Draft:Global tilted irradiance

Comment: There is already a page Solar irradiance where this is defined. I do not see a rationale to duplicate that with what is really an extended definition here. There are also issues of WP:NOTATEXTBOOK with the formulae, and WP:REFBOMB in the lead. Please use AfC as a new user if you want to pursue this. Ldm1954 (talk) 19:03, 9 December 2025 (UTC)

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The Global Tilted Irradiance (GTI), also known as the Plane-Of-Array (POA) irradiance, is the total hemispherical solar irradiance incident on a titled plane. The orientation of a tilted plane is normally defined by a tilt angle and an azimuth angle. When the condition allows, a plane is usually tilted equatorward. In broadband values, i.e. integrated over the whole Electromagnetic spectrum, it normally has SI units of W m⁻². In a sense, single-axis trackers and dual-axis trackers are tilted planes, only that their tilt angles and azimuth angles change with time.

The GTI is the sum of the beam (or direct), diffuse and ground reflected irradiances incident on that same tilted plane.^[1]

Information about time series of the GTI resource is useful for applications such as flat-plate collectors, which vary from photovoltaic (PV) modules, to passive collectors used as solar heaters for water or air applications. The emerging bifacial solar photovoltaics (BPV) have the ability to exploit the GTI incident on the front and rear sides of the module, and hence have an improved solar-cell efficiency per unit area as opposed to the more common monofacial PVs.^[2]

Pyranometers may measure the GTI when fixed on a tilted plane. If the tilt angle is 0°, this implies a flat plane, and hence the GTI is reduced to the Global Horizontal Irradiance (GHI). In the special scenario when a pyranometer is placed on a plane that is tracking the sun, then the Global Normal Irradiance (GNI) is the measured variable. Similarly, if a pyranometer is attached to a single-axis tracker, the measured variable is the GTI on the tracker orientation.

In the absence of such measurements, which are quite scarce,^[3][4] the GTI may be deduced from transposition models which require measurements or modelled values of the Direct (or Beam) Normal Irradiance (BNI or DNI), the Diffuse Horizontal Irradiance (DHI), the GHI, and the ground albedo.^[5] Sky models are an alternative, which utilize similar inputs, to provide the angular diffuse radiance distribution of the whole sky, from which the GTI on any tilted plane may be computed.^[6][7] In such models the beam component on the tilted plane is computed from the BNI. The GTI may also be computed by means of physical models solving the radiative transfer equation in the atmosphere,^[8][9] such models require very specific information on the composition of the atmosphere for accurate simulations.

An example of where to retrieve GTI data is NASA POWER, providing climatological monthly mean GTI derived from satellite-based hourly data for equatorward tilted planes with tilt angles equal to 0°, the latitude minus 15°, the latitude, the latitude plus 15°, and 90°.^[10]

Solar radiation components (oriented hemispherical irradiances) incident on the front and rear sides of a tilted plane.

Formulae

In the absence of measurements, the GTI may be calculated.

On either side of a tilted plane, the GTI is the sum of the Beam Tilted Irradiance (BTI), the Downward Diffuse Tilted Irradiance (DDTI), and the upward Reflected Tilted Irradiance (RTI). As both the DDTI and RTI are diffuse components, then the total Diffuse Tilted Irradiance (DTI) incident on the tilted plane is their sum.

The DDTI represents the contribution of radiation scattered by the sky onto the plane of interest. It is the result of the scattering of extraterrestrial solar radiation by the atmospheric components (aerosols, clouds, gases). The RTI represents the diffuse radiation reflected by the ground onto the plane of array. It is the results of the reflection of beam radiation, incoming from the Sun, and diffuse radiation, coming from the sky, by the surface. It depends on the optical properties of the surface.

The following equations present the relation between GTI, BTI, DDTI, RTI, DTI and BNI on either side of a plane:

${\displaystyle GTI^{+}=BTI+DDTI^{+}+RTI^{+}}$

${\displaystyle GTI^{-}=BTI+DDTI^{-}+RTI^{-}}$

${\displaystyle DTI=DDTI+RTI}$

${\displaystyle BTI=BNI*\max(\cos(\theta _{i}),0)}$

where + denotes the front side of the plane, − the rear side of the plane, and θ_i the angle of incidence.

Surface-based measurement

Solar radiation measurements by pyranometers in PV monitoring systems. The horizontally placed pyranometer is measuring the GHI, whereas the tilted one is measuring the GTI.

Field measurements are usually carried out with precision thermopile based pyranometers, which have a 180° field of view, calibrated against World Radiometric Reference (WRR) standards. When placed on a tilted plane, pyranometers directly measure the GTI.

Several Pyrheliometers fixed on a solar tracker. Pyrheliometers are used for BNI measurements.

Picture of the EKO MS-80 Pyranometer ISO 9060 Class A. If placed horizontally, and with a shading ball blocking the solar disc it is measuring the DHI. If placed on a tilted plane with the shading ball blocking the solar disc it would measure the DTI.

The GTI may also be computed from measurements of the BNI by means of pyrheliometers or equivalent pyranometric systems, and the DTI by means of pyranometers with a shading mechanism blocking the solar disc. From the BNI measurements the BTI is computed.

The DTI may be measured by a pyranometer with a shading mechanism to block the solar disc, like a shading ball or shadowband.

Alternative radiometric systems to measure the GTI, BTI and DTI include:

• Rotating shadowband irradiometers (RSI)^[11] — a photodiode-based pyranometer with a rotating shadowband. If placed on a tilted plane it would measure the GTI when the shadowband is not blocking the field-of-view of the pyranometer, and the DTI when the shadowband is totally blocking the solar disc. The BTI is computed from these two quantities.
• SPN1 sunshine pyranometer^[12] — a design with no moving parts including seven thermopiles and a unique static shading mask which blocks half the sky. At any point in time the shading mask is fully blocking the solar disc from at least one thermopile, and at least one other thermopile is fully viewing the solar disc. If placed on a tilted plane the GTI, DTI and BTI may be deduced.

Applications

• Photovoltaic systems
• BPVs
• Solar thermal collectors:
  • Solar water heating
  • Solar air heat
• Agrivoltaics
• Daylighting (architecture)

See also

• Sunlight
• Diffuse sky radiation
• Direct normal irradiance

References

1. M. Sengupta, A. Habte, S. Wilbert, C.A. Gueymard, J. Remund, E. Lorenz, W. van Sark, A.R. Jensen, Best practices handbook for the collection and use of solar resource data for solar energy applications, 4th ed., National Renewable Energy Laboratory: NREL/TP-5D00-88300, Golden, CO, 2024. https://www.nrel.gov/docs/fy24osti/88300.pdf.
2. Guerrero-Lemus, R.; Vega, R.; Kim, Taehyeon; Kimm, Amy; Shephard, L. E. (2016-07-01). "Bifacial solar photovoltaics – A technology review". Renewable and Sustainable Energy Reviews. 60: 1533–1549. Bibcode:2016RSERv..60.1533G. doi:10.1016/j.rser.2016.03.041. ISSN 1364-0321.
3. Jensen, Adam R.; Sifnaios, Ioannis; Anderson, Kevin S.; Gueymard, Christian A. (2025-07-15). "SolarStations.org—A global catalog of solar irradiance monitoring stations". Solar Energy. 295 113457. Bibcode:2025SoEn..29513457J. doi:10.1016/j.solener.2025.113457. ISSN 0038-092X.
4. Blanc, Philippe; Jolivet, Raphaël; Ménard, Lionel; Saint-Drenan, Yves-Marie (October 2022). Data sharing of in-situ measurements following GEO and FAIR principles in the solar energy sector. doi:10.23646/ac2m-8504.
5. Yang, Dazhi (2016-10-15). "Solar radiation on inclined surfaces: Corrections and benchmarks". Solar Energy. 136: 288–302. Bibcode:2016SoEn..136..288Y. doi:10.1016/j.solener.2016.06.062. ISSN 0038-092X.
6. Perez, R.; Seals, R.; Michalsky, J. (1993-03-01). "All-weather model for sky luminance distribution—Preliminary configuration and validation". Solar Energy. 50 (3): 235–245. Bibcode:1993SoEn...50..235P. doi:10.1016/0038-092X(93)90017-I. ISSN 0038-092X.
7. Igawa, Norio; Koga, Yasuko; Matsuzawa, Tomoko; Nakamura, Hiroshi (2004-01-01). "Models of sky radiance distribution and sky luminance distribution". Solar Energy. 77 (2): 137–157. Bibcode:2004SoEn...77..137I. doi:10.1016/j.solener.2004.04.016. ISSN 0038-092X.
8. Emde, Claudia; Buras-Schnell, Robert; Kylling, Arve; Mayer, Bernhard; Gasteiger, Josef; Hamann, Ulrich; Kylling, Jonas; Richter, Bettina; Pause, Christian; Dowling, Timothy; Bugliaro, Luca (2016-05-03). "The libRadtran software package for radiative transfer calculations (version 2.0.1)". Geoscientific Model Development. 9 (5): 1647–1672. Bibcode:2016GMD.....9.1647E. doi:10.5194/gmd-9-1647-2016. ISSN 1991-959X.
9. Gueymard, Christian A. (2019-07-15). "The SMARTS spectral irradiance model after 25 years: New developments and validation of reference spectra". Solar Energy. 187: 233–253. Bibcode:2019SoEn..187..233G. doi:10.1016/j.solener.2019.05.048. ISSN 0038-092X.
10. Zhang, T., Stackhouse Jr., P.W., Macpherson, B., and Mikovitz, J.C., 2024. A CERES-based dataset of hourly DNI, DHI and global tilted irradiance (GTI) on equatorward tilted surfaces: Derivation and comparison with the ground-based BSRN data. Sol. Energy, 274 (2024) 112538. doi: https://doi.org/10.1016/j.solener.2024.112538.
11. Jessen, Wilko; Wilbert, Stefan; Nouri, Bijan; Geuder, Norbert; Fritz, Holger (2016-04-12). "Calibration methods for rotating shadowband irradiometers and optimizing the calibration duration". Atmospheric Measurement Techniques. 9 (4): 1601–1612. Bibcode:2016AMT.....9.1601J. doi:10.5194/amt-9-1601-2016. ISSN 1867-1381.
12. "SPN1 Sunshine Pyranometer - Solar Radiation Measurement". Delta T. Retrieved 2025-12-17.

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