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Coupled EBM Project Update 10/4

Equations As of Now

C_{v}\frac{dT}{dt}= \psi(1-A)-I+\nabla \cdot \left (\kappa \nabla T \right)
\frac{dP}{dt}=\epsilon N
\frac{dN}{dt}=r(T)N
r(T) = E(r_{birth} (T) - r_{death} (T))=E[B_{0}e^{-(\frac{T-T_{max}}{\Delta T})^{2}}-D_{0}e^{(\frac{T-T_{max}}{\Delta T})^{2}}]

T = Temperature
P = pCO2
- \epsilon = per-capita carbon footprint
N = Population
- r(T) = per-capita growth rate, dependent on temperature
- T_{max}=temperature resulting in optimum growth rate
- \Delta T = exponential ramping distance
- E = proxy for technology, kept constant here

Methodology

Run energy balance model until equilibrium is reached, with an average global temperature of T_{eq}
Center the optimum growth rate for the civilization to that temperature, ie: set T_{max}=T_{eq}
Turn on coupling functionality, which allows population to rise, causing more CO2 to be in the atmosphere, which inevitably raises global temperatures past a habitable point