For a change of pace I have added Marcel Leroux's Global Warming - Myth Or Reality? to my bedtime reading. I don't recall why I chose this particular climate book from the shelf, but it is published by Springer, a publishing house respected by most mathematicians. In general it is difficult for an outsider to establish the reliability of a putative expert in a distant field. In fields in which I have some expertise, I frequently see the media promote extremely marginal scientists as expert spokesmen. Given the extent to which climatology appears to foster charlatanism, I am wary of all authors in the field.
I was especially eager to read Leroux's treatment of climate modelling. I have already written on why mathematicians are wary of the computer simulations responsible for the alarmist gloom and doom scenarios which lead so many people to advocate wrecking the world economy, abandoning democracy if necessary, in order to limit CO_2 output. My post on this subject dealt only with those universal features of the simulations that one could address without delving into the details of the models. I hope Leroux will shed more light on the nuts and bolts of the models.
Leroux's treatment of models (Chapter 7 of his book) is tinged with an antipathy to models qua models, which I consider misplaced. My objections are simply to the abuse of models. Leroux does provide us with more information about the models and their defects, although I assume that details such as grid sizes change monthly or yearly. I will rephrase and repackage Leroux's more coherent criticisms into a more mathematical framework.
Computer simulations of climate phenomena require dividing the atmosphere into a collection of volumes known as cells and assigning numerical data to each cell representing 'average' climate data for that cell for some time interval. At the time Leroux was writing, typical cell size ranged from hundreds to tens of thousands of cubic kilometers. He does not mention the typical time interval involved. Obviously, the smaller the cell and time step, the more reasonable is approximation of the climate within by some average. Ever increasing computer power is the only inherent limit on the number and therefore the size of the cells. Ideally, we would like to start with some initial approximate climate state, and compute the approximate evolution of the system by numerically approximating the solutions to the complex nonlinear fluid dynamics and other equations governing the system. Any phenomena which take place at smaller time or space scales than the time intervals or cells of our simulation cannot be modelled. Of course one can model such phenomena with a simulation adapted to the given phenomenon. Thus one could not use a simulation designed to model a century of global climate evolution to model the path of a hurricane. Instead, one uses a model adapted to the time and space scale of the hurricane, and corrects the simulation with new information several times a day.
In addition to errors arising from cell size and absence of real world initial data, climate evolution includes too many interactions to include in a realistic deterministic model. For example, the quantity of the main greenhouse gas, water vapor, depends on temperature, pressure, particulate matter, surface water, plant respiration, etc. These do not all admit simple modelling with numerical partial differential equations. Those features which are too complex for current deterministic models are ignored (the most honest path) or added into simulations by ad hoc mechanisms. These latter admit fine tuning to reach any desired conclusion.
Another source of error in simulations is the fact that the earth is not a closed system. Time varying solar radiation is the fundamental driver of our climate, but I am unaware of the existence of climate models that include realistic simulations of the complex dynamics of the sun's nuclear reactions.
Leroux appears to be bothered by the deterministic attitude of the climate modellers, a concern which I do not share. It seems reasonable to me that the extremely complex large scale dynamics of our climate stem result from small scale fundamental physical and chemical processes. Nonetheless, it is clear that since current climate models that are adapted to short time predictions are only crudely accurate for a few days, long term predictions have no value.
The more of Leroux I read, the less reliable he appears. His logic is generally quite poor. He frequently points out some weakness in the arguments of proponents of anthropogenic global warming, and then immediately concludes that CO_2 does not cause global warming, when, in fact, he has only countered an argument in support not actually presented an argument against. He also has a worrisome single factor explanation for most features of our climate. All phenomena of interest can be explained (according to Leroux) by his contribution to climatology: mobile polar highs. I have checked out a few books on atmospheric physics to make myself somewhat better able to analyze his claims. From my currently inexpert position, many of his assertions seem to be the atmospheric equivalent to the assertion that water runs down a mountain into a valley because the mountain is higher than the valley, and not because the valley is lower than the mountain. Such a distinction makes no sense to me; so, I need to learn more. Fortunately climate books are much lighter reading than math books, and hence can be read before bed without stimulating the brain enough to interfere with sleep.