Using wavelet based de-noising to identify the trend of ground water level (case study: Ardabil plain)

Ardabil plain)Groundwater is an important source of fresh water to meet the demands of growing industries such as agriculture, fisheries, mining, and manufacturing and the municipal water demands due to rise in population in different parts of the world. Efficient management of groundwater is an essential task in different regions, especially in arid and semi-arid climates that faces chronic shortage of fresh water. Thus, the detection of trends in groundwater levels is very essential in order to constantly monitor the levels of the ground water table. Nowadays, there are different statistical methods for trend analyzing hydrological time series such as t-test, regression analysis, Pearson correlation coefficient, the Spearman’s Rho, Sen’s slope, Wald–Wolfowitz and most commonly used method of Mann–Kendall (MK). Mann-Kendall (MK) test was introduced and developed by Mann (1945) and Kendall (1975), respectively. The advantage of this method is that it does not follow any specific statistical distribution. It has been widely used to analyze the monotonic trends in hydrological time series. The MK1 test for trend detection assumes that the sample data are serially independent, even though a few hydrological series show significant serial correlation. An alternative MK test is to remove first the serial correlation such as lag-1 auto regression or higher-order process from the time series prior to application of the test that its name is MK2. MK3 test is to remove all the serial correlation from the time series prior to application of the test.The objectives of the present study are: (1) to identify the trends and magnitude of trends in groundwater levels on monthly time scales with three variations of Mann-Kendall test include: (i) Mann–Kendall without autocorrelation, (ii) Mann–Kendall with lag-1 autocorrelation and trend-free pre-whitening, (iii) Mann–Kendall wi.