Tangent Linear Aspects of the Kain–Fritsch Moist Convective Parameterization Scheme

Abstract

Advanced operational four-dimensional variational data assimilation (4DVAR) schemes include a linearized version of moist convective parameterization and its adjoint. At the Meteorological Service of Canada, work is underway to implement 4DVAR for both global and regional operational data assimilation. Moreover, the Kain? Fritsch moist convective parameterization scheme is currently under operational testing for global and regional weather forecasting. Consequently, tangent linear and adjoint versions of this convective scheme have been developed. Sources of nonlinearities and accuracy of the tangent linear approximation of the convective scheme itself were examined. The procedure to test this latter aspect uses Monte Carlo simulations based on background error covariances from the operational three-dimensional variational data assimilation (3DVAR) system at the Canadian Meteorological Centre. It is shown that for a critical level of amplitudes of vertical perturbations of temperature or moisture greater than typically 0.1 K or 0.1 g kg?1, the tangent linear approximation becomes inaccurate (e.g., typical perturbation response having the wrong sign and amplitude errors larger than 100%). For such perturbation amplitudes, there is a rapid increase of convective points where the tangent linear convective approximation is very strongly in error. Deactivation of the Kain?Fritsch scheme becomes frequent and a significant source of invalid tangent linear approximation for input perturbations exceeding typically 0.3 K or 0.3 g kg?1. Potential implications of this study for linearized moist convection in the context of 4DVAR and moist singular vector computation are discussed.