Editorial Type:
Article
Article Type:
Research Article

A Comparison of Statistical Dynamical and Ensemble Prediction Methods during Blocking

Terence J. O’Kane CSIRO Marine and Atmospheric Research, Aspendale, Australia

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Jorgen S. Frederiksen CSIRO Marine and Atmospheric Research, Aspendale, Australia

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Print Publication:
01 Feb 2008
DOI:
https://doi.org/10.1175/2007JAS2300.1
Page(s):
426–447
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Abstract

In this paper error growth is examined using a family of inhomogeneous statistical closure models based on the quasi-diagonal direct interaction approximation (QDIA), and the results are compared with those based on ensembles of direct numerical simulations using bred perturbations. The closure model herein includes contributions from non-Gaussian terms, is realizable, and conserves kinetic energy and enstrophy. Further, unlike previous approximations, such as those based on cumulant-discard (CD) and quasi-normal (QN) hypotheses (Epstein and Fleming), the QDIA closure is stable for long integration times and is valid for both strongly non-Gaussian and strongly inhomogeneous flows. The performance of a number of variants of the closure model, incorporating different approximations to the higher-order cumulants, is examined. The roles of non-Gaussian initial perturbations and small-scale noise in determining error growth are examined. The importance of the cumulative contribution of non-Gaussian terms to the evolved error tendency is demonstrated, as well as the role of the off-diagonal covariances in the growth of errors. Cumulative and instantaneous errors are quantified using kinetic energy spectra and a small-scale palinstrophy production measure, respectively. As a severe test of the methodology herein, synoptic situations during a rapid regime transition associated with the formation of a block over the Gulf of Alaska are considered. In general, the full QDIA closure results compare well with the statistics of direct numerical simulations.

* Current affiliation: Centre for Australian Weather and Climate Research, Bureau of Meteorology, Melbourne, Australia

Corresponding author address: Terence J. O’Kane, CAWCR, Bureau of Meteorology, 700 Collins St., Docklands 3008, Australia. Email: t.okane@bom.gov.au

Abstract

In this paper error growth is examined using a family of inhomogeneous statistical closure models based on the quasi-diagonal direct interaction approximation (QDIA), and the results are compared with those based on ensembles of direct numerical simulations using bred perturbations. The closure model herein includes contributions from non-Gaussian terms, is realizable, and conserves kinetic energy and enstrophy. Further, unlike previous approximations, such as those based on cumulant-discard (CD) and quasi-normal (QN) hypotheses (Epstein and Fleming), the QDIA closure is stable for long integration times and is valid for both strongly non-Gaussian and strongly inhomogeneous flows. The performance of a number of variants of the closure model, incorporating different approximations to the higher-order cumulants, is examined. The roles of non-Gaussian initial perturbations and small-scale noise in determining error growth are examined. The importance of the cumulative contribution of non-Gaussian terms to the evolved error tendency is demonstrated, as well as the role of the off-diagonal covariances in the growth of errors. Cumulative and instantaneous errors are quantified using kinetic energy spectra and a small-scale palinstrophy production measure, respectively. As a severe test of the methodology herein, synoptic situations during a rapid regime transition associated with the formation of a block over the Gulf of Alaska are considered. In general, the full QDIA closure results compare well with the statistics of direct numerical simulations.

* Current affiliation: Centre for Australian Weather and Climate Research, Bureau of Meteorology, Melbourne, Australia

Corresponding author address: Terence J. O’Kane, CAWCR, Bureau of Meteorology, 700 Collins St., Docklands 3008, Australia. Email: t.okane@bom.gov.au

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