|Stochastic Systems Group|
Professor Dennis McLaughlin - Parsons Laboratory Professor of Water Resource Management, MIT
Many of the data assimilation problems encountered in the earth sciences are characterized by 1) nonlinearity, 2) high dimensionality, and 3) measurement and model uncertainty. To illustrate concepts we consider a hydrologic example -- estimation of fluxes between the land and atmosphere. The land surface system is quite heterogeneous, exhibiting significant spatial variations in topography, soil properties, and vegetation over a wide range of scales. Meteorological inputs to land surface systems (e.g. precipitation, air temperature, wind speed, etc.) vary over both time and space, also over a wide range of scales. A number of land surface states are constrained by thresholds (e.g. potential evapotranspiration) which themselves depend on the states. Finally, the relationships between land surface states and measurements can be nonlinear and are often influenced by state-dependent errors. All of these effects combine to create complex behavior that can be difficult to capture with traditional data assimilation methods. Alternatives to traditional methods are conceptually attractive but also tend to be more computationally demanding. This paper considers some computationally efficient techniques for dealing with large nonlinear hydrologic data assimilation problems. The methods of interest are developed from a Bayesian perspective that relies on ensemble statistics. Particular emphasis is given to multi-scale extensions of ensemble Kalman filtering. These techniques exploit changing space-time correlations in land surface states by introducing continually changing low-dimensional approximations for the update step of the filter. Other potentially promising methods for dealing with large nonlinear problems are also considered, with an emphasis on the tradeoffs implied whenever approximations are introduced to improve efficiency.
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