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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Co-Optimization of Sustainable Aviation Fuel: Cost, Emissions, and Performance

The combustion of petroleum-based fuels contributes to increases in atmospheric CO2, contributing to climate change. As other sectors electrify, current battery technology makes this impractical for the aviation industry. The fastest pathway to reducing the carbon contributions of aviation is to create low or no net carbon-emitting drop-in petroleum alternatives. This research explores 3 potential sorghum derived jet fuel molecules from 4 different production routes, hydro-processed esters and fatty acids (HEFA), and Jet A, to identify how blends including these fuels could offer improved performance (MJ/kg, MJ/L) and improved emissions (gCO2/MJ) while minimizing costs. Different applications will value each target metric differently. This research utilizes the Jet Fuel Blend Optimizer (JudO) to create a 4-dimensional Pareto front across potential solutions. The molecules considered will not offer reduced cost compared to conventional jet fuel (Jet A), but they can be utilized to create blends with higher specific energy, greater energy density, and reduced greenhouse gas emissions. Considerations including carbon credits, the sale of byproducts, and the valuation of improved performance will make the proposed molecules more commercially viable. At the lowest region of GHG solutions, coupled with equivalent LCFS approximations, JudO determined blends that could achieve as high as 69% overall carbon reductions at a premium of $0.34/L.

Feldhausen, John J.↗
NASA NTRS2020

Evaluating China's fossil-fuel CO2 emissions from a comprehensive dataset of nine inventories

China's fossil-fuel CO2 (FFCO2) emissions accounted for approximately 28 % of the global total FFCO2 in 2016. An accurate estimate of China's FFCO2 emissions is a prerequisite for global and regional carbon budget analyses and the monitoring of carbon emission reduction efforts. However, significant uncertainties and discrepancies exist in estimations of China's FFCO2 emissions due to a lack of detailed traceable emission factors (EFs) and multiple statistical data sources. Here, we evaluated China's FFCO2 emissions from nine published global and regional emission datasets. These datasets show that the total emissions increased from 3.4 (3.0–3.7) in 2000 to 9.8 (9.2–10.4) Gt CO2 per yr in 2016. The variations in these estimates were largely due to the different EF (0.491–0.746 t C per t of coal) and activity data. The large-scale patterns of gridded emissions showed a reasonable agreement, with high emissions being concentrated in major city clusters, and the standard deviation mostly ranged from 10 % to 40 % at the provincial level. However, patterns beyond the provincial scale varied significantly, with the top 5 % of the grid level accounting for 50 %–90 % of total emissions in these datasets. Our findings highlight the significance of using locally measured EF for Chinese coal. To reduce uncertainty, we recommend using physical CO2 measurements and use these values for dataset validation, key input data sharing (e.g., point sources), and finer-resolution validations at various levels.

Pengfei Han↗
NASA NTRS2017

Young People's Burden: Requirement of Negative CO2 Emissions

Global temperature is a fundamental climate metric highly correlated with sea level, which implies that keeping shorelines near their present location requires keeping global temperature within or close to its preindustrial Holocene range. However, global temperature excluding short-term variability now exceeds +1 C relative to the 1880 - 1920 mean and annual 2016 global temperature was almost +1.3 C. We show that global temperature has risen well out of the Holocene range and Earth is now as warm as it was during the prior (Eemian) interglacial period, when sea level reached 6 - 9 m higher than today. Further, Earth is out of energy balance with present atmospheric composition, implying that more warming is in the pipeline, and we show that the growth rate of greenhouse gas climate forcing has accelerated markedly in the past decade. The rapidity of ice sheet and sea level response to global temperature is difficult to predict, but is dependent on the magnitude of warming. Targets for limiting global warming thus, at minimum, should aim to avoid leaving global temperature at Eemian or higher levels for centuries. Such targets now require "negative emissions", i.e., extraction of CO2 from the air. If phasedown of fossil fuel emissions begins soon, improved agricultural and forestry practices, including reforestation and steps to improve soil fertility and increase its carbon content, may provide much of the necessary CO2 extraction. In that case, the magnitude and duration of global temperature excursion above the natural range of the current interglacial (Holocene) could be limited and irreversible climate impacts could be minimized. In contrast, continued high fossil fuel emissions today place a burden on young people to undertake massive technological CO2 extraction if they are to limit climate change and its consequences. Proposed methods of extraction such as bioenergy with carbon capture and storage (BECCS) or air capture of CO2 have minimal estimated costs of USD 89 - 535 trillion this century and also have large risks and uncertain feasibility. Continued high fossil fuel emissions unarguably sentences young people to either a massive, implausible cleanup or growing deleterious climate impacts or both.

Hansen, James↗
DOE OSTI2023

Analysis of Uncertainty Impacts on Emissions and Fuel Economy Evaluation for Chassis Dynamometer Testing

This study illustrates a methodology for quantifying the uncertainties encountered in the measurement of tailpipe emissions and in the fuel consumption measurements for light-duty conventional vehicles tested on a four-wheel drive chassis dynamometer. The study leverages high-fidelity experimental data collected over three standard drive cycles, UDDS, HWY and US06, intended to simulate a wide range of operating conditions. Here, a method is developed to estimate the measurement uncertainties in fuel consumption for a test cycle, which occur due to the accumulation of measurement uncertainties propagated through the system. The uncertainty determination model uses statistical analysis and standard propagation techniques to evaluate and combine the uncertainties introduced from various sources (including the vehicle, chassis dynamometer, driver, and instrumentation). The analysis also examines three different experimental methods for determining the fuel consumption: 1) carbon mass balance, 2) volumetric fuel scale and 3) gravimetric fuel scale, and takes into consideration the properties of the instrumentation used. The results show that the most significant influence on the determination of the emissions comes from the concentration measurement, and similarly the biggest impact on the total fuel consumption uncertainty comes from the uncertainty in the determination of the carbon dioxide mass, due to the large presence of this pollutant in the overall emissions. It was found that the fuel consumption uncertainties are in the range of ±1-2% for all three methods analyzed, with the lowest values being obtained for measurements performed using the gravimetric method for all three drive cycles considered.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS2018

The Use of Gridded Fossil Fuel CO2 Emissions (FFCO2) Inventory for Climate Mitigation Applications: Errors, Uncertainties, and Current and Future Challenges

Emission Inventory (EI) is a fundamental tool to monitor global compliance of greenhouse gases (GHGs) emissions reduction actions. Inventory guidelines provide a best practice to help EI compilers to make comparable national emission estimates, in spite of the differences in data availability across countries and regions. There are a variety of sources of errors and uncertainties, however, that originate beyond what the inventory guidelines define. For example, spatially-explicit EIs, which are a key product for atmospheric modeling applications, are often developed for research purposes, and there are no specific guidelines to disaggregate emission estimates from country scale. On top of that, EIs are fundamentally prone to systematic biases due to the simple calculation methodology and thus an objective evaluation (e.g. atmospheric top-down estimates) is needed to assure the accuracy of the estimates. ODIAC is a global high-resolution (1x1 km) fossil fuel carbon dioxide (CO2) gridded EI that is now often used in atmospheric CO2 modeling. ODIAC is based on disaggregation of national emission estimates made by CDIAC, which is the well accepted standard in the community. The ODIAC emission data product is updated on an annual basis using best available statistical data. Subnational spatial emission patterns are estimated using power plant profiles and satellite-observations of nighttime lights. In addition to the conventional CDIAC gridded data product, ODIAC carries international bunker emissions (shipping and aviation), which allows flux inversion modelers to accurately impose the global total fossil fuel emissions and their horizontal and vertical distribution. We have extensively evaluated ODIAC emissions using fine-grained EIs as well as a high-resolution atmospheric model simulation across different scales (national, subnational/regional, and urban policy relevant) with a focus on the uncertainties associated with the emission disaggregation. We have examined the use of NASA's Black Marble Suomi-NPP/VIIRS nightlight data.

Oda, Tomohiro↗
DOE OSTI2024

Hydrogen Infrastructure Analysis for the Port Applications [Slides]

The International Maritime Organization has committed to 50% reduction in GHG emissions by 2050 worldwide as of 2023. This analysis includes performing an inventory and modeling efforts to understand the energy, equipment and cost requirements to support decarbonization of cargo handling and shore power at U.S. Ports, along with assessment of zero- and near- zero emission fuel supplies at or near U.S. ports focused upon Hydrogen technologies. Initial market assessment for ocean going vessels for harbor support and ocean-going vessels is explored. An energy analysis is performed on the port system using a holistic approach and considering the port as an entire ecosystem that functions as a transportation and energy node. Presently, a comprehensive view is lacking for future analysis efforts, this analysis seeks to address this gap in data by evaluating four representative port types and the potential for utilizing hydrogen for the maritime industry. Every port is different, but broadly they could be bracketed into reference cases with scaling factors for the relative size of the port operations. These reference ports are for future use, potentially as baselines for analysis and development of demonstration programs. An equipment inventory for each reference port type (container, bulk, breakbulk, and inland waterway) is presented. A comparative analysis of fuel cell electric and battery electric equipment is conducted based on the following criteria: technology readiness level, refueling/charging time, operational range, energy consumption, and fuel cost savings compared to baseline internal combustion engine equipment. The tradeoffs and synergies between two alternative powertrains is highlighted. Based on energy and infrastructure analysis, average and high equipment utilization profiles across different port types is identified and quantified baseline fuel and electricity demand for various decarbonization scenarios. Based on the portfolio of equipment converted to fuel cell electric, the estimates of initial capital investment are provided for hydrogen refueling stations across ports. An energy demand model is developed that predicts well the all-electric cargo handling equipment annual energy consumption for ports with annual tonnage under 2 million twenty-foot equivalent units (TEUs). The model is a good rubric to follow for further energy demand models that can create a scalable solution to understand the energy needs of cargo handling equipment, whether they are all-electric, hydrogen fuel cell, or powered by another fuel-type. Zero and near-zero emission fuel supply at ports is evaluated looking into the characteristics of hydrogen, ammonia, and methanol as an alternative fuel, as well as the bunkering status. The readiness of reference ports to produce ammonia or methanol and bunker the fuel is examined based on the framework developed by the Global Maritime Forum and Rocky Mountain Institute.

08 HYDROGEN↗
DOE OSTI2021

Multi-scale evaluation of diesel commuter rail fuel use, emissions, and eco-driving

Diesel commuter rail emissions affect populations near rail corridors. An approach is demonstrated to quantify mesoscale and microscale diesel commuter rail fuel use and emission rates (FUERs) of CO 2 , CO, NO x , particulate matter, and total hydrocarbons based on two U.S. systems. A speed trajectory simulator, an energy model, and an emissions model were calibrated, evaluated, and applied. FUERs and potential reductions from eco-driving were quantified based on simulated trajectories. Hotspots were defined as sections with ≥ 90 th percentile of section-average FUERs by species. A few key variables explain 74–80% of variability in mesoscopic and microscopic FUERs. On average, FUERs are 7–8 times greater for hotspots than non-hotspots. Eco-driving was estimated to reduce segment-average FUERs by 3–33% and eliminate 2–11% hotspots. However, mesoscale oriented eco-driving can, at some locations, increase microscopic FUERs. The approach is adaptable to other diesel commuter rail systems.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2020

Constraining Fossil Fuel CO2 Emissions from Urban Area Using OCO-2 Observations of Total Column CO2

Satellite observations of the total column dry-air CO2(XCO2) are expected to support the quantification and monitoring of fossil fuel CO2 (ffCO2) emissions from urban areas. We evaluate the utility of the Orbiting Carbon Observatory 2 (OCO-2) XCO2 retrievals to optimize whole-city emissions, using a Bayesian inversion system and high-resolution transport modeling. The uncertainties of constrained emissions related to transport model, satellite measurements, and local biospheric fluxes are quantified. For the first two uncertainty sources, we examine cities of different landscapes: “plume city” located in relatively flat terrain, represented by Riyadh and Cairo; “basin city” located in basin terrain, represented by Los Angeles (LA). The retrieved scaling factors of emissions and their uncertainties show prominent variabilities from track to track, due to the varying meteorological conditions and relative locations of the tracks transecting plumes. To explore the performance of multiple tracks in retrieving emissions, pseudo data experiments are carried out. The estimated least number of tracks required to constrain the total emissions for Riyadh (<10% uncertainty), Cairo (<10%), and LA (<5%) are 5, 8, and 7, respectively. Additionally, to evaluate the impact of biospheric fluxes on derivation of the ffXCO2 enhancements, we conduct simulations for Pearl River Delta metropolitan area. Significant fractions of local XCO2 enhancements associated with local biospheric XCO2 variations are shown, which potentially lead to biased estimates of ffCO2 emissions. We demonstrate that satellite measurements can be used to improve urban ffCO2 emissions with a sufficient amount of measurements and appropriate representations of the uncertainty components.

Xinxin Ye↗
NASA NTRS1999

Effects of Passive Fuel-Air Mixing Control on Burner Emissions Via Lobed Fuel Injectors

The present experimental study examines the effects of differing levels of passive fuel-air premixing on flame structures and their associated NO(x) and CO emissions. Four alternative fuel injector geometries were explored, three of which have lobed shapes. These lobed injectors mix fuel and air and strain species inter-faces to differing extents due to streamwise vorticity generation, thus creating different local or core equivalence ratios within flow regions upstream of flame ignition and stabilization. Prior experimental studies of two of these lobed injector flowfields focused on non-reactive mixing characteristics and emissions measurements for the case where air speeds were matched above and below the fuel injector, effectively generating stronger streamwise vorticity than spanwise vorticity. The present studies examine the effects of airstream mismatch (and hence additional spanwise vorticity generation), effects of confinement of the crossflow to reduce the local equivalence ratio, and the effects of altering the geometry and position of the flameholders. NO(x) and CO emissions as well as planar laser-induced fluorescence imaging (PLIF) of seeded acetone are used to characterize injector performance and reactive flow evolution.

Mitchell, M. G.↗
NASA NTRS2013

Assessing 'Dangerous Climate Change': Required Reduction of Carbon Emissions to Protect Young People, Future Generations and Nature

We assess climate impacts of global warming using ongoing observations and paleoclimate data. We use Earth's measured energy imbalance, paleoclimate data, and simple representations of the global carbon cycle and temperature to define emission reductions needed to stabilize climate and avoid potentially disastrous impacts on today's young people, future generations, and nature. A cumulative industrial-era limit of approx.500 GtC fossil fuel emissions and 100 GtC storage in the biosphere and soil would keep climate close to the Holocene range to which humanity and other species are adapted. Cumulative emissions of approx.1000 GtC, sometimes associated with 2 C global warming, would spur "slow" feedbacks and eventual warming of 3-4 C with disastrous consequences. Rapid emissions reduction is required to restore Earth's energy balance and avoid ocean heat uptake that would practically guarantee irreversible effects. Continuation of high fossil fuel emissions, given current knowledge of the consequences, would be an act of extraordinary witting intergenerational injustice. Responsible policymaking requires a rising price on carbon emissions that would preclude emissions from most remaining coal and unconventional fossil fuels and phase down emissions from conventional fossil fuels.

climate↗
NASA NTRS2007

Ultra High Bypass Ratio Engine Research for Reducing Noise, Emissions, and Fuel Consumption

A pictorial history of NASA development of advanced engine technologies for reducing environmental emissions and increasing performance from the 1970s to 2000s is presented. The goals of the Subsonic Fixed Wing Program portion of the NASA Fundamental Aeronautics Program are discussed, along with the areas of investigation currently being pursued by the Ultra High Bypass Partnership Element of the Subsonic Fixed Wing Program.

Hughes, Christopher E.↗
NASA NTRS2008

Collaborative Research on the Ultra High Bypass Ratio Engine Cycle to Reduce Noise, Emissions and Fuel Consumption

A pictorial history of NASA development of advanced engine technologies for reducing environmental emissions and increasing performance from the 1970s to present is presented. The goals of the Subsonic Fixed Wing Program portion of the NASA Fundamental Aeronautics Program are addressed, along with the areas of investigation currently being pursued by the Ultra High Bypass Partnership Element of the Subsonic Fixed Wing Program to meet the goals. Ultra High Bypass cycle research collaboration successes with Pratt & Whitney are presented.

Hughes, Christopher↗
NASA NTRS2018

Future of the North American Carbon Cycle: Chapter - 19

Rising atmospheric carbon dioxide (CO2) concentrations, primarily due to fossil fuel emissions and land-use change, are expected to continue to drive changes in both climate and the terrestrial and ocean carbon cycles. Over the past two-to-three decades, there has been considerable effort to understand how terrestrial and oceanic systems behave (in response to rising atmospheric CO2 and changing climate conditions), quantify the dynamics of system responses to environmental change, and project how the ocean and terrestrial carbon cycle will interact with, and influence, future atmospheric CO2 concentrations and climate. In this presentation, we will summarize key findings related to projected changes to the North American carbon cycle and drivers and associated consequences of these changes, as reported in Chapter 19 of the Second State of the Carbon Cycle Report (SOCCR-2). The findings not only capture projections of emissions from fossil fuel and changes in land cover and land use, but also highlight the decline in future carbon uptake capacity of North American carbon reservoirs and soil carbon losses from the Northern high-latitudes. Such a discussion of future carbon cycle changes is new in SOCCR-2, yet timely. It underlines the progress made since the release of the First State of the Carbon Cycle Report (SOCCR-1) in 2007 in identifying the vulnerability of key carbon pools and their co-evolution with changing climatic conditions. We will also discuss key knowledge gaps and outline a set of future research priorities, including both monitoring and modeling activities, that are necessary to improve projections of future changes to the North American carbon cycle and associated adaptation and resource-management decisions.

North America↗
NASA NTRS1980

Cogeneration Technology Alternatives Study (CTAS). Volume 3: Energy conversion system characteristics

Six current and thirty-six advanced energy conversion systems were defined and combined with appropriate balance of plant equipment. Twenty-six industrial processes were selected from among the high energy consuming industries to serve as a frame work for the study. Each conversion system was analyzed as a cogenerator with each industrial plant. Fuel consumption, costs, and environmental intrusion were evaluated and compared to corresponding traditional values. The advanced energy conversion technologies indicated reduced fuel consumption, costs, and emissions. Fuel energy savings of 10 to 25 percent were predicted compared to traditional on site furnaces and utility electricity. With the variety of industrial requirements, each advanced technology had attractive applications. Fuel cells indicated the greatest fuel energy savings and emission reductions. Gas turbines and combined cycles indicated high overall annual savings. Steam turbines and gas turbines produced high estimated returns. In some applications, diesels were most efficient. The advanced technologies used coal derived fuels, or coal with advanced fluid bed combustion or on site gasifications. Data and information for both current and advanced energy conversion technology are presented. Schematic and physical descriptions, performance data, equipment cost estimates, and predicted emissions are included. Technical developments which are needed to achieve commercialization in the 1985-2000 period are identified.

Source record↗
DOE OSTI2024

Zero Emission Cargo Transport (ZECT) II Demonstration: South Coast Air Quality Management District (Final Report)

The South Coast Air Quality Management District (South Coast AQMD), California Air Resources Board (CARB) and Southern California Association of Governments (SCAG) — the agencies responsible for preparing the State Implementation Plan required under the federal Clean Air Act — have agreed that attainment of federal air quality standards for the region will require a transition to the broad use of zero and near-zero emission energy sources in cars, trucks and other equipment. Accordingly, the 2012 South Coast AQMD Air Quality Management Plan, the SCAG 2012 Regional Transportation Plan, and the “Vision for Clean Air: A Framework for Air Quality and Climate Control Planning” all identify the need to immediately enact a phasing in of zero and near-zero emission technologies to meet air quality goals. In 2014, South Coast AQMD was awarded grant funding under the US Department of Energy Zero Emission Cargo Transport (ZECT) II Demonstration program to develop and demonstrate zero-emission drayage trucks for goods movement operations between the Port of Los Angeles (POLA) and Port of Long Beach (POLB) near dock rail yards and warehouses: 1) development and demonstration of zero-emission fuel cell range extended electric drayage trucks and 2) development and demonstration of hybrid electric drayage trucks. The purpose of this project was to accelerate deployment of zero emission cargo transport technologies to reduce harmful diesel emissions, petroleum consumption and greenhouse gases in the surrounding communities along the goods movement corridors that are impacted by heavy diesel traffic and the associated air pollution. Between 2014 – 2024, six ZECT II zero-emission fuel cell drayage truck platforms, including fuel cell range extended and CNG hybrid trucks, were successfully designed, developed, integrated, built, tested, and demonstrated with drayage fleet operators in transportation corridors within areas of the South Coast AQMD jurisdiction in Southern California such as in and around POLA and POLB. Portable hydrogen refueling was deployed to support the fuel cell vehicles. The project had real-time improvement with on-going debugging and optimizations while the vehicles were under demonstration. All platforms demonstrated sufficient or excess power, torque, and energy to support 82,000lbs Gross Vehicle Weight Rating and gradeability to perform their daily duty cycles. Collectively, the trucks drove over 23,000 miles during their respective demonstration phases. The ZECT II project was the first of its kind to demonstrate the commercial viability that supported the additional technology breakthroughs for Class 8 zero emission trucks and validations as well as the regulatory basis for all the zero-emission regulation that we know today, such as the Innovative Clean Transit regulation, Advanced Clean Trucks and Clean Fleet regulations.

08 HYDROGEN↗
DOE OSTI2025

Quantification of regional net CO 2 flux errors in the Orbiting Carbon Observatory-2 (OCO-2) v10 model intercomparison project (MIP) ensemble using airborne measurements

Inverse model intercomparison projects (MIPs) provide a chance to assess the uncertainties in inversion estimates arising from various sources. However, accurately quantifying ensemble CO 2 flux errors remains challenging and often relies on the ensemble spread. This study proposes a method for quantifying the errors in regional net surface–atmosphere CO 2 flux estimates from models taken from the Orbiting Carbon Observatory-2 (OCO-2) v10 MIP by using independent airborne CO 2 measurements for the period 2015–2017. We first calculate the root mean square error (RMSE) between the ensemble mean of posterior CO 2 concentrations and airborne observations and then isolate the CO 2 concentration errors caused solely by the ensemble mean of posterior net fluxes by subtracting the observation, representation, and transport errors from seven regions. Our analysis reveals that the flux errors projected onto CO 2 space account for 55 %–85 % of the regional average RMSE over the 3 years, ranging from 0.88 to 1.91 ppm. In five regions, the error estimates based on observations exceed those computed from the ensemble spread of posterior fluxes by a factor of 1.33–1.93, implying an underestimation of the actual flux errors, while their magnitudes are comparable in two regions. The adjoint sensitivity analysis identifies that the underestimation of flux errors is prominent where the magnitudes of fossil fuel emissions exceed those of terrestrial-biosphere fluxes by a factor of 3–31 over the 3 years. This suggests the presence of systematic biases in the inversion estimates associated with errors in the prescribed fossil fuel emissions common to all models. Our study emphasizes the value of airborne measurements for quantifying regional errors in ensemble net CO 2 flux estimates.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2017

System-of-Systems Considerations in the Notional Development of a Metropolitan Aerial Transportation System

There are substantial future challenges related to sustaining and improving efficient, cost-effective, and environmentally friendly transportation options for urban regions. Over the past several decades there has been a worldwide trend towards increasing urbanization of society. Accompanying this urbanization are increasing surface transportation infrastructure costs and, despite public infrastructure investments, increasing surface transportation "gridlock." In addition to this global urbanization trend, there has been a substantial increase in concern regarding energy sustainability, fossil fuel emissions, and the potential implications of global climate change. A recently completed study investigated the feasibility of an aviation solution for future urban transportation (refs. 1, 2). Such an aerial transportation system could ideally address some of the above noted concerns related to urbanization, transportation gridlock, and fossil fuel emissions (ref. 3). A metro/regional aerial transportation system could also provide enhanced transportation flexibility to accommodate extraordinary events such as surface (rail/road) transportation network disruptions and emergency/disaster relief responses.

Alonso, Juan J.↗
DOE OSTI2025

On a simplified solution of climate-carbon dynamics in idealized flat10MIP simulations

Abstract. Idealized experiments with coupled climate-carbon Earth system models (ESMs) provide a basis for understanding the response of the carbon cycle to external forcing and for quantifying climate-carbon feedbacks. Here, we analyze globally-averaged results from idealized esm-flat10 experiments and show that most models exhibit a quasi-linear relationship between cumulative carbon uptake on land and in the ocean during a period of constant fossil fuel emissions of 10 Pg C yr−1. We hypothesize that this relationship does not depend on emission pathways. Further, as a simplification, we quantify the relationship between cumulative ocean carbon uptake and changes in ocean heat content using a linear approximation. In this way, changes in oceanic heat content and atmospheric CO2 concentration become interdependent variables, reducing the coupled temperature-CO2 system to just one differential equation. The equation can be solved analytically or numerically for the atmospheric CO2 concentration as a function of fossil fuel emissions. This approach leads to a simplified description of global carbon and climate dynamics, which could be used for applications beyond existing analytical frameworks.

Brovkin, Victor↗