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An estuary is the thin zone including bays, lagoons, sounds, salt marshes, mangrove forests, mud flats, swamps, inlets, and sloughs. It is a partly enclosed coastal body of water with one or more rivers or streams flowing into it, and with a free connection to the open sea. As freshwater rivers and streams flow into the ocean, mixing with the incoming seawater, the area is some of the most productive ecosystems. Estuaries are subject to both marine and riverine influences. The former includes tides, waves, and saltwater inflow while the latter includes freshwater flow and land-borne sediment. Seawater and freshwater inflows provide high levels of nutrients in both the water column and sediment, making estuaries among the most productive natural habitats. Human communities also rely on estuaries: these areas were generally used for agricultural, industrial, and commercial purposes, but more recently recreation and tourism have increased activity. Human activities have led to a decline in the health of estuaries, making them one of the most threatened ecosystems. The degradation includes many factors such as sedimentation, drainage, eutrophication, and pollution. The environment of estuary is mainly influenced by a tidal induced flow and river water discharge. Therefore, saline intrusion into rivers is an important issue in management and protection of freshwater resource and hazard prevention. It is a dynamic movement of salt and freshwater under natural conditions, and is caused by advection, dispersion, and diffusion of the saline solute into the freshwater body. The total discharge of freshwater, the tidal range, and the river geometry influence an extent of salt intrusion (Nguyen et al. 2008; Gay and O'Donnell 2009). The process is often caused by the actions of humans, with excessive extraction of water in the upstream. Saline intrusion is likely to become an increasing problem as sea level rises. The modeling can play an important role in the preventing future hazards.
Numerous analytical theories have been developed in the past century to seek physical aspects of the interaction between freshwater and saltwater in estuaries. Hansen and Rattray (1965) derived an analytical solution for the estuarine circulation and salinity intrusion. They discussed the significance of theoretical parameters that determine the partition of upstream salt flux among the river discharge, gravitational convection, and diffusive modes for coastal plain estuaries. Their solution still embodies the essential elements of the estuarine exchange flow, although it has limitation: for instance, the vertical mixing coefficients are assumed constant in time and space, and tidal advection is not considered. Later, Van den Burgh (1972) has developed a predictive model that gave a satisfactory solution for salinity intrusion. In the model, the dispersion coefficient was a function of hydrologic, hydraulic, and topographic parameters that could be empirically determined after its calibration with observed data in estuaries. In contrast, to construct the predictive equation, Rigter (1973), Fischer (1974), and Van Os and Abraham (1990) developed different empirical formulas based on flume data of Delft Hydraulics Laboratory and the Waterways Experiment Station. All these are one-dimensional tidal-averaged solutions assuming a constant cross-section. Savenije (1986, 1989, 1993) proposed an improved formula of salt intrusion taking into account of estuary geometry. The major advantage is that Savenije introduced the mathematical equations for cross-sectional area, width and depth that vary exponentially along the channel. Later, Prandle (2004) described the bathymetry as a function of power. Nguyen (2008) pointed out that his bathymetric approximation seems unrealistic from the comparison with the observed geometries.
The exponentially varying of geometric characteristics have been widely used to derive analytical equations to model estuaries (Prandle, 1981; Kranenburg, 1986; Jay, 1991; McCarthy, 1991; Lewis and Uncles, 2003; Brockway et al., 2006). It has also been conjectured that interactions between geometric and hydrologic factors express by an exponential function (Dyer, 1997; Savenije, 2005). However, with regard to estuary shape, Prandle (1981) obtained that in funnel-shaped estuaries constant longitudinal dispersion coefficient produced the best agreement with the observed salinity distribution. While in flumes and in estuaries with almost constant cross-section, very good results were obtained with the dispersion related to the concentration gradient along the estuary. Lewis and Uncles (2003) developed an analytical model for exponentially tapered estuaries to investigate the axial salinity distribution, magnitude and location of the maximum salinity gradient, and the axial variation in dispersive salt flux. They found that the spatially uniform dispersion is more consistent with observations than that of dispersion increasing exponentially toward the mouth. On the other hand, based on the measurements and testing in about 20 estuaries worldwide, Savenije (2005) clearly demonstrated how the dispersion varies along the estuary that is the highest near the mouth and zero near the toe of the salt intrusion curve. In a strongly funnel-shape estuary, where the salinity decreases steeply in upstream direction, the dispersion curve has an exponential decline. Many researchers, such as Ippen and Haleman (1961), Van den Burgh (1972), and McCarthy (1993) also recognized the similarity in longitudinal variation of dispersion coefficient. The Savenije's method has been successfully applied to a wide range of estuaries, including the Gambia (Savenije, 1988; Risley et al., 1993; Ervine et al., 2007), the Chao Phya (Savenije, 1989), the Casamance (Savenije and Pagès, 1992), the Mekong (Nguyen and Savenije, 2006; Nguyen et al., 2008), Flushing Bay (Eaton, 2007), the Pungue (Grass and Savenije, 2008), and the Sumjin River (Shara and Cho, 2009). The model calculates three different salt intrusion distances from the mouth. The length of salt intrusion can be obtained at the low water slack (LWS), high water slack (HWS), and tidal average (TA) that is an average of LWS and HWS. In this paper, we extend Savenije's approach to investigate the salinity distribution in an alluvial estuary system in the Red River Delta (RRD) and then use it to infer the resultant effect of tidal amplitude, estuary geometry, and freshwater discharge. Wind forcing is also important at various timescales, but in a narrow estuary, where the flow is predominated by the tide, the wind has minimum influence on the flow in long-term and it will not be treated in this paper.
Similar to general use of model, the salinity distribution has been commonly computed for an indicator to know the physical quantities such as tidal range, river flow, bathymetry, and local mixing and turbulence, because it represents the resultant effect of several complex processes occurred in an estuary. The estuary is assumed to converge or expand over its length and regularly is resolved with one spatial scale at tidally averaged state. Generally, as the tides dominated the longitudinal salt flux in estuaries, the results from previous steady solutions contradict the common observation of spring-neap variability. To know the salinity variations during a tidal month, Jay and Smith (1990) observer the density and velocity fields from one extreme of tidal range to another in the Columbia River Estuary. The corresponding salt transport calculations show that spring-neap variability for the salinity intrusion in the lower estuary is limited by compensating adjustment of the tidal advection and mean-flow salt transports in most river flow conditions. In contrast, the absence of such balancing mechanisms in combination with substantial spring-neap changes in vertical mixing allows larger variations in the density field and salinity intrusion length in the upper estuary. Spring-neap variability is much higher during the low flow season than during the high flow season. Their investigations also showed that during low-flow neap conditions the estuary appeared as a salt wedge on flood but became well mixed by the end of ebb, while in the tidally averaged condition, the estuary was partially mixed but this was not a representative state. Prandel (2004) formulated a single-point numerical model to assess the validity of associated analytical solutions for the tidal-mean vertical structure of salinity and residual velocities. An expression for saline intrusion length was derived by equating the rate of mixing associated with vertical diffusion with river flow. This formulation agrees with an earlier derivation based on flume tests and showed reasonable agreement with observed values in several estuaries. However, only limited agreement was found between observation and model results for the sensitivity of saline intrusion to tidal range (spring to neap) and river flow. The tidal-averaged view can be misleading in an estuary with strong tidal forcing.
In some estuaries with complicated geometry, the spatial variation of cross-sectional area, width, and depth varies significantly between high and low tidal levels and that the channel geometry influences on the distance of salt intrusion. Lewis and Uncles (2003) and Brockway et al. (2006) solved the salt balance equation in a quasi-equilibrium state and obtained practical results for forecasting salinity intrusion. Their investigations showed that in addition to tidal range and freshwater discharge, other factors such as geometric characteristics affect the predicting of model results. Gay and O'Donnell (2007) used a lineally-geometry based model to investigate the dependence of the curvature and gradient of the longitudinal salinity distribution on runoff, dispersion coefficient, and channel convergence. They split the channel estuary into several segments in order to simulate the effect of additional freshwater resources in each segment. They found that the salinity gradient depends on variation in channel cross-section and that a change of channel convergence is required to reverse the curvature of the longitudinal salinity profile. Our approach is similar in philosophy to Gay and O'Donnell (2007) since the use of a small number of segments fits the complicated geometry better than a single exponential form, which was suggested by Savenije (1986, 1989, 1993, 2005). However, in this paper we prefer to use the exponential-geometry based model. While the predictive models of salt intrusion with the variation of channel shape and tidal amplitude have been developed, the complicated geometry of real estuaries has limited the empirical evidence for these models. Since there is little compelling evidence for the influence of cross-sectional area, width, and depth variations on the salinity distribution, we set out to analyze salinity distribution in the spring high water, spring low water, neap high water, and neap low water for an estuarine system in the RRD. Prescribing the geometric characteristics to vary exponentially at different tidal conditions allows the analytical solution to estimate the salt transport and other response to the changes in external forcing, which is not carried out by either Savenije (1986, 1989, 1993, 2005) or Gay and O'Donnell (2007). In this paper, we explored a steady one-dimensional advection-diffusion model, which developed by Savenije (2005) to investigate the distribution of salinity but we shall present some modifications to the method for the estuary that have complex geometry.
2 Study area
The site of the study is located in northern Vietnam where the Red river and its tributaries flow into the Tonkin Gulf after a distance of approximately 1,200 km (Fig.1). The Red river has its source in the mountains south of Dali in China's Yunnan province, and enters Vietnam at Lap Cai province. Once reaching the lowlands near Viet Tri, the river splits into two main estuarine systems: The Red River system and the Thai Binh river system. Both river systems form a delta so-called the Red River Delta (RRD), which is a populous low-lying area in Vietnam. The total catchment area of the Red river is 169,000 km2, of which 86,600 km2 lies in Vietnam, and the RRD itself covers 16,444 km2. The Red river system is located in the south of the RRD, while the The Thai Binh river system is located in the northwest of it. These two systems link each other by the Duong river and the Luoc river. The Red river estuary system has four tributaries (Tra Ly, Hong, Ninh Co, and Day), while the Thai Binh river estuary system has five tributaries (...). The present study focuses on the former estuary system.
The whole area is subject to the tropical monsoon weather, the two main seasons are formed in one year. The south monsoon is dominated by south to southeasterly winds from May to October in the wet season, but the north monsoon is dominated by northerly to northeasterly winds from November to April in the dry season. Of course, there is a transition period in which it breezed from all directions all day. According to the data by MONRE (1996-2006), the annual precipitation varies from 700 to 4,800 mm/yr. The mean precipitation in the rainy season is mm, while that in the dry season is mm. The river discharge data have been obtained since 1996 to 2006 at the Son Tay station, which located about 30 km upstream from Hanoi operated by the Ministry of Agriculture and Rural Development. The average river discharge from 1996 to 2006 was about 1,200 m3s-1 in the dry season and 14,000 m3s-1 in the wet season. The tidal cycle is diurnal, with mean spring and neap ranges of 4.0 and 0.6 m, respectively. In the wet season the rivers play roles in evacuating the floodwater from upstream to East Sea and also supplying a considered amount of freshwater for the drinking demand of the area. On the other hand, in the dry season seawater intrudes through the estuaries into the rivers, resulting in the impossibility of the surface water supply system. Minh et al. (2009) found that at the distance of 120 km from the river mouth the water variation due to the tide was 1.0 m in the dry season and 0.6 in the wet season.
The Red river system is one of the largest river basin located in the northeastern and northern part of Vietnam. The RRD consists of 9 provinces: Hanoi, Hai Phong, Bac Ninh, Hung Yen, Hai Duong, Ha Nam, Nam Dinh, Thai Binh and Ninh Binh. As a major river representative of the national production, it has an important role in the development of the social-economy of the country. The land is very flat; more than 50% is less than 2 m above the mean sea level. To prevent it from river floods, dykes have been constructed at the many locations along rivers since the mid 20-centery. Now the total length of the dyke system is 2,700 km, and the average height is 6-8 m. In the Red river basin, there are two dams: Thac Ba dam on the Chay river, with an active storage capacity of 1.2 billion m3 and Hoa Binh dam on the Da tributary. Approximately 54% of the RRD surface is cropland, and 82% of this is rice-paddy. The delta depends heavily on pumping for drainage. The average population density for the entire basin is about 280-person/km2 in 2010. Almost 17 million people living in the RRD.
The extent of saltwater intrusion has a pronounced effect on agriculture in the RRD. In fact, a vast amount of paddy fields in the region has been in an awkward situation of mixing between fresh and salt waters. Especially in the dry season, the quantity of river discharge is so small that large quantities of seawaters intrude into the lower reaches.
Recently, the total amount of freshwater in the RRD has decreased because of climate change (MONRE, 2009). The river flow in the dry season has been decreased during the last fifteen years, as a result, the water environment has threatened by human activities that require much water for multi-purpose uses such as domestics, agriculture, industry, and bio-ecology (Hien et al., 2009). Saltwater penetrates further in all estuaries, the salt intrusion length during the period of 1993-2007 increases from 7% to 15% when compare with the observed data during the period of 1965-1985. The saline of 1 ppt is obtained throughout the south estuarine system up to 34 km landwards from the Tra Ly mouth, 30 km from the Hong mouth, 52 km from the Ninh Co mouth, and 41 km from the Day mouth (IMH, 2009). The longitudinal salinity distribution is subjected to a strong dependent on seasonal variation of river discharge and tidal regime. The maximum salt intrusion length usually occurs in January and February, two driest months of the year.
3 Data sets
The data used in this study consists of three sets. The first set is from the field measurements, which were carried out in the Red river system in January 2006 for water depth, water level, and salinity. The second set is from the collections taken by the Vietnam Institute of Meteorology and Hydrology (IMH) for water level and discharge at 12 stations along the Red river and its tributaries, and for salinity at the river mouths. The third set is from the survey for bathymetry, which was provided by the Ministry of Agriculture and Rural Development (MARD).
The field measurements were carried out from January 3 to 19 in 2006 to obtain the spatial distribution of salinity during the spring-neap tides. The measurements were conducted simultaneously at eight locations on the four channel estuaries (see Fig. 1 and Table 1). For each location, we measured the water depth, water level, and salinity at the time during high water and low water. In the flood tide, the water depth and water level were measured hourly, while in the ebb tide they were obtained every two hours. Based on the determined water depth, the water samples at three points over the depth: 0.5 m from the surface, 0.5 m from the bottom and mid-water column were taken to determine salinity. We selected the measurement periods due to the difference in time between rising and falling stages of the tide. In the Red river estuarine system, the falling stage period is longer than the rising stage period, it takes 59% of the time in the former one compare to that of 41% in the latter one.
Table 1. Location of the measured stations.
Distance from sea
tidal range (m)
The second data set was taken from the official database of the IMH. Water level was collected in the period of 1996-2006 at 12 hydrological stations in the south river system. Tidal level and salinity at four river mouths were also provided by the IMH. River discharges were obtained at three stations in the upstream, e.g.: Son Tay, Hanoi and Thuong Cat. In the RRD, only three upstream stations observe the discharge during the dry season, no other systematic records are available for downstream stations except for water level. Therefore, for the purpose of this study we used the empirical relationships between water level and discharge established at downstream stations to determine the distribution of river flow over the estuary branches and its influence on mixing process and transport of saltwater. The third data set was collected from the project: "Flood protection for the Red River Delta" supported by the MARD. The bathymetry survey was carried out in the dry season in 1999 and 2000 for all rivers in the RRD including four channel estuaries in the Red river system. The data contains a series of 2-dimentional points describing each cross-sectional profile along the rivers. This official bathymetry is the most reliable source so far, most Vietnamese research institutes have depended on this database.
In a convergence estuary, the geometrical variations can be described by the exponential functions (Savenije, 1993, 2005) as follow:
where A0, B0 and h0 are the cross-sectional area, width and depth at the mouth (x=0). A, B and h are the cross-sectional area, width and depth at a distance x (km) from the mouth. a, b and d are the cross-sectional area, width and depth convergence length, respectively. Since the positive x-direction is chosen in upstream direction, the cross-sectional area and the width decrease exponentially in landward direction. In estuaries with complex geometry, often accounts for strongly funnel-shaped near the mouth as a trumpet shape, the geometry cannot be described by a single exponential function. In this case, it can be solved as:
if 0<xâ‰¤x1 (4)
if x>x1 (5)
if 0<xx1 (6)
if x>x1 (7)
if 0<xx1 (8)
if x>x1 (9)
where A1, B1 and h1 are the cross-sectional area, width and depth at the inflection location, x1. a1, b1 and d1 are the convergence length of cross-sectional area, width and depth of the downstream segment. a2, b2 and d2 are the cross-sectional area width and depth convergence length of the upstream segment, respectively.
For an estuary, the advection-diffusion equation for salinity can be written as follow:
where t is time and x is the distance along the estuary, S is mean salinity in the cross-section, Q is the river discharge and D is the dispersion coefficient. If the long-term variation in salinity is negligible, in a situation of equilibrium we can neglect the first term resulting the balance between the second and the third terms. In that case, Equation 10 can be integrated with respect to x, we have:
in which i=1,2,3 indicates the three different states HWS, LWS and TA. Sf is the freshwater salinity.
Van den Burgh (1972) provided the relationship between salinity and dispersion coefficient based on salt measurements in the Rotterdam Waterway. It is expressed as:
where K is the Van den Burgh's coefficient, which is a hydraulic characteristic of an estuary. The K value lies between 0 and 1. Combination of Equation 11 and 12, and, integrating once with respect to x leads to:
where S0i and D0i are the salinity and the dispersion coefficient at the mouth for the HWS, LWS or TA condition. Considering the exponentially variation of the cross-sectional area and using the expression of Van de Burgh, Equation 13 can be integrated, yielding:
The above equation is the core of the steady one-dimensional advection-diffusion model for salinity intrusion in a convergence estuary. Solutions of this form have been presented by Savenije (1993, 2005), Nguyen and Savenije (2006) considered the geometry decrease exponential and allowed the dispersion coefficient to vary along the estuary. In the estuary with a trumpet shape, the Equation 14 can be rewritten separately for two segments as follow:
if 0<xâ‰¤x1 (15)
if x>x1 (16)
In case two segments are required to fit the exponential function, the salt intrusion length, Li, can be obtained by substitution Si=Sf in Equation (16) adding with the distance from the estuary mouth to where the segment intersect, yielding:
To solve the Equation 15, 16 and 17 one should know the K and the Di, Qi for the downstream and upstream segments, respectively. The two latter parameters, which in an estuary, are the most difficult parameters for determining. Fortunately, in the above equations, Qi always occurs in the same term as the Di, which permits them to be combined into single variable, the mixing coefficient Î±i (Î±i=-Di/Qi). The Van den Bergh's K is the time-independent factor characterised for a certain estuary depending on the geometry, tidal characteristics and channel roughness. Whereas, Di is time-dependent factor that depending on both river discharge and tidal range. Savenije (1993, 2005) developed the empirical equations for K and Di based on large number of observations in real estuaries. The K and Di are expressed particularly for HWS as follows:
where E is the tidal excursion at the estuary mouth, which is obtained by , Ï… is the tidal velocity amplitude, T is the tidal period, C is the coefficient of Chezy, Î´ is the damping rate of tidal range, H is the tidal range, is the average depth over the salt intrusion length and NR is the Estuarine Richardson number given by:
5.1 Shape of the estuarine branches
The Tra Ly, Hong, Ninh Co and Day are the channel estuaries in the south estuarine system of the RRD. The cross-sectional area, width and average depth of these branches were defined at different tidal level, e.g.: the spring high water, spring low water, neap high water and neap low water. The convergence lengths, which are the length scale of the exponential function, were obtained by calibration of Equation 4-9 against measured data. It can be seen in Fig. 3 the seaward expanding of the estuary branches. One can see that the longitudinal cross-sectional areas in spring high water are significant larger than those in spring low water. While the difference in the neap tides is negligible. The channel size is completely governed by the variation of tidal level.
Estuaries, according to Dyer (1973), are sediment trap. The sediment supplied by the river flood is deposited in the estuary as soon as the channel becomes wider and shallower. The tendency of larger opening of the mouth to the peculiar feature of the RRD estuaries is presented in Fig. 4. There is a remarkable trend in the variation of estuary width due to the tidal fluctuations. The estuaries are strong funnel-shaped near the mouths, it then decreases gradually from the inflection point to the upper stream. It could very well be that separating a channel estuary into two branches is more in agreement with the physical laws that guide the formation of ebb and flood channels than combining into a single branch. The estuarine geometry can be described reasonably well by the exponential function, which separately treated for two branches (downstream and upstream branches). The geometric characteristics of the four channel estuaries are calibrated and summarised in table 2.
Table 2. Geometric characteristics of the Tra Ly, Hong, Ninh Co and Day branches in the south estuarine system in the Red River Delta.
5.2 Salinity computations
Using the observed salinity during the spring tides (3-6 January, 2006) and neap tides (11-15 January, 2006) and the calibrated parameters for the geometry, Equation 15 and 16 can be used to calibrate the model parameters. We measured the vertical salinity distribution at fixed locations along the Tra Ly, Hong, Ninh Co and Day branches. It appeared that these branches were well mixed. This is understandable since the river discharge in the dry season is relatively small. Therefore, the averaged salinities over the water column have been used to compare with the computations. In order to obtain the theoretical longitudinal salinity distributions, we have to calibrate two parameters, i.e. K and a. First, the Van den Burgh s K is estimated from the predictive equation, e.g. Equation 18. However, K should be refined on the basis of salinity measurements (Nguyen et al., 2008). K particularly determines the shape of the toe of the salt intrusion curve and its magnitude is depends on the geometry and tidal characteristics. Second, the mixing coefficient, a, can be obtained through calibration of the Equation 15 and 16 against the observations. The calibration of K and a in the Tra Ly, Hong, Ninh Co and Day branhches during both spring and neap tides are presented in Fig. 5.
The performance of the salt intrusion computations for the estuary branches is satisfactory. Especially, the complete set of measurements at high water and low water during the spring tides from 3 to 6 January, 2006 and during the neap tides from 11 to 14 January, 2006 give a good result. Most measurements show some fluctuations around the theoretical curve, which obtained from the averaged calibration parameters. We can observe that the Van den Burgh's coefficient, K, in four branches is relatively small, which indicated that tide-driven mixing is the dominant mechanism of the estuary system (Savenije, 2005). In the individual estuary branches, the mixing coefficient, a, is distributed spatially which is higher in the downstream segment compare to that in the upstream one. This is understandable since the cross-sectional area near the mouth is larger and the influence of river discharge tends to be weaker. During spring tides, large amount of seawater flows forth and back though different cross-sectional areas at the mouths that results in larger variation of salinity. Therefore, the a value at the downstream part are significant different between high water and low water. While during neap tides, lower tidal current that allows the freshwater discharge increased in the downstream segment. In addition, the variation of geometry characteristics and tidal amplitudes is relatively small that leads to a decrease of the mixing coefficient.
Considering the upstream segment, there is a noticeable decrease of a value at the high water. In the Hong and Ninh Co branches, the two largest estuaries in the RRD, the tidal range is almost the same while the a value in the former branch is much smaller than that in the latter one. Higher river discharge always occurs in the Hong branch during both spring and neap tides. This would explain why in the same tidal conditions the salinity in the Hong branch decreases rapidly after the inflection point while in the Ninh Co branch the density profile decreases gradually from the estuary mouth to the upper stream.
In the RRD, the freshwater discharge distributes through a complex hydraulic channel system strongly depend on the magnitude of the discharge in the upstream. Salinity distribution in each estuary branches, therefore, has distinct characteristics. Before reaching the Tonkin Gulf, the main Hong river distributes its flow through six branches with 25% of the total volume is discharged into the Hong branch, 10% into the Tra Ly branch, 6 % into the Ninh Co branch, 22% into the Day branch and the other water volume is discharged into the Duong and the Luoc river (Pruszak el al., 2005). Since the freshwater discharge is not measured directly in the tidal region, it is usually derived from the discharge-water level relationship (Minh et al., 2009) or from the hydraulic model (Tran, 2006; Ngo et al., 2006). In this study, we approached the former method to estimate the discharge for the downstream branches. Based on the collected data at the hydro-meteorological stations, we defined the average freshwater discharge in the downstream branches of the RRD during the field measurements (Table 3). The discharge rate in each river is defined as the percentage ratio between the average discharge distributed in a river branch and the average discharge measured at the Son Tay station.
Table 3. Distribution of discharge rate over the RRD branches
Hong (at Son Tay station)
Hong (at Ha Noi station)
Duong (at Thuong Cat station)
Luoc (at Trieu Duong station)
Hong (downstream branch)
* The average measured discharge at Son Tay station during the field measurements.
One can see clearly from table 3 that the highest discharge rate, 21.2%, is distributed through the Hong branch. The amount of freshwater transported into the Tra Ly and Day branches was in the order of 10.7% and 15.5%, respectively. The lowest discharge rate was obtained in the Ninh Co branch with only 6.9% of the average discharge measured at Son Tay station. Obviously, the discharge can alter the salt intrusion in the receiving branches at the downstream. Our measured data reflected that highest salinity in accordance with the lowest discharge rate. The salinity in Ninh Co branch always remains in a higher value compared to that in other estuary branches.
5.3 Tidal level and salinity intrusion
As the salt intrusion along a river is very sensitive to the tidal conditions, in this study we examined the effect of tidal variations on the longitudinal salinity distributions for the spring tides and neap tides. The salinity visualisations as the result of computations at spring high water and spring low water on January 4, 2006 and at neap high water and neap low water on January 12, 2006 are plotted in Fig. 6. During the flood tides, when the river discharge is small, the salt water reaches much further. One can find that the water keeps the high saline density from the river mouths to the distance of 10 km at spring high water. This is probably due to the wider and shallower of the mouths. Alter the channel characteristics and river discharge in the upstream segments that reduce the salt density quickly to the next 10 km and slowly to the end of calculation segment for the Tra Ly, Hong and Day branches. The salinity of 1 ppt reaches approximately 29 km from the mouth in the Tra Ly branch, 23 km in the Hong branch, 46 km in Ninh Co branch and 33 km in the Day branch. While at neap high water, the salinity is relatively high within the first 2-3 km from the mouths. The narrower width together with the smaller discharge from the sea due to the lower tidal level contributes much to the distribution of salinity. The distance from the mouths that salinity of 1 ppt reaches in order of 15 km, 13 km, 30 km and 20 km in the Tra Ly, Hong, Ninh Co and Day branches, respectively.
In contrast, during the ebb tides the salinity decreases rapidly from the mouths to the upper stream. The extent of salinity of 1 ppt at neap low water is smaller than that at spring low water. The salinity of 1 ppt reaches 6-10 km from the mouth, although it depends upon the branch. Generally, the results illustrate the strong tidal effect to the variation of salinity. As the river discharge is rather small in the dry season, the tidal level mainly affect the damage from saltwater.
5.4 Salinity predictions
On 15 December 2008, the Institute of Hydro-Meteorology of Vietnam had conducted a field measurement for salinity using the moving boat method. The measurements that started at 0.5 km from the mouth of the Tra Ly, Hong, Ninh Co and Day branch were carried out for both HWS and LWS. Using calibrated Van den Burgh's coefficient, K, the averaged mixing coefficient, ai, for the downstream and upstream segments and the calibrated geometric parameters, we can estimate the salinity distribution in the South RRD estuary branches. The computed results against the measurements are presented in Fig. 7. One can see that the application of calibrated parameters produces very good results. The salinity distributions were approximately the same as for the measurements during the dry season in 2006 when no significant variations in the river discharge and tide appeared.
5.5 Model intrusion length
The most important output of analytical model is the salt intrusion length (Savenije, 1993). In the South estuarine system, due the complex geometry that two segments are required to fit the exponential function, the salt intrusion length can be obtained by the Equation 17. In Fig. 8, the measured and computed intrusion length of the Mekong estuaries in Vietnam, Pungue estuary in Mozambique, Schelde estuary in the Netherlands and Sumjin estuary in Korea are plotted together with the new data for the estuary branches in the South RRD. What we observe is that the salt intrusion length, which computed at spring high water in the dry season 2006, plot very well within the set, but it gives a small overestimation. This difference can be caused by the influence of meandering channel, which typically observed in alluvial estuaries.