A Sequential Hybrid 4DVAR System ImplementedUsing a Multi-Grid Technique

Yuanfu Xie1, Steven E. Koch1, and Steve Albers1,2

1NOAA Earth System Research Laboratory (ESRL)/Global Systems Division (GSD), Boulder, Colorado USA2Cooperative Institute for Research in the Atmosphere (CIRA), Colorado State University, Fort Collins, Colorado USA

For a multi-scale analysis, inaccurate error covariance (A. – small scale or B. – large scale) cannot provide a good analysis. STMAS then can no matter what numerical schemes are used (D., E., and F.).

B. C.

F.

A.

D. E.

• A Single VAR of Small Scale• A Single VAR of Large Scale• Truth• STMAS with Recursive Filter• STMAS with Wavelet• STMAS with Multi-Grid

Why a Sequential Data AssimilationError covariance is a difficult parameter to compute. Variational methods or EnKF cannot yield a good analysis with inaccurate covariance or limited ensemble members. For given observational net-works, some relatively large scale meteorological information is available to retrieve. A sequential analysis system could retrieve the large scale information and reduce to a standard variational or even EnKF at its last stage of the sequence analyses.

A simple example of a multi-scale analysis shows the difference between a single variational analysis vs. a sequential analysis follows below.

Space and Time Multi-ScaleAnalysis System (STMAS)

STMAS is implemented using a multi-grid technique. Coarser Grid: 4DVAR with an approximation model and use of a differentiable optimization method with the model adjoint;Finer Grid: 4DVAR with a numerical model and use of a non-differentiable optimization method without an adjoint; Finest Grid: EnKF with small scale localization scheme as large scales retrieved.

AdvantageThe multi-grid helps not only efficiency but control analysis scales so that adjoint system is valid and applicable on coarser grids.Model constraints can be applied according to the analysis scales.STMAS can handle all modern datasets, such as radar, micro-wave, and satellite radiance data.

A model adjoint does not exist for many mesoscale models and thus a 4DVAR minimization is usually inefficient. STMAS uses an approximate model that has adjoint over coarser grids to obtain better analysis guesses for its fine grid analysis. The non-differentiable 4DVAR of STMAS at its finest levels would be better to solve.

ApplicationsSTMAS has been applied to provide surface analysis for FAA storm boundary detection. It runs in real time with 15 minute update and 5km resolution over CONUS.It analyzes eight variables and a dozen of derived fields on a single processor.STMAS is also running full 4-D analysis using wide range datasets for hurricanes/typhoons in real time.

Future- Adjoint development for the approximation

model- Radar reflectivity analysis- Satellite radiance analysis- Non-differentiable 4DVAR/EnKF

STMAS multi-grid implementation is efficient and fits many frequent analysis applications. For example, an STMAS surface analysis of eight state variables over a 5-km resolution on a CONUS domain takes less than three minutes using a single 3.2GHz Intel processor. Now we are considering to test a 2-km resolution with 5-minute update cycle.