Impact of “variable localization” in the background error covariance matrix within the Local Ensemble Transform Kalman Filter

The Ensemble Kalman Filter data assimilation produces an analysis from a multivariate background error covariance matrix which contains the error correlation between the dynamic variables in the analysis. When the variables are physically related to each other, the multivariate background error can help the analysis to efficiently correct the errors. Here we address the problem of augmenting an analysis with a variable that is uncorrelated with some of the other dynamic variables.

We have a carbon cycle data assimilation system which assimilates the observations of meteorological variables (wind, temperature, humidity and surface pressure) as well as atmospheric CO2 and then analyzes not only those atmospheric variables, the atmospheric CO2 but also the surface CO2 fluxes. The fully multivariate data assimilation allows all error correlations among the dynamic variables in the analysis. However, the nature run used in this study does not include the radiative properties of atmospheric CO2 so that the atmospheric CO2 is determined by only the wind fields. That is, the error correlation of atmospheric CO2 with temperature and humidity is not present in this experimental setting. Furthermore, we found that the surface CO2 fluxes are significantly linked to only the atmospheric CO2 in our experiments. Thus, we build an analysis system with “variable localization” according to the physical relations among the variables, by zeroing out the background error covariance between irrelevant variables. The results show that impact of “variable localization” is positive.