Maybe, you could start with a broader analysis, like number of rain events, per season. Then you could add the amount of rain, its intensity, duration of the rain event and previous time that did not rained. Once you have build up that data, compare seasons using a priori statistical analyses like Kruskall-Wallis or ANOVA, and then a posteriori analysis of tukey, or one that suits your assumptions.
Analyze weekly 20 to 30 years data of rainfall during monsoon period using PSS statistical software. You could easily detect the pattern / change in the pattern.. Suppose change occurs after 12 years then consider those 12 years as standard and quantify the change in pattern during 13th years consider mentioned 12 years. I don't think that this is a difficult task..
I think this paper may help you.
https://www.researchgate.net/publication/237020123_Adaptation_of_climate_variabilityextreme_in_arid_environment_of_the_Arabian_peninsula_by_rainwater_harvesting_and_management?ev=prf_pub
Article Adaptation of Climate Variability/Extreme in Arid Environmen...
This may help too.
https://www.researchgate.net/publication/237020136_Rainwater_Harvesting_and_Management_as_an_Adaptive_Strategy_to_Cope_With_The_Extreme_Climate_Events_in_The_Arid_Environment_of_The_Arabian_Peninsula?ev=prf_pub
Conference Paper Rainwater Harvesting and Management as an Adaptive Strategy ...
From historical data, arithmetic can be done to know the long term mean or normalized amount of rainfall say over 10, 15 and 20 years. So, the long -term mean and period should be first defining point. Total monthly and annual can be compared with the longterm mean. Statistical anlaysis will give the root meran square of the deviations. Graphical prsentation can bring out the mesage well
The question is I beleive not how to analysis periodcity by to detrmine if there has been a change in the trend or natural variability. For this you need to apply change point analsysis. For the simplest try CUSUM analsysis (Taylor software) however to yuse this you need to remove the autocorrelation within the timeseries by Whitening the data. Aletrantively yhere is a change point dtermination in the spectral analysis proceedure SINgular Spectrum Analysis (principal components in time). Tjhe altter is best accessed through the software Catepillar, it a ree ware intially to try your data set out. What else? a rolling t test less subject to autocorrelation errors I think is possible or a moving wndow analysis with another corrrelated variable cnage indicate changes in correlation over vtime as indicating changes to structure and function (mirror correlation in a time series along an attractor see latest nature paper on cause and effect - google it).
Hope that helps in soem way
Barry
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