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
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.
Julia L. A. Knapp, Wouter R. Berghuijs, Marius G. Floriancic, and James W. Kirchner
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-371, https://doi.org/10.5194/hess-2024-371, 2024
Revised manuscript accepted for HESS
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, it shows 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.
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
Marius G. Floriancic, Wouter R. Berghuijs, Tobias Jonas, James W. Kirchner, and Peter Molnar
Hydrol. Earth Syst. Sci., 24, 5423–5438, https://doi.org/10.5194/hess-24-5423-2020, https://doi.org/10.5194/hess-24-5423-2020, 2020
Short summary
Short summary
Low river flows affect societies and ecosystems. Here we study how precipitation and potential evapotranspiration shape low flows across a network of 380 Swiss catchments. Low flows in these rivers typically result from below-average precipitation and above-average potential evapotranspiration. Extreme low flows result from long periods of the combined effects of both drivers.
Scott T. Allen, Scott Jasechko, Wouter R. Berghuijs, Jeffrey M. Welker, Gregory R. Goldsmith, and James W. Kirchner
Hydrol. Earth Syst. Sci., 23, 3423–3436, https://doi.org/10.5194/hess-23-3423-2019, https://doi.org/10.5194/hess-23-3423-2019, 2019
Short summary
Short summary
We developed global maps that concisely quantify the seasonality of stable isotope ratios in precipitation, using data from 653 meteorological stations across all seven continents. We make these gridded global maps publicly available to support diverse stable isotope applications.
Koen Hilgersom, Tim van Emmerik, Anna Solcerova, Wouter Berghuijs, John Selker, and Nick van de Giesen
Geosci. Instrum. Method. Data Syst., 5, 151–162, https://doi.org/10.5194/gi-5-151-2016, https://doi.org/10.5194/gi-5-151-2016, 2016
Short summary
Short summary
Fibre optic distributed temperature sensing allows one to measure temperature patterns along a fibre optic cable with resolutions down to 25 cm. In geosciences, we sometimes wrap the cable to a coil to measure temperature at even smaller scales. We show that coils with narrow bends affect the measured temperatures. This also holds for the object to which the coil is attached, when heated by solar radiation. We therefore recommend the necessity to carefully design such distributed temperature probes.
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.
Julia L. A. Knapp, Wouter R. Berghuijs, Marius G. Floriancic, and James W. Kirchner
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-371, https://doi.org/10.5194/hess-2024-371, 2024
Revised manuscript accepted for HESS
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, it shows 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.
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
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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.
Marius G. Floriancic, Wouter R. Berghuijs, Tobias Jonas, James W. Kirchner, and Peter Molnar
Hydrol. Earth Syst. Sci., 24, 5423–5438, https://doi.org/10.5194/hess-24-5423-2020, https://doi.org/10.5194/hess-24-5423-2020, 2020
Short summary
Short summary
Low river flows affect societies and ecosystems. Here we study how precipitation and potential evapotranspiration shape low flows across a network of 380 Swiss catchments. Low flows in these rivers typically result from below-average precipitation and above-average potential evapotranspiration. Extreme low flows result from long periods of the combined effects of both drivers.
Harsh Beria, Joshua R. Larsen, Anthony Michelon, Natalie C. Ceperley, and Bettina Schaefli
Geosci. Model Dev., 13, 2433–2450, https://doi.org/10.5194/gmd-13-2433-2020, https://doi.org/10.5194/gmd-13-2433-2020, 2020
Short summary
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We develop a Bayesian mixing model to address the issue of small sample sizes to describe different sources in hydrological mixing applications. Using composite likelihood functions, the model accounts for an often overlooked bias arising due to unweighted mixing. We test the model efficacy using a series of statistical benchmarking tests and demonstrate its real-life applicability by applying it to a Swiss Alpine catchment to obtain the proportion of groundwater recharged from rain vs. snow.
Anthony Michelon, Lionel Benoit, Harsh Beria, Natalie Ceperley, and Bettina Schaefli
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2019-683, https://doi.org/10.5194/hess-2019-683, 2020
Manuscript not accepted for further review
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 rely on measures from a network of 12 low-cost raingauges over 3 months. It assesses the importance of high-density rainfall observations to inform hydrological processes and help to design a permanent raingauge network.
Scott T. Allen, Scott Jasechko, Wouter R. Berghuijs, Jeffrey M. Welker, Gregory R. Goldsmith, and James W. Kirchner
Hydrol. Earth Syst. Sci., 23, 3423–3436, https://doi.org/10.5194/hess-23-3423-2019, https://doi.org/10.5194/hess-23-3423-2019, 2019
Short summary
Short summary
We developed global maps that concisely quantify the seasonality of stable isotope ratios in precipitation, using data from 653 meteorological stations across all seven continents. We make these gridded global maps publicly available to support diverse stable isotope applications.
Harsh Beria, Trushnamayee Nanda, Deepak Singh Bisht, and Chandranath Chatterjee
Hydrol. Earth Syst. Sci., 21, 6117–6134, https://doi.org/10.5194/hess-21-6117-2017, https://doi.org/10.5194/hess-21-6117-2017, 2017
Short summary
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High-quality satellite precipitation forcings have provided a viable alternative to hydrologic modeling in data-scarce regions. Ageing TRMM sensors have recently been upgraded to GPM, promising enhanced spatio-temporal resolutions. Statistical and hydrologic evaluation of GPM measurements across 86 Indian river basins revealed improved low rainfall estimates with reduced effects of climatology and topography.
Koen Hilgersom, Tim van Emmerik, Anna Solcerova, Wouter Berghuijs, John Selker, and Nick van de Giesen
Geosci. Instrum. Method. Data Syst., 5, 151–162, https://doi.org/10.5194/gi-5-151-2016, https://doi.org/10.5194/gi-5-151-2016, 2016
Short summary
Short summary
Fibre optic distributed temperature sensing allows one to measure temperature patterns along a fibre optic cable with resolutions down to 25 cm. In geosciences, we sometimes wrap the cable to a coil to measure temperature at even smaller scales. We show that coils with narrow bends affect the measured temperatures. This also holds for the object to which the coil is attached, when heated by solar radiation. We therefore recommend the necessity to carefully design such distributed temperature probes.
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Mathematical applications
Technical note: Quadratic Solution of the Approximate Reservoir Equation (QuaSoARe)
Two-dimensional Differential-form of Distributed Xinanjiang Model
Climatic, topographic, and groundwater controls on runoff response to precipitation: evidence from a large-sample data set
Processes and controls of regional floods over eastern China
Imprints of Increases in Evapotranspiration on Decreases in Streamflow during dry Periods, a large-sample Analysis in Germany
A national-scale hybrid model for enhanced streamflow estimation – consolidating a physically based hydrological model with long short-term memory (LSTM) networks
Understanding meteorological and physio-geographical controls of variability of flood event classes in China
Inferring heavy tails of flood distributions through hydrograph recession analysis
Landscape structures regulate the contrasting response of recession along rainfall amounts
Hydrological objective functions and ensemble averaging with the Wasserstein distance
Spatial variability in Alpine reservoir regulation: deriving reservoir operations from streamflow using generalized additive models
Regional significance of historical trends and step changes in Australian streamflow
River flooding mechanisms and their changes in Europe revealed by explainable machine learning
Changes in nonlinearity and stability of streamflow recession characteristics under climate warming in a large glaciated basin of the Tibetan Plateau
A data-driven method for estimating the composition of end-members from stream water chemistry time series
Evaporation loss estimation of the river-lake continuum of arid inland river: Evidence from stable isotopes
Technical note: PMR – a proxy metric to assess hydrological model robustness in a changing climate
Causal effects of dams and land cover changes on flood changes in mainland China
Can the two-parameter recursive digital filter baseflow separation method really be calibrated by the conductivity mass balance method?
Simultaneously determining global sensitivities of model parameters and model structure
Technical note: Calculation scripts for ensemble hydrograph separation
Specific climate classification for Mediterranean hydrology and future evolution under Med-CORDEX regional climate model scenarios
A line-integral-based method to partition climate and catchment effects on runoff
Technical note: A two-sided affine power scaling relationship to represent the concentration–discharge relationship
On the flood peak distributions over China
New water fractions and transit time distributions at Plynlimon, Wales, estimated from stable water isotopes in precipitation and streamflow
Does the weighting of climate simulations result in a better quantification of hydrological impacts?
A 50-year analysis of hydrological trends and processes in a Mediterranean catchment
Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu
Climate or land cover variations: what is driving observed changes in river peak flows? A data-based attribution study
Quantifying new water fractions and transit time distributions using ensemble hydrograph separation: theory and benchmark tests
Land cover effects on hydrologic services under a precipitation gradient
Technical note: Long-term persistence loss of urban streams as a metric for catchment classification
Responses of runoff to historical and future climate variability over China
Characterization and evaluation of controls on post-fire streamflow response across western US watersheds
Analysis and modelling of a 9.3 kyr palaeoflood record: correlations, clustering, and cycles
Climate change impacts on Yangtze River discharge at the Three Gorges Dam
Can assimilation of crowdsourced data in hydrological modelling improve flood prediction?
Delineation of homogenous regions using hydrological variables predicted by projection pursuit regression
Multivariate hydrological data assimilation of soil moisture and groundwater head
On the propagation of diel signals in river networks using analytic solutions of flow equations
Dominant climatic factors driving annual runoff changes at the catchment scale across China
Data assimilation in integrated hydrological modelling in the presence of observation bias
Recent changes in climate, hydrology and sediment load in the Wadi Abd, Algeria (1970–2010)
Technical Note: Testing an improved index for analysing storm discharge–concentration hysteresis
Estimating spatially distributed soil water content at small watershed scales based on decomposition of temporal anomaly and time stability analysis
Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization
Time series analysis of the long-term hydrologic impacts of afforestation in the Águeda watershed of north-central Portugal
Data assimilation in integrated hydrological modeling using ensemble Kalman filtering: evaluating the effect of ensemble size and localization on filter performance
Attribution of high resolution streamflow trends in Western Austria – an approach based on climate and discharge station data
Julien Lerat
Hydrol. Earth Syst. Sci., 29, 2003–2021, https://doi.org/10.5194/hess-29-2003-2025, https://doi.org/10.5194/hess-29-2003-2025, 2025
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This paper presents a method to solve a certain type of equation controlling the storage of water in hydrological models. This equation is often solved with complex numerical methods that may lead to slow runtimes. The method, called the Quadratic Solution of the Approximate Reservoir Equation (QuaSoARe), is both fast and applicable to any equation of this kind regardless of its complexity. The method reduces runtime by a factor of 10 to 50 depending on the model.
Jianfei Zhao, Zhongmin Liang, Vijay P. Singh, Taiyi Wen, Yiming Hu, Binquan Li, and Jun Wang
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-377, https://doi.org/10.5194/hess-2024-377, 2025
Revised manuscript accepted for HESS
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Distributed hydrological models often evolve from lumped models, but this shift can overlook important issues. By revisiting the distributed Xinanjiang model, we show that numerical errors persist and terrain representation is constrained by one-dimensional slope routing methods. These limitations can be addressed by combining purely differential-form equations, two-dimensional slope routing methods, and proper numerical implementation, resulting in an improved distributed Xinanjiang model.
Zahra Eslami, Hansjörg Seybold, and James W. Kirchner
EGUsphere, https://doi.org/10.5194/egusphere-2025-35, https://doi.org/10.5194/egusphere-2025-35, 2025
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We used a new method to measure how streamflow responds to precipitation across a network of watersheds in Iran. Our analysis shows that streamflow is more sensitive to precipitation when groundwater levels are shallower, climates are more humid, topography is steeper, and drainage basins are smaller. These results are a step toward more sustainable water resource management and more effective flood risk mitigation.
Yixin Yang, Long Yang, Jinghan Zhang, and Qiang Wang
Hydrol. Earth Syst. Sci., 28, 4883–4902, https://doi.org/10.5194/hess-28-4883-2024, https://doi.org/10.5194/hess-28-4883-2024, 2024
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We introduce a machine-learning framework to study spatial characteristics and drivers of regional floods in eastern China, using 38 years of flood peak data from a vast gauging network. Our analyses provide better understanding of contrasting flood behaviors by explicitly characterizing their spatial extents. This knowledge can help improve flood risk management.
Giulia Bruno, Laurent Strohmenger, and Doris Duethmann
EGUsphere, https://doi.org/10.5194/egusphere-2024-2678, https://doi.org/10.5194/egusphere-2024-2678, 2024
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Decreases in streamflow during dry periods threaten ecosystems and society, and increases in evapotranspiration may contribute to them. From data for small catchments in Germany, summer low flows decreased over 1970–2019 and increases in evapotranspiration relevantly contributed. Stronger-than-expected decreases in streamflow during the 1989–1993 drought occurred in catchments with increases in evapotranspiration. Increases in evapotranspiration need full consideration for streamflow prediction.
Jun Liu, Julian Koch, Simon Stisen, Lars Troldborg, and Raphael J. M. Schneider
Hydrol. Earth Syst. Sci., 28, 2871–2893, https://doi.org/10.5194/hess-28-2871-2024, https://doi.org/10.5194/hess-28-2871-2024, 2024
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We developed hybrid schemes to enhance national-scale streamflow predictions, combining long short-term memory (LSTM) with a physically based hydrological model (PBM). A comprehensive evaluation of hybrid setups across Denmark indicates that LSTM models forced by climate data and catchment attributes perform well in many regions but face challenges in groundwater-dependent basins. The hybrid schemes supported by PBMs perform better in reproducing long-term streamflow behavior and extreme events.
Yongyong Zhang, Yongqiang Zhang, Xiaoyan Zhai, Jun Xia, Qiuhong Tang, Wei Wang, Jian Wu, Xiaoyu Niu, and Bing Han
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-126, https://doi.org/10.5194/hess-2024-126, 2024
Revised manuscript accepted for HESS
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It is challenging to investigate flood variabilities and their formation mechanisms from massive event samples. This study explores spatiotemporal variabilities of 1446 flood events using hierarchical and partitional clustering methods. Control mechanisms of meteorological and physio-geographical factors are explored for individual flood event classes using constrained rank analysis. It provides insights into comprehensive changes of flood events, and aids in flood prediction and control.
Hsing-Jui Wang, Ralf Merz, Soohyun Yang, and Stefano Basso
Hydrol. Earth Syst. Sci., 27, 4369–4384, https://doi.org/10.5194/hess-27-4369-2023, https://doi.org/10.5194/hess-27-4369-2023, 2023
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Accurately assessing heavy-tailed flood behavior with limited data records is challenging and can lead to inaccurate hazard estimates. Our research introduces a new index that uses hydrograph recession to identify heavy-tailed flood behavior, compare severity, and produce reliable results with short data records. This index overcomes the limitations of current metrics, which lack physical meaning and require long records. It thus provides valuable insight into the flood hazard of river basins.
Jun-Yi Lee, Ci-Jian Yang, Tsung-Ren Peng, Tsung-Yu Lee, and Jr-Chuan Huang
Hydrol. Earth Syst. Sci., 27, 4279–4294, https://doi.org/10.5194/hess-27-4279-2023, https://doi.org/10.5194/hess-27-4279-2023, 2023
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Streamflow recession, shaped by landscape and rainfall, is not well understood. This study examines their combined impact using data from 19 mountainous rivers. Longer, gentler hillslopes promote flow and reduce nonlinearity, while larger catchments with more rainfall show increased landscape heterogeneity. In small catchments, the exponent decreases with rainfall, indicating less landscape and runoff variation. Further research is needed to validate these findings across diverse regions.
Jared C. Magyar and Malcolm Sambridge
Hydrol. Earth Syst. Sci., 27, 991–1010, https://doi.org/10.5194/hess-27-991-2023, https://doi.org/10.5194/hess-27-991-2023, 2023
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Measuring the similarity of distributions of water is a useful tool for model calibration and assessment. We provide a new way of measuring this similarity for streamflow time series. It is derived from the concept of the amount of
workrequired to rearrange one mass distribution into the other. We also use similar mathematical techniques for defining a type of
averagebetween water distributions.
Manuela Irene Brunner and Philippe Naveau
Hydrol. Earth Syst. Sci., 27, 673–687, https://doi.org/10.5194/hess-27-673-2023, https://doi.org/10.5194/hess-27-673-2023, 2023
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Reservoir regulation affects various streamflow characteristics. Still, information on when water is stored in and released from reservoirs is hardly available. We develop a statistical model to reconstruct reservoir operation signals from observed streamflow time series. By applying this approach to 74 catchments in the Alps, we find that reservoir management varies by catchment elevation and that seasonal redistribution from summer to winter is strongest in high-elevation catchments.
Gnanathikkam Emmanuel Amirthanathan, Mohammed Abdul Bari, Fitsum Markos Woldemeskel, Narendra Kumar Tuteja, and Paul Martinus Feikema
Hydrol. Earth Syst. Sci., 27, 229–254, https://doi.org/10.5194/hess-27-229-2023, https://doi.org/10.5194/hess-27-229-2023, 2023
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We used statistical tests to detect annual and seasonal streamflow trends and step changes across Australia. The Murray–Darling Basin and other rivers in the southern and north-eastern areas showed decreasing trends. Only rivers in the Timor Sea region in northern Australia showed significant increasing trends. Our results assist with infrastructure planning and management of water resources. This study was undertaken by the Bureau of Meteorology with its responsibility under the Water Act 2007.
Shijie Jiang, Emanuele Bevacqua, and Jakob Zscheischler
Hydrol. Earth Syst. Sci., 26, 6339–6359, https://doi.org/10.5194/hess-26-6339-2022, https://doi.org/10.5194/hess-26-6339-2022, 2022
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Using a novel explainable machine learning approach, we investigated the contributions of precipitation, temperature, and day length to different peak discharges, thereby uncovering three primary flooding mechanisms widespread in European catchments. The results indicate that flooding mechanisms have changed in numerous catchments over the past 70 years. The study highlights the potential of artificial intelligence in revealing complex changes in extreme events related to climate change.
Jiarong Wang, Xi Chen, Man Gao, Qi Hu, and Jintao Liu
Hydrol. Earth Syst. Sci., 26, 3901–3920, https://doi.org/10.5194/hess-26-3901-2022, https://doi.org/10.5194/hess-26-3901-2022, 2022
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The accelerated climate warming in the Tibetan Plateau after 1997 has strong consequences for hydrology, geography, and social wellbeing. In hydrology, the change in streamflow as a result of changes in dynamic water storage originating from glacier melt and permafrost thawing in a warming climate directly affects the available water resources for societies of some of the most populated nations in the world.
Esther Xu Fei and Ciaran Joseph Harman
Hydrol. Earth Syst. Sci., 26, 1977–1991, https://doi.org/10.5194/hess-26-1977-2022, https://doi.org/10.5194/hess-26-1977-2022, 2022
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Water in streams is a mixture of water from many sources. It is sometimes possible to identify the chemical fingerprint of each source and track the time-varying contribution of that source to the total flow rate. But what if you do not know the chemical fingerprint of each source? Can you simultaneously identify the sources (called end-members), and separate the water into contributions from each, using only samples of water from the stream? Here we suggest a method for doing just that.
Guofeng Zhu, Zhigang Sun, Yuanxiao Xu, Yuwei Liu, Zhuanxia Zhang, Liyuan Sang, and Lei Wang
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2022-75, https://doi.org/10.5194/hess-2022-75, 2022
Revised manuscript not accepted
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We analyzed the stable isotopic composition of surface water and estimated its evaporative loss in the Shiyang River Basin. The characteristics of stable isotopes in surface water show a gradual enrichment from mountainous areas to deserts, and the evaporation loss of surface water also shows a gradually increasing trend from upstream to downstream. The study of evaporative losses in the river-lake continuum contributes to the sustainable use of water resources.
Paul Royer-Gaspard, Vazken Andréassian, and Guillaume Thirel
Hydrol. Earth Syst. Sci., 25, 5703–5716, https://doi.org/10.5194/hess-25-5703-2021, https://doi.org/10.5194/hess-25-5703-2021, 2021
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Most evaluation studies based on the differential split-sample test (DSST) endorse the consensus that rainfall–runoff models lack climatic robustness. In this technical note, we propose a new performance metric to evaluate model robustness without applying the DSST and which can be used with a single hydrological model calibration. Our work makes it possible to evaluate the temporal transferability of any hydrological model, including uncalibrated models, at a very low computational cost.
Wencong Yang, Hanbo Yang, Dawen Yang, and Aizhong Hou
Hydrol. Earth Syst. Sci., 25, 2705–2720, https://doi.org/10.5194/hess-25-2705-2021, https://doi.org/10.5194/hess-25-2705-2021, 2021
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This study quantified the causal effects of land cover changes and dams on the changes in annual maximum discharges (Q) in 757 catchments of China using panel regressions. We found that a 1 % point increase in urban areas causes a 3.9 % increase in Q, and a 1 unit increase in reservoir index causes a 21.4 % decrease in Q for catchments with no dam before. This study takes the first step to explain the human-caused flood changes on a national scale in China.
Weifei Yang, Changlai Xiao, Zhihao Zhang, and Xiujuan Liang
Hydrol. Earth Syst. Sci., 25, 1747–1760, https://doi.org/10.5194/hess-25-1747-2021, https://doi.org/10.5194/hess-25-1747-2021, 2021
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This study analyzed the effectiveness of the conductivity mass balance (CMB) method for correcting the Eckhardt method. The results showed that the approach of calibrating the Eckhardt method against the CMB method provides a
falsecalibration of total baseflow by offsetting the inherent biases in the baseflow sequences generated by the two methods. The reason for this phenomenon is the baseflow series generated by the two methods containing different transient water sources.
Juliane Mai, James R. Craig, and Bryan A. Tolson
Hydrol. Earth Syst. Sci., 24, 5835–5858, https://doi.org/10.5194/hess-24-5835-2020, https://doi.org/10.5194/hess-24-5835-2020, 2020
James W. Kirchner and Julia L. A. Knapp
Hydrol. Earth Syst. Sci., 24, 5539–5558, https://doi.org/10.5194/hess-24-5539-2020, https://doi.org/10.5194/hess-24-5539-2020, 2020
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Ensemble hydrograph separation is a powerful new tool for measuring the age distribution of streamwater. However, the calculations are complex and may be difficult for researchers to implement on their own. Here we present scripts that perform these calculations in either MATLAB or R so that researchers do not need to write their own codes. We explain how these scripts work and how to use them. We demonstrate several potential applications using a synthetic catchment data set.
Antoine Allam, Roger Moussa, Wajdi Najem, and Claude Bocquillon
Hydrol. Earth Syst. Sci., 24, 4503–4521, https://doi.org/10.5194/hess-24-4503-2020, https://doi.org/10.5194/hess-24-4503-2020, 2020
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With serious concerns about global change rising in the Mediterranean, we established a new climatic classification to follow hydrological and ecohydrological activities. The classification coincided with a geographical distribution ranging from the most seasonal and driest class in the south to the least seasonal and most humid in the north. RCM scenarios showed that northern classes evolve to southern ones with shorter humid seasons and earlier snowmelt which might affect hydrologic regimes.
Mingguo Zheng
Hydrol. Earth Syst. Sci., 24, 2365–2378, https://doi.org/10.5194/hess-24-2365-2020, https://doi.org/10.5194/hess-24-2365-2020, 2020
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This paper developed a mathematically precise method to partition climate and catchment effects on streamflow. The method reveals that both the change magnitude and pathway (timing of change), not the magnitude alone, dictate the partition unless for a linear system. The method has wide relevance. For example, it suggests that the global warming effect of carbon emission is path dependent, and an optimal pathway would facilitate a higher global budget of carbon emission.
José Manuel Tunqui Neira, Vazken Andréassian, Gaëlle Tallec, and Jean-Marie Mouchel
Hydrol. Earth Syst. Sci., 24, 1823–1830, https://doi.org/10.5194/hess-24-1823-2020, https://doi.org/10.5194/hess-24-1823-2020, 2020
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This paper deals with the mathematical representation of concentration–discharge relationships. We propose a two-sided affine power scaling relationship (2S-APS) as an alternative to the classic one-sided power scaling relationship (commonly known as
power law). We also discuss the identification of the parameters of the proposed relationship, using an appropriate numerical criterion, based on high-frequency chemical time series of the Orgeval-ORACLE observatory.
Long Yang, Lachun Wang, Xiang Li, and Jie Gao
Hydrol. Earth Syst. Sci., 23, 5133–5149, https://doi.org/10.5194/hess-23-5133-2019, https://doi.org/10.5194/hess-23-5133-2019, 2019
Julia L. A. Knapp, Colin Neal, Alessandro Schlumpf, Margaret Neal, and James W. Kirchner
Hydrol. Earth Syst. Sci., 23, 4367–4388, https://doi.org/10.5194/hess-23-4367-2019, https://doi.org/10.5194/hess-23-4367-2019, 2019
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We describe, present, and make publicly available two extensive data sets of stable water isotopes in streamwater and precipitation at Plynlimon, Wales, consisting of measurements at 7-hourly intervals for 17 months and at weekly intervals for 4.25 years. We use these data to calculate new water fractions and transit time distributions for different discharge rates and seasons, thus quantifying the contribution of recent precipitation to streamflow under different conditions.
Hui-Min Wang, Jie Chen, Chong-Yu Xu, Hua Chen, Shenglian Guo, Ping Xie, and Xiangquan Li
Hydrol. Earth Syst. Sci., 23, 4033–4050, https://doi.org/10.5194/hess-23-4033-2019, https://doi.org/10.5194/hess-23-4033-2019, 2019
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When using large ensembles of global climate models in hydrological impact studies, there are pragmatic questions on whether it is necessary to weight climate models and how to weight them. We use eight methods to weight climate models straightforwardly, based on their performances in hydrological simulations, and investigate the influences of the assigned weights. This study concludes that using bias correction and equal weighting is likely viable and sufficient for hydrological impact studies.
Nathalie Folton, Eric Martin, Patrick Arnaud, Pierre L'Hermite, and Mathieu Tolsa
Hydrol. Earth Syst. Sci., 23, 2699–2714, https://doi.org/10.5194/hess-23-2699-2019, https://doi.org/10.5194/hess-23-2699-2019, 2019
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The long-term study of precipitation, flows, flood or drought mechanisms, in the Réal Collobrier research Watershed, located in South-East France, in the Mediterranean forest, improves knowledge of the water cycle and is unique tool for understanding of how catchments function. This study shows a small decrease in rainfall and a marked tendency towards a decrease in the water resources of the catchment in response to climate trends, with a consistent increase in drought severity and duration.
Vazken Andréassian and Tewfik Sari
Hydrol. Earth Syst. Sci., 23, 2339–2350, https://doi.org/10.5194/hess-23-2339-2019, https://doi.org/10.5194/hess-23-2339-2019, 2019
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In this Technical Note, we present two water balance formulas: the Turc–Mezentsev and Tixeront–Fu formulas. These formulas have a puzzling numerical similarity, which we discuss in detail and try to interpret mathematically and hydrologically.
Jan De Niel and Patrick Willems
Hydrol. Earth Syst. Sci., 23, 871–882, https://doi.org/10.5194/hess-23-871-2019, https://doi.org/10.5194/hess-23-871-2019, 2019
James W. Kirchner
Hydrol. Earth Syst. Sci., 23, 303–349, https://doi.org/10.5194/hess-23-303-2019, https://doi.org/10.5194/hess-23-303-2019, 2019
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How long does it take for raindrops to become streamflow? Here I propose a new approach to this old problem. I show how we can use time series of isotope data to measure the average fraction of same-day rainfall appearing in streamflow, even if this fraction varies greatly from rainstorm to rainstorm. I show that we can quantify how this fraction changes from small rainstorms to big ones, and from high flows to low flows, and how it changes with the lag time between rainfall and streamflow.
Ane Zabaleta, Eneko Garmendia, Petr Mariel, Ibon Tamayo, and Iñaki Antigüedad
Hydrol. Earth Syst. Sci., 22, 5227–5241, https://doi.org/10.5194/hess-22-5227-2018, https://doi.org/10.5194/hess-22-5227-2018, 2018
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This study establishes relationships between land cover and river discharge. Using discharge data from 20 catchments of the Bay of Biscay findings showed the influence of land cover on discharge changes with the amount of precipitation, with lower annual water resources associated with the greater presence of forests. Results obtained illustrate the relevance of land planning to the management of water resources and the opportunity to consider it in future climate-change adaptation strategies.
Dusan Jovanovic, Tijana Jovanovic, Alfonso Mejía, Jon Hathaway, and Edoardo Daly
Hydrol. Earth Syst. Sci., 22, 3551–3559, https://doi.org/10.5194/hess-22-3551-2018, https://doi.org/10.5194/hess-22-3551-2018, 2018
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A relationship between the Hurst (H) exponent (a long-term correlation coefficient) within a flow time series and various catchment characteristics for a number of catchments in the USA and Australia was investigated. A negative relationship with imperviousness was identified, which allowed for an efficient catchment classification, thus making the H exponent a useful metric to quantitatively assess the impact of catchment imperviousness on streamflow regime.
Chuanhao Wu, Bill X. Hu, Guoru Huang, Peng Wang, and Kai Xu
Hydrol. Earth Syst. Sci., 22, 1971–1991, https://doi.org/10.5194/hess-22-1971-2018, https://doi.org/10.5194/hess-22-1971-2018, 2018
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China has suffered some of the effects of global warming, and one of the potential implications of climate warming is the alteration of the temporal–spatial patterns of water resources. In this paper, the Budyko-based elasticity method was used to investigate the responses of runoff to historical and future climate variability over China at both grid and catchment scales. The results help to better understand the hydrological effects of climate change and adapt to a changing environment.
Samuel Saxe, Terri S. Hogue, and Lauren Hay
Hydrol. Earth Syst. Sci., 22, 1221–1237, https://doi.org/10.5194/hess-22-1221-2018, https://doi.org/10.5194/hess-22-1221-2018, 2018
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We investigate the impact of wildfire on watershed flow regimes, examining responses across the western United States. On a national scale, our results confirm the work of prior studies: that low, high, and peak flows typically increase following a wildfire. Regionally, results are more variable and sometimes contradictory. Our results may be significant in justifying the calibration of watershed models and in contributing to the overall observational analysis of post-fire streamflow response.
Annette Witt, Bruce D. Malamud, Clara Mangili, and Achim Brauer
Hydrol. Earth Syst. Sci., 21, 5547–5581, https://doi.org/10.5194/hess-21-5547-2017, https://doi.org/10.5194/hess-21-5547-2017, 2017
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Here we present a unique 9.5 m palaeo-lacustrine record of 771 palaeofloods which occurred over a period of 10 000 years in the Piànico–Sèllere basin (southern Alps) during an interglacial period in the Pleistocene (sometime between 400 000 and 800 000 years ago). We analyse the palaeoflood series correlation, clustering, and cyclicity properties, finding a long-range cyclicity with a period of about 2030 years superimposed onto a fractional noise.
Steve J. Birkinshaw, Selma B. Guerreiro, Alex Nicholson, Qiuhua Liang, Paul Quinn, Lili Zhang, Bin He, Junxian Yin, and Hayley J. Fowler
Hydrol. Earth Syst. Sci., 21, 1911–1927, https://doi.org/10.5194/hess-21-1911-2017, https://doi.org/10.5194/hess-21-1911-2017, 2017
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The Yangtze River basin in China is home to more than 400 million people and susceptible to major floods. We used projections of future precipitation and temperature from 35 of the most recent global climate models and applied this to a hydrological model of the Yangtze. Changes in the annual discharge varied between a 29.8 % decrease and a 16.0 % increase. The main reason for the difference between the models was the predicted expansion of the summer monsoon north and and west into the basin.
Maurizio Mazzoleni, Martin Verlaan, Leonardo Alfonso, Martina Monego, Daniele Norbiato, Miche Ferri, and Dimitri P. Solomatine
Hydrol. Earth Syst. Sci., 21, 839–861, https://doi.org/10.5194/hess-21-839-2017, https://doi.org/10.5194/hess-21-839-2017, 2017
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This study assesses the potential use of crowdsourced data in hydrological modeling, which are characterized by irregular availability and variable accuracy. We show that even data with these characteristics can improve flood prediction if properly integrated into hydrological models. This study provides technological support to citizen observatories of water, in which citizens can play an active role in capturing information, leading to improved model forecasts and better flood management.
Martin Durocher, Fateh Chebana, and Taha B. M. J. Ouarda
Hydrol. Earth Syst. Sci., 20, 4717–4729, https://doi.org/10.5194/hess-20-4717-2016, https://doi.org/10.5194/hess-20-4717-2016, 2016
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For regional flood frequency, it is challenging to identify regions with similar hydrological properties. Therefore, previous works have mainly proposed to use regions with similar physiographical properties. This research proposes instead to nonlinearly predict the desired hydrological properties before using them for delineation. The presented method is applied to a case study in Québec, Canada, and leads to hydrologically relevant regions, while enhancing predictions made inside them.
Donghua Zhang, Henrik Madsen, Marc E. Ridler, Jacob Kidmose, Karsten H. Jensen, and Jens C. Refsgaard
Hydrol. Earth Syst. Sci., 20, 4341–4357, https://doi.org/10.5194/hess-20-4341-2016, https://doi.org/10.5194/hess-20-4341-2016, 2016
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We present a method to assimilate observed groundwater head and soil moisture profiles into an integrated hydrological model. The study uses the ensemble transform Kalman filter method and the MIKE SHE hydrological model code. The proposed method is shown to be more robust and provide better results for two cases in Denmark, and is also validated using real data. The hydrological model with assimilation overall improved performance compared to the model without assimilation.
Morgan Fonley, Ricardo Mantilla, Scott J. Small, and Rodica Curtu
Hydrol. Earth Syst. Sci., 20, 2899–2912, https://doi.org/10.5194/hess-20-2899-2016, https://doi.org/10.5194/hess-20-2899-2016, 2016
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We design and implement a theoretical experiment to show that, under low-flow conditions, observed streamflow discrepancies between early and late summer can be attributed to different flow velocities in the river network. By developing an analytic solution to represent flow along a given river network, we emphasize the dependence of streamflow amplitude and time delay on the geomorphology of the network. We also simulate using a realistic river network to highlight the effects of scale.
Zhongwei Huang, Hanbo Yang, and Dawen Yang
Hydrol. Earth Syst. Sci., 20, 2573–2587, https://doi.org/10.5194/hess-20-2573-2016, https://doi.org/10.5194/hess-20-2573-2016, 2016
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The hydrologic processes have been influenced by different climatic factors. However, the dominant climatic factor driving annual runoff change is still unknown in many catchments in China. By using the climate elasticity method proposed by Yang and Yang (2011), the elasticity of runoff to climatic factors was estimated, and the dominant climatic factors driving annual runoff change were detected at catchment scale over China.
Jørn Rasmussen, Henrik Madsen, Karsten Høgh Jensen, and Jens Christian Refsgaard
Hydrol. Earth Syst. Sci., 20, 2103–2118, https://doi.org/10.5194/hess-20-2103-2016, https://doi.org/10.5194/hess-20-2103-2016, 2016
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In the paper, observations are assimilated into a hydrological model in order to improve the model performance. Two methods for detecting and correcting systematic errors (bias) in groundwater head observations are used leading to improved results compared to standard assimilation methods which ignores any bias. This is demonstrated using both synthetic (user generated) observations and real-world observations.
Mohammed Achite and Sylvain Ouillon
Hydrol. Earth Syst. Sci., 20, 1355–1372, https://doi.org/10.5194/hess-20-1355-2016, https://doi.org/10.5194/hess-20-1355-2016, 2016
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Changes of T, P, Q and sediment fluxes in a semi-arid basin little affected by human activities are analyzed from 40 years of measurements. T increased, P decreased, an earlier onset of first summer rains occurred. The flow regime shifted from perennial to intermittent. Sediment flux almost doubled every decade. The sediment regime shifted from two equivalent seasons of sediment delivery to a single major season regime. The C–Q rating curve ability declined due to enhanced hysteresis effects.
C. E. M. Lloyd, J. E. Freer, P. J. Johnes, and A. L. Collins
Hydrol. Earth Syst. Sci., 20, 625–632, https://doi.org/10.5194/hess-20-625-2016, https://doi.org/10.5194/hess-20-625-2016, 2016
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This paper examines the current methodologies for quantifying storm behaviour through hysteresis analysis, and explores a new method. Each method is systematically tested and the impact on the results is examined. Recommendations are made regarding the most effective method of calculating a hysteresis index. This new method allows storm hysteresis behaviour to be directly compared between storms, parameters, and catchments, meaning it has wide application potential in water quality research.
W. Hu and B. C. Si
Hydrol. Earth Syst. Sci., 20, 571–587, https://doi.org/10.5194/hess-20-571-2016, https://doi.org/10.5194/hess-20-571-2016, 2016
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Spatiotemporal SWC was decomposed into into three terms (spatial forcing, temporal forcing, and interactions between spatial and temporal forcing) for near surface and root zone; Empirical orthogonal function indicated that underlying patterns exist in the interaction term at small watershed scales; Estimation of spatially distributed SWC benefits from decomposition of the interaction term; The suggested decomposition of SWC with time stability analysis has potential in SWC downscaling.
Y. Chen, J. Li, and H. Xu
Hydrol. Earth Syst. Sci., 20, 375–392, https://doi.org/10.5194/hess-20-375-2016, https://doi.org/10.5194/hess-20-375-2016, 2016
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Parameter optimization is necessary to improve the flood forecasting capability of physically based distributed hydrological model. A method for parameter optimization with particle swam optimization (PSO) algorithm has been proposed for physically based distributed hydrological model in catchment flood forecasting and validated in southern China. It has found that the appropriate particle number and maximum evolution number of PSO algorithm are 20 and 30 respectively.
D. Hawtree, J. P. Nunes, J. J. Keizer, R. Jacinto, J. Santos, M. E. Rial-Rivas, A.-K. Boulet, F. Tavares-Wahren, and K.-H. Feger
Hydrol. Earth Syst. Sci., 19, 3033–3045, https://doi.org/10.5194/hess-19-3033-2015, https://doi.org/10.5194/hess-19-3033-2015, 2015
J. Rasmussen, H. Madsen, K. H. Jensen, and J. C. Refsgaard
Hydrol. Earth Syst. Sci., 19, 2999–3013, https://doi.org/10.5194/hess-19-2999-2015, https://doi.org/10.5194/hess-19-2999-2015, 2015
C. Kormann, T. Francke, M. Renner, and A. Bronstert
Hydrol. Earth Syst. Sci., 19, 1225–1245, https://doi.org/10.5194/hess-19-1225-2015, https://doi.org/10.5194/hess-19-1225-2015, 2015
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...
