Estimating model error covariances using particle filters

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 144; no. 713; pp. 1310 - 1320
• Main Authors: Zhu, Mengbin, van Leeuwen, Peter J., Zhang, Weimin
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.04.2018; Wiley Subscription Services, Inc
• Subjects: Advances in Data Assimilation Methods; Data; Data assimilation; Data collection; Errors; Estimates; localization; Methods; model error covariance; non‐degeneracy; particle filter; Physics; localization; non‐degeneracy; particle filter; model error covariance
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.3132

A method is presented for estimating the error covariance of the errors in the model equations in observation space. Estimating model errors in this systematic way opens up the possibility to use data assimilation for systematic model improvement at the level of the model equations, which would be a huge step forward. This model error covariance is perhaps the hardest covariance matrix to estimate. It represents how the missing physics and errors in parametrizations manifest themselves at the scales the model can resolve. A new element is that we use an efficient particle filter to avoid the need to estimate the error covariance of the state as well, which most other data assimilation methods do require. Starting from a reasonable first estimate, the method generates new estimates iteratively during the data assimilation run, and the method is shown to converge to the correct model error matrix. We also investigate the influence of the accuracy of the observation error covariance on the estimation of the model error covariance and show that, when the observation errors are known, the model error covariance can be estimated well, but, as expected and perhaps unavoidably, the diagonal elements are estimated too low when the observation errors are estimated too high, and vice versa. Modelling detailed atmospheric physical processes, such as stratocumulus clouds, is extremely difficult, and present‐day parametrizations are failing. To improve the models one could add stochastic model errors. We use a fully nonlinear particle filter to estimate model error characteristics, avoiding the need also to estimate the state covariance.