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