Parameter optimization using algorithmic differentiation in a reduced-form model of the Atlantic thermohaline circulation

Optimizing some model parameters a reduced-form model of the Atlantic thermohaline circulation (THC) is fitted to data provided by a comprehensive climate model. Different techniques to compute stationary states of the reduced-form model are discussed. The fitting problem is formulated as weighted least squares optimization problem with non-linear constraints that enforce a proper representation of the present climate. Possible formulations of the optimization problem are presented and compared with respect to their numerical treatment. The technique of Algorithmic or Automatic Differentiation (AD) is used to provide gradient information that can be used in the optimization. The application of the AD software is described in detail and numerical results are given

Path independence of carbon budgets when meeting a stringent global mean temperature target after an overshoot

Emission pathways that are consistent with meeting the Paris Agreement goal of holding global mean temperature rise well below 2 °C often assume a temperature overshoot. In such overshoot scenarios, a given temperature limit is first exceeded and later returned to, under the assumption of large‐scale deliberate carbon dioxide removal from the atmosphere. Here we show that although such strategy might result in a reversal of global mean temperature, the carbon cycle exhibits path dependence. After an overshoot, more carbon is stored in the ocean and less on land compared to a scenario with the same cumulative CO2 emissions but no overshoot. The near‐path independence of surface air temperature arises despite the path dependence in the carbon cycle, as it is offset by path dependence in the thermal response of the ocean. Such behavior has important implications for carbon budgets (i.e. the total amount of CO2 emissions consistent with holding warming to a given level), which do not differ much among scenarios that entail different levels of overshoot. Therefore, the concept of a carbon budget remains robust for scenarios with low levels of overshoot (up to 300 Pg C overshoot considered here) but should be used with caution for higher levels of overshoot, particularly for limiting the environmental change in dimensions other than global mean temperature rise

The Zero Emissions Commitment Model Intercomparison Project (ZECMIP) contribution to C4MIP: Quantifying committed climate changes following zero carbon emissions

The amount of additional future temperature change following a complete cessation of CO2 emissions is a measure of the unrealized warming to which we are committed due to CO2 already emitted to the atmosphere. This “zero emissions commitment” (ZEC) is also an important quantity when estimating the remaining carbon budget – a limit on the total amount of CO2 emissions consistent with limiting global mean temperature at a particular level. In the recent IPCC Special Report on Global Warming of 1.5 ∘C, the carbon budget framework used to calculate the remaining carbon budget for 1.5 ∘C included the assumption that the ZEC due to CO2 emissions is negligible and close to zero. Previous research has shown significant uncertainty even in the sign of the ZEC. To close this knowledge gap, we propose the Zero Emissions Commitment Model Intercomparison Project (ZECMIP), which will quantify the amount of unrealized temperature change that occurs after CO2 emissions cease and investigate the geophysical drivers behind this climate response. Quantitative information on ZEC is a key gap in our knowledge, and one that will not be addressed by currently planned CMIP6 simulations, yet it is crucial for verifying whether carbon budgets need to be adjusted to account for any unrealized temperature change resulting from past CO2 emissions. We request only one top-priority simulation from comprehensive general circulation Earth system models (ESMs) and Earth system models of intermediate complexity (EMICs) – a branch from the 1 % CO2 run with CO2 emissions set to zero at the point of 1000 PgC of total CO2 emissions in the simulation – with the possibility for additional simulations, if resources allow. ZECMIP is part of CMIP6, under joint sponsorship by C4MIP and CDRMIP, with associated experiment names to enable data submissions to the Earth System Grid Federation. All data will be published and made freely available

Long-term climate change commitment and reversibility: an EMIC intercomparison

This paper summarizes the results of an intercomparison project with Earth System Models of Intermediate Complexity (EMICs) undertaken in support of the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5). The focus is on long-term climate projections designed to: (i) quantify the climate change commitment of different radiative forcing trajectories, and (ii) explore the extent to which climate change is reversible on human timescales. All commitment simulations follow the four Representative Concentration Pathways (RCPs) and their extensions to 2300. Most EMICs simulate substantial surface air temperature and thermosteric sea level rise commitment following stabilization of the atmospheric composition at year-2300 levels. The meridional overturning circulation (MOC) is weakened temporarily and recovers to near pre-industrial values in most models for RCPs 2.6–6.0. The MOC weakening is more persistent for RCP 8.5. Elimination of anthropogenic CO2 emissions after 2300 results in slowly decreasing atmospheric CO2 concentrations. At year 3000 atmospheric CO2 is still at more than half its year-2300 level in all EMICs for RCPs 4.5–8.5. Surface air temperature remains constant or decreases slightly and thermosteric sea level rise continues for centuries after elimination of CO2 emissions in all EMICs. Restoration of atmospheric CO2 from RCP to pre-industrial levels over 100–1000 years requires large artificial removal of CO2 from the atmosphere and does not result in the simultaneous return to pre-industrial climate conditions, as surface air temperature and sea level response exhibit a substantial time lag relative to atmospheric CO2

Is there warming in the pipeline? A multi-model analysis of the Zero Emissions Commitment from CO₂

The Zero Emissions Commitment (ZEC) is the change in global mean temperature expected to occur following the cessation of net CO2 emissions and as such is a critical parameter for calculating the remaining carbon budget. The Zero Emissions Commitment Model Intercomparison Project (ZECMIP) was established to gain a better understanding of the potential magnitude and sign of ZEC, in addition to the processes that underlie this metric. A total of 18 Earth system models of both full and intermediate complexity participated in ZECMIP. All models conducted an experiment where atmospheric CO2 concentration increases exponentially until 1000 PgC has been emitted. Thereafter emissions are set to zero and models are configured to allow free evolution of atmospheric CO2 concentration. Many models conducted additional second-priority simulations with different cumulative emission totals and an alternative idealized emissions pathway with a gradual transition to zero emissions. The inter-model range of ZEC 50 years after emissions cease for the 1000 PgC experiment is −0.36 to 0.29 ∘C, with a model ensemble mean of −0.07 ∘C, median of −0.05 ∘C, and standard deviation of 0.19 ∘C. Models exhibit a wide variety of behaviours after emissions cease, with some models continuing to warm for decades to millennia and others cooling substantially. Analysis shows that both the carbon uptake by the ocean and the terrestrial biosphere are important for counteracting the warming effect from the reduction in ocean heat uptake in the decades after emissions cease. This warming effect is difficult to constrain due to high uncertainty in the efficacy of ocean heat uptake. Overall, the most likely value of ZEC on multi-decadal timescales is close to zero, consistent with previous model experiments and simple theory

Irreversible Ocean Thermal Expansion under Carbon Dioxide Removal

In the Paris Agreement in 2015 countries agreed on holding global mean surface air warming to “well below 2 ◦C above pre-industrial” levels, but the emission reduction pledges under that agreement are not ambitious enough to meet this target. Therefore, the question arises of whether restoring global warming to this target after exceeding it by artificially removing CO2 from the atmosphere is possible. One important aspect is the reversibility of ocean heat uptake and associated sea level rise, which have very long (centennial to millennial) response timescales. In this study the response of sea level rise due to thermal expansion to a 1 % yearly increase of atmospheric CO2 up to a quadrupling of the pre-industrial concentration followed by a 1 % yearly decline back to the pre-industrial CO2 concentration is examined using the University of Victoria Earth System Climate Model (UVic ESCM). We find that global mean thermosteric sea level (GMTSL) continues to rise for several decades after atmospheric CO2 starts to decline and does not return to pre-industrial levels for over 1000 years after atmospheric CO2 is restored to the pre-industrial concentration. This finding is independent of the strength of vertical sub-grid-scale ocean mixing implemented in the model. Furthermore, GMTSL rises faster than it declines in response to a symmetric rise and decline in atmospheric CO2 concentration partly because the deep ocean continues to warm for centuries after atmospheric CO2 returns to the pre-industrial concentration. Both GMTSL rise and decline rates increase with increasing vertical ocean mixing. Exceptions from this behaviour arise if the overturning circulations in the North Atlantic and Southern Ocean intensify beyond pre-industrial levels in model versions with lower vertical mixing, which leads to rapid cooling of the deep ocean