The air mass coefficient defines the direct
optical path length In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the product of the geometric length of the optical path followed by light and the refractive index of homogeneous medium through ...
through the
Earth's atmosphere
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
, expressed as a ratio relative to the path length vertically upwards, i.e. at the
zenith
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
. The air mass coefficient can be used to help characterize the solar spectrum after
solar radiation
Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre (W/m ...
has traveled through the atmosphere.
The air mass coefficient is commonly used to characterize the performance of
solar cell
A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon. s under standardized conditions, and is often referred to using the syntax "AM" followed by a number. "AM1.5" is almost universal when characterizing terrestrial power-generating
panels.
Description
![EffectiveTemperature 300dpi e](https://upload.wikimedia.org/wikipedia/commons/0/0d/EffectiveTemperature_300dpi_e.png)
Solar radiation closely matches a
black body radiator at about 5,800 K.
[or more precisely 5,777 K as reported i]
NASA Solar System Exploration - Sun: Facts & Figures
retrieved 27 April 2011 "Effective Temperature ... 5777 K"
As it passes through the atmosphere, sunlight is attenuated by
scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
and
absorption
Absorption may refer to:
Chemistry and biology
* Absorption (biology), digestion
**Absorption (small intestine)
*Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials
*Absorption (skin), a route by which ...
; the more atmosphere through which it passes, the greater the
attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable att ...
.
As the sunlight travels through the atmosphere, chemicals interact with the sunlight and absorb certain wavelengths changing the amount of short-wavelength light reaching the Earth's surface.
A more active component of this process is water vapor, which results in a wide variety of absorption bands at many wavelengths, while molecular nitrogen, oxygen and carbon dioxide add to this process. By the time it reaches the Earth's surface, the spectrum is strongly confined between the far infrared and near ultraviolet.
Atmospheric scattering plays a role in removing higher frequencies from direct sunlight and scattering it about the sky.
This is why the sky appears blue and the sun yellow — more of the higher-frequency blue light arrives at the observer via indirect scattered paths; and less blue light follows the direct path, giving the sun a yellow tinge.
The greater the distance in the atmosphere through which the sunlight travels, the greater this effect, which is why the sun looks orange or red at dawn and sunset when the sunlight is travelling very obliquely through the atmosphere — progressively more of the blues and greens are removed from the direct rays, giving an orange or red appearance to the sun; and the sky appears pink — because the blues and greens are scattered over such long paths that they are highly attenuated before arriving at the observer, resulting in characteristic pink skies at dawn and sunset.
Definition
For a path length
through the atmosphere, and solar radiation incident at angle
relative to the normal to the Earth's surface, the air mass coefficient is:
where
is the path length at
zenith
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
(i.e., normal to the Earth's surface) at
sea level
Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardised g ...
.
The air mass number is thus dependent on the Sun's elevation path through the sky and therefore varies with time of day and with the passing seasons of the year, and with the latitude of the observer.
Calculation
![Airmass geometry](https://upload.wikimedia.org/wikipedia/commons/8/88/Airmass_geometry.png)
A first-order approximation for air mass is given by
where
is the
zenith angle
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
in degrees.
The above approximation overlooks the atmosphere's finite height, and predicts an infinite air mass at the horizon. However, it is reasonably accurate for values of
up to around 75°. A number of refinements have been proposed to more accurately model the path thickness towards the horizon, such as that proposed by Kasten and Young (1989):
A more comprehensive list of such models is provided in the main article
Airmass, for various atmospheric models and experimental data sets.
At sea level the air mass towards the horizon (
= 90°) is approximately 38.
[The main article Airmass reports values in the range 36 to 40 for different atmospheric models]
Modelling the atmosphere as a simple spherical shell provides a reasonable approximation:
where the radius of the Earth
= 6371 km, the effective height of the atmosphere
≈ 9 km, and their ratio
≈ 708.
These models are compared in the table below:
These simple models assume that for these purposes the atmosphere can be considered to be effectively concentrated into around the bottom 9 km, i.e. essentially all the atmospheric effects are due to the atmospheric mass in the lower half of the
Troposphere
The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
. This is a useful and simple model when considering the atmospheric effects on solar intensity.
Cases
*AM0
The spectrum outside the atmosphere, approximated by the 5,800 K black body, is referred to as "AM0", meaning "zero atmospheres". Solar cells used for space power applications, like those on
communications satellite
A communications satellite is an artificial satellite that relays and amplifies radio telecommunication signals via a transponder; it creates a communication channel between a source transmitter and a receiver at different locations on Earth. C ...
s, are generally characterized using AM0.
*AM1
The spectrum after travelling through the atmosphere to sea level with the sun directly overhead is referred to, by definition, as "AM1". This means "one atmosphere".
AM1 (
=0°) to AM1.1 (
=25°) is a useful range for estimating performance of solar cells in
equatorial Equatorial may refer to something related to:
*Earth's equator
**the tropics, the Earth's equatorial region
**tropical climate
*the Celestial equator
** equatorial orbit
**equatorial coordinate system
** equatorial mount, of telescopes
* equatorial ...
and
tropical
The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in
the Southern Hemisphere at S. The tropics are also referred to ...
regions.
*AM1.5
Solar panels do not generally operate under exactly one atmosphere's thickness: if the sun is at an angle to the Earth's surface the effective thickness will be greater. Many of the world's major population centres, and hence solar installations and industry, across Europe, China, Japan, the United States of America and elsewhere (including northern India, southern Africa and Australia) lie in
temperate
In geography, the temperate climates of Earth occur in the middle latitudes (23.5° to 66.5° N/S of Equator), which span between the tropics and the polar regions of Earth. These zones generally have wider temperature ranges throughout t ...
latitudes. An AM number representing the spectrum at mid-latitudes is therefore much more common.
"AM1.5", 1.5 atmosphere thickness, corresponds to a solar zenith angle of
=48.2°. While the summertime AM number for mid-latitudes during the middle parts of the day is less than 1.5, higher figures apply in the morning and evening and at other times of the year. Therefore, AM1.5 is useful to represent the overall yearly average for mid-latitudes. The specific value of 1.5 has been selected in the 1970s for standardization purposes, based on an analysis of solar irradiance data in the conterminous United States.
[
] Since then, the solar industry has been using AM1.5 for all standardized testing or rating of terrestrial solar cells or modules, including those used in concentrating systems. The latest AM1.5 standards pertaining to photovoltaic applications are the ASTM G-173
[Reference Solar Spectral Irradiance: Air Mass 1.5](_blank)
NREL retrieved 1 May 2011
ASTM retrieved 1 May 2011 and IEC 60904, all derived from simulations obtained with the
SMARTS code.
The illuminance for
Daylight
Daylight is the combination of all direct and indirect sunlight during the daytime. This includes direct sunlight, diffuse sky radiation, and (often) both of these reflected by Earth and terrestrial objects, like landforms and buildings. Sunligh ...
(
this version) under AM1.5 is given as 109,870 lux (corresponding with the AM1.5 spectrum to 1000.4 W/m
2).
*AM2~3
AM2 (
=60°) to AM3 (
=70°) is a useful range for estimating the overall average performance of solar cells installed at high latitudes such as in northern Europe.
Similarly AM2 to AM3 is useful to estimate wintertime performance in temperate latitudes, e.g. airmass coefficient is greater than 2 at all hours of the day in winter at latitudes as low as 37°.
*AM38
AM38 is generally regarded as being the airmass in the horizontal direction (
=90°, i.e. sunset) at sea level.
However, in practice there is a high degree of variability in the solar intensity received at angles close to the horizon as described in the next section
Solar intensity
Solar may refer to:
Astronomy
* Of or relating to the Sun
** Solar telescope, a special purpose telescope used to observe the Sun
** A device that utilizes solar energy (e.g. "solar panels")
** Solar calendar, a calendar whose dates indicate t ...
.
*At higher altitudes
The ''relative'' air mass is only a function of the sun's zenith angle, and therefore does not change with local elevation. Conversely, the ''absolute'' air mass, equal to the relative air mass multiplied by the local atmospheric pressure and divided by the standard (sea-level) pressure, decreases with elevation above sea level. For solar panels installed at high altitudes, e.g. in an
Altiplano
The Altiplano (Spanish for "high plain"), Collao (Quechua and Aymara: Qullaw, meaning "place of the Qulla") or Andean Plateau, in west-central South America, is the most extensive high plateau on Earth outside Tibet. The plateau is located at the ...
region, it is possible to use a lower absolute AM numbers than for the corresponding latitude at sea level: AM numbers less than 1 towards the equator, and correspondingly lower numbers than listed above for other latitudes. However, this approach is approximate and not recommended. It is best to simulate the actual spectrum based on the relative air mass (e.g., 1.5) and the ''actual'' atmospheric conditions for the specific elevation of the site under scrutiny.
Solar intensity
Solar intensity at the collector reduces with increasing airmass coefficient, but due to the complex and variable atmospheric factors involved, not in a simple or linear fashion.
For example, almost all high energy radiation is removed in the upper atmosphere (between AM0 and AM1) and so AM2 is not twice as bad as AM1.
Furthermore, there is great variability in many of the factors contributing to atmospheric attenuation,
[''Planning and installing photovoltaic systems: a guide for installers, architects and engineers'', 2nd Ed. (2008), Table 1.1]
Earthscan
with the International Institute for Environment and Development, Deutsche Gesellschaft für Sonnenenergie. .
such as water vapor, aerosols,
photochemical smog
Smog, or smoke fog, is a type of intense air pollution. The word "smog" was coined in the early 20th century, and is a portmanteau of the words ''smoke'' and ''fog'' to refer to smoky fog due to its opacity, and odor. The word was then inten ...
and the effects of
temperature inversions.
Depending on level of pollution in the air, overall attenuation can change by up to ±70% towards the horizon, greatly affecting performance particularly towards the horizon where effects of the lower layers of atmosphere are amplified manyfold.
One empirical approximation model for solar intensity versus airmass is given by:
[PVCDROM](_blank)
retrieved 1 May 2011, Stuart Bowden and Christiana Honsberg
Solar Power Labs, Arizona State University
/ref>[Meinel, A. B. and Meinel, M. P. (1976). ''Applied Solar Energy'' Addison Wesley Publishing Co.]
where solar intensity external to the Earth's atmosphere = 1.353 kW/m2, and the factor of 1.1 is derived assuming that the diffuse component is 10% of the direct component.
This formula fits comfortably within the mid-range of the expected pollution-based variability:
This illustrates that significant power is available at only a few degrees above the horizon. For example, when the sun is more than about 60° above the horizon ( <30°) the solar intensity is about 1000 W/m2 (from equation as shown in the above table), whereas when the sun is only 15° above the horizon ( =75°) the solar intensity is still about 600 W/m2 or 60% of its maximum level; and at only 5° above the horizon still 27% of the maximum.
At higher altitudes
One approximate model for intensity increase with altitude and accurate to a few kilometres above sea level is given by:
where is the solar collector's height above sea level in km and is the airmass (from ) ''as if'' the collector was installed at sea level.
Alternatively, given the significant practical variabilities involved, the homogeneous spherical model could be applied to estimate AM, using:
where the normalized heights of the atmosphere and of the collector are respectively ≈ 708 (as above) and .
And then the above table or the appropriate equation ( or or for average, polluted or clean air respectively) can be used to estimate intensity from AM in the normal way.
These approximations at and are suitable for use only to altitudes of a few kilometres above sea level, implying as they do reduction to AM0 performance levels at only around 6 and 9 km respectively.
By contrast much of the attenuation of the high energy components occurs in the ozone layer - at higher altitudes around 30 km.[R.L.F. Boyd (Ed.) (1992). ''Astronomical photometry: a guide'', section 6.4. Kluwer Academic Publishers. .]
Hence these approximations are suitable only for estimating the performance of ground-based collectors.
Solar cell efficiency
Silicon solar cells are not very sensitive to the portions of the spectrum lost in the atmosphere. The resulting spectrum at the Earth's surface more closely matches the bandgap of silicon
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
so silicon solar cells are more efficient at AM1 than AM0. This apparently counter-intuitive result arises simply because silicon cells can't make much use of the high energy radiation which the atmosphere filters out.
As illustrated below, even though the ''efficiency'' is lower at AM0 the ''total output power'' (Pout) for a typical solar cell is still highest at AM0.
Conversely, the shape of the spectrum does not significantly change with further increases in atmospheric thickness, and hence cell efficiency does not greatly change for AM numbers above 1.
This illustrates the more general point that given that solar energy is "free", and where available space is not a limitation, other factors such as total Pout and Pout are often more important considerations than efficiency (Pout/Pin).
See also
* Air mass (astronomy)
* Diffuse sky radiation
Diffuse sky radiation is solar radiation reaching the Earth's surface after having been scattered from the direct solar beam by molecules or particulates in the atmosphere. It is also called sky radiation, the determinative process for chan ...
* Earth's atmosphere
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
* Insolation
Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre (W/m ...
* Mie scattering
The Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the f ...
* Photovoltaics
Photovoltaics (PV) is the conversion of light into electricity using semiconducting materials that exhibit the photovoltaic effect, a phenomenon studied in physics, photochemistry, and electrochemistry. The photovoltaic effect is commercially us ...
* Rayleigh scattering
* Solar cell
A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.
* Solar cell efficiency
* Solar energy
Solar energy is radiant light and heat from the Sun that is harnessed using a range of technologies such as solar power to generate electricity, solar thermal energy (including solar water heating), and solar architecture. It is an essenti ...
* Solar power
Solar power is the conversion of energy from sunlight into electricity, either directly using photovoltaics (PV) or indirectly using concentrated solar power. Photovoltaic cells convert light into an electric current using the photovoltaic e ...
* Solar radiation
Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre (W/m ...
* Solar tracker
A solar tracker is a device that orients a payload toward the Sun. Payloads are usually solar panels, parabolic troughs, fresnel reflectors, lenses or the mirrors of a heliostat.
For flat-panel photovoltaic systems, trackers are used to mi ...
* Sun
* Sun chart
A Sun chart is a graph of the ecliptic of the Sun through the sky throughout the year at a particular latitude.
Most sun charts plot azimuth versus altitude throughout the days of the winter solstice and summer solstice, as well as a number of in ...
* Sun path
Notes and references
{{Reflist
Solar energy
Solar cells