the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Mar 2025
Climate change impacts on floods in West Africa: New insight from two large-scale hydrological models
Abstract. West Africa is projected to face unprecedented shifts in temperature and extreme precipitation patterns as a result of climate change. The devastating impacts of river flooding are already being felt in most West African countries, emphasizing the urgent need for comprehensive insights into the frequency and magnitude of floods to guide the design of hydraulic infrastructure for effective flood risk mitigation and water resource management. Despite its significant socio-economic and environmental impacts, flood hazards remain poorly documented in West Africa due to the data-related challenges. This study aims to fill this knowledge gap by providing a large-scale analysis of flood frequency and magnitudes across West Africa, focusing on how climate change may influence future flood trends. To achieve this, we have used two large-scale hydrological models driven by five bias-corrected CMIP6 climate models under two Shared Socioeconomic Pathways (SSPs). The Generalized Extreme Value (GEV) distribution was utilized to analyze trends and detect change points by comparing multiple non-stationary GEV models across historical and future periods for a set of 58 catchments. Both hydrological models consistently projected increases in flood frequency and magnitude across West Africa, despite their differences in hydrological processes representation and calibration schemes. Flood magnitude is projected to increase for 94 % of the stations, with some locations experiencing increases exceeding 45 % in magnitude. In addition, the majority of trends are starting from the historical period, under both SSP2-4.5 and SSP5-8.5. The findings from this study provide regional-scale insights into the evolving flood risks across West Africa and highlight the urgent need for climate-resilient strategies to safeguard populations and infrastructure against the increasing threat of flood hazards.
-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
-
Preprint
(3057 KB)
-
Supplement
(543 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(3057 KB) - Metadata XML
-
Supplement
(543 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-130', Anonymous Referee #1, 14 Apr 2025
This manuscript presents an interesting analysis of possible future flood hazard in West Africa under climate change. Overall, the manuscript is well written and the material is well presented. It contains a few typos that I have not listed here, but I have listed a few spots below where I ask for clarification.
The manuscript builds on a range of methods that are mostly well established in the scientific literature. Thus, its methodological novelty is limited. However, I don’t see this as reason for concern here. The authors have developed a meaningful workflow, integrating a rather wide range of methods. In particular, I like the systematic approach of section 2.6.3 where they determine the appropriate temporal function for the non-stationary GEV – in most papers that use the non-stationary GEV, the choice of the temporal function is based on ad-hoc decisions.
The manuscript provides important data for a region which is highly vulnerable to flooding and is characterized by data-scarcity. Hence, I would like to see this study being published.
Major comments:
Line 243: The study uses 2 SSPs, namely SSP2-4.5 and SSP5-8.5. Is this really a good choice? Please justify why you have selected (only) 2 SSPs, and particularly these 2 SSPs. Specifically, SSP5-8.5 is often criticised for being overly pessimistic.
Line 299: If I understand correctly, you use the flood time series of the region to first estimate the distribution of the GEV shape parameter via L-moments, assuming a normal distribution. Then you use this result as prior for fitting the GEV to the same flood time series. In that way, you seem to the use the same data for estimating the prior and the posterior distribution. But does this approach not violate the principle that the prior should represent information independent of the observed data? Please clarify this point.
Line 422: I feel that the paragraph on the field significance and FDR requires a bit more explanation to be easily followed. For example, it should be made very clear that here you look at the significance of trends when you look at all stations in your region. Also, explain what the local null hypotheses and the global null hypotheses are.
Line 462: I would like to see a more detailed discussion about the causes of the difference in performance of the 2 models. The manuscript nicely lists 3 possible reasons, but it is unclear what the contribution of these reasons is. I understand that it may not be possible (within the scope of this manuscript) to estimate these contributions, but it would be helpful for the reader to better understand how important spatial resolution vs hydrological processes vs calibration is.
Line 613: The authors find that their “… results are consistent with previous studies that argued for the ongoing rising trend in extreme streamflow across the West African catchments ...”. I assume that the current manuscript goes well beyond the papers cited that have already argued that extreme streamflow is rising. It would be good to add some explanation in what regard the current manuscript goes beyond existing studies.
Line 631 and Figure 8: Why do you use here mean streamflow? Shouldn’t you use AMF series?
Minor comments:
Line 91: “ … updating these hydrological standards …”: Please clarify what you mean by hydrological standards. Do you mean the databases?
Line 108: Please clarify what you mean by “… the sensitivity of different climate models contrasting warming in the North Atlantic and Mediterranean Sea, which are known to influence the West African Monsoon (Bichet et al., 2020; Monerie et al., 2023), and due to contrasting emission scenarios …”: Do you mean that GCMs are sensitive to the warming of both seas, and that this warming is differently simulated by different models?
Line 152: What stands the I for in “… Inter-ITCZ …”?
Line 164: What do you mean by “… nearly half of Africa's continental watersheds are located in West Africa …”? West Africa covers about one-fifth of the African continent, but contains nearly half of the watersheds? What do you mean by continental here?
Line 184: “… the white lines …”: The lines are not really white.
Line 209: These numbers are the longitude, latitude ranges? Please clarify.
Line 231: What is the reason for using different datasets to bias-correct the GCM output for the HMF-WA and the LISFLOOD model? I propose that you also add a bit more explanation about these 2 datasets. In which regards are they different?
Line 277: “… each GEV parameter […] thus guiding effective flood risk management (Lawrence, 2020)…”. I was triggered by this statement and checked the associated reference (Lawrence). However, I could not find any discussion in this reference how different values of the 3 GEV parameters would guide risk management. Your following sentences explain the parameters, and you give one link between the shape parameter and design, but still I find it hard to speak of “… guiding…” in this regard. In case you want to keep this statement, then I propose that you are more explicit. For instance, would you increase the freebord of embankments for catchments/stations that have a higher scale parameter (and thus uncertainty)? Or what would you do for a catchment with a high shape parameter? Only increasing the embankments or also invest more in disaster management in contrast to a catchment with a low shape parameter?
Line 315: “… stations at which the null hypothesis … is rejected …”: Please specify what exactly the null hypothesis is. Is it that the simulated annual flood peaks follow the same distribution as the observed flood peaks? If yes, does this mean that you use all stations, independent of whether the models represent the observed floods well?
Line 362: Here SGEV occurs, but this abbreviation is only explained later.
Line 44.2: What exactly do you mean by “… the hydrological model is considered to perform poorly at that station…”? Have you discarded these models? If yes, what does this mean for the following analyses and metrics? For instance, then you probably do not have 5 models at each station in Figure 2.
Figure 2: I find the markers a bit disturbing, and the color not easy to see. Wouldn’t it be easier to have filled markers (circles and real squares – not these squares divided into 4 smaller squares)?
Line 472: Circles and squares show 60-100% and 0-20%, respectively. How about stations with 20-40% failure rate? And you do you use these 2 classes? Why not using 6 classes (from 5 out of 5 models fail to 0 out of 5 models fail)?
Figure 5: Please explain in the figure caption what ‘climate signal’ is – I assume it is the ratio that you have introduced in Line 324, but this should be clear.
Line 579: Delta Flood is mentioned here, but the exact definition follows only a few lines later.
Figure 6: You could add the correlation coefficients in the sub-plots. That would substitute Table S1, and the reader would have the summary metrics directly when he/she looks at Figure 6.
Figure 9: You could add pie charts in the sub-plots as in Figure 8. That would summarize the information for the reader.
Figure 10: (1) The GEV1 model shows a linear trend over the entire time period, correct? Then its starting year will be in the first year of the time period. Does it really make sense to say there is a significant breakpoint? A linear trend has no breakpoint. (2) The GEV3 model has 2 linear trends with a breakpoint in-between. Wouldn’t it be more interesting to show the breakpoint in-between? And I think it would be interesting to understand how these 2 trends look like, for example, do we have cases where floods decrease before the breakpoint and increase after it? (3) The starting years / colors are not so easy to see. Maybe use filled markers.
Citation: https://doi.org/10.5194/egusphere-2025-130-RC1 - AC1: 'Reply on RC1', Yves Tramblay, 13 May 2025
-
RC2: 'Comment on egusphere-2025-130', Anonymous Referee #2, 15 Apr 2025
This study performed a regional-scale assessment of climate change impacts on flood for Western Africa, using two large-scale hydrological models with the bias-corrected CMIP6 climate projections. I think the study has high potential to form valuable knowledge base of the likely changes in flood in Western Africa, but I have some major concerns on the approach taken in hydrologically modelling, which limited my capacity to assess the results presented. As such, I’d like to seek further clarification and justification from the authors on their chosen approach, or reconsideration of alternative approach, before proceeding to further review of the results.
General comments:
- Given the substantial lack of data in the study region, I’m wondering about the value of using rather complicated hydrological models (distributed and semi-physical) rather than simpler models (e.g., lumped conceptual models)? There is a lack of 1) motivation for exploring distributed and semi-physical modeling approach within the study objective (in the Introduction); 2) justification of modelling approach within Section 2.3 of the Materials and Methods. The start of the Introduction also touched on the challenge with data scarcity for the study region, which seems to suggest that uncertainties from input data might affect modelling (especially for more complex models which has higher data requirement) to some large degree - some assessments and/or discussion on this aspect would be useful.
- In the current analyses, the HMF-WA model has not been calibrated, while calibration for LISFLOOD seems to be done previously which are not part of this study. This attracts several major questions on the modelling approach:
- The disadvantage of not calibrating HMF-WA is clearly demonstrated in the results (Figure 2), the largely unsatisfactory performance of the model suggests that we have low confidence that it could even well represent the historical flood events. Although the results is accompanied by brief discussion on this issue that ‘projections of climate change impacts on African hydrological trends were produced using…’ – the decision to use an uncalibrated model is generally not standard in the international literature and require much more justification.
- On the LISFLOOD model, further justifications and details are required on the calibration process, including the input data, objective function, and cross-validation (if any). Such information on calibration is necessary for the reviewers/readers to assess the suitability of these models for the purpose of the study.
- Further, it is not clear whether the LISFLOOD models have been explicitly calibrated/evaluated to a flood context. Please see an example of calibration of hydrological models tailored to rarer floods, would the models used in this study benefit from a flood-centered calibration? Wasko et al., 2023. https://doi.org/10.1016/j.jhydrol.2023.129403
- Section 2.2 on data: given the substantial challenges in data availability for the study region, I think specific attention should be paid to the representativeness of the data to ensure they are not biased towards a specific type of catchment, and/or specific time periods. I think this can be achieved by adding the following details:
- A summary table (possibly in the Supplementary) of the selected study sites, with information on their catchment areas, mean annual catchment-averaged rainfall, mean annual streamflow, and the range of years over which streamflow data is available.
- The study site selection criteria mentioned ‘a minimum of 10 years streamflow time series between 1950 and 2018’ – does this allow for data gaps (i.e., days with missing or low-quality streamflow data), and if so, what is the maximum length of gaps allowed?
- How variable is the land uses in this study region? If they are rather heterogeneous, a summary of key land use types in each catchment would also be useful.
- Sources of input data for the hydrological models e.g., rainfall, temperature – it is unclear where they are from, it is implied from the later Section 2.5 that rainfall and temperature were from GCM rather than observed, but it would be helpful to clarify this earlier in the data section.
- Section 2.3: I understand that the details of the two hydrological models are presented in the corresponding papers cited, but I think the readers could benefit from some additional background on these models, at least covering the key processes represented in each model on converting rainfall to runoff. This information is currently only partly available for the HWF-WA model (with only the recently added process representations listed) and not communicated for the LISFLOOD model. After presenting these, I’d also love to see a quick summary of the key differences between the models to justify your point in the Abstract that the two models ‘differ in their hydrological process representation’.
Specific comments:
- Line 51 – it will be clearer if the change in flood magnitude can be summarized specific to the flood return period(s) investigated.
- 1 caption: ‘grey lines’ instead of ‘white lines’?
- Line 177 – decision on ‘low regulation’ catchments: the Supplementary Fig. 1 suggested that this is based on whether there is a dam located near the watershed outlet, with no information what defines a dam ‘near’ or ‘far from’ the outlet – was this based on visual inspection, or a threshold distance used? If the latter, how was the threshold distance determined?
- Section 2.6.1 – the introductory section for GEV is very informative, however, I think it could benefit from additional information on what positive and negative shape parameters mean, which seem to be useful context to the subsequent discussion on the plausible values of the shape parameter.
- Line 293: ‘…estimate the GEV parameters in a non-stationary context’ – can you elaborate a bit on what exactly this refers to – is it about fitting multiple GEVs to different periods of the data to represent non-stationary conditions?
Citation: https://doi.org/10.5194/egusphere-2025-130-RC2 - AC2: 'Reply on RC2', Yves Tramblay, 13 May 2025
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-130', Anonymous Referee #1, 14 Apr 2025
This manuscript presents an interesting analysis of possible future flood hazard in West Africa under climate change. Overall, the manuscript is well written and the material is well presented. It contains a few typos that I have not listed here, but I have listed a few spots below where I ask for clarification.
The manuscript builds on a range of methods that are mostly well established in the scientific literature. Thus, its methodological novelty is limited. However, I don’t see this as reason for concern here. The authors have developed a meaningful workflow, integrating a rather wide range of methods. In particular, I like the systematic approach of section 2.6.3 where they determine the appropriate temporal function for the non-stationary GEV – in most papers that use the non-stationary GEV, the choice of the temporal function is based on ad-hoc decisions.
The manuscript provides important data for a region which is highly vulnerable to flooding and is characterized by data-scarcity. Hence, I would like to see this study being published.
Major comments:
Line 243: The study uses 2 SSPs, namely SSP2-4.5 and SSP5-8.5. Is this really a good choice? Please justify why you have selected (only) 2 SSPs, and particularly these 2 SSPs. Specifically, SSP5-8.5 is often criticised for being overly pessimistic.
Line 299: If I understand correctly, you use the flood time series of the region to first estimate the distribution of the GEV shape parameter via L-moments, assuming a normal distribution. Then you use this result as prior for fitting the GEV to the same flood time series. In that way, you seem to the use the same data for estimating the prior and the posterior distribution. But does this approach not violate the principle that the prior should represent information independent of the observed data? Please clarify this point.
Line 422: I feel that the paragraph on the field significance and FDR requires a bit more explanation to be easily followed. For example, it should be made very clear that here you look at the significance of trends when you look at all stations in your region. Also, explain what the local null hypotheses and the global null hypotheses are.
Line 462: I would like to see a more detailed discussion about the causes of the difference in performance of the 2 models. The manuscript nicely lists 3 possible reasons, but it is unclear what the contribution of these reasons is. I understand that it may not be possible (within the scope of this manuscript) to estimate these contributions, but it would be helpful for the reader to better understand how important spatial resolution vs hydrological processes vs calibration is.
Line 613: The authors find that their “… results are consistent with previous studies that argued for the ongoing rising trend in extreme streamflow across the West African catchments ...”. I assume that the current manuscript goes well beyond the papers cited that have already argued that extreme streamflow is rising. It would be good to add some explanation in what regard the current manuscript goes beyond existing studies.
Line 631 and Figure 8: Why do you use here mean streamflow? Shouldn’t you use AMF series?
Minor comments:
Line 91: “ … updating these hydrological standards …”: Please clarify what you mean by hydrological standards. Do you mean the databases?
Line 108: Please clarify what you mean by “… the sensitivity of different climate models contrasting warming in the North Atlantic and Mediterranean Sea, which are known to influence the West African Monsoon (Bichet et al., 2020; Monerie et al., 2023), and due to contrasting emission scenarios …”: Do you mean that GCMs are sensitive to the warming of both seas, and that this warming is differently simulated by different models?
Line 152: What stands the I for in “… Inter-ITCZ …”?
Line 164: What do you mean by “… nearly half of Africa's continental watersheds are located in West Africa …”? West Africa covers about one-fifth of the African continent, but contains nearly half of the watersheds? What do you mean by continental here?
Line 184: “… the white lines …”: The lines are not really white.
Line 209: These numbers are the longitude, latitude ranges? Please clarify.
Line 231: What is the reason for using different datasets to bias-correct the GCM output for the HMF-WA and the LISFLOOD model? I propose that you also add a bit more explanation about these 2 datasets. In which regards are they different?
Line 277: “… each GEV parameter […] thus guiding effective flood risk management (Lawrence, 2020)…”. I was triggered by this statement and checked the associated reference (Lawrence). However, I could not find any discussion in this reference how different values of the 3 GEV parameters would guide risk management. Your following sentences explain the parameters, and you give one link between the shape parameter and design, but still I find it hard to speak of “… guiding…” in this regard. In case you want to keep this statement, then I propose that you are more explicit. For instance, would you increase the freebord of embankments for catchments/stations that have a higher scale parameter (and thus uncertainty)? Or what would you do for a catchment with a high shape parameter? Only increasing the embankments or also invest more in disaster management in contrast to a catchment with a low shape parameter?
Line 315: “… stations at which the null hypothesis … is rejected …”: Please specify what exactly the null hypothesis is. Is it that the simulated annual flood peaks follow the same distribution as the observed flood peaks? If yes, does this mean that you use all stations, independent of whether the models represent the observed floods well?
Line 362: Here SGEV occurs, but this abbreviation is only explained later.
Line 44.2: What exactly do you mean by “… the hydrological model is considered to perform poorly at that station…”? Have you discarded these models? If yes, what does this mean for the following analyses and metrics? For instance, then you probably do not have 5 models at each station in Figure 2.
Figure 2: I find the markers a bit disturbing, and the color not easy to see. Wouldn’t it be easier to have filled markers (circles and real squares – not these squares divided into 4 smaller squares)?
Line 472: Circles and squares show 60-100% and 0-20%, respectively. How about stations with 20-40% failure rate? And you do you use these 2 classes? Why not using 6 classes (from 5 out of 5 models fail to 0 out of 5 models fail)?
Figure 5: Please explain in the figure caption what ‘climate signal’ is – I assume it is the ratio that you have introduced in Line 324, but this should be clear.
Line 579: Delta Flood is mentioned here, but the exact definition follows only a few lines later.
Figure 6: You could add the correlation coefficients in the sub-plots. That would substitute Table S1, and the reader would have the summary metrics directly when he/she looks at Figure 6.
Figure 9: You could add pie charts in the sub-plots as in Figure 8. That would summarize the information for the reader.
Figure 10: (1) The GEV1 model shows a linear trend over the entire time period, correct? Then its starting year will be in the first year of the time period. Does it really make sense to say there is a significant breakpoint? A linear trend has no breakpoint. (2) The GEV3 model has 2 linear trends with a breakpoint in-between. Wouldn’t it be more interesting to show the breakpoint in-between? And I think it would be interesting to understand how these 2 trends look like, for example, do we have cases where floods decrease before the breakpoint and increase after it? (3) The starting years / colors are not so easy to see. Maybe use filled markers.
Citation: https://doi.org/10.5194/egusphere-2025-130-RC1 - AC1: 'Reply on RC1', Yves Tramblay, 13 May 2025
-
RC2: 'Comment on egusphere-2025-130', Anonymous Referee #2, 15 Apr 2025
This study performed a regional-scale assessment of climate change impacts on flood for Western Africa, using two large-scale hydrological models with the bias-corrected CMIP6 climate projections. I think the study has high potential to form valuable knowledge base of the likely changes in flood in Western Africa, but I have some major concerns on the approach taken in hydrologically modelling, which limited my capacity to assess the results presented. As such, I’d like to seek further clarification and justification from the authors on their chosen approach, or reconsideration of alternative approach, before proceeding to further review of the results.
General comments:
- Given the substantial lack of data in the study region, I’m wondering about the value of using rather complicated hydrological models (distributed and semi-physical) rather than simpler models (e.g., lumped conceptual models)? There is a lack of 1) motivation for exploring distributed and semi-physical modeling approach within the study objective (in the Introduction); 2) justification of modelling approach within Section 2.3 of the Materials and Methods. The start of the Introduction also touched on the challenge with data scarcity for the study region, which seems to suggest that uncertainties from input data might affect modelling (especially for more complex models which has higher data requirement) to some large degree - some assessments and/or discussion on this aspect would be useful.
- In the current analyses, the HMF-WA model has not been calibrated, while calibration for LISFLOOD seems to be done previously which are not part of this study. This attracts several major questions on the modelling approach:
- The disadvantage of not calibrating HMF-WA is clearly demonstrated in the results (Figure 2), the largely unsatisfactory performance of the model suggests that we have low confidence that it could even well represent the historical flood events. Although the results is accompanied by brief discussion on this issue that ‘projections of climate change impacts on African hydrological trends were produced using…’ – the decision to use an uncalibrated model is generally not standard in the international literature and require much more justification.
- On the LISFLOOD model, further justifications and details are required on the calibration process, including the input data, objective function, and cross-validation (if any). Such information on calibration is necessary for the reviewers/readers to assess the suitability of these models for the purpose of the study.
- Further, it is not clear whether the LISFLOOD models have been explicitly calibrated/evaluated to a flood context. Please see an example of calibration of hydrological models tailored to rarer floods, would the models used in this study benefit from a flood-centered calibration? Wasko et al., 2023. https://doi.org/10.1016/j.jhydrol.2023.129403
- Section 2.2 on data: given the substantial challenges in data availability for the study region, I think specific attention should be paid to the representativeness of the data to ensure they are not biased towards a specific type of catchment, and/or specific time periods. I think this can be achieved by adding the following details:
- A summary table (possibly in the Supplementary) of the selected study sites, with information on their catchment areas, mean annual catchment-averaged rainfall, mean annual streamflow, and the range of years over which streamflow data is available.
- The study site selection criteria mentioned ‘a minimum of 10 years streamflow time series between 1950 and 2018’ – does this allow for data gaps (i.e., days with missing or low-quality streamflow data), and if so, what is the maximum length of gaps allowed?
- How variable is the land uses in this study region? If they are rather heterogeneous, a summary of key land use types in each catchment would also be useful.
- Sources of input data for the hydrological models e.g., rainfall, temperature – it is unclear where they are from, it is implied from the later Section 2.5 that rainfall and temperature were from GCM rather than observed, but it would be helpful to clarify this earlier in the data section.
- Section 2.3: I understand that the details of the two hydrological models are presented in the corresponding papers cited, but I think the readers could benefit from some additional background on these models, at least covering the key processes represented in each model on converting rainfall to runoff. This information is currently only partly available for the HWF-WA model (with only the recently added process representations listed) and not communicated for the LISFLOOD model. After presenting these, I’d also love to see a quick summary of the key differences between the models to justify your point in the Abstract that the two models ‘differ in their hydrological process representation’.
Specific comments:
- Line 51 – it will be clearer if the change in flood magnitude can be summarized specific to the flood return period(s) investigated.
- 1 caption: ‘grey lines’ instead of ‘white lines’?
- Line 177 – decision on ‘low regulation’ catchments: the Supplementary Fig. 1 suggested that this is based on whether there is a dam located near the watershed outlet, with no information what defines a dam ‘near’ or ‘far from’ the outlet – was this based on visual inspection, or a threshold distance used? If the latter, how was the threshold distance determined?
- Section 2.6.1 – the introductory section for GEV is very informative, however, I think it could benefit from additional information on what positive and negative shape parameters mean, which seem to be useful context to the subsequent discussion on the plausible values of the shape parameter.
- Line 293: ‘…estimate the GEV parameters in a non-stationary context’ – can you elaborate a bit on what exactly this refers to – is it about fitting multiple GEVs to different periods of the data to represent non-stationary conditions?
Citation: https://doi.org/10.5194/egusphere-2025-130-RC2 - AC2: 'Reply on RC2', Yves Tramblay, 13 May 2025
Peer review completion
Journal article(s) based on this preprint
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 699 | 165 | 20 | 884 | 55 | 15 | 37 |
- HTML: 699
- PDF: 165
- XML: 20
- Total: 884
- Supplement: 55
- BibTeX: 15
- EndNote: 37
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Cited
Serigne Bassirou Diop
Job Ekolu
Yves Tramblay
Bastien Dieppois
Stefania Grimaldi
Ansoumana Bodian
Juliette Blanchet
Ponnambalam Rameshwaran
Peter Salamon
Benjamin Sultan
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(3057 KB) - Metadata XML
-
Supplement
(543 KB) - BibTeX
- EndNote
- Final revised paper