Three-dimensional volume averaged soil-moisture transport model: A scalable scheme for representing subgrid topographic control in land-atmosphere interactions
Climate models, both global and regional, have increased in sophistication and are being run at increasingly higher resolutions. The land surface models (LSMs) coupled to these climate models have also evolved from simple bucket models to the new generation models needed to support sophisticated linkages and process interactions at small scales to assess their cumulative impact at larger scales. This is possible by substantially improving the land-surface parameterization in these models to account for subgrid processes. Although topographic data is one of the most readily available high resolution products with continental and global coverage, heterogeneity induced by topographic characteristics, such as slopes and curvatures, is generally not well represented in the models. These data offer unprecedented opportunity for representing the scaling issues of the processes, which are controlled by topographic attributes, such as subsurface moisture transport. In most current LSMs, however, soil-moisture transport equations limited to the vertical soil-moisture transport are unable to capture the spatial variability of soil water induced by topography, and models are thus limited in predictability for land surface fluxes as well. Some recent models use the Topmodel framework based on a basin or catchment scale to overcome these shortcomings, but the underpinning assumptions remain questionable at the scale of regional climate model (RCM) applications. Moreover, although the surface runoff is also one of the important components for the terrestrial hydrologic cycle, most LSMs simplistically estimate it using the soil water budget without any explicit simulation or routing schemes regarding runoff travel time over the basins. Even this roughly generated runoff is not used as the boundary condition for the subsurface flow calculation, which may result in a mass balance error in water cycle. The model errors, in the absence of appropriate parameterizations, often manifest as non-linear drifts in the dynamical response. For the significant improvement in these crude parameterizations in current terrestrial hydrologic schemes of LSMs, the following research tasks are explored in this study. The 3-dimensional (3-D) volume averaged soil-moisture transport (VAST) formulation is derived from the Richards equation to incorporate the lateral flow and subgrid heterogeneity due to topographic characteristics. Parameters characterizing subgrid variability are represented as scale dependent statistical functions, of soil-moisture variability dependence on subgrid topographic attributes, with second order approximations. These parameterizations based on limited data sets serve to illustrate the role of subgrid variability, although they are not meant to serve as a universal model. I hope that this illustration will serve to catalyze a more consistent data collection. I find that the lateral and subgrid flux contribution plays a significant role in total soil-moisture dynamics, and the flux due to subgrid spatial variability is as much or larger than grid averaged flux, especially in drier condition. One of the approximated forms of the Saint-Venant equations is the non-inertia diffusion wave (DW) model, which can account for the downstream backwater effect and is known as an efficient method in accuracy and computational time. I have developed a conjunctive surface-subsurface flow model at a large scale, a 1-D diffusion wave (DW) model for the surface flow interacting with the 3-D VAST model for the subsurface flow, for the comprehensive terrestrial water and energy predictions in LSMs. This conjunctive flow model can explicitly simulate the surface runoff due to both rainfall excess and soil-surface saturation. A selection of numerical implementation schemes is employed for each flow component. The 3-D VAST model is implemented using a time splitting scheme applying an explicit method for lateral flow after a fully implicit method for the vertical flow. The 1-D DW model is then solved by the MacCormack finite difference scheme with the second-order accuracy in both space and time. For the implementation of the new developed model, this study also focuses on the de¬velopment and construction of appropriate data sets, especially surface boundary conditions (SBCs) specifically designed for mesoscale RCM applications. The new SBCs development motivated by the limitations and inconsistencies of existing SBCs can be readily incorporated into any RCM suitable for U.S. climate and hydrology modeling studies. The primary SBCs are currently presented in a RCM domain for the U.S applications at 30-km spacing. The raw data sources and processing procedures, however, are elaborated in detail, by which the SBCs can be readily constructed for any specific RCM domain anywhere in the world. The new conjunctive surface-subsurface flow model is substituted for the existing hydro-logic scheme in the CLM model, the state-of-the-art LSM, to improve the model predictability and to understand the topographic impact on the terrestrial water and energy balance. Model simulations are performed at the time step of 10 minutes for a study domain with a basin size of 450,000 km2 around the Ohio Valley region using the North American regional reanalysis (NARR) forcing dataset from 1995 to 2000 in the off-line mode. All model simulations are performed using the published model parameter values without calibration, except for the hydraulic conductivity reference depth Zr and anisotropy ratio ( which are estimated through the sensitivity analyses. The predicted stream flow hydrographs are compared with the observations at the four United States geological survey (USGS) stream gauges selected within the study domain. The simulation results show that the lateral and subgrid fluxes play a significant role in total the soil-moisture dynamics and the spatial distribution of soil water that has a large impact on the surface energy balance as well. It is also found from the new coupled model simulations that the interaction between surface and subsurface flows and the flow routing scheme improve the stream flow predictions significantly. Ignoring the role of surface flow depth on the infiltration rate causes errors in both surface and subsurface flow predictions. The new CLM model coupled to the improved terrestrial hydrologic scheme using realistic SBCs provides a full suite of modeling capability to characterize surface water and energy fluxes for regional, continental, and global hydrologic studies.