## Temperature

We will begin with estimates of the climate sensitivity, AT2x. The IPCC Third Assessment Report (2001) (IPCC as an organization is described in Chapter 13) reports that the mean of the climate sensitivity, AT2x, of 15 climate models is 3.5°C. The standard deviation of the climate sensitivities, denoted by the Greek letter sigma (a), is 0.9°C.

A standard deviation describes the variability or spread of a list of numbers, in this case model AT2x values. If the values are distributed in a normal "bell" curve, then the meaning of the standard deviation would be that 63% of the AT2x estimates should fall within 1a of the mean (in this case ±0.9°C), and about 95% of the estimates would fall within 2a (± 1.8°C). The statistics imply that with 95% certainty, a new estimate of

AT2x, such as from some new model, should probably fall between 1.9°C and 4.1°C. This range of model results in one measure of how well we can forecast the future.

Another approach to estimating how well we know A T2x uses a bit more brute force. Climate models have knobs, numbers that are not known precisely which affect the behavior of the model. These numbers are called tunable parameters. Cloud droplets, for example, do not form immediately when the relative humidity exceeds 100%. They may start forming at 110% relative humidity, or 120%. The best value of this parameter to use in a model is not known precisely. It varies from cloud to cloud, no doubt. Our model does not resolve all of the processes that would enable it to predict cloud droplet formation. The model must be told what value to use.

A brute force method for estimating the uncertainty in the model forecast is to run a climate model many times using a range of values of many different tunable parameters, varying multiple parameters at the same time. Climateprediction.net uses donated "screen saver" computer time to tackle this job. Each set of model parameters was run multiple times, with slightly varying initial conditions, to generate an ensemble (Chapter 7). Stainforth et al. (2005) analyze over 2000 model runs, over 100,000 years of model time. The URL for this project is www.climateprediction.net. Perhaps you would like to contribute to the effort yourself.

The distribution of model runs is shown in Fig. 12.1a. Most of the model combinations predicted a AT2x of about 3.4°C. There is a long "tail" to the distribution (this is not a normal "bell" curve), with a few very high AT2x estimates, ranging to 11°C. On the other side, there were very few parameter settings that came up with A T2x of much less than 2°C.

Each run included a control period, where CO2 concentration remains constant, and a period with doubled CO2. The climate of the control period was compared with meteorological data, and all the misfits added up into a single number. The misfit numbers from the runs are compared with the errors of a hand-tuned ("standard") model run. The misfits from the low-AT2x models tended to be a bit higher than the error from high-AT2x models (Fig. 12.1b) but none of the errors was bad enough to declare any of the models to be obviously wrong.

Uncertainty in A T2x is only the beginning of the uncertainty in the temperature forecast for the coming century. AT2x gauges the equilibrium response to doubling CO2, but it takes quite some time for the climate system to reach equilibrium. Predicting the temperature in the year 2100 requires modeling what is called the transient response. IPCC uses a standard benchmark for comparing the transient responses of models, which they call Transient Climate Response (TCR) and define as the model temperature at doubled CO2 concentration when the CO2 has been rising at a rate of 1% per year (Fig. 12.2). Real atmospheric pCO2 itself is not rising at 1% per year, but the idea is to raise CO2 a bit faster, to account for the greenhouse forcing from methane and other greenhouse gases. If the radiative forcing in the future doesn't go up as fast as 1% per year, then the TCR would be more appropriate to compare with the radiation = doubled CO2 year, whatever year that turns out to be. The average TCR values from 20 models is 1.8°C with a standard deviation of 0.4°C.

Climate takes a long time to change, that is to say, it has a long transient response to the change, in part because the ocean stores a lot of heat. During this time when we are