**3. Study area**

**2.4. Mann‐Whitney‐Pettit test**

32 Groundwater - Contaminant and Resource Management

, Order {*X1, X2,…, Xt*

ì ï ï í ï ï î

significant changing point.

confidence level.

change point *Xt*

The Mann‐Whitney‐Pettit (MWP) test [32] can be used to search for significant change points in a data series. The definition of a change point is when a data series {*X1, X2,…, Xn*} has a

The definition of is as shown in Eq. (7) shown. If there is not a change point in the data series, |*Ut*,*<sup>n</sup>* | on the function of time, *t* will continue to rise, and there will be no turning point. On the contrary, if there is a change point, |*Ut*,*<sup>n</sup>* | on the function of time *t*, there will be a decreasing turning point. In the same data series, the turning point may occur several times

( ) 0, 0 , ( ) , 1 1 1, 0

To confirm that change points exist, Eq. (8) is used to calculate the extreme value of |*Ut*,*<sup>n</sup>* | that is turning point as *Kn*>. Equation (9) is used to calculate the probability of a change point. In this study, *P* = 0.95 is set the as confidence level, where *P* > 0.95 judges that the time is a

2

, 2

2 3

æ ö ç ÷ ç ÷ ç ÷ ç ÷ è ø

*n n*

+

6

2 3

æ ö ç ÷ ç ÷ è ø

*n n*

However, in some data series, a change point may not exist by itself; thus, Eq. (10) is used to calculate each year's *P*(*t*) value. The *P*(*t*) value is identified when it is greater than the

+

<sup>6</sup> 1 exp *Kn <sup>P</sup>*


( ) 1 exp *Ut n P t*


*ij ij i j*


*Sign X X X X U Sign X X t n i jt X X*

on behalf of this data series, and there may be more than one change point.

1, 0

*i j*

*i j*

+ ->

*X X*

} is *F1*(*X*) and {*Xt+1, Xt+2, …, Xn*} is *F2*(*X*), then *F1*(*X*)*≠F2*(*X*).

*t n*

, *<sup>n</sup>* , 1 *K Max U t n t n* = £< (8)

(7)

(9)

(10)

The northern region of Taiwan includes several administrative districts, namely Yilan County, Keelung City, New Taipei City, Taipei City, Taoyuan County, and Hsinchu City. There are five types of terrains in this region: plains (mainly distributed in the Taoyuan Alluvial Fan and the Hsinchu Plain in the west, as well as the Yilan River Delta in the east); hills (mainly the Chutung Hill in Keelung); tablelands (the Linkou Plateau); basins (the Taipei Basin); and mountainous areas (the Tatun Mountain range in the north and the Central Mountain range). With these varied topographic features, this region ranges significantly in height from the <100 m above mean sea level (AMSL) plain areas to the <500 m AMSL hilly areas and to the >1000 m AMSL mountainous areas. The main rivers in the region are the Tamsui River, Lanyang River, Fengshan River, and Touqian River, with drainage areas of 2726, 978, 250.1, and 565.9 km2 , respectively. The annual average overall stream flow in the region is less than 15.1 billion m3 , which is less than that of the central, southern, and eastern regions. The data for the past several years indicate that the stream flow of the northern region during the dry season is different from that of the wet season. The total stream flow of the dry season (from November to April) is approximately 5.62 billion m3 ; while during the wet season (from May to October), it is 9.48 billion m3 [33].

The long‐term data on stream flow in Northern Taiwan were collected from the Water Resources Agency, Ministry of Economic Affairs. We selected stream flow stations that are not affected by artificial irrigation facilities and for which recorded data go as far back as 30 years. The eight gauging stations studied were Niudou and Ximen Bridge (Lanyang river basin); Fushan, Gaoyi, and Hengxi (Tamsui river basin); Xinpu (Fengshan river basin); and Neiwan and Shangping (Touqian river basin). Detailed information and geographical location of the various stations are shown in **Table 1** and **Figure 2**, respectively.


Note: a is Taiwan triangulation points' coordinates.

**Table 1.** Information on gauging stations in Northern Taiwan.

**Figure 2.** Spatial distribution of gauging stations in Northern Taiwan.
