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This article is about the theories and mathematics of climate modeling. For computer-driven prediction of Earth's climate, see Global climate model. This article is about computer-driven prediction of Earth's climate for the theories and mathematics of climate modeling please see Climate model.
Climate models are systems of differential equations based on the basic laws of physics, fluid motion, and chemistry. To “run” a model, scientists divide the planet into a 3-dimensional grid, apply the basic equations, and evaluate the results. Atmospheric models calculate winds, heat transfer, radiation, relative humidity, and surface hydrology within each grid and evaluate interactions with neighboring points.
Climate models are systems of differential equations based on the basic laws of physics, fluid motion, and chemistry. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties To “run” a model, scientists divide the planet into a 3-dimensional grid, apply the basic equations, and evaluate the results. Atmospheric models calculate winds, heat transfer, radiation, relative humidity, and surface hydrology within each grid and evaluate interactions with neighboring points. In thermal physics, heat transfer is the passage of Thermal energy from a hot to a colder body Radiation, as in Physics, is Energy in the form of waves or moving Subatomic particles emitted by an atom or other body as it changes from a higher energy Relative humidity is a measurement of the amount of Water vapor that exists in a gaseous mixture of air and water Hydrology (from Greek Yδωρ hudōr, "water" and λόγος logos, "study" is the study of the movement distribution and quality of

Climate models use quantitative methods to simulate the interactions of the atmosphere, oceans, land surface, and ice. Quantitative research is the systematic scientific investigation of Quantitative properties and Phenomena and their relationships The objective of quantitative Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. Terrain, or relief, is the third or vertical dimension of land surface. They are used for a variety of purposes from study of the dynamics of the weather and climate system to projections of future climate. The weather is a set of all the phenomena occurring in a given Atmosphere at a given Time. Climate encompasses the temperatures humidity rainfall atmospheric particle count and numerous other meteorogical factors in a given region over long periods of

All climate models balance, or very nearly balance, incoming energy as short wave electromagnetic radiation (which in this context means visible and ultraviolet, not to be confused with shortwave) to the earth with outgoing energy as long wave (infrared) electromagnetic radiation from the earth. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays Shortwave Radio operates between the frequencies of 3000 KHz (3 Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of Any imbalance results in a change in the average temperature of the earth.

The most talked-about models of recent years have been those relating temperature to emissions of carbon dioxide (see greenhouse gas). Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Greenhouse gases are gaseous constituents of the atmosphere bothnatural and anthropogenic that absorb and emit radiation at specific wavelengths within the spectrum of thermal infrared These models project an upward trend in the surface temperature record, as well as a more rapid increase in temperature at higher altitudes. See also Temperature record. The instrumental temperature record shows the fluctuations of the Temperature of the atmosphere and the oceans as

Models can range from relatively simple to quite complex:

This is not a full list; for example "box models" can be written to treat flows across and within ocean basins.

Contents

Zero-dimensional models

A very simple model of the radiative equilibrium of the Earth is

(1 − a)Sπr2 = 4πr2εσT4

where

and

The constant πr2 can be factored out, giving

(1 − a)S = 4εσT4

This yields an average earth temperature of 288 K [3]. This is because the above equation represents the effective radiative temperature of the Earth (including the clouds and atmosphere). The use of effective emissivity accounts for the greenhouse effect. The Greenhouse effect refers to the change in the Thermal equilibrium temperature of a planet or moon by the presence of an Atmosphere containing gas that absorbs

This very simple model is quite instructive, and the only model that could fit on a page. For example, it easily determines the effect on average earth temperature of changes in solar constant or change of albedo or effective earth emissivity. Using the simple formula, the percent change of the average amount of each parameter, considered independently, to cause a one degree Celsius change in steady-state average earth temperature is as follows:

Solar constant 1. 4% Albedo 3. 3% Effective emissivity 1. 4%

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 [4] [5] (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 [6] (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 258 K [7]. Taking all this properly into account results in an effective earth emissivity of about 0. 64 (earth average temperature 285 K).

This simple model readily determines the effect of changes in solar output or change of earth albedo or effective earth emissivity on average earth temperature. It says nothing, however about what might cause these things to change. Zero-dimensional models do not address the temperature distribution on the earth or the factors that move energy about the earth.

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 zero-dimensional radiative-convective model, which considers two processes of energy transport:

The radiative-convective models have advantages over the simple model: they can determine the effects of varying greenhouse gas concentrations on effective emissivity and therefore the surface temperature. Greenhouse gases are gaseous constituents of the atmosphere bothnatural and anthropogenic that absorb and emit radiation at specific wavelengths within the spectrum of thermal infrared But added parameters are needed to determine local emissivity and albedo and address the factors that move energy about the earth.

Links:

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. The terms zonal and meridional are used to describe directions on a Globe. 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 models operating at the highest spatial and temporal resolution currently feasible. This article is about computer-driven prediction of Earth's climate for the theories and mathematics of climate modeling please see Climate model. 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 1/2 a day; the ocean is MOM-3 (Modular Ocean Model) with a 3. The Modular Ocean Model (MOM is a three-dimensional Ocean circulation model designed primarily for studying the Ocean Climate system 75° × 3. 75° grid and 24 vertical levels.

GCMs (Global Climate Models or General circulation models)

Main article: Global climate model

Three (or more properly, four since time is also considered) dimensional GCM's discretise the equations for fluid motion and energy transfer and integrate these forward in time. This article is about computer-driven prediction of Earth's climate for the theories and mathematics of climate modeling please see Climate model. They also contain parametrisations for processes - such as convection - that occur on scales too small to be resolved directly.

Atmospheric GCMs (AGCMs) model the atmosphere and impose sea surface temperatures. Coupled atmosphere-ocean GCMs (AOGCMs, e. g. HadCM3, EdGCM, GFDL CM2.X, ARPEGE-Climat[8]) combine the two models. HadCM3 (Hadley Centre Coupled Model version 3 is a coupled atmosphere-ocean General circulation model (AOGCM developed at the Hadley Centre in the United Kingdom EdGCM is a Global climate model (GCM that has been ported for use on desktop computers and integrated with a Relational database, a Graphical user interface GFDL CM2X ( G eophysical F luid Dynamics L aboratory C oupled M odel version 2. The first general circulation climate model that combined both oceanic and atmospheric processes was developed in the late 1960s at the NOAA Geophysical Fluid Dynamics Laboratory [9] AOGCMs represent the pinnacle of complexity in climate models and internalise as many processes as possible. The National Oceanic and Atmospheric Administration ( NOAA) is a scientific agency within the United States Department of Commerce focused on the conditions of the The Geophysical Fluid Dynamics Laboratory (GFDL is a laboratory in the National Oceanic and Atmospheric Administration (NOAA/ Office of Oceanic and Atmospheric Research However, they are still under development and uncertainties remain.

Most recent simulations show "plausible" agreement with the measured temperature anomalies over the past 150 years, when forced by observed changes in "Greenhouse" gases and aerosols, but better agreement is achieved when natural forcings are also included [10] [11].

Climate modellers

A climate modeller is a person who designs, develops, implements, tests, maintains or exploits climate models. There are three major types of institutions where a climate modeller may be found:

See also

Climate models on the web

References

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