Articles | Volume 23, issue 5
https://doi.org/10.5194/hess-23-2339-2019
© Author(s) 2019. 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-23-2339-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note
| 
14 May 2019
Technical note |
| 14 May 2019
| 14 May 2019
Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu
Vazken Andréassian
CORRESPONDING AUTHOR
Irstea, HYCAR Research Unit, Antony, France
Tewfik Sari
ITAP, Univ. Montpellier, Irstea, Montpellier SupAgro, Montpellier, France
Related authors
Vazken Andréassian, Guilherme Mendoza Guimarães, Alban de Lavenne, and Julien Lerat
EGUsphere, https://doi.org/10.5194/egusphere-2025-414, https://doi.org/10.5194/egusphere-2025-414, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Using 4122 catchments from four continents, we investigate how annual streamflow depends on climate variables (rainfall and potential evaporation) and on the season when precipitation occurs, using and index representing the synchronicity between precipitation and potential evaporation. In all countries and under the main climates represented, synchronicity is, after precipitation, the second most important factor to explain annual streamflow variations.
Léonard Santos, Vazken Andréassian, Torben O. Sonnenborg, Göran Lindström, Alban de Lavenne, Charles Perrin, Lila Collet, and Guillaume Thirel
Hydrol. Earth Syst. Sci., 29, 683–700, https://doi.org/10.5194/hess-29-683-2025, https://doi.org/10.5194/hess-29-683-2025, 2025
Short summary
Short summary
This work investigates how hydrological models are transferred to a period in which climate conditions are different to the ones of the period in which they were set up. The robustness assessment test built to detect dependencies between model error and climatic drivers was applied to three hydrological models in 352 catchments in Denmark, France and Sweden. Potential issues are seen in a significant number of catchments for the models, even though the catchments differ for each model.
Olivier Delaigue, Guilherme Mendoza Guimarães, Pierre Brigode, Benoît Génot, Charles Perrin, Jean-Michel Soubeyroux, Bruno Janet, Nans Addor, and Vazken Andréassian
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-415, https://doi.org/10.5194/essd-2024-415, 2024
Revised manuscript accepted for ESSD
Short summary
Short summary
This dataset covers 654 rivers all flowing in France. The provided time series and catchment attributes will be of interest to those modelers wishing to analyse hydrological behavior, perform model assessments.
Thibault Hallouin, François Bourgin, Charles Perrin, Maria-Helena Ramos, and Vazken Andréassian
Geosci. Model Dev., 17, 4561–4578, https://doi.org/10.5194/gmd-17-4561-2024, https://doi.org/10.5194/gmd-17-4561-2024, 2024
Short summary
Short summary
The evaluation of the quality of hydrological model outputs against streamflow observations is widespread in the hydrological literature. In order to improve on the reproducibility of published studies, a new evaluation tool dedicated to hydrological applications is presented. It is open source and usable in a variety of programming languages to make it as accessible as possible to the community. Thus, authors and readers alike can use the same tool to produce and reproduce the results.
Ralph Bathelemy, Pierre Brigode, Vazken Andréassian, Charles Perrin, Vincent Moron, Cédric Gaucherel, Emmanuel Tric, and Dominique Boisson
Earth Syst. Sci. Data, 16, 2073–2098, https://doi.org/10.5194/essd-16-2073-2024, https://doi.org/10.5194/essd-16-2073-2024, 2024
Short summary
Short summary
The aim of this work is to provide the first hydroclimatic database for Haiti, a Caribbean country particularly vulnerable to meteorological and hydrological hazards. The resulting database, named Simbi, provides hydroclimatic time series for around 150 stations and 24 catchment areas.
Cyril Thébault, Charles Perrin, Vazken Andréassian, Guillaume Thirel, Sébastien Legrand, and Olivier Delaigue
Hydrol. Earth Syst. Sci., 28, 1539–1566, https://doi.org/10.5194/hess-28-1539-2024, https://doi.org/10.5194/hess-28-1539-2024, 2024
Short summary
Short summary
Streamflow forecasting is useful for many applications, ranging from population safety (e.g. floods) to water resource management (e.g. agriculture or hydropower). To this end, hydrological models must be optimized. However, a model is inherently wrong. This study aims to analyse the contribution of a multi-model approach within a variable spatial framework to improve streamflow simulations. The underlying idea is to take advantage of the strength of each modelling framework tested.
Alban de Lavenne, Vazken Andréassian, Louise Crochemore, Göran Lindström, and Berit Arheimer
Hydrol. Earth Syst. Sci., 26, 2715–2732, https://doi.org/10.5194/hess-26-2715-2022, https://doi.org/10.5194/hess-26-2715-2022, 2022
Short summary
Short summary
A watershed remembers the past to some extent, and this memory influences its behavior. This memory is defined by the ability to store past rainfall for several years. By releasing this water into the river or the atmosphere, it tends to forget. We describe how this memory fades over time in France and Sweden. A few watersheds show a multi-year memory. It increases with the influence of groundwater or dry conditions. After 3 or 4 years, they behave independently of the past.
Antoine Pelletier and Vazken Andréassian
Hydrol. Earth Syst. Sci., 26, 2733–2758, https://doi.org/10.5194/hess-26-2733-2022, https://doi.org/10.5194/hess-26-2733-2022, 2022
Short summary
Short summary
A large part of the water cycle takes place underground. In many places, the soil stores water during the wet periods and can release it all year long, which is particularly visible when the river level is low. Modelling tools that are used to simulate and forecast the behaviour of the river struggle to represent this. We improved an existing model to take underground water into account using measurements of the soil water content. Results allow us make recommendations for model users.
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
Short summary
Short summary
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.
Pierre Nicolle, Vazken Andréassian, Paul Royer-Gaspard, Charles Perrin, Guillaume Thirel, Laurent Coron, and Léonard Santos
Hydrol. Earth Syst. Sci., 25, 5013–5027, https://doi.org/10.5194/hess-25-5013-2021, https://doi.org/10.5194/hess-25-5013-2021, 2021
Short summary
Short summary
In this note, a new method (RAT) is proposed to assess the robustness of hydrological models. The RAT method is particularly interesting because it does not require multiple calibrations (it is therefore applicable to uncalibrated models), and it can be used to determine whether a hydrological model may be safely used for climate change impact studies. Success at the robustness assessment test is a necessary (but not sufficient) condition of model robustness.
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
Short summary
Short summary
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.
Antoine Pelletier and Vazken Andréassian
Hydrol. Earth Syst. Sci., 24, 1171–1187, https://doi.org/10.5194/hess-24-1171-2020, https://doi.org/10.5194/hess-24-1171-2020, 2020
Short summary
Short summary
There are many ways for water to join a river after a rainfall event, but they can be split into two categories: the quick ones that remain in the surface and the slow ones that use other trajectories. Thus, measured streamflow of a river can be split into two components: quickflow and baseflow. We present a new method to perform this separation, using only streamflow and rainfall data, which are generally broadly available. It is then used as an analysis tool of river dynamics over France.
José Manuel Tunqui Neira, Vazken Andréassian, Gaëlle Tallec, and Jean-Marie Mouchel
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2019-325, https://doi.org/10.5194/hess-2019-325, 2019
Manuscript not accepted for further review
Short summary
Short summary
This Technical Note deals with the mathematical representation of concentration-discharge relationships and with the identification of its parameters. We propose a two-sided power transformation alternative to the classical log-log transformation, and a multicriterion identification procedure allowing determining parameters that are efficient, both from the concentration and the load points of view.
Cédric Rebolho, Vazken Andréassian, and Nicolas Le Moine
Hydrol. Earth Syst. Sci., 22, 5967–5985, https://doi.org/10.5194/hess-22-5967-2018, https://doi.org/10.5194/hess-22-5967-2018, 2018
Short summary
Short summary
Inundation models are useful for hazard management and prevention. They are traditionally based on hydraulic partial differential equations (with satisfying results but large data and computational requirements). This study presents a simplified approach combining reach-scale geometric properties with steady uniform flow equations. The model shows promising results overall, although difficulties persist in the most complex urbanised reaches.
Vazken Andréassian, Laurent Coron, Julien Lerat, and Nicolas Le Moine
Hydrol. Earth Syst. Sci., 20, 4503–4524, https://doi.org/10.5194/hess-20-4503-2016, https://doi.org/10.5194/hess-20-4503-2016, 2016
Short summary
Short summary
We present a new method to derive the empirical (i.e., data-based) elasticity of streamflow to precipitation and potential evaporation. This method, which uses long-term hydrometeorological records, is tested on a set of 519 French catchments. We compare our method with the classical approach found in the literature and demonstrate its robustness and efficiency. Empirical elasticity is a powerful tool to test the extrapolation capacity of hydrological models.
Alban de Lavenne, Guillaume Thirel, Vazken Andréassian, Charles Perrin, and Maria-Helena Ramos
Proc. IAHS, 373, 87–94, https://doi.org/10.5194/piahs-373-87-2016, https://doi.org/10.5194/piahs-373-87-2016, 2016
Short summary
Short summary
Developing modelling tools that help to understand the spatial distribution of water resources is a key issue for better management. Ideally, hydrological models which discretise catchment space into sub-catchments should offer better streamflow simulations than lumped models, along with spatially-relevant water resources management solutions. However we demonstrate that those model raise other issues related to the calibration strategy and to the identifiability of the parameters.
F. Bourgin, V. Andréassian, C. Perrin, and L. Oudin
Hydrol. Earth Syst. Sci., 19, 2535–2546, https://doi.org/10.5194/hess-19-2535-2015, https://doi.org/10.5194/hess-19-2535-2015, 2015
D. Defrance, P. Javelle, D. Organde, S. Ecrepont, V. Andréassian, and P. Arnaud
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-11-4365-2014, https://doi.org/10.5194/hessd-11-4365-2014, 2014
Revised manuscript has not been submitted
Vazken Andréassian, Guilherme Mendoza Guimarães, Alban de Lavenne, and Julien Lerat
EGUsphere, https://doi.org/10.5194/egusphere-2025-414, https://doi.org/10.5194/egusphere-2025-414, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Using 4122 catchments from four continents, we investigate how annual streamflow depends on climate variables (rainfall and potential evaporation) and on the season when precipitation occurs, using and index representing the synchronicity between precipitation and potential evaporation. In all countries and under the main climates represented, synchronicity is, after precipitation, the second most important factor to explain annual streamflow variations.
Léonard Santos, Vazken Andréassian, Torben O. Sonnenborg, Göran Lindström, Alban de Lavenne, Charles Perrin, Lila Collet, and Guillaume Thirel
Hydrol. Earth Syst. Sci., 29, 683–700, https://doi.org/10.5194/hess-29-683-2025, https://doi.org/10.5194/hess-29-683-2025, 2025
Short summary
Short summary
This work investigates how hydrological models are transferred to a period in which climate conditions are different to the ones of the period in which they were set up. The robustness assessment test built to detect dependencies between model error and climatic drivers was applied to three hydrological models in 352 catchments in Denmark, France and Sweden. Potential issues are seen in a significant number of catchments for the models, even though the catchments differ for each model.
Olivier Delaigue, Guilherme Mendoza Guimarães, Pierre Brigode, Benoît Génot, Charles Perrin, Jean-Michel Soubeyroux, Bruno Janet, Nans Addor, and Vazken Andréassian
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-415, https://doi.org/10.5194/essd-2024-415, 2024
Revised manuscript accepted for ESSD
Short summary
Short summary
This dataset covers 654 rivers all flowing in France. The provided time series and catchment attributes will be of interest to those modelers wishing to analyse hydrological behavior, perform model assessments.
Thibault Hallouin, François Bourgin, Charles Perrin, Maria-Helena Ramos, and Vazken Andréassian
Geosci. Model Dev., 17, 4561–4578, https://doi.org/10.5194/gmd-17-4561-2024, https://doi.org/10.5194/gmd-17-4561-2024, 2024
Short summary
Short summary
The evaluation of the quality of hydrological model outputs against streamflow observations is widespread in the hydrological literature. In order to improve on the reproducibility of published studies, a new evaluation tool dedicated to hydrological applications is presented. It is open source and usable in a variety of programming languages to make it as accessible as possible to the community. Thus, authors and readers alike can use the same tool to produce and reproduce the results.
Ralph Bathelemy, Pierre Brigode, Vazken Andréassian, Charles Perrin, Vincent Moron, Cédric Gaucherel, Emmanuel Tric, and Dominique Boisson
Earth Syst. Sci. Data, 16, 2073–2098, https://doi.org/10.5194/essd-16-2073-2024, https://doi.org/10.5194/essd-16-2073-2024, 2024
Short summary
Short summary
The aim of this work is to provide the first hydroclimatic database for Haiti, a Caribbean country particularly vulnerable to meteorological and hydrological hazards. The resulting database, named Simbi, provides hydroclimatic time series for around 150 stations and 24 catchment areas.
Cyril Thébault, Charles Perrin, Vazken Andréassian, Guillaume Thirel, Sébastien Legrand, and Olivier Delaigue
Hydrol. Earth Syst. Sci., 28, 1539–1566, https://doi.org/10.5194/hess-28-1539-2024, https://doi.org/10.5194/hess-28-1539-2024, 2024
Short summary
Short summary
Streamflow forecasting is useful for many applications, ranging from population safety (e.g. floods) to water resource management (e.g. agriculture or hydropower). To this end, hydrological models must be optimized. However, a model is inherently wrong. This study aims to analyse the contribution of a multi-model approach within a variable spatial framework to improve streamflow simulations. The underlying idea is to take advantage of the strength of each modelling framework tested.
Alban de Lavenne, Vazken Andréassian, Louise Crochemore, Göran Lindström, and Berit Arheimer
Hydrol. Earth Syst. Sci., 26, 2715–2732, https://doi.org/10.5194/hess-26-2715-2022, https://doi.org/10.5194/hess-26-2715-2022, 2022
Short summary
Short summary
A watershed remembers the past to some extent, and this memory influences its behavior. This memory is defined by the ability to store past rainfall for several years. By releasing this water into the river or the atmosphere, it tends to forget. We describe how this memory fades over time in France and Sweden. A few watersheds show a multi-year memory. It increases with the influence of groundwater or dry conditions. After 3 or 4 years, they behave independently of the past.
Antoine Pelletier and Vazken Andréassian
Hydrol. Earth Syst. Sci., 26, 2733–2758, https://doi.org/10.5194/hess-26-2733-2022, https://doi.org/10.5194/hess-26-2733-2022, 2022
Short summary
Short summary
A large part of the water cycle takes place underground. In many places, the soil stores water during the wet periods and can release it all year long, which is particularly visible when the river level is low. Modelling tools that are used to simulate and forecast the behaviour of the river struggle to represent this. We improved an existing model to take underground water into account using measurements of the soil water content. Results allow us make recommendations for model users.
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
Short summary
Short summary
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.
Pierre Nicolle, Vazken Andréassian, Paul Royer-Gaspard, Charles Perrin, Guillaume Thirel, Laurent Coron, and Léonard Santos
Hydrol. Earth Syst. Sci., 25, 5013–5027, https://doi.org/10.5194/hess-25-5013-2021, https://doi.org/10.5194/hess-25-5013-2021, 2021
Short summary
Short summary
In this note, a new method (RAT) is proposed to assess the robustness of hydrological models. The RAT method is particularly interesting because it does not require multiple calibrations (it is therefore applicable to uncalibrated models), and it can be used to determine whether a hydrological model may be safely used for climate change impact studies. Success at the robustness assessment test is a necessary (but not sufficient) condition of model robustness.
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
Short summary
Short summary
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.
Antoine Pelletier and Vazken Andréassian
Hydrol. Earth Syst. Sci., 24, 1171–1187, https://doi.org/10.5194/hess-24-1171-2020, https://doi.org/10.5194/hess-24-1171-2020, 2020
Short summary
Short summary
There are many ways for water to join a river after a rainfall event, but they can be split into two categories: the quick ones that remain in the surface and the slow ones that use other trajectories. Thus, measured streamflow of a river can be split into two components: quickflow and baseflow. We present a new method to perform this separation, using only streamflow and rainfall data, which are generally broadly available. It is then used as an analysis tool of river dynamics over France.
José Manuel Tunqui Neira, Vazken Andréassian, Gaëlle Tallec, and Jean-Marie Mouchel
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2019-325, https://doi.org/10.5194/hess-2019-325, 2019
Manuscript not accepted for further review
Short summary
Short summary
This Technical Note deals with the mathematical representation of concentration-discharge relationships and with the identification of its parameters. We propose a two-sided power transformation alternative to the classical log-log transformation, and a multicriterion identification procedure allowing determining parameters that are efficient, both from the concentration and the load points of view.
Cédric Rebolho, Vazken Andréassian, and Nicolas Le Moine
Hydrol. Earth Syst. Sci., 22, 5967–5985, https://doi.org/10.5194/hess-22-5967-2018, https://doi.org/10.5194/hess-22-5967-2018, 2018
Short summary
Short summary
Inundation models are useful for hazard management and prevention. They are traditionally based on hydraulic partial differential equations (with satisfying results but large data and computational requirements). This study presents a simplified approach combining reach-scale geometric properties with steady uniform flow equations. The model shows promising results overall, although difficulties persist in the most complex urbanised reaches.
Vazken Andréassian, Laurent Coron, Julien Lerat, and Nicolas Le Moine
Hydrol. Earth Syst. Sci., 20, 4503–4524, https://doi.org/10.5194/hess-20-4503-2016, https://doi.org/10.5194/hess-20-4503-2016, 2016
Short summary
Short summary
We present a new method to derive the empirical (i.e., data-based) elasticity of streamflow to precipitation and potential evaporation. This method, which uses long-term hydrometeorological records, is tested on a set of 519 French catchments. We compare our method with the classical approach found in the literature and demonstrate its robustness and efficiency. Empirical elasticity is a powerful tool to test the extrapolation capacity of hydrological models.
Alban de Lavenne, Guillaume Thirel, Vazken Andréassian, Charles Perrin, and Maria-Helena Ramos
Proc. IAHS, 373, 87–94, https://doi.org/10.5194/piahs-373-87-2016, https://doi.org/10.5194/piahs-373-87-2016, 2016
Short summary
Short summary
Developing modelling tools that help to understand the spatial distribution of water resources is a key issue for better management. Ideally, hydrological models which discretise catchment space into sub-catchments should offer better streamflow simulations than lumped models, along with spatially-relevant water resources management solutions. However we demonstrate that those model raise other issues related to the calibration strategy and to the identifiability of the parameters.
F. Bourgin, V. Andréassian, C. Perrin, and L. Oudin
Hydrol. Earth Syst. Sci., 19, 2535–2546, https://doi.org/10.5194/hess-19-2535-2015, https://doi.org/10.5194/hess-19-2535-2015, 2015
D. Defrance, P. Javelle, D. Organde, S. Ecrepont, V. Andréassian, and P. Arnaud
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-11-4365-2014, https://doi.org/10.5194/hessd-11-4365-2014, 2014
Revised manuscript has not been submitted
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Mathematical applications
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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
Short summary
Short summary
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.
Julien Lerat
EGUsphere, https://doi.org/10.5194/egusphere-2024-3184, https://doi.org/10.5194/egusphere-2024-3184, 2024
Short summary
Short summary
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. Our method called “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.
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
Short summary
Short summary
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.
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.
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
S. Gharari, M. Shafiei, M. Hrachowitz, R. Kumar, F. Fenicia, H. V. Gupta, and H. H. G. Savenije
Hydrol. Earth Syst. Sci., 18, 4861–4870, https://doi.org/10.5194/hess-18-4861-2014, https://doi.org/10.5194/hess-18-4861-2014, 2014
S. G. Leibowitz, R. L. Comeleo, P. J. Wigington Jr., C. P. Weaver, P. E. Morefield, E. A. Sproles, and J. L. Ebersole
Hydrol. Earth Syst. Sci., 18, 3367–3392, https://doi.org/10.5194/hess-18-3367-2014, https://doi.org/10.5194/hess-18-3367-2014, 2014
J. Niu, J. Chen, and B. Sivakumar
Hydrol. Earth Syst. Sci., 18, 1475–1492, https://doi.org/10.5194/hess-18-1475-2014, https://doi.org/10.5194/hess-18-1475-2014, 2014
S. Galelli and A. Castelletti
Hydrol. Earth Syst. Sci., 17, 2669–2684, https://doi.org/10.5194/hess-17-2669-2013, https://doi.org/10.5194/hess-17-2669-2013, 2013
K. Rasouli, M. A. Hernández-Henríquez, and S. J. Déry
Hydrol. Earth Syst. Sci., 17, 1681–1691, https://doi.org/10.5194/hess-17-1681-2013, https://doi.org/10.5194/hess-17-1681-2013, 2013
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Short summary
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.
In this Technical Note, we present two water balance formulas: the Turc–Mezentsev and...
