Application of physically-based and experimentally calibrated method for flood hazard assessment: Case study of Zaio, Morocco.

. This study aims to assess the urban flood hazard in Zaio, Morocco by utilizing a rainfall-runo ff transformation and hydrodynamic modelling. We utilized a statistical adjustment and The Soil Conservation Service–Curve Number (SCS-CN) method to estimate the 100-year return period flood hydrograph, which itself served as input for the Iber numerical model. Flood hazard assessment for human adults was calculated using a physically-based and experimentally calibrated method, a method that takes into consideration all physical forces acting on a human body during a flood, i.e., drag and buoyancy, and thereby facilitate a more precise assessment of urban flood hazard.


Introduction
The frequency of floods as the primary natural disaster is alarming, representing 43% of recorded global disasters and resulting in over 20,000 annual deaths while affecting around 75 million people worldwide [1].Despite its geographical location, Morocco has not escaped the impacts of floods, evident from the identification of nearly 1,000 flood-prone sites, including the vulnerable Oriental region of Morocco.Flood hazard maps serve as critical tools in the identification of areas at risk of potential flooding disasters.These maps characterize floodwaters' depth and velocity.By offering comprehensive information on flood characteristics, these maps play an important role in provisioning the extent of damage caused by flood hazards and facilitate proactive measures [2].Ensuring the accuracy of information provided by flood hazard maps is paramount in the context of flood management and mitigation practices.Various studies have sought to quantify flood hazard through empirical formulas, relying on various factors such as flood depth, velocity [3], or its probability of occurrence [4].This study presents a flood hazard assessment in the city of Zaio, Morocco, taking into account the human body' stability to toppling and sliding.Combining rainfall runoff modeling with the physically-based and experimentally calibrated method for hazard assessment provides an accurate approach for flood risk management.The physically-based rainfall runoff model captures hydrodynamic processes, leading to realistic flood discharge estimates.While statistical adjustment provides return period design rainfall information that accounts for historical data and long-term trends, utilizing it alone does not yield discharge data.In contrast, the SCS-CN method transforms rainfall into a design flood hydrograph, bridging the gap between rainfall and discharge.The new criterion for human body stability considers factors like body buoyancy and upstream velocity profiles, improving accuracy [5].This integrated approach ensures precise flood risk assessment and enhances safety measures for people in floodplains and urban areas.

Study area
Zaio, situated in the southern part of Nador province (figure 1), is characterized by an altitude of 190 meters above sea level and experiences an average annual rainfall of 330 mm [6].The city is surrounded by the Kebdana Range to the north and the Sebra River to the south, forming a valley dominated by hills that act as a watershed for several small rivers known as Châaba.These rivers originate in the small basins of Mount Kebdana, approximately 2 km upstream from Zaio.Experiencing an arid climate, with an average annual precipitation of 330 mm/year.The total amount of rainfall varies significantly from year to year, depending on the dominance of maritime or continental influences [6].The combination of topographic contrast and urban development in Zaio City contributes to frequent and severe flooding events, as evidenced by the flood recorded in 2007.

Rainfall-runoff transformation
To estimate the maximum daily precipitation for a 100-year return period, a statistical adjustment of the daily maximum precipitation, recorded by the hydraulic basin of Oued Moulouya E3S Web of Conferences 469, 00013 (2023) ICEGC'2023 https://doi.org/10.1051/e3sconf/202346900013agency between 1984 and 2017, was performed using the Gumbel distribution, giving a 100year return period daily rainfall of 110 mm.Subsequently, the HEC-HMS software was used to obtain the 100-year flood hyetograph.Given Zaio's location as a city within a slope zone rather than a large watershed, we chose to dis-aggregate the maximum 100-year rainfall value into A SCS type II 2-hour duration with 6 minutes intervals instead of the conventional 24 hours.This approach is crucial to capture the rapid nature of flash floods, the predominant flood type in the city.HEC-HMS simulations allowed then to model the rainfall-runoff processes for each river in Zaio, giving the flood hydrographs of each stream crossing the city.Figure 2 demonstrates the 100-year return period rainfall hyetograph for Zaio.The flood hydrographs for the seven rivers numbered from 1 to 7 are shown in figure 3.

Iber hydrodynamic model
Iber is a two-dimensional numerical model with a primary purpose of replicating and studying free surface water flows and transport processes in rivers and channels [7].At its core lies the implementation of the Saint-Venant equations, which play a fundamental role in integrating the principles of mass conservation and quantity of motion.These governing equations are E3S Web of Conferences 469, 00013 (2023) ICEGC'2023 https://doi.org/10.1051/e3sconf/202346900013specifically tailored to account for essential factors that significantly influence the behavior of water in natural environments.Saint-Venant equations can be expressed as follows [8]: h represents the water depth in meters, U x and U y are the average flow velocities in the x and y directions in meters per second (m/s), respectively, g represents the acceleration due to gravity in (m/s²), q indicates the density of water (kg/m³), z b stands for the elevation of the channel bottom in meters, τ sy refers to the free surface friction caused by wind, τ by accounts for the friction with the channel bottom, and v t represents the turbulent viscosity.In this study, Iber 3.1 software was used.The selection of Iber was driven by the convenience of its ability to seamlessly convert formats to GIS interfaces, along with its accessibility at no cost [6].

Physically-based and experimentally calibrated hazard assessment method
Developed through extensive theoretical and experimental studies by Xia et al. [9], The physically based and experimentally calibrated flood hazard assessment method evaluates the safety of individuals in contact with flood flow.It incorporates a set of forces acting on the human body, including buoyancy, drag, gravity, and normal reaction forces (figure 4).The method introduces two distinct formulae for assessing sliding and toppling instabilities [5]: The incipient velocity of sliding instability: The incipient velocity of toppling instability: Where: U s and U t represent the incipient velocity of sliding and toppling, repectively.h f denotes the water depth (m), h p corresponds to the height of a person (m), m p represents the weight of a person (kg), ρ f indicates the density of water (kg/m 3 ), a 1 , a 2 , b 1 , and b 2 are empirical coefficients depending on the characteristics of a human body.Finally, the flood hazard for instability mechanisms can be assessed using the following expression:   Unlike conventional empirically derived approaches that consider only water depth and velocity multiplication (hv) as the proportional term to the destabilizing or the "overturning" force on the body [3,5], this method considers depth x velocity squared (hv 2 ), making it more sensitive to higher velocities and momentum often encountered during extreme flood events.For this paper we considered a real human body with a 1.7-m height and 60-kg weight [10], the other parameters are demonstrated in table 1 [9].

Spatio-temporal Flood depth and velocity maps
Figure 5 displays the flood depth and velocity data obtained from the Iber hydrodynamic model at: 3000, 6000, 9000, and 12000 seconds.Notably, both flood depth and velocity reach their peak values at 6000 seconds, measuring 2.17 meters and 6.34 meters per second, respectively.The highest flood depth and velocity readings are predominantly observed in rivers n°1 and n°7.This can be attributed to the upstream river n°7 being the outlet for the largest watershed compared to the upstreams of other rivers.As a result, river n°7 contributes a significant amount of water discharge to the system, leading to bigger flood levels and velocities along its course.Furthermore, it is worth noting that river n°4 converges with river n°3 (figure3), introducing additional discharge to the mid-eastern part of Zaio.Further adding more flood elevation in that specific part of the city.

Flood hazard maps
The physically-based and experimentally calibrated flood hazard maps for the city of Zaio were obtained using the raster calculator tool in ArcMap 10.8, wherein hazard ratings were calculated for each time step using the mathematical algebra expressions represented by equations ( 4) and ( 5). Figure 6 presents the flood hazard maps corresponding to different time steps (3000, 6000, and 9000 seconds) across three distinct zones in Zaio.Notably, the main river courses exhibit the highest flood hazard, while most of the floodplains were found to have a low hazard rating.An additional area of concern lies along the main road in Zone 2, where instability hazard was detected.In Zones 1 and 3, specific residential buildings were identified as having a high hazard rating.

Conclusion
Accurate flood hazard maps have become the focus of hydrologists and decision makers alike, improving the accuracy of flood hazard maps helps stakeholders, authorities, and urban planners to better understand this potential natural hazard and take protective mesures.
In this study we generated urban flood hazard maps for Zaio, Morocco for a 100-year return period flood.Combining rainfall-runoff transformation, high-resolution hydrodynamic modelling, and the physical-process that intervene during a flood-human body interaction, accurate flood maps were obtained across different zones across the city.Conclusively, the research indicates a pressing necessity to enhance our understanding and modeling capabilities regarding flooding processes and flood hazard assessment.This could be achieved by fostering a more unified approach and embracing a more rigorous, physically-based analysis as the foundation for flood hazard assessment.

Figure 1 .
Figure 1.Location of the city of Zaio.

Figure 2 .
Figure 2. 100-year return period rainfall hyetograph of the city of Zaio.

Figure 3 .
Figure 3.The locations of the upstreams (left) and the flood hydrographs (right) of the seven rivers.

Figure 4 .
Figure 4. Forces acting on an individual in a flood situation, showing the two modes of instability: sliding (a) and toppling (b) (Xia et al., 2014).

E3SFigure 5 .
Figure 5. Flood depth and velocity maps at different time steps.