Articles | Volume 24, issue 4
https://doi.org/10.5194/hess-24-1823-2020
© Author(s) 2020. 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-24-1823-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note: A two-sided affine power scaling relationship to represent the concentration–discharge relationship
José Manuel Tunqui Neira
Université Paris-Saclay, INRAE, HYCAR Research Unit, 92761
Antony, France
Sorbonne Université, CNRS, EPHE, UMR Metis 7619, Paris, France
Vazken Andréassian
CORRESPONDING AUTHOR
Université Paris-Saclay, INRAE, HYCAR Research Unit, 92761
Antony, France
Gaëlle Tallec
Université Paris-Saclay, INRAE, HYCAR Research Unit, 92761
Antony, France
Jean-Marie Mouchel
Sorbonne Université, CNRS, EPHE, UMR Metis 7619, Paris, France
Related authors
No articles found.
Paul Zarpas, Maria-Helena Ramos, Gaëlle Tallec, Denis Allard, and Fanny J. Sarrazin
EGUsphere, https://doi.org/10.5194/egusphere-2026-4287, https://doi.org/10.5194/egusphere-2026-4287, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Long-term information on irrigation water withdrawal is crucial to understand how agriculture affects water resources, but observations are often too short. We developed a statistical model to reconstruct annual irrigation water withdrawal in France from 2000 to 2022 at the catchment scale using a national database. The reconstructed time series reveal widespread increases in irrigation water withdrawal and provide a basis for water management and climate change impact studies.
Taha-Abderrahman El Ouahabi, François Bourgin, Charles Perrin, and Vazken Andréassian
Hydrol. Earth Syst. Sci., 30, 3549–3574, https://doi.org/10.5194/hess-30-3549-2026, https://doi.org/10.5194/hess-30-3549-2026, 2026
Short summary
Short summary
To improve hydrological uncertainty estimation, recent studies have explored machine learning (ML)-based post-processing approaches. Among these, quantile random forests (QRF) are increasingly used for their balance between interpretability and performance. We develop a hydrologically informed QRF trained in a multi-site setting. Our results show that the regional QRF approach is beneficial, particularly in catchments where local information is insufficient.
Léonard Santos, Anthony Thomas, Gaëlle Tallec, Laurent Mounereau, Aaron Bluche, Bruno J. Lemaire, Rania Louafi, and Guillaume Thirel
Hydrol. Earth Syst. Sci., 30, 1915–1949, https://doi.org/10.5194/hess-30-1915-2026, https://doi.org/10.5194/hess-30-1915-2026, 2026
Short summary
Short summary
Water resources will be heavily impacted by climate change in the future, with low flows and water demand satisfaction expected to decline. This study uses an integrated water resources management model to examine future water demand scenarios, revealing that climate change will be the primary driver of changes. While adapting water uses could mitigate negative impacts, this will not be enough to adapt to climate change. The irrigation sector is expected to be the most impacted.
Vazken Andréassian, Guilherme M. Guimarães, Julien Lerat, and Alban de Lavenne
Hydrol. Earth Syst. Sci., 30, 1865–1876, https://doi.org/10.5194/hess-30-1865-2026, https://doi.org/10.5194/hess-30-1865-2026, 2026
Short summary
Short summary
We study the variations in annual streamflow and explicit their dependence to climate variations, in order to understand their causes and to provide tools for a rapid assessment of the impact of climate change on water resources. By making explicit the dependency of streamflow elasticity to aridity, we are able to propose a regionalized elasticity formula with physically-realistic elasticity coefficients.
Antoine Degenne, François Bourgin, Charles Perrin, and Vazken Andréassian
EGUsphere, https://doi.org/10.5194/egusphere-2026-1197, https://doi.org/10.5194/egusphere-2026-1197, 2026
Short summary
Short summary
We tested whether a simple model combining basic water balance principles with artificial intelligence can predict yearly river flow across many regions and years. Using data from over 3,000 river basins in eight countries, we found that the model works well when predicting future years in the same basin, but is less accurate in new regions because estimating long-term average flow remains difficult. This highlights both the promise and limits of this approach for large-scale water management.
Vazken Andréassian, Guilherme Mendoza Guimarães, Alban de Lavenne, and Julien Lerat
Hydrol. Earth Syst. Sci., 29, 5477–5491, https://doi.org/10.5194/hess-29-5477-2025, https://doi.org/10.5194/hess-29-5477-2025, 2025
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 an 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 in explaining annual streamflow variations.
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, 17, 1461–1479, https://doi.org/10.5194/essd-17-1461-2025, https://doi.org/10.5194/essd-17-1461-2025, 2025
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 analyze hydrological behavior and perform model assessments.
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.
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.
Cited articles
Andréassian, V., Lerat, J., Loumagne, C., Mathevet, T., Michel, C.,
Oudin, L., and Perrin, C.: What is really undermining hydrologic science
today?, Hydrol. Process., 21, 2819–2822, https://doi.org/10.1002/hyp.6854, 2007.
Bieroza, M. Z., Heathwaite, A. L., Bechmann, M., Kyllmar, K., and Jordan,
P.: The concentration-discharge slope as a tool for water quality
management, Sci. Total Environ., 630, 738–749,
https://doi.org/10.1016/j.scitotenv.2018.02.256, 2018.
Botter, M., Burlando, P., and Fatichi, S.: Anthropogenic and catchment characteristic signatures in the water quality of Swiss rivers: a quantitative assessment, Hydrol. Earth Syst. Sci., 23, 1885–1904, https://doi.org/10.5194/hess-23-1885-2019, 2019.
Box, G. E. and Cox, D. R.: An analysis of transformations, J.
Roy. Stat. Soc. B Met., 26, 211–243, 1964.
Box, G. E., Jenkins, G. M., Reinsel, G. C., and Ljung, G. M.: Analysis of Seasonal Time Series, in: Time series analysis. Forecasting and Control, 5th edn., John Wiley & Sons Inc., Hoboken, New Jersey, USA, 305–351, 2016.
Durum, W. H.: Relationship of the mineral constituents in solution to stream
flow, Saline River near Russell, Kansas, Eos, Transactions American
Geophysical Union, 34, 435–442, https://doi.org/10.1029/TR034i003p00435, 1953.
Edwards, A. M. C.: The variation of dissolved constituents with discharge in
some Norfolk rivers, J. Hydrol., 18, 219–242,
https://doi.org/10.1016/0022-1694(73)90049-8, 1973.
Floury, P., Gaillardet, J., Gayer, E., Bouchez, J., Tallec, G., Ansart, P., Koch, F., Gorge, C., Blanchouin, A., and Roubaty, J.-L.: The potamochemical symphony: new progress in the high-frequency acquisition of stream chemical data, Hydrol. Earth Syst. Sci., 21, 6153–6165, https://doi.org/10.5194/hess-21-6153-2017, 2017.
Godsey, S. E., Kirchner, J. W., and Clow, D. W.: Concentration-discharge
relationships reflect chemostatic characteristics of US catchments,
Hydrol. Process., 23, 1844–1864, https://doi.org/10.1002/hyp.7315, 2009.
Gunnerson, C. G.: Streamflow and quality in the Columbia River basin,
J. Sanit. Eng. Div.-ASCE, 93, 1–16, 1967.
Hall, F. R.: Dissolved solids-discharge relationships .1. Mixing models,
Water Resour. Res., 6, 845–850, https://doi.org/10.1029/WR006i003p00845, 1970.
Hall, F. R.: Dissolved solids-discharge relationships .2. Applications to
field data, Water Resour. Res., 7, 591–601, https://doi.org/10.1029/WR007i003p00591,
1971.
Hem, J. D.: Fluctuations in concentration of dissolved solids of some
southwestern streams, Eos, Transactions American Geophysical Union, 29,
80–84, https://doi.org/10.1029/TR029i001p00080, 1948.
Hirsch, R. M., Moyer, D. L., and Archfield, S. A.: Weighted Regressions on
Time, Discharge, and Season (WRTDS), with an Application to Chesapeake Bay
River Inputs, J. Am. Water Resour. As.,
46, 857–880, https://doi.org/10.1111/j.1752-1688.2010.00482.x, 2010.
Howarth, R. and Earle, S.: Application of a generalized power
transformation to geochemical data, J. Int. Ass. Math. Geol., 11, 45–62, 1979.
Jonnston, J.: Econometric Methods, McGraw – Hill Book Company, New York, USA, 437 pp.,
1972.
Kirchner, J. W., Feng, X., Neal, C., and Robson, A. J.: The fine structure
of water-quality dynamics: the (high-frequency) wave of the future,
Hydrol. Process., 18, 1353–1359, 2004.
Klemeš, V.: Dilettantism in Hydrology: transition or destiny?, Water
Resour. Res., 22, 177S–188S, 1986.
Lenz, A. and Sawyer, C. N.: Estimation of stream-flow from
alkalinity-determinations, Eos, Transactions American Geophysical Union, 25,
1005–1011, https://doi.org/10.1029/TR025i006p01005, 1944.
Mathevet, T., Michel, C., Andreassian, V., and Perrin, C.: A bounded version
of the Nash-Sutcliffe criterion for better model assessment on large sets of
basins, IAHS Publication, 307, 211–219, 2006.
Minaudo, C., Dupas, R., Gascuel-Odoux, C., Roubeix, V., Danis, P.-A., and
Moatar, F.: Seasonal and event-based concentration-discharge relationships
to identify catchment controls on nutrient export regimes, Adv. Water
Resour., 131, 103379, https://doi.org/10.1016/j.advwatres.2019.103379,
2019.
Moatar, F., Abbott, B., Minaudo, C., Curie, F., and Pinay, G.: Elemental
properties, hydrology, and biology interact to shape concentration-discharge
curves for carbon, nutrients, sediment, and major ions, Water Resour. Res., 53, 1270–1287, 2017.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual
models part I – A discussion of principles, J. Hydrol., 10,
282–290, 1970.
Tallec, G., Ansard, P., Guérin, A., Delaigue, O., and Blanchouin, A.:
Observatoire Oracle, Data set, Irstea, https://doi.org/10.17180/obs.oracle,
2015.
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.
This paper deals with the mathematical representation of concentration–discharge relationships....