Volume 1 photovoltaic solar energy 1 12 – solar radiation resource assessment for renewable energy conversion

Volume 1 photovoltaic solar energy 1 12 – solar radiation resource assessment for renewable energy conversion Volume 1 photovoltaic solar energy 1 12 – solar radiation resource assessment for renewable energy conversion Volume 1 photovoltaic solar energy 1 12 – solar radiation resource assessment for renewable energy conversion Volume 1 photovoltaic solar energy 1 12 – solar radiation resource assessment for renewable energy conversion Volume 1 photovoltaic solar energy 1 12 – solar radiation resource assessment for renewable energy conversion

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DR Myers, National Renewable Energy Laboratory, USA

© 2012 Elsevier Ltd All rights reserved

1.12.1 Introduction

1.12.1.1 The Sun as Star

1.12.1.2 The Earth and the Sun

1.12.2 Fundamentals of Solar Radiation

1.12.2.1 Solar Geometry

1.12.2.2 The Atmospheric Filter

1.12.2.3 Spectral Considerations

1.12.3 Fuel for Solar Energy Collectors

1.12.3.1 Photovoltaic and Solar Thermal Flat Panels

1.12.3.2 Solar Thermal Systems

1.12.3.3 Sustainable Applications

1.12.4 Measuring Solar Radiation

1.12.4.1 Solar Radiometers and Detectors

1.12.4.7 Radiometric Uncertainty and Performance

1.12.5 Modeling Solar Radiation

1.12.5.1 Physics-Based Models

1.12.5.2 Empirical Models

1.12.5.3 Satellite-Based Models

1.12.5.4 Geographical Information System Models

1.12.6 Converting Solar Radiation Data to Application-Specific Data

1.12.6.1 Estimating Hemispherical Radiation on a Tilt

1.12.6.2 Estimating Direct Beam (DNI) from Global Horizontal Radiation

1.12.6.3 Estimating Diffuse Hemispherical Radiation from Global or DNI

1.12.7 Measured and Model Data Set Properties

1.12.7.1 Period of Record

1.12.7.2 Temporal Resolution

1.12.7.3 Spatial Coverage

1.12.7.4 Modeled Data Sets

1.12.8 Model Estimate Uncertainties

1.12.9 Developing Solar Radiation Resource Databases

1.12.9.2.6 Filling gaps in the data record

1.12.9.2.7 Deriving precipitable water data

1.12.9.2.8 Deriving broadband aerosol optical depth

1.12.9.2.9 Modeling cloud transmittance, scattering, and statistical effects

1.12.9.2.10 Output products and data quality checks

1.12.9.2.11 Updating the database

1.12.10 Applications: Calculating Solar Radiation for Flat-Plate and Concentrating Collectors

1.12.11 Future Directions

quantifying the extinction of solar radiation by scattering Electron volt (eV) Measure of photon energy, dependent

on wavelength of the light

particulates and absorption between the point of

observation and the top of the atmosphere Extinction Loss of amplitude or attenuation in a signal Air mass (AM) The path length from an observer’s propagating through an absorbing or scattering medium

Extraterrestrial solar

radiation at through the center of the sun, relative to the zenith the top of the Earth’s atmosphere

(perpendicular to the local horizontal = air mass 1) Global hemispherical radiation (G) The combination of Albedo (r) For the ground The ratio of the magnitude of photons from the sky dome and solar disk (diffuse

reflected radiation to incident radiation The bulk hemisphericaland projection of thedirect normal

Broadband radiation Photons in a wide electromagnetic Incidence angle (i) The angle between the center of thespectral wavelength range, typically several hundred solar disk and the foot of the normal (perpendicular) of a

Circumsolar radiation (CSR) The solar aureole, sky Pyranometer A radiometer with a 2π steradian

radiation surrounding the solar disk which is scattered out (hemispherical) field of view used to measure global

of the direct normal irradiance hemispherical or diffuse hemispherical radiation

Diffuse hemispherical radiation ( ) Photons scattered in F Pyrheliometer A radiometer with a restricted fi d of viewelthe atmosphere, excluding those from the solar disk, (typic ly 5°al –6°) used to measure direct normal radiation arriving on a horizontal surface originating from the 2π Responsivity (Rs) The ratio of the output signal of a steradian hemisphere of the sky dome radiometer to the optical power intercepted by the sensor Direct beam irradiance (B) See Glossaryterm ‘Direct Solar radiation Electromagnetic emissions from the sun

between 250 and 2500

Direct normal irradiance (DNI) Nearly parallel rays of Zenith angle (Z) The angle between the local vertical and photons arriving on a surface perpendicular to the line the center of the solar disk; complement of the solarfrom the observer to the center of the solar disk originating elevation angle (angle from the center of the solar disk tofrom within the 0.5°solid angle centered on the solar disk, the horizon)

1.12.1 Introduction

With the present recognition that fossil fuels are not sustainable and that their use damages the planetary environment, alternative, noncarbon emitting sources of energy such as solar energy are recognized as a path to a clean and sustainable energy sources It has long been recognized that the sun is the ultimate source of all of our energy sources, whether for fuel for the economy or food as fuel for our bodies This chapter addresses the measurement and modeling of solar energy as fuel for solar energy conversion systems In this sense, the sun provides unlimited ‘reserves’, relatively easy to access and harvest, for a truly sustainable energy supply Despite the intermittent and relatively low energy density of sunlight, information on the quantity and quality of terrestrial solar radiation can be used to optimize solar conversion systems Developing innovative designs for capturing and converting solar radiation is only one-half of the equation Identifying, locating, and prospecting for the appropriate quantity and quality of solar resources to fuel these systems is critical to designers, investors, financiers, and owner/operators This chapter addresses the fundamental elements and state of the art for measuring, modeling, and evaluating solar radiation resources and applications to system design

1.12.1.1 The Sun as Star

Modern classification of stars is similar to the classification of species in the plant, animal, and insect kingdoms The astrophysical classification scheme is used to express the approximate age, size, and luminosity, or energy content, of stars Presently, the classification consists of single letter designations OBAFGKMN The letters represent, in order, young, hot, energetic stars to old, cool, low energy stars Subclassification numbers and small letter designations are used for subdividing the stellar classes according

to sometimes esoteric features of the stellar spectra Our sun is a typical ‘average’ star classified by astronomers as a ‘G2-V dwarf’, in the middle of its evolutionary lifetime of about 20
109

years The sun emits 2.009

watts per square meter per steradian (Wm -sr−1) from its surface, and 2.845
1026 W in all directions The Earth resides in an elliptical orbit about the sun with an eccentricity of 0.0167 (1.4710
106

km at perihelion, 1.5210
106

km at aphelion) At the mean Earth–sun distance, the sun

subtends a solid angle of 9.24 mrad, or 0.529° Thus, the sun is not truly a point source, and the rays from the sun are not truly parallel, but diverge into a cone with a nominal half angle of 0.529° Many scientists have investigated the energy output of the sun, sometimes referred to as the ‘solar constant’, or the magnitude of the energy reaching the top of the Earth’s atmosphere, referred to here as ‘extraterrestrial radiation’, or ETR Since the late 1970s, measurements from earth orbit by orbiting ‘total solar irradiance’ sensors have attempted to measure ‘solar constant’ at the Earth Despite the identification of the ‘sunspot’ cycle of approximately 11 years, and rather small (less than one-fifth of 1%) variation in solar emission as a result of sunspots, there is a widely accepted definition of the solar constant, at 1 astronomical unit or 1.495979
109 km, as 1366.1 Wm−2  7.0 Wm−2

1.12.1.2 The Earth and the Sun

As mentioned above, the Earth’s orbit about the sun is elliptical Treating the sun as a point source, the variation in the Earth–sun distance produces a ‘1 over R-square’ variation in the ETR defined above This 1/R2

effect increases the ETR above the mean value by 3% at perihelion (December) and decreases the ETR by 3% at aphelion (July) This effect must be taken into account when modeling, or mathematically computing, solar radiation resources throughout the year The 23° tilt of the Earth’s rotation axis with respect to the plane of the Earth orbit about the sun results in variations in the solar path through the daytime sky dome throughout the year (as well as the procession of the seasons)

1.12.2 Fundamentals of Solar Radiation

The Earth intercepts the ETR within a very slender cone, or beam, of photons, called the direct normal irradiance (DNI), or direct beam radiation, since it is typically measured on a surface perpendicular to the quasi-collimated ‘beam’ of photons within the cone The flux density of this beam at the top of the atmosphere (at the average Earth–sun distance) is the ETR, or solar constant defined above The atmosphere acts as an absorbing and scattering medium through which the beam propagates to the ground Photons are scattered (their directed of propagation is changed) or absorbed by molecules and particles in the atmosphere Photons that are not absorbed contribute to uncollimated diffuse irradiance of the sky dome The changing constituents of the atmosphere (clouds, water vapor, aerosols, smoke, pollutants, etc.) change the optical properties of the atmosphere This in turn affects the distribution of power as a function of the wavelength (or energy) of the photons moving through the atmosphere The combination of direct normal and diffuse sky radiation constitutes the total solar radiation impinging on surface The geometrical relationship between the surface or plane of interest, the sky dome and ground, and the direction of the direct beam from the solar disk determine the relative contribution of each component to the total solar radiation available to a surface The optical properties of the surfaces or system elements also affect the amount of solar energy that can be converted to useful energy Each of these elementary contribu­tions to the modification of solar energy available to solar conversion systems are discussed below

1.12.2.1 Solar Geometry

Solar radiation flux on a horizontal surface is referred to as total hemispherical solar radiation; sometimes ‘global horizontal’ radiation, G This hemispherical radiation is comprised of a combination of the nearly collimated direct beam radiation (B) from the solar disk and some portion of the diffuse sky radiation (F) Solar flux on an arbitrarily tilted surface is referred to as total hemispherical radiation on a tilted surface, generally shortened to ‘global tilt’ radiation (GT) For tilted surfaces, contributions from the sky radiation are reduced because of the ‘unseen’ part of the sky radiation Ground-reflected radiation (R) may contribute to the global tilt radiation, and its magnitude depends on the optical properties (albedo) of the ground in the field of view In all cases, the contribution of the direct beam to the radiation on the surface depends upon the incidence angle (i), the angle between the normal

to the surface, and the projection of the direct beam radiation on the surface This component is computed as the direct beam magnitude multiplied by the cosine of the incidence angle i For a horizontal surface, the incidence angle for the beam is the zenith angle, Z, defined as the angle between the center of the solar disk and the normal to the surface, which points to the zenith Figure 1 illustrates the terms utilized in solar geometry calculations

For incidence angle i, direct beam magnitude B, diffuse sky radiation value F, and possibly ground-reflected radiation R, the total hemispherical radiation on a surface is

G ¼ B cos ið Þ þ F þ R From Figure 1, note that as the solar elevation angle (e) increases, or the zenith angle decreases, the effective path length (through a plane atmosphere) decreases The reference altitude for the path length calculation is sea level Geometrically, the path length is a function of the reciprocal of the sine of the incidence angle sin(i), or cosine of the zenith angle cos(Z) The common term for this path length in the solar energy community is the air mass, (AM), and AM = 1/sin(e) = 1/cos(Z) Thus, a solar elevation of 30° (Z = 60°) results in AM = 2.0, and AM = 1.0 means the elevation angle is 90°, the zenith angle is 0°, and the sun is directly overhead Note this definition is appropriate for a plane atmosphere only The curvature of the Earth’s atmosphere and refraction, or bending of the beam radiation due to optical properties of the atmosphere, cause deviations from this ‘geometrical’ AM and the

‘absolute AM’, represented by an integration over the (curved) path through the atmosphere, accounting for the decrease in atmospheric pressure with height above the ground For solar Z less than about 70° (elevations above 20°), the geometrical

Zenith Beam Zenith angle

Figure 1 Example of solar geometry terms for a general case For horizontal surfaces, the surface tilt is zero, and the normal points to the zenith, the

‘surface azimuth’ is undefined, and the incidence angle is equal to the zenith angle, Z, (complement of the solar elevation angle) Thus, the total hemispherical radiation becomes G = B cos (Z) + F

approximation is very good, as the atmosphere approximates a flat plate, due to the large curvature of the Earth For solar Z greater than 70° (elevations < 20°), corrections are often applied to account for the effects of refraction, which always increase the AM Lastly, absolute AM is a function of elevation, since the density of the atmosphere decreases with altitude

1.12.2.2 The Atmospheric Filter

The Earth’s atmosphere acts as a continuous variable filter, changing the relative magnitudes of the direct beam and diffuse sky radiation (and thus the total global radiation), as well as modifying the spectral distribution, or amplitude as a function of wavelength of the light, for each of these components The changes induced on the ETR beam and resulting global total and diffuse sky radiation are functions of many factors, including the solar geometry (AM) and constituents of the atmosphere

1.12.2.3 Spectral Considerations

Figure 2 is a graph of the extraterrestrial spectral distribution of sunlight at the top of the atmosphere, and typical direct beam, diffuse sky, and total hemispherical spectral distributions for a specific set of atmospheric conditions and single given air mass = 1.5 The ETR spectrum in Figure 2 can be approximated by a smooth blackbody radiation curve for a body at a temperature of about

5400 K However, the sun is not truly a blackbody radiator The ETR curve contains various absorption features (‘valleys’ in the curve), especially apparent below 500 nm These result from various elements and conditions such as gradients in temperature and density in the solar atmosphere These features were first identified and associated with the physics of the solar atmosphere by Fraunhofer, and are named in his honor Most are apparent in the wavelengths below 500 nm For longer wavelengths, the ETR curve is relatively smooth

Conversely, the terrestrial beam and total hemispherical curves show absorption features that depend on the path length between the top of the atmosphere and the observation site Basic atmospheric gases such as oxygen and nitrogen, and mainly water vapor, ozone, and pollutants have their own absorption features Gas molecules in the atmosphere that are approximately the same size as the wavelength of light within the spectrum are more efficient at scattering radiation out of the beam This is Rayleigh scattering, after Lord Rayleigh, who first investigated this phenomenon Lastly, suspended particulates of varying sizes and optical properties scatter some wavelengths better than others These particulates are usually lumped together as ‘aerosols’ The Swedish scientist Kurt Ångstrom related the extinction due to aerosols to two parameters, α (related to the size of the aerosols) and β (related

to the optical properties of the aerosols) Once the effects of Rayleigh scattering, atmospheric gas absorption, and water vapor absorption are accounted for, the formula for the relationship of collected incident radiation I to incident radiation Io is

I ¼ I expð−tmÞ where t ¼ βλα:

500 0.00 0.50 1.00 1.50 2.00

1000 1500 2000 2500 3000

Extraterrestrial Direct beam Global hemispherical on horizontal Diffuse hemispherical on horizontal

where t is often referred to as ‘turbidity’, m = air mass AM, and λ is wavelength The more correct term for t is aerosol optical depth The phrase optical depth refers to the attenuation of radiation passing through a plane parallel medium

A typical range for α is 0.5–2.5, with an average for natural atmospheres of around 1.3  0.5 Larger values of α, when the t value for longer wavelengths is much smaller than the t value for the shorter wavelengths, imply a relatively high ratio of small particles to large (r > 0.5 µm) particles As t for a longer wavelength approaches the t for a shorter wavelength, larger particles dominate the distribution and α becomes smaller It is not physically reasonable for the t value of longer wavelengths to equal or exceed the t value

of shorter wavelengths

For both broadband and spectral solar radiation, if one considers the transmittance, Tx, or ratio of collected to incoming ETR irradiance, for each atmospheric constituent ‘x’ described above, such as

Rayleigh scattering transmittance: Tr

Mixed gas transmittance: Tg

Water vapor transmittance: Tw

Ozone transmittance: To

Aerosol scattering transmittance: Ta

each of which is dependent on the AM and concentration, or amount of the constituents present

Then an expression for the dependence of clear-sky direct beam terrestrial solar radiation on these parameters can be written as the product of transmittances and the direct beam ETR, (Io):

For cloudy or partly cloudy skies, the situation becomes more complex Absolute or relative ‘effective’ cloud ‘transmittance’ is difficult to parameterize Various types of clouds have different optical properties (‘cloud optical depth’, similar to aerosol optical depth) The spatial distribution (in three dimensions) of clouds with respect to the position of the sun, mixture of cloud types present, and varying physical structure of clouds present formidable barriers to precise calculation of the impact of clouds on the transfer of solar radiation through the atmosphere That topic is discussed in more detail below in the section on Modeling Solar Radiation

1.12.3 Fuel for Solar Energy Collectors

Estimating or quantifying the available fuel for solar conversion systems is the aim of solar resource assessment The ‘quantity’ or magnitude of the resource is often of first concern The ‘quality’ of the resource is represented by inherent properties of the radiation, such as the spectral distribution, relative contribution of direct beam, diffuse, and total hemispherical components, duration, and

400 600 0.00

0.50 1.00 1.50 2.00

temporal and spatial variability The relative importance of each of these aspects of solar radiation resources depends on the technology of the conversions systems in question A few examples of the most common applications for solar radiation resource assessment are discussed next

1.12.3.1 Photovoltaic and Solar Thermal Flat Panels

Photovoltaic technologies utilize various semiconductor materials that release electrons from their constituent atomic structure that become available for conduction, or for the production of electric current The electrons are kicked out of there orbital bands by absorbing photons of above a suitable threshold energy The ‘suitable energy’ of course depends on the materials used

Most photovoltaic panels deployed today are made of crystalline silicon If a silicon atom absorbs a photon of wavelength shorter than about 1100 nm, or a photon with energy of at least 1.1 eV, an electron may be released into the conduction band of the material Less expensive cells, such as ‘thin film’ amorphous (i.e., noncrystalline) silicon, or more easily produced ‘multicrystalline’ silicon response differently Cadmium telluride (CdTe), copper indium gallium selenide (CuInGaSe2, or CIGS), and gallium arsenide (GaAs) cells use photons from different spectral bands into conduction electrons Some materials can be stacked to produce ‘multijunction’ cells Each layer absorbs and converts a specific part of the spectrum, thus using more of the solar spectrum Figure 4 plots the spectral response functions for several materials systems

0.6 0.5 0.4 0.3 0.2 0.1 0.0

GalnP a-Si CdTe GaAs InP multi-Si mono-Si ZnO/CIGS

Wavelength (nm) Figure 4 PV material system spectral responses GaInP = gallium indium phosphide; a-Si = amorphous silicon thin film; CdTe = cadmium telluride; GaAs = gallium arsenide; InP = indium phosphide; multi-Si = multicrystalline silicon; mono-Si = monocrystalline silicon; ZnO/CIGS = zinc oxide-coated copper indium gallium diselenide film Source: Field H (1997) Solar cell spectral response measurement errors related to spectral band width and chopped light waveform 26th IEEE Photovoltaic Specialists Conference, Anaheim, California, NREL/CP-530-22969, 29 September–3 October 1997 Golden CO: National Renewable Energy Laboratory [1]

The challenge for photovoltaic conversion systems is to find a combination of material conversion efficiency manufacturing processes and deployment applications for optimum economic and or energy impact The spectral quality of the sunlight available becomes important for photovoltaic systems, in that it is the integral of the product of the spectral response of the materials and the available spectral distribution that determines the total number of electrons that become available for conduction Energy outside the spectral response of the materials is absorbed to produce heat, or if the material is thin enough, and the wavelength long enough, passes through the material to be absorbed by the substrate holding the material

1.12.3.2 Solar Thermal Systems

Solar thermal collectors use the concept of ‘selective absorber’ materials to absorb as much of the solar spectrum as possible These are essentially black absorbers that convert the photon energy to heat The heat then is used in thermal applications to produce hot water or steam, sometimes at high pressure and temperatures Flat plate absorbers are commonly used to produce domestic hot water By using parabolic reflectors, either as long troughs with absorbers running through the focal axis of the trough or dishes with absorbers at the focus of the parabola, the flux density of the solar radiation (energy per unit area) can be increased several orders of magnitude (powers of 10) Similarly, Fresnel lenses or other focusing optical systems can also be used to concentrate solar radiation For thermal systems, part of the overall efficiency of the systems is the optical efficiency of the reflectors and absorbers Heat transfer and energy transport through the system contribute to the overall system efficiency It is critical to note that concentrating collectors can only utilize the direct beam irradiance These are the only photons that are redirected to the absorbers by the reflecting or lens components Diffuse sky and ground-reflected radiation propagate in random directions, and cannot be focused Thus, the relative contribution of direct beam to the total available solar radiation resource becomes important for concentrating systems

1.12.3.3 Sustainable Applications

Solar radiation resources are important for other sustainable energy applications, such as daylighting, solar desalinization, and detoxification of contaminated water, ‘passive solar’ construction (which manages the heat loads for buildings based on architecture and materials) For building applications it is usually necessary to have solar radiation information in combination with weather or climate data The solar radiation in combination with the exposure, materials, and orientation of buildings, and the parameters defining the comfort of the occupants, generates the heating and cooling loads that must be met

For daylighting applications, the substitution of natural sunlight for artificial lighting, the relevant solar geometry for a location,

in combination with the relative contributions of sky and direct beam radiation, and spectral transmittance of window materials become important The human eye has a limited spectral response (the photopic response) between 380 and 800 nm, peaking at

550 nm, which also has to be considered The ‘luminous efficacy’ of a source, such as the sun or a lamp, is the ratio of the integration

of the eye response multiplied by the spectral distribution of the source divided by the integrated source spectral distribution over the eye response region The variation of the spectral distribution of daylight is dependent on location and atmospheric conditions, and can impact the quality of available illumination for lighting applications

Water quality and availability can be improved through the use of solar energy to evaporate sea water, leaving behind salt, and then recondensing the water vapor Water contaminated with toxic compounds can be purified by using titanium dioxide (TiO2) as

a catalyst in combination with the ultraviolet part of the solar spectrum (or an artificial source) to remove the contaminants For these applications, the relative availability and amplitude of broadband and ultraviolet spectral components of solar radiation are important

The following sections discuss the measurement, modeling, and organization of solar radiation to meet the needs of these sustainable technologies

1.12.4 Measuring Solar Radiation

1.12.4.1 Solar Radiometers and Detectors

Radiometers for measuring total hemispherical or diffuse hemispherical radiation are called pyranometers Two types of sensors, thermal sensors using thermopiles or other thermoelectric generating sensors, such as resistance thermometers, or solid-state sensors using photovoltaic devices, typically silicon photodiodes, are most often used

Thermal sensors are in thermal contact with a black absorbing surface that heats up proportionally to the incident radiation A thermopile sensor generates voltages when junctions of dissimilar metals such as copper and constantan are heated A second set of reference junctions are held at a reference temperature The voltage generated by the thermopile is proportional to the temperature difference of the heated and reference junctions Thermal devices respond over the entire solar spectral range of wavelengths, though they may be protected by windows or domes with broad spectral transmittance range from 285 to 2500 nm When calibrated with respect to a reference radiometer with no window, a small missing part of the spectrum beyond 2500 nm in the test unit is accounted for

Silicon detectors generate a photocurrent proportional to the solar incident radiation The photocurrent can be passed through stable ‘dropping’ resistors to generate a voltage These radiometers have the same limited spectral response range as crystalline silicon photovoltaic cells, from 300 to 1100 nm The energy within this range represents only about 75% of that in the total solar

Total hemispherical Diffuse HZ TP Radiometer Li200 (Si)

spectrum The solar terrestrial solar spectrum beyond 1000 nm is susceptible to considerable variation due to water vapor absorption The silicon detectors do not respond to these variations This leads to additional uncertainty in the measurement of total solar radiation above that for thermal radiometers Figure 5 shows the relative spectral response windows for a thermal detector under a quartz dome and a silicon photodiode detector under an acrylic diffuser Figure 6 shows typical examples of radiometers used to measure hemispherical radiation

A pyrheliometer is used to measure the direct beam or direct normal irradiance (DNI) These instruments are designed with sensors at the bottom of view limiting tubes with field of view limiting apertures These apertures are designed to provide acceptance angles of 5–5.7° This permits some limited error in pointing or tracking of the 0.5° diameter of the solar disk, which should be centered in the field of view These designs were defined before the availability of highly accurate computer-controlled solar tracking equipment, so  2° tolerance for tracking were needed The geometry of the tube designs are defined by the World Meterorological Organization (WMO) Committee on Instrumentation, Measurements, and Observations (CIMO) Guide No 8, published by the WMO This reference has an excellent chapter, number 8, on the measurement of solar radiation That chapter also includes a classification scheme and specifications for solar radiometer quality

Within the 5–5.7° total field of view, the area of scattered radiation near the solar disk, the solar aureole or circumsolar radiation

is within the field seen by the pyrheliometer This sometimes raises questions as to the impact of comparing DNI measurements from pyrheliometers with different fields of view However, the decline in radiance or brightness of sky within the solar aureole is very steep, falling by a factor of 1000 over a very short angular distance from the solar disk limb The small amplitude of the aureole,

in combination with the additional 0.35° increment on the outer edge of the field of view of a 5.7° field results in the additional radiation below the noise level of the detectors involved

Diffuse hemispherical radiation, F, is measured using pyranometers behind shading devices that block at least the same 5 or 5.7° field of view, centered on the sun, that the pyrheliometer uses This conserves the component summation relation G = B cos(Z) + F for measured data, as the missing part of F is included in B Shade devices that produce the most accurate diffuse measurements are opaque disks or balls mounted on solar trackers that follow the sun and shade the pyranometer through the day An older alternative is band, oriented to obscure the entire path of the sun through the day This approach shades part of the diffuse sky where

Figure 5 Total hemispherical and diffuse spectral solar radiation distributions with spectral response regions for thermal detector (TP) under quartz window (with large flat region), and silicon photodiode (curve cutoff at 1100 nm)

Figure 6 Examples of silicon detector (left) and thermopile detector pyranometers (right) for measuring total hemispherical solar radiation on a horizontal

Total (global) G, Direct beam, B, Diffuse sky (scattered), F

G = B cos(i ) + F i = incidence angle

Pyrheliometer

Shaded Pyranometer

Pyranometer

Figure 7 Typical solar radiation sensors for the three solar components

the solar disk is not located Many algorithms for correcting for this source of error, which varies according to cloud cover and seasons have been published, but most are no more accurate than about  25% of the diffuse magnitude Figure 7 shows examples

of typical instrumentation for measuring solar radiation components

1.12.4.2 Radiometer Calibration

In 1970, Kendall [2] and later Willson [3] at the Jet Propulsion Laboratory developed electrical compensation radiometers utilizing conical blackened silver cavities with thermojunctions attached that could be calibrated using electrical heating in place of heating from solar radiation These and instruments of similar design by Crommelynck [4], Brusa and Frohlich [5], and Hickey [6] became the standard for the current World Radiometric Reference (WRR) now in use [7, 8] Figure 8 is a photograph of the instruments that constitute the World Standard Group, or WSG, which are used to define the present scale for solar radiation measurements These standard pyrheliometers are the foundation of the radiation scale and calibration of field pyrheliometers and pyranometers as described in more detail below

1.12.4.3 World Radiometric Reference: the Calibration Reference

The International System or SI unit of solar irradiance is the WRR established and maintained by the WMO at the Physical Meteorological Observatory, Davos, Switzerland, World Radiation Center (PMOD/WRC) WRR was introduced in 1977 in order to ensure homogeneity of solar radiation measurements WRR is determined from the weighted mean of the measurements of a group

of six absolute cavity radiometers, which were fully characterized for electrical performance and physical attributes (such as limiting aperture area) It has an estimated accuracy of 0.3% The WRR is realized by a group of absolute cavity pyrheliometers designated the World Standard Group (WSG) There have been laboratory comparisons between a WMO/WRC cavity radiometer and a cryogenic absolute cavity radiometer, the SI standard for realizing the radiometric scale for laboratory measurements The comparisons showed that the WRR radiometer reproduced the SI laboratory irradiance scale to within 0.05% [9–11]

Figure 8 Photo of the Working Standard Group (WSG) of the WRR at PMOD/WRC

Uncertainities

World Radiation

Cavity A Reference (WRR) ± 0.15%

Cavity B Reference (WRR) ± 0.15%

Calibrate Pyrheliometer

±WRR ± 0.15% ± 0.5%

±WRR ± 0.15% ± 0.5% ± 1.0%

± 2.0% of DIFFUSE 0.2% of REF IRRADIANCE

Every 5 years, since 1970, WMO sponsors the International Pyrheliometer Comparisons (IPC) The WMO representatives of any country bring their reference solar radiometers to Davos to compare them with the WSG and derive a WRR correction factor As of this writing, the latest IPC was IPC XI, conducted in 2010 The test radiometers are compared with the WSG using a rigorous data collection and processing protocol [12]

1.12.4.4 Traceability

Traceability of measurements requires an unbroken chain of comparisons with defined uncertainties to stated references The traceability of the WSG cavity radiometers to SI units is with respect to electrical (volt, ohm, and ampere) and physical-dimensional (length, area) standards maintained by national standardizing laboratories Detailed characterization of the aperture area, absorp­tion of the cavity, and electrical components of the measurement system substantiates the ‘absolute’ nature of the WSG measurements WMO representatives and reference pyrheliometer manufacturers of any country are invited to bring reference pyrheliometers to IPCs to compare them with the WSG and derive a WRR correction factor Figure 9 shows the traceability path for

Figure 9 Traceability diagram of the transfer of WRR scale and propagation of uncertainty from reference to field radiometers

working field radiometers to WRR through the WSG Increasing uncertainty at each level for field radiometer calibrations including transfer process and test radiometer stability is indicated

1.12.4.5 Pyrheliometer Calibrations

Pyrheliometer responsivities (Rs, or output signal per stimulus unit) are derived by direct comparisons with reference cavity pyrheliometers traceable to WRR The approach is much like the transfer of WRR between cavity radiometers The ratio of test pyrheliometer signals to the reference irradiance from the reference cavity pyrheliometer is computed over the course of a clear day

or several clear days Figure 10 shows typical data for such a ‘Broadband Outdoor Radiometer Calibration’ (BORCAL) at the National Renewable Energy Laboratory Example calibration reports are available online at http://www.nrel.gov/aim/borcal.html National and international standards documents describe the procedures for calibration of field pyrheliometers from primary (absolute cavity) pyrheliometers and reference pyrheliometers [13–15]

The shape of the response function seen in Figure 10 is of concern, as the distribution of the responsivities is not random but biased differently in the morning and afternoon The cause for this bias is a current topic of research Possible explanations are the different fields of view of the reference (5°) and test (5.7°) pyrheliometers, environmental influences (ambient temperature, wind speed, and direction), and test instrument design (thermal gradients between detector and reference thermocouples)

Shade/unshade calibrations are subject to several sources of uncertainty The pyranometer under test has several time constants, caused by differing heating and cooling rates of the domes and detectors as the shade is imposed and removed For the shaded pyranometer, sky radiation, particularly the infrared (IR) radiation temperature, remains relatively constant, while the detector cools down significantly Therefore, the net IR exchange between the instrument and the sky is different in the shade and unshade condition [16, 17] This produces thermal offsets in the detector Variations in the direct beam radiation over the shade and unshade periods (at the beginning and end of the shade period) can lead to errors A modified shade/unshade pyranometer calibration that determines an average responsivity at 45° zenith angle for three instrument azimuths averages out azimuth response variations [18]

–90 –80 –70 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90

7.00 7.50 8.00 8.50 9.00 9.50 10.00

Z = ±60° Upper limit

Z = ±60° Lower limit

For a ‘component summation’ calibration of a pyranometer, the reference global irradiance (Gr) is derived from an absolute cavity radiometer beam measurement (B) and shaded pyranometer (diffuse) measurement (F) using Gr= B cos(Z) + F The ratio of the test pyranometer signal to the reference global irradiance is the responsivity, or calibration value, for the pyranometer This technique requires a shade/unshade calibrated pyranometer to measure the ‘reference diffuse’ irradiance, F, during the calibration The instantaneous voltage signals of the test radiometers are divided by the reference global irradiance Gr to generate instantaneous responsivities typically in units of microvolts per watt per square meter (μV Wm−2) Figure 11 shows a typical plot of responsivity versus zenith angle throughout a day

As with the pyrheliometer example discussed above, the response of the pyranometer is not constant with respect to the solar incidence angle Every individual pyranometer will have a distinct, unique, individual ‘signature’, even for a given model designa­tion Similar signatures are obtained from pyranometers calibrated if the shade/unshade techniques are used over a large range of zenith angles Selection criteria for a reported responsivity (or calibration factor, Cf, equal to 1/Rs), and range of Rs (or Cf) must be described to adequately characterize the uncertainty in solar radiation measured with the pyranometer

1.12.4.7 Radiometric Uncertainty and Performance

Using the shade/unshade technique the direct beam irradiance can be measured with an absolute cavity pyrheliometer to about 0.4% The clear-sky diffuse irradiance can be measured with an uncertainty of (3% of reading + 1.0 Wm−2) Under clear-sky calibration conditions, the diffuse irradiance is on the order of 10–15% of the total global hemispherical irradiance This means that the contribution of uncertainties in the diffuse to the total global reference irradiance is rather small, about 0.3%, comparable to the uncertainty in the direct beam irradiance measured with an absolute cavity radiometer of 0.4% Thus, the very lowest uncertainty in

a reference irradiance or total global hemispheric irradiance in general is about 0.7%

In combination with the precision and accuracy of a (very good) data logger system, of about 0.1%, the uncertainty in the determination of each individual Rs computation is about 0.5–0.7% This represents about 1 standard deviation, or 1-sigma

‘standard uncertainty’ In accordance with the processes of uncertainty analysis spelled out in the International Bureau of Weights and Measures (French acronym BIPM) Guide to the Uncertainty in Measurements (GUM) [19] an expanded uncertainty is obtained

by multiplying this standard uncertainty by a coverage factor k, resulting in an expanded uncertainty with a specified confidence interval A confidence interval of 95%, assuming a normal or Gaussian distribution of errors sources, requires a k = 2 Thus, the expanded uncertainty about each individual Rs data point is about 1.8%

This 1.8% is the smallest uncertainty that can be expected of a pyranometer under conditions identical to the calibration conditions, including the infrared thermal offset (generated by infrared exchange between the cold sky and warm radiometer), at a specific zenith angle It is possible to estimate the thermal offset during calibration, using long-wave radiometers (Pyrgeometers, with their own inherent uncertainties) and compensate for this effect during the calibration Responsivity at a given zenith angle at the time of measurement, Rs(Z), can be obtained from a fit to the response curve from calibration data versus zenith angle

To simplify data collection and logging, an average responsivity is used to compute the calibration factor to convert sensor signal

to engineering units Since the average zenith angle for an isotropic, homogeneous, uniform irradiance distribution in the sky dome

is 45°, this is usually the preferred Z for reporting Rs(Z) If used, there will be a regular pattern of systematic errors introduced into the pyranometer measurements, especially of clear-sky data, from morning to afternoon and winter to summer These errors result from the deviation of the true instrument responsivity signature from the Z = 45° Rs(Z) as a function of Z, and can exceed 5% for

Z > 60°, and grow beyond 10% for Z > 70° [20] Compensation for these errors can occur by averaging data over a day Morning and

Figure 11 Typical pyranometer response as function of zenith angle throughout a day Negative Z angles correspond to morning 1.8% error bar on each

Rs, and limits of +2% and 5% bound data between 30° < Z < 60°