A Comparison of Statistical Dynamical and Ensemble Prediction Methods during Blocking

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.

The Australian community climate and earth system simulator global and regional ensemble prediction scheme

“…O'Kane & Frederiksen [9] considered cases for which fast growing disturbances occur and examined the role of higher order moments in non-Gaussian flows. Such cases are typified by the reduced predictability associated with the formation and decay of large scale coherent structures in the atmosphere evident as high-low blocking dipoles [8].…”

“…More recent approaches endeavor to generate independent initial perturbations as fast growing disturbances with structures and growth rates typical of the analysis errors such as the 'breeding' method developed by Toth & Kalnay [13]. This method of bred initial forecast perturbations allows information about the fast growing errors to be incorporated into the initial perturbations for the forecast [8]. For particularly dynamic flows, such as when emergent coherent structures are developing, errors arise due to fast growing large scale instabilities.…”

Entropy, Closures and Subgrid Modeling

“…Recently, subgrid-scale parameterizations based on a stochastic modeling approach have also been shown by Frederiksen & Kepert (2006) [133] to yield results very similar to those based on renormalized closures [57]. In recent years there has also been increasing interest in exploring how parameterizations of stochastic backscatter may improve weather and climate predictions and simulations (Frederiksen & Davies (1997) [71]). Holloway (1992) [140], hereafter H1992, developed a simple heuristic parameterization for the interaction of subgrid-scale eddies in oceanic flows with resolved scale topography.…”

“…Their performance has been compared with direct numerical simulations and experimental data (e.g., Herring et al (1974) [62], Pouquet et al (1975) [63], Kraichnan & Herring (1978) [64], McComb (1990) [65], McComb et al (1992) [46], Frederiksen, Davies & Bell (1994) [52], Frederiksen & Davies (2000, 2004 [66,67]). Importantly turbulence closures allow the study of the statistics of the predictability of homogeneous turbulent flows (Kraichnan (1970) [68], Leith (1971Leith ( , 1974 [55,69], Leith & Kraichnan (1972) [60], Métais & Lesieur (1986) [70]) and most recently of inhomogeneous turbulent flows (O'Kane & Frederiksen (2008a) [71]). Kraichnan's (1958 [41,42] DIA closure was derived through heuristic methods as reviewed by Frederiksen (2003) [72].…”

“…However, a one parameter regularization of the DIA, or empirical vertex renormalization, following the suggestion of [90], results in good agreement between the regularized DIA (RDIA) and DNS (Frederiksen & Davies (2004) [67]). Furthermore, the regularization parameter is almost universal for both homogeneous (Frederiksen & Davies (2004) [67]) and inhomogeneous turbulence (O' Kane & Frederiksen (2004, 2008a [71,88]). Frederiksen & Davies (2004) [67] note that their RDIA closure generally performs better than quasi-Lagrangian closures.…”