Performance assessment of two-dimensional hydraulic models for generation of f lood inundation maps in mountain river basins

Juan Pinos*,Luis Timbe

Department of Water Resources and Environmental Sciences,University of Cuenca,Cuenca 010207,Ecuador

Received 13 June 2018;accepted 3 January 2019 Available online 20 March 2019

AbstractHydraulic models for the generation of f lood inundation maps are not commonly applied in mountain river basins because of the diff iculty in modeling the hydraulic behavior and the complex topography.This paper presents a comparative analysis of the performance of four twodimensional hydraulic models(HEC-RAS 2D,Iber 2D,Flood Modeller 2D,and PCSWMM 2D)with respect to the generation of f lood inundation maps.The study area covers a 5-km reach of the Santa Barbara River located in the Ecuadorian Andes,at 2330 masl,in Gualaceo.The model's performance was evaluated based on the water surface elevation and f lood extent,in terms of the mean absolute difference and measure of f it.The analysis revealed that,for a given case,Iber 2D has the best performance in simulating the water level and inundation for f lood events with 20-and 50-year return periods,respectively,followed by Flood Modeller 2D,HEC-RAS 2D,and PCSWMM 2D in terms of their performance.Grid resolution,theway in which hydraulic structuresaremimicked,themodel code,and the default valueof the parameters are considered the main sources of prediction uncertainty.

Keywords:Two-dimensional hydraulic models;Flood modeling;Flood extent;Water surface elevation;High mountain river;Ecuador

1.Introduction

Floods are natural processes caused by weather extremes,which inundate f loodplains,and their impacts include economic losses,environmental problems,and human casualties(Cook and Merwade,2009;Hartnett and Nash,2017).It is expected that climate change will affect the frequency and hazard of f looding,through its impact on the intensif ication and acceleration of the hydrological cycle(Hirabayashi et al.,2013).Effective f lood management requires f lood inundation mapping,probabilistic estimates of potential damage and risks in f lood zones,and the design of a master plan for f lood risk mitigation.Inundation mapping has become a key measure due to the important information it provides,such as the water depth and f lood extent,which are essential for eff icient f lood risk management(ShahiriParsa et al.,2016).

Hydrodynamic modeling of a river with f loodplains requires the use of numerical methods to solve the conservation equations for free-surface f low under usual complex conditions.Since numerical models are a simplif ied representation of reality,a key feature of hydrodynamic modeling is an adequate representation of the topography of the river channel and adjacent f loodplains(Casaset al.,2006).There are several numerical tools which allow rivers and f loodplains to be modeled with one-dimensional(1D),two-dimensional(2D),or three-dimensional(3D)approaches(Blade et al.,2014a).Despite differences in model capacity and accuracy,to study the effects of f lood propagation on rivers,and in particular to estimate f low velocities and water levels,1D models have been used most often(Papaioannou et al.,2016).In 1D modeling it is common to consider a river as a line and channel geometry as a property of each node on the river line.On the other hand,in a 2D model a river is no longer discretized as a line with a series of cross-sections,but as a mesh consisting of a series of polygonal cells representing the topography of the main channel and f loodplains.

In more complex river systems it is likely that a 1D model will deviate too far from reality,whereas a 2D model with horizontal dimensionspredominating over vertical dimensions can lead to a more realistic description of the case.The evolution of numerical methods and the development of powerful computational tools,which facilitate the application of more complex approaches,have led to increasing use of 2D hydraulic models(Blade et al.,2014a).Recently,several studies have compared the performance of 1D and 2D hydraulic models for river f lood simulations(e.g.,Horritt and Bates,2002;Papaioannou et al.,2016;ShahiriParsa et al.,2016).

Digital elevation models(DEMs)and numerical solution schemes are essential requirements in 2D hydrodynamic modeling.The recent growth in the availability of DEMsfrom different sources(with spatial resolution and accuracy varying with sources)has facilitated their incorporation into hydrodynamic modeling(Horritt and Bates,2002).There is a wide range of 2D packagesdeveloped by commercial organizations,government agencies,research groups,and universities(e.g.,HEC-RAS in Brunner(2016),Iber in Blade et al.(2014b),TUFLOW in Syme(2001),TELEMAC in Hervouet(2000),MSN_Flood in Hartnett and Nash (2017),rapid f lood spreading method-explicit diffusion wave with acceleration term(RFSM-EDA)in Jamieson et al.(2012),and the Wolf software in Archambeau et al.(2002)).Merwade et al.(2008)claimed that thenumerical solution schemesof models are the most important source of uncertainty.Furthermore,hydraulic models are sensitive to the description of geometry,the value of model parameters,and the representation of hydraulic structures such as bridges,culverts,and embankments.

Hunter et al.(2008)reported one of the few studies of the performanceof different 2D hydraulic modelsin termsof their ability to simulate surfacef low in adensely urbanized area.To the knowledge of the authors,no research has been conducted to assess the performance of 2D models in simulation of the hydrodynamic behavior of high mountain rivers above 2000 masl.This study aimed at testing the performance of different 2D hydraulic modelsin termsof prediction of thef looded area and water surface elevation of an Andean river.

2.Materials and methods

2.1.Study area

This study was carried out in the Santa Barbara River subbasin located in Azuay Province(within the Andes region),in southern Ecuador,at latitude 2.87°S to 2.91°S and longitude 78.76°Wto 78.79°W(Fig.1).The study areacomprises ariver reach approximately 5 km long that f lows across Gualaceo,with an average slope of 0.25%.The western f loodplain comprisesan urban area,whiletheeastern f loodplain ismainly dominated by agricultural and recreational uses.The elevation is around 2330 masl with an average temperature of 17.6°C and annual rainfall around 960 mm(INAMHI,2015).This area was chosen because it is prone to frequent f looding.

2.2.2D models

The hydraulic models used in this study were selected based on the accessibility of existing 2D software packages.Table 1 summarizes brief ly the main characteristics of the selected models.Themethodsarefully described in thecited references.Essentially,each model represents a distinct trade-off between physical representation and potential computational cost,based on the developers’assumptions(Hunter et al.,2008).

2.3.Data and model implementation

Fig.1.Study area and high-resolution topography.

In a previous study,a one-dimensional HEC-RAS model,hereafter called HEC-RAS 1D,was validated with historical data from the f looded area along a 10-km reach of the Santa Barbara River for f lood events with a return period varying between 2 and 10 years(SENAGUA,2014).The results of HEC-RAS 1D were used as a reference to evaluate the performance of the tested 2D models in this study.

Table 1Main features of selected hydraulic models.

A DEM was obtained from the National System of Rural Land Information and Technological Infrastructure Project with a high spatial resolution of 3 m×3 m(http://www.sigtierras.gob.ec).This DEM was produced using the light detection and ranging(LiDAR)technique.Two f lood events from SENAGUA(2014)with return periods of 20 and 50 years,respectively,were selected for model evaluation.Synthetic hydrographs were implemented for discharge values of each f lood event.A preliminary time step analysis was carried out in order to solve stability problems.In addition,Manning roughness coeff icients were selected in correspondence to the type of land coverage,in which a land cover map was used.The land cover map was developed using a geographical information system(GIS)software,and the assigned Manning roughness coeff icients for different land coverage types(e.g.,forest,crop,grass,and urban areas)were derived from SENAGUA(2014).Table 2 describes brief ly the main conditions considered and implemented in each model.

A calibration process can be implemented for each model,with the risk that the Manning roughness coeff icients change drastically for each model.The lack or non-existence of historical recordsof f loodsseriously hindersmodel calibration.In this study the authors decided to reconstruct the water surface elevation and f lood extent for f lood eventsusing the calibrated HEC-RAS 1D.

The default mesh of HEC-RAS 2D consists of nonoverlapping polygons limited to a maximum of eight sides(Brunner,2016).Iber 2D works with structured and unstructured meshes formed by elements that can have three or four sides;this enables the combination of irregular elements with three and four sides within the same mesh(Blade et al.,2014b).In addition,in Iber 2D,different tools have been developed for creating and editing meshes that are most suited to the needs of river f lood study.For irregular or complex topography,the methodology of geometry creation in the RTIN format isimplemented,adapting the approach presented in Evanset al.(2001),where the mesh consistssolely of rightangled isosceles triangles.Although PCSWMM 2D can work with an unlimited number of nodes,for extensive areas it requires high computational power and more processing time,which are limitations in common use.Given this constraint,in thisstudy a7 m×7 m resolution grid wasused.For roughness implementation in PCSWMM 2D we followed the method described in Beck(2016)for a single mesh.

In Iber 2D,bridges were added by editing the mesh manually,while in HEC-RAS 2D,PCSWMM 2D,and Flood Modeller 2D,this option was not available.Nevertheless,culverts can be implemented as an approximation,mimicking the openings of simple bridge structures.Thus,in HEC-RAS 2D,culverts were implemented for the simulation of the openings under bridges.While bridge approximations could also be included in PCSWMM 2D and Flood Modeller 2D,they were not added becausetheprocedurewasmore complex than it was for the other tested packages.

2.4.Statistical analysis

Table 2Parameters considered for setting up 2D hydraulic models.

For the evaluation of the model's performance,simulation results of the selected models were compared to those of the previously validated HEC-RAS 1D (SENAGUA,2014),referred to here asthe reference.Thus,water surface elevation estimation from each tested model along the river reach was compared to that from the reference model,and the mean absolute difference(E)was expressed as

where Lriis the water surface elevation simulated by the reference model,Lmiis the water surface elevation estimated by the 2D models,and N is the total number of points where simulation results were compared.

To evaluate thesensitivity of the model structurein termsof f lood extent,we used themeasureof f it(F)proposed by Bates and De Roo(2000):

where M1and M2are the simulated and observed f lood extents,respectively,whereby the simulated result of the f looded area with the reference model was used as the observed value;and∪and∩are the union and intersection in GISoperations,respectively.An F value equal to 100%indicates that the two areas are exactly the same,quantitatively and spatially.

3.Results and discussion

3.1.Water surface elevation

Fig.2 depicts the water surface elevations simulated by the reference model versus the results obtained with the four 2D hydraulic models(HEC-RAS 2D,Iber 2D,Flood Modeller 2D,and PCSWMM 2D).The water prof iles were obtained by simulating the f lood events with return periods of 20 and 50 years,respectively.In Fig.2 the impacts of the three implemented culverts on the simulation result of HEC-RAS 2D are visible.This effect increases for the higher return period(with higher f low discharge).Therefore,HEC-RAS 2D is highly sensitive to the inclusion of culverts as an approximation of bridges,with a difference of up to 1 m at B1 ascompared to the results of the reference model.Iber 2D presents the best performance in thewater surfaceelevation estimation,asshown in Fig.2.Flood Modeller 2D shows a relatively poor performance(underestimation)in the upstream reach for both f lood events,but from 820 m(location of B1),the model estimates the water surface elevation adequately.PCSWMM 2D shows the poorest performance for both return periods with signif icant and systematic underestimation for the entire river reach.

The goodness of f it between the 2D models and the reference model shown in Fig.2 is quantif ied in terms of the mean absolute difference.Table 3 depicts the E values in terms of the simulated water surface elevation.The results show that Iber 2D has the lowest E values for both return periods,followed by Flood Modeller 2D.Higher disagreement was found for HEC-RAS 2D and PCSWMM 2D,with the latter yielding the largest E values.For the best model,the mean absolute differencesof water surfaceelevation were0.32 m and 0.36 m,while for the poorest model,the mean absolute differences were 1.32 m and 1.61 m for the f lood events with 20-and 50-year return periods,respectively.

Fig.2.Water surface elevations along study reach obtained with 2D hydraulic models compared to those simulated with reference model for f lood events with 20-and 50-year return periods,respectively.

Table 3E values in terms of water surface elevation estimations between reference model and 2D tested models for f lood events with 20-and 50-year return periods,respectively.

The considerable differences between the water surface elevations obtained by PCSWMM 2D and HEC-RAS 1D may be partly due to the lower grid resolution(7 m×7 m).This is corroborated by Li and Wong(2010)who found decreases in the water surface elevation and f lood extent when coarsening the terrain dataset resolution.On the other hand,Wang and Zheng(2005)and Cook and Merwade(2009)found that coarsening the resolution of the topographic dataset increased the f lood extent as well as the water depth.In contrast,Flood Modeller 2D produced better results in comparison to PCSWMM 2D using the same grid resolution of 7 m×7 m.This result suggests that the difference between numerical methodsisaplausibleexplanation of the noticed disparities,as both models use the same grid resolution.

Fig.3.Flood inundation maps for f lood event with 50-year return period.

3.2.Flood extent

This section discusses the sensitivity of f lood mapping resultsasa function of the applied solution schemeusing default model parameters.Fig.3 showsthe simulated f lood inundation maps of the f lood event with a return period of 50 years,and the reference f lood inundation map used for evaluation is presented in Fig.3(a).For a more detailed analysis of the f lood extent,we divided the river reach into seven critical zones(Fig.4).Thiszonif ication was based mainly on thetopographic conditions.Table 4 shows the inundation area of different zonesobtained by HEC-RAS 1D for f lood eventswith 20-and 50-year return periods,respectively.Zones6 and 7 are themost important due to their extension.The f loodplain delineation and the areas of different zones estimated by the four 2D hydraulic modelsaresubstantially different,ascan beobserved in Fig.3(b)through Fig.3(e).

Table 5 shows a comparison of simulated f lood extents between the reference model and the four 2D models for the seven zones of the river reach.The measure of f it and estimate of f lood extent for each critical zonevary with themodel used,return period,and critical zone.For example,for the f lood event with a20-year return period in Zone1,thebest model in terms of performance is Iber 2D,followed by HEC-RAS 2D,PCSWMM 2D,and Flood Modeller 2D.For the f lood event with a 50-year return period,Iber 2D has the best performance,followed by HEC-RAS 2D,Flood Modeller 2D,and PCSWMM 2D.In contrast,for Zone6,Iber 2D yields thebest f it for both events,followed by HEC-RAS 2D for the f lood event with a 20-year return period and Flood Modeller 2D for the f lood event with a 50-year return period,respectively.In this zone PCSWMM 2D shows the least agreement for both events.Finally,the results indicate that all the tested models show the poorest performance in Zone 5.This result may be explained by the inf luence of a tributary river at this point(e.g.,backwater effect).The San Francisco River was considered in the HEC-RAS 1D modeling but not considered in the tested 2D models.Despite the use of a f ine DEM resolution(3 m×3 m),the resolution was not enough to mimic in detail the San Francisco River channel,which has a width varying between 1 and 3 m.However,in all cases the discharge of the San Francisco River was added to the Santa Barbara River to simulate the full f low in the main zones(zones 6 and 7)downstream of the conf luence.The discharge of the San Francisco River varied at around 6%of the total discharge.

Fig.4.Delineation of seven critical zones along river reach based on f lood inundation map obtained with HEC-RAS 1D for f lood event with 50-year return period.

Globally,Iber 2D performs best in terms of prediction of the extent of f looded area with the maximum F values of 92.6%and 94.1%for the f lood events with 20-and 50-year return periods,respectively.PCSWMM 2D shows the smallest f looded area,with the maximum F values of 71.7%and 76.4%for thef lood eventswith 20-and 50-year return periods,respectively.Flood Modeller 2D presents complex behavior with varying performance and without a clear trend,the maximum F valueswere89.9%and 91.2%for thef lood events with 20-and 50-year return periods,respectively.In addition,HEC-RAS 2D presents an acceptable eff iciency with the maximum F values of 88.2%and 86.7%for the f lood events with 20-and 50-year return periods,respectively.

Even though we tried to represent equal conditions in model parameterization(e.g.,the Manning roughness coeff icients,boundary conditions,etc.),the differences in the model code(e.g.,the numerical scheme)and default calibration parameters are sources of uncertainty.This interpretation is in agreement with the research of Merwade et al.(2008).Despite the fact that the Manning roughnesscoeff icients in the channel and f loodplains have a signif icant impact on the estimation of water levels,this aspect was excluded in the performance assessment of the models because all of them used the same land cover map as an input.

While in the literature a debate still exists about whether a 1D or a 2D model provides a better representation of a f lood event(Horritt and Bates,2002;Tayef i et al.,2007;Papaioannou et al.,2016),it should be noted that even for the most sophisticated models,the performance of models is inf luenced by the quality of source of information that is available for their parameterization,calibration,and validation.Thisisespecially critical in undeveloped countrieswhere f inancial and data sources are scarce.

Table 4Inundation areas of different zones simulated with HEC-RAS 1D.

4.Conclusions

In this study we compared the performance of four 2D hydraulic models(HEC-RAS 2D,Iber 2D,Flood Modeller 2D,and PCSWMM 2D)for the estimation of thewater surface elevation and f lood extent in a mountain river basin located in southern Ecuador.The 2D model results were compared with those of a validated 1D reference model.The comparison provided valuable insights into the framework of f lood modeling and the implementation of appropriate 2D hydraulic models in high mountain rivers.

In terms of water surface elevation estimation,Iber 2D shows the best performance with mean absolute differences of 0.32 m and 0.36 m for the f lood events with 20-and 50-year return periods,respectively,while PCSWMM 2D presents the largest mean absolute differences(approximately four times higher than those of Iber 2D).The same pattern is observed for the f lood extent delineation.For the f lood event with a 50-year return period,Iber 2D has the best f it,with the highest average F value(82%,considering the seven critical zones),while PCSWMM 2D has the lowest average F value(68%).In contrast,Flood Modeller 2D and HEC-RAS 2D present similar and acceptable performance,with the average F values of 78%and 76%,respectively.Similar results are obtained for the f lood event with a 20-year return period.

According to the f indings of this study the following conclusions can be drawn:

(1)The tested 2D hydraulic models can predict the f lood extent and water surface elevation of mountain rivers with different levels of accuracy,under the same parameterization conditions.The model code,the default parameters,and the solution scheme are the likely causes of the observed differences.

(2)Iber 2D presents the best 2D hydraulic model for the studied conditions,followed by Flood Modeller 2D,HECRAS 2D,and PCSWMM 2D.

(3)Results should be treated with caution,since the application of the tested models to other reaches and f lood events may reveal different behaviors.

(4)The poorer performance of PCSWMM 2D is not necessarily due to the inaccuracy of the model.A possible explanation for thismight bethelower grid resolution used and by the fact that bridges were not implemented in this model.

(5)The main restriction of the 2D models remains the high computation requirements,resulting in a considerable amount of time required for calculation.

Acknowledgements

The authors would like to thank Chris Goodell,Hans Sanchez,John Beck,and Mark Randall,for their important support in the use of different modeling softwares.We would also like to thank Computational Hydraulics International(CHI)for the University Grant Program,which gave us access to PCSWMM Professional 2D.