the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Jan 2025
Technical Note: Streamflow Seasonality using Directional Statistics
Abstract. Hydrological fluxes typically vary across seasons, with several existing metrics available to characterize their seasonality. These metrics are beneficial when many catchments across diverse climates and landscapes are studied concurrently. Here, we present directional statistics to characterize streamflow seasonality, capturing the timing of streamflow (center of mass) and the strength of its seasonal cycle (concentration). We show that directional statistics is mathematically more robust than several widely used metrics to quantify streamflow seasonality. We extend the application of directional statistics to analyse seasonality in other hydrological fluxes, including precipitation, evapotranspiration, and snowmelt, and we introduce a trend analysis framework for both the timing and strength of seasonal cycles. Using an Alpine catchment (Dischma, Switzerland) as a testbed for this methodology, we identify a shift in the streamflow center of mass to earlier in the year and a weakening of the seasonal cycle. Additionally, we apply directional statistics to streamflow data from 11,118 European catchments, highlighting its utility for large-scale hydrological analyses. The introduced metrics, leveraging directional statistics, can improve our understanding of streamflow seasonality and associated changes, and can also be used to study the seasonality of other environmental fluxes, within and beyond hydrology.
-
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
(5479 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5479 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2024-4117', Gabriele Villarini, 27 Jan 2025
I have given a quick look at the manuscript, and believe that authors may have missed several relevant papers that already get to some of the core of their arguments and actually move them forward:
- Barth, Nancy A., et al. "Changes in streamflow seasonality associated with hydroclimatic variability in the north-central United States among three discrete temporal periods, 1946–2020." Journal of Hydrology: Regional Studies 57 (2025): 102084.
- Dhakal, Nirajan, et al. "Nonstationarity in seasonality of extreme precipitation: A nonparametric circular statistical approach and its application." Water Resources Research 51.6 (2015): 4499-4515.
- Treppiedi, D., G. Villarini, J. Bender, and L.V. Noto, Precipitation extremes projected to increase and to occur in different times of the year, Environmental Research Letters, 20(1), 014014, 2025.
- Veatch, W., and G. Villarini, Modeling riverine flood seasonality with mixtures of circular probability density functions, Journal of Hydrology, 613, 1-11, 2022.
- Villarini, G., On the seasonality of flooding across the continental United States, Advances in Water Resources, 87, 80-91, 2016.
This is not an exhaustive list and I hope these suggestions will help the authors to better contextualize their results with respect to the broader literature.
Citation: https://doi.org/10.5194/egusphere-2024-4117-CC1 -
AC1: 'Reply on CC1', Wouter Berghuijs, 27 Jan 2025
We appreciate the reminder that many studies use circular/directional statistics to characterize the seasonality of extremes, as evidenced by the suggested references. In our manuscript, we acknowledge this development by stating:
“Directional statistics have been widely used to characterize the seasonality of extreme flows (e.g., Burn et al., 1997; Young et al., 2000; Merz & Blöschl, 2003; Laaha and Blöschl, 2006; Blöschl et al., 2017; Berghuijs et al., 2016, 2019; Floriancic et al., 2021; Chagas et al., 2022).”
We will incorporate some of the suggested references, although an exhaustive list of all studies that could be cited here would be far more extensive than what is provided by us and these suggestions.
Importantly, our manuscript develops and applies directional statistics to characterize (continous) seasonal flow regimes, rather than focusing on the seasonality of annual extremes or peaks-over-threshold events. Our approach thereby unifies the concepts of seasonal flow regimes, center of mass, and directional statistics—which is not covered by the referenced studies. These developments are probably not complicated to someone familiar with directional statistics for characterizing extreme events, but have not been shown in the (suggested) literature, and do have many potential applications (also beyond hydrology).
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC1 -
CC2: 'Reply on AC1', Gabriele Villarini, 28 Jan 2025
Thank you for the quick reply. I appreciate the clarification and found this technical note interesting and well-suited for this venue.
Citation: https://doi.org/10.5194/egusphere-2024-4117-CC2
-
CC2: 'Reply on AC1', Gabriele Villarini, 28 Jan 2025
-
AC1: 'Reply on CC1', Wouter Berghuijs, 27 Jan 2025
-
RC1: 'Comment on egusphere-2024-4117', Anonymous Referee #1, 09 Feb 2025
This study proposed a new metric based on directional statistics to quantify the streamflow seasonality, which is a significant contribution of hydrology since the streamflow seasonality is an important characteristic of hydrograph. The paper is overall well written and organized. However, I would like to post some questions and suggestions regarding the applicability, novelty and robustness of the proposed metrics. The major concerns are as followed:
- Could the authors provide a discrete form of the calculation equation in addition to the integral form? This would make the adopting of the equation more practical, since the streamflow data is always in discrete form, such as daily.
- I’ve seen a similar metric called concentration ratio (CR) and concentration period (CP) in some studies (e.g., Nan & Tian 2024; Jiang et al., 2022). If I understand correctly, CR and CP seems to be a simplified form of the R and tQ proposed in this study, which only uses the monthly data. I think the authors can conducted more literature reviews to illustrate the origin and the novelty of the proposed metric.
- The authors illustrate that tQ remains stable regardless of the shift start data, which is indeed an advantage. However, it seems that when interpreting the calculated tQ, we still cannot clealy understand the seasonality pattern if we don’t know the start date of water year. For example, if the tQ of catchment A and B are 0.4 and 0.5, we cannot say the mass center of A catchment is earlier than B catchment in the corresponding water year if we don’t know the start date.
- Regarding the robustness of seasonality strengths, a normalization based on the maximum variation range of each metric is needed. Otherwise, for the example in Figure 3, it’s difficult to say whether the change of Is3 from 14.53 to 3.21 is more significant than the change of R from 0.427 to 0.421.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC1 -
AC2: 'Reply on RC1', Wouter Berghuijs, 10 Feb 2025
Response to Reviewer #1 (in bold)
This study proposed a new metric based on directional statistics to quantify the streamflow seasonality, which is a significant contribution of hydrology since the streamflow seasonality is an important characteristic of hydrograph. The paper is overall well written and organized. However, I would like to post some questions and suggestions regarding the applicability, novelty and robustness of the proposed metrics. The major concerns are as followed:
We thank the reviewer for this constructive report and address these individual points below
- Could the authors provide a discrete form of the calculation equation in addition to the integral form? This would make the adopting of the equation more practical, since the streamflow data is always in discrete form, such as daily.
We will add a discrete form of these equations in the revised manuscript.
- I’ve seen a similar metric called concentration ratio (CR) and concentration period (CP) in some studies (e.g., Nan & Tian 2024; Jiang et al., 2022). If I understand correctly, CR and CP seems to be a simplified form of the R and tQ proposed in this study, which only uses the monthly data. I think the authors can conducted more literature reviews to illustrate the origin and the novelty of the proposed metric.
We indeed did not notice the interesting works by Nan & Tian (2024) and Jiang et al. (2022).
In these works, a simplified form of mass center and concentration are provided, and we will explicitly acknowledge that in our revised manuscript.
We will state how Jiang et al. (2022) already provides a (monthly) version of the proposed work, which is later adopted by Nan & Tian (2024).
We, however, believe that providing a more generalized form, including several applications, and robustness tests, can catalyze its uptake in hydrological (and other fields’) research.
- The authors illustrate that tQ remains stable regardless of the shift start data, which is indeed an advantage. However, it seems that when interpreting the calculated tQ, we still cannot clealy understand the seasonality pattern if we don’t know the start date of water year. For example, if the tQ of catchment A and B are 0.4 and 0.5, we cannot say the mass center of A catchment is earlier than B catchment in the corresponding water year if we don’t know the start date.
For questions that require timings compared to a water year, it is inherently impossible to do this without defining the start date of that water year. For particular questions or problems, this may be very helpful to do.
To understand mass center shifts or differences between places (either in space or time), one can compare differences in the timing (irrespective of the water year start).
We will better emphasize both these aspects in the revised manuscript.
- Regarding the robustness of seasonality strengths, a normalization based on the maximum variation range of each metric is needed. Otherwise, for the example in Figure 3, it’s difficult to say whether the change of Is3 from 14.53 to 3.21 is more significant than the change of R from 0.427 to 0.421.
In the revised manuscript, we will provide a normalized comparison of all metrics. Additionally, we will highlight that, regardless of the specific outcomes of this normalization, directional statistics metrics have the advantage of yielding values that remain unaffected by the data's time resolution, enhancing communication and interpretability of seasonality strength.
Nan, Y., & Tian, F. (2024). Glaciers determine the sensitivity of hydrological processes to perturbed climate in a large mountainous basin on the Tibetan Plateau. Hydrology and Earth System Sciences, 28(3), 669-689.
Jiang, Y., Xu, Z., & Xiong, L. (2022). Runoff variation and response to precipitation on multi-spatial and temporal scales in the southern Tibetan Plateau. Journal of Hydrology: Regional Studies, 42, 101157.
No further comments.
We thank the Reviewer for this helpful review.
We will provide detailed versions of all our changes once the discussion is closed and if the editor indicates we can revise our manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC2
-
RC2: 'Comment on egusphere-2024-4117', Anonymous Referee #1, 09 Feb 2025
I am sorry that the reference in my referee report is missed. Please find them below:
Nan, Y., & Tian, F. (2024). Glaciers determine the sensitivity of hydrological processes to perturbed climate in a large mountainous basin on the Tibetan Plateau. Hydrology and Earth System Sciences, 28(3), 669-689.
Jiang, Y., Xu, Z., & Xiong, L. (2022). Runoff variation and response to precipitation on multi-spatial and temporal scales in the southern Tibetan Plateau. Journal of Hydrology: Regional Studies, 42, 101157.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC2 -
AC5: 'Reply on RC2', Wouter Berghuijs, 14 Mar 2025
No further reply needed
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC5 -
AC6: 'Reply on RC2', Wouter Berghuijs, 14 Mar 2025
No further reply needed
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC6
-
AC5: 'Reply on RC2', Wouter Berghuijs, 14 Mar 2025
-
RC3: 'Comment on egusphere-2024-4117', Anonymous Referee #2, 02 Mar 2025
This study proposes the use of directional statistics to characterize both the timing and strength of the seasonal streamflow cycle. It begins with a series of idealized comparisons to illustrate the methodology and then applies the statistics to real-world streamflow data. While prior studies (e.g., Nan & Tian, 2024; Jiang et al., 2022, indicated by another reviewer) have employed similar forms of directional statistics, this work advances the field by presenting a more generalized framework that is applicable to any temporal resolution. Additionally, it provides a comprehensive discussion on the advantages of directional statistics, including its ability to robustly capture seasonal timings and shifts (Section 3.1) and seasonal strength (Section 3.2). I believe this study makes a valuable contribution to the field of streamflow seasonality research.
I have only one suggestion for further improvement. Sections 4.1–4.3 effectively demonstrate the application of directional statistics. However, it would be highly informative to include a comparison with non-directional metrics, similar to what was done in Figures 1 and 2. Such a comparison would provide deeper insights into the practical differences between these metrics in streamflow analysis. In particular, I would be interested in seeing these comparisons extended to Figures 6 and 7, as they would help readers better understand the unique advantages of directional statistics in real-world scenarios.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC3 -
AC3: 'Reply on RC3', Wouter Berghuijs, 02 Mar 2025
We thank the reviewer for this positive and constructive evaluation
This study proposes the use of directional statistics to characterize both the timing and strength of the seasonal streamflow cycle. It begins with a series of idealized comparisons to illustrate the methodology and then applies the statistics to real-world streamflow data. While prior studies (e.g., Nan & Tian, 2024; Jiang et al., 2022, indicated by another reviewer) have employed similar forms of directional statistics, this work advances the field by presenting a more generalized framework that is applicable to any temporal resolution. Additionally, it provides a comprehensive discussion on the advantages of directional statistics, including its ability to robustly capture seasonal timings and shifts (Section 3.1) and seasonal strength (Section 3.2). I believe this study makes a valuable contribution to the field of streamflow seasonality research.
Thank you.
I have only one suggestion for further improvement. Sections 4.1–4.3 effectively demonstrate the application of directional statistics. However, it would be highly informative to include a comparison with non-directional metrics, similar to what was done in Figures 1 and 2. Such a comparison would provide deeper insights into the practical differences between these metrics in streamflow analysis. In particular, I would be interested in seeing these comparisons extended to Figures 6 and 7, as they would help readers better understand the unique advantages of directional statistics in real-world scenarios.
We could provide a comparison with non-directional statistics for timing using the half-flow date and the center of mass (Eqs. 1 and 2). However, displaying these metrics in maps in the main paper seems problematic, as these new maps would lack physical meaning. This is because either the metrics use different starting dates of the water year regionally (and then the units of the metric differ, which makes them incomparable) or they begin at unrealistic times of the year (e.g., not matching the low flow season) which is not informative either. Consequently, we are hesitant to present these metrics in a Figure, as they may distract from the more meaningful examples shown (which is the purpose of Sections 4.1-4.3). Instead, we propose addressing this issue through a textual discussion in Sections 4.2 and 4.3.
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC3 -
RC4: 'Reply on AC3', Anonymous Referee #2, 03 Mar 2025
Thanks to the authors for the prompt response. It is fine to add comparisons in the discussion part. However, I think adding figures based on non-directional statistics will still be useful. Showing the problems is as valuable as showing the advantages. You can adpot the normal Oct-Sep water year, even though Germany may use a different norm, and combine the trend and spatial distributions in one figure to avoid extended length. Such kind of comparison will be necessary to validate the distinct features of the directional statistics and show how problematic the non-directional statistics could be if those problems do exist. About the unit problem, its impact won't be not huge if you aim to compare the spatial patterns and trends. There is no need to create differences or calculate metrics between those statistics.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC4 - AC4: 'Reply on RC4', Wouter Berghuijs, 03 Mar 2025
-
RC4: 'Reply on AC3', Anonymous Referee #2, 03 Mar 2025
-
AC3: 'Reply on RC3', Wouter Berghuijs, 02 Mar 2025
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2024-4117', Gabriele Villarini, 27 Jan 2025
I have given a quick look at the manuscript, and believe that authors may have missed several relevant papers that already get to some of the core of their arguments and actually move them forward:
- Barth, Nancy A., et al. "Changes in streamflow seasonality associated with hydroclimatic variability in the north-central United States among three discrete temporal periods, 1946–2020." Journal of Hydrology: Regional Studies 57 (2025): 102084.
- Dhakal, Nirajan, et al. "Nonstationarity in seasonality of extreme precipitation: A nonparametric circular statistical approach and its application." Water Resources Research 51.6 (2015): 4499-4515.
- Treppiedi, D., G. Villarini, J. Bender, and L.V. Noto, Precipitation extremes projected to increase and to occur in different times of the year, Environmental Research Letters, 20(1), 014014, 2025.
- Veatch, W., and G. Villarini, Modeling riverine flood seasonality with mixtures of circular probability density functions, Journal of Hydrology, 613, 1-11, 2022.
- Villarini, G., On the seasonality of flooding across the continental United States, Advances in Water Resources, 87, 80-91, 2016.
This is not an exhaustive list and I hope these suggestions will help the authors to better contextualize their results with respect to the broader literature.
Citation: https://doi.org/10.5194/egusphere-2024-4117-CC1 -
AC1: 'Reply on CC1', Wouter Berghuijs, 27 Jan 2025
We appreciate the reminder that many studies use circular/directional statistics to characterize the seasonality of extremes, as evidenced by the suggested references. In our manuscript, we acknowledge this development by stating:
“Directional statistics have been widely used to characterize the seasonality of extreme flows (e.g., Burn et al., 1997; Young et al., 2000; Merz & Blöschl, 2003; Laaha and Blöschl, 2006; Blöschl et al., 2017; Berghuijs et al., 2016, 2019; Floriancic et al., 2021; Chagas et al., 2022).”
We will incorporate some of the suggested references, although an exhaustive list of all studies that could be cited here would be far more extensive than what is provided by us and these suggestions.
Importantly, our manuscript develops and applies directional statistics to characterize (continous) seasonal flow regimes, rather than focusing on the seasonality of annual extremes or peaks-over-threshold events. Our approach thereby unifies the concepts of seasonal flow regimes, center of mass, and directional statistics—which is not covered by the referenced studies. These developments are probably not complicated to someone familiar with directional statistics for characterizing extreme events, but have not been shown in the (suggested) literature, and do have many potential applications (also beyond hydrology).
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC1 -
CC2: 'Reply on AC1', Gabriele Villarini, 28 Jan 2025
Thank you for the quick reply. I appreciate the clarification and found this technical note interesting and well-suited for this venue.
Citation: https://doi.org/10.5194/egusphere-2024-4117-CC2
-
CC2: 'Reply on AC1', Gabriele Villarini, 28 Jan 2025
-
AC1: 'Reply on CC1', Wouter Berghuijs, 27 Jan 2025
-
RC1: 'Comment on egusphere-2024-4117', Anonymous Referee #1, 09 Feb 2025
This study proposed a new metric based on directional statistics to quantify the streamflow seasonality, which is a significant contribution of hydrology since the streamflow seasonality is an important characteristic of hydrograph. The paper is overall well written and organized. However, I would like to post some questions and suggestions regarding the applicability, novelty and robustness of the proposed metrics. The major concerns are as followed:
- Could the authors provide a discrete form of the calculation equation in addition to the integral form? This would make the adopting of the equation more practical, since the streamflow data is always in discrete form, such as daily.
- I’ve seen a similar metric called concentration ratio (CR) and concentration period (CP) in some studies (e.g., Nan & Tian 2024; Jiang et al., 2022). If I understand correctly, CR and CP seems to be a simplified form of the R and tQ proposed in this study, which only uses the monthly data. I think the authors can conducted more literature reviews to illustrate the origin and the novelty of the proposed metric.
- The authors illustrate that tQ remains stable regardless of the shift start data, which is indeed an advantage. However, it seems that when interpreting the calculated tQ, we still cannot clealy understand the seasonality pattern if we don’t know the start date of water year. For example, if the tQ of catchment A and B are 0.4 and 0.5, we cannot say the mass center of A catchment is earlier than B catchment in the corresponding water year if we don’t know the start date.
- Regarding the robustness of seasonality strengths, a normalization based on the maximum variation range of each metric is needed. Otherwise, for the example in Figure 3, it’s difficult to say whether the change of Is3 from 14.53 to 3.21 is more significant than the change of R from 0.427 to 0.421.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC1 -
AC2: 'Reply on RC1', Wouter Berghuijs, 10 Feb 2025
Response to Reviewer #1 (in bold)
This study proposed a new metric based on directional statistics to quantify the streamflow seasonality, which is a significant contribution of hydrology since the streamflow seasonality is an important characteristic of hydrograph. The paper is overall well written and organized. However, I would like to post some questions and suggestions regarding the applicability, novelty and robustness of the proposed metrics. The major concerns are as followed:
We thank the reviewer for this constructive report and address these individual points below
- Could the authors provide a discrete form of the calculation equation in addition to the integral form? This would make the adopting of the equation more practical, since the streamflow data is always in discrete form, such as daily.
We will add a discrete form of these equations in the revised manuscript.
- I’ve seen a similar metric called concentration ratio (CR) and concentration period (CP) in some studies (e.g., Nan & Tian 2024; Jiang et al., 2022). If I understand correctly, CR and CP seems to be a simplified form of the R and tQ proposed in this study, which only uses the monthly data. I think the authors can conducted more literature reviews to illustrate the origin and the novelty of the proposed metric.
We indeed did not notice the interesting works by Nan & Tian (2024) and Jiang et al. (2022).
In these works, a simplified form of mass center and concentration are provided, and we will explicitly acknowledge that in our revised manuscript.
We will state how Jiang et al. (2022) already provides a (monthly) version of the proposed work, which is later adopted by Nan & Tian (2024).
We, however, believe that providing a more generalized form, including several applications, and robustness tests, can catalyze its uptake in hydrological (and other fields’) research.
- The authors illustrate that tQ remains stable regardless of the shift start data, which is indeed an advantage. However, it seems that when interpreting the calculated tQ, we still cannot clealy understand the seasonality pattern if we don’t know the start date of water year. For example, if the tQ of catchment A and B are 0.4 and 0.5, we cannot say the mass center of A catchment is earlier than B catchment in the corresponding water year if we don’t know the start date.
For questions that require timings compared to a water year, it is inherently impossible to do this without defining the start date of that water year. For particular questions or problems, this may be very helpful to do.
To understand mass center shifts or differences between places (either in space or time), one can compare differences in the timing (irrespective of the water year start).
We will better emphasize both these aspects in the revised manuscript.
- Regarding the robustness of seasonality strengths, a normalization based on the maximum variation range of each metric is needed. Otherwise, for the example in Figure 3, it’s difficult to say whether the change of Is3 from 14.53 to 3.21 is more significant than the change of R from 0.427 to 0.421.
In the revised manuscript, we will provide a normalized comparison of all metrics. Additionally, we will highlight that, regardless of the specific outcomes of this normalization, directional statistics metrics have the advantage of yielding values that remain unaffected by the data's time resolution, enhancing communication and interpretability of seasonality strength.
Nan, Y., & Tian, F. (2024). Glaciers determine the sensitivity of hydrological processes to perturbed climate in a large mountainous basin on the Tibetan Plateau. Hydrology and Earth System Sciences, 28(3), 669-689.
Jiang, Y., Xu, Z., & Xiong, L. (2022). Runoff variation and response to precipitation on multi-spatial and temporal scales in the southern Tibetan Plateau. Journal of Hydrology: Regional Studies, 42, 101157.
No further comments.
We thank the Reviewer for this helpful review.
We will provide detailed versions of all our changes once the discussion is closed and if the editor indicates we can revise our manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC2
-
RC2: 'Comment on egusphere-2024-4117', Anonymous Referee #1, 09 Feb 2025
I am sorry that the reference in my referee report is missed. Please find them below:
Nan, Y., & Tian, F. (2024). Glaciers determine the sensitivity of hydrological processes to perturbed climate in a large mountainous basin on the Tibetan Plateau. Hydrology and Earth System Sciences, 28(3), 669-689.
Jiang, Y., Xu, Z., & Xiong, L. (2022). Runoff variation and response to precipitation on multi-spatial and temporal scales in the southern Tibetan Plateau. Journal of Hydrology: Regional Studies, 42, 101157.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC2 -
AC5: 'Reply on RC2', Wouter Berghuijs, 14 Mar 2025
No further reply needed
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC5 -
AC6: 'Reply on RC2', Wouter Berghuijs, 14 Mar 2025
No further reply needed
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC6
-
AC5: 'Reply on RC2', Wouter Berghuijs, 14 Mar 2025
-
RC3: 'Comment on egusphere-2024-4117', Anonymous Referee #2, 02 Mar 2025
This study proposes the use of directional statistics to characterize both the timing and strength of the seasonal streamflow cycle. It begins with a series of idealized comparisons to illustrate the methodology and then applies the statistics to real-world streamflow data. While prior studies (e.g., Nan & Tian, 2024; Jiang et al., 2022, indicated by another reviewer) have employed similar forms of directional statistics, this work advances the field by presenting a more generalized framework that is applicable to any temporal resolution. Additionally, it provides a comprehensive discussion on the advantages of directional statistics, including its ability to robustly capture seasonal timings and shifts (Section 3.1) and seasonal strength (Section 3.2). I believe this study makes a valuable contribution to the field of streamflow seasonality research.
I have only one suggestion for further improvement. Sections 4.1–4.3 effectively demonstrate the application of directional statistics. However, it would be highly informative to include a comparison with non-directional metrics, similar to what was done in Figures 1 and 2. Such a comparison would provide deeper insights into the practical differences between these metrics in streamflow analysis. In particular, I would be interested in seeing these comparisons extended to Figures 6 and 7, as they would help readers better understand the unique advantages of directional statistics in real-world scenarios.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC3 -
AC3: 'Reply on RC3', Wouter Berghuijs, 02 Mar 2025
We thank the reviewer for this positive and constructive evaluation
This study proposes the use of directional statistics to characterize both the timing and strength of the seasonal streamflow cycle. It begins with a series of idealized comparisons to illustrate the methodology and then applies the statistics to real-world streamflow data. While prior studies (e.g., Nan & Tian, 2024; Jiang et al., 2022, indicated by another reviewer) have employed similar forms of directional statistics, this work advances the field by presenting a more generalized framework that is applicable to any temporal resolution. Additionally, it provides a comprehensive discussion on the advantages of directional statistics, including its ability to robustly capture seasonal timings and shifts (Section 3.1) and seasonal strength (Section 3.2). I believe this study makes a valuable contribution to the field of streamflow seasonality research.
Thank you.
I have only one suggestion for further improvement. Sections 4.1–4.3 effectively demonstrate the application of directional statistics. However, it would be highly informative to include a comparison with non-directional metrics, similar to what was done in Figures 1 and 2. Such a comparison would provide deeper insights into the practical differences between these metrics in streamflow analysis. In particular, I would be interested in seeing these comparisons extended to Figures 6 and 7, as they would help readers better understand the unique advantages of directional statistics in real-world scenarios.
We could provide a comparison with non-directional statistics for timing using the half-flow date and the center of mass (Eqs. 1 and 2). However, displaying these metrics in maps in the main paper seems problematic, as these new maps would lack physical meaning. This is because either the metrics use different starting dates of the water year regionally (and then the units of the metric differ, which makes them incomparable) or they begin at unrealistic times of the year (e.g., not matching the low flow season) which is not informative either. Consequently, we are hesitant to present these metrics in a Figure, as they may distract from the more meaningful examples shown (which is the purpose of Sections 4.1-4.3). Instead, we propose addressing this issue through a textual discussion in Sections 4.2 and 4.3.
Citation: https://doi.org/10.5194/egusphere-2024-4117-AC3 -
RC4: 'Reply on AC3', Anonymous Referee #2, 03 Mar 2025
Thanks to the authors for the prompt response. It is fine to add comparisons in the discussion part. However, I think adding figures based on non-directional statistics will still be useful. Showing the problems is as valuable as showing the advantages. You can adpot the normal Oct-Sep water year, even though Germany may use a different norm, and combine the trend and spatial distributions in one figure to avoid extended length. Such kind of comparison will be necessary to validate the distinct features of the directional statistics and show how problematic the non-directional statistics could be if those problems do exist. About the unit problem, its impact won't be not huge if you aim to compare the spatial patterns and trends. There is no need to create differences or calculate metrics between those statistics.
Citation: https://doi.org/10.5194/egusphere-2024-4117-RC4 - AC4: 'Reply on RC4', Wouter Berghuijs, 03 Mar 2025
-
RC4: 'Reply on AC3', Anonymous Referee #2, 03 Mar 2025
-
AC3: 'Reply on RC3', Wouter Berghuijs, 02 Mar 2025
Peer review completion
Journal article(s) based on this preprint
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 537 | 160 | 27 | 724 | 12 | 19 |
- HTML: 537
- PDF: 160
- XML: 27
- Total: 724
- BibTeX: 12
- EndNote: 19
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Kate Hale
Harsh Beria
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5479 KB) - Metadata XML