The estimation of analysis error characteristics using an observation systems simulation experiment

Abstract

Observation system simulation experiments (OSSEs) have been performed at the National Centers for Environmental Prediction primarily for the purpose of evaluating the forecast improvement potential of proposed new observation instruments. The simulations have been validated primarily by comparing results from corresponding data denial experiments in both simulated and real data assimilation contexts. Additional validation is presented here using comparisons of some statistics of analysis increments determined from a baseline simulation using the entire suite of observations utilized during a reanalysis for February 1993. By exploiting the availability of a data set representing "truth" in the simulations, the background and analysis errors produced for the baseline simulation are computed. Several statistics of these errors are then determined, including time means and variances as functions of location or spherical harmonic wave number, vertical correlations, Kalman gains, and balance as measured by projections onto normal modes. Use of an OSSE in this way is one of the few means of estimating analysis error characteristics. Although these simulation experiments are among the best calibrated ones existing, the additional validation here indicates that some unrealism remains present. With this caveat, several interesting characteristics of analysis error have been revealed. Among these are that: longitudinal variations of error variances in the Northern Hemisphere have a similar range as latitudinal variations; corresponding background and analysis error variances are very similar in most regions so that the Kalman gains are generally small with the notable exception of regions and times well observed by rawindsondes; correlation lengths (both vertical and horizontal) are very similar for background and analysis errors; error variances at horizontal scales shorter than those corresponding to approximately spherical harmonic wavenumber 70 are as large as corresponding variances of the fields themselves; approximately 30 % of the error energy resides in gravitational normal modes; and the variance spectrum of the wind error is approximately white for scales below its peak near wavenumber 20.