Use of confidence curves to represent uncertainty in hydro-meteorological time series analysis

Abstract

Climate change is incompatible with the assumption of stationarity. This has lead to a sharp increase in the detection and study of nonstationarity in hydro-meteorological processes. Most hydro-meteorological processes are still analyzed by studying time series of observations. From the perspective of statistical characteristics, a stationary time series does not show significant changes. On the contrary, a nonstationarity time series often shows a slowly increasing/decreasing trend or a sudden change. A sudden change or a change point is a time point that a time series shows a great change in its statistical characteristics, for instance in themean or the standard deviation. For stationary cases, hydrologists have a large number of statistical tools to analyse these time series. These tools can not only help hydrologists to gain a deep insight into time series, but they can also analyse the corresponding uncertainty. For nonstationary cases, the detection of changes has drawn the majority of attention, however, the uncertainty associated with the detection has still been rarely studied. Therefore, this PhD research aims at bridging the gap between nonstationarity detection and the uncertainty of detection. To be more specific the main scope is rooted in analysing the uncertainty associated with detecting a change point in hydro-meteorological time series. When it comes to representing uncertainties, a traditional choice is using a confidence interval with a certain confidence level. In this research instead, the uncertainty is represented by confidence curves because they are capable of capturing more information by including all confidence intervals at all confidence levels and they visualize uncertainty in a curve. To verify the general applicability of a confidence curve in representing uncertainties, both a discrete parameter and a continuous parameter are considered in this research. The location of a change point is considered as a discrete parameter, and the dependence parameter in copula models will be considered as a continuous one. Additionally, in order to simplify the construction of a confidence curve, several new approaches have been presented in this research. Based on results and findings, confidence curves have been proven to be more informative and theoretically they can represent uncertainties of all types of parameter of interest. With a confidence curve, hydrologists can easily read the uncertainty of the detected change point and this would also provide decision-makers a better insight into the nonstationarity of a time series of a hydro-meteorological observations.