H. Tyralis, and D. Koutsoyiannis, Simultaneous use of observations and deterministic model outputs to forecast persistent stochastic processes, Facets of Uncertainty: 5th EGU Leonardo Conference – Hydrofractals 2013 – STAHY 2013, Kos Island, Greece, doi:10.13140/RG.2.1.3230.4889, European Geosciences Union, International Association of Hydrological Sciences, International Union of Geodesy and Geophysics, 2013.
We combine a time series of a geophysical process with the output of a deterministic model, which simulates the aforementioned process in the past also providing future predictions. The purpose is to convert the single prediction of the deterministic model for the future evolution of the time series into a stochastic prediction. The time series is modelled by a stationary persistent normal stochastic process. The output of the deterministic model comprises the simulation of the historical part of the process and its deterministic future prediction. The complexity of the deterministic model is assumed to be irrelevant to our framework. A multivariate stochastic process, whose first variable is the true (observable) process and the second variable is a process representing the deterministic model, is formed. The covariance matrix function is computed and the distribution of the unobserved part of the stochastic process is calculated conditional on the observations and the output of the deterministic model.