The Mann-Kendall test is a notable test among the non-parametric tests widely used to analyse the trend of a time series phenomenon (Mann, 1945; Jeremy, 1987; Das et al.2019). This test is useful for analysing the trend of time series data especially when the sample size is small. The test statistic(S) of the series x₁,x₂, x₃…., and x_n are calculated using equation:

1S=∑k=1n-1⋮∑j=k+1nsign(xj-xk)

Where n is the quantity of data points, sign signifies signum work x_j and x_k represents data points of time j and k.

2Signxi-xk=+1 if xi-xk>00 if xi-xk=0-1 if xi-xk<0

The variance of S, VAR(S) is computed by the following equation:

VAR(S)=118n(n-1)(2n+5)-∑p=1gtptp-12tp+5 (3)

Where, ‘g’ denotes the quantity of tied group’s number which is a set of sample data with similar value and t_p denotes the extend of p^th tie number.

The estimation of (S) and VAR(S) are used to estimate process the standardized test measurement Z as:

4Z=(S-1)Var(S), if S>00, if S=0(S+1)Var(S), if S<0

Positive and negative Z value indicates increasing and decreasing trends. The test contains two hypotheses null (H₀) hypothesis meaning ‘no trend’ in series and alternative (H₁) hypothesis indicating an upward or downward trend. Null hypothesis is rejected if the |Z| value is greater than Zα/2 (at α=0.001, α=0.01 and α=0.05 respective significance level) (Mann, 1945; Das et al.2019). In the present study the null hypothesis is tested at 95% confidence level.

Sen’s slope is another non-parametric test which gives quantity of slope (magnitude) in a time-series data. (Sen, 1 968; Pal et al.2017; Das et al.2019). To find the slope estimate (Q), the slopes of N pairs of data are computed using the following formula:

Qi= xk-xjk-j, i=1,2,……..N, k>j (5)

Where, x_k and x_j are the values of data at time k_j and k_i is the median slope respectively.

In the present study, test statistic in both tests is significant at 0.05 level.

The mean annual rainfall was computed by taking the sum of twelve-month long term monthly mean. The average annual precipitation of the Nambiyar watershed is 1027 mm and it varied from 639.6mm to 1881.3mm. The relief of a region was one of the most important factors which influenced the rainfall distribution. The two stations Balamore and Keeiparai located in the northwestern part of the watershed which lies in the Western Ghats receives highest annual rainfall throughout the year. Out of the four stations, Northeast Monsoon season had significant influence in the rainfall distribution all over the watershed, where it contributed about 47 per cent of the total rainfall received in that area. Southwest monsoon constituted around 30 per cent of the total rainfall received in the watershed. During summer through convectional rainfall, the watershed received rain and its contribution was about18.23 per cent and the winter season comes with a low percentage share which is 5 per cent of total annual rainfall. The Figure 2 illustrated the distribution of average rainfall in the watershed.

Figure 2

The following Table 1 showed the results of Mann-Kendall and Sen’s slope estimated for mean annual rainfall of different stations in Nambiyar Watershed.

The calculated Z values for the annual rainfall among different stations indicate there is no significant trend in temporal precipitation in the study area. The Sen’s slope estimate gives the magnitude of trend which is useful for identifying the linear relationships. Considering the Q values it is evident that four stations Keeriparai (-4.10 mm), Nanguneri (-4.11 mm), Radhapuram (-4.38 mm), and Sathankulam (-1.91 mm) shows negative Q values which implies a negative trend in the quantity of rainfall received. Kendall Tau value gives the correlation strength between the ranks of two variables considering the positive and negative values. These same stations exhibit a negative Kendall tau value indicating a negative trend between year and amount of rainfall received in these stations. The Figure 3 represents the Z and Q values calculated for all rainfall stations in Nambiyar Watershed. The Table 2 and Figure 3 shows the graphical representation of annual rainfall trend in Nambiyar Watershed.

In the present study it is evident that the winter season contributed (5 per cent) less amount of rainfall (47 mm) to the annual precipitation. In this season rainfall varied from 36.70 mm to 56.20 mm recorded in Panakudi and Nanguneri stations, respectively. Winter rainfall showed a decreasing spatially from from north to southern portion of study area.

The mean rainfall of the summer season constituted about 187.14 mm (18.23 per cent) of the total rainfall of the area. The amount of summer rainfall varied from 109.72 mm at Sathankulam to 369.79 mm at Keeriparai. The spatial pattern of summer rainfall showed a decreasing trend from Western Ghats in western portion towards the coastal region in the eastern part of the watershed.

The southern part of the country received more amount of rainfall from the Arabian Sea branch of the southwest monsoon. Even though major portion of Tamil Nadu state received more rainfall during the northeast monsoon, some districts in the western and southern part of the states were more influenced by the southwest monsoon. The western part of the Nambiyar watershed had received more rainfall from southwest monsoon which constitutes around 30.22 per cent (310.31 mm) of total rainfall.

The northeast monsoon also called as retreating monsoon starts form October and last till December. Most of the interior parts of Tamil Nadu received heavy rainfall from the northeast monsoon. The Nambiyar watershed also received abundant rainfall from the northeast monsoon which varies from 647.99 mm in Keeriparai to 393.31 at Radhapuram. The watershed receives more rainfall from northeast season i.e is 47 per cent (482.57 mm) of total rainfall. The Figure 4 illustrates the distribution of average rainfall in the watershed during different seasons.

Figure 4

The Mann Kendall and Sen’s slope was estimated to analyse the signigicance and magnitude of trend for each season in all stations. In general, all the seasons does not exhibit a significant trend in the rainfall over all stations.However, as an exception Winter, Summer and Southwest monsoon shows an significant incerasing trend in Kalakkadu station.It is evident that magnitude of winter rain is incerases with time except in Sathankulam station where it declines at a rate of -0.28 mm (Sen’s slope Q Value) annually.Similarly, quantity of summer rain decreases at a rate of -0.67 mm, and -0.49 mm at Nanguneri and Radhapuram respectively.

The quantity of southwest monsoon exhibits a declining trend in Keeriaparai(-8.98 mm),Nanguneri (-1 mm ), Sathkulam (-1.60 mm) stations. Eventhough northeast monsoon does indicate any significant trend all the stations have upward magnitude of rainfall except for Radhapuram station where it is decreasing at a rate of -1.72 mm (Sen’s slope Q value). The estimated Mann Kendall statistic, Kendall Tau and Sen’s slope value of different seasons are given in the Table 3 and represented in the Figure 5.

The months of January, February and March received average rainfall of less than 50 mm which constitutes 5 per cent of the total annual rainfall. During the month of May the watershed received greater amount of rainfall from convectional rains i.e an average of 75 mm which is 7.36 per cent of the total annual rainfall. The June month recorded highest rainfall among southwest monsoon months i.e an average of 100.39 mm and constitutes about 9.78 per cent of total rainfall. The monthly rainfall of June varies form 8.46 mm in Sathankulam to 174.84 mm in Balamore. Since the watershed receives more rainfall in northeast monsoon November month records highest average rainfall of about 217.52 mm which is 21.18 per cent of total rainfall. During the November month rainfall varies from 196.74 mm in Sathankulam to 248.68 mm in Keeriparai. The spatial distributions of rainfall in watershed during twelve months are shown in Figure 6.

Figure 6

The Mann Kendall test and Sen’s slope estimated for different months of all stations reveals that particular months exhibit a significant upward trend of temporal rainfall distribution in the Nambiyar Watershed.

The Mann Kendall test and Sen’s slope estimated for different months of all stations reveals that particular months exhibit a significant upward trend of temporal rainfall distribution in the Nambiyar Watershed. The rainfall recorded in March and December months shows an increasing significant trend with a magnitude of 1.25mm (Q Value) and 1.64mm (Q Value) respectively at Balamore station. The temporal pattern of rainfall received in month of January and March exhibits a significant upward trend at the rate of 0.24mm and 0.59mm (Q Values) at Kalakkadu station. Even though rest of the months does not exhibit significant trend magnitude of the rainfall shows an upward trend. The rainfall received during the month of May, July and December reveals the existence of significant increasing trend at Keeriparai station. The Q values estimated for the months of April (-1.40mm), June (-1.40mm), (-5.01mm), September (-2.82mm) and October (-4.86mm) indicate a fall in the quantity of rainfall in this station. At station Nanguneri, temporal rainfall does not reveal any significant trend. The Sen’s slope estimation of this station indicates the fact that for most of the months such January, February, March, May and August magnitude of rainfall is constant. Also a decreasing trend in magnitude is visible in months of April (-0.77mm), June (-0.07mm), July (-0.25mm) and October (-1.06mm). The rainfall trend is positively significant only for the month of December in Panakudi. During other months magnitude of rainfall is either constant or shows a upward trend. The rainfall received at Radhapuram is highly randomized where no months show any presence of trend.

The month of September exhibits significant negative trend where rainfall is decreasing at a rate of -0.72 (Q Value). Also rainfall pattern during April, May and November months exhibit downward magnitude in the quantity of rainfall. The estimated Mann Kendall statistic, Kendall Tau and Sen’s slope value of different seasons are given in the following Table 4.