A simulation of daily solar irradiance in Italy using exponentially distributed white noise

Cloud cover distributions are analysed at a Mediterranean station (Naples) using 20 years of observations. The variable we use to define the state of the sky is the clearness index, i.e., the ratio of daily solar irradiance at the ground level to that at the top of the atmosphere. We show that the daily sequences of k(t) (the clearness index), t=1, ..., n, ..., when analysed on a monthly basis are well modelled by a linear Markov process: k(t) = ck (t-1) + w(t) where w(t) is an exponentially distributed white noise, rather than a Gaussian noise, as often assumed in literature. The exponential nature of w(t) explains well the asymmetric features of the k(t) distributions and the cloud cover climatology observed in Naples. The results can be generalized introducing linear Markov processes with w(t) distributed according to: f(w) = A exp(-aw) + B exp(bw) where A, B, a and b are positive constants. This model is able to simulate the bimodal distribution of k(t) as often observed at Northern Hemisphere middle latitudes.