I am using Mann-Kendall test and Sen slope to assess the trends in monthly rainfall datasets for 64 years, e.g., Jan 1957, Jan 1958, ..., Jan 2020. Since the region is a semi arid one, there are a lot of zero values (NOT missing values) in the time series. For example, the time series for rainfall in January has only 15 non-zero values out of 64 data points. My question is how this will effect the trend test (Mann-Kendall) and the trend slope (Theil-Sen)?
Hello Harsh Upadhyay
My suggestion is to delete the months that have zero data. Then analyze the remaining data (15 months).
These tests are sensitive to zero numbers and strongly affect the results.
You must have at least 10 observations for the Normal approximation to be appropriate.
You could try aggregating the months into 3 month chunks for example, hopefully removing the large number of zeros at the cost of less granularity.
I agree with Abolfazl Ghoodjani
The model might be:
rainfall_t = max(a x_t + b, 0)
whiel the x_t can have any value.
NOT removing the zero rainfall data gives a wrong estimate of a.
I would argue that removing the zeros may significantly bias the results
Abolfazl Ghoodjani Thank you for replying. I was thinking of doing what you suggested but it didn't feel like the right thing to do as the new time series probably wouldn't be a true representative of the actual rainfall scenario in the area. I did read a lot of papers on semi-arid regions and they either haven't calculated the Sen slope for monthly time series data or they skipped over the months of non-rainy season in their respective study areas and just computed the Sen slope for rainy period months.
Jamie Wallis Thank you for replying. I had determined the trends for the seasonal periods in a year as well. Instead of 3 months however, I chose a 4-month period which, I guess, matched better with the periods of pre-rainy, rainy and post-rainy season (e.g., rainy season 1957, rainy season 1958, ....., rainy season 2020) and i was able to obtain decent results with it too. Does this correspond with what you suggested or did I misunderstood your comment?
To me this sounds like a Point Process with (say) Time intervals between the Rain event (A Procedure in Genstat software gives following description):
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A point process, or series of events, is characterized both by the times at which events occur, and the intervals between events. The Poisson process is the most basic point process, with Poisson counts in any interval, and independent exponentially distributed intervals between events.
A comprehensive account of methods for analysing point processes is given by Cox & Lewis (1966). PTDESCRIBE implements many of the test and summary statistics they give and should be used in conjunction with the text for a full discussion of the motivation and context of their use. All equations referred to below are from Cox & Lewis (1966).
The DATA variate may contain either the times at which events occur, the intervals between events, or a sequence of 0's and 1's, with 1's indicating the times of events on an integer time scale. The option REPRESENTATION specifies which of these is used. If REPRESENTATION=time and the process is measured from some time other than zero, the initial time should be given in the parameter START. Otherwise the START time is assumed to be zero. The first interval is taken to lie between the START time and the first event. If the process is observed beyond the last event, the total duration of the process should be given in the parameter LENGTH. Checks are carried out on START, LENGTH and the length of each interval, and the procedure terminates if these are inconsistent. If REPRESENTATION=time, the DATA variate may be restricted, facilitating the analysis of truncated or thinned point processes.
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Reference
Cox, D.R. & Lewis, P.A.W. (1966). The Statistical Analysis of Series of Events. Methuen, London.
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