Improving ensemble data assimilation through Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC)

Small forecast ensemble sizes (< 100) are common in the ensemble data assimilation (EnsDA) component of geophysical forecast systems, thus limiting the error-constraining power of EnsDA. This study proposes an efficient and embarrassingly parallel method to generate additional ensemble members: the Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC; "peace gee see"). Such members are called "virtual members". PESE-GC utilizes the users' knowledge of the marginal distributions of forecast model variables. Virtual members can be generated from any (potentially non-Gaussian) multivariate forecast distribution that has a Gaussian copula. PESE-GC's impact on EnsDA is evaluated using the 40-variable Lorenz 1996 model, several EnsDA algorithms, several observation operators, a range of EnsDA cycling intervals, and a range of forecast ensemble sizes. 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 improve the forecast model variable statistics, and/or (3) the rank histogram filter is used with non-parametric priors in high-forecast-spread situations. These results motivate development and testing of PESE-GC for EnsDA with high-order geophysical models.

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Related Software #1 : Data Assimilation Research Testbed

Related Software #2 : Code for PESE-GC Lorenz 96 study [Software]

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Author Chan, Man Yau
Publisher UCAR/NCAR - Library
Publication Date 2024-07-01T00:00:00
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Metadata Date 2025-07-10T20:00:32.288953
Metadata Record Identifier edu.ucar.opensky::articles:27325
Metadata Language eng; USA
Suggested Citation Chan, Man Yau. (2024). Improving ensemble data assimilation through Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC). UCAR/NCAR - Library. https://n2t.org/ark:/85065/d70r9tm4. Accessed 01 August 2025.

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