The term “morphometry” refers to the branch of science that is concerned with the quantitative measurements of any natural form’s shape. The pioneer in this field, Horton [
36], contributed to this contemporary method of quantitative morphological analysis of the basin. Several geomorphologists further developed and modified Horton’s laws, including Strahler [
39,
40] and Schumn [
41]. These basin’s morphometric parameters can provide information on a basin’s topography, geology, and hydrological behavior. Additionally, it also has a significant impact on the flood peak [
42]. In the current study, each basin was highlighted separately to extract its morphometric parameters in detail using ArcGIS and TOPAZ modules in a watershed modeling system (WMS) based on DEM data (
Figure 8). As shown in
Table 1, the main morphometric parameters of the drainage basins were calculated using the equations and methods. The linear, areal, and relief morphometric characteristics of the basins are summarized in
Table 2 and explained below.
Table 1.
Morphometric parameters selected for the current analysis.
Table 1.
Morphometric parameters selected for the current analysis.
| Morphometric Parameters | Mathematical Expression | References |
---|
A | Linear measurements of the drainage watershed |
1 | Stream order (Su) | Hierarchical ordering | [37] |
2 | Stream number (Nu) | Nu = N1 + N2 + Nn | [36] |
3 | Stream length (Lu) km | Lu = L1 + L2……Ln | [40] |
4 | Drainage basin length (Lb) | The longest dimension of the basin, which is parallel to the principal drainage (km) | [41] |
5 | Average basin width (Wb) | Basin area (A) divided by its length (Lb) | |
6 | Mean bifurcation ratio (MRb) | MRb = Average of bifurcation ratios Rb of all orders; Rb=Nu/N(u+1); Nu is number of streams of any given order, and (u+1) is the next higher order | [36] |
7 | Length of overland flow (Lg) | Lg = 1/(2 × Dd) | [36] |
B | Areal measurements of the drainage watershed |
1 | The area of drainage (A) km2 | GIS software analysis | [41] |
2 | Basin perimeter (P) km | Total length of outer boundary of drainage basin | [41] |
3 | Stream frequency (Fs) km2 | Fs = (ΣNu)/A | [36] |
4 | Drainage density (Dd) km/km2 | Dd = (ΣLu)/A | [36] |
5 | Circularity ratio (Rc) | Rc = 12.57 × (A/P2) | [43] |
6 | Elongation ratio (Re) | Re = 2/Lb × (A/π) 0.5 | [41] |
7 | Form factor (Ff) | Ff = A/Lb2 | [36] |
8 | Infiltration number (If) | If = Dd × Fs | [44] |
C | Relief measurements of the drainage watershed |
1 | Basin relief (R) | R = H − h; H is maximum elevation and h is minimum elevation of the basin | [40] |
2 | Relief ratio (Rr) | Rr = R/Lb | [41] |
3 | Drainage texture (T) | T = (ΣNu)/p | [45] |
4 | Ruggedness number (Rn) | Rn = R × Dd/1000 | [41] |
5 | Basin Slope (Bs) | WMS software “topaz model” | |
4.3.1. Linear Measurements of the Basins
Stream orders (Su) and stream numbers (Nu) are two of the most significant morphometric parameters in morphometric analysis if there are two basins with the same amount of rain falling and have the same area. They may differ in the runoff due to the difference in their stream order. However, the higher the network’s stream order, the higher the runoff and, consequently, the higher the risk of flooding. That is because a raindrop takes less time to travel from any point in the basin to the outlet, causing runoff to accumulate quickly and produce a high hydrograph peak. The stream orders of the studied basins range between the 4th and 7th orders. The Wadi A, B, C, and Abu Gherban have the lowest rank (4th order), and the Umm Gheig and Hamrat Ghannam basins have the highest rank (7th order). On the other hand, the total number of streams in the studied basins is the maximum (3310 streams) in Wadi Umm Gheig and the minimum (47 streams) in Wadi Abu Gherban.
Total stream lengths (Lu) differ significantly from one wadi to the other—they depend on the area of the basins and the number of streams. The morphometric analysis indicates that Wadi Umm Gheig is the longest one in terms of total stream lengths of 2560 km, while Wadi B is the shortest one in terms of total stream lengths of 30.8 km. These values varied between basins, indicating a difference in infiltration capacity that might be caused by changes in slope and terrain. The stream’s length reveals how climate, vegetation, and rock erosion resistance are related [
46]. In the same context, under the same conditions, impervious rocks support longer stream lengths [
47].
Basin length (Lb) is defined as the tallest length of the watershed that lies parallel to the mainstream [
41]. Gregory [
48] described the length of the basin as the tallest pass of the watershed, in which one end of the passage is at the basin’s outlet. According to the morphometric analysis, the highest basin length is 49.97 km for watershed Umm Gheig, while the shortest one is for watershed Rizq Awad of 6.27 km.
One important morphometric parameter used to estimate the basin’s shape is the width of the basin (Wb). The outcomes of the analysis indicate that the width of the wadis differs widely, from 1.5 km in Abu Gherban to 17.1 km in Umm Gheig.
The bifurcation ratio (Rb) is a dimensionless property, defined as a metric of how branched the hydrographic network [
36,
39]. Generally, the mean of all the bifurcation ratios of the basin (MRb) falls between the value of 2 for basins that are flat terrain and 3–4 for basins that are mountainous [
36]. The MRb of the basins covering the study area ranges from 2.79 for Rizq Awad to 4.92 for Sharm El-Bahari. According to Zuchiewicz [
49], the higher MRb is a result of the region having recently been exposed to tectonic uplift. On the other hand, basins with lower MRb tend to have experienced fewer structural disturbances [
40], and the geological or structural control has not distorted their drainage pattern [
41,
50]. In this regard, Strahler [
40] mentioned that areas with narrow valleys confined between steeply dipping rock might be expected to have an abnormally high MRb. Generally, MRb in the study area is relatively high when they are higher than the suggested normal range by Horton [
36] due to structure distortions. From the viewpoint of flood risk, a higher MRb value denotes a slow run of rainwater that allows water to penetrate under the surface, reducing runoff and flash floods [
51].
The overland flow length (Lg), which is significantly influenced by infiltration through the soil, is the distance that rainwater travels above the land surface before being accumulated in the basin’s stream channels. It has an opposite relationship with flash flood hazards and a direct relationship with infiltration rate [
7]. The basins of the study area have a length overland flow with values ranging from 0.159 km of wadi A to 0.223 km of wadi B. Lower Lg values mean a shorter flow distance, which indicates runoff will accumulate more quickly and arrive at the outlet in less time, increasing the risk of flooding.
4.3.2. Areal Measurements of the Basins
Watershed area (A): According to Strahler [
37], wadis having the same area and form characteristics have similar geomorphological properties. The outlined area of the basins covering the study area ranges between 855.3 km
2 in the Umm Gheig basin and 13.71 km
2 in basin B. Generally, assuming that infiltration, slope, and precipitation are the same for two watersheds, a watershed with a large area will receive a large amount of rains, and thus will cause significant runoff and may result in high hazard. Horton (1932) classified the basins on the basis of their surface area into three groups: the larger e basin > 100 km
2, the medium basin ranged from 50 to100 km
2, and the smaller basin < 50 km
2. The study area watersheds fall into the small to large area category.
The watershed perimeter (P) represents the outer frame of the watershed that separates it from other adjacent basins. The basins’ perimeter varies greatly from one to another, ranging from 20.27 km in Rizq Awad to 229.63 km in Umm Gheig.
The basin shape mainly reflects how surface water will flow out of the basin. The circular basins, which differ from elongated ones, will cause runoff from different directions of the wadi that reach the mainstream at roughly the same time. In this regard, the circular basin is characterized by a large drain in a shorter amount of time [
52,
53] additionally, the flooding peak is higher than the elongated one. Accordingly, the elongated basins have less runoff possibility [
54], which takes their chance to infiltrate, and also, the runoff will spread out over time. Hence, the elongated basins are simpler to manage and control than the circular basins, and their waters have a higher probability of infiltration into the water table [
55]. The ratio of elongation, ratio of circulatory, and shape factor represent the three key indices used to assess basin shape.
The elongation ratio (Re), according to Schumm [
41], measures the shape of the catchment and ranges from 0 to 1, where a value of 0 indicates that the catchment is highly elongated and a value of 1 indicates that it is circular. AnRe near one is typical for areas that have low relief, while Re < 0.8 is assumed to be elongated and is typically connected to steep slopes and moderate to high relief [
40]. In general, basins with an elongation ratio of <0.7 reflect that the lag time is longer and that flooding hazards are consequently reduced [
17,
40,
54]. The morphometric analysis results indicate that the basins in the area of study have elongation ratios that range between 0.42 and 0.73 for Wadi Abu Gherban and Wadi Hamrat Ghannam, respectively. According to the standard classification of the basin shape given in (
Appendix A,
Table A2), the study area’s basins tend to be elongated in shape.
Miller [
43] described the circularity ratio (Rc) as the ratio of the catchment’s surface area to the surface area of a circle with the same perimeter as the catchment. The Rc varies from 0 to 1. If it is close to or equal to 1, the catchment is circular in shape, while the catchment is elongated in shape if the Rc is closer to zero. The morphometric analysis results indicate that the Rc of the basins covering the study area ranges from 0.19 for Abu Gherban to 0.46 forRizq Awad. In this context, the lower circularity ratio of the basins means that they are close to the elongated in shape.
The form factor (Ff) parameter was suggested by Horton [
36], and it can be measured as the ratio between the surface area of the watershed and its length squared. Ff values range from 0 to 1. A higher Ff suggests that the watershed is close to being circular in shape, while a lower value suggests that the watershed is close to being elongated. The results of the analysis indicate that the drainage basin’s form factor ranged from 0.14 for Wadi Abu Gherban to 0.42 for Wadi Hamrat Ghannam. It indicates that the shape of basins that cover the area of study tends to be elongated.
Drainage density (Dd) indicates how far apart or close the streams are within the basin [
40]. Eze and Efong [
56] reported that low drainage density denotes fractured hard rocks, suggesting that a large percentage of rainstorms will infiltrate to recharge the aquifer, while high drainage density suggests great runoff of precipitation. In the present study, the Dd differed from 2.25 km/km
2 for wadi B to 2.99 km/km
2 for Umm Gheig. Accordingly, these basins have poor drainage and have a rough texture. When comparing basement rocks, the granite of the central Eastern Desert has a lower mean drainage density, and thus, basins with lower Dd are better for groundwater storage.
Stream frequency or channel frequency (Fs), described by Horton [
36], is the total number of channels in a network of all orders in a watershed per unit area. The stream frequency differs from one to 6 or maybe more based on the basin lithology. In the current study, Fs ranges from 3.12 to 4.74 streams per km
2 for Wadi Abu Gherban and Rizq Awad, respectively. As a result, the basins covering the study have relatively moderate stream frequency, which means they represent moderate surface runoff because it means the basin keeps an amount of water without draining.
The infiltration number (If), which depends on stream density and frequency, gives useful information on the basin’s infiltration characteristics. A low drainage density and frequency increases soil infiltration capacity [
57]. The infiltration number is directly related to the runoff potential and inversely related to the infiltration [
40]. The results reveal that the infiltration of the study area ranged between 8.1 (Wadi Abu Gherban) and 13.2 (Wadi Rizq Awad). As a result, the surface runoff increases in the Wadi Rizq Awad more than in the other—this means a high hazard.
4.3.3. Relief Characteristics of the Drainage Watersheds
Basin Relief (R): According to the study results, the basin relief varies greatly between 207 m for Abu Gherban and 1452 m above sea level for Sharm El-Bahari. As an outcome, the relief of basins covering the area under investigation ranges from high to very high as the erosional forces are relatively greater. According to Kadam et al., [
58], the basin with higher relief leads to the high gravity of rainfall flow, less soil penetration conditions, and great surface runoff.
The relief ratio (Rr) is a significant factor for measuring a watershed’s general slope [
59]. According to Schumm [
41], Rr has a direct relationship with flash floods and an inverse relationship with concentration time. Abdelkader et al., [
47] reported that the watersheds that cover the basement and Tertiary rocks contain high Rr values. The relief ratio in the present study, according to the morphometric measurements, differs from 0.020 m/km to 0.049 m/km for the Wadis Abu Gherban and Sharm EL-Qibli, respectively. Generally, lower Rr indicates the slope of the wadi is light; thus, runoff will decrease, while larger Rr indicates the slope of the wadi is steep; thus, runoff will increase.
Drainage texture (T), an essential element of the morphometric measurements, is significantly influenced by soil type, relief aspect, and infiltration [
60]. It is useful in describing how close or far away the streams are from each other and thus indicates the texture of the terrain. The study revealed that the texture ratio in Wadi Abu Gherban and Wadi Umm Gheig, respectively, ranges from 1.5 to 14.4 km. Based on Smith’s classification [
45] (
Appendix A,
Table A3), the studied basins are listed under the very fine to very coarse texture category. According to Smith [
45] and Sujatha et al., [
61], fine drainage texture appears in soft rocks or permeable surfaces without vegetation cover, while coarse drainage texture appears in hard rocks or impermeable soil.
The ruggedness number (Rn) of the watersheds covering the area under investigation varies between 0.47 and 4.11 in basin B and Hamrat Ghannam, respectively. Based on Melton [
62], the high Rn implies a rough topography, complex structural features in the area, and high drainage density. It means that high Rn values may cause an increase in watershed peak discharge.
Basin Slope (BS), one of the main morphometric measurements, is essential in assessing the risk of flooding as surface water flows along the direction of a steep slope. The basins’ slope was calculated using the WMS software’s TOPAZ model and varies from 0.043 to 0.180 for basin B and basin Sharm El-Bahari, respectively. In steep basin slopes, water infiltration is low, and overland flow velocity is high; it means faster runoff and the possibility of flood hazards. Basins with higher slopes have rapid runoff volume and potential soil erosion.