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.

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.

 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.

## Modeling Solar Radiation at the Earth’s Surface

### Quality Assessment Based Upon Comparison with Models

Many models based on the physics of radiation transfer through the clear atmo­sphere have been developed (Lacis and Hansen 1974; Atwater and Ball 1978; Hoyt 1978; Bird and Hulstrom 1981a, …

### Solar Horizontal Diffuse and Beam Irradiation on Clear Days

There exist a number of models to determine the solar horizontal diffuse irradia­tion on a clear day (Kondratyev 1969) but they are complex and have very stringent conditions. Similarly, there …

### Foreword

Reading the twenty chapters of this book caused me mixed reactions, though all were positive. My responses were shaped by several factors. Although I have main­tained a “watching brief’ on …

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