A heuristic study on the importance of anisotropic error distributions in data assimilation

A challenging problem in numerical weather prediction is to optimize the use of meteorological observations in data assimilation. Even assimilation techniques considered "optimal'' in the "least squares'' sense usually involve a set of assumptions that prescribes the horizontal and vertical distributions of analysis increments used to update the background analysis. These assumptions may impose limitations on the use of the data that can adversely affect the data assimilation and any subsequent forecast. Virtually all widely used operational analysis and dynamic-initialization techniques assume, at some level, that the errors are isotropic and so the data can be applied within circular regions of influence around measurement sites. Whether implied or used directly, circular isotropic regions of influence are indiscriminate toward thermal and wind gradients that may reflect changes of air mass. That is, the analytic process may ignore key flow-dependent information available about the physical error structures of an individual case. Although this simplification is widely recognized, many data assimilation schemes currently offer no practical remedy. To explore the potential value of case-adaptive, noncircular weighting in a computationally efficient manner, an approach for structure-dependent weighting of observations (SWOBS) is investigated in a continuous data assimilation scheme. In this study, SWOBS is used to dynamically initialize the PSU-NCAR Mesoscale Model using temperature and wind data in a series of observing-system simulation experiments. Results of this heuristic study suggest that improvements in analysis and forecast skill are possible with case-specific, flow-dependent, anisotropic weighting of observations.