Time Series Analysis of Temperature and Precipitation Dynamics Using CETA and MCETA Methods

ABSTRACT

In order to comprehend climate variability and extremes, it is essential to evaluate hydro‐climatic trends at various risk levels. The annual mean temperature and total precipitation data from 11 meteorological stations in the Khyber Pakhtunkhwa region of Pakistan were subjected to the Crossing Empirical Trend Analysis (CETA) and Modified Crossing Empirical Trend Analysis (MCETA) methods in this investigation. In CETA framework, upper and lower trend slopes are derived from maximum and minimum values identified in the first and second halves of the time series. In contrast, MCETA determines pivot values directly from cumulative distribution function (CDF)–based critical thresholds corresponding to selected risk levels (5%, 50% and 95%), enabling a risk‐oriented trend assessment. The results show that temperature series generally exhibit increasing trends across most stations, particularly at median and higher risk levels, indicating intensified thermal conditions. Precipitation trends display greater spatial variability, with several stations showing increasing trends at higher risk levels and decreasing trends at lower levels, suggesting a tendency towards more intense but less frequent precipitation events. The results indicate that MCETA outperforms both CETA and conventional trend analysis methods by offering a more comprehensive and distribution‐sensitive assessment of hydro‐climatic trends. MCETA, in contrast to conventional methods, effectively captures slope variability across various segments of the data distribution, thereby facilitating the identification of heterogeneous trend behaviours that are associated with differing risk levels. The implementation of CETA and MCETA in conjunction demonstrates that hydro‐climatic trends are not consistent throughout the distribution. This underscores the importance of risk level specific trend assessment in order to enhance hydro‐climatic analysis, climate variability interpretation and climate risk evaluation.