Database
The data sets used for the current investigation consist of the average monthly
rainfall of 36 meteorological subdivisions from 1901 to 2015. The meteorological
subdivision rainfall data were collected from the open-source platform-https://water.
india.gov.in/content/water/en/waterresourcesdepartment/WaterManagement/
IWRM.html. The hydrological year in India starts in April and ends in March. The
missing data in the time series were observed less than 1%, which have been
calculated using multiple imputation methods. R 3.5.1 and Arc 10.3 software have
been used for statistical analysis and mapping purposes, respectively. The various
methods used in this study are described in the following sections.
Methods
In this study, to detect the trends in historical rainfall data, ITA (Şen 2012) is used.
Further, the results of ITA are equated with the MK test (Mann 1945; Kendall 1975)
or mMK test (Hameed and Rao). The slope of changes is estimated by Sen’s slope
estimator (Şen 1968). However, a modified Mann–Kendell test (mMK) (Güçlü
2020; Phuong et al. 2020) has been performed for the serially correlated dataset as
the performance of the ordinary MK test in such conditions is very poor and gives
erroneous estimations (Sharma and Goyal 2020) because these statistics increase the
risk of overestimates or underestimates of the Z statistic if the time series has
significant autocorrelation (Ay and Kisi 2015; Rahman et al. 2017). Therefore,
MK autocorrelation lag-1 should be executed first to confirm the reliability of the
Z statistic. If significant autocorrelation exists in the data series, researchers suggests
moving to the modified Mann–Kendall test (Güçlü 2020).
Innovative Trend Analysis
To perform ITA, first the monthly mean rainfall of a subdivision (j) is split into two
subseries of equal numbers of observations. Then, each series is rearranged in
ascending order and plotted against the other into a Cartesian coordinate system
(Girma et al. 2020) wherein the first half is plotted on the x-axis and the second half
on the y-axis. In the third step, a straight line is fitted with the scatter plot that
represents ‘monotonic trend or no trend.’ If the scatter is concentrated above the 45
line (1:1), the time series exhibits an increasing trend; if the scatter points concentrate
below the 1:1 line, a decreasing trend is indicated (Cui et al. 2017). If the scatter
7 Comparison of Classical Mann–Kendal Test and Graphical Innovative Trend. . .
159
The data sets used for the current investigation consist of the average monthly
rainfall of 36 meteorological subdivisions from 1901 to 2015. The meteorological
subdivision rainfall data were collected from the open-source platform-https://water.
india.gov.in/content/water/en/waterresourcesdepartment/WaterManagement/
IWRM.html. The hydrological year in India starts in April and ends in March. The
missing data in the time series were observed less than 1%, which have been
calculated using multiple imputation methods. R 3.5.1 and Arc 10.3 software have
been used for statistical analysis and mapping purposes, respectively. The various
methods used in this study are described in the following sections.
Methods
In this study, to detect the trends in historical rainfall data, ITA (Şen 2012) is used.
Further, the results of ITA are equated with the MK test (Mann 1945; Kendall 1975)
or mMK test (Hameed and Rao). The slope of changes is estimated by Sen’s slope
estimator (Şen 1968). However, a modified Mann–Kendell test (mMK) (Güçlü
2020; Phuong et al. 2020) has been performed for the serially correlated dataset as
the performance of the ordinary MK test in such conditions is very poor and gives
erroneous estimations (Sharma and Goyal 2020) because these statistics increase the
risk of overestimates or underestimates of the Z statistic if the time series has
significant autocorrelation (Ay and Kisi 2015; Rahman et al. 2017). Therefore,
MK autocorrelation lag-1 should be executed first to confirm the reliability of the
Z statistic. If significant autocorrelation exists in the data series, researchers suggests
moving to the modified Mann–Kendall test (Güçlü 2020).
Innovative Trend Analysis
To perform ITA, first the monthly mean rainfall of a subdivision (j) is split into two
subseries of equal numbers of observations. Then, each series is rearranged in
ascending order and plotted against the other into a Cartesian coordinate system
(Girma et al. 2020) wherein the first half is plotted on the x-axis and the second half
on the y-axis. In the third step, a straight line is fitted with the scatter plot that
represents ‘monotonic trend or no trend.’ If the scatter is concentrated above the 45
line (1:1), the time series exhibits an increasing trend; if the scatter points concentrate
below the 1:1 line, a decreasing trend is indicated (Cui et al. 2017). If the scatter
7 Comparison of Classical Mann–Kendal Test and Graphical Innovative Trend. . .
159