The Gumbel distribution is the best-fitting distribution law for rainfall variables among the distribution laws that can account for the statistics of extreme phenomena (Laborde 2000). Table 4 shows the maximum daily rainfall for different return periods at Ajdir, Barrage, and Takenfoust stations. The return period is the average number of years between events of a given magnitude. For example, a 20-year return period means that an event of that magnitude is expected to occur on average once every 20 years. It is observed that the maximum daily rainfall increases with the return period because more intense extreme events are less likely to occur. For example, in a 20-year return period the extreme event is expected to be of 80 mm approximately in Ajdir, while in a 1000-year return period it is expected to be of 156 mm (Table 4).
Table 4
Maximum daily rainfall for different return periods.
Return Period | 10 | 20 | 50 | 100 | 1000 |
Fréquency F | 0.9 | 0.95 | 0.98 | 0.99 | 0.999 |
Gumbel Variable | 2.25 | 2.97 | 3.9 | 4.6 | 6.91 |
P in 24 hours (mm) - Ajdir Station | 80.31 | 92.02 | 107 | 118.53 | 156.01 |
P in 24 hours (mm) - MBA Dam Station | 107.66 | 129.4 | 157 | 178.52 | 248.17 |
P in 24 hours (mm) - Takenfoust Station | 89.31 | 106.2 | 128 | 144.33 | 198.41 |
The variability in maximum daily rainfall across different stations can be attributed to various factors influencing regional precipitation patterns. Despite Ajdir station (coastal) received a higher annual average precipitation than the MBA Dam Station (inland), the latter experienced more frequent extreme weather events. The discrepancy in rainfall between coastal and inland areas is attributed to the Mediterranean backflow phenomenon (Table 4 and Table 1) which occurs when cold air from the sea flows back into the continent, causing moisture to condense and form thunderstorms. These thunderstorms are most common at the beginning of autumn and the end of spring and are likely to cause more intense rainfall.
The Table 5 provides time of concentration (Tc) values calculated using different empirical formulas, namely Kirpich, Spanish, Turraza Passini, and Venture. Each method employs its own set of parameters and assumptions to estimate the time it takes for water to travel from the hydraulically farthest point to the watershed outlet. The Tc values obtained from different estimation methods vary across the watersheds, indicating the sensitivity and uncertainty associated with Tc estimation.
Table 5
Concentration time assessment results.
Watershed | Area km² | Long en km | Slope m/m | Kirpich | Espagnole | Turraza Passini | Venture | Average (minutes) | Average (Hours) |
Seftoula | 36.38 | 13.51 | 0.05 | 95.11 | 97.60 | - | 211.43 | 134.72 | 2.25 |
Ikaltoumene | 5.30 | 4.98 | 0.06 | 39.87 | 43.50 | - | - | 41.68 | 0.69 |
Chaâbat Agadir 2 | 1.21 | 3.92 | 0.04 | 38.77 | 39.17 | - | - | 38.97 | 0.65 |
Chaâbat Agadir 1 | 0.45 | 1.10 | 0.14 | 9.00 | 11.75 | - | - | 10.37 | 0.17 |
Nekor | 779.00 | 69.23 | 0.03 | 412.88 | 374.80 | 1477.43 | 1285.14 | 887.56 | 14.79 |
Through a comparison between the average flood flows and the values obtained from the empirical methods listed in Table 6, clear trends emerge in terms of the most effective approach for estimating river outflows across different return periods and watershed characteristics. It was assumed that the techniques exhibiting the closest values to the average for each return period are considered the most effective. Consequently, the Fuller II method is likely the most effective for river watersheds with a medium and a small area (less than 40 km²) and a 20-year return period. The Maillet et Gautier method also demonstrates good performance in this scenario. When considering a 50-year return period for all river watersheds, Fuller II remains the most effective method together with the Rational method. In the case of a 100-year return period, the choice of an effective method depends on the size of the river watershed. The Rational method is the most effective for small and medium-sized watersheds and the Fuller II method is best for large watersheds (greater than 40 km²). It should be noted that both the rational method and the Gradex technique do not provide calculated flow values for the 1000-year return period. These methods rely on the Montana coefficient parameters which are estimated only for return periods of 2, 5, 10, 20, 50, and 100 years (Table 8).
Table 6
Flood flows after the empirical analysis (m3/s).
| | Empirical techniques |
Return period (years) | Watershed | Maillet and Gautier | Rational | Hazan lazaravic | Fuller II | Possenti | Average |
20 | Seftoula | 75 | 49 | 59 | 81 | 151 | 83 |
Ikaltoumene | 20 | 14 | 12 | 24 | 60 | 26 |
Agadir 2 | 6 | 7 | 4 | 10 | 17 | 8,8 |
Agadir 1 | - | 1 | 2 | 6 | 23 | 8 |
Nekor | 554 | - | 705 | 672 | 633 | 641 |
50 | Seftoula | 101 | 114 | 87 | 106 | 202 | 122 |
Ikaltoumene | 26 | 28 | 18 | 31 | 80 | 36,6 |
Agadir 2 | 7 | 11 | 6 | 13 | 23 | 12 |
Agadir 1 | - | 3 | 2 | 7 | 31 | 8,6 |
Nekor | 844 | - | 1033 | 881 | 844 | 900,5 |
100 | Seftoula | 110 | 135 | 99 | 117 | 223 | 136,8 |
Ikaltoumene | 28 | 41 | 21 | 34 | 88 | 42,4 |
Agadir 2 | 7 | 14 | 6 | 14 | 26 | 13,4 |
Agadir 1 | - | 4 | 3 | 8 | 34 | 9,8 |
Nekor | 942 | - | 1175 | 971 | 934 | 1005,5 |
1000 | Seftoula | 136 | - | 138 | 153 | 294 | 180,25 |
Ikaltoumene | 34 | - | 29 | 45 | 116 | 56 |
Agadir 2 | 9 | - | 9 | 19 | 34 | 17,75 |
Agadir 1 | - | - | 4 | 11 | 45 | 15 |
Nekor | 1212 | - | 1644 | 1270 | 1229 | 1338,75 |
Table 8
Parameters of the Montana for the Al-Hoceima hydrograph (1972–2008).
T | a (mm/min) | b |
2 | 2.580 | 0.599 |
5 | 3.527 | 0.577 |
10 | 4.172 | 0.570 |
20 | 4.579 | 0.566 |
50 | 5.606 | 0.562 |
100 | 6.215 | 0.560 |
Table 7 compares flood flow values for different return periods and provides modeled flow estimates using the average of the empirical analysis and the Gradex technique. For the 10-year return period, the average modeled flows based on the empirical analysis are higher than those obtained from the Gradex technique across all watersheds. The same trend is observed for the 50-year and 100-year return periods, where the average modeled flows from the empirical analysis exceed the Gradex estimates. Specifically, the Seftoula watershed has an average modeled flow of 65.5 m³/s for the 20-year return period, 104 m³/s for the 50-year return period, and 119.4 m³/s for the 100-year return period (Table 7). Ikaltoumene, Agadir 2, Agadir 1, and Nekor also exhibit similar patterns with higher average modeled flows from the empirical analysis compared to the Gradex technique. Overall, the results demonstrates that the average of the empirical analysis consistently yields higher flow estimates for the examined return periods when compared to the Gradex technique.
Table 7
Modeled flows after the average of the empirical analysis and hydrometeorological Gradex techniques.
Return period (years) | Watershed | Average the empirical analysis | Gradex | Modeled |
20 | Seftoula | 83 | 48 | 65,5 |
Ikaltoumene | 26 | 11 | 18,5 |
Agadir 2 | 8,8 | 5 | 6,9 |
Agadir 1 | 8 | 1 | 4,5 |
Nekor | 641 | 517 | 579 |
50 | Seftoula | 122 | 86 | 104 |
Ikaltoumene | 36,6 | 22 | 29,3 |
Agadir 2 | 12 | 8 | 10 |
Agadir 1 | 8,6 | 3 | 5,8 |
Nekor | 900,5 | 794 | 847,25 |
100 | Seftoula | 136,8 | 102 | 119,4 |
Ikaltoumene | 42,4 | 26 | 34,2 |
Agadir 2 | 13,4 | 9 | 11,2 |
Agadir 1 | 9,8 | 4 | 6,9 |
Nekor | 1005,5 | 912 | 958,75 |
1000 | Seftoula | 180,25 | - | 180,25 |
Ikaltoumene | 56 | - | 56 |
Agadir 2 | 17,75 | - | 17,75 |
Agadir 1 | 15 | - | 15 |
Nekor | 1338,75 | - | 1338,75 |
It is concluded that the Gradex technique was the most accurate, but the empirical analysis of flood flows was also accurate and can be used in conjunction with the Gradex technique to improve the accuracy of the results.
The final phase of the simulation involved the cartography of hydraulic characteristics of floods, such as water levels and flood-prone areas. Regarding the hydraulic behavior, two distinct sectors were identified in the Nekor River:
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Left tributaries of the Nekor River: for this sector, the 1D-2D modeling was carried out using the flow flood of different return periods, including 20, 50 and 100-year. These tributaries pass through the Agadir and Hammou Ezzyani districts. Before crossing the N2 national road, overflows from 50-year and 100-year flood events are frequent, with water levels ranging from 0.5 to 2 meters (Fig. 6). Flow velocities during these floods have exceeded 3 m/s. The main road and streets in the area are frequently submerged during flood events.
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Downstream: a 1D-2D modeling technique was employed, utilizing the maximum flow data from the Tamellaht station in 1968 and 1000-year return period, and 20, 50 and 100-year for the industrial zone. The estimated flow for the 1000-year flood event was 1,338.75 m³/s (Table 7). The floods associated with this event pose varying levels of danger and affect extensive areas, potentially covering 2,017 Ha (Fig. 4). The industrial zone, which covers an area of 5 hectares, was partially built on the main course of the Nekor river. The 50-year return period covered 3 Ha of the zone (60% of the industrial zone) (Fig. 5). This flooding engenders significant damage to the buildings and protective structures.
Based on field surveys and archival research, significant historical floods that have affected different parts of the Nekor plain were identified. Notable floods include those in the 1960s (1962 and 1968), February 1982, November 2003, and October 2008. The most significant and violent floods in the Nekor plain were observed during the 1960s; From January 31 to March 3, 1968, the flow in the Nekor plain reached 1,700 m³/s at the Tamellaht station and 1,822 m³/s at the MBE dam (Fig. 3). In 1962, the flood was remarkable in the plain, with the Nekor river inundating significant parts, which housed various infrastructures. The Nekor and Ghis rivers converged in the commune of Ait Youssef Ou Ali. The volumes recorded at the Tamellaht station were similar as for the floods in January 31 to March 3, 1968 (Fig. 3 and Fig. 4). The floods on February 22, 1966 (1 hour and 30 minutes), and March 10–11, 1968 (1 hour) had the fastest rise in water levels and flow. The recorded damages mainly affected agricultural lands and livestock.
Since these historical floods had water quantities comparable to millennial return period flood events, the spatial extent of the 1968 flood was chosen for comparison with the results of the millennial return period to validate the findings. The 1968 flood covered an area of 2,483 Ha with a flow of 1,700 m³/s, while the millennial return flow covered an area of 2,017 hectare with a water quantity of 1,338.75 m³/s (Table 7 and Fig. 4). The relatively similar results demonstrate the reliability of the employed procedures.
Based on the provided information, calibration and validation of the simulation model were conducted using the hydrograph data from the flood seasons of 1968. The simulation was performed under unsteady flow conditions to replicate the flood events accurately. The floodplain area was defined by extending the cross-section, and the flood was considered to occur when the river water exceeded the main channel.
A Triangulated Irregular Network (TIN) was used to perform the calculations. TINs are a used for representing the river channel and floodplain topography using a network of interconnected triangles. This allows for the accurate calculation of various parameters and characteristics of the flow, such as velocity, depth, and discharge. The model's predictions of peak levels and their timing were found to be of good quality, indicating that the simulated results align well with the observed data (Fig. 3). Additionally, the Mean Square Error (MSE) (Eq. 15) was reported to fall between 10 and 20 cm. The MSE is a measure of the average squared differences between the observed and simulated values, and a lower MSE suggests better agreement between the two.