MODEL ERROR ESTIMATION USING PEARSON SYSTEM WITH APPLICATION TO NONLINEAR WAVES IN COMPRESSIBLE FLOWS

In data assimilation, the description of the model error uncertainty is of the utmost importance because, when incorrectly defined, it may lead to information loss about the real state of the system. In this work, we proposed a novel approach that finds the optimal distribution for describing the model error uncertainty within a particle filtering framework. The method was applied to nonlinear waves in compressible flows. We investigated the influence of observation noise statistics, resolution of the numerical model, smoothness of the solutions, and sensor location. The results showed that in almost all situations the Pearson Type I is preferred, but with different curve-shape characteristics, namely, skewed, nearly symmetric, boolean AND-, U-, and J-shaped. The distributions became, in most cases, U-shaped when the sensors were located near the discontinuities.