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:\(KG=\frac{P}{2\sqrt{\pi}\text{.A}}\approx 0.28.\frac{P}{\sqrt{}A}\)
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:
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:
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 = \(\sum_{1}^{4}\frac{\text{Lm}}{n}\)\(\sum_{1}^{4}\frac{\text{Lm}}{n}\)
\(lm=298,207\ km\) , 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:
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.

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:
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:
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:
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:
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
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:
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:
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:
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.