The relation between CO₂ emissions and atmospheric CO₂ concentration has traditionally been treated with more or less complex models with several boxes. Our approach is motivated by the question of how much CO₂ must necessarily be absorbed by sinks. This is determined by accepted measurements and the global carbon budget. Observations lead to the model assumption that carbon sinks, similar to oceans or the biosphere, are linearly dependent on CO₂ concentration on a decadal scale. In particular, this implies the falsifiable hypothesis that oceanic and biological CO₂ buffers have not significantly changed in the past 70 years and are not saturated in the foreseeable future. A statistical model with two parameters is built from the global carbon budget and two testable assumptions. This model explains the relation between CO₂ emission and historical CO₂ concentration data very well. The model gives estimates of the natural emissions, the pre-industrial CO₂ equilibrium concentration levels, the half-life time of an emission pulse, and the future CO₂ concentration level from a given emission scenario. It is validated by an ex-post forecast of the last 20 years. The important result is that, with the stated polices emission scenario of the International Energy Agency (IEA), the future CO₂ concentrations will not rise above 475 ppm. The model is compared with the carbon module of the Bern model, mapping their complex impulse response functions (IRFs) to a single time variant absorption parameter.

While the simple model of the total atmospheric carbon sink effect as a linear function of concentration has provided excellent prediction results, several problems remained to be investigated and solved. The most obvious open issue is the correct treatment of land use change emissions. It turns out that the model improves by mostly neglecting these emissions after 1950. This effectively implies that land use change emissions have been constant and small since then. The key investigation starts with the observation that the total carbon sink has a short-term component that can be explained by temperature changes. The apparent paradox, why contrary to the short-term changes no temperature-caused trend can be detected, despite the fact that several contributing processes exhibit clear temperature dependency, is analyzed and explained. The result of this analysis leads to the model extension, where the total effect of absorptions and natural emissions are a linear function of concentration and temperature. This extended model not only explains current measurements but also paleo-climate data from ice core time series.

While the simple model of the total atmospheric carbon sink effect as a linear function of concentration has provided excellent prediction results, several problems remained to be investigated and solved. The most obvious open issue is the correct treatment of land use change emssions. It turns out that the model improves by mostly neglecting them after 1959. This effectively implies that land use change emissions have been constant and small since then. The key investigation starts with the observation, that the total carbon sink has a short term component which be explained by temperature changes commonly known as El Nin˜o. The apparent paradox is analysed and explained, why contrary to the short term changes no temperature caused trend can be detected in the model, despite the fact that several contributing processes exhibit temperature dependency. The result of this analysis leads to the model extension, where the total effect of sinks and natural emissions are a linear function of concentration and temperature. This model not only explains current measurements but also paleo climate from ice-core time series.

The relation between CO2 emissions and atmospheric CO2 concentration has traditionally been treated with more or less complex models with several boxes. Our approach is motivated by the question of how much CO2 must necessarily be absorbed by sinks. Observations lead to the model assumption, that carbon sinks like oceans or biosphere are linearly dependent on CO2 concentration on a decadal scale. In particular this implies the falsifiable hypothesis that oceanic and biological CO2 buffers have not significantly changed in the past 50 years and are not saturated in the forseeable future. The simple model with 2 parameters explains very well the CO2 emission and historical CO2 concentration data. The model gives estimates of the natural emissions, the pre-industrial CO2 equilibrium concentration levels, the half-life time of an emission pulse, and the future CO2 concentration level from a given emission scenario. This is validated by an ex-post forecast of the last 20 years. The important result is that with the stated polices scenario of the IEA future CO2 concentrations will not rise above 475 ppm. The model is compared with the Carbon modul of the Bern model, mapping their complex IRFs to a single time variant parameter.

Weather-dependent, volatile energy sources, such as wind power and solar photovoltaics (PV), contribute considerably to the German electric energy supply. The current German government aims to substantially increase their market share. Using high-resolution time-series data from energy production and demand measurements, we replicate and analyze scenarios from the “Klimaneutrales Deutschland 2045” (KND2045) study. KND2045 was the basis for the German Government’s 2021 decision to move the abolition of CO₂ emissions from 2050 to 2045. The primary question in KND2045 is whether security of supply can be maintained by relying primarily on an effective duopoly of wind and solar power. We simulate scenarios for 2023, 2030, and 2045 using 15-min time-resolved measurements of wind and solar energy production and demand from 2023 and 2024, incorporating battery and gas storage systems into our model. We assess the overall economic costs for these scenarios. Our calculations demonstrate that the KND2045 scenarios are infeasible, as significant supply gaps persist during dark wind lulls, compromising security of supply. Instead, we propose improvements to these scenarios by incorporating nuclear energy as a backup to address KND2045’s shortcomings.

The successful application of simple statistical methods in economic modelling suggest that similar methods could provide insight into global climate. We apply an autoregressive method to observed time series to determine the dependence of atmospheric CO2 concentration on carbon emissions and, in turn, the dependence of globally averaged temperature on atmospheric CO2 concentration. We ascribe physical meaning to the regression parameters in terms of first order differential equations describing the diffusion of CO2 and temperature between reservoirs, viz.: the diffusion of CO2 between the atmosphere and the deep ocean and the transport of heat from the mixed layer. A strong feature of regression models is their built-in mechanism for deciding when a model provides an adequate description of the given data. Two implications of this statistically robust approach are that CO2 diffuses from the atmosphere within a time scale of decades and that global average temperatures are unlikely to exceed 2 deg C above pre-industrial values.