A Hessian-Based Method for Uncertainty Quantification of Parameters of Terrestrial Water and Energy Balance Equations

Abstract:

All land parameterizations used in hydrologic, ecological and climate models or assimilation systems contain key closure functions that relate water and energy balances. Key among these closure functions is reduction of evapotranspiration (latent heat flux) due to deficit in soil water availability (EF, the fraction of available energy released as latent heat), This closure is a flux-based diagnostic that can be calculated for any model. Its estimation as a function of soil moisture state (S) can be used to diagnose compatibility and fidelity of parameterizations. Important as this closure is, it remains empirical and mostly untested especially across diverse landscapes and climates. In this study we develop and apply mapping estimation capability for key unknown parameters that link the terrestrial water and energy balance equations. A single cost function is posed that measures moisture and temperature dependent errors solely in terms of observed forcings, surface states and unknown parameters. This cost function is minimized with respect to parameters to estimate key parameters of water and energy balance equation. The uncertainty of the estimated parameters (and associated statistical confidence limits) is obtained through the inverse of Hessian of the cost function, which is an approximation of the covariance matrix. The hessian of the cost function will be used to guide the formulation of a well-posed estimation problem. This calibration free method is verified at point scale and at regional scale using remote sensing measurements. The focus is to find the functional form of the evaporative fraction dependence on soil moisture, the key closure function for surface and subsurface heat and moisture dynamics, using remote sensing data. Accurate estimation of key parameters and closure function of water and energy balance equation can be used to guide the refinement of Land Surface Models and enhance weather and climate forecast skill.