The small ice cap instability in seasonal energy balance models

Results from a two-dimensional energy balance model with a realistic land-ocean distribution show that the small ice cap instability exists in the Southern Hemisphere, but not in the Northern Hemisphere. A series of experiments with a one-dimensional energy balance model with idealized geography are used to study the roles of the seasonal cycle and the land-ocean distribution. The results indicate that the seasonal cycle and land-ocean distribution can influence the strength of the albedo feedback, which is responsible for the small ice cap instability, through two factors: the temperature gradient and the amplitude of the seasonal cycle. The land-ocean distribution in the Southern Hemisphere favors the small ice cap instability, while the land-ocean distribution in the Northern Hemisphere does not. Because of the longitudinal variations of land-ocean distribution in the Northern Hemisphere, the behavior of ice lines in the Northern Hemisphere cannot be simulated and explained by the model with zonally symmetric land-ocean distribution. Model results suggest that the small ice cap instability may be a possible mechanism for the formation of the Antarctic icesheet. The model results cast doubt, however, on the role of the small ice cap instability in Northern Hemisphere glaciations. Offprint requests to: J Huang     

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

Summary 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.With 13 Figures     

A nonlinear stochastic low-order energy balance climate model

The effects of stochastic forcing on a one-dimensional, energy balance climate model are considered. A linear, stochastic model is reviewed in analogy with the Brownian motion problem from classical statistical mechanics. An analogous nonlinear model is studied and shows different behavior from the linear model. The source of the nonlinearity is the dynamical heat transport. The role of nonlinearity in coupling different temporal and spatial scales of the atmosphere is examined. The Fokker-Planck equation from statistical mechanics is used to obtain a time evolution equation for the probability density function for the climate, and the climatic potential function is calculated. Analytical solutions to the steady-state Fokker-Planck equation are obtained, while the time-dependent solution is obtained numerically. The spread of the energy produced by a stochastic forcing element is found to be characterized by movement mainly from smaller to larger scales. Forced and free variations of climate are also explicitly considered.     

Use of an upwelling-diffusion energy balance climate model to simulate and diagnose A/OGCM results

 We demonstrate that a hemispherically averaged upwelling-diffusion energy-balance climate model (UD/EBM) can emulate the surface air temperature change and sea-level rise due to thermal expansion, predicted by the HadCM2 coupled atmosphere-ocean general circulation model, for various scenarios of anthropogenic radiative forcing over 1860–2100. A climate sensitivity of 2.6 °C is assumed, and a representation of the effect of sea-ice retreat on surface air temperature is required. In an extended experiment, with CO₂ concentration held constant at twice the control run value, the HadCM2 effective climate sensitivity is found to increase from about 2.0 °C at the beginning of the integration to 3.85 °C after 900 years. The sea-level rise by this time is almost 1.0 m and the rate of rise fairly steady, implying that the final equilibrium value (the `commitment') is large. The base UD/EBM can fit the 900-year simulation of surface temperature change and thermal expansion provided that the time-dependent climate sensitivity is specified, but the vertical profile of warming in the ocean is not well reproduced. The main discrepancy is the relatively large mid-depth warming in the HadCM2 ocean, that can be emulated by (1) diagnosing depth-dependent diffusivities that increase through time; (2) diagnosing depth-dependent diffusivities for a pure-diffusion (zero upwelling) model; or (3) diagnosing higher depth-dependent diffusivities that are applied to temperature perturbations only. The latter two models can be run to equilibrium, and with a climate sensitivity of 3.85 °C, they give sea-level rise commitments of 1.7 m and 1.3 m, respectively. Received: 27 April 1999 / Accepted: 13 September 2000     

A microscale three-dimensional urban energy balance model for studying surface temperatures

A microscale three-dimensional (3-D) urban energy balance model, Temperatures of Urban Facets in 3-D (TUF-3D), is developed to predict urban surface temperatures for a variety of surface geometries and properties, weather conditions, and solar angles. The surface is composed of plane-parallel facets: roofs, walls, and streets, which are further sub-divided into identical square patches, resulting in a 3-D raster-type model geometry. The model code is structured into radiation, conduction and convection sub-models. The radiation sub-model uses the radiosity approach and accounts for multiple reflections and shading of direct solar radiation. Conduction is solved by finite differencing of the heat conduction equation, and convection is modelled by empirically relating patch heat transfer coefficients to the momentum forcing and the building morphology. The radiation and conduction sub-models are tested individually against measurements, and the complete model is tested against full-scale urban surface temperature and energy balance observations. Modelled surface temperatures perform well at both the facet-average and the sub-facet scales given the precision of the observations and the uncertainties in the model inputs. The model has several potential applications, such as the calculation of radiative loads, and the investigation of effective thermal anisotropy (when combined with a sensor-view model).     

A 1-D atmospheric energy balance model developed for ocean modelling

Summary We present a simple, deterministic energy balance model. The model is designed to represent the atmospheric component of the coupled atmosphere-ocean system. It is a one dimensional, global model with time and space resolutions of one year and 10° of latitude respectively. The model predicts the surface air temperature and estimates the surface freshwater flux diagnostically. The coupling between the atmospheric model and an ocean model is accomplished by heat and freshwater fluxes at their interface. The heat flux is calculated according to the difference in the surface air temperature and ocean surface temperature, while the freshwater flux is estimated from the latent heat transport in the atmosphere by a diagnostic equation. Two parameterizations for the latent heat transport are proposed, which distinguishes the two versions of the model.Before proceeding with interactive runs, we study the behaviour of the model in a decoupled mode. Some experiments with initial conditions altered and external forcings changed ar carried out to investigate the sensitivity and stability of the model. In particular, the influence of the ice-albedo feedback on model solutions is examined. The results of these experiments may be helpful both in understanding the characteristics of the model and in interpreting results when the model is coupled to an OGCM.With 9 Figures     

对二维气候能量平衡模式中辐射和动力学参数化的一些看法

全球性气候及其变化在很大程度上依赖于各种物理过程之间的相互反馈.Budyko和Sellers首先分别提出了南北方向一维气候能量平衡模式来研究极冰-反照率的反馈对气候的影响.由于水汽和云层是决定对流层内短波和红外辐射收支的主要因子,而地面温度又直接影响水汽的含量,故各种辐射-对流方案也已被广泛地应用在垂直方向的一维气候模式中.陈英仪和巢纪平近几年来设计了同时含有南北和垂直方向变化的二维     

Phillips模式的斜压不稳定的非线性饱和问题:能量情形

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model-the case of energy-is studied within the context of Arnold's second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd's; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances φ'i at any time.     

Seasonal oceanic heat transports computed from an atmospheric model

Seasonal estimates of the oceanic poleward heat transport are obtained using a climate model that is a global atmospheric general circulation model on an 8° × 10° grid. The climate model is used to calculate the surface heat flux into each ocean grid point for each day of the year. The rate of ocean heat storage is calculated using climatological surface temperatures, mixed layer depths, and ice amounts. By assuming that the rate of change of heat storage in the deep ocean is spatially constant, the horizontal transports are calculated from the vertical fluxes and the upper ocean storage rates. The oceanic meridional transport for each latitude and for each ocean basin are derived, and results are compared with other calculations of the seasonal transports. In the Northern Hemisphere, comparisons between the simulated seasonal transports indicate that the annual variation is much greater in the Pacific than in the Atlantic.     

A two-dimensional energy balance climate model including radiation and ice caps-albedo feedback

A simplified two-dimensional energy balance climate model including the solar and infrared radiation transports, the turbulent exchanges of heat in vertical and horizontal directions and the ice caps-albedo feedback is developed The solutions show that if the atmosphere is considered as a grey body and the grey coefficient depends upon the distributions of absorption medium and cloudiness, both horizontal and vertical distributions of temperature are identical to the observation.On the other hand, comparing the models that the atmosphere is considered as a grey body with ones that the infrared radiation is parameterized as a linear function of temperature, as was considered by Budyko, Sellers(1969), then the results show that even though both of them can obtain the earth's surface temperature in agreement with the observation, the sensitiv ity of the climate to the changes of solar constant is very different. In the former case,the requirement for the ice edge to move southward from the normal 72°N to 50°N(i.e. where the glacial climate would take place) is that the solar constant should decrease by 13% to 16%. However, in the latter case, the climate is highly sensitive to the changes of solar radiation. In this case, the requirement of solar radiation occurring in the glacial climate should decrease by 2% to 6%. According to the investigations mentioned above we must be careful when the parameterizations of the radiation and other processes are conducted in a climate model, otherwise the reliability of the results is suspicious.     

Conceptual understanding of climate change with a globally resolved energy balance model

The future climate change projections are essentially based on coupled general circulation model (CGCM) simulations, which give a distinct global warming pattern with arctic winter amplification, an equilibrium land-sea warming contrast and an inter-hemispheric warming gradient. While these simulations are the most important tool of the Intergovernmental Panel on Climate Change (IPCC) predictions, the conceptual understanding of these predicted structures of climate change and the causes of their uncertainties is very difficult to reach if only based on these highly complex CGCM simulations. In the study presented here we will introduce a very simple, globally resolved energy balance (GREB) model, which is capable of simulating the main characteristics of global warming. The model shall give a bridge between the strongly simplified energy balance models and the fully coupled 4-dimensional complex CGCMs. It provides a fast tool for the conceptual understanding and development of hypotheses for climate change studies, which shall build a basis or starting point for more detailed studies of observations and CGCM simulations. It is based on the surface energy balance by very simple representations of solar and thermal radiation, the atmospheric hydrological cycle, sensible turbulent heat flux, transport by the mean atmospheric circulation and heat exchange with the deeper ocean. Despite some limitations in the representations of the basic processes, the models climate sensitivity and the spatial structure of the warming pattern are within the uncertainties of the IPCC models simulations. It is capable of simulating aspects of the arctic winter amplification, the equilibrium land-sea warming contrast and the inter-hemispheric warming gradient with good agreement to the IPCC models in amplitude and structure. The results give some insight into the understanding of the land-sea contrast and the polar amplification. The GREB model suggests that the regional inhomogeneous distribution of atmospheric water vapor and the non-linear sensitivity of the downward thermal radiation to changes in the atmospheric water vapor concentration partly cause the land-sea contrast and may also contribute to the polar amplification. The combination of these characteristics causes, in general, dry and cold regions to warm more than other regions.     

Response of a stochastically-perturbed 1-D surface energy balance model to increased temperature

Summary The response of the climatic system to changes in its radiative forcing has been the subject of much study. Climate models of various complexity have been used to demonstrate that a small increase in the solar constant, or doubling of the atmospheric CO₂, would lead to a warmer surface. Very little scientific attention, however, has been given to the effect such a change in radiative balance might have on climatic variability. That is, would an earth warmed in this way be more temperate or more variable? To move one step closer to answering this question, we employed a simple one-dimensional surface energy balance climate model and forced it with random Gaussian white noise to simulate interannual variability. We integrated the model using 0, 2, and 4% increases in the solar constant. The results of these numerical experiments indicate that, under a warmer surface radiative balance, interannual variability of the surface temperature is reduced.     

The energy balance in the Ramdas layer

On calm clear nights, air at a height of a few decimetres above bare soil can be cooler than the surface by several degrees in what we shall call the Ramdas layer (Ramdas and Atmanathan, 1932). The authors have recently offered a logical explanation for such a lifted temperature minimum, together with a detailed numerical model. In this paper, we provide physical insight into the phenomenon by a detailed discussion of the energy budget in four typical cases, including one with a lifted minimum. It is shown that the net cooling rate near ground is the small difference between two dominant terms, representing respectively radiative upflux from the ground and from the air layers just above ground. The delicate energy balance that leads to the lifted minimum is upset by turbulent transport, by surface emissivity approaching unity, or by high ground cooling rates. The rapid variation of the flux emissivity of humid air is shown to dominate radiative transport near the ground.     

A study of the seasonal migration of ITCZ and the quasi-periodic oscillations in a simple monsoon system using an energy balance model

Summary A zonally averaged global energy balance model with feedback mechanisms was constructed to simulate (i) the poleward limits of ITCZ over the continent and over the ocean and (ii) a simple monsoon system as a result of differential heating between the continent and the ocean. Three numerical experiments were performed with lower boundary as (1) global continent, (2) global ocean and (3) continent-ocean, with freezing latitudes near the poles. Over the continent, midlatitude deserts were found and the ITCZ migrates 25° north and south with seasons. Over a global swamp ocean results do not show migration of ITCZ with time but once the ocean currents are introduced the ITCZ migrates 5° north and south with seasons. It was found that the seasonal migration of ITCZ strongly depends on the meridional distribution of the surface temperature. It was also found that continent influences the location of the oceanic ITCZ. In the tropics northward progression of quasi-periodic oscillations called events are found during the pre- and post-monsoon periods with a period of 8 to 15 days. This result is consistent with the observed quasi-periodic oscillations in the tropical region. Northward propagation of the surface temperature perturbation appears to cause changes in the sensible heat flux which in turn causes perturbations in vertical velocity and latent heat flux fields.List of Symbols vertical average - ₀ zonal average - vertical mean of the zonal average - _0s zonal average at the surface - _0a zonal average at 500 mb level - latitude We now define the various symbols used in the model rate of atmospheric heating due to convective cloud formation (K/sec) - dp/dt (N/m²/sec) - density - potential temperature (K) - rate of rotation of the earth (rad/sec) - empirical constant - humidity mixing ratio - ^* saturated humidity mixing ratio - opacity of the atmosphere - ₁,₂ factors for downward and upward effective black body long wave radiation from the atmosphere - Stefan-Boltzmann constant - emissivity of the surface - _D subsurface temperature (K) - a specific volume - _0xs ,_0ys eastward and northward components of surface frictional stress - ^* vertical velocity at the top of the boundary layer (N/m²/sec) - P Thickness of the boundary layer (mb) - nondimensional function of pressure - P pressure - P _a pressure of the model atmosphere (N/m²) - P _s pressure at the surface (N/m²) - t time (sec) - U eastward wind speed (m/sec) - V northward wind speed (m/sec) - surface water availability - T absolute temperature (K) - heat addition due to water phase changes - g acceleration due to gravity (m²/sec) - a radius of the earth (m) - R gas constant for dry air (J/Kg/K) - C _p specific heat of air at constant pressure (J/Kg/K) - k R/C _p - L latent heat of condensation (J/Kg) - f coriolis parameter (rad/sec) - H _s H _0s ⁽¹⁾ +H _0s ⁽²⁾ +H _0s ⁽³⁾ +H _0s ⁽⁴⁾ +H _0s ⁽⁵⁾ (J/m²/Sec)=sum of the rates of vertical heat fluxes per unit surface area, directed toward the surface - H _a H _0a ⁽¹⁾ +H _0a ⁽²⁾ +H _0a ⁽³⁾ +H _0a ⁽⁴⁾ (J/m²/Sec)=sum of the rates of heat additions to the atmospheric column per unit horizontal area by all processes - H _0s ⁽¹⁾ ,H _0a ⁽¹⁾ heat flux due to short wave radiation - H _0s ⁽²⁾ ,H _0a ⁽²⁾ heat flux due to long wave radiation - H _0s ⁽³⁾ ,H _0a ⁽³⁾ heat flux due to small scale convection - H _0s ⁽⁴⁾ heat flux due to evaporation - H _0a ⁽⁴⁾ heat flux due to condensation - H _0s ⁽⁵⁾ heat flux due to subsurface conduction and convection - e ^* saturation vapor pressure - R solar constant (W/m²) - r _a albedo of the atmosphere - r _s albedo of the surface - b ₂ empirical constant (J/m²/sec) - c ₂ empirical constant (J/m²/sec) - e ₂ nondimensional empirical constant - f ₂ empirical constant (J/m₂/sec) - factor proportional to the conductive capacity of the surface medium - a _s constant used in Sellers model - b _s positive constant of proportionality used in the Sellers model (kg m²/J/sec²) - K _HT coefficient for eddy diffusivity of heat (m²/sec) - K _HE exchange coefficient for water vapor (m²/sec) - h depth of the water column (m) - z height (m) - V _0ws meridional component of surface current (m/sec) - n cloud amount - G _0,n long wave radiation form the atmosphere for cloud amount n (W/m²) - B ₀ long wave radiation from the surface (W/m²) - S _0,n short wave radiation from the atmosphere for cloud amount n (W/m²) - A _n albedo factor for a cloud amount n - R _f1 large scale rainfall (mm/day) - R _f2 small scale rainfall (mm/day) With 22 Figures     

Seasonal temperature variations and energy demand

This paper presents an empirical study of the relationship between residential energy demand and temperature. Unlike previous studies in this field, the data sample has a global coverage and special emphasis is given to the heterogeneous response of different regions and to the contrasting effects on energy demand for cooling and heating purposes. To account for this we distinguish between different regions, seasons, and energy sources. Short- and long-run temperature demand elasticities are estimated. These features make the model results especially valuable in the analysis of climate change impacts as they provide an empirical basis for the study of the impact of climate change on energy demand. To illustrate the potential of the results as a basis for the study of climate change impacts, the estimates are used in a simple exercise that projects changes in energy demand due to temperatures increase in 2085.     

Some maps of isanomalies in energy balance climatology

Summary A series of world maps of isanomalies of annual and seasonal global radiation, net radiation, latent heat flux, sensible heat flux, maps of residuals from regression, radiation efficiency, and the Bowen Ratio have been constructed on the data base ofBudyko's Atlas of the Heat Balance of the Earth, 1963. Among the major features observed was the dissimilarity in patterns of isanomalies for the eastern and western sectors of the world's semi-permanent subtropical highs and the great difference between oceanic and continental surfaces.

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Zusammenfassung Auf Grund der Werte vonBudykos Atlas der Wärmebilanz der Erde (1963) wurden eine Anzahl Weltkarten der Isanomalien der jährlichen und der jahreszeitlichen Werte für die Globalstrahlung, die totale Strahlungsbilanz, den latenten und den fühlbaren Wärmefluß sowie Karten für die Abweichungen von der Regressionsgeraden, für den Strahlungsgenuß und für den Bowen-Quotienten konstruiert. Als Hauptergebnisse sind die Unähnlichkeit im Verlauf der Isanomalien zwischen dem östlichen und dem westlichen Sektor der semipermanenten Hochdruckgebiete der Subtropen sowie die großen Unterschiede zwischen ozeanischen und kontinentalen Gebieten zu nennen.

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Résumé En partant des valeurs publiées parBudyko dans son Atlas du bilan thermique de la Terre (1963), on a établi un certain nombre de cartes du globe. Sur celles-ci, on a reporté les isanomalies des valeurs annuelles et saisonières de la radiation globale, du bilan total radiatif, du flux des chaleurs latente et sensible ainsi que l'écart à la droite de régression pour le rayonnement reçu et pour le rapport de Bowen. Le résultat principal en est l'appararition de dissemblances dans le cours des isanomalies entre les secteurs oriental et occidental des anticyclones semipermanents des zones subtropicales ainsi que de différences importantes entre les régions océaniques et continentales.

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With 28 Figures     

A high-resolution analysis method of instability energy

This paper describes a geopotential thickness difference method for computing instability energy E. EP1P2 =g0 ( ΔHsP1P2-ΔHP1P2 , where ΔHP1P2 is the geopotential thickness of P1-P2 level; ΔHsP1P2 is called adia-batic geopotential thickness, based on which a computational method for high resolution of instability energy is proposed. E(x,y)≈g0(A(x,y) - B(x,y)), where A is interpolating polynomial of ΔHSP2P2 and it is afunction ofθe, of surface observing stations (x, y); B(x,y) is the thickness over corresponding stations (x, y) obtained using surface fitting method. Therefore, data of METAR can be used by computer to produce hourly horizontal distribution chart of E of surface observing station density. With the result that the temporal and spatial resolution of stability analysis has been improved. Practical use has shown that this method is an effective tool for very short range forecast of severe convective storms.     

A new one-dimensional simple energy balance and carbon cycle coupled model for global warming simulation

Global warming and accompanying climate change may be caused by an increase in atmospheric greenhouse gasses generated by anthropogenic activities. In order to supply such a mechanism of global warming with a quantitative underpinning, we need to understand the multifaceted roles of the Earth's energy balance and material cycles. In this study, we propose a new one-dimensional simple Earth system model. The model consists of carbon and energy balance submodels with a north–south zonal structure. The two submodels are coupled by interactive feedback processes such as CO₂ fertilization of net primary production (NPP) and temperature dependencies of NPP, soil respiration, and ocean surface chemistry. The most important characteristics of the model are not only that the model requires a relatively short calculation time for carbon and energy simulation compared with a General Circulation Model (GCM) and an Earth system Model of Intermediate Complexity (EMIC), but also that the model can simulate average latitudinal variations. In order to analyze the response of the Earth system due to increasing greenhouse gasses, several simulations were conducted in one dimension from the years 1750 to 2000. Evaluating terrestrial and oceanic carbon uptake output of the model in the meridional direction through comparison with observations and satellite data, we analyzed the time variation patterns of air temperature in low- and middle-latitude belts. The model successfully reproduced the temporal variation in each latitude belt and the latitudinal distribution pattern of carbon uptake. Therefore, this model could more accurately demonstrate a difference in the latitudinal response of air temperature than existing models. As a result of the model evaluations, we concluded that this new one-dimensional simple Earth system model is a good tool for conducting global warming simulations. From future projections using various emission scenarios, we showed that the spatial distribution of terrestrial carbon uptake may vary greatly, not only among models used for climate change simulations, but also amongst emission scenarios.     

二维能量平衡模式中大气温度对二氧化碳增温效应的响应

利用一个考虑了辐射能传输的二维能量平衡气候模式,解析地分析了二氧化碳浓度改变后冰界纬度的变化,得到了冰界纬度随CO2浓度变化的关系以及全球平均温度的变化曲线.结果表明,当CO2浓度由工业革命前的280×10-6增加到700×10-6时,冰界仅后退(北半球向北)几个纬度;当CO2的浓度继续增加时,冰界纬度会加速向极地退缩,直至出现全球无极冰覆盖的现象.同样地,当CO2浓度由280×10-6增加到700×10-6时,全球地表平均温度虽然在增加,但增加的速率很小,并且增加的速率在减小,而当大于700×10-6之后,温度增加的速率会快速增大,温度将加速上升.对不同反照率进行敏感性试验,发现当反照率从0.1到0.32时,结果并没有显著地改变,即结果对反照率的变化并不敏感.这一计算结果表明,在目前的状态下,由CO2引起的增温作用似乎处于变化很小的准饱和状态,即目前气候不会因为CO2浓度的增加而迅速变暖.较为实际的情形可能是大气温度在缓慢增加到一定程度后才会迅速升高.这并不意味着可以忽视CO2的增温效应,因为根据计算结果,这个临界值大概在700×10-6左右,当CO2浓度增加到超过临界值之后,气温会剧烈上升,气候将会处在一个非常温暖的阶段.