Construction of Mesoscale Error Covariance in a Data Assimilation System using Time-Lagged Ensembles

Abstract

One of the most important factors that determine meteorological analysis fields for numerical weather prediction is the background error covariance matrix. Not only do the correlations in this background covariance matrix will perform the spatial spreading of information from the observation points to a finite domain surrounding in the data-sparse areas, but it also takes a decisive role in how to smooth the analysis increments in data-dense area. There are empirical methods to estimate the background error covariance mainly based on the study of forecasts started from the analyses, like the NMC method or the adjoint sensitivity studies, but their theoretical foundation is rather unclear for the time being. In this research, I proposed a new method to estimate background error covariances, namely a time-lagged ensemble forecast system, which is recently developed in the NOAA/ESRL/GSD (The U. S. National Oceanic and Atmospheric Administration, Earth System Research Laboratory, Global System Division). These system pools forecasts are initialized at different times but validated at the same time, forming an ensemble system. Since each members of this ensemble system may be obtained in a time-sequential way, the model error covariance computed from such a statistical sample possesses crucial flow-dependent error information in the background model. This method makes possible economical computing because it can be easily implemented in on-line system at a lesser expense compared to NMC or ensemble perturbation method. The first goal is to evaluate the flow-dependent features of background error covariance fields estimated from time-lagged ensembles by comparing the background balanced dynamics (PV). The structure of mesoscale error covariance estimated from the time-lagged ensemble method is subsequently flow-dependent and highly anisotropic, which is determined by the underlying governing dynamics and associated error growth. The next aim is to demonstrate how well such background error covariance structure can be recovered from time-lagged ensemble method comparing with that from the NMC method. Typically, the NMC method renders a much smoothed, large-scale structure in background error covariance due to near-climatological averaging of day-to-day weather variances. The analysis increment propagated from two points of which one is located near the trough and the other one is located near the ridge has totally different weights for an observation near the trough for the time-lagged ensemble method, but it has similar or even too-spread weights in the NMC method. The last goal is to show that if this background error covariance can improve forecast as well as analysis by ingesting background wind and temperature error covariances in the LAPS (Local Analysis and Prediction System) data assimilation. In addition, more forecast experiments are performed by using these LAPS initial conditions. The VAR verification result of wind and temperature analysis / forecasts shows a mixed picture at some extent, in which it is improved at some points and deteriorated at others. But this result would make nice contribution to the research on ensemble error statistics in data assimilation but also to short-range forecasting in the domain of simulating initial condition uncertainties.