Calculation of Diffuse Angular Correction Voltages

Last Updated: January 2015

The methodology for this algorithm is from: Leszscynski et al., Erythemal weighted radiometers . . . Photochem. and Photobiology, 67(2), 212-221, 1998. Eqn 1. This explanation is for one channel for simplicity. All channels are processed in the same manner.

Retrieve the instrument's most recent angular responses that were determined in the laboratory of the testing agency (YES, CUCF or UVMRP) prior to the date of the data being corrected.

Organize the angular responses in a 2-dimensional array with 4 rows and 91 columns. Each row will contain angular responses from 0 through 90 degrees for one direction in the order shown below. The angles 0 - 90 are referred to as Θ.

           P0, M1, M2, M3, M4 ... M90
           P0, P1, P2, P3, P4 ... P90
           P0, M1, M2, M3, M4 ... M90
           P0, P1, P2, P3, P4 ... P90
The first two rows contain responses from the south to north scan; The last two rows contain responses from the west to east scan. Note that the SN P0 and WE P0 values are duplicated one time each.

For the first row, compute a product for each value in the row:

product=angular response × cosθ × sinθ × (2π/360)

For example, if we were doing the 5th value in the row, theta would be 4°;

product=M4 × cos4° × sin4° × (2π/360)

Sum the 91 products for the row. Repeat for the other 3 rows. This will result in 4 sums of products.

Add the 4 sums of products together and divide the total by pi. The result is the diffuse angular correction factor for the channel. The correction is applied by dividing the bias-corrected diffuse voltages by the correction factor.