Multigrid Beta Function Approach for Modeling of Background Error Covariance in the Real Time Mesoscale Analysis (RTMA)

The Real Time Mesoscale Analysis (RTMA) provides hourly and sub-hourly 2D analyses of surface variables, cloud fields and precipitation on the National Weather Service’s National Digital Forecast Database grid, which are used for situational awareness, providing current conditions for transportation customers, verification of forecasts and as the reference for bias correction in the National Blend of Models.

The major development underway is a fully three-dimensional RTMA system, which will replace the current two-dimensional system within the next year or two with 3D analyses performed at very high horizontal resolutions (~2.5 km) issued at very frequent time intervals (~15 min). The key prerequisite for the success of this enterprise is a vastly improved computational efficiency in producing those analyses.

The new approach to modeling of background covariance error is based on the application of “Beta filters” (filters possessing compact-support kernels in the form of the beta distribution of probability theory) within a multigrid approach. As will be discussed here, this development is one of the key components for the success of the 3D-RTMA development. The new method replaces the recursive filter of Purser et al. (2003 a and b) which, though in itself is an efficient and a very good approximation to the Gaussian, and able to account for the inhomogeneity and anisotropy of background errors, is an inherently sequential operator, ill-fitted to parallelization owing to its infinite support. The recursive filter has limited ability to describe covariances ranging across widely varying scales and is neither able to account for cross-correlations nor to exhibit negative lobes, which realistic covariance do possess. These are the defects that the multigrid Beta filter successfully solves.

We will present the development of the new technique and show preliminary results.