Typical irradiances integrated over spectral intervals in cloudy conditions

Table 7.3 gives some typical irradiances E_ci_0Uj(X/, 2^) integrated over various spectral intervals [Я/, 2?] at normal incidence for two atmospheres composed of a cloud of optical depth of, respectively 5 and 15. This table is similar to Table 7.1 giving spectrally integrated irradiances but for clear-sky conditions. In addition. Table 7.4 quantifies the relative contribution of spectrally integrated E_c/_oue/(li, 2^) to the total irradiance Echurl at normal incidence for the two cases of cloudy sky. For the sake of comparison, I also reported the fractions compared to the total radiation Ersi tit the top of the atmosphere, already presented in Table 3.3 (Chapter 3).

The irradiance E_cj_0U<i(Aj, Aft in a given interval decreases as the optical depth of the cloud increases (Table 7.3). This decrease is not constant over wavelengths. As done previously for Table 7.1, this can be illustrated by calculating the ratio between the irradiances for the two optical depths in Table 7.3. For example, the ratio between the total irradiances for the two optical depths (Table 7.3, first line) is about 0.61 (= 493/802). The ratio is also 0.61 (= 490/797) for the interval [250,4000] nm (Table 7.3, second line). It is around 0.62 (= 484/784) for the typical spectral band of pyranometers (Table 7.3, last line). As a whole, this ratio remains approximately constant at wavelengths shorter

Table 7.3 Typical irradiances (W m^-2) received at ground at normal incidence integrated over various spectral intervals for two cloudy atmospheres composed of a cloud of optical depth of respectively S and 15

PAR stands for photosynthetically active radiation. CIE stands for International Commission on Illumination. Results from the numerical code libRadtran simulating the radiative transfer in the atmosphere.

than around 2000nm. It can be concluded that as a first approximation, the effects of clouds are spectrally neutral at wavelengths shorter than around 2000nm. In other words, the depletion by the clouds does not depend on the wavelength at wavelengths shorter than around 2000 nm as a first approximation. At greater wavelengths, the ratio is less than 0.6 and depends on the interval.

As for the clear sky, approximately 99 % of the total irradiance E_ci_OUd received at ground is in the interval [250, 4000] nm (Table 7.4); the share of the interval [4000, 20,000] nm is very small. In general, since wavelengths greater than 900nm have the broadest absorption lines, the relative contributions of the longest wavelengths are less at ground level than at the top of the atmosphere. Correlatively, the relative contributions of wavelengths less than 900 nm are greater at ground level than at the top of the atmosphere. For example, the irradiance E_c/_oue/(l/, li) in the interval [380, 2100] nm accounts for approximately 94 % of E₍./_ouci, while at the top of the atmosphere the contribution of this interval is only 89 % of Ersi- Likewise, the irradiance E_c/_ouei(Xj, Я2) in the interval [400, 1100] nm accounts for approximately 80 % of E_c/_OU(i, while the fraction is only 67 % of Efsi at the top of the atmosphere.

The irradiance in the UV-B, in the range [280, 315] nm, is very low, around 2 W m^-2 (Table 7.3). There is very little variation in the attenuation in UV-B depending on the optical depth of the clouds. According to Table 7.1, the UV-B irradiance is 3 W m^-2 for clear and turbid cloudless atmospheres. The influence of the constituents of the tropospheric atmosphere on UV-B radiation is therefore weak; it is the content of the stratospheric ozone layer, between 20 and 40 km above sea level that matters most. The UV-B irradiance represents less than 1 % of the total irradiance E_c/_OUii (Table 7.4). The UV-A irradiance ([315, 400] nm) is much greater. It is a few tens of W m^-2 (Table 7.3) and

Table 7.4 Typical values of the fraction (%) of the irradiance received at normal incidence at the top of the atmosphere (left column) and on the ground (right columns) in various spectral ranges relative to the respective total irradiance under cloudy conditions

PAR stands for photosynthetically active radiation. CIE stands for International Commission on Illumination. Fractions are rounded up to the nearest integer. Results from the numerical code libRadtran simulating the radiative transfer in the atmosphere.

represents around 7 % of Е_с/_ош/ (Table 7.4). These proportions for ultraviolet are close to those observed at the top of the atmosphere. The radiation in UV-A is weaker in the presence of cloud than in cloudless conditions and decreases as the optical depth of the cloud increases.

If the irradiance in the visible range [380, 780] nm decreases when the cloud optical depth increases, on the other hand, the relative contribution of this interval to Е_с/_ОШ1 increases with the optical depth. It is 59 % and 62 %, respectively, in the simulations here, much more than that at the top of the atmosphere (49 %). In general, the relative contributions of the intervals to E_ct_oud increase as the cloud optical depth increases. For example, the PAR in the interval [400, 700] nm contributes in these simulations to 48 % and 51 %, respectively of E_ci_OU(f. This is more than for the clear sky (46 % and 45 % of E_cear, Table 7.2) and much more than at the top of the atmosphere (39 % of £7-57).

For very large intervals, the contributions relating to E_c/_ouj are similar to those relating to E_c/_ear For example, for the interval [380, 2100] nm, the contributions relating to E_ci_olHi are 93 % and 94 % and similar to those relating to E_c/_ear (92 %). Another example is that of the typical spectral range of pyranometers, i.e. [330, 2200] nm. The contributions relating to E_ci_ouj (98 %) and E_c/_ear (97 %) are very close: These instruments capture a very large part of the total radiation and do so homogeneously for all types of sky.