Modeling Solar Radiation at the Earth’s Surface

Solar Radiation Measurement Fundamentals

Solar radiation consists of electromagnetic radiation emitted by the Sun in spectral regions ranging from X-rays to radio waves. Terrestrial applications of renewable energy utilizing solar radiation generally rely on radiation, or photons, referred to as “optical radiation”, with a spectral range of about 300-4000 nm. Broadband mea­surements in this range are the most common and are described further in the next sections. Figure 1.1 shows the extraterrestrial solar spectrum (ETS) at the mean Sun - Earth distance, with extra detail for the ultraviolet (UV), i. e., below 400 nm, where a lot of spectral structure is obvious.

Christian A. Gueymard

Solar Consulting Services, ColebrookNH, USA, e-mail: chris@solarconsultingservices. com Daryl R. Myers

National Renewable Energy Laboratory, Golden CO, USA, e-mail: daryLmyers@nrel. gov

Fig. 1.1 Extraterrestrial solar spectrum in the shortwave at low resolution (0.5 to 5 nm). The highly-structured UV part of this spectrum is detailed in the inset at low (0.5 nm; thick black dots) and high (0.05 nm; thin gray line) resolution

The determination of ETS has evolved over time (Gueymard 2006), based on measurements from terrestrial observatories and spaceborne instruments, model calculations, or their combination. The low-resolution ETS in Fig. 1.1 is suffi­ciently detailed for most solar energy applications. It is a composite spectrum that uses all the types of data sources just mentioned, with proper weighting (Guey­mard 2004). This dataset is provided in the file ‘Gueymard_spectrum_2003.txt’ on the accompanying CD. [It is also available, along with other similar datasets, from http://rredc. nrel. gov/solar/spectra/am0/].

The spectral integration of the ETS over all possible wavelengths (0 to infinity) is usually referred to as the “solar constant” or “air mass zero” (AM0) spectrum. In recent years, a more proper name, Total Solar Irradiance (TSI), has been introduced, since the Sun’s output is not constant but varies slightly over short (daily) to long (decadal or more) periods (Frdhlich 1998). These variations have been monitored from space since 1978 with various broadband instruments, called absolute cavity radiometers (ACR). ACR uncertainty is about an order of magnitude lower than that of instruments used to measure the spectral distribution of the ETS, therefore TSI is more precisely known than its spectral details, shown in Fig. 1.1. Over a typical 11-year Sun cycle, there is a variation about ±1Wm~2 around the solar constant. Short-term variations of about ±4Wm~2 due to sunspots, solar flares, and other phenomena have been observed. The current best estimate of the average TSI based on 25 years of data is 1366.1Wm~2 (ASTM 2000; Gueymard 2004). However, recent measurements using a different type of instrument from the Solar Radiation and Climate Experiment (SORCE) satellite indicate a systematically lower value, of «1361Wm~2 (Rottman 2005). Work is underway to understand and resolve this discrepancy. It is highly probable that the revised value of the solar constant to be proposed in the near future will be somewhere between 1361 and 1366Wm~2. The daily or yearly excursions in TSI (±0.1 to 0.2%) are small compared to all the other uncertainties involved in measuring or modeling solar radiation, and hence are usually not considered in terrestrial applications. In what follows, only the solar constant value matters, along with its predictable daily variation induced by the Sun-Earth distance, as described in Sect. 3.

The spectral distribution shown in Fig. 1.1 is modified and segregated into var­ious component elements by the passage of the radiation through various layers of the Earth’s atmosphere. A discussion of these spectral features or their measurement is beyond the scope of this chapter. Further information may be obtained elsewhere (e. g., Gueymard and Kambezidis 2004).

The science behind the measurement of electromagnetic radiation is called ra­diometry. Historically, simple instrumentation has been long used to evaluate the duration of bright sunshine in relation to day length. Radiometers of various de­signs have then been perfected to measure the energy in specific “components” of terrestrial solar radiation, as will be defined in Sect. 3. The interested reader should consult other textbooks (e. g., Coulson 1975; Iqbal 1983) for historical and technical details about common instruments used in solar radiometry.

Radiometers are constituted of different parts, mainly a casing or body, a radiation detector, and some electronics, including electrical circuits. For the instruments un­der scrutiny here, whose main purpose is to measure shortwave radiation (as op­posed to UV or thermal radiation), detectors can be of three main types: thermopile, blackbody cavity, and solid state (semiconductor). The detector has a known spec­tral response to incident radiation. It is generally protected from the environment with some type of optical window, which can be transparent (e. g., glass or quartz), colored (e. g., interference filter), or translucent (e. g., white diffuser). The win­dow optical transmission further limits the spectral range of the radiation actually measured.

In the following sections, we discuss solar radiation components, the measure­ment scale and reference against which solar instrumentation are calibrated, mea­surement principles used for the instrumentation, and—of greatest importance for the modeler of solar radiation—the uncertainty or accuracy to be expected from typical instrumentation. Recent advances in radiometric techniques are explained in detail. We begin with a description of the components of solar radiation that are created by the interaction of extraterrestrial solar radiation with various extinction processes within the Earth’s atmosphere.

Modeling Solar Radiation at the Earth’s Surface

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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 …


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