Articles | Volume 22, issue 2
https://doi.org/10.5194/hess-22-1175-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/hess-22-1175-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
12 Feb 2018
Research article |
| 12 Feb 2018
Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling
University of Maryland Center for Environmental Science, US
Environmental Protection Agency Chesapeake Bay Program Office, 410 Severn
Avenue, Suite 112, Annapolis, Maryland 21403, USA
Ciaran J. Harman
Department of Environmental Health and Engineering, Johns Hopkins
University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
James W. Kirchner
Department of Environmental System Sciences, ETH Zurich,
Universitätstrasse 16, 8092 Zurich, Switzerland
Swiss Federal Research Institute WSL, Zürcherstrasse 111,
8903 Birmensdorf, Switzerland
Department of Earth and Planetary Science, University of
California, Berkeley, Berkeley, California 94720, USA
Related authors
Camille Minaudo, Andras Abonyi, Carles Alcaraz, Jacob Diamond, Nicholas J. K. Howden, Michael Rode, Estela Romero, Vincent Thieu, Fred Worrall, Qian Zhang, and Xavier Benito
Earth Syst. Sci. Data, 17, 3411–3430, https://doi.org/10.5194/essd-17-3411-2025, https://doi.org/10.5194/essd-17-3411-2025, 2025
Short summary
Short summary
Many waterbodies undergo nutrient decline, called oligotrophication, globally, but a comprehensive dataset to understand ecosystem responses is lacking. The OLIGOTREND database comprises multi-decadal chlorophyll a and nutrient time series from rivers, lakes, and estuaries with 4.3 million observations from 1894 unique measurement locations. The database provides empirical evidence for oligotrophication responses with a spatial and temporal coverage that exceeds previous efforts.
Camille Minaudo, Andras Abonyi, Carles Alcaraz, Jacob Diamond, Nicholas J. K. Howden, Michael Rode, Estela Romero, Vincent Thieu, Fred Worrall, Qian Zhang, and Xavier Benito
Earth Syst. Sci. Data, 17, 3411–3430, https://doi.org/10.5194/essd-17-3411-2025, https://doi.org/10.5194/essd-17-3411-2025, 2025
Short summary
Short summary
Many waterbodies undergo nutrient decline, called oligotrophication, globally, but a comprehensive dataset to understand ecosystem responses is lacking. The OLIGOTREND database comprises multi-decadal chlorophyll a and nutrient time series from rivers, lakes, and estuaries with 4.3 million observations from 1894 unique measurement locations. The database provides empirical evidence for oligotrophication responses with a spatial and temporal coverage that exceeds previous efforts.
Ciaran J. Harman and Esther Xu Fei
Geosci. Model Dev., 17, 477–495, https://doi.org/10.5194/gmd-17-477-2024, https://doi.org/10.5194/gmd-17-477-2024, 2024
Short summary
Short summary
Over the last 10 years, scientists have developed StorAge Selection: a new way of modeling how material is transported through complex systems. Here, we present some new, easy-to-use, flexible, and very accurate code for implementing this method. We show that, in cases where we know exactly what the answer should be, our code gets the right answer. We also show that our code is closer than some other codes to the right answer in an important way: it conserves mass.
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
Short summary
Short summary
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.
Adam S. Ward, Steven M. Wondzell, Noah M. Schmadel, Skuyler Herzog, Jay P. Zarnetske, Viktor Baranov, Phillip J. Blaen, Nicolai Brekenfeld, Rosalie Chu, Romain Derelle, Jennifer Drummond, Jan H. Fleckenstein, Vanessa Garayburu-Caruso, Emily Graham, David Hannah, Ciaran J. Harman, Jase Hixson, Julia L. A. Knapp, Stefan Krause, Marie J. Kurz, Jörg Lewandowski, Angang Li, Eugènia Martí, Melinda Miller, Alexander M. Milner, Kerry Neil, Luisa Orsini, Aaron I. Packman, Stephen Plont, Lupita Renteria, Kevin Roche, Todd Royer, Catalina Segura, James Stegen, Jason Toyoda, Jacqueline Hager, and Nathan I. Wisnoski
Hydrol. Earth Syst. Sci., 23, 5199–5225, https://doi.org/10.5194/hess-23-5199-2019, https://doi.org/10.5194/hess-23-5199-2019, 2019
Short summary
Short summary
The movement of water and solutes between streams and their shallow, connected subsurface is important to many ecosystem functions. These exchanges are widely expected to vary with stream flow across space and time, but these assumptions are seldom tested across basin scales. We completed more than 60 experiments across a 5th-order river basin to document these changes, finding patterns in space but not time. We conclude space-for-time and time-for-space substitutions are not good assumptions.
Adam S. Ward, Jay P. Zarnetske, Viktor Baranov, Phillip J. Blaen, Nicolai Brekenfeld, Rosalie Chu, Romain Derelle, Jennifer Drummond, Jan H. Fleckenstein, Vanessa Garayburu-Caruso, Emily Graham, David Hannah, Ciaran J. Harman, Skuyler Herzog, Jase Hixson, Julia L. A. Knapp, Stefan Krause, Marie J. Kurz, Jörg Lewandowski, Angang Li, Eugènia Martí, Melinda Miller, Alexander M. Milner, Kerry Neil, Luisa Orsini, Aaron I. Packman, Stephen Plont, Lupita Renteria, Kevin Roche, Todd Royer, Noah M. Schmadel, Catalina Segura, James Stegen, Jason Toyoda, Jacqueline Hager, Nathan I. Wisnoski, and Steven M. Wondzell
Earth Syst. Sci. Data, 11, 1567–1581, https://doi.org/10.5194/essd-11-1567-2019, https://doi.org/10.5194/essd-11-1567-2019, 2019
Short summary
Short summary
Studies of river corridor exchange commonly focus on characterization of the physical, chemical, or biological system. As a result, complimentary systems and context are often lacking, which may limit interpretation. Here, we present a characterization of all three systems at 62 sites in a 5th-order river basin, including samples of surface water, hyporheic water, and sediment. These data will allow assessment of interacting processes in the river corridor.
U. Ehret, H. V. Gupta, M. Sivapalan, S. V. Weijs, S. J. Schymanski, G. Blöschl, A. N. Gelfan, C. Harman, A. Kleidon, T. A. Bogaard, D. Wang, T. Wagener, U. Scherer, E. Zehe, M. F. P. Bierkens, G. Di Baldassarre, J. Parajka, L. P. H. van Beek, A. van Griensven, M. C. Westhoff, and H. C. Winsemius
Hydrol. Earth Syst. Sci., 18, 649–671, https://doi.org/10.5194/hess-18-649-2014, https://doi.org/10.5194/hess-18-649-2014, 2014
C. Harman and P. A. Troch
Hydrol. Earth Syst. Sci., 18, 417–433, https://doi.org/10.5194/hess-18-417-2014, https://doi.org/10.5194/hess-18-417-2014, 2014
S. E. Thompson, M. Sivapalan, C. J. Harman, V. Srinivasan, M. R. Hipsey, P. Reed, A. Montanari, and G. Blöschl
Hydrol. Earth Syst. Sci., 17, 5013–5039, https://doi.org/10.5194/hess-17-5013-2013, https://doi.org/10.5194/hess-17-5013-2013, 2013
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Modelling approaches
Hydrological regime index for non-perennial rivers
Assessing the adequacy of traditional hydrological models for climate change impact studies: a case for long short-term memory (LSTM) neural networks
Assessing the value of high-resolution data and parameter transferability across temporal scales in hydrological modeling: a case study in northern China
Technical note: How many models do we need to simulate hydrologic processes across large geographical domains?
CONCN: a high-resolution, integrated surface water–groundwater ParFlow modeling platform of continental China
Evaluating the effects of topography and land use change on hydrological signatures: a comparative study of two adjacent watersheds
Technical note: What does the Standardized Streamflow Index actually reflect? Insights and implications for hydrological drought analysis
Long short-term memory networks for enhancing real-time flood forecasts: a case study for an underperforming hydrologic model
Assessing the value of high-resolution rainfall and streamflow data for hydrological modeling: an analysis based on 63 catchments in southeast China
Catchments do not strictly follow Budyko curves over multiple decades, but deviations are minor and predictable
Scale dependency in modeling nivo-glacial hydrological systems: the case of the Arolla basin, Switzerland
Extended-range forecasting of stream water temperature with deep-learning models
Technical note: An approach for handling multiple temporal frequencies with different input dimensions using a single LSTM cell
Projections of streamflow intermittence under climate change in European drying river networks
Economic valuation of subsurface water contributions to watershed ecosystem services using a fully integrated groundwater–surface-water model
Analyzing the generalization capabilities of a hybrid hydrological model for extrapolation to extreme events
CH-RUN: a deep-learning-based spatially contiguous runoff reconstruction for Switzerland
Runoff component quantification and future streamflow projection in a large mountainous basin based on a multidata-constrained cryospheric–hydrological model
Multi-variable process-based calibration of a behavioural hydrological model
Exploring the potential processes controlling changes in precipitation–runoff relationships in non-stationary environments
A diversity-centric strategy for the selection of spatio-temporal training data for LSTM-based streamflow forecasting
Simulating the Tone River eastward diversion project in Japan carried out 4 centuries ago
Lack of robustness of hydrological models: a large-sample diagnosis and an attempt to identify hydrological and climatic drivers
Achieving water budget closure through physical hydrological process modelling: insights from a large-sample study
Heavy-tailed flood peak distributions: what is the effect of the spatial variability of rainfall and runoff generation?
A Distributed Hybrid Physics-AI Framework for Learning Corrections of Internal Hydrological Fluxes and Enhancing High-Resolution Regionalized Flood Modeling
State updating of the Xin'anjiang model: joint assimilating streamflow and multi-source soil moisture data via the asynchronous ensemble Kalman filter with enhanced error models
Improving the hydrological consistency of a process-based solute-transport model by simultaneous calibration of streamflow and stream concentrations
Understanding the relationship between streamflow forecast skill and value across the western US
Leveraging soil diversity to mitigate hydrological extremes with nature-based solutions in productive catchments
Leveraging a time-series event separation method to disentangle time-varying hydrologic controls on streamflow – application to wildfire-affected catchments
The significance of the leaf area index for evapotranspiration estimation in SWAT-T for characteristic land cover types of West Africa
Improved representation of soil moisture processes through incorporation of cosmic-ray neutron count measurements in a large-scale hydrologic model
Spatio-temporal patterns and trends of streamflow in water-scarce Mediterranean basins
A large-sample modelling approach towards integrating streamflow and evaporation data for the Spanish catchments
Seasonal variation in land cover estimates reveals sensitivities and opportunities for environmental models
Soil moisture and precipitation intensity control the transit time distribution of quick flow in a flashy headwater catchment
Estimating response times, flow velocities, and roughness coefficients of Canadian Prairie basins
Learning landscape features from streamflow with autoencoders
Constraining pesticide degradation in conceptual distributed catchment models with compound-specific isotope analysis (CSIA)
On the use of streamflow transformations for hydrological model calibration
Unveiling the Impact of Potential Evapotranspiration Method Selection on Trends in Hydrological Cycle Components Across Europe
Simulation-based inference for parameter estimation of complex watershed simulators
Comparative Hydrological Modeling of Snow-Cover and Frozen Ground Impacts Under Topographically Complex Conditions
Multi-scale soil moisture data and process-based modeling reveal the importance of lateral groundwater flow in a subarctic catchment
Catchment response to climatic variability: implications for root zone storage and streamflow predictions
Hybrid hydrological modeling for large alpine basins: a semi-distributed approach
Controls on spatial and temporal variability of soil moisture across a heterogeneous boreal forest landscape
Where can rewetting of forested peatland reduce extreme flows?
Karst aquifer discharge response to rainfall interpreted as anomalous transport
Pablo Fernando Dornes and Rocío Noelia Comas
Hydrol. Earth Syst. Sci., 29, 2901–2923, https://doi.org/10.5194/hess-29-2901-2025, https://doi.org/10.5194/hess-29-2901-2025, 2025
Short summary
Short summary
The Desaguadero–Salado–Chadiluevú–Curacó (DSCC) River is a semiarid river which is heavily dammed at its tributaries which collect the snowmelt runoff. This runoff feeds mostly gravitational irrigation systems of very low efficiency. As a result, the DSCC River does not have natural runoff. The proposed hydrological regime index (HRI) is able to discriminate and quantify regime alterations under permanent and non-permanent flow conditions and with low- and high-impoundment conditions.
Jean-Luc Martel, François Brissette, Richard Arsenault, Richard Turcotte, Mariana Castañeda-Gonzalez, William Armstrong, Edouard Mailhot, Jasmine Pelletier-Dumont, Gabriel Rondeau-Genesse, and Louis-Philippe Caron
Hydrol. Earth Syst. Sci., 29, 2811–2836, https://doi.org/10.5194/hess-29-2811-2025, https://doi.org/10.5194/hess-29-2811-2025, 2025
Short summary
Short summary
This study compares long short-term memory (LSTM) neural networks with traditional hydrological models to predict future streamflow under climate change. Using data from 148 catchments, it finds that LSTM models, which learn from extensive data sequences, perform differently and often better than traditional hydrological models. The continental LSTM model, which includes data from diverse climate zones, is particularly effective for understanding climate impacts on water resources.
Mahmut Tudaji, Yi Nan, and Fuqiang Tian
Hydrol. Earth Syst. Sci., 29, 2633–2654, https://doi.org/10.5194/hess-29-2633-2025, https://doi.org/10.5194/hess-29-2633-2025, 2025
Short summary
Short summary
We assessed the value of high-resolution data and parameter transferability across temporal scales based on seven catchments in northern China. We found that higher-resolution data do not always improve model performance, questioning the need for such data. Model parameters are transferable across different data resolutions but not across computational time steps. It is recommended to utilize a smaller computational time step when building hydrological models even without high-resolution data.
Wouter J. M. Knoben, Ashwin Raman, Gaby J. Gründemann, Mukesh Kumar, Alain Pietroniro, Chaopeng Shen, Yalan Song, Cyril Thébault, Katie van Werkhoven, Andrew W. Wood, and Martyn P. Clark
Hydrol. Earth Syst. Sci., 29, 2361–2375, https://doi.org/10.5194/hess-29-2361-2025, https://doi.org/10.5194/hess-29-2361-2025, 2025
Short summary
Short summary
Hydrologic models are needed to provide simulations of water availability, floods, and droughts. The accuracy of these simulations is often quantified with so-called performance scores. A common thought is that different models are more or less applicable to different landscapes, depending on how the model works. We show that performance scores are not helpful in distinguishing between different models and thus cannot easily be used to select an appropriate model for a specific place.
Chen Yang, Zitong Jia, Wenjie Xu, Zhongwang Wei, Xiaolang Zhang, Yiguang Zou, Jeffrey McDonnell, Laura Condon, Yongjiu Dai, and Reed Maxwell
Hydrol. Earth Syst. Sci., 29, 2201–2218, https://doi.org/10.5194/hess-29-2201-2025, https://doi.org/10.5194/hess-29-2201-2025, 2025
Short summary
Short summary
We developed the first high-resolution, integrated surface water–groundwater hydrologic model of the entirety of continental China using ParFlow. The model shows good performance in terms of streamflow and water table depth when compared to global data products and observations. It is essential for water resources management and decision-making in China within a consistent framework in the changing world. It also has significant implications for similar modeling in other places in the world.
Haifan Liu, Haochen Yan, and Mingfu Guan
Hydrol. Earth Syst. Sci., 29, 2109–2132, https://doi.org/10.5194/hess-29-2109-2025, https://doi.org/10.5194/hess-29-2109-2025, 2025
Short summary
Short summary
Land changes and landscape features critically impact water systems. Studying two watersheds in China’s Greater Bay Area, we found slope strongly influences water processes in mountainous areas. However, this relationship is weak in the lower regions of steeper watersheds. Urbanization leads to an increase in annual surface runoff, while flatter watersheds exhibit a buffering capacity against this effect. However, this buffering capacity diminishes with increasing annual rainfall intensity.
Fabián Lema, Pablo A. Mendoza, Nicolás A. Vásquez, Naoki Mizukami, Mauricio Zambrano-Bigiarini, and Ximena Vargas
Hydrol. Earth Syst. Sci., 29, 1981–2002, https://doi.org/10.5194/hess-29-1981-2025, https://doi.org/10.5194/hess-29-1981-2025, 2025
Short summary
Short summary
Hydrological droughts affect ecosystems and socioeconomic activities worldwide. Despite the fact that they are commonly described with the Standardized Streamflow Index (SSI), there is limited understanding of what they truly reflect in terms of water cycle processes. Here, we used state-of-the-art hydrological models in Andean basins to examine drivers of SSI fluctuations. The results highlight the importance of careful selection of indices and timescales for accurate drought characterization and monitoring.
Sebastian Gegenleithner, Manuel Pirker, Clemens Dorfmann, Roman Kern, and Josef Schneider
Hydrol. Earth Syst. Sci., 29, 1939–1962, https://doi.org/10.5194/hess-29-1939-2025, https://doi.org/10.5194/hess-29-1939-2025, 2025
Short summary
Short summary
Accurate early-warning systems are crucial for reducing the damage caused by flooding events. In this study, we explored the potential of long short-term memory networks for enhancing the forecast accuracy of hydrologic models employed in operational flood forecasting. The presented approach elevated the investigated hydrologic model’s forecast accuracy for further ahead predictions and at flood event runoff.
Mahmut Tudaji, Yi Nan, and Fuqiang Tian
Hydrol. Earth Syst. Sci., 29, 1919–1937, https://doi.org/10.5194/hess-29-1919-2025, https://doi.org/10.5194/hess-29-1919-2025, 2025
Short summary
Short summary
Common intuition holds that higher input data resolution leads to better results. To assess the benefits of high-resolution data, we conduct simulation experiments using data with various temporal resolutions across multiple catchments and find that higher-resolution data do not always improve model performance, challenging the necessity of pursuing such data. In catchments with small areas or significant flow variability, high-resolution data is more valuable.
Muhammad Ibrahim, Miriam Coenders-Gerrits, Ruud van der Ent, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 29, 1703–1723, https://doi.org/10.5194/hess-29-1703-2025, https://doi.org/10.5194/hess-29-1703-2025, 2025
Short summary
Short summary
The quantification of precipitation into evaporation and runoff is vital for water resources management. The Budyko framework, based on aridity and evaporative indices of a catchment, can be an ideal tool for that. However, recent research highlights deviations of catchments from the expected evaporative index, casting doubt on its reliability. This study quantifies deviations of 2387 catchments, finding them minor and predictable. Integrating these into predictions upholds the framework's efficacy.
Anne-Laure Argentin, Pascal Horton, Bettina Schaefli, Jamal Shokory, Felix Pitscheider, Leona Repnik, Mattia Gianini, Simone Bizzi, Stuart N. Lane, and Francesco Comiti
Hydrol. Earth Syst. Sci., 29, 1725–1748, https://doi.org/10.5194/hess-29-1725-2025, https://doi.org/10.5194/hess-29-1725-2025, 2025
Short summary
Short summary
In this article, we show that by taking the optimal parameters calibrated with a semi-lumped model for the discharge at a catchment's outlet, we can accurately simulate runoff at various points within the study area, including three nested and three neighboring catchments. In addition, we demonstrate that employing more intricate melt models, which better represent physical processes, enhances the transfer of parameters in the simulation, until we observe overparameterization.
Ryan S. Padrón, Massimiliano Zappa, Luzi Bernhard, and Konrad Bogner
Hydrol. Earth Syst. Sci., 29, 1685–1702, https://doi.org/10.5194/hess-29-1685-2025, https://doi.org/10.5194/hess-29-1685-2025, 2025
Short summary
Short summary
We generate operational forecasts of daily maximum stream water temperature for 32 consecutive days at 54 stations in Switzerland with our best-performing data-driven model. The average forecast error is 0.38 °C for 1 d ahead and increases to 0.90 °C for 32 d ahead given the uncertainty in the meteorological variables influencing water temperature. Here we compare the skill of several models, how well they can forecast at new and ungauged stations, and the importance of different model inputs.
Eduardo Acuña Espinoza, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, Ralf Loritz, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1749–1758, https://doi.org/10.5194/hess-29-1749-2025, https://doi.org/10.5194/hess-29-1749-2025, 2025
Short summary
Short summary
Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for rainfall-runoff hydrological modelling. However, most studies focus on predictions at a daily scale, limiting the benefits of sub-daily (e.g. hourly) predictions in applications like flood forecasting. In this study, we introduce a new architecture, multi-frequency LSTM (MF-LSTM), designed to use inputs of various temporal frequencies to produce sub-daily (e.g. hourly) predictions at a moderate computational cost.
Louise Mimeau, Annika Künne, Alexandre Devers, Flora Branger, Sven Kralisch, Claire Lauvernet, Jean-Philippe Vidal, Núria Bonada, Zoltán Csabai, Heikki Mykrä, Petr Pařil, Luka Polović, and Thibault Datry
Hydrol. Earth Syst. Sci., 29, 1615–1636, https://doi.org/10.5194/hess-29-1615-2025, https://doi.org/10.5194/hess-29-1615-2025, 2025
Short summary
Short summary
Our study projects how climate change will affect the drying of river segments and stream networks in Europe, using advanced modelling techniques to assess changes in six river networks across diverse ecoregions. We found that drying events will become more frequent and intense and will start earlier or last longer, potentially turning some river sections from perennial to intermittent. The results are valuable for river ecologists for evaluating the ecological health of river ecosystem.
Tariq Aziz, Steven K. Frey, David R. Lapen, Susan Preston, Hazen A. J. Russell, Omar Khader, Andre R. Erler, and Edward A. Sudicky
Hydrol. Earth Syst. Sci., 29, 1549–1568, https://doi.org/10.5194/hess-29-1549-2025, https://doi.org/10.5194/hess-29-1549-2025, 2025
Short summary
Short summary
This study determines the value of subsurface water for ecosystem services' supply in an agricultural watershed in Ontario, Canada. Using a fully integrated water model and an economic valuation approach, the research highlights subsurface water's critical role in maintaining watershed ecosystem services. The study informs on the sustainable use of subsurface water and introduces a new method for managing watershed ecosystem services.
Eduardo Acuña Espinoza, Ralf Loritz, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1277–1294, https://doi.org/10.5194/hess-29-1277-2025, https://doi.org/10.5194/hess-29-1277-2025, 2025
Short summary
Short summary
Data-driven techniques have shown the potential to outperform process-based models in rainfall–runoff simulations. Hybrid models, combining both approaches, aim to enhance accuracy and maintain interpretability. Expanding the set of test cases to evaluate hybrid models under different conditions, we test their generalization capabilities for extreme hydrological events.
Basil Kraft, Michael Schirmer, William H. Aeberhard, Massimiliano Zappa, Sonia I. Seneviratne, and Lukas Gudmundsson
Hydrol. Earth Syst. Sci., 29, 1061–1082, https://doi.org/10.5194/hess-29-1061-2025, https://doi.org/10.5194/hess-29-1061-2025, 2025
Short summary
Short summary
This study reconstructs daily runoff in Switzerland (1962–2023) using a deep-learning model, providing a spatially contiguous dataset on a medium-sized catchment grid. The model outperforms traditional hydrological methods, revealing shifts in Swiss water resources, including more frequent dry years and declining summer runoff. The reconstruction is publicly available.
Mengjiao Zhang, Yi Nan, and Fuqiang Tian
Hydrol. Earth Syst. Sci., 29, 1033–1060, https://doi.org/10.5194/hess-29-1033-2025, https://doi.org/10.5194/hess-29-1033-2025, 2025
Short summary
Short summary
Owing to differences in the existing published results, we conducted a detailed analysis of the runoff components and future trends in the Yarlung Tsangpo River basin and found that the contributions of snowmelt and glacier melt runoff to streamflow (both ~5 %) are limited and much lower than previous results. The streamflow in this area will continuously increase in the future, but the overestimated contribution of glacier melt could lead to an underestimation of this increasing trend.
Moritz Maximilian Heuer, Hadysa Mohajerani, and Markus Christian Casper
EGUsphere, https://doi.org/10.5194/egusphere-2025-636, https://doi.org/10.5194/egusphere-2025-636, 2025
Short summary
Short summary
This study presents a calibration approach for water balance models. The different calibration steps aim at calibrating different hydrological processes: evapotranspiration, the runoff partitioning into surface runoff, interflow and groundwater recharge, as well as the groundwater behaviour. This allows for selection of a model parameterisation that correctly predicts the discharge at catchment outlet and simultaneously correctly depicts the underlying hydrological processes.
Tian Lan, Tongfang Li, Hongbo Zhang, Jiefeng Wu, Yongqin David Chen, and Chong-Yu Xu
Hydrol. Earth Syst. Sci., 29, 903–924, https://doi.org/10.5194/hess-29-903-2025, https://doi.org/10.5194/hess-29-903-2025, 2025
Short summary
Short summary
This study develops an integrated framework based on the novel Driving index for changes in Precipitation–Runoff Relationships (DPRR) to explore the controlling changes in precipitation–runoff relationships in non-stationary environments. According to the quantitative results of the candidate driving factors, the possible process explanations for changes in the precipitation–runoff relationships are deduced. The main contribution offers a comprehensive understanding of hydrological processes.
Everett Snieder and Usman T. Khan
Hydrol. Earth Syst. Sci., 29, 785–798, https://doi.org/10.5194/hess-29-785-2025, https://doi.org/10.5194/hess-29-785-2025, 2025
Short summary
Short summary
Improving the accuracy of flood forecasts is paramount to minimising flood damage. Machine learning (ML) models are increasingly being applied for flood forecasting. Such models are typically trained on large historic hydrometeorological datasets. In this work, we evaluate methods for selecting training datasets that maximise the spatio-temporal diversity of the represented hydrological processes. Empirical results showcase the importance of hydrological diversity in training ML models.
Joško Trošelj and Naota Hanasaki
Hydrol. Earth Syst. Sci., 29, 753–766, https://doi.org/10.5194/hess-29-753-2025, https://doi.org/10.5194/hess-29-753-2025, 2025
Short summary
Short summary
This study presents the first distributed hydrological simulation which confirms claims raised by historians that the eastward diversion project of the Tone River in Japan was conducted 4 centuries ago to increase low flows and subsequent travelling possibilities surrounding the capital, Edo (Tokyo), using inland navigation. We showed that great steps forward can be made for improving quality of life with small human engineering waterworks and small interventions in the regime of natural flows.
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.
Xudong Zheng, Dengfeng Liu, Shengzhi Huang, Hao Wang, and Xianmeng Meng
Hydrol. Earth Syst. Sci., 29, 627–653, https://doi.org/10.5194/hess-29-627-2025, https://doi.org/10.5194/hess-29-627-2025, 2025
Short summary
Short summary
Water budget non-closure is a widespread phenomenon among multisource datasets which undermines the robustness of hydrological inferences. This study proposes a Multisource Dataset Correction Framework grounded in Physical Hydrological Process Modelling to enhance water budget closure, termed PHPM-MDCF. We examined the efficiency and robustness of the framework using the CAMELS dataset and achieved an average reduction of 49 % in total water budget residuals across 475 CONUS basins.
Elena Macdonald, Bruno Merz, Viet Dung Nguyen, and Sergiy Vorogushyn
Hydrol. Earth Syst. Sci., 29, 447–463, https://doi.org/10.5194/hess-29-447-2025, https://doi.org/10.5194/hess-29-447-2025, 2025
Short summary
Short summary
Flood peak distributions indicate how likely the occurrence of an extreme flood is at a certain river. If the distribution has a so-called heavy tail, extreme floods are more likely than might be anticipated. We find heavier tails in small catchments compared to large catchments, and spatially variable rainfall leads to a lower occurrence probability of extreme floods. Spatially variable runoff does not show effects. The results can improve estimations of probabilities of extreme floods.
Ngo Nghi Truyen Huynh, Pierre-André Garambois, Benjamin Renard, François Colleoni, Jérôme Monnier, and Hélène Roux
EGUsphere, https://doi.org/10.5194/egusphere-2024-3665, https://doi.org/10.5194/egusphere-2024-3665, 2025
Short summary
Short summary
Understanding and modeling flash flood-prone areas remains challenging due to limited data and scale-relevant hydrological theory. While machine learning shows promise, its integration with process-based models is difficult. We present an approach incorporating machine learning into a high-resolution hydrological model to correct internal fluxes and transfer parameters between watersheds. Results show improved accuracy, advancing development of learnable and interpretable process-based models.
Junfu Gong, Xingwen Liu, Cheng Yao, Zhijia Li, Albrecht H. Weerts, Qiaoling Li, Satish Bastola, Yingchun Huang, and Junzeng Xu
Hydrol. Earth Syst. Sci., 29, 335–360, https://doi.org/10.5194/hess-29-335-2025, https://doi.org/10.5194/hess-29-335-2025, 2025
Short summary
Short summary
Our study introduces a new method to improve flood forecasting by combining soil moisture and streamflow data using an advanced data assimilation technique. By integrating field and reanalysis soil moisture data and assimilating this with streamflow measurements, we aim to enhance the accuracy of flood predictions. This approach reduces the accumulation of past errors in the initial conditions at the start of the forecast, helping to better prepare for and respond to floods.
Jordy Salmon-Monviola, Ophélie Fovet, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 29, 127–158, https://doi.org/10.5194/hess-29-127-2025, https://doi.org/10.5194/hess-29-127-2025, 2025
Short summary
Short summary
To increase the predictive power of hydrological models, it is necessary to improve their consistency, i.e. their physical realism, which is measured by the ability of the model to reproduce observed system dynamics. Using a model to represent the dynamics of water and nitrate and dissolved organic carbon concentrations in an agricultural catchment, we showed that using solute-concentration data for calibration is useful to improve the hydrological consistency of the model.
Parthkumar A. Modi, Jared C. Carbone, Keith S. Jennings, Hannah Kamen, Joseph R. Kasprzyk, Bill Szafranski, Cameron W. Wobus, and Ben Livneh
EGUsphere, https://doi.org/10.5194/egusphere-2024-4046, https://doi.org/10.5194/egusphere-2024-4046, 2025
Short summary
Short summary
This study shows that in unmanaged snow-dominated basins, high forecast accuracy doesn’t always lead to high economic value, especially during extreme conditions like droughts. It highlights how irregular errors in modern forecasting systems weaken the connection between accuracy and value. These findings call for forecast evaluations to focus not only on accuracy but also on economic impacts, providing valuable guidance for better water resource management under uncertainty.
Benjamin Guillaume, Adrien Michez, and Aurore Degré
EGUsphere, https://doi.org/10.5194/egusphere-2024-3978, https://doi.org/10.5194/egusphere-2024-3978, 2025
Short summary
Short summary
Nature-based solutions (NbS) can mitigate floods and agricultural droughts by enhancing soil health and restoring hydrological cycles. This study highlights that leveraging soil diversity is key to optimizing NbS performance.
Haley A. Canham, Belize Lane, Colin B. Phillips, and Brendan P. Murphy
Hydrol. Earth Syst. Sci., 29, 27–43, https://doi.org/10.5194/hess-29-27-2025, https://doi.org/10.5194/hess-29-27-2025, 2025
Short summary
Short summary
The influence of watershed disturbances has proved challenging to disentangle from natural streamflow variability. This study evaluates the influence of time-varying hydrologic controls on rainfall–runoff in undisturbed and wildfire-disturbed watersheds using a novel time-series event separation method. Across watersheds, water year type and season influenced rainfall–runoff patterns. Accounting for these controls enabled clearer isolation of wildfire effects.
Fabian Merk, Timo Schaffhauser, Faizan Anwar, Ye Tuo, Jean-Martial Cohard, and Markus Disse
Hydrol. Earth Syst. Sci., 28, 5511–5539, https://doi.org/10.5194/hess-28-5511-2024, https://doi.org/10.5194/hess-28-5511-2024, 2024
Short summary
Short summary
Evapotranspiration (ET) is computed from the vegetation (plant transpiration) and soil (soil evaporation). In western Africa, plant transpiration correlates with vegetation growth. Vegetation is often represented using the leaf area index (LAI). In this study, we evaluate the importance of the LAI for ET calculation. We take a close look at this interaction and highlight its relevance. Our work contributes to the understanding of terrestrial water cycle processes .
Eshrat Fatima, Rohini Kumar, Sabine Attinger, Maren Kaluza, Oldrich Rakovec, Corinna Rebmann, Rafael Rosolem, Sascha E. Oswald, Luis Samaniego, Steffen Zacharias, and Martin Schrön
Hydrol. Earth Syst. Sci., 28, 5419–5441, https://doi.org/10.5194/hess-28-5419-2024, https://doi.org/10.5194/hess-28-5419-2024, 2024
Short summary
Short summary
This study establishes a framework to incorporate cosmic-ray neutron measurements into the mesoscale Hydrological Model (mHM). We evaluate different approaches to estimate neutron counts within the mHM using the Desilets equation, with uniformly and non-uniformly weighted average soil moisture, and the physically based code COSMIC. The data improved not only soil moisture simulations but also the parameterisation of evapotranspiration in the model.
Laia Estrada, Xavier Garcia, Joan Saló-Grau, Rafael Marcé, Antoni Munné, and Vicenç Acuña
Hydrol. Earth Syst. Sci., 28, 5353–5373, https://doi.org/10.5194/hess-28-5353-2024, https://doi.org/10.5194/hess-28-5353-2024, 2024
Short summary
Short summary
Hydrological modelling is a powerful tool to support decision-making. We assessed spatio-temporal patterns and trends of streamflow for 2001–2022 with a hydrological model, integrating stakeholder expert knowledge on management operations. The results provide insight into how climate change and anthropogenic pressures affect water resources availability in regions vulnerable to water scarcity, thus raising the need for sustainable management practices and integrated hydrological modelling.
Patricio Yeste, Matilde García-Valdecasas Ojeda, Sonia R. Gámiz-Fortis, Yolanda Castro-Díez, Axel Bronstert, and María Jesús Esteban-Parra
Hydrol. Earth Syst. Sci., 28, 5331–5352, https://doi.org/10.5194/hess-28-5331-2024, https://doi.org/10.5194/hess-28-5331-2024, 2024
Short summary
Short summary
Integrating streamflow and evaporation data can help improve the physical realism of hydrologic models. We investigate the capabilities of the Variable Infiltration Capacity (VIC) to reproduce both hydrologic variables for 189 headwater located in Spain. Results from sensitivity analyses indicate that adding two vegetation parameters is enough to improve the representation of evaporation and that the performance of VIC exceeded that of the largest modelling effort currently available in Spain.
Daniel T. Myers, David Jones, Diana Oviedo-Vargas, John Paul Schmit, Darren L. Ficklin, and Xuesong Zhang
Hydrol. Earth Syst. Sci., 28, 5295–5310, https://doi.org/10.5194/hess-28-5295-2024, https://doi.org/10.5194/hess-28-5295-2024, 2024
Short summary
Short summary
We studied how streamflow and water quality models respond to land cover data collected by satellites during the growing season versus the non-growing season. The land cover data showed more trees during the growing season and more built areas during the non-growing season. We next found that the use of non-growing season data resulted in a higher modeled nutrient export to streams. Knowledge of these sensitivities would be particularly important when models inform water resource management.
Hatice Türk, Christine Stumpp, Markus Hrachowitz, Karsten Schulz, Peter Strauss, Günter Blöschl, and Michael Stockinger
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-359, https://doi.org/10.5194/hess-2024-359, 2024
Revised manuscript accepted for HESS
Short summary
Short summary
Using advances in transit time estimation and tracer data, we tested if fast-flow transit times are controlled solely by soil moisture or are also controlled by precipitation intensity. We used soil moisture-dependent and precipitation intensity-conditional transfer functions. We showed that significant portion of event water bypasses the soil matrix through fast flow paths (overland flow, tile drains, preferential flow paths) in dry soil conditions for both low and high-intensity precipitation.
Kevin R. Shook, Paul H. Whitfield, Christopher Spence, and John W. Pomeroy
Hydrol. Earth Syst. Sci., 28, 5173–5192, https://doi.org/10.5194/hess-28-5173-2024, https://doi.org/10.5194/hess-28-5173-2024, 2024
Short summary
Short summary
Recent studies suggest that the velocities of water running off landscapes in the Canadian Prairies may be much smaller than generally assumed. Analyses of historical flows for 23 basins in central Alberta show that many of the rivers responded more slowly and that the flows are much slower than would be estimated from equations developed elsewhere. The effects of slow flow velocities on the development of hydrological models of the region are discussed, as are the possible causes.
Alberto Bassi, Marvin Höge, Antonietta Mira, Fabrizio Fenicia, and Carlo Albert
Hydrol. Earth Syst. Sci., 28, 4971–4988, https://doi.org/10.5194/hess-28-4971-2024, https://doi.org/10.5194/hess-28-4971-2024, 2024
Short summary
Short summary
The goal is to remove the impact of meteorological drivers in order to uncover the unique landscape fingerprints of a catchment from streamflow data. Our results reveal an optimal two-feature summary for most catchments, with a third feature associated with aridity and intermittent flow that is needed for challenging cases. Baseflow index, aridity, and soil or vegetation attributes strongly correlate with learnt features, indicating their importance for streamflow prediction.
Sylvain Payraudeau, Pablo Alvarez-Zaldivar, Paul van Dijk, and Gwenaël Imfeld
EGUsphere, https://doi.org/10.5194/egusphere-2024-2840, https://doi.org/10.5194/egusphere-2024-2840, 2024
Short summary
Short summary
Our study focuses on the rising concern of pesticides damaging aquatic ecosystems, which puts drinking water, the environment, and human health at risk. We provided more accurate estimates of how pesticides break down and spread in small water systems, helping to improve pesticide management practices. By using unique chemical markers in our analysis, we enhanced the accuracy of our predictions, offering important insights for better protection of water sources and natural ecosystems.
Guillaume Thirel, Léonard Santos, Olivier Delaigue, and Charles Perrin
Hydrol. Earth Syst. Sci., 28, 4837–4860, https://doi.org/10.5194/hess-28-4837-2024, https://doi.org/10.5194/hess-28-4837-2024, 2024
Short summary
Short summary
We discuss how mathematical transformations impact calibrated hydrological model simulations. We assess how 11 transformations behave over the complete range of streamflows. Extreme transformations lead to models that are specialized for extreme streamflows but show poor performance outside the range of targeted streamflows and are less robust. We show that no a priori assumption about transformations can be taken as warranted.
Vishal Thakur, Yannis Markonis, Rohini Kumar, Johanna Ruth Thomson, Mijael Rodrigo Vargas Godoy, Martin Hanel, and Oldrich Rakovec
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-341, https://doi.org/10.5194/hess-2024-341, 2024
Revised manuscript accepted for HESS
Short summary
Short summary
Understanding the changes in water movement in earth is crucial for everyone. To quantify this water movement there are several techniques. We examined how different methods of estimating evaporation impact predictions of various types of water movement across Europe. We found that, while these methods generally agree on whether changes are increasing or decreasing, they differ in magnitude. This means selecting the right evaporation method is crucial for accurate predictions of water movement.
Robert Hull, Elena Leonarduzzi, Luis De La Fuente, Hoang Viet Tran, Andrew Bennett, Peter Melchior, Reed M. Maxwell, and Laura E. Condon
Hydrol. Earth Syst. Sci., 28, 4685–4713, https://doi.org/10.5194/hess-28-4685-2024, https://doi.org/10.5194/hess-28-4685-2024, 2024
Short summary
Short summary
Large-scale hydrologic simulators are a needed tool to explore complex watershed processes and how they may evolve with a changing climate. However, calibrating them can be difficult because they are costly to run and have many unknown parameters. We implement a state-of-the-art approach to model calibration using neural networks with a set of experiments based on streamflow in the upper Colorado River basin.
Nan Wu, Ke Zhang, Amir Naghibi, Hossein Hashemi, Zhongrui Ning, Qinuo Zhang, Xuejun Yi, Haijun Wang, Wei Liu, Wei Gao, and Jerker Jarsjö
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-324, https://doi.org/10.5194/hess-2024-324, 2024
Revised manuscript accepted for HESS
Short summary
Short summary
The hydrology of cold regions in the human population is poorly understood due to complex motion and limited data, hindering streamflow analysis. Using existing models, we compared runoff from an extended model with snowmelt and frozen ground, validating its reliability and integration. This study focuses on the effects of snowmelt and frozen ground on runoff, affecting precipitation type, surface-groundwater partitioning, and evapotranspiration.
Jari-Pekka Nousu, Kersti Leppä, Hannu Marttila, Pertti Ala-aho, Giulia Mazzotti, Terhikki Manninen, Mika Korkiakoski, Mika Aurela, Annalea Lohila, and Samuli Launiainen
Hydrol. Earth Syst. Sci., 28, 4643–4666, https://doi.org/10.5194/hess-28-4643-2024, https://doi.org/10.5194/hess-28-4643-2024, 2024
Short summary
Short summary
We used hydrological models, field measurements, and satellite-based data to study the soil moisture dynamics in a subarctic catchment. The role of groundwater was studied with different ways to model the groundwater dynamics and via comparisons to the observational data. The choice of groundwater model was shown to have a strong impact, and representation of lateral flow was important to capture wet soil conditions. Our results provide insights for ecohydrological studies in boreal regions.
Nienke Tempel, Laurène Bouaziz, Riccardo Taormina, Ellis van Noppen, Jasper Stam, Eric Sprokkereef, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 28, 4577–4597, https://doi.org/10.5194/hess-28-4577-2024, https://doi.org/10.5194/hess-28-4577-2024, 2024
Short summary
Short summary
This study explores the impact of climatic variability on root zone water storage capacities and, thus, on hydrological predictions. Analysing data from 286 areas in Europe and the US, we found that, despite some variations in root zone storage capacity due to changing climatic conditions over multiple decades, these changes are generally minor and have a limited effect on water storage and river flow predictions.
Bu Li, Ting Sun, Fuqiang Tian, Mahmut Tudaji, Li Qin, and Guangheng Ni
Hydrol. Earth Syst. Sci., 28, 4521–4538, https://doi.org/10.5194/hess-28-4521-2024, https://doi.org/10.5194/hess-28-4521-2024, 2024
Short summary
Short summary
This paper developed hybrid semi-distributed hydrological models by employing a process-based model as the backbone and utilizing deep learning to parameterize and replace internal modules. The main contribution is to provide a high-performance tool enriched with explicit hydrological knowledge for hydrological prediction and to improve understanding about the hydrological sensitivities to climate change in large alpine basins.
Francesco Zignol, William Lidberg, Caroline Greiser, Johannes Larson, Raúl Hoffrén, and Anneli M. Ågren
EGUsphere, https://doi.org/10.5194/egusphere-2024-2909, https://doi.org/10.5194/egusphere-2024-2909, 2024
Short summary
Short summary
We investigated the factors influencing soil moisture variations across a boreal forest catchment in northern Sweden, where data is usually scarce. We found that soil moisture is shaped by topographical features, vegetation and soil characteristics, and weather conditions. The insights presented in this study will help improve models that predict soil moisture over space and time, which is crucial for forest management and nature conservation in the face of climate change and biodiversity loss.
Maria Elenius, Charlotta Pers, Sara Schützer, and Berit Arheimer
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-271, https://doi.org/10.5194/hess-2024-271, 2024
Revised manuscript accepted for HESS
Short summary
Short summary
Simulations of peatland rewetting in Sweden under various conditions of climate, local hydrology and rewetting practices showed insubstantial changes in landscape flow extremes due to mixing with runoff from various landcover. The impact on local hydrological extremes are governed by groundwater levels prior to rewetting and reduced tree cover, hence wetland allocation and management practices are crucial if the purpose is to reduce flow extremes in peatland streams.
Dan Elhanati, Nadine Goeppert, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 28, 4239–4249, https://doi.org/10.5194/hess-28-4239-2024, https://doi.org/10.5194/hess-28-4239-2024, 2024
Short summary
Short summary
A continuous time random walk framework was developed to allow modeling of a karst aquifer discharge response to measured rainfall. The application of the numerical model yielded robust fits between modeled and measured discharge values, especially for the distinctive long tails found during recession times. The findings shed light on the interplay of slow and fast flow in the karst system and establish the application of the model for simulating flow and transport in such systems.
Cited articles
Aubert, A. H., Kirchner, J. W., Gascuel-Odoux, C., Faucheux, M., Gruau, G., and Mérot, P.: Fractal water quality fluctuations spanning the periodic table in an intensively farmed watershed, Environ. Sci. Technol., 48, 930–937, https://doi.org/10.1021/es403723r, 2014.
Beran, J.: Long-range dependence, Wiley Interdiscip. Rev. Comput. Stat., 2, 26–35, https://doi.org/10.1002/wics.52, 2010.
Beran, J., Feng, Y., Ghosh, S., and Kulik, R.: Long-Memory Processes: Probabilistic Properties and Statistical Methods, Berlin, Heidelberg, Springer Berlin Heidelberg, 884 pp., 2013.
Boutahar, M., Marimoutou, V., and Nouira, L.: Estimation Methods of the Long Memory Parameter: Monte Carlo Analysis and Application, J. Appl. Stat., 34, 261–301, https://doi.org/10.1080/02664760601004874, 2007.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C.: Time Series Analysis, Fourth Edition. Hoboken, NJ, John Wiley & Sons, Inc., 47–92, 2008.
Clarke, R. T.: Calculating uncertainty in regional estimates of trend in streamflow with both serial and spatial correlations, Water Resour. Res., 49, 7120–7125, https://doi.org/10.1002/wrcr.20465, 2013.
Cleveland, W. S.: LOWESS: A program for smoothing scatterplots by robust locally weighted regression, Am. Stat., 35, 54, https://doi.org/10.2307/2683591, 1981.
Cohn, T. A. and Lins, H. F.: Nature's style: Naturally trendy, Geophys. Res. Lett., 32, L23402, https://doi.org/10.1029/2005GL024476, 2005.
Constantine, W. and Percival, D.: fractal: Fractal Time Series Modeling and Analysis, available at: https://cran.r-project.org/web/packages/fractal (last access: 6 April 2015.), 2014.
Darken, P. F., Zipper, C. E., Holtzman, G. I., and Smith, E. P.: Serial correlation in water quality variables: Estimation and implications for trend analysis, Water Resour. Res., 38, 1117, https://doi.org/10.1029/2001WR001065, 2002.
Delignette-Muller, M. L. and Dutang, C.: fitdistrplus: An R Package for Fitting Distributions, J. Stat. Softw., 64, 1–34, 2015.
Ehsanzadeh, E. and Adamowski, K.: Trends in timing of low stream flows in Canada: impact of autocorrelation and long-term persistence, Hydrol. Process., 24, 970–980, https://doi.org/10.1002/hyp.7533, 2010.
Fatichi, S., Barbosa, S. M., Caporali, E., and Silva, M. E.: Deterministic versus stochastic trends: Detection and challenges, J. Geophys. Res., 114, D18121, https://doi.org/10.1029/2009JD011960, 2009.
Foster, G.: Wavelets for period analysis of unevenly sampled time series, Astron. J., 112, 1709–1729, 1996.
Franzke, C.: Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature, J. Clim., 25, 4172–4183, https://doi.org/10.1175/JCLI-D-11-00293.1, 2012a.
Franzke, C.: On the statistical significance of surface air temperature trends in the Eurasian Arctic region, Geophys. Res. Lett., 39, L23705, https://doi.org/10.1029/2012GL054244, 2012b.
Godsey, S. E., Aas, W., Clair, T. A., de Wit, H. A., Fernandez, I. J., Kahl, J. S., Malcolm, I. A., Neal, C., Neal, M., Nelson, S. J., Norton, S. A., Palucis, M. C., Skjelkvåle, B. L., Soulsby, C., Tetzlaff, D., and Kirchner, J. W.: Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions, Hydrol. Process., 24, 1660–1671, https://doi.org/10.1002/hyp.7677, 2010.
Graham, J.: Missing Data Analysis: Making It Work in the Real World, Annu. Rev. Psychol., 60, 549–576, https://doi.org/10.1146/annurev.psych.58.110405.085530, 2009.
Helsel, D. R. and Hirsch, R. M.: Statistical Methods in Water Resources, US Geological Survey Techniques of Water-Resources Investigations Book 4, Chapter A3, US Geological Survey, Reston, VA, p. 522, http://pubs.usgs.gov/twri/twri4a3/ (last access: 11 June 2016.), 2002.
Hirsch, R. M., Alexander, R. B., and Smith, R. A.: Selection of methods for the detection and estimation of trends in water quality, Water Resour. Res., 27, 803–813, https://doi.org/10.1029/91WR00259, 1991.
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. Assoc., 46, 857–880, https://doi.org/10.1111/j.1752-1688.2010.00482.x, 2010.
Hurst, H. E.: Long-term storage capacity of reservoirs, Trans. Amer. Soc. Civil Eng., 116, 770–808, 1951.
Kasmarek, M. C. and Ramage, J. K.: Water-Level Measurement Data Collected during 2015-2016 and Approximate Long-term Water-Level Altitude Changes of Wells Screened in the Chicot, Evangeline, and Jasper Aquifers, Houston-Galveston Region, Texas: US Geological Survey data release, https://doi.org/10.5066/F77H1GP3, 2016.
Khaliq, M. N., Ouarda, T. B. M. J., and Gachon, P.: Identification of temporal trends in annual and seasonal low flows occurring in Canadian rivers: The effect of short- and long-term persistence, J. Hydrol., 369, 183–197, https://doi.org/10.1016/j.jhydrol.2009.02.045, 2009.
Khaliq, M. N., Ouarda, T. B. M. J., Gachon, P., and Sushama, L.: Temporal evolution of low-flow regimes in Canadian rivers, Water Resour. Res., 44, W08436, https://doi.org/10.1029/2007WR006132, 2008.
Kirchner, J.: Aliasing in 1?f\{̂α} noise spectra: Origins, consequences, and remedies, Phys. Rev. E, 71, 066110, https://doi.org/10.1103/PhysRevE.71.066110, 2005.
Kirchner, J. W. and Neal, C.: Universal fractal scaling in stream chemistry and its implications for solute transport and water quality trend detection, P. Natl. Acad. Sci. USA, 110, 12213–12218, https://doi.org/10.1073/pnas.1304328110, 2013.
Kirchner, J. W. and Weil, A.: No fractals in fossil extinction statistics, Nature, 395, 337–338, https://doi.org/10.1038/26384, 1998.
Kirchner, J. W., Feng, X., and Neal, C.: Fractal stream chemistry and its implications for contaminant transport in catchments, Nature, 403, 524–527, https://doi.org/10.1038/35000537, 2000.
Kirchner, J. W., Feng, X., and Neal, C.: Catchment-scale advection and dispersion as a mechanism for fractal scaling in stream tracer concentrations, J. Hydrol., 254, 82–101, https://doi.org/10.1016/s0022-1694(01)00487-5, 2001.
Langland, M. J., Blomquist, J. D., Moyer, D. L., and Hyer, K. E.: Nutrient and suspended-sediment trends, loads, and yields and development of an indicator of streamwater quality at nontidal sites in the Chesapeake Bay watershed, 1985–2010, US Geological Survey Scientific Investigations Report 2012-5093, Reston, VA, p. 26., available at: http://pubs.usgs.gov/sir/2012/5093/pdf/sir2012-5093.pdf (last access: 6 April 2015), 2012.
Lennartz, S. and Bunde, A.: Trend evaluation in records with long-term memory: Application to global warming, Geophys. Res. Lett., 36, L16706, https://doi.org/10.1029/2009GL039516, 2009.
Lomb, N. R.: Least-squares frequency analysis of unequally spaced data, Astrophys. Space Sci., 39, 447–462, https://doi.org/10.1007/BF00648343, 1976.
Montanari, A., Rosso, R., and Taqqu, M. S.: Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation, Water Resour. Res., 33, 1035–1044, https://doi.org/10.1029/97WR00043, 1997.
Montanari, A., Taqqu, M. S., and Teverovsky, V.: Estimating long-range dependence in the presence of periodicity: An empirical study, Math. Comput. Model., 29, 217–228, https://doi.org/10.1016/S0895-7177(99)00104-1, 1999.
Montanari, A., Rosso, R., and Taqqu, M. S.: A seasonal fractional ARIMA Model applied to the Nile River monthly flows at Aswan, Water Resour. Res., 36, 1249–1259, https://doi.org/10.1029/2000WR900012, 2000.
National Center for Water Quality Research: Tributary Data Download, https://ncwqr.org/monitoring/data/ (last access: 23 July 2015), 2015.
Noguchi, K., Gel, Y. R., and Duguay, C. R.: Bootstrap-based tests for trends in hydrological time series, with application to ice phenology data, J. Hydro., 410, 150–161, https://doi.org/10.1016/j.jhydrol.2011.09.008, 2011.
R Development Core Team: R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, http://www.r-project.org (last access: 6 April 2015), , 2014.
Rea, W., Oxley, L., Reale, M., and Brown, J.: Estimators for Long Range Dependence: An Empirical Study, Electron. J. Stat., http://arxiv.org/abs/0901.0762 (last access: 6 April 2015), 2009.
Sang, Y.-F., Wang, Z., and Liu, C.: Comparison of the MK test and EMD method for trend identification in hydrological time series, J. Hydrol., 510, 293–298, https://doi.org/10.1016/j.jhydrol.2013.12.039, 2014.
Scargle, J. D.: Studies in Astronomical Time-Series Analysis. II. Statistical Aspects of Spectral-Analysis of Unevenly Spaced Data, Astrophys. J., 263, 835–853, https://doi.org/10.1086/160554, 1982.
Stroe-Kunold, E., Stadnytska, T., Werner, J., and Braun, S.: Estimating long-range dependence in time series: an evaluation of estimators implemented in R, Behav. Res. Meth., 41, 909–923, https://doi.org/10.3758/BRM.41.3.909, 2009.
Taqqu, M. S., Teverovsky, V., and Willinger, W.: Estimators for long-range dependence: an empirical study, Fractals, 3, 785–798, https://doi.org/10.1142/S0218348X95000692, 1995.
Wang, Z.: cts: An R Package for Continuous Time Autoregressive Models via Kalman Filter, J. Stat. Softw., 53, 1–19, 2013.
Witt, A. and Malamud, B. D.: Quantification of Long-Range Persistence in Geophysical Time Series: Conventional and Benchmark-Based Improvement Techniques, Surv. Geophys., 34, 541–651, https://doi.org/10.1007/s10712-012-9217-8, 2013.
Yue, S., Pilon, P., Phinney, B., and Cavadias, G.: The influence of autocorrelation on the ability to detect trend in hydrological series, Hydrol. Process., 16, 1807–1829, https://doi.org/10.1002/hyp.1095, 2002.
Zeileis, A. and Grothendieck, G.: zoo: S3 Infrastructure for Regular and Irregular Time Series, J. Stat. Softw., 14, 1–27, 2005.
Zetterqvist, L.: Statistical Estimation and Interpretation of Trends in Water Quality Time Series, Water Resour. Res., 27, 1637–1648, https://doi.org/10.1029/91wr00478, 1991.
Zhang, Q. and Ball, W. P.: Improving Riverine Constituent Concentration and Flux Estimation by Accounting for Antecedent Discharge Conditions, J. Hydrol., 547, 387–402, https://doi.org/10.1016/j.jhydrol.2016.12.052, 2017.
Zhang, Q., Brady, D. C., Boynton, W. R., and Ball, W. P.: Long-Term Trends of Nutrients and Sediment from the Nontidal Chesapeake Watershed: An Assessment of Progress by River and Season, J. Am. Water Resour. Assoc., 51, 1534–1555, https://doi.org/10.1111/1752-1688.12327, 2015.
Short summary
River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. This paper provides a comprehensive overview of the various approaches for quantifying fractal scaling in irregularly sampled data and provides new understanding and quantification of the methods’ performances. More generally, the findings and approaches may be broadly applicable to irregularly sampled data in other scientific disciplines.
River water-quality time series often exhibit fractal scaling, which here refers to...
