A monthly, two-soil-layer statistical-dynamical water balance model for hydroecologically focused climate impact assessments

Abstract

An operational version of a statistical-dynamical water balance model is developed which is applicable to hydroecologically focused regional-scale climate impact assessments. Major improvements to the model include implementation at a monthly scale, addition of snow and frozen soil, division of vadose-zone soil into two layers, and a more realistic representation of vegetation. The latter is achieved by coupling the water balance model to the Shuttleworth-Wallace evapotranspiration model. The coupled model is applied to the central United States over a half-degree grid using vegetation, soil and climate data from the Vegetation Ecosystem Modeling and Analysis Project. After detailed review of the literature, careful estimation of the parameters of the evapotranspiration, soil-hydraulic and stochastic-precipitation sub-models is performed. An excellent match of modeled mean annual runoff to contours of streamflow is achieved with only minimal calibration of two evapotranspiration parameters. Model validity is further established through comparison of results for the mean and interannual variability of the water balance with observations of leaf area index (LAI), vegetation productivity and soil moisture. Surprising little dependence of the percentage of total evapotranspiration that is bare-soil evaporation on climate and vegetation type is found, with most of the variation across the study area attributable to soil texture and the resultant differences in vegetation density. The implication is that the higher (lower) soil moisture content in humid (dry) climates is more-or-less offset by the greater (lower) vegetation density. The partitioning of evapotranspiration in the model is highly dependent on vegetation density in the form of LAI. The spatial and interannual variation in LAI is captured in the model through application of the hypothesis that, in any year in which water is significantly limiting, vegetation will draw soil moisture down in the latter half of the growing season approximately to the point at which the vegetation just begins to experience water stress. This "LAI-maximization" hypothesis is supported through the analysis of observed soil moisture, soil-moisture retention data and water-stress studies in the plant physiology literature. Analysis of the sensitivity of model-maximized LAI to soil texture shows that the model is able to reproduce the inverse texture effect, which consists of the observation that natural vegetation in dry climates tends to be most productivity in sandy soils. Comparison of model results to interpolated estimates of storm flow from USGS gauging stations shows that, for most combinations of climate and soil, the one-dimensional formulation of infiltration dynamics does a reasonable job of approximating the spatially complex process of surface runoff generation at the regional scale. However, overestimation of surface runoff in dry climates is substantial if subgrid variability in soil hydraulic properties is included. This may be a scale issue in that much surface runoff in dry climates never reaches a gauged stream channel. In contrast, subgrid variability of soil hydraulic properties appears to be much less important in humid climates. Rather, the model tends to underestimate surface runoff in those climates owing to the unaccounted for connection of the vadose zone to shallow groundwater and the resulting Dunne (i.e., saturation excess) runoff and enhancement of Hortonian runoff. Although the model tends to underestimate the interannual variability in surface runoff and overestimate the interannual variability in base flow, it matches the overall structure in the observations. Specifically, it reproduces the linear decrease in the coefficients of variation of storm flow with the means, as well the peak in the coefficients of variation of base flow for means around one cm. The later is seen to be associated with a region of high interannual variability of precipitation over the central Great Plains. The model also reproduces the positive correlation between the skewness coefficients and the coefficients of variation in both storm flow and base flow. The tendency of the model to underestimate the interannual variability in storm flow is attributed to subgrid variability in precipitation and runoff processes, and to the spatiotemporal variability of antecedent soil moisture. The less severe overestimation of the interannual variability of base flow is attributed more to groundwater storage than to scale issues. Appendix A: Integrated hydrological/ecological/economic modeling for examining the vulnerability of water resources to climate change. A methodology for assessing regional-scale hydrologic vulnerability to climate variability that incorporates ecologic and economic factors is presented. A simple economic model of damages due to hydrologic drought and the decision to invest in "augmented" yield to mitigate these damages is coupled to a statistical-dynamical, soil-vegetation- climate model of the annual water balance. The coupling is through the cumulative distribution function (CDF) of annual basin yield as estimated by the model. Using Bayesian concepts for optimal decision-making under uncertainty, uncertainty in the yield CDF is propagated through the drought damage model to the hypothetical investment decision. Appendix B: The impact of land-atmosphere interactions on the temporal variability of soil moisture at the regional scale. This study examines the impact of the nonlinear dynamics of soil-moisture feedbacks to precipitation on the temporal variability of soil moisture at the regional scale. Our approach first formulates the large-scale soil-water balance as an ordinary differential equation and then recasts it as a stochastic differential equation by incorporating colored noise representing the high-frequency temporal variability and correlation of precipitation. The underlying model couples the atmospheric and surface-water balances and accounts for both precipitation recycling and precipitation-efficiency feedbacks, which arise from the surface energy balance. Based on the governing Fokker-Planck equation, we derive three different analytical solutions ( corresponding to differing forms and combinations of feedbacks) for the steady-state probability density function of soil moisture. Using NCEP/NCAR reanalysis data, estimates of potential evapotranspiration, and long-term observations of precipitation, streamflow and soil moisture, the model is parameterized for a 5°x5° region encompassing the State of Illinois. We show that precipitation-efficiency feedbacks can be significant contributors to the variability of soil moisture at the regional scale. Precipitation recycling, on the other hand, increases the variability by a negligible amount. For all feedback cases, the probability density function is unimodal and nearly symmetric. The analysis concludes with an examination of the dependence of the shape of the probability density functions on spatial scale. It is shown that the associated increases in either the correlation time scale or the variance of the noise will produce a bimodal distribution when precipitation-efficiency feedbacks are included. However, the magnitudes of the necessary increases are of an unrealistic magnitude.