Considering the impact of observation error correlation in ensemble square-root Kalman filter

Jichao Wang,Shaodong Zang

doi:10.1590/s1679-87592019026106717

Abstract

Data assimilation has been developed into an effective technology that can utilize a large number of multisource unconventional data. It cannot only provide the initial field for the ocean numerical prediction model, but also construct the ocean reanalysis datasets and provide the design basis for the ocean observation plan. In data assimilation, the estimation of the observation error is of paramount importance, because the quality of the analysis depends on it. In general, the observation error covariance matrix is diagonal or assumed to be diagonal, which means that the observation errors are independent from one another. However, there are indeed correlations in the observation errors. A diagnostic method has been developed, which can estimate a correlated and more accurate observation error covariance matrix. The proposed method combines an ensemble squareroot Kalman filter with the diagnostic method, providing an estimation of the observation error covariance matrix. In order to test the performance of the method, the numerical experiments are performed with the Lorenz 96 model and a Shallow water model. The more accurate observation error covariance matrix can be obtained to use in ensemble square-root Kalman filter by using the new method. We could find using the estimated correlated observation error in the data assimilation improves the analysis.

Highlights

Data assimilation is the process of combining observations with a prior forecast state of the model, known as background, to produce an accurate estimate of the current state, known as analysis
For a data assimilation process, in order to obtain an optimal estimation of the true state for ocean numerical models, the observation error covariance and the background error covariance must have more accurate estimation
Miyoshi et al (2013) introduced and demonstrated the beneficial effect of correlated observation error covariance matrix used in data assimilation, which means the observation error correlation is worthy of further study

Summary

Introduction

Data assimilation is the process of combining observations with a prior forecast state of the model, known as background, to produce an accurate estimate of the current state, known as analysis. It is important to effectively incorporate the observations into the numerical model to improve the accuracy of ocean prediction, when data assimilation is widely used in the field of ocean science. More and more researchers concentrate on ensemble filters, as well as the ensemble variational method. Most ocean numerical prediction models are high-dimensional nonlinear systems and Kalman filter cannot do anything about it. The ensemble filters are able to help us to deal with non-linear systems very well and the formulas of ensemble filters are much more computationally efficient than the Kalman filter.

Methods

Results

Conclusion