A joint stochastic-deterministic approach for long-term and short-term modelling of monthly flow rates

The authors present a detailed procedure for modelling of mean monthly flow time-series using records of the Great Morava River (Serbia). The proposed procedure overcomes a major challenge of other available methods by disaggregating the time series in order to capture the main properties of the hydrologic process in both long-run and short-run, The main assumption of the conducted research is that a time series of monthly flow rates represents a stochastic process comprised of deterministic, stochastic and random components, the former of which can be further decomposed into a composite trend and two periodic components (short-term or seasonal periodicity and long-term or multi-annual periodicity). In the present paper, the deterministic component of a monthly flow time-series is assessed by spectral analysis, whereas its stochastic component is modelled using cross-correlation transfer functions, artificial neural networks and polynomial regression. The results suggest that the deterministic component can be expressed solely as a function of time, whereas the stochastic component changes as a nonlinear function of climatic factors (rainfall and temperature). For the calibration period, the results of the analysis infers a lower value of Kling-Gupta Efficiency in the case of transfer functions (0.736), whereas artificial neural networks and polynomial regression suggest a significantly better match between the observed and simulated values, 0.841 and 0.891, respectively. It seems that transfer functions fail to capture high monthly flow rates, whereas the model based on polynomial regression reproduces high monthly flows much better because it is able to successfully capture a highly nonlinear relationship between the inputs and the output. The proposed methodology that uses a combination of artificial neural networks, spectral analysis and polynomial regression for deterministic and stochastic components can be applied to forecast monthly or seasonal flow rates.