CHAPTER 4: A Simple Climate Model
• First step to understanding climate to do an energy budget calculation, which requires calculating
energy in and energy out for the Earth
o First step calculating energy in to determine intensity of sunlight at Earth’s orbit
▪ 1360W/m2 the solar constant for the Earth, frequently represented in equations
by symbol S
• Function of how far the planet is from the Sun
o Easiest way to quantitatively calculate solar energy falling on Earth to realize that if you
set up a screen behind the Earth, Earth would cast circular shadow, with radius equal to
radius of Earth
▪ Amount of sunlight falling on Earth equal to amount that would have fallen into
the shadow area if Earth not there
▪ Solar energy falling on Earth at rate of 1.8 x 1017W
• If we could capture just 0.01% of solar energy falling on Earth, we could
satisfy all of the world’s current energy needs
• Reflectivity of a planet called the albedo, frequently represented by symbol α
o Fraction of incident photons reflected back to space
• Earth absorbs an average of 238W/m2 from the Sun, but that doesn’t mean every square meter of
Earth absorbs this amount
o Amount of solar energy varies widely across planet
▪ Mid-latitudes receive less solar radiation per square meter than tropics, and polar
regions receive even less solar energy
o In addition to variations in incoming sunlight with latitude, the albedo of planet also
varies widely
▪ Tropics are mainly open ocean, which is dark and has low albedo
• Combined with large amount of solar energy per square meter, tropics
experience far more solar heating than anywhere else
▪ High latitudes generally covered by snow and ice, so high albedo
• Combined with small amount of solar energy received, means they
receive the least amount of solar energy, so coldest regions
Greenhouse Effect
• Assumptions to understand impact of atmosphere on planet’s temperature:
o Earth’s atmosphere is transparent to visible photons emitted by Sun (which have
wavelengths from 0.3-0.8 microns) so these photons pass through the atmosphere and are
absorbed by the surface
o Atmosphere is opaque to infrared photons emitted by the surface (wavelengths longer
than 4 microns) so all photons are absorbed by atmosphere
o The atmosphere also behaves like a blackbody so it emits photons based on its
temperature… Emits equally both upward and downward
o Photons emitted by atmosphere in upward direction escape to space and carry energy
away from Earth, photons emitted downward are absorbed by surface
• To calculate surface temperature, assume planet as whole, as well as surface and atmosphere
individually, must all be in energy balance where energy in equals energy out
• Addition of an atmosphere that is opaque to infrared radiation has significantly warmed the
planet’s surface
o Conceptually occurs because surface of planet with atmosphere is heated not just by the
Sun but also by the atmosphere
• Another way to think about greenhouse effect is that atmosphere warms the surface by making it
harder for the surface to lose energy to space