Intrinsic Low-frequency Variability Research Articles

Intrinsic Low-Frequency Variability in the Upper-Layer Circulation of the East Sea (Sea of Japan)

Abstract The effects of external forcing variation on the intrinsic variability in the upper-layer circulation occurring within the East Sea (Sea of Japan) and its physical mechanism are analyzed using numerical experiments. In this study, the experiments were conducted with climatological annual/monthly mean forcings (constant/seasonal forcings). The intrinsic variability is mainly distributed in the meandering regions around the main current path with the comparatively large variability limited to the southern region. The reason of greater intrinsic variability mainly in the southern part of the East Sea than in the northern part is that more energy is required from external forcings to change the thicker upper layer formed in the northern part due to seasonal forcings (strong wind stress and surface heat flux). Although the experiments show slight differences, westward propagation of the Rossby wave appears in areas where the variability is large. The transport of the eddy momentum flux associated with the Rossby wave modulates the strength of the eastward jet and the north–south shift of its axis. Among the external forcings, the volume transport through the Korea/Tsushima Strait is the most important driver of intrinsic variability, and wind stress plays an important role in expanding and strengthening intrinsic variability. Significance Statement Intrinsic variability is an important factor in understanding the total variability in the upper-layer circulation in the East Sea (Sea of Japan). However, the physical mechanisms of intrinsic variability remain unclear. This study investigates the physical mechanisms of intrinsic variability occurring within the East Sea. The intrinsic variability occurs mainly around the main current path, especially the meandering current. Based on numerical experiments, the mechanism of the intrinsic variability is represented by the fluctuation in the strength of the eastward current or the north–south movement of its axis caused by the Rossby wave.

Toward a Turbulence Closure Based on Energy Modes

AbstractA new approach to parameterizing subgrid-scale processes is proposed: The impact of the unresolved dynamics on the resolved dynamics (i.e., the eddy forcing) is represented by a series expansion in dynamical spatial modes that stem from the energy budget of the resolved dynamics. It is demonstrated that the convergence in these so-called energy modes is faster by orders of magnitude than the convergence in Fourier-type modes. Moreover, a novel way to test parameterizations in models is explored. The resolved dynamics and the corresponding instantaneous eddy forcing are defined via spatial filtering that accounts for the representation error of the equations of motion on the low-resolution model grid. In this way, closures can be tested within the high-resolution model, and the effects of different parameterizations related to different energy pathways can be isolated. In this study, the focus is on parameterizations of the baroclinic energy pathway. The corresponding standard closure in ocean models, the Gent–McWilliams (GM) parameterization, is also tested, and it is found that the GM field acts like a stabilizing direction in phase space. The GM field does not project well on the eddy forcing and hence fails to excite the model’s intrinsic low-frequency variability, but it is able to stabilize the model.

Ocean modelling and altimeter data reveal the possible occurrence of intrinsic low-frequency variability of the Kuroshio Extension

ABSTRACT In this paper the combined use of model simulations and altimeter data suggests that, during the interval 1998–2006, the Kuroshio Extension (KE) low-frequency variability was mainly of intrinsic origin. The model is based on the primitive equations for a reduced-gravity ocean, is eddy-permitting and relatively idealized, but it includes essential elements of realism and is driven by a time-independent climatological wind field, so that the modelled variability is necessarily of intrinsic oceanic origin. The altimeter data are provided by AVISO and include all the data available to date. A new composite index Λ[Φ] specifically conceived for the KE is used in the analysis of both model and altimeter data (Φ gives the mean latitudinal position of the KE jet and Λ is a measure of the high-frequency variability of the KE path). A set of sensitivity numerical experiments shows that the frontal dynamics is extremely sensitive to the horizontal eddy viscosity. A self-sustained relaxation oscillation emerging from a reference simulation is represented by a loop in the (Λ, Φ)-plane and is characterized by four phases, each one being controlled by a specific dynamical mechanism. An interval ranging from January 1998 to March 2006 is identified in the altimeter data, during which the altimeter-derived index is very similar to the modelled one. A detailed analysis based also on sea surface height maps shows that the real KE evolution possesses four phases characterized by basically the same dynamical behaviour recognized in the model loop. The conclusion is that, during that interval, the KE dynamics was controlled by an oceanic intrinsic mode of low-frequency variability and that the directly driven dynamics and ocean-atmosphere coupled modes of variability did not overshadow the intrinsic evolution. The self-sustained vs excited character of the relaxation oscillation is finally discussed.

Intrinsic low-frequency variability and predictability of the Kuroshio Current and of its extension

Investigations of the intrinsic low-frequency variability and predictability of the Kuroshio Current and of its extension jet (the Kuroshio Extension, KE) are reviewed. The Kuroshio and KE in the North Pacific constitute a western boundary current system of great relevance from climatological and ecological viewpoints. Both the Kuroshio south of Japan and the KE display remarkable changes of bimodal character on interannual time scales that are believed to be intrinsic, i.e., basically generated by nonlinear oceanic mechanisms rather than by direct atmospheric forcing. Model studies of the Kuroshio and KE with climatological forcing are thus reviewed. Moreover, as these changes are chaotic, their predictability requires peculiar mathematical approaches: theoretical results concerning this important issue are therefore reviewed as well. Model studies aimed at determining the optimal precursors and optimally growing initial errors for the Kuroshio are described. Techniques based on Lyapunov exponents (including their Lagrangian extension) and on data assimilation techniques (namely, sequential importance sampling using a particle-filtering approach) are reviewed for the KE. The key problem of how to identify the areas where targeted observations can improve the forecast is also addressed. The role of wind forcing in triggering the KE oscillations is finally considered.

Geostrophic Turbulence in the Frequency–Wavenumber Domain: Eddy-Driven Low-Frequency Variability*

Abstract Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

Intrinsic low-frequency variability and predictability of the Kuroshio Current and of its extension

Intrinsic low-frequency variability and predictability of the Kuroshio Current and of its extension

Low frequency variability in an coupled ocean-sea ice general circulation model of the Southern Ocean

A coupled ocean-sea ice general circulation model is used to identify a Southern Ocean southeast Pacific intrinsic mode of low frequency variability and its response to inter-annual atmospheric forcing. Using forcing data from the co-ordinated ocean-ice reference experiment, a comprehensive suite of experiments elucidated excitation and amplification mechanisms of this intrinsic mode by low frequency forcing and stochastic forcing due to high frequency winds. Subsurface thermocline anomalies are found to teleconnect the Pacific and Atlantic regions of the Antarctic circumpolar current (ACC). It is found that the Pacific region of the ACC is characterised by intrinsic baroclinic disturbances that respond to both zonal and latitudinal wind variations, while the Atlantic sector of the ACC is sensitive to higher frequency synoptic winds that act to amplify thermocline anomalies propagating downstream from the Pacific resonant with eastward travelling Rossby waves. This simulation study identifies plausible mechanisms that determine the predictability of the Southern Ocean climate on multi-decadal timescales. References T. Delworth, A. J. Broccoli, A. Rosati, R. J. Stouffer, V. Balaji, J. A. Beesley, W. F. Cooke, and K. W. Dixon. GFDL's CM2 global coupled climate models. Part 1: Formulation and simulation characteristics. J. Climate, 19:643--674, 2006. doi:10.1175/JCLI3629.1 H. Dijkstra and M. Ghil. Low-frequency variability of the largescale ocean circulation: A dynamical systems approach. Rev. Geophys., 43 RG3002, 2005. doi:10.1029/2002RG000122 C. W. Hughes. Rossby waves in the Southern Ocean: A comparison of TOPEX/POSEIDON altimetry with model predictions. J. Geophys. Res., 100:15933--15950, 1995. doi:10.1029/95JC01380 W. G. Large, J. C. McWilliams, and S. C. Doney. Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32:363--403, 1994. doi:10.1029/94RG01872 W. G. Large and S. G. Yeager. Diurnal to decadal global forcing for ocean and sea-ice models: the datasets and flux climatologies. NCAR Technical Note:, NCAR/TN-460+STR, CGD Division of the National Centre for Atmospheric Research, 2004. doi:10.5065/D6KK98Q6 T. J. McDougall and P. C. McIntosh. The temporal-residual-mean velocity. Part I: Derivation and the scalar conservation equations. J. Phys. Oceanogr., 26:2653--2665, 1996. doi:10.1175/1520-0485(1996)026<2653:TTRMVP>2.0.CO;2 R. J. Murray. Explicit generation of orthogonal grids for ocean models. Journal of Computational Physics, 126:251--273, 1996. doi:10.1006/jcph.1996.0136 A. B. Pezza, H. A. Rashid, and I. Simmonds. Climate links and recent extremes in antarctic sea ice, high-latitude cyclones, southern annular mode and ENSO. Climate Dynamics, 38:57--73, 2012. doi:10.1007/s00382-011-1044-y G. Quattrocchi, S. Pierini, and H. A. Dijkstra. Intrinsic low-frequency variability of the gulf stream. Nonlinear Processes in Geophysics, 19:155--164, 2012. doi:10.5194/npg-19-155-2012 A. Timmermann. Changes of ENSO stability due to greenhouse warming. Geophys. Res. Let., 28:2061--2064, 2001. doi:10.1029/2001GL012879

Intrinsic low-frequency variability of the Gulf Stream

Abstract. In this paper a process study aimed at analyzing the low-frequency variability of intrinsically oceanic origin of the Gulf Stream (GS) and GS extension (GSE) is presented. An eddy-permitting reduced-gravity nonlinear shallow water model is implemented in an idealized North Atlantic Ocean, with schematic boundaries including the essential geometric features of the coastline and a realistic zonal basin width at all latitudes. The forcing is provided by a time-independent climatological surface wind stress obtained from 41 years of monthly ECMWF fields. The model response yields strong intrinsic low-frequency fluctuations on the interannual to decadal time scales. The modelled time-averaged GS/GSE flows are found to exhibit several features that can also be deduced from satellite altimeter data, such as the Florida Current seaward deflection, the GS separation at Cape Hatteras, and the overall structure of the GSE. The intrinsic low-frequency variability yields two preferred states of the GSE differing in latitudinal location that also have their counterpart in the altimeter data. A preliminary analysis of the variability in terms of dynamical systems theory is carried out by using the lateral eddy viscosity as the control parameter. A complex transition sequence from a steady state to irregular low-frequency variability emerges, in which Hopf and global bifurcations can be identified.

Low-Frequency Variability, Coherence Resonance, and Phase Selection in a Low-Order Model of the Wind-Driven Ocean Circulation

Abstract In this paper, a low-order spectral quasigeostrophic (QG) model of the wind-driven ocean circulation is derived and used to analyze the low-order character of the intrinsic low-frequency variability of the midlatitude double-gyre ocean circulation and of the related coherence resonance and phase selection phenomena. The model includes an exponential in the basis functions that allows for westward intensification, retains only four modes in the Galerkin projection, is defined in a rectangular domain, and is forced by deterministic and stochastic winds, thus extending previous low-order QG ocean models. The solution under steady forcing is first obtained, and the results are also analyzed in terms of dynamical systems theory. A homoclinic bifurcation (with the wind amplitude chosen as the control parameter) leads to intrinsic decadal relaxation oscillations (ROs) similar in several respects to those obtained with primitive equation models. The system is then forced with an additional red noise wind, and, in a parameter range preceding the global bifurcation, a coherence resonance scenario very similar to the one found with a primitive equation model of the Kuroshio Extension is obtained: this suggests that such a phenomenon is of low-order character. To study the RO excitation mechanism, a method denoted as phase selection is proposed. The system is forced with additional fictitious periodic winds that produce an emergence of ROs yielding strong phase dependence with the periodic forcing. The subsequent analysis reveals the character of the wind forcing that is most likely to excite a RO. All the results are discussed within the general framework of climate dynamics.

Low-Frequency Variability, Coherence Resonance and Phase Selection in a Low-Order Model of the Wind-Driven Ocean Circulation

In this paper, a low-order spectral quasigeostrophic (QG) model of the wind-driven ocean circulation is derived and used to analyze the low-order character of the intrinsic low-frequency variability of the midlatitude double-gyre ocean circulation and of the related coherence resonance and phase selection phenomena. The model includes an exponential in the basis functions that allows for westward intensification, retains only four modes in the Galerkin projection, is defined in a rectangular domain, and is forced by deterministic and stochastic winds, thus extending previous low-order QG ocean models. The solution under steady forcing is first obtained, and the results are also analyzed in terms of dynamical systems theory. A homoclinic bifurcation (with the wind amplitude chosen as the control parameter) leads to intrinsic decadal relaxation oscillations (ROs) similar in several respects to those obtained with primitive equation models. The system is then forced with an additional red noise wind, and, in a parameter range preceding the global bifurcation, a coherence resonance scenario very similar to the one found with a primitive equation model of the Kuroshio Extension is obtained: this suggests that such a phenomenon is of low-order character. To study the RO excitation mechanism, a method denoted as phase selection is proposed. The system is forced with additional fictitious periodic winds that produce an emergence of ROs yielding strong phase dependence with the periodic forcing. The subsequent analysis reveals the character of the wind forcing that is most likely to excite a RO. All the results are discussed within the general framework of climate dynamics.

Coherence Resonance in a Double-Gyre Model of the Kuroshio Extension

Abstract The effect of stochastic winds on the intrinsic low-frequency variability of the Kuroshio Extension (KE) is analyzed through a double-gyre (DG) model forced by a steady climatological wind plus an idealized Ornstein–Uhlenbeck wind noise. A DG model of the KE bimodality, whose results compare well to altimeter data, is first shown to be an excitable system. In fact, the relaxation oscillation (forced by steady winds) with decadal time scale that describes the bimodality is recognized to be an internal mode of the system, which can be excited also in a dissipative parameter range (PR) in which it does not arise spontaneously, provided appropriate initial conditions are chosen. It is then shown that, if the additive wind noise is included in the forcing, the actual excitation of the relaxation oscillation in PR occurs if the noise is red with a decorrelation time greater than a minimum time scale ranging from 1 month to 1 year, depending on the dissipation. This behavior, known as “coherence resonance,” is likely to be paradigmatic of the low-frequency variability of western boundary current extensions of intrinsic origin, when it is in the form of relaxation oscillations resulting from a homoclinic bifurcation. General considerations concerning the interpretation of model results obtained within different parameter ranges are applied to this study.

On the Crucial Role of Basin Geometry in Double-Gyre Models of the Kuroshio Extension

Abstract The decadal chaotic relaxation oscillation obtained in a recent double-gyre model study of the Kuroshio Extension intrinsic low-frequency variability was found to compare surprisingly well with the real variability of the jet as revealed by altimeter data, despite the high degree of idealization of the model. In this note it is shown that elements of realism in the basin geometry, present in that study and absent in previous double-gyre models applied to the Kuroshio Extension, play a crucial role in shaping the low-frequency variability of the jet, and can explain the good performance of the model. A series of numerical experiments with different basin geometries of increasing degrees of simplicity are analyzed. If the schematic western boundary representing the coastline south of Japan is removed, the strong decadal variability completely disappears and only a very weak periodic oscillation about an elongated state of the jet is found. If the large zonal width of the basin (representing correctly the extension of the North Pacific Ocean) is reduced by a half, then the total meridional Sverdrup transport is reduced by the same factor, and so is the intensity of the Kuroshio and Oyashio western boundary currents: as a result, the modeled Kuroshio Extension is totally unrealistic in shape and is steady. If both simplifications are introduced the resulting jet is, again, totally unrealistic, yielding a weak periodic bimodal cycle. On the basis of these results, two main conclusions are drawn: (i) the introduction of appropriate geometrical elements of realism in double-gyre model studies of the Kuroshio Extension is essential, and (ii) the Kuroshio Extension intrinsic low-frequency variability would be dramatically different if the southwestern coastline of Japan were more meridionally oriented.

A highly nonlinear coupled mode of decadal variability in a mid-latitude ocean–atmosphere model

This study examines mid-latitude climate variability in a model that couples turbulent oceanic and atmospheric flows through an active oceanic mixed layer. Intrinsic ocean dynamics of the inertial recirculation regions combines with nonlinear atmospheric sensitivity to sea-surface temperature (SST) anomalies to play a dominant role in the variability of the coupled system. Intrinsic low-frequency variability arises in the model atmosphere; when run in a stand-alone mode, it is characterized by irregular transitions between preferred high-latitude and less frequent low-latitude zonal-flow states. When the atmosphere is coupled to the ocean, the low-latitude state occurrences exhibit a statistically significant signal in a broad 5–15-year band. A similar signal is found in the time series of the model ocean's energy in this coupled simulation. Accompanying uncoupled ocean-only and atmosphere-only integrations are characterized by a decrease in the decadal-band variability, relative to the coupled integration; their spectra are indistinguishable from a red spectrum. The time scale of the coupled interdecadal oscillation is set by the nonlinear adjustment of the ocean's inertial recirculations to the high-latitude and low-latitude atmospheric forcing regimes. This adjustment involves, in turn, SST changes resulting in long-term ocean–atmosphere heat-flux anomalies that induce the atmospheric regime transitions.

Wind-driven ocean circulation in shallow water lattice Boltzmann model

A lattice Boltzmann (LB) model with overall second-order accuracy is applied to the 1.5-layer shallow water equation for a wind-driven double-gyre ocean circulation. By introducing the second-order integral approximation for the collision operator, the model becomes fully explicit. In this case, any iterative technique is not needed. The Coriolis force and other external forces are included in the model with second-order accuracy, which is consistent with the discretized accuracy of the LB equation. The numerical results show correct physics of the ocean circulation driven by the double-gyre wind stress with different Reynolds numbers and different spatial resolutions. An intrinsic low-frequency variability of the shallow water model is also found. The wind-driven ocean circulation exhibits subannual and interannual oscillations, which are comparable to those of models in which the conventional numerical methods are used.

Exploring Coupled Atmosphere-Ocean Models Using Vis5D

A distributed client/server system can be used to visualize very large simulation data sets. An example of a very large simulation data set is a 100-year simulation of the Earth's coupled atmosphere-ocean system. This model run was produced by an Argonne National Laboratory/University of Wisconsin collaborative project that is studying atmosphere-ocean coupling dynamics to understand the intrinsic low-frequency variability of the climate system. This understanding is crucial for the prediction and detec tion of human impacts on the Earth's climate. To visually explore this simulation, an IBM SP-2 is used as a data server and a pair of SGI Onyxes driving a CAVE are used as a graphics client. The SP-2 server divides the data set into sections that will fit in the memory of the graphics client. The data set is divided along the time axis. One data set section covers the entire 100-year span of the simula tion at reduced-time resolution, while the other data set sections cover short subintervals at full-time resolution. The visualization user interface allows users to switch between low and high time resolution.