A Survey of Statistical-Dynamical Models of the Terrestrial Climate

Publisher Summary This chapter discusses statistical dynamic models and explains how these models stem from the most general statements of the hydro thermodynamic laws and fit into a hierarchy of increasing complexity and simulation capability. The chapter discusses the physical foundation and reviews the development of an important group of models known as statistical-dynamical models. It also presents a review of the fundamental equations (namely, continuity equations, the equations of motion, the thermodynamical energy equation, and constitutive equations) that are the basis of both the explicit- and statistical-dynamical climate models. Climatic averaging is also discussed. The chapter then discusses the vertically integrated, thermodynamic models and describes its foundations and applications. It illustrates equations for the axially symmetric and asymmetric mean states, symmetric (zonal) models, asymmetric (nonzonal) models, and the complete time average state. Finally, the chapter explains modeling the evolution of climate, its general concepts and studies of forced climatic change, studies of free climatic change, and climatic prediction.

[1]  R. Reck Aerosols and Polar Temperature Changes , 1975, Science.

[2]  C. Su,et al.  Stability of the Budyko Climate Model , 1976 .

[3]  J. Wells Coral Growth and Geochronometry , 1963, Nature.

[4]  R. F. Strickler,et al.  Thermal Equilibrium of the Atmosphere with a Convective Adjustment , 1964 .

[5]  WATER VAPOR BALANCE OF THE ATMOSPHERE FROM FIVE YEARS OF HEMISPHERIC DATA , 1970 .

[6]  J. Namias Longevity of a Coupled Air-Sea-Continent System , 1974 .

[7]  P. Webster Response of the Tropical Atmosphere to Local, Steady Forcing , 1972 .

[8]  R. Dickinson,et al.  ANALYTIC MODEL FOR ZONAL WINDS IN THE TROPICS , 1971 .

[9]  J. Hansen,et al.  A parameterization for the absorption of solar radiation in the earth's atmosphere , 1974 .

[10]  Edward N. Lorenz,et al.  Climatic Change as a Mathematical Problem , 1970 .

[11]  Robert D. Cess,et al.  Radiative transfer due to atmospheric water vapor: Global considerations of the earth's energy balance , 1974 .

[12]  J. Adem EXPERIMENTS AIMING AT MONTHLY AND SEASONAL NUMERICAL WEATHER PREDICTION1 , 1965 .

[13]  A. L. BERGER,et al.  Support for the astronomical theory of climatic change , 1977, Nature.

[14]  E. Barrett Depletion of short-wave irradiance at the ground by particles suspended in the atmosphere , 1971 .

[15]  A. Pike Response of a Tropical Atmosphere and Ocean Model to Seasonally Variable Forcing1,,2 , 1972 .

[16]  T. H. Haar,et al.  On the Observed Annual Cycle in the Ocean-Atmosphere Heat Balance Over the Northern Hemisphere , 1976 .

[17]  Roger G. Barry,et al.  Simulation of the Atmospheric Circulation Using the NCAR Global Circulation Model with Ice Age Boundary Conditions , 1974 .

[18]  Robert J. Charlson,et al.  Climate: The Influence of Aerosols , 1969 .

[19]  J. Pollack,et al.  Estimates of the Climatic Impact of Aerosols Produced by Space Shuttles, SST's, and other High Flying Aircraft , 1976 .

[20]  R. Newell Changes in the Poleward Energy Flux by the Atmosphere and Ocean as a Possible Cause for Ice Ages , 1974, Quaternary Research.

[21]  V. Ramanathan Radiative Transfer Within the Earth's Troposphere and Stratosphere: A Simplified Radiative-Convective Model , 1976 .

[22]  M. J. Newman,et al.  Climatic effects during passage of the Solar System through interstellar clouds , 1976, Nature.

[23]  B. Saltzman Global mass and energy requirements for glacial oscillations and their implications for mean ocean temperature oscillations , 1977 .

[24]  G. E. Birchfield A study of the stability of a model continental ice sheet subject to periodic variations in heat input , 1977 .

[25]  A. Vernekar An Equilibrium Solution for the Axially Symmetric Component of the , 1971 .

[26]  J. Egger On the theory of the steady perturbations in the troposphere , 1976 .

[27]  D. Wuebbles,et al.  Temperature feedback in a stratospheric model , 1977 .

[28]  R. Cess Global climate change: an investigation of atmospheric feedback mechanisms , 1975 .

[29]  William D. Sellers,et al.  A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System. , 1969 .

[30]  G. Paltridge Global Cloud Cover and Earth Surface Temperature , 1974 .

[31]  B. Farrell,et al.  Some Realistic Modifications of Simple Climate Models , 1977 .

[32]  K. Hasselmann,et al.  Stochastic climate models , Part I 1 Application to sea-surface temperature anomalies and thermocline variability , 2010 .

[33]  M. A. Atwater Planetary Albedo Changes Due to Aerosols , 1970, Science.

[34]  P. Lemke Stochastic climate models, part 3. Application to zonally averaged energy models , 1977 .

[35]  A. Berger Obliquity and precession for the last 5000000 years , 1976 .

[36]  F. Luther,et al.  Climate studies using a zonal atmospheric model , 1974 .

[37]  D. R. Davies,et al.  On the problem of formulating a realistic model of the general atmospheric circulation , 1962 .

[38]  P. Drazin,et al.  On the Branching Structure of Diffusive Climatological Models , 1977 .

[39]  G. Kukla Missing link between Milankovitch and climate , 1975, Nature.

[40]  B. Saltzman,et al.  On a steady state theory of global monsoons , 1969 .

[41]  W. Gates The Numerical Simulation of Ice-Age Climate with a Global General Circulation Model. , 1976 .

[42]  Max J. Suarez,et al.  Simple albedo feedback models of the icecaps , 1974 .

[43]  A. Ingersoll The Runaway Greenhouse: A History of Water on Venus , 1969 .

[44]  W. D. Sellers A New Global Climatic Model. , 1973 .

[45]  A. Vernekar,et al.  A Statistical-Dynamical Model for Stationary Perturbations in the Atmosphere , 1978 .

[46]  A. Defant Die Zirkulation der Atmosphäre in den Gemässigten Breiten der Erde , 1921 .

[47]  J. R. Bray Volcanic triggering of glaciation , 1976, Nature.

[48]  W. D. Sellers The Effect of Changes in the Earth's Obliquity on the Distribution of Mean Annual Sea-Level Temperatures , 1970 .

[49]  A. Faegre An Intransitive Model of the Earth-Atmosphere-Ocean System , 1972 .

[50]  F. M. Snell,et al.  An Annual Zonally Averaged Hemispherical Climatic Model with Diffuse Cloudiness Feedback , 1976 .

[51]  J. Egger On the Linear Theory of the Atmospheric Response to Sea Surface Temperature Anomalies , 1977 .

[52]  Julius Chang,et al.  General circulation models of the atmosphere , 1977 .

[53]  J. Smagorinsky,et al.  Some aspects of the general circulation , 1964 .

[54]  Stephen H. Schneider,et al.  Cloudiness as a Global Climatic Feedback Mechanism: The Effects on the Radiation Balance and Surface Temperature of Variations in Cloudiness , 1972 .

[55]  Michael Ghil,et al.  Climate stability for a Sellers-type model , 1976 .

[56]  M. I. Budyko On present-day climatic changes , 1977 .

[57]  S. Schneider,et al.  Atmospheric Carbon Dioxide and Aerosols: Effects of Large Increases on Global Climate , 1971, Science.

[58]  H. L. Penman Natural evaporation from open water, bare soil and grass , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[59]  J. Bates Dynamics of stationary ultra‐long waves in middle latitudes , 1977 .

[60]  P. Stone The Meridional Variation of the Eddy Heat Fluxes by Baroclinic Waves and Their Parameterization , 1974 .

[61]  Lawrence N. Lahiff A Low-Latitude Atmosphere-Ocean Climate Model , 1975 .

[62]  T. Sasamori A Statistical Model for Stationary Atmospheric Cloudiness, Liquid Water Content, and Rate of Precipitation , 1975 .

[63]  B. Hunt Zonally symmetric global general circulation models with and without the hydrologic cycle , 1973 .

[64]  P. Webster,et al.  A Simple Ocean-Atmosphere Climate Model: Basic Model and a Simple Experiment , 1977 .

[65]  T. Wigley,et al.  Spectral analysis and the astronomical theory of climatic change , 1976, Nature.

[66]  F. M. Snell,et al.  A Diffuse Thin Cloud Atmospheric Structure as a Feedback Mechanism in Global Climatic Modeling. , 1974 .

[67]  J. Coakley Feedbacks in Vertical-Column Energy Balance Models , 1977 .

[68]  J. Adem Numerical-thermodynamical prediction of mean monthly ocean temperatures , 1975 .

[69]  P. Webster Temporal Variation of Low-Latitude Zonal Circulations , 1973 .

[70]  R. Reck Influence of surface albedo on the change in the atmospheric radiation balance due to aerosols , 1974 .

[71]  S. Schneider,et al.  A Comment on “Climate: The Influence of Aerosols” , 1971 .

[72]  G. S. Golitsyn,et al.  A similarity approach to the general circulation of planetary atmospheres , 1970 .

[73]  K. Taylor The Influence of Subsurface Energy Storage on Seasonal Temperature Variations , 1976 .

[74]  M. Suárez,et al.  Modelling climatic response to orbital parameter variations , 1976, Nature.

[75]  J. Coakley,et al.  Relative Influence of Visible and Infrared Optical Properties of a Stratospheric Aerosol Layer on the Global Climate. , 1976 .

[76]  A. Wiin-nielsen A theoretical study of the annual variation of atmospheric energy , 1970 .

[77]  H. Kuo,et al.  FORCED AND FREE MERIDIONAL CIRCULATIONS IN THE ATMOSPHERE , 1956 .

[78]  G. W. Paltridge,et al.  Global dynamics and climate - a system of minimum entropy exchange , 1975 .

[79]  B. Saltzman Surface Boundary Effects on the General Circulation and Macroclimate: A Review of the Theory of the Quasi-Stationary Perturbations in the Atmosphere , 1968 .

[80]  P. Stone The effect of large-scale eddies on climatic change. , 1973 .

[81]  R. Reck Stratospheric Ozone Effects on Temperature , 1976, Science.

[82]  W. Donn,et al.  A Theory of Ice Ages. , 1956, Science.

[83]  B. Saltzman On the theory of the mean temperature of the Earth's surface , 1967 .

[84]  J. Adem On the theory of the general circulation of the atmosphere , 1962 .

[85]  E. Lorenz The problem of deducing the climate from the governing equations , 1964 .

[86]  C. Frankignoul On the Noise Level of Climate Models , 1977 .

[87]  D. R. Davies,et al.  The effect of changes in solar radiation on climate , 1974 .

[88]  J. Frederiksen NONLINEAR ALBEDO-TEMPERATURE COUPLING IN CLIMATE MODELS. , 1976 .

[89]  Peter H. Stone,et al.  A Simplified Radiative-Dynamical Model for the Static Stability of Rotating Atmospheres , 1972 .

[90]  E. T. Eady,et al.  Long Waves and Cyclone Waves , 1949 .

[91]  V. Ramanathan,et al.  A Radiative-Convective Model Study of the CO2 Climate Problem , 1977 .

[92]  K. Hasselmann Stochastic climate models Part I. Theory , 1976 .

[93]  Sensitivity of the Diurnal Surface Temperature Range to Changes in Physical Parameters , 1977 .

[94]  R. Emden Über Strahlungsgleichgewicht und atmosphärische Strahlung : ein Beitrag zur Theorie der oberen Inversion , 1913 .

[95]  A. Pike INTERTROPICAL CONVERGENCE ZONE STUDIED WITH AN INTERACTING ATMOSPHERE AND OCEAN MODEL1 , 1971 .

[96]  E. Schneider Axially symmetric steady-state models of the basic state for instability and climate studies , 1977 .

[97]  G. Maykut,et al.  Some results from a time‐dependent thermodynamic model of sea ice , 1971 .

[98]  P. Webster Remote Forcing of the Time-Independent Tropical Atmosphere , 1973 .

[99]  F. M. Snell,et al.  An Annual Zonally Averaged Global Climatic Model with Diffuse Cloudiness Feedback , 1977 .

[100]  M. Budyko The future climate , 1972 .

[101]  Harshvardhan R. D. Cess Stratospheric aerosols: Effect upon atmospheric temperature and global climate , 1976 .

[102]  J. Egger The Linear Response of a Hemispheric Two–Level Primitive Equation Model to Forcing by Topography , 1976 .

[103]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[104]  John F Nye,et al.  The response of glaciers and ice-sheets to seasonal and climatic changes , 1960, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[105]  Johannes Weertman,et al.  Milankovitch solar radiation variations and ice age ice sheet sizes , 1976, Nature.

[106]  S. Schneider,et al.  Numerical experiments in climate stability. , 1973 .

[107]  A. Berger Power and limitation of an energy-balance climate model as applied to the astronomical theory of palaeoclimates , 1977 .

[108]  H. Kuo THREE-DIMENSIONAL DISTURBANCES IN A BAROCLINIC ZONAL CURRENT , 1952 .

[109]  A. J. Meadows,et al.  Long term variations in the albedo and surface temperature of the Earth , 1975, Nature.

[110]  B. Saltzman,et al.  Note on the effect of earth orbital radiation variations on climate , 1971 .

[111]  R. A. Bryson,et al.  A Non-Equilibrium Model of Hemispheric Mean Surface Temperature , 1976 .

[112]  W. Donn,et al.  Milankovitch Radiation Variations: A Quantitative Evaluation , 1968, Science.

[113]  A. T. Wilson Origin of Ice Ages: An Ice Shelf Theory for Pleistocene Glaciation , 1964, Nature.

[114]  Gilbert N. Plass,et al.  The Carbon Dioxide Theory of Climatic Change , 1956 .

[115]  Andrew F. Bunker,et al.  Computations of Surface Energy Flux and Annual Air–Sea Interaction Cycles of the North Atlantic Ocean , 1976 .

[116]  G. Plass The influence of the 15μ carbon‐dioxide band on the atmospheric infra‐red cooling rate , 1956 .

[117]  J. Adem ON THE PHYSICAL BASIS FOR THE NUMERICAL PREDICTION OF MONTHLY AND SEASONAL TEMPERATURES IN THE TROPOSPHERE-OCEAN-CONTINENT SYSTEM , 1964 .

[118]  Y. Kurihara A Statistical-Dynamical Model of the General Circulation of the Atmosphere , 1970 .

[119]  W. D. Sellers A Two Dimensional Global Climatic Model , 1976 .

[120]  S. Schneider,et al.  Energy balance climate modeling: Comparison of radiative and dynamic feedback mechanisms , 1976 .

[121]  R. Reck,et al.  Aerosols and Polar Temperature , 1975, Science.

[122]  F. Defant Das mittlere meridionale Temperaturprofil in der Troposphäre als Effekt von vertikalen und horizontalen Austauschvorgängen und Kondensationswärme , 1950 .

[123]  G. North Theory of Energy-Balance Climate Models. , 1975 .

[124]  J. Sela,et al.  ON THE TRANSPORT OF QUASI-GEOSTROPHIC POTENTIAL VORTICITY1 , 1971 .

[125]  S. Manabe,et al.  The Effects of Mountains on the General Circulation of the Atmosphere as Identified by Numerical Experiments , 1974 .

[126]  W. Donn,et al.  Model of climate evolution based on continental drift and polar wandering , 1977 .

[127]  J. S. A. Green,et al.  THE WEATHER DURING JULY 1976: SOME DYNAMICAL CONSIDERATIONS OF THE DROUGHT , 1977 .

[128]  B. Saltzman Perturbation equations for the time-average state of the atmosphere including the effects of transient disturbances , 1961 .

[129]  J. G. Charney,et al.  THE DYNAMICS OF LONG WAVES IN A BAROCLINIC WESTERLY CURRENT , 1947 .

[130]  J. Adem On the prediction of mean monthly ocean temperatures , 1970 .

[131]  M. Budyko The effect of solar radiation variations on the climate of the Earth , 1969 .

[132]  S. Schneider,et al.  Volcanic Dust, Sunspots, and Temperature Trends , 1975, Science.

[133]  J. Green,et al.  Transfer properties of the large‐scale eddies and the general circulation of the atmosphere , 1970 .

[134]  W. Dabberdt A Selective Climatology of Plateau Station, Antarctica , 1970 .

[135]  B. Saltzman A Generalized Solution for the Large-Scale, Time-Average Perturbations in the Atmosphere , 1963 .

[136]  PRELIMINARY COMPUTATIONS ON THE MAINTENANCE AND PREDICTION OF SEASONAL TEMPERATURES IN THE TROPOSPHERE1 , 1963 .

[137]  J. Weertman,et al.  Rate of Growth or Shrinkage of Nonequilibrium Ice Sheets , 1964, Journal of Glaciology.

[138]  J. D. Hays,et al.  Variations in the Earth ' s Orbit : Pacemaker of the Ice Ages Author ( s ) : , 2022 .

[139]  A Theory of the Consolidation of Snow , 1966 .

[140]  G. Maykut,et al.  Numerical Prediction of the Thermodynamic Response of Arctic Sea Ice to Environmental Changes , 1969 .

[141]  Masayuki Tanaka,et al.  Increase of Global Albedo Due to Air Pollution , 1972 .

[142]  R. Cess,et al.  Energy Balance Climate Models: A Reappraisal of Ice-Albedo Feedback , 1977 .

[143]  Bo R. Döös The influence of exchange of sensible heat with the earth's surface on the planetary flow , 1962 .

[144]  B. Saltzman,et al.  A Solution for the Northern Hemisphere Climatic Zonation During a Glacial Maximum , 1975, Quaternary Research.

[145]  S. Fritz THE HEATING DISTRIBUTION IN THE ATMOSPHERE AND CLIMATIC CHANGE , 1960 .

[146]  S. Schneider,et al.  On the Carbon Dioxide-Climate Confusion. , 1975 .

[147]  Julian Adem,et al.  INCORPORATION OF ADVECTION OF HEAT BY MEAN WINDS AND BY OCEAN CURRENTS IN A THERMODYNAMIC MODEL FOR LONG-RANGE WEATHER PREDICTION , 1970 .

[148]  Syukuro Manabe,et al.  On the Radiative Equilibrium and Heat Balance of the Atmosphere , 1961 .

[149]  Isao Kubota Seasonal Variation of Energy Sources in the Earth Surface Layer and in the Atmosphere over the Northern Hemisphere , 1970 .

[150]  A. Vernekar ON MEAN MERIDIONAL CIRCULATIONS IN THE ATMOSPHERE1 , 1967 .

[151]  J. Sela,et al.  SIMULATION OF THE ATMOSPHERIC ANNUAL ENERGY CYCLE1 , 1971 .

[152]  E. Opik Climatic change in cosmic perspective , 1965 .

[153]  Syukuro Manabe,et al.  Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity , 1967 .

[154]  A. Vernekar Long-Period Global Variations of Incoming Solar Radiation , 1972 .

[155]  B. Saltzman On the theory of the axially-symmetric, time-average, state of the atmosphere , 1964 .

[156]  R. Lindzen Wave-CISK in the Tropics , 1974 .

[157]  D. R. Davies,et al.  A mean motion model of the general circulation , 1965 .

[158]  Barry Saltzman,et al.  Global equilibrium solutions for the zonally averaged macroclimate , 1972 .

[159]  S. Schneider,et al.  Parameterization of Fractional Cloud Amounts in Climatic Models: The Importance of Modeling Multiple Reflections , 1976 .

[160]  A Calculation of Normal Temperature at the Earth's Surface , 1975 .

[161]  A. Defant Die Zirkulation Der AtmosphÄRe in Den GemÄSsigten Breiten Der Erde: Grundzüge Einer Theorie Der Klimaschwankungen , 1921 .

[162]  V. Ramanathan,et al.  Sensitivity of surface temperature and atmospheric temperature to perturbations in the stratospheric concentration of ozone and nitrogen dioxide , 1976 .

[163]  E. Kessler On the distribution and continuity of water substance in atmospheric circulations , 1969 .

[164]  B. Saltzman Empirical forcing functions for the large-scale mean disturbances in the atmosphere , 1962 .

[165]  E. Lorenz Maximum Simplification of the Dynamic Equations , 1960 .

[166]  B. Saltzman,et al.  A PARAMETERIZATION OF THE LARGE-SCALE TRANSIENT EDDY FLUX OF RELATIVE ANGULAR MOMENTUM , 1968 .

[167]  P. Chylek,et al.  Analytical Analysis of a Budyko-Type Climate Model , 1975 .

[168]  J. M. Mitchell,et al.  The Effect of Atmospheric Aerosols on Climate with Special Reference to Temperature near the Earth's Surface. , 1971 .

[169]  F. Möller On the influence of changes in the CO2 concentration in air on the radiation balance of the Earth's surface and on the climate , 1963 .

[170]  Isao Kubota Calculation of Seasonal Variation in the Lower Tropospheric Temperature with Heat Budget Equations , 1972 .

[171]  R. Bryson “All Other Factors Being Constant…”: A Reconciliation of Several Theories of Climatic Change , 1968 .

[172]  G. Ohring,et al.  Some Experiments with a Zonally Averaged Climate Model , 1978 .

[173]  B. Saltzman Steady state solutions for axially-symmetric climatic variables , 1968 .

[174]  Wei‐Chyung Wang,et al.  The radiative effect of aerosols in the earth's atmosphere , 1974 .

[175]  W. Donn,et al.  A Thermodynamic Study of Arctic Paleoclimatology , 1971, Quaternary Research.

[176]  Robert D. Cess,et al.  Climate Change: An Appraisal of Atmospheric Feedback Mechanisms Employing Zonal Climatology. , 1976 .

[177]  C. Leovy Simple Models of Thermally Driven Mesopheric Circulation , 1964 .

[178]  G. North Analytical Solution to a Simple Climate Model with Diffusive Heat Transport. , 1975 .

[179]  B. Saltzman,et al.  Parameterization of the monthly mean vertical heat transfer at the earth's surface , 1976 .

[180]  André Berger,et al.  Long-term variations of the Earth's orbital elements , 1977 .

[181]  W. D. Sellers A Reassessment of the Effect of CO2 Variations on a Simple Global Climatic Model , 1974 .

[182]  Takashi Sasamori,et al.  The Radiative Cooling Calculation for Application to General Circulation Experiments , 1968 .

[183]  Veerabhadran Ramanathan,et al.  Greenhouse Effect Due to Chlorofluorocarbons: Climatic Implications , 1975, Science.

[184]  J. Derome,et al.  On the maintenance of the axisymmetric part of the flow in the atmosphere , 1972 .