Solar spectral diffuse radiance for a specified atmosphere

Abstract

In many applications such as the design and performance evaluation of solar energy devices, remote sensing studies, meteorological and climatological studies, it is necessary to know the values of solar radiation reaching the surface of the earth. Depending on the application, either the global solar radiation or the diffuse and beam components of radiation are separately required, along with their spectral and angular distributions. While tabulations of mean beam and diffuse radiation reaching the earth’s surface are available in handbooks of solar radiation for many stations, neither the angular nor the spectral distribution is commonly available. Furthermore, when these quantities are required for a specific meteorological situation, it becomes necessary to carry out local measurements or rely on empirical correlations.

A technique has been developed for computing the spectral diffuse solar radiation and its angular distribution reaching a surface placed at any altitude within the atmosphere. It uses values of extraterrestrial radiation and actual local meteorological parameters such as profiles of temperature, humidity, ozone, and aerosols, or standard atmospheric models specifying average conditions.

For computing radiation scattered by atmospheric constituents, two techniques have been studied in detail:

The Eddington approximation, which is simple but provides only angularly integrated spectral radiative flux.

The adding method developed by van de Hulst, which calculates scattered radiation for any observer angle and azimuth.

In the calculations, the earth’s atmosphere is divided into a number of plane-parallel homogeneous layers. Their spectral optical thicknesses (transmittances) for absorption and scattering are found using a comprehensive numerical scheme — the LOWTRAN 5 transmittance code. For computing radiation scattered by aerosols, the phase functions (or angular asymmetry parameters) for complex polydispersions of particles in the atmosphere are taken to be standard Henyey–Greenstein phase functions, along with Rayleigh scattering functions for gas molecules.

When applying the Eddington approximation, the atmosphere is divided into just four layers. The adding method is used when angular distribution of diffuse radiation is required, and here the atmosphere is divided into many horizontal layers such that the optical thickness of each layer is less than 10?³, so that single scattering can be assumed.

The computational scheme developed has subroutines for each of the Eddington and adding methods, which can be coupled to the LOWTRAN 5 program so that diffuse radiation reaching an observer at any altitude or orientation can be computed for any specified meteorological condition. Spectral diffuse radiation has been computed for a tropical atmosphere under several visibility conditions. The results show excellent agreement between the Eddington and adding methods for integrated angular quantities. Since very short computer time is required for the Eddington method, whenever angularly integrated spectral diffuse radiation is needed, this technique may be utilized.

Comparison of diffuse radiation computed with other techniques, such as that of Dave or empirical methods using the Ångström coefficient, and also with experimental measurements, shows good agreement. Hence, for accurate computation of angular and spectral diffuse and beam solar radiation, programs have been developed that require only local meteorological data as input.