Stochastic investigation of the utility of multiple hydrological records for improving the reliability of estimation

In the case that more than one natural time series are available in different measuring stations, or in the same station for different timescales, the issue of the simultaneous study of the all samples arises in order to improve the reliability of the estimations, assuming that the homogeneity hypothesis stands for the study region. If the at-site statistical samples are assumed independent and identically distributed (IID), the unification of samples results in a significant increase of the reliability of the results since the length of the overall sample, which represents the reliability of the statistical estimations, equals the sum of the at-site lengths (station-years method). However, the unification is acceptable and in the cases that intersite correlation exists but in such cases the reliability does not increase in the same manner as in the cases of stochastically independent samples. In the present master thesis, the possibility of unification and the respective increase of reliability are investigated. The latter is quantified in terms of the effective number of independent sites, whose uncertainty is equal to that in the case of intersite correlation. It turns out that the intersite correlations results in a dramatic increase of uncertainty in statistical estimation in comparison to the results produced by the simplifying assumption of serially independent samples. This indicates the weakness of the classical statistics to define the stochastic nature of the hydrological processes and the importance of considering the autocorrelation and cross-correlation properties of hydrological processes.