Articles | Volume 29, issue 13
https://doi.org/10.5194/hess-29-2851-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-29-2851-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note
| 
08 Jul 2025
Technical note |
| 08 Jul 2025
| 08 Jul 2025
Technical note: Streamflow seasonality using directional statistics
Department of Earth Sciences, Free University Amsterdam, Amsterdam, the Netherlands
Kate Hale
Department of Geography, University of British Columbia, Vancouver, Canada
Harsh Beria
WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland
Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, Zurich, Switzerland
Related authors
Anna Luisa Hemshorn de Sánchez, Wouter R. Berghuijs, Anne F. Van Loon, Dimmie Hendriks, and Ype van der Velde
EGUsphere, https://doi.org/10.5194/egusphere-2025-5139, https://doi.org/10.5194/egusphere-2025-5139, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
This study explores how mean and extreme river flows respond to annual climate variability. Maps show where river flow is more sensitive to climate in Europe. Maximum flows are generally the most sensitive and minimum flows the least sensitive to precipitation changes. Sensitivities are influenced by many factors like climate, soil, and terrain. These findings improve our understanding of how rivers respond to climate and can support water management and disaster risk reduction across Europe.
Julia L. A. Knapp, Wouter R. Berghuijs, Marius G. Floriancic, and James W. Kirchner
Hydrol. Earth Syst. Sci., 29, 3673–3685, https://doi.org/10.5194/hess-29-3673-2025, https://doi.org/10.5194/hess-29-3673-2025, 2025
Short summary
Short summary
This study explores how streams react to rain and how water travels through the landscape to reach them, two processes rarely studied together. Using detailed data from two temperate areas, we show that streams respond to rain much faster than rainwater travels to them. Wetter conditions lead to stronger runoff by releasing older stored water, while heavy rainfall moves newer rainwater to streams faster. These findings offer new insights into how water moves through the environment.
Wouter R. Berghuijs, Ross A. Woods, Bailey J. Anderson, Anna Luisa Hemshorn de Sánchez, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 29, 1319–1333, https://doi.org/10.5194/hess-29-1319-2025, https://doi.org/10.5194/hess-29-1319-2025, 2025
Short summary
Short summary
Water balances of catchments will often strongly depend on their state in the recent past, but such memory effects may persist at annual timescales. We use global data sets to show that annual memory is typically absent in precipitation but strong in terrestrial water stores and also present in evaporation and streamflow (including low flows and floods). Our experiments show that hysteretic models provide behaviour that is consistent with these observed memory behaviours.
Alexa Marion Hinzman, Ylva Sjöberg, Steve W. Lyon, Wouter R. Berghuijs, and Ype van der Velde
EGUsphere, https://doi.org/10.5194/egusphere-2023-2391, https://doi.org/10.5194/egusphere-2023-2391, 2023
Preprint archived
Short summary
Short summary
An Arctic catchment with permafrost responds in a linear fashion: water in=water out. As permafrost thaws, 9 of 10 nested catchments become more non-linear over time. We find upstream catchments have stronger streamflow seasonality and exhibit the most nonlinear storage-discharge relationships. Downstream catchments have the greatest increases in non-linearity over time. These long-term shifts in the storage-discharge relationship are not typically seen in current hydrological models.
Niek Jesse Speetjens, Gustaf Hugelius, Thomas Gumbricht, Hugues Lantuit, Wouter R. Berghuijs, Philip A. Pika, Amanda Poste, and Jorien E. Vonk
Earth Syst. Sci. Data, 15, 541–554, https://doi.org/10.5194/essd-15-541-2023, https://doi.org/10.5194/essd-15-541-2023, 2023
Short summary
Short summary
The Arctic is rapidly changing. Outside the Arctic, large databases changed how researchers look at river systems and land-to-ocean processes. We present the first integrated pan-ARctic CAtchments summary DatabasE (ARCADE) (> 40 000 river catchments draining into the Arctic Ocean). It incorporates information about the drainage area with 103 geospatial, environmental, climatic, and physiographic properties and covers small watersheds , which are especially subject to change, at a high resolution
Anna Luisa Hemshorn de Sánchez, Wouter R. Berghuijs, Anne F. Van Loon, Dimmie Hendriks, and Ype van der Velde
EGUsphere, https://doi.org/10.5194/egusphere-2025-5139, https://doi.org/10.5194/egusphere-2025-5139, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
This study explores how mean and extreme river flows respond to annual climate variability. Maps show where river flow is more sensitive to climate in Europe. Maximum flows are generally the most sensitive and minimum flows the least sensitive to precipitation changes. Sensitivities are influenced by many factors like climate, soil, and terrain. These findings improve our understanding of how rivers respond to climate and can support water management and disaster risk reduction across Europe.
Julia L. A. Knapp, Wouter R. Berghuijs, Marius G. Floriancic, and James W. Kirchner
Hydrol. Earth Syst. Sci., 29, 3673–3685, https://doi.org/10.5194/hess-29-3673-2025, https://doi.org/10.5194/hess-29-3673-2025, 2025
Short summary
Short summary
This study explores how streams react to rain and how water travels through the landscape to reach them, two processes rarely studied together. Using detailed data from two temperate areas, we show that streams respond to rain much faster than rainwater travels to them. Wetter conditions lead to stronger runoff by releasing older stored water, while heavy rainfall moves newer rainwater to streams faster. These findings offer new insights into how water moves through the environment.
Wouter R. Berghuijs, Ross A. Woods, Bailey J. Anderson, Anna Luisa Hemshorn de Sánchez, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 29, 1319–1333, https://doi.org/10.5194/hess-29-1319-2025, https://doi.org/10.5194/hess-29-1319-2025, 2025
Short summary
Short summary
Water balances of catchments will often strongly depend on their state in the recent past, but such memory effects may persist at annual timescales. We use global data sets to show that annual memory is typically absent in precipitation but strong in terrestrial water stores and also present in evaporation and streamflow (including low flows and floods). Our experiments show that hysteretic models provide behaviour that is consistent with these observed memory behaviours.
Matthias Sprenger, Rosemary W. H. Carroll, David Marchetti, Carleton Bern, Harsh Beria, Wendy Brown, Alexander Newman, Curtis Beutler, and Kenneth H. Williams
Hydrol. Earth Syst. Sci., 28, 1711–1723, https://doi.org/10.5194/hess-28-1711-2024, https://doi.org/10.5194/hess-28-1711-2024, 2024
Short summary
Short summary
Stable isotopes of water (described as d-excess) in mountain snowpack can be used to infer proportions of high-elevation snowmelt in stream water. In a Colorado River headwater catchment, nearly half of the water during peak streamflow is derived from melted snow at elevations greater than 3200 m. High-elevation snowpack contributions were higher for years with lower snowpack and warmer spring temperatures. Thus, we suggest that d-excess could serve to assess high-elevation snowpack changes.
Alexa Marion Hinzman, Ylva Sjöberg, Steve W. Lyon, Wouter R. Berghuijs, and Ype van der Velde
EGUsphere, https://doi.org/10.5194/egusphere-2023-2391, https://doi.org/10.5194/egusphere-2023-2391, 2023
Preprint archived
Short summary
Short summary
An Arctic catchment with permafrost responds in a linear fashion: water in=water out. As permafrost thaws, 9 of 10 nested catchments become more non-linear over time. We find upstream catchments have stronger streamflow seasonality and exhibit the most nonlinear storage-discharge relationships. Downstream catchments have the greatest increases in non-linearity over time. These long-term shifts in the storage-discharge relationship are not typically seen in current hydrological models.
Anthony Michelon, Natalie Ceperley, Harsh Beria, Joshua Larsen, Torsten Vennemann, and Bettina Schaefli
Hydrol. Earth Syst. Sci., 27, 1403–1430, https://doi.org/10.5194/hess-27-1403-2023, https://doi.org/10.5194/hess-27-1403-2023, 2023
Short summary
Short summary
Streamflow generation processes in high-elevation catchments are largely influenced by snow accumulation and melt. For this work, we collected and analyzed more than 2800 water samples (temperature, electric conductivity, and stable isotopes of water) to characterize the hydrological processes in such a high Alpine environment. Our results underline the critical role of subsurface flow during all melt periods and the presence of snowmelt even during the winter periods.
Niek Jesse Speetjens, Gustaf Hugelius, Thomas Gumbricht, Hugues Lantuit, Wouter R. Berghuijs, Philip A. Pika, Amanda Poste, and Jorien E. Vonk
Earth Syst. Sci. Data, 15, 541–554, https://doi.org/10.5194/essd-15-541-2023, https://doi.org/10.5194/essd-15-541-2023, 2023
Short summary
Short summary
The Arctic is rapidly changing. Outside the Arctic, large databases changed how researchers look at river systems and land-to-ocean processes. We present the first integrated pan-ARctic CAtchments summary DatabasE (ARCADE) (> 40 000 river catchments draining into the Arctic Ocean). It incorporates information about the drainage area with 103 geospatial, environmental, climatic, and physiographic properties and covers small watersheds , which are especially subject to change, at a high resolution
Anthony Michelon, Lionel Benoit, Harsh Beria, Natalie Ceperley, and Bettina Schaefli
Hydrol. Earth Syst. Sci., 25, 2301–2325, https://doi.org/10.5194/hess-25-2301-2021, https://doi.org/10.5194/hess-25-2301-2021, 2021
Short summary
Short summary
Rainfall observation remains a challenge, particularly in mountain environments. Unlike most studies which are model based, this analysis of the rainfall–runoff response of a 13.4 km2 alpine catchment is purely data based and relies on measurements from a network of 12 low-cost rain gauges over 3 months. It assesses the importance of high-density rainfall observations in informing hydrological processes and helps in designing a permanent rain gauge network.
Cited articles
Almagro, A., Meira Neto, A. A., Vergopolan, N., Roy, T., Troch, P. A., and Oliveira, P. T. S.: The drivers of hydrologic behavior in Brazil: Insights from a catchment classification, Water Resour. Res., 60, e2024WR037212, https://doi.org/10.1029/2024WR037212, 2024.
Bai, L. and Breen, D.: Calculating center of mass in an unbounded 2D environment, Journal of Graphics Tools, 13, 53–60, https://doi.org/10.1080/2151237X.2008.10129266, 2008.
Barnett, T. P., Adam, J. C., and Lettenmaier, D. P.: Potential impacts of a warming climate on water availability in snow-dominated regions, Nature, 438, 303–309, https://doi.org/10.1038/nature04141, 2005.
Bastrup-Birk, A. and Gundersen, P.: Water quality improvements from afforestation in an agricultural catchment in Denmark illustrated with the INCA model, Hydrol. Earth Syst. Sci., 8, 764–777, https://doi.org/10.5194/hess-8-764-2004, 2004.
Berghuijs, W.: Streamflow seasonality using directional statistics workflow figures, Zenodo [code], https://doi.org/10.5281/zenodo.15264750, 2025.
Berghuijs, W. R., Sivapalan, M., Woods, R. A., and Savenije, H. H. G.: Patterns of similarity of seasonal water balances: A window into streamflow variability over a range of time scales, Water Resour. Res., 50, 5638–5661, https://doi.org/10.1002/2014WR015692, 2014.
Berghuijs, W. R. and Woods, R.: A simple framework to quantitatively describe monthly precipitation and temperature climatology, Int. J. Climatol., 36, 3161–3174, https://doi.org/10.1002/joc.4544, 2016.
Berghuijs, W. R., Woods, R. A., Hutton, C. J., and Sivapalan, M.: Dominant flood generating mechanisms across the United States, Geophys. Res. Lett., 43, 4382–4390, https://doi.org/10.1002/2016GL068070, 2016.
Berghuijs, W. R., Harrigan, S., Molnar, P., Slater, L. J., and Kirchner, J. W.: The relative importance of different flood-generating mechanisms across Europe, Water Resour. Res., 55, 4582–4593, https://doi.org/10.1029/2019WR024841, 2019.
Berghuijs, W. R. and Hale, K.: Streamflow shifts with declining snowfall, Nature, 638, E35–E37, https://doi.org/10.1038/s41586-024-08523-5, 2025.
Botterill, T. E. and McMillan, H. K.: Using machine learning to identify hydrologic signatures with an encoder–decoder framework, Water Resour. Res., 59, e2022WR033091, https://doi.org/10.1029/2022WR033091, 2023.
Blöschl, G., Hall, J., Parajka, J., Perdigão, R. A. P., Merz, B., Arheimer, B., Aronica, G. T., Bilibashi, A., Bonacci, O., Borga, M., Čanjevac, I., Castellarin, A., Chirico, G. B., Claps, P., Fiala, K., Frolova, N., Gorbachova, L., Gül, A., Hannaford, J., Harrigan, S., Kireeva, M., Kiss, A., Kjeldsen, T. R., Kohnová, S., Koskela, J. J., Ledvinka, O., Macdonald, N., Mavrova-Guirguinova, M., Mediero, L., Merz, R., Molnar, P., Montanari, A., Murphy, C., Osuch, M., Ovcharuk, V., Radevski, I., Rogger, M., Salinas, J. L., Sauquet, E., Šraj, M., Szolgay, J., Viglione, A., Volpi, E., Wilson, D., Zaimi, K., and Živković, N.: Changing climate shifts timing of European floods, Science, 357, 588–590, https://doi.org/10.1126/science.aan2506, 2017.
Burn, D. H.: Catchment similarity for regional flood frequency analysis using seasonality measures, J. Hydrol., 202, 212–230, https://doi.org/10.1016/S0022-1694(97)00068-1, 1997.
Chagas, V. B., Chaffe, P. L., and Blöschl, G.: Process controls on flood seasonality in Brazil, Geophys. Res. Lett., 49, e2021GL096754, https://doi.org/10.1029/2021GL096754, 2022.
Chalise, D. R., Sankarasubramanian, A., and Ruhi, A.: Dams and climate interact to alter river flow regimes across the United States, Earths Future, 9, e2020EF001816, https://doi.org/10.1029/2020EF001816, 2021.
Chen, X., Jiang, L., Luo, Y., and Liu, J.: A global streamflow indices time series dataset for large-sample hydrological analyses on streamflow regime (until 2022), Earth Syst. Sci. Data, 15, 4463–4479, https://doi.org/10.5194/essd-15-4463-2023, 2023.
Clow, D. W.: Changes in the timing of snowmelt and streamflow in Colorado: A response to recent warming, J. Climate, 23, 2293–2306, https://doi.org/10.1175/2009JCLI2951.1, 2010.
Court, A.: Measures of streamflow timing, J. Geophys. Res., 67, 4335–4339, https://doi.org/10.1029/JZ067i011p04335, 1962.
Dhakal, N., Jain, S., Gray, A., Dandy, M., and Stancioff, E.: Nonstationarity in seasonality of extreme precipitation: A nonparametric circular statistical approach and its application, Water Resour. Res., 51, 4499–4515, https://doi.org/10.1002/2014WR016399, 2015.
do Nascimento, T. V. M., Rudlang, J., Höge, M., van der Ent, R., Chappon, M., Seibert, J., Hrachowitz, M., and Fenicia, F.: EStreams: An integrated dataset and catalogue of stream- flow, hydro-climatic and landscape variables for Europe, Scientific Data, 11, 879, https://doi.org/10.1038/s41597-024-03706-1, 2024.
Eisner, S., Flörke, M., Chamorro, A., Daggupati, P., Donnelly, C., Huang, J., Hundecha, Y., Koch, H., Kalugin, A., Krylenko, I., Mishra, V., Piniewski, M., Samaniego, L., Seidou, O., Wallner, M., and Krysanova, V.: An ensemble analysis of climate change impacts on streamflow seasonality across 11 large river basins, Climatic Change, 141, 401–417, https://doi.org/10.1007/s10584-016-1844-5, 2017.
Feng, X., Porporato, A., and Rodriguez-Iturbe, I.: Changes in rainfall seasonality in the tropics, Nat. Clim. Change, 3, 811–815, https://doi.org/10.1038/nclimate1907, 2013.
Floriancic, M. G., Berghuijs, W. R., Molnar, P., and Kirchner, J. W.: Seasonality and drivers of low flows across Europe and the United States, Water Resour. Res., 57, e2019WR026928, https://doi.org/10.1029/2019WR026928, 2021.
Gnann, S. J., Howden, N. J. K., and Woods, R. A.: Hydrological signatures describing the translation of climate seasonality into streamflow seasonality, Hydrol. Earth Syst. Sci., 24, 561–580, https://doi.org/10.5194/hess-24-561-2020, 2020.
Gnann, S. J., Coxon, G., Woods, R. A., Howden, N. J., and McMillan, H. K.: TOSSH: A toolbox for streamflow signatures in hydrology, Environ. Modell. Softw., 138, 104983, https://doi.org/10.1016/j.envsoft.2021.104983, 2021.
Haines, A. T., Finlayson, B. L., and McMahon, T. A.: A global classification of river regimes, Appl. Geogr., 8, 255–272, https://doi.org/10.1016/0143-6228(88)90035-5, 1988.
Han, J., Liu, Z., Woods, R., McVicar, T. R., Yang, D., Wang, T., Hou, Y., Guo, Y., Li, C., and Yang, Y.: Streamflow seasonality in a snow-dwindling world, Nature, 629, 1075–1081, https://doi.org/10.1038/s41586-024-07299-y, 2024.
Hanus, S., Burek, P., Smilovic, M., Seibert, J., and Viviroli, D.: Seasonal variability in the global relevance of mountains to satisfy lowland water demand, Environ. Res. Lett., 19, 114078, https://doi.org/10.1088/1748-9326/ad8507, 2024.
Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M. H., Brett, M., Haldane, A., Fernández del Río, J., Wiebe, M., Peterson, P., Gérard-Marchant, P., Sheppard, K., Reddy, T., Weckesser, W., Abbasi, H., Gohlke, C., and Oliphant, T. E.: Array programming with NumPy, Nature, 585, 357–362, https://doi.org/10.1038/s41586-020-2649-2, 2020.
Hodgkins, G., Dudley, R., and Huntington, T.: Changes in the timing of high river flows in New England over the 20th century, J. Hydrol., 278, 244–252, https://doi.org/10.1016/S0022-1694(03)00155-0, 2003.
Hörtnagl, L., Buchmann, N., Meier, P., Gharun, M., Baur, T., Eugster, W., and Feigenwinter, I.: CH-DAV FP2022.5 (1997–2022), ETH Zurich [data set], https://doi.org/10.3929/ETHZ-B-000597213, 2023.
Jiang, Y., Xu, Z., and Xiong, L.: Runoff variation and response to precipitation on multi-spatial and temporal scales in the southern Tibetan Plateau, J. Hydrol., 42, 101157, https://doi.org/10.1016/j.ejrh.2022.101157, 2022.
Knoben, W. J., Woods, R. A., and Freer, J. E.: A quantitative hydrological climate classification evaluated with independent streamflow data, Water Resour. Res., 54, 5088–5109, https://doi.org/10.1029/2018WR022913, 2018.
Kormos, P. R., Luce, C. H., Wenger, S. J., and Berghuijs, W. R.: Trends and sensitivities of low streamflow extremes to discharge timing and magnitude in Pacific Northwest mountain streams, Water Resour. Res., 52, 4990–5007, https://doi.org/10.1002/2015WR018125, 2016.
Laaha, G. and Blöschl, G.: Seasonality indices for regionalizing low flows, Hydrol. Process., 20, 3851–3878, https://doi.org/10.1002/hyp.6161, 2006.
Luce, C. H. and Holden, Z. A.: Declining annual streamflow distributions in the Pacific Northwest United States, 1948–2006, Geophys. Res. Lett., 36, L16401, https://doi.org/10.1029/2009GL039407, 2009.
Magnusson, J., Bühler, Y., Quéno, L., Cluzet, B., Mazzotti, G., Webster, C., Mott, R., and Jonas, T.: High-resolution hydrometeorological and snow data for the Dischma catchment in Switzerland, Earth Syst. Sci. Data, 17, 703–717, https://doi.org/10.5194/essd-17-703-2025, 2025.
Mardia, K. V. and Jupp, P. E.: Directional Statistics, Academic Press Inc., London, England, ISBN 9780470316979, 1972.
Marvel, K., Cook, B. I., Bonfils, C., Smerdon, J. E., Williams, A. P., and Liu, H.: Projected changes to hydroclimate seasonality in the continental United States, Earths Future, 9, e2021EF002019, https://doi.org/10.1029/2021EF002019, 2021.
Merz, R. and Blöschl, G.: A process typology of regional floods, Water Resour. Res., 39, 1340–1359, https://doi.org/10.1029/2002WR001952, 2003.
Mott, R.: Climatological snow data since 1998, OSHD, EnviDat [data set], https://doi.org/10.16904/envidat.401, 2023.
Nan, Y. and Tian, F.: Glaciers determine the sensitivity of hydrological processes to perturbed climate in a large mountainous basin on the Tibetan Plateau, Hydrol. Earth Syst. Sci., 28, 669–689, https://doi.org/10.5194/hess-28-669-2024, 2024.
Oliver, J. E.: Monthly precipitation distribution: a comparative index, Prof. Geogr., 32, 300–309, https://doi.org/10.1111/j.0033-0124.1980.00300.x, 1980.
Pardé, M.: Fleuves et Rivières, Armand Colin, Paris, France, p. 224, 1933.
Patil, R., Wei, Y., and Shulmeister, J.: Change in center of timing of streamflow and its implications for environmental water allocation and river ecosystem management, Ecol. Indic., 153, 110444, https://doi.org/10.1016/j.ecolind.2023.110444, 2023.
Poff, N. L., Allan, J. D., Bain, M. B., Karr, J. R., Prestegaard, K. L., Richter, B. D., Sparks, R. E., and Stromberg, J. C.: The natural flow regime, BioScience, 47, 769–784, https://doi.org/10.2307/1313099, 1997.
Regonda, S., Rajagopalan, B., Clark, M., and Pitlick, J.: Seasonal cycle shifts in hydroclimatology over the western United States, J. Climate, 18, 372–384, https://doi.org/10.1175/JCLI-3272.1, 2005.
Renner, M. and Bernhofer, C.: Long term variability of the annual hydrological regime and sensitivity to temperature phase shifts in Saxony/Germany, Hydrol. Earth Syst. Sci., 15, 1819–1833, https://doi.org/10.5194/hess-15-1819-2011, 2011.
Sivapalan, M., Blöschl, G., Merz, R., and Gutknecht, D.: Linking flood frequency to long-term water balance: Incorporating effects of seasonality, Water Resour. Res., 41, W06012, https://doi.org/10.1029/2004WR003439, 2005.
Stewart, I. T., Cayan, D. R., and Dettinger, M. D.: Changes toward earlier streamflow timing across western North America, J. Climate, 18, 1136–1155, https://doi.org/10.1175/JCLI3321.1, 2005.
Stine, A. R., Huybers, P., and Fung, I. Y.: Changes in the phase of the annual cycle of surface temperature, Nature, 457, 435–440, https://doi.org/10.1038/nature07675, 2009.
Sun, X. and Cheruvelil, K. S.: Local water year values for the conterminous United States, EarthArxiv [preprint], https://doi.org/10.31223/X5Q121, 2024.
Villarini, G.: On the seasonality of flooding across the continental United States, Adv. Water Resour., 87, 80–91, 2016.
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, İ., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors: SciPy 1.0: fundamental algorithms for scientific computing in Python, Nat. Methods, 17, 261–272, https://doi.org/10.1038/s41592-019-0686-2, 2020.
Wang, H., Liu, J., Klaar, M., Chen, A., Gudmundsson, L., and Holden, J.: Anthropogenic climate change has influenced global river flow seasonality, Science, 383, 1009–1014, https://doi.org/10.1126/science.adi9501, 2024.
Whitfield, P. H.: Is “Centre of Volume” a robust indicator of changes in snowmelt timing?, Hydrol. Process., 27, 2691–2698, https://doi.org/10.1002/hyp.9817, 2013.
Walsh, R. P. D. and Lawler, D. M.: Rainfall seasonality: description, spatial patterns and change through time, Weather, 36, 201–208, https://doi.org/10.1002/j.1477-8696.1981.tb05400.x, 1981.
Wasko, C., Nathan, R., and Peel, M. C.: Trends in global flood and streamflow timing based on local water year, Water Resour. Res., 56, e2020WR027233, https://doi.org/10.1029/2020WR027233, 2020.
Yang, D., Zhao, Y., Armstrong, R., Robinson, D. and Brodzik, M. J.: Streamflow response to seasonal snow cover mass changes over large Siberian watersheds, J. Geophys. Res.-Earth., 112, F02s22, https://doi.org/10.1029/2006jf000518, 2007.
Young, A. R., Round, C. E., and Gustard, A.: Spatial and temporal variations in the occurrence of low flow events in the UK, Hydrol. Earth Syst. Sci., 4, 35–45, https://doi.org/10.5194/hess-4-35-2000, 2000.
Short summary
We present directional statistics to characterize seasonality, capturing the timing of streamflow (center of mass timing) and the strength of its seasonal cycle (concentration). Directional statistics are more robust than several widely used metrics to quantify streamflow seasonality. The introduced metrics 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.
We present directional statistics to characterize seasonality, capturing the timing of...
