the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Sep 2023
Assessing the impact of climate change on high return levels of peak flows in Bavaria applying the CRCM5 Large Ensemble
Abstract. Severe floods with extreme return periods of 100 years and beyond have been observed in several large rivers in Bavaria in the last three decades. Flood protection structures are typically designed based on a 100-year event, relying on statistical extrapolations of relatively short observation time series while ignoring potential temporal non-stationarity. However, future precipitation projections indicate an increase in the frequency and intensity of extreme rainfall events, as well as a shift in seasonality. This study aims to examine the impact of climate change on the 100-year flood (HF100) events on 98 hydrometric gauges within the Hydrological Bavaria. A hydrological climate change impact (CCI) modelling chain consisting of a regional single model initial condition large ensemble (SMILE) and a single hydrological model was created. The 50 equally probable members of the CRCM5-LE were used to drive the hydrological model WaSiM to create a hydro-SMILE. As a result, a database of 1,500 model years (50 members x 30 years) per investigated time period was established for extreme value analysis (EVA) to illustrate the benefit of the hydro-SMILE approach for a robust estimation of the HF100 based on annual maxima (AM), and to examine the CCI on the frequency and intensity of HF100 in different discharge regimes under a strong emission scenario (RCP8.5). The results demonstrate that the hydro-SMILE approach provides a clear advantage for a robust estimation of the HF100 using empirical probability on 1,500 AM compared to its estimation using the generalized extreme value (GEV) distribution on 1,000 samples of typically available time series size of 30, 100, and 200 years. Thereby, by applying the hydro-SMILE framework the uncertainty from statistical estimation can be reduced. The CCI on the HF100 varies for different flow regimes, with snowmelt-driven catchments experiencing severe increases in frequency and intensity, leading to unseen extremes that impact the distribution. Pluvial regimes show a lower intensification or even decline. The study highlights the added value of using hydrological SMILEs to project future flood return levels.
-
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
(1545 KB)
-
Supplement
(179 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1545 KB) - Metadata XML
-
Supplement
(179 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2019', Anonymous Referee #1, 26 Oct 2023
In this study, the authors assess the impacts of climate change on the 100-year flood events in several rivers in Bavaria region, in which most of the flood protection infrastructures are designed based on the 100-year flood events. Specifically, the authors explore a large ensemble of 50 members of CanESM2 climate model, which are produced using different initial conditions but the same model structure, parameters, and a high emission scenario (RCP8.5). A hydrological model is then used to simulate river discharge, followed by a dataset of 1500 model years (30 years of the reference period x 50 members), which are used for extreme value analysis. Also, the authors show the benefit of using hydro-SMILE in providing a more robust extreme hydrological discharge values under climate change impacts. In overall the study is beneficial for the study region. However, there are still some concerns, which require further improvements. My detailed comments are below.
- The fourth paragraph in Introduction (Lines 73-77, Page 3) is vague. The two first sentences do not seem to be the reason for the choice of study area.
- Can the authors explain the choices of CanESM2 and the use of RCP8.5 only?
- The study area has abundant in situ data. Should model parameters (i.e., soil properties) be calibrated?
- Since the reliability of the hydrological model affects the simulated discharge and the further analysis, the performance of the hydrological model should be presented and discussed in more detail. For example, for 16 gauges having NSE lower than 0.5 and 5 gauges having KGE lower than 0.5 (Lines 203-204, Page 7), an explanation is needed to show that the unsatisfactory is acceptable. For the other gauges with NSE and KGE higher than 0.5, how much higher than 0.5 are they? I think it is worth having maps that show the value of model performance metrics at all gauges.
- Panels c, d, and e in Fig. 7 do not show the entire variation ranges.
- I think it is worth having a map that visualizes the spatial variation of the change in return period under climate change impacts, some interesting insights might be found. I am curious about the difference between the changes in return period in mainstream and tributaries. Similar to the change in magnitude/intensity of the 100-year flood events under climate change impacts.
- The authors show that using hydro-SMILE provides a more robust extreme hydrological discharge values under climate change impacts, but do not discuss on how to make use of that finding in designing flood protection infrastructures, the problem that authors state from the beginning of the paper.
- [Technical correction] Line 297, Page 12: “0.49 and 1.91 for 100 AM values (panel c) and 0.56 and 1.60 for 200 AM values (panel e)”. Should it be (panel b) and (panel c)?
Citation: https://doi.org/10.5194/egusphere-2023-2019-RC1 - AC2: 'Reply on RC1', Florian Willkofer, 28 Nov 2023
-
RC2: 'Comment on egusphere-2023-2019', Anonymous Referee #2, 30 Oct 2023
Summary: The manuscript employed a large ensemble of hydrologic simulations driven by a climate model (Hydro-SMILE) to investigate the future changes in peak flow characteristics and dynamics. Hydro-SMILE can be a powerful tool for extreme value estimates in hydrology. The approach, based on validated physics-based hydrologic models and large ensemble climate data, is especially helpful for understanding the changes in magnitude, frequency, and dynamics in high-return level peak flow events. However, the authors did not fully utilize the data they generated and the focus of the manuscript has been on how beneficial such a tool can be. Further and more in-depth analyses on the changes in the characteristics of high return level peak flow events are needed to improve the manuscript. See below my major comments. In addition, I provide language edits/suggestions in minor comments for places where I think clarity is lacking.
Major comments:
1. The manuscript has a title of “…high return levels of peak flows…” but specifically focused on 100-year floods. With a large ensemble, the authors could investigate a range of high return levels of peak flows and see how the frequency, magnitude, and dynamics are projected to change in the future climate.
2. The manuscript focused on proving that it is beneficial to have a large ensemble to estimate extreme peak flow events (Sections 3.1 and Figures 4 and 5), which, I think, is very obvious so I suggest moving them to the supplementary. The authors have generated a powerful dataset for extreme peak flow estimation, however, there is no analysis of the changes in flood frequency and magnitude. The authors are suggested to substantially expand the analysis on flood frequency and characteristics. See Yu et al. (2020) for an example of flood frequency analysis.
Yu, G., Wright, D. B., & Li, Z. (2020). The upper tail of precipitation in convection-permitting regional climate models and their utility in nonstationary rainfall and flood frequency analysis. Earth's Future, 8, e2020EF001613. https://doi.org/10.1029/2020EF001613
3. The authors only gave limited information on the evaluation results of the hydrologic model which are essential for building confidence in the following analysis. I suggest including figures and/or tables showing the evaluation results such as time series of flow events with other quantitative metrics such as correlation coefficient, % bias, root mean square error, KGE, NSE, etc. One related question would be how the level of trust (LOT) is calculated.
4. The changing dynamics in the future climate (Section 3.2) are very interesting and worth digging into. The authors could dig into it with a mechanistic investigation of possible explanations for why they see such changes in future projections. For example, linking snow water equivalent and rain characteristics to the dynamical changes that are projected at the nivo-pluvial stations.
Minor comments:
Lines 57-59: it is unclear how prediction is a reason for challenges in modeling and predicting high flows by Brunner et al. (2021a).
Line 71: change “extraordinary” to “extreme”.
The paragraph starting from line 73: Needs substantial rephrasing. 1) Rephrase the sentence “This approach of high spatiotemporal resolution for climate and hydrological modeling is computationally demanding.” Do the authors mean “This ensemble-based climate and hydrological modeling approach is computationally demanding because of the high spatio-temporal resolution”?
2) Rephrase sentence “However, considering spatially refined catchment features (e.g., slopes, soil characteristics, land use), precise values due to higher temporal resolution, and the application of a SMILE for hydrological modeling supports an enhanced representation of extreme values within models.” Do the authors mean high spatio-temporal resolution of hydro-SMILE is particularly valuable for an enhanced representation of extreme values in models because hydro-SMILE considers spatially-refined catchment features at high temporal resolutions?
3) Rephrase “Thus, this study focuses on the major Bavarian river basins (upper Danube, Main, Inn) with all their tributaries”. It is unclear to me what your study area has to do with the above two statements.
Line 84: Remove “Therefore”.
The paragraph that starts from Line 84: add section numbers throughout the paragraph.
Line 85: Confusing sentence. Remove “…to meet the requirements for the hydrological modeling.”
Line 86: “…hydro-SMILE along...” should be “…along with…”.
Line 95: Remove “As a result”
Line 102: “…(up to 1100 mm precipitation sums in the north, 2500 mm in the south; an average temperature of 10 °C in the north, down to 5 °C (-8 °C on alpine summits)…”. Are the authors referring to annual total precipitation and annual mean temperature? Be clear on that. Also, be sure to mention the data sources for these numbers - are they from Poschlod et al. (2020) as well?
Line 108: “The major river catchments were divided into a total of 98 smaller sub-catchments based
on a common interest in flood protection and a more detailed variation in catchment characteristics, using a selection of gauges (Willkofer et al., 2020).” Rephrase this sentence. It is unclear to me whether the 98 sub-catchments were divided based on the spatial distribution of the 98 selected gauges or whether the gauges were selected because of the division of the 98 sub-catchments.
Line 125: Figure caption of Figure 2: Also introduce what are SDCLIREF and WaSiM in the Figure caption.
Line 142: What is “T63”?
Line 149: “Furthermore, the individual members of the CRCM5-LE are considered independent for the hydrological evaluation period from 1981 to 2099, as the analysis of variations in temperature and precipitation over land and ocean shows (Leduc et al., 2019).” This is the first time the authors mention “hydrological evaluation period”. This is a confusing sentence. Aren’t the CRCM5-LE individual members independent no matter what time period?
Line 152: “…showing regional and seasonal variations in magnitude over Europe (Leduc et al., 2019).” What variables do the authors mean?
Line 156: add “match” after “were adjusted to”.
Line 157: Change “RCM scale” to “RCM grid”. Did the authors do the interpolation onto the RCM grid? If yes, be clear on what interpolation scheme is used.
Line 160: “…3-hourly correction factors for every quantile and month”. Unclear how the 3-hourly correction factor is applied.
Sentence starting on Line 162: I think the authors want to stress that bias correction is inevitable. Rephrase it to “Despite the benefits (increasing reliability of climate change projections of the hydrological impact model, reducing bias in mean annual discharge) and shortcomings (disrupting feedbacks between fluxes, modification of change signals, assumption of a stationary bias) of bias correction are highly debatable (e.g., Teutschbein and Seibert, 2012; Maraun, 2016; Ehret et al., 2012; Dettinger et al., 2004; Chen et al., 2021; Huang et al., 2014), bias correction is often inevitable for climate change impact studies (Gampe et al., 2019).”
Line 168: For such a topographically complex region as described in the “Study area” section, I’m concerned the statistical downscaling between grids that are so different (from 12 km in RCMs to 500 m in hydrologic models) will lose important spatial heterogeneity across the domain. Does the mass-preserving approach address this problem?
Line 171: “The interpolation result was then applied to the SDCLIREF reference fields (Brunner et al., 2021b)”. Unclear. Do the authors mean the SDCLIREF reference fields are also interpolated using the same method?
Line 194: “minimizing a weighted combination of performance metrics, including Nash and Sutcliff efficiency (NSE; Nash 195 and Sutcliffe, 1970), Kling-Gupta efficiency (KGE; Gupta et al., 2009), the logarithmic NSE and the ratio of root mean squared error to standard deviation (RSR; Moriasi et al. (2007)) (Eq. (1))”. Introducing the overall metric (OM) equation first and then describe what is in the equation. Then, give a threshold - what OM value is considered “good” or “bad”?
Line 203: “(NSE: 16; KGE: 5)” Unclear. What does this mean?
Line 208: “Consequently, the level of trust (LOT) for peak flows of return periods of 5, 10, and 20 years of flood events, introduced in Willkofer et al. (2020) showed a moderate to high confindence for most catchments, with gauges of poor simulated performance yielding a lower LOT with increasing return levels.” Do the authors mean gauges with good performance have higher LOT for peak flows with return periods of 5, 10, and 20 years, whereas gauges with poor performance have lower LOT, especially for peak flows at longer return periods?
Line 214: “The entire modeling period is shortened by ten years to account for the time span it takes the RCM to produce fully independent realizations due to the inertia of the ocean model (Leduc et al., 2019).” I have two comments: 1) I saw that the authors partially address my question for Line 149 here. It would be better to rearrange this part and the sentence on Line 149 such that the 10-year spin-up period and the choice of the evaluation time period are more clearly lined up and explained. 2) Rephrase this sentence to “We focus on 1961—2099 as opposed to 1950 – 2099 to account for the time it takes for the RCM to produce fully independent realizations due to the inertia of the ocean model (Leduc et al., 2019).”
Figure 3: What is “HF T,BM” on the far right?
Line 256 and thereafter: Change “intensity” to magnitude throughout the manuscript.
Line 293: “…as indicated by the spread of the blue markers around the black benchmark
line.” I think the authors mean “… as indicated by the decreasing spread of the blue markers around the benchmark line with increasing sample size.”
Lines 296-297: What are panels a, c, and e?
Figures 1&6: What do “balanced” and “unbalanced” pluvial mean?
Citation: https://doi.org/10.5194/egusphere-2023-2019-RC2 - AC1: 'Reply on RC2', Florian Willkofer, 28 Nov 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2019', Anonymous Referee #1, 26 Oct 2023
In this study, the authors assess the impacts of climate change on the 100-year flood events in several rivers in Bavaria region, in which most of the flood protection infrastructures are designed based on the 100-year flood events. Specifically, the authors explore a large ensemble of 50 members of CanESM2 climate model, which are produced using different initial conditions but the same model structure, parameters, and a high emission scenario (RCP8.5). A hydrological model is then used to simulate river discharge, followed by a dataset of 1500 model years (30 years of the reference period x 50 members), which are used for extreme value analysis. Also, the authors show the benefit of using hydro-SMILE in providing a more robust extreme hydrological discharge values under climate change impacts. In overall the study is beneficial for the study region. However, there are still some concerns, which require further improvements. My detailed comments are below.
- The fourth paragraph in Introduction (Lines 73-77, Page 3) is vague. The two first sentences do not seem to be the reason for the choice of study area.
- Can the authors explain the choices of CanESM2 and the use of RCP8.5 only?
- The study area has abundant in situ data. Should model parameters (i.e., soil properties) be calibrated?
- Since the reliability of the hydrological model affects the simulated discharge and the further analysis, the performance of the hydrological model should be presented and discussed in more detail. For example, for 16 gauges having NSE lower than 0.5 and 5 gauges having KGE lower than 0.5 (Lines 203-204, Page 7), an explanation is needed to show that the unsatisfactory is acceptable. For the other gauges with NSE and KGE higher than 0.5, how much higher than 0.5 are they? I think it is worth having maps that show the value of model performance metrics at all gauges.
- Panels c, d, and e in Fig. 7 do not show the entire variation ranges.
- I think it is worth having a map that visualizes the spatial variation of the change in return period under climate change impacts, some interesting insights might be found. I am curious about the difference between the changes in return period in mainstream and tributaries. Similar to the change in magnitude/intensity of the 100-year flood events under climate change impacts.
- The authors show that using hydro-SMILE provides a more robust extreme hydrological discharge values under climate change impacts, but do not discuss on how to make use of that finding in designing flood protection infrastructures, the problem that authors state from the beginning of the paper.
- [Technical correction] Line 297, Page 12: “0.49 and 1.91 for 100 AM values (panel c) and 0.56 and 1.60 for 200 AM values (panel e)”. Should it be (panel b) and (panel c)?
Citation: https://doi.org/10.5194/egusphere-2023-2019-RC1 - AC2: 'Reply on RC1', Florian Willkofer, 28 Nov 2023
-
RC2: 'Comment on egusphere-2023-2019', Anonymous Referee #2, 30 Oct 2023
Summary: The manuscript employed a large ensemble of hydrologic simulations driven by a climate model (Hydro-SMILE) to investigate the future changes in peak flow characteristics and dynamics. Hydro-SMILE can be a powerful tool for extreme value estimates in hydrology. The approach, based on validated physics-based hydrologic models and large ensemble climate data, is especially helpful for understanding the changes in magnitude, frequency, and dynamics in high-return level peak flow events. However, the authors did not fully utilize the data they generated and the focus of the manuscript has been on how beneficial such a tool can be. Further and more in-depth analyses on the changes in the characteristics of high return level peak flow events are needed to improve the manuscript. See below my major comments. In addition, I provide language edits/suggestions in minor comments for places where I think clarity is lacking.
Major comments:
1. The manuscript has a title of “…high return levels of peak flows…” but specifically focused on 100-year floods. With a large ensemble, the authors could investigate a range of high return levels of peak flows and see how the frequency, magnitude, and dynamics are projected to change in the future climate.
2. The manuscript focused on proving that it is beneficial to have a large ensemble to estimate extreme peak flow events (Sections 3.1 and Figures 4 and 5), which, I think, is very obvious so I suggest moving them to the supplementary. The authors have generated a powerful dataset for extreme peak flow estimation, however, there is no analysis of the changes in flood frequency and magnitude. The authors are suggested to substantially expand the analysis on flood frequency and characteristics. See Yu et al. (2020) for an example of flood frequency analysis.
Yu, G., Wright, D. B., & Li, Z. (2020). The upper tail of precipitation in convection-permitting regional climate models and their utility in nonstationary rainfall and flood frequency analysis. Earth's Future, 8, e2020EF001613. https://doi.org/10.1029/2020EF001613
3. The authors only gave limited information on the evaluation results of the hydrologic model which are essential for building confidence in the following analysis. I suggest including figures and/or tables showing the evaluation results such as time series of flow events with other quantitative metrics such as correlation coefficient, % bias, root mean square error, KGE, NSE, etc. One related question would be how the level of trust (LOT) is calculated.
4. The changing dynamics in the future climate (Section 3.2) are very interesting and worth digging into. The authors could dig into it with a mechanistic investigation of possible explanations for why they see such changes in future projections. For example, linking snow water equivalent and rain characteristics to the dynamical changes that are projected at the nivo-pluvial stations.
Minor comments:
Lines 57-59: it is unclear how prediction is a reason for challenges in modeling and predicting high flows by Brunner et al. (2021a).
Line 71: change “extraordinary” to “extreme”.
The paragraph starting from line 73: Needs substantial rephrasing. 1) Rephrase the sentence “This approach of high spatiotemporal resolution for climate and hydrological modeling is computationally demanding.” Do the authors mean “This ensemble-based climate and hydrological modeling approach is computationally demanding because of the high spatio-temporal resolution”?
2) Rephrase sentence “However, considering spatially refined catchment features (e.g., slopes, soil characteristics, land use), precise values due to higher temporal resolution, and the application of a SMILE for hydrological modeling supports an enhanced representation of extreme values within models.” Do the authors mean high spatio-temporal resolution of hydro-SMILE is particularly valuable for an enhanced representation of extreme values in models because hydro-SMILE considers spatially-refined catchment features at high temporal resolutions?
3) Rephrase “Thus, this study focuses on the major Bavarian river basins (upper Danube, Main, Inn) with all their tributaries”. It is unclear to me what your study area has to do with the above two statements.
Line 84: Remove “Therefore”.
The paragraph that starts from Line 84: add section numbers throughout the paragraph.
Line 85: Confusing sentence. Remove “…to meet the requirements for the hydrological modeling.”
Line 86: “…hydro-SMILE along...” should be “…along with…”.
Line 95: Remove “As a result”
Line 102: “…(up to 1100 mm precipitation sums in the north, 2500 mm in the south; an average temperature of 10 °C in the north, down to 5 °C (-8 °C on alpine summits)…”. Are the authors referring to annual total precipitation and annual mean temperature? Be clear on that. Also, be sure to mention the data sources for these numbers - are they from Poschlod et al. (2020) as well?
Line 108: “The major river catchments were divided into a total of 98 smaller sub-catchments based
on a common interest in flood protection and a more detailed variation in catchment characteristics, using a selection of gauges (Willkofer et al., 2020).” Rephrase this sentence. It is unclear to me whether the 98 sub-catchments were divided based on the spatial distribution of the 98 selected gauges or whether the gauges were selected because of the division of the 98 sub-catchments.
Line 125: Figure caption of Figure 2: Also introduce what are SDCLIREF and WaSiM in the Figure caption.
Line 142: What is “T63”?
Line 149: “Furthermore, the individual members of the CRCM5-LE are considered independent for the hydrological evaluation period from 1981 to 2099, as the analysis of variations in temperature and precipitation over land and ocean shows (Leduc et al., 2019).” This is the first time the authors mention “hydrological evaluation period”. This is a confusing sentence. Aren’t the CRCM5-LE individual members independent no matter what time period?
Line 152: “…showing regional and seasonal variations in magnitude over Europe (Leduc et al., 2019).” What variables do the authors mean?
Line 156: add “match” after “were adjusted to”.
Line 157: Change “RCM scale” to “RCM grid”. Did the authors do the interpolation onto the RCM grid? If yes, be clear on what interpolation scheme is used.
Line 160: “…3-hourly correction factors for every quantile and month”. Unclear how the 3-hourly correction factor is applied.
Sentence starting on Line 162: I think the authors want to stress that bias correction is inevitable. Rephrase it to “Despite the benefits (increasing reliability of climate change projections of the hydrological impact model, reducing bias in mean annual discharge) and shortcomings (disrupting feedbacks between fluxes, modification of change signals, assumption of a stationary bias) of bias correction are highly debatable (e.g., Teutschbein and Seibert, 2012; Maraun, 2016; Ehret et al., 2012; Dettinger et al., 2004; Chen et al., 2021; Huang et al., 2014), bias correction is often inevitable for climate change impact studies (Gampe et al., 2019).”
Line 168: For such a topographically complex region as described in the “Study area” section, I’m concerned the statistical downscaling between grids that are so different (from 12 km in RCMs to 500 m in hydrologic models) will lose important spatial heterogeneity across the domain. Does the mass-preserving approach address this problem?
Line 171: “The interpolation result was then applied to the SDCLIREF reference fields (Brunner et al., 2021b)”. Unclear. Do the authors mean the SDCLIREF reference fields are also interpolated using the same method?
Line 194: “minimizing a weighted combination of performance metrics, including Nash and Sutcliff efficiency (NSE; Nash 195 and Sutcliffe, 1970), Kling-Gupta efficiency (KGE; Gupta et al., 2009), the logarithmic NSE and the ratio of root mean squared error to standard deviation (RSR; Moriasi et al. (2007)) (Eq. (1))”. Introducing the overall metric (OM) equation first and then describe what is in the equation. Then, give a threshold - what OM value is considered “good” or “bad”?
Line 203: “(NSE: 16; KGE: 5)” Unclear. What does this mean?
Line 208: “Consequently, the level of trust (LOT) for peak flows of return periods of 5, 10, and 20 years of flood events, introduced in Willkofer et al. (2020) showed a moderate to high confindence for most catchments, with gauges of poor simulated performance yielding a lower LOT with increasing return levels.” Do the authors mean gauges with good performance have higher LOT for peak flows with return periods of 5, 10, and 20 years, whereas gauges with poor performance have lower LOT, especially for peak flows at longer return periods?
Line 214: “The entire modeling period is shortened by ten years to account for the time span it takes the RCM to produce fully independent realizations due to the inertia of the ocean model (Leduc et al., 2019).” I have two comments: 1) I saw that the authors partially address my question for Line 149 here. It would be better to rearrange this part and the sentence on Line 149 such that the 10-year spin-up period and the choice of the evaluation time period are more clearly lined up and explained. 2) Rephrase this sentence to “We focus on 1961—2099 as opposed to 1950 – 2099 to account for the time it takes for the RCM to produce fully independent realizations due to the inertia of the ocean model (Leduc et al., 2019).”
Figure 3: What is “HF T,BM” on the far right?
Line 256 and thereafter: Change “intensity” to magnitude throughout the manuscript.
Line 293: “…as indicated by the spread of the blue markers around the black benchmark
line.” I think the authors mean “… as indicated by the decreasing spread of the blue markers around the benchmark line with increasing sample size.”
Lines 296-297: What are panels a, c, and e?
Figures 1&6: What do “balanced” and “unbalanced” pluvial mean?
Citation: https://doi.org/10.5194/egusphere-2023-2019-RC2 - AC1: 'Reply on RC2', Florian Willkofer, 28 Nov 2023
Peer review completion
Journal article(s) based on this preprint
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 260 | 99 | 31 | 390 | 45 | 22 | 22 |
- HTML: 260
- PDF: 99
- XML: 31
- Total: 390
- Supplement: 45
- BibTeX: 22
- EndNote: 22
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Florian Willkofer
Raul Roger Wood
Ralf Ludwig
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1545 KB) - Metadata XML
-
Supplement
(179 KB) - BibTeX
- EndNote
- Final revised paper