Study area
The Pasur River bifurcates into two branches, the Shibsa River and the Pasur River, at Akram Point before entering the Bay of Bengal (Fig. 1b). The Chunkhuri Channel connects the Pasur River to the Shibsa River, approximately 70 km upstream from Hiron Point, at Chalna. The interconnecting channel complicates the morphology of the Pasur-Shibsa estuarine system (Fig. 1b) and likely contributes to complex water circulation (Shaha and Cho 2016).
The Pasur River is directly linked to the main freshwater source of the Ganges through the Gorai-Madhumati-Nabaganga-Rupsha-Pasur (GMNRP) river system (Fig. 1a) that acts as the largest freshwater supplier for the Sundarbans, the world’s largest mangrove ecosystem. The Ganges originates in the Himalayas and flows through India and Bangladesh and empties into the Bay of Bengal through the GMNRP river system.
Data
River discharge data from January to December in 2014 and 2019 were collected from a non-tidal discharge station (at 23.5396°N and 89.5159°E, Kamarkhali, Faridpur) on the Gorai River, which is operated by the Bangladesh Water Development Board (BWDB). The highest discharge occurs during the wet season, which extends from July to October (Fig. 2). By contrast, river discharge is negligible in the dry season (November to June). The bathymetric chart of the PRE from Harbaria to Chalna was collected from Mongla Port Authority. The tidal information was collected from Mongla Port Authority. The tidal height varied from 4 to 6 m.
The vertical salinity was collected using a conductivity-temperature-depth (CTD) profiler (Model: In-situ Aqua TROLL 200, In-situ Inc., Fort Collins, Colorado, USA). The longitudinal salinity transects were taken along the main axis of the Pasur River from Harbaria to Batiaghata. No research vessel was available to collect data from the downstream area of this strongly tidally influenced estuary, especially southward from Harbaria to the estuary mouth, where speed boats or mechanized boats are not allowed to operate because of safety concerns. Eight longitudinal transects at high water were taken during both spring and neap tides, covering the dry and wet seasons from Januray to December of 2014 and 2019 (Table 1). A global positioning system (GPS) was used to obtain the exact locations along the estuary. The nominal distance between stations was approximately 3 km owing to the low salinity gradient (~ 0.05 km−1) along the estuary. The seawater from the mouth of the PRE was collected by the vessel of Mongla Port Authority that is routinely used for carrying ship crew from Hiron Point. The salinity was 27.6 and 5.8 during the dry and wet seasons, respectively.
Table 1 Sampling scheme during spring and neap tides in dry and wet seasons in the Pasur River estuary Water samples were collected at selected depths (0–0.5 m, euphotic layer)) along and across the length of the estuary with a 1.5 L water sampler (Wildco instruments, Wildlife supply company, USA). The samples were gravity-filtered through glass-fibre filters (Whatman© GF/C) using a vacuum system, and subsequently filtered through hydrophilic polyvinylidene difluoride (PVDF) 0.47 µm pore-size syringe filters. The filtrates were stored in the dark and frozen until analyses could commence (i.e. within a week after sampling). The levels of dissolved inorganic nutrients (nitrate—NO3−, nitrite—NO2−, ammonium—NH4+, orthophosphates—PO43− and dissolved silicon compounds—DSi) were analysed with classic spectrophotometric methods (Grasshoff et al. 2009). Absorbance was measured by a spectrophotometer (Model: DR6000 HACH, USA). The water samples were analysed for soluble reactive phosphorus (PO43−) and ammonium (NH4+) using standard spectrophotometric methods (Parsons et al. 1984; Scor-Unesco 1966). Total oxidised nitrogen (NO3− and NO2−) was analysed using the reduced copper cadmium method. For classification purposes, inorganic nutrients were categorised as dissolved inorganic nitrogen (DIN≈ NH4+, NO3− and NO2−) and phosphorus (DIP ≈ PO43−).
Estuarine volume calculation
The study area of the PRE was selected from Harbaria to Chalna for calculating flushing time due to the availability of bathymetry and salinity data. The lowest-low-water bathymetric data were collected from the Mongla Port Authority. The 36 km-long study area was divided into 12 segments, and each segment comprised of 3 km (Fig. 3). The extended trapezoidal and Simpson's rules (Press et al. 1988; Yesuf et al. 2012) of Golden Software Surfer 11 (Golden Software Inc., CO, USA) were used to calculate the volume (Vi) of each segment at high water during both spring and neap tides. An approximate high-water depth was obtained by adding the tidal range of both spring and neap tides to the lowest-low-water depth. The segment volumes were calculated using the high-water depths H (x, y) as follows:
$$V_{i} = \int\limits_{{x_{\min } }}^{{x_{\max } }} {\int\limits_{{y_{\min } }}^{{y_{\max } }} {H\left( {x,y} \right)dxdy} }$$
(1)
where x is the length of the estuary and y is the cross-estuary width. The volumes (Vi) of each segment during both spring and neap tides is shown in Fig. 4. The volume of each segment ranged from 13.78 × 106 m3 to 45.93 × 106 m3 during spring tide, and from 11.89 × 106 m3 to 40.54 × 106 m3 during neap tide. The salinity (Si) for each segment (Vi) was determined by using the vertical mean salinity of the two CTD stations allocated.
Freshwater fraction method to calculate flushing time
Though there are many methods to calculate flushing time (Dyer 1997; Valle-Levinson 2010), the flushing time was calculated using freshwater fraction method in the present study. In this method, the freshwater volume is estimated from the measurements of salinity at different sections in an estuary.
If we assume a linear mixing process, the freshwater fraction f can be written as follows (Dyer 1997; Officer 1976; Officer and Kester 1991):
$$f_{i} = \sum\limits_{i = 1}^{n} {\left( {1 - \frac{{S_{i} }}{{S_{SW} }}} \right)}$$
(2)
where fi is the freshwater fraction, Ssw is the seawater salinity adjacent to the estuary mouth, Si is the salinity at given location inside the estuary, and n is the total estuarine segments. As estuaries constantly exchange with the sea, the flushing time is focused on the freshwater and its transport in estuaries. Therefore, the freshwater volume of particular section or an entire estuary is calculated using an integration over the estuarine volume (Shaha et al. 2012; Priya et al. 2012; Sridevi et al. 2015):
$$F_{i} = \sum\limits_{i = 1}^{n} {f_{i} V_{i} }$$
(3)
where Fi is the freshwater volume of each segment. The freshwater fraction approach, as in Eq. (3), can be applied not only to the whole estuary but also to different estuarine segments (Shaha et al. 2012; Valle-Levinson 2010; Williams 1986).
Therefore, the flushing time (T) of an estuary can be calculated as follows (Dyer 1997; Ji 2008; Officer 1976; Shaha et al. 2012; Williams 1986):
$$T = \frac{F}{{Q_{f} }} = \frac{{\sum\limits_{i = 1}^{n} {F_{i} } }}{{Q_{f} }}$$
(4)
where Qf is the freshwater discharge.
The flushing time (Ti) of each estuarine segment can then be calculated as follows (Shaha et al. 2012; Williams 1986):
$$T_{i} = \frac{{V_{i} }}{{Q_{f} }}\left( {1 - \frac{{S_{i} }}{{S_{sw} }}} \right) = \frac{{F_{i} }}{{Q_{f} }}$$
(5)
The flushing time is not inversely proportional to the freshwater inflow in Eq. (4), as the freshwater inflow also changes the mean salinity, which is determined by the complex hydrodynamic process in the estuary. Therefore, the selection of freshwater discharge rate Qf can be challenging because it is infrequently in a steady state. For instances, to calculate flushing time in the earlier research works, some researchers use the freshwater discharge on the day of field observation, some use an averaged discharge of few days before the field observation, and others use monthly or seasonally mean discharges (Alber and Sheldon 1999). The flushing time is different for each of these approaches. In the present work, the flushing times were calculated using the monthly median river discharge of the respective month of field observation. Qf was assumed constant for each segment. The segment flushing times were considered as a spatially varying flushing time. In the present work, we emphasized on the spatially varying flushing time calculated by the FFM, as done by Williams (1986) and Shaha et al. (2012). This is because no single flushing time of an estuarine system is valid for all time periods and locations (Monsen et al. 2002). Therefore, some earlier researchers (Monsen et al. 2002; Shaha et al. 2012; Uriarte et al. 2014) suggest that a spatially varying calculation of the flushing time is more accurate to examine the effects of river discharge and tidal amplitude on the estuarine water quality. To examine the effects of freshwater discharge on the spatially varying flushing time of the PRE, simple power-law functions were used.
Flushing time may also be estimated most simply as Vol /q, where Vol is the estuarine volume and q is the flow rate of water in or out of the estuary (Monsen et al. 2002; Sheldon and Alber 2006; Valle-Levinson 2010). For the relatively simple Vol /q approach, the required quantities may not be known for the aquatic system of interest. In such a case, the “e-folding” flushing time (FTe) may be calculated empirically with an exponential fit with salinity concentration Sc (Monsen et al. 2002). This approach assumes instantaneous and complete mixing within the basin and given its exponential form, implicitly assumes the introduced mass is never completely flushed.
$${FT}_{e}={S}_{c}\mathrm{exp}\left(-\frac{q}{Vol}t\right)$$
With this approach, t is the tidal period and only 63% (1 − e−1) of the initial mass has been flushed. Because the e-folding flushing time is an empirical approach, all processes helping the scalar to flush, including tidal dispersion, are implicitly included.