**3. Data and methods**

#### **3.1. Data**

There are 18 rain gauge stations, including one meteorological station in Rajshahi in the study area. However, 15 stations have long-term (1971–2011) good records (**Figure 1**). Rahman et al. [8] collected rainfall data from the Bangladesh Water Development Board (BWDB) and meteorological data from the Bangladesh Meteorological Department (BMD). The study prepared a complete rainfall dataset by estimating missing values by Multiple Imputations Method. Moreover, data of Bogra meteorological station have also been analyzed as it is located very close to the study area. Details regarding the rainfall data can be found in Rahman et al. [8]. There are about 150 groundwater monitoring wells in the study area. However, only 15 wells have long-term (1971–2011) good records and 73 monitoring stations have good records for the period of 1991–2011 (**Figure 1**). These data have also been collected from the BWDB. Details of groundwater level monitoring data can be found in Rahman et al. [7, 9].

#### **3.2. Methods**

Rainfall climatological characteristics, such as rainfall seasonality index, (SI) has been calculated by Walsh and Lawer [12] formula. Time series of seasonality index (¯ SIk ) and precipitation concentration index (PCI) have been estimated by Pryor and Schoof [13] and Oliver [14] formulas, respectively.

#### *3.2.1. Trend analysis*

In the present study, trends have been detected by non-parametric Mann–Kendall [15, 16] (MK) test. MK test shows a good performance for identifying trends in hydrological variable [7–9]. If there is a significant serial correlation at lag-1 in the climatic data, MK test cannot calculate the exact value of test statistic [17]. In the study, lag-1 serial correlation has been evaluated before analyzing the trends. If there is a significant serial correlation at lag-1, the trend free pre-whitening method [17] has been applied to eliminate the influence of serial correlation before estimating the test statistic (Z). Moreover, the sequential values of the MK test have been used [18] to find out the change point. The rate of change has been calculated by Sen's slope estimator [19]. The details of the methods can be found in [7–9, 15–19].

#### *3.2.2. Drought risk ranking*

(BT). There exists a significant lithological variation in the BT and the adjacent floodplain areas. BT is comprised of thick clay surface lithology which is underlined by thick coarser sediments of Early Pleistocene to Late Paleocene. The materials are dense and compact, and the hydraulic conductivity of the surface clay layer is low [11]. Two different aquifer units have been identified based on hydro-stratigraphic data in the area [11]. The upper-shallow aquifer exists just beneath thick surface silty clay layer. The thickness of this aquifer ranges from 10 to 35 m and it consists of very fine-to-fine sand with lenses of fine to medium sand and occasionally clay, silt, and trace mica lenses. Below the upper-shallow aquifer, there is a lower-shallow aquifer. The thickness of this unit ranges from 20 to 70 m, and it is composed

There are 18 rain gauge stations, including one meteorological station in Rajshahi in the study area. However, 15 stations have long-term (1971–2011) good records (**Figure 1**). Rahman et al. [8] collected rainfall data from the Bangladesh Water Development Board (BWDB) and meteorological data from the Bangladesh Meteorological Department (BMD). The study prepared a complete rainfall dataset by estimating missing values by Multiple Imputations Method. Moreover, data of Bogra meteorological station have also been analyzed as it is located very close to the study area. Details regarding the rainfall data can be found in Rahman et al. [8]. There are about 150 groundwater monitoring wells in the study area. However, only 15 wells have long-term (1971–2011) good records and 73 monitoring stations have good records for the period of 1991–2011 (**Figure 1**). These data have also been collected from the BWDB. Details of

Rainfall climatological characteristics, such as rainfall seasonality index, (SI) has been calcu-

tion concentration index (PCI) have been estimated by Pryor and Schoof [13] and Oliver [14]

In the present study, trends have been detected by non-parametric Mann–Kendall [15, 16] (MK) test. MK test shows a good performance for identifying trends in hydrological variable [7–9]. If there is a significant serial correlation at lag-1 in the climatic data, MK test cannot calculate the exact value of test statistic [17]. In the study, lag-1 serial correlation has been evaluated before analyzing the trends. If there is a significant serial correlation at lag-1, the trend free pre-whitening method [17] has been applied to eliminate the influence of serial correlation before estimating the test statistic (Z). Moreover, the sequential values of the MK test

SIk

) and precipita-

of medium to coarse grain sand with occasional fine sediment lenses.

104 Achievements and Challenges of Integrated River Basin Management

groundwater level monitoring data can be found in Rahman et al. [7, 9].

lated by Walsh and Lawer [12] formula. Time series of seasonality index (¯

**3. Data and methods**

**3.1. Data**

**3.2. Methods**

formulas, respectively.

*3.2.1. Trend analysis*

Our previous study characterized the drought in the study area [8] using the standardized precipitation index (SPI) [20]. Drought risk ranking is necessary to prepare the viable adaptation measures of an area. This study has ranked the risk of drought using the drought risk ranking diagram [21] to know the risk condition of the area.

#### *3.2.3. Groundwater recharge and abstraction*

The groundwater budget of an area can be written as [22]:

$$R = \ \Delta S^{gv} + \mathcal{Q}^{b\dagger} + ET^{gv} + \left(\mathcal{Q}\_{out}^{gv} - \mathcal{Q}\_{in}^{gw}\right) \tag{1}$$

Here, *R =* recharge; ∆*S gw* = change in groundwater storage; *Qbf* = baseflow to river channel; *ETgw* = evapotranspiration from groundwater, and *Qout gw* − *Qin gw* = net subsurface flow from the area. The *Qbf* and *ETgw* are negligible for Bangladesh as river stage during the monsoon is higher than the groundwater level and land cover dominated by the shallow rooting depth crops [23]. Moreover, groundwater flow (*Qout gw* − *Qin gw*) is also negligible due to the absence of substantial hydraulic gradients in water level in shallow aquifer during monsoon [24]. Shamsudduha et al. [23] simplified Eq. (1) and calculated groundwater recharge (R) as:

$$\mathcal{R} = \Delta S^{\text{op}} = S\_y \frac{\partial h}{\partial t} = S\_y \frac{\Delta h}{\Delta t} \tag{2}$$

where, *Sy* is the specific yield, ∆*h* is the water-level height between annual maxima and minima, and ∆*t* is time period (a year). Eq. (2) is similar to water table fluctuation (WTF) method and recharge is referred as "net" recharge [25]. In WTF method, ∆*h* is the difference between the peak water level and the theoretical lowest level [25]. However, Shamsudduha et al. [23] calculated ∆*h* as an annual range between the annual maxima and minima from weekly measured data. Groundwater recharge calculation using Eq. (2) did not provide good results for recent periods (1985–2007 and 2002–2007) for some particular areas (Dhaka City and BT) as the seasonality in groundwater fluctuation suppressed by the long-term trend associated with intensive abstraction [23]. For these areas in Bangladesh, net groundwater recharge was calculated [23] as:

$$\mathcal{R} = \Delta S^{\otimes n} + \mathcal{Q}^{\mathcal{P}} \tag{3}$$

where *Q<sup>P</sup>* is the annual groundwater abstraction. In the study, groundwater recharge has been calculated by Eq. (3) for the BT. However, *Q<sup>P</sup>* is the groundwater abstraction for supplementary irrigation during the rainy season as a huge amount of groundwater withdrawn during the dry season for *Boro* rice cultivation about 1 m per square meter in Bangladesh [24, 26]. Therefore, adding the annual groundwater abstraction misleading the net recharge calculation.

The groundwater abstraction for irrigation in Bangladesh estimated from the irrigated proportion of the surface area and the amount of water applied to an irrigated field during the growing season [24, 26]. The time series data of the total irrigated area of the greater Rajshahi district, which includes the study area and Natore district, have been collected from the book published by Bangladesh Bureau of Statistics (BBS) for the period of 1993–2010. The groundwater abstraction has been calculated as the irrigated area is multiplied by an estimated 1.0 m [24] of abstraction per pumping season per square meter of irrigated area.

confidence levels are found in Rajshahi (−8.02 mm/year) and Mohadevpur (−10.82 mm/year) stations, respectively. On the other hand, a significant increasing (+11.17 mm/year) trend is found in Nawabganj at 99% confidence level. The plots of sequential MK test statistics of u(d) and u′(d) (**Figure 3a**–**c**) indicate downward trends started in 1981 and 1988 in Rajshahi and Mohadevpur, respectively, and significant upward trend in Nawabganj starts in 1991. The spatial distribution of the Z statistic reveals that the declining trend mostly occurred in the eastern part of the area (**Figure 2b**) and magnitude (slope Q) varies from −0.25 to −10.82 mm/year (**Figure 2c**). Significant negative trends are detected in the northeast and southeast. However, the majority of the stations located in the BT shows insignificant positive trends. The projected rainfall of Bangladesh at different emission scenarios shows an increase in rainfall, but the

Sustainable Groundwater Management in Context of Climate Change in Northwest Bangladesh

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107

Trend analysis of seasonal rainfall shows a declining trend in rainfall for all seasons. The estimated Z statistics are −0.94, −0.12, and −2.13 for winter, summer, and rainy seasons, respectively. The declining trend in rainy season rainfall in the area is significant at 95% confidence

**Figure 2.** Distribution of (a) annual rainfall, (b) Z statistic of annual rainfall, and (c) Sen's slope (*Q*) of annual rainfall.

**Figure 3.** Sequential MK statistic u(d) and u′(d) of annual rainfall (a) Rajshahi, (b) Mohadevpur, and (c) Chapai Nawabganj.

study found decreasing rainfall in Rajshahi [21].

*4.1.2.2. Seasonal rainfall*

#### *3.2.4. Vertical electric soundings (VES)*

Vertical electric soundings (VES) survey following the Schlumberger electrode configuration using a direct current resistivity meter has been carried out in six areas in Nachole Upazila (**Figure 1**) in Chapai Nawabganj district. The VES data has been analyzed using resistivity meter compatible software IGIS 2.0 which follows the inverse slope method for analyzing the resistivity data. Inversion is a mathematical iterative process and study [27] showed that the inverse method is quite a powerful scheme to interpret the resistivity data. Two bore holes have also been done and bore logs data have been used for validation of the lithology interpreted from resistivity data. These bore holes later have been used as MAR wells (**Figure 1**).
