Development of wavelet methodology for weather Data Assimilation
Seminar Room 2, Newton Institute Gatehouse
AbstractThis 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.