The longitudinal variation of salinity and the maximum salinity intrusion length in an alluvial estuary are important environmental concerns for policy makers and managers since they influence water quality, water utilization and agricultural development in estuarine environments and the potential use of water resources in general. The supermoon total lunar eclipse is a rare event. According to NASA, they have only occurred 5 times in the 1900s – in 1910, 1928, 1946, 1964 and 1982. After the 28 September 2015 total lunar eclipse, a Super Blood Moon eclipse will not recur before 8 October 2033. In this paper, for the first time, the impact of the combination of a supermoon and a total lunar eclipse on the salinity intrusion along an estuary is studied. The 28 September 2015 supermoon total lunar eclipse is the focus of this study and the Sebou river estuary (Morocco) is used as an application area. The Sebou estuary is an area with high agricultural potential, is becoming one of the most important industrial zones in Morocco and it is experiencing a salt intrusion problem. Hydrodynamic equations for tidal wave propagation coupled with the Savenije theory and a numerical salinity transport model (HEC-RAS software “Hydrologic Engineering Center River Analysis System”) are applied to study the impact of the supermoon total lunar eclipse on the salinity intrusion. Intensive salinity measurements during this extreme event were recorded along the Sebou estuary. Measurements showed a modification of the shape of axial salinity profiles and a notable water elevation rise, compared with normal situations. The two optimization parameters (Van der Burgh's and dispersion coefficients) of the analytical model are estimated based on the Levenberg–Marquardt's algorithm (i.e., solving nonlinear least-squares problems). The salinity transport model was calibrated and validated using field data. The results show that the two models described very well the salt intrusion during the supermoon total lunar eclipse day. A good fit between computed salinity and measurements is obtained, as verified by statistical performance tests. These two models can give a rapid assessment of salinity distribution and consequently help to ensure the safety of the water supply, even during such infrequent astronomical phenomenon.

Total lunar eclipse calculation by Fred Espenak, NASA/GSFC.

Illustrating the position of the moon (total lunar eclipse).

A supermoon total lunar eclipse is one of nature's loveliest celestial events (Espenak, 2000). During this event, three things will occur at once. First, the moon will be both full and at its closest point to Earth (356 877 km); this is known as a supermoon or perigee Moon (NASA, 2015). Second, this will occur at the same time as a total lunar eclipse; that means the Moon, Sun and Earth will be aligned. Because of its proximity to Earth, the Moon will appear brighter and larger (14 % larger and 30 % brighter than other full moons) in the sky (NASA, 2015). Third, the moon will appear a dark, coppery red, caused by the Earth blocking the sun light that is refracted by the atmosphere into the umbra (Hughes et al., 2015) (Fig. 1). Furthermore, tidal motions are controlled by changes in the position and alignment of the Moon and Sun relative to Earth (Stronach, 1989) (Fig. 2). Therefore, tidal forces are strengthened if the moon is closest to Earth in its elliptical orbit and when the Sun and Moon are directly over the Equator (NOC, 2015).

Estuaries form essential parts of the human–Earth system (Savenije, 2015). As the connecting element between marine water and river, estuaries have properties of both: they contain both fresh and saline water, they experience not only tides but also river floods, and they host both saline and fresh ecosystems (Savenije, 2015). The diverse estuarine environment plays not only an important role in the life cycle of many species but also serves as a site for many human activities. In short, estuaries are important water bodies where many dynamic factors interact and unfold (Xu et al., 2015). For decades, explosive increases in industrial and agricultural productivity, as well as the growing population in estuary regions, have led to numerous environmental concerns (Mai et al., 2002). Salinity intrusion is an important phenomenon in an estuary, and can constitute a serious problem. It influences the water quality and threatens potential water resource use. Intake of fresh water for consumption, agricultural purposes or use by industries may take place within a region not far landward of the limit of salt intrusion. To support policy and managerial decisions, a profound knowledge of processes associated with the salinity structure in estuaries is required (Kuijper and Van Rijn, 2011). Models have been widely used to research salinity intrusion. Two kinds of models are typically used: numerical models and analytical models. Presently, numerical models are more popular especially two-dimensional (2-D) and 3-D models (Kärnä et al., 2015; Elias et al., 2012; Zhao et al., 2012; Li et al., 2012; Jeong et al., 2010; Wu and Zhu, 2010; Xue et al., 2009; An et al., 2009, etc.) because they can provide more spatial and temporal detail.

Analytical models are also widely used, such as Prandle (1981), Savenije (1986, 1989, 1993a, 2005, 2012, 2015), Lewis and Uncles (2003), Gay and O'Donnell (2007, 2009), Kuijper and Van Rijn (2011), Aertsl et al. (2000), Brockway et al. (2006), Nguyen and Savenije (2006), Nguyen (2008), Nguyen et al. (2008), Cai et al. (2016), Gisen et al. (2015a, b), and Xu et al. (2015). These tools are based on the steady-state conservation of mass equation, which indicates that the dispersive and advective transports of salt are in equilibrium and the effective longitudinal dispersion coefficient incorporates all mixing mechanisms, where the dispersion coefficient along the estuary axis is either constant (e.g., Brockway et al., 2006; Gay and O'Donnell, 2007) or variable (e.g., Van der Burgh, 1972; Savenije, 1986).

In fact, 1-D mathematical models, i.e. analytical or numerical, can constitute the appropriate tools for quick-scan actions in a pre-phase of a project or for instructive purposes. In addition, it is methodologically correct to start with the simplest description of the phenomena under study and to evaluate the limits of this approximation before investigating more complications.

Our previous studies on the Sebou river estuary have shown that the 1-D (analytical or numerical) methods properly compute salt intrusion (Haddout et al., 2015, 2016). Also, Haddout et al. (2015) showed that salinity profiles of Sebou estuary show steep decrease. This characteristic is specific to narrow estuaries, i.e., having a near-prismatic shape and significant freshwater discharge. Such estuaries are called positive estuaries.

The aims of this paper it to investigate the applicability of these two
methods, analytical or numerical, during the supermoon total lunar eclipse
day of 28 September 2015. Measurements have shown a modification of
the shape of the salinity profiles along the estuary and a notable water
level increase, compared with normal situations studied in our earlier
works. In addition, calculations during the supermoon total lunar eclipse
using the coupled analytical hydrodynamic–salt intrusion model required the
recalculation of the geometric parameters of the estuary i.e.,
cross-sectional area

Even in these extreme conditions, a good-fit was obtained between the computed and observed salinity distribution for the two models. These models constitute powerful tools for evaluating salinity intrusion patterns in the Sebou river estuary, even during extreme events inducing sea level rise like the supermoon eclipse or climate change.

The analytical salinity intrusion model of Savenije (2005) has been adopted
to predict the salinity distribution and salinity intrusion length in
alluvial estuaries. This method is fully analytical, although it makes use of
certain assumptions, the most important being: the exponential shape of the
estuary, the longitudinal variation of the dispersion according to Van der
Burgh (1972), and the predictive equations for the boundary condition and the
Van der Burgh coefficient. The equations are based on the 1-D
cross-sectionally averaged, and tidally averaged, steady-state salt balance
equation, in which the advective salt transport is caused by the seaward
freshwater discharge, counteracted by the landward dispersive salt transport
induced by the different mixing processes (Cai et al., 2015). In a convergent
estuary, the main geometric parameters: cross-sectional area

In a steady-state situation, the partial temporal derivative in the salt
balance equation is zero (Gisen et al., 2015b). Considering constant
freshwater discharge

Since dispersion depends both on the river discharge and the salinity
distribution itself, the constant dispersion is not a correct solution. An
efficient and accurate approach to simulate the longitudinal variation of
dispersion is presented by Van der Burgh (1972), and also adopted by
Savenije (1986, 1989, 1993a, 2005, 2012):

Integrating Eq. (3) in combination with Eq. (2.38) in
Savenije (2012) yields

This 1-D steady advection–diffusion model has been applied to describe the salinity distribution along numerous well-mixed and partially-mixed estuaries (i.e. the adopted salt intrusion model assumes a partially to well mixed situation, which under low flow is the dominant process) (Nguyen and Savenije, 2006) for the HWS, LWS or TA condition.

The salt intrusion length

The roughness coefficient can be estimated by

Since 1960s there has existed a long tradition of 1-D analytical solutions for tidal dynamics in estuaries (e.g., Dronkers, 1964; Ippen, 1966; Prandle and Rahman, 1980; Leblond, 1978; Godin, 1985, 1999; Jay, 1991; Savenije, 1993b; Friedrichs and Aubrey, 1994; Lanzoni and Seminara, 1998; Kukulka and Jay, 2003; Horrevoets et al., 2004; Jay et al., 2011; Cai et al., 2012a). These analytical solutions usually made assumptions to simplify or linearize the nonlinear set of equations (Zhang et al., 2012). Of these, most authors used perturbation analysis, where scaled equations are simplified by discarding higher-order terms, generally neglecting the advective acceleration term and linearizing the friction term higher-order terms, whereas Savenije (2005) uses a simple harmonic solution without simplifying the equations (Cai et al., 2013). Others used a regression model to determine the relationship between river discharge and tide. Exceptions are the approaches by Horrevoets et al. (2004) and Cai et al. (2012b), who provided analytical solutions accounting for river discharge, based on the envelope method originally developed by Savenije (1998) (Cai et al., 2013). Recently, Cai et al. (2012a) proposed a new analytical framework for understanding the tidal damping in estuaries. They concluded that the main differences between the examined models (e.g., Savenije et al., 2008; Toffolon and Savenije, 2011; Kuijper and Van Rijn, 2011) lies in the treatment of the friction term in the momentum equation. Furthermore, Cai et al. (2012a) presented a new “hybrid” expression for tidal damping as a weighted average of the linearized and fully nonlinear friction term (Cai et al., 2013). Additionally, Cai et al. (2014b) included for the first time the effect of river discharge in a hybrid model that performs better.

Definition of dimensionless parameters (Cai et al., 2015).

Hybrid solution of tidal wave propagation in convergent estuaries (Cai et al., 2015).

It can be demonstrated that tidal hydrodynamics is controlled by three-dimensionless parameters that depend on localized geometry and external
forcing (e.g., Toffolon et al., 2006; Savenije et al., 2008), i.e.,

Note that the friction number reflects the nonlinear effect of the varying
depth (Savenije, 2012). The tidal hydrodynamics analytical solution can be
obtained by solving a set of four analytical equations, i.e., the phase lag
equation, the scaling equation, the damping equation and the celerity
equation (Cai et al., 2013). In Table 2, we present these equations for the
general case as well as the special case of the ideal estuary (

Since tidal dynamics in convergent alluvial estuaries can be reproduced
reasonably well by 1-D analytical solutions, in principle the output of such
a model can be used to predict the longitudinal tidal excursion

Moreover, Van der Burgh (1972) assumed that the salinity curves for
the HWS and LWS situations can be obtained by applying a horizontal
translation over half the tidal excursion in the landward and seaward
direction from TA situation and subsequently was demonstrated by Savenije (1986, 1989, 2005, 2012). Thus, Eq. (6) can be used to describe the two
situations of

The proposed analytical model by Cai et al. (2012a) for tidal hydrodynamics
can be used to predict a variable velocity amplitude

Salinity distribution is influenced by the hydrodynamic regime, which in
turn depends highly on the river estuary morphology. In the hydrodynamics
module, HEC-RAS solves the following 1-D equations of continuity
and momentum, known as the Saint-Venant equations (Brunner, 2010):

Manning's roughness coefficient used in the momentum equation is evaluated
initially by the empirical formula Eq. (16) proposed by Cowan (1956) and
Chow (1959):

Equations (14) and (15) are solved using the well-known four-point implicit box finite difference scheme (Brunner, 2010).

This numerical scheme has been shown to be completely non-dissipative but
marginally stable when run in a semi-implicit form, which corresponds to
weighting factor (

In the advection–dispersion module, the basic equation is the
1-D advection–dispersion one of a conservative constituent
(Brunner, 2010):

Geometric characteristics in the Sebou estuary.

Inputs of the transport model are initial and boundary salinity
concentrations and the dispersion coefficient (parameter

Study area and measurements sites in the Sebou river estuary.

Freshwater discharge release by Lalla Aïcha dam (from 1 January 2014 to 1 January 2016).

The Sebou is the largest Moroccan river, draining approximately 40 000 km

The tidal height varies from 0.9 to 3.10 m depending on the condition of the
tide and the average flow is about 200 m

Geometry of the Sebou estuary, showing the cross-sectional
area

Salinity evolution in the Sebou river estuary during 12 h (surveyed on 28 September 2015).

The entire estuary can be divided into two reaches with different convergence
length for cross-sectional area, width and depth. The first inflection point
is located at

The convergence length is shorter in the seaward reaches (

In this study, five locations: Mehdia, Oulad Berjel, Kenitra, Oulad Salma,
and M'Rabeh along the Sebou estuary are chosen for salt measurements (Fig. 6)
during 12 h of 28 September 2015 (supermoon total lunar eclipse day). A
W-P600 conductivity meter is used in each location. The salinity can be
expressed in parts per thousand (ppt or g L

Salinity evolution in the Sebou river estuary during spring tide (surveyed on 11 February 2016).

Water level measurements at Kenitra location from 27 to 29 September 2015.

The maximum and minimum salinity curves at HWS and LWS were thus observed,
representing the envelopes of the salinity variation during tidal cycle.
Figure 6 shows vertically averaged salinity concentration measurements
conducted at the five locations, during 12 h with 12 min interval. A
maximum salinity concentration is recorded during high tides with
35.5 g L

Calibrated parameters for the hydrodynamic model of the Sebou estuary.

Furthermore, Fig. 7 shows vertically averaged salinity concentration
measurements at normal situation during spring tide in three locations (Oulad
Berjel, Kenitra and Oulad Salma). A maximum salinity concentration is
recorded during high tides with 28.5 g L

The mixing mechanisms in estuaries are guided by tidal dynamics, the dispersion mechanisms and the amount of freshwater discharge from the river estuary. Dispersion includes longitudinal mixing, that takes place by mass traveling in streamlines at different velocities (Nylén and Ramel, 2012) and vertical mixing. Earlier measurements on Sebou estuary (Haddout et al., 2015) has shown vertical salinity and temperature stratification, essentially for locations near the estuary mouth (Mehdia, Oulad Berjel and Kenitra), classifying Sebou estuary as a partially mixed river. In addition, Fig. 8 shows water level measurements at the Kenitra location from 27 to 29 September 2015.

The water level drops in the low tide and then rises and peaks with the high tide to 4 m at supermoon total lunar eclipse day (less than 3.2 m in normal situation). This indicates the supermoon total lunar eclipse influence on the estuary hydrodynamic regime.

In this paper, the analytical (tidal propagation and salt intrusion) and numerical models introduced in the previous sections are applied to the Sebou estuary to evaluate the supermoon total lunar eclipse effect on salinity distribution.

To turn the steady-state model into a predictive model, semi-empirical
relations (Eq. 6) are required that relate the two optimization
parameters

Field measurements of salt intrusion along the Sebou estuary axis, which were
conducted at the 7–18–27 May 2015 (covering a spring–neap cycle) and at the
28th supermoon total lunar eclipse day, are used to test the predictive
method. Each tidal cycle consists of two HWS and two LWS salinity
observations, which corresponds to the tidal wave periods. The hybrid
(hydrodynamic) model presented in Sect. 1 was calibrated during
7–18–27 May 2015 and at supermoon total lunar eclipse day. The calibrated
parameters, the Manning–Strickler friction coefficient

Observed and analytically computed longitudinal salinity
distribution along the Sebou estuary (surveyed on 28 September 2015)
during 1st cycle

Longitudinal variation of salinity gradient

Comparison of computed and optimized dispersion

Based on the hydrodynamic parameters (e.g., tidal amplitude and velocity
amplitude) from the hybrid (hydrodynamic) model, it is possible to estimate the
main parameters that determine the salinity intrusion from predictive
Eqs. (8) and (9) at the inflection point. In most estuaries, there usually
exists an inflection point near the mouth, where the geometry changes (e.g.,
Gisen et al., 2015b). Moreover, the Van Der Burgh's (

Salt intrusion lengths computed against observed lengths (at HWS) for different predictive formulae found in the literature (Savenije, 2005) compared with results of the actual study on Sebou estuary.

Water level comparisons at Kenitra location in
calibration

Salinity comparisons at Oulad Berjel

The Levenberg–Marquardt algorithm adaptively varies the parameter updates between the gradient descent update and the Gauss–Newton update.

Salinity distribution data showing the salinity at the mouth
(

Values of the optimized parameters are summarized in Table 5 (at HWS), where
the dispersion coefficient at the estuary mouth

We attribute this difference to the dominance of tidal mixing in the Sebou
estuary for the eclipse period. Because the optimized value of

Additionally, salt intrusion exhibits three distinct tendencies: a dome shape at HWS and TA, a recession and bell shapes at LWS (see Appendix A). These three salinity shapes were observed during the eclipse day.

Furthermore, in a positive estuary, the salinity gradient is always negative due to the decreasing salinity in the landward direction as is the case for the Sebou river estuary (Fig. 11a). The dome shaped intrusion curves have a negative curvature in the seaward part of the estuary. As water level increases, the position of the maximum salinity gradient moves towards the estuary seaward, after which it has a dome shape with monotonous increasing of the salinity gradient. In addition, Fig. 11b shows curves of the second derivative of salinity gradient.

Additionally, the scatter plot of the computed vs. optimized results for the dispersion coefficient at high water slack is shown in Fig. 12.

This salinity intrusion model has been applied in different estuaries all over the world and by several methods (e.g. Van den Burgh, 1972; Rigter, 1973; Fischer, 1974; Van Os and Abraham, 1990; Savenije, 1993a, 2005; see Appendix B).

Figure 13 shows the computed salt intrusion lengths against observed lengths (at HWS) with data specific to Sebou estuary compared to different predictive formulae found in the literature. We observe that the Savenije solution for salt intrusion lengths fits very well with the observed data compared to all others solutions. The results of Savenije model are considered most accurate.

The hydrodynamic regime was first studied and modeled in HEC-RAS. Outputs from the hydrodynamic model (velocity and water level evolution) were used in the salt transport study. The final resolution of hydrodynamic model Eqs. (14) and (15) requires spatial discretization of the study area. The river reach (62 km) was discretized into 203 grids with a length varying between 58 and 996 m (Haddout et al., 2016). Data on cross-sectional areas from the ANP and other sources were used. The upstream boundary at the Lalla Aïcha dam was given values of discharge as a function of time from 27 to 29 September 2015. Also, the seaward boundary at the mouth was given values of the water level as a function of time.

The factor

The hydrodynamic model has been calibrated and validated using data from 27 to 29 September 2015. The calibrated parameter is Manning's roughness in the estuary. The calibration and validation are performed using the water level data at Kenitra location. The 27 September 2015 day has been used for calibration. The roughness coefficients were adjusted by a trial and error approach until the simulated and observed water levels were satisfactory.

Figure 14a shows the comparison of the simulated water level at Kenitra location with the observed data where the water levels are measured based on the datum of the ANP. For the model validation, water levels during 28 and 29 September 2015 have been used. Figure 14b shows good correspondence between the observed and simulated water levels at the Kenitra location.

Statistical indicators of analytical hydrodynamic model performance during the supermoon total lunar eclipse day.

Statistical indicators of analytical salinity intrusion model performance at HWS during the supermoon total lunar eclipse day.

Salinity distributions in the Sebou estuary during spring tide, neap tide and supermoon total lunar eclipse day.

Statistical indicators of Hydrodynamic model performance in calibration and validation.

Statistical indicators of transport model performance in calibration.

Comparisons salinity variation at HWS in different locations.

The salinity model has been calibrated by systematically adjusting the values
of the dispersion coefficient to achieve an acceptable match between the
measured salinity and the corresponding values computed by the 1-D advection–dispersion model. The dispersion coefficient was
modified to the same degree along the studied reach because we assumed that
the sources of errors involved in its evaluation are identical for all the
grids. The calibrated values of the coefficient “

The statistical indicators used for evaluating the performance of the
numerical and analytical models are root mean squared error (RMSE); mean
absolute error (ABSERR); the Nash–Sutcliffe modeling efficiency index (EF);
the goodness-of-fit (

The closer the values of RMSE and ABSERR to zero, and

The indicators of the hydrodynamic–salinity intrusion model are summarized
in Tables 6 and 7. In two models, the EF and

The statistical performances of the numerical model use water level for comparison. Values of statistical parameters indicated in Table 8 show good correlation model calculations and measurements during calibration and validation. These indicate that the model can estimate the water level at Kenitra fairly well.

The statistical indicators for the transport model are summarized in Table 9. The results show that the computed salinity concentration follows observed data, which suggest that the presented mass transport model is a reasonably efficient tool for predicting the impact of the supermoon total lunar eclipse on salt intrusion in alluvial estuaries.

The impact of the combination of a supermoon and a total lunar eclipse on
river hydrodynamics is mainly caused by the moon being at its closest point to Earth, which
gives extra gravitational pulling, and the alignment of Sun–Earth–Moon. The
maximum salinity at high water along the Sebou estuary has been described in
Sect. 4. Supermoon and total lunar eclipse impact on the maximum salinity at
different locations compared to the normal situation is given in Table 10.
The results clearly show that the astronomical event's impact on salinity
intrusion is highly significant. The salinity increments in the four stations
relative to the normal situation were 4.1 g L

Furthermore, Fig. 16 shows the profiles of salinity during supermoon total lunar eclipse compared with spring–neap tides. It appears that the salt intrusion curve computed in the neap–spring tides are recession type, while it becomes a dome-type shape at eclipse day. According to Nguyen et al. (2012), this is subjected to changes in the degree of convergence of the cross-sectional profile, and the effect of the mixing due to freshwater discharge (i.e. that increasing the tidal amplitude at the mouth tends to produce shorter convergence lengths of the cross-sectional area and width). The convergence or divergence of the channel can dramatically change the shape of the salt intrusion curve (Gay and O'Donnell, 2007; Cai et al., 2015). In addition, Savenije (2005) shows that the recession-type curve occurs in narrow estuaries having a near-prismatic shape, high river discharge and dome-type shape, which occurs in strong funnel-shaped estuaries (with a short convergence length) (see Appendix A). At eclipse day, when the channel converges strongly, the mixed water retains relatively higher salinity from the estuary mouth. However, salinity profiles under all spring–neap tides show a gradual decrease from the mouth to the upstream reach.

Additionally, it can be shown that the part of the Sebou estuary that is
affected by the supermoon total lunar eclipse is from 20 to 25 km upstream
of the river mouth. A water level rise as showed above during this
exceptional event moves the excessive salinity (25 g L

Computations using hybrid (hydrodynamic) and salt intrusion models during the
supermoon total lunar eclipse required the recalculation of the geometric
parameters of the estuary, i.e., cross-sectional area

The purpose of this paper was to study the impact of the supermoon total
lunar eclipse of 28 September 2015 on salt intrusion in Sebou river estuary.
It is, to our knowledge, the first time that this infrequent phenomenon has
been
studied in terms of its influence on water quality. Field measurements showed
a change of the salinity profiles form along the estuary axis and a notable
water level rise, compared with normal situations studied in our earlier
works. In addition, results show that the average salt content increased in
the reach between 0 and 25 km, as a result of water volume rise at the mouth. A
hybrid model proposed by Cai et al. (2014) coupled to an analytical salt
intrusion model in alluvial estuaries (Savenije, 2005) and a numerical model
(HEC-RAS) have been applied in the Sebou river estuary. Calculations during
the supermoon total lunar eclipse using the coupled hybrid–salt intrusion
model required the recalculation of the geometric parameters of the estuary,
i.e., cross-sectional area

A comparison between the two applied models is not the objective of this study since each one can be applied for specific management purposes. The analytical models are helpful for situations where a quick longitudinal salinity profile is needed. Furthermore, the numerical 1-D model is powerful where a temporal salinity variation is carried out in a specific location, but it needs more data and time for its implementation. Hence, these tools can be very helpful for water managers and engineering to make preliminary estimates on the salt intrusion along the estuary axis even during extreme events. These extreme events can concern similar the supermoon total lunar eclipse, see level rise due to climate change, a sea tsunami.

Finally, the impact of extreme events on the water quality of Sebou estuary should be considered by managers. Rapid interventions, based on the predictions of our mathematical models can thus be taken. These interventions may involve the pumping station closure for example.

The data used in the study (analytical and numerical models) were provided by local water authorities (i.e. ANP, National Agency of Ports and Water Services of Kenitra town) in a row format (AutoCAD files). On the other hand, some topographic and satellite maps were exploited.

Salinity distribution is a veritable fingerprint of each estuary and in
direct relation to both its geometric form and hydrology. For partially mixed
and well-mixed estuaries, a number of designations are used to classify
salinity profiles into three types depending on their shape. The following
types are distinguished (Savenije, 2005, 2012) (see Fig. A1):

Recession shape, which occurs in narrow estuaries with a near-prismatic shape and a high river discharge (Savenije, 2005, 2012).

Bell shape, which occurs in estuaries that have a trumpet shape, i.e. a long convergence length in the upstream part, but a short convergence length near the mouth (Savenije, 2005, 2012).

Dome shape, which occurs in strong funnel-shaped estuaries (with a short convergence length) (Savenije, 2005, 2012).

Three types of salt intrusion curves, in which

Rigter (1973):

Fischer (1974):

Van der Burgh (1972):

Van Os and Abraham (1990):

The authors would like to express their gratitude to O. Khabali, H. Qanza, M. Hachimi, O. El Mountassir and I. Baimik for the efforts in the field measurements during the supermoon total lunar eclipse day. The authors would also like to acknowledge the technicians at the water services of Kenitra, and the engineers of the National Agency of Ports for their availability and collaboration. Edited by: A. Ghadouani Reviewed by: two anonymous referees