A bi-variable probability density function for the daily clearness index

The assumption that probability density functions of daily clearness indices are unimodal was tested. Bimodal behaviour was observed in almost 60% of 600 monthly data sets and was shown to be the most usual shape at 50 locations between latitudes 18.438N and 64.818N and at between 2 and 2297 m above sea level. A bi-exponential probability density function was proposed that fits the observed behaviour of daily clearness indices. The proposed function uses the mean monthly clearness index K¯and the mean monthly solar height at noon h¯as inputs. The bi-exponential method for predicting daily t max distributions is shown to reduce the RMS error by over 20% compared with earlier methods. Parametric representations of monthly maximum and minimum clearness index using K¯and h¯ are combined with the bi-exponential function to obtain t max a bi-variable probability density function f(K , K¯ , h¯ ) and a cumulative distribution function F(K , K¯ , h¯ ), analogous to t t max t t max those of Liu and Jordan.  2003 Elsevier Ltd. All rights reserved.