You have to distinguish clearly between sunshine intensity measured as
direct irradiance and as global irradiance. Direct irradiance
involves, most simply, a sensor pointing directly at the sun and
tracking it across the sky through the day. This requires an expensive
instrument, although there are more cost-effective methods of
simulating the measurement of direct irradiance eg by using two fixed
sensors, one fitted with shade bands, but this is still not simple or
cheap.

But if you can measure direct irradiance then any value 120W/sqm
(IIRC) qualifies as bright sunshine.

The solar sensors of more affordable stations such as the Davis VP/VP2
measure global or whole-sky irradiance. There is then no simple
threshold value that can be used to enumerate bright sunshine hours.

However, it is possible to estimate the predicted global irradiance
for a given location and a given date/time given clear-sky conditions.
Then by comparing the actual and predicted values and defining a %
value above which you consider the sun to be shining brightly then you
can certainly estimate bright sunshine hours. It takes some analysis
to get a good value for the % cutoff. But the results over a month can
agree well with CS data, though totals on any given day have a larger
error.

John Dann
www.weatherstations.co.uk