Planet-Civ Evolution Project Update 11/6

Energy Balance Model (EBM)

The EBM reaches equilibrium at Teq. Below are plots of this for varying distances and partial CO2 pressures (pCO2):
​3D Plot (top view)
​3D Plot (side view)
​Contour Plot

Numerical Model

​Code Location on GitHub (Initial Conditions: t=1880, pCO2=284ppm, N=1.13 Billion People)

General Simulation Steps

  1. Run program with Earth like inputs as they were before the Anthropocene (in 1880), until an equilibrium temperature is reached.
  2. Set the populations peak growth rate to this temperature ​as shown here.
  3. Then turn on population growth; exponential rise in population results in exponentially increasing partial CO2 pressures, ultimately triggering a global climate change. Once the global temperatures pass a certain point, the growth rate of the population becomes negative, which results in mass extinction.

Goal #1

Repeat steps 1-3 for four different values of initial partial CO2 pressure, ranging from a tenth of ours to one hundred times ours. At each new value of pCO2, determine the habitable zone for that point, defined here to be where water can be liquid (273-373K).
Then repeat steps 1-3 for 4 different values of orbital distance, spanning the entirety of that habitable zone.
​Results Shown Here (as 4x4 grid)

Goal #2

Choose 3 different orbital distances. For each one, increase pCO2 until the equilibrium temperature reaches 287.09K (the temperature of earth at 1AU).
​Results Shown Here (Earth included for reference)

Next Steps

  1. Model 1: Introduce constant carrying capacity (maximum population)
  2. Model 2: Introduce a temperature-dependence to the carrying capacity, to emulate reduction of habitable regions due to global climate change.
  3. Model 3: Introduce a time-dependence to the carrying capacity, to emulate environmental sensitivity to climate change. So environments with low sensitivity could exceed their carrying capacities for a longer time than ones with higher sensitivity before climate change begins.

Analytical Model

​Current state of the Equations and Nondimensionalization Process
​Phase Diagrams of Analytic Model

Comments

No comments.