Long Window Assimilation of Martian Meteorology

A major goal of the data assimilation of planetary spacecraft atmospheric data is the determination of a ``best-fit'' state of meteorological variables consistent with all of the measurements and with the physical constraints imposed by a general circulation model, so that inferences about indirectly observed quantities --- winds --- can be made. For this purpose, it is necessary that the assimilation model produce not only a credible zonal mean state, but a realistic spectrum of baroclinic waves, while limiting gravity waves (which are sometimes spurious byproducts of the assimilation process). This motivates the use of higher resolution models (not truncated to the low zonal resolution of the observations) and longer assimilation windows (i.e., longer periods over which data is accumulated for each assimilation calculation). M. Fisher of ECMWF has recently shown that such long window, weak constraint, variational assimilation (with a window of 3 to 10 days in the terrestrial case) is the equivalent of Kalman smoothing, but does not require the estimation or propagation of the forecast error covariance matrix (a considerable savings in computational cost). Based on the short effective time constant of the radiatively active martian atmosphere, an even shorter window should be adequate for martian meteorology. The use of overlapping windows eliminates transients --- those undesired gravity waves --- at the start of the assimilation and minimizes the importance of the background term in the variational cost function. Preliminary calculations with this approach, using 100 sols of Mars Global Surveyor Thermal Emission Spectrometer team retrieved temperature profiles, show a reduction in the 1-sol forecast root-mean-square error from 3.45 K to 3.05 K. The root-mean-square error of the analysis is 1.68 K. There is a strong correlation between the analysis errors and the topography, suggesting that direct assimilation of the infrared observations is preferable, at least in the vicinity of Tharsis. The assimilated mean zonal circulation is qualitatively similar to that produced by ab initio general circulation models. Traveling wave amplitudes are enhanced compared to those assimilated with a severely truncated (maximum zonal wavenumber 6) model.