Impact of observation error structure on satellite soil moisture assimilation into a rainfall-runoff model

In the Ensemble Kalman Filter (EnKF) - based data assimilation, the background prediction of a model is updated using observations and relative weights based on the model prediction and observation uncertainties. In practice, both model and observation uncertainties are difficult to quantify thus have been often assumed to be spatially and temporally independent Gaussian random variables. Nevertheless, it has been shown that incorrect assumptions regarding the structure of these errors can degrade the performance of the stochastic data assimilation. This work investigates the autocorrelation structure of the microwave satellite soil moisture retrievals and explores how assumed observation error structure affects streamflow prediction skill when assimilating these observations into a rainfall-runoff model. An AMSR-E soil moisture product and the Probability Distribution Model (PDM) are used for this purpose. Satellite soil moisture data is transformed with an exponential filter to make it comparable to the root zone soil moisture state of the model. The exponential filter formulation explicitly incorporates an autocorrelation component in the rescaled observation, however, the error structure of this operator has been treated until now as an independent Gaussian process. In this work, the variance of the rescaled observation error is estimated based on the residuals from the rescaled satellite soil moisture and the calibrated model soil moisture state. Next, the observation error structure is treated as a Gaussian independent process with time-variant variance; a weakly autocorrelated random process (with autocorrelation coefficient of 0.2) and a strongly autocorrelated random process (with autocorrelation coefficient of 0.8). These experiments are compared with a control case which corresponds to the commonly used assumption of Gaussian independent observation error with time-fixed variance. Model error is represented by perturbing rainfall forcing data and soil moisture state. These perturbations are assumed to represent all forcing and model structural/parameter errors. Error parameters are calibrated by applying two discharge ensemble verification criteria. Assimilation results are compared and the impacts of the observation error structure assumptions are assessed. The study area is the semi-arid 42,870 km(2) Warrego at Wyandra River catchment, located in Queensland, Australia. This catchment is chosen for its flooding history, along with having geographical and climatological conditions that enable soil moisture satellite retrievals to have higher accuracy than in other areas. These conditions include large area, semi-arid climate and low vegetation cover. Moreover, the catchment is poorly instrumented, thus satellite data provides valuable information. Results show a consistent improvement of the model forecast accuracy of the control case and in all experiments. However, given that a stochastic assimilation is designed to correct stochastic errors, the systematic errors in model prediction (probably due to the inaccurate forcing data within the catchment) are not addressed by these experiments. The assumed observation error structures tested in the different experiments do not exhibit significant effect in the assimilation results. This case study provides useful insight into the assimilation of satellite soil moisture retrievals in poorly instrumented semi-arid catchments.