Meridional Energy Flux Research Articles

The Influence of Meridional Gradients in Insolation and Longwave Optical Depth on the Climate of a Gray Radiation GCM

The relative contributions of the meridional gradients in insolation and in longwave optical depth (caused by gradients in water vapor) to the equator-to-pole temperature difference, and to Earth’s climate in general, have not been quantified before. As a first step to understanding these contributions, this study investigates simulations with an idealized general circulation model in which the gradients are eliminated individually or jointly, while keeping the global means fixed. The insolation gradient has a larger influence on the model’s climate than the gradient in optical depth, but both make sizeable contributions and the changes are largest when the gradients are reduced simultaneously. Removing either gradient increases global-mean surface temperature due to an increase in the tropospheric lapse rate, while the meridional surface temperature gradients are reduced. “Global warming” experiments with these configurations suggest similar climate sensitivities; however, the warming patterns and feedbacks are quite different. Changes in the meridional energy fluxes lead to polar amplification of the response in all but the setup in which both gradients are removed. The lapse-rate feedback acts to polar amplify the responses in the Earth-like setup, but is uniformly negative in the other setups. Simple models are used to interpret the results, including a prognostic model that can accurately predict regional surface temperatures, given the meridional distributions of insolation and longwave optical depths.

Linking Hadley Circulation and Storm Tracks in a Conceptual Model of the Atmospheric Energy Balance

Abstract Midlatitude storm tracks shift in response to climate change and natural climate variations such as El Niño, but the dynamical mechanisms controlling these shifts are not well established. This paper develops an energy balance model that shows how shifts of the Hadley cell terminus and changes of the meridional energy flux out of the Hadley cell can drive shifts of storm tracks, identified as extrema of the atmospheric meridional eddy energy flux. The distance between the Hadley cell terminus and the storm tracks is primarily controlled by the energy flux out of the Hadley cell. Because tropical forcings alone can modify the Hadley cell terminus, they can also shift extratropical storm tracks, as demonstrated through simulations with an idealized GCM. Additionally, a strengthening of the meridional temperature gradient at the terminus and hence of the energy flux out of the Hadley cell can reduce the distance between the Hadley cell terminus and the storm tracks, enabling storm-track shifts that do not parallel shifts of the Hadley cell terminus. Thus, with the aid of the energy balance model and supporting GCM simulations, a closed theory of storm-track shifts emerges.

Regional energy budget control of the intertropical convergence zone and application to mid-Holocene rainfall

Shifts in the latitude of the intertropical convergence zone—a region of intense tropical rainfall—have often been explained through changes in the atmospheric energy budget, specifically through theories that tie rainfall to meridional energy fluxes. These quantitative theories can explain shifts in the zonal mean, but often have limited relevance for regional climate shifts, such as a period of enhanced precipitation over Saharan Africa during the mid-Holocene. Here we present a theory for regional tropical rainfall shifts that utilizes both zonal and meridional energy fluxes. We first identify a qualitative link between zonal and meridional energy fluxes and rainfall variations associated with the seasonal cycle and the El Nino/Southern Oscillation. We then develop a quantitative theory based on these fluxes that relates atmospheric energy transport to tropical rainfall. When applied to the orbital configuration of the mid-Holocene, our theory predicts continental rainfall shifts over Africa and Southeast Asia that are consistent with complex model simulations. However, the predicted rainfall over the Sahara is not sufficient to sustain vegetation at a level seen in the palaeo-record, which instead requires an additional large energy source such as that due to reductions in Saharan surface albedo. We thus conclude that additional feedbacks, such as those involving changes in vegetation or soil type, are required to explain changes in rainfall over Africa during the mid-Holocene. Shifts in the latitude of the tropical rainfall band are constrained by meridional energy fluxes. Calculations show that combining zonal and meridional energy fluxes can explain past regional rainfall variations like the African Humid Period.

Seasonal and Interannual Variations of the Energy Flux Equator and ITCZ. Part I: Zonally Averaged ITCZ Position

Abstract In the zonal mean, the ITCZ lies at the foot of the ascending branch of the tropical mean meridional circulation, close to where the near-surface meridional mass flux vanishes. The ITCZ also lies near the energy flux equator (EFE), where the column-integrated meridional energy flux vanishes. This latter observation makes it possible to relate the ITCZ position to the energy balance, specifically the atmospheric net energy input near the equator and the cross-equatorial energy flux. Here the validity of the resulting relations between the ITCZ position and energetic quantities is examined with reanalysis data for the years 1979–2014. In the reanalysis data, the EFE and ITCZ position indeed covary on time scales of seasons and longer. Consistent with theory, the ITCZ position is proportional to the cross-equatorial atmospheric energy flux and inversely proportional to atmospheric net energy input at the equator. Variations of the cross-equatorial energy flux dominate seasonal variations of the ITCZ position. By contrast, variations of the equatorial net energy input, driven by ocean energy uptake variations, dominate interannual variations of the ITCZ position (e.g., those associated with ENSO).

The Equatorial Energy Balance, ITCZ Position, and Double-ITCZ Bifurcations

Abstract The intertropical convergence zone (ITCZ) migrates north–south on seasonal and longer time scales. Previous studies have shown that the zonal-mean ITCZ displacement off the equator is negatively correlated with the energy flux across the equator; when the ITCZ lies in the Northern Hemisphere, energy flows southward across the equator, and vice versa. The hemisphere that exports energy across the equator is the hemisphere with more net energy input, and it is usually the warmer hemisphere. But states with a double ITCZ straddling the equator also occur, for example, seasonally over the eastern Pacific and frequently in climate models. Here it is shown how the ITCZ position is connected to the energy balance near the equator in a broad range of circumstances, including states with single and double ITCZs. Taylor expansion of the variation of the meridional energy flux around the equator leads to the conclusion that for large positive net energy input into the equatorial atmosphere, the ITCZ position depends linearly on the cross-equatorial energy flux. For small positive equatorial net energy input, the dependence of the ITCZ position on the cross-equatorial energy flux weakens to the third root. When the equatorial net energy input or its curvature become negative, a bifurcation to double-ITCZ states occurs. Simulations with an idealized aquaplanet general circulation model (GCM) confirm the quantitative adequacy of these relations. The results provide a framework for assessing and understanding causes of common climate model biases and for interpreting tropical precipitation changes, such as those evident in records of climates of the past.

Mechanisms of Forced Tropical Meridional Energy Flux Change

Abstract Anthropogenically forced changes to the mean and spatial pattern of sea surface temperatures (SSTs) alter tropical atmospheric meridional energy transport throughout the seasonal cycle—in total, its partitioning between the Hadley cells and eddies and, for the Hadley cells, the relative roles of the mass flux and the gross moist stability (GMS). The authors investigate this behavior using an atmospheric general circulation model forced with SST anomalies caused by either historical greenhouse gas or aerosol forcing, dividing the SST anomalies into two components: the tropical mean SST anomaly applied uniformly and the full SST anomalies minus the tropical mean. For greenhouse gases, the polar-amplified SST spatial pattern partially negates enhanced eddy poleward energy transport driven by mean warming. Both SST components weaken winter Hadley cell circulation and alter GMS. The Northern Hemisphere–focused aerosol cooling induces northward energy flux anomalies in the deep tropics, which manifest partially via strengthened northern and weakened southern Hadley cell overturning. Aerosol-induced GMS changes also contribute to the northward energy fluxes. A simple thermodynamic scaling qualitatively captures these changes, although it performs less well for the greenhouse gas simulations. The scaling provides an explanation for the tight correlation demonstrated in previous studies between shifts in the intertropical convergence zone and cross-equatorial energy fluxes.

Comparison of the main characteristics of the daily zonally averaged surface air temperature as represented by reanalysis and seven CMIP3 models

This paper analyses the ability exhibited by seven coupled global climate models of the Climate Model Inter-comparison Project 3 used in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change to simulate current zonally averaged surface air temperature (ZASAT) meridional profiles. The expansion in second order of ZASAT profiles by means of Legendre polynomials was compared with the same expansion carried out over the ZASAT profiles provided by the ERA40 and National Centers for Environmental Prediction reanalysis from 1961 to 1998. According to the theoretical support provided by the one-dimensional energy balance models (1D-EBMs), the Legendre coefficients corresponding to the ZASAT profile can be qualitatively interpreted as the independent modes that represent the meridional energy flux from the equator to the poles. We find that three models, MIROC3.2-MR, MIROC3.2-HR and MPI-ECHAM5 may be considered as the models that best reproduce the meridional structure of current ZASAT, although the differences between the models are not really large. Consequently, the results shown in this paper support the accuracy of the models in representing the poleward meridional heat fluxes and global thermal inertia under the qualitative interpretation provided by the 1D-EBM approach.

Solar irradiance modulation of Equator-to-Pole (Arctic) temperature gradients: Empirical evidence for climate variation on multi-decadal timescales

Using thermometer-based air temperature records for the period 1850–2010, we present empirical evidence for a direct relationship between total solar irradiance (TSI) and the Equator-to-Pole (Arctic) surface temperature gradient (EPTG). Modulation of the EPTG by TSI is also shown to exist, in variable ways, for each of the four seasons. Interpretation of the positive relationship between the TSI and EPTG indices suggests that solar-forced changes in the EPTG may represent a hemispheric-scale relaxation response of the system to a reduced Equator-to-Pole temperature gradient, which occurs in response to an increasing gradient of incoming solar insolation. Physical bases for the TSI-EPTG relationship are discussed with respect to their connections with large-scale climate dynamics, especially a critical relationship with the total meridional poleward energy transport. Overall, evidence suggests that a net increase in the TSI, or in the projected solar insolation gradient which reflects any net increase in solar radiation, has caused an increase in both oceanic and atmospheric heat transport to the Arctic in the warm period since the 1970s, resulting in a reduced temperature gradient between the Equator and the Arctic. We suggest that this new interpretative framework, which involves the extrinsic modulation of the total meridional energy flux beyond the implicit assumptions of the Bjerknes Compensation rule, may lead to a better understanding of how global and regional climate has varied through the Holocene and even the Quaternary (the most recent 2.6 million years of Earth's history). Similarly, a reassessment is now required of the underlying mechanisms that may have governed the equable climate dynamics of the Eocene (35–55 million years ago) and late Cretaceous (65–100 million years ago), both of which were warm geological epochs. This newly discovered relationship between TSI and the EPTG represents the “missing link” that was implicit in the empirical relationship that Soon (2009) recently demonstrated to exist between multi-decadal TSI and Arctic and North Atlantic climatic change.

Meridional energy flux in the Arctic from data of the radiosonde archive IGRA

face to 30 hPa is 70.6 W m –2 . The fraction of the sensible heat flux is 23.2 W m –2 , i.e., 33% of the total energy flux; the fraction of the latent heat flux is 28.0 W m –2 (40% of the total energy flux); the fraction of the poten� tial energy is 20.0 W m –2 (27%); and the fraction of the kinetic energy is 0.53 W m –2 , i.e., less than 1% of the total energy flux. The vertical structure of the flux shows that the main energy transport into the Arctic takes place in the middle troposphere–lower stratosphere layer, whereas the energy is transported mainly out of the Arctic in the lower troposphere, which agrees well with the schematic notion about the polar circulation cell. The spatial structure of the flux shows that the key regions with a positive (directed into the Arctic) energy flux are located in the vicinity of 160° E (the northwestern part of Eurasia, Pacific sector) and 50° W (Green� land sector). The regions with a negative (directed out of the Arctic) energy flux are located near 120° W (Canadian Arctic Archipelago) and from 20° E to 90° E (Atlantic sector). In the period from 1992 to 2007, the meridional energy transport into the Arctic weakened by –0.26 W m –2 yr –1 . The changes were mutually correlated; namely, positive and negative energy fluxes weakened in amplitude, almost without changing their locations.

Present and Last Glacial Maximum climates as states of maximum entropy production

AbstractThe Earth, like other planets with a relatively thick atmosphere, is not locally in radiative equilibrium and the transport of energy by the geophysical fluids (atmosphere and ocean) plays a fundamental role in determining its climate. Using simple energy‐balance models, it was suggested a few decades ago that the meridional energy fluxes might follow a thermodynamic Maximum Entropy Production (MEP) principle. In the present study, we assess the MEP hypothesis in the framework of a minimal climate model based solely on a robust radiative scheme and the MEP principle, with no extra assumptions. Specifically, we show that by choosing an adequate radiative exchange formulation, the Net Exchange Formulation, a rigorous derivation of all the physical parameters can be performed. The MEP principle is also extended to surface energy fluxes, in addition to meridional energy fluxes. The climate model presented here is extremely fast, needs very little empirical data and does not rely on ad hoc parameterizations. We investigate its range of validity by comparing its performances for pre‐industrial climate and Last Glacial Maximum climate with corresponding simulations with the IPSL coupled atmosphere‐ocean General Circulation Model IPSL_CM4, finding reasonable agreement. Beyond the practical interest of this result for climate modelling, it supports the idea that, to a certain extent, climate can be characterized by macroscale features with no need to compute the underlying microscale dynamics. Copyright © 2011 Royal Meteorological Society

Meridional mass and energy fluxes in the vicinity of the Arctic border

The air exchange between the Arctic and midlatitude regions is one of the processes forming the climate of the whole Northern Hemisphere. Analysis of the wind regime in the vicinity of the Arctic border (70° N) at the boundary between the 20th and 21st (1997–2004) centuries showed significant changes in the conditions of a meridional air transport between the Arctic and midlatitude regions as compared to the previous years (1960–1990). In this study, the wind fluxes of mass and heat (internal) and kinetic energies are estimated without consideration for turbulent and convective processes. The importance of spatial, seasonal, and interannual variations in wind velocity and air temperature in the formation of these fluxes is analyzed. It is shown that, during the period 1997–2004, an advective transport of energy from the northern latitudes occurred in the lower 6-km tropospheric layer at 70° N latitude over almost a whole year. Only in spring (April) did the wind fluxes bring heat energy from the south. The total amount of both heat and kinetic energies transported from the Arctic region in this way during a year is comparable to the mean amount of these energies contained in the whole atmosphere over the area bounded by 70° N latitude. The current spatial and temporal distributions of wind velocity and meridional mass and energy fluxes, which are presented in this study, may serve as additional information for interpreting data obtained from different on-site measurements in Arctic regions.

Water vapour transport from the tropical Atlantic and summer rainfall in tropical southern Africa

An empirical orthogonal functions analysis of the onshore flow of moisture along the west coast of southern Africa using NCEP-DOE AMIP II Re-analyses suggests two dominant modes of variability that are linked to (a) variations in the circulation linked with the South Atlantic anticyclone (b) the intensity of the flow that penetrates from the tropical Atlantic. The second mode, referred as the Equatorial Westerly mode, contributes the most to moisture input from the Atlantic onto the subcontinent at tropical latitudes. Substantial correlations in austral summer between the Atlantic moisture flux in the tropics and rainfall over the upper lands surrounding the Congo basin suggest the potential role played by this zonal mode of water vapour transport. Composites for austral summer months when this Equatorial Westerly mode had a particularly strong expression, show an enhanced moisture input at tropical latitudes that feeds into the deep convection occurring over the Congo basin. Sustained meridional energy fluxes result in above normal rainfall east and south of the Congo belt. During years of reduced equatorial westerly moisture flux, a deficit of available humidity occurs in the southern tropics. A concomitant eastward shift of deep convection to the southwest Indian ocean and southeastern Africa, leads to below normal rainfall over the uplands surrounding the Congo basin.

An Energy Balance Model Based on Potential Vorticity Homogenization

It has long been suggested that the extratropical eddies originating in baroclinic instability act to neutralize the atmosphere with respect to baroclinic instability. These studies focused on the Charney–Stern condition for stability, and since the implication of this condition was the elimination of meridional temperature gradients at the surface, contrary to observations, there appeared little possibility that the hypothesis was correct. However, Lindzen found that potential vorticity (PV) mixing along isentropic surfaces accompanied by elevated tropopause height and/or reduced jet width could also lead to baroclinic neutralization. Since it is not obvious what implications such a neutral state would have for meridional structure of wind and especially temperature, the authors examine, as a first step, in this paper the implications of an assumed fixed PV gradient in the extratropical troposphere. It is shown that this assumption, combined with an assumption of a moist adiabatic temperature structure in the Tropics, a constraint on surface static stability, and overall radiative equilibrium, suffices to constrain a model earth’s zonal mean climate. Comparison of the model climate with the observed climate, and variation of certain of the model’s assumptions to resolve differences, allow the authors to consider the role of deep convection in the climate of the midlatitudes, to investigate the connection between surface turbulent heat fluxes and meridional energy fluxes carried by baroclinic eddies, and to deduce the role of the stratosphere’s overturning circulation in determining the height of the tropopause.

Far-field acoustic holography onto cylindrical surfaces using pressure measured on semicircles

A simple formula was recently proposed by Williams [J. Acoust. Soc. Am. 99, 2022–2032 (1996)] for imaging pressure and velocity on a vibrating circular cylindrical shell using the far-field pressure measured along a meridional semicircle. The method is discussed and some new results are presented. The procedure is generalized to handle cylindrical surfaces of a noncircular but convex cross section. It is demonstrated that Williams’ formula predicts a supersonic surface intensity, which gives the same meridional energy flux as the exact radiated far-field pressure. A modification of Williams’ formula is suggested, which uses pressure data from several neighboring semicircles, although complete spherical coverage is not required. The modified imaging formula is based upon the first two terms in an asymptotic expansion in the dimensionless wave number. The leading-order term yields the original formula, and the second term results in a boundary layer type of correction in the circumferential direction. Numerical examples compare the exact supersonic acoustic intensity on a cylinder with that from the original and the modified formula. These indicate that the circumferential on-surface resolution is significantly enhanced by combining data from neighboring semicircles, even when the total far-field spherical coverage is small. [Work supported by ONR.]

Far-field acoustic holography onto cylindrical surfaces using pressure measured on semicircles

A simple formula was recently proposed by Williams [J. Acoust. Soc. Am. 99, 2022–2032 (1996)] for imaging pressure and velocity on a vibrating circular cylindrical shell using the far-field pressure measured along a meridional semicircle. The method is examined and some new results are obtained. The procedure is generalized to handle cylindrical surfaces of noncircular but convex cross section. It is demonstrated that Williams’ formula predicts a supersonic surface intensity which gives the same meridional energy flux as the exact radiated far-field pressure. A modification of Williams’ formula is suggested which uses pressure data from several neighboring semicircles, although complete spherical coverage is not required. The modified imaging formula is based upon the first two terms in an asymptotic expansion in the dimensionless wave number. The leading-order term yields the original formula, and the second term results in a boundary layer type of correction in the circumferential direction. Numerical examples are presented which compare the exact supersonic acoustic intensity on a cylinder with that from the original and the modified formula. These indicate that the circumferential on-surface resolution is significantly enhanced by combining data from neighboring semicircles, even when the total far-field spherical coverage is small.

Sensitivity experiments performed with an energy balance atmosphere model coupled to an advection-diffusion ocean model

In this paper a simple climate model is presented which is used to perform some sensitivity experiments. The atmospheric part is represented by a vertically and zonally averaged layer in which the surface air temperature, radiative fluxes at the surface and at the top of the atmosphere, the turbulent fluxes between atmosphere and surface and the snow cover are calculated. This atmospheric layer is coupled to a two-dimensional advection-diffusion ocean model in which the zonal overturning pattern is prescribed. The ocean model evaluates the temperature distribution, the amount of sea-ice and the meridional and vertical heat fluxes. The present-day climate simulated by the model compares reasonably well with observations of the seasonal and latitudinal distribution of temperature, radiation, surface alebdo, sea-ice and snow cover and meridional energy fluxes. Then, the sensitivity of the model-simulated present-day climate to perturbations in the incident solar radiation at the top of the atmosphere is investigated. The temperature response displays large latitudinal and seasonal variations, which is in qualitative agreement with results obtained with other climate models. It is found that the seasonal variation of sea-ice cover (and hence, the effective oceanic heat capacity) is one of the most important elements determining seasonal variations in climate sensitivity. Differences in sensitivity between the seasonal and annual mean version of the model are discussed. Finally, the equilibrium response to perturbations in some selected model variables is presented; these variables include meridional diffusion coefficients, drag coefficient, sea-ice thickness, atmospheric CO2-concentration and cloud optical thickness.

Annual mean meridional energy transport modelled by a general circulation model for present and 2 × CO2 equilibrium climates

The meridional energy flux modelled by the Bureau of Meteorology Research Centre general circulation model is examined. It is divided into atmospheric and oceanic components, and the resolved atmospheric components in turn into mean and eddy circulations. Comparison with observations shows the modelled total planetary meridional energy transport to be low, but shows better agreement for the resolved atmospheric component alone. The overall patterns of the individual circulation and energy components of the model also agree well, although strengths and locations do show some discrepancies. The doubled CO2 climate change is analyzed in terms of the changes in each of the circulation and energy components. It is found that the changes are the relatively small residual of larger, and generally opposing changes in sensible heat and potential energy fluxes. Despite the general decrease in poleward energy flux, the poleward latent heat flux is found to increase. The reduction in poleward transport is found to be dominated by changes in the mean meridional circulation at low southern latitudes, and changes in both mean circulations and eddy fluxes elsewhere.

Recent Oceanic Meridional Flux Estimates and Their Relationship with Temperature Gradients

Recent estimates of oceanic meridional energy flux are compared with previous work and shown to he somewhat smaller and have a different annual cycle. When combined with temperature gradient data they show a down-gradient flux in the Pacific and Indian oceans between the hemispheres and possibly a similar flux at 1 5°N. Elsewhere there is no significant association between these quantities and therefore parameterization of the oceanic flux by the temperature gradient is not appropriate.

Parameterization of meridional energy flux in a one-dimensional climate model

The zonally averaged meridional energy transport is parameterized in terms of the zonally averaged temperature gradient and its radiative equilibrium value. Two climate regimes are identified: radiative equilibrium and isothermal climates. The transport and temperature gradient are intermediate between corresponding quantities of these two climates. The parameterization assumes a linear increase of transport as temperature gradient departs from its radiative equilibrium value. The parameterization is formulated using a one-dimensional climate model. Ice-albedo feedback provides the mechanism for climate changes. The parameterization works well for climates associated with seasonal changes.

The Noninteraction of Waves with the Zonally Averaged Flow on a Spherical Earth and the Interrelationships on Eddy Fluxes of Energy, Heat and Momentum

Abstract For linearized hydrostatic waves on a spherical earth with a zonal mean wind which is a function of latitude and pressure I derive, without further approximations, expressions for the vertical and meridional energy fluxes in terms of the meridional heat flux and the vertical and meridional fluxes of zonal momentum. Using these expressions, I prove that in the absence of critical surfaces, dissipation, thermal heating and nonharmonic time dependence, that the waves and mean flow do not interact: the wave Reynold's stresses are exactly balanced by a mean meridional circulation whose streamfunction is simply the meridional beat flux divided by the static stability. In the presence of dissipation, thermal heating or transience, 1 am able to express the net forcing of the mean blow by the waves as expressions which are explicitly proportional to the coefficients of dissipation and heating and to the imaginary part of the phase speed. My work significantly extends earlier theorems on the noninteraction...