A stochastic methodology for generation of seasonal time series reproducing overyear scaling behaviour

Abstract

In generating synthetic time series of hydrological processes at sub-annual scales, it is important to preserve seasonal characteristics and short-term persistence. At the same time, it is equally important to preserve annual characteristics and overyear scaling behaviour. This scaling behaviour, which is equivalent to the Hurst phenomenon and has been interpreted by many as nonstationarity of processes, has been detected in a large number of hydroclimatic series and has important effects on the planning and design of hydrosystems. However, when seasonal models are used the preservation of annual characteristics and overyear scaling is a difficult task and is often ignored unless disaggregation techniques are applied, which, however, involve several difficulties (e.g. in parameter estimation) and inaccuracies. As an alternative, a new methodology is proposed that directly operates on seasonal time scale, avoiding disaggregation, and that simultaneously preserves annual statistics and the scaling properties on overyear time scales. Two specific stochastic models are proposed, a simple widely used seasonal model with short memory to which long-term persistence is imposed using a linear filter, and a combination of two sub-models, a stationary one with long memory and a cyclostationary one with short memory. Both models are capable of generating spatially correlated synthetic time series for more than one location simultaneously. The models are tested in a real world case and found to be accurate in reproducing all the desired statistical properties and virtually equivalent from an operational point of view.