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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
numbers
on any Important Exams unless you have checked them out!
Dr Viau says, "Gerald Nordley and Mark Wistey
were kind enough to help with this, but I made the mistakes all
by myself!"
The Solar Constant
How much of the sun's energy gets to the surface of the earth?
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 0.023% 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 amount of energy that gets to the earth's surface
at the equator at noon is called
The rate at which
radiant solar energy is received at the outer layer of the earth's
atmosphere.
the average amount of radiant energy received by the
earth's atmosphere from the sun; its value is about 2 calories per min
incident on each square centimeter of the upper atmosphere. The actual
value of the energy varies with several factors; the most important factor
is the earth's distance from the sun, which changes because of the earth's
elliptical orbit. For computing the value of the solar constant, the
astronomical
unit , or average earth-sun distance, is used.
100 cm = 1 meter
Therefore 100 * 100 = 10000 * 2 = 20,000 per minute
12 hours * 60 minutes = 720 minutes * 20000
= 1,4400,000 calories
1 Kilocalorie (food calorie) = 1000 physicst's calories
per 12 hour day
14400 Kilocalories * 0.023% =
14000 Kilocalories * 0.00023 = 3.312 KiloCalories
per square meter per 12 hour day.
maximum per 365 day year = 1208.88
The Solar Constant.
The solar constant ( as defined for planet Earth ) is
the power collected at the top of the atmosphere by a unit area
perpendicular to the light path. In what follows, the unit area will be 1
m˛
Let's think about this on a small scale that will
make sense to us.
Let's think about how many of the KiloCalories
(the calories hat
we measure food fwith) fall onto an area that is one meter square.
(A meter is pretty close
to a yard in length, so a square yard and a square meter are roughly the same size.)
At the Equator:
We find how many KiloCalories
fall s
onto 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.
Most of this energy is used up by the plant just
being a plant: it has to use energy to do its life processes,
an activity which is called respiration. Under ideal conditions plants might be able to turn
up to about 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, except by detritovores such as bacteria and fungi.
Let's take 10% of the 3000 calories,
remembering that plant tissue may not always be produced at the maximum rate.
3000 kilocalories per day divided by 10 = 300 kilocalories
per square meter per day.
So there are 300 KiloCalories 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?
300 Kilocalories * 365 days =
109500 Kilocalories per square
meter per year.
Well, there are clouds and rainstorms that would bring that
number down. Dr Viau found this table which will be very helpful
to all world builders!
At 60 Degrees of Latitude we calculate 4/9 times 3,300 which
equals
Kilocalories per square meter at 60 Degrees = 1500 kilocalories
per day
These figures are about maximum possible
production during a day which has 12 hours of daylight and12
hours of darkness.
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. There will be more discussion of this
further down on the page.
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 brilliant 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.
Formulas:
Kcal yield for year = (Calories per
day per square meter) multiplied by (number of days in growing
season).
|
Latitude |
Maximum Kcal for plants per square meter per
24 hour day |
Plants use 4/9 of the available
light |
Biome |
Growing Season in days per
year |
Maximum possible light received per square meter
per year |
10% turned into plant tissue per
square meter per year |
10% turned into animal tissue
by grazing animals per square meter per year |
Predator eats animal,
10% becomes predator tissue
|
| 0 Equator |
6000 (average) |
2666 |
Rain Forest, desert |
365 days |
973090 |
97309
K/Cal |
97* 5 = 500 K/cal |
|
| 30 Degrees |
5200 (average) |
2311 |
Deciduous
Forest |
120-250
days |
843515 |
|
|
|
| 60 Degrees |
4800(midsummer)
3000 (average)
731 (midwinter) |
|
Grasslands |
120-200
days |
70,000
kcal |
|
|
|
| 70 Degrees |
4100(midsummer)
0 (midwinter) |
|
Coniferous
Forest |
90-120
days |
|
|
|
|
| 80 Degrees |
3300(midsummer)
0 (midwinter)
|
|
Tundra |
60-100
days |
42,000 - |
|
|
|
| 90 Degrees |
|
|
|
At and below a possible
120 days,
earth photo
synthesis is very difficult. This is true in all zones
where plants cannot
get enough light. |
|
|
|
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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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