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Anthony C. Hirst

Abstract

Free equatorial modes for several simple coupled ocean-atmosphere models are determined. They are found to include unstable and damped modes of large zonal scale and long period. The influence of ocean thermo-dynamics on unstable modal behavior is systematically explored. The Model I ocean features a local thermal equilibrium. In Model II, linearized temperature advection is the sole ocean thermal process. The Model III ocean features both advective and local thermal processes, while that of Model IV features only local thermal processes. The ocean and atmosphere are each represented by linear shallow water equations on the equatorial β-plane, and are linked by traditional couplings. A finite difference method with variable resolution is used to find eigenvalues and eigenvectors of the coupled systems. Key results are checked via a series method.

Ocean modes are influenced most strongly by coupling, and are damped or destabilized depending on the configuration of induced atmospheric motion relative to oceanic velocities. In Model I, the oceanic Kelvin wave is destabilized while oceanic Rossby waves are damped by the coupling. In contrast, the gravest oceanic Rossby wave is destabilized while the Kelvin wave is damped in Model II. In Model III, coupling facilitates a slowly propagating unstable mode, which has structure intermediate between the Model I unstable Kelvin wave and the Model II unstable Rossby wave. A slow, unstable mode is also present in Model IV, but the growth rate is much reduced in the absence of ocean temperature advection. Growth rates of unstable modes are dependent on a variety of model coefficients. Further experiments include arbitrary shifting and meridional restriction of the atmospheric heating field. The latter experiment provides support for a conjecture concerning the seasonal timing of El Niño.

The results are applied to the equatorial Pacific; climatological background states do not permit unstable modes that seem relevant to El Niño onset. Unstable modes permitted by a background state based on conditions observed prior to an actual El Niño are discussed.

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Anthony C. Hirst

Abstract

The effect of ocean boundaries on instability in coupled ocean-natmosphere models is determined. Eigenvalues and eigenvectors are calculated for coupled systems featuring an ocean basin bounded zonally by a flat continent. The atmosphere is periodic zonally about the globe. The oceanic and atmospheric dynamics are both represented by linear shallow water equations on the equatorial β-plane. The calculation involves latitudinal series expansion and longitudinal finite differencing.

Certain of the modes (i.e., eigenvectors) have amplitudes that grow with time, the growth being a direct result of the ocean-atmosphere coupling. Comparison is made to modes previously determined for the theoretically simpler case where the ocean is zonally unbounded. Growing modes in the bounded ocean case correspond in aspects of behavior and structure to particular modes of appropriate wavelength in the unbounded ocean basin. The basic mechanism of instability is the same in both cases. Growing modes in the bounded ocean case feature wavelike disturbances that propagate slowly across the ocean basin. The direction of propagation and period of the oscillation are very sensitive to the values prescribed for oceanic thermodynamic coefficients. The period is set by the 1ength of time that the coupled disturbance takes to propagate across the basin, and, for a 15 000 km wide basin, ranges from about a year to many years. Dependence of modal behavior on other parameters is also documented. Instability occurs for a greater range of parameters, and growth rates are larger when the ocean basin is wide (e.g., 15 000 km) than when it is narrow. The zonal width of the continent has little effect on modal behavior. The Kelvin and symmetric low-n long Rossby components of the oceanic and atmospheric motion fields are of primary importance in modal growth.

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Anthony C. Hirst and Wenju Cai

Abstract

The sensitivity of a coarse-resolution model of the World Ocean to parameterization of subgrid-scale mixing is examined. The model is based on the GFDL code. Results are presented from a series of model runs where the subsurface mixing parameterization is sequentially upgraded toward a more physical representation. The surface forcing is the same for all principal model runs and features a strong relaxation of surface temperature and salinity toward perpetual wintertime observed values. One model version is rerun with a full annual cycle of surface forcing and verifies that use of the perpetual winter surface relaxation introduces only minor biases in the essential characteristics of the solution.

Runs 1 and 2 feature the diffusivity tensor in the traditional horizontal/vertical orientation, and examines the effect of different vertical diffusivity profiles on the solution. Results are compared with those of previous studies. In both cases, the water mass properties (espcially the salinity Acids) are rather poor. In runs 3–5, a standard parameterization is introduced that allows for enhanced diffusion along the isopycnal surfaces. Each of these runs feature a different prescribed profile of isopycnal diffusivity, though with the same profile of vertical diffusivity as for run 2. Introduction of isopycnal mixing considerably improves the water mass structure, in particular by freshening and cooling water at intermediate depths toward realistic levels. However, the vertical stratification and density fields are little changed from run 2. likewise. the current structure and meridional overturning are little changed. Thus isopycnal mixing has a major effect upon the temperature and salinity fields, but very minor effect on the ocean dynamics. Isopycnal mixing is found to modestly increase poleward oceanic heat transport in the midlatitudes via enhanced quasi-horizontal mixing of warm salty subtropical and cold fresh subpolar waters.

In run 6, the isopycnal diffusivity of run 4 is retained, but the vertical diffusivity is instead allowed to vary as the inverse of the local Brunt-Väisälä frequency. However, the resulting solution is little changed from that of run 4. Reasons for this small change are discussed. Also discussed are the impact of numerical problems associated with the use of realistically small vertical diffusivity, and problems inherent in deep water formation in coarse-resolution models.

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Anthony C. Hirst and J. S. Godfrey

Abstract

The effect of the Indonesian Throughflow on the World Ocean circulation is examined by a series of experiments with a global ocean GCM. The principal objective is to gain an understanding of how ocean flows respond to the throughflow, and how these changes result in changes in the pattern of surface heat flux and sea surface temperature. Four model runs are conducted. The first run features an open Indonesian passage through which a nonzero net throughflow is permitted. The second run features a complete blockage of the Indonesian passage. The third run is designed to isolate the effects of purely buoyancy-driven throughfiow: the Indonesian passage is open but the net volume transport is required to be zero. The fourth run is designed to isolate the effects of nonzero net throughflow on the Indian Ocean, independent of interocean buoyancy differences: the Indonesian passage is open but the throughflow water is cooled and salted toward profiles characteristic of the east Indian Ocean in the absence of throughflow.

Comparison of the first and second runs shows that the throughflow generally warms the Indian Ocean and cools the Pacific. However, large changes in the surface temperature and heat flux are restricted to certain well-defined regions: the Agulhas Current/outflow, the Leeuwin Current region off western Australia, the Tasman Sea, the equatorial Pacific, and two bands in the midlatitude South Pacific. In contrast, large subsurface temperature changes are widespread across both oceans. Heat budget analysis indicates that the large surface responses are dependent on the subsurface temperature change being brought to the surface, either by strong wind-forced upwelling (as in the equatorial Pacific) or by vigorous mixing in convective mixed layers (as in the other regions). Over most of both oceans, such mechanisms are absent and surface heat-flux changes are small (a few W m−2). There, subsurface temperature perturbations are largely insulated from the surface and may extend via direct advection or baroclinic wave propagation. The additional beat is released upon encounter with upwelling or a convective mixed layer, which may be far removed from the source of the perturbation. Atlantic and far Southern Ocean effects are mostly very small, possibly because of our use of restoring upper boundary conditions. The third and fourth runs break the throughflow into its baroclinic and barotropic components. The baroclinic (buoyancy-driven) component affects surface beat flux strongly in the Leeuwin Current region but relatively weakly in the Agulhas Current and Tasman Sea. The barotropic component has the converse effect. Interocean heat exchange is discussed; the full throughflow transports a net 0.63 petawatts out of the Pacific Ocean, which represents about one-third of the total heat input into the model's equatorial Pacific.

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David S. Battisti and Anthony C. Hirst

Abstract

The behavior of a tropical coupled atmosphere/ocean model is analyzed for a range of different background states and ocean geometries. The model is essentially that of Cane and Zebiak for the tropical Pacific, except only temporally constant background states are considered here. For realistic background states and ocean geometry, the model solutions feature oscillations of period of 3–5 yr. By comparing the full model solution with a linearized version of the model, it is shown that the basic mechanism of the oscillation is contained within linear theory.

A simple linear analog model is derived that describes the nature of the interannual variability in the coupled tropical atmosphere–ocean system. The analog model highlights the properties that produce coupled atmosphere–ocean instability in the eastern ocean basin, and the equatorial wave dynamics in the western ocean basin that are responsible for a delayed, negative feedback into this instability growth. The growth rate of the local instability c together with the magnitude b and lag of the wave-induced processes determine the nature of the interannual variability displayed in the coupled model. Specifically, these processes determine the growth rate of the coupled system and, when the solutions are oscillatory, the period of the oscillation. The terms b, c, and are set by the background state of the atmosphere and ocean, and the geometry of the ocean basin.

The simple analog model is used to design and interpret a set of experiments using the full linear and nonlinear numerical models of the coupled atmosphere ocean system in the Pacific. In these experiments, we examine the effects of the assumed basic state and ocean geometry on the interannual variability of the coupled system. The simple model is shown to be a remarkably good proxy of the full linear and nonlinear numerical models. The limiting nonlinearity in the full numerical model is shown to be the dependence of the temperature of the upward water on the thermocline depth. However, we find the essential processes that describe the local instability growth rate and period of the interannual oscillations in the coupled system are linear. Nonlinearities primarily act as a bound on the amplitude of the final state oscillations, and decrease the period of the firm state oscillations by about 10 percent from that obtained in the small amplitude regime of the full coupled model and the linear analog model. The nonlinear analog model for the full numerical model is derived, and compared with that proposed by Suarez and Schopf. The numerical and analog models help to explain why organized, large amplitude, interannual variability is prominent in the tropical Pacific basin, and not in Atlantic and Indian basins.

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Anthony C. Hirst and J. S. Godfrey

Abstract

The timescale and mechanisms of remote response in a global ocean GCM is investigated in the case of a sudden change in the rate of Indonesian Throughflow. In one experiment, the model is run to equilibrium with the Indonesian passage completely closed off. The passage is then opened, and the evolution of the system toward a new equilibrium is examined. In a second experiment, the model equilibrium solution with passage open is slightly perturbed by application of a body force to the water in the passage. The force is such that the change in throughflow (an increase of about 5%) has vertical profile almost identical to that of the original throughflow. The changes that evolve in the second experiment are, after appropriate scaling, quantitatively similar to those in the first, thereby verifying the approximate linearity of the response. The dynamics of this response are investigated with the aid of several idealized small-perturbation experiments, in which the model is reconfigured with a flat bottom and to be initially at rest with horizontally homogeneous density fields. It is shown that the extensive subsurface temperature responses in both the Indian and Pacific Oceans primarily result from a process of adjustment akin to baroclinic wave propagation of the first and second internal modes. The model's (approximate) first internal mode response is fairly similar to that expected from viscous linear theory. However, temperature perturbations associated with the second internal mode response are strongly distorted, in part by advection associated with the background currents. Temperature advection by the perturbation barotropic mode is unimportant except locally in the Tasman Sea and Agulhas Retroflection regions. Large differences in the patterns of response obtained previously for shallow and deep Indonesian sills, and for full versus buoyancy-driven-only throughflow, are interpreted in terms of preferential excitement of internal modes. Thus the model's baroclinic wave properties, and the spectrum of baroclinic modes excited by the throughflow change, appear very important to the pattern and timing of the subsurface (and hence surface) temperature response.

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Anthony C. Hirst and Trevor J. McDougall

Abstract

A parameterization for the adiabatic transport effect of eddies is introduced into a World Ocean model based on the Bryan-Cox code. The model topography is only lightly smoothed and retains realistic sill depths and representation of continental shelves commensurate with the model's 1.6° latitude by 2.8° longitude resolution. The parameterization allows the model to be run without horizontal diffusivity (though only under certain conditions as discussed). A first (control) run features a typical horizontal diffusivity and no eddy-induced transport. A second run features the eddy-induced transport scheme and zero horizontal diffusivity. Substantial changes occur between the runs in subsurface temperature, salinity, and density throughout the model ocean. The most profound changes occur in the deep ocean and feature a marked increase in density in the second run associated with a substantial decline in temperature (especially in the Atlantic) and an increase in salinity (especially in the Southern, Indian, and Pacific Oceans). The large changes in deep-water properties reflect a marked change in the relationship between dense sill/shelf overflow water and the water that reaches the deep ocean. Deep water in the second run much more closely resembles the source overflow water, because of elimination of local and remote effects of horizontal diffusivity, and because of reduced convection and isopycnal slope near downslope flows resulting from direct action by the transport scheme. The deep-water properties in the second run are clearly more realistic than in the first. The greater density in the second run is achieved despite substantial reductions in polar surface heat and salt fluxes from those in the first run. In particular, surface fluxes near Antarctica are generally small and smoothly varying in the second run.

Water mass Interactions important in the formation of model deep water are examined. The realistically high density of Circumpolar Deep Water in the second run prevents the occurrence of widespread deep convection near Antarctica, which, in the first run, seriously depletes the salinity of this water mass and consequently leads to marked salinity deficiencies in the deep Indian and Pacific Oceans. This convection also severely distorts the surface flux patterns near Antarctica. Practical implications of the marked reduction in Antarctic convection are discussed. Finally, a third run shows that much of the benefit of the eddy-induced transport scheme accrues upon its introduction even when the standard horizontal diffusivity is retained. This last result supports the use of the scheme even in models where the resolution is too come to allow for complete elimination of horizontal diffusivity.

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Anthony C. Hirst and K-M. Lau

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This study investigates the behavior of coupled ocean-atmosphere models in an environment where atmospheric wave speeds are considerably reduced from their dry atmospheric values, by, for example, condensation-moisture convergence. Preliminary coupled-model results presented earlier are verified and extended using more complete models and for a range of ocean thermodynamics. The models consist of linear coupled shallow-water equations for the equatorial β-plane and are distinguished by the form of the equation for sea-surface temperature. The ocean is forced by wind stress, and the atmosphere by latent heating resulting from (i) moisture convergence and (ii) evaporation. Modes are calculated for zonally periodic, unbounded, ocean-atmosphere systems. The results in this paper emphasize the importance of including prognostic atmospheric equations in simple, coupled ocean-atmosphere models, especially for the simulation of intraseasonal variability and its possible interaction with interannual variability.

Only low frequency modes (period ≥ 1.5 years) are destabilized by the coupling when atmospheric wave speeds are near dry atmospheric values. However, when atmospheric waves are slowed to a few meters per second and atmospheric dissipation rates are low [less than about (10 days)−1], coupling destabilizes both high frequency (period 30–70 days) and lower frequency modes. The dynamics of the two classes of modes are compared. The high frequency modes are essentially coupled oceanic and atmospheric Kelvin waves, and they rely on fundamentally nonequilibrium atmospheric dynamics for their growth. Their growth rates diminish rapidly with increased atmospheric wave speed or dissipation rate. The motion fields for the low frequency modes feature strong contributions from Rossby, as well as Kelvin, components; the associated atmospheric fields are generally in quasi-equilibrium with the sea surface temperature field, and the modes are not nearly so sensitive to changes in atmospheric wave speed or dissipation rate. Both classes of modes are sensitive to the degree to which surface wind anomalies are able to affect the evaporation rate. The possible relation of the high and low frequency modes to tropical intraseasonal and interannual variability is also discussed. The rapid diminution of growth rate with increased atmospheric dissipation makes it unlikely that the high-frequency coupled Kelvin instability can be by itself a major source of intraseasonal variability. More likely, ocean-atmosphere interaction may amplify intraseasonal variability of internal atmospheric origin; present results suggest that direct wind-evaporation feedback would be more important than the coupled Kelvin instability in such a case.

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Anthony C. Hirst and Trevor J. McDougall

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The present study examines the marked changes in the patterns of meridional overturning and dianeutral motion that occur upon introduction of the Gent and McWilliams (GM) scheme for eddy-induced transport into a coarse-resolution global ocean model. Results from two versions of the ocean model are compared. The first version does not have the GM scheme and uses a standard background horizontal diffusivity. The second version includes the GM scheme and has zero horizontal diffusivity. Both versions include a weak vertical diffusivity and isoneutral tracer diffusion as implemented by Cox. First, representations of the meridional overturning circulation computed via integration along (i) level, (ii) potential density, and (iii) neutral density (γ) surfaces are compared. Differences between the level surface representations are similar to those noted in previous studies. Differences between the density surface representations (not previously studied) are major at high densities (γ or σ θ > 27.0). The residual Deacon cell of the first version has completely vanished in the GM version. The separate direct Antarctic and deep circulation cells of the first version are fully merged in the GM version. In these respects, the solution of the GM version is broadly more consistent with that of the FRAM eddy-permitting simulation. However, introduction of the GM scheme does not aid long-standing model problems of excessive upwelling of deep water into the thermocline in the Pacific and excessive penetration of Antarctic Bottom Water into the North Atlantic. The marked differences between the versions noted above imply marked differences in the dianeutral transport of fluid. A direct calculation of dianeutral transport shows that this transport is much weaker in the Southern Ocean and in the western boundary currents in the GM run. A breakup of the dianeutral transport into components resulting from the individual model mixing processes shows that the sole factor responsible for these qualitative changes is the absence of dianeutral motion induced by horizontal diffusive fluxes in the GM version. The interior dianeutral transport in this version is characterized by widespread and gentle upward motion induced by vertical diffusive fluxes. The results are shown to be insensitive to details of the surface boundary restoration. Consequences for our understanding of (i) the role of the Deacon cell as a tracer transport mechanism and (ii) the nature of the eddy-induced transports as provided by the GM scheme are discussed. In particular, although the total effective transport in the ocean interior is nearly isoneutral in the GM case, the eddy-induced part of that transport is shown to have a large dianeutral component and so cannot be interpreted as an isoneutral “bolus” transport.

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Anthony C. Hirst, David R. Jackett, and Trevor J. McDougall

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A comparison is made of the meridional overturning circulation in a coarse-resolution World Ocean model when the integration is performed along (i) level, (ii) potential density, and (iii) neutral density surfaces. In the level-surface calculation, all the usual cells are evident, including the Atlantic “conveyor,” the Deacon cell, and the direct Antarctic cell. In the potential or neutral density calculations, all cells remain present; however, the Deacon cell is greatly reduced in strength (to just a few Sverdrups). An analysis of the thermodynamics underlying the dianeutral motion is conducted. Most dianeutral motion results from fluxes associated with the vertical diffusivity and the (unphysical) horizontal diffusivity. Caballing is not important, despite the inclusion of isopycnal diffusivity. The mechanism of the residual Deacon cell involves densification near 40°5 resulting from fluxes associated with the horizontal diffusivity. Horizontal diffusivity results in substantial dianeutral motion in several other parts of the ocean. Most significant is motion toward lesser density in the far Southern Ocean, which integrates zonally and between 67°S and 57°S to give a transport of about 25 Sv across density surfaces. This transport dominates other dianeutral transports at high density in the ocean interior and indicates serious distortion of the solution by the horizontal diffusivity.

A second model run is conducted where the horizontal diffusivity is reduced to near the (experimentally determined) limit for the numerical integrity of water properties on the large scale. Dianeutral transports associated with horizontal diffusivity generally decline modestly. In neutral density coordinates, the Deacon cell now vanishes almost completely. The Deacon cell of the level-surface integration results mainly from large-scale isopycnal motions occurring on sloping density surfaces, which superpose to yield a cell upon zonal integration at constant depth. Finally, it is apparent that the neutral density coordinate provides a clearer picture of the ocean circulation than do potential density coordinates, because of inherent ambiguity in choosing the reference pressure of potential density.

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