The Kalman smoother for a linear quasi-geostrophic model of ocean circulation

Abstract

An explicit algorithm is given for the generalized inverse or Kalman smoother of a time-dependent, linear, quasi-geostrophic model of ocean circulation. The algorithm requires computation of the Kalman filter but, if the smoother error covariance matrix. Thnot required, then it is not necessary to invert and store the filter error covariance matrix. That is, the algorithm yields smoother estimates of the system noise, the measurement noise and the state with relatively low computational effort. Theoretical estimates and computational practice show the integrations in the algorithm to be well conditioned. The theoretical investigation of the smoother shows the need to assume red wavenumber spectra for the system noise, in order to ensure the efficiency of the smoother at estimating noise, in order to achieve spatially regular and thus physically realizable estimates of the state, and in order to lower the computational burden. The smoother estimate of the system noise is shown not to have the unphysical non-linear boundary layer structure found in the filter estimate. The filter and smoother are compared with a series of numerical examples.