HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-20-3923-2016Analytical and numerical study of the salinity intrusion in the Sebou river
estuary (Morocco) – effect of the “Super Blood Moon” (total lunar eclipse) of
2015HaddoutSoufianehaddout.ens@gmail.comIgouzalMohammedMaslouhiAbdellatifInterdisciplinary Laboratory for Natural Resources and Environment,
Department of Physics, Faculty of Sciences, Ibn Tofail
University, B.P 242, 14000 Kenitra, MoroccoSoufiane Haddout (haddout.ens@gmail.com)26September20162093923394531May201613June201629August201612September2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://hess.copernicus.org/articles/20/3923/2016/hess-20-3923-2016.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/20/3923/2016/hess-20-3923-2016.pdf
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).
Introduction
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 A0 and convergence length a.
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.
Models formulations1-D salt intrusion model
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 A, width B
and depth h can be described by exponential functions (see
Eqs. (2.38)–(2.40) in Savenije, 2012).
In a steady-state situation, the partial temporal derivative in the salt
balance equation is zero (Gisen et al., 2015b). Considering constant
freshwater discharge Q and tidally averaged cross-sectional area
A, the salt balance equations for the high water slack (HWS), low water
slack (LWS) and tidal average (TA) situation can be rearranged as
∂SS=-QAD∂x.
If one assumes that D is constant along the length of an estuary,
i.e., D=D0, where D0 is the dispersion coefficient at the estuary
mouth, simple analytical solutions for axial distribution of salinity can be
derived.
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):
∂D∂x=-KQA,
which, using Eq. (1), can be demonstrated to be the same as the
following equation (Savenije, 2005, 2012):
DD0=SS0K,
where S0 (g L-1) is the boundary salinity at the estuary mouth,
D0 (m2 s-1) is the longitudinal dispersion at the estuary
mouth for the HWS, LWS or TA condition and K is the Van der Burgh's dimensionless
coefficient, which has a value between 0 and 1. If K=0, Eq. (3) reduces to
the case with constant dispersion D=D0. For the case where K=1, we see
that the curves D/D0 and S/S0 coincide. If K is small, then
tide-driven mixing is dominant near the toe of the intrusion curve; if K
approaches unity, then gravitational mixing is dominant (Savenije, 2006;
Shaha and Cho, 2011).
Integrating Eq. (3) in combination with Eq. (2.38) in
Savenije (2012) yields
DD0=1-KQaAD0exp(x/a)-1,
which determines the longitudinal variation of dispersion coefficient.
Combining Eqs. (3) and (4), the cross-sectionally averaged salinity
along an estuary with convergent cross-sectional area is given by Savenije (2005, 2012):
SS0=1-KQaD0A0exp(x/a)-11/K.
Making use of the dimensionless parameters (Cai et al., 2016), Eq. (5) can be
scaled as
S∗=1-KD∗γexp(x∗γ)-11/K,
where S∗ is dimensionless salinity that is normalized by the salinity
at the estuary mouth, γ is the estuary shape number representing the
convergence of an estuary, D∗ is the dimensionless dispersion at
seaward boundary condition and x∗ is the dimensionless longitudinal
coordinate that is scaled by the frictionless wavelength in prismatic
channels (Cai et al., 2016).
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 L∗, defined as the distance from the
estuary mouth to the location with freshwater salinity (assumed to be
<1 g L-1 isohaline) for the HWS, LWS or TA condition, can be determined by
setting S∗=0 in Eq. (6):
L∗=1γln(γD∗K+1).
Furthermore, in most estuaries, there usually exists an inflection
point near the mouth, where the geometry changes (e.g., Gisen et al.,
2015b). This inflection point is associated with the transition of a
wave-dominated regime to a tide-dominated regime (Gisen et al., 2015b).
Making use of this phenomenon, Gisen et al. (2015b) recently expanded the
underlying database and reanalyzed these equations, resulting in
D1v1E1=0.396×(g/C2)0.21(NR)0.57,K=8.03×10-6Bf0.30g0.93H10.13T0.97π0.71B10.30Cz0.18v10.71b10.11h10.15rs0.84,
where Bf is the river regime width (typical width in the river-dominated region), and Cz is the Chezy roughness coefficient. The
symbols H1 (m), B1 (m), v1 (m s-1), b1 (m), h1
(m), D1 (m2 s-1) and E1 (m) represent the tidal range, stream
width, velocity amplitude, width convergence length, depth, dispersion
coefficient and tidal excursion at the inflection point, respectively. If
there is no inflection point near the estuary mouth, then these parameters
refer to the situation at the mouth itself.
The roughness coefficient can be estimated by Cz=Ksh11/6 with Ks being the Manning–Strickler friction (Ks=1/n,
where n is the Manning's coefficient), while the tidal excursion can be
calculated by E1=v1T/π. The estuarine Richardson number
NR, which is defined as the ratio of potential energy of the
buoyant fresh water to the kinetic energy of the tide (Fischer et al., 1979),
is given by
NR=ΔρρghQTA0E0ν02,
where ρ (kg m-3) is the water density, Δρ is the density
difference of ocean and river water over the salt intrusion length (in
estuaries, the ratio Δρ/ρ is about 0.025).
Analytical hybrid model
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).
Dimensionless parameters Local variableDependent variableTidal amplitude ζ=η/h Estuary shape γ=c0/(ωa) Friction number χ=rsfc0ζ/(ωh) River discharge φ=Ur/vDamping number δ=c0dη/(ηωdx)
Velocity number μ=v/(rsζc0)=vh/(rsηc0) Celerity number λ=c0/c Phase lag ε=π/2-(ϕZ-ϕU)
Hybrid solution of tidal wave propagation in convergent estuaries
(Cai et al., 2015).
CasePhase lag tan(ε)Scaling μDamping δCelerity λ2Generalλ/(γ-δ)sin(ε)/λ=cos(ε)/(γ-δ)γ/ 2-4χμ/(9πλ)-χμ2/ 31-δ(γ-δ)Ideal estuary1/γ1/(1+γ2)01
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., ζ
the dimensionless tidal amplitude (indicating the seaward boundary
condition), γ the estuary shape number (representing the effect of
cross-sectional area convergence) and χ the friction number (describing
the role of the frictional dissipation). These parameters are defined in
Table 1, where η is the tidal amplitude and Ks is the
Manning–Strickler friction coefficient.
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 (δ=0).
Coupled model for salt intrusion
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 E∗;
i.e. E∗ is the dimensionless tidal excursion scaled by the
frictionless tidal wavelength (Cai et al., 2016) defined as
E∗=Eω/c0=2v/c0,v=rsc0μω,η/h,
where v is the velocity amplitude and ω is the tidal frequency,
c0 is the classical wave celerity of a frictionless progressive wave
defined as
c0=gh/rs,
where g is the acceleration due to gravity and rs the storage
width ratio (e.g., Savenije et al., 2008).
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
S∗HWS(x∗)=S∗TA(x∗+E∗/2),S∗LWS(x∗)=S∗TA(x∗-E∗/2).
Here the asterisk denotes a dimensionless variable.
The proposed analytical model by Cai et al. (2012a) for tidal hydrodynamics
can be used to predict a variable velocity amplitude v (and hence tidal
excursion E∗) for given tidal amplitude at the seaward boundary,
estuary shape and friction.
Numerical modelingHydrodynamic model
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):
∂Q∂x+∂A∂t-ql=0,∂Q∂t+∂(Q2/A)∂x+gA∂h∂x=gAnQAR2/32-β0,
where Q is the freshwater discharge (m3 s-1), A is the cross-sectional area (m2), x is the distance along the channel (m), t is
the time (s), ql is the lateral inflow per unit length
(m2 s-1), g is the acceleration due to gravity (m s-2),
h is the flow depth (m), β0 (–) is the bottom slope, n is
the Manning's roughness coefficient (n=1/Ks)
(m-1/3 s-1) and R is the hydraulic radius (m).
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):
n=(n0+n1+n2+n3+n4)m5,
where n0 is a basic value for a straight, uniform, smooth channel,
n1 is the adjustment for the effect of surface irregularity, n2 is
the adjustment for the effect of variation in shape and size of the channel
cross section, n3 is the adjustment for obstruction, n4 is the
adjustment for vegetation and m5 is a correction factor for meandering
channels.
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 (θ) of 0.5 for the unsteady solution. This value
represents a half weighting explicit to the previous time step's known
solution, and a half weighting implicit to the current time step's unknown
solution. However, practically speaking, due to its marginal stability for
the semi-implicit formulation, a θ weighting factor of 0.6 or
more is necessary, since the scheme is diffusive only at values of θ
greater than 0.5. In HEC-RAS, the default value of θ is 1. However,
the user can specify any value between 0.6 to 1 (Billah et al., 2015).
Mass transport model
In the advection–dispersion module, the basic equation is the
1-D advection–dispersion one of a conservative constituent
(Brunner, 2010):
∂(AC)∂t=∂∂xDA∂C∂x-∂(QC)∂x,
where C is the salinity concentration (g L-1), A is the cross-sectional
area of the river (m2), Q is the freshwater discharge (m3 s-1) and
D is the longitudinal dispersion coefficient (m2 s-1). This module
requires output from the hydrodynamics module in terms of discharge, water
level, cross-sectional area and hydraulic radius. The advection–dispersion
equation is solved using the ULTIMATE QUICKEST explicit upwind scheme
(Brunner, 2010). The resultant finite difference solution for Eq. (17)
is as follows:
Vn+1Cn+1=VnCn+Δt×QupCup∗-QdnCup∗+DdnAdn∂C∗∂xdn-DupAup∂C∗∂xup,
where Cn+1 is the concentration of a constituent at present time step
(g m-3), Cn is the concentration of a constituent at previous time
step (g m-3), Cup∗ is the QUICKEST concentration of a
constituent at upstream (g m-3), ∂C∗/∂xup is the QUICKEST derivative of a constituent at
upstream (g m4), Dup is the upstream dispersion coefficient
(m2 s-1), Vn+1: volume of the water quality cell at present
time step (m3), Vn is the volume of the water quality cell at
previous time step (m3), Qup is the upstream discharge
(m3 s-1) and Aup is the upstream cross-sectional area
(m2).
Inputs of the transport model are initial and boundary salinity
concentrations and the dispersion coefficient (parameter D in Eq. 17).
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).
Overview of the Sebou river estuary
The Sebou is the largest Moroccan river, draining approximately 40 000 km2,
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 (Fig. 3). Kenitra harbor, about 17 km from the ocean, has
commercial traffic, while Mehdia harbor at only 2 km from the mouth is busy
with fishing activities. The flow regime at the level of the Sebou estuary
is marked by considerable seasonal and interannual variations. It is under
the influence of the tide regime and under the control of many dams (Igouzal
and Maslouhi, 2005; Igouzal et al., 2005). During low-flow periods, the
hydrodynamic regime is controlled by the Lalla Aïcha dam situated 62 km
upstream. This dam has been constructed to preserve water for agricultural
pumping stations and to prevent the rise of salty water towards these stations.
Before the dam construction, excessive salinity reached up to 85 km upstream
(Combe, 1969). Figure 4 shows the flow release by Lalla Aïcha dam from
1 January 2014 to 1 January 2016.
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 m3 s-1 at the river mouth
(Combe, 1966). In addition, the tide near the estuary mouth is mainly
semi-diurnal with a 44 820 s tidal cycle (Haddout et al., 2014) and is a
meso-/micro-tidal estuary. The topography of the Sebou estuary is presented in
Fig. 5. Figure 5 shows the shapes of cross-sectional area, channel width and
depth during neap–spring and supermoon total lunar eclipse tides. The
cross-sectional area and width are plotted directly from bathymetric data,
and the water depth represents the ratio of these two geometric values. The
bathymetric data were provided by local water authorities (i.e., ANP:
National Agency of Ports and the Water Services of Kenitra
town).
Geometry of the Sebou estuary, showing the cross-sectional
area A (m2), the width B (m) and the estuary depth h (m) during
neap–spring and total lunar eclipse tides.
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 x=5 km (between the river mouth (Mehdia) and Kenitra). The
second inflection point is located at x=35 km (between Oulad Salma and
M'Rabeh), where
the convergence length switches and the estuary becomes more riverine.
Geometrical characteristics along the Sebou estuary are summarized in
Table 3, with the cross-sectional area; width and depth are well described by
exponential functions (Fig. 5).
The convergence length is shorter in the seaward reaches (x=0–5 km and
x=5–35 km) where the tidal influence is dominant over the river flow,
compared with that in the landward reach (x=35–62 km) where the influence
of river flow becomes important). The depth gradually increases from Lalla
Aïcha dam to seaward, while the cross-sectional area and width remains
roughly constant.
Field data interpretation
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-1) and the average value in
the ocean is 35 g L-1. The period of measurements included the LWS, TA and
HWS situations (HWS and LWS correspond to periods when water velocity changes
its directions and becomes nearly zero).
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-1 at the river mouth, 32.7 g L-1 at Oulad Berjel,
30 g L-1 at Kenitra, 1.2 g L-1 at Oulad Salma and
0.9 g L-1 at M'Rabeh. A minimum salinity concentration is recorded
during low tides with 17.5 g L-1 at the river mouth and less than
1 g L-1 in the other four locations.
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-1 at Oulad Berjel,
19.8 g L-1 at Kenitra and 0.9 g L-1 at Oulad Salma. A minimum
salinity concentration is recorded during low tides with 5 g L-1 at
Oulad Berjel and less than 3 g L-1 in the other two locations.
(a) Analytically computed tidal amplitude and traveling time
along the Sebou estuary at supermoon total lunar eclipse day.
(b) Analytically computed velocity amplitude and damping
number along the Sebou estuary at supermoon total lunar eclipse day.
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.
Results and analysis
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.
Application of the coupled salt intrusion analytical model
To turn the steady-state model into a predictive model, semi-empirical
relations (Eq. 6) are required that relate the two optimization
parameters K and D1 to hydrodynamic and geometrical bulk parameters.
These bulk parameters are dimensionless numbers composed of geometrical (a,
b, A0, B0, h0), hydrological (Q) and hydraulic (H, E,
Cz, υ, η) parameters that influence the process of mixing
and advection. An analytical hydrodynamic model for tidal wave propagation is
used to reproduce the main tidal dynamics along the estuary axis and
subsequently for predicting the main parameters (Van der Burgh's coefficient
K, dispersion coefficient D1 and tidal excursion E) that influence
the salt intrusion process, during supermoon total lunar eclipse day, of the
Sebou estuary.
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 Ks and the
storage width ratio rs, are presented in Table 4. It is worth
noting that the storage width ratio rs is different in the seaward
reaches for various tidal situations. It is important to point out that the
model uses a variable depth in order to account for variations of the
estuarine sections along the channel. Figure 9a shows the longitudinal
computations of tidal amplitude and traveling time along the Sebou estuary
for the selected periods (representing the spring tide, the moderate tide,
the neap tide and supermoon total lunar eclipse day). The agreement between
analytically computed and observed tidal amplitude and traveling time for HW
and LW is good. Furthermore, these results show that the difference
between supermoon total lunar eclipse day and spring–neap situation is very
remarkable. Additionally, Fig. 9b shows the velocity amplitude and damping
number at supermoon total lunar eclipse, which suggests that the hybrid
model proposed by Cai et al. (2012a, 2014a) can well reproduce the tidal
dynamics and velocity amplitude with a significant range of dam discharges.
Observed and analytically computed longitudinal salinity
distribution along the Sebou estuary (surveyed on 28 September 2015)
during 1st cycle (a, b, c) at LWS, TA and HWS, and 2nd cycle (d, e, f) at LWS TA and HWS.
Longitudinal variation of salinity gradient (a) and
curvature (second derivative) (b) along the Sebou estuary axis.
Comparison of computed and optimized dispersion D1
coefficient at HWS in the spring–neap and the supermoon total lunar eclipse
day tides.
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 (K) and
dispersion (D1) coefficients are initially estimated by Eqs. (8) and
(9). However, due to the large uncertainty of these predictive equations, the
K and D1 estimations should be refined on the basis of salinity
measurements. The optimization process of K and D1 has been carried
out using the Levenberg–Marquardt nonlinear minimization method (Marquardt,
1963). In this method, the following objective function ϕ is minimized
during the parameters optimization process:
minϕ((K,D1),S)=∑i=1m(Si-Si+(K,D1))2m,σS2,
where Si and Si+ are the measured and predicted salinity,
σS2 are variance of the measured salinity, m is number of
observation.
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 (a) and validation (b).
Salinity comparisons at Oulad Berjel (a), Kenitra (b) and
Oulad Salma (c) in calibration.
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
(S0), tidal excursion (E), Richardson number (NR),
dispersion coefficient at high water slack, Van Der Burgh's coefficient (K)
and salt intrusion length at high water slack (L). S.M. stands for
supermoon.
Tidal conditionsS0ENRD1HWSComputedD1HWSOptimzedKComputedKOptimzedLCompLObs[g L-1][km][–][m2 s-1][m2 s-1][–][–][km][km]S.M. eclipse (1st at HWS)35.812.310.047533.61590.900.180.2029.025.0S.M. eclipse (2nd at HWS)35.811.910.060742.59792.020.180.2025.627.0Spring HWS35.006.500.305440.48403.250.160.1523.121.5Neap HWS34.508.000.150415.40400.000.150.1523.320.0
Values of the optimized parameters are summarized in Table 5 (at HWS), where
the dispersion coefficient at the estuary mouth D0 can be obtained by
substituting D1; x1 and K into Eq. (4). It can be shown that the
estimated values of the parameters D1 and K are very close to their
reference values (Eqs. 8 and 9). This indicates that the predictive
equations developed by Savenije (1993a, 2012) and revised by Gisen et
al. (2015b) are appropriate to be applied in getting a first estimate of
D1 and K as starting values for the optimization process. At each
tidal condition (HWS, LWS, and TA), the optimized values of D1 are
greater that initial estimated values, whereas the optimized values of the
coefficient K have remained constant and equal to 0.20 for all tidal
conditions on the supermoon total lunar eclipse day. Also, in normal situations
Haddout et al. (2015) found a value of K=0.15, which is relatively small
compared to the value of K=0.20 during eclipse day.
We attribute this difference to the dominance of tidal mixing in the Sebou
estuary for the eclipse period. Because the optimized value of K remained
constant, fitted salinity curves were more sensitive to the dispersion
coefficient D at HWS, LWS, and TA (Haddout et al., 2015). Results of the
axial salinity analysis at HWS, TA and LWS are plotted in Fig. 10. On the
whole, it can be said that the analytical salt intrusion model performs well
in representing the salinity distribution in the Sebou estuary (surveyed on
28 September 2015).
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.
The predictive model compared to other methods
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.
Numerical modeling of salinity distributionHydrodynamic model
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 n0 Eq. (16) is evaluated from granulometric measurements that
were carried out from upstream to seaward in the studied reach. The others
coefficients were evaluated from observations of the river in aerial photos,
from the cross-sectional areas and available photos, and from field visits.
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 hybridRMSEABSERREFR2PBIASmodel during eclipse day[m, min][m, min][–][–][%]Tidal amplitude (1st and 2nd)0.42–0.490.37–0.530.79–0.890.91–0.921.42–1.7Travel time at HW (1st and 2nd)0.50–0.650.32–0.440.88–0.940.89–0.931.01–1.1Travel time at LW (1st and 2nd)0.55–0.610.30–0.470.97–0.950.95–0.970.98–1.0
Statistical indicators of analytical salinity intrusion
model performance at HWS during the supermoon total lunar eclipse day.
Statistical indicators of transport model performance in
calibration.
Statistical indicators of transportRMSE [g L-1]ABSERR [g L-1]EF [–]R2 [–]PBIAS [%]model in calibrationOulad Berjel0.690.710.960.910.92Kenitra0.880.860.920.861.04Oulad Salma0.920.890.920.841.12
Comparisons salinity variation at HWS in different
locations.
EstuaryNormal situationsupermoon eclipselocationsHWS salinity (g L-1)HWS salinity (g L-1)Oulad Berjel28.532.6Kenitra16.626.0Oulad Salma00.701.2M'Rabeh00.600.8Salt transport model
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 “D” ranges from 500 to
900 m2 s-1 along the river. Figure 15 shows the comparison of the
observed and computed salinity at three locations (Oulad Berjel, Kenitra and
Oulad Salma) during the supermoon total lunar eclipse day. The results show
that the simulated salinity concentration fits adequately the observed data.
Models performance verification
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 (R2) and the % of deviation from observed
streamflow (PBIAS). The statistical parameters were defined as follows
(Moriasi et al., 2007; Stehr et al., 2008; Conversa et al., 2015):
RMSE=∑i=1n(Omeas,i-Sperd,i)2N,ABSERR=∑i=1n(Omeas,i-Sperd,i)N,EF=1-∑i=1n(Omeas,i-Sperd,i)2∑i=1n(Omeas,i-Omeas‾)2,R2=∑i=1n(Omeas,i-Omeas‾)(Sperd,i-Sperd‾)(∑i=1n(Omeas,i-Omeas‾)2)1/2(∑i=1n(Sperd,i-Sperd‾)2)1/22,PBIAS=∑i=1n(Omeas,i-Sperd,i)∑i=1n(Omeas,i)100,
where Omeas,i is the observed value and
Sperd,i the computed value of salinity or water level.
O‾meas,i is the mean observed salinity or water level
data and Sperd‾ is the mean computed salinity or
water level.
The closer the values of RMSE and ABSERR to zero, and R2 to unity, the
better the model performance is evaluated (Abu El-Nasr et al., 2005). Percent bias (PBIAS) measures the average tendency, expressed as a
percentage of the simulated data to be larger or smaller than their observed
counterparts (Gupta et al., 1999). The optimal value of PBIAS is 0, with
low-magnitude values indicating accurate model simulation (Moriasi et al.,
2007). Positive values indicate model underestimation bias and negative
values indicate model overestimation bias (Gupta et al., 1999). The
EF (Nash and Sutcliffe, 1970) is a normalized
statistic that determines the relative magnitude of the residual variance
(noise) compared to the measured data variance (information). EF ranges
between -∞ and 1 (1 inclusive), with EF = 1; the closer the model
EF efficiency is to 1, the more accurate is the model. Values between 0 and 1
are generally viewed as acceptable levels of performance, whereas values
≤ 0 indicate an unacceptable performance (Moriasi et al., 2007).
The indicators of the hydrodynamic–salinity intrusion model are summarized
in Tables 6 and 7. In two models, the EF and R2 coefficients are very
near to unity. This result demonstrates the good performance of the
analytical model. Also, this shows that the proposed coupled analytical model
by Cai et al. (2016) is applicable and useful.
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.
Supermoon total lunar eclipse impact
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-1
(6.54 %), 9.4 g L-1 (22.06 %), 0.5 g L-1 (26.32 %)
and 0.2 g L-1 (14.29 %). This situation was unsuitable for
drinking and agricultural proposes.
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-1) until 20 km
upstream. Moreover, water level rise causes large augmentation of
salinity in the mesohaline zone of the Sebou estuary. Also, if we considerer
Kenitra location, an increase of water level for 0.8 m causes an increase of
9.4 g L-1 in salinity witch correspond to a salinity augmentation of
11.75 g L-1 per meter of increased water level. At the Oulad Salma
drinking water station salinity increased to a value of 1.2 g L-1 that
exceeds the limit value of 0.5 g L-1 recommended by the World Health
Organization (WHO) for drinking water.
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 A0, convergence
length a and the optimization of the dispersion coefficient D. Geometry
is one of the most important parameters in the hydrodynamic and salt
intrusion models. It affects the character of the salinity distribution and
appears prominently in the shape of salt intrusion curves during extreme
events. Computed results reveal that variations in the sensitivity of these
parameters are likely to depend on changes in geometric characteristics.
Conclusions
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 A0 and convergence length a. A good fit was
obtained between computed and observed salinity during this extreme event.
These models reproduce very well the salinity rise. Statistical indicators
show that these models fit adequately salinity observations in the Sebou
estuary.
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.
Nomenclature and abbreviations list
aConvergence length of cross-sectional area [m]ATidally averaged cross-sectional area [m]A0Tidally averaged cross-sectional area at the estuary mouth [m]bConvergence length of width [m]BEstuary width [m]B1Width at inflection point [m]BfStream width [m]CzCoefficient of Chezy [m0.5 s-1]dConvergence length of depth [m]DLongitudinal dispersion [m2 s-1]D0Longitudinal dispersion at estuary mouth [m2 s-1]D1Longitudinal dispersion at inflection point [m2 s-1]DupLongitudinal dispersion at upstream [m2 s-1]ETidal excursion [m]E0Tidal excursion starting from the estuary mouth [m]E1Tidal excursion starting from the inflection point [m]fDarcy–Weisbach friction factor [–]FFroude number [–]FDDensimetric Froude number [–]gAcceleration due to gravity [m s2]hAveraged estuary depth [m]h0Estuary depth at the mouth [m]HTidal range [m]H0Tidal range at estuary mouth [m]H1Tidal range at inflection point [m]HTidal range [m]KsManning–Strickler friction factor [m1/3 s-1]KVan der Burgh's coefficient [–]mNumber of observations [–]NCanter–Cremers' estuary number [–]NREstuarine Richardson number [–]QFreshwater discharge [m3 s-1]
QupFreshwater discharge at upstream [m3 s-1]RHydraulic radius [m]rsStorage width ratio [–]SSteady-state salinity [g L-1]S0Steady-state salinity at the estuary mouth [g L-1]S∗Steady-state salinity [–]CSalinity concentration [g L-1]Cn+1Concentration of a constituent at present time step [g m-3]Cup∗QUICKEST concentration of a constituent at upstream [g m-3]CnConcentration of a constituent at previous time step [g m-3]TTidal period [s]tTime [s]u0Velocity of the freshwater discharge at estuary mouth [m s-1]νTidal velocity amplitude [m s-1]ν0Tidal velocity amplitude at estuary mouth [m s-1]ν1Tidal velocity amplitude at inflection point[m s-1]Vn+1Volume of the water quality cell at present time step [m3]VnVolume of the water quality cell at previous time step [m3]LSalt intrusion length [m]L∗Salt intrusion length [–]xDistance from the estuary mouth [m]x∗Distance from the estuary mouth [–]x1First inflection point [m]ηTidal amplitude [m]c0Classical wave celerity [m s-1]β0Bottom slope [–]qlLateral inflow per unit length [m2 s-1]σsVariance of the measured salinity [m2 s-1]χFriction number [–]ωTidal frequency [s-1]ρFluid density [kg m-3]ΔρDensity difference over the intrusion length [kg m-3]δDamping number [–]εPhase lag between HW and HWS (or LW and LWS) [–]ζTidal amplitude to depth ratio [–]γEstuary shape number [–]φZPhase of water level [–]φUPhase of velocity [–]λCelerity number [–]μVelocity number [–]
Abbreviations list
LWSlow water slackHWShigh water slackLWlow waterHWhigh waterTAtidal averageRMSEroot mean squared errorABSERRmean absolute errorEFNash–Sutcliffe indexR2goodness-of-fitPBIAS% of deviation fromobserved streamflow
Data availability
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.
Types of salt intrusion and shape of salt intrusion curves
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 L is the salt
intrusion length, x is the distance from the mouth, S is the salinity at
the mouth and S0 is the salinity corresponding with the distance.
Van der Burgh (1972):
LTA=-26h0Kgh0v0v0u0N0.5=26.πh0KF-1.0N-0.5.
Van Os and Abraham (1990):
LLWS=4.4h0fFD-1N-1,
where h0 is the tidal average depth, v0 is the maximum tidal
velocity, u0 is the velocity of fresh water, N is the Canter–Cremers'
estuary number, K is the Van der Burgh's coefficient, f is the
Darcy–Weisbach's coefficient, F is the Froude number and FD is
the densimetric Froude number.
Acknowledgements
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
References
Aertsl, J. C. J. H., Hassan, A., Savenije, H. H. G., and Khan, M.: Using GIS
tools and rapid assessment techniques for determining salt intrusion: stream
a river basin management instrument, Phys. Chem. Earth, 25, 265–273, 2000.
An, Q., Wu, Y., Taylor, S., and Zhao, B.: Influence of the Three Gorges Project
on saltwater intrusion in the Yangtze River Estuary, Environ.
Geol., 56, 1679–1686, 2009.
Billah, M., Rahman, M. M., Paul, S., Hasan, M. A., and Islam, A. K. M. S. L.:
Impact of climate change on river flows in the southwest region of
Bangladesh, Proceedings of the 5th International Conference on Water and
Flood Management (ICWFM 2015), 6–8 March, 2015, IWFM, BUET, Dhaka,
Bangladesh, Vol. 1, 581–590, 2015.
Brockway, R., Bowers, D., Hoguane, A., Dove, V., and Vassele, V.: A note on salt
intrusion in funnel-shaped estuaries: Application to the Incomati estuary,
Mozambique, Estuar. Coast. Shelf S., 66, 1–5, 2006.
Brunner, G. W.: HEC-RAS River Analysis System Hydraulic Reference Manual
(version 4.1), US Army Corp of Engineers, Hydrologie Engineering Center (HEC),
Davis California, USA, 2010.Cai, H., Savenije, H. H. G., and Tofflon, M.: A new analytical framework for
assessing the effect of sea-level rise and dredging on tidal damping in
estuaries, J. Geophys. Res.-Ocean., 117, C09023, 10.1029/2012JC008000,
2012a.Cai, H., Savenije, H. H. G., Yang, Q., Ou, S., and Lei, Y.: Influence of river
discharge and dredging on tidal wave propagation; Modaomen estuary case, J.
Hydraul. Eng., 138, 885–896, 10.1061/(ASCE)HY.1943-7900.0000594, 2012b.Cai, H., Savenije, H. H. G., and Toffolon, M.: A hybrid analytical model for
assessing the effect of river discharge on tidal damping, applied to the
modaomen estuary, Coast. Dynam.,
http://www.coastaldynamics2013.fr/pdf_files/024_Cai_Huayang.pdf (last access: 11 March 2016), 2013.Cai, H., Savenije, H. H. G., and Jiang, C.: Analytical approach for predicting
fresh water discharge in an estuary based on tidal water level observations,
Hydrol. Earth Syst. Sci., 18, 4153–4168, 10.5194/hess-18-4153-2014, 2014a.Cai, H., Savenije, H. H. G., and Toffolon, M.: Linking the river to the estuary:
influence of river discharge on tidal damping, Hydrol. Earth Syst. Sci., 18,
287–304, 10.5194/hess-18-287-2014, 2014b.
Cai, H., Savenije, H. H. G., and Gisen, J. I. A.: A coupled analytical model
for salt intrusion and tides in convergent estuaries, Hydrol. Sci. J.,
Hydrological Sciences Journal, 61, 402–419, 2016.
Cai, H., Savenije, H. H., Zuo, S., Jiang, C., and Chua, V. P.: A predictive model
for salt intrusion in estuaries applied to the Yangtze estuary, J.
Hydrol., 529, 1336–1349, 2015b.
Chow, V. T.: Open-channel Hydraulics, McGraw-Hill International Editions,
McGraw-Hill Book Co., New York, 680 pp., 1959.
Combe, M.: Study of tidal cycle in the Sebou estuary
during low water, 108 pp., Rapport inédit, Rabat, MTPC/DH DRE, 1966.
Combe, M.: Hydrogeological maps of the Plain Gharb 1/100 000, Notes and
Memoirs of the Geological Service of Morocco, 221 bis, Rabat, Morocco, 1969.
Conversa, G., Bonasia, A., Di Gioia, F., and Elia, A.: A decision support
system (GesCoN) for managing fertigation in vegetable crops. Part II-model
calibration and validation under different environmental growing conditions
on field grown tomato, Frontiers in plant science, Vol. 6, 2015.
Cowan, W. L.: Estimating hydraulic roughness coefficients, Agr. Eng., 37,
473–475, 1956.
Dronkers, J. J.: Tidal computations in River and Coastal Waters, Elsevier,
518 pp., New York, Interscience Publishers, 1964.Espenak, F.: Lunar Eclipses,
http://eclipse.gsfc.nasa.gov/LEdecade/LEdecade1991.html (last access: 2 March 2016), 1991–2000.Elias, E. P., Gelfenbaum, G., and Van der Westhuysen, A. J.: Validation of a
coupled wave-flow model in a high-energy setting: The mouth of the Columbia
River, J. Geophys. Res.-Ocean., 117, 10.1029/2012JC008105, 2012.
El-Nasr, A. A., Arnold, J. G., Feyen, J., and Berlamont, J.: Modelling the
hydrology of a catchment using a distributed and a semi-distributed model,
Hydrol. Process., 19, 573–587, 2005.
Fischer, H. B.: Discussion of Minimum length of salt intrusion in estuaries, edited
by: Rigter, B. P., J. Hydraul. Div., 99, 1475–1496, 1974.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H.: Mixing in
Inland and Coastal Waters, Academic Press, New York, 483 pp., 1979.
Friedrichs, C. T. and Aubrey, D. G.: Tidal propagation in strongly convergent
channels, J. Geophys. Res. Oceans, 99, 3321–3336, 1994.Gay, P. and O'Donnell, J.: Comparison of the salinity structure of the
Chesapeake Bay, the Delaware Bay and Long Island Sound using a linearly
tapered advection-dispersion model, Estuar. Coast., 32, 68–87,
10.1007/s12237-008-9101-4 2009.Gay, P. S. and O'Donnell, J.: A simple advection-dispersion model for the salt
distribution in linearly tapered estuaries, J. Geophys. Res.,
112, C070201, 10.1029/2006JC003840, 2007.
Gisen, J. I. A., Savenije, H. H. G., Nijzink, R. C., and Wahab, A. K. Abd.:
Testing a 1-D analytical salt intrusion model and its predictive equations in
Malaysian estuaries, Hydrol. Sci. J., 60, 156–172, 2015a.Gisen, J. I. A., Savenije, H. H. G., and Nijzink, R. C.: Revised predictive
equations for salt intrusion modelling in estuaries, Hydrol. Earth
Syst. Sci., 19, 2791–2803, 10.5194/hess-19-2791-2015, 2015b.
Godin, G.: Modification of river tides by the discharge, J. Waterw. Port.
C-ASCE, 111, 257–274, 1985.
Godin, G.: The propagation of tides up rivers with special considerations on
the upper saint lawrence river, Estuar. Coast., 48, 307–324, 1999.
Gupta, H. V., Sorooshian, S., and Yapo, P. O.: Status of automatic calibration
for hydrologic models: comparison with multilevel expert calibration, J.
Hydrol. Eng., 4, 135–143, 1999.
Haddout, S., Maslouhi, A., and Igouzal, M.: Mathematical modeling of the flow
regime in the Sebou river estuary (Morocco), National Water Information System
Congress, NWIS 2014, 2–4 December, Rabat, 2014.Haddout, S., Maslouhi, A., and Igouzal, M.: Predicting of salt water
intrusion in the Sebou river estuary (Morocco), J. Appl. Water Eng. Res.,
1–11, 10.1080/23249676.2015.1124029, 2015.
Haddout, S., Maslouhi, A., Magrane, B., and Igouzal, M.: Study of salinity
variation in the Sebou River Estuary (Morocco), Desalination and Water Treatment,
57, 17075–17086, 2016.
Horrevoets, A. C., Savenije, H. H. G., Schuurman, J. N., and Graas, S.: The
influence of river discharge on tidal damping in alluvial estuaries, J.
Hydrol., 294, 213–228, 2004.
Hughes, S. W., Hosokawa, K., Carroll, J., Sawell, D., and Wilson, C.: In the
red shadow of the Earth, Phys. Educ., 50, p. 741, 2015.
Igouzal, M. and Maslouhi, A.: Elaboration of management tool of a reservoir dam
on the Sebou river (Morocco) using an implicit hydraulic model, J Hydraul. Res., 43, 125–130, 2005.
Igouzal, M., Mouchel, J. M., Tamoh, K., and Maslouhi, A.: Modelling the
hydraulic regime and the water quality of Sebou River (Morocco): first
results, IAHS Publ., 299, p. 75, 2005.
Ippen, A. T.: Tidal dynamics in estuaries, part I: Estuaries of rectangular
section, in Estuary and Coastline Hydrodynamics, edited by: Ippen, A. T.,
McGraw-Hill, New York, 493–521, 1966.
Jay, D. A.: Green law revisited-tidal long-wave propagation in channels with
strong topography, J. Geophys. Res., 96, 20585–20598, 1991.
Jay, D. A., Leffler, K., and Degens, S.: Long-term evolution of columbia river
tides, J. Waterw. Port C-ASCE, 137, 182–191, 2011.
Jeong, S., Yeon, K., Hur, Y., and Oh, K.: Salinity intrusion characteristics
analysis using EFDC model in the downstream of Geum River, J.
Environ. Sci., 22, 934–939, 2010.
Kärnä, T., Baptista, A. M., Lopez, J. E., Turner, P. J., McNeil, C.,
and Sanford, T. B.: Numerical modeling of circulation in high-energy estuaries: A
Columbia River estuary benchmar, Ocean Model., 88, 54–71, 2015.
Kuijper, K. and Van Rijn, L. C.: Analytical and numerical analysis of tides and
salinities in estuaries; part II: salinity distributions in prismatic and
convergent tidal channels, Ocean Dynam., 61, 1743–1765, 2011.Kukulka, T. and Jay, D. A.: Impacts of columbia river discharge on salmonid
habitat: 1. A nonstationary fluvial tide model, J. Geophys. Res.-Ocean.,
108, 3293, 10.1029/2002JC001382, 2003.
Lanzoni, S. and Seminara, G.: On tide propagation in convergent estuaries, J.
Geophys. Res.-Ocean., 103, 30793–30812, 1998.Lewis, R. E. and Uncles, R. J.: Factors affecting longitudinal dispersion in
estuaries of different scale, Ocean Dynam., 53, 197–207,
10.1007/s10236-003-0030-2, 2003.
Li, J., Li, D., and Wang, X.: Three-dimensional unstructured-mesh eutrophication
model and its application to the Xiangxi River, China, J.
Environ. Sci., 24, 1569–1578, 2012.
Leblond, P. H.: Tidal propagation in shallow rivers, J. Geophys. Res.-Ocean.,
83, 4717–4721, 1978.
Mai, B. X., Fu, J. M., Sheng, G. Y., Kang, Y. H., Lin, Z., Zhang, G., and Zeng,
E. Y.: Chlorinated and polycyclic aromatic hydrocarbons in riverine and
estuarine sediments from Pearl River Delta, China, Environ.
Poll., 117, 457–474, 2002.
Marquardt, D. W.: An algorithm for least-squares estimation of nonlinear
parameters, J. Soc. Indust. Appl. Math., 11, 431–441, 1963.
Moriasi, D. N., Arnold, J. G., Van Liew, M. W., Bingner, R. L., Harmel, R.
D., and Veith, T. L.: Model evaluation guidelines for systematic quantification
of accuracy in watershed simulations, Trans. Asabe, 50, 885–900, 2007.NASA (National Aeronautics and Space Administration): http://www.nasa.gov/
(last access: 18 August 2016), 2015.Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual
models part I-A discussion of principles, J. Hydrol., 10, 282–290,
10.1016/0022-1694(70)90255-6, 1970.
Nguyen, A. D.: Salt Intrusion, Tides and Mixing in Multi-Channel Estuaries:
PhD: UNESCO-IHE Institute, Delft, CRC Press, 176 pp., 2008.Nguyen, A. D. and Savenije, H. H.: Salt intrusion in multi-channel estuaries:
a case study in the Mekong Delta, Vietnam, Hydrol. Earth Syst. Sci., 10,
743–754, 10.5194/hess-10-743-2006, 2006.
Nguyen, A. D., Savenije, H. H., Pham, D. N., and Tang, D. T.: Using salt
intrusion measurements to determine the freshwater discharge distribution
over the branches of a multi-channel estuary: The Mekong Delta
case, Estuar. Coast. Shelf S., 77, 433–445, 2008.
Nguyen, D. H., Umeyama, M., and Shintani, T.: Importance of geometric
characteristics for salinity distribution in convergent estuaries, J.
Hydrol., 448, 1–13, 2012.NOC (National Oceanography Centre): http://noc.ac.uk/ (last access: 18
August 2016), 2015.
Nylén, L. and Ramel, E.: The effects of inlet sedimentation on water
exchange in Maha Oya Estuary, Sri Lanka, 130 pp., 2012.
Prandle, D.: Salinity intrusion in estuaries, J. Phys. Oceanogr., 11, 1311–1324, 1981.
Prandle, D. and Rahman, M.: Tidal response in estuaries, J. Phys. Oceanogr.,
10, 1552–1573, 1980.
Rigter, B. P.: Minimum length of salt intrusion in estuaries,
J. Hydr. Eng. Div.-ASCE, 99, 1475–1496, 1973.
Savenije, H. H. G.: A one-dimensional model for salinity intrusion in alluvial
estuaries, J. Hydrol., 85, 87–109, 1986.
Savenije, H. H. G.: Salt intrusion model for high-water slack, low-water
slack, and mean tide on spread sheet, J. Hydrol., 107, 9–18,
1989.
Savenije, H. H. G.: Predictive model for salt intrusion in estuaries,
J. Hydrol., 148, 203–218, 1993a.
Savenije, H. H. G.: Determination of estuary parameters on basis of
Lagrangian analysis, J. Hydraul. Eng.-ASCE, 119, 628–642, 1993b.
Savenije, H. H. G.: Analytical expression for tidal damping in alluvial
estuaries, J. Hydraul. Eng.-ASCE, 124, 615–618, 1998.
Savenije, H. H. G.: Salinity and tides in alluvial estuaries, Amsterdam,
Elsevier, 197 pp., 2005.
Savenije, H. H. G.: Comment on “A note on salt intrusion in funnelshaped
estuaries: Application to the Incomati estuary, Mozambique” by Brockway et
al. (2006), Estuar. Coast. Shelf S., 68, 703–706, 2006.Savenije, H. H. G., Toffolon, M., Haas, J., and Veling, E. J. M.: Analytical
description of tidal dynamics in convergent estuaries, J. Geophys. Res.-Ocean.,
113, C10025, 10.1029/2007JC004408, 2008.Savenije, H. H. G.: Salinity and Tides in Alluvial Estuaries, second ed.,
available at: www.salinityandtides.com (last access: 8 October 2015).
2012.
Savenije, H. H. G.: Prediction in ungauged estuaries: An integrated
theory, Water Resour. Res., 51, 2464–2476, 2015.Shaha, D. C. and Cho, Y.-K.: Determination of spatially varying Van der
Burgh's coefficient from estuarine parameter to describe salt transport in an
estuary, Hydrol. Earth Syst. Sci., 15, 1369–1377,
10.5194/hess-15-1369-2011, 2011.
Stehr, A., Debels, P., Romero, F., and Alcayaga, H.: Hydrological modelling with
SWAT under conditions of limited data availability: evaluation of results
from a Chilean case study, Hydrol. Sci. J., 53, 588–601,
2008.
Stronach, J. A. and Murty, T. S.: Nonlinear river-tidal interactions in the
Fraser River, Canada, Mar. Geod., 13, 313–339, 1989.Toffolon, M. and Savenije, H. H. G.: Revisiting linearized one-dimensional
tidal propagation, J. Geophys. Res.-Ocean., 116, C07007,
10.1029/2010JC006616, 2011.Toffolon, M., Vignoli, G., and Tubino, M.: Relevant parameters and finite
amplitude effects in estuarine hydrodynamics, J. Geophys. Res.-Ocean., 111,
C10014, 10.1029/2005JC003104, 2006.Van der Burgh, P.: Ontwikkeling van een methode voor het voorspellen van
zoutverdelingen in estuaria, kanalen en zeeen, Rijkwaterstaat, Rapport,
10–72, 1972.
Van Os, A. G. and Abraham, G.: Density currents and salt intrusion, Lecture
Note for Hydraulic Engineering Course at IHE-Delft, Delft Hydraulics, Delft,
the Netherlands, 1990.
Wu, H. and Zhu, J.: Advection scheme with 3rd high-order spatial interpolation at
the middle temporal level and its application to saltwater intrusion in the
Changjiang Estuary, Ocean Model., 33, 33–51, 2010.
Xu, Y., Zhang, W., Chen, X., Zheng, J., Chen, X., and Wu, H.: Comparison of
Analytical Solutions for Salt Intrusion Applied to the Modaomen
Estuary, J. Coast. Res., 31, 735–741, 2015.Xue, P., Chen, C., Ding, P., Beardsley, R. C., Lin, H., Ge, J., and Kong, Y.:
Saltwater intrusion into the Changjiang River: A model-guided mechanism
study, J. Geophys. Res.-Ocean., 114, 10.1029/2008JC004831, 2009.
Zhao, L., Zhang, X., Liu, Y., He, B., Zhu, X., Zou, R., and Zhu, Y.:
Three-dimensional hydrodynamic and water quality model for TMDL development
of Lake Fuxian, China, J. Environ. Sci., 24, 1355–1363, 2012.Zhang, E. F., Savenije, H. H. G., Chen, S. L., and Mao, X. H.: An analytical
solution for tidal propagation in the Yangtze Estuary, China, Hydrol. Earth Syst.
Sci., 16, 3327–3339, 10.5194/hess-16-3327-2012, 2012.