Discontinuous Forcing Generating Rough Initial Conditions in 4DVAR Data Assimilation

Abstract

The impact of discontinuous model forcing on the initial conditions obtained from 4DVAR data assimilation is studied with mathematic analyses, idealized numerical examples, and more realistic meteorological cases. The results show that a discontinuity in a parameterization, like a model bias, can introduce a systematic error in the assimilated initial fields. However, the most detrimental effect of a model discontinuity is the retention of roughness in the assimilated initial fields, although in some cases the 4DVAR procedure provides some smoothing effect. The obvious consequences of this roughness is that it will introduce spurious modes in the ensuing forecast, and 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 constraining model is also studied. Possible solutions to the problem of 4DVAR data assimilation with discontinuous model forcing are discussed.