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Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including
atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A ...
,
ocean The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wor ...
s,
land surface Terrain or relief (also topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The Latin wo ...
and ice. They are used for a variety of purposes from study of the dynamics of the climate system to projections of future
climate Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorologi ...
. Climate models may also be qualitative (i.e. not numerical) models and also narratives, largely descriptive, of possible futures. Quantitative climate models take account of incoming
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
from the sun as short wave
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
, chiefly visible and short-wave (near)
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...
, as well as outgoing long wave (far)
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...
electromagnetic. An imbalance results in a change in temperature. Quantitative models vary in complexity. For example, a simple
radiant heat Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
transfer model treats the earth as a single point and averages outgoing energy. This can be expanded vertically (radiative-convective models) and/or horizontally. Coupled atmosphere–ocean–
sea ice Sea ice arises as seawater freezes. Because ice is less dense than water, it floats on the ocean's surface (as does fresh water ice, which has an even lower density). Sea ice covers about 7% of the Earth's surface and about 12% of the world's o ...
global climate model A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic terms ...
s solve the full equations for mass and
energy transfer In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat ...
and radiant exchange. In addition, other types of modelling can be interlinked, such as
land use Land use involves the management and modification of natural environment or wilderness into built environment such as settlements and semi-natural habitats such as arable fields, pastures, and managed woods. Land use by humans has a long ...
, in Earth System Models, allowing researchers to predict the interaction between climate and
ecosystems An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
.


Box models

Box models are simplified versions of complex systems, reducing them to boxes (or
reservoir A reservoir (; from French ''réservoir'' ) is an enlarged lake behind a dam. Such a dam may be either artificial, built to store fresh water or it may be a natural formation. Reservoirs can be created in a number of ways, including contr ...
s) linked by fluxes. The boxes are assumed to be mixed homogeneously. Within a given box, the concentration of any
chemical species A chemical species is a chemical substance or ensemble composed of chemically identical molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale. These energy levels determine the wa ...
is therefore uniform. However, the abundance of a species within a given box may vary as a function of time due to the input to (or loss from) the box or due to the production, consumption or decay of this species within the box. Simple box models, i.e. box model with a small number of boxes whose properties (e.g. their volume) do not change with time, are often useful to derive analytical formulas describing the dynamics and steady-state abundance of a species. More complex box models are usually solved using numerical techniques. Box models are used extensively to model environmental systems or ecosystems and in studies of
ocean circulation An ocean current is a continuous, directed movement of sea water generated by a number of forces acting upon the water, including wind, the Coriolis effect, breaking waves, cabbeling, and temperature and salinity differences. Depth contours, ...
and the
carbon cycle The carbon cycle is the biogeochemical cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of the Earth. Carbon is the main component of biological compounds as well as a major compon ...
. They are instances of a
multi-compartment model A multi-compartment model is a type of mathematical model used for describing the way materials or energies are transmitted among the ''compartments'' of a system. Sometimes, the physical system that we try to model in equations is too complex, so ...
.


Zero-dimensional models

Zero-dimensional models are also commonly referred to as Energy Balance Models (or EBM's).


Model with combined surface and atmosphere

A very simple model of the
radiative equilibrium Radiative equilibrium is the condition where the total thermal radiation leaving an object is equal to the total thermal radiation entering it. It is one of the several requirements for thermodynamic equilibrium, but it can occur in the absence of ...
of the Earth is :(1-a)S \pi r^2 = 4 \pi r^2 \epsilon \sigma T^4 where * the left hand side represents the incoming energy from the Sun * the right hand side represents the outgoing energy from the Earth, calculated from the
Stefan–Boltzmann law The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths ...
assuming a model-fictive temperature, ''T'', sometimes called the 'equilibrium temperature of the Earth', that is to be found, and * '' S'' is the
solar constant The solar constant (''GSC'') is a flux density measuring mean solar electromagnetic radiation ( total solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical unit (au) from the Sun (roughly the ...
– the incoming solar radiation per unit area—about 1367 W·m−2 * ''a'' is the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
's average
albedo Albedo (; ) is the measure of the diffuse reflection of solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body that refle ...
, measured to be 0.3. * '' r'' is Earth's radius—approximately 6.371×106m * '' π'' is the mathematical constant (3.141...) * '' \sigma '' is the
Stefan–Boltzmann constant The Stefan–Boltzmann constant (also Stefan's constant), a physical constant denoted by the Greek letter ''σ'' (sigma), is the constant of proportionality in the Stefan–Boltzmann law: "the total intensity radiated over all wavelengths inc ...
—approximately 5.67×10−8 J·K−4·m−2·s−1 * '' \epsilon '' is the effective
emissivity The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that most commonly includes both visible radiation (light) and infrared radiation, which is n ...
of earth, about 0.612 The constant ''πr''2 can be factored out, giving :(1-a)S = 4 \epsilon \sigma T^4 Solving for the temperature, :T = \sqrt /math> This yields an apparent effective average Earth temperature of . This is because the above equation represents the effective ''radiative'' temperature of Earth's combined surface and atmosphere (including clouds). This very simple model is quite instructive. For example, it easily determines the change in the
effective temperature The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature ...
caused by changes in solar constant, Earth albedo, or effective Earth emissivity. The average emissivity of the earth is readily estimated from available data. The emissivities of terrestrial surfaces are all in the range of 0.96 to 0.99 (except for some small desert areas which may be as low as 0.7). Clouds, however, which cover about half of the earth's surface, have an average emissivity of about 0.5 (which must be reduced by the fourth power of the ratio of cloud absolute temperature to average earth absolute temperature) and an average cloud temperature of about . Taking all this properly into account results in an effective earth emissivity of about 0.64 (earth average temperature ).


Models with separated surface and atmospheric layers

upright=1, One-layer EBM with blackbody surface Dimensionless models have also been constructed with functionally separated atmospheric layers from the surface. The simplest of these is the zero-dimensional, one-layer model, which may be readily extended to an arbitrary number of atmospheric layers. The surface and atmospheric layer(s) are each characterized by a corresponding temperature and emissivity value, but no thickness. Applying radiative equilibrium (i.e
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means tha ...
) at the interfaces between layers produces a set of coupled equations which are solvable. Layered models produce temperatures that better estimate those observed for Earth's surface and atmospheric levels. They likewise illustrate the radiative
heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy ( heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conducti ...
processes which underlie the
greenhouse effect The greenhouse effect is a process that occurs when energy from a planet's host star goes through the planet's atmosphere and heats the planet's surface, but greenhouse gases in the atmosphere prevent some of the heat from returning directly ...
. Quantification of this phenomenon using a version of the one-layer model was first published by
Svante Arrhenius Svante August Arrhenius ( , ; 19 February 1859 – 2 October 1927) was a Swedish scientist. Originally a physicist, but often referred to as a chemist, Arrhenius was one of the founders of the science of physical chemistry. He received the Nob ...
in year 1896.


Radiative-convective models

The zero-dimensional model above, using the solar constant and given average earth temperature, determines the effective earth emissivity of long wave radiation emitted to space. This can be refined in the vertical to a one-dimensional radiative-convective model, which considers two processes of energy transport: * upwelling and downwelling radiative transfer through atmospheric layers that both absorb and emit infrared radiation * upward transport of heat by convection (especially important in the lower
troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. Fro ...
). The radiative-convective models have advantages over the simple model: they can determine the effects of varying
greenhouse gas A greenhouse gas (GHG or GhG) is a gas that absorbs and emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse gases in Earth's atmosphere are water vapor (), carbon dioxide (), methane ...
concentrations on effective emissivity and therefore the surface temperature. But added parameters are needed to determine local emissivity and albedo and address the factors that move energy about the earth. Effect of ice-albedo feedback on global sensitivity in a one-dimensional radiative-convective climate model.


Higher-dimension models

The zero-dimensional model may be expanded to consider the energy transported horizontally in the atmosphere. This kind of model may well be zonally averaged. This model has the advantage of allowing a rational dependence of local albedo and emissivity on temperature – the poles can be allowed to be icy and the equator warm – but the lack of true dynamics means that horizontal transports have to be specified.


EMICs (Earth-system models of intermediate complexity)

Depending on the nature of questions asked and the pertinent time scales, there are, on the one extreme, conceptual, more inductive models, and, on the other extreme,
general circulation model A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic ter ...
s operating at the highest spatial and temporal resolution currently feasible. Models of intermediate complexity bridge the gap. One example is the Climber-3 model. Its atmosphere is a 2.5-dimensional statistical-dynamical model with 7.5° × 22.5° resolution and time step of half a day; the ocean is MOM-3 ( Modular Ocean Model) with a 3.75° × 3.75° grid and 24 vertical levels.


GCMs (global climate models or general circulation models)

General Circulation Models (GCMs) discretise the equations for fluid motion and energy transfer and integrate these over time. Unlike simpler models, GCMs divide the atmosphere and/or oceans into grids of discrete "cells", which represent computational units. Unlike simpler models which make mixing assumptions, processes internal to a cell—such as convection—that occur on scales too small to be resolved directly are parameterised at the cell level, while other functions govern the interface between cells. Atmospheric GCMs (AGCMs) model the atmosphere and impose
sea surface temperature Sea surface temperature (SST), or ocean surface temperature, is the ocean temperature close to the surface. The exact meaning of ''surface'' varies according to the measurement method used, but it is between and below the sea surface. Air mas ...
s as boundary conditions. Coupled atmosphere-ocean GCMs (AOGCMs, e.g.
HadCM3 HadCM3 (abbreviation for ''Hadley Centre Coupled Model, version 3'') is a coupled atmosphere-ocean general circulation model (AOGCM) developed at the Hadley Centre in the United Kingdom. It was one of the major models used in the IPCC Third Asse ...
,
EdGCM The Educational Global Climate Model or EdGCM is a fully functional global climate model (GCM) that has been ported for use on desktop computers (Windows PCs and Macs). It operates through a graphical user interface and is integrated with a relatio ...
, GFDL CM2.X, ARPEGE-Climat) combine the two models. The first general circulation climate model that combined both oceanic and atmospheric processes was developed in the late 1960s at the
NOAA The National Oceanic and Atmospheric Administration (abbreviated as NOAA ) is an United States scientific and regulatory agency within the United States Department of Commerce that forecasts weather, monitors oceanic and atmospheric conditio ...
Geophysical Fluid Dynamics Laboratory The Geophysical Fluid Dynamics Laboratory (GFDL) is a laboratory in the National Oceanic and Atmospheric Administration (NOAA) Office of Oceanic and Atmospheric Research (OAR). The current director is Dr. Venkatachalam Ramaswamy. It is one of se ...
AOGCMs represent the pinnacle of complexity in climate models and internalise as many processes as possible. However, they are still under development and uncertainties remain. They may be coupled to models of other processes, such as the
carbon cycle The carbon cycle is the biogeochemical cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of the Earth. Carbon is the main component of biological compounds as well as a major compon ...
, so as to better model feedback effects. Such integrated multi-system models are sometimes referred to as either "earth system models" or "global climate models."


Research and development

There are three major types of institution where climate models are developed, implemented and used: * National meteorological services. Most national weather services have a
climatology Climatology (from Greek , ''klima'', "place, zone"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. This modern field of stu ...
section. * Universities. Relevant departments include atmospheric sciences, meteorology, climatology, and geography. * National and international research laboratories. Examples include the
National Center for Atmospheric Research The US National Center for Atmospheric Research (NCAR ) is a US federally funded research and development center (FFRDC) managed by the nonprofit University Corporation for Atmospheric Research (UCAR) and funded by the National Science Foundatio ...
(NCAR, in
Boulder, Colorado Boulder is a home rule city that is the county seat and most populous municipality of Boulder County, Colorado, United States. The city population was 108,250 at the 2020 United States census, making it the 12th most populous city in Colora ...
, USA), the
Geophysical Fluid Dynamics Laboratory The Geophysical Fluid Dynamics Laboratory (GFDL) is a laboratory in the National Oceanic and Atmospheric Administration (NOAA) Office of Oceanic and Atmospheric Research (OAR). The current director is Dr. Venkatachalam Ramaswamy. It is one of se ...
(GFDL, in
Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of w ...
, USA),
Los Alamos National Laboratory Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, ...
, the
Hadley Centre for Climate Prediction and Research The Met Office Hadley Centre — named in honour of George Hadley — is one of the United Kingdom's leading centres for the study of scientific issues associated with climate change. It is part of, and based at the headquarters of the Met Of ...
(in
Exeter Exeter () is a city in Devon, South West England. It is situated on the River Exe, approximately northeast of Plymouth and southwest of Bristol. In Roman Britain, Exeter was established as the base of Legio II Augusta under the personal comm ...
, UK), the
Max Planck Institute for Meteorology The Max Planck Institute for Meteorology (''Max-Planck-Institut für Meteorologie''; MPI-M) is an internationally renowned institute for climate research. Its mission is to understand Earth's changing climate. Founded in 1975, it is affiliated w ...
in Hamburg, Germany, or the
Laboratoire des Sciences du Climat et de l'Environnement The (LSCE, Climate and Environment Sciences Laboratory) is a laboratory for the study of climate and in particular climate change. It is part of the Institute Pierre Simon Laplace, and located on campuses in L'Orme des Merisiers and Gif sur Y ...
(LSCE), France, to name but a few. The
World Climate Research Programme The World Climate Research Programme (WCRP) is an international programme that helps to coordinate global climate research. The WCRP was established in 1980, under the joint sponsorship of the World Meteorological Organization (WMO) and the Inter ...
(WCRP), hosted by the
World Meteorological Organization The World Meteorological Organization (WMO) is a specialized agency of the United Nations responsible for promoting international cooperation on atmospheric science, climatology, hydrology and geophysics. The WMO originated from the Inter ...
(WMO), coordinates research activities on climate modelling worldwide. A 2012
U.S. National Research Council The National Academies of Sciences, Engineering, and Medicine (also known as NASEM or the National Academies) are the collective scientific national academy of the United States. The name is used interchangeably in two senses: (1) as an umbrell ...
report discussed how the large and diverse U.S. climate modeling enterprise could evolve to become more unified. Efficiencies could be gained by developing a common software infrastructure shared by all U.S. climate researchers, and holding an annual climate modeling forum, the report found.


See also

* Atmospheric reanalysis *
General circulation model A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic ter ...
*
Chemical transport model A chemical transport model (CTM) is a type of computer numerical model which typically simulates atmospheric chemistry and may give air pollution forecasting. Chemical transport models and general circulation models While related general circ ...
*
Atmospheric Radiation Measurement The Atmospheric Radiation Measurement Climate Research Facility (ARM Climate Research Facility) is a multi-laboratory United States Department of Energy scientific user facility used for national and international global climate research efforts. ...
(ARM) (in the US) * Climate Data Exchange *
Climateprediction.net climate''prediction''.net (CPDN) is a volunteer computing project to investigate and reduce uncertainties in climate modelling. It aims to do this by running hundreds of thousands of different models (a large climate ensemble) using the donate ...
* GFDL CM2.X *
GO-ESSP The Global Organization of Earth System Science Portals or (''GO-ESSP'') is an international collaboration, formed in 2003, that is developing software infrastructure to support the distribution, and analysis of climate model data and related obs ...
*
Numerical Weather Prediction Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in th ...
*
Static atmospheric model A reference atmospheric model describes how the ideal gas properties (namely: pressure, temperature, density, and molecular weight) of an atmosphere change, primarily as a function of altitude, and sometimes also as a function of latitude, day of ...
*
Tropical cyclone prediction model A tropical cyclone forecast model is a computer program that uses meteorological data to forecast aspects of the future state of tropical cyclones. There are three types of models: statistical, dynamical, or combined statistical-dynamic. Dyn ...
* Verification and validation of computer simulation models * CICE sea ice model


Climate models on the web


Dapper/DChart
— plot and download model data referenced by the Fourth Assessment Report (AR4) of the
Intergovernmental Panel on Climate Change The Intergovernmental Panel on Climate Change (IPCC) is an intergovernmental body of the United Nations. Its job is to advance scientific knowledge about climate change caused by human activities. The World Meteorological Organization (WMO) ...
. (No longer available)
NCAR/UCAR Community Climate System Model
(CCSM)
Do it yourself climate prediction

Primary research GCM developed by NASA/GISS (Goddard Institute for Space Studies)

Original NASA/GISS global climate model
(GCM) with a user-friendly interface for PCs and Macs
CCCma model info and interface to retrieve model data

NOAA/Geophysical Fluid Dynamics Laboratory
CM2 global climate model info and model output data files
Dry idealized AGCM
based on above GFDL CM2
Model of an idealized Moist Atmosphere (MiMA)
based on GFDL CM2. Complexity in-between dry models and full GCMsM. Jucker and E. P. Gerber: "Untangling the Annual Cycle of the Tropical Tropopause Layer with an Idealized Moist Model". Journal of Climate 2017 30 (18) 7339-7358;
University of Victoria Global climate model
free for download. Leading researcher was a contributing author to an
IPCC The Intergovernmental Panel on Climate Change (IPCC) is an intergovernmental body of the United Nations. Its job is to advance scientific knowledge about climate change caused by human activities. The World Meteorological Organization (WMO) ...
report on
climate change In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to ...
.
vimeo.com/user12523377/videos Visualizations of climate models of ETH Zurich

Empirical Climate Model


References


Bibliography

*


External links




On the Radiative and Dynamical Feedbacks over the Equatorial Pacific Cold Tongue


— The Discovery of Global Warming *
Climate Modeling 101 website
by the
U.S. National Research Council The National Academies of Sciences, Engineering, and Medicine (also known as NASEM or the National Academies) are the collective scientific national academy of the United States. The name is used interchangeably in two senses: (1) as an umbrell ...
— This site is a primer on how climate models work. The information is based on expert, consensus reports from the
U.S. National Research Council The National Academies of Sciences, Engineering, and Medicine (also known as NASEM or the National Academies) are the collective scientific national academy of the United States. The name is used interchangeably in two senses: (1) as an umbrell ...
's Board on Atmospheric Sciences and Climate. The most recent i
''A National Strategy for Advancing Climate Modeling''
.
Why results from the next generation of climate models matter
CarbonBrief, Guest post by Belcher, Boucher, Sutton, 21 March 2019
Builder Insight - Modelling the Future Climate in Passively Cooled Buildings
{{Portal bar, Energy, Global warming Numerical climate and weather models