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  • Author or Editor: Terence J. O’Kane x
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Terence J. O’Kane
and
Jorgen S. Frederiksen

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.

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Courtney Quinn
,
Dylan Harries
, and
Terence J. O’Kane

Abstract

The dynamics of the North Atlantic Oscillation (NAO) are analyzed through a data-driven model obtained from atmospheric reanalysis data. We apply a regularized vector autoregressive clustering technique to identify recurrent and persistent states of atmospheric circulation patterns in the North Atlantic sector (20°–90°N, 110°W–0°). To analyze the dynamics associated with the resulting cluster-based models, we define a time-dependent linear delayed map with a switching sequence set a priori by the cluster affiliations at each time step. Using a method for computing the covariant Lyapunov vectors (CLVs) over various time windows, we produce sets of mixed singular vectors (for short windows) and approximate the asymptotic CLVs (for longer windows). The growth rates and alignment of the resulting time-dependent vectors are then analyzed. We find that the window chosen to compute the vectors acts as a filter on the dynamics. For short windows, the alignment and changes in growth rates are indicative of individual transitions between persistent states. For long windows, we observe an emergent annual signal manifest in the alignment of the CLVs characteristic of the observed seasonality in the NAO index. Analysis of the average finite-time dimension reveals the NAO as the most unstable state relative to the NAO+, with persistent AR states largely stable. Our results agree with other recent theoretical and empirical studies that have shown blocking events to have less predictability than periods of enhanced zonal flow.

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Vassili Kitsios
,
Terence J. O’Kane
, and
Nedjeljka Žagar

Abstract

The Madden–Julian oscillation (MJO) is presented as a series of interacting Rossby and inertial gravity waves of varying vertical scales and meridional extents. These components are isolated by decomposing reanalysis fields into a set of normal mode functions (NMF), which are orthogonal eigenvectors of the linearized primitive equations on a sphere. The NMFs that demonstrate spatial properties compatible with the MJO are inertial gravity waves of zonal wavenumber k = 1 and the lowest meridional index n = 0, and Rossby waves with (k, n) = (1, 1). For these horizontal scales, there are multiple small vertical-scale baroclinic modes that have temporal properties indicative of the MJO. On the basis of one such eastward-propagating inertial gravity wave (i.e., a Kelvin wave), composite averages of the Japanese 55-year Reanalysis demonstrate an eastward propagation of the velocity potential, and oscillation of outgoing longwave radiation and precipitation fields over the Maritime Continent, with an MJO-appropriate temporal period. A cross-spectral analysis indicates that only the MJO time scale is coherent between this Kelvin wave and the more energetic modes. Four mode clusters are identified: Kelvin waves of correct phase period and direction, Rossby waves of correct phase period, energetic Kelvin waves of larger vertical scales and meridional extents extending into the extratropics, and energetic Rossby waves of spatial scales similar to that of the energetic Kelvin waves. We propose that within this normal mode framework, nonlinear interactions between the aforementioned mode groups are required to produce an energetic MJO propagating eastward with an intraseasonal phase period. By virtue of the selected mode groups, this theory encompasses both multiscale and tropical–extratropical interactions.

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Terence J. O’Kane
,
James S. Risbey
,
Christian Franzke
,
Illia Horenko
, and
Didier P. Monselesan

Abstract

Changes in the metastability of the Southern Hemisphere 500-hPa circulation are examined using both cluster analysis techniques and split-flow blocking indices. The cluster methodology is a purely data-driven approach for parameterization whereby a multiscale approximation to nonstationary dynamical processes is achieved through optimal sequences of locally stationary fast vector autoregressive factor (VARX) processes and some slow (or persistent) hidden process switching between them. Comparison is made with blocking indices commonly used in weather forecasting and climate analysis to identify dynamically relevant metastable regimes in the 500-hPa circulation in both reanalysis and Atmospheric Model Intercomparison Project (AMIP) datasets. The analysis characterizes the metastable regime in both reanalysis and model datasets prior to 1978 as positive and negative phases of a hemispheric midlatitude blocking state with the southern annular mode (SAM) associated with a transition state. Post-1978, the SAM emerges as a true metastable state replacing the negative phase of the hemispheric blocking pattern. The hidden state frequency of occurrences exhibits strong trends. The blocking pattern dominates in the early 1980s, and then gradually decreases. There is a corresponding increase in the SAM frequency of occurrence. This trend is largely evident in the reanalysis summer and spring but was not evident in the AMIP dataset. Further comparison with the split-flow blocking indices reveals a superficial correspondence between the cluster hidden state frequency of occurrences and split-flow indices. Examination of composite states shows that the blocking indices capture splitting of the zonal flow whereas the cluster composites reflect coherent block formation. Differences in blocking climatologies from the respective methods are discussed.

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James S. Risbey
,
Terence J. O’Kane
,
Didier P. Monselesan
,
Christian Franzke
, and
Illia Horenko

Abstract

This study applies a finite-element, bounded-variation, vector autoregressive method to assess midtropospheric flow regimes characterized by regime switches between metastable states. The flow is assessed in reanalysis data from three different reanalysis sets assimilating surface data only; surface and upper-air data; and ocean, surface, and upper-air data. Results are generally consistent across the reanalyses and confirm the utility of surface-only reanalyses for capturing midtropospheric variability. The method is applied to a set of regional domains in the Northern Hemisphere and for the full-hemispheric domain. Composites of the metastable states for each region yield structures that are consistent with the well-documented teleconnection modes: the North Atlantic Oscillation in the Atlantic Ocean, the Pacific–North America pattern (PNA) in the Pacific Ocean, and Scandinavian blocking over Eurasia. The PNA mode includes a clear waveguide structure in midlatitudes. The Northern Hemisphere domain yields a state composite that reflects aspects of an annular mode (Arctic Oscillation), where the annular component in midlatitudes comprises a circumglobal waveguide. The Northern Hemisphere waveguide is characterized by wavenumber 5. Some of the nodes in this circumglobal waveguide manifest as part of regional dipole structures like the PNA. This situation contrasts with the Southern Hemisphere, where the circumglobal waveguide exhibits wavenumbers 3 and 5 and is monopolar. For each of the regions and modes examined, the annual time series of residence percent in each state displays prominent decadal variability and provides a clear means of identifying regimes of the major teleconnection modes.

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