Climate Stabilization Targets: Emissions, Concentrations, and Impacts over Decades to Millennia (2011)

Models used in Section 2.1.

The UVIC model used here is ESCM version 2.8, which includes a 19-layer ocean general circulation model. The ocean model is coupled to a dynamic-thermodynamic sea-ice model and an energy-moisture balance model of the atmosphere. The land surface and terrestrial vegetation are represented by a simplified version of the Hadley Center’s MOSES land-surface scheme coupled to the dynamic vegetation model TRIFFID. Ocean carbon is simulated by means of an OCMIP-type inorganic carbon-cycle model (J. Orr, R. Najjar, C. Sabine, and F. Joos, Abiotic how-to document, 2000, available at http://www.ipsl.jussieu.fr/OCMIP) and a marine ecosystem model solving prognostic equations for nutrients, phyto-plankton, zooplankton, and detritus. The model has participated in a number of model intercomparison projects including the C4MIP, the Paleoclimate Modeling Intercomparison Project (PMIP), and the coordinated thermohaline circulation experiments. See Zickfeld et al. (2009) and references therein. The Bern model used in this study is the Bern2.5CC EMIC described in Plattner et al. (2008) and Joos et al. (2001); it is compared to other models in Plattner et al. It is a coupled climate-carbon cycle model of intermediate complexity that consists of a zonally averaged dynamic ocean model, a one-layer atmospheric energy-moisture balance model, and interactive representations of the marine and terrestrial carbon cycles.

Table 3.2 and associated discussion in text:

This section refers to two theoretical estimates of climate sensitivity carried out using realistic CO₂ and water vapor radiative transfer based

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.

Methods summary for food figure

Left-hand panel:

For broad regions, yield losses per ºC of local warming were taken from Figure 5.2 in the Working Group 2 reports of the Fourth Assessment Report of the IPCC (Easterling et al., 2007). These estimates include estimates of CO₂ effects but without explicit modeling of adaptation. The mean and one standard error for each level of warming were approximated from the figure. Local temperature changes were converted to global temperature levels using a value of 1.5ºC local per global ºC for mid-to-high latitudes and 1.2ºC local per global ºC for low latitudes.

Note that since several of these studies are based on experiments where climate is allowed to equilibrate with doubled CO₂levels, while others were taken from transient simulations (e.g., based on SRES scenarios), the CO₂levels for different amounts of warming likely varied by study, with the equilibrium studies likely underestimating CO₂levels for a given warming amount.

Right-hand panel:

Yield losses per ºC of local warming were taken from the following studies: U.S. maize and soybean (Schlenker and Roberts, 2009); Asia rice (Matthews et al., 1995); India wheat (Lal et al., 1998); Africa maize (Schlenker and Lobell, 2010). For each region, global temperatures were converted to local temperature change based on the patterns in Section 4.2. The yield effects of higher CO₂ were estimated based on a recent metaanalysis (Ainsworth et al., 2008). CO₂ levels for each temperature value were based on the values reported in Section 3.2, and assuming a ratio of CO₂ to CO₂-equivalent equal to the average of the SRES scenarios (ratio is 1.05 for 1ºC, 0.93 for 2ºC, and 0.8 for 3ºC and warmer).

Standard errors were estimated by propagating estimates of standard errors for (1) local temperature change for a given global temperature; (2) crop yield response to temperature; (3) CO₂ levels for a given global temperature; and (4) yield response at a CO₂ level. Propagation was done with the standard equations:

[1]

[2]

The shaded region in the figure corresponds to the likely range, which is defined as the 67% confidence interval or ± one standard error.

Figure 6.1 and associated discussion in text:

The very long-term warming in Figure 6.1 was computed on the basis of the CO₂ concentrations at 1,000, 5,000 and 10,000 years in the LTMIP ensemble of carbon-cycle models (Archer et al., 2009). The minimum, median, and maximum climate sensitivity from Table 3.1 was applied to each member of the ensemble in order to produce the range of estimated warming. Only ensemble members that included sediment dissolution feedback were used in the calculation, but the ensemble includes simulations with and without climate feedback on carbon uptake. Because the climate feedback invariably increases the long-term CO₂ value, the no-feedback case defines the lower end of the estimated warming, corresponding to a case in which the climate feedback on uptake is negligible. The upper end of the warming is underestimated in this calculation, because the climate feedback should increase when a climate sensitivity higher than that used in the carbon-cycle model is applied, but this effect was not taken into account because there was no reliable methodology for doing so within the ensemble of published results. The LTMIP ensemble states results for 1,000 GtC and 5,000 GtC cumulative emissions. Temperatures for intermediate values of cumulative emissions were obtained by interpolating log(CO₂) linearly in the cumulative emissions, based on the geochemical principles laid out in Caldeira and Kasting (1993).