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.
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.
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.
Compactness Index of
Gravelius
The Compactness Index KG of Gravelius (1914), defined as
the ratio of the perimeter of the watershed to the perimeter of the
circle having the same area:
Where:\(KG=\frac{P}{2\sqrt{\pi}\text{.A}}\approx 0.28.\frac{P}{\sqrt{}A}\)
- KG is the index of compactness of Gravelius,
- A: surface area of the catchment area [km2],
- P: watershed perimeter [km].
In our case: KG =1,77
From the value of KG 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.
Horton Compactness Index
The Horton Compactness Index (Horton, 1932) is calculated as the ratio
of the average width lm to the length of the mainstream L by the
following relationship:
Kh= \(=\frac{\text{lm}}{L}\)
With:
- lm : the average width of the watershed (km).
- L : the length of the main watercourse (km).
In our catchment area: lm =13.56km and L =45.76km
Kh = 0.0065 Km(-1)
As the Kh value is very low this confirms that the watershed is
elongated.
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:
- lm: the average width of the watershed (km);
- La: axial length (km).
At the level of our watershed, we have: lm=13.56km and L =29.76km².
Kf=0.45
This implies an elongated shape of the catchment area.
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 = \(\sum_{1}^{4}\frac{\text{Lm}}{n}\)\(\sum_{1}^{4}\frac{\text{Lm}}{n}\)
- A: Area of the watershed in km², A=405 km²;
- n: number of order = 4;
- Lmx: maximum length of watercourses in the watershed Lmx= 74.55;
- lm: average length of rivers.
\(lm=298,207\ km\) , 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.
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:
- Kg: Gravelius index of compactness.
- S: catchment area (Km);
- L: length of the equivalent rectangle (Km);
- l: width of the equivalent rectangle (Km);
- For our pool we have the following characteristics.
The values of the dimensions (figure 7) of the watershed allow us to
deduce that we have a relatively elongated watershed.
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:
Calculation of the angle α1=\(Arctg(\frac{2Ai}{L^{2}})\)
With:
- A: the area of the right bank; A = 224, 033km²;
- L: the length of the main watercourse; L = 45.76km².
α1: the angle of the right bank triangle
α1 = 12.077 °.
For the left bank:
Calculation of the angle α2=\(Arctg(\frac{2Ai}{L^{2}})\)
With:
- A: the area of the left bank; A = 180, 97km² ;
- L: the length of the main watercourse; L = 45.76km².
α1: the angle of the right bank triangle
α2 = 9.81 °
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.
Altitude Characteristics
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 ….). 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” (> 1500m), however further north
towards the downstream part (<300m).
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…
the average altitude is calculated according to the following formula:
Hm= \(\sum_{1}^{i}\frac{\text{Aihi}}{A}\)
With:
- Ai: this is the area between two contour lines (Km²)
- hi: Average altitude between two contour lines (m)
- A: Total area of the watershed (km²)
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
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:
- Tc concentration time (hours);
- A: area of the watershed in km²; A = 405km²;
- The length of the main Thalweg watercourse in (km); L = 45.68km.
- Hm: average altitude (m); Hm = 928.36m.
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.
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%.
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
- H5% the altitude which corresponds to 5% of cumulative surface
- H95% the altitude which corresponds to 95% of cumulative surface
- From: Height difference H5% - H95%, Du = 1080m
- L: equivalent rectangle length in (km), L = 56.43km
- Ig = 20m / km
- Ig = 0.02
According to the table of Ostrom the value of Ig allows us to deduce
that the relief of the watershed is quite strong.
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:
- Ig: global slope index Ig = 20m / km
- A: area in km² A = 405 km²
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.
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.
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:
- Li: Accumulated length of thalwegs (permanent and temporary) in Km.
- A: Area of the watershed in km².
For the Sefrou watershed: ∑Li = 298.207km and A = 405 km².
Hence Dd = 0.73km -1
This value gives us an idea that the hydrographic network of the
watershed is dense.
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:
- Dd: drainage density, Dd = 0.73 km - 1
- F1: designates the frequency of elementary thalwegs F1 = N1 / A; F1 =
0.21
- N1: number of streams of order 1.
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.)
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).
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.
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.