Jacobian mapping between vertical coordinate systems in data assimilation

Abstract

AbstractRadiances measured by remote‐sensing instruments are now the largest component of the atmospheric observation network. The assimilation of radiances from nadir sounders involves fast radiative transfer (RT) models which project profiles provided by forecast models onto the observation space for direct comparison with the measurements. One of the features typically characterizing fast RT models is the use of a fixed vertical coordinate. If the vertical coordinate of the RT model is not identical to that used by the forecast model, an interpolation of forecast profiles to the RT model coordinate is necessary. In variational data assimilation, the mapping of the Jacobians (derivatives of the RT model output with respect to its inputs) from the RT model coordinate to the forecast model coordinate is also required. This mapping of Jacobians is accomplished through the adjoint of the forecast profile interpolator. As shown, the nearest‐neighbour log‐linear interpolator commonly used operationally can lead to incorrect mapping of Jacobians and, consequently, to incorrect assimilation. This incorrect mapping occurs as a result of leaving out intermediate levels in the interpolation. This problem has been previously masked in part through the smoothing effect of forecast‐error vertical correlations on the analysis increments. To solve this problem, two simple versions of an interpolator relying on piecewise log‐linear weighted averaging over the layers are investigated. Both markedly improve Jacobian mappings in the assimilation of observations, with one being slightly favoured over the other. This interpolator is being incorporated into the RTTOV model used by several operational weather forecasting centres. Copyright © 2007 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.