Coupled EBM Project Update 7/15

EBM (Energy Balance Model) = climate model that balances the incoming solar radiation with outgoing infrared radiation (IR) to approximate the temporal progression of planetary temperature

  • Simplifications (from Williams & Kasting (1997))
    • ebm averages heat capacity, surface albedo, and temperature over 10 deg wide latitudinal areas…
      • causes us to overestimate the amplitude of the seasonal cycle over the continents
      • also in doing this we ignore meridional land-sea temperature gradients which affect dynamic heat transport and weather
        • becomes more of an issue with higher obliquity, as these types of planets have very large latitudinal temperature gradient
    • ebm models latitudinal heat transport as diffusion, where in reality, wind patterns and energy transport are much more complicated

Initial IR calculation: linear relationship for outgoing IR, based off of North et al. 1981 (A+BT)

New IR calculation: higher-order polynomial parameterization of outgoing longwave radiation and planetary albedo, from Williams & Kasting (1997) paper, obtained from fits to Jim Kasting's radiative-convective model earthtem_ir

  • Benefits:
    • lets us specify atmospheric co2 levels with variable=pco2 (unit bar)
  • Limitations:
    • error is 4.56 W*m-2
    • this version of ir can be applied for…
      • 190 K < Temperatures < 370 K
      • .00001 bars < pco2 < 10 bars

Exploring the EBM

Goal: Use our Energy Balance Model (EBM) to approximate the width of the habitable zone of our solar system

Method

  • Assuming all other parameters of the Earth are held constant, we change the effective orbital distance (d) by altering the input corresponding to the relative solar constant
    • the solar constant (S) is normally a function of stellar Luminosity and orbital distance, but with Luminosity being constant, it reduces to an inverse square law:

  • The Habitable ("Goldilocks") Zone is defined to be any orbital distance that can result in liquid water:
    • Water Freezes: (blue dotted line)
    • Water Boils: (red dotted line)
  • I then run our uncoupled EBM, with default, deterministic, Earth-like inputs, for three years, and then plot the final global temperatures, discretized by latitude
    • black dotted line is the final globally averaged temperature

https://www.pas.rochester.edu/~esavitch/plots/d0.61.PNG https://www.pas.rochester.edu/~esavitch/plots/d1.PNG https://www.pas.rochester.edu/~esavitch/plots/d1.2.PNG
The table below summarizes the findings from the plots above…

Orbital Distance (AU) Relative Solar Constant (relsolcon) New Solar Constant (Wm-2) Final Globally Averaged Temperature (Kelvin)
.61 2.69 3,658.4 371.94 Too Hot (left plot)
1 1 1,360 287 Just Right (middle plot)
1.2 0.69 938.4 274.05 Too Cold (right plot)

Conclusion: This data lets us give an approximate width for our habitable zone of 0.59 AU
(Williams and Kastings (1997) estimated a width of our habitable zone of approximately 0.4 AU)

Next Steps

  1. Add complexity to the population logistic growth equation
  2. Then couple the updated EBM to the updated population model
  3. Explore Results!

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