Adaptive mobile firefighting resources: stochastic dynamic optimization of international cooperation

Lohmander, Peter

doi:10.15406/iratj.2020.06.00213

Cited by 2 publications

(4 citation statements)

References 9 publications

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“…First, we study how the CO 2 equilibrium level in the atmosphere changes if the natural emissions increase. This is found in equation (14). Equation ( 15) follows.…”

Section: Methodsmentioning

confidence: 99%

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

Lohmander¹

2022

BJSTR

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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.

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“…First, we study how the CO 2 equilibrium level in the atmosphere changes if the natural emissions increase. This is found in equation (14). Equation ( 15) follows.…”

Section: Methodsmentioning

confidence: 99%

“…Forest fires cause severe problems in many countries. Forest fire areas in nine European countries were investigated by Lohmander [14] with respect to yearly averages, standard deviations and correlations between nations.…”

Section: Introductionmentioning

confidence: 99%

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

Lohmander¹

2022

BJSTR

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“…In case we can show that the second order minimum condition ( 9) is satisfied, then we have a unique minimum (10). However, this will be investigated in detail before we can be sure.…”

Section: ( ) ( )mentioning

confidence: 97%

“…The optimal use of such resources and optimal international cooperation in this area has been analyzed via stochastic dynamic programming, by Lohmander. 10 In many cases, conditions of relevance to fire management change rapidly. For instance, in Canada and Russia, the probabilities of severe wild fires are very low during the winter, when snow covers the forests.…”

Section: Introductionmentioning

confidence: 99%

Optimization of distance between fire stations: effects of fire ignition probabilities, fire engine speed and road limitations, property values and weather conditions

Lohmander¹

2021

IRATJ

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A general spatial fire brigade unit network density optimization problem has been solved. The distance to a particular road, from a fire station, is approximated as a continuous variable. It is proved, via integral convolution, that the probability density function of the total travel time, PDFT, is triangular. The size of the fire, when it stopped, is a function of the time it takes until the fire brigade reaches the fire location. An explicit continuous function for the expected total cost per square kilometer, based on the cost per fire station, the PDFT, the exponential fire cost function parameters, the distance between fire stations, and the speed of fire engines, is derived. It is proved that the optimal distance between fire brigade unit positions, OFD, which minimizes the total expected cost, is unique. Then, the OFDs are replaced by integers, OFDIs, for different parameter assumptions. In this process, also the optimal expected total costs are determined. It is proved that the OFD is a strictly decreasing function of the expected number of fires per area unit, a strictly increasing function of the speed of the fire engines, a strictly decreasing function of the parameters of the exponential fire cost function, and a strictly increasing function of the cost per fire station. These effects of parameter changes are also illustrated via graphs in the numerical section.

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Adaptive mobile firefighting resources: stochastic dynamic optimization of international cooperation

Cited by 2 publications

References 9 publications

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

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

Optimization of distance between fire stations: effects of fire ignition probabilities, fire engine speed and road limitations, property values and weather conditions

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