Using OPTiMEM and the Heat Conjecture to Estimate Future Social Cost of Greenhouse Gases

TL;DR

OPTiMEM presents a physics-based framework to estimate the social cost of greenhouse gases by linking ocean heat content to weather damages through the heat conjecture, producing gas-specific, year-by-year phase-space representations rather than a single SCC value. It replaces traditional IAM-driven SCC with multi-dimensional surfaces for CO$_2$, CH$_4$, N$_2$O, and Fgas and introduces long-term carbon bonds to implement real discounting, addressing persistent debates over discount rates. The approach leverages 18 emission scenarios, NOAA weather-damages data, and a present value of future losses, $PV_{FL}$, to map costs across 10–1500 year horizons and quantify risk via Chebyshev bounds and stochastic damage curves. The work also argues against relying on CO$_2$-equivalents, emphasizes energy as the monetary foundation, and advocates a rapid, high-EROEI energy transition funded by carbon bonds, with attention to energy poverty and long-term security considerations.

Abstract

We present an entirely new physics founded approach to estimating the social cost of carbon (SCC). For this, we developed our Ocean-Heat-Content Physics and Time Macro Economic Model (OPTiMEM) to estimate future heat content (separately published). The heat conjecture assumes that weather damages curves are stochastically proportional to ocean heat increase. We model carbon combustion, validate to datasets for greenhouse gas (GHG), temperature, and ocean heat content (OHC). We show that the social cost of 4 GHGs: CO2, CH4, N2O and halogenated hydrocarbons, cannot be single values, but must be represented by a kind of economic phase space. We propose very long-term carbon bonds to implement real discounting. This obviates the Gordian knot of the descriptivist versus prescriptivist discount disagreement that is unsolvable. Implementing these bonds leads to a new monitoring metric: real-dollar spending and bond discount rates compared to SC-GHG cost with variation on the discount scale, where the discount has no relationship to the pure rate of time preference (PRTP). This heat conjecture is based on OPTiMEM. OPTiMEM initiates from a fossil fuel consumption function to produce CO2, with 18 scenarios implemented to provide the uncertainty range. We provide 1:N year loss risk models (1:10, 1:100, 1:1000) that government, engineers, and actuaries should find useful. A scenario implementing DICE family of models carbon and growth assumptions shows +18° C is breached by 2210 CE, and +110° C by 2300 CE -- both of which outcomes are obviously not compatible with the fairly rosy conclusions of DICE models. Concerns are raised about having enough low-cost fossil fuel for conversion to minimal CO$_2$ maximal energy return on energy invested (EROEI) power if nations wait too long, and low EROEI power is questioned because monetary value is dependent on energy.

Figures (8)

• Figure 1: Scenarios tree, that sets the range of uncertainty. Upper solid box shows the 18 primary scenarios for this study. (https://doi.org/10.48550/arXiv.2601.06085 §6). Lower dashed box shows the 3 DICE family of models scenarios for the DICE implicit assumptions test.
• Figure 2: Fig 1 of Burke et al 2018 Burke2018Plio reproduced by permission in entirety with caption Temperature trends for the past 65 Mya and potential geohistorical analogs for future climates. Six geohistorical states (red arrows) of the climate system are analyzed as potential analogs for future climates. For context, they are situated next to a multi-timescale time series of global mean annual temperatures for the last 65 Ma. Major patterns include a long-term cooling trend, periodic fluctuations driven by changes in the Earth’s orbit at periods of $10^4$ – $10^5$ y, and recent and projected warming trends. Temperature anomalies are relative to 1961–1990 global means and are composited from five proxy-based reconstructions, modern observations, and future temperature projections for four emissions pathways. Pal, Paleocene; Mio, Miocene; Oli, Oligocene.
• Figure 3: OPTiMEM atmospheric physics schema. This diagram describes the climate model used for this work. Shaded ocean heat box is where heat in OPTiMEM is stored. This OHC is validated by von Shuckmann and NASA datasets, representing 88.0% of planetary heat energy relevant to climate/weather. Cross hatched atmosphere heat box is modelled as a pseudo-surface in contact with the ocean that does not store the 0.9% that is atmospheric heat. Dashed boxes for land and cryosphere indicate these are not used. Land and cryosphere are much more difficult to model and it was not attempted. (https://doi.org/10.48550/arXiv.2601.06085 §10.2-10.3, fig. 44) We start with carbon extraction limits driving CO$_2$ emissions which translates to CO$_2$ parts per million. NOx is not a forcing of climate in OPTiMEM. N$_2$O is driven by population and Gross World Product (GWP). Methane emissions are historical fractions of CO$_2$ with the addition of permafrost emissions (https://doi.org/10.48550/arXiv.2601.06085 §6.2.5). Methane converts to CO$_2$ based on its e-fold chemical lifetime (https://doi.org/10.48550/arXiv.2601.06085 §6.3.2, §11.3 & eq. 18). Fgases also participate in changing the heat flux (EEI), which in turn heats land, ice, atmosphere, and ocean. The ocean is the largest heat reservoir by far, and the only one for which we have a usable dataset for validation. Thus, ocean heat content (OHC) is our chosen heat curve.
• Figure 4: Remaining CO$_2$ by year fitted to Archer Archer2009AtmosphericLifetimeOfCO2. Upper blue long-dash curve is fitted to points from highest Archer results C$_{RH}$. Central solid black curve is harmonic mean of all data C$_{RC}$. Lower short-dash red curve is fitted to lowest remainder points, C$_{RL}$. Grey circles are density plot of Archer data sampled at intervals. Upper and lower crosses are calibration points for upper and lower curve fits. Central boxes are computed calibration points for harmonic mean. These three CO$_2$ remainder equations provide the fraction for future years. (https://doi.org/10.48550/arXiv.2601.06085 §6.21
• Figure 5: Heat conjecture weather damages curves estimating uncertainty. This graph is a slice at Tab A through figure \ref{['figPVDrateNumYears']}, extending approximately 475 years. Blue datapoints, NOAA weather damages. Blue curve is the trajectory of $WDe(y)$ (https://doi.org/10.48550/arXiv.2601.06085 §11.11) exponential fit equation to NOAA data, provided to show the fit to the scaled OHC curves. Shaded curve regions are weather damages curves. Light grey region, shows the outer limits from lowest to highest scenarios. Inner peach colored region shows the high and low central scenarios.