164
Radiation Basics
the formula:
Brutsaert (1984) reconciled Eqs. (10.10) and (10.1 1) using an empirical
correlation of temperature and vapor pressure. We use Eq. (10.11) for
most of our computations, and values are listed in Table A.3. If vapor
pressure data are available, Eq. (10.10) is probably preferable.
Clouds have an emissivity of one, so when clouds are present, atmospheric emissivity is higher than for a clear sky. The atmospheric
emittance on cloudy days can be estimated by adding the energy emitted by the clear portions of the sky to the energy emitted by the clouds.
Monteith and Unsworth (1990) give the simple relationship
where c is the fraction of the sky covered by cloud and .sac is given by
Eq. (10.1 1) or (10.10). When c is zero, .sa(c) = .sac. When c = 1,
E,(c) = 0.84 + 0.16.sac. At a temperature of 20" C, this gives a sky
emissivity of 0.97.
Example 10.6. Compare clear sky and completely overcast sky emittance when air temperature is 20" C.
Solution. Using Eq. (10.7) or Table A.3 the black body emittance can
be found. Equation (10.7) gives
The clear sky emissivity (Eq. (10.11) or Table A.3) is 9.2 x
x
(273.16 + 20)' = 0.79. The emissivity for a completely overcast sky
(Eq. (10.12), c = 1) is 0.16 x 0.79 f 0.84 = 0.97. The emittances are
clearsky: 0.79 x 419 = 331 Wm-'
cloudy sky: 0.97 x 419 = 406 W m-2.
The cooling and frost that occur on clear nights are sometimes explained
as "radiation being lost to outer space." This description is both overly
dramatic and wrong. The difference between a clear night and a cloudy
night is not the outgoing but the incoming radiation. The ground receives
less radiation from the atmosphere on clear nights (and days) than on
cloudy ones.
We could compute the ernittance of the sun just as we do the earth and
atmosphere, but this has little value for environmental biophysics. We
assume the output of the sun is constant and use that constant, measured
value for all of our calculations. The mean radiant flux density outside
the atmosphere of the earth and normal to the solar beam is about 1360
W m-2. This value is known as the solar constant. The actual flux density
varies by about f 1.5 percent due to random variations in solar activity
and f 3.5 percent annually due to the predictable variation in earth-sun
Radiation Basics
the formula:
Brutsaert (1984) reconciled Eqs. (10.10) and (10.1 1) using an empirical
correlation of temperature and vapor pressure. We use Eq. (10.11) for
most of our computations, and values are listed in Table A.3. If vapor
pressure data are available, Eq. (10.10) is probably preferable.
Clouds have an emissivity of one, so when clouds are present, atmospheric emissivity is higher than for a clear sky. The atmospheric
emittance on cloudy days can be estimated by adding the energy emitted by the clear portions of the sky to the energy emitted by the clouds.
Monteith and Unsworth (1990) give the simple relationship
where c is the fraction of the sky covered by cloud and .sac is given by
Eq. (10.1 1) or (10.10). When c is zero, .sa(c) = .sac. When c = 1,
E,(c) = 0.84 + 0.16.sac. At a temperature of 20" C, this gives a sky
emissivity of 0.97.
Example 10.6. Compare clear sky and completely overcast sky emittance when air temperature is 20" C.
Solution. Using Eq. (10.7) or Table A.3 the black body emittance can
be found. Equation (10.7) gives
The clear sky emissivity (Eq. (10.11) or Table A.3) is 9.2 x
x
(273.16 + 20)' = 0.79. The emissivity for a completely overcast sky
(Eq. (10.12), c = 1) is 0.16 x 0.79 f 0.84 = 0.97. The emittances are
clearsky: 0.79 x 419 = 331 Wm-'
cloudy sky: 0.97 x 419 = 406 W m-2.
The cooling and frost that occur on clear nights are sometimes explained
as "radiation being lost to outer space." This description is both overly
dramatic and wrong. The difference between a clear night and a cloudy
night is not the outgoing but the incoming radiation. The ground receives
less radiation from the atmosphere on clear nights (and days) than on
cloudy ones.
We could compute the ernittance of the sun just as we do the earth and
atmosphere, but this has little value for environmental biophysics. We
assume the output of the sun is constant and use that constant, measured
value for all of our calculations. The mean radiant flux density outside
the atmosphere of the earth and normal to the solar beam is about 1360
W m-2. This value is known as the solar constant. The actual flux density
varies by about f 1.5 percent due to random variations in solar activity
and f 3.5 percent annually due to the predictable variation in earth-sun