Nothing Special   »   [go: up one dir, main page]
Next Article in Journal
Analysis of the Spatiotemporal Trends of Standardized Drought Indices in Sicily Using ERA5-Land Reanalysis Data (1950–2023)
Previous Article in Journal
Flood Susceptibility Assessment for Improving the Resilience Capacity of Railway Infrastructure Networks
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Water
Volume 16
Issue 18
10.3390/w16182594
water-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Flood Modeling of the June 2023 Flooding of Léogâne City by the Overflow of the Rouyonne River in Haiti

by
Rotchild Louis
1,2,
Yves Zech
2,
Adermus Joseph
1,
Nyankona Gonomy
1 and
Sandra Soares-Frazao
2,*
1
Département de Génie Rural, Université d’Etat d’Haïti, Port-au-Prince HT 6122, Haiti
2
Institute of Mechanics, Materials and Civil Engineering, UCLouvain, 1348 Louvain-la-Neuve, Belgium
*
Author to whom correspondence should be addressed.
Water 2024, 16(18), 2594; https://doi.org/10.3390/w16182594
Submission received: 22 July 2024 / Revised: 1 September 2024 / Accepted: 9 September 2024 / Published: 13 September 2024
Browse Figures
Figure 1
<p>Study area: (<b>a</b>) Study site location in Haiti; (<b>b</b>) Rouyonne river channel and its upper watershed; (<b>c</b>) Altitude distribution in the upper watershed.</p> "> Figure 1 Cont.
<p>Study area: (<b>a</b>) Study site location in Haiti; (<b>b</b>) Rouyonne river channel and its upper watershed; (<b>c</b>) Altitude distribution in the upper watershed.</p> "> Figure 2
<p>Illustration of image acquisition: (<b>a</b>) Aerial image of the river during the dry season; (<b>b</b>) DJI drone equipped with a GoPro camera (sensor type: 1/2.3” CMOS; camera type: sport/action camera; equivalent focal length: 16.41 mm; lens type: wide angle; aperture: f/2.8).</p> "> Figure 3
<p>Illustration of the morphological changes in the Rouyonne river channel: (<b>a</b>) Cross-section 54—54 of the Rouyonne River; (<b>b</b>) Bathymetric data comparison between UAV photogrammetry DTM (2022) and the manual survey (2022); (<b>c</b>) Evolution of morphological changes between 2014 and 2022 in cross-section 54—54.</p> "> Figure 4
<p>Illustration of the damage caused by the 3 June 2023 event: (<b>a</b>) Buildings destroyed by the flood in the town of Léogâne; (<b>b</b>) Pressure sensor broken by flood at the measuring section; (<b>c</b>) High-water mark measurement; (<b>d</b>) Spatial distribution of high-water marks measured for the 2–3 June 2023 event.</p> "> Figure 4 Cont.
<p>Illustration of the damage caused by the 3 June 2023 event: (<b>a</b>) Buildings destroyed by the flood in the town of Léogâne; (<b>b</b>) Pressure sensor broken by flood at the measuring section; (<b>c</b>) High-water mark measurement; (<b>d</b>) Spatial distribution of high-water marks measured for the 2–3 June 2023 event.</p> "> Figure 5
<p>Illustration of the unstructured mesh of the study area.</p> "> Figure 6
<p>Cross-section at the limnimetric station with the equivalent rectangle (discontinuous black line) used in the BaRatin method.</p> "> Figure 7
<p>Relationships between water depth and discharge at the measurement section: comparison of the Bayesian rating curve with uncertainties and the uniform-flow assumption.</p> "> Figure 8
<p>Hydrological modeling: (<b>a</b>) Calibration (August 2022); (<b>b</b>) Validation (September 2022).</p> "> Figure 9
<p>Hydrological modeling applied to the event of 2–3 June 2023.</p> "> Figure 10
<p>Illustration of the 2–3 June 2023 event simulation.</p> "> Figure 11
<p>Model evaluation: Comparison between the observed and modeled water depths.</p> "> Figure 12
<p>Identification of the overflow points on the Rouyonne river: (<b>a</b>) Right bank overtopping to downtown Léogâne; (<b>b</b>) Left bank overtopping where the probe was installed.</p> ">
Versions Notes

Abstract

:
Evaluating flood risk though numerical simulations in areas where hydrometric and bathymetric data are scarcely available is a challenge. This is, however, of paramount importance, particularly in urban areas, where huge losses of human life and extensive damage can occur. This paper focuses on the 2–3 June 2023 event at Léogâne in Haiti, where the Rouyonne River partly flooded the city. Water depths in the river have been recorded since April 2022, and a few discharges were measured manually, but these were not sufficient to produce a reliable rating curve. Using a uniform-flow assumption combined with the Bayesian rating curve (BaRatin) method, it was possible to extrapolate the existing data to higher discharges. From there, a rainfall–runoff relation was developed for the site using a distributed hydrological model, which allowed the discharge of the June 2023 event to be determined, which was estimated as twice the maximum conveying capacity of the river in the measurement section. Bathymetric data were obtained using drone-based photogrammetry, and two-dimensional simulations were carried out to represent the flooded area and the associated water depths. By comparing the water depths of 21 measured high-water marks with the simulation results, we obtained a Kling–Gupta Efficiency (KGE) and Nash–Sutcliffe Efficiency (NSE) values of 0.890 and 0.882, respectively. This allows us to conclude that even when only scarce official data are available, it is possible to use field data acquired by low-cost methodologies to build a model that is sufficiently accurate and that can be used by flood managers and decision makers to assess flood risk and vulnerability in Haiti.

1. Introduction

Urban flooding is a subject of major concern to both the scientific community and the public. To improve urban planning and to manage these risks, it is important to have digital tools capable of simulating flood events for better decision making. Hydraulic modeling tools can predict the spatial and temporal evolution of river behavior during a flood event and the resulting flood extent [1,2,3], provided that prior calibration of the model can be achieved. There are various approaches for modeling river flooding events, including simpler one-dimensional models [4,5], which require less data, and more detailed two-dimensional [6,7,8] models. The choice of approach must be consistent with the scale under study and with the risks involved [9]. Moreover, for accurate modeling, updated and good-quality topographic data are needed [10], as well as high-resolution water level and flow measurements to capture rapid flood variations [9]. For ungauged sites, hydrological models are often used to estimate flows based on precipitation data and watershed characteristics [11,12]. However, these models need to be calibrated for the specific site under study, and appropriate criteria, such as the KGE (Kling–Gupta Efficiency) and the NSE (Nash–Sutcliffe Efficiency), should be used to evaluate these models.
In the present case, the study site, namely the Léogâne City in Haiti, lies in a region where only scarce or inaccurate and incomplete data are available, resulting in additional modeling challenges. Indeed, the only official topographical data in the country dates back to 2014–2016, but since then, the country has undergone several natural hazards, such as Hurricane Matthew in 2016, which resulted in strong morphological changes in the rivers in the affected regions. Moreover, due to the complex political situation and the lack of means of the local authorities, many measurement devices have not been able to be maintained or replaced in the case of failure, resulting in important gaps in hydrological and hydraulic data.
The aim of this study is thus to develop hydraulic modeling combined with hydrologic tools to reconstruct the missing data in order to reproduce the June 2023 event in Léogâne, and from there, to initiate a methodology to characterize the flood risk in the region. Specifically, the proposed modeling strategy is based on the contribution of (i) low-cost drone-based photogrammetry to complement existing but inaccurate bathymetric data; (ii) the uniform-flow approach to construct a rating curve for poorly gauged rivers for which only scarce measurements are available; and (iii) hydrological modeling for the reconstruction of flood hydrographs corresponding to extreme events in weakly instrumented watersheds, as is often the case for Haitian watersheds.
Hydraulic modeling in such cases is usually performed by solving the two-dimensional shallow-water equations [7,13,14,15,16,17,18,19] on structured or unstructured grids constructed using available topographic and bathymetric data. While a wide range of software is available for such purposes (e.g., HEC-RAS, TUFLOW, MIKE-FLOOD, etc.), here, the WATLAB open-modeling environment developed by our research group “https://sites.uclouvain.be/hydraulics-group/watlab/index.html (accessed on 11 June 2024)” was used, which is based on reported developments, e.g., in [20,21,22,23], and widely validated by comparison with other existing tools. To validate the model in our study, measurements of water depth in the flooded zone were taken from the high-water marks shortly after the June 2023 event.
As regards stage–discharge relations, these are normally obtained from a series of direct measurements of the flow and water depth for a range of flows at a gauging station. During floods, it is easier to measure water depth than flow with reasonable accuracy, because water velocities and levels pose a safety problem. In such situations, extrapolation of the rating curve is often used [24,25] or alternatively, rating curves of similar rivers in the region are used for ungauged watersheds [26]. However, the uncertainty associated with any stage–discharge relations is often assessed [24,27,28,29,30], because extrapolating errors can be responsible for unrealistic river roughness estimates [31].
Finally, hydrological modeling allows flood hydrographs to be derived from rainfall data when discharge measurements are not available. Either lumped, semi-distributed or distributed models can be used (e.g., GR4J, GRSD, HEC-HMS, Mike-SHE, etc.) [32,33,34,35], all of which have different data requirements. Lumped models are easier to set up but need accurate discharge data for the calibration of the transfer functions as no physical transfer processes are considered. In the present case, the distributed model AtHyS (Atelier Hydrologique Spatialisé) was used [36], which takes into account the actual topographical data in a physically sound way for the transfer from runoff to the outlet of the catchment, considering evaporation and infiltration losses according to the curve number model [36].
The results of this modeling strategy are expected to provide critical insights for urban flood managers and policy makers to assess the flood risk in Haiti, and, ultimately, to contribute to the design of development and flood-risk management plans. The June 2023 event is expected to recur, especially in cyclonic periods. Depending on the data availability, synthetic extreme rainfall data with given return periods could be determined based on a statistical analysis of past events to construct corresponding design hydrographs and to design preventive risk management strategies in Haiti and hydro-climatically similar regions.
The paper is organized as follows: first, the study area and data collection are presented, including drone-based measurements for the bathymetry and hydrological modeling to evaluate the discharges; then, a hydraulic model is constructed, and simulations of the June 2023 event are conducted. The results are compared to field measurements, and, finally, conclusions are drawn on the long-term perspective regarding possible flood forecasting systems for the city of Léogâne to predict what might happen when heavy rainfall is announced and to establish risk maps.

2. Materials and Methods

2.1. Study Area

This research study concerns a stretch of the Rouyonne River along the town of Léogâne in Haiti (Figure 1a,b). Fed by a mountainous upper watershed of 46.45 km2 (Figure 1b), the river flows into the Caribbean Sea via an 8.2 km long channelized reach that begins at the upper watershed outlet (X = 754,280 m; Y = 2,044,471 m; coordinate system WGS 84/UTM zone 18N) and ends at the sea (X = 747,693 m; Y = 2,049,408 m). While the river is rather sinuous in the mountainous upper watershed, the downstream part of the Rouyonne River (the channel) is nearly straight, with an average slope of 0.62%. The lower course of the river was, in fact, artificially channelized and confined by embankments specifically to prevent inundations. The upper watershed is very hilly, with 75% of its surface area situated between 250 and 950 m above sea level (Figure 1c). The city of Léogâne lies in the flood plain zone, close to the channelized part of the river. Unfortunately, the embankments experience frequent overflows, which explains the recurrent flooding of the city.

2.2. Data Acquisition

The topographical and bathymetric data available for the site were the official data from the National Center for Geospatial Information—Centre National des Informations Géospatiales (CNIGS) covering the entire country, which dated back to 2016 and were issued from a measurement campaign that was started in January 2014 by IGN France International (IGN FI), with funding from the World Bank. The 1.5 m resolution digital terrain model (DTM) from the CNIGS was used for the hydrological modeling of the upper watershed. However, since the data acquisition, many major morphological changes were observed in the main rivers of Haiti, which were caused by extreme climatic events in the last years in the lower reach. This DTM has, thus, become too inaccurate for hydraulic modeling of the Rouyonne River reach. Therefore, a drone-based survey of the river was conducted during the dry season, when the river is empty (Figure 2a), to capture aerial images to measure the bathymetry and surrounding topography using photogrammetry through the image processing software “Agisoft Metashape pro version 1.8.0”. Aerial images were taken from a drone (DJI marvic Air 2) equipped with a GoPro Hero 4 camera (Figure 2b), which are all low-cost and easy-to-handle devices that are well suited to such field conditions.
Each drone flight had a duration of about 10 min, depending on the battery autonomy, with a speed of 5 m/s and a capture frequency of one image every two seconds. The image overlap between successive flights is 80% at the front and 60% at the side [37]. These overlaps provide sufficient information for the spatial reconstruction of the scenes studied, with a total of 300 images, on average, for a flight plan. The accurate georeferencing of the imagery was performed by the global navigation satellite system (GNSS) positioning of at least 15 ground control points (GCPs) for each flight plan, which were used for image georeferencing during the photogrammetric processing. For more information on the processing procedure and assessment of this method at sites in Haiti, see [38,39,40,41,42,43].
Two drone-based surveys were conducted in 2020 and 2022, respectively. The drone-based technique was found to be very accurate, with a root mean square error (RMSE) of 0.18 m at 80 verification points. A comparison between a manual survey of cross-section 54–54 and the photogrammetric data is illustrated in Figure 3a,b. The marked morphological evolution of the river at this cross-section is illustrated in Figure 3c, where the official DTM (2014–2016) is compared to that from the 2020 and 2022 surveys. It can be observed that the left bank, which was destroyed during Hurricane Matthew in 2016 and then reconstructed, was again completely eroded between 2020 and 2022.
The 3 June 2023 event resulted in the death of almost twenty people in the city of Léogâne, a lot of injuries and considerable damage (Figure 4a,b). In just 32 h and 30 min, the average rainfall recorded in the watershed amounted to 142.1 mm. This value exceeds the monthly average rainfall of around 100 mm for the month of June in the municipality of Léogâne. Consequently, significant overflows were observed during this event, inundating the flood plains and, finally, a part of the city. One day after the June 2023 event, 21 high-water marks were measured in the city and along the river, as illustrated in Figure 4c,d. These were subsequently used to validate the hydraulic model.

2.3. Discharge Estimation

To run the hydraulic model, we needed the flood hydrograph at the system inlet for the 2–3 June 2023 event. Ideally, the discharge should have been obtained from a hydrometric station, which was, unfortunately, not the case at Léogâne. Only data from a limnimeter (OTT PLS probe: pressure sensor) installed at the measurement section (at the channel inlet) since April 2022 were available. At this location, an OTT “MF Pro” magnetic induction current meter was used to take a range of flow measurements at shallow water depths of below 40 cm. Beyond this depth, measurements become dangerous; therefore, the number of stage–discharge points available to construct a rating curve were not sufficient. It was thus necessary to extrapolate the few points of the rating curve for greater water depths. The construction of the rating curve was based on the assumption of uniform flow in the measurement section and was complemented by the Bayesian rating curve (BaRatin) method [44,45] developed by the National Research Institute for Agriculture, Food and the Environment (INRAE) in 2010, which allowed the uncertainty associated with this approach to be assessed.
However, it is also important to be able to predict the flow from rainfall measurements when the water-level station is dysfunctional, as was indeed the case during the 2–3 June 2023 event as the probe was destroyed. To achieve this, the rainfall data recorded at three rain gauges on the Rouyonne river catchment were used to establish a rainfall–discharge relationship for this watershed using version 6.0 of the AtHyS software developed at the Research Institute for Development (IRD), Montpelier, France [36]. This distributed hydrological model was used because of its physical basis in terms of water propagation and infiltration modeling, and it has provided good-quality results in previous studies in similar poorly gauged environments [46,47,48]. The key parameters of this hydrological model are the following: V0 (m/s), which can be estimated as the velocity of flood wave propagation; S (mm), the total ground reservoir capacity, which depends on soil characteristics; ds (day−1), the proportionality coefficient between the reservoir level and the emptying intensity; ω (dimensionless), the fraction of the underground reservoir emptying that participates in hypodermic flow; and K0 (dimensionless), a proportionality constant between the diffusion time and the transfer time. These parameters were calibrated and validated using two other events that occurred before the June 2023 event. The performance of the hydrological model was assessed using the classic criteria most widely used in hydrology studies [49,50,51,52], i.e., the Nash–Sutcliffe Efficiency (NSE) proposed by [53] and the Kling–Gupta Efficiency (KGE) [54], used in other hydrological studies [55,56]. The KGE criterion was used to select the best parameter set during the calibration and to assess the hydrological model performance. Once validated, the rainfall–discharge relationship can be used to predict flows resulting from given rainfall events.

2.4. Hydraulic Model and Simulation Tool

Based on the DTM, a hydraulic model was built using a triangular mesh (Figure 5), with the advantage that different mesh resolutions could be used for the computational cells: (1) the riverbed with a 1 m resolution; (2) the floodplain with a 40 m resolution; and (3) the transition zone between the Rouyonne riverbed and the floodplain, where the dikes can be identified, with an intermediate 3 m resolution. This mesh was then used for numerical simulations within the WATLAB environment developed at UCLouvain/iMMC “https://sites.uclouvain.be/hydraulics-group/watlab/index.html (accessed on 11 June 2024)”, solving the two-dimensional shallow-water equations using a finite-volume scheme for unstructured meshes:
𝜕 h 𝜕 t + 𝜕 q x 𝜕 x + 𝜕 q y 𝜕 y = 0
𝜕 q x 𝜕 t + 𝜕 𝜕 x q x 2 h + g h 2 2 + 𝜕 𝜕 y q x q y h = g h S 0 , x − S f , x
𝜕 q y 𝜕 t + 𝜕 𝜕 x q x q y h + 𝜕 𝜕 y q y 2 h + g h 2 2 = g h S 0 , y − S f , y
where h is the water depth; qx and qy are the unit discharge in the x and y directions; S0,x, S0,y, Sf,x, and Sf,y are the x and y components of the bed slope S0 and of the friction slope Sf that is calculated using the Manning equation. The WATLAB modeling environment is based on previous works, e.g., [20,21,22,23], and provides an open-source environment that allows the creation of a computational mesh using GIS tools and the version 4.8.4 of the GMSH software in a unified Python framework, while the core computational code is run in C++ with a parallel implementation. The advantage of this open-source environment is that it can be easily adapted to the user needs or to specific features of the studied environment.
The hydraulic model roughness was characterized through two different values of Manning’s coefficient: nc = 0.048 sm−1/3 for the main channel, and nf = 0.05 sm−1/3 for the floodplain. As regards the upstream boundary conditions, the flood hydrograph generated using AtHyS was used, because no complete hydrograph could be established from the limnimetric data recording as this had stopped at the time when the probe cable broke.

2.5. Summary of Data Used in This Study

All the data used in this study are summarized in Table 1, which describes the origin of the data and the time or space resolution applied in the simulations. It is worth noting that the drone-based topography has a finer resolution than the official DTM from CNIGS.

3. Results

3.1. Rating Curve for the Rouyonne River

The cross-section of the Rouyonne River at the location of the limnimetric station is illustrated in Figure 6. It has an almost regular trapezoidal shape, and based on the uniform-flow assumption, a stage–discharge relation could be constructed using Manning’s equations, after calibrating the roughness using the eight manually measured stage–discharge values for water depths of up to 0.40 m. As the maximum discharge that was manually measured was well below the probable discharge that occurred during the June 2023 event, it was necessary to assess the quality of the rating curve established using the uniform-flow assumption. Therefore, the BaRatin method [44,45], combining all the sources of uncertainties related to the rating curves, was used.
Figure 7 shows the rating curve obtained with the uniform-flow assumption calibrated using the few measured points and the rating curve calculated with the Baratin method, as well as the associated uncertainties. Parametric uncertainty expresses the uncertainty related only to the estimation of the curve parameters, while the total uncertainty is the combination of the parametric uncertainty and the uncertainty induced by the remnant error.
Unfortunately, the water-level gauge failed during the June 2023 event when the water level reached 2.43 m, making it impossible to use the rating curve to calculate the corresponding hydrograph. Therefore, a rainfall–discharge relation is required.

3.2. Rainfall–Discharge Relationship

The AtHyS hydrological model was run on one event that occurred in August 2022 to calibrate the model parameters and then applied to an event in September 2022 for validation. The comparisons between the estimated flows using the rating curve of Figure 7 and the hydrological model results are shown in Figure 8. The values of the calibrated parameters are given in Table 2, as well as the KGE and NSE scores.
Using this validated model, the complete hydrograph of the 2–3 June 2023 event was built, and the results are illustrated in Figure 9. It can already be observed that the agreement between the observations and the model is very good during the period when the limnimetric station was working properly. The simulated maximum flow (Q = 168 m3/s) at the measuring section for this event is two times larger than the maximum flow (Q = 84 m3/s) that the river can convey without overflowing at this section.

3.3. Hydraulic Modeling of the 3 June 2023 Flood Hydrograph

The simulation results are illustrated in Figure 10. It can be observed that the Rouyonne River indeed overflows the dikes and induces severe flooding of the surrounding areas, including the city of Léogâne. The extent of the inundated area appears to be well reproduced by the model, as the points where high-water marks were recorded are indeed located in the inundated area (red points in Figure 10).
The comparison of the simulated and measured water depths at the 21 high-water marks (Figure 11) shows that the model provides a good estimate of the water depth in the study area. With KGE and NSE values of 0.890 and 0.882, respectively, based on these 21 comparison points, the model is considered satisfactory.

4. Discussion

The rating curve was established using a few measured points and considering a uniform-flow assumption, which is a questionable assumption as the flow is highly unsteady, especially during rapid floods. Nonetheless, the validity of the curve was confirmed by the use of Baratin method, which allowed the related uncertainty to be estimated, especially considering the limited number of gauging points. A similar situation was observed in [57], where the authors verified the beginning of their rating curve with water depths of no more than 0.50 m for a total section height of around 1.20 m.
This rating curve was then successfully applied to determine the parameters of the AtHyS hydrological model. The optimal parameters (Table 2) allow for a very good reproduction of both the validation case and the beginning of the June 2023 hydrograph. However, the very high value of the velocity V0, equal to 5.43 m/s, is questionable. It could be explained by the very steep slopes in the upper catchment, as well as by significant deforestation that prevents the slowing down of runoff water by vegetation. The calibrated value of S = 82.44 mm corresponds to a CN of close to 75, which is in agreement with classical values for the type of soil and vegetation cover in the catchment, where the hydrological conditions of the cultivated surfaces are medium. However, it can be observed that the model underestimates the peak discharge in the calibration stage; nonetheless, it reflects well the hydrological behavior of the Rouyonne river watershed, as the curves are very close, and the statistical scores are very good (Table 2). The same situation was described in [46,58], where the peaks of the hydrographs were also underestimated while the curves followed each other in the rising and falling limbs of the hydrographs. As the extent of the inundated area is more related to the volume of the hydrograph than to the peak discharge, the calibration with the parameters found as providing the highest KGE and NSE was retained. In the validation case presented in Figure 8b, the peak discharge is better estimated, but a time lag appears in the hydrograph. This can be related to the velocity parameter V0, which could also depend on the initial conditions of the watershed, which were not considered here. However, considering the high KGE and NSE values, and the good fit with the measured data in Figure 9, it was decided to keep the calibrated parameters to reconstruct the missing part of the 23 June 2023 hydrograph.
The hydraulic simulation based on this hydrograph identified three major overflow points on the Rouyonne river, which are highlighted in Figure 12: two points on the right bank (Figure 12a), responsible for flooding the town center, and one point on the left bank (Figure 12b), upstream of and close to the gauging station. This last overflow point explains why the probe was torn off, interrupting the water-depth recording at the measuring section.
From the good agreement between the simulated and measured water depths (Figure 11), the hydraulic model can be considered as satisfactory. However, the accuracy of the results could be further improved by using a more refined mesh (for example, by reducing the size of the cells in the floodplain); however, this would come at the cost of a great increase in calculation time. Also, the buildings in the city of Léogâne are not properly accounted for. As shown in the work of [6,7], various local aspects can influence the modeled water height, such as spatialized roughness in the floodplain and the effect of buildings in the city. Consequently, our results may underestimate the water depth in some places. This is a prospect for further studies in Haiti.

5. Conclusions

By combining different sources of data and low-cost field measurement techniques, it was possible to develop a hydraulic model for the Rouyonne catchment that reproduced well the inundation of the city following the June 2023 event. This shows that the model could be used to draw up flood zone maps for the city of Léogâne. By using rainfall events or synthetic rainfalls with given return periods, it will be possible to derive corresponding hydrographs and to characterize the possible flooded area for different return periods. Such rainfall data with known return periods are not available at the moment but could be used in the future.

Author Contributions

Conceptualization, methodology and validation, R.L., S.S.-F. and Y.Z.; software and investigation, R.L., A.J., Y.Z., S.S.-F. and N.G.; formal analysis, resources and data curation, R.L., S.S.-F. and Y.Z.; writing—original draft preparation, R.L.; writing—review and editing, S.S.-F. and Y.Z.; visualization and supervision, N.G. and A.J.; project administration and funding acquisition, N.G., Y.Z. and S.S.-F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the ARES (Académie de Recherche et d’Enseignement Supérieur) RISCRUE project (grant number COOP-CONV-22-190).

Data Availability Statement

Data supporting the results of this study are available from the authors upon reasonable request.

Acknowledgments

The authors would like to thank ARES-CCD for funding this study through the RISCRUE research project in Haiti and also thank Dauphin Géthro, Asie Louis Raymond, Jacky Dolciné and Lamour Frantz for their assistance in the data collection in the field, the team at the Civil and Environmental Engineering Department of UCLouvain and the team at the Rural Engineering Department of the State University of Haiti for their help in the realization of this study.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Lhomme, J. Modélisation des Inondations en Milieu Urbain: Approches Unidimensionnelle, Bidimensionnelle et Macroscopique. Ph.D. Thesis, Université de Montpellier II, Sciences et Techniques du Languedoc, Montpellier, France, December 2006. [Google Scholar]
  2. Mathieu, G. Développement d’une Méthodologie Pour la Cartographie du Risque D’inondation: Application à la Rivière de Cavaillon en Haïti. Ph.D. Thesis, Université Catholique de Louvain, Ottignies-Louvain-la-Neuve, Belgium, January 2023. [Google Scholar]
  3. Joseph, A.; Gonomy, N.; Zech, Y.; Soares-Frazão, S. Modelling and analysis of the flood risk at Cavaillon City, Haiti. Houille Blanche 2018, 104, 68–75. [Google Scholar] [CrossRef]
  4. Crispino, G.; Gisonni, C.; Iervolino, M. Flood hazard assessment: Comparison of 1D and 2D hydraulic models. Int. J. River Basin Manag. 2015, 13, 153–166. [Google Scholar] [CrossRef]
  5. Horritt, M.S.; Bates, P.D. Evaluation of 1D and 2D numerical models for predicting river flood inundation. J. Hydrol. 2002, 268, 87–99. [Google Scholar] [CrossRef]
  6. Lhomme, J.; Soares-Frazão, S.; Guinot, V.; Zech, Y. Large scale modelling of urban floods and 2D shallow-water model with porosity. Houille Blanche 2007, 93, 104–110. [Google Scholar] [CrossRef]
  7. Van Emelen, S.; Soares Frazao, S.; Riahi-Nezhad, C.; Chaudhry, M.H.; Imran, J.; Zech, Y. Simulations of the New Orleans 17th Street Canal breach flood. J. Hydraul. Res. 2012, 50, 70–81. [Google Scholar] [CrossRef]
  8. Pinos, J.; Timbe, L. Performance assessment of two-dimensional hydraulic models for generation of flood inundation maps in mountain river basins. Water Sci. Eng. 2019, 12, 11–18. [Google Scholar] [CrossRef]
  9. Apel, H.; Aronica, G.T.; Kreibich, H.; Thieken, A. Flood risk analyses—How detailed do we need to be? Nat. Hazards 2009, 49, 79–98. [Google Scholar] [CrossRef]
  10. Dewals, B.J.; Detrembleur, S.; Archambeau, P.; Erpicum, S.; Ernst, J.; Pirotton, M. Caractérisation micro-echelle du risque d’inondation: Modélisation hydraulique détaillée et quantification des impacts socio-économiques. Houille Blanche 2011, 97, 28–34. [Google Scholar] [CrossRef]
  11. Hrachowitz, M.; Savenije, H.H.G.; Blöschl, G.; McDonnell, J.J.; Sivapalan, M.; Pomeroy, J.W.; Arheimer, B.; Blume, T.; Clark, M.P.; Ehret, U.; et al. A decade of Predictions in Ungauged Basins (PUB)—A review. Hydrol. Sci. J. 2013, 58, 1198–1255. [Google Scholar] [CrossRef]
  12. Blöschl, G.; Bierkens, M.F.P.; Chambel, A.; Cudennec, C.; Destouni, G.; Fiori, A.; Kirchner, J.W.; McDonnell, J.J.; Savenije, H.H.; Sivapalan, M.; et al. Twenty-three Unsolved Problems in Hydrology (UPH)—A Community Perspective. Hydrol. Sci. J. 2019, 64, 1141–1158. [Google Scholar] [CrossRef]
  13. Buwalda, F.J.L.; De Goede, E.; Knepflé, M.; Vuik, C. Comparison of an Explicit and Implicit Time Integration Method on GPUs for Shallow Water Flows on Structured Grids. Water 2023, 15, 1165. [Google Scholar] [CrossRef]
  14. Mitsopoulos, G.; Panagiotatou, E.; Sant, V.; Baltas, E.; Diakakis, M.; Lekkas, E.; Stamou, A. Optimizing the Performance of Coupled 1D/2D Hydrodynamic Models for Early Warning of Flash Floods. Water 2022, 14, 2356. [Google Scholar] [CrossRef]
  15. Guo, W.; Zhai, M.; Lei, X.; Huang, H.; Long, Y.; Li, S. Two-Dimensional Hydrodynamic Simulation of the Effect of Stormwater Inlet Blockage on Urban Waterlogging. Water 2024, 16, 2029. [Google Scholar] [CrossRef]
  16. Martínez-Aranda, S.; Meurice, R.; Soares-Frazão, S.; García-Navarro, P. Comparative Analysis of HLLC- and Roe-Based Models for the Simulation of a Dam-Break Flow in an Erodible Channel with a 90° Bend. Water 2021, 13, 1840. [Google Scholar] [CrossRef]
  17. Guan, M.; Guo, K.; Yan, H.; Wright, N. Bottom-up multilevel flood hazard mapping by integrated inundation modelling in data scarce cities. J. Hydrol. 2023, 617, 129114. [Google Scholar] [CrossRef]
  18. Yang, Q.; Ma, Z.; Zhang, S. Urban Pluvial Flood Modeling by Coupling Raster-Based Two-Dimensional Hydrodynamic Model and SWMM. Water 2022, 14, 1760. [Google Scholar] [CrossRef]
  19. Delis, A.I.; Nikolos, I.K. Shallow Water Equations in Hydraulics: Modeling, Numerics and Applications. Water 2021, 13, 3598. [Google Scholar] [CrossRef]
  20. Soares-Frazão, S.; Zech, Y. HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed. Int. J. Numer. Methods Fluids 2010, 66, 1019–1036. [Google Scholar] [CrossRef]
  21. Meurice, R.; Soares-Frazão, S. A 2D HLL-based weakly coupled model for transient flows on mobile beds. J. Hydroinform. 2020, 22, 1351–1369. [Google Scholar] [CrossRef]
  22. Sandra, S.F.; Yves, Z. Dam break in channels with 90 degrees bend. J. Hydraul. Eng. 2002, 128, 956–968. [Google Scholar]
  23. Soares-Frazao, S.; Zech, Y. Dam-break flow through an idealized city. J. Hydraul. Res. 2008, 46, 648–658. [Google Scholar] [CrossRef]
  24. Westerberg, I.K.; Sikorska-Senoner, A.E.; Viviroli, D.; Vis, M.; Seibert, J. Hydrological model calibration with uncertain discharge data. Hydrol. Sci. J. 2020, 67, 2441–2456. [Google Scholar] [CrossRef]
  25. Lee, M.; Yoo, Y.; Joo, H.; Kim, K.T.; Kim, H.S.; Kim, S. Construction of rating curve at high water level considering rainfall effect in a tidal river. J. Hydrol. 2021, 37, 100907. [Google Scholar] [CrossRef]
  26. Jafarzadegan, K.; Moradkhani, H. Regionalization of stage-discharge rating curves for hydrodynamic modeling in ungauged basins. J. Hydrol. 2020, 589, 125165. [Google Scholar] [CrossRef]
  27. Kumar, V.; Sen, S. Rating curve development and uncertainty analysis in mountainous watersheds for informed hydrology and resource management. Front. Water 2024, 5, 1323139. [Google Scholar] [CrossRef]
  28. Ocio, D.; Le Vine, N.; Westerberg, I.; Pappenberger, F.; Buytaert, W. The role of rating curve uncertainty in real-time flood forecasting. Water Resour. Res. 2017, 53, 4197–4213. [Google Scholar] [CrossRef]
  29. Garcia, R.; Costa, V.; Silva, F. Bayesian Rating Curve Modeling: Alternative Error Model to Improve Low-Flow Uncertainty Estimation. J. Hydrol. Eng. 2020, 25, 04020012. [Google Scholar] [CrossRef]
  30. Qiu, J.; Liu, B.; Yu, X.; Yang, Z. Combining a segmentation procedure and the BaRatin stationary model to estimate nonstationary rating curves and the associated uncertainties. J. Hydrol. 2021, 597, 126168. [Google Scholar] [CrossRef]
  31. Domeneghetti, A.; Castellarin, A.; Brath, A. Assessing rating-curve uncertainty and its effects on hydraulic model calibration. Hydrol. Earth Syst. Sci. 2012, 16, 1191–1202. [Google Scholar] [CrossRef]
  32. Reed, S.; Schaake, J.; Zhang, Z. A distributed hydrologic model and threshold frequency-based method for flash flood forecasting at ungauged locations. J. Hydrol. 2007, 337, 402–420. [Google Scholar] [CrossRef]
  33. Montaldo, N.; Mancini, M.; Rosso, R. Flood hydrograph attenuation induced by a reservoir system: Analysis with a distributed rainfall-runoff model. Hydrol. Process. 2004, 18, 545–563. [Google Scholar] [CrossRef]
  34. Peredo, D.; Ramos, M.H.; Andréassian, V.; Oudin, L. Investigating hydrological model versatility to simulate extreme flood events. Hydrol. Sci. J. 2022, 67, 628–645. [Google Scholar] [CrossRef]
  35. Azizi, S.; Ilderomi, A.R.; Noori, H. Investigating the effects of land use change on flood hydrograph using HEC-HMS hydrologic model (case study: Ekbatan Dam). Nat. Hazards 2021, 109, 145–160. [Google Scholar] [CrossRef]
  36. Bourvier, C.; Delclaux, F. ATHYS: A hydrological environment for spatial modelling and coupling with GIS. In HydroGIS 96: Application of Geographic Information Systems in Hydrology and Water Resources Management (Proceedings of the Vienna Conference, April 1996); IAHS Publication: Wallingford, UK, 1996; Volume 235, pp. 19–28. [Google Scholar]
  37. Agisoft Metashape. Available online: https://www.agisoft.com/pdf/metashape-pro_1_8_en.pdf (accessed on 14 March 2023).
  38. Louis, R.; Dauphin, G.; Zech, Y.; Joseph, A.; Gonomy, N.; Soares-Frazão, S. Assessment of UAV-Based Photogrammetry for Bathymetry Measurements in Haiti: Comparison with Manual Surveys and Official Data. In Proceedings of the 39th IAHR World Congress from Snow to Sea, Granada, Spain, 19–24 June 2022; pp. 565–574, ISBN 978-90-832612-1-8. [Google Scholar]
  39. Verhoeven, G. Taking computer vision aloft—Archaeological three-dimensional reconstructions from aerial photographs with photoscan. Archaeol. Prospect. 2011, 18, 67–73. [Google Scholar] [CrossRef]
  40. Lowe, D.G. Distinctive Image Features from Scale-Invariant Keypoints. Int. J. Comput. Vis. 2004, 60, 91–110. [Google Scholar] [CrossRef]
  41. Snavely, N.; Seitz, S.M.; Szeliski, R. Photo Tourism: Exploring Photo Collections in 3D. ACM Trans. Graph. 2006, 25, 835–846. [Google Scholar] [CrossRef]
  42. Snavely, N.; Seitz, S.M.; Szeliski, R. Modeling the World from Internet Photo Collections. Int. J. Comput. Vis. 2008, 80, 189–210. [Google Scholar] [CrossRef]
  43. Westoby, M.J.; Brasington, J.; Glasser, N.F.; Hambrey, M.J.; Reynolds, J.M. ‘Structure-from-Motion’ photogrammetry: A low-cost, effective tool for geoscience applications. Geomorphology 2012, 179, 300–314. [Google Scholar] [CrossRef]
  44. Le Coz, J.; Renard, B.; Bonnifait, L.; Branger, F.; Le Boursicaud, R. Combining hydraulic knowledge and uncertain gaugings in the estimation of hydrometric rating curves: A Bayesian approach. J. Hydrol. 2014, 509, 573–587. [Google Scholar] [CrossRef]
  45. Horner, I.; Renard, B.; Le Coz, J.; Branger, F.; McMillan, H.K.; Pierrefeu, G. Impact of stage measurement errors on streamflow uncertainty. Water Resour. Res. 2018, 54, 1952–1976. [Google Scholar]
  46. Bouadila, A.; Bouizrou, I.; Aqnouy, M.; En-nagre, K.; El Yousfi, Y.; Khafouri, A.; Hilal, I.; Abdelrahman, K.; Benaabidate, L.; Abu-Alam, T.; et al. Streamflow Simulation in Semiarid Data-Scarce Regions: A Comparative Study of Distributed and Lumped Models at Aguenza Watershed (Morocco). Water 2023, 15, 1602. [Google Scholar] [CrossRef]
  47. Nguyen, S.; Bouvier, C. Flood modelling using the distributed event-based SCS-LR model in the Mediterranean Real Collobrier catchment. Hydrol. Sci. J. 2019, 64, 1351–1369. [Google Scholar] [CrossRef]
  48. Mourad, A.; El Messari, J.E.S.; Bouadila, A.; Morabbi, A.; Benaabidate, L.; Al-Djazouli, M.O. Modeling of Continuous and Extreme Hydrological Processes Using Spatially Distributed Models MERCEDES, VICAIR and VISHYR in a Mediterranean Watershed. Ecol. Eng. Environ. Tech. 2021, 22, 9–23. [Google Scholar] [CrossRef]
  49. Mathevet, T.; Gupta, H.; Perrin, C.; Andréassian, V.; Le Moine, N. Assessing the performance and robustness of two conceptual rainfall-runoff models on a worldwide sample of watersheds. J. Hydrol. 2020, 585, 124698. [Google Scholar] [CrossRef]
  50. Orth, R.; Staudinger, M.; Seneviratne, S.I.; Seibert, J.; Zappa, M. Does model performance improve with complexity? A case study with three hydrological models. J. Hydrol. 2015, 523, 147–159. [Google Scholar] [CrossRef]
  51. Worqlul, A.W.; Ayana, E.K.; Maathuis, B.H.P.; MacAlister, C.; Philpot, W.D.; Osorio Leyton, J.M.; Steenhuis, T.S. Performance of bias corrected MPEG rainfall estimate for rainfall-runoff simulation in the upper Blue Nile Basin, Ethiopia. J. Hydrol. 2018, 556, 1182–1191. [Google Scholar] [CrossRef]
  52. Tegegne, G.; Park, D.K.; Kim, Y.O. Comparison of hydrological models for the assessment of water resources in a data-scarce region, the Upper Blue Nile River Basin. J. Hydrol. 2017, 14, 49–66. [Google Scholar] [CrossRef]
  53. Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol. 1970, 10, 282–290. [Google Scholar] [CrossRef]
  54. Gupta, H.V.; Kling, H.; Yilmaz, K.K.; Martinez, G.F. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. J. Hydrol. 2009, 377, 80–91. [Google Scholar] [CrossRef]
  55. Reis, A.A.; Weerts, A.; Ramos, M.H.; Wetterhall, F.; Fernandes, W.S. Hydrological data and modeling to combine and validate precipitation datasets relevant to hydrological applications. J. Hydrol. 2022, 44, 101–200. [Google Scholar] [CrossRef]
  56. de Lavenne, A.; Lindström, G.; Strömqvist, J.; Pers, C.; Bartosova, A.; Arheimer, B. Evaluation of overland flow modelling hypotheses with a multi-objective calibration using discharge and sediment data. Hydrol. Process. 2022, 36, e14767. [Google Scholar] [CrossRef] [PubMed]
  57. Langhammer, J.; Bernsteinová, J.; Miřijovský, J. Building a High-Precision 2D Hydrodynamic Flood Model Using UAV Photogrammetry and Sensor Network Monitoring. Water 2017, 9, 861. [Google Scholar] [CrossRef]
  58. Bouizrou, I.; Chahinian, N.; Perrin, J.L.; Müller, R.; Rais, N. Network Representation in Hydrological Modelling on Urban Catchments in Data-Scarce Contexts: A Case Study on the Oued Fez Catchment (Morocco). J. Hydrol. Reg. Stud. 2021, 34, 100800. [Google Scholar] [CrossRef]
Water 16 02594 g001aWater 16 02594 g001b
Figure 1. Study area: (a) Study site location in Haiti; (b) Rouyonne river channel and its upper watershed; (c) Altitude distribution in the upper watershed.
Figure 1. Study area: (a) Study site location in Haiti; (b) Rouyonne river channel and its upper watershed; (c) Altitude distribution in the upper watershed.
Water 16 02594 g001aWater 16 02594 g001b
Water 16 02594 g002
Figure 2. Illustration of image acquisition: (a) Aerial image of the river during the dry season; (b) DJI drone equipped with a GoPro camera (sensor type: 1/2.3” CMOS; camera type: sport/action camera; equivalent focal length: 16.41 mm; lens type: wide angle; aperture: f/2.8).
Figure 2. Illustration of image acquisition: (a) Aerial image of the river during the dry season; (b) DJI drone equipped with a GoPro camera (sensor type: 1/2.3” CMOS; camera type: sport/action camera; equivalent focal length: 16.41 mm; lens type: wide angle; aperture: f/2.8).
Water 16 02594 g002
Water 16 02594 g003
Figure 3. Illustration of the morphological changes in the Rouyonne river channel: (a) Cross-section 54—54 of the Rouyonne River; (b) Bathymetric data comparison between UAV photogrammetry DTM (2022) and the manual survey (2022); (c) Evolution of morphological changes between 2014 and 2022 in cross-section 54—54.
Figure 3. Illustration of the morphological changes in the Rouyonne river channel: (a) Cross-section 54—54 of the Rouyonne River; (b) Bathymetric data comparison between UAV photogrammetry DTM (2022) and the manual survey (2022); (c) Evolution of morphological changes between 2014 and 2022 in cross-section 54—54.
Water 16 02594 g003
Water 16 02594 g004aWater 16 02594 g004b
Figure 4. Illustration of the damage caused by the 3 June 2023 event: (a) Buildings destroyed by the flood in the town of Léogâne; (b) Pressure sensor broken by flood at the measuring section; (c) High-water mark measurement; (d) Spatial distribution of high-water marks measured for the 2–3 June 2023 event.
Figure 4. Illustration of the damage caused by the 3 June 2023 event: (a) Buildings destroyed by the flood in the town of Léogâne; (b) Pressure sensor broken by flood at the measuring section; (c) High-water mark measurement; (d) Spatial distribution of high-water marks measured for the 2–3 June 2023 event.
Water 16 02594 g004aWater 16 02594 g004b
Water 16 02594 g005
Figure 5. Illustration of the unstructured mesh of the study area.
Figure 5. Illustration of the unstructured mesh of the study area.
Water 16 02594 g005
Water 16 02594 g006
Figure 6. Cross-section at the limnimetric station with the equivalent rectangle (discontinuous black line) used in the BaRatin method.
Figure 6. Cross-section at the limnimetric station with the equivalent rectangle (discontinuous black line) used in the BaRatin method.
Water 16 02594 g006
Water 16 02594 g007
Figure 7. Relationships between water depth and discharge at the measurement section: comparison of the Bayesian rating curve with uncertainties and the uniform-flow assumption.
Figure 7. Relationships between water depth and discharge at the measurement section: comparison of the Bayesian rating curve with uncertainties and the uniform-flow assumption.
Water 16 02594 g007
Water 16 02594 g008
Figure 8. Hydrological modeling: (a) Calibration (August 2022); (b) Validation (September 2022).
Figure 8. Hydrological modeling: (a) Calibration (August 2022); (b) Validation (September 2022).
Water 16 02594 g008
Water 16 02594 g009
Figure 9. Hydrological modeling applied to the event of 2–3 June 2023.
Figure 9. Hydrological modeling applied to the event of 2–3 June 2023.
Water 16 02594 g009
Water 16 02594 g010
Figure 10. Illustration of the 2–3 June 2023 event simulation.
Figure 10. Illustration of the 2–3 June 2023 event simulation.
Water 16 02594 g010
Water 16 02594 g011
Figure 11. Model evaluation: Comparison between the observed and modeled water depths.
Figure 11. Model evaluation: Comparison between the observed and modeled water depths.
Water 16 02594 g011
Water 16 02594 g012
Figure 12. Identification of the overflow points on the Rouyonne river: (a) Right bank overtopping to downtown Léogâne; (b) Left bank overtopping where the probe was installed.
Figure 12. Identification of the overflow points on the Rouyonne river: (a) Right bank overtopping to downtown Léogâne; (b) Left bank overtopping where the probe was installed.
Water 16 02594 g012
Table 1. Data used in this study.
Table 1. Data used in this study.
Data SourcesResolution Explanations
Terrain dataDTM of CNIGS1.5 mOfficial data based on a LiDAR survey in 2014–2016 by IGN FI.
Drone photogrammetry0.1 mData were constructed during this study to update the bathymetry of the Rouyonne River.
Rainfall data3 rain gauges1 minCalibration of the hydrological model (21–22 August 2022), validation (20 September 2022), and application to the flood event (2–3 June 2023).
Hydrometric dataOTT PLS pressure sensor;1 minThree sets of water-level data for the same dates at the measuring station.
magnetic induction current meter “MF Pro” Maximum water depth sampled for construction of the water depth–discharge relationship: 0.40 m.
Inundation dataField measurement 21 water-level measurement points were collected (24 h after the 2–3 June 2023 event) from high-water marks.
Table 2. Hydrological model assessment.
Table 2. Hydrological model assessment.
Calibrated Parameters
S = 82.44 mmV0 = 5.43 m/sds = 1ω = 0.02K0 = 0.73
Statistical scores: calibration
KGE = 0.923
NSE = 0.878
Statistical scores: validation
KGE = 0.906
NSE = 0.925
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Louis, R.; Zech, Y.; Joseph, A.; Gonomy, N.; Soares-Frazao, S. Flood Modeling of the June 2023 Flooding of Léogâne City by the Overflow of the Rouyonne River in Haiti. Water 2024, 16, 2594. https://doi.org/10.3390/w16182594

AMA Style

Louis R, Zech Y, Joseph A, Gonomy N, Soares-Frazao S. Flood Modeling of the June 2023 Flooding of Léogâne City by the Overflow of the Rouyonne River in Haiti. Water. 2024; 16(18):2594. https://doi.org/10.3390/w16182594

Chicago/Turabian Style

Louis, Rotchild, Yves Zech, Adermus Joseph, Nyankona Gonomy, and Sandra Soares-Frazao. 2024. "Flood Modeling of the June 2023 Flooding of Léogâne City by the Overflow of the Rouyonne River in Haiti" Water 16, no. 18: 2594. https://doi.org/10.3390/w16182594

APA Style

Louis, R., Zech, Y., Joseph, A., Gonomy, N., & Soares-Frazao, S. (2024). Flood Modeling of the June 2023 Flooding of Léogâne City by the Overflow of the Rouyonne River in Haiti. Water, 16(18), 2594. https://doi.org/10.3390/w16182594

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop