Following
the Energy Trail
Let's see how the sun's energy flows in the Biosphere.
Warning: I am making a lot of assumptions and doing a lot of rounding in the math here. My numbers may be off by several thousand percent, but I think the process is all right.
Try to understand the basic idea, and don't use my math on any Important Exams unless you have checked it out!
The earth gets only 2 billionths of the sun's energy, but that is still a lot. However, you can see on the chart that life (through photosynthesis) uses only .023% of the energy that reaches the surface of the earth
34% of the sun's energy is reflected back into space by snow and clouds. This reflective quality of a planet is called its albedo.
42% of the energy goes to warm the land and water. The warmth of the earth is constantly being radiated into space, and the sun's energy replenishes this warmth.
The water cycle -- evaporation and precipitation -- uses 23% of the solar energy.
Winds and ocean currents use 1%.
The Solar Constant.
At the Equator:
We find how many KiloCalories falls ont one square meter each day
This turns out to be about 19.7 kilocalories per minute on each square meter at the equator above the atmosphere.
A kilocalorie (kcal) is a food Calorie, the kind of Calorie that we count when we are on diets.
19.7 kilocalories per meter squared per minute multiplied by 60 minutes = 1,180 kilocalories per hour
1,180 kilocalories per hour multiplied by 24 hours = 28,320 kilocalories per square meter per 24 hour day (about).
(We will adjust for the night in the next step!)We correct for the rotation of the earth
However, because the sunlight is slanted in the morning and the evening, and because of night, we need to divide this 28,320 kilocalories per square meter per 24 hour day by 3.
28,320 kilocalories per square meter per 24 hour day divided by 3 = 9,440 kilocalories per square meter per 24 hour day.
We correct for the presence of the atmosphere
However, all this has been going on at the very top of our atmosphere. Only about 70% of that energy gets down to sea level.
70% of 9440 kilocalories = 6,600 kilocalories
More Adjustments:
About 4/9 of the solar energy that actually falls on a plant is energy that the plant can use. (Some of the radiation does not help with photosynthesis.)
Let's figure out how much energy is actually useful.
At the equator, a square meter densely covered with plants is receiving useful radiation of about 4/9 of 6,600 kilocalories per square meter per 24 hour day.
6,600 * 4/9 =2933 kilocalories per day
We will round this up to 3000 kilocalories per day for the sale of simplicity.
However, most of this energy is used up by the plant just being a plant: it has to use energy to do it's life processes, an activity which is called respiration. Under ideal conditions very efficient crop plants might be able to turn between 3% and 10% of those 3000 kilocalories into biomass, which is food that the animals could eat and also stalks and thorns and roots that may not be digestible.
Let's take 1% of the 3000 calories because plant tissue is not going to be produced at the maximum rate in the wild.
This is how many calories there are in the new plant tissue that was added that day. This is called the Net Primary Productivity per day.
Over a year, how many calories of primary productivity are produced in our square?
30 Kilocalories * 365 days = 10950 Kilocalories per square meter per year.
Clouds and rainstorms that would bring that number down.
Check out the table that is at http://www.geog.ouc.bc.ca/physgeog/contents/9l.html
an online Geology course created by Dr,
Michael Pidwirny at Okanagan College, British Columbia,
Canada. This table will give you the number of Kilocalories of
food for herbivores produced by the plants growing on one square
meter over a year. Find your biome and the number of Kilocalories
that will be produced there.
At 60 Degrees Latitude:
As we travel away from the equator, the curvature of the earth causes the solar energy to be spread out over a larger area.
At 60 degrees North the amount of energy received is about half that at the equator. The table about the biomes adjusts for this.
Additional Variables:
There are spaces between leaves: the energy falling there is not used.
There are rocks and bare patches on the ground.
Water and nutrients affect growth -- abundant solar energy is not enough.
Plants grow when it is warm. Brilliant sunlight on a frosty day is not as effective as brillliant sunlight at the equator!
Animals must eat all year.
Probably the plant yield will usually be lower than the maximum possible.
These figures are for the energy budget of the earth -sun system: Check the AU Equivalent in the Star Tables for your world.
Special Cases
The earth's axis is tilted at 23 degrees to the plane of its rotation around the sun. In the high latitudes near the poles, winters are dark, and summers have long days. We have heard of "the midnight sun", which refers to the period when the sun does not set at the poles. When we think about the high latitudes, both north and south, we must remember that, although light is available in abundance, temperatures remain low. Life processes are chemical processes, which work more quickly as temperatures rise.
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© Elizabeth Anne Viau, 1999. This material may be used freely for instructional purposes but not sold for a price beyond the cost of reproduction. Please inform the author if you use it at eviau@earthlink.net