The detection, estimation and prediction of trends and associated statistical and physical significance are important aspects  of climate research. Given a time series of (say) temperatures, the trend is the rate at which temperature changes over a time period. The trend may be linear or non-linear. However, generally, it is synonymous with the linear slope of the line fit to the time series. Simple linear regression is most commonly used to estimate the linear trend (slope) and statistical significance (via a  Student-t test). The null hypothesis is no trend (ie, an unchanging climate). The non-parametric (ie., distribution free) Mann-Kendall (M-K) test can also used to assess monotonic trend (linear or non-linear) significance.

See: https://climatedataguide.ucar.edu/climate-data-tools-and-analysis/trend-analysis

Rainfall trends in south eastern australia are now so obvious that changes can be seen without advanced statistics. We are lucky here to have 150 years of good rainfall data from many locations. A simple analysis calculating a running 10 year average of annual rain over the 150 year period shows stable rainfall until about 1960 then a steady decrease of 2-3 mm / year since then. Not a big change , but it adds up over 60 years.

I find this type of analysis is more convincing for climate change dis believers than advanced statistics.

There is no definite method to your problem. It depends very much of what you are looking at and other conditions of your work, e.g. geographical coverage, analysis of an meteorological region, or narrow area... Besides what you mentioned, you may also compute the mean value for the 30 years, and then, compute the difference of each year vs this mean. Hence rather than dealing with the original values, you deal with "anomalies". It coud be useful.

I am very thankful to the researchers who addressed my need and commented here. All of your answers have introduced me to consider new aspects in my analysis and to presentation. I felt like it saved me reading of a whole book on the subject. I will be back with additional questions once i explored these suggestions.

Dear Colleagues,

Can I use XLstat for Mann Kedall trend analysis. I have seen many researchers using R-software for this test. Is there difference of results with both software. Or will you recommend some specific software for this Mann-Kendall test.

Hello

The problem with any statistical test (including regression fit with time as predictor and MK test) is the sensitivity on the first and last available dates and 30 years is short for a trend analysis. If you use statistical test, you need to check that your results are not too sensitive on first and last dates (for example by computing scores on year 1-30, but also on year 1-28, 2-29 and 3-30 and so on). I fully agree with the comment of Cliff here above, but we need a lot of available decades to look at trends with such a method.

Vincent

Firstly, I'd consider you re-phrase the question. A trend is a feature that may be local forcing based, a long term climate mode (longer than your avaiable data) or both. You can apply Dominant Frequency State Analysis (Article Heartbeat of the Southern Oscillation explains ENSO climatic...

you can simply shuffle (many times) the 30 values randomly and derive a population (PDF) of the slope. Then, you can test if the non-shuffled slope lies within e.g. the 95% integral of the shuffled, or outside the PDF. This may avoid problems with the limited sample size (Vincent's comment).

Thanks for the answers!

Innovative Polygon Trend Analysis Method which the newest trend analysis method of Zekai Şen.

We just published an article (INNOVATIVE TREND ANALYSIS OF HYDRO-METEOROLOGICAL VARIABLES IN IBADAN, NIGERIA) using the recently developed Innovative Trend Analysis Method (ITAM) and Mann-Kendall (M-K) with Sen’s slope test. Precipitation trend during the period of 45 years was analyzed using these methods. You may wish to check it out if interested.

Hi,

I have developed two R-Packages namely 'modifiedmk' and 'trendchange' to perform various trend tests.

In case if the timeseries is not affected by Auto-Correlation (also called as - Serial Correlation), I would suggest using:

· Non-Parametric Mann-Kendall Trend Test (mkttest) from modifiedmk package

· Non-Parametric Spearman’s Rank Correlation Trend Test (spear) from modifiedmk package

· Innovative Trend Analysis (innovtrend) from trendchange package

· Innovative Polygon Trend Analysis (ipta) from trendchange package

If the series is affected by serial correlation, I would suggest using an ensemble of methods instead of using just one modified version of non-parametric test from ‘modifiedmk’ package:

· Pre-Whitening with Mann-Kendall Test (pwmk)

· Trend Free Pre-Whitening with Mann-Kendall Test (tfpwmk)

· Bias-Corrected Pre-Whitening with Mann-Kendall Test (bcpw)

· Bootstrapped Mann-Kendall Trend Test with Optional Bias Corrected Prewhitening (pbmk)

· Block Bootstrapped Mann-Kendall Trend Test (bbsmk)

· Block Bootstrapped Spearman’s Rank Correlation Trend Test (bbssr)

· Modified Mann-Kendall Test Using the Hamed and Rao (1998) Variance Correction Approach (mmkh)

· Modified Mann-Kendall Test Using the Yue and Wang (2004) Variance Correction Approach (mmky)

It is also important to indicate the trend change points in the time series (When the changes in the trend occurred) along with the trend results. Trend Change Points can be analysed using the following functions from ‘trendchange’ package:

· Distribution Free CUSUM Test (dfcusum)

· Sequential Mann-Kendall Test (sqmk)

Refer attached links for further reference.

https://www.researchgate.net/publication/338553931_Long-Term_Homogeneity_Trend_and_Change-Point_Analysis_of_Rainfall_in_the_Arid_District_of_Ananthapuramu_Andhra_Pradesh_State_India

https://www.researchgate.net/publication/359081739_Modified_versions_of_Mann_Kendall_and_Spearman's_Rho_trend_tests

https://www.researchgate.net/publication/337674307_trendchange_Innovative_Trend_Analysis_and_Time-Series_Change_Point_Analysis

https://www.researchgate.net/publication/321885655_On_using_CRAN-R_package_'modifiedmk'_to_perform_Mann-Kendall_and_Modified_Mann-Kendall_trend_tests_for_beginners_in_R?_sg%5B0%5D=wjz70jYH6xY7mzyYQGJVP0I93u8cH_R9LABNJ8_bEuN662nkdTDn3Zfvtf-dkZVSf-vN_WK-Uq_9iXRFhcLPAtUe-EG1xRdMBOGv8kyR.cgnBeBh8xR9XBf8QmE6rNoO-7gRN8pc4JCl5SN7g5hcZBOk-DcnsW5sPxOe5VTC0zv0SJdxirEpaUDZcuBn7wQ

https://www.youtube.com/watch?v=lfGIdtr8oPA

https://www.youtube.com/watch?v=uh4-uOJ7lB0

Hi,

I have posted the following answer in several other questions related to trend analysis. For the sake of new visitors, I am posting the following again:

I have developed two R-Packages namely 'modifiedmk' and 'trendchange' to perform various trend tests.

In case if the timeseries is not affected by Auto-Correlation (also called as - Serial Correlation), I would suggest using Mann-Kendall Test, Spearman's Rho test or Innovative Trend Analysis etc.,

If the series is affected by serial correlation, I would suggest using an ensemble of methods instead of using just one modified version of non-parametric test. It is also important to indicate the trend change points in the time series (When the changes in the trend occurred) along with the trend results. Refer attached research paper for further reference.