USE OF 2D MODELS TO CALCULATE FLOOD WATER LEVELS: CALIBRATION AND SENSITIVITY ANALYSIS

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1 USE OF 2D MODELS TO CALCULATE FLOOD WATER LEVELS: CALIBRATION AND SENSITIVITY ANALYSIS A. PAQUIER 1, E. MIGNOT 1 1 Cemagref, Hydrology Hydraulics Research Unit, 3 bis, quai Chauveau, CP220, Lyon Cedex 09, France, andre.paquier@cemagref.fr, mignot@lyon.cemagref.fr ABSTRACT In case of wide and built-up flood plains, 2D modelling is necessary to obtain a convenient view of the flows during flooding. The complexity of these flows requires possible modelling of supercritical and specific representation of hydraulic structures. Uncertainty of the results remain high because of hazardous events as dike breaching or because of lack of data such as the local rainfall. Calibration is usually performed by adjusting calculated peak water levels to flood marks. Information about extent of the flooded area or time of arrival or any other information should also be used to reduce uncertainty. Two flood events, the 1999 flood of the coastal Agly river flood plain and the 1988 flood in the city of Nîmes are described. On the first event, results of the calibration accuracy are provided in term of average deviation; locally, the difference between calculated peak water level and corresponding flood mark is high because the description of the flood plain does not take into account the buildings in a detailed way and because the influence of infiltration and other secondary processes could not be modelled. On the second example, representing a dense built-up area, a sensitivity analysis was performed in order to identify the parameters that may explain local differences in spite of the representation of the buildings. Higher uncertainty seems to come from the topography including description of the possible storage areas, from flow and rainfall inputs and from specific hazardous events (car blockage or any event due to fixed or mobile obstacle). KEY WORDS: 2D model, shallow water equations, calibration, uncertainty, sensitivity analysis, flood INTRODUCTION Within the framework of the Flooding Risk Program (RIO) supported by the French Ministry of Ecology and Lasting Development (MEDD), Cemagref and his partners are developing tools to estimate the risks of flood in the inhabited areas. These last decades, the urban or suburban development often occurred on the most flat surfaces situated in the plains next to streams. This led to the increase of the number of obstacles opposing to the flow in flood plains such as buildings and embankments. In parallel, the rivers themselves were often channelled and embanked to reduce overflows. Indeed, these works decreased strongly the overflow frequencies, but on the other hand, they let a stronger occupation of the plain develop as people forget the flood risk whereas it remains present. Indeed, floods may still occur, for example if the design discharge is exceeded, or if the main channel capacity is reduced by sediment deposits or vegetation development, or if some dikes break caused by overflows or erosions at the feet of the dike. In order to inform the population and limit this risk by figuring out the best measures or organizations to apply, it is necessary to be aware of the various possible scenarios of flood and to model their consequences (Paquier et Farissier, 1996).

2 The complexity of the flows in the plain during these events requires at least a description of the main obstacles and of the preferential routes of flows. Besides, the possible modification of the directions of the flows during and after the floods makes a 2D modelling more accurate than a one-dimensional modelling based on a network of reaches and storage areas. The values of the parameters to calibrate come at the same time from identified physical processes and from simplifications due to the modelling; furthermore, these simplifications vary in term of places depending both on the stakes and on the precision of the data. The objective is to show how to use a hydrodynamic modelling in this context and especially how to proceed for the calibration. So after a brief description of the software, two large flood events are described: the flood of Agly of November 1999 and the flood of Nîmes of October 1988, and the bases of the modelling and procedures of calibration are detailed. PRESENTATION OF THE CODE The 2-D computations were performed using the code Rubar 20 developed by Cemagref. It solves 2-D shallow water equations by an explicit finite volume scheme (Paquier, 1998). The cells, triangles or quadrangles, are considered as dry cells as long as the water level is below a minimal value within the cells. A hydraulic structure is defined as a set of a few cells where fluxes through one edge are computed from the relations linking discharge and water levels upstream and downstream. However, as the code can calculate the supercritical flow, some structures may be modelled by their geometry. The numerical scheme is generally stable under the Courant Friedrichs Levy condition that limits the Courant number to values below unity. Rough variations of time steps or of cells dimensions are usually responsible for numerical perturbations, even though in the presented cases, a dimensional ratio of 200 between two adjacent cells did not create major instabilities. The validity of the numerical method was checked on a lot of tests including 1-D and 2-D situations, steady and unsteady flows, cases with or without analytical solutions, comparisons with laboratory experiments. THE 1999 FLOOD OF THE AGLY RIVER The high flood that occurred in the southern part of France in November 1999 after rainfalls between 200 and 400 mm was one of the highest of the 20 th century in the lower reach of Agly river. The dam at the higher catchment of the river did not prevent the discharge to reach very high values further downstream where the rainfalls were the strongest. In Rivesaltes (main city at the entrance of the coastal plain), the peak discharge reached about 2000 m 3 /s which is as high as the historical 1940 flood. Then, as the dikes and the channel widening were designed for a maximal discharge of 1500 m 3 /s, several overflows occurred which flooded large areas but only with a few centimetres of water. However, one of these overflows was the origin of a breach that suddenly released a 2 meters high wave that destroyed a sewage plant in Saint Laurent de la Salanque, further downstream. In 1996, a 2-D model was built in order to simulate the 100 years flood that could inundate the coastal plain and to define the areas that may be considered as safe enough for extension of villages or of commercial areas. The study (BRL Ingénierie et Cemagref, 1996) calculated the areas flooded after a breaching of the dikes at various locations. Immediately after the 1999 flood, the Authorities gathered observations concerning the event and particularly the higher water level marks. Topographical campaigns permitted to level 43 cross sections of the main channel and the longitudinal profiles of the dikes. In parallel, some urgent works were performed to repair the damage to the dikes and a study was carried out in order to get a diagnosis about the state of the dikes and to define the short term and long term works necessary to increase their safety. It was decided to set a numerical model that would be

3 calibrated from the 1999 flood and that would permit to decide some additional works. To obtain the detailed calibration required, the 1996 model s 2-D grid was densified (the number of cells increased from 8848 to so the space step was limited to 100 meters) in order to represent the main channel of Agly river in a more detailed way as well as some places in the right bank near the town of Rivesaltes which were flooded in The structuring lines of the mesh are the major embankments and streams. On the other hand, localized structures such as culverts are modelled by defining the relations linking discharge and water levels upstream and downstream. On the other hand, embankments and weirs on the rivers were described by the topography of ground level and modelled using shallow water equations in which only a Manning coefficient has to be specified and can be estimated by the same method as elsewhere. Although there was a heavy rain over the area of the model, a simplification was to introduce only one discharge hydrograph at the entrance of this area in the Agly main channel. This hydrograph was determined from the measurements of water levels at the hydrometric station of Rivesaltes, and their extrapolations (from the measurements at an upstream station) after the failure of the device. During the calibration, it was checked that the water levels computed at that point were in agreement with the measured and then extrapolated ones. The Manning friction coefficient values in the flood plain generally do not influence the results too much as the flows depend mainly on the discharges over the dikes and through the embankments. The calibration of the friction coefficients is more difficult in the main channel of the river, especially because of two uncertainties: the discharge entering the embanked channel is not exactly known (± 10 to 20 %) and the topography of the main channel at the time of the peak flow was different from the results of the topographic survey a few weeks after the flood because of deposits. Locally, some other parameters also have to be calibrated: the sea water level, the wind effect on the flooded areas, infiltration in the ground and the dikes and the coarse representation of the drainage network. The modelling of the Saint Laurent breach in the dike supposed a very rapid opening with the full cross section of the breach as measured (about 40 m wide and 3 m high) and a relatively low Manning coefficient (0.02 s/m 1/3 ). The peak discharge through the breach was estimated to 170 m 3 /s. After calibration, the water levels remain low compared to the observed ones, which may be related to the presence before the opening of the breach of some water from rain and infiltration through (or below) the dikes or to the South East wind. It can be also guessed that the buildings, not represented in the model, locally increase the water level and that this increase is impossible to get only by increasing the friction coefficient. For the same reason and despite the introduction of walls in the model, calculated water levels differ from observed ones in the built-up area in the upstream Rivesaltes. After calibration, the mean difference between observed and calculated maximum water levels was about 0.1 m in the flood plain. It reaches 0.15 m in the main channel because the water level was decreased in order to prevent overflows where flood marks were inconsistent with the dikes height. However, within this limit of uncertainty of a few centimetres, the flooded area is calculated in a suitable way (Fig. 1).

4 Figure 1 Calculated flooded areas and estimated limit for the 1999 s flood THE 1988 FLOOD IN THE CITY OF NIMES The flood of October the 3 rd, 1988 in Nîmes was caused by a rainstorm that generated up to 250 mm of rain in about six hours. This led to the overflow of the watercourses to the north of the city and the subsequent inundation of various localities causing extensive damages to property and human life. A statistical analysis of the rainfalls showed that the return period of this event is 150 to 250 years but according to the historical meteorological information in the region, this return period may be lowered to 60 to 120 years (Desbordes et al., 1989). The zone Richelieu that was selected to test the models was an area 1.2 km long and less than 1 km wide in the North Eastern part of the city. A railway embankment runs all the way along its northern side, and the western and eastern flanks are formed by hills. Structurally the zone is varied, characterised by a rather steep upper part on the North passing below the railway where most of the buildings are of large area (army barracks, hospital ), followed by a southern zone of narrow straight streets (width down to 6 meters) crossing at right angles. During the 1988 flood, some water levels have locally exceeded 2 meters and the maximal water levels in most streets reached 1 meter. For the basic calculations, (Haider, 2001) considered that all the buildings were closed and then impermeable: thus the storage areas available within the buildings were neglected. Moreover, the sewage water network was not modelled; this hypothesis was justified by the amount of uncertainty concerning the rainfall data and by the limitation of the inputs to two discharges (Fig. 2) coming from specific structures below the railway embankment on the North of the modelled zone without considering the rainfall over the whole city neighbourhood and the downstream entering basins.

5 Discharge (m 3 /s) Hydrograph 1 (West) Hydrograph 2 (East) Time (hours) Figure 2 Upstream discharge hydrographs entering the Richelieu zone The grid for each street was built from the seven points cross sectional profiles with a space step of about 25 meters along the streets and a maximum of 50 meters in some specific places. On the other hand, the crossroads are described from the crossing of the seven profiles of each meeting street and the space step is then much lower, down to 0.1 m. The time step remains constant at 0.01 second and the computational time is then several hours on PC. The streets are supposed totally dry before the beginning of the flood, the initial conditions of the simulation are then a water depth of zero in the whole area. The definition of the downstream boundary conditions are complicated as the downstream adjacent areas are also flooded, but as the streets are orientated North South, it was admitted that no exchange of water with the adjacent streets occurred and the free outlet boundary was selected. A constant Strickler coefficient of 40 m 1/3 /s was applied to model the bottom friction. Finally, the following parameters were neglected: the friction on the walls of the buildings, the influence of some obstacles such as the cars parked and the diffusion coefficient that was set to zero. The limits of the flooded area are quite well simulated (Figure 3). However, small deviations come from the uncertainties of observed limits and of topographical data. Local comparison between the calculated water levels and the flood marks are also possible but one should remind that the observed water levels may vary within a street (up to 1 meter) whereas calculation results are more homogeneous. From the 82 available observation points, the mean maximum water level was different by 0.2 m from flood marks although standard deviation reaches 0.8 m. This relatively high value seems to be mainly caused by the errors or uncertainties in the bottom elevation and the distance between the observation and calculation points.

6 Figure 3 Calculated peak water depths and computational grid In order to calibrate this model, it was decided to examine its sensitivity to different parameters: reducing the number of points used in the street profile until a rectangular section, increasing the friction (Strickler coefficient from 40 to 30 m 1/3 /s), introducing diffusion, increasing the upstream input discharge, adding rainfall over the whole area. For example, at P1 point (Fig. 4) in South-Western part of the modelled zone or at point P2 (Fig. 5) in North- Western part, the evolution of water level during the flood depends more on the space step (numerical diffusion) than on the friction coefficient or additional diffusion (ν) that keep the same graph shape. The results generally confirm our expectations: for instance, increasing friction and diffusion increases the water levels and reduces the velocities. It is important to note that the influence of all these global changes is the same on the whole modelled area and that it usually does not modify the mean maximal water level too much (for instance, 0.1 m if the Strickler coefficient goes from 40 to 30 m 1/3 /s). These modifications do not change the standard deviation between calculations and measurements but they can be used to adjust the average values.

7 2 Water depth (m) 1 Flood marks Increased space step Strickler = 30 nu=0 Strickler = 40 nu=0 (Ref.) Strickler = 40 nu=1 Strickler = 40 nu= Time (hours) Figure 4 Water depths at point P1 Flood marks Strickler = 30 nu=0 Strickler = 40 nu=0 (Ref.) Water depth (m) 1 Strickler = 40 nu=1 Strickler = 40 nu=0.01 Increased space step Time (hours) Figure 5 Water depths at point P2 On the other hand, introducing obstacles (for example, representing parked cars) or storage areas (places, gardens, parks ) in a street leads to local strong modifications but have only some consequences on the neighbouring water levels if the volume stored or evacuated is important compared to the global volume of the flood. For instance, when parked cars are added in one street, the water level is increased (0.1 m) only in that street, whereas if a storage volume is added (in the hospital at the North West part of the area) representing 10% of the whole volume of the flood, the mean peak water level is increased by 0.3 m in the whole modelled zone. Then, it can be guessed that model calibration is possible by introducing such local singularities except in the zones where the flood marks give very heterogeneous values.

8 CONCLUSIONS Occurrence of floods in the urban environment is much more devastating than in any other area and simulating such events become necessary in order to better protect the buildings and populations by forecasting flood advance in cities. But to model such complex flows, it is necessary to develop models specially adapted to these areas and in particular capable to deal with waves and sub-critical to supercritical flows evolution. The case of the Agly flood of 1999 showed the possibility of the model to integrate several structures and a breach in a dike. Unfortunately, the lack of precise description of the buildings makes the calibration in the plain difficult and the sediment transport in the main channel and uncertainties about the overflows above the dikes make the calculation of discharge and water level between the dikes more complicated. The 1988 Nîmes flood study showed that the Rubar 20 software permitted to simulate an urban flood in a network of streets with very quick flows (velocities up to 2 m/s). However, the local calibration in this case is particularly difficult. A more accurate pre-processing is necessary in order to integrate the details of the buildings that can be found in the urban databases or in aerial or satellite photographs. On the other hand, the influence of obstacles, sewage water networks, rainfalls, ground infiltration and storage in the buildings still have to be introduced in the modelling. ACKNOWLEDGEMENTS The authors thank all the partners of the project Estimation of the surface flows for an extreme flood in urbanised environment of the Flooding Risk Program (RIO) funded by the French Ministry of Ecology and Lasting Development (MEDD). REFERENCES BRL Ingénierie et Cemagref, Etude des débordements de l'agly en aval de Rivesaltes, DDE Pyrénées Orientales. Desbordes, M., Durepaire, P., Gilly, J.C., Masson, J.M. et Maurin, Y., Octobre 1988: Inondations sur Nîmes et sa Région: Manifestations, Causes et Conséquences. Lacour, Nîmes, France, 96 pp. Haider, S., Contribution à la modélisation d'une inondation en zone urbanisée. Approche bidimensionnelle par les équations de Saint Venant. Ph D Thesis, Institut National des Sciences Appliquées, Lyon, 173 pp. Paquier, A., D and 2-D models for simulating dam-break waves and natural floods. In: M. Morris, J.-C. Galland and P. Balabanis (Editors), Concerted action on dambreak modelling, proceedings of the CADAM meeting, Wallingford, United Kingdom. European Commission, Science Research Development, Hydrological and hydrogeological risks., L2985, Luxembourg, pp Paquier, A. et Farissier, P., Assessment of risks of flooding by use of a 2-D model, Destructive water: Water-Caused Natural Disasters-Their Abatment and Control. IAHS, Anaheim, California, pp