Solar Irradiance

Overview¶

Solar Irradiance is the power per unit area (surface power density) received from the Sun as electromagnetic radiation, within the wavelength band of the measuring instrument.

Quantity	SI unit	Note
Solar irradiance	W/m²	Power incident per unit surface area

(Source: Wikipedia.)

Global irradiance¶

Global irradiance is the total solar radiation incident on a surface—the sum of its direct and diffuse parts. It may refer to a horizontal reference plane or to a tilted (in-plane) collector.

Geometry	Abbreviation	Meaning
Horizontal	GHI	Global horizontal irradiance
Inclined	GII	Global in-plane (inclined) irradiance

GHI is the usual input when transposing irradiance onto tilted surfaces.

PVGIS treats in-plane global irradiance as direct plus diffuse on the tilted plane:

\[ \text{GII} = \text{DII} + \text{Diffuse}_{\text{inclined}} \]

Here GII is global in-plane irradiance and DII is direct inclined irradiance. The diffuse inclined term splits into sky and ground contributions:

\[ \text{GII} = \text{DII} + \text{Diffuse}^{\mathrm{sky}}_{\text{inclined}} + \text{Diffuse}^{\mathrm{ground}}_{\text{inclined}} \]

Reflected irradiance in PVGIS ≤ 5.3

In PVGIS 5.3 and earlier, the ground-related diffuse term is often labelled Ground-reflected. In this documentation, ground-diffuse and ground-reflected denote the same quantity.

The same relationship may be written as:

\[ \text{GII} = \text{DII} + \text{Diffuse}_{\text{inclined}} + \text{Reflected} \]

Irradiance data in the PVGIS Web application

The PVGIS Web application uses SARAH-3 global and direct horizontal products. The software can ingest any compatible time series supported by Xarray, not only SARAH.

Component processes¶

Each term corresponds to a distinct physical mechanism:

Component	Role
Direct	Radiation from the solar disk, without scattering
Diffuse (sky)	Radiation scattered by the atmosphere and clouds
Diffuse (ground)	Radiation reflected from the ground onto the collector

Real-sky or clear-sky?

Mode	Inputs used
Real-sky	Measured or supplied series (e.g. GHI, DNI, temperature, wind, Linke turbidity, albedo) where available
Clear-sky	Modelled components (global, direct, sky-diffuse, ground-diffuse) plus climatological temperature, wind, turbidity, and albedo when series are missing

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flowchart TB
    GHI["<img src='../../icons/sun-wireless-outline.svg' width='18' height='18'/><br/>Global horizontal irradiance (GHI)"]
    DII["<img src='../../icons/sun-angle-outline.svg' width='18' height='18'/><br/>Direct inclined irradiance (DII)"]
    SKY["<img src='../../icons/weather-partly-cloudy.svg' width='18' height='18'/><br/>Sky-diffuse inclined irradiance"]
    GRI["<img src='../../icons/noun_global_horizontal_irradiance_new.svg' width='18' height='18'/><br/>Ground-reflected diffuse (GRI)"]
    GII["<img src='../../icons/sun-wireless-outline.svg' width='18' height='18'/><br/>Global in-plane irradiance (GII)"]

    ALB["<img src='../../icons/noun-sun-525998_modified.svg' width='18' height='18'/><br/>Albedo (ρ)"]
    GVF["<img src='../../icons/radius-outline.svg' width='18' height='18'/><br/>Ground view fraction (GVF)"]
    GVF_EQ["GVF = (1 - cos(β)) / 2"]
    GRI_EQ["GRI = ρ * GHI * GVF"]
    GII_EQ["GII = DII + SKY + GRI"]

    GVF --> GVF_EQ --> GRI_EQ
    ALB --> GRI_EQ
    GHI --> GRI_EQ
    GRI_EQ --> GRI

    DII --> GII_EQ
    SKY --> GII_EQ
    GRI --> GII_EQ
    GII_EQ --> GII
    classDef noBox fill:transparent,stroke:transparent,color:#000000;
    class GHI,DII,SKY,GRI,GII,ALB,GVF noBox;

Terminology and CLI

Component	Incidence	CLI command	Subcommands	Meaning
Global	Horizontal, inclined	`global`	`horizontal`, `inclined`	Total incident irradiance
Direct	Horizontal, inclined	`direct`	`horizontal`, `inclined`	Beam from the solar disk
Diffuse (sky-reflected)	Horizontal, inclined	`diffuse`	`horizontal`, `inclined`	Atmospherically scattered
Diffuse (ground-reflected)	Inclined only	`reflected`	—	Reflected from the ground surface

Horizontal vs. inclined irradiance¶

PVGIS reports both horizontal and inclined components. Transposition maps each component from the horizontal plane to the tilted plane using solar position and surface orientation.

Type	Definition
Horizontal	Irradiance on a flat horizontal reference surface
Inclined (in-plane)	Irradiance on a surface with given tilt and azimuth

Direct irradiance¶

Direct irradiance is radiation from the solar disk that reaches the surface without having been scattered. Its magnitude depends on sun position, atmosphere (clouds, aerosols), and collector geometry.

Symbol	Name	Definition
DNI	Direct normal irradiance	Flux on a plane normal to the sun’s rays
BHI	Beam (direct) horizontal irradiance	Direct component on a horizontal plane — do not confuse with DHI (diffuse horizontal irradiance)
DII	Direct inclined irradiance	Direct component on the tilted plane

With solar altitude \(\alpha\) and incidence angle \(\theta\) (between sun direction and surface normal):

\[ \text{BHI} = \text{DNI} \cdot \sin(\alpha) \]

\[ \text{DII} = \text{BHI} \cdot \frac{\sin(\theta)}{\sin(\alpha)} \]

Near sunrise and sunset (\(\alpha \to 0\)), implementations use a limiting formulation; the ratio \(\sin(\theta)/\sin(\alpha)\) expresses the geometric transposition.

Driver	Influence on direct
Solar position	Altitude and azimuth set geometric factors
Atmosphere	Clouds and aerosols attenuate the beam
Surface	Tilt and orientation set \(\theta\)

Diffuse irradiance¶

Diffuse irradiance is radiation that has been scattered or reflected before reaching the collector. In PVGIS it is split into a sky term and a ground term.

Part	Source
Sky-diffuse	Scattering in the atmosphere and by clouds
Ground-reflected	Reflection from the ground into the tilted surface

Sky-reflected (sky-diffuse) irradiance¶

Sky-diffuse radiation has not travelled directly from the disk; it arrives from the sky vault and is strongest under cloudy skies. For inclined surfaces, models use sky visibility, shading, and scattering properties.

Property	Sky-diffuse
Origin	Atmosphere (molecules, aerosols, clouds), not the disk
Geometry	Contributions from the visible sky hemisphere
Weather	Larger under cloud; sensitive to turbidity

Diffuse vs. sky-diffuse

In PVGIS docs and CLI output, diffuse and sky-diffuse both mean diffuse sky-reflected irradiance, as distinct from ground-reflected diffuse.

Ground-reflected irradiance¶

Ground-reflected (ground-diffuse) irradiance is sunlight reflected from the terrain onto the collector. It depends on GHI, ground view fraction, and albedo \(\rho\).

Input	Role
GHI	Irradiance available at the ground for reflection
GVF	Fraction of the ground seen by the tilted surface (function of tilt \(\beta\))
Albedo \(\rho\)	Ground reflectivity

Calculation¶

PVGIS uses time series of global and direct horizontal irradiance to derive diffuse components (sky and ground). Following Hofierka (2002), the ground view fraction is a function of surface tilt \(\beta\). The ground-reflected component is set to 0 for a horizontal (or nearly horizontal) surface.

\[ \mathrm{GVF} = \frac{1 - \cos(\beta)}{2} \]

\[ \text{GRI} = \rho \cdot \text{GHI} \cdot \mathrm{GVF} \]

Tilt	Ground-reflected behaviour
\(\beta \approx 0°\)	≈ 0 (no ground in field of view)
\(\beta = 90°\)	GVF = 0.5 (maximum for this geometry)
Increasing \(\beta\)	More ground visible; term grows with tilt

When ground-reflected irradiance matters

Situation	Why it matters
Tilt > ~30°	Larger ground fraction in view
High albedo (snow, sand, water)	More reflected power
Bifacial PV	Rear side also sees ground albedo
Vertical façades	Large tilt → stronger ground coupling

Effects and corrections¶

Reflectivity¶

PV performance models apply reflectivity losses at the glazing (or module) surface for direct and for diffuse (sky and ground) irradiance. Losses increase with incidence angle and depend on glass and coatings (Martin and Ruiz, 2005).

\[ R(\theta) = f(\theta) \]

\(R(\theta)\) is a reflectivity-related factor; the function \(f\) differs for direct (single incidence \(\theta\)) and for diffuse hemispherical sky and ground terms.

Spectral effect¶

The spectral effect compares natural spectra (air mass, aerosols, clouds) to the AM1.5 reference used under STC.

\[ M_{\mathrm{sp}} = \frac{\displaystyle\int E_{\mathrm{actual}}(\lambda)\,R(\lambda)\,\mathrm{d}\lambda}{\displaystyle\int E_{\mathrm{STC}}(\lambda)\,R(\lambda)\,\mathrm{d}\lambda} \]

Symbol	Meaning
\(E(\lambda)\)	Spectral irradiance
\(R(\lambda)\)	Relative spectral response (device or weighting)
\(M_{\mathrm{sp}}\)	Spectral correction factor (implementation detail may vary)

Technology-specific spectral responses make this term important for comparing module types.

References¶

Hofierka, J. (2002). Solar radiation model. In Distributed GRASS Modules for Solar Irradiance Modelling.
Martin, N., & Ruiz, J. M. (2005). Annual angular reflection losses in PV modules. Progress in Photovoltaics: Research and Applications, 13(1), 75–84.
SARAH-3 Climate Data Records: Surface Solar Radiation. CM SAF, EUMETSAT.