PREDICTING SOIL MOISTURE WITH MODELS AND OBSERVATIONS THROUGH AN ENSEMBLE QUASI STEADY-STATE FILTER

Soil moisture is a critical land surface variable that links the energy, water, and carbon cycles. High spatial resolution (10 - 100 m) soil moisture predictions are critical to hydrologic and geomorphic applications such as rainfall-runoff and landslide forecasting. Ensemble-based data assimilation provides a mechanism to combine estimates of soil moisture from nonlinear physically-based models with noisy remote sensing observations. However, a challenge of applying these methodologies to soil moisture estimation is the high dimensionality of the soil moisture simulation model imposed by the need for high spatial resolution. We suggest an ensemble quasi steady-state filter in which the state error covariance matrices are estimated through offline simulation. Three distinct regimes of soil moisture state are considered: (1) prior to rainfall initiation, (2) after rainfall cessation, and (3) during watershed dry-down. Evolution of rainfall is simulated stochastically by sampling the climatic distributions of storm inter-arrival time, duration and depth. Storm events are then disaggregated in space. These synthetic rainfall fields are used to force the TIN-based Realtime Integrated Basin Simulator (tRIBS) model, yielding an ensemble of realizations of the soil moisture field evolution. Ensemble steady-state error covariance matrices for each of the three hydrologic regimes are constructed by sampling from the soil moisture ensemble at appropriate times (e.g., immediately prior to every storm) and stored. During online data assimilation, the ensemble quasi steady-state filter algorithm selects the most appropriate of the three state error covariance matrices based on recent rainfall history and short-term rainfall forecast. With the appropriate state error covariance matrix and the error covariance of the noisy observation, the algorithm updates an evolved soil moisture ensemble of reasonable computational size through a least-squares approximation.