Modeling Solar Radiation at the Earth’s Surface
Components of Solar Radiation in the Atmosphere
From the Earth, the solar disk subtends a solid angle of about 0.5° on average. Due to the eccentricity of the Earth’s elliptical orbit (0.0167), the distance from the Earth to the Sun varies throughout the year by ±1.7%, resulting in a ±3.4% variation in the intensity of the solar radiation at the top of the atmosphere. The Sun thus acts as a quasi point source, illuminating the Earth with very nearly parallel rays of radiation. This quasi-collimated beam is the extraterrestrial direct beam, or extraterrestrial radiation, referred to as ETR.
As the ETR beam traverses the atmosphere, interaction between the photons in the beam and the atmosphere result in scattering and absorption of photons out of the beam into random paths in the atmosphere. Scattered photons (mostly at short wavelengths) produce the diffuse sky radiation, which we will denote by D. The remaining unabsorbed and unscattered photons, still nearly collimated, constitute the direct beam radiation, responsible for the casting of shadows, which we will denote as B. The total radiation flux on a horizontal surface in the presence of diffuse and beam radiation is often called “total” or “global” radiation. We will denote this global solar radiation on a horizontal surface as G. The term “global” refers to the concept that the radiation on a horizontal surface is received from the entire 2n solid angle of the sky dome. The difference between G at ground level and its corresponding value at the top of the atmosphere is what has been absorbed or reflected away by the atmosphere. On average, the Earth reflects about 29% of the incident solar irradiance back to space.
The total solar radiation received by a tilted (non-horizontal) surface is a combination of direct beam, diffuse sky, and additional radiation reflected from the ground (which we will denote as R), and should be referred to as total hemispherical radiation on a tilted surface. However, it is most often described by the simpler term “global tilted” radiation. Figure 1.2 illustrates the various components of solar radiation on intercepting surfaces.
The nearly collimated rays of the solar direct beam, in combination with the constantly changing altitude and azimuth of the Sun throughout the day, produces a constantly changing angle of incidence of the direct beam on a horizontal or tilted surface. Lambert’s cosine law states that the flux on a plane surface produced by a collimated beam is proportional to the cosine of the incidence angle of the beam with the surface.
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Fig. 1.2 Solar radiation components segregated by the atmosphere and surface |
The incidence angle (i) of the solar beam upon a horizontal surface is equal to the solar zenith angle (z), i. e., the complement of the solar elevation (h). Thus the basic relation between the total global horizontal radiation G, direct beam radiation B at normal incidence, and diffuse radiation D on a horizontal surface can be described by Eq. (1.1):
G = B cos(z)+D = B sin(h)+D. (1.1)
Equation (1.1) is fundamental to the calibration of solar instrumentation. For tilted surfaces, Eq. (1.1) needs to be rewritten as:
G = B cos(9)+RdD + R (1.2)
where в is the incidence angle with respect to the normal of the tilted surface, and Rd is a conversion factor that accounts for the reduction of the sky view factor and anisotropic scattering, and R is radiation reflected from the ground that is intercepted by the tilted surface (Iqbal 1983). Modeling each of the components of Eqs. (1.1) or (1.2) is the objective of many investigations and of other chapters in this book.
