Discontinuous forcing generating rough initial conditions in 4DVAR data assimilation

The impact of discontinuous model forcing on the initial conditions obtaine d from 4DVAR data assimilation is studied with mathematic analyses, idealiz ed numerical examples, and more realistic meteorological cases. The results show that a discontinuity in a parameterization, like a model bias, can in troduce a systematic error in the assimilated initial fields. However, the most detrimental effect of a model discontinuity is the retention of roughn ess in the assimilated initial fields, although in some cases the 4DVAR pro cedure provides some smoothing effect. The obvious consequences of this rou ghness is that it will introduce spurious modes in the ensuing forecast, an d derivatives of the assimilated initial data will be unrealistically large , which can lead to large errors in data analysis. The smoothing effect on the initial conditions with the addition of artificial diffusion to the con straining model is also studied. Possible solutions to the problem of 4DVAR data assimilation with discontinuous model forcing are discussed.