Seasonally adjusted periodic time series for Mann-Kendall trend test

In this study, temperature data trend analysis is conducted, which is thought to be influenced by global warming, climate change, and local factor impacts. The main objective of this paper is to obtain an acceptable autoregressive correlation value for the MK test. For this purpose, seasonality (periodicity) especially in monthly time series is adjusted. Autoregressive correlation and homogeneity test values decrease after seasonal adjusting, but reasonable results are not achieved. Then, prewhitening procedure is also applied to the seasonally adjusted data. This process resulted in the data becoming both homogeneous and free autoregressive correlation. The final version of the time series is suitable for the MK test. Furthermore, the time series are divided into different time intervals, and the efficacy of the method is investigated. The results demonstrated that the method is suitable for time series with less than 30 years of data. The study demonstrated that the proposed method enhances the reliability of the data. Also, multiplication by 12 (months) allows the MK test with Z score in place of the Student's t-test in short-term data sets. This suggested methodology can be used to identify MK trend conditions in monthly time series. The application is based on monthly and annual average temperature data between 1957 and 2022 from three stations within the Kızılırmak basin (Çankırı, Kırşehir, Sivas stations) and one station within Seyhan Basin (Adana station) in Türkiye. The test results exhibited a significant increasing trend.