Dear Behnam Ababei,

I can say that hydrologists traditionally apply rather non-parametric tests mainly due to the potential non-Gaussianity (and sometimes missing values) of the samples regarding drought. For instance, the Mann-Kendall tests is very popular in this field. Definitely, I would recommend you to treat ties (equal values) properly in this case because in regularly sampled (annual) time series a lot of zeroes may occur due the fact that the drought does not need to develop in some years.

Some authors have pointed out that the presence of autocorrelation (serial correlation) and specifically long-term persistence in the case of drought may have adverse influence on the Mann-Kendall test results. So, there are a lot of modifications of this test dealing with this issue. See some references in my recent paper that can be found at the link provided below. A few of them can be downloaded directly from ResearchGate (e.g. Eghbal Ehsanzadeh's papers).

The following papers may be considered somewhat pioneering as regards the identification of trends in drought-related characteristics in hydrology:

Douglas, E.M., Vogel, R.M., Kroll, C.N., 2000. Trends in floods and low flows in the United States: Impact of spatial correlation. J. Hydrol. 240, 90–105. doi:10.1016/S0022-1694(00)00336-X

Hisdal, H., Stahl, K., Tallaksen, L.M., Demuth, S., 2001. Have streamflow droughts in Europe become more severe or frequent? Int. J. Climatol. 21, 317–333. doi:10.1002/joc.619

You will certainly find some older references therein.

Nowadays, new techniques for the detection of trends primarily connected with the wavelet analysis and the empirical mode decomposition have been developed (see e.g. Yan-Fang Sang's papers). However, personally, I am not so familiar with them. Nevertheless, I cannot say which technique is the best because every characteristic has its own specific features. It is necessary to explore them properly before applying a trend test that has several assumptions.

Hope this helps at least a little bit.

Best regards from Czechia,

Ondrej

http://www.proc-iahs.net/369/

Thank you Ondrej. That was comprehensive and helpful. Regards.

SPI is a simple and well recognized method. Yes, you have to select one, which will feasible with you and your objective. Dr Ondrej Ledvinka has discussed nicely too. I prefer simple technique, which can help to discuss and interpret the situation best. 

Dear Mr. Rowshon, 

Thank you very much for the response. Would you mind making our idea more clear to me, as you mentioned SPI. Do you mean Standardized Precipitation Index? Because my questions was about trend analysis, not the drought index themselves, and I am not sure if I am aware of this SPI technique of trend analysts. 

Regards.

Dear Behnam,

You could use R in order to calculate SPI and perform a modified Mann-Kendall test. I have used these packages:

For SPI: ‘SCI’ (Standardized Climate Indices such as SPI, SRI or SPEI)

For modified Mann-Kendall test: ‘zyp’ (Prewhitened Nonlinear Trend Analysis)

Regards

Thanks Franklin, I think it will be very helpful.

Mann-Kendall is a good method, the only thing I am not sure about is if we can use it for drought indices or other variables without any preprocessing, as these indices have seasonal fluctuations. Of course, we have a package in R to run seasonal Mann-Kendall, however I am not sure whether this can be used for drought indices which have been smoothed using a moving average of 6 or 12 months.

Actually this question of min applies to all trend analysis methods. Which one can be used for variables with seasonal fluctuations?

Regards.

Dear Behnam,

You should explore if your time series have a significant statistically autocorrelation. Here, there is an R-based script:

http://stats.stackexchange.com/questions/10947/formula-for-autocorrelation-in-r-vs-excel

Group 1: For your time series with significant statistically autocorrelation, apply a Prewhitened Nonlinear Trend Analysis (e.g. zyp for R)

Group 2: For your time series without significant statistically autocorrelation, apply a Traditional Trend Analysis (e.g. Kendall for R)

Regards

Thank you Franklin. Just a question: in order to reduce the number of testing the data, do you think it is advisable that we use the zyp package in all situations, without checking for significant auto-correlation? What happens if this method is used for a time series without significant auto-correlation?

Behnam.

just a linear regression between time and drought index(SPI/PDSI) will be fine