Solar Radiation

© 2005 Dr Ron Nielsen

IN PLAIN ENGLISH (A summary for those who like it short and simple)

We need energy to support all our activities but most of our energy comes now from fossil fuels. Do we have to use them?

For a time being we have to use them because we do not yet have a convenient replacement, but we have to work harder and faster to develop alternative sources of energy; otherwise the damage we do to the environment is likely to have catastrophic consequences.

One of these alternative sources of energy comes from nuclear fusion reactions in the Sun. The Sun delivers about 7000 times more energy to the Earth's surface than we currently need for our global consumption.Even if we could use only a small fraction of the solar energy, we could reduce our dependence on fossil fuels. In time we might even eliminate them altogether. We could clean the environment and improve the living conditions on our planet.

NUCLEAR FUSION REACTOR

The Sun is a powerful nuclear fusion reactor producing staggering amounts of energy, which unfortunately is dispersed in space and practically all of it is lost. The Earth is 149,596,000 km from the Sun and at this distance solar flux is relatively small.

The energy intercepted by the Earth over a period of one year is equal to the energy emitted by the Sun in just 14 milliseconds. To put it another way, solar energy captured by the Earth over a period of 1000 years is equal to the energy produced by the Sun in just only 14 seconds.

SOLAR RADIATION REACHING THE EARTH

The intensity of the solar radiation reaching us is about 1369 watts per square metre [W/m2]. This is known as the Solar Constant. It is important to understand that it is not the intensity per square metre of the Earth’s surface but per square metre on a sphere with the radius of 149,596.000 km and with the Sun at its centre.

The total solar radiation intercepted by the Earth is the Solar Constant multiplied by the cross section area of the Earth. If we now divide the calculated number by the surface area of the Earth, we shall find how much solar radiation is received, on average, by a square metre of the Earth's surface. Thus, the average solar radiation S per square metre of the Earth’s surface is,


where S in the Solar Constant in W/m2 and r is the Earth's radius.

 

SOLAR RADIATION REACHING THE EARTH SURFACE

However, our calculations are not yet finished because we have not yet considered the influence of the Earth's atmosphere. The value we have calculated is for the average solar radiation intensity at the outer regions of the Earth’s atmosphere. What we want to know is how much of this radiation reaches the earth surface where we are.

The atmosphere absorbs about 68 W/m2 and reflects 77 W/m2 (Wallace and Hobbs 1977). The radiation reaching the Earth’s surface is therefore on average 198 W/m2, i.e. 58% of the radiation intercepted by the Earth.

Distribution of solar radiation

Figure 1. The distribution of the solar radiation. On average, each square metre of the upper regions of the atmosphere receives 342 watts of solar radiation [W/m2]. The atmosphere absorbs on average 67 W/m2 and reflects 77 W/m2. About 198 W/m2 reaches the Earth's surface, of which 168 W/m2 is absorbed and 30 W/m2 is reflected back to space. The total of the reflected radiation is 107 W/m2, or 31% of the incoming radiation.

Source: Modified figure of Houghton et al. 2001

The intensity of solar radiation depends on the time of the year and geographical positions as illustrated in Figure 2.

Figure 2: The intensity of solar radiation (solar power) in various parts of the world depending on the season, measured in watts per square metre [ W/m2].

Source: Sofia (Sharing of Free Intellectual Assets).

 

SOLAR ENERGY

Using the Solar Constant we can calculate (see the formula below) that the total solar energy intercepted by the Earth in one year is 5.5 million exajoules [EJ/y]. To appreciate this figure we have to compare it with the global energy consumption in 2005, which was only 463 EJ/y. Thus, even though the Sun is so far from us, we still receive huge amounts of energy from this immensely powerful source.

The energy reaching the Earth surface is 3.2 million EJ/y, which is close to 7000 times the global energy consumption. If we could harvest even a small fraction of this energy we could solve our energy problems. Global energy consumption in2005 was only 0.014% of the solar energy reaching the Earth surface. The projected global consumption in 2100 is 0.051%. We should therefore expect that we should be able to harvest enough of solar energy to replace the harmful fossil fuels.

HANDY FORMULA

Here is the formula you can use to calculate how much energy we receive from the Sun:

where E is the solar energy in EJ, S is the Solar Constant in W/m2, n is the number of hours, r is the Earth's radius in km.

This formula is for the total solar energy intercepted by the Earth in n hours. If you want to calculate how much of the solar energy reaches the Earth's surface, multiply the result by 0.58.

You can use this formula and Figure 1 to calculate how much solar energy is reflected or absorbed by the Earth and the atmosphere. Using information contained in The Little Green Handbook you can also calculate that our current global annual consumption of energy is equal to the average solar energy reaching the Earth's surface over a period of only one hour and 16 minutes. Add to it an extra 30 minutes and you'll have enough energy for the annual global consumption in 2020.

How much solar energy can we harvest? Can it be enough to satisfy our global energy needs? See my estimations in another section.


Copyright

You may use the information contained in this article as long as you refer to it as Nielsen, R. 2005, 'Solar Radiation', http://home.iprimus.com.au/nielsens/.

For more information and for a discussion of all critical global trends shaping our future see The Little Green Handbook.

References

Houghton, J. T., Ding, Y., Griggs, D. J., Noguer, M., Linden, P. J. van der, and Xiaosu, D. (eds) 2001, Climate Change 2001: The Scientific Basis, IPCC, Cambridge University Press, Cambridge, UK.

Wallace, J. M. and Hobbs, P. V. 1977, Atmospheric Science: An introductory survey, Academic Press, New York.


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