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Coupled EBM Project Update 7/22

The above graph details what range of temperatures an unprotected human can survive in…

Minimum Temperature: 70^{o}F=21^{o}C
Maximum Temperature: 140^{o}F=60^{o}C

Coupling Population Growth Equation to EBM

Goal: Couple the logistic growth equation to the energy balence model (EBM) by putting a temperature dependence on the relative growth rate

\qquad \qquad \qquad \qquad \qquad \qquad \quad \qquad \frac{dN}{dt}=\alpha (T,E)N(1-\frac{N}{N_{max}})

N = current population
N_{max} = maximum population
\alpha (T,E) = relative growth rate
- T = temperature
- E = technological efficiency (ie: measurement of how much technology a civilization has)

Method: the behavior we desire can be modelled by the difference of two gaussian functions, corresponding to the average birth rate and death rate of a civilization:

\quad \alpha_{net} (T,E) = \alpha_{birth} (T,E) - \alpha_{death} (T,E)=E(B_{0}e^{-(\frac{T-T_{max}}{\Delta t})^{2}}-D_{0}e^{(\frac{T-T_{max}}{\Delta t})^{2}})

T_{max} = global temperature resulting in maximum growth rates \approx 98^{o}F
B_{0} = initial growth rate \approx 1/40
D_{0} = initial death rate \approx 1/70
- assuming a 70 year avg lifespan
\Delta t = width of gaussian (or exponential ramping distance)
- \approx 33\ for\ T<T_{max}
- \approx 50\ for\ T\geq T_{max}

astrobear

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Coupled EBM Project Update 7/22

Coupling Population Growth Equation to EBM

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