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Reading: Ensemble covariances adaptively localized with ECO-RAP. Part 2: a strategy for the atmosphere

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Original Research Papers

Ensemble covariances adaptively localized with ECO-RAP. Part 2: a strategy for the atmosphere

Authors:

Craig H. Bishop ,

Naval Research Laboratory, Marine Meteorology Division, 7 Grace Hopper Ave, Stop 2, Building 702, Room 212, Monterey, CA 93943-5502, US
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Daniel Hodyss

Naval Research Laboratory, Marine Meteorology Division, 7 Grace Hopper Ave, Stop 2, Building 702, Room 212, Monterey, CA 93943-5502, US
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Abstract

Part 1’s localization method, Ensemble COrrelations Raised to A Power (ECO-RAP), is incorporated into a Local Ensemble Transform Kalman Filter (LETKF). Because brute force incorporation would be too expensive, we demonstrate a factorization property for Part 1’s Covariances Adaptively Localized with ECO-rap (CALECO) forecast error covariance matrix that, together with other simplifications, reduces the cost. The property inexpensively provides a large CALECO ensemble whose covariance is the CALECO matrix. Each member of the CALECO ensemble is an element-wise product between one raw ensemble member and one column of the square root of the ECO-RAP matrix. The LETKF is applied to the CALECO ensemble rather than the raw ensemble. The approach enables the update of large numbers of variables within each observation volume at little additional computational cost. Under plausible assumptions, this makes the CALECO and standard LETKF costs similar. The CALECO LETKF does not require artificial observation error inflation or vertically confined observation volumes both of which confound the assimilation of non-local observations such as satellite observations. Using a 27 member ensemble from a global NumericalWeather Prediction (NWP) system, we depict four-dimensional (4-D) flow-adaptive error covariance localization and test the ability of the CALECO LETKF to reduce analysis error.

How to Cite: Bishop, C.H. and Hodyss, D., 2009. Ensemble covariances adaptively localized with ECO-RAP. Part 2: a strategy for the atmosphere. Tellus A: Dynamic Meteorology and Oceanography, 61(1), pp.97–111. DOI: http://doi.org/10.1111/j.1600-0870.2007.00372.x
  Published on 01 Jan 2009
 Accepted on 30 Sep 2008            Submitted on 17 Apr 2008

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