Variational Assimilation of Precipitation Data and Gravity Wave Excitation

Abstract

The degree of imbalance forced by deep convection in a three-dimensional variational analysis scheme (3DVAR) is examined. Simulated surface precipitation rates are used with various degree of errors together with different background atmospheric fields. Dynamical imbalances are defined only for the fastest timescales associated with gravity waves and diagnosed according to the implicit normal mode framework. Local measures of ageostrophic perturbations are also considered over rainy areas. Slow timescale perturbations on internal gravitational modes introduced by convection during 3DVAR are also monitored using temporal evidence of their presence. The diagnostic quantities used here are more appropriate for deep vertical scales where Machenhauer's balance scheme can be justified but must be used with care when discussing possible imbalance for shallow vertical gravity modes (especially for mesoscale data assimilation). These diagnostic measures are not actually used as an explicit constraint in the 3DVAR analysis but only serve as diagnostic tools. These measures are not meant as optimal penalty terms to be used in variational analysis schemes however since this aspect is not considered in this study. It is found that gravity wave imbalance is introduced early in the minimization process when no balance constraint is imposed (other than the simple geostrophic constraint used in the background error statistics). Precipitation observations localized over a restricted horizontal domain are sufficient to trigger non-negligible imbalances. A challenging issue is the introduction by 3DVAR of slow timescale internal modes that significantly differ from those already present in the background trajectory. Whether these oscillations need to be controlled in some ways in order to ensure that the variational adjustment of convective forcing leads to slow timescales within some neighborhood of those of the background trajectory remains an open question. Traditional normal mode tools as those used in implicit normal mode initialization (especially for the first two internal vertical modes) can be used for such constraining problems in principle. For operational applications, the now widely used digital time-filtering approach presumably would need some extension in order to achieve the same controlling effect on slow timescales.