Cloud cover effect of clear-sky index distributions and differences between human and automatic cloud observations

The statistics of clear-sky index can be used to determine solar irradiance when the theoretical clear sky irradiance and the cloud cover are known. In this paper, observations of hourly clear-sky index for the years of 2010--2013 at 63 locations in the UK are analysed for over 1 million data hours. The aggregated distribution of clear-sky index is bimodal, with strong contributions from mostly-cloudy and mostly-clear hours, as well as a lower number of intermediate hours. The clear-sky index exhibits a distribution of values for each cloud cover bin, measured in eighths of the sky covered (oktas), and also depends on solar elevation angle. Cloud cover is measured either by a human observer or automatically with a cloud ceilometer. Irradiation (time-integrated irradiance) values corresponding to human observations of "cloudless" skies (0 oktas) tend to agree better with theoretical clear-sky values, which are calculated with a radiative transfer model, than irradiation values corresponding to automated observations of 0 oktas. It is apparent that the cloud ceilometers incorrectly categorise more non-cloudless hours as cloudless than human observers do. This leads to notable differences in the distributions of clear-sky index for each okta class, and between human and automated observations. Two probability density functions---the Burr (type III) for mostly-clear situations, and generalised gamma for mostly-cloudy situations---are suggested as analytical fits for each cloud coverage, observation type, and solar elevation angle bin. For human observations of overcast skies (8 oktas) where solar elevation angle exceeds 10°, there is no significant difference between the observed clear-sky indices and the generalised gamma distribution fits.