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Dynamics and control of the CO2 level via a differential equation and alternative global emission strategies


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Abstract

The analysis in this paper shows that the fundamental theory of the CO2 level in the atmosphere, under the influence of changing CO2 emissions, can be modeled as a first order linear differential equation with a forcing function, describing industrial emissions. 
 
Observations of the CO2 level at the Mauna Loa CO2 observatory and official statistics of global CO2 emissions, from Edgar, the Joint Research Centre at the European Commission, are used to estimate all parameters of the forced CO2 differential equation.
 
The estimated differential equation has a logical theoretical foundation and convincing statistical properties. It is used to reproduce the time path of the CO2 data from Mauna Loa, from year 1990 to 2018, with very small errors. Furthermore, the differential equation shows that the global CO2 level, without emissions, has a stable equilibrium at 280 ppm. This value has earlier been reported by IPCC as the pre-industrial CO2 level.
 
The differential function is applied to derive four dynamic cases of the global CO2 level, from the year 2020 until 2100, conditional on four different strategies concerning the development of global CO2 emissions: 
i. Emissions continue to increase according to the trend during 1990–2018
ii. Emissions stay for ever at the 2020 level
iii. Emissions are reduced with a linear trend to become zero year 2100
iv. Emissions are reduced with a linear trend to become zero year 2050
In case i., the CO2 level year 2100 will be 688 ppm. In cases ii. and iii., the CO2 levels in 2100 will be 517 ppm and 389 respectively. In case iv., the CO2 level in 2050 is 408 ppm and then rapidly falls.

Keywords

global warming, dynamics, global emissions, emissions strategies, atmosphere, transformations, factors, european commission, precision, equation, precision, probability, equilibrium, parameters

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