Land surface data assimilation problems are often limited by the high dimensionality of states created by spatial discretization over large high-resolution computational grids. Yet field observations and simulation both confirm that soil moisture can have pronounced spatial structure, especially after extensive rainfall. This suggests that the high dimensionality of the problem could be reduced during wet periods if spatial patterns could be more efficiently represented. After prolonged drydown, when spatial structure is determined primarily by small-scale soil and vegetation variability rather than rainfall, the original high-dimensional problem can be effectively replaced by many independent low-dimensional problems that can be solved in parallel with relatively little effort. In reality, conditions are continually varying between these two extremes. This is confirmed by a singular value decomposition of the replicate matrix (covariance square root) produced in an ensemble forecasting simulation experiment. The singular value spectrum drops off quickly after rainfall events, when a few leading modes dominate the spatial structure of soil moisture. The spectrum is much flatter after a prolonged drydown period, when spatial structure is less significant. Deterministic reduced-rank Kalman filters can achieve significant computational efficiency by focusing on the leading modes of a system with large-scale spatial structure. But these methods are not well suited for land surface problems with complex uncertain inputs and rapidly changing spectra. Local ensemble Kalman filters are suitable for such problems during dry periods but give less accurate results after rainfall. The most promising option for achieving computational efficiency and accuracy is to develop generalized localization methods that dynamically aggregate states, reflecting structural changes in the ensemble.

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ABSTRACT:The main objective of this paper is to improve the accuracy of radar rainfall estimation by accounting for a storm movement into a radar rainfall accumulation process. The multi-resolution viscous alignment (MVA) technique was used to estimate the velocity of a rain field from two consecutively measured radar images. The analysis used the 10-min radar reflectivity of the Pasicharoen radar and the corresponding 47 rain gauges measurements of 41 rainfall events that occurred in Bangkok during [2005][2006][2007]. The 28 rainfall events occurring during 2005-2006 were used for calibration, and the 13 rainfall events recorded in 2007 were used for validation. Finer temporal resolutions of radar reflectivity data, taken at 1-9 min intervals, were generated using the MVA technique in order to investigate the optimal temporal resolution of the Pasicharoen radar when the MVA technique was integrated into an hourly radar rainfall estimation algorithm to account for a storm movement within a sampling interval. The results showed that using the generated 5-min MVA reflectivity data for estimating hourly radar rainfall gave the smallest root mean square error (RMSE) between hourly radar rainfall estimates and corresponding rain gauge data when compared to other temporal resolutions of generated MVA reflectivity. Hourly radar rainfall obtained from the proposed algorithm, which integrates the MVA technique into the accumulation approach, was compared with the traditional simple linear interpolation (SLI) technique and conventional method. Using the 5-min generated MVA reflectivity data to estimate hourly radar rainfall can reduce RMSEs between hourly radar and rain gauge rainfall by 10% and 17% for the calibration period, and by 27% and 29% for the validation period when compared to the SLI and conventional methods, respectively.