Types Of Models

There are many types of models used in paleoclimatology and the GCMs referred to in the introduction are most complex. Hydrological balance models, used to understand the paleorecord of lake sediments and lake level changes, have already been discussed in Chapter 7. Models of the changes in forest growth that might be expected with climatic changes of different duration and magnitude were described in Chapter 9. One could also argue that the various approaches to calibrating faunal data from the oceans, and pollen and tree-ring data from the continents, constitute statistical models, which may produce different reconstructions as methodologies are refined and improved. Models are thus embedded in a conceptual framework of how systems work, and as our understanding of such systems improves so we can expect models to be revised. In this sense, model experiments produce results that are moving targets. Some results may be robust and demonstrably correct; others may turn out to be erroneous. By the constant interaction between data-generators (empiricists) and modelers (theorists) the results eventually will converge on a consensus of how (and why) climates varied in the past.

Various types of atmospheric models have been developed with varying levels of complexity. Coupled ocean-atmosphere general circulation models are at the high end of this range but consequently require immense amounts of computer time, making the number of runs and potential applications somewhat limited. Less complex models have the advantage of being much faster to run (allowing many more options to be examined) but the trade-off is in limiting the processes, feedbacks, and/or dimensions being examined.

A very brief summary is provided of the types of models that have been used in climate and paleoclimatic applications, with an emphasis on GCMs. For a much more comprehensive introduction to the theory of paleoclimate modeling, see Saltzman (1985). An introduction to climate models in general, with CD-based examples of different models, is provided by McGuffie and Henderson-Sellers (1997). The volumes edited by Schlesinger (1987) and Trenberth (1992) also provide in-depth discussion of climate models and their components. All of the relatively simple models described here have a role to play in understanding how the climate system works and indeed complex general circulation models have been constructed using insights obtained from the development of simpler, faster models (Schneider, 1992).

12.2.1 Energy Balance Models and Statistical Dynamical Models

Energy balance models (EBMs) consider only surface temperature as a consequence of energy exchange. The simplest are zero-dimensional (i.e., consider the energy balance of the earth as a whole; Budyko, 1969; Sellers, 1969, 1973). One-dimensional EBMs consider the earth in terms of zonal bands, with energy exchanged latitudinally from one zone to the next by diffusive horizontal heat transfer. Two-dimensional EBMs add additional complexity by considering latitude/altitude or latitude/longitude differences (e.g., land vs ocean). Further detail may be added, for example, by considering the earth as a series of linked boxes with different properties (atmosphere-land-mixed layer ocean-deep ocean), and with energy transfers taking place between them by advection and diffusion (Harvey and Schneider, 1985a). Such models enable changes in feedbacks to be investigated in a computationally efficient way, allowing many slightly different simulations (sensitivity experiments) to be carried out. The effects of changes in albedo, solar input to the earth, greenhouse gas increases, and net poleward heat transport have also been investigated with EBMs (North et al., 1981; Harvey and Schneider, 1985b; Wigley, 1991; Wigley and Kelley, 1990).

Statistical-dynamical models (SDMs) are designed to capture the observed record of climate without explicitly creating that record, ab initio, from basic physical laws at a network of points, as occurs in general circulation models. Unlike GCMs (considered in what follows), they do not consider explicitly all the synoptic scale variability and atmospheric changes that take place at high frequencies (30-min time steps). Instead, they use equations that describe changes over long time periods, requiring parameterization of many of the phenomena that are dealt with explicitly in GCMs. Consequently, SDMs require less computer time and can be used to examine the long-term evolution of climate, taking into account some of the more slowly responding parts of the climate system (Saltzman, 1985). For example, Gallee et al. (1991) developed a quite complex two-dimensional (latitude/altitude) time-dependent climate model of the northern hemisphere, with the surface subdivided into up to 7 different categories, each with distinct properties (ocean, sea ice, snow-covered or snow-free land, and three areas of land ice, representing the Laurentide, Fennoscandian, and Greenland ice sheets). Atmospheric dynamics in the model were zonally averaged, and meridional fluxes, oceanic heat transport, mixed layer dynamics, and land surface hydrology were all parameterized. The atmosphere-land-ocean model was coupled asynchronously to an ice-sheet-bedrock model; this allowed the different response times of these systems to be taken into account. The atmosphere-land-ocean model was run every day for a 20-yr simulation, and the resulting climate was the input to the ice-sheet-bedrock model, which ran at 1-yr time steps for 1000 yr. The procedure was then repeated, taking into account the altered surface boundary conditions, changes in orbital forcing, and C02 levels (as deduced from the Vos-tok ice core) (Gallee etal., 1992; Berger et al., 1993). Figure 12.1 shows the resulting simulation of northern hemisphere continental ice volume for the last 200,000 yr, compared to 8lsO variations in benthic forams, according to SPECMAP (Martinson et al., 1987). Although the model is not correct in absolute terms (e.g., it reconstructs zero ice in the northern hemisphere at the last interglacial, at -100 ka and -70-84 ka B.P., which is not supported by the paleorecord) it does well at reproducing the general time evolution of the SPECMAP record. Considering SPECMAP 8180 represents a global ice volume signal, and the model is based only on conditions in the northern hemisphere, the comparison is very favorable. Further improvements in the parameterizations, and incorporation of a southern hemisphere model should make the comparison even better (Berger and Loutre, 1997a,b).

12.2.2 Radiative Convective Models

These models examine radiation processes in a vertical column of the atmosphere; vertical temperature profiles (lapse rates) are maintained within a reasonable range

FIGURE 12.1 Variations in northern hemisphere ice volume over the last 200,000 yr simulated by the Louvain-la-Neuve 2D climate model (Gallee et al., 1991) forced by insolation and C02 variations (solid line) compared to the SPECMAP 8I80 variations, representing ice volume changes over the entire earth (dashed line) (Berger and Loutre, 1997a).

FIGURE 12.1 Variations in northern hemisphere ice volume over the last 200,000 yr simulated by the Louvain-la-Neuve 2D climate model (Gallee et al., 1991) forced by insolation and C02 variations (solid line) compared to the SPECMAP 8I80 variations, representing ice volume changes over the entire earth (dashed line) (Berger and Loutre, 1997a).

by convective adjustments (movement of air vertically). Such models have been used to investigate the effects of atmospheric aerosols and clouds on temperature and the effects of changing greenhouse gases (C02, CH4, 03) (Manabe and Wetherald, 1967; Reck, 1974; Hansen et al., 1978). Radiative convective models (RCMs) have been used extensively to perform sensitivity tests in which the value of one parameter (e.g., greenhouse gas amount) is varied in different model simulations to examine how such changes might lead to feedbacks with other parts of the system (Ramanathan and Coakley, 1978; Kiehl, 1992).

12.2.3 General Circulation Models

Atmospheric general circulation models (AGCMs) simulate atmospheric processes in three dimensions, explicitly taking into account dynamical processes. Basic equations solved in GCMs involve the conservation of energy, mass, and momentum. The earth's surface is divided into a series of grid boxes, extending vertically into the atmosphere (Fig. 12.2). The atmospheric column is also divided into a series of levels (commonly 10-20) with more levels near the earth's surface. Equations are solved at each grid point and at each vertical level at a preset time interval (typically 20-30 min) with vertical and horizontal exchanges of energy, mass, and momentum computed for all points at each time interval. Clearly, this procedure requires immense amounts of computer time and so the most sophisticated GCMs have to run on the fastest computers available, and even then it may take weeks of dedicated computer time to carry out a simulation. For example, the National Center for Atmospheric Research (NCAR) Climate System Model, comprising a 3.75°x 3.75° grid, 18-level atmospheric model, coupled to a 3°x 3° mixed layer ocean, with 30-min time steps requires -15 h of dedicated time on a CRAY J90 computer (one of the fastest supercomputers currently available) to simulate one yr. The problem is even more acute in ocean general circulation models (OGCMs) where finer spatial resolution is required to simulate effectively the important scale of motion (oceanic eddies) that are < 50 km across (more than an order of magnitude smaller than the typical atmospheric eddies). Massively parallel computers (employing >100 processors simultaneously) are now being used to solve such problems (Chervin and Semtner, 1991).

These GCMs vary considerably in their resolution. Many paleoclimatic simulations have been carried out at a scale of 8° (latitude) x 10° (longitude). Such models have relatively crude geography (for example, small details like the United Kingdom or New Zealand would not be represented!) and poor topographical representation. In such a model, a single grid box in midlatitudes is equivalent in size to the states of Colorado and Utah, or of France and Germany, together. More complex models may have spatial resolution up to 2° x 2° with more highly resolved surface relief. However, such models inevitably trade computational speed for the added sophistication provided by a denser grid network, so the analyst must determine if the nature of the problem being investigated warrants the added time and expense of a high-resolution GCM. Even in the highest resolution AGCMs, many atmospheric processes cannot be represented as they are below the grid scale of the model. Convective thunderstorms, for example, play a critical role on a global scale in latent and sensible heat transfer from the surface to the atmosphere, but individually they

Horizontal exchange between columns

IN THE ATMOSPHERIC COLUMN wind vectors, humidity, clouds, temperature, and chemical species

Geography and orography

Horizontal exchange between columns

IN THE ATMOSPHERIC COLUMN wind vectors, humidity, clouds, temperature, and chemical species

Geography and orography

Atmospheric grid

Vertical exchange between levels

Bathymetry

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