Climate model

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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.
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 use quantitative methods to simulate the interactions of the atmosphere, oceans, land surface, and ice. They are used for a variety of purposes from study of the dynamics of the climate system to projections of future climate. The most talked-about use of climate models in recent years has been to project temperature changes resulting from increases in atmospheric concentrations of greenhouse gases.

All climate models take account of incoming energy from the sun as short wave electromagnetic radiation, chiefly visible and short-wave (near) infrared, as well as outgoing energy as long wave (far) infrared electromagnetic radiation from the earth. Any imbalance results in a change in temperature.

Models can range from relatively simple to quite complex:

  • A simple radiant heat transfer model that treats the earth as a single point and averages outgoing energy
  • this can be expanded vertically (radiative-convective models), or horizontally
  • finally, (coupled) atmosphere–ocean–sea ice global climate models discretise and solve the full equations for mass and energy transfer and radiant exchange.

This is not a full list; for example "box models" can be written to treat flows across and within ocean basins. Furthermore, other types of modelling can be interlinked, such as land use, allowing researchers to predict the interaction between climate and ecosystems.

Box models[edit]

Box models are simplified versions of complex systems, reducing them to boxes (or reservoirs) linked by fluxes. The boxes are assumed to be mixed homogeneously. Within a given box, the concentration of any chemical species 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 and the carbon cycle.[1]

Zero-dimensional models[edit]

A very simple model of the radiative equilibrium 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 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 incoming solar radiation per unit area—about 1367 W·m−2
  • a is the Earth's average albedo, measured to be 0.3.[2][3]
  • r is Earth's radius—approximately 6.371×106m
  • π is the mathematical constant (3.141...)
  •  \sigma is the Stefan-Boltzmann constant—approximately 5.67×10−8 J·K−4·m−2·s−1
  •  \epsilon is the effective emissivity of earth, about 0.612

The constant πr2 can be factored out, giving

(1-a)S = 4 \epsilon \sigma T^4

Solving for the temperature,

T = \sqrt[4]{ \frac{(1-a)S}{4 \epsilon \sigma}}

This yields an apparent effective average earth temperature of 288 K (15 °C; 59 °F).[4] This is because the above equation represents the effective radiative temperature of the Earth (including the clouds and atmosphere). The use of effective emissivity and albedo account for the greenhouse effect.

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.

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[5][6] (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[7] (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 (−15 °C; 5 °F).[8] Taking all this properly into account results in an effective earth emissivity of about 0.64 (earth average temperature 285 K (12 °C; 53 °F)).

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[edit]

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 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. 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.[9][10][11]

Higher-dimension models[edit]

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.[12]

EMICs (Earth-system models of intermediate complexity)[edit]

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. 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.[13]

GCMs (global climate models or general circulation models)[edit]

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 temperatures as boundary conditions. Coupled atmosphere-ocean GCMs (AOGCMs, e.g. HadCM3, EdGCM, GFDL CM2.X, ARPEGE-Climat)[14] 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 Geophysical Fluid Dynamics Laboratory[15] 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, 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[edit]

There are three major types of institution where climate models are developed, implemented and used:

The World Climate Research Programme (WCRP), hosted by the World Meteorological Organization (WMO), coordinates research activities on climate modelling worldwide.

A 2012 U.S. National Research Council report discussed how the large and diverse U.S. climate modeling enterprise could evolve to become more unified.[16] 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.[17]

See also[edit]

Climate models on the web[edit]

Notes and references[edit]

  1. ^ Sarmiento, J.L.; Toggweiler, J.R. (1984). "A new model for the role of the oceans in determining atmospheric P CO 2". Nature 308 (5960): 621–24. Bibcode:1984Natur.308..621S. doi:10.1038/308621a0. 
  2. ^ Goode, P. R.; et al. (2001). "Earthshine Observations of the Earth’s Reflectance". Geophys. Res. Lett. 28 (9): 1671–4. Bibcode:2001GeoRL..28.1671G. doi:10.1029/2000GL012580. 
  3. ^ "Scientists Watch Dark Side of the Moon to Monitor Earth's Climate". American Geophysical Union. April 17, 2001. 
  4. ^ eospso.gsfc.nasa.gov
  5. ^ icess.ucsb.edu
  6. ^ Jin M, Liang S (15 June 2006). "An Improved Land Surface Emissivity Parameter for Land Surface Models Using Global Remote Sensing Observations". J. Climate 19 (12): 2867–81. Bibcode:2006JCli...19.2867J. doi:10.1175/JCLI3720.1. 
  7. ^ T.R. Shippert, S.A. Clough, P.D. Brown, W.L. Smith, R.O. Knuteson, and S.A. Ackerman. "Spectral Cloud Emissivities from LBLRTM/AERI QME". Proceedings of the Eighth Atmospheric Radiation Measurement (ARM) Science Team Meeting March 1998 Tucson, Arizona. 
  8. ^ A.G. Gorelik, V. Sterljadkin, E. Kadygrov, and A. Koldaev. "Microwave and IR Radiometry for Estimation of Atmospheric Radiation Balance and Sea Ice Formation". Proceedings of the Eleventh Atmospheric Radiation Measurement (ARM) Science Team Meeting March 2001 Atlanta, Georgia. 
  9. ^ pubs.giss.nasa.gov
  10. ^ Wang, W.C.; P.H. Stone (1980). "Effect of ice-albedo feedback on global sensitivity in a one-dimensional radiative-convective climate model". J. Atmos. Sci. 37: 545–52. Bibcode:1980JAtS...37..545W. doi:10.1175/1520-0469(1980)037<0545:EOIAFO>2.0.CO;2. Retrieved 2010-04-22. 
  11. ^ grida.no
  12. ^ shodor.org
  13. ^ pik-potsdam.de
  14. ^ cnrm.meteo.fr
  15. ^ celebrating200years.noaa.gov
  16. ^ "U.S. National Research Council Report, A National Strategy for Advancing Climate Modeling". 
  17. ^ "U.S. National Research Council Report-in-Brief, A National Strategy for Advancing Climate Modeling". 

Bibliography[edit]

External links[edit]