The effects of discontinuities in the Betts-Miller cumulus convection scheme on four-dimensional variational data assimilation

A tangent linear and an adjoint of the large-scale precipitation and the cumulus convection processes in the National Meteorological Center's NMC/ETA regional forecast model are developed. The effects of discontinuities in the Betts’Miller cumulus convection scheme are examined and applicability of derivative minimization methods in four-dimensional variational (4D VAR) data assimilation is considered. It is demonstrated that discontinuities present in the control Betts’Miller cumulus convection scheme increase linearization errors to a large extent and have adverse effects on 4D VAR data assimilation. In the experiments performed, discontinuities in the cumulus convection scheme have the most serious effect in low layers. These problems can be reduced by modifying the scheme to make it more continuous in low layers. Positive effects of inclusion of cumulus convection in 4D VAR data assimilation are found in upper layers, especially in humidity fields. The “observations” used are optimal interpolation analyses of temperature, surface pressure, wind and specific humidity. By inclusion of other data, more closely related to the convective processes, such as precipitation and clouds, more benefits should be expected. Even with the difficulties caused by discontinuities, derivative minimization techniques appear to work for the data assimilation problems. In order to get more general conclusions, more experiments are needed with different synoptic situations. The inclusion of other important physical processes such as radiation, surface friction and turbulence in the forecast and the corresponding adjoint models could alter the results since they may reinforce the effects of discontinuities.