Space-Time Mesoscale Analysis System

A sequential 3DVAR approach

Yuanfu Xie, Steve Koch

John McGinley 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 4D) and will be a new data assimilation technique.

Background

Observation Long wave

Resolvable Information for a Given Observation Network

Single solution of a 3DVAR

• It builds the grid value correlation by statistical estimation;

• It may not resolve the frontal or boundary correctly that 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 3DVAR approach

A recursive filter is usually used to approximate the error covariance;

After selecting the parameter of recursive filter , it solves one variational problem:

min1

2u ub T B 1 u ub 1

2Hu y TO 1 Hu y

0.5 0.7 0.9

A single 3DVAR with different RF

These analyses tend toapproximate the truth:

Recursive filter version of STMAS

A sequential 3DVAR implemented through a recursive filter.

1. Solve the 3DVAR with large , e.g. 0.999;2. Subtract the analysis from observation

values used in previous 3DVAR 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 3DVARWith =0.5 or 0.9

STMAS-RF Truth

Multigrid application in STMASReplacing 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

Since the multigrid determines the wavelength, there is no correlation involved in STMAS variational analysis over a given grid.

Only computation for the cost function is simple interpolations.

A STMAS 5 km surface analysis of 6 state variables 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

STMAS-MG (multigrid) is an efficient, multiscale grid analysis system;

It can use all possible data sources, including radar, satellite and so on;

It can also impose balances or constraints to its analysis directly;

STMAS 4D is under development.