The Tarrawarra project

Introduction

At present, spatially distributed hydrologic models offer great promise for synergistic measurement and model development. Accounting for spatial variability is critical for simulating many processes such as pathways of pollutants through watersheds, hydrologic responses to changes in land cover, or landscape erosion and sediment transport. Distributed hydrologic models are designed to simulate the spatial distribution of important watershed variables such as soil water content and snow cover. They also offer a structure for incorporating spatial data from geographic information systems or remote sensing, which makes them particularly valuable in areas with limited instrumentation. Although distributed models have been effective tools for hydrologic simulations in a variety of settings, we have yet to determine how well the existing models can simulate internal watershed processes, and we have yet to use the models effectively to inform network design.

We introduce a methodology for evaluating distributed hydrologic models based on a 'hypothetical reality' of hydrologic response. This hypothetical reality presents a useful method of improving our ability to design effective hydrologic measurement networks and begin synergistically using measurements and modeling to advance understanding of hydrologic processes.

Although we recognize the importance of field-based research in advancing hydrologic understanding, analyses based solely on unique field sites are inhibited by many factors including data limitations, process complexity and heterogeneity, and discrepancies in scale between measurements and simulations.

The proposed research has three primary objectives:

ï¿ *Create an experimental framework for testing distributed hydrologic models

We introduce a procedure for rigorous distributed hydrologic model testing that can easily be used to test any model and modified to assess many different physical processes or watershed structures. The testing will be conducted based on a detailed numerical simulation or 'hypothetical reality' of hydrologic response with the watershed characteristics and hydrologic response behavior of a real, extensively measured zero-order catchment. Using this experimental framework, we will test the performance of two distributed hydrologic models. The tests will be designed to assess the suitability of the distributed model structure for accurately representing spatial and temporal patterns of bulk water movement through the watershed.

ï¿ *Use the framework to address particular measurement and modeling questions

The experimental framework will offer an ideal structure for testing a range of science questions, and the structured testing methodology will greatly facilitate comparisons between results of different model tests. Tests will particularly consider the types and scales of measurements that most effectively help characterize water movement through the watershed.

Prior research in distributed model testing and hypothetical realities

The importance of evaluating distributed models is widely recognized, and extensive efforts have been undertaken to compare how different distributed models simulate discharge. For example, in the National Weather Service's Distributed Model Intercomparison Project (DMIP) (Smith et al., 2004), a number of different distributed and quasi-distributed models were applied to the same basins, yielding useful insights as to which models might be most suitable for a particular type of watershed. Most model intercomparison projects, including DMIP, have focused on simulations of discharge but have not considered how well the models simulate internal watershed processes. To get at these internal processes requires an alternate scheme. Several studies have considered the sensitivity of internal watershed states and fluxes to distributed model parameter values (e.g. Christiaens and Feyen, 2002; Anderton et al., 2002) or examined how simulated internal watershed states relate to geographic and terrain attributes (e.g. Ivanov et al., 2004b). Troch et al. (1993) evaluated a topographic index-based conceptual distributed model against 3D numerical simulations of two eastern Pennsylvania catchments. They compared water table depth trends at particular points in the conceptual and numerical model simulations and assessed how well the conceptual model would be able to represent soil water content and root zone processes. That work is closest in spirit to the proposed research and fits within the scope of the types of distributed model tests we will conduct based on the hypothetical realities of hydrologic response.

Tools: Models to be used

Integrated Hydrology Model (InHM)

To construct the hypothetical realities of hydrologic response we will use the comprehensive InHM [VanderKwaak, 1999], which was designed to simulate quantitatively, in a fully-coupled approach, 3D variably-saturated flow in porous media and/or macropores and 2D flow over the surface and in open channels. Infiltration and exfiltration rates are determined in space and time by spatially variable subsurface properties, spatially and temporally variable subsurface pressure-head gradients, and spatially and temporally variable surface water depths. The flow of water in both the surface and subsurface continua is therefore intimately coupled. The governing equations are given in VanderKwaak and Loague (2001) and Loague et al. (2005). These equations are discretized in space using the control volume finite-element method, which combines the geometric flexibility of finite elements with the local conservation characteristics of control volumes. InHM has been successfully employed by Loague and co-workers for catchment scale, event-based rainfall-runoff simulation [VanderKwaak and Loague, 2001; Loague and VanderKwaak, 2002; Loague et al., 2005]. Read more on this model on the InHM website.

The InHM model runs were performed by Ben Mirus at Stanford University, Department of Geological and Environmental Sciences.

The hypothetical realities will be used as the basis for evaluating other distributed hydrologic models. For this evaluation, we chose two models that fit three important criteria:

1. Scale independent: Models can be used for a range of spatial scales, enabling extension of the results and methodology to larger scale watersheds and allowing direct examination of the effects of model scale.

2. Full process representation: Models have the ability to represent all hydrologic processes in all subsurface and surface domains, enabling both isolation of particular processes in model testing and expansion of testing to include additional processes such as snow accumulation and melt.

3. Representative: Model structures are physically-based and non-unique, so findings will provide general guidance regarding distributed model application and parameterization.

Penn State Integrated Hydrology Model (PIHM)

PIHM (Qu and Duffy, 2004) is an example of a physically-based distributed model that does not require as much computational capacity as an end member model like InHM. The model domain is divided into a TIN with prismatic finite volume elements, and it simulates fully coupled 2D overland flow, 1D channel flow, 1D vertical unsaturated zone, and 2D saturated flow. It is capable of simulating the location of the water table and tracking both unsaturated and saturated zone moisture movement, but the subsurface states are averaged over depth. Otherwise, the physical processes are represented in the same way as in InHM, except the solutions are determined using ODE's instead of PDE's, thus making the model much more computationally feasible for simulating a large watershed. PIHM additionally simulates interception, snowmelt based on a temperature index, and evapotranspiration based on the Penman Monteith equation. This model is new and has yet to be widely applied, but it offers a simple, robust structure that will integrate well with GIS, accommodate a range of scales, and easily incorporate additional hydrologic processes without compromising the fundamental physics of fluid flow through and between the surface and subsurface domains. Read more on the PIHM/PIHMgis website.

MODHMS

MODHMS (Panday and Huyakorn, 2004) is a physically based fully integrated surface-subsurface model based on the USGS MODFLOW groundwater code for which additional modules have been developed to simulate 3-D variably saturated flow (Richards equation) and 2-D overland flow (diffusion wave approximation). Read more on the MODHMS website.

Data: Tarrawarra watershed

The hypothetical reality created in this study will be based on a well-understood, extensively measured catchment. We have chosen the Tarrawarra catchment in southern Victoria, Australia (Figure 1). This is an area where water movement through the soil is important, and as such it is representative of the conditions in a large number of hillslopes throughout the world. Although other watersheds have hydrologic responses controlled by other factors such as overland flow, at this preliminary stage, our focus is on understanding building blocks of fluid movement through hillslopes, so the Tarrawarra catchment represents an ideal starting case.

Tarrawarra is a 10.5 ha catchment consisting of undulating hills used as pasture for cattle (Western and Grayson, 1998). Soils in the catchment are silty loams and silty clay loams ranging from 0.5 to 1.5 m deep over siltstone interbedded with sandstone and limestone. The climate is temperate, with an average of 820 mm of annual precipitation. Rainfall exceeds evapotranspiration in the winter, but there is a significant rainfall deficit in the summer. The catchment does not have any stream channels, but ephemeral surface runoff occurs and is measured at the catchment outlet.

Western and Grayson (1998) conducted detailed measurements of the spatial distribution of soil water contents using a "Terrain Data Acquisition System" (TDAS), which allowed collection of soil water content measurements using Time Domain Reflectometry (TDR) over a large spatial area. Over a one year period, they collected 13 distributions, each with 500 measurements on a 10x20 m grid. This data set is an important resource for analyzing soil moisture patterns of the dry and wet conditions at Tarrawarra. Read more on the Tarrawarra dataset website.

Figure 1 - Tarrawarra catchment, Australia - 30 cm integrated measured soil moisture states (Western and Grayson, 1998)

Generating hypothetical realities: InHm simulations of Tarrawarra

InHM is an internally consistent, valid representation of flow physics in three dimensions, so it can provide a 'hypothetical reality' of hydrologic response. The particular 'hypothetical reality' to be generated will have all the physical and hydrologic response characteristics of the well-measured Tarrawarra watershed. The InHM simulations will be based on the dimensions, topography, and soil, geologic, vegetation and climate characteristics of Tarrawarra, and simulations will be run using existing meteorological data at and near Tarrawarra.

A boundary-value problem (BVP) was already established for the Tarrawarra catchment by Ben Mirus at Stanford University, Department of Geological and Environmental Sciences. For the BVP, a finite-element mesh [i.e., three uniform layers with spatially uniform near-surface soil-hydraulic properties (e.g., saturated hydraulic conductivity) and adequate nodal spacing] was constructed based upon the Tarrawarra DEM and easily acquired information. This mesh contains spatial increments of 5-15 m in the horizontal direction, with tighter mesh spacing close to the catchment outlet. A regional sink boundary condition was defined for the catchment outlet. Figure 2 shows an example surface soil water content distribution that resulted from draining the catchment.

Figure 2a - Example of 'hypothetical reality': degree of saturation on April 15, 0:00AM, 1996

Meteorological data collected at the Coldstream weather station near Tarrawarra was used to force the model and produce eleven-year continuous simulations of hydrologic response. The daily output including spatial patterns of soil-water contents was stored. Animations of the saturation levels in the top 2 cm are shown to illustrate the dynamics of the wetting and drying patterns of the Tarrawarra system.

Figure 2b - Example of 'hypothetical reality': degree of saturation in the top 2 cm - sequence of daily output snapshots

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