Spectral distribution of the irradiance in a cloudy atmosphere
Clouds are made up of many water droplets or ice crystals, or a combination of both. The intensity of the scattering is very strong, and the radiation directed toward the ground can be strongly attenuated when passing through a cloud. The greater the optical depth of the cloud, the greater the attenuation. There is a great diversity of clouds and therefore a great diversity of effects. However, the general properties of these effects can be presented with the help of simple simulations.
Influence of the cloud optical depth
Figure 7.7 illustrates the influence of the optical depth of the cloud on the spectral distribution of the solar radiation, at wavelengths between 200 and 2300 nm. The receiving surface on the ground is horizontal, and the solar zenithal angle is 30°. Three cases are simulated: a cloud layer of optical depth 5, another of optical depth 15, and, for comparison, a limpid cloudless atmosphere. The corresponding clearness indices are plotted in Figure 7.8.
Figure 7.7 Typical spectral distributions of the solar irradiance received on a horizontal surface located at ground in limpid clear-sky conditions, and in cloudy conditions with cloud optical depths of 5 and 15, between 200 and 2300 nm. Solar zenithal angle is 30°. Results from the numerical code libRadtran simulating the radiative transfer in the atmosphere.
Figure 7.8 Typical spectral distributions of the clearness index in limpid clear-sky conditions, and in cloudy conditions with cloud optical depths of 5 and 15, between 200 and 2300 nm. Solar zenithal angle is 30°. Results from the numerical code libRadtran simulating the radiative transfer in the atmosphere.
The three curves in Figure 7.7 have the same shape: zero irradiance at wavelengths A less than 280 nm, strong growth when A increases to around 500nm, and then a slow decay, marked by different absorption lines. The different absorption lines are the same as for the clear atmosphere. They have been detailed previously, and I do not repeat them.
As expected, the irradiance under a cloudy atmosphere is less than that for the clear atmosphere, at all wavelengths. As the optical depth of the cloud increases, the irradiance decreases at all wavelengths. A cloud of optical depth 3-5 does not allow an observer on the ground to see the sun: The direct component is zero. As soon as the cloud optical depth is greater than about 3, only the diffuse component composes the irradiance and the spectral diffuse fraction is equal to 1 at all wavelengths.
The clearness index for a cloudy atmosphere (Figure 7.8) is less than that for the clear atmosphere, at all wavelengths. The shapes of the spectral distributions are quite similar to those of the clearness indices for a clear atmosphere. The same absorption lines are found there.
The similarity in shapes in both Figures 7.7 and 7.8 shows that the shapes do not depend on the cloud optical depths. In other words, the presence of clouds does not induce any modification in the shape of the spectral distributions of the irradiance. This is in agreement with what I wrote in Chapter 4, on the scattering of the solar rays by water droplets in the clouds, which is non-selective, that is to say, that it affects in a uniform way all wavelengths, except the longest in the infrared. This is why the shape of the spectral distribution is unchanged by the clouds as a first approximation; only the intensity of the attenuation changes.
Influence of the solar zenithal angle
Figure 7.9 shows the spectral distribution of the irradiance E(./oll(/ received at ground for three solar zenithal angles 0°, 30°, and 60°, for a cloudy atmosphere, with a cloud optical depth set to 5. Figure 7.10 shows the corresponding clearness indices.
Figure 7.9 Typical spectral distributions of the solar irradiance received on a horizontal surface located at ground in cloudy conditions, between 200 and 2300 nm, for three solar zenithal angles: 0°, 30°, and 60°. The cloud optical depth is 5. Results from the numerical code libRadtran simulating the radiative transfer in the atmosphere.
Figure 7.10 Typical spectral distributions of the clearness index Kt in cloudy conditions, between 200 and 2300 nm, for three solar zenithal angles: 0°, 30°, and 60°. The cloud optical depth is 5. Results from the numerical code libRadtran simulating the radiative transfer in the atmosphere.
The spectral distributions in Figure 7.9, respectively Figure 7.10, have the same general shape. The spectral irradiance, respectively the spectral clearness index, decreases when increases at each wavelength. These graphs illustrate in particular the great importance of the solar zenithal angle on the attenuation of radiation, including in a cloudy atmosphere.
