Climate Modelling and the Cold Continental Interior Paradox of Greenhouse Worlds

The principal tools for predicting future climate change are climate models. The most sophisticated versions are called general circulation models (GCM). These models attempt to simulate climate and climate change, starting from the basic physical laws which govern fluid motion. These include Newtons Laws of motion and the first and second laws of thermodynamics. For the climate system, these equations can not be solved exactly, but require a number of approximations. Many of these approximations are well justified and clearly have not changed in the past and will not change in the future. An example of this type of approximation is to assume that the atmosphere is an ideal gas. This approximation is a reasonable one, except perhaps for the very earliest primordial atmosphere. However, there are other approximations that are more uncertain yet potentially crucial for climate.

Many of the uncertainties in climate models arise from the method for solving the governing equations. Even with the largest computers, the equations can only be solved on a relatively coarse grid. The spacing of this grid is typically a few hundred kilometres yet there are many processes which are potentially important for climate but which act on scales smaller than the grid. Some of the most obvious examples of this include clouds, convection, and the coastlines (Fig.1). Their effects are of fundamental importance for climate and cannot be ignored. Therefore GCM's attempt to include these processes, based partly on an understanding of the physics of the process but also in part based on empirical studies of present day climate. This is called parameterisation and is the principle cause of uncertainties in modelling climate.

Figure 1. Top - modern day coastlines as seen at the grid scale of a typical palaeoclimate GCM with topography.

Bottom - mid Cretaceous (95 million years ago) coastlines and topography.

Again it is useful to illustrate the problems of parameterisations with a concrete example. Clouds play a vital part in the basic energy balance of the climate. They are highly reflective and thus act to reduce the amount of absorbed incoming solar radiation, effectively acting to cool the Earth system. Clouds also absorb outgoing longwave radiation and thus limits the amount of cooling. Observations from satellites indicate that the magnitude of these effects are very important and cannot be ignored (and that currently the net effect is to cool climates). However clouds are generally a lot smaller than the model grids and therefore have to be parameterised. Typical cloud parameterisations consider the physical processes responsible for cloud formation, such as large scale ascent of warm, moist air and it is possible to devise a cloud parameterisation scheme based on these resolved dynamics. Alas, at the large scale, resolved physics cannot "close" the problem and there are a number of semi-empirical constants which can only be based on observations. In this sense, climate models are based on the present state of the climate system.

Further, the reflectivenes of clouds depends on the total cloud amount, and also the size (and type) of the water droplets, and the warming effect of clouds also depends on cloud height. Thus a "perfect" climate model would require treatment of spatial scales from global to microphysical. A crude calculation suggests that to explicitly encompass all of these scales would require computing power many orders of magnitudes greater than currently available (as much as 1040 times present speeds). Thus even with the phenomenal growth of the power of computers, we will not achieve such feats for many decades. Therefore the conclusion is that climate models will always have a degree of uncertainty and will be based, in part, on our observations of the present climate system. If we are ever to have confidence in climate models, it is essential that these models are tested against climate regimes different to the present.

The recent geological past (the last 100,000 years) provides one possible period for testing models and there is an extensive literature on this subject. However, climates during this period were either cooler than present (e.g. the last glacial maximum at 21,000 years ago) or were seasonally warmer by a few °C. By contrast the distant past, and especially the Cretaceous, is thought to have been significantly warmer than present and hence provides a demanding test of the climate models in a warm climate regime. Estimates of atmospheric CO2 concentration suggest that levels were high (typically 4 x present values) and hence the Cretaceous warmth has potential parallels with possible future climate change. Direct comparisons between the Cretaceous and the future are not valid because CO2 is not the only climatically important change. The continents and mountains are also substantially different. Therefore the Cretaceous should not be used as a direct "climate analogue". Instead, the climate proxy data can be used to test the same climate models that are used to predict the future.

To simulate the Cretaceous climate, and more specifically the Cenomanian, a number of input parameters (so called boundary conditions) are needed for the models. These are either external processes, or those processes which act on very long time scales. These include:

1. The solar constant which is thought to be approximately 0.5% less than present. This has generally been ignored in GCM simulation of the period. Simple energy balance models would suggest that a 0.5% decrease would result in approximately a 0.5-1oC globally cooler climate.

2. The orbital parameters are specified, but sensitivity experiments using different values can be performed to investigate the likely effects of changes of these parameters. It is currently not possible to calculate orbital variations beyond the last 5 million years and hence typical sensitivity experiments use estimates of extremes of the orbital parameters, based on recent experience.

3. The palaeogeography and orographies are required. In particular, an atmospheric model requires knowledge of the coastlines and the mean height of the mountains. Some more recent climate models also require estimates of the sub-grid scale variability of the mountains. Ocean models require detailed bathymetry.

4. Atmospheric CO2 (and other radiatively active gases) also need to be specified. Estimates of CO2 concentrations are generally based on the geochemical model of Berner. Other radiatively active gases (such as CH4 or NO2) are generally not included because of insufficient knowledge, but error bars associated with their potential effect can be estimated if desired. Atmospheric O3 (and O2) are assumed to have the same concentration as today. Water vapour concentrations are "fast" physics and thus are predicted by the model. In practice, the importance of the CO2 depends on the treatment of the oceans. If sea surface temperature is specified, then the climate model is remarkably insensitive to changes in most radiatively active gases.

5. Surface type (such as forest, grassland, or ice sheet) is also required because it effects the amount of reflected solar radiation, as well as the exchange of momentum, heat and moisture between the surface and the lower atmosphere. Ice sheets are particularly important because of their highly reflective nature. Models predict the seasonal distribution of snow (and sea ice) but an ice sheet can take many thousands of years to grow and is therefore "slow" physics which requires to be specified. For the Cretaceous, the evidence suggests that there were no permanent ice sheets and thus no ice sheet are included within the models. The distribution of vegetation can be specified or predicted.

6. Finally, the treatment of the oceans must be considered. The ideal is to simulate the ocean as well as the atmosphere. However for an accurate treatment of the oceans, a good knowledge of the bathymetry is required. Simulations of the present day ocean circulation (and especially the Atlantic thermohaline circulation) suggests that the ocean bathymetry is required to greater accuracy than the terrestrial mountains. The ocean can be very sensitive to extremely small features (such as the opening of the straights of Gibraltar or the closing of the Panama isthmuth. In contrast the atmosphere has no obvious threshold-like behaviour and so detailed orography is not quite so important.

To model the oceans, a further problem exists. The ocean requires knowledge of the heat and fresh water flux at the surface as well as the surface wind stress. For the Cretaceous, these can only be specified from knowledge of the atmosphere based on climate models. An atmospheric model requires the sea surface temperature and thus the only way to completely model the oceans is to couple an atmospheric GCM to an oceanic GCM. This is currently at the limits of our modelling ability. Even for present day climate there are a number of problems, let alone simulations of the Cretaceous oceans. Not least of the problems is the large timescale for the ocean to come into equilibrium. For this reason, simulations of Cretaceous oceans should be viewed as tentative only.

An alternative approach is to use a highly simplified ocean model and to specify the horizontal heat transport within the ocean. In such models, the ocean is represented as a "slab" of water typically 50m thick and this warms and cools depending on the atmospheric models prediction of heat exchange and the amount of ocean heat transport. Thus the "slab" model only considers the thermodynamic properties of the mixed layer of the ocean. The advantage of this approach is that it is computationally cheaper than the full ocean GCM yet the model is still predicting sea surface temperature. The disadvantage is that there is no observational basis for choosing the ocean heat transport in the Cretaceous and hence most simulations to date have based their ocean heat transport on present day conditions. Such a method means that this type of model is heavily constrained towards the present.

For this reason, a number of authors have chosen to specify sea surface temperatures, rather than ocean heat transport. These temperatures can be based on oxygen isotope estimates and therefore, at least in part, can be justified. In addition, sensitivity experiments can examine the importance of the assumption. It should be emphasised that the atmospheric model does not need to know how the surface temperatures arise (i.e. what were the ocean circulation). All that the atmosphere needs is the sea surface temperature. However after the simulation is completed, it is possible to examine the total energy balance of the model. If the sea surface temperatures are reasonable, then the amount of net incoming solar radiation should exactly balance the net outgoing longwave radiation. If it does not balance, then either the sea surface temperature or radiatively active gases are incorrect.

The above list gives the impression that the resulting predictions of Cretaceous climate will be highly uncertain because of uncertainties and lack of knowledge of the appropriate boundary conditions. To illustrate that there are some robust features, we show results from a Cenomanian simulation using the GCM of the UK Universities Global Atmospheric Modelling Programme (UGAMP). This is a typical GCM and is relatively high resolution. The boundary conditions are (1) present solar constant, (2) present day orbital parameters, (3) coastlines and orography based on Smith (pers. comm.), and see fig.1. (4) atmospheric CO2 concentrations 4 x present day values, (5) uniform shrubland everywhere, no permanent ice sheets, and (6) a simple zonally symmetric sea surface temperature given by 27 x cos (latitude), loosely based on oxygen isotope estimates. This results in tropical temperatures being very similar to the present, but with mid and high latitudes much warmer.

Figure 2 shows the prediction of January and July monthly mean surface air temperature and fig.3 shows the corresponding precipitation maps. Winter continental temperatures drop to below zero in N.America, Northern Eurasia, and Antarctica. In the Northern hemisphere, there is a particularly cold spot in the east which is related to high orography. However even if this were removed, there would still be a large region of below zero temperatures. Similar considerations apply to the other regions, in that orography plays only a small part in the cold continental interiors. The mean annual range of temperatures is generally considerably smaller than the present, but remains substantial. Over the Eurasian continent, the range of temperature is of the order of 40oC (c.f. nearer 60oC for the present day). Such ranges of temperatures, and especially the cold month temperatures appear to be inconsistent with the geological data.

 Figure 2. A - July monthly mean surface temperatures (2m above ground level) for the Cenomanian (95 million years ago).

B - January monthly mean surface temperatures for the Cenomanian.

The precipitation patterns show a number of very clear features. The tropics are dominated by a narrow Inter Tropical Convergence Zone (ITCZ), and with strong precipitation over land occurring during the summer (monsoon) season. The peak values of rainfall are larger than the present day equivalents, and is this is associated with the generally warmer climate (a warmer atmosphere can hold more water vapour and this generally results in increased rainfall). However over tropical South America and South Africa, the winter seasons are much drier. Therefore most of the tropics experience a very seasonal climate with the wet season being marked than present day, but with a pronounced dry season.

Figure 3. A - July mean monthly precipitation for the Cenomanian. B - January mean monthly precipitation for the Cenomanian.

On each side of the ITCZ there is a dry region which can be associated with the descending branch of the Hadley cell. It is most clearly delineated in the winter hemisphere, as in the present day. Further North, the mid-latitude storm belt is clearly seen in the winter hemispheres. The warmth of the mid and high latitudes in the Cenomanian results in these regions being a lot wetter than the equivalent present day locations, even though the temperature gradients are reduced.

The cold winter temperatures result in heavy snow cover and a key question is whether the summers are warm enough for the snow to melt in the subsequent warm summer. Figure 4 shows the predicted seasonal snow depth. It can be seen that in the both hemispheres, winter snow totally melts in the summer. Thus the model is predicting no permanent ice caps in the Northern hemisphere, although we cannot discount the possibility of a few mountain glaciers (which cannot be resolved in the GCM). In the Southern hemisphere, closer examination shows that the snow is present in December but not in January or February. Thus the model is very close to predicting an ice sheet in the Southern hemisphere, although it should be cautioned that the GCM does not include a proper representation of the compaction of snow into ice and hence the gradual formation of an ice sheet and this could effect the speed of summer melting. The nearness of a permanent snow cover also suggests that for orbital parameters with cool southern hemispheres, then the development of an ice sheet is extremely likely.

Figure 4. A - Mean July snow depth for the Cenomanian. B - Mean January snow depth for the Cenomanian.

The results above can be usefully summarised in terms of a simple climate classification scheme. Here we use a simplified Koppen scheme ( Fig. 5) which can be associated with biome types. However, extreme caution should be used in linking to the biomes because, as discussed earlier, there are some climate regimes which have no parallel in the present, such as seasonally dry rain forests.

 Figure 5. Modified Koppen scheme showing major biome types for the Cenomanian.

The results shown above are similar, but not identical, to previous simulations using the NCAR Genesis model. In particular, the UGAMP model appears to be somewhat warmer and more equable, especially at high latitudes in winter. One of the major differences between the two models is that the Genesis model included a simple slab ocean model as described earlier. We therefore have repeated the simulation but included a slab ocean model within the UGAMP GCM. With this addition, the simulated temperatures increase by approximately 1.5°C, and with an amplification at high latitudes. There is substantial warming (fig 6) in both hemispheres during their winter (up to 8°C) but considerably smaller changes, and even some cooling in summer. The generally warmer climate is because the original simulation was not in energy balance. More solar energy was being received than longwave radiation was being emitted. The net imbalance resulted in warming once the sea surface temperatures were allowed to vary. The conclusion is that the slab ocean version of the UGAMP GCM is more equable than the specified sea surface temperature, and has only exacerbated the apparent differences between the two models.

Figure 6. Temperature differences between a UGAMP model run using a simple specified sea surface temperature (A) and a slab ocean (B) for the Cenomanian.

One interpretation of this result is that there are some potentially big differences between climate model simulations. However, the two simulations did not use exactly the same boundary conditions. It is therefore of interest to try and evaluate the magnitude of the differences between models using exactly the same boundary conditions. We have performed a simulation using the Hadley Centre model from the UK Meteorological office. This model is widely used for future climate change simulations but has not previously been used for pre-Quaternary work. It is approximately the same spatial resolution as the UGAMP model. We used the same boundary conditions in both models and imposed a relatively warm SST based on the sea surface temperature from the UGAMP slab ocean run.

The resulting temperature predictions are shown in fig. 7 for the UGAMP model, and fig. 8 for the Hadley centre model. The regions of sub-freezing temperatures are very similar but the extent of the cooling is more dramatic. The Hadley centre model is colder by more than 12°C in some regions. Tropical regions are also colder, by a similar amount. Such substantial differences are bigger than the intermodel differences seen for the present day (AMIP reference needed) which suggests that the GCM's have all been "tuned" to get good present day climatologies but have profoundly different climate sensitivities. Unfortunately, there are many differences between the two climate models and a definitive explanation will be difficult to achieve. However, examination of the surface energy balance suggests that the principle differences arise from the treatment of clouds and the surface parameterisation. In the UGAMP model, the soil dries out much more rapidly than in the Hadley Centre model.

Figure 7. Cenomanian surface temperature predictions using the UGAMP GCM. A - mean monthly July temperatures. B - mean monthly January temperatures.

Figure 8. Cenomanian surface temperature predictions using the Hadley Centre GCM. A - mean monthly July temperatures. B - mean monthly January temperatures.