# GTI DIRINT

This function derives direct normal irradiance (*G*_{B,n}) and diffuse horizontal irradiance (*G*_{D}) from the global tilted irradiance (*G*_{Ti}) using modifications to the DIRINT decomposition model and Perez transposition model. This allows for *G*_{Ti} to be input into an energy prediction, largely avoiding decomposition and transposition model errors (with the exception of calculations that require the direct/diffuse components, i.e. shading and IAM).

## Inputs

## Outputs

## Algorithm

This model implementation calculates a solution for incidence angles (θ) over and under 90° separately to allow solutions at times when the *G*_{Ti }measurement does not include any component of *G*_{D}.

### 1. GTI DIRINT model for θ < 90°

Note that this model uses a modified (tilted) clearness index as described in the Clearness Index section. Unmodified DIRINT equations (see DIRINT Model) are used to calculate *G*_{B,n}. *G*_{D} can then be calculated using:

Known errors are introduced when using the *G*_{Ti }as an input into the GTI DIRINT model (i.e. differences in proportions of diffuse and direct irradiance between global horizontal irradiance and *G*_{Ti }and the fact that *G*_{Ti} also includes ground reflected radiation). So, after *G*_{D }and *G*_{B,n }are calculated from the measured *G*_{Ti} using the reverse decomposition of GTI DIRINT, the forward transposition using Perez is used to calculate *G*_{Ti} as a check. The measured *G*_{Ti }and calculated *G*_{Ti }can then be compared and used as the iteration criteria in an optimization loop.

In the optimization loop, the initial calculation uses the measured *G*_{Ti} to calculate *K*_{t}. Subsequent iterations adjust the *G*_{Ti }until the *K*_{t} provides a *G*_{B,n }and *G*_{D }value such that a modeled *G*_{Ti} matches the measured *G*_{Ti}. The *G*_{Ti }value is adjusted using:

Where *i* is the index corresponding to the iteration number, *D* is the difference between the modeled and measured *G*_{Ti}, and *C* is a coefficient to ensure an iterative solution (1.0 for *i *<3, 0.5 for 3 ≤ *i* < 10, 0.25 for 10 ≤ *i* < 20, and 0.125 for 20 ≤ *i* < 30). Often, only two iterations are needed. The following illustrates the flow chart for the model when θ < 90°.

## 2. GTI DIRINT model for θ ≥ 90°

After *G*_{B,n} and *G*_{D }are calculated for θ < 90°, average early morning and late afternoon *K*_{t}‘ values are determined by averaging *K*_{t}‘ values for morning and afternoon instances when θ is between 65° and 85°. Besides *K*_{t}‘, the solution for *G*_{B,n} requires *K*_{t} which is rearranged from the original DIRINT equation to solve for *K*_{t} instead of *K*_{t}‘:

The *G*_{D }can then be determined using:

## Reference

Marion, B., *A model for deriving the direct normal and diffuse horizontal irradiance from the global tilted irradiance.* Solar Energy 122 (2015), pp. 1037-1046.