Markov Models in Discrete and Continuous Time for Hourly Observations of Cloud Cover

Abstract

An analysis of 15 years of hourly observations of cloud cover at an airport location near Copenhagen, Denmark shows that the main part of the variations can be described by first-order homogeneous Markov models. Models in both discrete and continuous time are considered. Special emphasis is laid upon the representation of the variation by a Markov model in continuous time. The physical restrictions for transitions of cloud cover are investigated and it is shown that the natural restrictions imply a very simple structure for the matrix of transition rates corresponding to the embedded Markov process in continuous time. The maximum likelihood estimate of the matrix of transition rates is found by numerical methods and an indication of the estimation error under the model is given.