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Patrick Haertel
and
Alexey Fedorov

Abstract

Adiabatic theories of ocean circulation and density structure have a long tradition, from the concept of the ventilated thermocline to the notion that deep ocean ventilation is controlled by westerly winds over the Southern Ocean. This study explores these ideas using a recently developed Lagrangian ocean model (LOM), which simulates ocean motions by computing trajectories of water parcels. A unique feature of the LOM is its capacity to model ocean circulations in the adiabatic limit, in which water parcels exactly conserve their densities when they are not in contact with the ocean surface. The authors take advantage of this property of the LOM and consider the circulation and stratification that develop in an ocean with a fully adiabatic interior (with both isopycnal and diapycnal diffusivities set to zero). The ocean basin in the study mimics that of the Atlantic Ocean and includes a circumpolar channel. The model is forced by zonal wind stress and a density restoring at the surface.

Despite the idealized geometry, the relatively coarse model resolution, and the lack of atmospheric coupling, the nondiffusive ocean maintains a density structure and meridional overturning that are broadly in line with those observed in the Atlantic Ocean. These are generated by just a handful of key water pathways, including shallow tropical cells described by ventilated thermocline theory; a deep overturning cell in which sinking North Atlantic Deep Water eventually upwells in the Southern Ocean before returning northward as Antarctic Intermediate Water; a Deacon cell that results from a topographically steered and corkscrewing circumpolar current; and weakly overturning Antarctic Bottom Water, which is effectively ventilated only in the Southern Hemisphere.

The main conclusion of this study is that the adiabatic limit for the ocean interior provides the leading-order solution for ocean overturning and density structure, with tracer diffusion contributing first-order perturbations. Comparing nondiffusive and diffusive experiments helps to quantify the changes in stratification and circulation that result from adding a moderate amount of tracer diffusion in the ocean model, and these include an increase in the amplitude of the deep meridional overturning cell of several Sverdrups, a 10%–20% increase in Northern Hemispheric northward heat transport, a stronger stratification just below the main thermocline, and a more realistic bottom overturning cell.

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Alexey V. Fedorov

Abstract

How unstable is the tropical ocean–atmosphere system? Are two successive El Niño events independent, or are they part of a continual (perhaps weakly damped) cycle sustained by random atmospheric disturbances? How important is energy dissipation for ENSO dynamics? These closely related questions are frequently raised in connection with several climate problems ranging from El Niño predictability to the impact of atmospheric “noise” on ENSO. One of the factors influencing the system’s stability and other relevant properties is the damping (decay) time scale for the thermocline anomalies associated with the large-scale oceanic motion. Here this time scale is estimated by considering energy balance and net energy dissipation in the tropical ocean and it is shown that there are two distinct dissipative regimes: in the interannual frequency band the damping rate is approximately (2.3 yr)−1; however, in a near-annual frequency range the damping appears to be much stronger, roughly (8 months)−1.

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Alexey V. Fedorov

Abstract

Physical processes that control ENSO are relatively fast. For instance, it takes only several months for a Kelvin wave to cross the Pacific basin (Tk ≈ 2 months), while Rossby waves travel the same distance in about half a year. Compared to such short time scales, the typical periodicity of El Niño is much longer (T ≈ 2–7 yr). Thus, ENSO is fundamentally a low-frequency phenomenon in the context of these faster processes. Here, the author takes advantage of this fact and uses the smallness of the ratio ε k = Tk /T to expand solutions of the ocean shallow-water equations into power series (the actual parameter of expansion also includes the oceanic damping rate). Using such an expansion, referred to here as the low-frequency approximation, the author relates thermocline depth anomalies to temperature variations in the eastern equatorial Pacific via an explicit integral operator. This allows a simplified formulation of ENSO dynamics based on an integro-differential equation. Within this formulation, the author shows how the interplay between wind stress curl and oceanic damping rates affects 1) the amplitude and periodicity of El Niño and 2) the phase lag between variations in the equatorial warm water volume and SST in the eastern Pacific. A simple analytical expression is derived for the phase lag. Further, applying the low-frequency approximation to the observed variations in SST, the author computes thermocline depth anomalies in the western and eastern equatorial Pacific to show a good agreement with the observed variations in warm water volume. Ultimately, this approach provides a rigorous framework for deriving other simple models of ENSO (the delayed and recharge oscillators), highlights the limitations of such models, and can be easily used for decadal climate variability in the Pacific.

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Bowen Zhao
and
Alexey Fedorov

Abstract

Changes in background zonal wind in the tropical Pacific are often invoked to explain changes in ENSO properties. However, the sensitivity of ENSO to mean zonal winds has been thoroughly explored only in intermediate coupled models (following Zebiak and Cane), not in coupled GCMs. The role of mean meridional winds has received even less attention. Accordingly, the goal of this study is to examine systematically the effects of both zonal (equatorial) and meridional (cross-equatorial) background winds on ENSO using targeted experiments with a comprehensive climate model (CESM). Changes in the mean winds are generated by imposing heat flux forcing in two confined regions at a sufficient distance north and south of the equator. We find that the strengthening of either wind component reduces ENSO amplitude, especially eastern Pacific SST variability, and inhibits meridional swings of the intertropical convergence zone (ITCZ). The effect of zonal winds is generally stronger than that of meridional winds. A stability analysis reveals that the strengthening of zonal and meridional winds weakens the ENSO key positive feedbacks, specifically the zonal advection and thermocline feedbacks, which explains these changes. Zonal wind enhancement also intensifies mean upwelling and hence dynamical damping, leading to a further weakening of El Niño events. Ultimately, this study argues that the zonal and, to a lesser extent, meridional wind strengthening of the past decades may have contributed to the observed shift of El Niño characteristics after the year 2000.

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Alexey V. Fedorov
and
W. Kendall Melville

Abstract

A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist steady wave solutions characterized by confined regions of wave breaking alternating with relatively long intervals where the wave profiles change monotonically. In the former regions the flow is decelerated; in the latter it is accelerated. The regions of breaking are akin to hydraulic jumps of finite width necessary to join the smooth “interior” flows and have periodic waves. In contrast to classical hydraulic jumps, the strongly forced waves lose both energy and momentum across the jumps. The flow in the upper layer is driven by the balance between the wind stress at the surface, the turbulent drag applied at the layer interface, and the wave drag induced at the layer interface by quasi-steady breaking waves. Propagating in the downwind direction, the strongly forced waves significantly modify the flow in both layers, lead to enhanced turbulence, and reduce the speed of the near-surface flow. According to this model, a large fraction of the work done by the surface wind stress on the ocean in high winds may go directly into wave breaking and surface turbulence.

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Alexey V. Fedorov
and
S. George Philander

Abstract

Interactions between the tropical oceans and atmosphere permit a spectrum of natural modes of oscillation whose properties—period, intensity, spatial structure, and direction of propagation—depend on the background climatic state (i.e., the mean state). This mean state can be described by parameters that include the following: the time-averaged intensity τ of the Pacific trade winds, the mean depth (H) of the thermocline, and the temperature difference across the thermocline (ΔT). A stability analysis by means of a simple coupled ocean–atmosphere model indicates two distinct families of unstable modes. One has long periods of several years, involves sea surface temperature variations determined by vertical movements of the thermocline that are part of the adjustment of the ocean basin to the fluctuating winds, requires a relatively deep thermocline, and corresponds to the delayed oscillator. The other family requires a shallow thermocline, has short periods of a year or two, has sea surface temperature variations determined by advection and by entrainment across the thermocline, and is associated with westward phase propagation. For the modes to be unstable, both families require that the background zonal wind exceed a certain intensity. An increase in ΔT, and in H beyond a certain value, are stabilizing. For intermediate values of H, between large values that favor the one mode and small values that favor the other, the modes are of a hybrid type with some properties of each family. The observed Southern Oscillation has been of this type for the past few decades, but some paleorecords suggest that, in the distant past, the oscillation was strictly of the delayed oscillator type and had a very long period on the order of a decade.

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Georgy E. Manucharyan
and
Alexey V. Fedorov

Abstract

El Niño–Southern Oscillation (ENSO) is a pronounced mode of climate variability that originates in the tropical Pacific and affects weather patterns worldwide. Growing evidence suggests that despite extensive changes in tropical climate, ENSO was active over vast geological epochs stretching millions of years from the late Cretaceous to the Holocene. In particular, ENSO persisted during the Pliocene, when a dramatic reduction occurred in the mean east–west temperature gradient in the equatorial Pacific. The mechanisms for sustained ENSO in such climates are poorly understood. Here a comprehensive climate model is used to simulate ENSO for a broad range of tropical Pacific mean climates characterized by different climatological SST gradients. It is found that the simulated ENSO remains surprisingly robust: when the east–west gradient is reduced from 6° to 1°C, the amplitude of ENSO decreases only by 30%–40%, its dominant period remains close to 3–4 yr, and the spectral peak stays above red noise. To explain these results, the magnitude of ocean–atmosphere feedbacks that control the stability of the natural mode of ENSO (the Bjerknes stability index) is evaluated. It is found that as a result of reorganization of the atmospheric Walker circulation in response to changes in the mean surface temperature gradient, the growth/decay rates of the ENSO mode stay nearly constant throughout different climates. These results explain the persistence of ENSO in the past and, in particular, reconcile the seemingly contradictory findings of ENSO occurrence and the small mean east–west temperature gradient during the Pliocene.

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Florian Sévellec
and
Alexey V. Fedorov

Abstract

Ocean general circulation models (GCMs), as part of comprehensive climate models, are extensively used for experimental decadal climate prediction. Understanding the limits of decadal ocean predictability is critical for making progress in these efforts. However, when forced with observed fields at the surface, ocean models develop biases in temperature and salinity. Here, the authors ask two complementary questions related to both decadal prediction and model bias: 1) Can the bias be temporarily reduced and the prediction improved by perturbing the initial conditions? 2) How fast will such initial perturbations grow? To answer these questions, the authors use a realistic ocean GCM and compute temperature and salinity perturbations that reduce the model bias most efficiently during a given time interval. The authors find that to reduce this bias, especially pronounced in the upper ocean above 1000 m, initial perturbations should be imposed in the deep ocean (specifically, in the Southern Ocean). Over 14 yr, a 0.1-K perturbation in the deep ocean can induce a temperature anomaly of several kelvins in the upper ocean, partially reducing the bias. A corollary of these results is that small initialization errors in the deep ocean can produce large errors in the upper-ocean temperature on decadal time scales, which can be interpreted as a decadal predictability barrier associated with ocean dynamics. To study the mechanisms of the perturbation growth, the authors formulate an idealized model describing temperature anomalies in the Southern Ocean. The results indicate that the strong mean meridional temperature gradient in this region enhances the sensitivity of the upper ocean to deep-ocean perturbations through nonnormal dynamics generating pronounced stationary-wave patterns.

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Florian Sévellec
and
Alexey V. Fedorov

Abstract

A salient feature of paleorecords of the last glacial interval in the North Atlantic is pronounced millennial variability, commonly known as Dansgaard–Oeschger events. It is believed that these events are related to variations in the Atlantic meridional overturning circulation and heat transport. Here, the authors formulate a new low-order model, based on the Howard–Malkus loop representation of ocean circulation, capable of reproducing millennial variability and its chaotic dynamics realistically. It is shown that even in this chaotic model changes in the state of the meridional overturning circulation are predictable. Accordingly, the authors define two predictive indices which give accurate predictions for the time the circulation should remain in the on phase and then stay in the subsequent off phase. These indices depend mainly on ocean stratification and describe the linear growth of small perturbations in the system. Thus, monitoring particular indices of the ocean state could help predict a potential shutdown of the overturning circulation.

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Florian Sévellec
and
Alexey V. Fedorov

Abstract

Variations in the strength of the Atlantic meridional overturning circulation (AMOC) are a major potential source of decadal and longer climate variability in the Atlantic. This study analyzes continuous integrations of tangent linear and adjoint versions of an ocean general circulation model [Océan Parallélisé (OPA)] and rigorously shows the existence of a weakly damped oscillatory eigenmode of the AMOC centered in the North Atlantic Ocean and controlled solely by linearized ocean dynamics. In this particular GCM, the mode period is roughly 24 years, its e-folding decay time scale is 40 years, and it is the least-damped oscillatory mode in the system. Its mechanism is related to the westward propagation of large-scale temperature anomalies in the northern Atlantic in the latitudinal band between 30° and 60°N. The westward propagation results from a competition among mean eastward zonal advection, equivalent anomalous westward advection caused by the mean meridional temperature gradient, and westward propagation typical of long baroclinic Rossby waves. The zonal structure of temperature anomalies alternates between a dipole (corresponding to an anomalous AMOC) and anomalies of one sign (yielding no changes in the AMOC). Further, it is shown that the system is nonnormal, which implies that the structure of the least-damped eigenmode of the tangent linear model is different from that of the adjoint model. The “adjoint” mode describes the sensitivity of the system (i.e., it gives the most efficient patterns for exciting the leading eigenmode). An idealized model is formulated to highlight the role of the background meridional temperature gradient in the North Atlantic for the mode mechanism and the system nonnormality.

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