Non-Gaussian variational data assimilation with reverse-lognormal errors

doi:10.1002/qj.4965

Non-Gaussian variational data assimilation with reverse-lognormal errors

2025-04-01

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DOI：10.1002/qj.4965

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For the majority of data assimilation (DA) applications, a Gaussian assumption is made to model the behaviour of errors associated with the specific situation. This assumption is generally false in geoscience fields, especially for variables that are positive (semi-)definite. The three-dimensional variational (3DVar) data-assimilation method was traditionally generated through Bayes' theorem with Gaussian multivariate probability density functions; however, over the last 15 years this assumption has been modified to allow for a lognormal distribution, as well as combining the Gaussian and lognormal distributions to form a mixed Gaussian-lognormal distribution. In this article, we adapt this assumption and allow these errors to be reverse-lognormally distributed. This is done by applying the Bayesian probability framework to derive a reverse-lognormal 3DVar cost function. With the new reverse-lognormally distributed 3DVar, we use machine-learning methods to detect which 3DVar method (Gaussian, lognormal, reverse-lognormal) is suitable to minimise the errors in that region of the Lorenz 1963 model.

Keyword:

data assimilation

Gaussianity

lognormal

non-Gaussianity

reverse-lognormal

Non-Gaussian variational data assimilation with reverse-lognormal errors

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