Improving Ensemble Data Assimilation with Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC)

Ensemble data assimilation (EnsDA) in numerical weather prediction (NWP) typically uses small ensemble sizes (<100). Such sizes lead to two important challenges in EnsDA: 1) sampling errors in the ensemble statistics, and for certain EnsDA methods, 2) inaccuracies in representing the observation likelihood function.

In this talk, I will introduce a method to mitigate these issues: the Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC). PESE-GC leverages the users’ knowledge of the NWP model variables’ marginal forecast distributions to create additional (virtual) ensemble members. Unlike methods that draw additional members from climatology, virtual members have flow-dependent statistics. Furthermore, PESE-GC can handle a range of user knowledge (knowing the marginal distributions’ parametric form versus only knowing about those distributions’ bounds), and a large range of multivariate distributions (anything with a Gaussian copula). Finally, PESE-GC is efficient and embarrassingly parallel.

PESE-GC is tested with the Lorenz 1996 model, with a variety of observation operators, EnsDA algorithms, cycling intervals, forecast ensemble sizes, and expanded ensemble sizes (> 1,000 configurations). Significant improvements to EnsDA (p<0.01) are observed when either 1) the forecast ensemble size is small (<20 members), 2) the user selects marginal distributions that introduce information into the forecast model variable statistics, and/or 3) the rank histogram filter is used in high forecast spread situations. These results, and PESE-GC’s efficiency and scalability, motivate developing and testing of PESE-GC for EnsDA with high-order NWP models.