Dear Pritha Datta,

first, it is necessary to realize what you consider by the term 'trend'. If you used the Mann-Kendall test, I guess the trend component of your precipitation series was defined as a monotonic gradual change of the totals. Then, the result highly depends on the time period you chose (or you had at hand). Of course, as Raoof Mostafazadeh says, the longer the series is, the better it reflects the long-term behaviour of the series. However, one must admit that in many cases instrumental time series are often too short and there is a high risk that the record may represent only a part of much longer cycle that is a result of long-term climate variability (that could be revealed if you had much longer, perhaps reconstructed, time series). There is also a discussion among hydrologists whether the 'trends' found by hypothesis tests are really deterministic trends (reflecting climate change) or they are a result of stochastic processes generating the series. Such stochastic processes may mimic the deterministic components of a series such as trends. Therefore, it is necessary to carefully select between various modifications of the tests taking into account these stochastic processes. Probably, the most difficult is the detection of so-called long-term persistence (LTP, sometimes also referred to as long-range dependence) triggered likely by a long-memory process. However, in practice, the purpose of your work should be superior. For instance, do you need to proceed further with short-term forecasts or long-term forecasts? For further discussion, I would recommend that you read some papers on the topic by Demetris Koutsoyiannis, Alberto Montanari, Khaled H. Hamed or Harry F. Lins (hydrologists) or A. Ian McLeod (statistician).

Hope this helps.

Ondrej

In my opinion! The longer, The better, Which provide a better realistic picture of the data and climatic condition and the test of hypothesis.

As a rule of thumb, the WMO have recommended a time series longer than 30.

Although, the trend in short time series may have a higher probability.

Dear Pritha Datta,

first, it is necessary to realize what you consider by the term 'trend'. If you used the Mann-Kendall test, I guess the trend component of your precipitation series was defined as a monotonic gradual change of the totals. Then, the result highly depends on the time period you chose (or you had at hand). Of course, as Raoof Mostafazadeh says, the longer the series is, the better it reflects the long-term behaviour of the series. However, one must admit that in many cases instrumental time series are often too short and there is a high risk that the record may represent only a part of much longer cycle that is a result of long-term climate variability (that could be revealed if you had much longer, perhaps reconstructed, time series). There is also a discussion among hydrologists whether the 'trends' found by hypothesis tests are really deterministic trends (reflecting climate change) or they are a result of stochastic processes generating the series. Such stochastic processes may mimic the deterministic components of a series such as trends. Therefore, it is necessary to carefully select between various modifications of the tests taking into account these stochastic processes. Probably, the most difficult is the detection of so-called long-term persistence (LTP, sometimes also referred to as long-range dependence) triggered likely by a long-memory process. However, in practice, the purpose of your work should be superior. For instance, do you need to proceed further with short-term forecasts or long-term forecasts? For further discussion, I would recommend that you read some papers on the topic by Demetris Koutsoyiannis, Alberto Montanari, Khaled H. Hamed or Harry F. Lins (hydrologists) or A. Ian McLeod (statistician).

Hope this helps.

Ondrej

Dear Pritha,

I'd add to the extended comment of Ondrej the following well-known circumstance. That is true that instrumental data are usually too short and noisy to extract reliably the deterministic components in the available time series. Even if you formally extract them at some confidence level it does not mean that one can use the obtained parameters for the reliable forecast because the statistical structure of the time series can change. It is especially true for the precipitation.

So, it seems to me that the best strategy is as follows. To study carefully the statistical structure of the available time series. To put the special attention to the non stationarity of them. After that to choose the suitable statistical technique to separate the stochastic and deterministic components (if possible).

Thanks to all for the answers. Dear Raoof Mostafazadeh , A. B. Polonskii, and Ondrej Ledvinka, I have used the modified version (Hamed & Rao, 1998) of the Mann-Kendall test and as I mentioned that in recent years (the recent series is more than 30 years), precipitation has decreased to a great extent and is also significant in the modified Mann-Kendall Test. However, the trend of the entire series remained non-significant positive. From the perspective of policy formulation for adaptation measures, what one should suggest for that region?

If I take the trend result of the entire series, then it is non-significant positive and the recent is significant negative. What I should recommend for that region?

Dear Pritha datta,

I can suggest you that, make your data into windows with a length of 30 years and calculate the Mann-kendall trends of each window. Then you can clearly differentiate the variation in trends of each window.

Yes, I almost forgot about the approach mentioned by B. Padmavathi. The Mann-Kendall test applied to the sliding windows of time series can be beneficial if you want to see how the values of the standardized Mann-Kendall test statistic varied in the past. Note also that Hannaford and Buys (2012; Article Trends in seasonal river flow in the UK

I would also like to add my voice on your question. Coming from a climate perspective, short term trends may be good for tactical decisions while long term trends could useful for strategic decisions or plans. Since you mentioned that you would like to use your results for policy makers or policy decisions for a region, you can calculate the trends considering their use in the two decision dimensions. For example, short term patterns/trends of rainfall e.g. seasonal may be useful in planning of farm activities --crop and pasture production..

Dear Richard Muita , thanks for your opinion. It was helpful.

Dear Pritha Datta,

I think you can check seasonality in the time-series. Split the entire time-series into summer and winter and see the trend again. It is normal you can find an increasing trend for one season and a decrease in the second one. If one season (e.g. summer) is dominating the regime ad follows -ve trend then the entire series will be -ve trend. You can also try parametric methods to find a trend, see this paper: Article A comparison of three approaches to non-stationary flood fre...

Dear Ondrej,

Thanks for referring to my papers.

For your information, the brand new paper by Theano (Any) Iliopoulou and me (part of her PhD thesis) shows in a comprehensive and exhaustive manner that there is no meaning/usefulness in looking for trends in hydrological series.

The paper is Projecting the future of rainfall extremes: better classic than trendy, https://www.researchgate.net/publication/340994016

Kind regards,

Demetris

You can split the long time series into a span of 30 years each, also check seasonality change in time series.

relevant papers-

Kumar V, Jain SK, Singh Y.2010.Analysis of long-term precipitation trends in India.

Devi et al., 2020. Analyzing precipitation and temperature trends of Kanha and Satpura Tiger Reserve, Central India

Yadava et al., 2019. Analyzing long term seasonal and annual trends for precipitation and temperature in Central India

Thanks to all for sharing your valuable thoughts on my question. Besides, I would like to ask Dr. Richard Muita , that as you have mentioned " long term trends could be useful for strategic decisions or plans", in this regard can you please give a few examples of such plans! It can actually provide a precise understanding of your thought.

Dr. Yavuz Selim Güçlü Hello sir, can you provide some insights here? Thank you very much.

Dear Pritha Datta

Hydrologists and meteorologists often face this type of problems while interpreting the trend results of long-term data. In your case, you should divide your entire time series (1900-2019) into sub-series (say 25 or 30 years). Then apply Mann-Kendall test on each sub-series separately. Try to find out any cyclic pattern or seasonality in your data. One should not draw the conclusion on the basis of entire time-series in this type of cases.

You can also apply the Change Detection Tests, to identify the change points in the entire time-series (1900-2019). A long time-series often contains more than one change points.

Moreover, recent trend (past 2-3 decades) is more important for policy makers than long-term trend. For example, If you will draw your conclusion based on entire time-series (1900-2019), it will definitely mislead the policy makers.

Dear Pankaj Bhardwaj , thanks for your answer.

Dear Pritha Datta,

I am just seeing this question. It is my opinion that in the consideration of trends in climatic parameters that a minimum of 30 - 35 years data should be considered.