Recovery of mesoscale covariance using time-phased ensembles

In most data-assimilation systems in the operational numerical weather forecast centers around the world, the background error covariance (BEC) is either computed off-line and/or modeled with some empirical fitting functions. When BEC is computed off-line or modeled, it requires a large and long-period statistical sample of verification of model forecasts and analyses (e.g., the well-known NMC method). Typically, such methods render a very smoothed, large-scale structure in BEC due to near-climatological averaging of day-to-day weather variances. There are questions whether a data-assimilation system will produce any realistic mesoscale structure in the analysis if such constructed BEC is used, and whether such an analysis suitable for generating a short-range numerical weather prediction of 1-2 days.

In this study, we present a method to compute BEC, which can be not only done effectively on-line (in the sense of parallel with model runs), but the BEC can also capture the detailed mesoscale structure. The method uses a set of time-phased ensembles. We will demonstrate how such BEC can be calculated within a frequent data-assimilation cycle, and also compare the covariance structure recovered using this method with that from the NMC method.