VIRTUAL RESEARCH INSTRUCTIONS

EARTH'S ZONAL ENERGY FLOW: THE CLASSIC BUDYKO-SELLERS MODEL

To simulate the behavior and interaction of basic climate system parameters on Earth, Budyko (1969) and Sellers (1969) developed a one-dimensional energy balance model to examine the sensitivity of a predicted equilibrium climate to changes in the solar constant S, and in basic feedbacks imposed by the Earth's variable albedo a, surface heat transport C, and greenhouse gases (A, B).

For each latitudinal zone:

(Shortwave in) = (Transport out) + (Longwave out)

i.e.,

S(q) [1-a(q)] = F(q) + R(q)
S(q) [1-a(q)] = C[T(q) - Tavg] + [A + BT(q)]

where

C = horizontal transport coefficient (default set to 3.81 W/m²ºK)
T(q) = the surface temperature at latitude q
Tavg = mean global surface temperature
A, B = constants governing longwave radiation loss (default set to A = 204.0 W/m2 and B = 2.17 W/m²ºC)
S(q) = mean annual radiation at latitude q (default value 1370 cosz W/m²)
a(T(q),q) = albedo at latitude q (set at 0.62 for T < -10 ºC, 0.3 otherwise)

ELEMENTARY EXERCISES (after McGuffie & Henderson-Sellers (1997):

Go to the website: Shodor's Energy Balance Models and RUN the model, which computes the above equation to equilibrium across 10º latitudinal zones, with the provided default values.

(a) Sensitivity to solar luminosity: Using the default values of albedo, A,B, and C, determine the decrease in solar constant required just to glaciate the entire Earth , i.e., find approximate highest fractional value of S.

(b) Perturbations in heat transport: There is considerable argument about the transport coefficient C. Investigate the effect of changing C to values below and above the default value C=3.81. Try 3 values above, and 3 values below. For each of these values, also investigate the sensitivity of this new parameterized climate to changes in the solar constant.

(c) Sea ice vs. land ice and snow: The Northern Hemisphere is dominated by land masses, the Southern Hemisphere by oceans. It has been observed that ice and snow on land begin to accumulate at the critical temperature Tcrit = 0ºC. In contrast, sea ice begins to form over the oceans at Tcrit = -13ºC. Investigate the development (sensitivity) of North vs. South hemispheric glaciaton for these two cases by varying the solar constant.

(d) Longwave emission: A and B model the longwave emission of the Earth. Holding A constant, vary the B parameter and investigate the effect on the climate. What does the variation in B correspond to physically?