on the NCAR Community Climate Model radiation code, but employing an idealized vertical profile of temperature and humidity. The general approach is the same as that outlined in Chapter 4 of Pierrehumbert (2010). The temperature profile consists of a moist adiabat patched on to an isothermal stratosphere. The stratospheric water vapor mixing ratio was assumed vertically uniform, at a value equal to the mixing ratio at the tropopause. For the case of fixed water vapor content (no water vapor feedback) the tropospheric water vapor mixing ratio was held fixed at a value corresponding to 50% relative humidity computed for the unperturbed temperature. For the case including water vapor feedback, the mixing ratio was allowed to increase with temperature so as to hold the tropospheric relative humidity fixed at 50%. In both cases, the radiation calculation was done for clear-sky conditions.


The steps of the analysis, which we applied to the grid point scale, are:

  1. From the 22 CMIP3 models’ runs available for 20C3M we extract annual values of average TAS in June-July-August and December-January-February.

  2. We then form anomalies from the 1971-2000 mean and compute their distribution (i.e., a set of quantiles).

  3. We choose a high quantile (95%, 100%) as benchmark against which to evaluate the change in likelihood of exceedances in a warmer climate.

  4. We then superimpose spatial patterns of change in seasonal average temperature derived through pattern scaling for a series of representative changes in global average temperature. (Pattern scaling gives us a robust geographical pattern of seasonal temperature changes that scales linearly with values of global average temperature.) For each choice of global average temperature change, this will shift uniformly the quantiles of the distribution to the right. In our example below we choose additive patterns corresponding to 1ºC, 2ºC, and 3ºC global average warming.

  5. We finally compute what fraction of the newly derived distribution lays to the right of the chosen threshold/benchmark.

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