Non-differentiable Minimization in the Context of the Maximum Likelihood Ensemble Filter (mlef)

The Maximum Likelihood Ensemble Filter (MLEF) is a control theory based ensemble data assimilation algorithm. The MLEF is presented and its basic equations discussed. Its relation to Kalman filtering is examined, indicating that the MLEF can be viewed as a nonlinear extension of the Kalman filter in the sense that it reduces to the standard Kalman filter for linear operators and Gaussian Probability Density Function assumption. In the analysis step, the MLEF employs an unconstrained iterative minimization. It is shown that the MLEF minimization can be used as a stand-alone non-differentiable minimization. The MLEF non-differentiable minimization is tested with a “spike” nondifferentiable function, and it was shown that it outperforms the nonlinear conjugate-gradient minimization for a given example.