Mean meridional circulations of the stratosphere and mesosphere

Observations from the Nimbus 6 pressure modulator radiometer (PMR) have been used to estimate monthly mean planetary wave fluxes of heat and momentum in the stratosphere and mesosphere. While the eddy heat fluxes play an important role in the mean meridional circulation of the winter stratosphere they are shown to be less important in the upper mesosphere. Incorporation of the observed momentum fluxes into the Oxford two-dimensional circulation model has shown that they are incapable of providing the momentum transport necessary to balance the zonal flow accelerations induced by the mean meridional motion. Other unspecified transfer processes represented by Rayleigh frictional damping of the zonal fow are shown to dominate. In contrast the observed fluxes in the stratosphere achieve the necessary redistribution of momentum. Moreover their interannual variability profoundly influences the stratospheric circulation, as demonstrated in the model by the use of two different annual sets of observed momentum fluxes. The desirability of calculating the planetary wave behaviour within the model is indicated.     

Effects of the earth's rotation and the balance of zonal kinetic energy

Summary According to the symmetric formulation of the zonal kinetic energy equation, positive generations arise through countergradient transports of angular momentum. Five years of northern hemispheric upper air data are used to investigate two of the terms in the equation, which represent the effects of the transport, by the mean general circulation cells, of the angular momentum associated with the earth's rotation. These two -generation terms do not usually appear in the more traditional form of the conservation equation, and results of their evaluation have not appeared previously. It is found that positive generation largely dominates in the -term involving horizontal (meridional) transports of angular momentum, and negative generation in the -term involving vertical transport. In fall and particularly winter, both terms are responsible for very large amounts of generation of opposing sign for the whole atmosphere.The five years of data are also used to evaluate the balance of zonal kinetic energy implied by the symmetric equation in northern hemispheric polar caps of various pressure thicknesses. The vertical processes involved are not directly measured but rather are obtained from observed horizontal motions through use of continuity of mass and angular momentum requirements. Possible reasons for the lack of a perfect balance are offered, but in any case the residuals are generally not large enough to be of too much concern. Vertical eddies are found to play an important role in the balance of zonal kinetic energy. A study of the balance in the upper half of the atmosphere reveals that in spring the vertical eddies (summed for all scales) must tranport angular momentum and zonal kinetic energy upward toward the jet in order to counter the net effect of the mean cells in reducing the zonal kinetic energy in this volume. In the fall however, there is a dramatic change in the direction in which these vertical eddies act, as they now remove zonal kineticenergy from the upper half of the atmosphere in this season.The research reported in this paper was sponsored by the U.S. National Science Foundation under Grant No. GA-1310X.     

Ocean eddy momentum fluxes at the latitudes of the Gulf Stream and the Kuroshio extensions as revealed by satellite data

Eddy momentum fluxes, i.e. Reynold stresses, are computed for the latitude bands of the Gulf Stream and Kuroshio extensions using 13 years of data from the merged satellite altimeter product of Le Traon et al. The spatial pattern and amplitude of the fluxes is remarkably similar to that found by Ducet and Le Traon using the 5 years of data that were available to them. In addition to updating the work of Ducet and Le Traon, we provide new insight into the role played by the underlying variable bottom topography, both for determining the structure of the eddy momentum fluxes seen in the satellite data and for influencing the way these fluxes feedback on the mean flow. While there is no clear evidence that eddies locally flux momentum into the eastward jets of the Gulf Stream and Kuroshio extensions, a clearer picture emerges after zonally integrating across each of the North Atlantic and North Pacific basins. We argue that the eddy momentum fluxes do indeed drive significant transport, a conclusion supported by preliminary results from a 3-D model calculation. We also present evidence that in the North Pacific, the Reynolds stresses are important for driving the recirculation gyres associated with the Kuroshio extension, taking advantage of new data from both observations and high-resolution model simulations.     

The topographically forced component of the atmospheric motion

Summary The zonally asymmetric stationary component of the general circulation is studied for small Rossby number without the beta-plane approximation. The equations for this component are linearized about a mean flow. An analytic solution for the meridional wind is found when the zonal wind and static stability of the mean flow are independent of the vertical coordinate. The solution is used to compute the transports of angular momentum and heat. The angular momentum transports give rise to a net convergence of the order of Rossby number and are balanced by the zonal mean Coriolis torque. However, the heat transports vanish at this order of magnitude.     

On the three-dimensional oceanic density distribution in a millennium integration with an AO-GCM

 The three-dimensional time-mean density distribution in the ocean is determined not only by the time-mean fluxes of heat and freshwater at the sea surface, but also by time-mean vertical currents and time-mean density fluxes due to oceanic transients excited by fluctuating fluxes at the sea surface. The effects of these various processes on the global density fields are assessed using a balance equation of the variance of spatial density anomalies and a millennium integration with an atmosphere–ocean general circulation model. It is found that spatial density anomalies are generated by the time-mean heat fluxes at the sea surface and destroyed by the time-mean surface freshwater flux, by sinking of dense water and rising of less dense water, and finally by density fluxes associated with transients. The last two processes take place essentially in the oceanic interior. Since density fluxes of transient eddies act to reduce the existing density differences between the Atlantic/Southern Oceans and the other oceans, their presence could affect the global density balance, and from that the thermohaline circulation and the stability of this circulation. Received: 4 October 2001 / Accepted: 10 October 2002 Responsible Editor: Richard J. Greatbatch Acknowledgements I thank Ulrich Cubasch and his colleagues for providing me with the ECHAM3/LSG integration, Peter Müller and Richard Greatbatch for valuable suggestions.     

Effects of cyclonic mesoscale eddies on the marine ecosystem in the Kuroshio Extension region using an eddy-resolving coupled physical-biological model

Effects of mesoscale eddies on the marine ecosystem in the Kuroshio Extension (KE) region are investigated using an eddy-resolving coupled physical-biological model. The model captures the seasonal and intra-seasonal variability of chlorophyll distribution associated with the mesoscale eddies, front variability, Kuroshio meanders, and upwelling. The model also reproduces the observed interannual variability of sea surface height anomaly (SSHA) in the KE region along a zonal band of 32–34°N from 2002 to 2006. The distribution of high surface chlorophyll corresponds to low SSHA. Cyclonic eddies are found to detach from the KE jet near 150°E and 158°E and propagate westward. The westward propagating cyclonic eddies lift the nutrient-rich thermocline into the euphotic zone and maintain high levels of chlorophyll in summer. In the subsurface layer, the pattern in chlorophyll is influenced by both lateral and vertical advection. In winter, convection inside the eddy entrains high levels of nutrients into the mixed layer, increasing production, and resulting in high chlorophyll concentration throughout the surface mixed layer. There is significant interannual variability in both the cyclonic eddy activity and the surface phytoplankton bloom south of the KE jet, although whether or not there is a causal link is unclear.     

Numerical studies of transient planetary circulations in a wind-driven ocean

Summary The time-dependent primitive equations for a shallow homogeneous ocean with a free surface are solved for a bounded basin on the sphere, driven by a steady zonal wind stress and subject to lateral viscous dissipation. These are the vertically integrated equations for a free-surface model, and are integrated to 60 days from an initial state of rest by an explicit centered-difference method with zero-slip lateral boundary conditions. In a series of comparative numerical solutions it is shown that at least a 2-deg resolution is needed to resolve the western boundary currents adequately and to avoid undue distortion of the transient (Rossby waves. The -plane formulation is shown to be an adequate approximation for the mean circulation in the lower and middle latitudes, but noticeably intensifies the transports poleward of about 50 deg and both slows and distorts the transients in the central basin. The influence of the (southern) zonal boundary on the transport solutions is confined to the southernmost gyre, except in the region of the western boundary currents where its influence spreads to the northern edge of the basin by 30 days. The total boundary current transport is shown to be approximately proportional to the zonal width of the basin and independent of the basin's (uniform) depth, while the elevation of the free water surface is inversely proportional to the basin depth, in accordance with linear theory. The introduction of bottom friction has a marked damping effect on the transient Rossby waves, and also reduces the maximum boundary-current transport. The solutions throughout are approximately geostrophic and are only slightly nonlinear.The root-mean-square (rms) transport variability during the period 30 to 60 days is concentrated in the southwest portion of the basin through the reflection of the transient Rossby waves from the western shore and has a maximum corresponding to an rms current variability of about 3 cm sec^–1. The transport variabilities are about 10 percent of the mean zonal transport and more than 100 percent of the mean meridional transport over a considerable region of the western basin (outside the western boundary current regime). Some 99 percent of the total kinetic energy is associated with the zonal mean and standing zonal waves, which are also responsible for the bulk of the meridional transport of zonal angular momentum. Although the transient Rossby waves systematically produce a momentum flux convergence at the latitude of the maximum eastward current, much in the manner of their atmospheric counterparts, this is only a relatively small contribution to the zonal oceanic momentum balance; the bulk of the mean zonal stress is here balanced by a nearly stationary net pressure torque exerted against the meridional boundaries by the wind-raised water. In an ocean without such boundaries the role of the transient circulations may be somewhat more important.     

Stochastic Models of Quasigeostrophic Turbulence

Atmospheric and oceanic eddies are believed to be manifestations of quasigeostrophic turbulence — turbulence that occurs in rapidly rotating, vertically stratified fluid systems. The heat, momentum, and water transport by these eddies constitute a significant component of the climate balance, without which climate change cannot be understood. A major, unsolved problem is whether the turbulent eddy fluxes can be parameterized in terms of the large-scale, background flow. In the past, stochastic models have been used quite extensively to investigate quasigeostrophic turbulence in the case in which the eddy statistics are isotropic and homogeneous. Unfortunately, these models ignore the background shear which is absolutely essential to maintaining the eddies in the presence of dissipation. Recent attempts to extend stochastic models to shear flows have shown significant skill in predicting the structure of the eddy fluxes in arbitrary, three-dimensionally varying flows. This paper provides an accessible introduction to these models. The topics reviewed include quasigeostrophic turbulence and two-dimensional turbulence, non-modal andoptimal perturbations, mathematical theory of stochastic models, stochastic model simulations with realistic background states, and recent closure theories. A list of unsolved problems concludes this review.     

Existence of eddies at crossroad of the Indonesian seas

An eddy-resolving Indo-Pacific ocean circulation model was applied to highlight the behavior of eddies throughout the Indonesian seas. The complexity of the topography and coastline at the entrance of the Makassar Strait induce an eddy-type throughflow, instead of a straightforward flow. A sill and a narrow passage in the Makassar strait creates a barrier and impedes the continuation of eddies from the Pacific ocean, but the existence of a steep deep basin (>500 m depth) between the Java and Flores seas indicates a possible area for eddies. Based on our numerical results, we described the presence of a unique eddy structure north of Lombok Island, which we designated the “Lombok Eddy” and verified it by performing a drifter release field experiment and reviewing monthly mean climatology data from the World Ocean Atlas 2001 and XBT PX2 track data. NCEP/NCAR reanalysis, satellite observation data, and mixed layer depth analysis were also used to confirm these processes. By analyzing numerical simulation results and available temperature datasets, two additional eddies were found. All eddies form primarily due to eastward local winds correlated with seasonal monsoon winds during the austral summer. These eddies vary synchronously at an interannual time scale. Together, they are referred to as the Lombok Eddy Train (LET), which affects the surface layer down to a depth of 60 m, and the intensity of the eddy system is strongly affected by mixed layer depth variability from December to February.     

A numerical model of the zonal mean circulation of the middle atmosphere

The annual cycle of the zonally averaged circulation in the middle atmosphere (16–96 km) is simulated using a numerical model based on the primitive equations in log pressure coordinates. The circulation is driven radiatively by heating due to solar ultraviolet absorption by ozone and infrared cooling due to carbon dioxide and ozone (parameterized as a Newtonian cooling). Since eddy fluxes due to planetary waves are neglected in the model, the computed mean meridional circulation must be interpreted as thediabatic circulation, not as the total eulerian mean. Rayleigh friction with a short (2–4 day) time constant above 70 km is included to simulate the strong mechanical dissipation which is hypothesized to exist in the vicinity of the mesopause due to turbulence associated with gravity waves and tides near the mesopause.Computed mean winds and temperatures are in general agreement with observations for both equinox and solstice conditions. In particular, the strong mechanical damping specified near the mesopause makes it possible to simulate the cold summer and warm winter mesopause temperatures without generating excessive mean zonal winds. In addition, the model exhibits a strong semiannual cycle in the mean zonal wind at the equator, with both amplitude and vertical structure in agreement with the easterly phase of the observed equatorial semiannual oscillation.Contribution No. 497, Department of Atmospheric Sciences, University of Washington, Seattle.     

On Production of Long-term Mean Zonal Current and Eddy Momentum and Heat Transports in Atmosphere

— The mean zonal velocity in the atmosphere is taken as being created continually by the global scale Hadley circulation produced by the differential solar heating through the balance between the Coriolis effect and vertical diffusion, and not by conservation of absolute momentum. Hence a proper determination of the diffusion coefficient becomes the key to the solution of the zonal flow problem. In this study we take the flow field as composed of a primary global scale Hadley circulation, and a secondary flow created by the convergences of the eddy transports of heat and momentum and surface friction, which give rise to the classical three cell structure of the meridional circulation but which only modifies the zonal velocity distribution slightly.¶Finally, we use the equilibrium solution of the perturbation potential vorticity equation to obtain the eddy transports of momentum and heat, with the zonal velocity given by the primary Hadley flow as the basic flow, and we found that they are close to the statistically observed values, demonstrating that the system can maintain itself.     

Impact of the surface temperature and vertical shear of zonal wind on the dynamics of a simple two-layer model of the atmosphere

The paper presents and analyzes, from the point of view of smooth dynamic systems theory, a two-layer baroclinic model of the troposphere in geostrophic approximation. The model describes airflow in β-channel within the tropospheric part of the main Hadley circulation cell. It enables to obtain, after application of the Galerkin method, a fairly simple low-parametric dynamic system describing the phenomena of non-linear interactions, bifurcations and blocking in the atmosphere. This enables to take into consideration such basic factors influencing the atmospheric dynamics like the heat exchange within the surface, orography, vertical variability of zonal wind and hydrostatic stability. Impact of zonal thermal variability of the surface and vertical shear of zonal wind in the troposphere on the orographic bifurcation was investigated and the oscillation character in the dynamic system after Hopf bifurcation of the second kind was analyzed. Additionally, the model dynamics was investigated in conditions including momentum forcing in the upper and lower parts of the troposphere and excluding orographic interaction, as well as in the conditions of thermal interaction between the troposphere and the surface for the vertical shear of zonal wind in both tropospheric layers. Impact of the mean zonal wind in the troposphere on the properties of model dynamics was assessed. It was proved that zonally varied surface temperature and layered mean zonal wind in the atmosphere are the parameters that have basic influence on the model dynamics. They cause numerous bifurcations and strongly influence the periods of oscillations of the model variables. They are often Hopf bifurcations of the second kind during which tropospheric states fairly distant from the ones before the bifurcations are generated. This significantly influences the model predictability.     

A numerical study of the circulation and monthly-to-seasonal variability in the Caribbean Sea: the role of Caribbean eddies

This study examines the circulation and associated monthly-to-seasonal variability in the Caribbean Sea using a regional ocean circulation model. The model domain covers the region between 99.0 and 54.0°W and between 8.0 and 30.3°N, with a horizontal resolution of 1/6°. The ocean circulation model is driven by 6-hourly atmospheric reanalysis data from the National Center for Environmental Prediction and boundary forcing extracted from 5-day global ocean reanalysis data produced by Smith et al. (Mercator Newsletter 36:39–49, 2010), and integrated for 7 years. A comparison of model results with observations demonstrates that the regional ocean circulation model has skill in simulating circulation and associated variability in the study region. Analysis of the model results, as well as a companion model run that uses steady annual mean forcing, illustrates the role of Caribbean eddies for driving monthly-to-seasonal circulation variability in the model. It is found that vertically integrated transport between Nicaragua and Jamaica is influenced by the interaction between the density perturbations associated with Caribbean eddies and the Nicaraguan Ridge. The impact of Caribbean eddies squeezing through the Yucatan Channel is also discussed.     

A new barotropic model of the wind-driven circulation

Rationalized by the observational circulation pattern in the upper ocean of the North Pacific, meridional friction term is first incorporated in a barotropic theoretical model of the wind-driven circulation. The governing potential vorticity equation thence has β term and wind stress curl term (the two of the Sverdrup balance), zonal friction term and meridional friction term. The analytical solution satisfactorily captures many important features of the wind-driven circulation in the North Pacific: Kuroshio, Oyashio, Kuroshio extension, North Equatorial Current, and especially the eastern boundary currents in the North Pacific, i.e. California current and Alaska current.     

Three-dimensional structure of mesoscale eddies in the western tropical Pacific as revealed by a high-resolution ocean simulation

The three-dimensional structure of mesoscale eddies in the western tropical Pacific(6°S–20°N, 120°E–150°E)is investigated using a high-resolution ocean model simulation. Eddy detection and eddy tracking algorithms are applied to simulated horizontal velocity vectors, and the anticyclonic and cyclonic eddies identified are composited to obtain their three-dimensional structures. The mean lifetime of all long-lived eddies is about 52 days, and their mean diameter is 147 km. Two typical characteristics of mesoscale eddies are revealed and possible dynamic explanations are analyzed. One typical characteristic is that surface eddies are generally separated from subthermocline eddies along the bifurcation latitude(~13°N) of the North Equatorial Current in the western tropical Pacific, which may be associated with different eddy energy sources and vertical eddy energy fluxes in subtropical and tropical gyres. Surface eddies have maximum swirl velocities of 8–9 cm s~(-1) and can extend to about 1500 m depth. Subthermocline eddies occur below 200 m, with their cores at about 400–600 m depth, and their maximum swirl velocities can reach 10 cm s~(-1). The other typical characteristic is that the meridional velocity component of the eddy is much larger than the zonal component. This characteristic might be due to more zonal eddy pairs(two eddies at the same latitude),which is also supported by the zonal wavelength(about 200 km) in the high-frequency meridional velocity component of the horizontal velocity.     

Decadal variability of the Kuroshio Extension: mesoscale eddies and recirculations

An eddy-resolving multidecadal ocean model hindcast simulation is analyzed to investigate time-varying signals of the two recirculation gyres present respectively to the north and south of the Kuroshio Extension (KE) jet. The northern recirculation gyre (NRG), which has been detected at middepth recently by profiling float and moored current meter observations, is a major focus of the present study. Low-frequency variations in the intensity of the recirculation gyres are overall highly correlated with decadal variations of the KE jet induced by the basin-wide wind change. Modulation of the simulated mesoscale eddies and its relationship with the time-varying recirculation gyres are also evaluated. The simulated eddy kinetic energy in the upstream KE region is inversely correlated with the intensity of the NRG, consistent with previous observational studies. Eddy influence on the low-frequency modulation of the NRG intensity at middepth is further examined by a composite analysis of turbulent Sverdrup balance, assuming a potential vorticity balance between the mean advection and the convergent eddy fluxes during the different states of the recirculation gyre. The change in the NRG intensity is adequately explained by that inferred by the turbulent Sverdrup balance, suggesting that the eddy feedback triggers the low-frequency modulation of the NRG intensity at middepth.     

On the interaction between a radiatively damped planetary wave and the zonally averaged circulation in the middle atmosphere

The interaction between a planetary wave damped by cooling to space and the zonally averaged circulation in the middle atmosphere is examined for a steady-state situation in middle latitudes. Quasi-geostrophic scaling of Type 2 is assumed (i.e. the space scales are planetary and the superrotation is small).A set of mean equations is derived for this scaling which is complementary to the set of perturbation equations previously studied. The mean equations show that a planetary wave induces a mean meridional circulation which is balanced by an eddy momentum forcing function and a mean diabatic heating which is balanced by an eddy heat flux forcing function. The vertical eddy fluxes enter the forcing at the same order as the horizontal eddy fluxes.An analytical wave solution is found for the case of an atmosphere in constant superrotation. The eddy fluxes and forcing functions are evaluated for this special case. It is found that they are very sensitive to the values of the radiative damping coefficient and the superrotation. Since the damping coefficient depends on the ozone concentration and the intensity of the solar ultraviolet flux, the results suggest that changes in these quantities can strongly modify the wave-mean flow interaction in the middle atmosphere. Possible implications for climate change are discussed.     

Wave-induced topographic formstress in baroclinic channel flow

Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ ^–2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ ² acts as a vertical eddy viscosity, and the transport is λ ²/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.     

On the maintenance of the axisymmetric part of the flow in the atmosphere

Summary The maintenance of the axisymmetric component of the flow in the atmosphere is investigated by means of a steady-state, quasi-geostrophic formulation of the meteorological equations. It is shown that the meridional variations in the time-averaged axisymmetric variables can be expressed as the sum of three contributions, one being due to the eddy heat transport, another to the eddy momentum transport, and a third to the convective-radiative equilibrium temperature which enters the problem through the specification of a Newtonian form of diabatic heating. The contributions by the large scale eddies are evaluated through the use of observed values for the eddy heat and momentum transports.The contributions from each of the three forcing mechanisms to the temperature and zonal wind fields are invstigated individually and found to be of about equal importance. The sum of the three contributions are also presented for the temperature, the zonal wind, the stream function associated with the mean meridional circulation and the corresponding vertical motion. Although the results fail to reproduce the main observed features of the lower stratosphere, they are found to be in good agreement with observations in the middle latitude troposphere. At any pressure level, for example, the computed mean zonal wind has a jet-like profile and the axis of the jet is found to slope to the south with height, as observed in the atmosphere.Based in part on a thesis submitted by the first author as partial fulfillment of the requirements for the Ph.D. degree at the University of Michigan. — Publication No. 194 from the Department of Meteorology and Oceanography, The University of Michigan.     

Evapotranspiration and runoff from large land areas: Land surface hydrology for atmospheric general circulation models

A land surface hydrology parameterization for use in atmospheric GCMs is presented. The parameterization incorporates subgrid scale variability in topography, soils, soil moisture and precipitation. The framework of the model is the statistical distribution of a topography-soils index, which controls the local water balance fluxes, and is therefore taken to represent the large land area. Spatially variable water balance fluxes are integrated with respect to the topography-soils index to yield our large scale parameterizations: water balance calculations are performed for a number of intervals of the topography-soils distribution, and interval responses are weighted by the probability of occurrence of the interval. Grid square averaged land surface fluxes result. The model functions independently as a macroscale water balance model. Runoff ratio and evapotranspiration efficiency parameterizations are derived and are shown to depend on the spatial variability of the above mentioned properties and processes, as well at the dynamics of land surface-atmosphere interactions.