ECMWF flow dependent workshop, June 2007. Slide 1 of 14. A regime-dependent balanced control variable based on potential vorticity Ross Bannister, Data Assimilation Research Centre, University of Reading Mike Cullen, Numerical Weather Prediction, Met Office Funding: NERC and Met Office ECMWF Workshop on Flow-dependent Aspects of Data Assimilation, 11-13 th June 2007
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ECMWF flow dependent workshop, June 2007. Slide 1 of 14. A regime-dependent balanced control variable based on potential vorticity Ross Bannister, Data.
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ECMWF flow dependent workshop, June 2007. Slide 1 of 14.
A regime-dependent balanced control variable based on
potential vorticity
Ross Bannister, Data Assimilation Research Centre, University of ReadingMike Cullen, Numerical Weather Prediction, Met Office
Funding: NERC and Met Office
ECMWF Workshop on Flow-dependent Aspects of Data Assimilation, 11-13 th June 2007
ECMWF flow dependent workshop, June 2007. Slide 2 of 14.
Flow-dependence in data assimilation
• A-priori (background) information in the form of a forecast, xb.
• Flow dependent forecast error covariance matrix (Pf or B).
ECMWF flow dependent workshop, June 2007. Slide 14 of 14.
Summary
Acknowledgements: Thanks to Paul Berrisford, Mark Dixon, Dingmin Li, David Pearson, Ian Roulstone, and Marek Wlasak for scientific or technical discussions.Funded by NERC and the Met Office.
www.met.rdg.ac.uk/~ross/DARC/DataAssim.html
• Many VAR schemes use rotational wind as the leading control variable (a proxy for PV –- the
balanced vorticity approximation, BVA).
• The BVA is invalid for small Bu regimes, NH/fL0 < 1.
• Introduce new control variables.
• PV-based balanced variable (b).
• anti-PV-based unbalanced variable (pu).
b shows larger vertical scales than at large horizontal scales.
pu shows larger vertical scales than pr at large horizontal scales.
• cor(b, pu) < cor(, pr).
• Anti-balance equation (zero PV) amplifies features of large horiz/small vert scales in pu.
• The scheme is expected to work better with the Charney-Phillips than the Lorenz vertical grid.
ECMWF flow dependent workshop, June 2007. Slide 15 of 14.
End
ECMWF flow dependent workshop, June 2007. Slide 16 of 14.
At large horizontal scales, b and pu have larger vertical scales than and pr.
• Expect b < • Expect pu 0
(apart from at large vertical scales).
ECMWF flow dependent workshop, June 2007. Slide 17 of 14.