The background and hourly flare indices are based on the X-ray index (see the SET Technical Report for a detailed description of the GOES X-ray data), which is a way to convienently describe the more general charactersitics of solar X-ray flux. Solar X-rays have two dominant characteristics: A slowly-varying total-disk background component (on the order of days to months), and rapidly-varying flare component (on the order of seconds to hours). It is often helpful visually and statistically to take a time series measurement that varies exponentially and convert it to a linear time series index. It is especially helpful when comparing variations of X-rays to the daily quantities F10.7, E10, etc.
To convert the GOES 0.1-0.8 nm flux (in the physical units of Watts / square meter / second) into the dimensionless "X-ray Index"
To convert from the "X-ray Index" back to physical units:
The X-ray index is used to determine the Daily Background Index Xb10 and the Hourly Flare Index Xhf. The details on how this is done can be found in the SET Technical Report. The figure below shows the results during a period of high solar activity. These indices can more effectively used in certain applications to describe the terrestrial effects of solar X-ray variations.