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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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Jiale Lou
,
Terence J. O’Kane
, and
Neil J. Holbrook

Abstract

A stochastically forced linear inverse model (LIM) of the combined modes of variability from the tropical and South Pacific Oceans is used to investigate the linear growth of optimal initial perturbations and to identify the spatiotemporal features of the stochastic forcing associated with the atmospheric Pacific–South American patterns 1 and 2 (PSA1 and PSA2). Optimal initial perturbations are shown to project onto El Niño–Southern Oscillation (ENSO) and South Pacific decadal oscillation (SPDO), where the inclusion of subsurface South Pacific Ocean temperature variability significantly increases the multiyear linear predictability of the deterministic system. We show that the optimal extratropical sea surface temperature (SST) precursor is associated with the South Pacific meridional mode, which takes from 7 to 9 months to linearly evolve into the final ENSO and SPDO peaks in both the observations and as simulated in an atmosphere-forced ocean model. The optimal subsurface precursor resembles its peak phase, but with a weak amplitude, representing oceanic Rossby waves in the extratropical South Pacific. The stochastic forcing is estimated as the residual by removing the deterministic dynamics from the actual tendency under a centered difference approximation. The resulting stochastic forcing time series satisfies the Gaussian white noise assumption of the LIM. We show that the PSA-like variability is strongly associated with stochastic SST forcing in the tropical and South Pacific Oceans and contributes not only to excite the optimal initial perturbations associated with ENSO and the SPDO but in general to activate the entire stochastic SST forcing, especially in austral summer.

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Jiale Lou
,
Neil J. Holbrook
, and
Terence J. O’Kane

Abstract

The South Pacific decadal oscillation (SPDO) characterizes the Southern Hemisphere contribution to the Pacific-wide interdecadal Pacific oscillation (IPO) and is analogous to the Pacific decadal oscillation (PDO) centered in the North Pacific. In this study, upper ocean variability and potential predictability of the SPDO is examined in HadISST data and an atmosphere-forced ocean general circulation model. The potential predictability of the IPO-related variability is investigated in terms of both the fractional contribution made by the decadal component in the South, tropical and North Pacific Oceans and in terms of a doubly integrated first-order autoregressive (AR1) model. Despite explaining a smaller fraction of the total variance, we find larger potential predictability of the SPDO relative to the PDO. We identify distinct local drivers in the western subtropical South Pacific, where nonlinear baroclinic Rossby wave–topographic interactions act to low-pass filter decadal variability. In particular, we show that the Kermadec Ridge in the southwest Pacific enhances the decadal signature more prominently than anywhere else in the Pacific basin. Applying the doubly integrated AR1 model, we demonstrate that variability associated with the Pacific–South American pattern is a critically important atmospheric driver of the SPDO via a reddening process analogous to the relationship between the Aleutian low and PDO in the North Pacific—albeit that the relationship in the South Pacific appears to be even stronger. Our results point to the largely unrecognized importance of South Pacific processes as a key source of decadal variability and predictability.

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Jiale Lou
,
Terence J. O’Kane
, and
Neil J. Holbrook

Abstract

A multivariate linear inverse model (LIM) is developed to demonstrate the mechanisms and seasonal predictability of the dominant modes of variability from the tropical and South Pacific Oceans. We construct a LIM whose covariance matrix is a combination of principal components derived from tropical and extratropical sea surface temperature, and South Pacific Ocean vertically averaged temperature anomalies. Eigen-decomposition of the linear deterministic system yields stationary and/or propagating eigenmodes, of which the least damped modes resemble El Niño–Southern Oscillation (ENSO) and the South Pacific decadal oscillation (SPDO). We show that although the oscillatory periods of ENSO and SPDO are distinct, they have very close damping time scales, indicating that the predictive skill of the surface ENSO and SPDO is comparable. The most damped noise modes occur in the midlatitude South Pacific Ocean, reflecting atmospheric eastward-propagating Rossby wave train variability. We argue that these ocean wave trains occur due to the high-frequency atmospheric variability of the Pacific–South American pattern imprinting onto the surface ocean. The ENSO spring predictability barrier is apparent in LIM predictions initialized in March–May (MAM) but displays a significant correlation skill of up to ~3 months. For the SPDO, the predictability barrier tends to appear in June–September (JAS), indicating remote but delayed influences from the tropics. We demonstrate that subsurface processes in the South Pacific Ocean are the main source of decadal variability and further that by characterizing the upper ocean temperature contribution in the LIM, the seasonal predictability of both ENSO and the SPDO variability is increased.

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Terence J. O’Kane
,
Russell Fiedler
,
Mark A. Collier
, and
Vassili Kitsios

Abstract

Recent studies of various stochastic forcing and subgrid-scale parameterization schemes applied to climate and atmospheric models have revealed a diversity of model responses. These responses include degeneracy in the response to different forcings and compensating model errors. While stochastic parameterization of the ocean eddies is an active area, this has mainly involved idealized models with fewer studies employing ocean general circulation models. Here we examine the sensitivity of a low-resolution climate model to stochastic forcing of the momentum fluxes restricted to regions of the three-dimensional ocean where an eddy-resolving ocean model configuration has high variability. We consider the changes in the modeled energetics of low-resolution simulations in response to increased stochastic forcing. We find that as forcing amplitudes are increased there is enhanced conversion of transient to seasonal potential energy. Additionally, there is a systematic redistribution from seasonal to small-scale transient kinetic energy. Our approach has zero mean noise such that the total kinetic energy spectra remain largely unchanged even as small-scale eddy kinetic energy is increased in the targeted regions. However, we also show that strong stochastic forcing, particularly when applied in the tropics, can induce substantial changes to the ocean steady state that are undesirable. These changes include overly strong vertical mixing leading to unrealistic increases in ocean heat content and latitudinally dependent changes to sea level. We show that judicious selection of the magnitude and spatial extent of the stochastic forcing is required for desirable results. Our results point to the importance of a comprehensive evaluation of ocean model responses to stochastic parameterizations.

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Terence J. O’Kane
,
Didier P. Monselesan
, and
James S. Risbey

Abstract

The authors undertake a multiscale spectral reexamination of the variability of the Pacific–South American (PSA) pattern and the mechanisms by which this variability occurs. Time scales from synoptic to interannual are investigated, focusing on the means by which tropical variability is communicated to the midlatitudes and on in situ forcing within the midlatitude waveguides. Particular interest is paid to what fraction of the total variability associated with the PSA, occurring on interannual time scales, is attributable to tropical forcing relative to that occurring on synoptic and intraseasonal time scales via internal waveguide dynamics. In general, it is found that the eastward-propagating wave train pattern typically associated with the PSA manifests across time scales from synoptic to interannual, with the majority of the variability occurring on synoptic-to-intraseasonal time scales largely independent of tropical convection. It is found that the small fraction of the total variance with a tropical signal occurs via the zonal component of the thermal wind modulating both the subtropical and polar jets. The respective roles of the Hadley circulation and stationary Rossby wave sources are also examined. Further, a PSA-like mode is identified in terms of the slow components of higher-order modes of tropospheric geopotential height. This study reestablishes the multiscale nonlinear nature of the PSA modes arising largely as a manifestation of internal midlatitude waveguide dynamics and local disturbances.

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Paul A. Sandery
,
Terence J. O’Kane
,
Vassili Kitsios
, and
Pavel Sakov

Abstract

Data assimilation (DA) experiments are performed to assess impacts of observations in climate model state estimation through the cross-domain ocean–atmosphere forecast error covariances (cross covariances). Specifically, we explore strongly and weakly coupled DA variants using the Climate Analysis Forecast Ensemble (CAFE) system. This comprises 96 ensemble members of the Geophysical Fluid Dynamics Laboratory (GFDL) CM2.1 climate model assimilating observational data from the ocean, atmosphere, and sea ice realms with the ensemble Kalman filter (EnKF). Sequences of atmospheric synoptic time-scale coupled forecasts (7 days) are carried out with model consistent initialization. Unassimilated forward-independent observations are used to quantify forecast innovation error-growth rates. The results show benefit for the slow components of the atmosphere and ocean subsurface when strongly coupling ocean observations to the atmosphere. In the present system, projecting fast atmospheric observations onto the ocean subsurface through the cross covariances benefits the oceanic and atmospheric near-surface layers; however, this leads to deterioration in the ocean subsurface. Particular variants of coupled DA are able to constrain the ocean and atmosphere. The forecasts initialized with these variants have predictability at intraseasonal time scales. Errors associated with the dominant intraseasonal mode of variability, the Madden–Julian oscillation (MJO), are decomposed into normal mode functions. Consistent with recent studies showing large MJO events are concurrent with rapid error growth associated with nonlinear interactions, we find a clear relationship between the strength of a given MJO event and the related forecast innovations. Our results demonstrate consistent system behavior in relation to capturing real-world disturbances that affect climate predictability.

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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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