Correcting biased observation model error in data assimilation

TL;DR

This paper introduces a nonparametric Bayesian method to learn and correct biases in observation models within data assimilation, enabling the use of previously discarded biased observations to improve forecast accuracy.

Contribution

It proposes a novel nonparametric Bayesian scheme that learns observation model error distributions and corrects biases, compatible with any data assimilation system.

Findings

Successfully modeled bimodal error distributions in synthetic tests.

Improved data assimilation by utilizing biased cloudy satellite observations.

Demonstrated effectiveness with realistic cloud and radiative transfer models.

Abstract

While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications, model error with nontrivial biases is unavoidable. A practical example is the error in the radiative transfer model (which is used to assimilate satellite measurements) in the presence of clouds. As a consequence, many (in fact 99\%) of the cloudy observed measurements are not being used although they may contain useful information. This paper presents a novel nonparametric Bayesian scheme which is able to learn the observation model error distribution and correct the bias in incoming observations. This scheme can be used in tandem with any data assimilation forecasting system. The proposed model error estimator uses nonparametric likelihood functions constructed with data-driven basis functions based on the theory of kernel embeddings of conditional distributions developed in the machine learning community. Numerically, we show positive results with two examples. The first example is designed to produce a bimodality in the observation model error (typical of "cloudy" observations) by introducing obstructions to the observations which occur randomly in space and time. The second example, which is physically more realistic, is to assimilate cloudy satellite brightness temperature-like quantities, generated from a stochastic cloud model for tropical convection and a simple radiative transfer model.