Abstract
Nice Metropolis in Alpes Maritimes, France is prone to flood. The city is crossed by the Lower Paillons River (LPR). Its discharge for a return period of 100 years is estimated at 794 m3/s. Part of the river is covered by 2 km. In addition, there are two retention storages in the river bed and a floodable road tunnel on the left bank. Due to the increase in urban development, flood management is challenging. An existing decision support system, Aquavar, uses DHI Mike tools to reproduce runoff for the Lower Var River in the same region. To extend this system to the LPR and reinforce flood management, a new modelling tool adapted to the characteristics of the LPR is needed. Consequently, this research utilizes the DHI MIKEPLUS tool to develop a 1D -2D coupled model for real-time flood management. The results demonstrate that flood events like those in 2017 and 2019 were correctly reproduced. The linear regression R2 is above 0.8 for all stations. It was also estimated that the covered river should stay clean to avoid widespread flooding in the urban area. Overall, the model is useful for simulating flow in real time and can help sustain urban development.
HIGHLIGHTS
Coupled 1D–2D hydraulic models are implemented using DHI MIKEPLUS 2023.
Assessments of operational management, data and flood risks of the Lower Paillons River.
Modelling complex river hydraulics for real-time decision support systems.
INTRODUCTION
In the southeastern region of France, floods and droughts affect the mountainous catchments including the Paillons and the Var on the west and east of Nice City, France. The Var valley is one of the main fresh water resources of the Nice metropolis (or Metropole Nice Côte d'Azur (MNCA)). The Paillons River is covered and crosses the dense urban centre. On the French Riviera, as in many Mediterranean coastal cities, urbanization and economic development are on the rise and can be deeply affected during extreme convective events such as the Alex storm recorded in October 2020 or the major flood of 2019. On top of that, demand for water resources is increasing (Salvan et al. 2016, 2018; Chochon et al. 2022; Gourbesville & Ghulami 2022; Wacheux 2022). Therefore, the region needs an integrated modelling approach that provides reliable information to protect its people, functions and assets.
This situation motivated the development of the AquaVar decision support system since 2014 (Gourbesville et al. 2016; Ma et al. 2016; Du et al. 2018, 2019; Zavattero 2019). Four main needs were to be met: represent the hydrological characteristics of the Var, be useful for predicting the impacts of future construction projects on the river and groundwater hydraulics, implement long-term scenarios for climate changes impacts, forecast the impacts of extreme hydrological events and consider pollutant leakage into the river or unconfined aquifer. To achieve those goals, three deterministic models were implemented. A hydrological model based on the DHI MIKE SHE was calibrated to represent complex hydrogeological processes in the entire catchment. Using observed or estimated discharges from the hydrological model, a hydraulic model was designed with the DHI MIKE21FM to simulate surface flow and river-aquifer exchange in the lower Var valley. And the flow in the unconfined aquifer located in the lower Var valley was modelled with FEFLOW to accurately represent river-aquifer exchange. This tool successfully coupled hydrological, hydraulic, and groundwater modules to optimize management of collected data and provide useful information for real-time management of water hazards and resources (Gourbesville et al. 2022). To this date, the system has been used in several technical applications related to groundwater resources and extreme flood management in the Var catchment (Ma & Gourbesville 2020). However, other parts of the MNCA including the Paillons facing similar issues are not covered. Hence, the tool can be extended to the Paillons to address the risk of urban flooding and fill the gap in knowledge of the dynamics of the unconfined aquifer.
To develop a similar tool for the Paillons catchment, specificities of the study area must be considered. The main issue with the Paillons is flooding. In 2000, 2014, and 2019 major flood events caused damages to infrastructures in the Lower Paillons River (LPR) and its valley. Existing monitoring systems are used to manage water-related issues, but gaps and errors in collected information are present. The unconfined aquifer is used by some neighbourhoods for drinking and by a few industries. Its dynamics are not well known due to a lack of monitoring information (Tennevin et al. 2017). The surface hydraulic component of AquaVar is based on open channel modelling. Game et al. (2023) studied open channel modelling of the LPR. The study showed the possibility to reproduce flow processes and inundations maps by representing the covered portion of the river as open channels. However, in real-time, pressurized flow or clogging that may happen cannot be considered. Also, the geometry of the covered river (CR) is not respected; therefore, the effect of the artificial underground waterways reaching maximum capacity is not integrated. Other challenges include the high computation time needed to properly represent the riverbed with a 2 m mesh size. With such fine resolution riverbed, more computing power is needed for the tool to be integrated into a real-time forecasting system. Maintenance of such tools like updating river geometry or recalibrating models will require even greater resources.
Unlike the Var river, the LPR is partially covered. Within the riverbed, two retention storages exist. On the left bank, an underground road can be flooded and reduce flood risk in urban Nice. In fact, in urbanized areas where space is limited, CR and underground roads are used to create more space on the surface for urban development, on the one hand. On the other hand, they are useful for flood reduction and making urban spaces safer. The steep tributaries of the river and densely urbanized floodplains present a challenge for runoff water management. Approximately 16 km2 area is channelled into the urban drainage network. Sediment deposition is a significant problem for the LPR, while erosion is prevalent in its steep tributaries. The riverbed channelization further exacerbates these issues. The region's geological layers consist mainly of marl and limestone, which provide irrigation and industry with groundwater (Le Gouz de Saint-Seine 1995; Tennevin et al. 2017). Extreme events from September to February are common. Every year, the river is dredged to reduce flood risk and to replenish the nearby beach, which is exposed to winter coastal erosion. Consequently, a flexible model that can integrate frequent and localized changes in the riverbed geometry will be an efficient tool for real-time flood modelling.
Due to the need to extend AquaVar DSS to the LPR and the capabilities of DHI Mike tools to meet the specific modelling objectives for this river, the surface hydraulic model will be based on DHI MIKEPLUS and will be used for the LPR. The DHI MIKEPLUS integrates modules for 1D and 2D surface models, collection systems and rainfall-runoff modelling. Coupling 1D–2D has been applied to river networks, urban drainages and urban flood zones (Li et al. 2018; Salvan et al. 2016, 2018; Zavattero 2019). Depending on the modelling objectives, each approach can generate useful information for management purposes. Input data required for the MIKEPLUS includes topography, land use, runoff, and weather information. The modelling results generated by this tool are used in flood management activities, and it can be coupled with hydrological and groundwater modelling tools like DHI Mike SHE and FEFLOW. This coupling enables the assessment of flood extents and river-aquifer exchanges. When monitored runoff data are not available or of low quality, hydrological modelling results are used as inputs to hydraulic models. Many parameters required for model set up can be retrieved from literature, and calibrated sets of parameters can be obtained for areas of interest (DHI 2023a, 2023d, 2023b).
This paper focuses on assessing the use of 1D–2D coupling in river hydraulics and flood mapping in a complex hydraulic environment. This model will be an important component of the DSS tool for the Paillons. It must be flexible, fast computing set up and be able to be integrated with the other components of the DSS. An emphasis is made on how to accurately model flow in open and CR channels. Then, the potential applications of the calibrated tool to flood mapping are tested. To achieve these study objectives, the operational management of the river and runoff data are analysed. Next, a Gumbel method is used to determine return periods and magnitude of extreme discharges. After that, a 1D–2D model is set up and calibrated. The sensitivity of the model to surface roughness and maximum distance between cross-sections is analysed. In addition, the performance of the model is evaluated using five statistical parameters. The results are compared and discussed for the selected events and measurement locations. Finally, an application of the model to flood mapping is presented.
DATA AND METHODS
Study area and data used
Within the modelling area, there are monitoring stations that are overseen by the local water authorities of the MNCA. The stream gauges are integrated into a flood warning system that operates in real-time. Three stations keep track of the water depth and discharge in the OR. The stations, namely Abattoirs (ABA), Passerelles (PAS), and Coty, have 6-min interval records available. In the longest covered section of the river connected to the sea, measurements are implemented at the entrance, middle and end of the river. However, due to data quality issues, only a few flood events could be selected for model calibration and validation.
In addition to runoff records used as boundary conditions or for calibration and validation, hydraulic models require other inputs like topography, land use, infrastructures, meteorological data, and sea level. Data characteristics are summarized in Table 1. Topographic data provided by MNCA are available at 0.25 m × 0.25 m or 1 m × 1 m resolutions. Land use, infrastructures and part of meteorological data were also obtained from MNCA. Sealevel data and bathymetry required for downstream boundary conditions were downloaded from Service Hydrographique et Océanographique de la Marine (SHOM) () platform (https://data.shom.fr/).
Data . | Source . | Characteristics . |
---|---|---|
Topography | MNCA | Resolution :0.25 m × 0.25 m and 1 m × 1 m |
Land use | Detailed at building units | |
Buildings/roads | All types | |
Runoff discharges/water depths | Timestep: 6 min | |
Period: 2010–2021 | ||
Rainfall/temperature/potential evapotranspiration | MNCA & METEO-FRANCE | 1921–2021 (daily) |
1993–2021 (hourly) | ||
2010_2021 (per 6-min) | ||
Sea levels | SHOM | 2010–2021 (per 10-min) |
Bathymetry | Resolution :1 m × 1 m |
Data . | Source . | Characteristics . |
---|---|---|
Topography | MNCA | Resolution :0.25 m × 0.25 m and 1 m × 1 m |
Land use | Detailed at building units | |
Buildings/roads | All types | |
Runoff discharges/water depths | Timestep: 6 min | |
Period: 2010–2021 | ||
Rainfall/temperature/potential evapotranspiration | MNCA & METEO-FRANCE | 1921–2021 (daily) |
1993–2021 (hourly) | ||
2010_2021 (per 6-min) | ||
Sea levels | SHOM | 2010–2021 (per 10-min) |
Bathymetry | Resolution :1 m × 1 m |
Analysis of operational management of the LPR
. | Bridge openings . | 1 . | 2 . | 3 . | 4 . | 5 . | Average . |
---|---|---|---|---|---|---|---|
Before dredging | Upstream | 23.32 | 23.76 | 23.05 | 23.15 | 23.88 | 23.43 |
Downstream | 23.43 | 23.44 | 23.37 | 23.73 | 23.71 | 23.54 | |
After dredging | Upstream | 22.71 | 23.53 | 23.07 | 22.64 | 23.77 | 23.14 |
Downstream | 22.68 | 23.02 | 23.06 | 22.80 | 23.37 | 22.99 | |
Difference | Upstream | 0.61 | 0.23 | −0.02 | 0.51 | 0.11 | 0.29 |
Downstream | 0.75 | 0.43 | 0.31 | 0.93 | 0.34 | 0.55 |
. | Bridge openings . | 1 . | 2 . | 3 . | 4 . | 5 . | Average . |
---|---|---|---|---|---|---|---|
Before dredging | Upstream | 23.32 | 23.76 | 23.05 | 23.15 | 23.88 | 23.43 |
Downstream | 23.43 | 23.44 | 23.37 | 23.73 | 23.71 | 23.54 | |
After dredging | Upstream | 22.71 | 23.53 | 23.07 | 22.64 | 23.77 | 23.14 |
Downstream | 22.68 | 23.02 | 23.06 | 22.80 | 23.37 | 22.99 | |
Difference | Upstream | 0.61 | 0.23 | −0.02 | 0.51 | 0.11 | 0.29 |
Downstream | 0.75 | 0.43 | 0.31 | 0.93 | 0.34 | 0.55 |
The existing flooding monitoring system is used to manage the TAL located in the riverbed. The nine rainfall and ten runoff gauges across the associated river basin; and four cameras (two at ABA bridge, two at Pont Anatole France) provided the needed information for real-time flood monitoring. Limitations in quantifying the flood events and the need to reduce false alerts require a new hydraulic model that can in real-time give water depths and discharge estimates with updated geometry of the river.
Analysis of available runoff data
Available records from 2010 to 2021 can be separated into two periods, 2010–2016 and 2017–2021. The maximum difference in discharge for the same water depth is 100 m3/s for estimated discharges less than 400 m3/s. The raw datasets include systematic errors that should be corrected. From 0 to 1 m water depths, the curves are very similar. The values diverge when water depths increase from 1 m upward. In addition, all values above 2.5 m or 300 m3/s of discharge are incorrect because they rise and drop within 6 min, unrealistically. Plotting with wrong values allows one to have an idea of the rating curve validity range. Possible reasons for decreasing discharge for a given water depth are changes in river geometry or utilization of new methods. In the period 2010–2021, only up to 55 cm of sediment deposits or removal have been observed, with no change in the width of the bridge under which measurements are implemented. This is not sufficient to explain such changes in rating curves. The likely explanation lies in the technic used and the fact that after some years of experience, discharge was overestimated at that location. Direct field measurements to validate automated records are sparse and only available for discharges during drought or low flow periods. This is an opportunity to harmonize the data before comparing it to model results.
From runoff data providers, uncertainties exist in the water depth measurements. At the ABA gauge, errors in measured water depth fluctuate up to 12, 20 or 40 cm depending on the location. Runoff data often vary from high values during the flood to low values during drought or no rain, but in the raw data available, water depths in summer with no rain are higher than water depth with rain at several dates. This is a challenge in calibrating or validating modelling results for continuous and long periods. It is also delicate to use the raw data directly to assess the flow characteristics and river response to flood events. For hydraulic modelling, it is possible to select a few events for calibration and validation. The strategy is to select several events after making the data consistent over the period of availability. A statistical approach can therefore be used to generate synthetic hydrographs for creating flood maps for different return periods.
Besides the ABA station, PAS and Coty are two other gauging stations available in the LPR with water depths records only. In the CR, the entrance, the middle, and the junction with the sea are also gauged, but water depths are only available in 2017 and 2018. Table 3 shows some statistics of the raw datasets. ABA is the station with the most available data (90%). PAS and COTY have less than 28 and 33% of data available between 2010 and 2021. Min and Max of the raw data represent erroneous records and are not representative of the period of data. Factors like hardware issues, sediment transport and removal, waves on the free water surface and land use can explain gaps and errors in automatic data measurements. Lower Paillon is a torrential river. Flow processes can generate waves of up to 1 m on the water surface during extreme events. In dry periods, artificial ponds at ABA, Coty or PAS bridges happen regularly due to erosion or anthropic activities. Ponded water increases measured water depths by the automatic system which does not reflect the flow conditions. In addition, erosion of the riverbed can decrease the bottom elevation and lead to wrong measurements of water depths. In consequence, unrealistic discharges are computed using rating curves.
Station _ Parameter . | Min . | Max . | Mean . | Std . | Missing (%) . |
---|---|---|---|---|---|
ABA_depth (m) | 0.00 | 5.07 | 0.66 | 0.43 | 11 |
ABA_Q (m3/s) | 0 | 500 | 27 | 60 | 10 |
PAS_depth (m) | −1.00 | 4.75 | 0.80 | 1.63 | 73 |
PAS_Q (m3/s) | 0 | 22 | 5 | 8 | 72 |
Coty_depth (m) | 0.00 | 4.00 | 0.25 | 0.45 | 67 |
Coty_Q (m3/s) | 0 | 0 | 0 | 0 | 100 |
Station _ Parameter . | Min . | Max . | Mean . | Std . | Missing (%) . |
---|---|---|---|---|---|
ABA_depth (m) | 0.00 | 5.07 | 0.66 | 0.43 | 11 |
ABA_Q (m3/s) | 0 | 500 | 27 | 60 | 10 |
PAS_depth (m) | −1.00 | 4.75 | 0.80 | 1.63 | 73 |
PAS_Q (m3/s) | 0 | 22 | 5 | 8 | 72 |
Coty_depth (m) | 0.00 | 4.00 | 0.25 | 0.45 | 67 |
Coty_Q (m3/s) | 0 | 0 | 0 | 0 | 100 |
Combining automatic runoff records, baseflow measurements and rating curves, this approach improved the quality of the time series of water depths and discharge estimates needed for model calibration and validation. Discharge is recomputed with the most recent rating curve. First, water depths and discharge values that do not fit the rating curves are excluded from the datasets. Second, the unrealistic rises between three timesteps are replaced by the average of the lowest values. Then, discharge is recomputed using the most recent rating curve. For non-rainy periods, the discharge is decreased to reflect the observed baseflow without recomputing equivalent baseflow water depths. The minimum discharge for driest months like in July is assumed to be 0.02 m3/s, except for periods with flood events. This threshold reflects an almost dry river. The raw data have an undeniable quality, regarding the shape of the hydrographs and the timing of the pics. The calibration and validation of the hydraulic model rely on selected hydrographs that fit the above quality criteria.
Characteristics of runoff hydrographs
Return period in years . | Gumbel variable . | Estimated peak discharge (m3/s) . | PPRI 1999 . | Gradex 1999 (m3/s) . | Tennevin et al. (2017) (m3/s) . |
---|---|---|---|---|---|
2 | 0.3665 | 131 | x | x | x |
5 | 1.4999 | 234 | x | x | x |
10 | 2.2504 | 332 | 260 | 260 | 373 |
100 | 4.6001 | 794 | 750 | 825 | 794 |
200 | 5.2958 | 975 | x | x | x |
1,000 | 6.9073 | 1,475 | x | x | x |
Return period in years . | Gumbel variable . | Estimated peak discharge (m3/s) . | PPRI 1999 . | Gradex 1999 (m3/s) . | Tennevin et al. (2017) (m3/s) . |
---|---|---|---|---|---|
2 | 0.3665 | 131 | x | x | x |
5 | 1.4999 | 234 | x | x | x |
10 | 2.2504 | 332 | 260 | 260 | 373 |
100 | 4.6001 | 794 | 750 | 825 | 794 |
200 | 5.2958 | 975 | x | x | x |
1,000 | 6.9073 | 1,475 | x | x | x |
Modelling strategy
In the complex hydraulic environment of the LPR, this study develops a model tailored to real-time DSS. DHI MIKE+ 2D overland module is coupled with the 1D pipe flow module to assess the risk of flooding of the TAL and the capacity of CR to drain runoff water to the sea. Calibration and validation rely on observed water depths and runoff at different locations in the riverbed. Model set up included processing mesh and river geometry with a 0.25 m digital elevation model (DEM) data.
This assessment focuses on using the coupled 1D–2D hydrodynamic modules. Strickler coefficients describe bed resistance for each land use type. The critical Courant (CFL) number is set at 0.8. Time steps for solving shallow water equations range between 0.01 and 1 s. Mesh size is 25 m in the flood plain. Building blocks are extruded from the mesh to reduce the number of cell elements and optimize the computation time. The 1D model's longest flow path is 4.9 km. It is divided into two ORs and two CR interconnected to storages and the TAL. Lateral links are implemented to couple the 1D cross-sections to the 2D cell elements. The model is designed in a way that it can be directly coupled, in the future, with the urban drainage model in the Mike + .
The selection of 2D floodplain grid resolution is based on computation time. The objective was to be able to run on a classical desktop computer an event of 2 days duration within 12 h. It is assumed that with a fast-running hydrological model that can compute the same duration event in less than an hour, the tool can be used in nowcasting and forecasting. For case studies, it is possible to increase the 2D mesh resolution for detailed assessments of fluvial flooding in the urban area. An assessment of grid resolution allows selecting the most suitable one for this project. Other physical processes like direct precipitation, evapotranspiration, and effects of wind, tide, infiltration, or precipitation are not considered. In this case, only flow from the runoff hydrograph imposed at the upstream boundary is evaluated.
Runoff information from monitoring stations is not always available. In many cases, and especially for real-time forecasting, DHI MIKE SHE hydrological model results can be used as input to hydraulic models. This paper presents the analysis of flow processes in the riverbed and the risk of flooding in the TAL and in Nice's urban area. The advantage of using Mike+ is that it can integrate urban drainage and river network modelling into surface flow modelling. It is also possible to couple the river network from Mike+ as a Mike1D pipe flow module to MIKESHE (DHI 2023b).
1D Hydraulic model
According to DHI (2023a) Mike1D models unsteady flow based on an implicit, finite difference numerical solution of one-dimensional Saint-Venant water equations.
Due to computational challenges, this tool cannot solve the problem of an arbitrary flow of water through three-dimensional canals. However, the geometry of pipes and canals lends itself to a set of approximations that are well suited to the problem at hand. These approximations are based on four assumptions:
Water has a uniform density and is considered incompressible; its density does not significantly vary along such a short distance.
The slope of pipes and canals is gentle, which allows us to approximate the cosine of the angle it makes with the horizontal as 1.
The water depth is small compared to the wavelength; therefore, the flow can be considered to have a direction parallel to the bottom. As a result, vertical accelerations can be ignored, and a hydrostatic pressure variation along the vertical axis can be assumed.
- In each stretch of water, there is no perpendicular acceleration to the flow direction. Based on this premise, two simplified equations from the Navier–Stokes equations known as the Saint–Venant equations or Shallow Water Equations can be derived:where q (discharge), Afl (flow area or cross-section area), qin (lateral inflow, per length unit), h (water level) and α (momentum distribution coefficient), lf (flow resistance term, in form of friction slope), f (momentum forcing, per length unit) and ρw (density of water).
The numerical algorithms (DHI 2023a) used can provide precise and efficient solutions for branched and looped pipe and river networks. The computational scheme is suitable for vertically homogeneous flow conditions observed in various pipe types, ranging from small profile collectors used for detailed urban drainage and pressurized sewer mains influenced by varying water levels at the outlet, to OR, channels, and floodplains extending from steep rivers to tidal-influenced estuaries. The numerical scheme is adaptable to both subcritical and supercritical flows, considering local flow conditions. Flow characteristics such as backwater effects and surcharges can be simulated accurately. However, hydraulic jumps are not described in detail. Nevertheless, the scheme can accurately describe flow conditions both upstream and downstream of hydraulic jumps.
The computational modelling of pressurized flows involves using a narrow vertical extension of closed pipes. This method allows for describing free surface and pressurized flows with the same numerical scheme, resulting in a smooth and stable transition between the two flow types. Moreover, advanced models are incorporated to describe flow over hydraulic structures, including structure control. The modelling features facilitate realistic and dependable simulations of the performance of both existing sewage and river networks as well as those currently under design (DHI 2023a).
2D Hydraulic model
Mike+ 2D overland module is based on the DHI MIKE21 FM (DHI 2023d) suitable for surface hydraulic modelling. It uses a flexible mesh approach to reproduce flow processes. The mesh is based on a cell-centred Finite Volume method. A strict stability criterion is required to solve the explicit numerical solution of the two-dimensional shallow water equations (Equations (3) and (4)). The first-order Euler and second-order explicit Runge–Kutta methods are two options that can be applied. The interface convective fluxes are computed based on an approximate Riemann solver. This scheme is suitable for robust and stable simulation of flows that have shocks and discontinuities such as hydraulic jumps and bores. The Froud-Number must be less than 1. Its hydrodynamic module solves the two-dimensional Shallow Water Equations.
Coupling 1D and 2D hydraulic models
MIKE+ is a system that integrates water distribution, wastewater, and stormwater collection systems, as well as 2D overland domains and river networks (DHI 2023c). Different features including Catchments, Collection system network, River network, and 2D overland can be interconnected. Couplings between the network and overland models using the 1D-2D Couplings editor allows for the linkage of different 1D model components such as stormwater pipes, open channels, streams, rivers, and the overland surface. In this study, only 1D riverbanks are coupled with 2D floodplains using lateral links. All the other above-mentioned capabilities of the software are not tested.
Models' set up
Calibration and validation of models
Calibration and validation of the model require observed data. The Strickler coefficient is the primary variable that is adjusted to replicate flow velocities and depths in the modelling domain. To evaluate flow conditions initially, a Strickler coefficient is utilized in the range of 20–60. Despite having topographic data, uncertainties may exist in the geometry of the riverbed and flood protection structures. 1D river cross-sections at bridge locations were modified during pre-processing and initial testing of the model. The modifications consisted in updating the cross-sections with the field topographic measurements provided by MNCA and satellite imageries. Uncertainties in riverbank and riverbed levels exist. The model results are compared to observed data at various locations, and the flow maps are evaluated.
Model evaluation criteria
RESULTS AND DISCUSSIONS
Sensitivity analysis of hydraulic model parameters
Parameters . | Value range . | Constant parameters . |
---|---|---|
Strickler coefficient, S (m1/3/s) | OR 20–60 | Floodplain WD = 0.2 m |
Floodplain DD = 0. 5 m | ||
OR Max dx = 50 | ||
CR 20–60 | CR Max dx = 1,000 | |
Maximum dx, Maxdx (m) | 10–100 | WD = 0.2 m and DD = 0.5 m |
SOR = 20 and SCR = 20 |
Parameters . | Value range . | Constant parameters . |
---|---|---|
Strickler coefficient, S (m1/3/s) | OR 20–60 | Floodplain WD = 0.2 m |
Floodplain DD = 0. 5 m | ||
OR Max dx = 50 | ||
CR 20–60 | CR Max dx = 1,000 | |
Maximum dx, Maxdx (m) | 10–100 | WD = 0.2 m and DD = 0.5 m |
SOR = 20 and SCR = 20 |
Parameters . | Strickler coefficient, S . | Maximum dx, Max dx . | ||
---|---|---|---|---|
Range . | 20–60 . | 10–100 . | ||
Variation of simulated water depths (m) . | Average . | Maximum . | Average . | Maximum . |
ABA station | 0.27 | 0.55 | 0.00 | 0.05 |
Coty station | 0.21 | 0.49 | 0.01 | 0.03 |
PAS station | 0.22 | 0.62 | 0.00 | 0.01 |
CR entrance | 0.14 | 0.28 | ||
CR middle | 0.20 | 0.35 |
Parameters . | Strickler coefficient, S . | Maximum dx, Max dx . | ||
---|---|---|---|---|
Range . | 20–60 . | 10–100 . | ||
Variation of simulated water depths (m) . | Average . | Maximum . | Average . | Maximum . |
ABA station | 0.27 | 0.55 | 0.00 | 0.05 |
Coty station | 0.21 | 0.49 | 0.01 | 0.03 |
PAS station | 0.22 | 0.62 | 0.00 | 0.01 |
CR entrance | 0.14 | 0.28 | ||
CR middle | 0.20 | 0.35 |
In Figure 10, two flood events reached a peak discharge of 140 and 38 m3/s, respectively. The event on 11 December 2017 lasted 40 h. On 5 February 2017, the event was a small flood with data only available over 7 h. The more intense flood has however a smaller baseflow. These events were selected because of the availability of water depths in the OR and CR for sensitivity analysis. Unfortunately, records for more intense events in the CR were not available. The range of parameters as shown in Table 5 varies from 20 to 60 m1/3/s for the Strickler coefficient and from 10 to 100 for the Max dx. In this coupled 1D–2D hydraulic model, the floodplain in 2D is set up with fixed parameters. In fact, the WD and DD were, respectively, 0.2 and 0.5 m.
In Figure 11, six graphs present changes in water depths due to variations in S and Max dx at three stations ABA, Coty and PAS for the event of 11 December 2017. The peak water depth is 1.6 m for ABA, 1.1 m for Coty and 1.15 m for PAS. The curves were plotted after filtering raw data. The model was set up with constant parameters and each time the value for one of the selected parameters was changed to get the results in the figure. As expected, an increase in S decreases water depths. The max increase of water depth when S is changed from 20 to 60 is 0.6 m. Little change is observed with Max dx varying between 10 and 100. To further investigated flow characteristics, an analysis is conducted in the CR as displayed in Figure 11. Measurements available at the entrance and middle of the CR were used for this purpose. At the entrance, the peak water depth was 0.5 m for a baseflow of 0.2 m. The same was observed in the middle of the CR. A change in S from 20 to 60, decreases the peak water depths by 0.4 at the entrance and by 0.6 m at the middle. This can be explained by the differences in geometry along the CR. For stability reasons, the Max dx in the CR is set at 1000, and all the cross-sections describing the geometry are included.
In Table 6, the average and maximum change in water depths at ABA, Coty, PAS, CR entrance and middle are summarized. The average change is between 0.14 and 0.27 m. for S and less than 0.05 for Max dx. This implies that S has a strong impact on water depths. Calibrating the model based on S will be sufficient to get a good model.
Based on the outcomes of sensitivity analysis, the range of roughness coefficient was determined. Then the model was calibrated by making some adjustments to parameters and numerical settings. Table 7 summarizes the results of the calibration process. The optimized S values are 20 for OR 20 for floodplain and 60 for CR during flood periods. During drought periods, the floodplain has higher roughness. Therefore, vegetation is assigned 15 and urban areas get 70. The numerical settings were set as default values of 0.005 and 0.05 m for WD and DD, respectively.
Parameters . | Flood period . | Drought period . |
---|---|---|
S (m1/3/s) | OR = 20 | OR = 20 |
CR = 60 | ||
CR = 60 | Floodplain forests = 10 | |
Floodplain Grass 1 vegetation = 15 | ||
Floodplain = 20 | Floodplain urban areas = 70 | |
Water = 20 | ||
Max dx (m) | OR = 10 | |
CR = 1,000 | ||
Numerical settings values (m) | WD = 0.005 m | |
DD = 0.05 m |
Parameters . | Flood period . | Drought period . |
---|---|---|
S (m1/3/s) | OR = 20 | OR = 20 |
CR = 60 | ||
CR = 60 | Floodplain forests = 10 | |
Floodplain Grass 1 vegetation = 15 | ||
Floodplain = 20 | Floodplain urban areas = 70 | |
Water = 20 | ||
Max dx (m) | OR = 10 | |
CR = 1,000 | ||
Numerical settings values (m) | WD = 0.005 m | |
DD = 0.05 m |
Evaluation of model performance and validation
The flood event of 20 December 2019 generated 184 m3/s discharge. It is one of the most intense events of the last decade in the LPR. Two other modest events, on 2 February 2019 and on 12 May 2020 were included in model validation. Their intensities are, respectively, 50 and 28 m3/s. It can be noted that some events in the LPR can last more than 24 h.
Overall, results show that the model performs better at some stations than at other stations. The linear regression R2 is good (above 0.8) for all stations. At ABA station, the NSE and KGE are always higher than 0.9. And the RMSE is close to 0.02. At PAS and Coty stations, NSE is very low, but KGE varies between 0.4 and 0.8. For Coty station, the model underestimated the observations by more than 30% during two important flood events. The difference in timing of the peak varies from 0 to 12 min. If the observed discharges can be erroneous due to the use of rating curves and uncertainties in water depths, the timing of the peak is considered reliable. Accordingly, the model is efficient to reproduce flow processes in the LPR. Low performance at Coty station may be caused by errors in the geometry of the cross-sections. Sediment transport and dredging activities can also introduce large errors in water depth measurements. These factors can affect the magnitude of the base flow. In summary, the high and low flow events are correctly modelled by the 1D-2D Mike+ coupled model.
The modelling tool based on 1D-2D coupling was implemented on a classical desktop computer intel Core i7-4790 CPU 3.60GHZ, RAM 16 Go. Compared to the fully 2D modelled, the 1D–2D model is faster and can accurately reproduce a 48-h intense event within 12 h. This was not possible with the 2D model (Game et al. 2023), which has a high computing time. Another advantage is that the CR was properly modelled with its varying geometry. Connecting open and closed channels was made possible thanks to the DH MIKE PLUS coupling systems. With such a tool, quantification of overflow in the TAL and other storages is possible in real time. The model is also flexible. Changing cross-section geometry to integrate river bathymetry evolution will be much faster than in a fully 2D model. However, bidirectional flows within the river bed are not well represented. The LPR is a small torrential river. The importance of a 2D flow toward riverbanks in overflow is not studied. During low flows, meandering occurs and can influence water levels and discharge measurements. In addition, measurement stations are located under bridges. Flow interactions with piers generate perturbations that affect measurements. In this context, it is interesting to note that the developed model can reproduce flow processes in the LPR. Future developments will investigate adding the urban drainage system to the model. In MIKEPLUS, this integration is possible and allows to make river and pipe flow modelling a part of an integrated tool for global management of floods in complex urban environments.
The 2D floodplain was implemented with a coarse resolution in this model. This is sufficient for an overall evaluation of flow directions, speed and water depths. However, in urban areas, street level details may be necessary to better represent flooding. In the following section, an application of the calibrated model to flood mapping is implemented. The stability and calculation speed of the model for extreme events such as a 1,000-year flood event makes it a reliable tool for real-time extreme event management. The current model is limited to the confluence of all major tributaries of the Paillons River. The flexibility of the model allows future integration of upstream floodplains as well. All vulnerable areas of the east side of the MNCA will therefore be covered by this tool and provide real-time flood information.
Application of calibrated model to mapping of flood events
Flooding occurs mostly on the left bank of the river and flows toward the Port of Nice. The road on the left bank started being flooded at 480 m3/s near the ABA bridge. At Coty bridge, the river overflows on the left bank at 900 m3/s. At the inlet of the domain, overflow occurs from 1,190 m3/s. The floodable road tunnel, TAL, is inundated when the river discharge reaches 480 m3/s. At the PAS bridge, overflow to an existing flood retention storage starts at 250 m3/s. Then, the left and right banks of the OR near PAS are inundated from 570 m3/s. The extended TAL plays an important role in reducing inundation in the urban area. In fact, with the 100-year return period peak discharge of 794 m3/s, localized overflow occurs in the floodplain, but most of the excess water is drained out to the sea by the TAL.
In an urban area that is constantly changing with some building blocks surrounded by fences, it is challenging to reproduce flood routes. The model can reproduce flow at street level, but the floodplain grid resolution can be increased to better represent flow processes. In addition, the riverbed geometry is constantly changing due to sediment transport and anthropic removal every year. The 1D riverbed and 2D floodplain models should therefore be updated whenever new topographic data are available. Errors in the riverbank elevation should be reduced as much as possible before assessing flooding.
CONCLUSIONS
This study built and evaluated a surface hydraulic model for the LPR by employing the MIKEPLUS river network and 2D overland modules. Using 1D representation for open and CR allowed to optimized computation time without decreasing the quality of the results. It can model high fluxes without numerical instabilities. The model is an efficient tool for simulating free surface and pressurized flow conditions. It is a fact that the pressurized flow of the CR will have a disastrous effect on the infrastructure in Nice. Results show that the model can reproduce flow processes and inundation maps. The tool is useful for modelling flow conditions in the CR and the TAL as well as generating flood maps in the urban Nice. It can be incorporated into a flood warning system for real-time management of TAL and flood risk.
An analysis of the management practices and data quality demonstrated that model performance is highly dependent on the quality of input information and validation data. Sediment transport and dredging activities are important factors in flow processes. To improve data quality, implementing a periodical on-site verification of water depths and discharges would be valuable. Since discharge values are estimated automatically from measured water depths, reducing uncertainties in water depths would improve the overall data quality. However, ground-based runoff gauges can stop recording for numerous reasons, especially at the highest discharges. Therefore, new technics for discharge estimates can be implemented. The area has several cameras for river flood monitoring. Image-based methods could provide reliable estimates of discharges using camera records (Chahrour et al. 2021).
This model is designed for river flooding in urban area but urban drainage is not included. In fact, to fully understand flood processes, the floodplain mesh should be refined to street level and the model coupled with an urban drainage model. The current version removed buildings, and thus can accurately reproduce river floods in the main streets and places. Limitations in the model include the choice of calibration and validation events and river geometry resolution. A 1D representation of the river does not account for bidirectional flows in the river that can increase overflow risks. Clogging and sediment transport are not included either. The scenario with reduced roughness due to clogging or material deposits highlights the necessity to keep the CR clean. During non-rainy periods, the river gets dry due to evapotranspiration and infiltration. In fact, subsurface flow is estimated to be important in the LPR. This model does not include leakages to groundwater. A groundwater model is developed to evaluate river-aquifer exchanges.
Additional work is needed to integrate the model into a real-time DSS. The model can simulate an event of 2 days in 12 h. It is suitable for nowcasting and forecasting in real time. Due to the gaps and errors in monitoring runoff data, an integrated hydrological model is developed to provide boundary conditions in real time. MIKE SHE has the advantage of including different modules to generate surface and subsurface flow conditions.
ACKNOWLEDGEMENTS
This work is part of a PhD project under the AquaVar framework funded by Metropole Nice Côte d'Azur (MNCA) and MNCA Eau et Assainissement (the local water utility), with the participation of the University of Côte d'Azur.
DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.