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A process-based distributed hydrologic model and its application to a Michigan watershed

ProQuest Dissertations and Theses, 2009
Dissertation
Author: Chaopeng Shen
Abstract:
The PAWS (Process-based Adaptive Watershed Simulator) model is a novel distributed hydrologic model that is based on solving partial differential equations (PDE) for physical conservation laws of the hydrologic cycle. The objective is to create an efficient physically-based modeling framework to describe the linkages between processes at different scales and to improve the applicability of physically-based models. The model simulates evapotranspiration, overland flow, channel flow, unsaturated soil moisture, groundwater flow, depression storage, vegetation growth and snowpack. PAWS focuses on the dynamic surface- subsurface interactions and integrated responses by efficiently coupling runoff and groundwater flow to the vadose zone processes governed by the Richards equation. This novel approach solves a long-standing bottleneck in PDE-based subsurface flow modeling by removing the computational limitations while maintaining physically consistent solutions. Surface flow is solved by ail efficient Runge-Kutta Finite Volume (RKFV) scheme. We follow the Freeze and Harlan (1969) blueprint in that we believe each component of the model should be verifiable by itself. All flow components have been independently verified using analytical solutions and experimental data where applicable. PAWS utilizes readily available data from national databases. The model is applied to a medium-sized watershed in Michigan achieving high performance metrics in terms of streamflow prediction at two gages during the calibration period and the verification period. The baseflow flow periods are described particularly well. Starting from a rough initial estimate of the groundwater heads, the model describes the observed groundwater heads well (R 2 =0.98). The annual hydrologic fluxes are close to those estimated by a calibrated SWAT model. The model is considerably less expensive than previous physically-based models of similar complexity. The model is able to elucidate the complex interactions of processes in space and time. Such detailed, quantitative and mechanistic descriptions cannot be produced by conceptual models. The watershed is found to be a subsurface-dominated system with saturation excess being the main runoff generation mechanism. Infiltration, recharge and ET are also found to be strongly related to topography and groundwater flow. The large seasonal variation of energy input drives the strong annual cycle and markedly different responses in streamflow.

Table of Contents List of Tables x List of Figures xii Chapter 1. Background and literature review 1 1.1. Motivation for a new hydrologic model 1 1.2. Review of hydrologic models 4 Chapter 2. Development of the Hydrologic Model: Mathematical Bases and Test Cases : 12 2.1. Model Processes 13 2.2. Discretization and Representations 15 2.3. Hydrologic Processes and Solution to each flow domain 20 2.3.1. Evapotranspiration 20 2.3.2. Vegetation 29 2.3.3. Overland flow 31 2.3.4. Channel flow 43 2.3.5. Unsaturated vadose zone model 48 2.3.6. Saturated groundwater flow model 54 2.4. Interactions between domains 61 2.4.1. Coupling of the Unsaturated Richards equation and the groundwater flow equation: 61 2.4.2. Coupling of the vadose zone and surface flow: 75 2.4.3. Interaction between overland flow and channel flow 79 2.4.4. Interaction between groundwater and channel flow 84 2.5. Data preparation steps general to all watersheds 86 2.5.1. Digital elevation data 86 2.5.3. Soils 91 2.5.4. Climatic data 91 2.6. Model Flow Diagram 93 2.7. Test cases 95 2.8. Summary and Conclusions 112 Chapter 3. Development of the Hydrologic Model: Model Applications and Comparisons 114 3.1. The Red Cedar River watershed model 114 3.1.1. Study site and input data 114 Groundwater data 128 vn

3.1.2. Model Calibration 130 3.2. SWAT Model for comparison 131 3.2.1. Brief summary of SWAT mathematical bases 132 3.2.2. SWAT Model Setup 136 3.3. Results and Discussions 139 3.3.1. Model Evaluation 139 3.3.2. Model performance evaluations 139 3.3.3. Additional model results and hydrologic system of the RCR watershed ...151 3.3.4. Understanding the hydrology 153 3.4. Summary and Conclusions 167 3.5. Limitations and future research 168 3.6. Software package 168 Chapter 4. Estimating Longitudinal Dispersion and Surface Storage in Streams Using Acoustic Doppler Current Profilers 170 4.1. Introduction 170 4.2. Description of Sites 179 4.3. Materials and Methods 182 4.3.1. Transient Storage Modeling 188 4.3.2. Multi-resolution Wavelet Decomposition of ADCP Data 191 4.3.3. Estimating the Longitudinal Dispersion Coefficient 196 4.4. Results 200 4.4.4. Evaluation of Channel Features and Potential for Hyporheic Exchange in the RCR 200 4.4.5. Evaluation of TS Model Parameters for RCR 202 4.4.6. Results from ADCP Surveys and Wavelet Analysis 207 4.4.7. Estimating Longitudinal Dispersion in Rivers 215 4.5. Conclusions 229 Appendix A. Supplemental Tables 232 Appendix B. User's Manual for the model Graphical User Interface 238 B.l. Creating and Running the model in interactive mode 238 B.l.l. Installing and starting the model 239 B. 1.2. Loading the data 240 B.l.3. Setting up the grid 243 B.l.5. Setting up solution schemes and time steps 247 B.1.6. Final model setup 249 B.1.7. Saving and Loading model 250 B.l.8. Running the model 250 B.2. Running the model in non-interactive mode 252 vin

References 254 ix

List of Tables Table 2.1. Modeled Processes 13 Table 2.2. Major state variables and their symbols 15 Table 2.3. Supported land use types and their representations 18 Table 2.4. Simplied decision table for the atmospheric transmittance x from [Spokas and Forcella, 2006] 25 Table 2.5. Soil Parameters for the test case: Infiltration into very dry soils 103 Table 2.6. Soil Parameters for the test case: Vauclin experiment 108 Table 3.1. Climatic Data sources and data availability. The dates in YYYYMMDD format are the dates when a station starts to have records; Frac is the fraction of the RCR watershed that is controlled by this weather station; PRCP PCT is the percentage of valid precipitation records from 1998 to 2007 119 Table 3.2. Land use percentages from the NLCD database and the MDNR databse 122 Table 3.3. SWAT Land use class percentages after apply thresholds. URLD: Low Intensity Urban; URMD: Medium Intensity Urban; WETF: Forested Wetland; URHD: High Intensity Urban; HAY: Hay/Forage Crops; AGRR: General Agriculture; FRSD: Deciduous Forest 138 Table 3.4. Performance metrics evaluating the model applied to the RCR watershed 142 Table 3.5. Metric of Groundwater heads comparison to wellogic data 147 Table 3.6. Annual Average Fluxes compared to SWAT 151 Table 4.1. Parameters in the Transient Storage model estimated for four different flow rates 205 Table 4.2. Comparison of the Relative Sizes of the Transient storage zones estimated using tracer data and independently using the ADCP data for Reach A 213 Table A. 1. List of input data to the watershed model and format 232 x

Table A.2. An example transformation matrix from MDNR dataset to model classes 233 Table A.3. Summary of several watershed-scale hydrologic models 236 XI

List of Figures (Images in this dissertation are presented in color) Figure 2.1. Definition sketch of the model. T: transpiration, p: precipitation, EO Evaporation from overland flow/stream, EB: evaporation from bare soil; I: infiltration; R: Recharge 14 Figure 2.2. Illustration of Arakawa-C grid 37 Figure 2.3. Relationship between K, 8 and h at different parameter values with the van Genuchten formulation for a hypothetic soil type (a) at different a; (b): at different X; (c) at different N. THE in the figure heading means 9. The base parameter for this comparison is a= 2.49(l/m), N = 1.507, 9S = 0.43, 9r = 0.01; Ks = 0.175 (m/day); X = -0.14. Unit in the figure is the same as the base parameter set 49 Figure 2.4. sketch of the Vauclin 1979 test problem. HW(x) is the water table location at x, z is measured 0 at the bottom 65 Figure 2.5. Illustration of Assumptions 1 and 2 66 Figure 2.6. h(x,z) as a function of z and DR values 70 Figure 2.7. sketch of a river cell in the model, (a), cross-sectional view, (b) plane view 82 Figure 2.8. Calculation of River/Land exchange 83 Figure 2.9. Discrepancies between NED and DEM when aggregated into the same grid 87 Figure 2.10. the river bed elevations estimated based on the DEM and NED as compared to the groundwater head 90 Figure 2.11. Rainfall pattern of the Midwest from 92 Figure 2.12. Program Flow Chart for the proposed model 94 Figure 2.13. Outflow hydrograph of the inclined plane test problem compared to the analytical solution 97 xn

Figure 2.14. Sketch of the V-Catchment test problem 99 Figure 2.15. Solution to the V-Catchment test problem: Comparison of River outflow hydrograph with analytical solution and the finite element (FE) solution reported in [DiGiammarco]. (a) River outflow (b) Plane side outflow 100 Figure 2.16. Simulated channel flow vs measured data by [Irfan, 2002]. Red circle: measured data; blue solid line: Simulated 102 Figure 2.17. Infiltration into very dry soil test problem at t = 6hr. circle: Analytical solution; solid line: Ax= 0.075cm; dashed line: Ax= 0.25cm; dashed line with cross: Ax= 0.6cm 104 Figure 2.18. Pumping near impervious wall test problem 106 Figure 2.19. Solution to the pumping near impervious wall test problem: transient comparison; 107 Figure 2.20. Comparison of the proposed model with experimental results from [Vauclinetal, 1979] 109 Figure 2.21. Comparison of soil moisture profile obtained using the approach in the proposed and traditional method, 6S=0.3, EBC=Equation Boundary Condition (Present approach); DBC=Dirichlet Boundary Condition (Conventional approach) 111 Figure 3.1. Location of the Red Cedar River Watershed 116 Figure 3.2. Elevation map of the Red Cedar River watershed 117 Figure 3.3. Locations of weather stations used for climatic input data 118 Figure 3.4. Basin-average Annual precipitation for the years from 1988 to 2008 (mm) 119 Figure 3.5. NLCD Land use/Land cover map for the RCR watershed 121 Figure 3.6. River system of the RCR watershed with USGS flow gages 123 Figure 3.7. Geology maps of the RCR watershed, a. Land Systems; b. Bedrock Geology 125 xm

Figure 3.8. Soil property maps of the RCR watershed as reported in the STATSGO database, a. Sand percent; b. Soil Available Water Capacity; c. Saturated Hydraulic Conductivity (Ksat) 127 Figure 3.9. Watersheds delineated for the SWAT2005 model using the ArcSWAT GIS interface 138 Figure 3.10. Comparison of the observed and simulated daily flow at USGS gage 04112500 at East Lansing. Upper: Entire period from 1998/09/01 to 2005/12/31, Middle and lower: Close-up look of the hydrograph 141 Figure 3.11. Comparison of the observed and simulated daily flow at USGS gage 04111379 at Williamston... 142 Figure 3.12. Comparison of the simulated streamflow from PAWS and SWAT and observed USGS streamflow data. Upper: from 1999 to 2005, Lower: Close-up look of water year 2001 144 Figure 3.13. Comparison of the simulated streamflow from PAWS and SWAT and observed USGS streamflow data in log-scale 146 Figure 3.14. (a) 5 year averaged simulated groundwater, (b) observed heads interpolated from wellogic database, (c) initial groundwater heads used to start the model 148 Figure 3.15. Observed vs simulated groundwater heads, (a) Observed data vs 5 year averaged value, (b) Observed data vs the rough initial guess. X-axis is the observed data obtained from Kriging interpolation of the wellogic data 150 Figure 3.16. Pie chart showing the comparison of the average annual fluxes as a percentage of total precipitation between PAWS and SWAT 152 Figure 3.17. Hydrograph partitioning into streamflow generation mechanisms: Infiltration excess, saturation excess and groundwater contribution. X-axis are dates in YY/MM/DD format. SatE: Saturation Excess, InfE: Infiltration Excess, Qgc: Groundwater contribution, Qout: Red Cedar River outflow 154 Figure 3.18. Temporal dynamics of fluxes and state variables. Upper: Monthly mean fluxes (mm). Lower: Daily fluxes (close up of 2004). Inf: Infiltration; Qoc: Overland contribution to channel; Qgc: Groundwater contribution to channel; Rchrg: Recharge; InfE: Infiltration Excess; SatE: Saturation Excess; Dperc: Deep Percolation 155 xiv

Figure 3.19. Basin average state variables (a) Soil Water Content (change from initial state), (b) Snow Water Equivalent. X-axis marks the beginning of each year (YY). 157 Figure 3.20. Daily fluxes of recharge and groundwater baseflow. (a) Rising limb of baseflow, (b) falling limb of baseflow. Again, dates are in YY/MM/DD format. Unit of the figure is m 159 Figure 3.21. Average annual runoff generation (mm) (a) Saturation Excess (b) Topographic Index 163 Figure 3.22. Average Annual Infiltration Excess 164 Figure 3.23. Annual Infiltration (a) and recharge map (b). 165 Figure 3.24. Annual ET (a) and EvapG (b) map. EvapG is evaporation from the ground 166 Figure 4.1. Red Cedar River and the sampling locations 180 Figure 4.2. Red Cedar River and the study region showing the sampling locations of the Grand River tracer study 182 Figure 4.3. Comparison of the numerical solution with the analytical solution of De Smedtetal[2005]....' 191 Figure 4.4. Schematic diagram illustrating the concept of discrete wavelet decomposition. S denotes the original signal (the 2D image of the velocity field measured by ADCP). L and H denote the low-frequency approximations and high-frequency details, respectively. Suffixes denote wavelet scale levels 195 Figure 4.5. Comparison of observed and simulated tracer concentrations for four slug releases conducted during summer 2002. (a) Q=2.49 m3/s. Sampling locations at x=0.87km (Bogue Street Bridge) (b) Q = 14.41 m /s, sampling locations are, namely, Farm Lane Bridge (x = 1.40km). Kellogg Bridge (x = 3.10km) and the Kalamazoo Bridge (x=5.08km), respectively, (c) Q = 16.82km3/s, (d) Q= 19.06m3/s 203 Figure 4.6. Observed mean velocity fields at two different stations in reach A in the Red Cedar River obtained using a 1200 kHz ADCP (a and b) Q = 5.49m3/s (8 November 2003). (c and d) Q = 19.89 m3/s (19 March 2006). Note that during the high event the adjacent low lying areas near the banks were filled with relatively stagnant water which were not available during low discharge 209 xv

Figure 4.7. Multiresolution wavelet approximations for the images shown in Figure 4.6. After completing the wavelet analysis, the low-frequency content at wavelet levels 1 and 2 (denoted by LI and L2) was plotted in the physical space, (a and b) Hagadorn Bridge, (c andd) Farm Lane Bridge 211 Figure 4.8. Sample ADCP transect data used for computing the longitudinal dispersion coefficients 218 Figure 4.9. Vertical velocity profiles in the Ohio and St. Clair Rivers showing the effect of fitting a power law (black lines) and logarithmic profiles (red lines). The raw data from the ADCP is shown using symbols 220 Figure 4.10. Effects of smoothing (logarithmic, power-law or no-smoothing) and velocity projection methods (rotating velocities in the streamwise direction or projecting them in a direction normal to the transect track) on the dispersion estimates from ADCP 225 Figure 4.11. Comparisons between ADCP and tracer estimates of the dispersion coefficient: (a) Box plots denote the variability in D estimated using the ADCP method within a given river reach. Tracer estimates based on the ADE and the transient storage modeling are shown using different symbols, (b) Comparisons between ADCP and tracer estimates plotted on top of similar results reported in the literature 227 Figure 4.12. Comparison of ADCP estimates of the dispersion coefficient with tracer estimates and results from empirical relations, (b) Box plots showing the deviation between estimates of D based on the ADCP method and empirical relations 228 Figure 4.13. Depth-averaged longitudinal (u) velocity profiles plotted as a function of the transverse coordinate y 229 Figure B.l. GUI after the model is started 240 Figure B.2. Data GUI. (a) before loading data (b) after loading data files 242 Figure B.3. GUI after the model is started 244 Figure B.4. Discretization GUI 246 Figure B.5. Solvers GUI. (a) after it is opened (b) after dt file is loaded 248 Figure B.6. Loading solvers data into solvers functions GUI 249 xvi

Chapter 1. Background and literature review 1.1. Motivation for a new hydrologic model In the twenty-first century the management of water resources has gained unprecedented scientific as well as strategic importance. On one hand, the growing human population raises larger and larger demand for usable and available water resources. Satisfying such a need can be a serious challenge in many parts of the world. On the other hand, humans are equipped with the ability greater than ever to harness water in nature for their own end, and they often opt to do so. These interventions have led to some fundamental modifications to the hydrosphere. In the past century we have essentially transformed the Earth's ecosystem, even on the grandest scale, into a human-dominated one [Vitonsek et al., 1997]. While many of the large-scale hydraulic projects proved essential for the economic development and well-being of people and their positive impacts should not be downplayed or understated, the hydrological, ecological and environmental consequences are usually not fully understood. Today the Aral Sea in Central Asia, once the fourth largest inland lake in the world, has been desiccated to 1/10 of its original size with its entire ecological system destroyed. Studies reveal that this overwhelmingly owns to the diversions of water from the sea's tributaries for irrigation expansion [Cretaux et al, 2005; Micklin, 1986; 1988]. The impacts of such interventions are so far reaching, profound and irreversible that all aspects of the hydrologic system need to be 1

carefully assessed. The surface-subsurface water interactions are often overlooked. Due to the slow response of the subsurface water system, impacts of large-scale projects - benign, malign or neutral - can take a long time to manifest themselves. The Aswan Dam in Egypt and its reservoir, Lake Nasser, still witness newly discovered impacts that could not be predicted 30 years ago when the dam was constructed. Some have observed reduced carbon emission and more sustainable development [Prasad et ah, 2001; Strzepek et ah, 2008], while others reported erosion, salinization, and pollution that induced decline in agricultural productivity and loss of land and coastal lagoons [Stanley and Warne, 1993]. These challenges are further complicated by the more and more pronounced trend of climate change. Climate change is expected to exacerbate current water stresses [IPCC, 2007]. Semi-arid regions and drought-affected areas are projected with high confidence to suffer decreased water resources due to climate change. For example, the Lakes Mead and Powell created by the Hoover Dam, the lifeblood of U.S. southwest, are estimated to dry up by 2021 if no changes to the current water usage are made [Barnett and Pierce, 2008; 2009]. The study has attributed this result to global warming and current operating conditions. Understanding water fluxes is also important from a human health perspective. A variety of pollutants including chemical and biological agents pose threats to human and ecosystem health [U.S.EPA, 2000]. A well-known USGS study that involved 139 2

streams in 30 US states between 1999 and 2000 found pharmaceuticals, hormones and a number of emerging contaminants in 80 % of the streams sampled [Kolpin et al., 2002]. Similarly a majority of rivers sampled in Michigan tested positive for the presence of viable enteric viruses [Jenkins et al, 2005]. Therefore understanding factors that influence the fate and transport of contaminants in rivers and streams is extremely important from the point of predicting human health risks and protecting the public. The flow generation process governs the source and form of contamination. Pollutants can reach streams via point source discharge, non-point source (overland flow), or subsurface seepage [Jamieson et al, 2004]. All these challenges call for resolute but well-informed decision making. Sound decision making is best aided by good understanding of the complex and interrelated hydrologic systems. Better understanding comes most elucidated with the ability to explicitly describe the hydrologic processes in space and time. This is where a reliable and verifiable process-based hydrologic model with good predictive power could play an important role. The present study attempts to create a process-based hydrologic model that finds a good balance between process modeling and applicability. This model should link processes that occur at different scales and illustrate the interactions among the hydrologic domains, including, surface water, soil water, groundwater, river, canopy and atmosphere. It is hoped that this model will help address some of the challenges posed by human intervention as well as climate change. 3

1.2. Review of hydrologic models Many hydrologic models have been historically developed to study different hydrologic systems. Several models that are recently cited are reviewed in Table A.3. Models are often developed with specific scientific objectives in mind. Thus each model has its own strengths in some areas and may be inadequate in some other areas. For example, SWAT is designed as a long term water balance and non-point source pollution simulator [Arnold and Allen, 1996; Arnold and Fohrer, 2005]. Thus simulating short term point source pollution with SWAT may not be advantageous. Before developing our own model it is helpful to understand the current state of research. Broadly, there are two categories of models: conceptual and physically-based (or mechanistic). Generally, in conceptual hydrologic models (CHM), the modeler forms hypotheses, either from experience or his own perceptions, about the hydrologic processes and proposes mathematical formulations to represent these processes with sometimes strong simplifying assumptions. CHM are often based on empirical relations and conceptual state variables that cannot be always measured. Physically-based hydrologic models (PBHM), on the other hand, are derived deductively from established physical principles with appropriate assumptions and physically meaningful/measurable parameters [Beven, 2002]. Historically there have been heated discussions about the relative advantages and disadvantages of the two 4

approaches. In 1966, the paper [Freeze and Harlan, 1969] laid out a blueprint for physically based hydrologic modeling, writing out the equations for different flow processes and the linkages via common boundary conditions. The development of such a physically based model in the years followed, however, has been limited by the computational power, data availability, understanding of the complex hydrologic system and, to a lesser extent, the accumulation of mathematical technique. [Beven, 2002] has challenged that blueprint and provided an alternative blueprint to hydrologic modeling that is based on lumped conceptual models. These models do not use the process theory to build a model structure a priori, but rely on observed data to define an appropriate model structure (described by Beven as 'hypothesis testing'). He also stressed on the importance of quantifying the uncertainty of the models. With the advancement of computer power, Geographic Information System (GIS) and readily available databases, recently published models lean more and more toward the physically-based approach [Karvonen et al, 1999]. However, to date there does not seem to be a conclusion to that debate and the two schools of models continue to be created and advanced. In fact, both types of models have their own advantages and disadvantages. Some of the notable conceptual models include TOPMODEL [Beven and Kirkby, 1979], DLBRM [Croley and He, 2005], Sacramento Soil Moisture Accounting Model (SAC-SMA) [Burnash, 1995], HEC-HMS [HEC, 2000], VIC-3L [Liang and Xie, 2001; Reed et al, 2004], etc (also see [Borah and Bera, 2003; Reed et al, 2004]). 5

Usually, conceptual models require less physical input as its components are idealized. The models tend to be structurally simple, computationally inexpensive and more easily operational. However, they need long term monitoring data to calibrate. The parameters generally cannot be applied for ungauged watersheds. Moreover, the conceptualization process blurs the underlying dynamics and extension of conceptual models beyond the range of calibration is questionable [Beven, 1985]. It is not rare that a CHM that describes completely different physics from the study region and still get fair results after optimization, but the physics can be far from reality. In fact, a large number of papers have been published to quantify the uncertainties associated with the conceptual models (e.g. see [Beven, 2006; Beven and Binley, 1992; van Griensven and Bauwens, 2003; Vrngt et al, 2005; Yang et al, 2008], etc). The large uncertainties undermine the reliability of the model, especially since estimated parameters cannot be interpreted. A review of current physically-based models, on the other hand, reveals that there is still much room for improvement, especially in achieving the right balance between process descriptions and computational demands. PBHM generally tend to be data intensive and computationally expensive and thus their applicability tends to be limited. The reported results from PBHMs are often simulations for small areas during short periods of time. The published comparisons with observations indicate that these models, as commented by [Ivanov et al, 2004a], are yet to emerge as the preferred tool for prediction and analysis. Some well-documented physically based 6

hydrologic models include the MIKESHE model [DHI, 2001 ], Soil & Water Assessment Tool (SWAT) [Arnold and Fohrer, 2005], Water and Energy Transfer Process (WEP) model [Jia et al, 2001; Jia et al, 2006], CASC2D/GSSHA [Downer and Ogden, 2004b] and tRIBS [Ivanov et al, 2004b], etc. We must mention here that some regard SWAT as a semi-physically based model since considerable amount of empiricism is included in the model, as highlighted in section 3.2. Although almost all PBHMs still carry some level of empiricism, the models can be constrained much better by real data since most parameters are physically based. Here we review six watershed-scale and one macro-scale (VIC) PBHM. Table A.3 in the appendix lists, in alphabetical order, seven models that are currently being published and cited in the literature. This is by no means a complete list of hydrologic models that are of interest, but it does give a representative coverage. In its completeness, watershed hydrologic models should incorporate several flow domains that cover various flow paths possible after rain drops to the ground: overland flow, unsaturated subsurface flow (the vadose zone model), saturated subsurface flow (groundwater flow) and channel flow. Water also exists in canopy interception, snowpack, biomass and depression storage. Besides the flow domain, one of the processes of utmost importance is the evapotranspiration, which on average is estimated to take out 70% of the rainfall in North America [Jensen et al, 1990]. In order to account for the seasonal dynamics of a watershed, a reasonable vegetation growth module should also be included. A sufficient PBHM should contain all of the 7

relevant processes. Table A.3 also lists the spatial discretization method and solution schemes to the flow problems. The InHM [VanderKwaak and Loague, 2001] is a processe-based model that integrates overland flow with the mixed form three-dimensional Richards equation for the subsurface. InHM simulations in showed that both the Horton and Dunne overland flow mechanisms can be important streamflow generation processes. The InHM simulations also suggested that accurate accounting of soil water storage can be as important as exhaustive characterization of spatial variations in near-surface permeability. However, the InHM is very computationally demanding such that it can only applied at the plot-scale. The GSSHA model, developed for the Army Corps of Engineers, evolved from CASC2D [Downer and Ogden, 2004b]. CASC2D uses Green and Ampt infiltration method [Green and Ampt, 1911] with redistribution (GAR) for moisture accounting. However, it has been found that the processes modeled in the CASC2D model cannot adequately describe watersheds where saturation excess is important [Downer et al, 2002]. This research highlights the importance of incorporating the correct processes in physically-based models and applying hydrologic models in the settings where they are applicable. In GSSHA, the subsurface flow component is improved by coupling the Richards equation with the groundwater flow equation. The height of the water 8

table is provided as the lower boundary condition to the Richards equation. A constantly changing discretization is used to cope with the rise and fall of the groundwater table. As will be shown later in section 2.4.1, this coupling approach will cause soil moisture profile to be inconsistent with the location of the groundwater table. Moreover, it is difficult to evaluate the potential of GSSHA or CASC2D as a large-scale long term analysis tool as most of the published results are for small 2 2. 2 catchment areas (20 km and 3.64 Ion in [Downer and Ogden, 2004a] and 3 km in [Downer and Ogden, 2004b]) in a short time frame (<200 days). The comparison is also limited to streamflow measurements. The WEP was originally developed by [Jia et ah, 2001] and applied in Japan to a small size urban watershed. Later, it was expanded into a large scale version WEP-L and applied to a very large basin — the Yellow River Basin in China [Jia et ah, 2006]. The WEP model uses the mosaic approach which allows sub-grid heterogeneity to be parameterized. Three layers of soils are defined in the model and water is allowed to move only vertically in the soil. The soil layers are connected to the unconfmed aquifer which is modeled using the Boussinesq equation. The proposed model shares some similarities in the structure with the WEP model. The results reported for both the Japanese watershed and the Yellow River basin are promising. Unfortunately, this model is not available so direct comparison is not possible. It is felt that applications to some medium-sized watersheds with different hydrologic settings and geologic 9

Full document contains 288 pages
Abstract: The PAWS (Process-based Adaptive Watershed Simulator) model is a novel distributed hydrologic model that is based on solving partial differential equations (PDE) for physical conservation laws of the hydrologic cycle. The objective is to create an efficient physically-based modeling framework to describe the linkages between processes at different scales and to improve the applicability of physically-based models. The model simulates evapotranspiration, overland flow, channel flow, unsaturated soil moisture, groundwater flow, depression storage, vegetation growth and snowpack. PAWS focuses on the dynamic surface- subsurface interactions and integrated responses by efficiently coupling runoff and groundwater flow to the vadose zone processes governed by the Richards equation. This novel approach solves a long-standing bottleneck in PDE-based subsurface flow modeling by removing the computational limitations while maintaining physically consistent solutions. Surface flow is solved by ail efficient Runge-Kutta Finite Volume (RKFV) scheme. We follow the Freeze and Harlan (1969) blueprint in that we believe each component of the model should be verifiable by itself. All flow components have been independently verified using analytical solutions and experimental data where applicable. PAWS utilizes readily available data from national databases. The model is applied to a medium-sized watershed in Michigan achieving high performance metrics in terms of streamflow prediction at two gages during the calibration period and the verification period. The baseflow flow periods are described particularly well. Starting from a rough initial estimate of the groundwater heads, the model describes the observed groundwater heads well (R 2 =0.98). The annual hydrologic fluxes are close to those estimated by a calibrated SWAT model. The model is considerably less expensive than previous physically-based models of similar complexity. The model is able to elucidate the complex interactions of processes in space and time. Such detailed, quantitative and mechanistic descriptions cannot be produced by conceptual models. The watershed is found to be a subsurface-dominated system with saturation excess being the main runoff generation mechanism. Infiltration, recharge and ET are also found to be strongly related to topography and groundwater flow. The large seasonal variation of energy input drives the strong annual cycle and markedly different responses in streamflow.