In hydrological studies, it is very important to properly analyze the relationship among the different components of the water cycle, due to the complex feedback mechanisms typical of this system. The analysis of available time series is hence a fundamental step, which has to be performed before any modeling activity. Moreover, time series analysis can shed light over the spatial and temporal dynamics of correlated hydrological and climatological processes. In this work, we focus on three tools applied for time series analysis: homogeneity tests, wavelet analysis and copula analysis. Homogeneity tests allow to identify a first important kind of variability in the time series, which is not due to climate nor seasonal variability. Testing for inhomogeneities is therefore an important step that should be always performed on a time series before using it for any application. The homogenization of snow depth data, in particular, is a challenging task. Up to now, it has been performed analyzing available metadata, which often present contradictions and are rarely complete. In this work, we present a procedure to test the homogeneity of snow depth time series based on the Standard Normal Homogeneity Test (SNHT). The performance of the SNHT for the detection of inhomogeneities in snow depth data is further investigated with a comparison experiment, in which a dataset of snow depth time series relative to Austrian stations has been analyzed with both the SNHT and the HOMOP algorithm. The intercomparison study indicates that the two algorithms show comparable performance.
The wavelet transform analysis allows to obtain a different kind of information about the variability of a time series. In fact, it determines the different frequency content of a signal in different time intervals. Moreover, the wavelet coherence analysis allows to identify periods where two time series are correlated and their phase shift. We apply the wavelet transform to a dataset of snow depth time series of stations distributed in the Adige catchment and on a dataset of 16 discharge time series located in the Adige and in the Inn catchments. The same datasets are used to perform a wavelet coherence analysis considering the Mediterranean Oscillation Index (MOI) and the North Atlantic Oscillation Index (NAOI). This analysis highlights a difference in the behavior of the snow time series collected below and above 1650 m a.s.l.. We also observe a difference between low and high elevation sites in the amount of mean seasonal snow depth and snow cover duration. More interestingly, snow time series collected at different elevations respond differently to temperature and more in general to climate changes. The wavelet analysis allows us also to distinguish between gauging stations belonging to different catchments, while the wavelet coherence analysis revealed non-stationary correlations with the MOI and NAOI, indicating a very complex relation between the measured quantities and climatic indexes. Finally the application of copulas allows modeling the marginal of each variable and their dependence structure independently. We apply this technique to two relevant cases. First we study snow related variables in relation with temperature, the NAOI and the MOI, which we already investigated with the wavelet coherence analysis. Then we model flood events registered at two stations of the Inn river: Wasserburg and Passau. This last analysis is performed with the goal of predicting future flood events and derive construction parameters for retention basins. We test three different combinations of variables (direct peak discharge-direct volume, direct peak discharge-direct volume-rising time-base flow, direct peak discharge-direct volume-rising time-moving threshold) describing the flood events and compare the results. The consistency in the results indicates that the proposed methodology is robust and reliable. This study shows the importance of approaching the analysis to hydrological time series from several points of view: quality of the data, variability of the time series and relation between different variables. Moreover, it shows that integrating the use of various time series analysis methods can greatly improve our understanding of the system behavior
