The influence of spring and neap tide on salt intrusion and stratification in Sebou estuary (Morocco)

ABSTRACT Estuaries, which are coastal bodies of water connecting the riverine and marine environment, are among the most important ecosystems in the world. Saltwater intrusion is the movement of coastal saline water into an estuary, which makes up estuary water, becomes salty due to the mixing of freshwater with saltwater. It has become a serious environmental problem in the Sebou estuary (Morocco) during wet and dry seasons, which has a considerable impact on residential water supply, agricultural water supply as well as urban industrial production. The aim of this paper is to study longitudinal salinity and the vertical salinity stratification under different hydraulic conditions in the Sebou estuary. Field observations were done during May 2014 and February 2016 and were interpolated using a Geographic Information System (GIS). Measurements results show that the vertically averaged salinity during spring tide is higher than that during neap tide. Also, the stratification increases a larger during the low-flow periods than during the high-flow periods in the Sebou estuary. Based on results of the longitudinal and vertical salinity observations and historical data, empirical equations were obtained for estimation of the intrusion length as a function (1) of upstream freshwater discharge and (2) tidal range in the Sebou estuary. Additionally, a correlation equation between the surface salinity and the vertical average salinity in estuary (at Kenitra station) was proposed. Finally, this paper provides simple equations that are useful to provide first estimates of intrusion length and vertical average salinity in the Sebou estuary, which can be obtained by a simple desk study without the use of every measurements day.


Introduction
Salinity transport in estuaries is a highly complex process due to a number of factors, including the intricate geometries of the estuary (e.g. sinuous channel forms, islands, shoals, bridge piers, etc.) and the mixing of freshwater inflows with saline tides. Because of the density variations between the freshwater and denser seawater, salinity in estuaries typically stratifies which produces a two-layer circulation (Haddout and Maslouhi 2017). Estuaries are aquatic environments in the continent ocean interface where the marine and river water interact with each other (Priya et al. 2015;Priya et al. 2016a). They are semi-enclosed coastal water bodies, with one or more connections with the open sea, where the sea water mix in different ratios with fresh water from the drainage basin. Seawater is driven mostly by the tide and propagates up estuary with flood currents (Pritchard 1955;Cameron and Pritchard 1963;Fairbridge 1980;Dyer 1997;Haddout and Maslouhi 2018).
A quantitative understanding of the characteristics of salinity distribution and transport under various environmental conditions is essential for the interpretation of an estuary's physical, chemical, biological and ecological status. Salt water intrusion can be aggravated by decreasing river discharge resulting from upstream barrages required for drinking and irrigation water (Shaha and Cho 2016). Additionally, discharge of fresh river water into the ocean is closely related to vertical and longitudinal salinity variations along an estuary (e.g. MacKay and Schumann 1990;Wong 1995;Becker et al. 2010;Whitney 2010;Savenije et al. 2013). River discharge also has a noticeable effect on the tidal range, primarily through the friction term (the amount of energy per unit width lost by friction) (Savenije 2005). A decrease in river discharge into an estuary could increase the tidal range and the wave celerity, and consequent increase in salinity levels (Cai et al. 2012). Recently, more attention has been paid to the salinity stratification in estuaries, where a river enters into open sea and fresh water mixes with salt water (Zhou et al. 1999;Li et al. 2003;Yun and Jie 2005). Tides and freshwater inflows are the two major external forcing mechanisms controlling estuarine processes. The freshwater tends to float over the denser sea water, but tidal mixing reduces this stratification. Its driving mechanism is commonly attributed to longitudinal baroclinic pressure gradients and the viscosity acting against it. The gravitational circulation is further influenced by factors such as local topography, river flow, salinity intrusion, tide and wind forcing (Shen et al. 1994;Yong-ming and Murphy 1995;Zhou and Li 2005;Chen et al. 2007;Guo and Valle-Levinson 2007;Bin and Kai 2008). The level of stratification in the water column is crucial in controlling the intensity of vertical mixing and hence, the vertical fluxes of water properties (Simpson et al. 1990;Prandle 2004). Stratification plays a fundamental role, e.g. on nutrient transport in estuaries. Understanding the development and breakdown of stratification in a shallow estuary will provide a better understanding of the dynamical process of the estuary and its influence on living resources. In a partially stratified estuary, the estuarine stratification mixing process is often regulated by its springneap tidal cycles. The intensity of stratification depends on the buoyancy input and the mixing produced by tidal and wind stirrings. Studies of estuarine stratification showed that the freshwater buoyancy input is one of the most influential mechanisms of estuary circulation (Schroeder et al. 1990;Simpson et al. 1990).
On the other hand, the filtration efficiency of a given estuary depends on several factors, such as its morphology and flow regime, although estuary water circulation also plays a major role (Dyer 1995). Estuary systems dominated by river discharge characteristically exhibit a highly stratified vertical salinity distribution governed by fluvial advection and lower filtering efficiency (e.g. Schettini et al. 2006). In estuaries where there is a balance between river and tidal forcing, the vertical pattern of salinity is partially stratified, and estuarine circulation plays an important role in scalar transport inside the estuary, resulting in efficient systems for the retention of material (e.g. Geyer et al. 2000). The tide-dominated estuaries present a well-mixed vertical distribution of salinity, and the filtration efficiency may be low or high depending on the morphology and behaviour of the tide (e.g. Wolanski and Ridd 1986;Schettini and Miranda 2010).
On the other hand, longitudinal distribution of salt water intrusion in an estuary are important physical phenomena that affect the quality of both surface and ground water, and its variation determines the diversity of species in estuaries. In recent years, there has been an increasing concern about environmental degradation in estuaries as a result of human interventions, such as dredging for navigation, land reclamation, dam construction and fresh water withdrawal, which in turn has led to growing demands for developing rapid assessment techniques that assist policy maker and managers to make considered decisions for the protection and management of estuarine environment and to establish policies for sustainable management and governance rules of water resources so as to ensure their durability (Savenije 2015;Haddout et al. 2016a).
Regarding Morocco, conventional water resources are very limited and irregular. This is due to the increase in several activities using water and also to the influence of climate change. This situation imposes to look for other water resources, not yet exploited, as water available in estuaries. Estuarine water is constantly influenced by salinity coming from the ocean. On the other hand, estuaries are complex hydro-systems whose management needs information on several scales, as we will see through the study of the Sebou estuary.
The Sebou River (88°N and 35°N to 4°W and 7°W) covers an area of 40,000 km 2 . Sebou is the largest Moroccan river, stretching about 614 km from its source in the Middle Atlas Mountains to the Atlantic Ocean, which represents 6% of Morocco's total land area. Kenitra harbor, about 17 km from the ocean, has commercial traffic, while the Mehdia harbor at only 2 km from the mouth is busy with fishing activities. The mean annual rainfall is about 600 mm in the west and 450 mm in the southeast and its average flow is about 200 m 3 /s at the mouth. The annual input volume is about 5.109 m 3 of freshwater and may double in rainy seasons. The morphology of Sebou estuary is highly variable and influencing the river regime. In addition, the flow regime at the level of the Sebou estuary is marked by considerable seasonal and inter-annual variations. It is under the influence of the tide regime and under the control of many dams (Igouzal, and Maslouhi 2005). During low-flow periods, the hydrodynamic regime is controlled by the dam situated 62 km upstream. This dam has been constructed to preserve water for agricultural pumping stations, many land use, and to avoid that salty waters rise towards these stations. Before the dam construction, excessive salinity reached up to 85 km upstream (Combe 1969). The tidal height varies from 0.9 to 3.1 m depending on the condition of the tide and the average flow is about 200 m 3 /s at the river mouth (Combe 1966). The tide near the estuary mouth is mainly semi-diurnal with a 12.27-h tidal cycle (Haddout et al. 2016a;Haddout et al. 2016b). The tide regime in the estuary is characterized by a filling (at high tide) and an emptying (at low tide) by the bottom of the river; the emptying is less rapid than tide filling (El-Blidi and Fekhaoui 2003). In addition, the Sebou estuary is considered as a narrow estuary, so wind has minimum impact on the flow (Haddout et al. 2017b). Tidal excursions range between 6 and 10 km (i.e. is a distance that a water particle travels between low tide and high tide) (Haddout et al. 2017b). The channel width is about 600 m to 98 m with an average depth of 4.5 m (Haddout et al. 2016a;Haddout et al. 2017c). The waters in the Sebou river estuary are used by many industries (cooling, washing, manufacturing processes …) and agriculture. However, high-water salinity limits the development of these activities. The Sebou river estuaries have been the subject of several research projects. All these works have noticed the presence of a stratification of salinity and temperature at the estuary (El-Blidi and Fekhaoui 2003;Haddout et al. 2016a;Haddout et al. 2017b).
In this paper, we will study the longitudinal and vertical salinity in Sebou river estuary, based on intensive measurements during spring-neap tide of May 2014 and February 2016 periods. First, longitudinal and vertical salinity have been investigated along the river estuary in other to select the best station where intensive vertical measurements will be done in a next step of the study. Hence, a river station near Kenitra town (17 km from the mouth) has been chosen for stratification survey. Results show that river waters salinity is vertically stratified in this station. Stratification depends on tide cycle and is influenced by river flow. Based on results of the longitudinal and vertical salinity observations; and historical data an empirical equations were obtained for estimation of the intrusion length as a function (1) of upstream freshwater discharge and (2) tidal range in the Sebou estuary. Additionally, a correlation equation between the surface salinity and the vertical average salinity in estuary (at Kenitra station) was proposed. Geographic Information Systems (GIS) were used for visualizing the longitudinal and the vertical variations of salt intrusion measurements for various hydraulic conditions from upstream to downstream of the estuary. This approach permits to draw isohalines maps (areas of equal salinity) for different situations.

Data and processing methods
The studied reach (62 km) is situated between the Mouth of Sebou estuary and Lalla Aïcha dam ( Figure 1). The climatic, geological and soils characteristics of the study area are summarized in Table 1. Salinity measurements were made at specific stations reflecting the spatial variability (Table 2). On the other hand, salinity is a measure of the amount of dissolved salts in industrial or natural waters. In practice, it is determined indirectly by measuring the electrical conductivity of the water as an indicator. In our case, the salinity measurements, WATER METER TYPE 120-LTC Conductivity Meter attached with 120 m cable was employed is used and Global Positioning Systems (GPS) were used to record the locations of every measurement, they are adequate to carry out various measurements in cost-effective ways. This instrument is able to measure water temperature, conductivity, TDS and salinity simultaneously. It is worth to note that the conductivity and temperature have to be calibrated before use. The salinity can be expressed in parts per thousand (ppt, g/l or ‰) and the average value in the ocean is 35 g/l. All field measurements were conducted in normal situation during May 2014 (at dry season) and February 2016 (at wet season); and different hydraulic conditions. Additionally, a Geographic Information System (GIS) is a dynamic information tool to store, organize and spatialize data in a comprehensive manner, persistent and with less redundancy. The geographic information systems (GIS) implementation process starts with the initial decision to use a GIS (Adhikary et al. 2010), proceeds through system selection, information collection and classification data in two formats: spatial and attribute format, acquisition and processing installation, training and up to database development and product generation. This system has demonstrated its simplicity of use and its effectiveness in other works for the management of water resources; that is why we have chosen it to do our current study. The realization of the salt transport in the Sebou estuary in GIS requires different stages ( Figure 2).
The prediction of spatial variations from point's measurements over land surface requires some realistic interpolation techniques. Deterministic and geo-statistical techniques are two main groupings of interpolation techniques to produce a continuous surface from point's measurements. Deterministic interpolation techniques create surfaces from measured points using mathematical functions, which are based on either the extent of similarity (e.g. inverse distance weighted IDW) or the degree of smoothing (e.g. radial basis functions). Geo-statistical interpolation techniques (e.g. kriging) utilize both the mathematical and the statistical properties of the measured points (Goovaerts 1997). In this study, the ordinary kriging geo-statistical interpolation technique was used to develop maps of salt intrusion along the Sebou river estuary.

Results and discussion
The hydraulic regime of Sebou river estuary is influenced by the tide cycle (at the mouth of the river) and by water flow releases from the Lalla Aïcha dam, Figure 3 gives distribution of longitudinal measured salt intrusion, as interpolated by GIS approach during May 2014, for three characteristic flows: 33 m 3 /s, 60 m 3 /s, 100 m 3 /s. This type of figures give a cartography of the salinity called isohalines directly exploitable. Figure 3(a,b) shows that when low flow is released from Lalla Aïcha (upstream end), at high tide excessive salinity arrived up to S5 station 35 km from the mouth and varies between 12 and 34 g/l. At low tide, excessive salinity reached S3 station (10 g/l). An increase of the river freshwater flow to 60 m 3 /s forces back the excessive salinity, which does not exceed S2 station, in low tide and high tide; this is shown in Figure 3(c,d). A river flow of 100 m 3 /s stops the salinity in the vicinity of the river mouth and reduces its concentration to low values (9 and 29 g/l) (Figure 3(e,f)). Summarizing, it can be seen that tide and river discharge are the two dominant drivers for estuary salinity. The salinity distribution was observed by other authors (Combe 1969;El-Blidi and Fekhaoui 2003;Haddout et al. 2016a;Haddout et al. 2016b;Haddout et al. 2017b;Haddout et al. 2017d).
All measurements shown above enabled us to divide the river, according to the salinity categories (zones) of the Venice System (1958) (Table 3), from limnetic (0.5 g/l) to fully marine waters (>30 g/l). The limnetic zone is situated between stations S6 and S7 (∼9 Km) where salinity does not exceed ∼2 g/l and is not influenced by tidal dynamics. The mesohaline/oligohaline zone is situated between stations S3 and S6 (∼36 Km) where salinity is between 2 and 12 g/l. This zone is considered a transition zone influenced by tidal dynamics and river flow. The polyhaline/euhaline zone is situated between stations S1 and S3 (17 Km) where the oceanic influence is permanent, regardless of the river flow downstream Lalla Aïcha dam. The salinity in this area is between 12 and 34 g/l.
On the other hand, the estuarine type is a function of tidal mixing, bathymetry and river discharge. Estuaries are categorized according to their density stratification controlled primarily by salinity. In our case, we examined the vertical salinity and temperature of the Sebou estuary during the measurement period cited above. Figure 4 presents the results for high tides at 25 May 2014, with river discharge of 60 m 3 /s. A notable stratification is observed, essentially for stations near the estuary mouth (S1, S3 and S4). For S3 and S4 stations, Figure 4 shows a salinity difference of 6 and 3.5 g/l between the surface and the bottom of the river. Marine waters have a high density compared to fresh waters and tend to dive to the bottom of the river. The halocline is defined as a zone of rapid salinity increase with depth and is represented (in the same figure) by green circles in the figure. The upper part of the halocline has a very sharp gradient, and this is often visible to divers because of the neutrally buoyant organic matter that rests there (Dyer 1991). Figure 5 presents a GIS view of vertical salinity distribution along the Sebou estuary at high and low tides. Way, when the bottom water from the estuary encounters the saltier water from the oceanic region, there is an advection movement, causing the entrainment, which is responsible for transferring saltier waters from the bottom layers to the surface. The frontal pressure gradient caused by the encounter of waters with different densities causes a combination between friction force and entrainment, which results in a vertical circulation that characterizes active estuarine fronts (Garvine 1977;De Barros et al. 2014). The entrainment and the turbulent diffusion are the main responsible for causing vertical mixing in the water column.
A number of authors quantitatively classified estuaries on stratification by means of dimensionless numbers, such as Estuarine Richardson number N R (Fischer et al. 1979) and Estuary number N e (Thatcher and Harleman 1981). Table 4 gives a classification of estuaries according to the values of the N e and N R .
Estuarine Richardson number N R : Estuary number N e : where Δρ is the difference between freshwater and seawater density typically 25 kg/m 3 , ρ is the reference density typically 1000 kg/m 3 , g is the acceleration due to gravity (m/s 2 ), Q f is the river flow (m 3 /s), U t is the mean tidal velocity at river mouth (m/s), W is the width of the estuary (m). In estuaries with elevated freshwater discharge and stratification, the N R is high and the entrainment processes predominate. On the other hand, in partially stratified estuaries with elevated tide amplitude, the N R is low and the turbulent diffusion processes are dominant.
In the case of Sebou estuary, for a river flow of 60 m 3 /s, which corresponds to the flow during the measurement in Figure 4, the calculated values of N R and N e are 0.35 and 0.91, respectively. According to the classification above, these values of N R and N e corresponds to a partially mixed estuary which is consistent with observations at the same figure.
Additionally, the monitoring of the vertical variation of temperature shows a thermal stratification through the water column. A thermal gradient appears from 1 m from de surface. Surface waters are much warmer than the deep waters, a difference of 0.5°C and 0.3°C is observed between these two layers.
On the other hand, results in Figures 4 and 5 show that river waters at Kenitra station (S3) are more affected by stratification. This station is accessible compared to others and river hydraulic data are available. Hence, Kenitra station  In order to study the temporal variability of the salinity, a 22-h field measurement (1st and 2nd February 2016) was conducted at the S3 station, with a 10-min interval. Figure 6 shows a sinusoidal salinity evolution, which follows the tidal cycles. A maximum concentration of 13.5 g/l is recorded during high tides and a minimum concentration of 3.6 g/l is recorded during low tides, also the maximum concentration of salinity reached between 20 and 25 g/l during spring tide (Haddout et al. 2016a;Haddout et al. 2016b). Temperature evolution differs from that of salinity and does not follow directly the tidal cycle. The temperature tends to increase during the day, because of the sunshine.
Regarding, the vertical salinity at Kenitra station was carried for two periods (4th and 22nd February 2016) at every 0.5 m depth, with a time interval varied between 5 and 20 min.
During 4th February 2016 (at river flow 14 m 3 /s), the temporal evolution of the salinity and temperature during field measurement at the surface layer (20 cm), the middle layer and background are presented in more detail in Figures 7  and 8(a). For salinity, Figure 7 shows the layering of different salinity level of the water column. The salinity increases from  the surface to the bottom during the entire period. This figure also shows that the transition zone of the salinity varies depending on the state of the tide. Regarding the temperature, the bottom layers remain relatively cold (Figure 8). This situation is usually observed in summer (El-Blidi and Fekhaoui 2003;Hatje 2003;Yurkovskis 2004;Malki et al. 2008;El Morhit et al. 2012).
During the second field campaign 22nd February 2016 (at flow river 49 m 3 /s), the pace of changes in salinity is similar to that observed during the 4th February 2016. Salinity increases gradually from the surface to the bottom (Figure 7(b)). Regarding the temperature, Figure 8(b) shows that during this period, the temperature increases from the surface to the bottom. This is may be due to the influence of climatic conditions (air temperature). In addition, this type of temperature behaviour is always observed in winter (El-Blidi and Fekhaoui 2003;Hatje 2003;Yurkovskis 2004;Malki et al. 2008;El Morhit et al. 2012).
Measurements in the water column showed that the stratification changes according to the state of the tide. Figures 9  and 10 give a GIS view of these measurements. Stratification is outstanding during the ebb (Figure 9(a,b)). This stratification shows the superposition of two or three layers of different salinities. The position relative to the surface of the transition zone (halocline) changes according to the state of the tide. It varies between 1.5 and 2 m at high tide and between 5 and 8.5 m at low tide. In the other hand, the overall average temperature was 18.4°C (Figure 10(a)) and 16.1°C (Figure 10(b)); the temporal variation of temperature did not follow the tidal variation.
Also, comparing the salinity stratification measurements between the two periods (4th and 22nd February 2016) shows the significant impact of the river flow.
On the other hand, the vertical average salinity varies from 9.24 to 19.22 g/l during 4th February 2016 ( Figure 11) and between 0.7 and 12.82 g/l during the 22nd February 2016 (Same Figure 11). The vertical average salinity in the water column during 4th February 2016 is lower than that measured in 22nd February 2016. The cause is the river flow is equal to 14 m 3 /s for 4th February 2016 and 49 m 3 /s for 22nd February 2016.
The above results showed that the salinity level of the Sebou estuary experiencing a significant stratification. Measuring the salinity only at the water surface underestimates its mean vertical value. However, from a practical point of view, a quick estimation of the average salinity is always necessary for the different uses. Figure 12 shows the vertical average salinity of the water versus the surface salinity of the column, using data of 4th and 22nd February 2016 survey.
We note a strong correlation between these two variables (R 2 = 0.97). The average salinity at the Kenitra station can be deduced from the surface salinity by the following relation: where S m is the average salinity and S s is the surface salinity. The correlation between the average vertical salinity and surface salinity must be studied, in the future, for other stations along the estuary. Results from all correlations way permit a calculation of the average salinity at every station. In addition, this equation provides useful information on Table 4. Classification of estuaries according to the values of the N e and N R (Nguyen 2008   the average vertical salinity for water resources managers in understanding amount of minimum freshwater discharge needed to maintain acceptable salinity levels during high tide for pump stations.

Effect of important parameters
The influences of the effective dimensional parameters i.e. riverine discharge (Q) and tidal range (H 0 ) on the salinity intrusion length at high-water slack (HWS) in the Sebou estuary are described in this section. For this study, the salinity intrusion length is considered as the distance from the mouth to the point where the salinity becomes <1 g/l more than the river water salinity (Van der Tuin 1991; Parsa et al. 2007).

The response of salt intrusion to changes in river discharge
As riverine discharge increases, the salinity field is pushed downstream toward the mouth (Savenije 2005). The salt   intrusion length generally follows a power-law relationship to river discharge: L HWS ∼Q n , where the power dependence coefficient n varies in a wide range in different estuarine conditions. The response of the salinity intrusion length to the variation of river discharge was studied for flow ranging from Q = 3 to 160 m 3 /s. This range of river discharge is selected based on the historical records of the river discharge in different seasons (Haddout et al. 2016a;Haddout et al. 2016b). Figure 13 illustrates the salinity intrusion lengths versus the river discharge. This relationship can be presented in the form of a power function as L HWS ∼Q −0.25 with R 2 = 0.90. Increased freshwater discharge pushes the limits of salt intrusion toward the river mouth. Similarly, other studies also revealed the inverse relationship between salinity intrusion length and freshwater discharge. For example, recent numerical studies of Liu and Liu (2014) in the Wu River system in Taiwan showed that the salinity intrudes further during dry seasons. Similarly, Rice et al. (2012) found that in Chesapeake Bay, the salt intrusion is enhanced in dry periods compared with that of typical periods. The observed inverse relationship between salinity intrusion length and discharge is also in line with the results of previous studies of e.g. Oey (1984) carried out a theoretical investigation on the salinity intrusion in unstratified estuaries. His measurements in Hudson estuary indicated that L HWS ∼Q −0.2 . Theoretical arguments of Monismith et al. (2002) also showed that L HWS ∼Q −0.33 while the field measurements in San Francisco Bay showed that the salinity intrusion length is correlated with Q −0.14 . The theoretical arguments of Monismith et al. (2002) are based on the work of Hansen and Rattray (1966) in which they used constant bathymetry. The analysis of Ralston et al. (2008) indicated that the lower sensitivity of the salinity intrusion in San Francisco Bay to the discharge variation is mainly due to the along-channel bathymetry. Zahed et al. (2008) carried out a numerical study on Arvand estuary and showed that L HWS ∼Q −0.2 . Becker et al. (2010) studied the effect of riverine discharge on the salinity intrusion length in the Cape Fear River estuary using a power-law regression analysis. Their analysis indicated that this relationship can be approximated by L HWS ∼Q −0.2 . The importance of variation of channel bathymetry has been also echoed by other investigators (e.g. Gay and O'Donnell 2007;Etemad-Shahidi et al. 2011). It seems that the difference between the values of the exponents may be related to variations in bathymetry and width along the estuaries.
According to Figure 13, at the low flow (Q = 3 m 3 /s), the salinity intrusion length is ∼47 km. When the discharge is equal to 160 m 3 /s (high flow), salinity intrusion length is only ∼15.5 km.

The response of salt intrusion to changes in tidal range
The tide drives the flow which causes different mixing mechanisms in estuaries. The resultant mixing in an estuary originates from shear mixing, tidal trapping, gravitational circulation and tidal pumping . The shear mixing is not the important mixing mechanism in estuaries (Savenije 2005). Tidal trapping is the result of the irregularity of the estuary banks which is not the case (Savenije 2005). The key mixing mechanisms in the studied estuary are gravitational circulation and tidal pumping. A higher tidal range results in stronger tidal currents as well as enhanced horizontal mixing (Fischer et al. 1979).   . Variation and correlation between the salinity intrusion length and riverine discharge at HWS (high-water slack: the moment that the flow velocity is equal to zero is called slack. The moment of slack after HW is referred to as high-water slack (HWS)). Figure 14 indicates that the salinity intrusion length increases with the increase in the tidal range. The minimum tidal range occurs in neap tides when the tidal range is equal to 0.98 m, and the salinity intrusion length is ∼12 km (for Q = 60 m 3 /s). During spring tides, the tidal range and salinity intrusion length are 3.27 m and ∼46 km, respectively. Additionally, Figure 14 indicates that the relationship between the salinity intrusion length and tidal range can be demonstrated by L HWS H 0.96 0 with R 2 = 0.97. As expected, the salinity moves further upstream as the tidal range increases. Hence, all foregoing empirical models have indicated that the salinity intrusion length in LWS and TA are directly related to tidal range. Rigter (1973), Fischer (1974) and Van Os and Abraham (1990) models show that L HWS (H 0.25 0 − H 1 0 ) and Van der Burgh (1972) model shows that L TA H 0.5 0 . These findings imply that the obtained power function describes well the effect of tidal range on the salinity intrusion length. The obtained relationship also indicates that the salinity intrusion length is very sensitive to tidal range variations.

Water resources development and management
Water resources are necessary for the development of human societies. This development, mainly in the industrial and agricultural sectors, increasingly affects these resources at many levels. Lack of water is considered as a limiting factor of socio-economic development of a country. A major objective is to establish policies for sustainable management and governance rules of water resources so as to ensure their durability. In Morocco, conventional water resources are very limited and irregular. The consequence of population and economic growth, accentuated by an increased variability and scarcity of water resources, is the growth of requirements for the quantity and quality of water, their more intensive and comprehensive use. The emphasis in Moroccan development planning has been for the last five decades on maximizing the capture of the country's surface water resources and providing for their optimal use in irrigated agriculture, potable water supplies, industrialization and energy generation on a sustainable basis. Additionally, in this planning imposes to look for other water resources, not yet exploited, as water available in Moroccan estuaries.
Estuarine water is constantly influenced by salinity coming from the ocean. On the other hand, estuaries are complex hydro-systems whose management needs information on several scales, as we will see through the study of the Sebou estuary. This area is a coastal zone with an important agricultural and is becoming one of the most important industrial zones in Morocco. Additionally, this estuary supports industrial practices (At Kenitra City) and navigation activities. Water is diverted for irrigation purposes mainly for peanut production in the upper course of the Sebou estuary. However, high-water salinity limits the development of these activities. Therefore, determination of the salinity distribution along this estuary is the main interest for water managers in Morocco. Also, it is methodologically correct in the management context to start with the simplest description of the phenomena under study and to evaluate the limits of this approximation before investigating more complications.
Meanwhile, this paper provides simple equations (i.e. vertical average salinity and intrusion length) that are useful to provide first estimates of intrusion length and vertical average salinity (at Kenitra station) in the Sebou estuary, which can be obtained by a simple desk study without the use of every measurements day; and as a starting point in many management projects in Morocco relating to recreational, agricultural, commercial activities and safe water supply. Additionally, these formulas are completely transparent and practical, allowing direct assessment of the parameters (i.e. flow rate and tidal range) on the salt intrusion. For example, as long as we get the data of the discharge at upstream of the estuary and salt value at the river mouth, the length of the salt intrusion can be calculated by power-law regression equation for the discharge-salt intrusion relationships. On the contrary, according to the length of salt intrusion, the minimum daily discharge to prevent the salt water can be predicted. The regression equations can estimate the salinity intrusion and river discharge (or tidal range) quickly and simply, which provide a decision-making basis for quick response to deploy the corresponding preventive measures to minimize disasters when the salt intrusion happened. These sample predictive equations is an effective tool for water resources development in this area, and to assist the future management plans.

Conclusions
In this paper, longitudinal salinity evolution and the vertical salinity stratification under different hydrological conditions in the Sebou estuary was investigated. First measurements have shown that river waters at Kenitra station (S3) are more affected by stratification. Intensive observations at Kenitra station showed that the vertical salinity stratification depends both on tidal cycle and river flow. Measurements results show that the vertically averaged salinity during spring tide is higher than that during neap tide. Also, the stratification increases a larger during the low-flow periods than during the high-flow periods in the Sebou estuary. On the other hand, the impact of stratification changes overwhelms the impact of tidal changes. Finally, the equations with a high R 2 value was provided as a rapid tool for assessment of changing the intrusion length (or river discharge if not available), and average vertical salinity (at Kenitra station) in the Sebou estuary.