Stochastic models of solar radiation processes

Abstract : Characteristics of solar radiation highly depend on some unobserved meteorological events such as frequency, height and type of the clouds and their optical properties (atmospheric aerosols, ground albedo, water vapor, dust and atmospheric turbidity) while a sequence of solar radiation can be observed and measured at a given station. This has suggested us to model solar radiation (or clearness index) processes using a hidden Markov model (HMM), a pair of correlated stochastic processes. Our main model is a continuous-time HMM (Xt, yt)t_0 is such that the solar radiation process (yt)t_0 is a solution of the stochastic differential equation (SDE) : dyt = [g(Xt)It − yt]dt + _(Xt)ytdWt, where It is the extraterrestrial radiation received at time t, (Wt) is a standard Brownian motion and g(Xt), _(Xt) are functions of the unobserved Markov chain (Xt) modelling environmental regimes. To fit our models to observed real data, the estimation procedures combine the Expectation Maximization (EM) algorithm and the measure change method due to Girsanov theorem. Filtering equations are derived and continuous-time equations are approximated by robust versions. The models are applied to pdf comparison and classification and prediction purposes.
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van Ly Tran. Stochastic models of solar radiation processes. General Mathematics [math.GM]. Université d'Orléans, 2013. English. ⟨NNT : 2013ORLE2046⟩. ⟨tel-00994598⟩

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