LECTURE 3: ENERGY BALANCE
Solar and Terrestrial Radiation
Almost all the energy received by the earth comes from the sun. Its distribution is not even on
the surface of the earth but varies latitudinally and fluctuates seasonally. The influence of
seasons can be appreciated by the fact that the earth is tilted 23.5o from the vertical, and this
gives rise to winter and summer in different hemispheres as the earth revolves round the sun.
Two equinoxes occur, in March and September, when the sun is directly over the equator and
daylength and nigh-time durations are equal throughout the world. In June, the summer solstice
in the northern hemisphere, the sun appears directly overhead the Tropic of Cancer, and the
polar areas (north of 66 2/3o N) have 24 hours of daylight. Similarly, in December winter
solstice, the sun appears overhead the Tropic of Capricorn, and the south polar region receive 24
hours of daylight (Figure 1).
Obviously, seasons, and length of daylight affect the amount of radiation received at any point
on the earth's surface, but the angle of the sun's rays also influences the receipt of solar energy.
Radiation of energy comes in wavelengths. The complete range of radiation wavelengths is
called the electromagnetic spectrum (Figure 2), grouped into familiar bands such as visible
light, X-rays, and radio waves.
All objects radiate and following the Stefan-Boltzmann law, the radiation emitted by a perfect
radiating surface (a 'black body') depends on the fourth power of its absolute (Kelvin)
temperature. The sun radiates as a black body with a surface temperature of about 6000K.
Because of the high temperature of the sun, radiation emitted is in the form short wavelength.
The earth, on the other hand, with an average temperature of 288K (15 oC) radiates in the
infrared region of the spectrum, or long wave-length. Earth's radiation is called terrestrial
radiation as opposed to solar radiation for the sun.
About 46 % of the energy in the total solar spectrum is in the visible portion, ie between 0.4 and
0.7 um. Human eyes can detect radiation in this band. Radiation in much smaller wave-length
between 0.01 - 0.4 um (ultraviolet) accounts for some 8 %, but this is significant in that it is
responsible for some forms of skin cancer.
Global Radiation Balance
Solar radiation
In discussing global radiation balance it's good to look at the earth and atmosphere as one
system, hence the balance referred to is the earth-atmosphere radiation balance. The concept of
balance presupposes that input must equal output over a long-term period, and there should be
no deficit or surplus. This should be so because any surplus will lead to the earth-atmosphere
system becoming hotter with time, and the reverse is true if there are continuous deficits.
Figure 3 is useful in explaining this radiation balance. The figure is divided into two parts
horizontally - one refers to the incoming radiation, the other the outgoing. It is also divided into
two parts vertically - the stratosphere-troposphere medium and the surface of the earth. Seen as
a whole, input minus output must produce zero value.
Out of the 100 units of solar radiation moving to the earth 21 units are absorbed by the
stratosphere-tropospheric medium (3 units* by the ozone layer or stratospheric absorption, 15
units by water vapour and aerosols, 3 units by clouds). 21 units are reflected back to space by
clouds and 6 units back scattered by aerosols, etc. At the surface of the earth, 4 units are
reflected back to space. Out of the 100 units only 48 units finally reach the earth's
*
The sun is about 150 million km from the earth
surface in two forms as direct radiation (Q = 27 units) and diffuse radiation (q = 21 units).
The total amount of solar radiation that is sent back to space is 31 units, known as the planetary
albedo. Potentially, the amounts absorbed by the earth-atmosphere system is 69 (21 by
atmosphere and 48 by the earth's surface).
Terrestrial radiation
The earth being much cooler than the sun emits radiation in the long wavelength. From the
amount of short wave radiation received it emits an equivalent of 113 units of long wave
radiation upwards, out of which 97 is reflected by the atmospheric medium to the earth, called
back radiation, or counter radiation. 10 units are absorbed by the atmosphere. From the energy
received the earth's surface also releases to the atmosphere an equivalent of 22 units in the form
of latent heat through convection, and 10 units as sensible heat transfer through conduction. A
total of 69 units escape to space comprising 6 units through the atmospheric window, 37 water
vapour and CO2 emission, 26 through cloud emission.
Radiation balance
To appreciate this balance, it is useful to look at the gains and losses for each layer - the earth's
surface, the atmospheric medium, and space.
The earth's surface receives 48 units of short wave radiation and 97 units of long wave counter
radiation. It loses 113 units of long wave radiation, 22 units through convection, and 10 units
through conduction. The total gain of 145 units is equal to the total loss of 145 units.
The same approach applies to the atmosphere. It receives 21 units of short wave radiation, 107
units in long wave radiation, 22 units of latent heat and 10 units through conduction making a
total of 160 units. This atmospheric medium loses 63 units to space and 97 units to the earth's
surface, making a total of 160, hence ensuring a balance.
In the upper atmosphere 100 units are received from the sun, but losses back to space amount to
31 units of planetary albedo, and 69 units from the earth's surface and the atmospheric medium,
giving a total of 100 units each.
From the above it is clear that a balance of energy in the earth-atmosphere system is maintained.
Net Radiation Balance
The difference between the quantity of radiation received and lost by a surface at any place
determines the net radiation that remains at that surface. It can be calculated by using the
following formula:
Rn = Rs - Rs(a) - RL(t) + RL(c)
where Rn is net radiation, Rs is incoming solar radiation, a is the albedo, RL(t) is outgoing
terrestrial radiation, and RL(c) is the counter radiation.
Since there are many factors that influence the intensity and the quantity of solar radiation
received at different parts of the earth's surface, the net radiation therefore varies spatially and
temporally. Over the globe, as a rule of the thumb, the net radiation in the tropics at sea level
equals about two thirds of global radiation.
Some factors that affect net radiation are:
a,
b.
c.
d.
e.
Latitudinal location
Altitude, relief and aspect
Nature of the surface - land and sea
Seasons
Time of day
Energy Balance
While all energy received from the sun comes in the form of solar radiation, the earth transfers
the energy in three different forms - as long-wave radiation, convection and conduction. Water
vapour moves into the atmosphere through the process of evaporation, and the energy required
for it is supplied by radiation. The energy is stored in latent heat form only to be released when
condensation takes place. Air, land and water heat up as radiant energy is converted to sensible
heat.
Generally, areas below 37o latitude have a net radiation surplus and areas above 37o have a net
radiation deficit. Surplus energy carried to high latitudes through latent heat and sensible heat
transfer by wind and ocean currents (to be discussed later) keeps the global heat budget in
balance. Otherwise, the tropics will become progressively warmer and the polar regions
progressively cooler. Thus areas at the tropics are net importers of radiative energy and net
exporters of energy stored as sensible heat and latent heat.
The energy balance can be described by this equation:
Rn = LE + H + G + P
where Rn is net radiation, LE is latent heat absorbed in evaporation, H is the heat flux to the air,
G is the heat flux to the ground, and P is energy consumed in photosynthesis. Only LE and H
are the most important for they account for most of the available net radiation. Because of this
H:LE often called Bowen ratio, has been used as a means of classifying climate.
------------------------------------------------ALBEDO
Albedo of a surface is the percentage of incident radiation that is reflected back
by the surface.
reflected radiation
albedo = ------------------- X 100 %
incident radiation
Albedo is influenced by many factors:
a.
b.
c.
d.
type of surface particularly its colour and tone (soil, rocks, water, ice,
etc)
nature of the surface (smooth, rough, wavy, etc)
angle of the sun's radiation
for the same type of surface, albedo values are not constant even if the
angle of incident radiation is the same:
i.
fresh snow and old snow
ii
same crop but at different stages of growth
iii
effects of seasons on forest vegetation in temperate region
The table below shows some albedo values of different surfaces.
Surface
Albedo
(%)
Fresh snow
Dry (dune) sand
Dark soil
Blacktop road
Concrete surface
Clouds
Cumuliform
Stratus
Cirrostratus
Sea ice
Vegetation cover
Tundra
Desert
Coniferous
Deciduous
Savanna
Wet
Dry
Green meadows
79-95
30-35
10-15
5-17
17-27
70-90
59-84
44-50
30-40
15-20
25-30
5-15
10-20
15-20
25-30
10-20
Water
Zenith angle
of sun (o)
Albedo (%)
0
2
40
2.5
60
6
------------------------------------------------------
80
35
90
100