Trend Analysis of Rainfall, Runoff and Temperature

I am interested in doing trend analysis of rainfall, run-off and temperature using the parametric test.

My question is - is it essential to have normally distributed data or not?

Can I directly apply regression analysis and then check for significance and non-significance?

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8 Answers

1. Hi Sultan.

   If you do not want to normalize the data, you can use non-parametric tests like Man-Kendall trend test.

   I also agree ​with others on ​not forcing a ​particular ​distribution on ​the data. 

2. Hi Sultan, 

   I would suggest using 'linear transformation' to 'normalise' the data [(X-Xmin)/(Xmax-Xmin)] which will preserve the shape of the distribution. Parametric tests can be used on non-normal data if the sample size criteria can be met, more info at http://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test. So the answer to your question is that it is not essential to have normally distributed data. I agree with others on not forcing a particular distribution on the data  - use as is / find the distribution that fits your data.

3. I agree with Ian Pearson's perspective and approach. Meteorological/climatic data is not normally distributed as it varies spatially and temporally. Thus, for parametric testing, the data need to be normalized by fitting the data into a suitable PDF/CDF before transformation to a standard Gaussian multivariate. Otherwise, you may consider the non-parametric tests such as Spearman Rank correlation and Mann-Kendall trend test; although parametric statistical models are superior. 

   1 Comment

   1. can i email data to check? as i have some confusion. when i apply power tranfirmation some data is skewed some is normal. 

4. Hi

   New discovery incredible, never heard

   THE RAIN IS FORMED IN 7 PHASES, NOT 3.

   -https://pdf.lu/lsu5/ details in one page (EN.FR).

   "Lightning + thunder + rain = one operation"

5. Each statistical tests comes with certain pre requisites and normality test is one of the key prerequisite. If the data used is not normally distributed then the further test you conduct basically loss its power. It is like a Pre Qualification before you qualify to work for certain field. Like a Degree. So normality test is must. If data is not normal, you require to transform data to various forms like log or others and check whether the normality of data is improved it or not. 

   Try to run Linear regression on non normal data directly and transformed data . You will see the difference in the results you get. Indeed there are certain tests still available which are performed on non normal data like Z test for t-tests where Z test is used for non normal data.  

    

   2 Comments

   1. Hi My mail id is amit.christian@levapor.in

   2. can i email data to check? as i have some confusion. when i apply power tranfirmation some data is skewed some is normal. 

6. I understand your desire for testing. I might suggest that you take current rainfall data, soil types and permeability %. Regardless of ANY testing or censoring equipment or any area  there will only be 2 conclusions. You have too much rainfall causing floods or too little rain causing desertification and destruction of an agricultural industry. Both situations are easily resolved. A) flood control plant more trees especially next to the river banks. Trees respirate up to 300 gallons a day. B) if red clay or desert sand just collect all...ALL of the trash grind it up and make compost, add microbes and water. You have just created soil. Next the soil will hold the moisture Large areas will be come humid. Humidity conducts electricity, it will magnetically attract more moisture which will cause more rainfall. Weather pattern will spiral up reversing the desertification process. New fam land and later forests. Regardless of which desert in the entire world none can change the laws of nature. Nature is a good teacher. Been around for a few billion years.  

7. Hi

   In the regression analysis for the trend in hydrologic data the assumption of normality is a must. First of all you check with the kind of distribution your rainfall data has. Otherwise you may convert the data to Normally Distributed data if it differs from normality. You may use power transformation function.

   1 Comment

   1. can i email data to check? as i have some confusion. when i apply power tranfirmation some data is skewed some is normal. 

8. Hi Sultan,  you cannot stipulate that the data must be normally distributed - you must use the data that you have and assess what distribution pattern best fits it.  This then governs the regression analysis you will apply.  You are on track with applying a regression analysis and checking for level of significance.  If you have a number of rainfall and weather stations and streamflow gauges in the same catchment, you will also need to test for cross correlation.  I did this many years ago and modeled the system with a stochastic model.  The other option is using a deterministic model approach.  There are some off-the-shelf models you can use now days, but I am not familiar with them.