Estimation of model error covariance matrices for different land-atmosphere hydrology models

The model error covariance matrix Q is an often unknown, yet necessary parameter for the implementation of Kalman filtering. In the hydrologic data assimilation context Q is a measure of how much forcing noise needs to be included in the hydrology model used. While the measurement error covariance matrix R can in general be determined from instrument characteristics, there is little guidance for most hydrologic models as to how what value should be given for Q, or even how to model this error. In this work, we present the values of Q for several land-atmosphere hydrologic models, in which the state variables are soil moisture and temperature and canopy (intercepted) moisture. Precipitation and net radiation are used as forcing variables, while the desirability of using measured land surface energy fluxes as state variables is explored. The Q matrices are derived by applying maximum likelihood estimation techniques to the extended Kalman filter methodology of data assimilation, minimizing the residuals between the ideal (unknown) state variables and their filter estimates. Land surface measurements of micrometeorologic variables and energy fluxes taken during the Southern Great Plains 1999 (SGP99) experiment are used to drive the estimation. By explicitly calculating the model error covariance structure of different land-atmosphere hydrology models for a given set of environmental measurements, choices about which model may be appropriate for use in a data-assimilation framework can be clarified.