Efficient Characterization of Uncertain Model Parameters with a Reduced-Order Ensemble Kalman Filter

Spatially variable model parameters are often highly uncertain and difficult to observe. This has prompted the widespread use of Bayesian characterization methods that can infer parameter values from measurements of related variables, while explicitly accounting for uncertainty. Ensemble versions of Bayesian characterization are particularly convenient when uncertain variables have complex spatial structures that do not conform to Gaussian descriptions. However, ensemble methods can be time consuming for high-dimensional problems. This paper describes a reduced-order approach to ensemble characterization that is particularly well suited for subsurface flow and transport problems. It uses a truncated discrete cosine transform to reduce the dimensionality of spatially variable time-invariant model parameters and a nonlinear extension of principle orthogonal decomposition to reduce the dimensionality of dynamic model states. The resulting nonlinear reduced-order model can be included in the forecast step of ...

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