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Factors controlling flooding at the Tonal river mouth (Mexico)

A. Pedrozo-Acua1, A. Ruiz de Alegria-Arzaburu1, I. Mario-Tapia2, C. Enriquez1 andF.J. Gonzlez Villareal1

1 Instituto de Ingeniera, Universidad Nacional Autnoma de Mxico, Mexico City, Mxico

2 Centro de Investigacin y Estudios Avanzados (CINVESTAV), Unidad Mrida del Instituto Politcnico Nacional, Mrida, Mxico

Correspondence

Adrin Pedrozo-Acua, Instituto de

Ingeniera, Universidad Nacional

Autnoma de Mxico, Cd. Universitaria,

04510 Coyoacn, Mexico City, D.F., Mxico

Email: [email protected]

DOI: 10.1111/j.1753-318X.2012.01142.x

Key words

Coastal flood; field data; flood risk;floodplain; fluvial flood; hydrodynamic

model; inundation; river mouth.

Abstract

This investigation presents an integrated study for the identification of coastaland fluvial forcing, in the generation of flood events in the lower area of theTonal River. The methodology is designed to reduce some of the uncertaintiesin the results and is comprised by high-quality field measurements, a two-dimensional numerical model and light ranging and detection data. Undertypical conditions, results show good agreement between numerical and meas-ured data. Investigation of mesh resolution effects and roughness parameteri-sation along the floodplain demonstrates the grid independence of the results

and enabled the selection of a realistic roughness value for the floodplain.Results imply a sensitivity of the region to the combined river and coastalforcing. This study demonstrates that a good description of the terrain eleva-tion, acquisition of high-quality bathymetric data and proper calibration of theroughness parameters provide the adequate set-up for the identification ofvulnerable areas to flood events generated by river discharges and storm surges.The combined scenarios of high discharges and storm surges showed a delicatebalance between river and coastal fluxes within this system. The approach couldbe useful for both, the generation of flood management strategies and theunderstanding of the role of driving physical processes.

1. Introduction

It has been internationally acknowledged that both coastaland fluvial floods remain the most frequent and devastatingnatural hazards (e.g. Dawson et al., 2009; Gallien et al.,2011). Lowland regions are particularly vulnerable to flood-ing induced by both regional variation in sea-level rise andextreme discharges, and also sediment supply (e.g. Nicholls,2002; Pye and Blott, 2009).

In the case of river flood modelling, efforts have focusedon the forecast of floods based on measured precipitation(e.g. Goppert et al., 1998), and the incorporation of

numerical weather prediction models (ensemble predictionsystems) is considered necessary to obtain accurate day-to-week forecasts (Cloke and Pappenberger, 2009). Recently,flood modelling efforts have focused on wavelet-basedshort-term (days) river flood forecasting (Adamowski,2008); however, modelling floods in lowland rivers iscomplex and requires an accurate representation of thefluvial processes as well as the hydrological inflows intothe reach (Stewart et al., 1999). Indeed, a good flood riskmanagement strategy aims to control flood disasters, in the

sense of being prepared for a flood, and to minimise itsimpact (Reeve, 1998; Plate, 2002).

Floodplain inundation plays a key role in the generationof these strategies and for several ecological processes, suchas ecosystem productivity, species occurrence and distribu-tion and nutrient and sediment dynamics (Poffet al., 1997;Postel and Richter, 2003). Hence, being able to simulate thespatial inundation patterns through mathematical model-ling provides a valuable tool to water management as well asthe effects of human interventions such as water withdraw-als, embankments, dykes and dredging projects.

With the increasing availability of high-resolution

remote-sensing data sets, it seems that two-dimensional(2D) modelling is the way forward for floodplain inundationprediction (Horritt and Bates, 2001). However, the use of2-D models is still somewhat restricted due to its datarequirements. At the very minimum, they need validationdata and distributed topographic data (Bates et al., 1998).

Recent progress in remote-sensing techniques offers theopportunity to collect spatially distributed data rapidly andover large areas (Cobbyet al., 2001; Hodgson and Bresna-han, 2004). Digital elevation models (DEMs) can be derived

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2012 The AuthorsJournal of Flood Risk Management 2012 The Chartered Institution of Water and Environmental Management

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from airborne light ranging and detection (LiDAR) data(Marks and Bates, 2000; Cobbyet al., 2003), airborne inter-ferometric synthetic aperture radar data or the Shuttle RadarTopography Mission (SRTM) data (Sanders, 2007). In par-ticular, DEMs derived with high-resolution LiDAR data areuseful to input into hydrodynamic models and carry out

small-scale flood risk management studies (Fewtrell et al.,2011). Thus, the use of these technological advances enablesa better integration of high-quality data with numericalmodels, and consequently, generates appropriate flood miti-gation measures on the basis of accurate forecasts. Thisallows long-term planning for flood damage reduction andissuing of targeted early warning to downstream communi-ties located in the floodplains which will be affected(Popescu et al., 2010).

In addition, protection policies have evolved in differentways depending on the type of flood that is observed (e.g.flash floods or floods in alluvial plains) (Plate, 2002). Forinstance, in flood events associated to alluvial plains of largerivers, the main danger to life is from the wide lateral extentof inundated areas. In recent years, this has been experiencedin the Mexican state of Tabasco, during the severe floods of2007, 2008, 2009 and 2010. In all these events, different riversflooded a large part of the Mexican state of Tabasco. Inparticular, the 2007 event flooded 70% of the lowlands of thestate, with depths up to 4 m in some locations and withcirca~1.2 million of affected people (Aparicioet al., 2009).

After these experiences, the characterization of theresponse close to the river mouth (e.g. drainage) has beenpointed out as a valuable insight into the limiting processesfor extreme flood generation. In addition, local river-/coastal

flood-producing factors are more amenable to analysis thanin larger catchments where the regional combination of con-trols can be relatively more important (Merz and Blschl,2008). Indeed, there are very few studies focused on under-standing the causes of flood occurrence close to river mouthsin relation to extreme conditions (i.e. intense precipitation,extreme storm surges).

On river mouths subject to the incidence of high surges,both still water levels and river discharges can be importantin assessing flood risk. The simultaneous occurrence ofintense river discharges and a high still water level is there-fore important in estimating their combined effect control-

ling flooding. In the Gulf Coast of Mexico, the incidence oftropical storms (i.e. hurricanes) is expected each year fromJune 1st until November 30th. These extreme events inducehigh water levels at the coast and produce intense precipita-tion events. Under these conditions, water level variationsalong the rivers are due to a combination of upstream-propagating coastal surge and rainfall and run-off flow.Thus, in order to develop strategies of flood mitigation anddefence, it is necessary to carry out a careful assessment ofboth factors (fluvial and coastal). Indeed, floods are intrin-

sically multivariate random events, and the need for proce-dures that enable the simultaneous estimation of probabilityfor each of the variables involved has been recently recog-nised (i.e. Adamsonet al., 1999; Yue and Rasmussen, 2002).However, as pointed out by Hawkes et al. (2002), unlessboth driving factors are either completely independent or

dependent, multivariate extremes are difficult to predictdirectly from observational data.

Precisely, this is the case when linking flood events to highsurges and intense river discharges, as in the record period;there are too few events among the observations. In fact,some studies have started to look at the action of coastalsurge and river discharge, showing that in some cases, thesecan become decoupled (e.g. Reeve et al., 2008).

On the other hand, it is well known that the uncertaintyin the results of hydraulic modelling is generated by con-straints in the knowledge of the boundary conditions,topography, water surface elevations and appropriatechannel roughness (Beven, 2001). With the purpose ofreducing the uncertainties in river flood modelling, thisinvestigation follows the integrated two-prong approachpresented by Pedrozo-Acua et al. (2011). In this case, thisis applied to identify possible sources of flood risk in amajor river mouth in the Mexican state of Tabasco (TonalRiver). The methodology is comprised of the combinationof a high-quality data set obtained during an intensive fieldcampaign carried out in September 2010 and a validatedstandard two-D numerical model. Additionally, the currentstudy employs a LiDAR-based DEM for the accurate rep-resentation of elevation data with root mean square errorof 0.2 m in the horizontal and 0.15 m in the vertical

(INEGI, 2008).Within this context, the main aim of this work is to

analyse coastal and fluvial factors controlling flood genera-tion along the lower course of the Tonal River. For this, thehydraulic system will be characterised during normal condi-tions, which will then enable an analysis of flood-prone areasresulting from the incidence of extreme river discharge andstorm surges. This paper is organised as follows, Section 2provides a description of the study area; Section 3 presents adescription of the methodology comprised by field measure-ments and the numerical model. In Section 4, the modelset-up and validation are introduced; Section 5 presents the

hydrodynamic results under extreme events due to fluvialand coastal forcings as well as the description of the hydrau-lic consequences on the floodplain under the different sce-narios. Finally, conclusions and future work are summarisedin Section 6.

2. The Tonal river system

In Mexico, the eastern state of Tabasco represents one of themost vulnerable regions to flooding. Due to its size, many

Factors controlling flooding at Tonal river mouth 227

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rivers in this area are of a transboundary nature, as theircatchment includes not only Mexico but also Guatemala.Any event occurring in these rivers is advected downstreamto Tabasco, Mexico, where all the natural drainages (rivermouths and lagoons) are located. An example of this situ-ation was observed during 2009, when severe flooding wasproduced by the Tonal river. This natural watercourseflows into the Gulf of Mexico and defines the boundarybetween the states of Veracruz and Tabasco, with a totallength of approximately 150 km (Figure 1). Close to its river

mouth, the flow receives input from other streams, such asAgua Dulcita in Veracruz and Chicozapote in Tabasco, andit discharges more than 11 389 million m3/year towards theGulf of Mexico (CONAGUA, 2010). The study site is a low-lying area of ~350 km2 (Figure 1), exposed to a microtidalregime (~0.6 m mean spring tidal range) and low wave con-ditions (mean Hs < 1 m). The average mean temperature inTonal is between 24 C28 C, with a climate influenced byan intense wet season (SeptemberDecember) in combina-tion with the incidence of hurricanes and storms arriving

Figure 1 Location of Tonal River in relation to the Gulf of Mexico, Veracruz and Tabasco within Mxico, showing the location of both

the fixed intrumentation within the system ( Argonaut and CTD-diver; Acoustic Doppler V elocimeter currentmeter) and the

monitored cross-shore transects using the Acoustic Doppler Profiler (a,b,c,d).

228 Pedrozo-Acua et al.



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from the north. The relative humidity fluctuates between80%86%, and the cloudiness is high most of the year. Theregion has the highest mean precipitation rate in Mexico,with an average between 23 m/year. The hydrologic char-acteristics play in concert with the morphological setting ofthe lowland area to increase the susceptibility of the region

to flooding events during extreme scenarios.A recent hydrological study, presented by Fuentes et al.

(2010), indicated that extreme values of discharge for theTonal River are between 5001000 m3/s for return periodsin the interval of 5 to 1000 years. Furthermore, Durnet al.(2010) estimated probability distributions for the wind-induced storm surge in the coastal zone of Tabasco, report-ing that an increase of 0.8 m in thewater level corresponds toa return period of 500 years.

There are several urban areas and locations along bothsides of the river and river mouth: the towns of Tonal, AguaDulce and Gaviln in Veracruz and Cuauhtemoczin and LaVenta in Tabasco. In addition, the area is populated withindustrial facilities associated with the national oil company(PEMEX). Thus, severe floods may cause large socio-economical damage along this region. Because there is norecorded information about the flood magnitude or naturewithin the region, there is a clear need to increase the level ofunderstanding of the different factors increasing flood risk.These requirements are met nowadays by making use ofboth hydrodynamic models and high-quality data, which areused by water managers in both forecasting situations as wellas planning situations.

3. Methodology

The integrated approach used in this study is comprised bythe acquisition of high-quality field measurements, topo-graphic elevation from a LiDAR data source and standardtwo-D numerical modelling. The field data were collectedduring an intensive field campaign and were used to validatethe MIKE 21 flexible mesh (FM) two-D numerical model. Itis acknowledged that some of the uncertainties within themodelling results are generated by constraints in the knowl-edge of the boundary conditions, topography, water sur-

face elevations and appropriate channel roughness (Beven,2001). Therefore, in an attempt to reduce the uncertainties,this study employs in situ-measured river discharges,bathymetry, water levels and velocities. In addition, LiDARdata were utilised to establish an accurate representation ofthe topography in the study region. The utilisation of thisapproach allows the set-up and validation of the two-Dmodel, which can then be used for the determination offlood maps in the Tonal River floodplain under differenthydrodynamic conditions.

3.1 Field measurements

In September 2010, a 2-week field campaign was carried outalong the Tonal River with the aim of collecting topographicand bathymetric data, as well as water level, discharge, tem-perature and salinity measurements along the river and rivermouth. Bathymetric data and information on river dis-charges at localised points are necessary to define the initialand boundary conditions of the hydrodynamic model.Moreover, knowledge on water levels and fluxes is needed forthe validation of the numerical outputs and enablesthe useof

such model to obtain accurate numerical solutions.Detailed bathymetric data were collected along the Tonal

River using a double-frequency echo sounder (SyQuestBathy 500 DF, SyQwest Bathy 500 DF, SyQWest Inc.,Warwick, RI, USA) synchronised with a Leica 1200 (LeicaGeosystems AG, Heerbrugg, Switzerland) differential GPS(dGPS) and fixed on a motor boat (see trajectories inFigure 2). In addition, water levels were measured with aconductivity, temperature and depth (pressure)(CTD)-diver(Seabird SBE19plus, Sea-Bird Electronics, Inc., Bellevue,WA, USA) at the river mouth and corrected for atmosphericpressure variations with a baro-diver installed out of the

water, in order to determine a reference point for all topo-graphic and bathymetric measurements. Beach profiles weremeasured from the upper beach (dunes) up to the shorelineusing the dGPS on wheels. In addition, sediment sampleswere collected across the beach profile to enable a full mor-phological characterisation of different regions of the beachand river mouth. The shoreline and waterbodies along thestudy area were defined from digitised freely available geo-referenced satellite imagery from National Oceanic andAtmospheric Administration (Landsat 7 shown in Figure 1).

Figure 2 Digitised shoreline and waterbodies (blue line) along

with the motor-boat trajectories for the bathymetric survey

(red dots).



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Hydrodynamic and thermohaline measurements werecollected with moorings at the river mouth at 8.12 m depthand 12 km up the river at 4.8 m depth. The fixed instrumen-tation included an Acoustic Doppler Velocimeter (Nortek,

Nortek AS, Vangkroken, Norway) to record currents during1 min every 10 min with a sampling frequency of 1 Hz andCTD-diver to measure conductivity, temperature and pres-sure over a week (Figure 1). In addition, four river sectionswere monitored during 12-h tidal cycles recording continu-ous current profile measurements through the whole watercolumn during 30 min each hour followed by temperatureand salinity profiles at strategic points along the rivertransect. These measurements aimed to quantify waterexchange in the system (Figure 1) and were collected from awave runner with an Acoustic Doppler Profiler (1.2 MHzADP- Sontek, YSI Inc. / Xylem Inc. San Diego, CA, USA) and

a CTD Seabird SBE19plus.Instantaneous discharges at the different cross sectionswere estimated from the ADP measurements. The mean(entire cross section) discharge and the different water leveldischarges over the 12-h tidal cycle were obtained fromthe measurements (e.g. Figure 3 showing the mean andmaximum discharges at the river mouth). These types ofmeasurements were collected at the four open boundaries(Figure 1) and were used to define the model boundaryconditions.

3.2 LiDAR data

The LiDAR data provided by INEGI (2008) were utilised toconstruct three ground surface DEMs with different resolu-tion for the area of study. Following Masonet al. (2003), theraw data were processed in different ways depending on thetype and height of the vegetation. Thus, in regions of short

vegetation, ground hits are processed by subtracting anempirically determined fraction of the vegetation heightfrom theoriginaldata, then the topographic elevation map isconstructed. In regions of tall and intermediate vegetation(i.e. mangrove and palm trees), the topographic heightmap is constructed by interpolation between local minima(assumed to be ground hits) and topographic heights innearby short vegetation regions. The determination of thevegetation heights is derived by subtracting the groundheights from the canopy returns from the raw data, thismethod has been shown to be accurate to about 10% (Mag-nussen and Boudewyn, 1998). Ground height accuracy falls

off in wooded regions due to poor penetration of the LiDARthrough the canopy. Fortunately, the selected study regionand floodplain does not contain any large areas of woodland.

Figure 4 illustrates the three generated DEMs for thestudy region with resolutions of 5 m, 10 m and 20 m. Thearea of study contains the lower reach of the Tonal Riveralong with its floodplain. Due to the fact that the study isnot aimed at characterising floods in urban areas, the 10-mDEM is selected for the generation of the mesh in the flood-plain. This selection follows recommendations put forwardby the Committee on Floodplain Mapping Technologies,NRC (2007) and Prinos et al. (2008), whom state that a10-m DEM is acceptable for floodplain mapping, as itensures both accuracy and detail of the ground surface.

3.3 Numerical model

The MIKE 21 FM flow model is applied to investigate thephysical processes involved in the flood events along thefloodplain of the Tonal River. The hydrodynamic modelsolves the Reynolds-averaged two-D NavierStokes equa-tions subject to the assumptions of Boussinesq and of hydro-static pressure (http://www.dhigroup.com; DHI, 2009). Themodel solves the equations at the centre of each elementwithin the domain.

3.3.1 Model boundary conditions

Three boundary conditions are set: 1) where the inputhydrograph will be set, 2) at Tonals river mouth and 3) atthe Agua Dulcita river. The location of the first boundarycondition is at the south of the domain (blue dot inFigure 5).Upstream from this position, the river is limited bya national road that separates the studied lowland regionfrom the upper river. The second boundary located at the

600

800

1000

1200

1400

1600

Q(m

3/s)

06/10/2010 15:00hrs 07/10/2010 03:00hrs

-0.1

0

0.1

0.2

0.3

diver

(m)

Qmean

Qmax

Figure 3 Estimated discharges from acoustic doppler current pro-

filer measurements (mean and maximum, top panel) and water

surface elevation at the Tonal river mouth (bottom panel). Q

represents river discharge.




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river mouth is defined through measured temporal varia-tions of the water level during the field campaign from the27th of September to the 11th of October 2010 (green dotFigure 5). The third boundary located at the entrance ofAgua Dulcita river (red dot Figure 5) is estimated with flowmeasurements to a constant discharge of 100 m3/s.

The hydraulic behaviour of the river mouth is determinedby changes of the mean sea level due to tidal fluctuations orstorm surges generated by hurricanes or northerly winds. An

example of the obtained measurements is shown in Figure 6,where panel (a) illustrates the time series of water level andpanels (b), (c) and (d) present ADP measurements (velocity,discharge and depth) obtained at the same cross section inthe Tonal River.

3.3.2 Sensitivity analysis to numerical grids

It has been acknowledged that an understanding of meshresolution effects on the model results is vital for the accu-

rate representation of the physical systems (Hardy et al.,1999; Reeve et al., 2010). Following this reasoning, a sensi-tivity analysis is carried out in order to determine theoptimum model grid for the river channel, where the bathy-metric measurements are assimilated.

Five different grids are built and tested in order to ensurethe numerical independence of the results to the model dis-

cretisation. A summary of the characteristics of these meshesis presented in Table 1, while the difference in spatial reso-lution for the region of the river mouth is illustrated for grids1, 3 and 5 in Figure 7.

Results for this analysis are shown in Figure 8, where acomparison of numerical results for river discharges at twodifferent cross sections along the river stream is illustrated.The first of these is selected close to the river mouth toenable the comparison of numerical results against fieldmeasurements, while the other is defined at an intermediatesection along the river. The location of both cross sections isindicated in the small panel in the upper right corner of

Figure 8. Results for the point close to the river mouth showthat the selected meshes reproduce the same trend. Moreo-ver, these are in agreement with measurements from the fieldcampaign (root mean square error of 96 m3/s). The riverdischarge obtained at the cross section located in the centreof the domain also shows a very similar behaviour in all fivemeshes (comparison shown in bottom panel of Figure 8).These results indicate the grid independence of the numeri-cal results generated, providing confidence in the numericaldiscretisation of the study area.

Figure 4 Digital elevation models obtained from light ranging and detection data.

Table 1 Summary of the selected meshes for the sensitivity

analysis

Mesh no.

Maximum element

size (m2)

Number of

nodes

Number of

elements

1 6 400 9 874 14 202

2 2 500 11 498 17 371

3 1 600 13 365 20 972

4 900 17 826 29 555

5 625 22 428 38 369



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Figure 5 (a) Illustration of the computational mesh and zoom for details; (b) mesh with processed and interpolated light ranging and

detection data. Note that resolution is highest along the river stream (locations of boundary conditions are identified by the dots: blue

input hydrograph, green water level variation and red discharge at the river Agua Dulcita.




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-0.40

-0.20

0.00

0.20

0.40

Tidaleleva

on(m)

3-Oct-2010 5-Oct-2010 7-Oct-2010 9-Oct-2010

Number of observaons

(b)

(c)

(d)

(a)

Figure 6 (a) Measured astronomic tides at the Tonal river mouth from the 27th September to the 11th of October 2010; Acoustic

Doppler Profiler measurements (b) velocities, (c) discharges and (d) depths at the Tonal river mouth.



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Clearly, as spatial resolution is increased, particularterrain and flow features will no longer be adequately rep-resented. Therefore, in this study, mesh no. 3 is utilised inthe rest of the paper for the river channel. Although thedecision on the grid resolution is a much more subjectivechoice, the mesh selection is carried out following recom-

mendations put forward by Asselman et al. (2009), whomsuggest a medium resolution for a good characterisation ofthe velocity field in rural floodplains. The coarser grids no.4 and 5 are discarded, as their use in the river channelwould lead to coarser elements in the numerical discretisa-tion of the floodplain.

3.3.3 Floodplain discretisation and roughness

Once the mesh resolution was determined for the riverstream, the floodplain mesh was constructed through16 sub-domains, each with different resolution (finest andcoarserelements with a maximum area of 400 m2 and 1600 m2,

respectively). The selected resolutions guaranteed the properrepresentation of the elevation in the floodplain with a 10-mDEM. This provided a robust set-up for the definition of themodel domain (e.g. Hodgson and Bresnahan, 2004).

The model domain was determined in order to comprisethe lower basin of the Tonal River and additional mainwaterbodies (Figure 5). This enables flood modelling alongthe floodplain with adequate computational efficiency. Themain section of the Tonal River contains elements of400 m2, whereas the other waterbodies contain elements of900 m2 and 1600 m2.

It is recognised that in river floodplains, the hydraulicresistance may be conceptually divided into several zones,and the level of detail at which this process can be repre-sented is dependent on the scale of the simulation and theavailable data used for characterising the floodplain. Forinstance, Mason et al. (2003) introduced the use of LiDARdata to generate distributed friction maps. However, due tothe difficulty in justifying the roughness parameterisationalong the floodplain, this is assumed to be uniform.

The inundation extent to be simulated under the differentscenarios cannot be contrasted against any field data fromhistorical events. Therefore, in this investigation, we utilisetwo different values for the Manning number, one for themain river channel (n =0.0313 m1/3/s) and another for the

floodplain.In order to evaluate the effect of the friction value on the

resulting inundation extent, a hypothetical exercise is under-taken. Seven values for the Manning number on the flood-

Figure 7 Close up to Tonals river mouth showing three different

resolutions for model discretisation (highest resolution mesh

Mesh 1; middle resolution mesh Mesh 3; lowest resolution mesh

Mesh 5).

Table 2 Selected roughnesses for river channel and floodplain (n m1/3/s)

Region\case C1 C2 C3 C4 C5 C6 C7

River channel 0.0313 0.0313 0.0313 0.0313 0.0313 0.0313 0.0313

Floodplain 0.0526 0.0418 0.0313 0.0270 0.0238 0.0213 0.0192




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plain are tested under the forcing of an extreme dischargeon the river (Q =1300 m3/s). Following the work presentedby Werner et al. (2005), the roughness values are chosendepending on the land use in the floodplain (i.e. n =0.025

0.06 m1/3/s for the main channel and n =0.0250.05 m1/3/sfor pasture and cultivated fields). Table 2 presents the sevencoefficients employed in this experiment, where highervalues of the coefficient represent more roughness.

Figure 8 Numericalhydrographsat twocrosssections(a closeto theriver mouth andb intermediatepoint)alongthe Tonalriver stream

for the different selected resolutions (highest resolution mesh Mesh 1; lowest resolution mesh Mesh 5). Q represents river discharge.



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For each of these numerical runs, a flood map is obtainedand the affected area is estimated. Figure 9 presents theresulting inundation maps, where small differences are illus-trated among the selected floodplain roughnesses. In orderto get a better comparison of these results, the resultinginundation extent is digitised and quantified in order to beable to compare in a more quantitative manner. Figure 10presents the results of inundated area against roughnesscoefficient in the floodplain. In this figure, it is evident thatfor a Manning number between 0.05880.027 m1/3/s, theresulting flooded area does not change significantly. Theflooded area is naturally increased for the unrealistic caseswhere Manning numbers in the floodplain imply less rough-ness than in the river channel. The difference in inundatedarea between the cases of lower resistancen =0.0192 m1/3/sin the floodplain and a constant Manning number in riverand floodplainn =0.03125 m1/3/s is estimated in 10% moreaffected area. In contrast, the difference found in the com-parison between the cases of higher resistance n =0.0588m1/3/s in the floodplain and that using a constant Manning

number in river and floodplain is small. The affected area is2% smaller in the higher resistance case in comparison withthat of a uniform Manning number.

These results indicate that the use of a higher Manningnumber for the floodplain than that utilised for the riverchannel does not have a big impact on the resulting inunda-tion area for this case. Moreover, the inundation extent doesnot change significantly, when varying the Manning numberfor the floodplain in compliance with other literature (e.g.Werneret al., 2005). It should be noted that this holds onlyfor this particular case and only for the flood extent. Flood-plains with different vegetation and characteristics may

behave differently. Therefore, for the rest of the experimentshere presented, a value ofn =0.04545 m1/3/s is determinedfor the floodplain, while for the river channel, a constantvalue ofn =0.03125 m1/3/s is utilised.

4. Results under fluvial/coastalextreme forcing

The model performance is considered satisfactory under theconditions recorded during the field campaign. Therefore,

this section presents a qualitative evaluation of flood genera-tion along the river floodplain under the incidence ofextreme fluvial and/or coastal forcing. The model simula-tions here presented have a Courant number of 0.8 andvarying time-steps of 0.0115 s. The purpose of this numeri-cal experiment is the enhancement of the understanding of

how the hydraulic system responds to the occurrence ofextreme conditions. The combination of high-quality fieldand elevation data with a validated standard two-D model isnovel and relies on the latest scientific knowledge publishedon flood risk research.

The investigation here presented comprises the firstattempt of its kind in Mexico, in which by means of anintegrated methodology, the purpose is to provide usefulinformation to local authorities regarding flood-prone areasin terms of its forcing.

The selected extreme scenarios for both the discharge inthe river and water level at the river mouth are chosenunder the basis of reported values in previous studies pre-sented by Fuentes et al. (2010) and Durn et al. (2010). Inparticular, discharges of 800 m3/s, 1000 m3/s, 1300 m3/s,1600 m3/s and 2000 m3/s associated with return periodsbetween 510 000 years are evaluated. On the other hand,the influence of the storm surge on the system is examinedthrough the use of two surge peaks of 0.8 m and 1.2 mwith return periods of 500 and 1000 years, added to themeasured astronomical tide. These values are determinedfor a strong northerly wind and a hurricane class 2 in theSaffirSimpson scale. Moreover, the combined effect ofextreme fluvial and coastal forcing is also studied. Table 3comprises all the extreme cases simulated with the numeri-

cal model for the evaluation of the floods along the studyregion. All model runs comprise a simulation period of3 days, considering steady flow for the discharges (i.e. con-stant). The purpose of the numerical simulations is toidentify flood-prone areas under different extreme forcing,rather than accurate identification of flood extents.

4.1 Fluvial forcing extreme river discharge

The first scenarios comprise the study of stationary dis-charges of 800 m3/s, 1000 m3/s, 1300 m3/s and 1600 m3/sin combination with water level variations due to an

astronomical tide. Figure 11 illustrates the generated inun-dation maps for all these cases after 3 days of incidence.Numerical results indicate that under the two firstscenarios (800 m3/s and 1000 m3/s), the Tonal River is ableto drain and discharge the excess volume of water into theGulf of Mexico without causing relevant floods (panels (a)and (b)). Results of a stationary discharge of 1300 m3/s(during 3 days) show the existence of significant floods alongthe upper river and near the river input boundary. Thecentral part of the domain is flooded, but most of the floods

Table 3 Selected river discharges and storm surge conditions

modelled with MIKE 21 for the evaluation of extreme flood risk

scenarios

Discharges

[Q (m3/s)]

Measured

astronomic

tides

Moderate

storm surge

(~0.8 m)

Extreme

storm surge

(~1.2 m)

800

1000

1300

1600

2000




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Figure 9 Inundation maps obtained with different values of the roughness coefficient over the floodplain reported in Table 1 (from the

lowest C7 to the highest roughness C1) red circle indicates the region where subtle differences are identified snapshots are shown

after the forcing of four tidal cycles.



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extend along the eastern side of the river (panel (c) in Fig-ure 11). These results point towards a highly vulnerable areain the south of the domain to extreme fluvial scenarios(i.e. most of the villages located in this region are flooded).

In the cases of more intense discharges (1600 m3/s and2000 m3/s), large floods are observed at the upper section ofthe river, andseveral towns are affected (panels (d) and(e) inFigure 11). These results further confirm previous observa-tions under moderate river discharge conditions. For thesetwoscenarios, thetown of LaVenta(Tabasco)and Agua Dulce(Veracruz) are affected, and the central and upper sections of

the river are heavily flooded. Notably, the river mouth is notflooded, and the towns close to this area do not seem to beunder the flood hazard (panel (d) in Figure 11). The extremedischarge of 2000 m3/s shows severe floods along most of theregions within the floodplain (panel (e) in Figure 11), nearly50% of the domain gets flooded except again for the rivermouth area. These results illustrate that even during extremeprecipitations, the river mouth is able to drain the excessvolume of water without causing any flood damage in thevicinity. In order to betterassess thehydraulic efficiencyof theriver mouth, Figure 12 presents the estimated numerical dis-charge for all the fluvial scenarios. It is shown that in all the

cases, the river discharge, although modulated by the tide, isable to drain most of the water entering the system. In themost intense case, defined by Q =2000 m3/s, recorded dis-charge at the river mouth is 1900 m3/s.This confirmsa highlyefficient river mouth under fluvial scenarios.

4.2 Coastal forcing storm surge

Two conditions of storm surge are selected, one whichdefines a moderate storm surge and another with a more

intense peak level. These are depicted in Figure 13, wheresurge levels of 0.8 m and 1.3 m are defined. The selection ofthese values is done on the basis of historic events andreported values in Smith and Ward (1998). The forcing ofthis coastal surge conditions is studied in combined sce-narios with river discharges of 800 m3/s, 1000 m3/s and1600 m3/s over 3 days of model simulations.

Figure 14 presents a summary of the inundation mapsdetermined by the combined effects of river discharges andstorm surges incident on the study region. In particular, allinstants are shown at the time of maximum water level

recorded in the time series. It is observed that a coastal surgeof 0.8 m in combination with a river discharge of 800 m3/sreduces the hydraulic efficiency of the river mouth to drainthe excess volume of water. This is confirmed by the genera-tion of a flood event along the eastern side of the rivermouth. Notably, for the same instant, numerical results donot show evidence of a flood event in the region close to theriver input boundary. This further confirms that the originof the flood scenario registered for this case is a direct con-sequence of the moderate storm surge at the river mouth.Moreover, a similar result is obtained in the case of thiscoastal surge in combination with a river discharge of

1000 m

3

/s. However, when the river discharge increases to1600 m3/s, significant inundation is also recorded along theupper river close to the river input boundary (see left panelsin Figure 14).

Results related to the incidence of an extreme storm surgepeak level of 1.3 m (typical during hurricanes) are presentedin right panels of Figure 14. In the case of an extreme stormsurge in combination with a river discharge of 800 m 3/s, it isevident that the affected area has significantly increased. Thisresult points towards the importance of the balance between

2.50

2.55

2.60

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

0 0.01 0.02 0.03 0.04 0.05 0.06

Manning number in the floodplain, n (m1/3/s)

Inundatedare

a(106m2)

Figure 10 Extent of inundation area versus Manning number (n) over the floodplain.




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fluvial and coastal forcings within this system. A smallincrease in the water level at the river mouth considerablyraises the probability of a major flood event in the region.Similar results are shown for a river discharge of 1000 m3/s.While results for the combined action of an extreme surgewith a river discharge of 1600 m3/s show the worst case of aflood scenario with significant floods along the upper riverand the river mouth.

Results indicate that the storm surge level mainly gener-ates floods along the region close to the river mouth. This isshown in all results where a moderate storm surge of 0.8 mcauses floods in the eastern side of the river mouth, whereasa level of 1.3 m inundates both sides (Figure 14).

The recorded discharge at the river mouth under thestudied storm surge levels is presented in Figure 15. Toppanel introduces the time series registered under the pres-

Figure 11 Numerical outputs for the model simulations with water level variations at the river mouth induced by the astronomical tide

and river discharges (Q) of 800 m 3/s, 1000 m3/s, 1300 m3/s, 1600 m3/s and 2000 m3/s, from (a) to (e), respectively snapshots are shown

after the forcing of four tidal cycles. UTM, universal transverse mercator.



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ence of a moderate (0.8 m) peak surge level, while bottompanel illustrates the results under the incidence of anextreme surge (1.3 m). In the top panel of Figure 15, it isshown that a storm surge level of 0.8 m could considerablyreduce the river discharge into the Gulf of Mexico. From the

visual inspection of the balance between river and coastalfluxes within the river mouth, it is possible to identify thetime when the surge forcing is triggered. Indeed, for thelowest discharge tested, there is an instant (at peak surgelevel) at which the river discharge is nearly reduced to zero,indicating that there is no flow outside the domain.

Results related to the combined forcing of river dischargesand extreme storm surge levels (1.3 m) are shown in bottompanel of Figure 15. In the time series of river discharge at theriver mouth, it is shown that for this surge level, the direc-

tion of the flow is inverted in two cases (800 m 3/s and1000 m3/s), which indicates the predominance of coastalforcing and the entrance of coastal water into the system.For the case when the river discharge increases to 1600 m3/s,this increment in the river forcing works against the coastal

forcing recovering the draining ability of the river mouth.This is indicated by the red line in the bottom panel, whichis positive for most of the time, showing a direction of theflow towards the Gulf of Mexico (Figure 15). The maximumsurge level only reduces the draining ability to a minimumbut is not able to reverse the flow at the river mouth.

These results are in agreement with those presented byStewart et al.(1999),whomindicatedthatthefloodriskalonga river is largelydependent on its drainage, which at thesametime depends on river discharges and storm surge levels.

Figure 12 Tonal river mouth discharges during the 3-day simulations for discharges (Q) of 800 m 3/s, 1300 m3/s, 1600 m3/s and 2000 m3/s.

Figure 13 Water level at the Tonal river mouth for storm surge conditions of 0 m (black), 0.8 m (blue) and 1.2 m (red) for the model

simulations.




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5. Summary and conclusions

This study presented an analysis of factors controlling floodcharacteristics along the lower course of the Tonal River upto its discharge into the Gulf of Mexico. For this, the meth-odology was comprised of high-quality field measurements,elevation from a LiDAR data source and a standard two-Dnumerical model. These components were selected with the

purpose of reducing some of the well-known uncertaintieswithin modelling results (i.e. boundary conditions, terrainelevation, water surface elevations and appropriate channelroughness). The selected integrated approach is novel andfollows recommendations put forward in the latest scientificworks published on flood risk research.

The work included a sensitivity analysis on mesh resolu-tion effects, followed by an investigation of the roughness

Figure 14 Inundation maps generated for the combined forcing defined by storm surge levels of of 0.8 m and 1.3 m (left and right

columns, respectively) and river discharges of 800 m3/s, 1000 m3/s and 1600 m3/s snapshots are shown at the instant of peak water level.

Q represents river discharge; UTM, universal transverse mercator.



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parameterisation in the floodplain. This confirmed the gridindependence in the results and enabled an assessment of theuse of different roughness values for the river channel and

the floodplain. It was shown that the prescription of a real-istic higher Manning number for the floodplain than thatused for the river channel does not have a large impact on theresulting inundation area. Notably, this result may only bevalid for this particular case and only for the flood extent. Itis expected that floodplains with different vegetation andphysical characteristics (e.g. slope) may behave differently.

The reported accuracy of the comparisons between modelresults and measurements under normal conditions hasprovided good level of confidence in the approachutilised to characterise the hydraulic system. The validatedmodel was used to study the sensitivity of the region to

floods generated by the combined river and coastal forcing.Nevertheless, it should be noted that observation datasets for historical flood events were not available, whichrestricted a direct data model comparison under extremeconditions.

Despite the inability to validate the predicted flood extentdue to lack of available data, results were considered helpful,as they provided a first indicator of possible consequenceswithin the study region under extreme forcing conditions.The exercise allowed the identification of areas highly vul-

nerable to flood events generated by both extreme river dis-charges and storm surges. Furthermore, it was demonstratedthat flood events in the study region are more severe when

the drainage of the river is reduced by the presence of astorm surge at the river mouth.

High river discharges Q > 1000 m3/s, were identified as animportant forcing in the generation of large floods in theupper river (south region of the domain). On the otherhand, the lack of flood events in the region close to the rivermouth demonstrated the draining ability of the river duringsevere fluvial forcing.

Furthermore, results indicated that storm surge levelsmainly produce floods in the region close to the river mouth(north). A moderate surge level inundates the eastern area ofthe river mouth, whereas severe surges flood both sides of

the river mouth. Thus, the water level at the river mouth hasa direct effect on the ability of the river to drain the excessvolume of water. It was demonstrated that a moderate surgelevel can reduce the river discharge up to zero, while a moresevere storm surge can invert the direction of the flow at theriver mouth. The combined scenario of high discharges andsevere storm surge level indicated a delicate balance betweenriver and coastal fluxes within this system.

It should be noted that this type of investigation has notbeen undertaken in Mexico, therefore it is anticipated that

Figure 15 Tonal river mouth discharges during the 3-day simulations for discharges (Q) of 800 m3/s, 1000 m3/s and 1600 m3/s and storm

surge levels of 0.8 m (top panel) and 1.3 m (bottom panel).




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the generated information in terms of highly vulnerableareas to flood events is useful to local authorities in charge ofmanaging these risks. There is therefore a pressing require-ment for internal validation of two-D models and the col-lection of suitable field data of inundation extent. If suchdata were available, it may be possible to determine the rela-

tive impacts of individual processes and flow pathways onthe flood prediction.

Acknowledgements

Special thanks are due to our field assistants: Emmanuel Ucand Aleph Jimnez. Miguel A. Laverde Barajas and Irving J.lvarez Celso are acknowledged for the digitisation of inun-dation maps and estimation of flooded areas. Commentsmade by three anonymous reviewers are greatly acknowl-edged, as these led to improvements of the final manuscript.

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