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 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
The Solar Constant
How much of the sun's energy gets to the surface of
the earth, and what does that mean to a lemming?
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
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 Solar Constant.
Let's think about this on a small scale that will
make sense to us.
Let's think about how many of the KiloCalories that
we use to measure food 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
(very) roughly the same size.)
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 and
shape 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
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
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
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.
3000 kilocalories per day divided by 100 = 30 kilocalories
per square meter per day.
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.
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!
Net Primary Productivity
(Kilocalories / square meter / year)
per square meter per day
Rainfall per year in
More than 60
(the place where a river meets the sea
-may have many channels and be a delta.)
(grass, scattered trees,
or no winter snow)
Forest (Evergreen Coniferous Forest)
Grassland (cold winters)
| Polar Tundra
Less than 10
Less than 10
This table is from http://www.geog.ouc.bc.ca/physgeog/contents/9l.html
an online Geology course created by Dr,
Michael Pidwirny at Okanagan College, British Columbia,
(Dr Viau's additons are in red)
At 60 Degrees of Latitude we calculate 4/9 times 3,300 which
Kilocalories per square meter at 60 Degrees = 1500 kilocalories
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.
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
These figures are for the energy budget of the earth -sun
system: Check the AU Equivalent in the Star
Tables for your world.
Kcal yield for year = (Calories per
day per square meter) multiplied by (number of days in growing
Maximum Kcal for plants per square meter per
24 hour day
|| Plants use
4/9 of the available light
Maximum possible light received per square meter
||1% turned into
plant tissue per square meter per year
|| 5% turned
into animal tissue by grazing animals per square meter per year
| 0 Equator
Rain Forest, desert
|| 365 days
|| 97* 5 = 500
| 30 Degrees
| 120-250 days
| 60 Degrees
|| 120-200 days
| 70 Degrees
| 90-120 days
| 80 Degrees
|| 60-100 days
|| 42,000 -
| 90 Degrees
|| At and below
a possible 120, earth photosynthesis is very difficult. This
is true in all zones where plants cannot
get enough light.
Go on to
The Caloric Content of
Some Animal Weights and
Caloric Requirements on Earth
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.
© 1999 Elizabeth Anne Viau. All rights
reserved. 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 firstname.lastname@example.org