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F. L. Yin and E. S. Sarachik

Abstract

The implicit vertical diffusion (IVD) convective adjustment scheme in common use in ocean general circulation models (OGCMs) could have large residual static gravitational instability at each time step. An iterative and explicit scheme is devised, based on similar physical considerations as the ones for the IVD scheme. It guarantees a complete removal of static instability in a vertical water column and is more efficient than the IVD scheme in overall spinup of the model.

The two convective schemes are compared in an ocean model that is in a state of interdecadal limit cycles. While the model solution with either of these two schemes is characterized by interdecadal oscillations, the variability is different in each scheme. The primary oscillation has a period of about 11 years, but the basin mean kinetic energy shows large differences. The 11-year cycle is modulated by a 33-year oscillation with the IVD scheme, while it is modulated by a 22-year cycle with the complete scheme. The amplitude of the variation of kinetic energy with the IVD scheme is also about twice as large as that with a complete adjustment scheme. It is therefore suggested that complete and incomplete convective schemes can lead to different model variability when convective changes in temperature and salinity have large variations over a short period of time.

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Andrew J. Weaver and E. S. Sarachik

Abstract

In centered difference models of ocean circulation, two grid-point computational modes can be excited if grid Reynolds and Peclet numbers are greater than two. The Bryan-Cox General Circulation Model (GCM) is used to show the dramatic effect that this instability has on the equatorial thermohaline circulation. In many recent numerical calculations researchers have used 12 vertical levels. It is shown that this resolution produces an artificial cell at the equator when typical values of the vertical diffusivity and viscosity parameters are used. This artifical cell rotates counter to the primary cell driven by deep water formation at high latitudes, is driven by downwelling at the eastern boundary near the equator and is 40% the strength of the primary cell for the parameters used in the present study. When the vertical resolution is increased the cell vanishes. It is suggested therefore that higher vertical resolution should be used in Bryan-Cox GCM deep-ocean modeling studies when current values of the vertical diffusivity and viscosity parameters are used.

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F. L. Yin and E. S. Sarachik

Abstract

Oceanic interdecadal thermohaline oscillations are investigated with a coarse-resolution version of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model. The geometry of the model is a box with a depth of 5000 m and a longitudinal width of 60°, spanning latitudes from 14.5° to 66.5°N. The model ocean is forced by a zonal wind stress, a heat flux parameterized by restoring the surface temperature toward a reference value, and a specified surface freshwater flux. Zonal wind stress, reference temperature, and freshwater flux are all longitudinally uniform, time-independent, and vary meridionally.

It is shown that the ocean model can be in a state of interdecadal oscillations, and a physical mechanism is explained. For these oscillatory solutions, both surface mean heat flux and basin mean kinetic energy vary with interdecadal periods. Temperature and salinity budget analyses reveal that these oscillations depend primarily on advective and convective processes. Horizontal advective heat transports from the subtropical region warm the subsurface water in the subpolar region, destablize the water column, and thereby enhance convection. Convection, in turn, induces surface cyclonic and equatorward flows, which, together with horizontal diffusion and surface freshwater input, transport subpolar fresh water into convecting regions, subsequently weakening or suppressing convection. During an oscillation, convection vertically homogenizes the water column, increases the surface salinity, creates a larger meridional gradient of surface salinity, and increases the efficiency of surface advective freshening in the convective region. The periodic strengthening and weakening of convection caused by subsurface advective warming and surface freshening in the subpolar region results in model interdecadal oscillations.

These advective and convective interdecadal oscillations are not sensitive to either the detailed distribution of subpolar freshwater flux or the horizontal diffusivity. They are mainly a result of halocline and inverted thermocline structure in the subpolar region, maintained by horizontal advective subsurface heating and surface freshening processes.

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Igor V. Kamenkovich and E. S. Sarachik

Abstract

The authors identify and describe the important dynamical mechanisms that explain the significant sensitivity of the Atlantic thermohaline circulation to the parameterization of heat and salt transports by mesoscale eddies in numerical models. In particular, the effects of the Gent–McWilliams (GM) scheme, which has a strong flattening effect on isopycnals, and a simple horizontal diffusion scheme are considered and compared. Two control runs, one with each scheme, exhibit very different circulations and density structures. To analyze the dynamical reasons for the differences between the control runs, a number of numerical experiments with regionally varying diffusion coefficients are carried out, emphasizing the effects of different schemes in key regions. The main effect of eddies in the Southern Ocean in nature is to shoal the subsurface isopycnal surfaces, thus increasing the density of the northward inflow of relatively dense intermediate waters into the Atlantic—as will be seen, this is more effectively done by the GM parameterization of the eddies. The resulting increase in the subsurface density at low latitudes decreases the meridional density contrast with the high latitudes of the North Atlantic, shoals the pycnocline, and consequently weakens the meridional overturning. By contrast, the effect of the eddy transports in the western boundary current in the Northern Hemisphere on the strength of the North Atlantic Deep Water (NADW) formation is shown to be smaller. The Northern Hemisphere upwelling and horizontal flow structure is strongly affected by local eddy transports, and the outflow of the NADW is very sensitive to the Northern Hemisphere eddy transports as a result. The original scaling of Gnanadesikan is modified to include the effects of horizontal mixing in low latitudes. The results confirm the leading role of the Southern Ocean eddies in affecting the strength of NADW formation, while the Northern Hemisphere horizontal mixing mostly affects local upwelling. The eddy transports in the Southern Ocean also affect the properties of Antarctic Bottom Water, which influences the vertical penetration of the NADW overturning cell as well as the density of the deep ocean.

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Igor V. Kamenkovich and E. S. Sarachik

Abstract

Restoring boundary conditions, wherein the temperature and salinity are restored to surface target fields of temperature and salinity, are traditionally used for studies of the ocean circulation in ocean general circulation models. The canonical problem with these boundary conditions is that, when the target fields are chosen as the observed fields, accurate simulation of the surface fields of temperature and salinity would imply that the surface fluxes and therefore the ocean heat transports approach zero, a clearly unrealistic situation. It is clear that the target fields cannot be chosen as the observed fields. A simple but effective method of modifying conventional restoring boundary conditions is introduced, designed to keep the calculated values of surface temperature and salinity as close to observations as possible. The technique involves calculating the optimal target fields in the restoring boundary conditions by an iterative procedure. The method accounts for oceanic processes, such as advection and eddy mixing in the derivation of the new boundary conditions. A reduced version of this method is introduced that produces comparable results but offers greater simplicity in implementation. The simplicity of the method is particularly attractive in idealized studies, which often employ restoring surface boundary conditions. The success of the new method is, however, limited by several factors that cannot be easily compensated by the adjustment of the target profiles. These factors include inaccurate model dynamics, errors in the observations, and the too-simplified form of restoring surface boundary conditions themselves. The application of the method in this study with a coarse-resolution model leads to considerable improvements of the simulation of sea surface temperature (SST) and sea surface salinity (SSS). Both amplitude and phase of the annual cycle in SST greatly improve. The resulting magnitudes of surface heat and freshwater fluxes increase on average, and the meridional heat transport gets stronger. However, the fluxes in some regions remain unrealistic, notably the too-strong freshwater forcing of the western boundary currents in the Northern Hemisphere. Southern Ocean cooling and freshening are also likely to be too strong. The subsurface values of temperature improve greatly, proving that a large part of errors in the subsurface temperature distribution in our model can be corrected by reducing errors at the surface. In contrast, the reduction of errors in surface salinity fails to improve uniformly the simulated subsurface salinity values.

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D. E. Harrison, B. S. Giese, and E. S. Sarachik

Abstract

Four different datasets of monthly mean new-equatorial Pacific sea surface temperature for 1982–83 are compared, and the space-time regions for which there was consensus that cooling or warming took place, are determined. There was consensus that warming took place east of the date line, averaged over the period July-December 1982, and that the warming progressed eastward from the central Pacific. There was also consensus that weak cooling took place in April 1983, and that substantial cooling occurred in June-July 1983, generally over the central and eastern Pacific. However, the analyses tend to agree on the sign of SST change only in periods of cooling or warming in excess of 1°C/month; quantitative agreement at the level of 0.5°C/month or better is almost never found.

SST changes in five ocean-circulation model hindcasts of the 1982–83 period (differing only in that each used a different analyzed monthly mean surface wind stress field to drive the ocean), are compared with the observations and with each other. There is agreement that net warming occurred in the July-December 1982 period and cooling in mid-1983. The heat budgets of these experiments indicate that the major model central Pacific warmings occurred primarily from anomalous eastward surface advection of warm water. Further, east zonal advection remains significant but a diminished cooling tendency from meridional advection can also be important; different hindcasts differ on the relative importance of these terms. Surface heat flux changes do not contribute to the warmings. The reduced cooling tendency from meridional advection is consistent with diminished surface Ekman divergence, suggesting that southward transport of warm north equatorial counter current water was not a major factor in the model warmings. The hindcasts do not agree on the relative importance of local or remote forcing of the eastward surface currents; while there is clear evidence of remote forcing in some hindcasts in particular regions, local forcing is also often significant. The main 1983 midocean cooling began because of increased vertical advection of cool water; but once cooling began horizontal advection often contributed. Further east, where the easterlies generally return later than they do in midocean, upwelling and horizontal advection all can be important. Again no model consensus exists concerning the details of SST evolution.

Because the observations do not agree on the sign of SST change during much of the 1982–83 period, improved SST data is needed in order to document the behavior of the ocean through future ENSO periods. Better forcing data will be needed to carry out improved ocean-model validation studies, and to explore the mechanisms likely responsible for SST change through entire ENSO cycles.

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Ying-Quei Chen, D. S. Battisti, and E. S. Sarachik

Abstract

A 21/2-layer ocean model is developed to investigate the role of the first two baroclinic modes in determining the interannual variations of the sea surface temperature (SST) associated with the El Niño–Southern Oscillation (ENSO) phenomenon. Rather than simply adding an additional mode to the ocean component of the Zebiak–Cane coupled atmosphere–ocean model, it proved necessary to completely rethink all parts of the model. This allowed the external parameters to be specified more realistically. For example, the drag coefficient used in calculating the surface wind stress in the model is now consistent with that empirically derived, and the temperature of the water entrained in the surface layer that affects SST is now more carefully parameterized.

When forced by observed wind stress anomalies for 1961–93, the ocean model reproduces the interannual variations of SST satisfactorily. The quantitative discrepancies between the model hindcast and observed SST anomalies are limited to an excessive cooling of 0.5–1°C in the eastern/central Pacific during the period of 1989 to early 1991, and weaker warm phases in the central/western Pacific than observed. Both of the two gravest baroclinic modes are shown to be important in affecting the interannual variability in SST. A critique of the ocean model is presented at the end of this work.

When the ocean model is coupled with a simple atmosphere model, the resulting model exhibits quasi-periodic ENSO cycles with a period of ∼5 years. The variability in the coupled model is sensitive to the strength of the coupling and to the model parameterization of subsurface temperature. This model provides an opportunity to gain a better insight into the instability and variability of large-scale, low-frequency phenomena in the coupled atmosphere–ocean climate system and to bridge the gap between the simple Zebiak–Cane model and the more complex and computationally intensive coupled general circulation models in which more vertical modes are present.

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Zhaohua Wu, David S. Battisti, and E. S. Sarachik

Abstract

A series of studies are performed to examine the response of the tropical atmosphere to a prescribed steady, large-scale, elevated heat source (i.e., a region of persistent precipitation). Special emphasis is placed on the surface wind response in two idealized cases in which dissipation is achieved exclusively by Rayleigh friction or by Newtonian cooling. Starting from the linearized equations on an equatorial beta plane, theoretical arguments are presented that suggest there are qualitative differences in the solutions of these two models. A dry spectral primitive equation model of the atmosphere is employed and confirms the results obtained from the analytical studies.

The results from both the analytical study and the numerical simulations are consistent in showing that Rayleigh friction and Newtonian cooling play totally different roles in the tropical atmosphere. Newtonian cooling homogenizes the atmospheric motion in the vertical direction, and a strong, vertically uniform wind is found below the base of the heat source. When Rayleigh friction dominates, the circulation driven by the heat source is confined to the layer where the heat source is located. It is also shown that a strong Hadley circulation is associated with reasonable strong Rayleigh friction, but not with Newtonian cooling alone.

Finally, the numerical solution is found for the case where Newtonian cooling acts uniformly in the vertical and Rayleigh friction is included in the lower atmosphere to mimic crudely the dissipation of momentum in the boundary layer. The introduction of the simple boundary layer dramatically reduces the surface circulation that was supported in the Newtonian cooling alone case. Together these results suggest a significant surface circulation is unlikely to be driven by an elevated heat source if it resides above the top of the boundary layer.

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Scot D. Johnson, David S. Battisti, and E. S. Sarachik

Abstract

An empirically derived linear dynamical model is constructed using the Comprehensive Ocean–Atmosphere Data Set enhanced sea surface temperature data in the tropical Pacific during the period 1956–95. Annual variation in the Markov model is sought using various tests. A comparison of Niño-3.4 forecast skill using a seasonally varying Markov model to forecast skill in which the seasonal transition matrices are applied during opposite times of the year from which they were derived is made. As a result, it is determined that the seasonal transition matrices are probably not interchangeable, indicating that the Markov model is not annually constant. Stochastic forcing, which has been hypothesized to exhibit seasonality, is therefore not the sole source of the annual variation of El Niño–Southern Oscillation (ENSO) dynamics and the phase locking of ENSO events to peak during November.

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Zhaohua Wu, E. S. Sarachik, and David S. Battisti

Abstract

In this paper, the three-dimensional structure of the thermally forced atmosphere on an equatorial β plane is investigated. Special emphasis is placed on the relations between the vertical structure of heating and the horizontal structure of the forced response.

By solving the vertical eigenvalue–eigenfunction problem in a vertically semi-infinite domain, the authors obtain a complete set of vertical eigenfunctions that includes a single barotropic (external) mode and a continuous spectrum of baroclinic (internal) modes. These eigenfunctions are used to decompose vertical heating profiles for two types of tropical heating: 1) deep heating representing the convective plume (CP) heating and 2) shallow heating representing mature cloud (MC) cluster heating. By examining the spectral energy density of the heating profile, the contributions of each vertical mode (spectral interval) to the overall structure are explored for each case, and the difference between the responses to these two profiles of heating is discussed. A dry spectral primitive equation model of the atmosphere is employed to verify the analytical results.

The results from both the analytical approach and the numerical simulations are consistent in showing that the vertical structure of the heating is fundamental to the structure of the forced response. The CP is deep relative to the MC. Thus, the CP projects onto the vertical eigenfunctions of relatively larger equivalent depth more so than does the MC. As a result, the CP-forced signals propagate away from the heat source much faster than those forced by the MC. Hence, when the atmosphere is subjected to the same linear dampings (Rayleigh friction and Newtonain cooling), the spatial (mainly in the horizontal) decay rate of the CP-forced signals is significantly smaller than that of the MC-forced signals, and the CP-forced signals extend farther.

To what extent a shallow-water system of a specified vertical mode (e.g., the Gill model) can approximate the three-dimensional response is also examined. Results show that the effective gravity wave speed of the multimode system varies greatly with location. Hence, it is extremely difficult to select a globally suitable equivalent depth so that a one-mode shallow-water system can approximate the spatially three-dimensional structure of the response to a given heating.

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