Objective Analysis for Numerical Weather Prediction

 The field of objective analysis for numerical weather prediction is enjoying rapid development because of theoretical advances in analysis methods coupled with progress in observing and computing technology. This review considers current and projected work on objective analysis under three main headings: theory, verification and practice.<br> Recent developments in the theory suggest that there are close links between all analysis methods based on optimality principles. Moreover, simpler analysis methods such as successive correction can be modified to converge to an optimal method in simple circumstances. The basic job of any analysis algorithm is to filter random observation error from the data and then interpolate the filtered data to a regular grid. A new viewpoint on Optimum Interpolation shows the algorithm in a simple light with an intimate connection between the filtering and interpolation capabilites.<br> Verifications of observations, forecasts, and analyses are reviewed, using statistics on one-point and two-point height and velocity correlations. The two-point correlations are inter-related through the kinematic equations of two-dimensional turbulence. In the limit of vanishing spatial lag they degenrate to the one-point correlations. These diagnostics offer a means to compare the error characteristics of different observing systems. When used to verify short-range forecasts, they provide a complete description of the structure of the forecast errors. Phillips’ simple theory of forecast errors can reproduce many of the features of the empirically determined structures. New results indicate that there may be a need for anisotropic and non-separable correlation functions for analysis.<br> The correlation diagnostics offer new and rigorous ways to estimate analysis error at observation points. They provide a quick and easy measure of the efficiency of an analysis system. They should prove useful in identifying the reasons for system dependence in the results of observing system experiments.<br> In discussing current and future research we consider the special problems of analysis in data rich areas over land and near mountains; the problems of analysis over the mid-latitude oceans; and then the problems of tropical analysis. Extensions of O/I offer new approaches to these problems which will be explored in the near future. In the slightly longer term, new developments in the theory of 4-dimensional analysis may well supersede current methods. Finally we consider developments in data quality control, an area of great importance for all other developments. New developments here, using Bayesian methods, offer promise.