An Integrated Variational Data Assimilation Methodology for Robust Estimation of State and Parameters of the Coupled Terrestrial Water and Energy Cycle

Accurate estimation of land surface heat and moisture fluxes as well as root zone soil moisture is crucial in many hydrological, meteorological, and agricultural applications. “In situ” measurements of these fluxes are costly and cannot be readily scaled to large areas relevant to weather and climate studies. Therefore, there is a need for techniques to make quantitative estimates of these variables at different spatial and temporal scales.

In this research a novel approach based on the variational data assimilation (VDA) methodology is applied for coupled estimation of key parameters of land surface fluxes and profiles of soil moisture and temperature from observed land surface state variables of moisture and temperature. This study accounts for the strong linkage between terrestrial water and energy cycles by coupling the dual source energy balance equation with the water balance equation through the mass flux of evapotranspiration (ET).  Heat diffusion and moisture diffusion into the column of soil are adjoined to the cost function as constraints.

A hessian based uncertainty quantification (UQ) framework is developed to address a key limitation of the VDA technique, which is its tendency to be ill- posed. The proposed framework utilizes uncertainty analysis and analysis of error covariance approximation as a tool to quantify the uncertainty of estimated parameters and to guide the formulation of a well-posed estimation problem.

The proposed integrated variational data assimilation algorithm is tested at point scale using synthetic data sets generated by the simultaneous heat and water (SHAW) model. The (synthetic) true measurements, including the profile of soil moisture and temperature, land surface water and heat fluxes, and root zone water uptake are compared with the model estimated counterparts. In addition, the feasibility of extending the proposed approach to use remote sensing observations is examined by limiting the number of land surface temperature and moisture observations within the assimilation period.