Risk attachment Sen’s Slope calculation in hydrometeorological trend analysis

The effects of global warming and climate change appear as increasing or decreasing trends in hydrometeorological records in different locations. Identifying trends in long-term (more than 30 year) data is possible through a variety of methodologies as well as classical Mann–Kendall (MK), Regression (R), Spearman’s Rho (SR) methods in addition to the innovative trend analysis (ITA) approaches. The most used method in the literature is the MK trend determination test, but it has limited assumptions, and the trend slope is calculated according to Sen’s median procedure. However, Sen’s approach is an empirical methodology that considers a single median slope from all possible consecutive lag slopes. This paper provides the theoretical probability distribution function (PDF) that matches Sen’s slopes, and an innovative probabilistic trend slope methodology is proposed with a set of slope risk levels, rather than statistical slope calculation. The application of the proposed methodology is presented for long-term Danube River annual discharge data in Romania and precipitation records at Antalya resort center in the south along the Mediterranean coast of Turkey. A set of trend lines, objectively different risk levels, are obtained. It has been determined that there are decreasing and increasing monotonic trends in each historical time series record. Therefore, for extreme events, it is possible to consider a particular risk level trend characteristic, i.e., floods and droughts, rather than the classical mean or median level trend definition.