Functional data analysis to quantify and investigate controls on and changes in baseflow seasonality

Leeming, Kathryn A.; Bloomfield, John P.; Coxon, Gemma; Zheng, Yanchen

doi:https://doi.org/10.5194/hess-2023-202

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https://doi.org/10.5194/hess-2023-202

Preprints

29 Aug 2023

| 29 Aug 2023

Status: this preprint has been withdrawn by the authors.

Functional data analysis to quantify and investigate controls on and changes in baseflow seasonality

Kathryn A. Leeming, John P. Bloomfield, Gemma Coxon, and Yanchen Zheng

Abstract. Baseflow is the delayed component of streamflow from subsurface storage and is critical for sustaining ecological flows and ensuring water resource security. Understanding controls on and changes in baseflow, including the seasonality of baseflow, is therefore an important task. Baseflow seasonality has typically been investigated using pre-defined hydrological seasons. Instead, here, we investigate baseflow seasonality using data-led approaches that identify and cluster average annual baseflow hydrographs that exhibit early-, mid-, or late-seasonality. We apply a novel functional data analysis (FDA) approach and examine temporal changes in the timing of seasonal peaks in annual standardised baseflow hydrographs for 671 catchments across Great Britain (GB). We use data from the CAMELS-GB dataset for the period 1976 to 2015 split into two twenty-year time blocks (1976–1995 and 1996–2015). Functional clustering enables groups of catchments with similar distributions between time blocks to be identified. Changes in baseflow seasonality with time are investigated by identifying and characterising catchments that move between functional clusters and time blocks, while analysis of the timing of baseflow peaks provides additional temporal resolution to the early-, mid-, and late-season discretisation generated by the functional clustering. The analysis shows that baseflow seasonality has a spatio-temporally coherent structure across GB and catchment characteristics are a first order control on the form of seasonal baseflow clusters. Changes in climate are inferred to be the first order control on changes in baseflow seasonality between the two time blocks. A change to earlier seasonal baseflow in snow-melt influenced catchments in upland northern GB is associated with systematic warming across the two time blocks, and a move to earlier (later) baseflow seasonality across lowland southern, central and eastern (western, north-western and northern) catchments in GB is associated with earlier (later) seasonality in effective rainfall (defined as precipitation minus potential evapotranspiration). These changes in baseflow seasonality in non-snow-melt influenced catchments are consistent with the proposition that, in temperate environments, climate warming leading to vegetation phenology-mediated changes in evapotranspiration may be modifying the timing of hydrological cycles.

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Received: 17 Aug 2023 – Discussion started: 29 Aug 2023

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Kathryn A. Leeming, John P. Bloomfield, Gemma Coxon, and Yanchen Zheng

Interactive discussion

Status: closed

RC1:
'Comment on hess-2023-202', Anonymous Referee #1, 15 Sep 2023

General comments:
The authors of the manuscript entitled "Functional data analysis to quantify and investigate controls on and changes in baseflow seasonality" aims at applying a novel functional data analysis (FDA) approach and examine temporal changes in the timing of seasonal peaks in annual standardized baseflow hydrographs for 671 catchments across Great Britain (GB). It is an important topic about watershed management plans. Unfortunately, I find that the manuscript does not break new ground nor offer insightful new methodology to the field of water resources. In general, the manuscript does not meet the high standard of HESS journal due to many flaws as follow (Main concerns). I cannot support this version of manuscript.
Main concerns:
1. As the authors state baseflow is an important component of runoff during periods of low flow and drought, and it is critical to water security in the basin. However, how to accurately simulate baseflow has been a challenge in hydrology. The authors only mention very briefly in the manuscript the use of digital filtering to calculate baseflow, which is not very reasonable. Although the Lyne-Hollick digital filtering method is superior to the parameter less separation simplicity, the parameter selection as well as the number of filters need to be considered. Finally, the accuracy of the simulated values of the baseflow needs to be verified, and subsequent analyses should be performed after these tasks are completed to ensure the reliability of the research results.
2. The manuscript focuses on analyzing the seasonality of baseflow and splits the hydrologic data from all stations into two windows. This approach is too subjective, as hydrological processes are affected to different degrees in each basin due to human activities and climate change, and in some cases, the timing of hydrological surges may even occur. Therefore, it is recommended to analyze the abrupt changes in baseflow in each basin before performing temporal and spatial analyses.
3. The manuscript contains insufficient research and more analysis needs to be added subsequently. For example, the authors mention that there is some consistency or correlation between changes in effective rainfall and baseflow seasonality, and a quantitative result is needed. On the other hand, the effects of other factors on baseflow seasonality, such as TWS and NDVI, need to be analyzed.

Citation: https://doi.org/10.5194/hess-2023-202-RC1
- AC2: 'Reply on RC1', Kathryn Leeming, 23 Oct 2023
  
  Thank you for your feedback on our submission, we'd like to address the general and specific (numbered) comments as follows.
  Response to general comments: We are disappointed that we’ve not been able to convey the novelty of the work in the first submission of the paper. We believe that it is novel both in the methodological approach employed and in the insights that the work has provided into the functioning of the terrestrial water cycle under long-term (multi-decadal) change.
  
  There are two elements to the methodological novelty. Firstly, as described in the paper (L87-L92) we have for the first time applied Functional Data Analysis (FDA) methods to analyse seasonal change in a hydraulic time series (in this case to baseflow). Secondly, as we note (L167-L171), unlike the limited previous work that has applied FDA in other hydrological contexts, in our study the seasonal shapes are standardised to remove their mean and give unit variance for each curve. This is critical as it allows the shapes defining the baseflow seasonality to be compared (rather than the absolute values) and enables the clustering and spatio-temporal analysis to be undertaken.
  
  This novel methodological approach has allowed us for the first time to address the challenge, only recently formulated by workers such as Piao et al. (2019) and Chen et al., (2022), of characterising and then investigating the controls on potential decadal-scale changes seasonality in the terrestrial water cycle driven by climate warming. This is a new set of research challenges only raised in the last couple of years and ours is the first study of baseflow that we are aware of in this context – hence our belief that the work and it’s findings are novel and “break new ground”.
  
  In the revised version of the paper, we will ensure these novelties are clear by strengthening the abstract, discussion and conclusions.
  Response 1: The focus of this work is on a new application of the FDA method (see our response to the general comments above) and is not intended to be a further contribution to the long-standing debate on baseflow separation methods. We understand the concerns regarding baseflow separation methods and acknowledge that the resulting baseflow time series from different methods are not equal. However, in this work we calculate the annual patterns from the baseflow, which should be fairly robust to the choice of baseflow separation method. The baseflow separation was performed on daily flow timeseries, but the annual components were evaluated using monthly averages of the baseflow. This temporal downscaling should allow for resilience of the presented results to different baseflow separation approaches. Our choice of digital filtering method was motivated by the standardised approach proposed by Ladson et al (2013) which allowed for processing of all of the CAMELS-GB catchments in a uniform way and we will include further specification of this method in the text. It would be unfeasible to tune a baseflow separation method for each of the catchments separately for this work and would make the interpretation of the results questionable if the same analytical approach had not been applied to each catchment. We will add analysis to the manuscript and supplementary material to demonstrate that the changes in seasonality shown in the paper are not due to the baseflow separation method.
  Response 2: In this work we investigated changes over two twenty-year time blocks. We did not target specific temporal changes as we were trying to identify changes based upon the seasonal distributions in these time blocks alone. We agree that the hydrological processes are catchment-specific, and in the discussion advocated for an improvement in time-varying catchment attributes because changes such as anthropogenic factors do not have associated data available. Whilst the catchment-specific approach would offer valuable insight, it would be impractical to perform a study for each of the 671 CAMELS-GB catchments, so this study provides information at the GB-scale. We think that processing the data from all catchments in the same way is advantageous as it allows for differences between catchments and time blocks (such as those due to anthropogenic or climate factors) to be identified and compared across GB (eg Fig 6d).The median was used to calculate monthly values for evaluation of the seasonal patterns so extreme features such as surges are mitigated so that the general behaviour and patterns over time can be identified. Our analysis has provided insight into long time-scale changes in seasonality of baseflow within GB catchments. In the discussion section we will add a commentary on the implications and limitations of the time block splits.
  Response 3: Our analysis includes the concordance coefficient between the peak timing change for effective rainfall and baseflow (L350). As presented in the discussion section 4.3, the data availability of changing features of the catchments is poor, so many analyses we would like to investigate have not been possible due to lack of data. We emphasised the need for additional observational data to be included in large sample datasets to allow for such analyses, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.
  References:
  
  Chen, S., Fu, Y. H., Hao, F., Li, X., Zhou, S., Liu, C., and Tang, J.: Vegetation phenology and its ecohydrological implications from individual to global scales. Geogr. Sustain., 3, 334-338, https://doi.org/10.1016/j.geosus.2022.10.002, 2022
  
  Piao, S., Liu, Q., Chen, A., Janssens, I. A., Fu, Y., Dai, J., Liu, L., Lian, X., Shen, M., and Zhu, X.: Plant phenology and global climate change: Current progresses and challenges. Glob. Change Biol., 25 (6), 1922-1940, https://doi.org/10.1111/gcb.14619, 2019.
  
  Citation: https://doi.org/10.5194/hess-2023-202-AC2
RC2:
'Comment on hess-2023-202', Anonymous Referee #2, 20 Sep 2023
This manuscript introduced a functional data analysis (FDA) approach to examine how the timing of seasonal peaks in annual standardized baseflow changes. It is applied to >600 catchments across Great Britain (GB). Understanding changes in (base)flow conditions is relevant, but before the paper is publishable several concerns need to be addressed (in my opinion).
The split of data from all stations into two windows is very arbitrary and may overlook some of the actual changes occurring (but are associated with other timings).

It is unclear how the chosen method of baseflow would affect the results.

The association of vegetation-related (NDVI) causes is rather handwavy and qualitative in nature.

Color scales of Figures 1b and 2b could have a more informative range to highlight catchment differences better.

Could maps of figure 6 be enlarged so markers overlap less).

If these points are meaningfully addressed the paper seems publishable.
Citation: https://doi.org/10.5194/hess-2023-202-RC2
- AC1: 'Reply on RC2', Kathryn Leeming, 23 Oct 2023
  
  Many thanks for your comments, responses to numbered points are included below.
  1. Within this work we address the question of change over a coarse scale, twenty year time blocks. We agree that this time scale may not highlight all changes that are occurring, however long-scale changes have been identified within this work using these time windows and explored within the results section (Section 3.2: shifts to earlier seasonal patterns, including in snow-melt influenced catchments). This multi-decadal approach has enabled us to discover changes that are occurring across many catchments (movement to earlier clusters in Fig 2c, earlier seasonal peaks in Fig 6d) . Future follow-up work could consider differently targeted temporal blocks or spatial regions, however we think there is a lot of insight gained from the coarse scale, GB-wide approach we have used. We will add a discussion of the time window choice and the implications and limitations of this approach within the discussion section.
  2. In our work the baseflow separation is performed before monthly averages are calculated, and then the median annual signal is calculated across multiple years. These two stages of averaging mean that small differences in baseflow calculated using different separation methods would be mitigated in the final results. The Lyne-Hollick filter was chosen due to its suitability for processing large numbers of streamflow time series, and we expect the annual patterns to be broadly robust across baseflow separation methods. We will demonstrate this the revision of the manuscript and supplementary material by providing further analysis using alternative baseflow separation.
  3. We agree that some of the observations in the Discussion are by necessity qualitative, however, we took care to frame the statements based on new study observations and importantly highlighted the need for additional information that is currently not available.
  In the discussion (L373-376) we state that “given the absence of association between change in precipitation and baseflow seasonality, it is inferred that the change in effective rainfall seasonality is due to changes in the seasonality of PET, the latter presumably driven at least in part by long-term warming across the UK”. However, note that we were careful not to directly associate this to “vegetation-related (NDVI) causes” as stated by the reviewer. This was because there is currently insufficient data to constrain changes in vegetation-related NDVI over time period of our analysis. This is why we also emphasised at the end of the Conclusion section the need for additional observational data to be included in large sample datasets, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.
  4. Thank-you for this comment, we will adapt the colour scale for Fig 1b and 1c accordingly. Please clarify if Fig 2b was not sufficiently clear.
  5. We will adapt this figure for less overlap.
  
  Citation: https://doi.org/10.5194/hess-2023-202-AC1
AC3:
'Comment on hess-2023-202', Kathryn Leeming, 31 Oct 2023
Our work demonstrates the application of functional data analysis (FDA) to consider the seasonal patterns of baseflow and whether the seasonality is changing over time. Other FDA applications in hydrology have not addressed seasonality specifically, and our approach has enabled us to identify differences in timing of the seasonal pattern of baseflow over catchments in Great Britain, and changes over the time period (1976-2015). The CAMELS-GB dataset contains streamflow and meteorological time series and catchment attributes for 671 catchments, and our analysis has been performed on each catchment equally. This allows us to consider the GB catchments simultaneously, and identify coarse-scale temporal changes.
Following the reviewers' feedback we propose improvements to clarify and add to elements of the text: enhanced discussion of the motivation and novelty of the approach throughout, discussion of the benefits and limitations of the twenty-year time blocking, analysis of the impacts of baseflow separation method on the results, and clearer figures.
Our manuscript does not seek to contribute to the debate over baseflow separation methods, and in our improvements we will show that the presented findings are not specific to the choice of Lyne-Hollick filter separation (addressing comments from both reviewers). The FDA approach used here is also not specific to baseflow and could be applied to different hydrological and meteorological time series.
We will also extend the discussion sections to include the benefits and limitations of the time splits used in this work (addressing comments from both reviewers). These time splits have allowed us to identify coarse-scale changes in the catchments over time scales that will feature different changes in different catchments. Unfortunately, the data availability on temporal changes in catchment management processes and other catchment attributes is poor, so we have focussed on large scale changes and climate changes in our analysis. Improving the data availability for catchment attribute changes is of importance for future studies, and we have highlighted this in the discussion section.
We do not expect that our proposed changes will alter the fundamental observations in this work, but they will strengthen the justification for the approach and the conclusions reached.
Referee 1:

General comments:

The authors of the manuscript entitled "Functional data analysis to quantify and investigate controls on and changes in baseflow seasonality" aims at applying a novel functional data analysis (FDA) approach and examine temporal changes in the timing of seasonal peaks in annual standardized baseflow hydrographs for 671 catchments across Great Britain (GB). It is an important topic about watershed management plans. Unfortunately, I find that the manuscript does not break new ground nor offer insightful new methodology to the field of water resources. In general, the manuscript does not meet the high standard of HESS journal due to many flaws as follow (Main concerns). I cannot support this version of manuscript.
Response to general comments: We are disappointed that we’ve not been able to convey the novelty of the work in the first submission of the paper. We believe that it is novel both in the methodological approach employed and in the insights that the work has provided into the functioning of the terrestrial water cycle under long-term (multi-decadal) change.
There are two elements to the methodological novelty. Firstly, as described in the paper (L87-L92) we have for the first time applied Functional Data Analysis (FDA) methods to analyse seasonal change in a hydraulic time series (in this case to baseflow). Secondly, as we note (L167-L171), unlike the limited previous work that has applied FDA in other hydrological contexts, in our study the seasonal shapes are standardised to remove their mean and give unit variance for each curve. This is critical as it allows the shapes defining the baseflow seasonality to be compared (rather than the absolute values) and enables the clustering and spatio-temporal analysis to be undertaken.
This novel methodological approach has allowed us for the first time to address the challenge, only recently formulated by workers such as Piao et al. (2019) and Chen et al., (2022), of characterising and then investigating the controls on potential decadal-scale changes seasonality in the terrestrial water cycle driven by climate warming. This is a new set of research challenges only raised in the last couple of years and ours is the first study of baseflow that we are aware of in this context – hence our belief that the work and it’s findings are novel and “break new ground”.
In the revised version of the paper, we will ensure these novelties are clear by strengthening the abstract, discussion and conclusions.

References:
Chen, S., Fu, Y. H., Hao, F., Li, X., Zhou, S., Liu, C., and Tang, J.: Vegetation phenology and its ecohydrological implications from individual to global scales. Geogr. Sustain., 3, 334-338, https://doi.org/10.1016/j.geosus.2022.10.002, 2022
Piao, S., Liu, Q., Chen, A., Janssens, I. A., Fu, Y., Dai, J., Liu, L., Lian, X., Shen, M., and Zhu, X.: Plant phenology and global climate change: Current progresses and challenges. Glob. Change Biol., 25 (6), 1922-1940, https://doi.org/10.1111/gcb.14619, 2019.
Main concerns:

1. As the authors state baseflow is an important component of runoff during periods of low flow and drought, and it is critical to water security in the basin. However, how to accurately simulate baseflow has been a challenge in hydrology. The authors only mention very briefly in the manuscript the use of digital filtering to calculate baseflow, which is not very reasonable. Although the Lyne-Hollick digital filtering method is superior to the parameter less separation simplicity, the parameter selection as well as the number of filters need to be considered. Finally, the accuracy of the simulated values of the baseflow needs to be verified, and subsequent analyses should be performed after these tasks are completed to ensure the reliability of the research results.

Response 1: The focus of this work is on a new application of the FDA method (see our response to the general comments above) and is not intended to be a further contribution to the long-standing debate on baseflow separation methods. We understand the concerns regarding baseflow separation methods and acknowledge that the resulting baseflow time series from different methods are not equal. However, in this work we calculate the annual patterns from the baseflow, which should be fairly robust to the choice of baseflow separation method. The baseflow separation was performed on daily flow timeseries, but the annual components were evaluated using monthly averages of the baseflow. This temporal downscaling should allow for resilience of the presented results to different baseflow separation approaches. Our choice of digital filtering method was motivated by the standardised approach proposed by Ladson et al (2013) which allowed for processing of all of the CAMELS-GB catchments in a uniform way and we will include further specification of this method in the text. It would be unfeasible to tune a baseflow separation method for each of the catchments separately for this work and would make the interpretation of the results questionable if the same analytical approach had not been applied to each catchment. We will add analysis to the manuscript and supplementary material to demonstrate that the changes in seasonality shown in the paper are not due to the baseflow separation method.

Proposed changes 1: L150-152 will be extended to add further details on the Lyne-Hollick algorithmic approach. Further analysis will be performed using the UKCEH separation algorithm, and the similarity of the clustering outputs will be described in Section 3.1 (Characterisation of baseflow seasonality). Results of the clustering approach using this alternative baseflow separation method will be included in the Supplementary material in the same format as Fig S1-3. These additions will demonstrate that the choice of baseflow separation algorithm is not driving the results.

2. The manuscript focuses on analyzing the seasonality of baseflow and splits the hydrologic data from all stations into two windows. This approach is too subjective, as hydrological processes are affected to different degrees in each basin due to human activities and climate change, and in some cases, the timing of hydrological surges may even occur. Therefore, it is recommended to analyze the abrupt changes in baseflow in each basin before performing temporal and spatial analyses.

Response 2: In this work we investigated changes over two twenty-year time blocks. We did not target specific temporal changes as we were trying to identify changes based upon the seasonal distributions in these time blocks alone. We agree that the hydrological processes are catchment-specific, and in the discussion advocated for an improvement in time-varying catchment attributes because changes such as anthropogenic factors do not have associated data available. Whilst the catchment-specific approach would offer valuable insight, it would be impractical to perform a study for each of the 671 CAMELS-GB catchments, so this study provides information at the GB-scale. We think that processing the data from all catchments in the same way is advantageous as it allows for differences between catchments and time blocks (such as those due to anthropogenic or climate factors) to be identified and compared across GB (eg Fig 6d).The median was used to calculate monthly values for evaluation of the seasonal patterns so extreme features such as surges are mitigated so that the general behaviour and patterns over time can be identified. Our analysis has provided insight into long time-scale changes in seasonality of baseflow within GB catchments. In the discussion section we will add a commentary on the implications and limitations of the time block splits.

Proposed changes 2: We will extend the paragraph at L150-157 to motivate the choice of using the same algorithmic approach for each catchment, and describe how use of monthly values and median averaging will mitigate the influence of extreme years. We will add an additional paragraph to 4.1 (Controls on and changes in baseflow seasonality) to discuss the time-window blocks, and the changes that can be found due to this choice. Motivation for future work will be added to the conclusion (L428) to explore temporal changes that are not covered with the time block approach.

3. The manuscript contains insufficient research and more analysis needs to be added subsequently. For example, the authors mention that there is some consistency or correlation between changes in effective rainfall and baseflow seasonality, and a quantitative result is needed. On the other hand, the effects of other factors on baseflow seasonality, such as TWS and NDVI, need to be analyzed.
Response 3: Our analysis includes the concordance coefficient between the peak timing change for effective rainfall and baseflow (L350). As presented in the discussion section 4.3, the data availability of changing features of the catchments is poor, so many analyses we would like to investigate have not been possible due to lack of data. We emphasised the need for additional observational data to be included in large sample datasets to allow for such analyses, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.

Proposed changes 3: In L372-373 of the discussion section we will make the quantitative nature of the concordance result clear.

Referee 2:

This manuscript introduced a functional data analysis (FDA) approach to examine how the timing of seasonal peaks in annual standardized baseflow changes. It is applied to >600 catchments across Great Britain (GB). Understanding changes in (base)flow conditions is relevant, but before the paper is publishable several concerns need to be addressed (in my opinion).
The split of data from all stations into two windows is very arbitrary and may overlook some of the actual changes occurring (but are associated with other timings).

Response 1: Within this work we address the question of change over a coarse scale, twenty year time blocks. We agree that this time scale may not highlight all changes that are occurring, however long-scale changes have been identified within this work using these time windows and explored within the results section (Section 3.2: shifts to earlier seasonal patterns, including in snow-melt influenced catchments). This multi-decadal approach has enabled us to discover changes that are occurring across many catchments (movement to earlier clusters in Fig 2c, earlier seasonal peaks in Fig 6d) . Future follow-up work could consider differently targeted temporal blocks or spatial regions, however we think there is a lot of insight gained from the coarse scale, GB-wide approach we have used. We will add a discussion of the time window choice and the implications and limitations of this approach within the discussion section.

Proposed changes 1: (as above) We will add an additional paragraph to 4.1 (Controls on and changes in baseflow seasonality) to discuss the time-window blocks, and the changes that can be found due to this choice. Motivation for future work will be added to the conclusion (L428) to explore temporal changes that are not covered with the time block approach.

It is unclear how the chosen method of baseflow would affect the results.

Response 2: In our work the baseflow separation is performed before monthly averages are calculated, and then the median annual signal is calculated across multiple years. These two stages of averaging mean that small differences in baseflow calculated using different separation methods would be mitigated in the final results. The Lyne-Hollick filter was chosen due to its suitability for processing large numbers of streamflow time series, and we expect the annual patterns to be broadly robust across baseflow separation methods. We will demonstrate this the revision of the manuscript and supplementary material by providing further analysis using alternative baseflow separation.

Proposed changes 2: (as above) L150-152 will be extended to add further details on the Lyne-Hollick algorithmic approach. Further analysis will be performed using the UKCEH separation algorithm, and the similarity of the clustering outputs will be described in Section 3.1 (Characterisation of baseflow seasonality). Results of the clustering approach using this alternative baseflow separation method will be included in the Supplementary material in the same format as Fig S1-3. These additions will demonstrate that the choice of baseflow separation algorithm is not driving the results.

The association of vegetation-related (NDVI) causes is rather handwavy and qualitative in nature.

Response 3: We agree that some of the observations in the Discussion are by necessity qualitative, however, we took care to frame the statements based on new study observations and importantly highlighted the need for additional information that is currently not available.

In the discussion (L373-376) we state that “given the absence of association between change in precipitation and baseflow seasonality, it is inferred that the change in effective rainfall seasonality is due to changes in the seasonality of PET, the latter presumably driven at least in part by long-term warming across the UK”. However, note that we were careful not to directly associate this to “vegetation-related (NDVI) causes” as stated by the reviewer. This was because there is currently insufficient data to constrain changes in vegetation-related NDVI over time period of our analysis. This is why we also emphasised at the end of the Conclusion section the need for additional observational data to be included in large sample datasets, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.

Proposed changes 3: We will clarify at L376-377 that links to NDVI are not testable due to current data availability.

Color scales of Figures 1b and 2b could have a more informative range to highlight catchment differences better.

Response 4: Thank-you for this comment, we will adapt the colour scale for Fig 1b and 1c accordingly. Please clarify if Fig 2b was not sufficiently clear.

Proposed changes 4: Improvement of Figure 1b and 1c for a wider colour difference across the plots.

Could maps of figure 6 be enlarged so markers overlap less).

Response 5: We will adapt this figure for less overlap.

Proposed changes 5: Improvement of Figure 6, 2x2 grid of plots rather than 1x4 will allow for greater detail and larger individual plots.

If these points are meaningfully addressed the paper seems publishable.
Citation: https://doi.org/10.5194/hess-2023-202-AC3

Interactive discussion

Status: closed

RC1:
'Comment on hess-2023-202', Anonymous Referee #1, 15 Sep 2023

General comments:
The authors of the manuscript entitled "Functional data analysis to quantify and investigate controls on and changes in baseflow seasonality" aims at applying a novel functional data analysis (FDA) approach and examine temporal changes in the timing of seasonal peaks in annual standardized baseflow hydrographs for 671 catchments across Great Britain (GB). It is an important topic about watershed management plans. Unfortunately, I find that the manuscript does not break new ground nor offer insightful new methodology to the field of water resources. In general, the manuscript does not meet the high standard of HESS journal due to many flaws as follow (Main concerns). I cannot support this version of manuscript.
Main concerns:
1. As the authors state baseflow is an important component of runoff during periods of low flow and drought, and it is critical to water security in the basin. However, how to accurately simulate baseflow has been a challenge in hydrology. The authors only mention very briefly in the manuscript the use of digital filtering to calculate baseflow, which is not very reasonable. Although the Lyne-Hollick digital filtering method is superior to the parameter less separation simplicity, the parameter selection as well as the number of filters need to be considered. Finally, the accuracy of the simulated values of the baseflow needs to be verified, and subsequent analyses should be performed after these tasks are completed to ensure the reliability of the research results.
2. The manuscript focuses on analyzing the seasonality of baseflow and splits the hydrologic data from all stations into two windows. This approach is too subjective, as hydrological processes are affected to different degrees in each basin due to human activities and climate change, and in some cases, the timing of hydrological surges may even occur. Therefore, it is recommended to analyze the abrupt changes in baseflow in each basin before performing temporal and spatial analyses.
3. The manuscript contains insufficient research and more analysis needs to be added subsequently. For example, the authors mention that there is some consistency or correlation between changes in effective rainfall and baseflow seasonality, and a quantitative result is needed. On the other hand, the effects of other factors on baseflow seasonality, such as TWS and NDVI, need to be analyzed.

Citation: https://doi.org/10.5194/hess-2023-202-RC1
- AC2: 'Reply on RC1', Kathryn Leeming, 23 Oct 2023
  
  Thank you for your feedback on our submission, we'd like to address the general and specific (numbered) comments as follows.
  Response to general comments: We are disappointed that we’ve not been able to convey the novelty of the work in the first submission of the paper. We believe that it is novel both in the methodological approach employed and in the insights that the work has provided into the functioning of the terrestrial water cycle under long-term (multi-decadal) change.
  
  There are two elements to the methodological novelty. Firstly, as described in the paper (L87-L92) we have for the first time applied Functional Data Analysis (FDA) methods to analyse seasonal change in a hydraulic time series (in this case to baseflow). Secondly, as we note (L167-L171), unlike the limited previous work that has applied FDA in other hydrological contexts, in our study the seasonal shapes are standardised to remove their mean and give unit variance for each curve. This is critical as it allows the shapes defining the baseflow seasonality to be compared (rather than the absolute values) and enables the clustering and spatio-temporal analysis to be undertaken.
  
  This novel methodological approach has allowed us for the first time to address the challenge, only recently formulated by workers such as Piao et al. (2019) and Chen et al., (2022), of characterising and then investigating the controls on potential decadal-scale changes seasonality in the terrestrial water cycle driven by climate warming. This is a new set of research challenges only raised in the last couple of years and ours is the first study of baseflow that we are aware of in this context – hence our belief that the work and it’s findings are novel and “break new ground”.
  
  In the revised version of the paper, we will ensure these novelties are clear by strengthening the abstract, discussion and conclusions.
  Response 1: The focus of this work is on a new application of the FDA method (see our response to the general comments above) and is not intended to be a further contribution to the long-standing debate on baseflow separation methods. We understand the concerns regarding baseflow separation methods and acknowledge that the resulting baseflow time series from different methods are not equal. However, in this work we calculate the annual patterns from the baseflow, which should be fairly robust to the choice of baseflow separation method. The baseflow separation was performed on daily flow timeseries, but the annual components were evaluated using monthly averages of the baseflow. This temporal downscaling should allow for resilience of the presented results to different baseflow separation approaches. Our choice of digital filtering method was motivated by the standardised approach proposed by Ladson et al (2013) which allowed for processing of all of the CAMELS-GB catchments in a uniform way and we will include further specification of this method in the text. It would be unfeasible to tune a baseflow separation method for each of the catchments separately for this work and would make the interpretation of the results questionable if the same analytical approach had not been applied to each catchment. We will add analysis to the manuscript and supplementary material to demonstrate that the changes in seasonality shown in the paper are not due to the baseflow separation method.
  Response 2: In this work we investigated changes over two twenty-year time blocks. We did not target specific temporal changes as we were trying to identify changes based upon the seasonal distributions in these time blocks alone. We agree that the hydrological processes are catchment-specific, and in the discussion advocated for an improvement in time-varying catchment attributes because changes such as anthropogenic factors do not have associated data available. Whilst the catchment-specific approach would offer valuable insight, it would be impractical to perform a study for each of the 671 CAMELS-GB catchments, so this study provides information at the GB-scale. We think that processing the data from all catchments in the same way is advantageous as it allows for differences between catchments and time blocks (such as those due to anthropogenic or climate factors) to be identified and compared across GB (eg Fig 6d).The median was used to calculate monthly values for evaluation of the seasonal patterns so extreme features such as surges are mitigated so that the general behaviour and patterns over time can be identified. Our analysis has provided insight into long time-scale changes in seasonality of baseflow within GB catchments. In the discussion section we will add a commentary on the implications and limitations of the time block splits.
  Response 3: Our analysis includes the concordance coefficient between the peak timing change for effective rainfall and baseflow (L350). As presented in the discussion section 4.3, the data availability of changing features of the catchments is poor, so many analyses we would like to investigate have not been possible due to lack of data. We emphasised the need for additional observational data to be included in large sample datasets to allow for such analyses, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.
  References:
  
  Chen, S., Fu, Y. H., Hao, F., Li, X., Zhou, S., Liu, C., and Tang, J.: Vegetation phenology and its ecohydrological implications from individual to global scales. Geogr. Sustain., 3, 334-338, https://doi.org/10.1016/j.geosus.2022.10.002, 2022
  
  Piao, S., Liu, Q., Chen, A., Janssens, I. A., Fu, Y., Dai, J., Liu, L., Lian, X., Shen, M., and Zhu, X.: Plant phenology and global climate change: Current progresses and challenges. Glob. Change Biol., 25 (6), 1922-1940, https://doi.org/10.1111/gcb.14619, 2019.
  
  Citation: https://doi.org/10.5194/hess-2023-202-AC2
RC2:
'Comment on hess-2023-202', Anonymous Referee #2, 20 Sep 2023
This manuscript introduced a functional data analysis (FDA) approach to examine how the timing of seasonal peaks in annual standardized baseflow changes. It is applied to >600 catchments across Great Britain (GB). Understanding changes in (base)flow conditions is relevant, but before the paper is publishable several concerns need to be addressed (in my opinion).
The split of data from all stations into two windows is very arbitrary and may overlook some of the actual changes occurring (but are associated with other timings).

It is unclear how the chosen method of baseflow would affect the results.

The association of vegetation-related (NDVI) causes is rather handwavy and qualitative in nature.

Color scales of Figures 1b and 2b could have a more informative range to highlight catchment differences better.

Could maps of figure 6 be enlarged so markers overlap less).

If these points are meaningfully addressed the paper seems publishable.
Citation: https://doi.org/10.5194/hess-2023-202-RC2
- AC1: 'Reply on RC2', Kathryn Leeming, 23 Oct 2023
  
  Many thanks for your comments, responses to numbered points are included below.
  1. Within this work we address the question of change over a coarse scale, twenty year time blocks. We agree that this time scale may not highlight all changes that are occurring, however long-scale changes have been identified within this work using these time windows and explored within the results section (Section 3.2: shifts to earlier seasonal patterns, including in snow-melt influenced catchments). This multi-decadal approach has enabled us to discover changes that are occurring across many catchments (movement to earlier clusters in Fig 2c, earlier seasonal peaks in Fig 6d) . Future follow-up work could consider differently targeted temporal blocks or spatial regions, however we think there is a lot of insight gained from the coarse scale, GB-wide approach we have used. We will add a discussion of the time window choice and the implications and limitations of this approach within the discussion section.
  2. In our work the baseflow separation is performed before monthly averages are calculated, and then the median annual signal is calculated across multiple years. These two stages of averaging mean that small differences in baseflow calculated using different separation methods would be mitigated in the final results. The Lyne-Hollick filter was chosen due to its suitability for processing large numbers of streamflow time series, and we expect the annual patterns to be broadly robust across baseflow separation methods. We will demonstrate this the revision of the manuscript and supplementary material by providing further analysis using alternative baseflow separation.
  3. We agree that some of the observations in the Discussion are by necessity qualitative, however, we took care to frame the statements based on new study observations and importantly highlighted the need for additional information that is currently not available.
  In the discussion (L373-376) we state that “given the absence of association between change in precipitation and baseflow seasonality, it is inferred that the change in effective rainfall seasonality is due to changes in the seasonality of PET, the latter presumably driven at least in part by long-term warming across the UK”. However, note that we were careful not to directly associate this to “vegetation-related (NDVI) causes” as stated by the reviewer. This was because there is currently insufficient data to constrain changes in vegetation-related NDVI over time period of our analysis. This is why we also emphasised at the end of the Conclusion section the need for additional observational data to be included in large sample datasets, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.
  4. Thank-you for this comment, we will adapt the colour scale for Fig 1b and 1c accordingly. Please clarify if Fig 2b was not sufficiently clear.
  5. We will adapt this figure for less overlap.
  
  Citation: https://doi.org/10.5194/hess-2023-202-AC1
AC3:
'Comment on hess-2023-202', Kathryn Leeming, 31 Oct 2023
Our work demonstrates the application of functional data analysis (FDA) to consider the seasonal patterns of baseflow and whether the seasonality is changing over time. Other FDA applications in hydrology have not addressed seasonality specifically, and our approach has enabled us to identify differences in timing of the seasonal pattern of baseflow over catchments in Great Britain, and changes over the time period (1976-2015). The CAMELS-GB dataset contains streamflow and meteorological time series and catchment attributes for 671 catchments, and our analysis has been performed on each catchment equally. This allows us to consider the GB catchments simultaneously, and identify coarse-scale temporal changes.
Following the reviewers' feedback we propose improvements to clarify and add to elements of the text: enhanced discussion of the motivation and novelty of the approach throughout, discussion of the benefits and limitations of the twenty-year time blocking, analysis of the impacts of baseflow separation method on the results, and clearer figures.
Our manuscript does not seek to contribute to the debate over baseflow separation methods, and in our improvements we will show that the presented findings are not specific to the choice of Lyne-Hollick filter separation (addressing comments from both reviewers). The FDA approach used here is also not specific to baseflow and could be applied to different hydrological and meteorological time series.
We will also extend the discussion sections to include the benefits and limitations of the time splits used in this work (addressing comments from both reviewers). These time splits have allowed us to identify coarse-scale changes in the catchments over time scales that will feature different changes in different catchments. Unfortunately, the data availability on temporal changes in catchment management processes and other catchment attributes is poor, so we have focussed on large scale changes and climate changes in our analysis. Improving the data availability for catchment attribute changes is of importance for future studies, and we have highlighted this in the discussion section.
We do not expect that our proposed changes will alter the fundamental observations in this work, but they will strengthen the justification for the approach and the conclusions reached.
Referee 1:

General comments:

The authors of the manuscript entitled "Functional data analysis to quantify and investigate controls on and changes in baseflow seasonality" aims at applying a novel functional data analysis (FDA) approach and examine temporal changes in the timing of seasonal peaks in annual standardized baseflow hydrographs for 671 catchments across Great Britain (GB). It is an important topic about watershed management plans. Unfortunately, I find that the manuscript does not break new ground nor offer insightful new methodology to the field of water resources. In general, the manuscript does not meet the high standard of HESS journal due to many flaws as follow (Main concerns). I cannot support this version of manuscript.
Response to general comments: We are disappointed that we’ve not been able to convey the novelty of the work in the first submission of the paper. We believe that it is novel both in the methodological approach employed and in the insights that the work has provided into the functioning of the terrestrial water cycle under long-term (multi-decadal) change.
There are two elements to the methodological novelty. Firstly, as described in the paper (L87-L92) we have for the first time applied Functional Data Analysis (FDA) methods to analyse seasonal change in a hydraulic time series (in this case to baseflow). Secondly, as we note (L167-L171), unlike the limited previous work that has applied FDA in other hydrological contexts, in our study the seasonal shapes are standardised to remove their mean and give unit variance for each curve. This is critical as it allows the shapes defining the baseflow seasonality to be compared (rather than the absolute values) and enables the clustering and spatio-temporal analysis to be undertaken.
This novel methodological approach has allowed us for the first time to address the challenge, only recently formulated by workers such as Piao et al. (2019) and Chen et al., (2022), of characterising and then investigating the controls on potential decadal-scale changes seasonality in the terrestrial water cycle driven by climate warming. This is a new set of research challenges only raised in the last couple of years and ours is the first study of baseflow that we are aware of in this context – hence our belief that the work and it’s findings are novel and “break new ground”.
In the revised version of the paper, we will ensure these novelties are clear by strengthening the abstract, discussion and conclusions.

References:
Chen, S., Fu, Y. H., Hao, F., Li, X., Zhou, S., Liu, C., and Tang, J.: Vegetation phenology and its ecohydrological implications from individual to global scales. Geogr. Sustain., 3, 334-338, https://doi.org/10.1016/j.geosus.2022.10.002, 2022
Piao, S., Liu, Q., Chen, A., Janssens, I. A., Fu, Y., Dai, J., Liu, L., Lian, X., Shen, M., and Zhu, X.: Plant phenology and global climate change: Current progresses and challenges. Glob. Change Biol., 25 (6), 1922-1940, https://doi.org/10.1111/gcb.14619, 2019.
Main concerns:

1. As the authors state baseflow is an important component of runoff during periods of low flow and drought, and it is critical to water security in the basin. However, how to accurately simulate baseflow has been a challenge in hydrology. The authors only mention very briefly in the manuscript the use of digital filtering to calculate baseflow, which is not very reasonable. Although the Lyne-Hollick digital filtering method is superior to the parameter less separation simplicity, the parameter selection as well as the number of filters need to be considered. Finally, the accuracy of the simulated values of the baseflow needs to be verified, and subsequent analyses should be performed after these tasks are completed to ensure the reliability of the research results.

Response 1: The focus of this work is on a new application of the FDA method (see our response to the general comments above) and is not intended to be a further contribution to the long-standing debate on baseflow separation methods. We understand the concerns regarding baseflow separation methods and acknowledge that the resulting baseflow time series from different methods are not equal. However, in this work we calculate the annual patterns from the baseflow, which should be fairly robust to the choice of baseflow separation method. The baseflow separation was performed on daily flow timeseries, but the annual components were evaluated using monthly averages of the baseflow. This temporal downscaling should allow for resilience of the presented results to different baseflow separation approaches. Our choice of digital filtering method was motivated by the standardised approach proposed by Ladson et al (2013) which allowed for processing of all of the CAMELS-GB catchments in a uniform way and we will include further specification of this method in the text. It would be unfeasible to tune a baseflow separation method for each of the catchments separately for this work and would make the interpretation of the results questionable if the same analytical approach had not been applied to each catchment. We will add analysis to the manuscript and supplementary material to demonstrate that the changes in seasonality shown in the paper are not due to the baseflow separation method.

Proposed changes 1: L150-152 will be extended to add further details on the Lyne-Hollick algorithmic approach. Further analysis will be performed using the UKCEH separation algorithm, and the similarity of the clustering outputs will be described in Section 3.1 (Characterisation of baseflow seasonality). Results of the clustering approach using this alternative baseflow separation method will be included in the Supplementary material in the same format as Fig S1-3. These additions will demonstrate that the choice of baseflow separation algorithm is not driving the results.

2. The manuscript focuses on analyzing the seasonality of baseflow and splits the hydrologic data from all stations into two windows. This approach is too subjective, as hydrological processes are affected to different degrees in each basin due to human activities and climate change, and in some cases, the timing of hydrological surges may even occur. Therefore, it is recommended to analyze the abrupt changes in baseflow in each basin before performing temporal and spatial analyses.

Response 2: In this work we investigated changes over two twenty-year time blocks. We did not target specific temporal changes as we were trying to identify changes based upon the seasonal distributions in these time blocks alone. We agree that the hydrological processes are catchment-specific, and in the discussion advocated for an improvement in time-varying catchment attributes because changes such as anthropogenic factors do not have associated data available. Whilst the catchment-specific approach would offer valuable insight, it would be impractical to perform a study for each of the 671 CAMELS-GB catchments, so this study provides information at the GB-scale. We think that processing the data from all catchments in the same way is advantageous as it allows for differences between catchments and time blocks (such as those due to anthropogenic or climate factors) to be identified and compared across GB (eg Fig 6d).The median was used to calculate monthly values for evaluation of the seasonal patterns so extreme features such as surges are mitigated so that the general behaviour and patterns over time can be identified. Our analysis has provided insight into long time-scale changes in seasonality of baseflow within GB catchments. In the discussion section we will add a commentary on the implications and limitations of the time block splits.

Proposed changes 2: We will extend the paragraph at L150-157 to motivate the choice of using the same algorithmic approach for each catchment, and describe how use of monthly values and median averaging will mitigate the influence of extreme years. We will add an additional paragraph to 4.1 (Controls on and changes in baseflow seasonality) to discuss the time-window blocks, and the changes that can be found due to this choice. Motivation for future work will be added to the conclusion (L428) to explore temporal changes that are not covered with the time block approach.

3. The manuscript contains insufficient research and more analysis needs to be added subsequently. For example, the authors mention that there is some consistency or correlation between changes in effective rainfall and baseflow seasonality, and a quantitative result is needed. On the other hand, the effects of other factors on baseflow seasonality, such as TWS and NDVI, need to be analyzed.
Response 3: Our analysis includes the concordance coefficient between the peak timing change for effective rainfall and baseflow (L350). As presented in the discussion section 4.3, the data availability of changing features of the catchments is poor, so many analyses we would like to investigate have not been possible due to lack of data. We emphasised the need for additional observational data to be included in large sample datasets to allow for such analyses, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.

Proposed changes 3: In L372-373 of the discussion section we will make the quantitative nature of the concordance result clear.

Referee 2:

This manuscript introduced a functional data analysis (FDA) approach to examine how the timing of seasonal peaks in annual standardized baseflow changes. It is applied to >600 catchments across Great Britain (GB). Understanding changes in (base)flow conditions is relevant, but before the paper is publishable several concerns need to be addressed (in my opinion).
The split of data from all stations into two windows is very arbitrary and may overlook some of the actual changes occurring (but are associated with other timings).

Response 1: Within this work we address the question of change over a coarse scale, twenty year time blocks. We agree that this time scale may not highlight all changes that are occurring, however long-scale changes have been identified within this work using these time windows and explored within the results section (Section 3.2: shifts to earlier seasonal patterns, including in snow-melt influenced catchments). This multi-decadal approach has enabled us to discover changes that are occurring across many catchments (movement to earlier clusters in Fig 2c, earlier seasonal peaks in Fig 6d) . Future follow-up work could consider differently targeted temporal blocks or spatial regions, however we think there is a lot of insight gained from the coarse scale, GB-wide approach we have used. We will add a discussion of the time window choice and the implications and limitations of this approach within the discussion section.

Proposed changes 1: (as above) We will add an additional paragraph to 4.1 (Controls on and changes in baseflow seasonality) to discuss the time-window blocks, and the changes that can be found due to this choice. Motivation for future work will be added to the conclusion (L428) to explore temporal changes that are not covered with the time block approach.

It is unclear how the chosen method of baseflow would affect the results.

Response 2: In our work the baseflow separation is performed before monthly averages are calculated, and then the median annual signal is calculated across multiple years. These two stages of averaging mean that small differences in baseflow calculated using different separation methods would be mitigated in the final results. The Lyne-Hollick filter was chosen due to its suitability for processing large numbers of streamflow time series, and we expect the annual patterns to be broadly robust across baseflow separation methods. We will demonstrate this the revision of the manuscript and supplementary material by providing further analysis using alternative baseflow separation.

Proposed changes 2: (as above) L150-152 will be extended to add further details on the Lyne-Hollick algorithmic approach. Further analysis will be performed using the UKCEH separation algorithm, and the similarity of the clustering outputs will be described in Section 3.1 (Characterisation of baseflow seasonality). Results of the clustering approach using this alternative baseflow separation method will be included in the Supplementary material in the same format as Fig S1-3. These additions will demonstrate that the choice of baseflow separation algorithm is not driving the results.

The association of vegetation-related (NDVI) causes is rather handwavy and qualitative in nature.

Response 3: We agree that some of the observations in the Discussion are by necessity qualitative, however, we took care to frame the statements based on new study observations and importantly highlighted the need for additional information that is currently not available.

In the discussion (L373-376) we state that “given the absence of association between change in precipitation and baseflow seasonality, it is inferred that the change in effective rainfall seasonality is due to changes in the seasonality of PET, the latter presumably driven at least in part by long-term warming across the UK”. However, note that we were careful not to directly associate this to “vegetation-related (NDVI) causes” as stated by the reviewer. This was because there is currently insufficient data to constrain changes in vegetation-related NDVI over time period of our analysis. This is why we also emphasised at the end of the Conclusion section the need for additional observational data to be included in large sample datasets, see L417-420, e.g. “to investigate changes in seasonality and how these cascade through the terrestrial water cycle in different catchment settings there is a need for better linked environmental data sets, including both hydrological and phenological data, and continued production of and investment in future large sample data sets such as the CAMELS family of data sets.

Proposed changes 3: We will clarify at L376-377 that links to NDVI are not testable due to current data availability.

Color scales of Figures 1b and 2b could have a more informative range to highlight catchment differences better.

Response 4: Thank-you for this comment, we will adapt the colour scale for Fig 1b and 1c accordingly. Please clarify if Fig 2b was not sufficiently clear.

Proposed changes 4: Improvement of Figure 1b and 1c for a wider colour difference across the plots.

Could maps of figure 6 be enlarged so markers overlap less).

Response 5: We will adapt this figure for less overlap.

Proposed changes 5: Improvement of Figure 6, 2x2 grid of plots rather than 1x4 will allow for greater detail and larger individual plots.

If these points are meaningfully addressed the paper seems publishable.
Citation: https://doi.org/10.5194/hess-2023-202-AC3

Kathryn A. Leeming, John P. Bloomfield, Gemma Coxon, and Yanchen Zheng

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Kathryn A. Leeming, John P. Bloomfield, Gemma Coxon, and Yanchen Zheng

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Short summary

In this work we characterise annual patterns in baseflow, the component of streamflow that comes from subsurface storage. Our research identified early-, mid-, and late-seasonality of baseflow across catchments in Great Britain over two time blocks: 1976–1995 and 1996–2015, and found that many catchments have earlier seasonal patterns of baseflow in the second time period. These changes are linked to changes in climate signals: snow-melt in highland catchments and effective rainfall changes.


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