Space-Time Mesoscale Analysis System A sequential 3 DVAR approach Yuanfu Xie, Steve Koch John Mc. Ginley and Steve Albers Global Systems Division Earth System Research Laboratory

Space and time variational data assimilation system STMAS is a three-dimensional variational analysis, combining horizontal spatial and temporal observation to provide a temporally consistent surface grid analysis. It will be developed into a full three-dimensional spatial and temporal analysis (STMAS 4 D) and will be a new data assimilation technique.

Resolvable Information for a Given Observation Network

Single solution of a 3 DVAR • It builds the grid value correlation by statistical estimation; • It may not resolve the frontal or boundary correctly that is critical for the automatic front detection algorithm.

Surface Analysis: Ideal case Left: Mesonet surface stations; Right: An analysis function

Analytic function: A multi-scale frontal propagation testing function

Single 3 DVAR approach Ø A recursive filter is usually used to approximate the error covariance; Ø After selecting the parameter of recursive filter , it solves one variational problem:

A single 3 DVAR with different RF 0. 5 These analyses tend to approximate the truth: 0. 7 0. 9

Recursive filter version of STMAS A sequential 3 DVAR implemented through a recursive filter. 1. Solve the 3 DVAR with large , e. g. 0. 999; 2. Subtract the analysis from observation values used in previous 3 DVAR analysis; 3. Reduce by a fraction, say in (0. 5, 1); 4. Return to step 1 if it is necessary; 5. Add the previous analyses together.

Comparison: Single 3 DVAR With =0. 5 or 0. 9 STMAS-RF Truth

Multigrid application in STMAS Replacing the recursive filter in an early version of STMAS, a multigrid technique is implemented to obtain a multiscale analysis. The number of grid points over a given domain determines the shortest wavelength allowed. A multigrid uses the number of grid points to control the wavelength. STMAS solves its variational problem over the coarsest grid and obtains observation information for longest waves. By gradually increasing the number of grid points, STMAS multigrid gains shorter waves by each iterations.

An efficient analysis system Ø Since the multigrid determines the wavelength, there is no correlation involved in STMAS variational analysis over a given grid. Ø Only computation for the cost function is simple interpolations. Ø A STMAS 5 km surface analysis of 6 state variables Ø over eastern US (two-third of CONUS) using recursive filter spends 15 minutes; A multigrid STMAS analysis could take about 40 seconds.

Different Implementation of STMAS Recursive filter Wavelet Multigrid

STMAS-MG Ø STMAS-MG (multigrid) is an efficient, multiscale grid analysis system; Ø It can use all possible data sources, including radar, satellite and so on; Ø It can also impose balances or constraints to its analysis directly; Ø STMAS 4 D is under development.