Crossing empirical trend analysis (CETA) at risk levels in hydro-meteorological time series

Trend identification procedures are used to identify systematic monotonic trendlines in a given hydro-meteorological time series recording to represent time-dependent variations as increases or decreases. Different methodologies have been proposed for such descriptions, but most of them require restrictive assumptions such as normal (Gaussian) probability distribution function (PDF), serial independence, and long sample sizes. In particular, pre-whitening and over-whitening are recommended to meet the need for serial independence, but they cannot transform a serially dependent series into a completely independent one. In this paper, a new trend methodology is proposed based on the characteristics of crossings along any given straight line within the given time series, and the sought-after trend component is the one with the maximum number of crossings. This approach does not require any restrictive assumptions. Unlike previous trend algorithms, the proposed cross-empirical trend analysis (CETA) does not give a single trend, but a series of trends at different levels within the variation range of hydro-meteorological time series records. For the sake of brevity, only three levels are considered in this article, at 10%, 50%, and 90% risk levels. The comparison of the CETA approach is presented with the classical and frequently used Mann-Kendall (MK) trend determination procedure method based on Sen's slope calculation. For very small series correlation coefficients and normal PDF function cases, CETA and the classical technique give almost the same trendline within the +/- 5% error band. The application of this methodology is presented for monthly and annual discharge records of the Danube River and annual precipitation records from seven geographical regions of Turkey.