2-2: Climate Models

Eugene S. Takle
© 1997

Understanding climate change is complicated by the many interactions that occur within the climate system. The next image gives examples of what are known as "feedback" processes in climate. Feedback effects occur when a change in one climate parameter changes another, which, in turn, causes changes in the initial variable. The following are examples of feedback processes:

1. Temperature-radiation feedback.

2. Water-vapor/greenhouse feedback. 3. Snow and ice cover / albedo feedback. 4. Cloudiness / surface-temperature feedback. 5. Radiative-dynamic coupling.

These feedback processes are described by laws of physics and are naturally incorporated into climate models. We now focus our attention on the characteristics of such models.

Climate models are essentially the same models that are used every day for weather forecasting. They have some slight modifications made to make them adaptable to running for long periods of time (several years as opposed to a few days), but they use the same basic laws of physics: conservation of energy, conservation of momentum, conservation of mass, and an equation of state that describes the relationship of temperature to pressure and density.
Basic equations
of climate models.
Takle, G.S., 1995

The vector equations describing these motions and processes in the atmosphere are given in the accompanying image. In these equations, the wind has horizontal components u and v in the east and north directions, respectively, an vertical component w. T is temperature, p is pressure, rho is density, g is the acceleration due to gravity, R is the flux of radiation, omega is the vector describing the angular rotation of the earth on its axis, F is the frictional force of drag due to the earth's surface, cv is the specific heat capacity at constant volume, kT is the turbulent diffusion constant, C represents the effect of heating (or cooling) by condensation, St includes other unaccounted for sources of heat, q is specific humidity, S represents sources of water vapor, and Ro is the universal gas constant. Actual models have three equations rather than just one for H2O. Separate equations are needed for water vapor, liquid water, and cloud-ice particles.

Some physical process are too complicated or occur at such small scales that they cannot be resolved by the coarse grid spacing of model and must be approximated by what are called parameterizations. Cloud processes, the absorption and radiating properties of the atmosphere and clouds, and atmospheric interactions with vegetation and other surface features must be described by parameterizations. The next sketch shows some of the factors that are taken into account in surface parameterizations. Vegetation transpires water into the air and suspends liquid water from precipitation or dew deposition. The roots, stems, and leaves provide a pathway for subsurface water to be delivered to the atmosphere. The surface parameterization must account for seasonal change in vegetation and its change in transpiration, its change in reflective properties, and its change in drag forces on the atmosphere. Evaporation, infiltration of water to the deep soil, and surface runoff to streams and lakes must be taken into account at each time step.
Land-surface
parameterization
scheme.
NCAR/TN - 275 +STR
Biosphere-Atmosphere
Transfer Scheme (BATS)

For a global climate model we determine values of temperature, wind speed, pressure, density, and concentration of water vapor, liquid water, and ice crystals at each of about 50,000 to 150,000 grid points over the earth at each time step (typically an hour) for the duration of the simulation (corresponding to the number of pegs in our pinball analogy), which typically might be a 30-year period (262,800 time steps). As an estimate of the volume of numbers created by such a model, if 10 variables are saved for each of 150,000 grid points at 262,800 time steps, the data to be saved totals 400,000 megabytes.

A typical grid used in a global climate model is shown in the next figure. Each point on this grid has a vertical column of points at which variables are calculated. The number of points in the vertical direction ranges from as few as 2 to as many as about 20 levels. Note that typical global models have a have a horizontal grid spacing of about 500 km ( 300 miles). This means that a single surface grid point must represent all the surface processes in a box larger than the state of Iowa. Most global models have resolution too coarse to even recognize the existence of the Great Lakes, and some completely ignore the Florida peninsula.
Giss model

A more desirable grid is given in the accompanying image, but such fine resolution for a model spanning he entire globe is unmanageably large with present computational capabilities. Regional climate models, designed to cover a limited area of the globe as shown in the next image, allow resolution of more spatial details than global models but require information from some other source at their lateral boundaries. Using regional models to study climate change has become a more important approach in recent years. One such study here at ISU is the Project to Intercompare Regional Climate Simulations (PIRCS).

High resolution (hypothetical) grid. Cushman and Ferres,
Climate Change Quarterly, 77.

Computational domain for a regional climate model. NCAR/TN - 381 +1A. A user's guide to the Penn State/NCAR mesoscale modelling system.

We now follow the strategy outlined in the pinball analogy where we first examine how well the model simulates the characteristics of the present global climate. The accompanying plot shows the zonally averaged sea-level pressure. The horizontal axis on this plot gives the latitude from the North Pole (90o) to the South Pole (-90o). The upper graph gives the December-January-February (DJF) averages, and the bottom plot gives June-July-August (JJA) values. Each curve represents a different global climate model, including the results from the National Center for Atmospheric Research (NCAR), Geophysical Fluid Dynamics Laboratory high-resolution model (GFHI), United Kingdom Meteorological Office high-resolution model (UKHI), NASA Goddard Institute for Space Studies (GISS), Geophysical Fluid Dynamics Laboratory low-resolution model (GFLO), United Kingdom Meteorological Office low-resolution model (UKLO), and the Canadian Climate Centre (CCC). All models use the same basic equations in simulating climate, but differ in how they parameterize effects of clouds, radiation, and surface features. The red lines in each of the plots give the observed zonally averaged sea-level pressure against which results of all models are to be compared.
Zonal-average
mean sea-level
pressure. Adapted from Figure 4.1 IPCC, 1990.


Surface pressure is particularly a good variable to begin the model comparison because, representing the mass of the atmosphere, it gives the overall movement of mass over the planet. Notice that the pressure has maxima about 30o north and south of the Equator. Can you recall the dominant climatic characteristic of these regions 30o north and south of the Equator as discussed in an earlier lecture? The minimum near -70o marks the pressure minimum of the Southern Hemisphere ocean. Most models represent the pressure distribution reasonably well except near the polar regions, especially the South Pole. Recall that the Antarctic continent is very high with a very deep layer of ice. These factors create severe difficulties for simulation of pressure over this region. In some cases (such as UKLO in JJA) a low-resolution model gives results closer to the observations than high-resolution models. Note that the UKLO model does not give results as accurate in the DJF simulation.

The next plot compares model results for simulating temperature in for the same two seasons as the previous plot. All models do quite well in all regions except near the South Pole. Zonal-average precipitation produced by global models show some of the weakness of climate simulation. The observations show high-precipitation regions in the tropics (near latitude 0o) and the mid-latitudes (45o-60oN and S). Most models show the correct placement of the precipitation maxima, but close examination reveals that the relative size of the errors typically range from about 20 to 100%. The next plot of this series shows how well models simulate soil moisture. The models give poor representations of soil moisture in the Northern Hemisphere. In the tropics where the soil is moist most of the time, the models do much better. In the subtropical high pressure zones the soil is usually dry, so again the models do well. So in general, the models do quite well in areas where the soil moisture doesn't change much but not very well where there are large fluctuations.
Zonal-average air temperature. Adapted from Figure 4.8 IPCC, 1990. Zonal-average precipitation. Adapted from Figure 4.10 IPCC, 1990. Zonal-average soil moisture. Adapted from Figure 4.12 IPCC, 1990.


The final plot gives results of the latest generation of high-resolution models. The upper panel shows good agreement except over Antarctica. The lower panel shows that even the highest resolution for global models fails to capture such features as the peaks in the tropics and Southern Hemisphere midlatitudes. Zonally-averaged JJA and DJF sea-level pressure simulated by current high resolution GCMs. Adapted from Figure B27 IPCC, 1990.

Transcription by Theresa M. Nichols