Bryan, Kirk, February 2011: Coupling atmospheric general circulation to oceans In The Development of Atmospheric General Circulation Models: Complexity, Synthesis and Computation, New York, NY, Cambridge University Press, 148-201.
Bryan, Kirk, 2006: Modeling ocean circulation - 1960-1990: The Weather Bureau, and Princeton In Physical Oceanography: Developments Since 1950, Jochum, M., and R. Murtugudde, eds., New York, Springer, 29-44.
Factors controlling the position and strength of the surface winds during the Last Glacial Maximum (LGM) are examined using a global, multilevel, moist, atmospheric model. The idealized aquaplanet model is bounded below by a prescribed axisymmetric temperature distribution that corresponds to an ocean-covered surface. Various forms of this distribution are used to examine the influence of changes in the surface cooling and baroclinicity rates. The model omits seasonal variations.
Increasing the cooling lowers the tropopause and greatly reduces the moist convection in the Tropics, thereby causing a weakening and equatorward contraction of the Hadley cell. Such a cooling also weakens the surface westerlies and shifts the peak westerly stress equatorward. An extra surface baroclinicity in midlatitudes—implicitly associated with an increase in the polar sea ice—also shifts the peak westerly stress equatorward, but strengthens the surface westerlies.
Thus, calculations with combined surface cooling and baroclinicity increases, representative of the Last Glacial Maximum, reveal an absence of change in the amplitude of the peak westerly stress but exhibit a substantial equatorward shift in its position, 7° for a 3-K cooling and 11° for a 6-K cooling. The easterlies, however, always increase in strength when the surface westerlies move equatorward.
The application of these results to the LGM must take into account the model’s assumption of symmetry between the two hemispheres. Any changes in the climate’s hemispheric asymmetry could also cause comparable latitudinal shifts in the westerlies, probably of opposite sign in the two hemispheres. Published coupled-model simulations for the LGM give an equatorward shift for the peak westerlies in the Northern Hemisphere but give contradictory results for the Southern Hemisphere.
Cessi, P, Kirk Bryan, and Rong Zhang, 2004: Global seiching of thermocline waters between the Atlantic and the Indian-Pacific Ocean Basins. Geophysical Research Letters, 31, L04302, DOI:10.1029/2003GL019091. Abstract
Proxy climate data from the Greenland icecap and marine deposits in the Pacific indicate that warm conditions in the North Atlantic are linked to cool conditions in the Eastern Equatorial Pacific, and vice versa. Our ocean models show that the surface branch of the overturning circulation connecting the North Atlantic to the Equatorial Pacific adjusts by exchanging thermocline water between ocean basins in response to changes in deep water formation in the northern North Atlantic. Planetary ocean waves give rise to a global oceanic seiche, such that the volume of thermocline water decreases in the Pacific-Indian Ocean while increasing in the Atlantic Ocean. We conjecture that the remotely forced changes in the thermocline of the Eastern Equatorial Pacific may trigger El Niño events. These global seiches have been previously overlooked due to the difficulty of integrating high-resolution climate models for very long time-scales.
Park, Y-G, and Kirk Bryan, 2001: Comparison of thermally driven circulations from a depth-coordinate model and an isopycnal-layer model. Part II: The difference and structure of the circulations. Journal of Physical Oceanography, 31(9), 2612-2624. Abstract PDF
Thermally driven ocean circulations in idealized basins are calculated with two well-known model codes, one based on depth-level coordinates and the other based on isopycnal coordinates. In addition, the two models have very different representations of convection. In the level-coordinate model, convective adjustment is used, while in the isopycnal-coordinate model, convection is simulated by a transformation of the surface layer to the layer below. Both models indicate a three-layer structure in the circulation. The lower and middle layers have a flow structure that corresponds with the classical abyssal circulation models. The upper flow is strongly constrained by the buoyancy flux field at the upper surface and the convective parameterization. The model with convective adjustment and level coordinates is dominated by an eastward flow, which sinks to subsurface level at the eastern boundary. It lacks any indication of surface cyclonic flow, even in the vicinity of sinking at the northern wall. On the other hand, in the model based on density coordinates the eastward surface flow turns to the north at the eastern boundary and forms a pronounced cyclonic circulation at high latitudes. Due to the cyclonic circulation, the coldest surface water is found near the northwestern corner, while in the level model the coldest water is near the northeastern corner. The isopycnal model appears to be a more realistic representation of the real ocean since both wind and the thermohaline circulation are thought to contribute to the North Atlantic subarctic cyclonic gyre.
Although the zonally averaged buoyancy flux produced by the two model codes is the same, the actual patterns of buoyancy flux at the surface are not similar at high latitudes. This suggests that the two types of numerical models would indicate very different air-sea interaction if coupled to atmospheric models and used to simulate climate. The application of the Gent-McWilliams parameterization of mesoscale eddies to the model with z coordinates and convective adjustment reduces the differences between the surface circulation of the two models by a small amount.
Park, Y-G, and Kirk Bryan, 2000: Comparison of thermally driven circulations from a depth-coordinate model and an isopycnal-layer model. Part I: Scaling-law sensitivity to vertical diffusivity. Journal of Physical Oceanography, 30(3), 590-605. Abstract PDF
Two different types of numerical ocean circulation models are used in a classical idealized problem, the thermally induced circulation in an ocean basin bounded by two meridians to the east and west and by the equator and a line of constant latitude. A simple scaling theory exists for predicting poleward heat transport and the strength of meridional overturning as a function of vertical diffusivity and other external factors. However, previous studies have indicated conflicting results, and other scaling laws have been proposed. Experiments with two widely used types of numerical models, one based on depth coordinates and the other based on isopycnal layers, provide insight into the discrepancies of previous studies. In the numerical experiments vertical diffusivity is varied over a range of 200. The source of the difficulty in previous studies is in part traced to applying a fixed restoring coefficient at the upper boundary and considering the buoyancy forcing at the surface fixed irrespective of vertical diffusivity k. Globally or zonally averaged results show a robust agreement between the two models and support the simple scaling law in a flat-bottom basin and a bowl-shaped basin, as long as the meridional circulation is estimated along isopycnal surfaces and in situ rather than externally imposed restoring density differences are used to estimate the geostrophic-scale velocity. Over the thermocline the vertical mean of the zonally averaged zonal baroclinic pressure gradient has constant ratio to the vertical mean of the zonally averaged meridional baroclinic pressure gradient, consistent with the scaling assumptions for a diffusive thermocline.
Bryan, Kirk, J K Dukowicz, and R D Smith, 1999: On the mixing coefficient in the parameterization of bolus velocity. Journal of Physical Oceanography, 29(9), 2442-2456. Abstract PDF
Mesoscale eddies in the ocean play an important role in the ocean circulation. In order to simulate the ocean circulation, mesoscale eddies must be included explicitly or parameterized. The eddy permitting calculations of the Los Alamos ocean circulation model offer a special opportunity to test aspects of parameterizations that have recently been proposed. Although the calculations are for a model in level coordinates, averages over a five-year period have been carried out by interpolating to instantaneous isopycnal surfaces. The magnitude of "thickness mixing" or bolus velocity is found to coincide with areas of intense mesoscale activity in the western boundary currents of the Northern Hemisphere and the Antarctic Circumpolar Current. The model also predicts relatively large bolus fluxes in the equatorial region. The analysis does show that the rotational component of the bolus velocity is significant. Predictions of the magnitude of the bolus velocity, assuming downgradient mixing of thickness with various mixing coefficients, have been compared directly with the model. The coefficient proposed by Held and Larichev provides a rather poor fit to the model results because it predicts large bolus velocity magnitudes at high latitudes and in other areas in which there is only a small amount of mesoscale activity. A much better fit is obtained using a constant mixing coefficient or a mixing coefficient originally proposed by Stone in a somewhat different context. The best fit to the model is obtained with a coefficient proportional to λ² /T, where λ is the radius of deformation, and T is the Eady timescale for the growth of unstable baroclinic waves.
Bryan, Kirk, 1997: A numerical method for the study of the circulation of the world ocean. Journal of Computational Physics, 135(2), 154-169. Abstract PDF
A model is presented for studying ocean circulation problems taking into account the complicated outline and bottom topography of the World Ocean. To obtain an efficient scheme for the study of low-frequency, large-scale current systems, surface gravity-inertial waves are filtered out by the "rigid-lid" approximation. To resolve special features of the ocean circulation, such as the Equatorial Undercurrent, the numerical model allows for a variable spacing in either the zonal or meridional direction. The model is designed to be as consistent as possible with the continuous equations with respect to energy. It is demonstrated that no fictitious energy generation or decay is associated with the nonlinear terms in the finite difference form of the momentum equations. The energy generation by buoyancy forces for the numerical model is also designed in such a way that no energy "leak" occurs in the transformation from potential to kinetic energy.
Reprinted from Journal of Computational Physics, 4(3), 1969, pages 347-376.
Bryan, Kirk, and Stephen M Griffies, 1997: Predictability of North Atlantic climate on decadal times scales estimated using a coupled ocean-atmosphere model. International WOCE Newsletter, 26, 5-9.
Atmospheric weather systems become unpredictable beyond a few weeks, but climate variations can be predictable over much longer periods because of the coupling of the ocean and atmosphere. With the use of a global coupled ocean-atmosphere model, it is shown that the North Atlantic may have climatic predictability on the order of a decade or longer. These results suggest that variations of the dominant multidecadal sea surface temperature patterns in the North Atlantic, which have been associated with changes in climate over Eurasia, can be predicted if an adequate and sustainable system for monitoring the Atlantic Ocean exists.
The North Atlantic is one of the few places on the globe where the atmosphere is linked to the deep ocean through air-sea interaction. While the internal variability of the atmosphere by itself is only predictable over a period of one to two weeks, climate variations are potentially predictable for much longer periods of months or even years because of coupling with the ocean. This work presents details from the first study to quantify the predictability for simulated multidecadal climate variability over the North Atlantic. The model used for this purpose is the GFDL coupled ocean-atmosphere climate model used extensively for studies of global warming and natural climate variability. This model contains fluctuations of the North Atlantic and high-latitude oceanic circulation with variability concentrated in the 40-60 year range. Oceanic predictability is quantified through analysis of the time-dependent behavior of large-scale empirical orthogonal function (EOF) patterns for the meridional stream function, dynamic topography, 170 m temperature, surface temperature and surface salinity. The results indicate that predictability in the North Atlantic depends on three main physical mechanisms. The first involves the oceanic deep convection in the subpolar region which acts to integrate atmospheric fluctuations, thus providing for a red noise oceanic response as elaborated by Hasselmann. The second involves the large-scale dynamics of the thermohaline circulation, which can cause the oceanic variations to have an oscillatory character on the multidecadal time scale. The third involves non-local effects on the North Atlantic arising from periodic anomalous fresh water transport advecting southward from the polar regions in the East Greenland Current. When the multidecadal oscillatory variations of the thermohaline circulation are active, the first and second EOF patterns for the North Atlantic dynamic topography have predictability time scales on the order of 10-20 y, whereas EOF-1 of SST has predictability time scales of 5-7 y. When the thermohaline variability has weak multidecadal power, the Hasselmann mechanism is dominant and the predictability is reduced by at least a factor of two. When the third mechanism is in an extreme phase, the North Atlantic dynamic topography patterns realize a 10-20 year predictability time scale. Additional analysis of SST in the Greenland Sea, in a region associated with the southward propagating fresh water anomalies, indicates the potential for decadal scale predictability for this high latitude region as well. The model calculations also allow insight into regional variations of predictability, which might be useful information for the design of a monitoring system for the North Atlantic. Predictability appears to break down most rapidly in regions of active convection in the high-latitude regions of the North Atlantic.
Bryan, Kirk, 1996: The role of mesoscale eddies in the poleward transport of heat by the oceans: A review. Physica D, 98(2-4), 249-257. Abstract PDF
The poleward transport of heat by the ocean circulation plays a major role in the global heat balance, but many details of this process remain unclear. In particular, it is difficult to determine from observations what role energetic mesoscale eddies play in poleward heat transport. In place of missing long-term buoy measurements over extensive areas, eddy resolving numerical ocean circulation simulations offer some means to gain insight. For ocean models with specified meridional density distributions at the upper boundary it is possible to compare the poleward heat transport in eddy resolving and non-eddy-resolving simulations. While a change of vertical diffusion in models is known to be very important for poleward heat transport, the reduction of horizontal viscosity and diffusion, which allows mesoscale eddies to appear in the simulation, seems to have little effect. A possible explanation appears to be that the models for normal parameter ranges are very weakly driven thermal systems. The time dependent mesoscale eddies appear to set up nearly adiabatic flows in which eddy transport of heat is compensated by induced mean flows which transport heat in the opposite direction. For extremely strong forcing of the density fields in the upper ocean this is no longer true.
Bryan, Kirk, 1996: The steric component of sea level rise associated with enhanced greenhouse warming: A model study. Climate Dynamics, 12, 545-555. Abstract PDF
Climate change due to enhanced greenhouse warming has been calculated using the coupled GFDL general circulation model of the atmosphere and ocean. The results of the model for a sustained increase of atmospheric carbon dioxide of 1% per year over a century indicate a marked warming of the upper ocean. Results of the model are used to study the rise in sea level caused by increase in ocean temperatures and associated changes in ocean circulation. Neglecting possible contributions due to changes in the volume of polar ice sheets and mountain glaciers, the model predicts an average rise in sea level of approximately 15 ± 5 cm by the time atmospheric carbon dioxide doubles. Heating anomalies are greatest in subpolar latitudes. This effect leads to a weakening of the ocean thermohaline circulation. Changes in thermohaline circulation redistribute heat within the ocean from high latitudes toward the equator, and cause a more uniform sea level rise than would occur otherwise.
Hsieh, W W., and Kirk Bryan, 1996: Redistribution of sea level rise associated with enhanced greenhouse warming: A simple model study. Climate Dynamics, 12, 535-544. Abstract PDF
Future sea level rise from thermal expansion of the World Ocean due to global warming has been explored in several recent studies using coupled ocean-atmosphere models. These coupled models show that the heat input by the model atmosphere to the ocean in such an event could be quite non-uniform in different areas of the ocean. One of the most significant effects predicted by some of the models is a weakening of the thermohaline circulation, which normally transports heat poleward. Since the greatest heat input from enhanced greenhouse warming is in the higher latitudes, a weakening of the poleward heat transport effectively redistributes the heat anomaly and the associated sea level rise to lower latitudes. In this study, the mechanism of ocean circulation spindown and heat redistribution was studied in the context of a much simpler, linearized shallow water model. Although the model is much simpler than the three-dimensional ocean circulation models used in the coupled model experiments, and neglects several important physical effects, it has a nearly 10-fold increase in horizontal resolution and clearer dynamical interpretations. The results indicated that advanced signals of sea level rise propagated rapidly through the action of Kelvin and Rossby waves, but the full adjustment toward a more uniform sea level rise took place much more slowly. Long time scales were required to redistribute mass through narrow currents trapped along coasts and the equatorial wave guide. For realistic greenhouse warming, the model showed why the sea level rise due to ocean heating could be far from uniform over the globe and hence difficult to estimate from coastal tide gauge stations.
The comment by Rahmstorf suggests that a numerical problem in Tziperman et al. (1994, TTFB) leads to a noisy E - P field that invalidates TTFB's conclusions. The authors eliminate the noise, caused by the Fourier filtering used in the model, and show that TTFB's conclusions are still valid. Rahmstorf questions whether a critical value in the freshwater forcing separates TTFB's stable and unstable runs. By TTFB's original definition, the unstable runs in both TTFB and in Rahmstorf's comment have most definitely crossed a stability transition point upon switching to mixed boundary conditions. Rahmstorf finally suggests that the instability mechanism active in TTFB is a fast convective mechanism, not the slow advective mechanism proposed in TTFB. The authors show that the timescale of the instability is, in fact, consistent with the advective mechanism
Treguier, A M., J K Dukowicz, and Kirk Bryan, 1996: Properties of nonuniform grids used in ocean general circulation models. Journal of Geophysical Research, 101(C9), 20,877-20,881. Abstract PDF
Ocean general circulation models frequently use nonuniform grids, especially in the vertical direction. This paper clarifies the implications of using such grids on the consistency and accuracy of numerical schemes. It is emphasized that numerical schemes maintain their order of accuracy on a nonuniform grid provided the grid can be related to a smooth mapping. Additional metric terms appear in the truncation error, which should not be interpreted simply as a numerical diffusion.
Bryan, Kirk, 1995: Commentary on the paper of McWilliams In Natural Climate Variability on Decade-to-Century Time Scales, Washington, DC, National Academy Press, 353.
Bryan, Kirk, and F Hansen, 1995: A stochastic model of North Atlantic climate variability on decade-to-century time scales In Natural Climate Variability on Decade-to-Century Time Scales, Washington, DC, National Academy Press, 355-362; 363-364. Abstract
A conceptual model of North Atlantic climate variability is based on a simple two-box representation of the thermohaline circulation of the ocean. The model is linearized about a basic state, which corresponds approximately to the present ocean climate of the North Atlantic. Stochastic forcing, which represents the random effects of atmospheric cyclones and anticyclones passing over the ocean surface, drives the model away from its equilibrium state. The model transforms this stochastic forcing with equal power at all frequencies into a red-noise response in ocean temperature and salinity. At frequencies less than the thermohaline circulation's time scale, the solution is an equilibrium response and the amplitude of model ocean climate becomes independent of frequency.
Damping of salinity variations in the model is due to the thermohaline circulation. Ocean temperature variations are damped by both the thermohaline circulation and interaction with the atmosphere at the ocean surface.
The model illustrates how air-sea interaction involving the thermohaline circulation could produce a continuous spectrum without peaks. Stochastic forcing amplitudes corresponding to the climate of the last few thousand years produce a nearly linear response of the model. Large perturbations of the hydrological cycle typical of the close of the last ice age produce a chaotic response.
Griffies, Stephen M., and Kirk Bryan, 1994: Predictability of North Atlantic climate variability on multidecadal time scales In The Atlantic Climate Change Program, Proceedings from the principal investigators meeting, NOAA, University Corporation for Atmospheric Research, 77-80. Abstract
A major goal of the ACCP program is to gain the understanding of North Atlantic climate variability required for making predictions. An essential first step in this direction is to assess the predictability of Atlantic climate variability from models. A methodology for doing this was first proposed by Lorenz (1965) for atmospheric models. Recently, predictability studies have been extended to coupled atmosphere-ocean models in connection with the El Niño/Southern Oscillation phenomenon (e.g., Cane and Zebiak, 1987; Goswami and Shukla, 1991). At present, no operational monitoring system exists to provide proper initial conditions for the ocean on a global basis or even for the North Atlantic. The goal of this study is to use the GFDL climate model to determine the value, in terms of practical prediction of multi-decadal climate variability, of an operational, deep-sea observing system. We present here preliminary results toward this goal.
Molinari, R L., , Kirk Bryan, and J Walsh, 1994: The Atlantic Climate Change Program. Bulletin of the American Meteorological Society, 75(7), 1191-1199. Abstract PDF
The Atlantic Climate Change Program (ACCP) is a component of NOAA's Climate and Global Change Program. ACCP is directed at determining the role of the thermohaline circulation of the Atlantic Ocean on global atmospheric climate. Efforts and progress in four ACCP elements are described. Advances include 1) descriptions of decadal and longer-term variability in the coupled ocean-atmosphere-ice system of the North Atlantic; 2) development of tools needed to perform long-term model runs of coupled simulations of North Atlantic air-sea interaction; 3) definition of mean and time-dependent characteristics of the thermohaline circulation; and 4) development of monitoring strategies for various elements of the thermohaline circulation.
Tziperman, E, J R Toggweiler, Y Feliks, and Kirk Bryan, 1994: Instability of the thermohaline circulation with respect to mixed boundary conditions: Is it really a problem for realistic models?Journal of Physical Oceanography, 24(2), 217-232. Abstract PDF
A global primitive equations oceanic GCM and a simple four-box model of the meridional circulation are used to examine and analyze the instability of the thermohaline circulation in an ocean model with realistic geometry and forcing conditions under mixed boundary conditions. The purpose is to determine whether this instability should occur in such realistic GCMs.
It is found that the realistic GCM solution is near the stability transition point with respect to mixed boundary conditions. This proximity to the transition point allows the model to make a transition between the unstable and stable regimes induced by a relatively minor change in the surface freshwater flux and in the interior solution. Such a change in the surface flux may be induced, for example, by changing the salinity restoring time used to obtain the steady model solution under restoring conditions. Thus, the steady solution of the global GCM under restoring conditions may be either stable or unstable upon transition to mixed boundary conditions, depending on the magnitude of the salinity restoring time used to obtain this steady solution. The mechanism by which the salinity restoring time affects the model stability is further confirmed by carefully analyzing the stability regimes of a simple four-box model. The proximity of the realistic ocean model solution to the stability transition point is used to deduce that the real ocean may also be near the stability transition point with respect to the strength of the freshwater forcing.
Finally, it is argued that the use of too short restoring times in realistic models is inconsistent with the level of errors in the data and in the model dynamics, and that this inconsistency is a possible reason for the existence of the thermohaline instability in GCMs of realistic geometry and forcing. A consistency criterion for the magnitude of the restoring times in realistic models is formulated, that should result in steady states that are also stable under mixed boundary conditions. The results presented here may be relevant to climate studies that run an ocean model under restoring conditions in order to initialize a coupled ocean-atmosphere model.
Tziperman, E, and Kirk Bryan, 1993: Estimating global air-sea fluxes from surface properties and from climatological flux data using an oceanic general circulation model. Journal of Geophysical Research, 98(C12), 22,629-22,644. Abstract
A simple method is presented and demonstrated for estimating air-sea fluxes of heat and fresh water with the aid of a general circulation model (GCM), using both sea surface temperature and salinity data and climatological air-sea flux data. The approach is motivated by a least squares optimization problem in which the various data sets are combined to form an optimal solution for the air-sea fluxes. The method provides estimates of the surface properties and air-sea flux data that are as consistent as possible with the original data sets and with the model physics. The calculation of these estimates involves adding a simple equation for calculating the air-sea fluxes during the model run and then running the model to a steady state. The proposed method was applied to a coarse resolution global primitive equation model and annually averaged data sets. Both the spatial distribution of the global air-sea fluxes and the meridional fluxes carried by the ocean were estimated. The resulting air-sea fluxes seem smoother and significantly closer to the climatological flux estimates than do the air-sea fluxes obtained from the GCM by simply specifying the surface temperature and salinity. The better fit to the climatological fluxes was balanced by a larger deviation from the surface temperature and salinity. These surface fields were still close to the observations within the measurement error in most regions, except western boundary areas. The inconsistency of the model and data in western boundary areas is probably related to the inability of the coarse resolution GCM to appropriately simulate the large transports there. The meridional fluxes calculated by the proposed method differ very little from those obtained by simply specifying the surface temperature and salinity. We suggest therefore that these meridional fluxes are strongly influenced by the interior model dynamics; in particular, the too-weak model meridional circulation cell seems to be the reason for differences between the meridional transports in the model and those estimated from other sources. We discuss the implications for the calculation of air-sea fluxes by inverse models.
Gordon, A L., S E Zebiak, and Kirk Bryan, 1992: Climate variability and the Atlantic Ocean. EOS, 73(15), 161, 164-165.
Manabe, Syukuro, Ronald J Stouffer, Michael J Spelman, and Kirk Bryan, 1992: Response of a coupled ocean-atmosphere-land surface model to a gradual increase of atmospheric carbon dioxide In The Global Role of Tropical Rainfall, Hampton, Virginia, Deepak Publishing, 93-103. Abstract
This study investigates the response of a climate model to a gradual increase of atmospheric carbon dioxide. The model is a general circulation model of the coupled ocean-atmosphere-land surface system with a global computational domain, smoothed geography, and seasonal variation of insolation. It is found that the simulated warming of sea surface temperature is very slow over the northern North Atlantic and the circumpolar ocean of the Southern Hemisphere where the vertical mixing of water penetrates very deeply and the rate of deep water formation is relatively fast. With the exception of these two regions, the distribution of the change in surface temperature of the model is qualitatively similar to the equilibrium response of an atmospheric-mixed layer ocean model, which has been the subject of many previous studies.
The increase of atmospheric carbon dioxide affects not only the thermal structure of the coupled model, but also its hydrologic cycle. For example, the global mean rates of both precipitation and evaporation increase. The increase in evaporation rate is particularly large in low latitudes and decreases with increasing latitudes. On the other hand, the increase in the precipitation rate is substantial in high latitudes due to the increased penetration of warm, moisture-rich air into high latitudes. Thus, the rate of runoff in the subarctic basins is increased markedly.
In qualitative agreement with the results of equilibrium response studies, soil moisture is reduced in summer over extensive regions of the middle and high latitudes, such as the North American Great Plains, Western Europe, Northern Canada, and Siberia.
Manabe, Syukuro, Ronald J Stouffer, Michael J Spelman, and Kirk Bryan, 1992: Transient response of a coupled ocean-atmosphere-land surface model to increasing atmospheric carbon dioxide In Advances in Theoretical Hydrology: A Tribute to Jim Dooge, The Netherlands, Elsevier Science Publishers, 159-173. Abstract
This study investigates the response of a climate model to a gradual increase of atmospheric carbon dioxide. The model is a general circulation model of the coupled ocean-atmosphere-land surface system with a global computational domain, smoothed geography, and seasonal veriation of insolation. It is found that the simulated increase of sea surface temperature is very slow over the northern North Atlantic and the Circumpolar Ocean of the Southern Hemisphere where the vertical mixing of water penetrates very deeply and the rate of deep water formation is relatively fast. With the exception of these two regions identified above, the distribution of the change in surface temperature of the model is qualitatively similar to the equilibrium response of an atmospheric-mixed layer ocean model, which has been the subject of many previous studies. In most of the Northern Hemisphere, the seasonal dependence of surface air temperature change is also similar to the equilibrium response. For example, the temperature increase is at a maximum over the Arctic Ocean and its surroundings in the late fall and winter, whereas it is at a minimum in summer. However, the increase of surface air temperature and its seasonal variation is very small in the Circumpolar Ocean of the Southern Hemisphere and the northern North Atlantic.
The increase of atmospheric carbon dioxide affects not only the thermal structure of the coupled model but also its hydrologic cycle. For example, the global mean rates of both precipitation and evaporation increase. The increase in evaporation rate is particularly large in low latitudes and decreases with increasing latitudes. On the other hand, the increase in the precipitation rate is substantial in high latitudes due to the increased penetration of warm, moisture-rich air into high latitudes. Thus, the rate of runoff in the subarctic basin increases markedly.
In qualitative agreement with the results of equilibium response studies, soil moisture is reduced in summer over extensive regions of the middle and high latitudes, such as the North American Great Plains, Western Europe, Northern Canada, and Siberia.
Stephenson, D B., and Kirk Bryan, 1992: Large-scale electric and magnetic fields generated by the oceans. Journal of Geophysical Research, 97(C10), 15,467-15,480. Abstract
The magnetostatic equations are used to derive a consistent set of equations capable of describing the global-scale, low-frequency electric and magnetic fields induced by the motion of the ocean through the geomagnetic field. The equations are solved numerically with realistic 2° x 2° topography in a global domain with ocean flow simulated by a detailed ocean circulation model. Estimates of the annual mean and the first annual harmonic of the electric potential, the vertical component of the oceanic magnetic field, and the vertically integrated electric current density stream function are obtained. With the idea of using electric and magnetic fields to deduce large-scale oceanic flow, emphasis is placed on the geographical location of interesting features. The fields are not found to be basin-wide but rather are found to be localized and strongest in shallow regions. The magnetic fields generated by ocean currents are of the order of 1 nT, and while these can be measured by magnetometers, they would be difficult to detect owing to contamination from other sources of magnetic variation. In finding the electric field, electric currents cannot be neglected where ocean currents cut across isobaths. However, in regions where the ocean flow is aligned with the isobaths, measurement of electric fields is sufficient to find the ocean flow.
Tziperman, E, W C Thacker, and Kirk Bryan, 1992: Computing the steady oceanic circulation using an optimization approach. Dynamics of Atmospheres and Oceans, 16, 379-403. Abstract
The traditional method for computing the steady oceanic circulation has been by stepping an oceanic model forward in time until transients are damped by friction. An alternative method, which has the potential for being more economical is to minimize the sum of the squares of the residuals of the steady model equations. A variety of algorithms might be considered for computing the minimum; attention here is focused on preconditioned conjugate-gradient descent with the gradient computed using adjoint model. The choice of variables, i.e., the preconditioning transformation used in the optimization process, is found to be critical to the efficiency of the method. An appropriate preconditioning transformation can be suggested by a heuristic analysis similar to that commonly used to test the stability of numerical models. The method is demonstrated within the context of the barotropic vorticity equation.
Bryan, Kirk, 1991: Michael Cox (1941-1989): His pioneering contributions to ocean circulation modeling. Journal of Physical Oceanography, 21(9), 1259-1270. Abstract PDF
Michael Cox was a pioneer in the development and application of numerical models to the study of the ocean circulation. His simulation of the response of the Indian Ocean to the monsoons was one of the first applications of a numerical model to seasonal changes in circulation near the equator. Cox's finding that the seasonal reversal of the Somali Current was primarily due to local monsoon-driven coastal upwelling challenged a popular theory that the effects of remote forcing, propagating westward along the equatorial waveguide, were the most important mechnism. In a detailed follow-up study, he was able to demonstrate that remote forcing could only be important near the equator along the Somali Coast and that local driving was the only viable mechanism to explain the amplitude and phase of the main features of the seasonal reversal of the Somali Current.
In another pioneering calculation, Cox was the first to simulate the seasonal changes of the eastern equatorial Pacific, including the Legeckis waves between the South Equatorial Current and the Equatorial Counter Current. From his analysis, he concluded that the Legeckis waves were due to both baroclinic and barotropic instability.
Using observed temperature and salinity data, Cox carried out a new type of diagnostic study of the circulation of the World Ocean. His calculations demonstrated the great importance of adjusting the observed density field in a manner compatible with the constraints imposed by the conservation of mass, temperature, and salinity
In a detailed comparison of simulations of ocean circulation in eddy- and noneddy-resolving models of simplified geometry, Cox was able to demonstrate that mesoscale eddies could have some very important effects on midlatitude thermocline ventilation by wind-driven downwelling. In particular, the mixing by mesoscale eddies along isopycnal surfaces could be strong enough to erase tracer and potential vorticity gradients over trajectories of less than 2000 km. On the other hand, Cox found that poleward transport of buoyancy was approximately the same in similar runs, which did, or did not, include mesoscale eddies. He concluded that this was due to eddy-time mean flow compensation. A similar phenomenon exists in the weakly driven flows of the earth's stratosphere.
Bryan, Kirk, 1991: Ocean circulation models In Strategies for Future Climate Research, Hamburg, Germany, Max Planck Institut für Meteorologie, 265-285. Abstract
Ocean circulation may be characterized as a "stiff system" with a wide range of important frequencies and horizontal scales. The growing power of computers is allowing an exploration of this wide-banded system through numerical experiments. This review focuses on recent experiments with very high horizontal resolution. Examples are given of a high resolution model of the World Ocean used to assimilate existing observation of water mass properties, and a very detailed process study carried out in idealized geometry. These high resolution experiments offer an opportunity for exploring dynamic issues related to the ocean's role in climate and climate change. Many ideas based on the interpretation of tracers and water masses, can be placed in a more quantitative framework.
Bryan, Kirk, 1991: Poleward heat transport in the ocean. A review of a hierarchy of models of increasing resolution. Tellus, 43AB, 104-115. Abstract PDF
The large-scale transport of heat and carbon by the ocean circulation play an important role in the Earth's climate. Progress in developing realistic models of this process is reviewed. Sufficient numerical experiments have been carried out to indicate the role of subgrid scale mixing of temperature and salinity in the transport behavior of the models. The vertical component of subgrid diffusion in the models is essential for determining the amplitude of the thermohaline circulation of the ocean. In the case of simple geometrics, poleward heat transport in models is approximately proportional to vertical mixing to the two-thirds power. The horizontal component of the diffusion appears to play almost no role in the poleward transport of heat as long as the value is less than 1032/s. At low values of horizontal diffusion and viscosity, mesoscale eddies are generated spontaneously in the models through baroclinic and barotropic instability. In analogy with the atmosphere one would expect these mesoscale disturbances to play an important role in poleward heat transport. The results of numerical experiments show that this may not be the case. The mesoscale eddies in the models generate mean flows which tend to cancel the eddy fluxes in much the same way that eddy-mean flow compensation occurs fot atmospheric disturbances in the lower stratosphere.
On decadal time-scales the historical surface temperature record over land in the Northern Hemisphere is dominated by polar amplified variations. These variations are coherent with SST anomalies concentrated in the Northwest Atlantic, but extending with lesser amplitude in the North Pacific as well. Bjerknes suggested that multi-year SST anomalies in the subpolar North Atlantic were due to irregular changes in the intensity of the thermohaline circulation. In support of the Bjerknes hypothesis there is evidence that winter overturning in the Labrador Sea was suppressed for a brief period from 1967-1969 by a cap of relative fresh water at the surface. Cause and effect are unclear, but this event was associated with a marked cooling of the entire Northern Hemisphere.
The difference in SST averaged over the Northern Hemisphere oceans and SST averages over the Southern Hemisphere oceans from the equator to 40°S is coherent with Sahel summer rainfall on decadal time scales. Empirical evidence is supported by numerical experiments with the British Meteorological Office atmospheric climate model which simulate augmented monsoonal rainfall in the Sahel region of Africa in response to realistic warm SST anomalies in the Northwest Atlantic. A coupled ocean-atmosphere global model exhibits two equilibrium climate states. One has an active thermohaline circulation in the North Atlantic and the other does not. The two climate states provide an extreme example which illustrates the type of large scale air-sea interaction Bjerknes visualized as a mechanism for North Atlantic climate variability on decadal time-scales.
Dickinson, R, R Monastersky, J Eddy, Kirk Bryan, and S Matthews, 1991: In The Climate System, Boulder, CO, UCAR, 21 pp..
Manabe, Syukuro, Ronald J Stouffer, Michael J Spelman, and Kirk Bryan, 1991: Transient responses of a coupled ocean-atmosphere-land surface model to gradual changes of atmospheric CO2 In Global Change, Proceedings of the first Demetra meeting held at Chianciano Terme, Italy from 28 to 31 October 1991, Environment and Quality of Life, EUR 15158 EN, Directorate-General Science, Research and Development, European Commission, 82-93.
This study investigates the response of a climate model to a gradual increase or decrease of atmospheric carbon dioxide. The model is a general circulation model of the coupled atmosphere-ocean-land surface system with global geography and seasonal variation of insolation. To offset the bias of the coupled model toward settling into an unrealistic state, the fluxes of heat and water at the ocean-atmosphere interface are adjusted by amounts that vary with season and geography but do not change from one year to the next. Starting from a quasi-equilibrium climate, three numerical time integrations of the coupled model are performed with gradually increasing, constant, and gradually decreasing concentrations of atmospheric carbon dioxide.
It is noted that the simulated response of sea surface temperature is very slow over the northern North Atlantic and the Circumpolar Ocean of the Southern Hemisphere where vertical mixing of water penetrates very deply. However, in most of the Northern Hemisphere and low latitudes of the Southern Hemisphere, the distribution of the change in surface air temperature of the model at the time of doubling (or halving) of atmospheric carbon dioxide resembles the equilibrium response of an atmospheric-mixed layer ocean model to CO2 doubling (or halving). For example, the rise of annual mean surface air temperature in response to the gradual increase of atmospheric carbon dioxide increases with latitudes in the Northern Hemisphere and is larger over continents than oceans.
When time-dependent response of the model oceans to the increase of atmospheric carbon dioxide is compared with the corresponding response to the CO2 reduction at an identical rate, the penetration of the cold anomaly in the latter case is significantly deeper than that of the warm anomaly in the former case. The lack of symmetry in the penetration depth of a thermal anomaly between the two cases is associated with the difference in static stability, which is due mainly to the change in the vertical distribution of salinity in high latitudes and temperature changes in middle and low latitudes.
Despite the difference in penetration depth and accordingly, the effective thermal inertia of the oceans between two experiments, the time-dependent response of the global mean surface air temperature in the CO2 reduction experiment is similar in magnitude to the corresponding response in the CO2 growth experiment. In the former experiment with a colder climate, snow and sea ice with high surface albedo cover a much larger area, thereby enhancing their positive feedback effect upon surface air temperature. On the other hand, surface cooling is reduced due to the larger effective thermal inertia of the oceans. Because of the compensation between these two effects, the magnitude of surface air temperature response turned out to be similar between the two experiments.
Stouffer, Ronald J., Syukuro Manabe, and Kirk Bryan, 1991: Climatic response to a gradual increase of atmospheric carbon dioxide In Greenhouse-Gas-Induced Climatic Change: A Critical Appraisal of Simulations and Observations, The Netherlands, Elsevier Science Publishers, 129-136. Abstract
The transient response of a coupled ocean-atmosphere model to an increase of carbon dioxide has been the subject of several studies (Bryan et al., 1982; Spelman and Manabe, 1984; Bryan and Spelman, 1985; Schlesinger and Jiang, 1988; Schlesinger et al., 1985; Bryan et al., 1988; Manabe et al., 1990; Washington and Meehl, 1989). The models used in these studies explicitly incorporate the effect of heat transport by ocean currents and are different from the model used by Hansen et al. (1988). Here we evaluate the climatic influence of increasing atmospheric carbon dioxide using a coupled model recently developed at the NOAA Geophysical Fluid Dynamics Laboratory. The model response exhibits a marked and unexpected interhemispheric asymmetry. In the circumpolar ocean of the Southern Hemisphere, a region of deep vertical mixing, the increase of surface air temperature is very slow. In the Northern Hemisphere of the model, the rise of surface air temperature is faster and increases with latitude, with the exception of the northern North Atlantic, where it is relatively slow because of the weakening of the thermohaline circulation.
Bretherton, Christopher S., Kirk Bryan, and J D Woods, 1990: Time dependent greenhouse-gas-induced climate change In Climate Change: The IPCC Scientific Assessment, Cambridge, UK, Cambridge University Press, 173-194.
The transient response of climate to an instantaneous increase in the atmospheric concentration of carbon dioxide has been investigated by a general circulation model of the coupled ocean-atmosphere-land system with global geography and annual mean insolation. An equilibrium climate of the coupled model climate during the 60-year period after the doubling is compared with the result from a control integration of the model without the doubling. The increase of surface air temperature in middle and high latitudes is slower in the Southern Hemisphere than the Northern Hemisphere. The large thermal inertia of the ocean-dominated hemisphere is partly responsible for this difference. The effective thermal inertia of the oceans becomes particularly large in high southern latitudes. Owing to the absence of meridional barriers at the latitudes of the Drake Passage, a wind-driven, deep cell of meridional circulation is maintained in the Circumpolar Ocean of the model. In addition, a deep reverse cell develops in the immediate vicinity of the Antarctic Continent. The thermal advection by these cells and associated convective overturning result in a very efficient mixing of heat in the 2-km thick upper layer and increase the effective thermal inertia of the ocean, thereby contributing to the slowdown of the CO2- induced warming of the near-surface layer of the Circumpolar Ocean of the model. It is surprising that, during the last 15 years of the 60-year experiment, sea surface temperatures in the Circumpolar Ocean actually reduce with time. Because of the increase in precipitation caused by the enhanced penetration of warm, moisture-rich air aloft into high latitudes, the surface halocline of the Circumpolar Ocean intensifies, thereby suppressing the convective mixing between the surface layer and the warmer underlying water. Thus, sea surface temperature is reduced in the Circumpolar Ocean towards the end of the experiment. In the Northern Hemisphere, the CO2-induced warming of the lower troposphere increases with increasing latitudes and is at a maximum near the North Pole due partly to the albedo feedback process involving sea ice and snow cover. The warming of the upper ocean layer also increases with increasing latitudes up to about 65 degrees N where the absorption of solar radiation increases markedly due to the poleward retreat of sea ice. Over the Arctic Ocean, the warming is very large in the surface layer of the model atmosphere, whereas it is very small in the underlying water. Both sea ice and a stable surface halocline act as thermal insulators and are responsible for the large air-sea contrast of the warming in this region. In short, the CO2- induced warming of the sea surface has a large interhemispheric asymmetry, in qualitative agreement with the results from a previous study conducted by use of a coupled model with a sector computational domain and an idealized geography. This asymmetry induces an atmospheric response which is quite different between the two hemispheres.
Bryan, Kirk, 1989: Climate response to greenhouse warming: The role of the ocean In Climate and Geo-Sciences: A Challenge for Science and Society in the 21st Century, Amsterdam; The Netherlands, Kluwer Academic Publishers, 435-446.
Bryan, Kirk, 1989: The design of numerical models of the ocean circulation In Oceanic Circulation Models: Combining Data and Dynamics, Amsterdam; The Netherlands, Kluwer Academic Publishers, 465-500.
Bryan, Kirk, and Syukuro Manabe, 1989: Ocean circulation in warm and cold climates In Climatic Change Influences on Oceanic Circulation, Amsterdam; The Netherlands, Kluwer Academic Publishers, 951-966.
The transient response of a coupled ocean-atmosphere model to an increase of atmospheric carbon dioxide has been the subject of several studies. The models used in these studies explicitly incorporate the effect of heat transport by ocean currents and are different from the model used by Hansen et al. Here we evaluate the climatic influence of increasing atmospheric carbon dioxide using a coupled model recently developed at the NOAA Geophysical Fluid Dynamics Laboratory. The model response exhibits a marked and unexpected interhemispheric asymmetry. In the circumpolar ocean of the Southern Hemisphere, a region of deep vertical mixing, the increase of surface air temperature is very slow. In the Northern Hemisphere of the model, the warming of surface air is faster and increases with latitude, with the exception of the northern North Atlantic, where it is relatively slow because of the weakening of the thermohaline circulation.
Toggweiler, J R., Keith W Dixon, and Kirk Bryan, 1989: Simulations of radiocarbon in a coarse-resolution world ocean model 1. Steady state prebomb distributions. Journal of Geophysical Research, 94(C6), 8217-8242. Abstract PDF
This paper presents the results of five numerical simulations of the radiocarbon distribution in the ocean using the Geophysical Fluid Dynamics Laboratory primitive equation world ocean general circulation model. The model has a 4.5 degree latitude by 3.75 degree longitude grid, 12 vertical levels, and realistic continental boundaries and bottom topography. The model is forced at the surface by observed, annually averaged temperatures, salinities, and wind stresses. There are no chemical transformations or transport of 14C by biological processes in the model. Each simulation in this paper has been run out the equivalent of several thousand years to simulate the natural, steady state distribution of 14C in the ocean. In a companion paper the final state of these simulations is used as the starting point for simulations of the ocean's transient uptake of bomb-produced 14C. The model reproduces the mid-depth 14C minimum observed in the North Pacific and the strong front near 45 degrees S between old, deep Pacific waters and younger circumpolar waters. In the Atlantic, the model's deep 14C distribution is much too strongly layered with relatively old water from the Antarctic penetrating into the northern reaches of the North Atlantic basin. Two thirds of the decay of 14C between 35 degrees S and 35 degrees N is balanced by local 14C input from the atmosphere and downward transport by vertical mixing (both diffusion and advective stirring). Only one third is balanced by transport of 14C from high latitudes. A moderately small mixing coefficient of 0.3 cm2 s-1 adequately parameterizes vertical diffusion in the upper kilometer. Spatial variation in gas exchange rates is found to have a negligible effect on deepwater radiocarbon values. Ventilation of the circumpolar region is organized in the model as a deep overturning cell which penetrates as much as 3500 m below the surface. While allowing the circumpolar deep water to be relatively well ventilated, the overturning cell restricts the ventilation of the deep Pacific and Indian basins to the north. This study utilizes three different realizations of the ocean circulation. One is generated by a purely prognostic model, in which only surface temperatures and salinities are restored to observed values. Two are generated by a semidiagnostic model, in which interior temperatures and salinities are restored toward observed values with a 1/50 year-1 time constant. The prognostic version is found to produce a clearly superior deep circulation in spite of producing interior temperatures and salinities which deviate very noticeably from observed values. The weak restoring terms in the diagnostic model suppress convection and other vertical motions, causing major disruptions in the diagnostic model's deep sea ventilation.
Toggweiler, J R., Keith W Dixon, and Kirk Bryan, 1989: Simulations of radiocarbon in a coarse-resolution world ocean model 2. Distributions of bomb-produced carbon 14. Journal of Geophysical Research, 94(C6), 8243-8264. Abstract PDF
Part 1 of this study examined the ability of the Geophysical Fluid Dynamics Laboratory (GFDL) primitive equation ocean general circulation model to simulate the steady state distribution of naturally produced 14C in the ocean prior to the nuclear bomb tests of the 1950s and early 1960s. In part 2 we begin with the steady state distributions of part 1 and subject the model to the pulse of elevated atmospheric 14C concentrations observed since the 1950s. This study focuses on the processes and time scales which govern the transient distributions of bomb 14C in the upper kilometer of the ocean. Model projections through 1990 are compared with observations compiled by the Geochemical Ocean Sections Study (GEOSECS) in 1972, 1974, and 1978; the Transient Tracers in the Ocean (TTO) expedition in 1981, and the French INDIGO expeditions in 1985-1987. In their analysis of the GEOSECS 14C observations, Broecker et al. (1985) noted that much of the bomb 14C which entered the ocean's equatorial belts prior to GEOSECS accumulated in the adjacent subtropical zones. Broecker et al. argued that this displacement of bomb 14C inventories was caused by the wind-driven upwelling and surface divergence in the tropics combined with convergent flow and downwelling in the subtropics. Similar displacements were invoked to shift bomb 14C from the Antarctic circumpolar region into the southern temperate zone. The GFDL model successfully reproduces the observed GEOSECS inventories, but then predicts a significantly different pattern of bomb 14C uptake in the decade following GEOSECS. The post-GEOSECS buildup of bomb 14C inventories is largely confined to the subthermocline layers of the North Atlantic, the lower thermocline of the southern hemisphere, and down to 2000 m in the circumpolar region. A great deal of attention is devoted to detailed comparisons between the model and the available radiocarbon data. A number of flaws in the model are highlighted by this analysis. The Subantarctic Mode Waters forming along the northern edge of the circumpolar current are identified as a very important process for carrying bomb 14C into the thermoclines of the southern hemisphere. The model concentrates its mode water formation in a single sector of the circumpolar region and consequently fails to form its mode waters with the correct T-S properties. The model also moves bomb 14C into the deep North Atlantic and deep circumpolar region much too slowly.
Bryan, Kirk, 1988: Efficient methods for finding the equilibrium climate of coupled ocean-atmosphere models In Physically-based Modelling and Simulation of Climate and Climatic Change, Pt. I, Dordrecht, Holland, Kluwer Academic Publishers, 567-582. Abstract
Climate involves the interaction of the atmosphere, hydrosphere, and cryosphere, with an extremely wide range of significant time scales. Straightforward numerical integration of the time-dependent equations of a climate model is not a practical way to find equilibrium solutions of a more complete climate model. Methods that have been found useful for finding climate equilibrium in low-resolution coupled atmosphere-ocean models are described.
Bryan, Kirk, and Syukuro Manabe, 1988: Ocean circulation in warm and cold climates In Physically-based Modelling and Simulation of Climate Change, Part II, Dordrecht, Holland, Kluwer Academic Publishers, 951-966.
Bryan, Kirk, Syukuro Manabe, and Michael J Spelman, 1988: Interhemispheric asymmetry in the transient response of a coupled ocean-atmosphere model to a CO2 forcing. Journal of Physical Oceanography, 18(6), 851-867. Abstract PDF
Numerical experiments are carried out using a general circulation model of a coupled ocean-atmosphere system with idealized geography, exploring the transient response of climate to a rapid increase of atmospheric carbon dioxide. The computational domain of the model is bounded by meridians 120° apart, and includes two hemispheres. The ratio of land to sea at each latitude corresponds to the actual land-sea ratio for the present geography of the Earth. At the latitude of the Drake Passage the entire sector is occupied by ocean.
In the equivalent of the Northern Hemisphere the ocean delays the climate response to increased atmospheric carbon dioxide. The delay is of the order of several decades, a result corresponding to previous modeling studies. At high latitudes of the equivalent of the ocean-covered Southern Hemisphere, on the other hand, there is no warming at the sea surface, and even a slight cooling over the 50-year duration of the experiment. Two main factors appear to be involved. One is the very large ratio of ocean to land in the Southern Hemisphere. The other factor is the very deep penetration of a meridional overturning associated with the equatorward Ekman transport under the Southern Hemisphere westerlies. The deep cell delays the response to carbon-dioxide warming by upwelling unmodified waters from great depth. This deep cell disappears when the Drake Passage is removed from the model.
Bryan, Kirk, 1987: Man's great geophysical experiment: Can we model the consequences?Oceanus, 29(4), 36-42. Abstract PDF
Greenhouse gases in the atmosphere produced by modern man are changing the global radiation balance-Carbon Dioxide and Climate: A Scientific Assessment. Climate Research Board, National Academy of Sciences, 1979. Resulting climate trends, however, depend on complex interactions between the ocean, atmosphere, and biosphere. Is it possible to harness existing knowledge of ocean and atmosphere circulation to build models accurate enough to forecast the climate consequences of a probable buildup of greenhouse gases continuing well on into the 21st century?
Bryan, Kirk, 1987: Potential vorticity in models of the ocean circulation. Quarterly Journal of the Royal Meteorological Society, 113, 713-734. Abstract PDF
Existing observations suffice to give a qualitative description of the wind-driven and thermohaline components of the ocean circulation, but a hierarchy of analytical and numerical models is now needed for use in coupled ocean-atmosphere models of the earth's climate. Potential vorticity is a more appropriate diagnostic field variable than angular momentum for the ocean circulation because of the complicated geometry of ocean basins. Patterns of potential vorticity on surfaces of constant density help validate ocean circulation models, and give physical insight into how the ocean circulation works.
High resolution models suggest that the lateral mixing of potential vorticity by mesoscale eddies along isopycnal surfaces is of the same order as large-scale advection, and that the assumption of inviscid, potential-vorticity-conserving flow in the thermocline is not appropriate for the real ocean. A satisfactory test of this vorticity-conserving flow in the thermocline is not appropriate for the real ocean. A satisfactory test of this conjecture will require the extensive measurements planned for the World Ocean Circulation Experiment.
Models also indicate that the transport of water mass properties by mesoscale eddies is largely a mixing along isopycnal surfaces. The weak temperature gradients along isopycnal surfaces in most areas of the ocean limit the effectiveness of the mesoscale eddies in transporting significant amounts of heat across latitude circles.
Hibler III, W D., and Kirk Bryan, 1987: A diagnostic ice-ocean model. Journal of Physical Oceanography, 17(7), 987-1015. Abstract PDF
A coupled ice-ocean model suitable for simulating ice-ocean circulation over a seasonal cycle is developed by coupling the dynamic thermodynamic sea ice model of Hibler with a multilevel baroclinic ocean model (Bryan). This model is used to investigate the effect of ocean circulation on seasonal sea ice simulations by carrying out a simulation of the Arctic, Greenland and Norwegian seas. The ocean model contains a linear term that damps the ocean's temperature and salinity towards climatology. The damping term was chosen to have a three-year relaxation time, equivalent to the adjustment time of the pack ice. No damping, however, was applied to the uppermost layer of the ocean model, which is in direct contact with the moving pack ice. This damping procedure allows seasonal and shorter time-scale variability to be simulated in the ocean, but does not allow the model to drift away from ocean climatology on longer time scales.
For the standard experiment, an initial integration of five years was performed at one-day time steps and a 1.45° by 1.45° resolution in order to obtain a cycle equilibrium. For comparison, a five-year simulation with an ice-only model, and shorter one-year sensitivity simulations without surface salt fluxes and without ocean currents, were also carried out. Input fields consisted of climatological surface air temperatures and mixing ratios, together with daily geostrophic winds from 1979.
The surface-current structure at the end of the five-year simulation exhibits a stronger East Greenland Current and Beaufort Sea Gyre than the initial geostrophic estimates, and is in better agreement with observation. In the Greenland/Norwegian Sea the upper 0.5 km of the ocean becomes more isothermal, with a noticeable seasonal variation in temperature. This neutral density allows monthly averaged winter heat fluxes as large as 350 W m-2 to be delivered to the upper ocean, thus yielding a much more realistic ice edge than is obtainable by the ice-only model. Spatial variations in ice thickness and ice drift prediction are also in better agreement in the full ice-ocean model as compared to the ice-only model. Except in very shallow regions, month-to-month fluctuations in ice motion are much larger than upper ocean current fluctuations, which also tend to be smaller than mean annual currents. In the central basin, the ice interaction is found ro reduce by about 40% the wind stress transferred into the ocean.
Analysis of the advance and retreat of the East Greenland ice edge shows that while there is some initial freezing in the fall, on a monthly-averaged basis the ice tends to melt during the winter, thus partially off-setting the advection of ice into the region. The amount of melt tends to oscillate from month to month, with large melt ratios coinciding with large oceanic heat fluxes and vice versa. Examination of shorter sensitivity simulations shows this realistic ice edge to be especially dependent on the inclusion of the full three-dimensional circulation in the ocean, and to a lesser degree sensitive to the inclusion of ice melt fluxes. Analysis of the global budgets shows that an annual northward heat transport across the Denmark Strait and Iceland-Faeroe-Shetland passages of about 0.18 x 1015 W is required to balance the atmospheric heat gain.
Huang, R-X, and Kirk Bryan, 1987: A multilayer model of the thermohaline and wind-driven ocean circulation. Journal of Physical Oceanography, 17(11), 1909-1924. Abstract PDF
A hybrid, multilayer model for the oceanic general circulation is formulated and tested. The model includes a mixed layer at the surface which is specified by Eulerian coordinates, and three moving layers below which are specified by quasi-Lagrangian, isopycnal coordinates.
Initial tests have been carried out with a 22 x 22 horizontal grid mesh covering a subtropical-subpolar basin (6000 x 6000 km2). The numerical results demonstrate a strong interaction between the wind-driven and the thermally driven circulations, including outcropping of the lower isopycnal layers, a Gulf Stream-like interior boundary current, and convection which produces mode water and abyssal water. The model provides insight into the potential vorticity balance and its relation to both the wind-driven and thermohaline components of the circulation which has not been previously available from Eulerian numerical models or analytical models based on the assumption of an ideal fluid thermocline.
Bogue, N M., R-X Huang, and Kirk Bryan, 1986: Verification experiments with an isopycnal coordinate ocean model. Journal of Physical Oceanography, 16(5), 985-990. Abstract PDF
The approximate conservation of density along trajectories in the upper thermocline, indicated by the observed distribution of water mass properties, suggests that isopycnal coordinates would provide a more economical framework than conventional Eulerian coordinates. An approximate analytic solution for a wind-driven circulation in a reduced gravity model is used as a prototype for testing a numerical model based on isopycnal coordinates. The numerical solutions are successful in reproducing the outcropping pattern of the analytic solutions. The application of the flux-corrected transport algorithm significantly reduces implied diffusivity relative to a first-order donor cell scheme.
Bryan, Kirk, 1986: Poleward buoyancy transport in the ocean and mesoscale eddies. Journal of Physical Oceanography, 16(5), 927-933. Abstract PDF
There are many dynamic similarities between mesoscale eddies in the ocean, and cyclones and anticyclones in the earth's atmosphere. Observational data, however, are still not adequate to explore this analogy in detail. In the present study a new eddy-resolving ocean circulation model, which includes both wind-driving and buoyancy-driving, is used to determine whether mesoscale eddies play a role in poleward buoyancy transport in any way comparable to the role of synoptic scale motions in transporting heat in the atmosphere. Within an Eulerian reference frame, mesoscale eddies transport buoyancy poleward through two mechanisms. One involves the correlations of time-dependent fluctuations of horizontal velocity and buoyancy. The other transport mechanism involves wave-driven cells in the meridional plane. These cells are analogous to the Ferrel cell in the atmosphere, except that the geometry of the ocean basin allows them to be geostrophically balanced. In an eddy-resolving model of ocean circulation, the two mechanisms for buoyancy transport are almost perfectly compensating. Within a Lagrangian framework, the trajectories of the eddies are largely excursions on isopycnal surfaces. Heat transport may take place by eddies in the renal ocean without eddy buoyancy transport, since temperature gradients always exist on isopycnal surfaces and may be quite strong in polar regions. Mesoscale eddies and the thermohaline circulation in the model can be weakly coupled, because available potential energy created by the large-scale wind stirring provides a primary energy source for baroclinic instability. The model results indicate that the actial measurement of mesoscale eddy transports is extremely difficult, since it involves an accurate determination of the difference between transport by wave-driven, mean flows and by the correlation of the time-dependent fields.
Bryan, Kirk, and Syukuro Manabe, 1985: A coupled ocean-atmosphere and the response to increasing atmospheric CO2 In Coupled Ocean-Atmosphere Models, Amsterdam; The Netherlands, Elsevier Science Publishers, 1-6. PDF
The climate response to a large increase in atmospheric CO2 was investigated in a numerical experiment with a coupled ocean-atmosphere model. The study is focused on one aspect of the experiment, the predicted response of the ocean to the warming episode. A fourfold increase in atmospheric CO2 causes a warming sufficiently intense to produce a partial collapse of the thermohaline circulation of the ocean. Surprisingly, the wind-driven circulation of the ocean is maintained without appreciable change. The global hydrological cycle intensifies without a major shift of the pattern of net precipitation over the model ocean. In the warming episode the downward pathways for heat, which include diffusion and model ocean. In the warming episode the downward pathways for heat, which include diffusion and Ekman pumping, remain open. The partial collapse of the thermohaline circulation closes the normal upward pathways associated with abyssal upwelling and high-latitude convection. As a result the thermocline is able to sequester almost twice as much heat than would be predicted from the behavior of a neutrally buoyant tracer introduced at the surface under normal climatic conditions. An enhanced sequestering of heat would produce a negative feedback for greenhouse warming. However, the partial collapse of the thermohaline circulation found in the numerical experiment would also affect the global carbon cycle, possibly producing a climatic feedback as strong as that caused by an enhanced uptake of heat from the atmosphere.
Manabe, Syukuro, and Kirk Bryan, 1985: CO2 -induced change in a coupled ocean-atmosphere model and its paleoclimatic implications. Journal of Geophysical Research, 90(C6), 11,689-11,707. Abstract PDF
The climatic effects of very large changes of CO2 concentration in the atmosphere are explored using a general circulation model of the coupled ocean-atmosphere system. As a simplification the model has an annual mean insolation and a highly idealized geography. A series of climatic equilibria are obtained for cases with 1/2, 1/sq rt 2, 1, 2, 4, and 8 times the present CO2 concentration in the atmosphere. The results from these six numerical experiments indicate the climatic signatures of large CO2 changes in the atmosphere and in the abyssal and surface waters of the ocean. As the CO2 concentration in the model atmosphere increased from 1 to 8 times the normal value, the meridional gradient of surface air temperature decreased, while that of upper tropospheric temperature increased in agreement with the results of earlier CO2 climate sensitivity studies. However, the intensity and latitudinal placement of the atmospheric jet hardly changed. Despite the reduction of meridional temperature gradient, the meridional density gradient of water at the ocean surface changed little because of the increase of thermal expansion coefficient of seawater with increasing temperature. Thus the intensity of thermohaline circulation in the ocean model does not diminish as expected in the range from 1 to 8 times the normal atmospheric CO2 concentration. As was shown in an earlier study, the CO2-induced changes in the deep sea follow the change of sea surface temperature in high latitudes and thus are much larger than the globally averaged changes of sea surface temperature. The model predicts that the area mean rates of precipitation, evaporation, and runoff increase with increasing CO2 concentration in the atmosphere. The latitudes of the arid zone and the high surface pressure belt in the subtropics are almost constant in the entire range of 1-8 times normal CO2. In general, the climatic signature obtained from the model appears to be consistent with a CO2 hypothesis for the climatic changes in the Cenozoic with the following exception: the tropical sea surface temperature in the model has a small but significant increase with increasing atmospheric CO2 concentration, while tropical sea surface temperature as deduced from the isotopic record appears to have no systematic trend during the Tertiary. It is found that the climate corresponding to one-half normal CO2 is markedly different from the normal and high-CO2 cases. Sea ice extends to middle latitudes, and the thermohaline circulation in the model ocean loses its intensity and is largely confined to an area between the sea ice margin and the equator. The poleward heat transport by ocean currents is very small in high latitudes, markedly reducing the surface air temperature there. It is suggested that a similar process, which enhances the positive albedo feedback effect of sea ice, played a key role in reducing surface air temperatures over the North Atlantic during the last glacial maximum.
Bryan, Kirk, 1984: Accelerating the convergence to equilibrium of ocean-climate models. Journal of Physical Oceanography, 14(4), 666-673. Abstract PDF
Solutions corresponding to climatic equilibrium are usually obtained from atmospheric general circulation models by extended numerical integration with respect to time. Because the ocean contains a much wider range of time scales, the same procedure is not practical for ocean general circulation models. The ocean contains the same high frequency waves as the atmosphere and in addition, has ultra low frequencies associated with slow diffusion of water mass properties below the main thermocline. For the parameter range in which equilibrium solutions exist, a method based on distorted physics partially circumvents this difficulty. The distorted physics compresses the frequency band of the ocean model by slowing down gravity waves and speeding up abyssal processes. The acceleration of abyssal processes is accomplished by decreasing the local heat capacity without altering the transport and mixing of heat. Numerical integration of the distorted-physics ocean model then converges to equilibrium nearly as efficiently as an atmospheric model of comparable spatial reolution. Equilibrium solutions of the distored- and nondistorted-ocean models are equivalent because the distortion only involves derivatives with repect to time. A joint ocean-atmosphere model study provides a practical demonstration of the method.
Bryan, Kirk, 1984: Climate models related to Stream 3: Outstanding technical problems In Workshop on Global Observations and Understanding of the General Circulation of the Oceans, Washington, DC, National Academy Press, 76-93.
Bryan, Kirk, F G Komro, and C G H Rooth, 1984: The ocean's transient response to global surface temperature anomalies In Climate Processes and Climate Sensitivity, Geophysical Monograph 29, Maurice Ewing Volume 5, Washington, DC, American Geophysical Union, 29-38. Abstract
Transient tracers are not perfect analogues for the downward penetration of a heat anomaly associated with climate change. Buoyancy effects associated with a temperature anomaly can significantly alter the stratification and thermohaline circulation. To investigate these effects a three-dimensional model of the world ocean is perturbed by spatially uniform surface anomalies, and the response calculated over a 50 year period. The penetration depth for a negative temperature anomaly of 0.5 degrees C is 25% greater than that for a positive anomaly. The penetration depth is found to be approximately one half the pycnocline depth after 10 years, and one pycnocline depth after 40 years. Both a simple two box model, and a box diffusion model provide a reasonable fit to the globally averaged results of the more general three-dimensional model.
Cox, M D., and Kirk Bryan, 1984: A numerical model of the ventilated thermocline. Journal of Physical Oceanography, 14(4), 674-687. Abstract PDF
A steady state numerical solution is found for an idealized, rectangular ocean basin driven by wind and surface buoyancy flux. A three-dimensional primitive equation model is used. In agreement with recent analytical modeling, the thermocline in the numerical solution consists of three regions, quite distinct in their ventilation characteristics. Forming the greater part of the subtropical thermocline is an unventilated "pool" zone located in the core of the subtropical gyre, and a "ventilated" zone to the east. The unventilated "shadow" zone lies farther east and toward the equator. Analysis of potential vorticity on constant density surfaces is used to study the structure of the thermocline. A small but intense zone of convection located in the western boundary outflow, caused by rapid heat loss to the atmosphere, produces source water for the ventilated zone. This water of extremely low potential vorticity (mode water), is distributed widely into the subtropical thermocline. The pool zone forms equatorward of the convective influence, although lateral mixing in the western boundary current provides indirect ventilation within this region. Trajectory analysis is used to illustrate the effects of the individual terms in the density equation on potential vorticity.
Hibler III, W D., and Kirk Bryan, 1984: Ocean circulation: Its effects on seasonal sea-ice simulations. Science, 224(4648), 489-492. Abstract PDF
A diagnostic ice-ocean model of the Arctic, Greenland, and Norwegian seas is constructed and used to examine the role of ocean circulation in seasonal sea-ice simulations. The model includes a lateral ice motion and three-dimensional ocean circulation. The ocean portion of the model is weakly forced by observed temperature and salinity data. Simulation results show that including modeled ocean circulation in sea-ice simulations substantially improves the predicted ice drift and ice margin location. Simulations that do not include lateral ocean movement predict a much less realistic ice edge.
Bryan, Kirk, 1983: Poleward heat transport by the ocean. Reviews of Geophysics, 21(5), 1131-1137. PDF
Bryan, Kirk, 1982: Poleward heat transport by the ocean: Observations and models. Annual Review of Earth and Planetary Sciences, 10, 15-38.
Bryan, Kirk, 1982: Seasonal variation in meridional overturning and poleward heat transport in the Atlantic and Pacific Oceans: A model study. Journal of Marine Research, 40(Supplement), 39-53. Abstract
Numerical solutions for a model of the World Ocean are analyzed to illustrate the important changes in the meridional circulation of the ocean induced by seasonal changes in wind stress. Seasonal variations of meridional circulation and associated changes in poleward heat transport predicted by the model are most important in the Pacific where the background thermohaline circulation is relatively weak. Numerical experiments show that seasonal variations of cross-equatorial heat transport basically depend on the variations of the zonal component of the wind stress. Seasonal variations of the meridional wind stress exert an influence on cross-equatorial heat transport which is 180 degrees out of phase in the seasonal cycle from the more dominant influence of seasonal variations of the zonal wind stress.
The ocean's role in the delayed response of climate to increasing atmospheric carbon dioxide has been studied by means of a detailed three-dimensional climate model. A near-equilibrium state is perturbed by a fourfold, step-function increase in atmospheric carbon dioxide. The rise in the sea surface temperature was initially much more rapid in the tropics than at high latitudes. However, the fractional response, as normalized on the basis of the total difference between the high carbon dioxide and normal carbon dioxide climates, becomes almost uniform at all latitudes after 25 years. Because of the influence of a more rapid response over continents, the normalized response of the zonally averaged surface air temperature is faster and becomes nearly uniform with respect to latitude after only 10 years.
Three-dimensional solutions are obtained for the circulation of the North Atlantic using a robust diagnostic model. In contrast to previous diagnostic models the robust diagnostic model incorporates the conservation of the large-scale fields of heat and salinity as well as momentum. An approximate fit to observed fields of temperature and salinity is obtained by a closure condition. The method is robust in the sense that it does not have the extreme sensitivity to the density input fields of the classical diagnostic method. Equilibrium solutions are obtained by numerical integration of the time-dependent equations. Error estimates for the velocity field can be obtained indirectly from the numerical solutions. Temperature observations used as input have an effective resolution of 3 degrees x 3 degrees of latitude and longitude and a sampling error of plus or minus 0.15 degrees C. The equivalent vertically integrated velocity error is estimated to be plus or minus 0.5-1.0 cm/s depending on bottom topography. The suitability of the model for geochemical work is judged by comparison with heat and salinity balance estimates. Best results are obtained for the case in which the model has a minimum observational constraint below the surface.
Smagorinsky, Joseph, Kirk Bryan, and Syukuro Manabe, et al., 1982: CO2/Climate Review Panel In Carbon Dioxide and Climate: A Second Assessment, Washington, DC, National Academy Press, 1-72.
Anderson, D L., Kirk Bryan, A E Gill, and Ronald C Pacanowski, 1979: The transient response of the North Atlantic: Some model studies. Journal of Geophysical Research, 84(C8), 4795-4815. Abstract PDF
Four numerical experiments have been designed to clarify the role of stratification and topography on the transient response of the ocean to a change in wind forcing. The geometry and topography appropriate to the North Atlantic between the equator and 50 degrees N are used to make the study more appropriate to a real ocean. In all four experiments, zonally symmetric wind stresses are 'switched on' at the upper surface of a resting model ocean. Two short experiments, 1 and 2, with a duration of 100 days, are first discussed. These are for a homogeneous ocean with and without topography. The response in the flat-bottomed case can be described either in terms of planetary waves or basin modes, but when topography is present, no obvious wave propagation was identified. Higher-frequency basin modes are detectable, but their amplitude is much lower than that in the flat-bottomed case. They are damped out on a time scale of ~ 50 days. Two longer experiments, 3 and 4, are then analyzed. These are the analogs of 1 and 2, but stratification was included. The introduction of stratification for the ocean with topography leads to a new, longer time scale, not just for the baroclinic modes, but also for the barotropic. Despite the presence of topography, model analysis was found useful in analyzing the results. Propagation effects are analyzed, both on the moderately fast time scale of internal Kelvin waves and on the slow time scale of internal planetary waves. Kelvin waves are apparent along the equator, the northern boundary, and on the eastern coast in the Gulf of Guinea from the equator to 20 degrees N. They are not clearly visible anywhere on the west coast. Planetary waves can be detected in the interior both in the presence and absence of topography. When topography is present without stratification, the transport of the Gulf Stream is reduced from 30 to 14 million tons per second. This is a well-known result. With stratification there is no significant difference in transport between the case with or without topography.
Bryan, Kirk, 1979: Models of the ocean circulation and the global heat balance In Report of the JOC Study Conference on Climate Models: Performance, Intercomparison and Sensitivity Studies, Vol. I, Global Atmospheric Research Programme, Joint Organizing Committee, GARP Publications No. 22., World Meteorological Organization, 23-40.
Bryan, Kirk, 1979: Models of the world ocean. Dynamics of Atmospheres and Oceans, 3, 327-338.
A numerical model of the world ocean is developed to investigate the role of the ocean in the earth's heat balance. Climatological wind stress, temperature, and salinity are imposed as upper boundary conditions. An equilibrium solution is obtained based on an extended numerical integration over the equivalent of 1000 years. Seasonal variations are included. A series of numerical integrations over shorter periods indicate that quantitative aspects, such as the scale depth of the thermocline, are very sensitive to the closure parameterization representing the effect of unresolved scales of motion. The mean depth of the thermocline is found to be in proportion to the global available potential energy. Larger wind driving increases the scale depth of the thermocline, while larger lateral friction of diffusion leads to a shallower thermocline. The model predicts three major meridional cells of the atmosphere. The tropical and mid-latitude cells are largely wind driven. Thermohaline effects are dominant in the polar meridional cells. Seasonal changes in winds have a profound effect on the meridional circulation in the tropics and cause a flux of surface water from the summer to the winter hemisphere. It is suggested that this mechanism is an important factor in moderating climate by transferring excess heat from the summer hemisphere into the winter hemisphere.
Manabe, Syukuro, Kirk Bryan, and Michael J Spelman, 1979: A global ocean-atmosphere climate model with seasonal variation for future studies of climate sensitivity. Dynamics of Atmospheres and Oceans, 3, 393-426.
Siegel, A D., and Kirk Bryan, 1979: Seasonal redistribution of heat in the equatorial Atlantic. EOS, 60(18), 291.
Bryan, Kirk, 1978: Ocean Circulation In Geophysical Predictions, Washington, DC, National Academy of Sciences, 178-184. Abstract
Because of a scanty data base, research on ocean circulation is still in an exploratory stage relative to other areas in geophysics. Much of our knowledge of the ocean's circulation rests on indirect methods based on the interpretation of water mass distributions and radioactive tracers. Direct measurements of current are available for only a limited number of locations, but they indicate that the ocean circulation is often a weak background with time-varying eddies of 100-200-km scale containing the major share of the kinetic energy. How the transport of heat, momentum, and salinity is partitioned between the mesoscale eddies and the background circulation is not clear, but there is evidence that the level of partitioning must vary greatly from one location to another
Regional numerical models of the ocean circulation are playing an increasingly important role in the planning and analysis of field programs designed to study mesoscale dynamics, large-scale air-sea interaction, and major upwelling regions. Global models with somewhat lower horizontal resolution are being developed to interpret tracer data or, as one component of joint air-sea interaction models, to study climate impact problems.
In spite of intense interest in the subject, little is known about the role of the ocean circulation in large-scale interaction of the ocean and atmosphere. For time scales of the order of one year or less the most promising results are in connection with sea-surface temperature anomalies in the tropics. The oceanographic components of the First GARP (Global Atmospheric Research Program) Global Experiment (FGGE) and the North Pacific Experiment (NORPAX) and the Indian Ocean Experiment (INDEX) are major field efforts aimed at understanding the response of the ocean circulation in low latitudes to the atmosphere. Seasonal variations of the ocean circulation in the tropics are more important than at high latitudes. Detailed field work and modeling studies of the "phase-locked" seasonal variations is recommended as an excellent way to gain an understanding of other more random-phase anomalies in the tropics of approximately the same time scale.
While much more can be done with existing data to develop ocean circulation models for planning purposes and environmental impact studies, major strides forward can only be taken when more widespread direct measurements and more detailed tracer data become available. Drifting surface platforms tracked by satellites and sub-surface platforms tracked acoustically hold great promise as the basis of an instrument system that can survey large regions of the ocean at a reasonable cost. Computer models would play an essential role in a system of buoys by providing a means of converting information from drifting instruments into a usable synoptic framework. Several excellent pilot studies of such concepts are already being carried out.
Bryan, Kirk, and P Ripa, 1978: The vertical structure of North Pacific temperature anomalies. Journal of Geophysical Research, 83(C5), 2419-2429. Abstract
The existence of large-scale thermal anomalies in the North Pacific motivates a study of the reflection of a wind-driven anomaly at the eastern boundary. A continuously stratified, linear model is used to calculate the vertical and horizontal structure of large-scale waves forced by fluctuating wind stress patterns. Thermal anomalies caused by eastward, westward, and standing wind wave patterns are investigated. Although exact comparison with data is not possible, the model can predict downward phase propagation as observed at OWS station N without invoking friction or vertical mixing of heat. In the same solution, upward propagation is predicted at other locations. An eastward moving, forced anomaly in the thermocline transports energy toward the eastern boundary. In the model the anomaly is reflected at the wall in the form of westward moving, internal Rossby waves which have a much lower group velocity. A small amount of friction will attenuate the outgoing waves much more than the incoming waves, providing a mechanism for eastward intensification.
Huppert, H E., and Kirk Bryan, 1976: Topographically generated eddies. Deep-Sea Research, Part I, 23, 655-679. Abstract
The interaction between temporally varying currents and the bottom topography of the ocean is investigated by the numerical and analytic examination of the following simple model. The flow of an inviscid, statified fluid is initiated from relative rest in a uniformly rotating system containing an isolated topographic feature. The evolution of the flow redistributes vorticity and temperature in such a way that relatively cold water with anticyclonic vorticity exists over the topographic feature, while water shed from above the topographic feature sinks, thereby inducing a warm anomaly with cyclonic vorticity. For sufficiently strong oncoming flows, the shed fluid continually drifts downstream in the form of a relatively warm eddy. If the oncoming flow is relatively weak, the interaction between the anticyclonic and cyclonic vorticity distributions traps the warm eddy and it remains in the vicinity of the topographic feature
We suggest that recent observations of an eddy in the vicinity of the Atlantis II Seamount and the existence of the large amount of high frequency energy near the bottom of the ocean measured by the MODE experiment may be partly explained in terms of the above mechanism. We conclude by speculating that vorticity redistribution by topography may be a contributing factor to cyclogenesis in the atmosphere.
Pond, S, and Kirk Bryan, 1976: Numerical models of the ocean circulation. Reviews of Geophysics & Space Physics, 14(2), 243-263. Abstract
Numerical models of the large-scale circulation of the oceans have developed into a useful tool for the interpretation of oceanographic data and the planning of new observational programs. Idealized numerical models with simplified geometry and physics have extended the analytic theory of the wind-driven ocean circulation into the range in which inertial effects determine the solution. Recent numerical work has shown how stratification and baroclinic instability further modify a wind-driven ocean circulation. Other results obtained by simplified numerical models include important predictions about the spectral properties of geostrophic turbulence in the ocean. Another class of numerical models has been developed which attempts to model geometry and physics of the ocean circulation in a more detailed way, allowing a quantitative comparison with observations. Interesting results have been obtained for the Indian Ocean which simulate the seasonal variations of the Somali Current. Other Soviet and U.S. model studies using the observed density field as input show that presure torques acting on bottom topography can be as large as the torques exerted by the wind acting at the surface. As yet, detailed simulations of the ocean circulation in a major ocean basin which include the effect of mesoscale eddies have not been undertaken.
Bryan, Kirk, 1975: Three-dimensional numerical models of the ocean circulation In Numerical Models of Ocean Circulation, Washington, DC, National Academy of Sciences, 94-105; 105-106.
A numerical experiment has been carried out with a joint model of the ocean and atmosphere. The 12-level model of the world ocean predicts the fields of horizontal velocity, temperature and salinity. It includes the effects of bottom topography, and a simplified model of polar pack ice. The numerical experiment allows the joint ocean-atmosphere model to seek an equilibrium over the equivalent of 270 years in the ocean time scale. The initial state of the ocean is uniform stratification and complete rest. Although the final temperature distribution is more zonal than it should be, the major western boundary currents and the equatorial undercurrent are successfully predicted. The calculated salinity field has the correct observed range, and correctly indicates that the Atlantic is saltier than the Pacific. It also predicts that the surface waters of the North Pacific are less saline than the surface waters of the South Pacific in accordance with observations. The pack ice model predicts heavy ice in the Arctic Ocean, and only very light pack ice along the periphery of the Antarctic Continent.
The poleward heat transport of the model is very sensitive to the strength of the circulation in the vertical-meridional plane. The heat transport is strongest in the trade wind belt where Ekman drift and thermohaline forces act together to cause a net flow of surface water toward the poles. At higher latitudes in the westerly belt the wind and thermohaline forces on the meridional circulation tend to oppose each other. As a result, the heat transport is weaker. Heat balance computations made from observed data consistently show that the maximum heat transport by ocean currents is shifted 10 degrees - A numerical experiment has been carried out with a joint model of the ocean and atmosphere. The 12-level model of the world ocean predicts the fields of horizontal velocity, temperature and salinity. It includes the effects of bottom topography, and a simplified model of polar pack ice. The numerical experiment allows the joint ocean-atmosphere model to seek an equilibrium over the equivalent of 270 years in the ocean time scale. The initial state of the ocean is uniform stratification and complete rest. Although the final temperature distribution is more zonal than it should be, the major western boundary currents and the equatorial undercurrent are successfully predicted. The calculated salinity field has the correct observed range, and correctly indicates that the Atlantic is saltier than the Pacific. It also predicts that the surface waters of the North Pacific are less saline than the surface waters of the South Pacific in accordance with observations. The pack ice model predicts heavy ice in the Arctic Ocean, and only very light pack ice along the periphery of the Antarctic Continent.
The poleward heat transport of the model is very sensitive to the strength of the circulation in the vertical-meridional plane. The heat transport is strongest in the trade wind belt where Ekman drift and thermohaline forces act together to cause a net flow of surface water toward the poles. At higher latitudes in the westerly belt the wind and thermohaline forces on the meridional circulation tend to oppose each other. As a result, the heat transport is weaker. Heat balance computations made from observed data consistently show that the maximum heat transport by ocean currents is shifted 10 degrees - 20 degrees equatorward relative to the maximum poleward heat transport by the atmosphere in middle latitudes. The effect of the zonal wind in enhancing poleward heat transport at low latitudes and suppressing it in middle latitudes is offered as an explanation.
A joint ocean-atmosphere model covering the entire globe has been constructed at the Geophysical Fluid Dynamics Laboratory (GFDL) of NOAA. This model differs from the earlier version of the joint model of Bryan and Manabe both in global domain and inclusion of realistic rather than idealized topography. This part of the paper describes the structure of the atmospheric portion of the joint model and discusses the atmospheric circulation and climate that emerges from the time integration of the model. The details of the oceanic part are given by Bryan et al. (1974), hereafter referred to as Part II.
The atmospheric part of the model incorporates the primitive equations of motion in a spherical coordinate system. The numerical problems associated with the treatment of mountains are minimized by using the "sigma" coordinate system in which pressure, normalized by surface pressure, is the vertical coordinate. For vertical finite differencing, nine levels are chosen so as to represent the planetary boundary layer and the stratosphere as well as the troposphere. For horizontal finite differencing, the regular latitude-longitude grid is used. To prevent linear computational instability in the time integration, Fourier filtering is applied in the longitudinal direction to all prognostic variables in higher latitudes such that the effective grid size of the model is approximately 500 km everywhere.
For the computation of radiative transfer, the distribution of water vapor, which is determined by the prognostic system of water vapor is used. However, the distribution of carbon dioxide, ozone and cloudiness are prescribed as a function of latitude and height and assumed to be constant with time. The temperature of the ground surface is determined such that it satisfies the condition of heat balance.
The prognostic system of water vapor includes the contribution of three-dimensional advection of water vapor and condensation in case of supersaturation. To simulate moist convection, a highly idealized procedure of moist convective adjustment is introduced. The prediction of soil moisture and snow depth is based upon the budget of water, snow and heat. Snow cover and sea ice are assumed to have much larger albedos than soil surface or open sea, and have a very significant effect upon the heat balance of the surface of the model.
Starting from the initial conditions of an isothermal and dry atmosphere at rest, the long-term integration of the joint model is conducted with the economical method adopted by Bryan and Manabe in their earlier study. The climate that emerges from this integration includes some of the basic features of the actual climate. However, it has many unrealistic features, which underscores the necessity of further increasing the computational resolution of horizontal finite differencing.
In order to identify the effect of the ocean currents upon climate, the joint model climate is compared with another climate obtained from the time integration of a so-called "A-model" in which oceanic regions are occupied by wet swampy surfaces without any heat capacity. Based upon the comparison between these two climates, the possible effects of oceanic heat transport on the climate are discussed. For example, the results show that the total poleward transport of energy is affected little by the oceanic heat transport. Although ocean currents significantly contribute to the transport, the atmospheric transport of energy in the presence of the latter decreases by approximately the same magnitude. Therefore, the total transport in the joint model differs little from that in the A-model. Further comparison between the two models indicates that ocean currents significantly affect not only the horizontal distribution of surface temperature of both oceans and continents but also the global distribution of precipitation.
Reid, R O., A R Robinson, and Kirk Bryan, 1975: Summary, conclusions, and recommendations In Numerical Models of Ocean Circulation, Washington, DC, National Academy of Sciences, 361-362.
Stegen, G R., Kirk Bryan, J L Held, and F Ostapoff, 1975: Dropped horizontal coherence based on temperature profiles in the upper thermocline. Journal of Geophysical Research, 80(27), 3841-3847. Abstract
A series of 66 temperature profiles taken in the open ocean 350 km north of Puerto Rico are analyzed to determine the displacement spectrum and the dropped horizontal coherence. The results are not inconsistent with the Garrett and Munk model. One interesting exception is a tendency for the horizontal coherence not to fall off monotonically with decreasing vertical scales.
Bryan, Kirk, 1972: An approximate equation of state for numerical models of ocean circulation. Journal of Physical Oceanography, 2(4), 510-514. PDF
Bryan, Kirk, and M D Cox, 1972: The circulation of the world ocean: A numerical study. Part I, An homogenous model. Journal of Physical Oceanography, 2(4), 319-335. Abstract PDF
Calculations are carried out for an homogenous model of the World Ocean. Solutions for the large-scale, wind-driven circulation are obtained by numerical integration with respect to time of a numerical model. The model includes 9 levels in the vertical and has an horizontal resolution of 2 degrees x 2 degrees in latitude and longitude. Subgrid-scale motions are included implicitly through the eddy viscosity hypothesis. The level of viscosity is adjusted so that only scales of motion large enough to be resolved by the numerical model will have appreciable amplitude. Compared with available observations, the model with uniform depth tends to underpredict the strength of the transport in the Northern Hemisphere boundary currents, but overpredict the strength of the Antarctic Circumpolar Current and the East Australian Current. When bottom topography is taken into account, the Northern Hemisphere transport patterns are not greatly altered, but transport of the Antarctic Circumpolar Current and the East Australian Current are drastically reduced.
Gill, A E., and Kirk Bryan, 1971: Effects of geometry on the circulation of a three-dimensional southern-hemisphere ocean model. Deep-Sea Research, Part I, 18, 685-721. Abstract
A series of numerical experiments on the circulation of the Antarctic region have been carried out in order to study the effect of baroclinicity and geometry on the circumpolar current and the Antarctic Convergence. Comparisons are made between model ocean which do and do not have barrier free zones ('Drake Passage'). Limitations of computer storage require the parameters used to be somewhat different than those applicable to the ocean. However, certain conclusions can be drawn. The existence of the barrier free zone is offered as an explanation of the formation of Antarctic Intermediate Water in latitudes a little north of the latitude of Cape Horn. It is found that when the model 'Drake Passage' is as deep as the rest of the model ocean (which is of uniform depth), the circumpolar current is predominantly wind-driven. When the model 'Drake Passage' is only half as deep, the transport of the current is increased nearly three times and the predominant driving mechanism appears to be 'thermal'.
Bryan, Kirk, 1969: Climate and the ocean circulation climate and the ocean circulation III. The ocean model. Monthly Weather Review, 97(11), 806-827. Abstract PDF
The ocean model used in a calculation of the earth's climate is described in detail. Compared with earlier numerical models used in ocean circulation studies, the present model includes several new features. Temperature and salinity are treated separately. Density is calculated with an accurate equation of state for sea water. The model also includes a method for calculating the growth and movement of sea ice.
Due to the very slow adjustment of the deep water in the ocean model, a numerical integration extending over the equivalent of a century fails to reach a climatic equilibrium. At the termination of the run, the surface layers of the ocean show little change with respect to time, but the average heating rate for the ocean as a whole is 2 degrees per century. The salinity patterns at the termination of the run are highly realistic compared to observations. A halocline forms in the Arctic Zone and a surface salinity maximum is present in the subtropics. A weak salinity minimum at a depth of 1 km indicates an extensive water mass very similar to the Antarctic intermediate water of the Southern Hemisphere. Poleward heat transport is found to be closely related to the intensity of the thermohaline circulation. A vertical mixing coefficient, k, of 1.5 cm2 sec-1 leads to a very reasonable heat exchange with the atmosphere based on estimates of the heat balance of the North Atlantic.
The calculation indicates that the thermal "relaxation" time of the ocean is too long for a numerical integration of the time-dependent equations to be a practical method of finding an equilibrium solution, and new methods should be sought for future calculations of this type.
Bryan, Kirk, 1969: A numerical method for the study of the circulation of the world ocean. Journal of Computational Physics, 4, 347-376. Abstract PDF
A model is presented for studying ocean circulation problems taking into account the complicated outline and bottom topography of the World Ocean. To obtain an efficient scheme for the study of low-frequency, large-scale current systems, surface gravity-inertial waves are filtered out by the "rigid-lid" approximation. To resolve special features of the ocean circulation, such as the Equatorial Undercurrent, the numerical model allows for a variable spacing in either the zonal or meridional direction. The model is designed to be as consistent as possible with the continuous equations with respect to energy. It is demonstrated that no fictitious energy generation or decay is associated with the nonlinear terms in the finite difference form of the momentum equations. The energy generation by buoyancy forces for the numerical model is also designed in such a way that no energy "leak" occurs in the transformation from potential to kinetic energy.
Manabe, Syukuro, and Kirk Bryan, 1969: Climate calculations with a combined ocean-atmosphere model. Journal of the Atmospheric Sciences, 26(4), 786-789. PDF
Orlanski, Isidoro, and Kirk Bryan, 1969: Formation of the thermocline step structure by large-amplitude internal gravity waves. Journal of Geophysical Research, 74(28), 6975-6983. Abstract
It is suggested that a possible mechanism for the formation of the thermocline step structure is a sporadic overturning by rotors associated with finite-amplitude internal waves. A criterion for the required critical amplitude of an internal wave is derived, and good agreement is found with numerical experiments illustrating the mechanism. A scale analysis for the ocean shows that downward-propagating waves with a vertical wavelength of 10-20 meters would be most favored to 'break' by the convective instability mechanism. Examination of velocity spectra measured in the North Atlantic shows that more than enough energy exists in the internal wave frequency range for this type of instability to occur.
Bryan, Kirk, and M D Cox, 1968: A nonlinear model of an ocean driven by wind and differential heating: Part I. Description of the three-dimensional velocity and density fields. Journal of the Atmospheric Sciences, 25(6), 945-967. Abstract PDF
A numerical experiment is carried out to investigate the circulation of an ocean, driven by a prescribed density gradient and wind stress at the surface. The mathematical formulation includes in one model most of the physical effects that have been considered in previous theoretical studies. Starting out from conditions of uniform stratification and complete rest, an extensive numerical integration is carried out with respect to time. Care is taken in the final stages of the calculation to use a finite difference net which resolves the very narrow boundary layers which form along the side walls of the basin.
A detailed description is made of the three-dimensional velocity and temperature patterns obtained from the final stage of the run. Since inertial effects play an important role in the western boundary current, it is possible to verify with a baroclinic model two results obtained previously with barotropic ocean models: 1) a concentrated outflow from the western boundary takes place along the upper boundary of the subtropic wind gyre; and 2) inertial recirculation may increase the total transport of the boundary current to a value well above that given by linear theory. In addition to the western boundary current, a strong eastward flowing current is found along the equator. Taking into account a difference in Rossby number between model and prototype, the intensity of the computed currents agrees very closely to observations in the Gulf Stream and the Equatorial Current.
Bryan, Kirk, and M D Cox, 1968: A nonlinear model of an ocean driven by wind and differential heating: Part II. An analysis of the hear, vorticity and energy balance. Journal of the Atmospheric Sciences, 25(6), 968-978. Abstract PDF
An analysis is made of the heat and vorticity balance of a numerical model of a baroclinic ocean. The computation is carried out on a three-dimensional grid designed to resolve the thermocline, and the narrow sidewall boundary layers at the coasts. A vorticity analysis indicates almost perfect geostrophic balance in the interior. In the immediate vicinity of the western wall the vorticity balance at a given level is dominated by lateral friction and vortex stretching associated with upwelling. The "beta" effect plays an important, but somewhat lesser role. A study of the heat balance in the interior shows that lateral advection is of primary importance in the upper part of the model ocean as it removes heat received at the surface in areas of wind-induced downwelling. Some of this heat is carried to the western boundary where is compensates the cooling due to upwelling and convective transfer through the surface.
An examination of the time-dependent motion indicates a regular downstream movement of eddies in the western boundary current. These eddies extend throughout the water column and give rise to a Reynolds stress which acts to retard the time-averaged flow. In a test run with bottom friction included, these eddies are slowly damped.
Bryan, Kirk, and M D Cox, 1967: A numerical investigation of the oceanic general circulation. Tellus, 19(1), 54-80. Abstract
An oceanic basin of uniform depth is considered. It is bounded laterally by two meridians. Temperature and wind stress are specified as functions of latitude at the upper surface. The physical model is similar to that used in previous models of the oceanic thermocline, except that the momentum equations of the horizontal velocity components are retained in nearly complete form. Solutions are obtained by the direct numerical integration of a corresponding initial value problem using an electronic computer. Dimensional analysis indicates that the system depends on 5 basic parameters. The geophysically significant range of these parameters is investigated in 8 numerical experiments.
Computations with and without wind stress show the interaction of the thermohaline and the wind-driven components of the large scale circulation. Without wind a single large anticyclonic gyre extends over the entire surface of the basin. There is a shallow western boundary current, extending to high latitudes, and a vertically uniform southward drift in the interior from the surface down to the base of the thermocline. A sluggish cyclonic gyre exists below the thermocline. The addition of a wind stress pattern corresponding to a maximum in the westerlies at 45 degrees N leads to the formation of an additional cyclonic gyre in subarctic latitudes. In spite of the simplified boundary conditions the solutions with wind stress reproduce many details of the observed density structure in the North Atlantic, particularly in the subtropical gyre.
A more quantitative comparison with North Atlantic data indicates that choice of the vertical diffusion coefficient to be 1 cm2/s gives an approximate fit to the thermocline depth and estimates of the total poleward transport of heat. The corresponding renewal time for deep water, however, is considerably less than that indicated by C14 data.
Bryan, Kirk, 1966: A scheme for numerical integration of the equations of motion on an irregular grid free of nonlinear instability. Monthly Weather Review, 94(1), 39-40. PDF
Bryan, Kirk, and S Hellerman, 1966: A test of convergence of a numerical calculation of the wind-driven ocean circulation. Journal of the Atmospheric Sciences, 23, 360-361. PDF
Bryan, Kirk, 1965: Nonlinear effects in the theory of a wind-driven ocean circulation. Methods in Computational Physics, 4, 29-43.
