Adaptive estimation of inflation and observation errors in a simulated carbon cycle data assimilation

Ensemble Kalman Filter technique usually needs inflating background errors in order to prevent the analysis from underestimating them. In the study of carbon cycle data assimilation using Ensemble Kalman Filter, we found that inflation is a very important parameter, especially for estimating surface CO2 fluxes. Li et al. (2009) introduced an adaptive estimation of the inflation factor without manual tuning which is very expensive or sometimes infeasible. In addition, the method of Li et al. (2009) provides an accurate estimate of the observation error. In other words, this method can only be applied for the variables having observations.

We apply the methodology of Li et al. (2009) to our simulated carbon cycle data assimilation system so that the inflations for the atmospheric CO2 and the meteorological variables are estimated adaptively. Since we assume that surface CO2 fluxes have no observations, we calculate the adaptive inflation for it in a different way, similar to the relaxation to the prior covariance method: Zhang et al.(2004). With those adaptive inflation techniques, our data assimilation system simultaneously analyzes meteorological variables (wind, temperature, humidity, and surface pressure), atmospheric CO2, and surface CO2 fluxes.

The results from the OSSEs show that the estimation of adaptive inflation improves the analysis very significantly, especially for the surface CO2 fluxes. The resulting inflation factors agree with empirical experiments done with manual tuning: the inflation for the atmospheric CO2 has larger magnitude than that for the meteorological variables while the surface CO2 fluxes needs relatively small inflation.