The paper introduces the use of phase-state modelling as a means of estimating expected benefits or losses when dealing with decision processes under uncertainty of future events. For this reason the phase-space approach to time series, which generally aims at forecasting the expected value of a future event, is here also used to assess the forecasting uncertainty. Under the assumption of local stationarity the ensemble of generated future trajectories can be used to estimate a probability density that represents the a priori uncertainty of forecasts conditional on the latest measurements. This a priori density can then be used directly in the optimisation schemes if no additional information is available, or after deriving an a posteriori distribution in the Bayesian sense, by combining it with forecasts from deterministic models, here taken as noise-corrupted ‘pseudo-measurements’ of future events. Examples of application are given in the case of the Lake Como real-time management system as well as in the case of rainfall ensemble forecasts on the River Reno.

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