Introducing non-Gaussian observation errors into incremental variational data assimilation methods

doi:10.1002/qj.5050

Introducing non-Gaussian observation errors into incremental variational data assimilation methods

2025-07-16

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Peter Jan van Leeuwen

DOI：10.1002/qj.5050

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The probability density function (pdf) of the observation error can be non-Gaussian, with causes including representation error, bounded observables, or nonlinearity. However, it has been assumed to be Gaussian in most data assimilation applications. In this study, we propose a new method, called the evolving-Gaussian method, to incorporate non-Gaussian observation error into data assimilation methods that use Gauss–Newton-based outer loops, such as incremental variational methods and iterative ensemble Kalman filters. The key idea behind the evolving-Gaussian method is to approximate the gradient of the non-Gaussian cost function locally by using a chosen Gaussian cost function during the minimization. Because we do not require the cost function to change for different observation-error pdfs, the evolving-Gaussian method is not restricted to any parametric pdf form, which facilitates its implementation in a full-scale operational weather forecasting system without adding to the computational cost. We show in an idealized experiment that the evolving-Gaussian method is able to identify the mode of the posterior successfully for a non-Gaussian observation-error pdf. We also demonstrate the evolving-Gaussian method in an operational-quality weather forecast system, the Integrated Forecasting System (IFS), with the assimilation of all-sky microwave radiances. The results indicate promising signs of improvement for the short-term forecast of low-tropospheric water vapor, cloud, and precipitation in the Tropics, albeit with some degradations in temperature.

Keywords:

all-sky satellite radiance assimilation

data assimilation

non-Gaussian errors

variational data assimilation

Introducing non-Gaussian observation errors into incremental variational data assimilation methods

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