Atmospheric Energy Balance Model Research Articles

Impacts of Oceanic and Atmospheric Heat Transports on Sea Ice Extent

AbstractClimate-model biases in ocean heat transport (OHT) have been proposed as a major contributor to uncertainties in projections of sea ice extent. To better understand the impact of OHT on sea ice extent and compare it to that of atmospheric heat transport (AHT), an idealized, zonally averaged energy balance model (EBM) is developed. This is distinguished from previous EBM work by coupling a diffusive mixed layer OHT and a prescribed OHT contribution, with an atmospheric EBM and a reduced-complexity sea ice model. The ice-edge latitude is roughly linearly related to the convergence of each heat transport component, with different sensitivities depending on whether the ice cover is perennial or seasonal. In both regimes, Bjerknes compensation (BC) occurs such that the response of AHT partially offsets the impact of changing OHT. As a result, the effective sensitivity of ice-edge retreat to increasing OHT is only ~2/3 of the actual sensitivity (i.e., eliminating the BC effect). In the perennial regime, the sensitivity of the ice edge to OHT is about twice that to AHT, while in the seasonal regime they are similar. The ratio of sensitivities is, to leading order, determined by atmospheric longwave feedback parameters in the perennial regime. Here, there is no parameter range in which the ice edge is more sensitive to AHT than OHT.

Milankovitch Forcing and Meridional Moisture Flux in the Atmosphere: Insight from a Zonally Averaged Ocean–Atmosphere Model

Abstract A 1-Myr-long time-dependent solution of a zonally averaged ocean–atmosphere model subject to Milankovitch forcing is examined to gain insight into long-term changes in the planetary-scale meridional moisture flux in the atmosphere. The model components are a one-dimensional (latitudinal) atmospheric energy balance model with an active hydrological cycle and an ocean circulation model representing four basins (Atlantic, Indian, Pacific, and Southern Oceans). This study finds that the inclusion of an active hydrological cycle does not significantly modify the responses of annual-mean air and ocean temperatures to Milankovitch forcing found in previous integrations with a fixed hydrological cycle. Likewise, the meridional overturning circulation of the North Atlantic Ocean is not significantly affected by hydrological changes. Rather, it mainly responds to precessionally driven variations of ocean temperature in subsurface layers (between 70- and 500-m depth) of this basin. On the other hand, annual and zonal means of evaporation rate and meridional flux of moisture in the atmosphere respond notably to obliquity-driven changes in the meridional gradient of annual-mean insolation. Thus, when obliquity is decreased (increased), the meridional moisture flux in the atmosphere is intensified (weakened). This hydrological response is consistent with deuterium excess records from polar ice cores, which are characterized by dominant obliquity cycles.

The Instability of the Thermohaline Circulation in a Low-Order Model

Abstract Although the instability of the thermohaline circulation has been widely observed in numerical ocean models, theoretical advances have been hindered by the nonlinearity of heat and salt transports, a circulation governed by lateral temperature, and salinity gradients. Because the instability occurs initially in polar waters through the formation of haloclines and the halt of convection, any explanatory model must have at least a surface and a deep layer. The model proposed here (two surface boxes above a deep one) reduces to a 2 degrees-of-freedom dynamical system when convection is active and 3 degrees when it is interrupted. The instability that is induced by a negative freshwater perturbation in polar waters has three stages. The first stage is a rapid 5-yr adjustment to a transient thermal attractor that results from an approximate balance between heat advection and air–sea heat fluxes. The second stage is a slow evolution that self-organizes near this attractor, which preconditions the instability, as it can be shown that the circulation becomes more sensitive to changes in salinity gradients than in temperature gradients. The slow O(100 yr) growth of salinity in the subtropics is the critical precursor of the instability while at the same time the subpolar salinity rises against the initial perturbation to stabilize the system by increasing the overturning and restoring convection. When the overturning becomes smaller than the value at the unstable fixed point, the third stage occurs, which is when the subpolar salinity decreases at last on a fast O(10 yr) time scale, precipitating the fall of the overturning. During the last two stages of the instability, the horizontal thermal gradient increases, but its stabilizing effect is just barely unable to prevent the outcome. The return to stability occurs frequently through a regime of multidecadal oscillations with intermittent convection. The hypothesis of mixed boundary conditions has been relaxed by coupling the ocean box model to an atmospheric energy balance model to show that the coupling increases the stability of the oceanic circulation; however, the precursors of the instability are unchanged.

Ergodic dynamics of the coupled quasigeostrophic-flow-energy-balance system

The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic-flow-energy-balance model. This model consists of the large-scale quasigeostrophic oceanic flow model and the transport equation for oceanic temperature, coupled with an atmospheric energy-balance model. After reformulating this coupled model as a random dynamical system (cocycle property), it is shown that the coupled quasigeostrophic-energy balance fluid system has a random attractor, and under further conditions on the physical data and the covariance of the noise, the system is ergodic, namely, for any observable of the coupled atmosphere-ocean flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long.

The Role of Bottom Vortex Stretching on the Path of the North Atlantic Western Boundary Current and on the Northern Recirculation Gyre

Abstract The mechanisms affecting the path of the depth-integrated North Atlantic western boundary current and the formation of the northern recirculation gyre are investigated using a hierarchy of models, namely, a robust diagnostic model, a prognostic model using a global 1° ocean general circulation model coupled to a two-dimensional atmospheric energy balance model with a hydrological cycle, a simple numerical barotropic model, and an analytic model. The results herein suggest that the path of this boundary current and the formation of the northern recirculation gyre are sensitive to both the magnitude of lateral viscosity and the strength of the deep western boundary current (DWBC). In particular, it is shown that bottom vortex stretching induced by a downslope DWBC near the south of the Grand Banks leads to the formation of a cyclonic northern recirculation gyre and keeps the path of the depth-integrated western boundary current downstream of Cape Hatteras separated from the North American coast. Both south of the Grand Banks and at the crossover region of the DWBC and Gulf Stream, the downslope DWBC induces strong bottom downwelling over the steep continental slope, and the magnitude of the bottom downwelling is locally stronger than surface Ekman pumping velocity, providing strong positive vorticity through bottom vortex-stretching effects. The bottom vortex-stretching effect is also present in an extensive area in the North Atlantic, and the contribution to the North Atlantic subpolar and subtropical gyres is on the same order as the local surface wind stress curl. Analytic solutions show that the bottom vortex stretching is important near the western boundary only when the continental slope is wider than the Munk frictional layer scale.

An Adjoint Analysis of the Meridional Overturning Circulation in a Hybrid Coupled Model

Abstract Multicentury sensitivities in a realistic geometry global ocean general circulation model are analyzed using an adjoint technique. This paper takes advantage of the adjoint model’s ability to generate maps of the sensitivity of a diagnostic (i.e., the meridional overturning’s strength) to all model parameters. This property of adjoints is used to review several theories, which have been elaborated to explain the strength of the North Atlantic’s meridional overturning. This paper demonstrates the profound impact of boundary conditions in permitting or suppressing mechanisms within a realistic model of the contemporary ocean circulation. For example, the so-called Drake Passage Effect in which wind stress in the Southern Ocean acts as the main driver of the overturning’s strength, is shown to be an artifact of boundary conditions that restore the ocean’s surface temperature and salinity toward prescribed climatologies. Advective transports from the Indian and Pacific basins play an important role in setting the strength of the overturning circulation under “mixed” boundary conditions, in which a flux of freshwater is specified at the ocean’s surface. The most “realistic” regime couples an atmospheric energy and moisture balance model to the ocean. In this configuration, inspection of the global maps of sensitivity to wind stress and diapycnal mixing suggests a significant role for near-surface Ekman processes in the Tropics. Buoyancy also plays an important role in setting the overturning’s strength, through direct thermal forcing near the sites of convection, or through the advection of salinity anomalies in the Atlantic basin.

The effects on oceanic planetary waves of coupling with an atmospheric energy balance model

This paper shows the existence of a growing planetary-wave-like ocean mode, with a decadal period and growth rate, which appears when a stratified, diffusive ocean is coupled to a simple atmosphere via an energy balance model (EBM). Such modes are not found when simpler surface ocean conditions are applied. The mode is low order in the vertical and, because of its slow growth, is likely to be observed in Earth System Models using an EBM in place of a fuller set of atmospheric dynamics. There is no apparent physical energy source for such a mode, and therefore it should not be expected to arise in such a model. The mode is analysed through a hierarchy of simple models, which differ only through their surface boundary condition.

The effects on oceanic planetary waves of coupling with an atmospheric energy balance model

This paper shows the existence of a growing planetary-wave-like ocean mode, with a decadal period and growth rate, which appears when a stratified, diffusive ocean is coupled to a simple atmosphere via an energy balance model (EBM). Such modes are not found when simpler surface ocean conditions are applied. The mode is low order in the vertical and, because of its slow growth, is likely to be observed in Earth System Models using an EBM in place of a fuller set of atmospheric dynamics. There is no apparent physical energy source for such a mode, and therefore it should not be expected to arise in such a model. The mode is analysed through a hierarchy of simple models, which differ only through their surface boundary condition.

On the role of thermohaline advection and sea ice in glacial transitions

A two‐dimensional, one‐basin thermohaline oceanic circulation (THC) model coupled to an atmospheric energy balance model (EBM) with land ice albedo effect and a thermodynamic sea ice model is used to study global climate on centennial, and longer, timescales. The model is interpreted to represent the effect of the global ocean, rather than the Atlantic, as is commonly done. It is forced by symmetric insolation and includes a diagnostic parameterization of the hydrologic cycle. Here the strength of the ocean's haline forcing is controlled by a parameter, which reflects the effect of river runoff. This parameter is varied in a set of experiments, which also differ by the magnitude of solar insolation. In wide ranges of the hydrologic cycle, multiple climatic equilibria exist, consisting of circulations with different degrees of asymmetry. More symmetric states have a higher global atmospheric temperature, characteristic of modern climate, whereas less symmetric states are colder and resemble glacial conditions. The maximum global atmospheric temperature difference between such states is consistent with proxy‐data‐derived temperature drop of about 4°C during the glacial, in contrast to EBM‐only sensitivity of about 0.4°C. The mechanics of climate transitions in the model are due to amplification of the orbitally induced global heat budget changes by a major reorganization of the oceanic heat transport. In our model this reorganization is caused by the nonlinear dynamics of the ocean's THC, whose stability regime shifts subject to variable external forcing. Sea ice enhances model climate sensitivity by anchoring deep‐ocean temperature to be near freezing [Kravtsov, 2000] and by affecting atmospheric temperature and land ice extent near the poles because of sea ice insulating properties.

Simulated warm polar currents during the middle Permian

During Permian stage 6 (Wordian, Kazanian) the Pangaean supercontinent was surrounded by a superocean: Panthalassa. An ocean general circulation model has been coupled to an atmospheric energy balance model to simulate the sensitivity of the Wordian climate (∼265 million years ago) to changes in greenhouse gas concentrations, high‐latitude geography, and Earth orbital configurations. The model simulates significantly different circulation features with different levels of greenhouse gas forcing, ranging from a strong meridional overturning circulation in the Southern Hemisphere at low CO2concentration (present level) to more symmetric overturning circulation cells with deep water formation in polar latitudes of both hemispheres at high CO2concentration (8 times present level). The simulated climate with 4 times present level CO2concentration agrees generally well with climate‐sensitive sediments and phytogeographic patterns. The model simulates strong subtropical gyres with similarities to the modern South Pacific circulation and moderate surface temperatures on the southern continent Gondwana, resulting from a strong poleward heat transport in the ocean. An even more moderate climate is generated if high‐latitude land is removed from the southern continent so that ocean currents can penetrate into the polar regions of Gondwana.

Coupled climate modelling of ocean circulation changes during ice age inception

Freshening of high latitude surface waters can change the large-scale oceanic transport of heat and salt. Consequently, atmospheric and sea ice perturbations over the deep water production sites excite a large-scale response establishing an oceanic "teleconnection" with time scales of years to centuries. To study these feedbacks, a coupled atmosphere-ocean-sea ice model consisting of a two dimensional atmospheric energy and moisture balance model (EMBM) coupled to a thermodynamic sea ice model and an ocean general circulation model is utilised. The coupled model reproduces many aspects of the present oceanic circulation. We also investigate the climate impact of changes in fresh water balance during an ice age initiation. In this experiment part of the precipitation over continents is stored within continental ice sheets. During the buildup of ice sheets the oceanic stratification in the North Atlantic is weakened by a reduced continental run-off leading to an enhanced thermohaline circulation. Under these conditions salinity is redistributed such that deep water is more saline than under present conditions. Once the ice sheets built up, we simulate an ice age climate without net fresh water storage on the continents. In this case the coupled model reproduces the shallow and weak overturning cell, an ice edge advance insulating the upper ocean, and many other aspects of the glacial circulation.

Sensitivity of the thermohaline circulation to modern and glacial surface boundary conditions

We analyze the results from over 20 numerical experiments with a global ocean general circulation model (OGCM) under different present and last glacial maximum (LGM) surface boundary conditions. The model exhibits a large range of circulation strengths and patterns, including strong and deep overturning of North Atlantic Deep Water (NADW) under LGM boundary conditions. Parameterizations tuned for today's ocean and fixed atmospheric temperatures contribute to this failure. The experiments show a close relation between the NADW and Antarctic Bottom Water (AABW) overturning cells in the Atlantic. High transport in the NADW cell is associated with little or no transport of AABW. The strength of the AABW overturning cell depends sensitively on the treatment of sea ice in the Southern Ocean. An atmospheric energy balance model coupled with the OGCM allows a free response of the sea ice component. Because of the close link between NADW and AABW, the northern source of deep water must be relatively weak during the LGM. An ocean circulation consistent with paleoclimatic evidence only results when the surface salinity in the northern North Atlantic is reduced. The solution then shows a southward expansion of the Arctic domain and a southward shift of the deep water formation area in the North Atlantic. The glacial NADW is less dense than modern NADW, and AABW occupies a larger part of the abyssal ocean. Compared to modern distributions, there is almost no glacial Antarctic Intermediate Water causing middepth warming in the southern and tropical Atlantic.

On the Robustness of the Interdecadal Modes of the Thermohaline Circulation

Ocean models in box geometry forced by constant surface fluxes of density have been found to spontaneously generate interdecadal oscillations of the thermohaline circulation. This paper analyzes the sensitivity of these oscillations to various physical effects, including the presence of mesoscale turbulence, various thermal surface boundary conditions, and the presence of wind forcing or bottom topography. The role of unstable long baroclinic waves is also reexamined in an attempt to understand the oscillation period. In idealized geometry, it is found that the low-frequency variability of the thermohaline circulation under quasi-constant surface fluxes is a robust feature of the large-scale circulation. It is not strongly affected by energetic mesoscale turbulence; the oscillation period is relatively invariant with respect to varying resolution and momentum and tracer horizontal mixing coefficients, although it loses some regularity as shorter and longer periods of variability emerge when the mesoscale activity increases in strength with smaller mixing coefficients. The oscillations are also retained as the ocean model is coupled to an interactive atmospheric energy balance model; the thermohaline modes are robust to a range of exchange coefficients that widens with the amplitude of the mean circulation. The presence of an additional wind-forced component generally weakens the oscillation, and depending on the relative strength of thermodynamic and dynamic forcings, the oscillation may be completely killed. A simple interpretation is given, highlighting the role of upward Ekman pumping in damping density anomalies. Finally, the interaction of these baroclinic modes with bottom topography depends strongly on the relative directions of the mean topographic features and the mean currents and baroclinic waves, but usually results in a damping influence.

Simulation of ocean temperature change due to the opening of Drake Passage

An ocean general circulation model (GCM) is used to test the hypothesis that the opening of Drake Passage in the Oligocene may have lead to cooling in southern high latitudes. Results of previous studies show that no ocean models using restoring boundary conditions for the surface heat flux could reveal substantial southern high latitude cooling without prescribing atmospheric cooling a priori. To compute the surface heat flux that would be free from the restoring constraints we use another method, which is derived from an atmospheric energy balance model with lateral heat transport. In experiments conducted with both idealized and realistic topography the energy balance method produces substantial cooling not only in high latitudes but in deep waters as well.

Sea Ice and Climate. Part II: Model Climate Stability to Perturbations of the Hydrological Cycle

Abstract The sensitivity of a simple climate model to variations in a global hydrological cycle is studied. The model consists of a zonally averaged single basin, two-hemisphere ocean model coupled to an atmospheric energy balance model and a thermodynamic sea ice model. Land processes are reduced to considerations of the oceanic catchment basins, which serve to amplify or decrease the oceanic freshwater forcing. The model typically admits both symmetric and asymmetric equilibria. For sufficiently strong global freshwater forcing, the symmetric circulation is replaced by asymmetric states. This is accomplished by a supercritical pitchfork bifurcation. It is shown that sea ice enhances climate sensitivity in that larger changes of the hydrological cycle are required to induce instability if sea ice is neglected. This behavior comes from the strong damping of SST anomalies under ice, which is essential for suppressing deep ocean temperature anomalies. Thus, ocean temperature plays an important role in clima...

An investigation of the small ice cap instability in the Southern Hemisphere with a coupled atmosphere-sea ice-ocean-terrestrial ice model

A simple climate model has been developed to investigate the existence of the small ice cap instability in the Southern Hemisphere. The model consists of four coupled components: an atmospheric energy balance model, a thermodynamic snow-sea ice model, an oceanic mixed layer model and a terrestrial ice model. Results from a series of experiments involving different degrees of coupling in the model show that the instability appears only in those cases when an explicit representation of the Antarctic ice sheet is not included in the model. In order to determine which physical processes in the ice sheet model lead to a stabilization of the system we have conducted several sensitivity experiments in each of which a given ice sheet process has been removed from the control formulation of the model. Results from these experiments suggest that the feedback between the elevation of the ice sheet and the snow accumulation-ice ablation balance is responsible for the disappearance of the small ice cap instability in our simulation. In the model, the mass balance of the ice sheet depends on the air temperature at sea level corrected for altitude and it is, therefore, a function of surface elevation. This altitude-mass balance feedback effectively decouples the location of the ice edge from any specific sea level isotherm, thus decreasing the model sensitivity to the albedo-temperature feedback, which is responsible for the appearance of the instability. It is also shown that the elevation-radiative cooling feedback tends to stabilize the ice sheet, although its effect does not seem to be strong enough to remove the instability. Another interesting result is that for those simulations which include the terrestrial ice model with elevation-dependent surface mass balance, hysteresis is exhibited, where for a given level of external forcing, two stable solutions with different, non-zero ice-sheet volume and area and different air and ocean temperature fields occur. However, no unstable transition between the two solutions is ever observed. Our results suggest that the small ice cap instability mechanism could be unsuitable for explaining the inception of glaciation in Antarctica.

Response of a coupled ocean/energy balance model to restricted flow through the Central American Isthmus

Prior ocean modeling work suggested that an open central American isthmus would cause a collapse of the North Atlantic thermohaline circulation because of free exchange of low salinity water between the Atlantic and the Pacific. Geological data provide some support for this response, but the data also indicate that some North Atlantic Deep Water formation occurred before final closure of the isthmus. We previously postulated that this “early switch on” could reflect a more limited exchange of Atlantic waters with the Pacific. In this study we discuss model sensitivity experiments testing that hypothesis and interpret the response in terms of shifts between multiple steady states of the model. Two simulations are conducted with a version of the Hamburg large‐scale geostrophic ocean model that is coupled to an atmospheric energy balance model. Constrictions of throughflow through the central American isthmus is mimicked by locally changing the frictional drag coefficient in the ocean model. Results indicate that modest levels of throughflow can maintain some level of thermohaline circulation. These results support the conjecture in our earlier study. However, the overturning cell is about 300 m shallower than in the control run, with deep water production nearly eliminated in the Labrador Sea. These latter responses should be testable with marine data.

On Spatial Scales and Lifetimes of SST Anomalies beneath a Diffusive Atmosphere

Abstract The authors identify spatial and temporal scales in a one-dimensional linear, diffusive atmospheric energy balance model coupled everywhere to a slab mixed layer of fixed depth. Mathematically, the model is identical to a heat conducting rod, which over its entire length both radiates and is in contact with a large but finite“reservoir.” Three characteristic timescales mark, respectively, the atmosphere’s adjustment to a sea surface temperature (SST) anomaly, the decay of a pointwise SST anomaly, and the radiative decay of a large-scale SST anomaly. The first and the third of these timescales are associated with diffusive length scales characterizing, respectively, the distance over which heat is diffused in the atmosphere before being lost to the ocean beneath, and the distance over which heat is diffused in the coupled system before being radiated to space. For spatial scales between the two diffusive lengths, the SST anomaly does not decay exponentially but with the square root of time; this r...

Variability of the Thermohaline Circulation in an Ocean General Circulation Model Coupled to an Atmospheric Energy Balance Model

The variability of the ocean’s thermohaline circulation in an oceanic general circulation model (OGCM) coupled to a two-dimensional atmospheric energy balance model (EBM) is examined. The EBM calculates air temperatures by balancing heat fluxes, including that from the ocean surface; air temperature and ocean circulation evolve together without imposed temperature restrictions except specification of the solar constant. The heat coupling is scale dependent such that small-scale ocean temperature anomalies are damped quickly while large-scale ones lose heat slowly by longwave emission to space. These boundary conditions are more realistic than restoring conditions even when weak coupling is used, since they allow changes in air temperature and wholesale shifts in the planetary heat balance. It is found that coupling the EBM to the OGCM increases the stability of the ocean’s thermohaline circulation. This increased stability arises from the ability of the coupled model to develop a four times greater sea surface temperature response to a given change in thermohaline overturning than when traditional restoring boundary conditions are used. The sense of this increased response works to stabilize the thermohaline overturning. The specific value of the small-scale thermal coupling coefficient also influences the stability even though the large-scale coefficient is always small (2 W m−2 C−1); this suggests that small-scale processes might determine the large-scale stability.

The Role of Temperature Feedback in Stabilizing the Thermohaline Circulation

Abstract Ocean climate models traditionally compute the surface heat flux with a restoring boundary condition of the form Q = λ(T* − To). This implies an atmosphere of fixed temperature and breaks down when large-scale changes in the ocean circulation are considered, which have a feedback effect on atmospheric temperatures. To include this important feedback, a new thermal boundary condition of the form Q = γ(T* − To) − μ∇2(T* − To) is proposed. This is derived from an atmospheric energy balance model with diffusive lateral heat transport. The effects of this new parameterization are examined in experiments with the GFDL modular ocean model for two model basins. “Conveyor belt” circulation states are compared using traditional mixed boundary conditions and our new coupling. With the new coupling, a realistic temperature contrast is obtained between the North Atlantic and the Pacific, caused by free adjustment of surface temperature to the oceanic heat transport. The results show that a temperature feedbac...