There are two methods to calculate the UV Index from GUV measurements, a simple and a more advanced method. The UV Index discussed here refers to the action for erythema (sunburn) as defined in the CIE norm by McKinlay and Diffey [1987].
1. Simple method
The simple method is described in the BSI Application Note "GUV 'Diffey Dose' Calculations," available at GUV Diffey Dose Calculations.pdf. In brief, the UV Index is calculated from a linear combination of measurements of the GUV channels at 305, 320, and 340 nm:
UV Index = a1 E305 + a2 E320 + a3 E340
where a1 = 0.8911, a2 = 0.0818, and a3 = 0.007751. These coefficients refer to the "2B. Coefficients for 96 UV INDEX" listed in Table 1 of the aforementioned application note. E305, E320, and E340 are the spectral irradiances at 305, 320, and 340 nm, which are calculated by applying offsets and scale factors to the GUV's measurements as described in the instrument's calibration certificate.
If a GUV radiometer is equipped with a channel at 313 nm, the UV Index can also be calculated from a linear combination of measurements of four GUV channels, namely 305, 313, 320, and 340 nm:
UV Index = a1 E305 + a2 E313 + a3 E320 + a4 E340
where a1 = 0.8058, a2 = 0.0887, a3 = 0.0324, and a4= 0.0131. Using measurements of four, rather than three, channels leads to slightly more accurate results, in particular for low-Sun conditions.
2. Advanced method
An alternative method of calculating the UV Index from GUV measurements is described by Bernhard et al. (2005). The paper is available at http://www.biospherical.com/nsf/presentations/OEUV-12.pdf. This is the method implemented by the NSF UV Monitoring Network. The method requires measurements of the GUV's spectral response functions plus associated calibration factors.
References
Bernhard, G., C.R. Booth, and J.C. Ehramjian. (2005). Real-time ultraviolet and column ozone from multichannel ultraviolet radiometers deployed in the National Science Foundation’s ultraviolet monitoring network. Optical Eng., 44(4), 041011-1 – 041011-12.
McKinlay, A.F., and B.L. Diffey (Eds.). (1987). A reference action spectrum for ultraviolet induced erythema in human skin. CIE Res. Note, 6(1), 17–22.