Long range dependence in discharge time series and its relationship to external drivers

Abstract

Abweichender Titel laut Übersetzung der Verfasserin/des VerfassersZsfassung in dt. SpracheThe long term analysis of hydrological variables, such as discharge, is important given the recent interest in climate change effects on the water balance of catchments. The aim of this thesis is to a gain deeper understanding of the long term behaviour of discharge and its possible dependencies on various climate and storage related drivers from a long term perspective. There are several criteria that can be considered, when analysing time series from a long term perspective. Long range dependence, measured by the Hurst coefficient, gives information about the autocorrelation for high time lags. This phenomenon is investigated in Chapter 2, where the Hurst coefficient of 39 series of mean daily discharges of European rivers is estimated using different methods. The existence of long range dependence is identified in all time series. Furthermore, the correlations between the Hurst coefficient and several discharge related characteristics are investigated. Various significant correlations are found including a positive correlation between the Hurst coefficient and catchment area and air temperature. Another approach of analysing hydrological variables from a long term perspective are wavelet and cross-wavelet spectra. This methodology is used in Chapter 3 to analyse monthly time series from the Danube River in order to find long cycles. The correlations between the spectra are examined for discharge, air temperature and precipitation monthly data sets. Long cycles with over a decade long return periods are found in all discharge time series. Long cycles in selected precipitation time series are found as well. However, no long cycles can be identified in the air temperature time series. The cross-wavelet analysis shows strong correlations between the discharge and precipitation spectra, especially for low frequencies. The two approaches mentioned above are combined in Chapter 4, where a method for deseasonalisation of time series using discrete wavelet transformation is proposed. Long range dependence of the time series is taken into consideration by using an ARFIMA (autoregressive fractionally integrated moving average) model. Wavelet deseasonalisation is compared to a standard moving average deseasonalisation approach, using forecasting performance as a comparison criterion. The results show that, considering one to ten days ahead forecasting performance, the wavelet deseasonalisation approach improves the forecasting performance for longer forecasting horizons compared to the standard approach. The findings of this thesis give new insights into discharge and discharge related processes from the long term perspective. They form a basis for more accurate multivariate modelling, using discharge as dependent and possibly air temperature and precipitation as explanatory variables. The results of this thesis suggest that there are significant cycles with multidecadal time periods in European rivers. Furthermore, the results highlight the need to approach time series modelling on a case-by-case base, considering the specific periodic behaviour of each data set separately, emphasizing the need for future improvements of stochastic modelling of discharge processes.7