A Wavelet-Based Reduced Rank Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

Abstract

A suboptimal Kalman filter system that evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments, which lasted 24 days and used different degrees of truncation, were carried out. These experiments reduced the number of elements in the covariance matrix by 90%, 97%, and 99% and the computational cost of covariance propagation by 80%, 93%, and 96%, respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period was not found to be growing after about 5 days of assimilation. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients at times when observations were made in the immediate vicinity.