−26.0 × 10−16.1 × 10−1
420-hour2.0 × 10−1−2.4 × 10−24.0 × 10−26.0 × 10−24.8 × 10−1−2.9 × 100

[23] Figure 8 illustrates the computed transient response of the overland flow areas contributing to streamflow during rainfall inundation and subsequent drainage during the first 30 h of the simulation. Although somewhat arbitrary, the contributing areas are defined here as the regions where the calculated overland flow depths are 10−3 m or greater. Note that the mobile water depth was set in the model at 10−3 m so any water depth less than this amount does not flow over the land surface. As shown in Figure 8, contributing areas after 6 h into the simulation have formed in the valleys and near the bases of hillslopes in the vicinity of the streams. The contributing areas extend up to a few tens of meters from the axes of some of the streams at this point in time. After 30 h, the sizes of these contributing areas have diminished to the immediate environs of the drainage network and the surface flow regime is again approaching equilibrium pre-event conditions. The surface-subsurface exchange fluxes across the land surface are shown in Figure 9. Note that, on Figure 9, negative surface-subsurface exchange fluxes represent subsurface water exfiltrating to the land surface. After 6 h into the simulation, incoming rainfall is infiltrating into the subsurface in the upslope regions of system while groundwater is exfiltrating in the vicinity of the drainage network and in the neighboring lowland areas. These regions of exfiltrating groundwater also appear to be well-correlated with the contributing areas shown in Figure 8, which indicates that the contributing areas are composed of both incoming rainfall and exfiltrating groundwater. Figure 9 also shows some infiltration is ongoing in isolated pockets throughout the watershed after 30 h; however, the exfiltration is now largely confined primarily to zones along the stream drainage network itself. The spatial and temporal variability of the system's rainfall-runoff responses with respect to the contributing areas and the surface-subsurface exchange fluxes makes clear the dynamic nature of the interaction occurring between the surface and subsurface hydrologic regimes in the Laurel Creek Watershed.

image

Figure 8. Contributing areas after 6 h and 30 h, respectively, into the 900-h transient-flow simulation.

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image

Figure 9. Surface-subsurface exchange fluxes after 6 h and 30 h, respectively, into the 900-h transient-flow simulation. Note: negative values represent groundwater discharging to the surface.

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[24] To demonstrate that the model can also reasonably reproduce observed rainfall-runoff responses within the Laurel Creek Watershed for other time periods, a second transient simulation was performed. The same methodology described previously was used to establish a new steady state initial condition that matched the flow conditions observed at the Erbsville gauge station on 2 October 1999. Next, 420 h of net rainfall data were used as input to drive the model. In this simulation, the rainfall intensity rates for each individual, discrete event needed to be reduced by 52.5 percent to provide the best possible match between the computed and observed discharge hydrographs. The InHM-calculated and observed rainfall-runoff responses for this simulation are presented in Figure 10 and the corresponding statistics are presented in Table 3. A comparison of the calculated and observed discharge hydrographs in Figure 10 shows that the computed rainfall-runoff responses match the observed responses reasonably well. The values of the mean residual error, mean absolute error and percent error in peak discharge statistics for the 420-h transient simulation in Table 3 also indicate that the model is able to predict the watershed's observed rainfall-runoff responses with a relatively good degree of accuracy. However, the model efficiency for the 420-h simulation is lower than that of the 900-h simulation (see Table 3) which again indicates the calculated results could be improved upon. The calculated and observed cumulative volumes for the simulation period are approximately 2.0 × 105 m3 and 2.4 × 105 m3, respectively, which translates to a cumulative discharge error of about 15 percent. Again, the model is underpredicting the volume of runoff over the course of the simulation. Additionally, the timing of the largest computed peak of the hydrograph precedes the observed peak by about 7 h. It is believed that both the timing and underprediction issues discussed above are likely due to a combination of assuming that the incoming rainfall is uniform across the entire land surface and because the effects of evapotranspiration are represented in a very simplified manner. By accounting for evapotranspiration in this manner, it is unlikely that simulated soil-water moisture content in the unsaturated zone prior to a rainfall event will be an accurate reflection of the actual moisture content. If the calculated and actual soil-moisture distributions differ appreciably then the relative amounts of the computed overland flow and infiltration will be impacted; however, spatial and temporal data on soil-moisture content are unavailable to assess model errors in the shallow unsaturated zone.

image

Figure 10. InHM-calculated and observed rainfall-runoff responses for the 420-h transient-flow simulation at the Erbsville gauge station.

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[25] The steady state initial condition for each transient simulation was determined by applying a net rainfall rate to the surface of the initially saturated system that, after the system had equilibrated, produced a simulated streamflow rate that matched the observed rate. A difficulty with this methodology is that it fails to imbue the simulated flow system with the antecedent wetting and drying history of the actual flow system. The inclusion of this history is important because the initial condition of the system can affect the computed rainfall-runoff response. Although the approach used to establish an initial condition in this study might still be used as a starting point, the wetting and drying history of the subsurface could also be incorporated by subjecting the model to an extended spin-up period. During this spin-up period, the observed rainfall history, evapotranspiration, pumping and irrigation rates, etc. could be used to generate a more representative initial condition relevant to subsequent transient simulations.

[26] The computed and observed discharge hydrographs for the two transient simulations agreed moderately well, albeit by representing the effects of evapotranspiration in a very simplified manner. However, it is expected that a more rigorous representation of the effects of evapotranspiration, in conjunction with distributed rainfall data, would enhance these results significantly. The 900-h and 420-h transient simulations required approximately 48 and 35 h, respectively, to execute on a Pentium 4 desktop machine equipped with 3.0 Gb of main memory.

6. Summary and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[27] The level of agreement between the computed and observed hydraulic head and drainage network patterns indicates that the steady state model reasonably captures the essence of the surface and subsurface hydraulic characteristics of the watershed. It is reasonable to assume that the data used to populate the model are relatively representative of the conditions present in the watershed. If they were not, it is unlikely that the model would have reproduced the drainage network to the degree that it did. It should be noted that the steady state model can reproduce the drainage network well even when the major tributaries are not incised in the mesh [e.g., see Sudicky et al., 2000]. Quantitatively, the model performance statistics presented in Table 2 show the steady state model also performed fairly well in terms of the simulated subsurface hydraulic head patterns, albeit with some room for improvement. Overall, the steady state results highlight the strength of the fully integrated approach when simulating watershed-scale hydrodynamics. Traditional surface water models typically require the user to specify the groundwater contribution to streamflow generation because the model has no built in feedback from the subsurface. Conversely, most traditional groundwater models attempt to incorporate the drainage network contribution to the subsurface by assigning a constant-head or other type of boundary condition along the river channels on top of the groundwater model's numerical mesh. Both approaches lack adequate feedback between the surface and subsurface regimes. In the fully integrated approach employed in InHM, the model determines where water infiltrates, exfiltrates, or forms surface water in drainage channels or wetlands based on the physical interaction between the surface and subsurface hydrologic regimes. A fully integrated, three-dimensional framework which allows complete feedback between the two regimes is likely to be even more important in the context of contaminant migration as was illustrated by Di Iorio [2003].

[28] The simulated transient responses of the overland flow contributing areas and the surface-subsurface exchange fluxes during rainfall inundation and subsequent drainage periods shown in Figures 8 and 9 demonstrate the ability of a fully integrated model such as InHM to capture the dynamic response of a watershed during and following rainfall events. The spatial and temporal variation of these responses again highlights why the use of physically based, surface-subsurface models is desirable. For example, the recharge boundary in nearly all groundwater models is assumed to be either spatially uniform across the top of the numerical mesh or is subdivided into a number of uniform recharge zones. Moreover, as was discussed by Jyrkama and Sykes [2006], the recharge flux of each zone is often determined during the calibration process and seldom calculated explicitly. Even in cases where the spatially varying recharge rate is determined explicitly using site specific land use, soil property, temperature and precipitation rate information, it is still necessary to temporally lump the calculated rate into daily or greater increments [e.g., see Jyrkama et al., 2002]. However, the results presented in this study suggest that the temporal variability of that rate is quite significant on much smaller timescales. A similar argument can be made for traditional surface water models which often determine subsurface infiltration rates in an empirical or quasi-physically based manner and only consider the upper few meters of the vadose zone and ignore the transient response of the water table, especially where it is shallow. The degree of observed interaction between the surface and subsurface hydrologic regimes in this study highlights why the use of physically based, surface-subsurface models is desirable. This will be especially important for simulating the spatial and temporal patterns of, for example, contaminant and nutrient cycling within watersheds.

[29] There has been some discussion in the literature of abandoning models based on the Freeze and Harlan [1969] blueprint [see, e.g., Beven, 2002b]. One of the primary objections often brought up concerning the Freeze and Harlan [1969] blueprint concerns whether or not it is appropriate to use the variably saturated form of the Richards' equation at larger (i.e., watershed or greater) hydrologic scales. Although the results presented in this study do not unequivocally demonstrate that Richards' equation can be employed at larger scales, we do believe that they show some promise in this regard. Indeed, models such as InHM show great potential as tools for watershed management, source water protection planning, urbanization issues, non-point source pollution studies, hypothesis testing and focusing data collection efforts in field studies.

[30] The primary objective of this study was to gauge the performance of a complex, three-dimensional, fully integrated model to simulate transient flow processes at a scale larger than has been previously attempted. A secondary objective was to highlight the advantages of the fully integrated approach with regards to studying watershed scale hydrodynamics. Although the results presented here are promising, they must be considered preliminary because a number of improvements still need to be made regarding input data requirements and upscaling issues, process representation and computational performance. We are aware of these difficulties and expect that step-by-step improvements to such models and new data gathering strategies to populate them with the necessary input information will continue to evolve.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[31] The authors would like to sincerely thank Joel VanderKwaak for providing technical support with regard to the InHM code as well as the reviewers and editors whose suggestions helped improve this manuscript. This work was funded by grants from the Natural Sciences and Engineering Research Council of Canada (in partnership with the Grand River Conservation Authority, the Regional Municipality of Waterloo and the City of Waterloo), the Canadian Water Network and a Canada Research Chair in Quantitative Hydrogeology (Tier I) awarded to E. A. Sudicky. Funding was also provided to J. P. Jones from a number of scholarships awarded to him by the University of Waterloo.

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  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Site Description
  5. 3. Physical System
  6. 4. Steady State Results
  7. 5. Transient Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information
FilenameFormatSizeDescription
wrcr11129-sup-0001-t01.txtplain text document0KTab-delimited Table 1.
wrcr11129-sup-0002-t02.txtplain text document0KTab-delimited Table 2.
wrcr11129-sup-0003-t03.txtplain text document1KTab-delimited Table 3.

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