There are two general approaches in paleoclimatic analysis: an inverse- modeling, or reconstruction approach, and a forward-modeling, or hypothesis-testing approach. The first approach, which might also be called a "bottom-up" approach, is the classical one in paleoclimatic analysis. In this approach, paleoclimatic evidence, in the form of geological or paleoecological records, is interpreted in climatic terms by one means or another. These reconstructions are then used to infer (usually subjectively) the nature of the changes in the controls of climate responsible for the observed patterns. The second, or "top-down" approach has been less frequently applied in paleoclimatic analysis. In this approach, ideas about the changes in the large-scale controls of climate are applied to one or more models (conceptual as well as numerical) of the climate system, and the resulting simulations are then compared with paleoclimatic observations. This approach is synonymous with " paleoclimatic data-model comparison," or "hypothesis-testing."
The properties of the forward-modeling approach that favor its application in paleoclimatic analysis (of Pliocene climates in particular) will be discussed in the next section. Following this, an example of the application of the forward-modeling approach applied to the middle Pliocene distribution of several plant taxa in North America will be schematically illustrated.
There are a number of conditions and assumptions both statistical and ecological that must be satisfied when making inferences from paleoclimatic data; these have been discussed in detail by Sloan and Barron (1992), and Bartlein and Webb (1985). One major problem that arises in the reconstruction approach, even if the technical assumptions are satisfied, is the indeterminacy of the paleoclimatic data itself: the specific controls of a particular paleoclimatic record cannot always be uniquely or unambiguously determined from the data alone. In other words, even if the paleoclimatic reconstructions are correct, they alone may not reveal the controls of the past climates.
Indeterminacy of paleoclimatic records. Indeterminacy of paleoclimatic records arises from two sources: one intrinsic to the paleoclimatic indicators themselves, and one related to the nature of the climate system. The intrinsic source of indeterminacy arises because rarely will a particular biological or geological indicator of past climate reflect a single climatic variable. Vegetation, for example, is determined by a number of climatic variables, and interactions among these variables is typical. Vegetation is often limited by its moisture requirements as well as by temperature, and "effective moisture" reflects both precipitation and evapotranspiration. Evapotranspiration, in turn, is determined by a number of distinct climatic variables, as well as by the properties of the soil and vegetation. Consequently, it may be difficult to identify the particular individual or group of climatic variables that may have contributed to a particular feature of a paleoecological record. Derivations of the response functions (either empirical or theoretical) of the different paleoclimatic indicators can illustrate how a particular indicator depends on one or more controlling variable. Such information can be used to indicate when an observed response of a particular indicator may not be unambiguously interpretable in terms of a single climatic variable.
Example 1 shows how the similar regional patterns of effective moisture (dry in the Pacific Northwest, wet in the southwest) can result from two different large-scale controls. See Thompson et al. (in press) for further discussion. Example 2 shows how the multiple pathways by which a single large-scale control (uplift of western North America) can produce a signal in a regional paleoclimatic indicator (i.e. steppe replacing forest in the interior western United States; see Thompson (1991) for further discussion).
In the simulations for 9 ka, greater summer insolation than present heated the center of the continent and increased the land/ocean temperature contrast in summer. This thermal anomaly in turn affected circulation, strengthening the east Pacific subtropical high pressure system in summer, and producing a "heat low" over the continent (Kutzbach, 1987). The stronger subtropical high, and the greater regional-scale subsidence associated with it, consequently suppressed precipitation in the Pacific Northwest, while the greater onshore flow (than present) into the heat low increased summer precipitation.
The same regional paleoclimatic anomaly pattern drier than present in the Pacific Northwest and wetter than present in the Southwest apparently can result from two different sets of ultimate controls, and the reconstructed pattern of effective moisture alone cannot discriminate between the two. This situation exists despite the likelihood that the precipitation anomaly was best expressed in winter in one case and in summer in the other. Further paleoclimatic information, such as the status of the levels of former lakes (Guiot et al., 1993), or the variation in abundance of plant taxa with specific seasonal climatic requirements (Thompson, 1988) might be used to differentiate between the controls, but the effective moisture pattern alone cannot provide an unambiguous identification of the ultimate controls in each case.
A second example illustrates a case in which the ultimate control of a response observable in a particular paleoclimatic record is clear, but there are more than one proximate controls, and it is not apparent which or all are important. In this example, the specific paleoclimatic observation is the replacement of steppe vegetation by conifers in the basins in the interior western United States during the Pliocene, a vegetation change unambiguously interpretable as indicating a change toward drier conditions (Thompson, 1991). The ultimate control of this trend toward dryness clearly is the uplift of western North America. But there are at least two different pathways by which this large-scale control can produce drier conditions within the region, however, and there are intra-regional (positive) feedbacks that can reinforce the trend as well, adding a third pathway. At the continental scale, the uplift of western North America over the past several million years gradually strengthened the ridge in the upper-level westerly winds that now prevails over western North America (Ruddiman and Kutzbach, 1989; Raymo and Ruddiman, 1992). This circulation change in turn would have increased subsidence over western North America, and consequently suppressed precipitation. At the subcontinental scale, the uplift or formation of individual ranges such as the Sierra Nevada and Cascade Range would have increased the regional-scale rainshadows, by increasing orographic precipitation on the west side of the ranges and increasing subsidence on the east side. This mechanism would also reduce precipitation. Within the region, decreased precipitation would likely have reduced the size of the very large (relative to present) Pliocene lakes, further reinforcing the drying trend by reducing lake-effect precipitation.
In this second example, although the ultimate control of the change recorded by various paleoclimatic indicators is clear, the manner in which the regional response is actually determined is ambiguous. Both examples show how the bottom-up, inverse-modeling approach may be inadequate when the objective is to discover how changes in the large-scale controls of climate govern regional climatic responses.
The forward-modeling approach. The "top-down" or forward- modeling approach in paleoclimatic analysis begins with some information or assumptions regarding the state of the large-scale controls of climate (i.e. boundary conditions") and then applies these to a climate model. The model in turn makes projections of the potential response to this particular configuration of the controls. The projections made by the climate model can then be passed to an environmental "sub-model" (e.g. a hydrological (Hostetler and Giorgi, 1993), or a vegetational (Prentice et al., 1992a) model). The output of these succeeding models is then compared with the available paleoclimatic indicators.
The climate model, as well as the environmental sub-models, do not need to be numerical models; conceptual models may also be used (e.g. Bartlein et al., 1991), although these are generally viewed as inferior to numerical models. One objective of the forward-modeling approach is to expose inadequacies in any model. This information could be then used, for example, to advocate replacement of a conceptual model with a numerical one, or to revise elements of the model or the assumed state of the controls.
In an example of this approach, Webb et al. (1987) used output from the paleoclimatic simulations produced by Kutzbach and Guetter (1986) to simulate the changing distribution of vegetation in eastern North America over the past 18,000 years, as represented by fossil pollen data. The paleoclimatic simulations were based on the CLIMAP Project Members (1981) reconstruction of sea surface temperatures (SSTs) and ice sheet size for the last glacial maximum (LGM). Although there was broad-scale agreement between the simulations and observations, for some locations and time intervals (i.e. the southeastern United States during the interval between 18 ka and 12 ka) there was a serious mismatch between the two. There are three potential sources of the mismatch: 1) misinterpretation of the fossil data, 2) model inadequacy, or 3) the specification of inappropriate boundary conditions. In this case, the discrepancy seems assignable to the third source, in specific through: a) the adoption of the CLIMAP SSTs for the ocean adjacent to North America--these show little difference from present, particularly in the Gulf of Mexico; and b) the inclusion of a very large ice sheet in the model, which resulted in the simulation of relatively high temperatures in the southeastern U.S. produced by adiabatic heating of air that descended from the broad dome of the ice sheet. Consequently the paleoclimatic simulations in the southeastern U. S. also differed little from present, leading to the particular mismatch that was observed. In this example, the comparison of simulated paleoecological responses with the observed provides information that can be used to enhance our understanding of the how the patterns recorded in the paleoclimatic data were generated.
Forward-modeling can also be iteratively applied in order to resolve apparent inconsistencies among different sources of paleoclimatic data. For example, Prentice et al. (1992b) were able to resolve the apparent inconsistency between the observations in the Mediterranean region at the LGM of steppe vegetation (signaling dry conditions), and high lake levels (signaling wet conditions). They combined a simple numerical model of the regional-scale water balance with a conceptual model of atmospheric circulation changes (based in part on numerical GCM simulations, Harrison et al., 1992). By perturbing the present climate of the region in a set of sensitivity tests with a water-balance model, they were able to find a plausible configuration of precipitation, evapotranspiration and runoff that was consistent with both the paleoclimatic data and simulations.
The indeterminacy problem is greatly reduced in the forward-modeling approach. By requiring the use of models (that usually must be sufficient to explain the present climate and in turn its influence on geological and biological indicators), the approach implicitly recognizes the multivariate nature of the controls of the different indicators upon which paleoclimatic reconstructions are based. For example, trade-offs between such large-scale controls of regional climates as atmospheric circulation and insolation might be evaluated using regional or mesoscale climate models. Similarly, the application of a hydrological model might reveal the relative importance of increased precipitation as opposed to decreased evapotranspiration in producing an inferred increase in effective moisture.
Another advantage of the forward-modeling approach is its potential for allowing comparisons between model simulations and paleoclimatic evidence in regions of sparse data coverage. Kutzbach and Guetter (1980) examined the role that the distribution of sites that register the response to large-scale controls has in reconstructing those controls. In their analysis, they examined the degree to which (controlling) sea-level pressure patterns could be estimated using a network of sites with observations of temperature and precipitation responses. They found that the level of explained variance of the pressure patterns was dependent on the uniformity, density and extent of spatial coverage of the temperature and precipitation sites. At "low" site densities (below those of late Quaternary fossil pollen sites in eastern North America or western Europe, and roughly equal to the density of late Quaternary sites from western North America), less than half of the variance of January sea-level pressure patterns could be explained. These results imply that where the density of sites with paleoclimatic evidence is low, it may not be feasible to recover by inverse modeling the nature of the proximate controls of the climatic variations recorded at those sites.
Forward-modeling, in contrast, permits the simulation of paleoenvironmental responses at a resolution determined only by the practical limits of application of the associated environmental sub- models. In other words, the forward-modeling approach could be used to generate, for example, a very high-resolution spatial pattern of vegetation types across a region, regardless of how dense the network of fossil pollen sites in that region is. Point-by-point comparisons between the simulations and observations could be made where fossil data is available. A more telling comparison would likely result from a subjective evaluation (in light of the observed fossil pollen data) of the predicted vegetation pattern.
The forward-modeling approach has the advantages of reducing the indeterminacy problem, and allowing paleoclimatic hypotheses to be tested even in regions of sparse coverage of paleoclimatic evidence. The inverse- modeling approach, although based on "observed" or "real," as opposed to simulated data, suffers from indeterminacy, and problems of applicability in regions of sparse coverage of fossil data. In summary, the forward- modeling approach can be applied over the entire domain of interest (e.g. North America), generating predictions of, for example, the past distributions of different taxa that can be tested wherever data does exit. The inverse-modeling approach can be usefully applied in those regions where data is sufficiently dense, multiple paleoclimatic are available, and the assumptions that underlie the techniques used are not violated. In such regions, the approach can provide quantitative reconstructions of past climates with relatively low uncertainties.
Dowsett et al. (n.d.) have compiled a data set of boundary conditions for the middle Pliocene that includes paleogeography, sea-surface temperatures, sea-ice and land-ice extents, and surface cover. These boundary conditions were then used by Chandler et al. (n.d.) as input to the GISS (Goddard Institute of Space Science) general circulation model (GCM), to produce a simulation of middle Pliocene climates. In the simulation of Chandler et al., the concentration of carbon dioxide in the atmosphere was kept at modern values, because they were not certain that CO2 concentrations during the Pliocene were greater than present. This "Pliocene" simulation can therefore be considered to represent a "non- elevated-CO2" portrayal of middle Pliocene climates. Another simulation with the GISS model, performed by Hansen et al. (1984), can be used to illustrate the response of the simulated climate to a doubling of carbon dioxide alone (i.e. without any other changes in boundary conditions). This "2xCO2" simulation can therefore be used to represent a Pliocene climate that differs from the present one only because of variations in the composition of the atmosphere. The extent to which either simulation can correctly reproduce the observed difference in vegetation between the middle Pliocene and present can then be used to differentiate between the two controls altered boundary conditions as opposed to elevated CO2-- in explaining the nature of the middle Pliocene climate. This example, although rather forced, does illustrate the general approach of using the forward-modeling approach to analyze the causes of past climates.
Relationships between the incidence of different plant taxa and climate are summarized here using response surfaces (Bartlein et al., 1986; Prentice and Solomon, 1991). Response surfaces for presence-absence data (as obtained from range maps) illustrate the probability of occurrence of a particular taxon at different locations in the climate space defined by the four climatic variables. Response surfaces represent a type of equilibrium (as opposed to dynamic) vegetation model (Prentice et al., 1993; Prentice and Solomon, 1991). Such models are appropriate for simulating the broad-scale distributions of plants under slowly changing climates.
The diagram shows sixteen two-dimensional slices through a four- dimensional climate space. Each slice shows the probability of observing P. mariana as a function of January and July temperatures for the specific values of January and July precipitation given in the margin. The probabilities are shown by shading, with the lightest shade indicating zero probability. Unshaded areas represent combinations of the four variables that do not occur over North America.
The response surfaces may be used to simulate the distributions of the different taxa under a particular climate by "plugging in" the values of the climate variables for each of the 25 km grid cells and then mapping the estimated probabilities of occurrence. In the examples here, the "Pliocene" and "2xCO2" climates that were input to the response surfaces consisted of the simulated anomalies (paleoclimatic experiment minus control) applied to the observed modern values on the 25 km grid.
The upper left-hand map shows the present distribution of P. mariana as digitized onto a 25-km grid from the range maps in Little (1971). The upper right-hand map shows the present distribution of P. mariana as simulated by plugging in the observed values of the four climate variables that define the response surface for this taxon. The probability of occurrence of this taxon at each grid point is shown by shading. The lower left-hand map shows the probability of occurrence of P. mariana as simulated by plugging in the climate values generated by the "Pliocene" simulation, and the lower right-hand map shows the probability of occurrence of P. mariana as simulated by plugging in the climate values generated by the "2xCO2" simulation.
Which of two climate simulations best reproduces these patterns? The simulated distributions of Picea for the "Pliocene" and "2xCO2" simulations are quite similar to one another. The distributions of Picea under both simulations advance at their northern edges, and there is a slight increase (although probably not significant) in Picea in the Northern Rocky Mountain. region in the "Pliocene" simulation. Both simulations seem consistent with the reconstructions (Dowsett et al., n.d.), and there is little to distinguish between them.
The simulated patterns of Quercus in eastern North America are quite similar under the two simulations as well. Both show a northward shift in the range of the Quercus, with the northward retreat of the southern range margin slightly greater under the 2xCO2 simulation. West of the Mississippi valley, however, the simulations are markedly different, with the "2xCO2" simulation showing a greater northward advance relative to present on the northern Great Plains, and the "Pliocene" simulation showing a greater incidence on the southern Great Plains and in the interior basins of the intermountain west, where steppe vegetation prevails at present. In eastern North America, as was the case with Picea, both simulations seem consistent with the reconstructions. In western North America, however, the high probabilities of Quercus under the "Pliocene" simulation seem inconsistent with the reconstructions.
The simulated patterns of Artemisia differ more overall between the two simulations than do the other taxa. Both patterns do show a decrease in the incidence of Artemisia, consistent with the reconstructions of less steppe and grassland during the Pliocene. Under the "2xCO2" simulation, the range of Artemisia is approximately the same as at present, while under the "Pliocene" simulation, the range and incidence maximum shift to the east.
Of the two simulations, the "2xCO2" simulation produces distributions of these tree taxa that seem more consistent with the vegetation reconstructions than does the "Pliocene" simulation. It should be pointed out that neither simulation (one with Pliocene surface boundary conditions, but no increase in CO2, and the other with increased CO2, but without Pliocene surface boundary conditions) should be considered to be a "full" simulation of Pliocene climates. It is also true that only three taxa have been examined, and simulations of other taxa could change the picture. In any case, this example shows the utility of the forward- modeling approach in comparing two climate model simulations.
In addition to testing specific paleoclimatic hypotheses, the forward- modeling approach can be used to discriminate among different climate models, or among different sets of boundary conditions for those models. In such an application, the sets of paleoenvironmental responses produced by the approach would be compared to syntheses of paleoclimatic data in order to identify which simulation was most consistent with the data. This type of application was illustrated here through an example of the simulation of three plant taxa by two different simulations of Pliocene climates for North America.