The social cost of atmospheric release

The first component of the SCAR is climate damages that are proportional to global mean surface temperature change (equivalent to the traditional SCC). Global mean temperature changes are driven by the global mean radiative forcing (RF) caused by each emitted compound. RF for most emissions is based on the IPCC AR5 (Myhre et al. 2013). RF attributable to individual aerosol precursors including indirect cloud effects was not provided in AR5, and hence to incorporate this important component for SO₂, BC and OC I use a combination of modeling and literature analysis (Shindell et al. 2012a; Shindell et al. 2009; United Nations Environment Programme and World Meteorological Organization 2011; hereafter UNEP 2011; see ESM). The relative uncertainties in RF presented in the AR5 (Myhre et al. 2013) are used for all emissions. These uncertainties, and all others used here, are assumed to be 5–95 % confidence intervals (CI).

Forcing by non-CO₂ emissions includes a component driven by the response of the carbon-cycle to temperature changes induced by those emissions (as in the calculations for CO₂ itself) based on a reduced carbon uptake of 1 GtC per degree warming (Arora et al. 2013; Collins et al. 2013b). The uncertainty in this effect is taken to be equal to the magnitude of the effect itself (Collins et al. 2013b).

Temperature responses to forcings by each individual pollutant are calculated using the time dependence of the impulse-response function from the Hadley Centre climate model (Boucher et al. 2009). The magnitude is set to yield an equilibrium climate sensitivity (ECS) of 3.2 °C for doubled CO₂, consistent with the AR5 (Collins et al. 2013a). As valuation depends strongly on the transient climate response, uncertainty in sensitivity is based on the range in a recent study of the AR5 models (1.3–3.15 °C; (Shindell 2014)) relative to the mean of those models (1.8 °C, hence −28 %/+75 %; those models also exhibited a mean ECS of 3.2 °C).

Basic climate damages for all pollutants in the SCAR are then calculated from their impact on global mean temperature as in the SCC for CO₂. The SCAR calculations presented here use the DICE 2007 IAM damage function (Nordhaus 2008), which has damages proportional to the square of the temperature change and equal to 1.8 % of world output at 2.5 °C (see ESM for context). AR4 suggested that valuation of non-economic and economic impacts at 2.5 °C together contributed ~65 % as much uncertainty to the SCC as did climate sensitivity (Yohe et al. 2007). Hence I set the uncertainty of the damage function to 65 % of the mean uncertainty associated with climate sensitivity.

GDP increases at 2 ± 1 %yr⁻¹, as in SRES scenarios, giving a mean 2100 value of $355 trillion, consistent with USG 2013. Reference temperature change follows a business-as-usual trend with projected increases of 0.015 °C yr⁻¹ (as in recent observations). These gradually increase with time, then slow to 0.008 °C yr⁻¹ after the total increase exceeds 4 °C and the maximum tolerated warming is 4.5 °C assuming massive societal response to large changes (similar to the ‘backstop’ technology deployed in DICE for large temperature changes). The modeled time horizon is 350 years, but results are minimally sensitive to variations beyond ~150 years due to the warming limit. Uncertainty in the trend is ±0.005 °C yr⁻¹. Mean reference temperatures are ~3.8 °C greater than preindustrial in 2100, in accord with projections for the higher end emissions pathways in recent simulations (Forster et al. 2013). Values are presented for 2010 emissions in 2007 $US (as in USG 2013).

The discount rate is an important choice in valuation of future damages. USG 2013 gives 2010 SCC values using three different constant discount rates, 5, 3 and 2.5 %, based on results from several IAMs examining multiple scenarios for emissions, population, GDP, etc. I use the same discount rates to facilitate comparison and as these reflect the consensus view of the US government about which values reflect plausible choices. I also include analysis using a constant discount rate of 1.4 %, the value used in Stern (2006). Although discount rate selection is subjective, involving growth projections, risk aversion, and ethical choices (e.g. future utility), the large wealth increase with 2–3 % annual GDP growth is less compatible with very low discount rates. Therefore, for the 1.4 % discount rate case only, GDP increases at 1.3 yr⁻¹, as in Stern (2006), with an uncertainty of +0.3/−0.5 % yr⁻¹. Finally, authors have argued for the use of a declining discount rate (DDR) (e.g. (Arrow et al. 2013; Gollier 2008)), and I therefore also use a rate that starts at 4 % and decreases exponentially with a 250 year time constant (i.e. the percentage rate is 4*exp(−t/250) where t is the time in years) which approximates the mean behavior seen in several prior studies discussed in Arrow et al. (2013). Note that the framework employed here does not directly include any economic response to environmental damages other than the backstop assumption.

The traditional SCC includes economic impacts of premature mortality and morbidity due to climate change, with these climate-health impacts causing ~10–50 % of total damages in the IAM studies summarized in Nordhaus and Boyer (2000). The DICE damage function used here includes climate-health impacts attributable to tropical diseases only (see ESM). Recent estimates of climate-health impacts by the World Health Organization (WHO) (Campbell-Lendrum and Woodruff 2007) find large impacts attributable to other causes, however, especially malnutrition, with 126,000 premature deaths attributed to the current warming (~0.8 °C) via causes other than tropical diseases. I therefore perform additional climate-health valuation calculations using this estimate, assuming these effects are also proportional to the temperature change squared. Both the magnitude and long-term trend of climate-health impacts clearly merit further study, however. As WHO provides only qualitative uncertainties, I use an uncertainty of ±80 %, as for the composition-health impacts.

A consistent valuation methodology is used for climate-health and composition-health impact calculations. The WHO found climate-health damages, especially malnutrition, to be heavily weighted towards poorer developing nations (where carbonaceous emissions are currently large). Climate-health calculations therefore use a Value of a Statistical Life (VSL) of $1.7 million (for 2010), which is the nominal US-based VSL of $7.5 million adjusted to account for carbonaceous aerosol exposure- and population-weighted country-specific income differences from prior analyses (UNEP 2011).

Socio-economic projections affect the climate-health damages. The VSL increases along with per capita growth in GDP since it’s associated with the willingness-to-pay. As in basic climate damage calculations, GDP increases at 2 ± 1 % yr⁻¹. Increases in population are 0.4 % yr⁻¹, increasing the number of people exposed to health impacts while reducing per capita GDP increases. Baseline mortality decreases by 0.45 ± 0.45 % yr⁻¹, with the mean value matching the optimistic scenario of Mathers and Loncar (2006) and the range spanning their baseline scenario (~0 %) and the more optimistic trend (~−0.9 %) in Murray and Lopez (1997).

In the WHO analysis, ~46 % of premature mortalities due to climate change are attributable to malnutrition. Agricultural responses to climate change are expected to be highly sensitive to CO₂ fertilization effects on plants (Yohe et al. 2007). In particular, ~3–10 times more people are at risk from hunger under future scenarios (across the high SRES A1F1 and low B1) when the beneficial effects of CO₂ fertilization at their maximum estimated effectiveness are excluded (Parry et al. 2004). I assume a mid-range effectiveness with 3 times more malnutrition cases for warming without CO₂ fertilization, and an uncertainty of 100 % so that the maximum (6 times more) is consistent with the central portion of the above estimate and the minimum excludes any fertilization effect. Since positive historical non-CO₂ RF has been largely offset by negative aerosol forcing, I assume the current WHO analysis includes CO₂ fertilization. Therefore, the climate-health effects of non-CO₂ emissions associated with malnutrition (46 %) are multiplied by 3 ± 3 to account for the CO₂ fertilization effect.

Multiple climate modeling studies have shown that both scattering and absorbing aerosols induce strong regional hydrologic cycle changes (e.g. (Levy et al. 2013; Ramanathan and Carmichael 2008; Wang et al. 2009)), and that there is typically a substantially greater precipitation response per unit RF than for well-mixed greenhouse gases (Shindell et al. 2012a, b). As many impacts are closely related to regional changes in precipitation that directly affect water and food, attribution of damages solely to temperature may be a less accurate approximation for regionally highly uneven forcings. Therefore, I include additional impacts stemming from regional disruption of the hydrologic cycle for aerosols.

I assume all precipitation changes lead to net damages as they cause shifts relative to traditional patterns to which human systems are aligned. These shifts can also alter the intensity distribution (e.g. wet areas getting wetter and dry areas drier (Held and Soden 2006)), potentially leading to more extremes either directly (Portmann et al. 2009) or indirectly via teleconnections (Kenyon and Hegerl 2010), which would again lead to damages even in cases where changes in mean precipitation could be beneficial. Hence I assign damages to both scattering aerosols and absorbing BC even though the sign of their impact is sometimes opposite. It is difficult to estimate precisely what portion of the climate-related damages is due to precipitation changes. Even for a particular impact such as human health, temperature and precipitation both play important roles by influencing malnutrition, vector borne diseases, etc. (Campbell-Lendrum and Woodruff 2007). I attribute 50 % of the climate-related damages to precipitation changes, and increase these by a factor of 4.2 for aerosols based on the mean ratio in prior modeling (see ESM). The portion of the global climate response attributable to carbon-cycle feedbacks is excluded. I assume this aerosol enhancement has an uncertainty of ±50 % of its mean value.

Premature deaths attributable to chronic PM_2.5 (particulate matter with a diameter less than 2.5 μm) exposure are calculated using the total current outdoor PM_2.5 impact on human health (3.2 million premature deaths annually (Lim et al. 2012)) and total current emissions, with the fractional contribution of each individual aerosol type given by the fractional contribution of each to population-weighted annual average surface PM_2.5 calculated on a worldwide 0.5 × 0.5° grid (UNEP 2011; Shindell et al. 2012a). Valuation uses the current global mean population- and PM_2.5 exposure-weighted VSL of $3.05 million, calculated using the same model and methods as for the climate-health VSL (UNEP 2011) (see ESM).

Impacts of methane on human health (via ozone) are drawn from results of two global composition-climate models (Shindell et al. 2012a), whereas impacts of CO and NO_x on health via ozone are drawn from one of those models (GISS). Impacts use population- and exposure-weighted country-specific VSL for the ozone-health impact calculated for each pollutant. I account for the time-dependence of the ozone response to methane and CO emissions, and thus these are affected by the discount rate and projected GDP and baseline mortality, which are the same as for climate-health impacts.

The uncertainty is ±80 % for the composition-health impacts based on uncertainty in the epidemiological concentration-response functions and differences in the modeled concentration response to emissions changes (UNEP 2011; Anenberg et al., 2012).

Impacts of methane on agriculture via the induced change in surface ozone are also included. These are incorporated based upon prior work using (1) the surface ozone response to methane emissions changes from two global composition-climate models, (2) the impact of ozone on yields of four staple crops, wheat, maize, soy and rice, based on the methodology of Van Dingenen et al. (2009), and (3) their valuation using world market prices, as described in Shindell et al. (2012a).

The calculations include the specified uncertainties associated with 11 factors, as discussed throughout this section: RF, climate sensitivity, carbon-cycle response to non-CO₂ forcing, damage function, regionally enhanced precipitation response to aerosols, climate-health, composition-health, baseline mortality projections, effects of CO₂ fertilization on agriculture/malnutrition, GDP projections, and reference temperature projections. I perform Monte Carlo calculations sampling each source of uncertainty randomly within its distribution. I present the median and the 5 and 95 % confidence levels from a 40,000-member sample (the median is lower than the mean owing primarily to the asymmetric distributions of climate sensitivity and GDP growth in real terms). Uncertainty attributable to individual factors is presented in the ESM.