A wavelet approach to representing background error covariances in a limited-area model

The use of orthogonal wavelets for the representation of background error covariances over a limited area is studied. Each wavelet function contains both information on position and information on scale: using a diagonal correlation matrix in wavelet space thus gives the possibility of representing the local variations of correlation scale. To this end, a generalized family of orthogonal Meyer wavelets that are not restricted to dyadic domains (i.e., powers of 2) is introduced. A three-bases approach is used, which allows one to take advantage of the respective properties of the spectral, wavelet, and gridpoint spaces. While the implied local anisotropies are relatively small, the local changes in the two-dimensional length scale are rather well represented.