The calculation of flushing time for the upper Pasur River Estuary, Bangladesh

Estimation of estuarine flushing time, a time required to transport of pollutants or any other properties from estuaries to the coast, is very important for its resource management. In this study, we estimated flushing time (T) of the upper Pasur River Estuary (UPRE) for understanding the water quality condition in the dry and wet seasons. High-resolution salinity data were collected from the PRE at high water in the dry and wet seasons in 2014 and 2019. Flushing time was calculated using the freshwater fraction method (FFM) as well as e-folding flushing time scales was estimated empirically using the salinity (non-reactive conservative) and monthly river discharge data. System flushing during the dry season was thirteen times weaker than flushing during the wet season owing to decreasing river discharge by nearly 94%. In addition, the daily exchange volume was decreased by eight times during the dry season than during the wet season. As a consequence, the conditions of the UPRE are more dynamic during the wet season due to receiving huge amount of river discharge. During the dry season, only the e-folding time scales showed higher values in the salinity maximum zone (salt plug area). This implied that the e-folding time scale is an empirical approach and was able to encompass the tidal dispersion process whereas the FFM was unable to include that process. As the PRE is a macrotidal estuary, the tide assists to flush dissolved substances from the UPRE to the coast during the dry season having negligible river discharge. In addition, there was no significant variation in water quality parameter between the salt plug area (SP) and downstream of salt plug area (DSP) during the dry season. In order to have more accuracy, a three-dimensional hydrodynamic model would be useful to compute estuarine time scales precisely. The daily exchange volume decreased by eight times during dry season. Salt plug did not trap nutrients and deteriorate water quality. The e-folding flushing time scale included the tidal dispersion process. The daily exchange volume decreased by eight times during dry season. Salt plug did not trap nutrients and deteriorate water quality. The e-folding flushing time scale included the tidal dispersion process.


Introduction
Flushing time is defined as the time required to replace the existing freshwater in an estuary at a rate equal to the river discharge As pollutant loadings are often linked to freshwater inflows, the flushing time describes a general feature of the estuary and is often used to estimate the removal rate of a pollutant carried by freshwater (Ji 2008). In general, the tidal exchange between the system and the

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Terrestrial, Atmospheric and Oceanic Sciences Page 2 of 15 Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 adjacent sea, the river discharge, stratification, bathymetry, and wind control the flushing time of a given system (Choi and Lee 2004;Ji et al. 2007;Pilson 1985). The low flushing time keeps an ecosystem free from the adverse effects of pollutants to a great extent. On the other hand, if flushing time is longer, pollutant requires long time to flush from an estuary which in turn may cause pollution (Ji 2008;Valle-Levinson 2010). For instances, the month-long flushing time caused the eutrophication and hypoxia/anoxia in the Chesapeake Bay for most of the anthropogenic nutrients discharged into the system (Cerco and Cole 1993). Typical flushing times range from days in small estuaries to months in large estuaries during low flow conditions (Ji 2008). There are numerous time scales relevant to biological and physical understanding of an estuary that are often used to characterize a system (Lucas 2010). Quantifying these time scales is especially necessary for understanding the potential exposure and risk from an industrial accident. Bulk time scales include the flushing time, freshwater turnover time, salinity turnover time, and the e-folding flushing time. Flushing time is a bulk or integrative parameter describing the general exchange characteristics of an estuary without identifying detailed underlying physical processes or their spatial distribution (Monsen et al. 2002). Flushing time may 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). In river-dominated systems, q may be approximated by R (river flow). 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 may be calculated empirically with an exponential fit to the concentration of salinity (Monsen et al. 2002). A three-dimensional hydrodynamic model is used to compute estuarine time scales including the turnover, e-folding time, the age and residence time of Galveston Bay, a low-flow, partially stratified estuary. Time scales are computed for river flow varied by several orders of magnitude and exhibited significant temporal variability because of the unsteadiness of the system (Rayson et al. 2016). The flushing times for a number of segments of the Sumjin River Estuary (SRE) was determined using the freshwater fraction method (FFM) with a spatially varying freshwater fraction in order to examine the effects of freshwater discharge and tidal amplitude on the spatially varying flushing time (Shaha et al. 2012).
The Pasur River is an important river for the world's largest Sundarbans mangrove ecosystem, irrigation, urban water supply and industry (Mirza 2004) in the southwestern coastal zone of Bangladesh. However, due to construction of Farakka barrage upstream of the Padma River (Fig. 1), the freshwater flow has decreased to a post-barrage mean flow of 10 m 3 s −1 in 2008 (Islam and Gnauck 2011) from a pre-barrage mean flow of 190 m 3 s −1 in 1973 during the dry season in the Pasur River estuary (Mirza 2004). Consequently, salt water intrusion has extended as far as ~ 164 km (29 March 2014) from the estuarine mouth (at Hiron Point) to a head at Lohagara (Narail District), during the spring tide in the dry season (Shaha and Cho 2016). In addition, the salt plug was formed near Chalna in the PRE by exporting salt water from the Shibsa River Estuary to the PRE through the Chunkhuri Channel when small river discharge occurred during the dry season (Shaha and Cho 2016). During the last two decades, the discharging rate of effluents into the Pasur River system from the third largest industrial city (Khulna) has increased to about 10 million gallons day −1 (World Bank 2006). Besides, the recent trend of heavy metals bioaccumulation in fish of the PRE has adversely affected the fishing industry (Samad et al. 2015;World Bank 2006). Though heavy metal concentrations such as Zn, Pb, and Mn in water and fish of the PRE are within the permissible limits, the bioaccumulation factor indicates that fish consumption from the PRE is likely to exert health hazards for human being (Samad et al. 2015). A long residence time of heavy metals in the PRE can increase the bioaccumulation rate in fish. However, no information is available on the transport timescales, such as flushing time, of the PRE to describe the time scales for transport and removal of materials. Being an ecosystem of important mangrove fishery activities and simultaneously exposed to effluents discharged from industries, the flushing time of the PRE needs to be well understood. In the present work, we calculated flushing time in the upper PRE using the freshwater fraction method (FFM) and e-folding flushing time empirically for examining the effects of river discharges and salinity maximum zone (salt plug area) on flushing time during the dry season. Knowledge of transport timescales can significantly aid the assessment of the environmental, ecological and water resources management strategies of the PRE.

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  Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 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 conductivitytemperature-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.
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-NO 3 − , nitrite-NO 2 − , ammonium-NH 4 + , orthophosphates-PO 4 3− 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 (PO 4 3− ) and ammonium (NH 4 + ) using standard spectrophotometric methods (Parsons et al. 1984;Scor-Unesco 1966). Total oxidised nitrogen (NO 3 − and NO 2 − ) was analysed using the reduced copper cadmium method. For classification purposes, inorganic nutrients were categorised as dissolved inorganic nitrogen (DIN≈ NH 4 + , NO 3 − and NO 2 − ) and phosphorus (DIP ≈ PO 4 3− ).

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 (V i ) 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: where x is the length of the estuary and y is the crossestuary width. The volumes (V i ) of each segment during both spring and neap tides is shown in Fig. 4. The volume of each segment ranged from 13.78 × 10 6 m 3 to 45.93 × 10 6 m 3 during spring tide, and from 11.89 × 10 6 m 3 to 40.54 × 10 6 m 3 during neap tide. The salinity (S i ) for each   Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 segment (V i ) 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): where f i is the freshwater fraction, S sw is the seawater salinity adjacent to the estuary mouth, S i 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): where F i 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): (2)  Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 where Q f is the freshwater discharge. The flushing time (T i ) of each estuarine segment can then be calculated as follows (Shaha et al. 2012;Williams 1986): 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 Q f 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. Q f 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 powerlaw 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 (FT e ) may be calculated empirically with an exponential fit with salinity concentration S c (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.
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.

Salinity distribution
The vertical salinity distribution obtained along the main axis of the PRE during dry (December-June) and wet (July-October) seasons in 2014 and 2019 are shown in Figs. 5 and 6. The large variations in salinity between dry and wet seasons were due to high river discharge during the wet season. By contrast, the salinity showed a salt plug or salinity maximum zone near Chalna in the PRE (34 km upstream from Harbaria) during the dry season. The salt plug area is denoted as SP and the downstream area of salt plug area is denoted as DSP. However, a typical estuarine condition (salinity decreases from the ocean toward the head of the estuary) was observed during the wet season. We calculated vertical average salinity along the PRE from vertical salinity profile, and we used this average salinity to calculate freshwater fraction and flushing time of the PRE.
The spatial and temporal distributions of salinity are useful indicators for understanding the hydrodynamic parameters of estuaries, including stratification (Lewis and Uncles 2003;Shaha et al. 2010), flushing (Shaha et al. 2012), the distribution patterns of ecological parameters (Shivaprasad et al. 2013). Water column stratification for each profile observed was assessed using the stratification parameter n s = ∂S/s m where ∂S = S bot − S sur , S m = (S bot − S sur )/2, with S sur and S bot the salinity at the surface and bottom of the water column, respectively and S m is the mean salinity of water column (from surface to bottom). In case n s < 0.1, then the water column is well mixed, when 0.1< n s < 1.0 then partial mixing occurs, while n s > 1.0 stratification occurs (Haralambidou et al. 2010). The PRE is a well-mixed estuary during the dry and wet season according to the stratification parameter (< 0.01). Based on the tidal range criterion (Dyer 1997), the PRE can be characterized as a macrotidal estuary where tidal range varies between 4 and 6 m (BIWTA, 2021). The tidal range supports the well mixed condition of the PRE and the distribution of ecological parameters is almost vertically homogeneous. Page 9 of 15 Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15

Spatio-temporal variation of flushing time in the PRE
Spatio-temporal variation of segment flushing times of the PRE during the dry and wet seasons is shown in Fig. 7. The segment flushing time varied with the changes in river discharges and estuarine circulation. The flushing times were comparatively longer during the dry season due to low freshwater discharge. By contrast, during the wet season, the flushing times became as short as less than one day and no significant variation in flushing time was observed among the estuarine segments. In general, a decreasing trend in flushing times was observed from Harbaria to Chalna. According to FFM, flushing time was approximately 4 days during the dry season, and from 0.4 day during the wet season. In contrast, average e-folding flushing times were about 10.9 days during the dry season and 0.97 day during the wet season (Fig. 8).
The e-folding flushing times is an empirical approach and assisted to include the tidal dispersion of the salinity (Fig. 8). The e-folding time scales showed higher values in the salinity maximum zone (salt plug area) during the dry season and take longer time to flush to the coast. This implies that the e-folding time scale is able to encompass the tidal dispersion (Rayson et al. 2016) whereas the FFM was unable to include the tidal dispersion process. Therefore, results from the e-folding flushing time approach might not be in conflict with those found with the residence time approach (Lucas 2010;Monsen et al. 2002). Rather, the approach provides more information about local processes and gives strong clues about the mechanisms of spatial heterogeneity (Fig. 8).
During the dry season, flushing time ranged from 2.0 to 3.0 days during spring tide, and from 1.0 to 3.0 days during neap tide. By contrast, during the wet season, flushing time ranged from 0.11 to 0.17 days during spring tide, and from 0.1 to 0.25 days during neap tide. Flushing time was less during neap tide than that during spring tide in all segments in the dry and wet seasons (Fig. 7). This is because the freshwater discharge was larger during neap tide than that during spring tide which might enhance the estuarine circulation. Moreover, the estuarine circulation during neap tide increases with a reduction in tidal amplitude, resulting in increasing the water exchange (Geyer 2010;Valle-Levinson 2010) and reducing the estuarine flushing time (Shaha et al. 2012).

Effects of river discharge and tide on flushing time
The low flushing time keeps an ecosystem free from the adverse effects of pollutants to a great extent.
To observe the effects of freshwater discharge on the spatial heterogeneity of estuarine flushing, the flushing times of the different segments were plotted against the freshwater discharge (Fig. 9). The best fit to the data is achieved with a power-law function, rather than an exponential function. At low freshwater discharges rates, the flushing time is reasonably sensitive (changes quickly). On the other hand, the shortest flushing times  Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 are related to the largest freshwater discharge rates. The power regression equations exhibited a significant correlation between flushing time and river discharge in all the estuarine segments with correlation co-efficient of R 2 ranged from 0.62 to 0.71 in all the segments (Fig. 9). A linear regression between flushing time and high-water level is shown in Fig. 10. A linear function with negative slope appears between the flushing time and the high-water level, with correlation coefficients varied between 0.12 and 0.26. According to this regression analysis, the flushing time in the PRE depends to a great extent on freshwater input. During the dry season, the flushing time in the PRE depends on tidal amplitude (tidal range varied between 4 and 6 m).

Inverse of the flushing time
The inverse of the flushing time is an important parameter in the estimation of quantities of dissolved anthropogenic Fig. 9 Comparison of the power-law relations between e-folding flushing time (days) and river discharge (m 3 s −1 ) for multiple estuarine segments Page 11 of 15 Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 inputs flushed from the coastal environment to the sea (Heggie and Skyring 1999). The fraction of water removed per unit time from the PRE is shown in Fig. 11. The exchange volume of water per unit time (day −1 ) increased twice upstream from Harbaria in both dry and wet seasons. In addition, the daily exchange volume of water was eight times greater during wet season than during dry season. Apart from this, the daily exchange volume was intensified during neap tide due to increasing river discharge resulting from weakening turbulence in comparison with spring tide. The seasonal variation in river discharge exerted major controls on daily exchange volume of the PRE during the wet season. As such, it is one important parameter for evaluating the estuarine water quality.

Sensitivity to changes in river discharge
The relationship between discharge and flushing time is not linear, but rather a negative power function. This Page 12 of 15 Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 pattern has been observed in all segments. The impact of changing river flow to an estuary depends on where the operative discharge range falls on the flushing versus discharge curve (Fig. 9). The anthropogenic changes in river inflow have effects on estuarine flushing time. Our study shows that siltation during the dry season at the mouth of the Gorai River, an entrance path of freshwater from the Padma River to the Pasur river, has reduced freshwater discharge and increased flushing times during the dry season. For example, a 30 m 3 s −1 decrease in freshwater flow to the Pasur river from the Padma River during the dry season would not have a measurable impact on flushing time in the Pasur River estuarine system, whereas it would increase flushing time in the Pasur estuary. Moreover, decreases in freshwater flow have a proportionately greater impact on flushing times. Understanding where an estuary falls on a flushing versus discharge curve will help in evaluating the relative impact of reducing surface water inflow to Pasur river estuarine system, and this type of information should be incorporated into management decisions. System flushing of the PRE during the dry season was comparatively weaker than flushing during the wet season. Low river discharge can lower the flushing rate during the dry season in the PRE (Shaha et al. 2012). However, dissolved inorganic nutrients did not trap in the salt plug area of the PRE for longer periods during the dry season (Fig. 12). As the PRE is a macrotidal estuary, the strong tidal action assisted to shorter the flushing of the dissolved substances from the UPRE to the coast.

Discussion
Flushing time usually denotes a local assessment and is generally recommended for dealing with questions of water quality and biological processes. In general, flushing time is a general measurement of water exchange in an estuary ( Table 2). The estimates of flushing time for the PRE are between 2 and 4 days during the dry season and less than 1 day during the wet season. The PRE, a macrotidal estuary, also has a high rate of water  Page 13 of 15 Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15 exchange during the dry season having negligible river discharge due to strong tidal action. This is because higher concentration of dissolved inorganic nutrients was not found in the salt plug area during the dry season. In addition, there was no significant variation in dissolved nutrients between SP and DSP (Fig. 12). While Ridd et al. (1988) found higher concentration of nutrients in the salt plug area in Australian arid estuary. Among the major nutrients, dissolved inorganic nitrogen (DIN), dissolved inorganic phosphorus (DIP), dissolved silica (DSi) and chlorophyll-a did not vary significantly between the salt plug area and downstream of the salt plug area (Fig. 12). In addition, the nutrients had low concentrations, in agreement with the tropical conditions (Bricker et al. 2003;Dodds 2006;Garmendia et al. 2012) and low anthropogenic impact (Table 3).

Limitations of the study
The limitations of this study and recommendations for future works are as follows. In practice the estuary is ordinarily subdivided into arbitrary segments to improve the precision of the freshwater volume estimation (Eq. 3). The method is simple in theory but not straight-forward in practice. Salinities must be measured precisely to avoid errors arising from the small differences in the S sw -S i term of Eq. 2. Ignorance of this stipulation can lead to wide deviations in the flushing time estimates. To overcome this limitation, we collected high-resolution salinity data from the PRE during the dry and wet seasons in 2014 and 2019. Bathymetry data may also have some errors. Page 14 of 15 Shaha et al. Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:15

Conclusions
The flushing time in an estuary is important for water quality analysis, and it is one of the major transport time scales used in estuaries to quantify the hydrodynamic processes and for water resources management strategies. The purpose of this work is to investigate the influence of tide and river discharge on the spatially varying flushing time and water quality of the upper PRE. Flushing time was quite sensitive to the freshwater inflow rate, with the larger flow rates associated with smaller flushing times. System flushing and the daily exchange volume during the dry season were thirteen and eight times weaker than flushing during the wet season owing to decreasing river discharge. Only the e-folding time scales showed higher values in the salinity maximum zone (salt plug area). This implied that the e-folding time scale is able to encompass the tidal dispersion process. The power regression equations can be used for rapid evaluation of the impact of the dry and wet season scenarios on flushing time in the UPRE. In order to have more accuracy, a three-dimensional hydrodynamic model would be useful to compute estuarine time scales precisely.