Open AccessA Wavelet Approach to Representing Background Error Covariances in a Limited-Area Model
Author(s) -
Alex Deckmyn,
Loïk Berre
Publication year - 2005
Publication title -
monthly weather review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.862
H-Index - 179
eISSN - 1520-0493
pISSN - 0027-0644
DOI - 10.1175/mwr2929.1
Subject(s) - wavelet , mathematics , scale (ratio) , diagonal , position (finance) , representation (politics) , space (punctuation) , wavelet transform , computer science , algorithm , statistical physics , mathematical analysis , artificial intelligence , geometry , physics , finance , quantum mechanics , politics , political science , law , economics , operating system
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.