What are the Recent Methodologies in Analyzing Trends in Rainfall and Temperature Data
As a starting point, two well-accepted nonparametric statistical tests for checking for the presence (or absence) of hydrologic trends are the Mann- Kendall and Spearman Rank tests.
If a statistically significant trend is found using these tests, then additional testing can be performed for identifying characteristics of the trend--for example, simple linear or nonlinear regressions to check for the presence of linear or nonlinear trends. Also more sophisticated statistical techniques are available to check for the presence or absence of 'break points' in time at which the trend may have initiated and/or terminated within the time span of the data series.
You may use the Mann-Kendall test, Sen's Slope, or Spearman's rank correlation. All of these are widely used by researchers.
If somebody is looking for a relatively new method for trend analysis or changepoint detection, one possibility is a Bayesian time series analysis package BEAST or 'Rbeast' , available in R, Python and Matlab (https://github.com/zhaokg/Rbeast). It is no better than other techniques or packages, but just providing an alternative choice and some different insights. Here is a recent study that compared BEAST and the M-K test: Di Nunno, Fabio, Giovanni de Marinis, and Francesco Granata. "Analysis of SPI index trend variations in the United Kingdom-A cluster-based and bayesian ensemble algorithms approach." Journal of Hydrology: Regional Studies 52 (2024): 101717.
