# Decomposition of the Radiation Components

Last update: Oct. 2016

## 1. Glossary

 GHI Global Horizontal Irradiation BHI Beam Horizontal Irradiation DHI Diffuse Horizontal Irradiation GTI (GNI) Global Tilted Irradiation (Global Normal Irradiation) BTI (BNI) Beam (or Direct) Tilted Irradiation (Beam Normal Irradiation) DTI (DNI) Diffuse Tilted Irradiation (Diffuse Normal Irradiation) RTI (RNI) Reflected Tilted Irradiation (Reflected Normal Irradiation) ToA Top of Atmosphere Kt Clearness Index (GHI/ToA) Kc Clearsky Index (GHI/GHI_clearsky)

 _m monthly _d daily _h hourly _15min every 15 minute _1min every 1 minute

## 2. In HelioClim-3

 Starting point: the 15 min Global Horizontal Irradiation data (GHI_15min). Case of HC-3. DHI_15min: The model used to compute DHI_15min depends on the version of HelioClim-3 you consider. (version 2 uses the equation 1 of Erbs, Klein and Duffie (eq 1, 1982)) Version 3, 4 and 5: the reference is Ruiz-Arias 2009. BHI_min: please read "In HelioClim-1". Computation over a tilted or normal plane: The model to compute the diffuse part of the radiation over an inclined surface is Muneer (1990). (Reminder: ESRA (2000): eq. 3.6.5a to eq. 3.6.7b, pp:142-143). Then, a temporal aggregation is performed if requested by the user and the components are summed up to formed the Global fraction. BTI_min: please read "In HelioClim-1". RTI_min: please read "In HelioClim-1". NB: since Apr. 2013, the algorithm of Muneer computes the DTI with or without horizon.

## 3. In HelioClim-1

 Starting point: the daily Global Irradiation data over the horizontal plane (GHI_d). Case of HC-1. DHI_d: The equation 6 of Erbs, Klein and Duffie (1982) is used to assess the diffuse fraction from the daily global irradiation values over the horizontal plane (GHI_d), or more precisely from the Clearness Index Kt ESRA (2000): eq. 3.4.5a and 3.4.5b p 118 and p 119 BHI_d: The direct component is assessed by removing the diffuse from the global irradiance: BHI_d = GHI_d - DHI_d GHI_min:Collares-Peirera and Rabl (1979). A large number of application fields required an intra-day time step for the irradiation values. But as it is often the case with archived data, the irradiation values are limited to monthly or daily values. This model proposes an estimation model to derive the hourly (or less) irradiation values from the daily ones. The idea is to start from a sinus shape profile in clear sky conditions, and to modulate the values to fit the given daily irradiation value. NB: no consideration of the historical weather of each day. Application fields: PVsyst exploits this model to derive hourly values when monthly ones are inputs, computation of the monthly HelioClim-1 values over a normal plane (soda webservice for free HC-1monthDNI), computation of the HC-1 data with a time step inferior to the day (on request only), computation of the HC-1 data over the tilted surface (on-request only), ... ESRA (2000): eq. 3.5.24a, eq. 3.5.24b, eq. 3.5.24c and eq. 3.5.25 p129

DHI_min: the algorithm of Liu and Jordan (1960), described in the ESRA (2000), permits to assess the hourly (or on smaller time intervals) diffuse fraction from the global irradiance. ESRA 2000: eq 3.5.25 and eq 3.5.26 p129

DTI_min: The algorithm of Muneer (1990) is exploited to extract the proportion of diffuse radiation collected by any inclined surface. At the origin, this model has been defined on a hourly basis. Nevertheless, it can be extended to an interval of time lower than the hour since it uses Kc. ESRA (2000): eq. 3.6.5a to eq. 3.6.7b, pp:142-143

BTI_min: the direct (Beam) component computation over the inclined surface is based on pure geometry, directly obtained from the BHI
RTI_min: the reflected component is a fonction of the GHI_min, the albedo and of the tilt of the plane (similar to the proportion of sky seen by the tilted surface): RTI_min = GHI_min*albedo*(1-cos(tilt))/2

Then, temporal aggregation is performed if requested by the user and the components are summed up to formed the Global fraction.
NB: since Apr. 2013, the algorithm of Muneer can compute the DTI with or without horizon.

## 4. Other models

Several other models exists to compute DTI from DHI. Among them, the most popular is Perez et al. 1987. This approach is similar to the one of Muneer 1990, since it exploits an anisotrope representation of the sky vault decomposing the sky in 3 zones: the diffuse "horizon", the diffuse "circumsolar" and the diffuse "isotrope" to represent the rest of the sky. The only difference resides in the use of different empirical functions, i.e. the parameters to describe the models have been estimated using different cases. There is no scientific or physical demonstration that would prefer one method from the other one.

The model described in Perez et al. 1987 is a simplification of the model of radiance of Perez et al. 1993, which proposes an analogical distribution of the sky. This approach is classic for daylighting applications, but not really for radiation. Moreover, as the numerical implementation of this model implies to decompose the sky into a very high number of very small elements, the code is very long to run and return a result, which is not suitable for an operational exploitation.

## 5. Bibliography

Main publications are: Erbs 1980, Erbs, Klein and Duffie, 1982, ESRA 2000, Muneer 1990, Perez and Seals 1987, and Perez et al. 1993.

Full references are available on the "publication" page.

## 6. Equations

 Erbs, Klein and Duffie (1982), eq 6. Collares-Peirera and Rabl (1979) Liu and Jordan (1960) Muneer (1990)