CLP

Abstract

This work aims at improved computation of covariances and of multiscale structures such as clouds, in the Weather Research and Forecasting (WRF) data-assimilation (WRFDA) system, in particular the horizontal factor of the control-variable transform used to optimize the forecast initialization. Better representation can be achieved in the horizontal transform by wavelet-compression techniques that have been proven in many other applications.

In this work, two past obstacles to effective incorporation of wavelets in limited-area models such as WRF are resolved: isometric-injective (i.e., energy preserving, left-invertible) wavelets avoid boundary-condition assumptions at any scale; and these wavelets can be applied to non-dyadic data lengths. A summary technical description of these improved wavelets and their implementation into WRFDA is presented. By retaining only a diagonal background-covariance matrix in wavelet space, appropriate heterogeneity is obtained for the model-space covariances.

A second wavelet application is to partition observation error into a part due to poor representation (e.g., too-coarse resolution), and a residual, using a novel criterion in wavelet space. Other methods to construct inhomogeneous anisotropic covariance models are cited, and other potential technical improvements are discussed.