GoKawiilDecades of scientific advances establish that human activities are changing Earth’s climate, that these changes are negatively impacting a range of human outcomes and that those experiencing the most harm are responsible for a small fraction of historical emissions1,2,8. These intersecting insights motivate calls that emitting entities pay for L&D, usually framed as the harms from climate change that parties were unable to avoid through adaptation or mitigation4,9,10,11. Similar claims have been made in ongoing litigation, in which claimants assert damages as a result of emissions from specific (and often distant) emitters12,13.
Substantial headway has been made in understanding how anthropogenic forcing and its effects on climate extremes can be linked to specific national, regional or corporate emitters14,15,16; however, with a few exceptions13,17, quantifying how these specific emissions can be linked to global and local damages has received less formal and empirical attention. A central empirical challenge is that emissions come from many sources and are well mixed in the atmosphere, and damages from these emissions must be inferred relative to a lower-emissions counterfactual that is unobserved. A key conceptual challenge is that since the language of L&D was agreed to18, there have been multiple interpretations of what this language means in practice5 and a formal definition has yet to be adopted6.
Building on IPCC documents4,9 and a growing academic literature10,11, we propose that L&D is computed as the net present value of economic and non-economic impacts attributable to the emissions of greenhouse gases through their effect on the climate, net of any adaptation that was undertaken. We show how this source-agnostic measure of L&D can be equivalently computed as the theoretical payment schedule that would completely reimburse all harmed parties for the damages (or benefits) that they have experienced or will experience from climate change, paid for by the emitting parties. However, we emphasize that—consistent with Article 8 of the Paris agreement—these damage estimates do not necessarily equal what is owed by one entity to another, as that is a moral and legal question beyond the scope of this analysis.
The basic idea is to consider the emission of a unit of greenhouse gas (GHG) as the creation of an asset that produces a subsequent stream of value (Fig. 1). Unlike many assets, this value might be negative (for example, a liability) and its flow accrues to individuals who did not create the asset. These features are not unique to GHG assets, and similar assets are commonly traded in markets. For example, household garbage generates a flow of costs for whoever takes ownership, and households typically must compensate a waste disposal firm to take the garbage and store it on their premises. We compute an analogue to the value of unpaid garbage collection bills that would be owed for past GHG emissions if individuals were paid for the costs imposed on them by this waste. The total sum of these costs are the residual loss and damages suffered by populations due to climate change.
Fig. 1: Framework for emissions damage accounting. Full size image a, A unit of emissions in year t e generates an annual flow of damages in future year(s) t in population i. These damages can be compensated (that is, paid for in transfer payment from the emitter to i) in settlement year t s . b, If the settlement year is after the damage year (t s > t), then the damage accrues interest. c, If the settlement is in advance of anticipated future damage (t s < t), then future damage is discounted back to the settlement year. d, A higher discount rate amplifies current value of past damages, and decreases present value of future damages, relative to a lower discount rate. e, Payment owed for multiple periods of uncompensated past damage (HD-CO 2 ) is additive. f, Past emission can continue to create future damage even if past damage is compensated (emissions remain in atmosphere), requiring additional compensation (FD-CO 2 ). g, SC-CO 2 is a special case in which settlement for future damages occurs at the time of emission.
We show how L&D from CO 2 emissions can be computed from three components: the discounted historical damages that have already occurred due to past CO 2 emissions, the discounted future damages expected to occur from these past emissions, and the discounted future damages expected to occur from present or future emissions (Supplementary Methods). Total L&D is then the sum of each of these components, written in its simplest form as:
$$\begin{array}{c}{\rm{T}}{\rm{o}}{\rm{t}}{\rm{a}}{\rm{l}}\,{\rm{l}}{\rm{o}}{\rm{s}}{\rm{s}}\,{\rm{a}}{\rm{n}}{\rm{d}}\,{\rm{d}}{\rm{a}}{\rm{m}}{\rm{a}}{\rm{g}}{\rm{e}}\,={\rm{h}}{\rm{i}}{\rm{s}}{\rm{t}}{\rm{o}}{\rm{r}}{\rm{i}}{\rm{c}}{\rm{a}}{\rm{l}}\,{\rm{d}}{\rm{a}}{\rm{m}}{\rm{a}}{\rm{g}}{\rm{e}}{\rm{s}}\,{\rm{f}}{\rm{r}}{\rm{o}}{\rm{m}}\,{\rm{h}}{\rm{i}}{\rm{s}}{\rm{t}}{\rm{o}}{\rm{r}}{\rm{i}}{\rm{c}}{\rm{a}}{\rm{l}}\,{\rm{e}}{\rm{m}}{\rm{i}}{\rm{s}}{\rm{s}}{\rm{i}}{\rm{o}}{\rm{n}}{\rm{s}}\\ \,+\,{\rm{f}}{\rm{u}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}}\,{\rm{d}}{\rm{a}}{\rm{m}}{\rm{a}}{\rm{g}}{\rm{e}}{\rm{s}}\,{\rm{f}}{\rm{r}}{\rm{o}}{\rm{m}}\,{\rm{h}}{\rm{i}}{\rm{s}}{\rm{t}}{\rm{o}}{\rm{r}}{\rm{i}}{\rm{c}}{\rm{a}}{\rm{l}}\,{\rm{e}}{\rm{m}}{\rm{i}}{\rm{s}}{\rm{s}}{\rm{i}}{\rm{o}}{\rm{n}}{\rm{s}}\\ \,+\,{\rm{f}}{\rm{u}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}}\,{\rm{d}}{\rm{a}}{\rm{m}}{\rm{a}}{\rm{g}}{\rm{e}}{\rm{s}}\,{\rm{f}}{\rm{r}}{\rm{o}}{\rm{m}}\,{\rm{f}}{\rm{u}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}}\,{\rm{e}}{\rm{m}}{\rm{i}}{\rm{s}}{\rm{s}}{\rm{i}}{\rm{o}}{\rm{n}}{\rm{s}}\end{array}$$ (1)
For a historical marginal emission—that is, an additional unit emitted above the existing background emissions in a given year—we denote the resulting discounted historical damages as HD-CO 2 and discounted future damages as FD-CO 2 . For a present or future marginal emission, we denote the resulting discounted future damages as SC-CO 2 . This approach enables decomposition of L&D into past and future damages, and aligns the financial accounting framework of L&D with the existing SC-CO 2 framework (refs. 7,19). The SC-CO 2 is commonly defined as the net-present value of total additional net future harm (or benefit) that accrues to society as a result of one additional unit of CO 2 emissions at a specific moment in time. Aligning the calculation of L&D with SC-CO 2 enables the application of established scientific tools used to compute SC-CO 2 (refs. 7,20), supports legal consistency around climate liability12, and helps avoid incentives to delay emissions accountability, for instance, if damages from past and future emissions are valued differently.
We develop a formal framework for estimating equation (1), and an implementation of the framework that: combines (1) emissions inventories; (2) the reduced complexity model Finite Amplitude Impulse Response (FaIR) to calculate the change in global mean surface temperature (GMST) from an emissions perturbation; (3) the CMIP6 ensemble of global climate models21 to ‘pattern scale’ GMST changes to country-level changes; and (4) an updated statistical model that relates country-level per-capita economic growth rates to changes in contemporaneous and lagged average temperatures22 to translate local temperature changes into damages (Extended Data Fig. 1 and Supplementary Methods). Relationships between mean annual temperature and GDP have been well explored in the literature22,23,24,25 and probably capture many (but not all) channels through which a warming climate affects economic outcomes. The reduced-form temperature–GDP damage function we use is robust across statistical models, has not changed appreciably in the past 60 years (Extended Data Fig. 2), and provides strong evidence that temperature is affecting the growth rate of GDP, not just the level (Extended Data Figs. 3 and 4 and Supplementary Methods).