Climate-change impact potentials as an alternative to global warming potentials

There are at least three different kinds of climate-change impacts (Kirschbaum 2003a, 2003b, 2006, Fuglestvedt et al 2003, Tanaka et al 2010) that can be categorized based on their functional relationship to increasing temperature as:

• (1)  
  the impact related directly to elevated temperature;
• (2)  
  the impact related to the rate of warming; and
• (3)  
  the impact related to cumulative warming.

2.1.1. Direct-temperature impacts

2.1.2. Rate-of-warming impacts

2.1.3. Cumulative-warming impacts

For devising optimal climate-change mitigation strategies, it is also necessary to quantify the importance of different kinds of impacts relative to each other. Without any formal assessment of their relative importance being available in the literature, they were therefore assigned here the same relative weighting. However, the different kinds of impacts change differently over time so that the importance of one kind of impact also changes over time relative to the importance of the others.

The notion of assigning them equal importance can therefore be implemented mathematically only under a specified emission pathway and at a defined point in time. This was done by expressing each impact relative to the most severe impact over the next 100 years under the 'representative concentration pathway' (RCP) with radiative forcing of 6 W m⁻² (RCP6; van Vuuren et al 2011).

Any focus on maximum temperature increases, such as the '2° target', explicitly targets the most extreme impacts. However, that ignores the lesser, but still important, impacts that occur before and after the most extreme impacts are experienced. Hence, the damage function used here sums all impacts over the next 100 years. Summing impacts is different from summing temperatures to derive initial impacts. For example, the damage from tropical cyclones is linked to sea-surface temperatures in a given year (Webster et al 2005). Total damages to society, however, are the sum of cyclone damages in all years over the defined assessment horizon.

Climate-change impacts clearly increase with increases in the underlying climate perturbation, but how strongly? By 2012, global temperatures had increased by nearly 1 °C above pre-industrial temperatures (Jones et al 2012), equivalent to about 0.01 °C yr⁻¹, with about 20 cm sea-level rise (Church and White 2011), and there are increasing numbers of unusual weather events that have been attributed to climate change (e.g. Schneider et al 2007, Trenberth and Fasullo 2012). By the time temperature increases reach 2°, or sea-level rise reaches 40 cm, would impacts be twice as bad or increase more sharply? If impacts increase sharply with increasing perturbations, then overall damages would be largely determined by impacts at the times of highest perturbations, whereas with a less steep impact response function, impacts at times with lesser perturbations would contribute more to overall damages.

Schneider et al (2007) comprehensively reviewed and discussed the quantification of climate-change impacts and their relationship to underlying climate perturbations but concluded that a formal quantification of impacts was not yet possible. This was due to remaining scientific uncertainty, and the intertwining of scientific assessments of the likelihood of the occurrence of certain events and value judgements as to their significance.

For example, Thomas et al (2004) quantified the likelihood of species extinction under climate change and concluded that by 2050, 18% of species would be 'committed to extinction' under a low-emission scenario, which approximately doubled to 35% under a high-emission scenario. Given the functional redundancy of species in natural ecosystems, their impact on ecosystem function, and their perceived value for society, doubling the loss of species would presumably more than double the perceived impact of the loss of those species. The scientifically derived estimate of species loss therefore does not automatically translate into a usable damage response function. It requires additional value judgements, such as an assessment of the importance of the survival of species, including those without economic value.

It is also difficult to quantify the impact related to the low probability of crossing key thresholds (Lenton et al 2008). It may be possible to agree on the importance of crossing some irreversible thresholds, but it is difficult to confidently derive probabilities of crossing them. But despite these uncertainties, some kind of damage response function must be used to quantify the marginal impact of extra emission units.

As it is difficult, if not impossible, to employ purely objective means of generating impact response functions, we have to resort to what Stern called a 'subjective probability approach. It is a pragmatic response to the fact that many of the true uncertainties around climate-change policy cannot themselves be observed and quantified precisely' (Stern 2006). Different workers have used some semi-quantitative approaches, such as polling of expert opinion (e.g. Nordhaus 1994), or the generation of complex uncertainty distributions from a limited range of existing studies (Tol 2012), but none of these overcomes the essentially subjective nature of devising impact response functions.

Figure 1 shows some possible response functions that relate an underlying climate perturbation to its resultant impact. This is quantified relative to maximum impacts anticipated over the next 100 years for perturbations such as temperature. The current temperature increase of about 1 °C is approximately 1/3 of the temperature increase expected under RCP6 over the next 100 years, giving a relative perturbation of 0.33. For the quantification of CCIPs, impacts had to be expressed as functions of relative climate perturbations to enable equal quantitative treatment of all three kinds of climatic impacts.

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Economic analyses tend to employ quadratic or cubic responses function (e.g. Nordhaus 1994, Hammitt et al 1996, Roughgarden and Schneider 1999, Tol 2012), but there is concern that these functions that are based only on readily quantifiable impacts may give insufficient weight to the small probability of extremely severe impacts (e.g. Weitzman 2012, 2013, Lemoine and McJeon 2013). A response function that includes these extreme impacts would increase much more sharply than quadratic or cubic response functions (e.g. Weitzman 2012).

The relationship used here uses an exponential increase in impacts with increasing perturbations to capture the sharply increasing damages with larger temperature increases (as shown by Hammitt et al 1996 and Weitzman 2012). Warming by 3/4 of the expected maximum warming, for example, would have about 10 times the impact as warming by only 1/4 of maximum warming. The graph also shows the often-used power relationships (e.g. Hammitt et al 1996, Boucher 2012), shown here with powers of 2 (quadratic) and 3 (cubic), and a more extreme impacts function (hockey-stick function) presented by Hammitt et al (1996). Compared to the power functions, the exponential relationship calculates relatively modest impacts for moderate climate perturbations that increase more sharply for more extreme climate perturbations. It is thus very similar to the 'hockey-stick' relationship of Hammitt et al (1996).

Should near-term impacts be treated as more important than more distant impacts? If one applies discount rates of 4%, for example, it would render impacts occurring in just 17 years as being only half as important as impacts occurring immediately. The choice of discount rates is hence one of the most critical components of any impact analysis, and the influential Stern report (Stern 2006) derived a fairly bleak outlook on the seriousness of climate change, largely due to using an unusually low discount rate of 1.4%.

While the use of large discount rates is warranted in purely economic analyses, it is questionable in environmental assessments as it essentially treats the lives and livelihood of our children and grandchildren as less important than our own, which is hard to justify ethically (e.g. Schelling 1995, Sterner and Persson 2008). On the other hand, using a 0 discount rate would treat impacts in perpetuity as equally important as short-term impacts. This raises at least the practical problem that it becomes increasingly difficult to predict events and their significance into the more distant future.

The calculation of GWPs essentially uses 0 discount rates, but ignores impacts beyond the end of the assessment period (Tanaka et al 2010). This avoids a preferential emphasis on the impacts on one generation over another, yet avoids the unmanageable requirement of having to assess impacts in perpetuity. This approach is also used here for calculating CCIPs.

To quantify the three different kinds of impacts, it is necessary to first calculate the climate perturbations underlying them. The perturbation P_{y, T} in year y, related to direct-temperature impacts, is simply calculated as:

$$\begin{eqnarray}&&\label {eq1} P_{{y},{T}} = T_{{y}}- T_{{p}} \end{eqnarray} \tag{ 1 }$$

where T_y and T_p are the temperatures in year y and pre-industrially. The temperature in 1900 is taken as the pre-industrial temperature.

The rate of temperature change, P_{y, Δ} , is calculated as the temperature increase over a specified time frame:

$$\begin{eqnarray}&&\label {eq2} P_{{y},\Delta } = (T_{{y}}-T_{{y}-{d}}) / d \end{eqnarray} \tag{ 2 }$$

where d is the length of the calculation interval, set here to 100 years. Shorter calculation intervals could be used, in principle, but extra emission units would then affect both the starting and end points for calculating rates of change, leading to complex and sometimes counter-intuitive consequences. The choice of 100 years is further discussed below.

The cumulative temperature perturbation, P_{y, Σ} , is calculated as the sum of temperatures above pre-industrial temperatures:

$$\begin{eqnarray}&&\label {eq3} P_{{y},\Sigma } = \sum _{i=p}^y {(T_{i} -T_{{p}} )} \end{eqnarray} \tag{ 3 }$$

where T_i is the temperature in every year i from pre-industrial times to the year y.

All three perturbations are then normalized to calculate relative perturbations, Q, as:

$$\begin{eqnarray}Q_{{y},{T}} &=& P_{{y},{T}}/\max (P_{{T}, {\rm RCP}6})\label {eq4a} \end{eqnarray} \tag{ 4a }$$

$$\begin{eqnarray}Q_{{y}, \Delta } &=& P_{{y}, \Delta }/ \max (P_{\Delta , {\rm RCP}6})\label {eq4b} \end{eqnarray} \tag{ 4b }$$

$$\begin{eqnarray}Q_{{y},\Sigma } &=& P_{{y},\Sigma }/\max (P_{\Sigma , {\rm RCP}6}) \label {eq4c} \end{eqnarray} \tag{ 4c }$$

where the P-terms are the calculated perturbations under a chosen emissions pathway, and the max-terms are the maximum perturbations calculated under RCP6 over the next 100 years. With this normalization, each kind of climate impact can be treated mathematically the same.

Impacts, I, are then derived from relative perturbations as:

$$\begin{eqnarray}&&I_{{y},{T}}={ [({\rm e} ^{Q_{{y},{T}}})}^{{\rm s}}]-1 \label {eq5a} \end{eqnarray} \tag{ 5a }$$

$$\begin{eqnarray}&&I_{{y}, \Delta } ={ [({\rm e} ^{Q_{{y},\Delta }})}^{{\rm s}}]-1 \label {eq5b} \end{eqnarray} \tag{ 5b }$$

$$\begin{eqnarray}&&I_{{y},\Sigma } ={ [({\rm e} ^{Q_{{y},\Sigma }})}^{{\rm s}}]-1 \label {eq5c} \end{eqnarray} \tag{ 5c }$$

where s is a severity term that describes the relationship between perturbations and impacts (figure 1). The work presented here uses s = 4 (as discussed in section 2.4 above).

Temperatures from 1900 to 2010 were based on the HadCRUT4 data set of Jones et al (2012). They were used to set initial temperatures for calculating rates of warming and cumulative warming up to 2010. Temperatures beyond 2010 were added to base temperatures and together determined respective perturbations over the next 100 years.

The relevant impacts were then calculated using equation (4), and summed over 100 years. To calculate CCIPs, these calculation steps were followed four times. The first set of calculations was based on RCP6 and was only used to derive max(P_RCP6) which was needed for subsequent normalizations. This normalization made it possible to assign each kind of impact equal importance at their highest perturbations over the next 100 years under RCP6.

The second set of calculations used a chosen emission pathway, RCP6, or a different one as specified below, to calculate background gas concentrations and perturbations. The final two sets of calculations used the same chosen emission pathway and added either 1 tonne of CO₂ or of a different gas. The calculations then derived marginal extra impacts of extra emission units under the three different kinds of impacts. CCIPs of each gas were then calculated as the ratios of marginal impacts of different gases relative to those of CO₂.

These calculations aim to estimate impacts over the coming 100 years, and how those impacts might be modified through pulse emissions of different GHGs. They use the best estimates of relevant background conditions based on emerging science and updated emission scenarios. These calculations would need to be repeated every few years with new scientific understanding and newer emission projections to provide updated guidance of the importance of different GHG over the next 100-year period.

The calculations of radiative forcing and temperature followed the approach of Kirschbaum et al (2013), including the carbon cycle based on the Bern model and radiative forcing calculations provided by the IPCC. Calculations also included the replacement of a molecule of CO₂ by CH₄ in the biogenic production of CH₄, and its partial conversion back to CO₂ when CH₄ was oxidized (Boucher et al 2009). Global temperature calculations included a term for the thermal inertia of the climate system. Full calculation details are given in the supplemental information (available at stacks.iop.org/ERL/9/034014/mmedia).

A quantification of the marginal impact of additional units of each gas must be based on background conditions that include quantification of the impacts that are expected to occur without those additional emission units. Figure 2 shows the relative perturbations underlying the three kinds of impacts and resultant calculated climate-change impacts.

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Under RCP6, direct and cumulative-warming impacts continue to increase throughout the 21st century, with greatest impacts reached by 2109. Rate-of-warming impacts reach their maximum by about 2080 and then start to fall slightly (figure 2(a)). While the underlying climate perturbations increase fairly linearly over the next 100 years, this leads to sharply increasing impacts towards the end of the assessment period (figure 2(b)). This pattern is most pronounced for cumulative-warming impacts. The irregular pattern in calculated rates of warming is related to the unevenness in the observed temperature records up to 2010 as rates of warming are calculated from the temperature difference over the preceding 100 years.

To calculate the marginal impact of pulse emissions of extra GHG units, it is necessary to first establish their physico-chemical consequences. Concentration increases are greatest immediately after the emission of extra units. They then decrease exponentially for CH₄ (figure 3(b)) and N₂O (figure 3(c)). CO₂ concentrations also decrease but follow a more complex pattern (figure 3(a)). For CH₄, the decrease is quite rapid, with a time constant of 12 years, but is more prolonged for N₂O, with a time constant of 120 years.

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These concentration changes exert radiative forcing. It is also highest immediately after the emission of each gas and decreases thereafter. It decreases proportionately faster than the concentration decrease because of increasing saturation of the relevant infrared absorption bands. This is most pronounced for CO₂ (figure 3(a)), for which RCP6 projects large concentration increases (figure 3(d)), which makes the remaining CO₂ molecules from 2010 pulse emissions progressively less effective (e.g. Reisinger et al 2011). For N₂O, RCP6 projects only moderate concentration increases. The infrared absorption bands of N₂O are also less saturated than for CO₂ so that the effectiveness of any remaining molecules remains high. RCP6 projects little change in the CH₄ concentration. Radiative forcing then drives temperature changes (figure 3) that lag radiative forcing by 15–20 years due to the thermal inertia of the climate system.

From the information in figures 2 and 3, one can calculate marginal increases in impacts due to a 2010 pulse emission of each gas (figure 4). Extra units of CO₂ emitted in 2010 cause the largest temperature increase in about 2025 (figure 3(a)). Base temperatures, however, are still fairly mild in 2025 (figure 2(a)) so that the extra warming at that time increases direct-temperature impacts only moderately (figure 4(a)). Even though the extra warming from CO₂ added in 2010 diminishes over time (figure 3(a)), it adds to increasing base temperatures (figure 2(a)) to cause increasing ultimate impacts (figure 4(a)). This pattern is strongest for cumulative-warming impacts. The patterns for N₂O (figure 4(c)) are similar to those for CO₂ because the longevity of N₂O in the atmosphere is similar to that of CO₂.

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CH₄ emitted in 2010, however, modifies direct-temperature impacts only over the first few decades after its emission (figure 3(b)). While later warming could potentially have greater impacts, the residual warming several decades after its emission becomes so small to have very little effect. For cumulative-warming impacts, however, the greatest marginal impact of CH₄ additions also occurs at the end of the assessment period. Even though CH₄ emissions exert their warming early in the 21st century, that warming is effectively remembered in the cumulative temperature record and leads to the largest ultimate impact when it combines with large cumulative-warming base impacts (figure 4(b)).

For rate-of-warming impacts and direct-temperature impacts, there are distinctly different patterns for the different gases that are principally related to the longevity of the gases in the atmosphere. For cumulative-warming impacts, however, the patterns are similar for all gases, with the marginal impact from a 2010 pulse emission being muted for the first 50–80 years and then increasing sharply over the remainder of the 100-year assessment period. This is because cumulative warming can be increased in much the same way for contributions made earlier as from on-going warming. Even though different gases make their additions to cumulative warming at different times, that increased perturbation has the largest impact when it adds to large base values (see figure 2(a)) so that for all gases, the largest marginal impacts occur at the end of the 100-year assessment period (figure 4).

Marginal impacts can then be summed over the 100 years after the pulse emission of each gas and expressed relative to CO₂ (table 1). Under RCP6, CCIPs for biogenic and fossil CH₄ are 20 and 23, respectively, compared to a 100-year GWP of 25. These lower values are due to the much lower direct-temperature and rate-of-warming impacts. Peak warming from CH₄ emissions in 2010 occurs at a time when background temperature increases are still fairly mild so that the extra warming from CH₄ (figure 4(b)) causes less severe impacts than the warming from CO₂ (figure 4(a)) that is still strong many decades later when it combines with higher background temperatures to cause more severe additional impacts.

In contrast, cumulative-warming impacts under RCP6 are 34 and 37 (for biogenic and fossil CH₄), which are greater than the corresponding values for cumulative radiative forcing. The earlier radiative forcing from CH₄ ensures that all radiative forcing leads to warming within the assessment period. For CO₂ and N₂O, on the other hand, radiative forcing overestimates their warming impact because of the thermal inertia of the climate system. Some of the radiative forcing exerted towards the end of the 100-year assessment period only leads to warming after the end of the assessment period providing relatively more cumulative radiative forcing than cumulative warming.

Fossil-fuel-derived CH₄ has higher CCIPs than biogenic CH₄ by about three units. Biogenic CH₄ production means that a molecule of carbon is converted to CH₄, which lowers the atmospheric CO₂ concentration and thereby reduces its overall climatic impact. After it has been oxidized, any CH₄, however, continues its radiative forcing as CO₂, which increases its overall impact (Boucher et al 2009), with the same effect for both fossil and biogenic CH₄.

CCIPs of CH₄ become progressively smaller when they are calculated under higher concentration pathways (table 1). This is caused by much higher impact damages being reached under higher concentration pathways so that the earlier warming contribution of CH₄ relative to CO₂ becomes increasingly less important. This affects direct-temperature impacts and rate-of-warming impacts, whereas cumulative temperature impacts remain similar under the different RCPs.

For N₂O, the CCIP is greater than the 100-year GWP (348 versus 298 under RCP6). This is mainly due to the reducing effectiveness of infrared absorption of extra CO₂ under increasing background concentrations, which increases the relative importance of the emission of other gases. This interaction with base-level gas concentrations is not included in GWPs as they are calculated under constant background gas concentrations.

The relative importance of different gases also depends strongly on the underlying climate-change severity term (figure 5). With increases in the severity term, the importance of short-lived CH₄ decreases considerably (figure 5(b)), whereas the importance of N₂O increases slightly (figure 5(a)). This is because the greatest temperature and rate of change perturbations are projected to occur at the end of the assessment period when CH₄ adds little to those perturbations, while N₂O adds even more than CO₂. As the climate-change severity term increases, it progressively increases the importance of impacts at these later periods and thereby greatly reduces the importance of CH₄.

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