Self-Consistent Stochastic Model Errors in Data Assimilation

Abstract: In using data assimilation to import information from observations to estimate parameters and state variables of a model, one must assume a distribution for the noise in the measurements and in the model errors. Using the path integral formulation of data assimilation~ cite{abar2009}, we introduce the idea of self consistency of the distribution of stochastic model errors: the distribution of model errors from the path integral with observed data should be consistent with the assumption made in formulating the the path integral. The path integral setting for data assimilation is discussed to provide the setting for the consistency test. Using two examples drawn from the 1996 Lorenz model, for $D = 100$ and for $D = 20$ we show how one can test for this inconsistency with essential no additional effort than that expended in extracting answers to interesting questions from data assimilation itself. \end{abstract}