Vertical Heat Transport Research Articles

Steady natural convection in a double layer of immiscible liquids with density inversion

Natural convection of a layered fluid system composed of two immiscible liquids, silicone oil on top of water, is studied numerically. The flow in the two layers is viscously and thermally coupled. Two counter-rotating natural convection roll cells of opposite vorticity develop when one side wall temperature in the density inversion fluid is above and the other below the density inversion temperature. In contrast, only one roll cell develops in a liquid layer with Boussinesq properties. The viscous coupling between both immiscible layers strengthens the roll cell with opposite vorticity in the density inversion layer. At large Rayleigh number the flow pattern in the density inversion layer becomes very complex. The largest heat transport occurs in the upper Boussinesq layer. The two-roll cell pattern in the density inversion layer is impeding the total horizontal heat transfer. A vertical heat transport exists across the interface from the density inversion layer into the encapsulating upper layer. The moving interface between the immiscible liquids improves the heat transfer in each layer when compared to the cavity cases.

Tropopause Height in Baroclinic Channel Flow

A wave–mean flow model of dry channel flow is used to investigate the processes that determine the height HT and the slope of the extratropical tropopause. Without baroclinic waves, differential radiative heating and a convective adjustment mechanism cooperate to establish a well-defined tropopause and a mean zonal wind with almost constant vertical shear. This reference state is neutrally stratified in the troposphere and, therefore, baroclinically unstable. It is shown that the meridional and vertical heat transports by the unstable linear eigenmodes induce a rise of the tropopause in the northern part of the channel, whereas there is little change of HT in the south. These predictions of the linear theory are verified by aid of the nonlinear model. Changes of HT are restricted to the jet region if a jet is enforced.

Lead‐induced atmospheric circulations

Leads provide a significant source of heat and moisture to the Arctic winter atmosphere, and plumes from wide leads have been observed to penetrate the Arctic inversion. We have developed a two‐dimensional, high‐resolution, deep anelastic numerical model to investigate the atmospheric convection from leads with widths ranging from 100 m to 10 km. A second‐order turbulence closure scheme is used to parameterize the atmospheric turbulence in the horizontally inhomogeneous system. This study describes how the lead‐induced circulations can enhance the vertical transport of heat into the atmospheric boundary layer. This model is compared with large‐eddy simulation results and with lidar observations of a lead‐induced ice crystal plume. The model is used to study the effect of varying lead widths and ambient atmospheric conditions on the resultant convection from leads, and some preliminary results are described.

Systematic errors in the medium range prediction of the Asian summer monsoon circulation

The present study describes an analysis of Asian summer monsoon forecasts with an operational general circulation model (GCM) of the European Centre for Medium Range Weather Forecasts (ECMWF), U.K. An attempt is made to examine the influence of improved treatment of physical processes on the reduction of systematic errors. As some of the major changes in the parameterization of physical processes, such as modification to the infrared radiation scheme, deep cumulus convection scheme, introduction of the shallow convection scheme etc., were introduced during 1985–88, a thorough systematic error analysis of the ECMWF monsoon forecasts is carried out for a period prior to the incorporation of such changes i.e. summer monsoon season (June–August) of 1984, and for the corresponding period after relevant changes were implemented (summer monsoon season of 1988). Monsoon forecasts of the ECMWF demonstrate an increasing trend of forecast skill after the implementation of the major changes in parameterizations of radiation, convection and land-surface processes. Further, the upper level flow is found to be more predictable than that of the lower level and wind forecasts display a better skill than temperature. Apart from this, a notable increase in the magnitudes of persistence error statistics indicates that the monsoon circulation in the analysed fields became more intense with the introduction of changes in the operational forecasting system. Although, considerable reduction in systematic errors of the Asian summer monsoon forecasts is observed (up to day-5) with the introduction of major changes in the treatment of physical processes, the nature of errors remain unchanged (by day-10). The forecast errors of temperature and moisture in the middle troposphere are also reduced due to the changes in treatment of longwave radiation. Moreover, the introduction of shallow convection helped it further by enhancing the vertical transports of heat and moisture from the lower troposphere. Though, the hydrological cycle in the operational forecasts appears to have enhanced with the major modifications and improvements to the physical parameterization schemes, certain regional peculiarities have developed in the simulated rainfall distribution over the monsoon region. Hence, this study suggests further attempts to improve the formulations of physical processes for further reduction of systematic forecast errors.

2つの積雲対流パラメタリゼーションのGCMによる感応実験

To examine the sensitivity of the simulated large-scale structures to the Betts-Miller and the Arakawa-Schubert cumulus parameterizations, a series of 6-month integrations are performed using the CCSR/NIES atmospheric general circulation model with a horizontal triangular resolution of 21 and 20 vertical levels. The model results are time-averaged for the last three months, that is, June-July-August mean. Comparisons between the simulations using the Betts-Miller scheme and the Arakawa-Schubert scheme indicate that although the simulated large-scale structures are generally similar to each other, there are some noticeable differences. These include the temperatures in the middle and upper troposphere at mid-latitudes in the northern hemisphere, the location of the maximum convective heating in the tropical deep connective region, the convective heating/cooling in the boundary layer, the precipitation distribution pattern over the tropical western Pacific and the vertical profile of the vertical turbulent heat transport. Sensitivity experiments with different adjustment parameters in the Betts-Miller scheme show that the precipitation distribution pattern over the tropical western Pacific is very sensitive to the adjustment time scale and stability weight as well as the saturation pressure departure. It is also shown that the partition between the convective precipitation and the large-scale precipitation is most sensitive to the saturation pressure departure.

Dependence of a Plume Heat Budget upon Lateral Advection

The structure and heat budget of a plume created by a linear heat source is investigated, demonstrating their dependence upon the larger-scale cross-source flow. A large-eddy model simulates individual thermal eddies produced by a source 200 m wide having an average surface temperature flux of 0.20 K m s−1, parameters appropriate to an Arctic lead—that is, to a break in the polar ice field. When the large-scale cross-flow is relatively weak, maximum turbulent development occurs over the source itself and the mean updraft is relatively strong. Thermally induced lateral inflow then concentrates the vertical heat transport over the source, and vertical advection accounts for over half the total heat transfer. Horizontal turbulent heat transport is important throughout the mean updraft. Turbulent vertical heat flux dominates the heat budget only in the near-surface region. With increasing externally forced cross-flow, mean and turbulent vertical velocities are weakened. Transport mechanisms are significantly altered when the cross-flow is sufficiently strong to move the region of maximum turbulence beyond the source. Turbulent vertical heat flux then becomes important through the entire plume depth, and its heat transfer becomes larger than that due to mean vertical transport. Maximum turbulent development occurs horizontally where the parcel transit time from the source centerline is approximately half the Brunt–Väisälä period of the surrounding environment. When this occurs over the source, its position coincides with that of the mean updraft. A criterion for strong updraft development, and consequent large vertical advective transport, is for the transit time of a parcel over the source to be less than the Brunt–Väisälä period.

Thermodynamic Balance of Three-Dimensional Stratospheric Winds Derived from a Data Assimilation Procedure

The NASA/Goddard three-dimensional chemistry and transport model is driven by winds from a stratospheric data assimilation system. Synoptic- and planetary-scale patterns, apparent in satellite observations of trace constituents, are successfully reproduced for seasonal integrations. As model integrations proceed, however, the quality of simulations decreases, and systematic differences between calculation and measurement appear. The differences are explained by examining the zonal-mean residual circulation. The vertical velocity w-bar (sup star) is calculated two ways: (1) from the diabatic heating rates and temperature tendency and (2) from the Eulerian vertical velocity and the horizontal eddy heat flux convergence. The results from these calculations differ substantially. Periodic insertion of observational data during the assimilation process continually shocks the general circulation model and produces these differences, which leads to an overestimate of the mean vertical heat and cconstituent transport. Such differences are expected to be general to all data assimilation products. This interpretation is corroborated by two-dimensional (2D) model calculations. When w-bar(sup star) is calculated from (2), the 2D ozone evolution is unrealistic and qualitatively similar to the 3D model simulation. The 2D ozone evolution is reasonable when w-bar (sup star) from (1).

Roll vortices in the planetary boundary layer: A review

Roll vortices may be loosely defined as quasi two-dimensional organized large eddies with their horizontal axis extending through the whole planetary boundary layer (PBL). Their indirect manifestation is most obvious in so-called cloud streets as can be seen in numerous satellite pictures. Although this phenomenon has been known for more than twenty years and has been treated in a review by one of us (R.A.Brown) in 1980, there has been a recent resurgence in interest and information. The interest in ocena/land-atmosphere interactions in the context of climate modeling has led to detailed observational and modeling efforts on this problem. The presence of rolls can have a large impact on flux modelling in the PBL. Hence, we shall review recent advances in our understanding of organized large eddies in the PBL and on their role in vertical transport of momentum, heat, moisture and chemical trace substances within the lowest part of the atmosphere.

An observational study on the energetics of the onsent monsoon vortex, 1979

AbstractTime variations, of the vertically integrated, and vertical distribution of time‐mean zonal and eddy components of the kinetic and available potential energy, and the associated energy conversions, are examined in order to understand the formation and growth mechanisms associated with the monsoon onset vortex during 14‐17 June 1979. For the computations, the area 0‐22.5°N and 48.75°E‐78.75°E and the vertical layer 1000‐300 hPa are considered. The dynamical characteristics of the large‐scale monsoon current surrounding the onset vortex are also investigated. Strengthening of the meridional and vertical shear of the mean zonal wind is noticed during the period. The vortex is formed to the north of the westerly jet, in the zone of maximum cyclonic shear. The northward shift of the large‐scale monsoon current is noticed in association with northward movement of the onset vortex.It is identified from the mean energetics that both barotropic and baroclinic energy conversions, and also the boundary terms, maintain the vortex. Baroclinic energy transfer to eddy kinetic energy (KE) takes place not only in the upper levels but also in the lower levels. Further, the energy conversion from zonal kinetic energy (KZ) to KE dominates over the energy conversion from eddy available potential energy (AE) to KE. The barotropic energy conversion due to the down‐gradient eddy transport of meridional momentum is more than that due to zonal momentum transport. The transfer of the vertical wave‐energy flux, due to the eddy pressure interaction, away from the middle level also contributes significantly to the maintenance of KE in the upper and lower levels. The generation rate of the zonal and eddy available potential energy and the frictional dissipation of KE are computed b the residue method; the values are 0.54 W m‐2, 0.25 W m−2 and 0.65 W m−2, respectively.The meridional and vertical transports of momentum and heat are examined in relation to the structure of the vortex. The requirement of minimum vertical resolution for the vortex modelling studies is indicated.

Dynamic Oxygen and Carbon Dioxide Exchange between Soil and Atmosphere: I. Model Development

AbstractThe rate of exchange of O2 and CO2 gases between soil and atmosphere is controlled by atmospheric and soil physical and biological conditions. Analysis and evaluation of problems in soil biology and soil ecology would be greatly facilitated by the availability of a mathematical model that predicts concentrations of these gases as a function of time and soil depth as well as the rate of gas exchange at the soil surface. Our objective was to develop such a model, driven by time‐dependent functions for solar radiation, rainfall, air temperature, and relative humidity of the atmosphere. Outputs of the model include concentrations of CO2 and O2, soil water content, soil temperature, and rate of consumption of O2 and production of CO2 by roots and soil microorganisms, all as functions of time and soil depth. Dissolution of O2 and CO2 in soil water, adsorption of O2 and CO2 onto colloidal surfaces of soil particles, and replacement of air by water due to soil wetting and vice versa are accounted for in the model. Rates of respiration by microorganisms and roots and rate of root growth are given as functions of O2 and CO2 concentrations. Not all of the processes or parameters could be included in the model development because of their large number and complexity. The structure of the model consists of time‐dependent simultaneous equations for vertical transport of water, heat, O2, and CO2 through unsaturated soils. Finite difference methods are used to solve the mathematical model.

On the transient response of a simple coupled climate system

This paper presents quasi‐analytical solutions to a class of coupled atmosphere‐ocean models for time‐dependent ramp‐ and step‐forced climate changes. The model consists of a conventional two‐dimensional energy balance model of the atmosphere with an oceanic mixed layer coupled to a deep ocean having vertical heat transports due to horizontally uniform vertical diffusion and upwelling. The solution is partitioned into the particular or asymptotic part and the homogeneous or transient part. This partitioning facilitates understanding the different time constants involved in the problem. For ramp forcing there are two time constants: the lag time in the asymptotic straight line warming solution and the characteristic adjustment time to the asymptotic curve. The lag behind the “no inertia” warming is a few decades, while the adjustment time to the asymptotic curve is several hundred years due to the restructuring of the thermal profile near the main thermocline. This is in strong contrast to the step‐forcing scenario where the adjustment time to the new constant steady state is only a few decades. The latter experiment suggests that step‐forcing scenarios are not very similar to ramp‐forcing scenarios. The model produces a warming of ∼ 0.5°C over the last hundred years provided the simulation is started 200 years ago. An interesting feature of the solutions is that the land surface areas lead the ocean surface areas in heating up by O (0.1°C). This may lead eventually to a fairly robust signature of the greenhouse forcing. Future models of this type probably need more horizontal dependence on the vertical heat transport parameters as well as horizontal transport mechanisms.

An energy balance climate model with hydrological cycle: 1. Model description and sensitivity to internal parameters

A thermodynamical model designed to illustrate the effect of a hydrological cycle on climate sensitivity is presented. The model contains three climatic variables: two temperatures referring to an idealized atmosphere and ocean, respectively, and atmospheric humidity. The independent variables are time and latitude. Atmosphere and ocean are coupled by radiation and convection at their interface. Some structure of the atmospheric circulation is retained by differentiating between the dynamics of a low latitude zone (0° ‐ ϕH) and that of a high latitude zone (ϕH‐90°), where ϕH ≈ 30° is the intersection of meridional temperature gradient and critical gradient for baroclinic instability. The atmospheric transport is split into an advective and a diffusive part, while the oceanic transport is approximated by pure diffusion. The coefficients associated with horizontal and vertical motion are modelled in terms of temperature gradients. The predicted water vapor gives rise to precipitation and clouds and influences (via cloud cover and greenhouse effect) the radiation balance of the system. The model is integrated for annual mean conditions until an asymptotic equilibrium is reached. The free (internal) parameters of the system are determined by optimization methods so that simulated temperature, heat flux and hydrological cycle are in close agreement with observations. The sensitivity of the model is governed by radiation parameters. Of these, the cloud albedo is the most sensitive quantity. By contrast, the model is relatively little affected by parameters associated with horizontal and vertical transport of heat.

Solar heating of a stratified ocean in the presence of a static ice cover

Conductivity, temperature, and depth measurements were carried out in an isolated transverse lead in static, shorefast ice in Mould Bay, Prince Patrick Island, Northwest Territories, during a 3‐week period at the height of the melt season. Currents beneath the ice appeared to be weak and largely tidal in nature. Initially, the water was vertically uniform and at the salinity‐determined freezing point down to a depth of at least 20 m. By the end of the experiment the water column consisted of three distinct layers: a well‐mixed, nearly fresh surface meltwater layer; a very stable half‐meter‐thick halocline centered somewhat below the bottom of the ice; and a thermally stratified layer of constant salinity extending down to at least 25 m. The halocline was characterized by a temperature maximum that was about 2°C warmer than the surrounding water. This temperature maximum in the pycnocline effectively trapped shortwave energy absorbed in the lower layer and prevented it from melting the overlying ice. Theoretical calculations demonstrate that the thermal structure observed beneath the pycnocline was controlled by the input of shortwave radiation and that vertical heat transport was largely the result of diffusive processes. The presence of leads drastically increases the amount of energy stored in the water. In regions where leads are common, it is likely that this energy will significantly accelerate the decay and removal of the ice once it becomes mobile and once the pycnocline is erased.

Double-Diffusive Fluxes in a Salt Gradient Solar Pond

The possible influence of double-diffusive stratification on the vertical transport of salt and heat in a mixed-layer simulation model for a salt gradient solar pond is examined. The study is concerned primarily with the interfacial fluxes across the boundary between the gradient zone and upper convecting zone of solar ponds, though the arguments presented should be applicable to other “diffusive” interfaces as well. In the absence of mechanical stirring in the upper convecting zone (e.g., by wind), double diffusive instabilities could govern the vertical flux of heat and salt by adjusting interfacial gradients of temperature and salinity which control transport by molecular diffusion. Because these gradients are generally too sharp to be resolved by numerical models, the fluxes can either be modeled directly or be parameterized by grid-dependent “effective diffusivities.” It is shown that when mechanical stirring is present in the mixed layer, double-diffusive instabilities will not be allowed to grow in the interfacial boundary layer region. Thus, double-diffusive fluxes become important only in the absence of stirring and, in effect, provide a lower bound to the fluxes that would be expected across the interface.

Heat Budget of the Siberian High and the Winter Monsoon

Abstract The heat budget of the Siberian high is investigated by using a compositing method. Ninteen cases of strong Siberian highs that moved over China from the northwest were selected from datasets covering five winters (December through February of 1980–1984). The apparent heat source (Q1)and the apparent moisture sink (Q2) were estimated via budget calculations. The diabatic heating terms were also calculated via direct use of physical parameterization schemes. The vertical transports of sensible and latent heat from subgrid-scale of motions were estimated as residuals from the thermodynamic energy equation. Over the region of the region of the Siberian high, strong radiative cooling and large-scale descending motion (with large-scale mass convergence over the upper and middle tropospheric and divergence over the lower troposphere) contributes to a rapid buildup of the Siberian high. Heating in the upper troposphere due to subgrid-scale sensible heat transfer is also an important factor in the mainte...

The effect of vertical transports of heat and moisture by cumulus convection in typhoon

By utilizing the denser upper-air observations from the Okinawa region and Japanese islands during August 17–23, 1975, the vertical transports of heat and moisture by cumulus convection in the typhoon No. 7507 have been calculated. It is found that there exist a large apparent heat source (Q1) and a moisture sink (Q2) in the southern part of the typhoon at the disturbance, growing and mature stages. The magnitudes of the apparent heat source and moisture sink are rather small, or turn into the apparent heat sink in the northern sector of the typhoon. In the southern part of the typhoon, the total cloud mass flux (Mc) is positive, whereas in the northern part of the typhoonMc is negative. The above-mentioned distributions ofQ1,Q2 andMc agree well with the major cloud patterns.

Observations of intermittent cumulus convection in the boundary layer

AbstractDuring the 1978 JASIN experiment radiosonde and tethered balloon measurements were performed from the R. V. Meteor. On 1 September, two cloud layers (cumulus below stratocumulus) were observed below an inversion at about 900m. Such a boundary layer situation occurred relatively often during the experiment. Cumulus clouds were not present all the time but alternately appeared and disappeared. When they occurred on 1 September, a relatively large vertical shear (about 0.006 s−1) together with an inflection point in the profile of the wind component normal to the mean wind direction was observed in the cumulus cloud layer. the airsea temperature difference was small (δT = −0.5 K) and there was a relatively large dynamical contribution to cloud generation. This may suggest the idea of an interaction between large‐scale processes generating a favourable mean wind shear profile and dynamically forced convection.Significant vertical transport of heat and momentum in the cloud layer occurred only in connection with cumulus clouds. Although in parts of some clouds the transports were locally as large as several 100W m−2 and 1N m−2, there were only a few events with such large excursions so that the transports averaged over the whole field of cumulus clouds were small.The relative air flow in and around active cumulus clouds was characterized by updraughts within the cloud and downdraughts at the cloud edges. the thermodynamic properties of updraughts and downdraughts are discussed.

Numerical simulation of vortex roll development during a cold air outbreak

Abstract Cold air outbreaks can be identified by the formation of cloud streets downwind from a land-sea boundary, as can be seen in numerous satellite pictures. These cloud streets are caused by horizontal roll vortices which in turn are due to dynamic and convective instability of the planetary boundary layer over sea. The development of these roll vortices is simulated with a numerical model and compared to observations obtained over the Bering Sea. Vertical heat transport is found to be due to turbulent diffusion in the initial stage of a cold air outbreak before organized roll vortices contribute to the heat flux in the higher levels of the boundary layer. The influence of a capping inversion on the dynamic and convective instability is also elucidated.

A linear stability theory of double-diffusive horizontal intrusions in a temperature–salinity front

The stability of a temperature–salinity front of finite width in which the density is exactly compensated for in the horizontal direction is studied by means of a linear theory. It is assumed that salt fingers are responsible for vertical transports of salinity and heat. The front is found to be always unstable even if viscosity is present. Horizontal intrusions are generated as a result of the instability, and cold/fresh water sinks while hot/salty water rises.The stability of the front is described by three dimensionless parameters: a frontal stability parameter G = [g(1 − γ)βΔS]6/κe2a2N10, a stratification parameter the vertical gradient of the basic salinity, κe the eddy diffusivity of salt due to salt fingers, and ν is either molecular or eddy kinematic viscosity. When ε is not zero it is found that a modified frontal stability parameter R defined by R = G/ε plays an important role in determining the stability for a fixed value of μ. In particular, when ε is larger than 10, the stability is almost completely determined by R if μ is specified.The dependence of the vertical scale h of the fastest-growing mode on external parameters varies according to the value of R for a given value of μ. When R is less than 40(1 + μ)5.4 (for ε = 10−3-103) h becomes independent of R and ε and is given by h = 2.2d/(1 + μ), where d = g(1 − γ)βΔS/N2 is the scale suggested by Ruddick & Turner (1979) who performed an experiment on horizontal intrusions across a narrow front. When R > 2 × 1055 (1 + μ)4.9, on the other hand, h becomes proportional to dR−1/4, the scale suggested by Toole & Georgi (1978), who considered the stability of a temperature–salinity front of infinite width. The constant of the proportionality is a weak function of ε and varies from 2π[(2 + μ)/4(1 + μ)2]−¼ to 2π[2(1 + μ + (1 + μ)½)]½ as ε goes from zero to infinity. Thus a front can be said to be narrow if R < 40(1 + μ)5.4 and wide if R > 2 × 105(1 + μ)4.9.The results of the theory explain those of Ruddick & Turner's experiment (1979) reasonably well.

Recombination of atomic oxygen near the mesopause: Interpretation of rocket data

From the observations of atomic oxygen concentrations during the Energy Budget Campaign 1980, heating rates in the lower thermosphere at high latitude for late fall are derived and are found to be rather high. Useful information is also inferred for the vertical transport of mass and heat at these heights. The eddy diffusion coefficient which is derived from the data decreases with decreasing altitude below 100 km and reaches a minimum value of the order of 10 m2 s−1 near the mesopause. Such low value implies a low minimum concentration of nitric oxide (105–106 cm−3) near 80 km.