Title: Deriving Optimal Combinations of Static and Flow Dependent Variances using Hidden Error Variance Theory

Author: David Kuhl (NRL, Washington DC)
Elizabeth Satterfield (NRL, Monterey, CA)
Craig H. Bishop (NRL, Monterey, CA)

Data assimilation systems such as Hybrid variational DA schemes employ forecast error covariance models that are linear combinations of static covariance models and flow-dependent ensemble based covariance models, we will refer to these systems as Hybrids. Currently, to determine the optimal weightingof the flow-dependent and static parts components, numerical weather prediction (NWP) centers must perform computationally expensive trials to compare each set of plausible weights. Since it is likely that the accuracy of ensemble based error covariances varies with vertical level and latitude, it also seems reasonable to assume that the optimal weights for a Hybrid covariance model would be a slowly varying function of latitude and height. However, the amount of tuning required to optimize such spatially varying weights would be even more computationally expensive. Here, we introduce and demonstrate a new method for deriving spatially varying weights for Hybrid error covariance models. This method is based on empirical techniques arising from hidden error variance theory which enable estimates of aspects of the climatological distribution of true error variances and the likelihood distribution of ensemble variances given a true error variance. If the assumptions of the approach are satisfied, the method would recover optimal weights for the ensemble and climatological estimates of the true error variance from archives of innovation and ensemble variance pairs. Here we evaluate the assumptions of the univariate model applied to the Lorenz '96 system as well as the Navy's 2016 operational DA scheme NAVDAS-AR-hybrid. Results indicate that the derived optimal weights perform comparably to the optimal weights found through brute force tuning.

GMAO Head: Steven Pawson Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: Feb 9 2015