A stable hothouse triggered by a tipping mechanism

TL;DR

This work introduces the temperature–carbon–vegetation (TCV) framework, a 0-D coupled set of equations linking globally averaged temperature $T$, atmospheric carbon $C_A$, ocean carbon $C_M$, and vegetation degradation $V$ to investigate global tipping to a hothouse climate. Through a four-ODE formulation and a reduced differential-algebraic (DAE) version, it incorporates two key biogeophysical feedbacks: a temperature-dependent albedo increase from terrestrial algal darkening and a degradation-driven reduction in vegetation carbon uptake, both of which can drive bistability between present and hothouse states. The model reproduces historical temperature and carbon fluxes and shows a bifurcation structure with a present-climate fixed point $P_1$ and a distant hothouse fixed point $P_2$, separated by an unstable $P_3$, with tipping triggered under high emissions such as RCP8.5 around the mid-21st century, accompanied by a near 10 K temperature jump. Validation against observations and ensemble GCMs indicates robust performance prior to tipping, while the regime diagram highlights emission thresholds and safety margins (for example an approximate buffer of $22.5$ GtC/yr at $T_{\alpha_L,\ell}=290$ K) that can inform policy. The analysis underscores the significance of regional feedbacks in shaping planetary-scale outcomes and demonstrates how a low-dimensional, mechanistically grounded framework can illuminate nonlinear climate dynamics alongside high-resolution climate models.

Abstract

The climate system's nonlinear dynamics is influenced by various external forcings and internal feedbacks that can give rise to regional and even global tipping points that may lead to significant and potentially irreversible changes. Paleoclimatic records reveal that Earth's climate has shifted between distinct equlibria, including a "hothouse Earth" state with temperatures about 10 K higher than present. However, a specific mechanism for a sudden tipping to an alternate stable state, several degrees warmer than the present climate, has yet to be presented. We introduce a temperature-carbon-vegetation (TCV) model comprising an energy balance model of global temperature, coupled with global terrestrial and ocean CO2 dynamics, and with vegetation ecosystem change. Our model exhibits a new tipping mechanism that leads to a hothouse Earth under a high-emissions scenario. Its simulations align with both observations and IPCC-class global climate models prior to tipping. The two processes that produce global tipping are: (i) temperature-albedo feedback due to darkening of the terrestrial cryosphere by glacial microalgae; and (ii) limits to vegetation adaptation that lead to reduced carbon absorption.

Figures (13)

• Figure 1: TCV model validation with respect to observational data and IPCC-class GCM simulations. In each panel, the TCV model's temperature simulation (heavy red line) is compared with observational data (heavy blue line), as well as with 42 different IPCC-class GCM models (light colors) subject to four RCP scenarios Taylor2012 and with their ensemble mean (heavy black line). The TCV model is benchmarked against individual GCMs using its RMSE with respect to either (a) observed data or (b--e) the GCM ensemble mean.
• Figure 2: Global terrestrial surface albedo darkening. Plots of climatological terrestrial albedo with and without algal darkening of ice sheets and midlatitude cryosphere. Grid-level values were computed using raw data from simulations of the CNRM-CM5 climate model coupled with the ISBA-ES snowpack dynamics and hydrology model Boone2001Boone2010 for the 2070--2100 interval, subject to the RCP 8.5 emission scenario. Panel (a) displays grid-level annual climatological terrestrial albedo with no algal darkening; and panel (b) displays grid-level albedo with maximum darkening of land cryosphere due to algal blooms. The minimum and maximum global average terrestrial albedo values used in $\alpha_{{\rm{L}}}(T)$ of Eq. \ref{['eq:TempEq']} (see Eq. \ref{['eq:alb_terrestrial']} in Methods) are obtained after performing a weighted spatial average of gridded data in (a) and (b) accounting for both the latitudinal gradient of annual cumulative radiation and the latitude dependence of gridded areas; see Fig. \ref{['Fig:Terrestrial-Albedo-Weights']} and Methods section.
• Figure 3: Phase portrait of the coupled DAE model \ref{['eq:TC-3box']} for two emissions levels, $e = 0$ and $e = 21$, and constant ecosystem degradation level, $V = 0$. The coordinates are global temperature $T$ in degrees K on the abscissa and total surface carbon $C_{\mathrm{S}}$ in GtC on the ordinate. The temperature and carbon nullclines $F_1(T, C_{\mathrm{S}})=0$ and $F_2(T, C_{\mathrm{S}})=0$ that correspond to equations \ref{['eq:TempEq3']} and \ref{['eq:TotalCarb']} are in blue and red, respectively. (a) The phase portrait for preindustrial conditions; (b) the phase portrait for $e = 21$ GtC/yr that illustrates the model's three steady states; and (c) blow-up of area in panel (b) that contains the model's three steady states. The blue-filled circle indicates the stable current climate $P_1$ (left) and the red-filled circle corresponds to the hothouse climate $P_2$ (right), with the unstable fixed point $P_3$ in orange in-between. The light vertical line in all three panels indicates a discontinuity in the derivative of $\alpha_{{\rm {O}}}$ at $T_{\alpha, \ell} = 290$ K that is explained in the Methods section; in panel (c) the temperatures $T$ and carbon stock $C_{\rm S}$ of the two stable steady states are also indicated by light dashed lines.
• Figure 4: Bifurcation diagrams of the TCV-DAE model with fixed vegetation degradation $V$. The two diagrams show the steady states' temperature $T$ as a function of the yearly carbon emissions $e$: (a) for intact ecosystems, $V=0$; and (b) for nonzero ecosystem degradation, $V=0.3$. In both panels, the stable branches are light blue for the current climate and light red for the hothouse; the intermediate, unstable solution branch is dashed black. The dark blue triangle indicates the preindustrial steady state $P_1$ for the standard parameter values of Tables \ref{['tab:param-temp']}, \ref{['tab:param-terrestrial-carbon']}, and \ref{['tab:param-ocean-carbon']}. The bifurcation point of the current climate $P_1$ and intermediate branch $P_3$ is shown as a filled blue circle $B_{\rm c}$ with coordinates $(T_c = 290$ K, $e_c = 31.5$ GtC/yr) for $V = 0$ and $(T_c = 290$ K, $e_c = 21.5)$ GtC/yr for $V = 0.3$, while the other bifurcation point $B_{d}$, shown as a filled red circle, has coordinates $(T_d = 294.2$ K, $e_d = 16.5$ GtC/yr) for both $V=0$ and $V=0.3$.
• Figure 5: Evolution of the global temperature anomalies, carbon stocks, and carbon fluxes in our TCV model with anthropogenic forcing. The parameter values used are given in Tables \ref{['tab:param-temp']}, \ref{['tab:param-terrestrial-carbon']}, and \ref{['tab:param-ocean-carbon']}. and the results are shown for Representative Carbon Pathways (RCPs) RCP 2.6 (blue), RCP 4.5 (orange), and RCP 6.0 (brown) Meinshausen2011. Preindustrial initial state is $(T_0 = 286.5\,{\rm K}, \,C_{A,0} = 589\,{\rm{GtC}})$. (a) Temperature anomaly evolution, with observed anomalies in solid black NOAA2023; (b) atmospheric carbon stock $C_{\rm A}$, with observed stock in solid black Friedlingstein_2022; (c) Fluxes $F_{{{\rm A}} \to {{\rm O}} }$ to the ocean mixed layer; and (d) fluxes $F_{{{\rm A}} \to {{\rm L}} }$ to the land vegetation. The minimum (dashed), maximum (dotted) and median (light solid) lines in panels (c) and (d) are based on different observation and model-based estimates of carbon fluxes aggregated in the Global Carbon Budget Friedlingstein_2022.