Temperature variability implies greater economic damages from climate change

Historical global mean temperature (GMT) records and climate models show substantial variability at annual to multi-decadal scales. Yet, widely used integrated assessment models (IAMs) and official assessments typically treat GMT deterministically, allowing them to capture epistemic uncertainty (uncertainty in model parameters such as equilibrium climate sensitivity, ECS) but not aleatory uncertainty (irreducible internal variability around the expected temperature trajectory). Because damages are computed by passing annual temperature anomalies through a nonlinear damage function and discounting over time, ignoring aleatory variability may bias damages downward and understate uncertainty. This study asks: What are the economic consequences of incorporating realistic inter-annual and multi-decadal temperature variability into IAM-style damage assessments? The authors propose a simple, physically grounded stochastic energy balance model to represent temperature variability and quantify its effect on total discounted climate damages and on a risk premium representing the cost of living with aleatory uncertainty. The work is important because it reveals large, previously unaccounted-for economic costs and highlights the amplified risks when aleatory and epistemic uncertainties interact, pointing to greater benefits of adaptation than previously recognized.

The paper builds on canonical climate physics and economics. It adopts Hasselmann’s (1976) stochastic climate framework to represent internal variability in a simple energy balance model. It contrasts with mainstream IAM applications used in policy (e.g., Interagency Working Group on SCC; Stern Review; methods in Greenstone et al.) that employ deterministic GMT trajectories, thereby capturing epistemic but not aleatory uncertainty. The damage mapping references Weitzman’s catastrophe-aware damage functions. The discussion connects to emergent constraints on ECS from variability (Cox et al.; Rypdal et al.) and parameter estimation for stochastic EBMs (Cummins et al.). It also relates to long-range dependence literature (Mandelbrot and Wallis; Fredriksen & Rypdal) and socio-environmental implications of persistent extremes (e.g., Syrian drought studies by Kelley et al.).

- Climate module: A stochastic one-layer energy balance model (EBM) is used to represent GMT anomalies (ΔT): C dΔT = F dt − λ ΔT dt + √2 σ0 dte, where C is effective heat capacity, F is radiative forcing (driven by RCP scenarios), λ is the climate feedback parameter, and e is a zero-mean Gaussian noise process with variance parameter σ0. - Parameterization: Parameters are calibrated to approximate historical variability (details in Supplementary Note 6). Values used in illustrative simulations include C = 10^9 J m−2 K−1, λ = 1.23 W m−2 K−1, and σ0 = 0.9375 × 10^8 W m−2 s. - Forcing scenarios: RCP2.6, RCP4.5, RCP6.0, and RCP8.5 are used to span a range of future radiative forcings. - Deterministic vs stochastic runs: Deterministic trajectories set σ0 = 0. Stochastic ensembles simulate 10,000 temperature trajectories per RCP with the calibrated σ0 to capture internal variability and autocorrelation. - Damages: Annual damages (share of global output) are computed by passing ΔT each year through a nonlinear damage function (consistent with Weitzman-type functional forms), then discounting and summing over time to obtain net present value of total climate damages. A discount rate of 4.25% is used (to match Nordhaus 2017). - Risk premium (aleatory only): The risk premium is defined as the difference in expected utility between the deterministic damage trajectory and the ensemble of stochastic damages, representing what a canonical social planner would pay today to eliminate aleatory variability (details in Supplementary Note 5). - Interacting uncertainties (aleatory + epistemic): Epistemic uncertainty is represented via a distribution over ECS. ECS is assumed log-normal with a most likely value of 3 °C and Pr(2 ≤ ECS ≤ 4.5) = 0.66 (consistent with IPCC AR4/AR5). Two ensembles are generated under each RCP: (1) deterministic EBM sampled over the ECS distribution; (2) stochastic EBM sampled over the same ECS distribution. The additional risk premium attributable to aleatory uncertainty under epistemic uncertainty is measured as the difference in expected utility between these two ensembles. The interaction effect is the increment beyond the aleatory-only premium due to dependence of both mean and variance of temperatures on λ (and thus ECS).

- Adding realistic temperature variability substantially widens the distribution of total discounted damages relative to deterministic forecasts. - RCP8.5 damages: Deterministic forecast ≈ $486 trillion. Under stochastic temperatures, there is a 5% chance damages exceed $563 trillion (+16% relative to deterministic). The 5–95% range for stochastic damages is −13% to +16% of deterministic. - RCP2.6 damages: Deterministic forecast ≈ $30 trillion. Stochastic 5–95% range is −30% to +52% of deterministic (lower forcing yields higher relative dispersion). - Aleatory-only risk premium (amount the social planner would pay today to eliminate internal variability; as level and % of current global output): - RCP8.5: $32 trillion (≈40% of current output); adds ~6–13% to deterministic damages. - RCP6.0: $15 trillion (≈19%). - RCP4.5: $9 trillion (≈11%). - RCP2.6: $3 trillion (≈4%). - With epistemic uncertainty over ECS (interaction of aleatory × epistemic): Risk premia rise markedly because higher ECS implies both greater mean warming and greater variability, fattening the right tail of damage distributions: - RCP8.5: $46 trillion total premium (≈58%), of which ≈$14 trillion from interaction beyond aleatory-only. - RCP6.0: $31 trillion (≈39%), ≈$16 trillion interaction. - RCP4.5: $25 trillion (≈31%), ≈$16 trillion interaction. - RCP2.6: $9 trillion (≈11%), ≈$6 trillion interaction. - Aleatory uncertainty likely has limited effect on the social cost of carbon (SCC) for a marginal tonne, since variability is present with or without that tonne. The large risk premium primarily reflects costs that are not avoidable by marginal abatement but rather call for adaptation.

The study directly addresses the omission of aleatory uncertainty in standard IAM assessments. By embedding a stochastic EBM for GMT into the damage calculation, the authors show that internal climate variability materially raises total discounted damages and generates a sizable risk premium—costs that deterministic models miss. The interaction with epistemic uncertainty over ECS further amplifies damages because draws of high ECS simultaneously increase mean warming and variability, producing fat-tailed damage distributions. These insights suggest that standard policy metrics focused solely on deterministic trajectories understate the benefits of policies and investments that reduce vulnerability to variability (adaptation). The authors argue that while aleatory uncertainty does not substantially affect the SCC for a marginal tonne, it creates large welfare losses that society must plan to absorb, highlighting adaptation’s elevated value. They also note that their quantitative estimates are conservative given the high discount rate used and the absence of true long-range dependence in the temperature process; real-world persistence of extremes could further elevate damages, even if the model’s risk premium metric is memoryless.

The paper integrates a physically grounded representation of temperature variability into an IAM-style damage framework and demonstrates that aleatory uncertainty adds trillions of dollars to climate damages, with even larger costs when combined with epistemic uncertainty over ECS. This reveals a major, previously unaccounted-for component of climate risk and underscores the importance of adaptation alongside mitigation. Future research should: (1) incorporate long-range dependence and more realistic persistence of extremes into damage assessments; (2) investigate damage accumulation and socio-economic tipping under prolonged adverse conditions; (3) explore sectoral and regional heterogeneity in vulnerability to variability; and (4) develop frameworks to value and prioritize adaptation strategies that specifically target variability-induced risks.

- Discounting: A relatively high discount rate (4.25%) is used; lower rates would increase present-valued damages and risk premia substantially. - Stochastic process: The temperature model is a continuous AR(1)-type process without true long-range dependence; if the climate exhibits long-range persistence, prolonged deviations and damages could be larger. - Memoryless damages and welfare: The damage function and social welfare function have no memory; they do not capture path-dependent or cumulative impacts of persistent extremes, potentially understating real-world costs. - Parameter calibration: Results depend on calibrated values of C, λ, and σ0 and on the assumed ECS distribution; alternative calibrations or structural uncertainty could change magnitudes. - Adaptation costs: The analysis quantifies the benefits of hypothetically eliminating aleatory variability (risk premium) but does not model the costs, feasibility, or dynamics of real-world adaptation measures. - Damage function form: Use of a particular nonlinear damage function entails functional-form uncertainty that can materially affect damage estimates.