Lecture 9 The Earth's Climate and Other Planets

Temperature Definition

• determines which way heat flows and represents the amount of heat a body contains, for this lecture climate is temperature

Heat (Energy) Definition

• the quantity of energy required to give an object its temperature (J)

(Heat) Flow/Flux Definition

• the rate of energy transfer (between objects) [Js-1=W], possibly per unit area [Wm-2]

(1) Simplest Model for Earth’s Average Temperature

• heat in -> T -> heat out (depending on T)

• heat in and out balance

• a simple energy balance model, equilibrium or ‘steady state’ model = no dependence on time

Temperature of a Planet Based only on Heating (5)

• simple model for Earth’s average temperature

• heating by incident sunlight

  • intrinsic brightness of the sun and distance from sun matter

  • 1/r2

• consider energy from sun

  • 1361Wm-2 if face on

  • but, half of Earth is in shadow, most of the day surface is obliquely lit, reduces intensity by factor 4 on average

  • Heat in = S0/4 = 340Wm^-2

• albedo

• so, what determines temperature of a plant?

  • power of incident sunlight (340Wm-2)

  • albedo of the planet (0.3)

  • net power absorbed = 340 x (1-0.3) = 340 x 0.7 = 238Wm-2

  • but if there were only heating, the planet would get hotter and hotter

    • but, Earth radiates heat

Total Solar Irradiance

• total energy/metre squared/second received by Earth’s orbit

Average Flux Density

• total power that strikes Earth passes through blue area A=R^2

• power is then spread over whole earth, with A=4R^2

• so, average flux density received by Earth’s surface is S0/4

Albedo

• on average Earth reflects about 30% of insolation back into space

• largely from clouds

Sun and Earth Temperatures

• Sun’s temperature is 6000K

  • emits radiation at visible wavelengths

• Earth’s temperature is ~255K 

  • emits radiation at infrared wavelengths

Thermal Radiation of Earth

• rate of radiation of energy

  • =Const. * (t+273C)^4

  • =Const. * T^4

• t = temperature in celsius

• T = temperature in Kelvin = t + 273C

• Const. =5.67 * 10-8Wm^-2K^-4

• fourth-power law is very rapid rise

  • if T increases by 1%, radiation increases by 4%

  • if T doubles, radiation increases to x16

(2) Equilibrium: Temperature of the Earth considering heating and cooling

• both heating (power of incident sunlight and albedo) and cooling (power radiated, depends on planetary temperature)

• new recipe for planetary temperature

  • calculate solar heating S0 at planet using distance from Sun =S0/4

  • multiply this by (1-albedo) to get radiation flux INTO climate system

  • find the temperature that gives a matching flux out using 

    • Constx * (t+273C)4

• dynamic equilibrium

  • point where radiation in and radiation out balance depending on t

• new energy balance model

  • (S0/4)*(1-a)=T4

  • T=(S0(1-a)/4))0.25

  • T = temperature in Kelvin

Calculating Temperature using Equilibrium Model

• (340Wm-2)*(1-03) = (5.67*10-8Wm-2K-4)*T4

• T4=(340Wm-2/5.67*10-8Wm-2K-4) 8 0.7

• T4=4.20*109K4

• T=254.5K or t=-18.5C

• graph of planetary temperature vs distance from sun varied by albedo

• Predicted planetary temperatures in Celsius

  • Venus: -46 -> 462

  • Earth: -18 -> 15

  • Mars: -57 -> -60

  • Enceladus: -213 -> -205

• very poor predictions for Venus and Earth -> why?

• Greenhouse Effect!

Importance of Atmosphere

• Mars has almost no atmosphere

  • volume 1% of Earth’s

• Enceladus has no atmosphere

• Earth and Venus do have atmosphere

  • Venus’s is 90 times that of Earth’s mass-wise and is mostly CO2

• where is outgoing energy coming from?

Where is outgoing energy coming from in the atmosphere?

• top of atmosphere receives S0/4=340Wm-2 on average

• about 30% of this is reflected back into space = the albedo

• the remaining 70% is absorbed by the ground and the atmosphere

• the atmosphere and clouds reflect, absorb, and reradiate radiation

• the amount of outgoing energy is characteristic of the temperature of the atmosphere and clouds at ~5.5 km

Natural Greenhouse Effect

• environmental lapse rate ~-6C per km in troposphere(up until 10km)

  • h = height, L = lapse rate

• radiative cooling to space comes on average from about 5.5km, fixing the mean temperature at this height

(3) Final Climate Model with Atmospheric Impact (6)

• T=(S0(1-a)/(4))0.25+hL

• one output -> global mean surface temperature

• one fundamental constant -> radiation constant =5.67 * 10-8Wm-2K-4

• four parameters -> solar constant, albedo, mean source height of outgoing radiation, atmosphere lapse rate

• S0=1360Wm2, a=0.3, h=5.5km, L=6Kkm-1

• T=254.2K+22.0K=287.5K=14.5C

Timescales (6)

• in the climate practical you will consider

  • Earth’s albedo changes

  • Solar activity changes

• the energy balance changes and so the temperature changes

• the oceans cover most of the Earth’s surface

• the oceans take time to respond to the change in energy balance and hence for the surface temperature to change

• the whole ocean takes a long time to respond

• the mixed layer (first 20m) responds much faster

Oceans and Absorption of Sunlight

• most radiation absorbed near the surface in the mixed layer, before the thermocline

• heat mixed to about 100m