Vertical and off-diagonal eddy diffusivities in the Northern Hemispheric stratosphere and lower mesosphere

Meteorological rocket soundings, launched between 1968–74 at six locations representative of low, middle, and high latitudes in the northern hemisphere, are employed to determine the vertical, meridional and off-diagonal components of the eddy diffusivity in the northern hemispheric statosphere and lower mesosphere.It is shown that the distribution of the vertical and meridional components of the eddy diffusivity are similar in the northern hemisphere, although the magnitude of the former is 10⁷ smaller than that of the latter; the magnitude of the off-diagonal eddy diffusivity is about 10³ smaller than that of the meridional eddy diffusivity. In the troposphere, a maximum eddy diffusivity occurs in the mid-latitude at about 7 km above the mean sea level for both the summer and winter seasons. In the stratosphere, a maximum eddy diffusivity occurs in the mid-latitude at about 33 km in the winter, but no maximum in the summer.Paper presented at the World Meterological Organization Technical Conference on Global Observations of Atmospheric Pollution Relative to Climate, Boulder, Colorado, 20–24 August 1979.     

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.     

Influence of the vertical motion field on ozone concentration in the stratosphere

Computations of the mean meridional motion field in the stratosphere are applied to ozone distributions to evaluate the associated ozone concentration changes. These changes are compared with those produced by photochemical and quasi-horizontal eddy processes. For the period January–April 1964 there is a cooperative action between the mean and eddy motions with mean subsidence in middle latitudes supplying ozone to be carried polawards and equatorwards by quasi-horizontal eddy processes. At low latitudes mean horizontal motions offset the eddy transport while at high latitudes mean rising motion is the offsetting term. The mean ozone flux through 50 mb, 3.5×10²⁹ molecules sec^–1, is comparable with the fluxes evaluated by other techniques.The spring maximum is thought to be due to a modulation of the energy supply to the stratospheric eddies which, in turn, force the mean motions. Longer-term changes are to be expected; for example during Ice Ages when increased tropospheric eddy activity is anticipated there should be higher total ozone.     

Horizontal eddy diffusivities in the northern hemispheric stratosphere and lower mesosphere

Meterological rocket soundings, launched between 1969–74 at six locations representative of low, middle, and high altitudes, are employed with the use of the statistical theory of diffusion, to determine the zonal and meridional component of eddy diffusivity between 30 and 55 km as a function of season, latitude, and altitude. A comparison is also made between annually-averaged eddy diffusivities above and below 30 km.It is shown that the zonal component of eddy diffusivity is approximately three to five times as large as the meridional component, in most cases. Both components of eddy diffusivity vary greatly with season, latitude, and altitude. Highest eddy diffusivities, found in the vicinity of the winter westerly jet, are approximately one order of magnitude higher than those present during the summer. Tropical eddy diffusivities, however, remain relatively small throughout the year. Annually, a minimum is indicated near 25 km between maximums located at the stratopause and tropopause.     

Meridional eddy flux of enthalpy in the Southern Hemisphere during the IGY

Summary From meteorological IGY data for the calendar year 1958, the mean meridional eddy transport of enthalpy was evaluated for the Southern Hemisphere. Levels chosen for the study were 1000, 850, 700, 500, 400, 300, 200, 150 and 100 mb. Data from 84 Southern Hemisphere and 25 equatorial Northern Hemisphere stations were used. Yearly mean quantities related to meridional eddy enthalpy flux were computed and analyzed.It was found that around 40° S there is a double-maximum zone of poleward, meridional, transient eddy enthalpy flux, the stronger transport occurring at 850 mb, and the weaker near 200 mb. The countergradient transient eddy flux regions in the low latitude mid-troposphere and in the middle and upper latitude lower stratosphere, found in previous Northern Hemisphere investigations, were observed to exist in the Southern Hemisphere also. The standing eddy heat transport, as expected, was very weak except at high latitudes where Antarctic continentality effected a large double-maximum poleward flux centered near the surface and in the lower stratosphere. The total vertically integrated enthalpy transport by the eddies was found to be poleward everywhere, reaching a maximum between 35° and 40° S.     

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.     

Observations of condensation growth determined by entity type mixing

It has been speculated for many years that the development of the droplet spectra in cloud is probably influenced by mixing processes. Various theoretical attempts to broaden the droplet spectra by mixing parcels with different velocity histories has shown that that particular effect is small. Similarly, very simpleuniform entrainment procedures did not lead to cloud drop size spectra which were broad enough, although by producing cloud drop size distributions with a double mode these models did substantially improve the drop size spectra of earlier adiabatic models which only exhibited a single mode.Recently a model based on entraining entities representing moving parcels of cloud air within the cloud was detailed byTelford andChai (1980). This study showed that the mixing in of dry air at cumulus turrets could lead to vertical cycling of diluted parcels, and that this cycling, with continual entrainment across the parcel boundaries, will produce much larger drops, as well as smaller drops of all sizes, in the droplet spectra. The entity entrainment concept studied there appears to apply to the observations of stratus cloud discussed in this paper.This paper presents data taken in marine stratus off the California coast which give a particularly clear example of how such droplet spectra modification occurs in practice. Both large drops, and the spread of the spectra to smaller sizes, occur in relation to other variables in such a way as to be consistent with an entity entrainment explanation, with no other obvious possibility.In a marine stratus cloud just over 200 m thick and many tens of miles in extent we find clear evidence that dry air is mixing in at cloud tops. Strong vertical motion is to be found in the cloud, large sized drops are found in cloud parcels where the mixing gives lower droplet concentrations, and there is evidence that newly formed cloud parcels are warmer and contain many more smaller droplets.The observations show that immediately following entrainment of dry air drop diameters are not reduced appreciably, but, in the same parcels, drop concentrations have been reduced by a factor of ten or more. Further down in the cloud big drops, able to start growth by coalescence, are found associated with low total droplet concentrations.Overall, it seems likely from the consideration of these observations that the formation of the large drops which lead to precipitation processes in clouds depends critically on the mixing in of dry air at cloud tops, and very little on the size of the small drops resulting from the condensation nucleus counts. As a conclusion it appears reasonable to state that if entrainment occurs at cloud tops, then big drops will be formed!     

Comment on “Complete Eulerian-mean tracer equation for coarse resolution OGCMs” by M. S. Dubovikov and V. M. Canuto

Dubovikov and Canuto (Dubovikov, M.S. and Canuto, V.M., Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. Astrophys. Fluid Dyn., 2006, 100, 197–214), after averaging the tracer conservation equation in density coordinates and transforming to height coordinates, concluded that present ocean models are missing important terms in their mean tracer equations. Here we point out some errors made by Dubovikov and Canuto (2006 Dubovikov, MS and Canuto, VM. 2006. Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. & Astrophys. Fluid Dynam., 100: 197–214. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in their isopycnal averaging procedure. We draw on the temporal-residual-mean (TRM) theory and show that when the isopycnal averaging and coordinate transformation are performed correctly, the tracer equations of present ocean circulation models are recovered. We therefore conclude that present ocean circulation models are not neglecting the leading order terms identified by Dubovikov and Canuto (2006 Dubovikov, MS and Canuto, VM. 2006. Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. & Astrophys. Fluid Dynam., 100: 197–214. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

Climatological Ertel’s potential-vorticity flux and mean meridional circulation in the extratropical troposphere – lower stratosphere

We investigated to what extent the isentropic, non-geostrophic formulation of zonally averaged circulation derived for stratospheric conditions is applicable to climatological transport in the extratropical troposphere and lower stratosphere. The study is based on 10 years of daily data of ECMWF analysis and on the ECHAM3 climate model of the German Climate Computing Centre. The main result is a scalar isentropic mixing coefficient, K_yy, and a mean meridional transport circulation consistently derived from the same data base. For both data sources, isentropic mean meridional circulation is derived from horizontal mass flow rate for 4 representative months. Alternatively, a mean meridional circulation is calculated from total diabatic heating rates of the ECHAM3 model. It is shown that only the latter is in good agreement with the ECMWF mean meridional circulation. Isentropic analysis also comprises the seasonal cycle of the climatological meridional gradient and flux of Ertels potential vorticity (PV). Application of Tungs flux-gradient relation yields that for all seasons K_yy is positive in height-latitude regions where statistical significance is reached. Large K_yy values, marking regions of more efficient mixing, have been found in the subtropical vertical band of weak westerly wind and in mid-latitudes in regions of upward-propagating baroclinic wave activity in the middle and upper troposphere. Based on the ECMWF data and results of baroclinic-wave behaviour, strong indications are presented that positive zonally averaged PV flux polewards of the jet core in the NH is strengthened by stationary waves and nonlinear effects. Reduced eddy transport is apparent in winter and spring slightly below the subtropical tropopause jet. The seasonal cycle of K_yy from ECHAM3 data is to a great extent in agreement with the result based on ECMWF analysis. In the model, reduced interannual variability enlarges the height-latitude range where sign of K_yy is significant.     

Partial ages: diagnosing transport processes by means of multiple clocks

The concept of age is widely used to quantify the transport rate of tracers - or pollutants - in the environment. The age focuses only on the time taken to reach a given location and disregards other aspects of the path followed by the tracer parcel. To keep track of the subregions visited by the tracer parcel along this path, partial ages are defined as the time spent in the different subregions. Partial ages can be computed in an Eulerian framework in much the same way as the usual age by extending the Constituent oriented Age and Residence Time theory (CART, www.climate.be/CART). In addition to the derivation of theoretical results and properties of partial ages, applications to a 1D model with lateral/transient storage, to the 1D advection-diffusion equation and to the diagnosis of the ventilation of the deep ocean are provided. They demonstrate the versatility of the concept of partial age and the potential new insights that can be gained with it.     

Water vapour transport and vergence patterns over India during two contrasting summer monsoons

Summary Using the daily upper air data of 00 GMT, the values of precipitable water, mean and eddy transport of moisture and the vergence patterns over the Indian sub-continent were evaluated for two contrasting summer monsoon seasons, 1966 and 1967. The precipitable water did not change markedly between the strong and weak monsoons. But there was a marked decrease in the zonal transport, up to 70%, in certain regions in the weak monsoon. In the strong monsoon, the meridional transport increased by a factor of 2 in certain regions and the vergence patterns also strengthened likewise in certain other regions.     

On the vertical transport of angular momentum in the atmosphere

Summary The possible modes of vertical transport of angular momentum in the atmosphere are considered. Momentum balance calculations for both hemispheres show the possibility of countergradient transport by vertical eddies in the region of the mid-latitude jet. As a consequence, it is pointed out that the transport of momentum downward from the region of maximum westerlies would have to be accomplished by the mean meridional motions, through the action of Coriolis torques. The same mechanism may account for a large part of the upward transport in the tropics. The very approximate nature of the calculations must, however, be borne clearly in mind.     

An analytical study of general hyper-diffusivity and barotropic eddies

An exact solution to the barotropic potential vorticity equation is used to examine the properties of barotropic vortices under arbitrary nth-order hyper-diffusivity. Analytical expressions are derived for an eddy's lifetime, meridional drift, decay in size, and energy, as functions of the Coriolis parameter, order and magnitude of diffusivity, and the eddy's size, shape and strength. These expressions provide a simple explanation for many observed features of oceanic and atmospheric vortices. For example, the competition between the Coriolis effect and eddy strength in giving permitted eddy geometries; the bias towards a zonal anisotropy for large vortices but not for small ones; energetic preference for axisymmetry; poleward meridional drift of cyclonic vortices; and meridional speed variation depending on eddy geometry and strength.     

Impact of horizontal eddy diffusivity on Lagrangian statistics for coastal pollution from a major marine fairway

Lagrangian trajectory methods are often applied as deterministic transport models, where transport is due strictly to advection without taking into account stochastic elements of particle dispersion, which raises questions about validity of the model results. The present work investigates the impact of horizontal eddy diffusivity for a case study of coastal pollution in the Gulf of Finland, where the pollutants are assumed to originate from a major fairway and are transported to the coast by surface currents. Lagrangian trajectories are calculated using the TRACMASS model from velocity fields calculated by the Rossby Centre circulation model for 1982 to 2001. Three cases are investigated: (1) trajectory calculation without eddy diffusivity, (2) stochastic modelling of eddy diffusivity with a constant diffusion coefficient and (3) stochastic modelling of eddy diffusivity with a time- and space-variable diffusion coefficient. It is found that the eddy diffusivity effect increases the spreading rate of initially closely packed trajectories and the number of trajectories that eventually reach the coast. The pattern of most frequently hit coastal sections, the probability of hit to each such section and the time the pollution spends offshore are virtually invariant with respect to inclusion of eddy diffusivity.     

Atmospheric eddy anomalies associated with the wintertime North Pacific subtropical front strength and their influences on the seasonal-mean atmosphere

This study investigates transient eddy activity anomalies in the mid-latitude upper troposphere associated with intensity variability of the wintertime North Pacific subtropical front. Our results show that the meridional gradient of air temperature and baroclinic instability in the mid-latitude atmosphere become stronger as the subtropical front intensifies, and the mid-latitude westerly jet accelerates with barotropic structure. We further divide the mid-latitude atmospheric eddy activities into high-(2–7 days) and low-frequency(10–90 days) eddy activities according to their life periods. We find that, when the oceanic subtropical front intensifies, the high-frequency atmospheric eddy activity in the mid-latitudes strengthens while the low-frequency eddy activity weakens. The stronger high-frequency eddy activity tends to moderate the air temperature gradient and baroclinicity in the mid-latitudes. High-frequency eddy anomalies accelerate the westerly jet on the northern side and downstream of the westerly jet, and enhance the jet with equivalent barotropic structure. In contrast, the weaker low-frequency eddy activity has a negative contribution to zonal wind speed tendency and attenuates the zonal homogenization of the jet. The anomalous thermodynamic forcing of the low-frequency eddy activity helps maintain the meridional gradient of air temperature in the mid-troposphere.     

Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases

To efficiently simulate the advection-diffusion processes along and across density surfaces, we need to deal with a diffusivity tensor containing off-diagonal elements (Redi, J Phys Oceanogr, 12:1154–1158, 1982). In the present paper, the Lagrangian model, in case of a space-varying diffusivity tensor, is developed. This random walk model is applied for two idealized test cases for which the analytical solutions are known. Results of the testing show that the Lagrangian approach provides accurate and effective solutions of advection-diffusion problems for general diffusivity tensor.     

The boundary layer of the residence time field

The residence time of a tracer in a control domain is usually computed by releasing tracer parcels and registering the time when each of these tracer parcels cross the boundary of the control domain. In this Lagrangian procedure, the particles are discarded or omitted as soon as they leave the control domain. In a Eulerian approach, the same approach can be implemented by integrating forward in time the advection–diffusion equation for a tracer. So far, the conditions to be applied at the boundary of the control domain were uncertain. We show here that it is necessary to prescribe that the tracer concentration vanishes at the boundary of the control domain to ensure the compatibility between the Lagrangian and Eulerian approaches. When we use the Constituent oriented Age and Residence time Theory (CART), this amounts to solving the differential equation for the residence time with boundary conditions forcing the residence time to vanish at the open boundaries of the control domain. Such boundary conditions are likely to induce the development of boundary layers (at outflow boundaries for the tracer concentration and at inflow boundaries for the residence time). The thickness of these boundary layers is of the order of the ratio of the diffusivity to the velocity. They can however be partly smoothed by tidal and other oscillating flows.     

A parcel formulation of Hamiltonian layer models

Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of Hamiltonian ordinary differential equations bound together by integral transport laws. In particular, we show that this parcel Hamiltonian structure is compatible with the stacking of layers under isentropic or isothermal constraints. The appeal of the parcel formulation is the simplification of various calculations, in particular the derivation of the continuum Poisson bracket and the proof of the Jacobi identity. A comparison and connection is made between the Hamiltonian dynamics of fluid parcels and the Hamiltonian system of partial differential equations. The parcel formulation can be seen as a precursor and tool for the study of Hamiltonian numerical schemes.     

Mean and eddy motion in the Skagerrak/northern North Sea: insight from a numerical model

Insight regarding the mean and eddy motion in the Skagerrak/northern North Sea area is gained through an analysis of model-simulated currents, hydrography, kinetic energy and relative vorticity for the 2 years 2000 and 2001. In this a -coordinate ocean model is used. Since the tidal currents are generally strong in the area, care is exercised to distinguish the mesoscale (eddy) motion from higher-frequency motion such as tides, before computing the mean and eddy kinetic energy. The model-simulated response is first compared with available knowledge of the circulation in the area, and when available, also with sea-surface temperature obtained from satellite imagery. It is concluded that the model appears to faithfully reproduce most of what is known, in particularly the upper mixed layer circulation. An analysis of the mean and eddy kinetic energy reveals that many of the mesoscale structures found in the area are recurrent. This is particularly true for the structures off the southern tip of Norway. Also in general, areas of strong mean and eddy kinetic energy are co-located. The exception is the area off the southern tip of Norway, where the eddy kinetic energy is much larger than its mean counterpart. An analysis of the relative vorticity reveals that the variability found is due to the occurrence of recurrent anticyclonic eddies. It is hypothesized that these eddies are generated due to an offshore veering of the Norwegian coastal current (NCC) as it reaches the eastern end of the Norwegian Trench plateau. Here it becomes a free jet, which is then vulnerable to either barotropic instability caused by the horizontal shear in the jet-like structure of the NCC at this point, or a baroclinic (frontal) instability. The latter may come into play when the NCC veers offshore and its relatively fresh water meets the inflowing saline water of Atlantic origin, a frontogenesis that may become strong enough for cyclogenesis to take place. Due to the depth-independent nature of the model-generated eddies, the barotropic instability is the most likely candidate. It remains to resolve the reason for the offshore veering of the NCC. The most likely candidate mechanisms are vortex squeezing or simply that the coastline curvature is large enough for the NCC to separate from the coast in a hydraulic sense.Responsible Editor: Phil Dyke     

Relation between the intensity of the stratospheric circumpolar vortex and the accumulation of ozone in the winter hemisphere

Summary The intensity of the polar vortex at 10 mb is used to calculate theoretical values of mean total ozone north of 40° latitude. A satisfactory fit is attained between the development in time of the theoretical ozone and that of the mean of the observed total ozone. The results lead to the conclusion, that a one-cell mean meridional motion relative to the polar night vortex is important for the transport of heat and ozone.