The daily rainfall data from 1988-2017 (30 years) of eight rainfall stations were

Fig 1 Map of the study area-showing flood inundated area

analyzed in this study (Table 1). The distribution of rainfall stations is shown in Figure 1. The rainfall data was acquired on request from Thai meteorological department, Thailand (TMD). The rainfall data was grouped into two 1988-2002 and 2003-2017 for further investigation of changes in spatial and temporal distribution over Uttaradit province. The changes over the province were observed with total annual rainfall, monsoonal rainfall and interpolation technique. Monthly average rainfall of two periods was used to investigate the temporal changes in precipitation [9].

Mann-Kendall is rank based non-parametric trend test was developed by [10] [11]. It is a commonly used the test to detect linear or nonlinear trend in time series data. It is based on two hypotheses, one is null (H₀) and the other is known as alternative hypothesis (H₁). The null hypothesis (H₀) confirms the nonexistence of any trend while the H₁ shows the existence of the trend in time series data. The MK is derived using the following equation:

S = ∑ i = j n − 1 ∑ j = i + 1 n sgn ( x j − x i ) (1)

where

sgn ( x j − x i ) = { + 1 ,         x j > x i 0 ,             x j = x i − 1 ,         x j < x i (2)

The statistics of variance has been calculated as:

V a r ( S ) = 1 18 [ n ( n − 1 ) ( 2 n + 5 ) − ∑ p = 1 q t p ( t p − 1 ) ( 2 t p + 5 ) ] (3)

Z M K = { S − 1 V a r ( S )       if   S > 0 0                               if   S = 0 S + 1 V a r ( S )       if   S < 0 (4)

In Equation (1) x i and x j are the observational data of the time series in the years i and j, n denotes the number of observation in the data series, t p is the number of ties for the pth value, and q denotes the number of tied values. The Z M K values can come both in positive and negatives, the positive shows the increasing trend while negative values indicates the decreasing trend in time series data. There are two hypotheses: one is the null hypothesis of no trend and the alternative hypothesis indicating significant trend in the data. When | Z M K | > Z 1 − α / 2 , the H₀ is rejected and H₁ is accepted that means a significant trend exists in the time series. Z 1 − α / 2 is the critical value of Z from the standard normal table, Z 1 − α / 2 value is 1.96 for 5% significance level.

Sen’s slope estimation test has been commonly used for climatic data [12] [13]. In this study, SS method was used for precipitation data for estimation of its slope. The slope of entire, associated data [14] was computed as:

F ( t ) = Q t + B (5)

Here, Q specifies slope, while B is a constant value. In order to get the slope estimation (Q), initially the slopes (value) of the entire time series data was calculated:

Q i = X i − X j / j − k (6)

In the above Equation (6), i = 1 , 2 , 3 , 4 , ⋯ , N , whereas, at time j and k (j > k), X_j and X_k are the values of data pairs, respectively. The median of N values of T_i has been expressed as the SSE, given as:

Q m e d = { Q [ ( N + 1 ) / 2 ]                                       if   N   is   odd Q [ N / 2 ] + Q [ ( N + 2 ) / 2 ] 2         if   N   is   even (7)

Therefore, if N appears odd, SS is analyzed as Q m e d = T ( N + 1 ) / 2 . However, if it appears even, then SS will eventually be analyzed as Q m e d = T ( N / 2 ) + T ( N + 2 ) / 2 . Thus, Q_med is computed to get the slope magnitude using non-parametric model. If Q_i is positive, it shows increasing trend while negative Q_i represents decreasing trend in time series data analysis.

Several indices like SPI, VCI, TCI, SPEI, RDI, PDSI and SSI etc. by drought experts to analyze drought condition and severity in an area [15] - [21]. In this study SPI is applied to assess drought condition in the study area. This index was first used and developed by McKee et al. (1993). SPI require only long term precipitation data to analyze the drought in an area [22] [23]. This index is considered more reliable for heterogeneous topographical area and can assess drought for different time scales [24]. The SPI and its categories are given below in (Table 2). Mathematical formulation of SPI is given below:

SPI = X − x ¯ σ [25] (8)

where X is the monthly precipitation, x ¯ is mean of monthly precipitation data and σ represents standard deviation. SPI were calculated by using SPI_SLX6 calculator. Table 1 shows the threshold values for different intensities of drought.

In this study trend analysis method was applied to annual and monsoonal rainfall over the eight rainfall stations and it was revealed from the trend that in near future the amount of rainfall will be decreasing. The average annual rainfall for the periods of 1988-2002 and 2003-2017 are 1179 and 1003 mm respectively.

It can be easily observed that amount of rainfall decreased by 14.92% from first half to the second and 15.50% of monsoonal rainfall decreased from 1988-2002 to 2003-2017. The total average annual rainfall during 1988-2017 is 1091 mm and it is estimated using linear regression method that by 2030 it will drop to 700 mm, which is 35% decrease from the average annual rainfall of 1988-2017. The average monsoonal rainfall between 1988-2017 is 956 mm and it is predicted using linear regression method that by 2030 it will drop to 630 mm. Trend analysis results are in good agreement with a study in North-Eastern Thailand [26] and are shown in Figure 2.

These predictions are indicating the rainfall shift; the amount of rainfall is rapidly decreasing in monsoon period as compared to annual rainfall. These alarming changes showed that the study area will face more severe meteorological drought conditions in the near future. These findings are useful for disaster managers, concerned government organizations and decision makers to take the necessary step in its response.

The time series of annual rainfall over eight rainfall stations plotted to represent the variation in rainfall crossways in the province. As the annual rainfall from 1988-2017 showed a decreasing trend but the variation (spatial variability) in rainfall showed an increasing trend from its first half to the second by 19.57%.

In this study, precipitation data of eight meteorological stations of Uttaradit province was analyzed to assess the trend. The results (Table 3) of all stations

shows negative Z M K values except Fakara met-station, it means there is a decreasing trend in the amount of rainfall. Except Tambon Tha Pla met station and no other met-station shows any significant trend.

The MK trend analysis was applied to seasonal rainfall to assess the trend and results shown that in winter season five station shows negative Z M K values and three stations (Ban Khok, Thong Saen Khan, & Fakara) shows the increasing trend (Figure 3(b)) but not a single met-station showed any significant increasing or decreasing trend. Moreover, when MK trend analysis was applied to summer season the same trend was found as of the annual rainfall but in summer season the met-station Tambon Tha Pla shows more significant decreasing trend in the amount of precipitation (Figure 3(c)). In monsoon season the amount of precipitation increase at the met-stations of ThaPla and Fakara. All other stations show decreasing trend but there is no significant trend found in amount of rainfall (Figure 3(d)). It means overall there is decreasing trend which is in a good agreement with the previous study [26].

Sen’s slope estimation test was applied to all meteorological stations for the annual, and three seasonal rainfall (Table 4). Sen’s slope estimation test applied to Q_annual, and results revealed that Fakara is the only station which adores the positive and the topmost slope magnitude (Q = 3.375), which is followed by ThaPla station (Q = −2.225). Except Fakara station, other seven stations show negative and fluctuating slope magnitude (Table 4; Figure 4(a)). Likewise, SS estimation test was applied on all met stations of Q_winter, and results discovered that Fakara met-station has the uppermost slope magnitude (Q = 0.775), followed by Ban Khok station (Q = 0.605). Thong Saen Khan and ThaPla have rather smaller values comparatively (Q = 0.475 and −0.07) respectively. Laplae met station which is at high elevation grasp the lowest slope magnitude i.e. Q = −0.594 (Table 4; Figure 4(b)). Using SS estimation test for Q_summer, results revealed that all stations have negative trend except Fakara met station which did not show any trend (Q = 0) but this station showed topmost and positive trend in Q_annual

Note: *Q is the Sen’s slope estimation for annual and seasonal rainfall.

and Q_winter, respectively (Table 4; Figure 4(a) & Figure 4(b)).

The lowermost slope magnitude (Q = −12.635) in Q_summer for Tambon Tha Pla station which is on the moderate elevated area. Correspondingly, by testing SS estimation on Q_monsoon on all meteorological stations, Fakara retains the superior slope magnitude (Q = 1.694), which is followed by ThaPla (Q = 0.428). The lowest slope magnitude retains by Tambon Tha Pla met-station (Q = −21) and other lasting met-stations specify inconsistency in case of Q_monsoon (Table 4; Figure 4(d)).

Spatial trend of average annual, monsoonal, summer and winter season rainfall distribution during 1988-2017 was assessed and presented into two groups 1988-2002 and 2003-2017 in Figures 5(a)-(f). Spatial trend of rainfall was

assessed using spline interpolation technique. It is clear from Figure 5(a) that average annual rainfall during 1988-2002 showed a rising trend from east to west and southwest; though, during 2003-2017 (Figure 5(d)) the magnitude of rainfall rising towards the west and north. The extent of average annual rainfall through 1988-2002 is higher than the period of 2003-2017 by 1100 mm.

The trend of monsoonal season rainfall during the periods of 1988-2002 and 2003-2017 are rising in southwest direction (Figure 5(b) and Figure 5(e)) but the amount of rainfall decreased from first period to second period by 500 mm. In summer and winter season, the average rainfall rising towards southwest for the period of 1988-2002 (Figure 5(c)) but for the period of 2003-2017 it is rising towards the north part (Figure 5(f)) and amount of rainfall decreased from first period to second period by 248 mm. The comparison of average monthly rainfall between 1988-2002 and 2003-2017 studied and showed in Figure 6. The differences in distribution of average monthly rainfall between the two dated showing that monsoonal season (May-October) receive more than 80% of average annual rainfall.

The average monthly rainfall is decreasing from the period of 1988-2002 to 2003-2017. There are two peaks in the first period, in the months of May and August; however, in the second period the peaks were found in the months of August and September (Figure 6). The average monsoonal season rainfall decreased by 15.26% from first period to the second. The trend of average monthly rainfall of the wet season (Monsoon) is exposing that it is moving towards the dry conditions and in near future the province will face the meteorological drought.

SPI for 12-month return period is used to assess the drought condition in an area that prevails for more than two seasons. It takes accumulated precipitation of whole year. Figure 7 indicates that the drought conditions in the Uttaradit Province are not the same both in temporal and spatial dimension. The Thong Saen Khan rainfall-station witnessed severe drought in 1996, 1997, 2017 and moderate drought in 2015. In the Ban Khok rainfall-station moderate drought was found from the analysis in the years of 2005, 2006, 2007 and 2017. Similarly, in Fakkai rainfall-station two moderate drought years (2006, & 2015) and three severe drought years was 2010, 2014 and 2017.

Similarly, the severe drought condition was also witnessed in Fakraa rainfall-station during 1988-2015 in the years of 1988, 1989 and same like other station in 2017 as well. In the rainfall-stations of Laplae, Huai Mo Mun and Tha Pla the year of 2017 witness the history extreme drought in the study region. Laplae also witnessed severe drought in 2015 and moderate drought in 2016. While the situation of drought in Tambon Tha Pla rainfall-station was totally different from other stations as up to 2011 the rainfall situation was more than higher than normal in almost all years but after 2011 there is a consecutive moderate type of drought prevailing in the area.