Computational Issues for Large-Scale Land Surface Data Assimilation Problems

Abstract

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.