Zonal Energy Balance Model

Directions: This model allows you to calculate the mean global temperature and the individual temperatures for nine latitudal zones. For this model, you will need these input parameters:

A, a constant that defines the longwave radiation loss, in units of watts meter^-2
B, another constant that defines the longwave radiation loss, in units of watts meter^-2 degrees C^-1
C, the transport coefficient, in units of watts meter^-2 degrees C^-1
the critical temperature, T_crit, the temperature (in degrees Celsius) at which land becomes covered with snow and/or water turns to ice
the latitude (in degrees North), which represents the middle of the zone (for example, 85 degrees north for the zone between 80-90 degrees North
the initial surface temperature at a particular latitude, or zone
S, the mean annual radiation (in watts) incident at a particular latitude
the initial albedo at a particular latitude

There are fundamentally three sets of calculations that you will need to do this case study:

Initial calculations of zonal temperature, surface albedo, and radiation in
Iterative (looping, or repeating) calculations
Final calculations of temperatures, albedoes, and radiation out

With this model, you can investigate a variety of scenarios, such as:

At what fraction of the solar constant does the hemisphere "ice over", that is, the surface temperatures in all the zones fall to or below the critical temperature? How sensitive is the model to changes in the solar constant fraction?
A variety of values for the transport constant has been reported:
1. K=3.81 W m-2 C-1
2. K=3.74 W m-2 C-1
How sensitive is the model to changes in this constant?
Holding A constant, vary B slightly and investigate the effect on the climate. What does a variation in B correspond to physically?

Once you have entered the values desired, scroll to the bottom of the page and hit the "Run EBM" button.

Input Values for Energy Balance Model

Number of iterations:	A (longwave radiation loss, in watts-m²):
B (longwave radiation loss, in watts-m²C^-1):	C (transport coefficient, in watts-m^-2-degrees C^-1):
Cloud Albedo:	Ice Albedo:
Critical Temperature (in degrees Celsius):	Fraction Solar Constant:
Solar Constant:


ZONE	S (annual radiation)	Initial Temp
80-90
70-80
60-70
50-60
40-50
30-40
20-30
10-20
0-10

Plotting Options

X axis minimum		X axis maximum		Y axis minimum		Y axis maximum
Style		Image proportion size

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NOTE! This run takes several minutes to run the code and generate the results graphics. Please be patient!