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\begin{document}
\title{Physical characteristics and their influences on water dynamics in the
Sefrou watershed, Northern Tabular Middle Atlas, Morocco}
\author[1]{Youssef Hattafi}%
\author[2]{Farah El Hassani}%
\author[1]{Abderrahim Lahrach}%
\affil[1]{Universite Sidi Mohamed Ben Abdellah Faculte des Sciences et Techniques de Fes}%
\affil[2]{Universite Euro-Mediterraneenne de Fes}%
\vspace{-1em}
\date{\today}
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\selectlanguage{english}
\begin{abstract}
The Sebou watershed is the main receiver of rainwater contributions in
the North of Morocco. The present study is interested in the knowledge
of the global Physical characteristics on water dynamics in the Sefrou
watershed at the level of the Sefrou sub-watershed which belongs to this
large hydrological unit and which occupies its south-western part. The
approach followed in this study consisted initially, in acquiring the
data, organizing it, and processing it by a geographic information
system (GIS), in order to obtain a global idea on the distribution of
the different parameters in the entourage concerned by this study. The
application of geographic information system tools makes it possible to
establish a set of maps that will help develop an excellent descriptive
analysis characteristic of the watershed. In this paper, we present the
analysis results of the geological, climatic and hydrological
characteristics of an important area of the Middle Atlas, with the
notable importance of precipitation, runoff and rivers for irrigation
and the supply of drinking water. of cities in the region. The
hydrological study of the Sefrou watershed has shown a typical
Mediterranean regime, the watershed receives an average annual rainfall
of 454.22 mm, with a volume input of 183,96*10 \^{}6 \^{}3/year and an
average annual temperature of 16.62\selectlanguage{ngerman}°C. The actual evapotranspiration in
the watershed is 389.22 mm/year which is 161,28.10\^{}6 m\^{}3/year.%
\end{abstract}\selectlanguage{ngerman}%
\sloppy
\selectlanguage{ngerman}\textbf{Résumé}
Le bassin versant de Sefrou qui occupe la zone Sud-Est du plus grand
bassin de Sebou, qui s'étend sur la partie septentrionale du Causse
Moyen Atlasique. L'étude a été abordée par une caractérisation
physiographique, morphologique de la zone étudiée, suivie par une
synthèse hydrologique.
La démarche suivie dans cette étude consistait dans un premier temps, à
acquérir les données, les organiser, et les traiter par un système
d'informations géographique (SIG), afin d'obtenir une idée globale sur
la répartition des différents paramètres dans l'entourage concerné par
cette étude. L'application des outils de systèmes d'informations
géographiques permet d'établir un ensemble des cartes qui vont aider à
développer une excellente analyse descriptive caractéristique du bassin
versant.
Dans cet article, nous présentons les résultats d'analyse des
caractéristiques géologiques, climatiques et hydrologiques d'une zone
importante du Moyen Atlas en apports pluviométriques et hydrologiques,
du ruissellement et des rivières pour l'irrigation et
l'approvisionnement en eau potable des villes de la région.
Le bassin reçoit une pluviométrie moyenne annuelle de 454,22 mm, avec un
apport de volume de \(183,96*10\ ^{6}\)\selectlanguage{english}?\(\ {}^{3}\)/an et une
temperature moyenne annuelle de 16,62degC. L'evapotranspiration reelle
dans le bassin versant est de 389,22 mm/an qui soient
161,28\(.10^{6}m^{3}/\text{an}\).
Mots cles : bassin versant de Sefrou, morphologie, hydrologie, Moyen
Atlas, physiographie, Sebou .
\section*{Introduction}
{\label{introduction}}
Geographically, Morocco is situated in North Africa precisely with the
African and the European plates which enforces a great richness, variety
and complexity of Moroccan geology seeing its different structural
domains.
The Middle Atlas region is characterized by its hugely diverse
landscapes. As a matter of fact, its geological wealth is a considerable
asset for the local development of the region. The quality of the
geological outcrops makes it easy to read the history of this part of
the Atlasic chain from the Paleozoic to the present day. The Middle
Atlas, which constitutes an intracontinental chain whose mountainous and
structural buildings are elongated essentially in the NE-SW direction,
this chain is longitudinally subdivided into two structural domains
separated by a major tectonic faults '' NMAF '', which separates the
tabular Middle Atlas to the NW from the folded Middle Atlas to the SE.
The Paleozoic outcrops there in several buttonholes like (Bsabis, El
Menzel, Tazekka, Beni Mellala\ldots{}).
The Sefrou watershed in its downstream part, spreads over an area close
to 405 km2 with a perimeter of 127.42 km. The main watercourse
originates from mountainous springs (Benima, J el Abed, Jbel l'Abd,
Chaabat-Mbarek \ldots{}) and drains the Middle Atlas tabular area
through the city of Sefrou towards its connection with the Oued Sebou
which exists at the level of the Rif southern corridor crossing
different geographical areas, and different bioclimatic environments.
Using a physical characterization method with a certain set of
parameters allows us to follow and better understand the hydrodynamic
behavior of the Watershed.
\section*{Geographic and Geological
settings}
{\label{geographic-and-geological-settings}}
\subsection*{Geographic and geological
aspects}
{\label{geographic-and-geological-aspects}}
The Atlas system extends over some 2000 km between the Moroccan Atlantic
margin in the West and Tunisia in the East. This system is bound by
major lineaments, called South and North Atlas Faults, with adjacent
subatlasic depressions and, is subdivided within Morocco in Middle and
High Atlas (figure 1).
The Atlas Mountains represent an intracratonic belt and consist of
Mesozoic and Cenozoic formations that accumulated in the foreland of the
Tell-Rif Thrust Belt during the Alpine/Atlasic Orogeny.
The Middle Atlas is limited to the North by the Sai\selectlanguage{english}s plain and the Rif
front-thrust, to the NE by the Guercif Basin, to the E and the SE by the
Moulouya depressions, and to the W by the Paleozoic massif of Central
Morocco (belonging to the Western Moroccan Meseta). It is composed of
the juxtaposition of two structural units: the tabular (or the ''Middle
Atlas Causse'' ; Termier, 1936) and the folded Middle Atlas. These two
units are separated by the North-Middle Atlas Fault as a major
lineament. The tabular Middle Atlas is a sub-horizontal structure,
composed mainly of neritic carbonates of the lower and middle Liassic.
It is organized into a tiered plateau reflecting tilted block structures
and consists of two sections (northern and southern), separated by the
Tizi n'Tretten Fault. The folded Middle Atlas, oriented NE-SW, is
composed of large syncline depressions delimited by narrow anticlinal
ridges. the syncline depressions are occupied, essentially, by Toarcian
and Dogger material. The Cretaceous and the Paleogene are confined to
depressions situated to the W of the Boulemane meridian, while Neogene
outcrops occur largely to the NE. Anticline ridges form. The hinge of
narrow anticlines, generally represented by Liassic carbonates, is often
affected by faults and injected with Triassic - Liassic shale and/or
intruded by Jurassic/Cretaceous magmatites (Fedan \& El Hassani, 2018).
\subsection*{Geological description}
{\label{geological-description}}
Reading the geological map of Sefrou 1:
100.000\textsuperscript{th}(Charri\selectlanguage{ngerman}ère 1989 : figure 2) and relative
documents (i.e. Termier \& Dubar, 1940 ; Martin 1981 ; Benshili, 1987 ;
Cirac, 1987 ; Charrière, 1984 and 1992 ; Fedan, 1988; Ahmamou 1987)
allows us to subdivide the stratigraphic series of this part of the
tabular Middle Atlas into four groups (figure 3):
A Paleozoic basement, with Ordovician to the Carboniferous series, in
particular a complete Devonian sequences of conglomerates, limestones,
reef limestones and carbonate marls (see Aboussalam et al., 2020).
Post-Paleozoic cover were sedimentation generally starts with the upper
Triassic clay-evaporite series (gypsiferous argillites and mixed
basalts);
\begin{itemize}
\tightlist
\item
followed by Kandar Dolomitic Formation of Sebkha's environment
(Charrière, 1992) of lower Liasic age dolomitic deposits. Then
brecciated dolomites, dolomitic sands and bedded dolomites;
\item
The Liasic series continues with massive limestones with Oncolites,
Gastropods, Terebratula and imperforate foraminifera, locally
dolomitized;
\item
Flint-bedded limestones with ammonites (Tropidoceras) at the base,
which is overcome by reef constructions (lumachel limestones and
epi-reef levels);
\item
Ammonite limestone (protogrammoceras celebratum and Fuciniceras);
\item
And finally, oolite limestones with reefs which shows frequent
dolomitization.
\end{itemize}
After a major unconformity, above the Jurassic series, outcrop north of
Sefrou (in the Sais plain and its borders) marly formations that filling
the basin (fig. 3) that shows from base to top:
\begin{itemize}
\tightlist
\item
Red formations with volcano-sedimentary levels and volcanic flows (in
the area of Zra wadi), then a formation composed of clays, marls and
lacustrine limestones; channeled sandstones and conglomerates
(fluvio-deltaic facies); finally rose marl showing silt-sandstone
intercalations with microfauna.
\item
The three Messinian formations:
\end{itemize}
\begin{itemize}
\tightlist
\item
Bhalil Formation (biocalcarenites, reef constructions and
conglomerates);
\item
Sefrou Formation of ocher silts with Globorotalia dutertrei;
\item
and finally, the Fez ``blue marls'' Formation which is rich in
planktonic foraminifera.
\end{itemize}
The stratigraphic series close, after an unconformity, by lacustrine
limestones of the Sais (middle to upper Pliocene) and finally the
Quaternary Formations (travertines, crusts, alluviums, glacis and
terraces).
\section*{Climate context of the
watershed}
{\label{climate-context-of-the-watershed}}
\subsection*{Annual precipitation}
{\label{annual-precipitation}}
Precipitation decreases towards the SE where the station of Anoceur is
located. It has an average of 504 mm, lower than that of Sefrou (517.2
mm), and that of Allal El Fassi dam (335.3 mm). This can be explained by
the orographic effect of the sequences of high ridges. The annual
average is 361 mm in Azzaba, 396.2 mm in Fez, 407.4 mm in Ain Timedrine.
Thus, from the results obtained for the 5 stations, it can be deduced
that the average rainfall for the sector studied is 417.8 mm, for the
period between 1957/58 and 2009/10.
\subsection*{Average monthly
precipitation}
{\label{average-monthly-precipitation}}
In the Sefrou watershed, there was a maximum average monthly rain
(figure 4) of 54.92 mm in December, which makes this month the wettest
of all the stations, while July is the driest. with an average rain of
3.86 mm, this will directly influence the runoff flows.
\subsection*{Assessment of the blade of water fallen on the
watershed}
{\label{assessment-of-the-blade-of-water-fallen-on-the-watershed}}
The fallen layer of water can be estimated by several methods, making it
possible to integrate into point data relating to the different
stations, a surface result, which makes it possible to estimate spatial
precipitation. `Thiessen polygon' is the applied methodology, as a
statistical method, which amounts to carrying out the weighted average
of the precipitation measured in the rainfall stations of the watershed.
The influence area of each station measurement ``called the Thiessen
polygon'' is the weighting factor. These polygons are obtained
graphically (figure 5), by plotting the perpendicular bisectors of the
segments connecting two neighboring rainfall stations, on a geographic
or topographic map.
\subsubsection*{Isohyet method}
{\label{isohyet-method}}
To make interpretation of precipitation easier, the map of isohyets
shows that there is a progressive precipitation gradient between the
different stations. From this figure, we notice that the rainfall
gradient increases from North to South in the direction of high
altitudes (figure 6).
Thus, precipitation becomes significant at the stations located at high
altitudes. We note that some summer months are characterized by the
predominance of rain mainly linked to the frequency of local
thunderstorms. These are due to the strong insolation on the ground
which sometimes gives rise to updrafts which causes the formation of
stormy precipitation.
\subsubsection*{Estimated mean of the water slide calculated by the three
methods}
{\label{estimated-mean-of-the-water-slide-calculated-by-the-three-methods}}
In order to reconcile between the three different values found by each
method (table 1), and to quantify the volume of the blade of water
fallen on the basin, it is recommended to calculate an average between
them. Annual volume of precipitated water (in m\textsuperscript{3}), for
the Sefrou watershed, can be estimated as follows:
V = 183, 96\(.10^{6}m^{3}\)/year
\par\null
\subsection*{Evaporation, Evapotranspiration and flow
deficit}
{\label{evaporation-evapotranspiration-and-flow-deficit}}
\subsubsection*{Real Evapotranspiration
(ETR)}
{\label{real-evapotranspiration-etr}}
Actual evapotranspiration (ETR) is the sum of the quantities of water
evaporated by the soil and by plants when the soil is at its current
specific humidity and the plants at a stage of real physiological and
sanitary development under real conditions and taking into account the
water available.
It turns out that the actual evapotranspiration is very important, it is
calculated from the average of the three methods (Thornthwaite, 1948;
Coutagne,1954; Turc, 1955) is 389.22 mm for the entire watershed, whose
annual average precipitation represents a value of 454.22mm. The
percentage of loss represents 85.69\% of inflows from the water system
having a volume close to 161.28 million m\textsuperscript{3}, while the
rest will represent the volume of water drained and the amount of
underground infiltration, the latter reaching 14, 31\% with a value of
22.68 million m\textsuperscript{3} /year.
\section*{Physiographic Characteristics of Sefrou
watershed}
{\label{physiographic-characteristics-of-sefrou-watershed}}
The study area is located in the Sefrou watershed between the parallels
(33.41°N; 34°N) and the meridians (4.43°W; 4.56°W). It is limited to the
North by the Allal El Fassi dam and to the South (upstream part) by
Chaabat Mbark and Jbel Beima.
\subsection*{Morphometric
Characteristics}
{\label{morphometric-characteristics}}
According to digitalization, the Sefrou watershed covers an area of 405
Km² and a perimeter of 127.42 Km. These are small sizes that make it
vulnerable to any rainfall.
\subsection*{Shape characteristic}
{\label{shape-characteristic}}
The shape of the hydrograph at the outlet of the watershed depends on
the shape of the latter. There are, thus, different morphological
indices which allow to characterize the environment, but also to compare
different basins.
\subsubsection*{Compactness Index of
Gravelius}
{\label{compactness-index-of-gravelius}}
The Compactness Index K\textsubscript{G} of Gravelius (1914), defined as
the ratio of the perimeter of the watershed to the perimeter of the
circle having the same area:
Where:\(KG=\frac{P}{2\sqrt{\pi}\text{.A}}\approx 0.28.\frac{P}{\sqrt{}A}\)
\begin{itemize}
\tightlist
\item
K\textsubscript{G} is the index of compactness of Gravelius,
\item
A: surface area of the catchment area {[}km\textsuperscript{2}{]},
\item
P: watershed perimeter {[}km{]}.
\end{itemize}
In our case: K\textsubscript{G} =1,77
From the value of K\textsubscript{G} it can be concluded that the
watershed is elongated with probable linear erosion, this favors, for
the same rainfall, low peak flood flows due to the delay of water
delivery to the outlet.
\subsubsection*{Horton Compactness Index}
{\label{horton-compactness-index}}
The Horton Compactness Index (Horton, 1932) is calculated as the ratio
of the average width \emph{lm} to the length of the mainstream L by the
following relationship:
Kh= \(=\frac{\text{lm}}{L}\)
With:
\begin{itemize}
\tightlist
\item
\emph{lm} : the average width of the watershed (km).
\item
\emph{L} : the length of the main watercourse (km).
\end{itemize}
In our catchment area: \emph{lm} =13.56km and \emph{L} =45.76km
Kh = 0.0065 Km\textsuperscript{(-1)}
As the Kh value is very low this confirms that the watershed is
elongated.
\subsubsection*{Shape Coefficient}
{\label{shape-coefficient}}
It is the ratio between the average width (lm) and the axial length at
watershed level (La).
Kf= \(\frac{\text{lm}}{\text{La}}\)
With:
\begin{itemize}
\tightlist
\item
lm: the average width of the watershed (km);
\item
La: axial length (km).
\end{itemize}
At the level of our watershed, we have: lm=13.56km and L =29.76km².
K\textsubscript{f}=0.45
This implies an elongated shape of the catchment area.
\subsubsection*{Coefficient of elongation of Shumm (E) (Shumm,
1956)}
{\label{coefficient-of-elongation-of-shumm-e-shumm-1956}}
It is calculated from the ratio of the diameter of a circle having the
same area as the catchment area to the maximum length of the catchment
area:
E\(=\frac{\sqrt[2]{A/\pi}}{\text{Lmx}}\)
With: Lmx = \(\sum_{1}^{4}\frac{\text{Lm}}{n}\)\(\sum_{1}^{4}\frac{\text{Lm}}{n}\)
\begin{itemize}
\tightlist
\item
A: Area of the watershed in km², A=405 km²;
\item
n: number of order = 4;
\item
Lmx: maximum length of watercourses in the watershed Lmx= 74.55;
\item
lm: average length of rivers.
\end{itemize}
\(lm=298,207\ km\) , So: E=0,16
The E coefficient shows a relatively low value, which may mean that the
watershed has not yet reached a mature phase in old age.
\subsubsection*{The equivalent rectangle}
{\label{the-equivalent-rectangle}}
The concept of the equivalent rectangle was first introduced by Roche
(1963), its interest is to compare the influence of watershed
characteristics on flow. This notion assimilates the watershed to a
rectangle with the same perimeter and surface area, the same compactness
index, and therefore the same hypsometric distribution. In this case,
the contours become parallel to the side of the equivalent rectangle.
Climatology, soil distribution, vegetation cover and drainage density
remain unchanged between contours. The longer the equivalent rectangle
is elongated, the less it will drain. The dimensions of the equivalent
rectangle are determined by the following formula:
\(L=\frac{\text{Kg}\sqrt{A}}{1,12}*(1+\sqrt{1-({\frac{1,12}{\text{Kg}})}^{2}}\ )\)with l=\(\frac{\text{Kg}\sqrt{A}}{1,12}*(1-\sqrt{1-({\frac{1,12}{\text{Kg}})}^{2}}\))
With:
\begin{itemize}
\tightlist
\item
Kg: Gravelius index of compactness.
\item
S: catchment area (Km);
\item
L: length of the equivalent rectangle (Km);
\item
l: width of the equivalent rectangle (Km);
\item
For our pool we have the following characteristics.
\end{itemize}
L=56,43km and l =7,18km
The values of the dimensions (figure 7) of the watershed allow us to
deduce that we have a relatively elongated watershed.
\subsubsection*{Trihedral representation}
{\label{trihedral-representation}}
The trihedral representation is a model of representation developed for
the first time by P.Verdeil (1988 ), it corresponds to the sum of two
right-angled triangles whose side of the corner line must be designated
by L which constitutes an adjacent side and represents the main
watercourse and therefore the watershed line between the two banks of
the watershed.
For this purpose, it is assumed that each bank of the main watercourse
is assimilated by a triangle of the same area as the bank.
For the right bank:
{\label{for-the-right-bank}}
Calculation of the angle \selectlanguage{greek}α\selectlanguage{english}1=\(Arctg(\frac{2Ai}{L^{2}})\)
With:
\begin{itemize}
\tightlist
\item
A: the area of the right bank; A = 224, 033km\selectlanguage{ngerman}²;
\item
L: the length of the main watercourse; L = 45.76km².
\end{itemize}
\selectlanguage{greek}α\selectlanguage{english}1: the angle of the right bank triangle
\selectlanguage{greek}α\selectlanguage{english}1 = 12.077 \selectlanguage{ngerman}°.
For the left bank:
{\label{for-the-left-bank}}
Calculation of the angle \selectlanguage{greek}α\selectlanguage{english}2=\(Arctg(\frac{2Ai}{L^{2}})\)
With:
\begin{itemize}
\tightlist
\item
A: the area of the left bank; A = 180, 97km\selectlanguage{ngerman}² ;
\item
L: the length of the main watercourse; L = 45.76km².
\end{itemize}
\selectlanguage{greek}α\selectlanguage{english}1: the angle of the right bank triangle
\selectlanguage{greek}α\selectlanguage{english}2 = 9.81 \selectlanguage{ngerman}°
According to the trihedral representation of the watershed(figure 8), we
can see that the two banks are relatively asymmetrical compared to the
main river, the right bank is more developed than the left bank, which
can lead us to believe that the drainage is distributed heterogeneously
on both sides of the Sefrou watershed.
\subsection*{Altitude Characteristics}
{\label{altitude-characteristics}}
\subsubsection*{Hypsometric Map}
{\label{hypsometric-map}}
The relief of the watershed is characterized by a hypsometric map and
curve. The study of the relief characteristics allows to determine the
morphology of the watershed, its interactions with meteorological
phenomena and its hydrological behavior, and as the relief directly
influences all hydro-climatic factors (precipitation, temperatures,
vegetation, flow \ldots{}.). The Hypsometric map is obtained by
delimiting altitude ranges of the watershed by 200 m equidistance level
curves. According to this map below (figure 9), we can see that the high
altitudes are located towards the southern part of the watershed within
the ``Causse Moyen Atlas'' (\textgreater{} 1500m), however further north
towards the downstream part (\textless{}300m).
\subsubsection*{Hypsometric curve}
{\label{hypsometric-curve}}
To understand the variations in altitudes within the Sefrou watershed
(figure 10), we determined a hypsometric curve which allowed us to
translate the distribution of altitudes within the study area and allows
to determine the characteristic altitudes.
From this curve, it can be concluded that the altitude varies enormously
despite the relatively small area of the watershed and the area is small
in relation to the change in altitude, characterizing a steep watershed.
The characteristic altitudes of the watershed: average altitude, median
altitude\ldots{}
the average altitude is calculated according to the following formula:
Hm= \(\sum_{1}^{i}\frac{\text{Aihi}}{A}\)
With:
\begin{itemize}
\tightlist
\item
Ai: this is the area between two contour lines (Km²)
\item
hi: Average altitude between two contour lines (m)
\item
A: Total area of the watershed (km²)
\end{itemize}
For the Sefrou watershed, the average altitude is: Hm = 928.36m
Note that this is almost equal to the same value given by the ArcGis
according to a classification of the DTM: 926.52m.
The median altitude is the value read at 50\% of the total surface of
the watershed on the hypsometric curve: Hmed = 905m
\subsubsection*{Concentration time}
{\label{concentration-time}}
Defined as the time after which the particle of water falling in the
area furthest from the outlet will reach it. The concentration-time is a
characteristic of the watershed which essentially depends on the surface
of the basin, the lithology, the rainfall, slopes, the length, and the
density of the hydrographic network. For its calculation, there are
several formulas. Some are in common use in Morocco. Using the Giandotti
formula (Giandotti M. 1937) we will quote:
Tc=\(\frac{4*\sqrt[\ ]{A}+1,5L}{0,8\sqrt{\text{Hmoy}}}\)
With:
\begin{itemize}
\tightlist
\item
Tc concentration time (hours);
\item
A: area of the watershed in km²; A = 405km²;
\item
The length of the main Thalweg watercourse in (km); L = 45.68km.
\item
Hm: average altitude (m); Hm = 928.36m.
\end{itemize}
For our watershed: Tc = 6h11min
Based on the value of the concentration time at the Sefrou watershed,
which makes it possible to classify the watershed among the watersheds
that have a relatively short concentration time.
\subsubsection*{Slope study}
{\label{slope-study}}
Our objective is to study the slope's indices and characteristics to
define their classification because the slope plays an important role in
the hydrological characterization of the watershed in order to establish
the hydrological balance. It directly influences the infiltration and
runoff for the same downpour and with the same permeability. In the
Sefrou watershed the following map is obtained ( figure 11):
At the level of the slope map, we can notice an abundance of moderate
slope values whose average value is 19\%. The degree of slope increases
rapidly at the level of major faults and which can reach values more
than 40\%.
\subsubsection*{The overall slope
indexes}
{\label{the-overall-slope-indexes}}
The global slope index Ig makes it possible to assess the importance of
the relief on the basin. It is defined as the ratio between the useful
drop (Du) and the length (L) of the equivalent rectangle. This Ig index
characterizes the relief of the pelvis. It is given by the following
formula:
Ig=\(\frac{\text{Du}}{\text{Leq}}=\frac{H5\%-H95\%}{\text{Leq}}\)
With Ig: overall slope index in m / km
\begin{itemize}
\tightlist
\item
H5\% the altitude which corresponds to 5\% of cumulative surface
\item
H95\% the altitude which corresponds to 95\% of cumulative surface
\item
From: Height difference H5\% - H95\%, Du = 1080m
\item
L: equivalent rectangle length in (km), L = 56.43km
\item
Ig = 20m / km
\item
Ig = 0.02
\end{itemize}
According to the table of Ostrom the value of Ig allows us to deduce
that the relief of the watershed is quite strong.
\subsubsection*{Specific drop Ds}
{\label{specific-drop-ds}}
The specific elevation considers the area of the watershed and the
global slope index Ig. This index allows us to compare the basins with
each other and is defined by the following formula:
Ds =Ig\(\sqrt{A}\)
With:
\begin{itemize}
\tightlist
\item
Ig: global slope index Ig = 20m / km
\item
A: area in km² A = 405 km²
\end{itemize}
Ds = 402.24m
According to the classification of the Ostrom (table 2), the value of Ds
at the level of the catchment area shows a relief which is relatively
strong.
\subsection*{Characteristics of the hydrological
network}
{\label{characteristics-of-the-hydrological-network}}
The hydrographic network designates a hierarchical and structured set of
channels that provide surface drainage, permanent or temporary, of a
watershed or a given region. The hierarchy of the hydrographic network
is manifested by the increasing importance of its elements, from the
original ramifications of the upstream devoid of tributaries (called
order 1 in the classification of Horton - Strahler, 1952), to the main
collector. The order number of this one increases (order 2, orders 3, 4,
5, etc.) with the size of the basin, the number of tributaries, and the
density of the drainage.
The density of the river system increases when the climate is wetter,
the steeper slopes, the rocks or surface formations less permeable.
At the level of our watershed (figure 12), the main river stretches
45.68 km from upstream and high altitudes towards the outlet. According
to the ArcHydro function at ArcGis, we were able to calculate the length
of the main watercourse and even for thalwegs of small extension with a
flow direction of the Sefrou watersheds from South to North.
\subsection*{Drainage density}
{\label{drainage-density}}
Each hydrographic network is characterized by a drainage density, which
is defined as the ratio between the sum of the lengths of the current
lines for a hydrographic network over the area of the watershed. It is
given by the following formula:
Dd=\(\frac{\sum Li\ }{A}\)
With:
\begin{itemize}
\tightlist
\item
Li: Accumulated length of thalwegs (permanent and temporary) in Km.
\item
A: Area of the watershed in km².
\end{itemize}
For the Sefrou watershed: \selectlanguage{english}[?]Li = 298.207km and A = 405 km2.
Hence Dd = 0.73km \textsuperscript{-1}
This value gives us an idea that the hydrographic network of the
watershed is dense.
\subsection*{Torrentiality coefficient}
{\label{torrentiality-coefficient}}
This coefficient considers the frequency of elementary thalwegs (of low
order, generally of order 1) by the density of drainage, the value is
given by the following relation:
Ct = Dd.F1
With:
\begin{itemize}
\tightlist
\item
Dd: drainage density, Dd = 0.73 km \textsuperscript{- 1}
\item
F1: designates the frequency of elementary thalwegs F1 = N1 / A; F1 =
0.21
\item
N1: number of streams of order 1.
\end{itemize}
Ct = 0.16
The value is relatively low since the torrentiality coefficient depends
directly on the concentration time (Tc = 6h11min), (this value is
related to the nature of the relief, slope, area of the basin,
precipitation, etc.)
\subsection*{Hierarchy of the network}
{\label{hierarchy-of-the-network}}
As the ramification of the network is complex, we proceed by a
classification on the set of ramifications of the network. In the
Strahler classification, any drain which has no tributary is assigned
the value 1. Then, the calculation of the value of each drain is done
according to the following method: a drain of order n + 1 is derived of
the confluence of two drains of order n. The Strahler order of a
watershed is the order from the main drain to the outlet. Improvements
have been made to this method by Scheidegger (1966) and developed by
Schriver-Mazzuoli (2012) and to match the Strehler order with the
importance of the flow on the main drain. The map (figure 13) clearly
shows that the total order of the Sefrou watershed is 4 which implies a
fairly developed and branched flow network. (Strehler, 1952).
\subsection*{Longitudinal profile of the
watershed}
{\label{longitudinal-profile-of-the-watershed}}
The use of the profile along the main river (figure 14) allows us to
estimate the average slope and then we can calculate the characteristic
Tc. We note that there are several slope breaks indicating erosion at
the level of the breaking section. These ruptures are generally due to
changes in facies. The main tributaries occupy the right bank with an
appreciable density.
\subsection*{Conclusion}
{\label{conclusion}}
The different physiographic characteristics (table 3) of the Sefrou
watershed are summarized in the table below. The parameters
characterizing the relief show an elongated catchment area. As L is
relatively small, the Tc value for a characteristic downpour is
relatively average. The hypsometric curve shows a relief which decreases
as it moves towards the outlet of the pelvis (northern part of the study
area). Relatively average altitudes (500 to 900 m) are the most
frequented.
The hydrographic network is relatively denser at the level of the right
bank than on the left bank, the two banks remain almost symmetrical
according to their surfaces and the trihedral representation.
\section*{Hydrological
characterization}
{\label{hydrological-characterization}}
\subsection*{Data collection}
{\label{data-collection}}
The available mean annual flows are those of the Ain Louali station
(figure 15), with the following geographical coordinates (X=555,650m; Y=
377,000m; Z= 245 m), located downstream of the catchment area towards
the outlet, these data were obtained on the basis of the monthly values
of the flows provided by the Sebou Hydraulic Watershed Agency. The
period runs from 1968 to 1970 and from 1979 to 2005, a period of 29
years.
It should be noted that the converting data for the 1970/79 period are
absent, to resolve this problem and to ensure data continuity, the
values for these nine years have been estimated, following the shape of
the flow curve by statistical correlation methods.
\subsection*{Study of the flow rate}
{\label{study-of-the-flow-rate}}
\subsubsection*{Average annual flow}
{\label{average-annual-flow}}
The series of observations thus taken shows that the average annual flow
is around 454 l/s. The following figure shows the evolution of annual
flows during the period considered(figure 16):
The specific flow or Qsp is a measure of the average flow of
precipitation within a river catchment area. It is defined as the number
of liters of water that flows on average every second per square
kilometer of the basin. Formulation: this is the value of the flow Q
(L/s or m\textsuperscript{3}/s) relative to the surface A of the
watershed (km\textsuperscript{2}):
Qsp = Q / A
The specific flow is also used to express peak flows during floods. In
general, the peak Qsp during floods decreases when the size of the
watershed increases.
Specific flow : Qsp = \(1.12\ l/s{/km}^{2}\)
The highest average interannual flow is 1000 l/s recorded in 1969/1970,
while the lowest is 300 l/s recorded in 1993/1994 and in 2002/2003.
\subsubsection*{Average monthly flows}
{\label{average-monthly-flows}}
The maximum monthly average flow appears in March (390 l/s), on the
other hand the minimum flow is observed in August (325 l/s), the
following hydrogram shows the variation of the average monthly flows in
Ain Louali (figure 17):
This figure shows that the water concentration requires seven months,
from September to March to reach its maximum which represents the peak
in March with a value of 390 l/s. The time of the recession begins from
the end of March to August, a period of five months to arrive at the
minimum quantity of flows. It should be noted that the flood and
recession times are approximate since we work with average monthly
flows.
\subsubsection*{Specific flows and height of the flow of
water}
{\label{specific-flows-and-height-of-the-flow-of-water}}
Many hydrological studies often focus on comparing the hydrological
regimes of different stations or streams. It is therefore advantageous
to give here the specific flows in l/s/Km2 for the period from 68/69 to
2003/04. The specific flow formula:
q = Q / S
\begin{itemize}
\tightlist
\item
q: specific flow in l/s/Km2.
\item
Q: average flow in l/s.
\item
S: area of the catchment area in Km2.
\end{itemize}
The height of the flow of water in mm is given as a function of q which
is the specific flow rate (Parade, 1974):
\begin{itemize}
\tightlist
\item
H = 31.536 x q for one year.
\item
H = 2,419 x q for a month of 28 days.
\item
H = 2,592 x q for a month of 30 days.
\item
H = 2,678 x q for a month of 31 days.
\end{itemize}
The monthly values of the specific flow rate and the height of the flow
of water flow are given in the following table (table 4):
The total volume of water flown is 27.73 mm/year, or approximately 6\%
of the average volume of water that fell into the watershed (454.22
mm/year). The H/P runoff coefficient (27.73 / 454.22) is 0.061.
\subsubsection*{Rainfall-discharge
relationship}
{\label{rainfall-discharge-relationship}}
The following table (table 5) shows the monthly flows and precipitation
for the period 68/69 to 2004/2005:
When we compare the hydrograph of average monthly flows with that of
average monthly precipitation (figure 18), we see that there is a
synchronism between flows and monthly precipitation. Indeed, the two
curves thus plotted for the same period roughly evolve in the same
meaning and in the same way:
\begin{itemize}
\tightlist
\item
The decrease in rainfall inputs is accompanied by a late decrease
inflow recorded around the summer months.
\item
These are maximum precipitation values in December and January
followed by a maximum flow in March, with a delay of one month; time
required for the arrival of significant inputs to the measurement
station which is located near the outlet of the watershed. This
discrepancy can be explained by the lithological nature of the
watershed or by its morphology.
\end{itemize}
In general, the flow of runoff is one of the most important components
of the outflow from a hydrological regime fed by precipitation.
\subsubsection*{Final water balance
estimate}
{\label{final-water-balance-estimate}}
The main purpose of any hydrological study is to estimate the water
balance of the region concerned, to establish a database corresponding
to local water reserves, as well as to guarantee integrated management
of these resources. The following table summarizes the results of the
Sefrou watershed water balance assessment (table 6):
According to the table (6), the maximum percentage is that of
evapotranspiration (87.67\%), which can be explained by the
high-temperature values during the dry period and by the evolution of
the vegetation in the area.
It is important to underline the fundamental points concerning the study
carried out under this paragraph. The aspects relating to the hydrology
of the Sefrou catchment area bear witness to the Mediterranean
hydrological character where the dry season is strongly pronounced. It
is therefore obvious to deduce that the hydrological drought has been
well marked during the previous 30 years, which has, moreover, been
confirmed by the method of differences in the average interannual flow
rates.
The study of the hydrological regime using the method of determining the
''precipitation-flow'' relationship has made it possible to define a
rainfall regime. The mean annual flow is 454 l/s.
The study of the monthly flows shows that there is a similar evolution
with a small delay between the maximum values of the flows and the
monthly flow coefficients show that the Sefrou catchment area is
characterized by an irregular regime. For its part, the study of the
specific flows and the height of the runoff water level made it possible
to estimate the runoff coefficient which is 0.061.
The water balance showed that the runoff estimation represents 6.06\% of
total precipitation. As for infiltration, it represents 6.23\% of
precipitation.
Sefrou watershed provides real water resources and thus ensures the
supply of drinking water for the inhabitants of the Middle Atlas regions
and more specifically for the habitats of the city of Sefrou. Despite
the usefulness of these important capacities, they were causing risks
represented by winter floods causing human and material damage, which is
solved by the establishment of development projects in the region.
\section*{Conclusion}
{\label{conclusion-1}}
The Sefrou watershed occupies the SW part of the Sebou watershed. It is
extended over a total area, up to the intersection with the famous Oued
Sebou, of 404.89 Km2 with a perimeter of 127.42 Km; that is 1\% of the
Sebou watershed.
The morphometric parameters show that the Sefrou watershed is elongated
(L=56.43 Km and l= 7.18 Km). The hypsometry is characterized by
altitudes that progressively decrease from the South to the northern
part of the basin. According to the hypsometric curve, the altitudes
between 500m and 900m occupy most of the surface of the basin. The
relief is relatively strong according to the global slope index and the
specific gradient. The hydrographic network is very important on the
eastern bank than on the western bank, and this is related to the
lithology and the vegetation cover.
In spite of the diversity of the lithological formations that outcrop in
the Sefrou catchment area, they can be grouped into two large units the
southern sector (the Middle Atlas ``cause'') which is characterized by
essentially carbonate formations constituting a highly developed karstic
system thus conditioning a high permeability in this part of the
catchment area.
The rainfall collected in the stations during 1970/2011 is characterized
by fluctuations between the different stations and hydrological cycles.
The mean annual and monthly precipitation is
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