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Markwick, P.J., Paul J. Valdes, Bruce Sellwood, Raymond T. Pierrehumbert (1999) 'Equability' in an unequal world: the early Eocene revisited Proceedings. Early Paleogene warm climates and biosphere dynamics, Göteborg, Sweden Abstract The Mesozoic and early Cenozoic are often referred to as "hot-house" worlds in reference to the interpreted greater warmth of these intervals, relative to the Recent, and the lack of appreciable polar ice-sheets. Synonymous with this warmth is the interpretation of thermal 'equability,' which computer climate modelling experiments have consistently had problems replicating, especially in mid-high latitude continental interiors. In this study we re-examine the Early Eocene "hot-house' world using two different General Circulation Models (GCMs): that of the UK Universities Modelling Project (UGAMP) and the more recent Hadley Centre GCM (UKMO). GCM's provide the best means of understanding the dynamics responsible for past climates, but can only be assessed for their veracity through comparisons with observations, which for palaeoclimate means the geological record. Palaeoclimate interpreted from geological data is invariably based on analogy with the Recent, the validity of which depends on corroboration from multiple lines of evidence. This requires the compilation and investigation of large, global datasets of well-constrained geological climate proxies. However, in too many data-model studies comparisons are qualitative: for example, a modelling experiment is considered successful if a 'warm' prediction coincides with a climate proxy that indicates 'warmth'. But while the qualitative comparison of model results against observations provides a broad indication of model success, or otherwise, there is a need for a more quantitative approach. Here we utilize a method derived by one of us (PJM) in which model results and data are directly compared one with another. In order to illustrate this method we concentrate on only one proxy (fossil crocodilians), while recognizing that it is only through intercomparison between the interpretations from multiple and diverse climate proxies that we can more confidently 'ground-truth' modelling experiments. The climate space defined by modern crocodilians has been found to be delimited by a minimum coldest month mean temperature (CMM) of 5°C and the presence of water bodies. Today this coincides with a mean annual temperature (MAT) or about 16°C, but whether this is also true for the past cannot be assumed. The method is as follows. First, the climate space occupied by each climate proxy is defined for the Recent, using a dataset of 1060 globally distributed climate stations: each proxy is 'recorded' for all climate stations that fall within the present geographic distribution of that proxy. Then the geological occurrences of each proxy (in this study, fossil crocodilians) are overlain onto the gridded GCM output, and for each proxy location the model output value extracted. These values are then replotted in climate space where they can be directly compared with that based on the present day (for this study of 'equability' that climate space is plotted on a graph of MAT versus mean annual range of temperature, MART; CMM can be illustrated on the same diagram). A statistical comparison between the distributions can then be made (using the Mann Witney non-parametric test, for example), although account must be made of differing sampling densities, given that the comparisons are made between recent and fossil records. This method also facilitates model-model comparisons: the position of fossil crocodilians for each GCM run are plotted in the same climate space and a vector drawn between corresponding crocodilian localities. This vector is then a measure of the difference between model results. For the current study we have used ArcView GIS Spatial Analyst for extracting the GCM values for each proxy location, which has the advantage that the underlying palaeogeographic context of the data can simultaneously be displayed, and StatView and StatisticaMac for the statistical analysis of results. Our results show the following. For both models about half of the Early Eocene fossil crocodilian localities fall outside of the climate space defined by modern crocodilians. These fossil localities are concentrated in mid-latitude continental settings, where the modelled CMM's are <5°C. This suggests that both models are underestimating CMM's in these areas. This may be due to a number of reasons including errors in specified GCM boundary conditions, such as incorrect orography (that CMM is too low in mid-latitude interiors might be due to the orography being too high), land-sea distribution (under-estimating seaway extents), or vegetation. Alternatively they may be a product of the model resolution (areas such as the Green River Basin, although low themselves, are surrounded by mountains that may bias the model). However, similar discrepancies are observed when this method is applied to GCM experiments of the Recent, which suggests a more systematic problem in the way these GCM's may be dealing with the mid-latitudes. The results for MAT and MART may indicate a further explanation. While the majority of fossil crocodilian sites in the UGAMP model fall within the MAT limits observed for the Recent (>16°C), in the UKMO results the majority fall below this limit. Paradoxically, the vector mapping (the vectors joining the different model results for the same crocodilian locality) indicates that not only are the annual UGAMP results 'warmer' than those of the UKMO model, but that the MART's are also greater (less 'equable'). This is contrary to the usual equation of greater warmth and increased thermal 'equability.' It is suggested the high MART values in the UGAMP model probably reflects the model's overall "dryness", which exacerbates summer warmth and winter cold. The better parameterization of moisture in the UKMO model therefore results in the lower MART values. But increased evaporation also has the effect of lowering temperatures (lower MAT). The fact that the results for CMM, MAT and MART do not follow the same relationships as observed in the Recent, highlights the need to distinguish between an actual limiting climate parameter (for crocodilians, CMM) and an autocorrelated metric (in this case MAT and MART). The methods and results outlined here further indicate the importance of using the Geological Record as a means of testing climate models, while further aiding our understanding of past climates.

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