"Rational Control of Global Warming Dynamics Via the CO2 Level, Emission Reductions and Forestry Expansion"

Abstract

First, the observed CO 2 level in the atmosphere, recorded by NOAA [1] at the Mauna Loa observatory, and the global industrial CO 2 emissions, reported by EDGAR [2], European Commission, are investigated, from 1990 until 2021. Then, a differential equation model is developed, based on two hypotheses, that explains how these time series interact. The hypotheses of the explaining model are tested with regression analysis, and it is demonstrated that no hypothesis can be rejected on statistical grounds. The parameters of the CO 2 concentration model are determined with high t-values and low p-values. The model is used to determine the time path of the CO 2 concentration of the natural system without industrial emissions, for arbitrary initial conditions. This system has a unique and stable equilibrium at 262 ppm. With constant industrial emissions, the equilibrium is found at a higher level, which is shown with an explicit equation. Comparative statics analysis shows how the equilibrium is affected by alternative parameter adjustments. An extended version of the natural differential equation, with a forcing function, representing the time paths of industrial emissions, is developed. The industrial emissions are modeled as a quadratic function of time. The general function of the time path of the CO 2 concentration of the natural system under the influence of industrial emissions, is determined for arbitrary initial conditions and parameters of the industrial emission function.The CO 2 time path function is analytically verified. Then, it is also empirically tested and found to be able to reproduce the historical CO 2 observations with high precision. Then, the time paths of the future CO 2 concentrations are calculated, for six alternative levels of change of the industrial emissions, from -1.5 Gt/year to +1.0 Gt/ year, from the year 2022 until 2100. These results are presented as a function and as graphs. The net CO 2 emissions can also be reduced over time, if forestry is gradually intensified. The rational intensity of this investment process is determined, taking the time path of the CO 2 level into consideration, during an arbitrary time interval. An explicit function for the optimal forestry intensification level, based on all CO 2 time path function parameters, the marginal cost of the CO 2 concentration, time interval parameters, rate of interest and different cost function parameters, is derived and presented.

Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations

“…The global warming problem, for instance, can be solved via optimal combinations of emission reductions and expansion of sustainable forestry. This is reported by Lohmander (2022a) and(2022b), where also a global CO2 model is defined, based on official atmospheric CO2 data series and dynamic global emission data. The future consequences of alternative global emission reduction levels, and forestry expansion strategies, are calculated and presented.…”

“…Hence, a nonlinear full system equilibrium analysis of the interdependent processes is performed. Lohmander, et al (2022b). The data have been organized in 8 diameter classes, and transformed to the relative frequency diagram found above.…”

“…The empirically estimated relative frequencies of trees in different diameter classes. Source: The empirical data have been obtained from the five graphs denoted Figure 1, in Fagerberg, Olsson,Lohmander, et al (2022b). The data have been organized in 8 diameter classes, and transformed to the relative frequency diagram found above.…”