ALBEDO AND ITS EFFECT

ALBEDO: a planet’s albedo is its ability to reflect incident sunlight back to space.  The greater the albedo, the less solar energy hits the earth’s surface, cooling it.  The reverse is also true, the lower the albedo, the greater the earth’s surface temperature.  The effect of albedo on earth’s surface temperature is very significant, comparable to the effect of carbon dioxide in the atmosphere.

Characteristics of Albedo

• Poles have high Albedo (around 70%) reflectance) due to ice and snow
• Oceans have low albedo (dark blue color is a good absorber of sunlight)
• Albedo of land varies with vegetation and soil color
• Albedo is highly dependent on cloud cover, hence fluctuates with time (especially seasons) and location
• Cloud cover strongly affects surface temperature.  See HERE
• Cosmic rays effects (seeds) cloud formation, thus affecting surface temperture.  See HERE

Due to low albedo and that higher water temperature increases cloud formation that the correlation of temperature to albedo is ocean. The first figure below shows that in the tropics (red) where clouds are plentiful because the warm waters generate more water vapor than cold water.  The opposite applies to the polar regions where the correlation between albedo and temperature is low.  The second figures shows the average albedo 15 period.

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  Temperature vs Albedo

  Click Figures to Enlarge

 

The intent of this parametric study is to determine the effect of increasing earth’s albedo from estimated present value of 0.30 to a value of 0.31

The result is the annual average temperature would be lowered by 0.01C if the albedo were increased by 0 1 units.

COMPUTATION OF SENSIVITY OF EARTH’S AVERAGE TEMPERATURE TO ITS ALBEDO.

CALCULATIONS

Heat Balance Equation

εσT_a⁴ = 1/4So (1-A) = H =εσ(kT_s)⁴                  Equation 1

Where  ε = emissivity = 0.97, σ  = 5.67E-8 watts/m²-K⁴, T_a = equivalent radiative temperature,
S_o = solar constant – sunlight incident on earth’s atmosphere = 1367 w/m², A = albedo,
H = net sunlight incident on earth’s surface = earth’s heat radiated to space = 235.47 w/m² for baseline
T_s = temperature of earth’s surface = 288.2K for baseline, k = T_a / _Ts

(From the first and last terms of Equation 1, k⁴ = Ta⁴/Ts⁴, or k =Ta/Ts )

Rearranging the middle components of Eqn. 1, and assuming A = 0.30:

H = 1367 * (1 – 0.3) / 4 = 239.2 w/m²

This is the H computed by ModTran for the no clouds condition.

Computing Ta for no clouds:

Ta = [S_o(1-A)/4εσ] ^¼ =[1367*(1-0.3)/(4*.97*5.67E-8)]^1/4 = 256.8 K

For Ts = 288.2 K, k = 256.8K / 288.2K = 0.8911, the same as for no-clouds from ModTran

If we use H from ModTran for the cloud condition Stratus-Stratocumulus 0.66 to 2 km top, then k would be that from the ModTran calcs = 0.8876, where H was 235.47 watts/m² (calculated from the two right hand elements of Equation 1.)

Compute k⁴ for 0.31 Albedo (increase of 0.1):

T_a = kTs = 0.8876 Ts

Using εσTs⁴ = So (1-A)/4

Then T_a⁴ = So (1-A)/(4εσ)

and since T_a = k T_s

k⁴Ts⁴ = So (1-A)/(4εσ)

Differentiate,

4k⁴T³ δT_s = – S_oδA/(4εσ)

Rearrange, and assume Ts approx = Ta, the difference being about 1 degree out of 288, is represented as a constant T in the denominator below.

δTs = – S_oδA/(16ϵσk⁴T³)

= -1367/(16*0.97*5.67E-8*(0.8876)⁴*288.2³)*δA = -104.7δA

δA = 0.31 – 0.30 = 0.01

δTs = –1.05C , that is temperature decreases as albedo increases by 0.01, and conversely increases +1.05C if albedo decreases by 0.01.

Because differentials are finite, the smaller the δA, the more accurate the δT_s.