GLOBAL ENERGY BUDGET - 2 The Greenhouse Effect

EARTH’S SURFACE TEMPERATURE Depends on: The solar flux (S) available at the distance of Earth’s orbit (30% of incident energy reflected) Earth’s reflectivity or albedo (A) – the fraction of the total incident sunlight that is reflected from the planet as a whole The amount of warming provided by the atmosphere (magnitude of the greenhouse effect)

PLANETARY ENERGY BALANCE energy emitted by Earth = energy absorbed by Earth

Effective Radiating Temperature (Te) The temperature that a true blackbody would need in order to radiate the same amount of energy that Earth radiates Use Stefan-Boltzmann Law to calculate energy emitted by Earth - Energy emitted = σ Te4 x 4 R2

Energy Absorbed by Earth energy absorbed = energy intercepted – energy reflected Energy Intercepted (Incident Energy) - the product of Earth’s projected area and the solar flux =  R2 S Energy Reflected - the product of Earth’s incident energy and albedo =  R2 S x A

ENERGY ABSORBED energy absorbed =  R2 S –  R2 S x A =  R2 S (1 – A) energy absorbed = energy intercepted – energy reflected energy absorbed =  R2 S –  R2 S x A =  R2 S (1 – A)

PLANETARY ENERGY BALANCE energy emitted by Earth = energy absorbed by Earth σ Te4 x 4  R2 =  R2 S (1 – A) σ Te4 = (S/4) (1 – A) where σ is 5.67 x 10-8 W/m2/K4 , T is temperature in Kelvin, S is solar flux, and A is albedo The planetary energy balance between outgoing infrared energy and incoming solar energy

MAGNITUDE OF THE GREENHOUSE EFFECT Effective Radiating Temperature Atmospheric temperature at which most outgoing infrared radiation is derived Average temperature that Earth’s surface would reach with no atmosphere Using planetary energy balance equation - Earth’ s effective radiating temperature = -18C or 0F

MAGNITUDE OF THE GREENHOUSE EFFECT Actual surface temperature of Earth = 15C Difference between actual surface temperature and effective is caused by greenhouse effect ∆ Tg = Ts – Te For Earth ∆ Tg = 15C –(–18C) = 33C By absorbing part of the infrared radiation radiated upward from the surface and re-emitting it in both upward and downward directions, the atmosphere allows the surface to be warmer that it would be if no atmosphere were present

THE GOLDLOCKS PROBLEM A planet’s greenhouse effect is at least as important in determining a planet’s surface temperature as is its distance from the Sun For Homework – Critical Thinking #2

FAINT YOUNG SUN PARADOX Solar luminosity, and flux (S), is estimated to be 30% lower early in Earth’s history Earth’s average surface temperature would have been below freezing (if albedo & greenhouse effect unchanged) The early Earth had liquid water and life HOMEWORK – Critical Thinking #5