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Eli Tziperman

Abstract

The relation between the circulation calculated from averaged hydrographic data (such as the Levitus data), and the actual time average circulation is examined using a CTD dataset which provides both time and space coverage of a region of the Mediterranean Sea. The connection between eddy mixing coefficients calculated from hydrographic data and the eddy fluxes (uT) they are intended to parameterize is also considered.

An inverse model is used to calculate circulation and mixing coefficients from the time average data. Then, the actual time averaged circulation is estimated by averaging six realizations of the instantaneous velocity field, and mixing coefficients are calculated by directly parameterizing the eddy fluxes of heat and salt.

Comparing the results obtained by the different procedures, it is concluded that the horizontal time average circulation can be reliably estimated from averaged and smoothed climatological data, but that it is nearly impossible to obtain physically meaningful mixing coefficient from such data.

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Eli Tziperman

Abstract

The relation between the mean state of the thermohaline circulation (THC) and its stability is examined using a realistic-geometry primitive equation coupled ocean–atmosphere–ice global general circulation model. The main finding is that a thermohaline circulation that is 25% weaker and less dominated by thermal forcing than that of today’s ocean is unstable within this coupled GCM. Unstable initial ocean climates lead in the coupled model to an increase of the THC, to strong oscillations, or to a THC collapse.

The existence of an unstable range of weak states of the THC provides a natural explanation for large-amplitude THC variability seen in the paleo record prior to the past 10 000 years: A weakening of the THC due to an external forcing (e.g., ice melting and freshening of the North Atlantic) may push it into the unstable regime. Once in this regime, the THC strongly oscillates due to the inherent instability of a weak THC. Hence the strong THC variability in this scenario does not result from switches between two or more quasi-stable steady states.

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Eli Tziperman

Abstract

The problem of determining the (eastern boundary) basic stratification and the buoyancy-driven circulation of the oceans is addressed. A global integral constraint relating the interior stratification and the air-sea heat fluxes is derived, based on the condition that the total mass of water of given density is constant in a steady state ocean. This constraint is then applied to two simple analytic models: The first is a continuous nonlinear diffusive model of the lower mid-depth and bottom circulation below the influence of the wind-driven circulation. It shows the tendency of the vertical density profile to look like an exponential profile in the presence of mixing. The integral constraint is used to relate the stratification and circulation of the bottom and mid-depth waters to the air-sea heat fluxes at the surface, where the deep densities outcrop. The second model is a layered one of the wind-driven circulation, mid-depth, and bottom water. The eastern boundary stratification of the model is determined from the air-sea heat fluxes, using the integral constraint and a parameterization of the mixing processes in layer models. A two gyre mid-depth circulation is found, driven by the cross-isopycnal diffusive velocities and affected by the variations in the depth of the main thermocline above it. The bottom circulation in both models is similar to that of the Stommel-Arons model.

Air-sea heat fluxes affect the deep buoyancy-driven flows not by direct cooling or heating, but through the formation of water masses that sink and spreak in the deep ocean. Thermal boundary conditions for the interior thermocline problem seem to require specification of the air-sea heat fluxes in addition to the specification of the density distribution at the base of the Ekman layer. Cross-isopycnal mixing processes are a crucial part of the dynamics, although numerically small. Together with the air-sea heat fluxes, they determine the basic vertical stratification of the wind-driven and deep circulation.

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Eli Galanti and Eli Tziperman

Abstract

The possibility of generating decadal ENSO variability via an ocean teleconnection to the midlatitude Pacific is studied. This is done by analyzing the sensitivity of the equatorial stratification to midlatitude processes using an ocean general circulation model, the adjoint method, and a quasigeostrophic normal-mode stability analysis. It is found that, on timescales of 2–15 yr, the equatorial Pacific is most sensitive to midlatitude planetary Rossby waves traveling from the midlatitudes toward the western boundary and then to the equator. Those waves that propagate through baroclinically unstable parts of the subtropical gyre are amplified by the baroclinic instability and therefore dominate the midlatitude signal arriving at the equator. This result implies that decadal variability in the midlatitude Pacific would be efficiently transmitted to the equatorial Pacific from specific areas of the midlatitude Pacific that are baroclinically unstable, such as the near-equatorial edges of the subtropical gyres (15°N and 12°S). The Rossby waves that propagate via the baroclinically unstable areas are of the advective mode type, which follow the gyre circulation to some degree and arrive from as far as 25°N and 30°S in the east Pacific. It is shown that the baroclinic instability amplifying these waves involves critical layers due to the vertical shear of the subtropical gyre circulation, at depths of 150–200 m.

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Eli Galanti and Eli Tziperman

Abstract

The physical mechanism underlying ENSO’s phase locking to the seasonal cycle is examined in three parameter regimes: the fast-SST limit, the fast-wave limit, and the mixed SST–wave dynamics regime. The seasonal cycle is imposed on simple ordinary differential equation models for each physical regime either as a seasonal ocean–atmosphere coupling strength obtained from the model of Zebiak and Cane or as a climatological seasonal upwelling. In all three parameter regimes, the seasonal variations in the ocean–atmosphere coupling strength force the events to peak toward the end of the calendar year, whereas the effect of upwelling is shown to be less important. The phase locking mechanism in the mixed-mode and fast-SST regimes relies on the seasonal excitation of the Kelvin and the Rossby waves by wind stress anomalies in the central Pacific basin. The peak time of the events is set by the dynamics to allow a balance between the warming and cooling trends due to downwelling Kelvin and upwelling Rossby waves. This balance is obtained because the warming trend due to the large-amplitude Kelvin waves, amplified by a weak Northern Hemisphere wintertime ocean–atmosphere coupling strength, balances the cooling trend due to weak Rossby waves, amplified by a strong summertime coupling strength. The difference between the locking mechanisms in the mixed-mode regime and in the fast-SST regime is used to understand the effect of the SST adjustment time on the timing of the phase locking. Finally, in the less realistic fast-wave regime, a different physical mechanism for ENSO’s phase locking is revealed through the SST adjustment time and the interaction between the east Pacific region and the central Pacific region.

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Ziv Sirkes and Eli Tziperman

Abstract

Adjoint models are used for atmospheric and oceanic sensitivity studies in order to efficiently evaluate the sensitivity of a cost function (e.g., the temperature or pressure at some target time t f, averaged over some region of interest) with respect to the three-dimensional model initial conditions. The time-dependent sensitivity, that is the sensitivity to initial conditions as function of the initial time t i, may be obtained directly and most efficiently from the adjoint model solution. There are two approaches to formulating an adjoint of a given model. In the first (“finite difference of adjoint”), one derives the continuous adjoint equations from the linearized continuous forward model equations and then formulates the finite-difference implementation of the continuous adjoint equations. In the second (“adjoint of finite difference”), one derives the finite-difference adjoint equations directly from the finite difference of the forward model. It is shown here that the time-dependent sensitivity obtained by using the second approach may result in a very strong nonphysical behavior such as a large-amplitude two-time-step leapfrog computational mode, which may prevent the solution from being used for time-dependent sensitivity studies. This is an especially relevant problem now, as this second approach is the one used by automatic adjoint compilers that are becoming widely used. The two approaches are analyzed in detail using both a simple model and the adjoint of a primitive equations ocean general circulation model. It is emphasized that both approaches are valid as long as they are used for obtaining the gradient or sensitivity at a single time, as needed in data assimilation, for example. Criteria are presented for the choice of the appropriate adjoint formulation for a given problem.

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Laure Zanna and Eli Tziperman

Abstract

A simple zonally averaged coupled ocean–atmosphere model, with a relatively high resolution in the meridional direction, is used to examine physical mechanisms leading to transient amplification of thermohaline circulation (THC) anomalies. It is found that in a stable regime, in which small perturbations eventually decay, there are optimal initial conditions leading to a dramatic amplification of initial temperature and salinity anomalies in addition to the THC amplification. The maximum amplification occurs after about 40 years, and the eventual decay is on a centennial time scale. The initial temperature and salinity anomalies are considerably amplified by factors of a few hundreds and 20, respectively. The initial conditions leading to this amplification are characterized by mutually canceling initial temperature and salinity anomalies contributions to the THC anomaly, such that the initial THC anomaly vanishes. The mechanism of amplification is analyzed and found to be the result of an interaction between a few damped (oscillatory and nonoscillatory) modes with decay time scales lying in a range of 20–800 years. The amplification mechanism is also found to be distinct from the advective feedback leading to THC instabilities for large freshwater forcing.

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Yosef Ashkenazy and Eli Tziperman

Abstract

Oceanic variability and eddy dynamics during snowball Earth events, under a kilometer of ice and driven by a very weak geothermal heat flux, are studied using a high-resolution sector model centered at the equator, where previous studies have shown the ocean circulation to be most prominent. The solution is characterized by an energetic eddy field, equatorward-propagating zonal jets, and a strongly variable equatorial meridional overturning circulation (EMOC), on the order of tens of Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1), restricted to be very close to the equator. The ocean is well mixed vertically by convective mixing, and horizontal mixing rates by currents and eddies are similar to present-day values. There are two main opposite-sign zonal jets near the equator that are not eddy driven, together with multiple secondary eddy-driven jets off the equator. Barotropic stability analyses, the Lorenz energy cycle (LEC), and barotropic-to-baroclinic energy conversion rates together indicate that both baroclinic and barotropic instabilities serve as eddy-generating mechanisms. The LEC shows a dominant input into the mean available potential energy (APE) by geothermal heat flux and by surface ice melting and then transformation to eddy APE, to eddy kinetic energy, and finally to mean kinetic energy via eddy–jet interaction, similarly to the present-day atmosphere and unlike the present-day ocean. The EMOC variability is due to the interaction of warm plumes driven by geothermal heating that reach the ocean surface, leading to ice-melt events that change the stratification and, therefore, the EMOC. The results presented here may be relevant to the ocean dynamics of planetary ice-covered moons such as Europa and Enceladus.

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Eli Tziperman and Hezi Gildor

Abstract

The meridional freshwater flux in the atmosphere, and hence the strength of the hydrological cycle, undergoes variations on glacial–interglacial as well as on some shorter timescales. A significant portion of these changes to the hydrological cycle are due to the temperature–precipitation feedback according to which there is more precipitation over the higher latitudes during warm periods when the moisture holding capacity of the atmosphere is higher.

It is proposed here that this feedback may play an important role in determining the stability of the thermohaline circulation (THC). The THC stability to different parameterizations of the meridional atmospheric freshwater flux is therefore investigated using a simple box model of the ocean, atmosphere, and sea ice. It is demonstrated that parameterizations that are consistent with the temperature–precipitation feedback, and hence with the observed variations of the hydrological cycle during glacial–interglacial cycles, stabilize the THC for a wide range of forcing parameters.

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Claudia Pasquero and Eli Tziperman

Abstract

A simplified model is used to study the possible effects of the horizontal upper-ocean wind-driven circulation (WDC) on the variability of the overturning meridional circulation driven by buoyancy fluxes. It is found that the added interaction with the WDC adds interesting new classes of variability. First, self-sustained variability of the thermohaline circulation (THC) becomes possible, on time scales of interdecades to a few centuries. Furthermore, these oscillations may be either small amplitude or large amplitude and either periodic or chaotic, depending on the amplitude of the freshwater forcing and on the strength of the WDC. Even a relatively weak WDC changes the well-known stability properties of the THC that are seen in numerous models of the THC alone. The variability modes found here may account for similar modes of variability observed in GCM studies.

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