Elsevier

Advances in Water Resources

Volume 33, Issue 12, December 2010, Pages 1524-1541
Advances in Water Resources

A process-based, distributed hydrologic model based on a large-scale method for surface–subsurface coupling

https://doi.org/10.1016/j.advwatres.2010.09.002Get rights and content

Abstract

Process-based watershed models are useful tools for understanding the impacts of natural and anthropogenic influences on water resources and for predicting water and solute fluxes exported from watersheds to receiving water bodies. The applicability of process-based hydrologic models has been previously limited to small catchments and short time frames. Computational demands, especially the solution to the three-dimensional subsurface flow domain, continue to pose significant constraints. This paper documents the mathematical development, numerical testing and the initial application of a new distributed hydrologic model PAWS (Process-based Adaptive Watershed Simulator). The model solves the governing equations for the major hydrologic processes efficiently so that large scale applications become relevant. PAWS evaluates the integrated hydrologic response of the surface–subsurface system using a novel non-iterative method that couples runoff and groundwater flow to vadose zone processes approximating the 3D Richards equation. The method is computationally efficient and produces physically consistent solutions. All flow components have been independently verified using analytical solutions and experimental data where applicable. The model is applied to a medium-sized watershed in Michigan (1169 km2) achieving high performance metrics in terms of streamflow prediction at two gages during the calibration and verification periods. PAWS uses public databases as input and possesses full capability to interact with GIS datasets. Future papers will describe applications to other watersheds and the development and application of fate and transport modules.

Research highlights

► A new process-based, distributed hydrologic model (PAWS) is described. ► PAWS uses a stable surface – subsurface coupling method. ► The coupling method is suitable for large-scale applications.

Introduction

In recent years, the focus of hydrologic modeling is shifting toward using models to predict future scenarios including the impacts of climate change and human interventions on water resources. The effects of these forcings are modulated by complex and interrelated responses of hydrologic processes which are often characterized by feedbacks and thresholds. Process-based models, derived deductively from established physical laws [1], can capture the underlying dynamics of watersheds and may produce better predictions across a range of scales. Understanding water and solute 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 [2]. Pollutants can reach streams via point source discharge, non-point source (overland flow), or subsurface seepage. Process-based hydrologic models explicitly detail the various flow paths and thus provide the necessary information to predict contaminant loads at downstream receiving bodies including lakes [3] and oceans [4].

Previous hydrologic models, especially those intended for large scale simulations, tend to use conceptual representations of the groundwater compartment, ignoring the complexity of the groundwater and vadose zone flow problems in space, e.g. SWAT [5]. Some large-scale land surface models (LSMs), e.g. the VIC model [6] and Noah LSM [7], assume a leaky bottom for the land surface domain. These methods over-simplify the groundwater flow dynamics and lead to prediction errors when the water table is shallow or saturation excess is an important mechanism. On the continental scale, [8], [9] added simple groundwater dynamics into LSMs and ran simulations for entire North America.

The subsurface flow is an integral component of the hydrologic cycle which should be studied using a holistic approach [10], [11], [12]. In shallow water table conditions, groundwater controls soil moisture and provides sources of water for ET. The soil moisture in turn exhibits heavy influences on surface energy fluxes and meterological phenomena with feedback loops which may amplify the anomalies [13]. Coupled climate-hydrologic modeling indicated that shallow groundwater conditions in the humid regions and intermountain valleys in arid regions enhanced ET and precipitation [9], [14]. Therefore, an accurate description of groundwater dynamics is crucial for understanding the nonlinear responses of the hydrologic system and to describe impacts on regional climate.

There has been a growing interest in integrated surface–subsurface modeling. However, such research is still limited by computational constraints. The governing equation for three-dimensional subsurface flow is the Richards equation (RE) [15]. Rainfall, surface ponding and groundwater interact via the variably saturated soil zone (the vadose zone) where crucial processes such as infiltration, soil evaporation, root extraction and groundwater recharge/discharge take place. The RE automatically handles all relevant processes in a seamless fashion [16]. A number of watershed/regional-scale process-based models that solve the three-dimensional Richards equation have been recently developed to examine the interactions between surface and subsurface flow, e.g., InHM [17], Hydrogeosphere [18], CATHY [19], ParFlow [20], [21], WASH123D [22], HYDRUS3D [23], MODHMS [24]. However, models that employ such a full 3D approach are faced with the problem of excessive computational demand, especially in large domains. Due to the strong non-linearity, the solution accuracy of the RE depends heavily on the spatial step size. In particular, the combination of heavy rain and a relatively dry soil surface can lead to the development of a steep wetting front along which soil moisture can change dramatically, making it necessary to use very fine grid cells. Downer and Ogden [25] studied the effect of vertical discretization on RE solution and concluded that to simulate infiltration accurately, the vertical cell size needs to be on the centimeter level near soil surfaces, but not throughout the soil column. The large matrix resulting from the 3-D discretization must be solved iteratively which is prohibitively expensive.

As a result, applications of the aforementioned process-based models were often restricted to small catchments (from plot scale to less than 100 km2) and short time frames. If the watershed size increased, the simulations took exceedingly long times. For example, the INHM model [17] or CAT3M [26] were only applied on a plot scale. The GSSHA model [27] was applied to small catchments (20 km2 and 3.64 km2 in [25] and 3 km2 in [27]) over short time frames (<200 days). The comparisons are also limited to streamflow measurements. The applications of the MIKE-SHE model also ranged from a few km2 [28], [29] to medium sized-watersheds of several hundred km2 [30]. Being a private-domain model, MIKE-SHE’s source code is not accessible, which may have limited its use for research that links with other sciences. For medium/small-sized watersheds, models such as HydroGeoSphere [18] and CATHY [19] required many days to run when 3D RE is enabled. Some recent research makes use of parallel computing systems, e.g., ParFlow [20], [21], WASH123D [22]. While such research offers useful insights, this means that the newly-available computing power will be consumed to solve the PDEs, making it difficult or impossible to carry out other equally important tasks such as model auto-calibration and uncertainty analysis. It is clear from the above review that widespread use of process-based models requires further advances in describing the subsurface physics in a computationally efficient manner. The aim of this paper is to describe a new process-based model for large watersheds that is based on a novel method for surface–subsurface coupling.

This paper documents the mathematical development, numerical testing and the initial application of a new process-based distributed hydrologic model, PAWS (Process-based Adaptive Watershed Simulator). The model solves governing equations for the major hydrologic processes efficiently so that large scale applications become relevant. PAWS is developed with the aims of long term simulations on medium (∼1000 km2) to large (>5000 km2) basins. With upscaling and parallelization, we expect to apply the model to larger (e.g., continental) scales in future. This paper serves as an introduction to the model and focuses mainly on the mathematical aspects of the model. Future papers will describe applications to other watersheds, data processing and the development and application of fate and transport modules.

Section snippets

General overview

PAWS solves physically-based conservation laws for major processes of the hydrologic cycle, which are depicted in Fig. 1 and summarized in Table 1. The eight compartments where most calculations take place are, respectively, surface ponding layer, canopy storage layer, impervious cover storage layer, overland flow layer, snowpack, soil moisture, groundwater aquifers and stream channels. The major state variables are summarized in Table 2. Clearly the vadose zone plays a central role in the

Test cases

Numerical codes must be carefully tested and verified before they can be put to use. Following the Freeze and Harlan blueprint [54], we require that each component be independently verified. There are two levels of code testing. In the first level, numerical code is compared to available analytical solutions to ensure that there are no bugs in the code and that the numerical schemes solve the PDEs with acceptable accuracy (within the range of parameters covered by the test problem). At this

Limitations/Future research

It is an assumption in our model that soil moisture does not flow laterally in the unsaturated part of the soil column. The model performance may deteriorate in catchments dominated by perched water table dynamics. Detailed analyses including comparisons with the SWAT model indicated that soil lateral flow is a minor component of the hydrologic cycle for the watershed described in this paper [56], however it may be important for other watersheds and the process will be added in a future version

Acknowledgements

This research was funded by the NOAA Center of Excellence for Great Lakes and Human Health. We thank Jie Niu for assistance with data processing and GUI development. Computer time on the High Performance Computer Center at MSU and help from HPCC staff Dirk Colbry and Andrew Keen are gratefully acknowledged.

References (71)

  • C.T. Lai et al.

    The dynamic role of root-water uptake in coupling potential to actual transpiration

    Adv Water Resour

    (2000)
  • I. Braud et al.

    Comparison of root water uptake modules using either the surface energy balance or potential transpiration

    J Hydrol

    (2005)
  • G. Gottardi et al.

    An accurate time integration method for simplified overland flow models

    Adv Water Resour

    (2008)
  • V. Casulli

    Semi-implicit finite-difference methods for the 2-dimensional shallow-water equations

    J Comput Phys

    (1990)
  • J.C. van Dam et al.

    Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation

    J Hydrol

    (2000)
  • O. Gunduz et al.

    River networks and groundwater flow: a simultaneous solution of a coupled system

    J Hydrol

    (2005)
  • R.A. Freeze et al.

    Blueprint for a physically-based, digitally-simulated hydrologic response model

    J Hydrol

    (1969)
  • P. DiGiammarco et al.

    A conservative finite elements approach to overland flow: the control volume finite element formulation

    J Hydrol

    (1996)
  • M. Sulis et al.

    A comparison of two physics-based numerical models for simulating surface water-groundwater interactions

    Adv Water Resour

    (2010)
  • D.M. Bjerklie

    Estimating the bankfull velocity and discharge for rivers using remotely sensed river morphology information

    J Hydrol

    (2007)
  • S.G. Li et al.

    An object-oriented hierarchical patch dynamics paradigm (HPDP) for modeling complex groundwater systems across multiple-scales

    Environ Model Software

    (2006)
  • K. Beven

    Towards an alternative blueprint for a physically based digitally simulated hydrologic response modelling system

    Hydrol Process

    (2002)
  • U.S.EPA. National Primary Drinking Water Regulations: Ground Water Rule; Proposed Rules. 40 CFR Parts 141 and 142....
  • P. Thupaki et al.

    Budget analysis of Escherichia coli at a Southern Lake Michigan Beach

    Environ Sci Technol

    (2010)
  • S.B. Grant et al.

    Surf zone entrainment, along-shore transport, and human health implications of pollution from tidal outlets

    J Geophys Res-Oceans

    (2005)
  • Neitsch SL, Arnold JG, Kiniry JR, Williams JR. Soil and water assessment tool theoretical documentation version 2005....
  • F. Chen et al.

    Coupling an advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system. Part I: Model implementation and sensitivity

    Mon Weather Rev

    (2001)
  • G. Miguez-Macho et al.

    Incorporating water table dynamics in climate modeling: 2. Formulation, validation, and soil moisture simulation

    J Geophys Res-Atmos

    (2007)
  • X.Y. Jiang et al.

    Impacts of vegetation and groundwater dynamics on warm season precipitation over the Central United States

    J Geophys Res-Atmos

    (2009)
  • R.M. Maxwell et al.

    Development of a coupled land surface and groundwater model

    J Hydrometeorol

    (2005)
  • L.E. Gulden et al.

    Improving land-surface model hydrology: is an explicit aquifer model better than a deeper soil profile?

    Geophys Res Lett

    (2007)
  • R.M. Maxwell et al.

    Interdependence of groundwater dynamics and land-energy feedbacks under climate change

    Nature Geosci

    (2008)
  • R.O. Anyah et al.

    Incorporating water table dynamics in climate modeling: 3. Simulated groundwater influence on coupled land-atmosphere variability

    J Geophys Res-Atmos

    (2008)
  • L.A. Richards

    Capillary conduction of liquids in porous mediums

    Physics

    (1931)
  • C.W. Downer et al.

    Theory, development, and applicability of the surface water hydrologic model CASC2D

    Hydrol Process

    (2002)
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