Articles | Volume 29, issue 15
https://doi.org/10.5194/hess-29-3745-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-29-3745-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
14 Aug 2025
Research article |
| 14 Aug 2025
| 14 Aug 2025
Two-dimensional differential form of distributed Xinanjiang model
Jianfei Zhao
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Zhongmin Liang
CORRESPONDING AUTHOR
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Vijay P. Singh
Department of Biological & Agricultural Engineering, Texas A & M University, College Station, TX 77843-2117, USA
Zachry Department of Civil & Environmental Engineering, Texas A & M University, College Station, TX 77843-3127, USA
National Water and Energy Center, UAE University, Al Ain, P.O. Box 15551, UAE
Taiyi Wen
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Yiming Hu
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Binquan Li
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Jun Wang
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Related authors
No articles found.
Taesam Lee, Jaewoo Park, Sunghyun Hwang, and Vijay Singh
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2023-57, https://doi.org/10.5194/gmd-2023-57, 2023
Revised manuscript not accepted
Short summary
Short summary
The current study presents a novel method to demarcate the cross-section of a river channel using a very flexible regression model, called K-nearest neighbor local linear regression (KLR). The proposed method draws the cross-section automatically based on the point cloud data taken from unmanned aerial vehicles (UAVs). The proposed model can provide a further development of 4th industy innovation by employding the UAV-based photogrammetry.
Tuantuan Zhang, Zhongmin Liang, Wentao Li, Jun Wang, Yiming Hu, and Binquan Li
Hydrol. Earth Syst. Sci., 27, 1945–1960, https://doi.org/10.5194/hess-27-1945-2023, https://doi.org/10.5194/hess-27-1945-2023, 2023
Short summary
Short summary
We use circulation classifications and spatiotemporal deep neural networks to correct raw daily forecast precipitation by combining large-scale circulation patterns with local spatiotemporal information. We find that the method not only captures the westward and northward movement of the western Pacific subtropical high but also shows substantially higher bias-correction capabilities than existing standard methods in terms of spatial scale, timescale, and intensity.
Dayang Li, Zhongmin Liang, Yan Zhou, Binquan Li, and Yupeng Fu
Nat. Hazards Earth Syst. Sci., 19, 2027–2037, https://doi.org/10.5194/nhess-19-2027-2019, https://doi.org/10.5194/nhess-19-2027-2019, 2019
Short summary
Short summary
Flood forecasting in semiarid regions is always poor, and a single-criterion assessment provides limited information for decision making. Here, we propose a multicriteria assessment framework (FCRA) to assess the most striking feature of an event-based flood – the peak flow. One hundred flood events are modeled in the middle Yellow River with four hydrological models. Our results show that the FCRA may help decision makers improve their diagnostic abilities in the early flood warning process.
Binquan Li, Changchang Zhu, Zhongmin Liang, Guoqing Wang, and Yu Zhang
Proc. IAHS, 379, 403–407, https://doi.org/10.5194/piahs-379-403-2018, https://doi.org/10.5194/piahs-379-403-2018, 2018
Short summary
Short summary
Differences between meteorological and hydrological droughts could reflect the regional water consumption by both natural elements and human water-use. The connections between these two drought types were analyzed using the Standardized Precipitation Evapotranspiration Index (SPEI) and Standardized Streamflow Index (SSI), respectively, in a typical semi-arid basin of the middle Yellow River.
Y. M. Hu, Z. M. Liang, X. L. Jiang, and H. Bu
Proc. IAHS, 371, 163–166, https://doi.org/10.5194/piahs-371-163-2015, https://doi.org/10.5194/piahs-371-163-2015, 2015
Short summary
Short summary
A approach for non-stationary hydrological frequency analysis is proposed. In this method, an assumption is done that the variation hydrological series in a big time window owns an expected vibration center (EVC), which is a linear combination of the two mean values of the two subsample series. Then using the EVC to reconstruct non-stationary series to meet the requirement of stationary.
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Mathematical applications
Understanding meteorological and physio-geographical controls of variability of flood event classes in headstream catchments of China
Technical note: Streamflow seasonality using directional statistics
Technical note: Quadratic Solution of the Approximate Reservoir Equation (QuaSoARe)
Climatic, topographic, and groundwater controls on runoff response to precipitation: evidence from a large-sample data set
Processes and controls of regional floods over eastern China
Imprints of Increases in Evapotranspiration on Decreases in Streamflow during dry Periods, a large-sample Analysis in Germany
A national-scale hybrid model for enhanced streamflow estimation – consolidating a physically based hydrological model with long short-term memory (LSTM) networks
Inferring heavy tails of flood distributions through hydrograph recession analysis
Landscape structures regulate the contrasting response of recession along rainfall amounts
Hydrological objective functions and ensemble averaging with the Wasserstein distance
Spatial variability in Alpine reservoir regulation: deriving reservoir operations from streamflow using generalized additive models
Regional significance of historical trends and step changes in Australian streamflow
River flooding mechanisms and their changes in Europe revealed by explainable machine learning
Changes in nonlinearity and stability of streamflow recession characteristics under climate warming in a large glaciated basin of the Tibetan Plateau
A data-driven method for estimating the composition of end-members from stream water chemistry time series
Evaporation loss estimation of the river-lake continuum of arid inland river: Evidence from stable isotopes
Technical note: PMR – a proxy metric to assess hydrological model robustness in a changing climate
Causal effects of dams and land cover changes on flood changes in mainland China
Can the two-parameter recursive digital filter baseflow separation method really be calibrated by the conductivity mass balance method?
Simultaneously determining global sensitivities of model parameters and model structure
Technical note: Calculation scripts for ensemble hydrograph separation
Specific climate classification for Mediterranean hydrology and future evolution under Med-CORDEX regional climate model scenarios
A line-integral-based method to partition climate and catchment effects on runoff
Technical note: A two-sided affine power scaling relationship to represent the concentration–discharge relationship
On the flood peak distributions over China
New water fractions and transit time distributions at Plynlimon, Wales, estimated from stable water isotopes in precipitation and streamflow
Does the weighting of climate simulations result in a better quantification of hydrological impacts?
A 50-year analysis of hydrological trends and processes in a Mediterranean catchment
Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu
Climate or land cover variations: what is driving observed changes in river peak flows? A data-based attribution study
Quantifying new water fractions and transit time distributions using ensemble hydrograph separation: theory and benchmark tests
Land cover effects on hydrologic services under a precipitation gradient
Technical note: Long-term persistence loss of urban streams as a metric for catchment classification
Responses of runoff to historical and future climate variability over China
Characterization and evaluation of controls on post-fire streamflow response across western US watersheds
Analysis and modelling of a 9.3 kyr palaeoflood record: correlations, clustering, and cycles
Climate change impacts on Yangtze River discharge at the Three Gorges Dam
Can assimilation of crowdsourced data in hydrological modelling improve flood prediction?
Delineation of homogenous regions using hydrological variables predicted by projection pursuit regression
Multivariate hydrological data assimilation of soil moisture and groundwater head
On the propagation of diel signals in river networks using analytic solutions of flow equations
Dominant climatic factors driving annual runoff changes at the catchment scale across China
Data assimilation in integrated hydrological modelling in the presence of observation bias
Recent changes in climate, hydrology and sediment load in the Wadi Abd, Algeria (1970–2010)
Technical Note: Testing an improved index for analysing storm discharge–concentration hysteresis
Estimating spatially distributed soil water content at small watershed scales based on decomposition of temporal anomaly and time stability analysis
Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization
Time series analysis of the long-term hydrologic impacts of afforestation in the Águeda watershed of north-central Portugal
Data assimilation in integrated hydrological modeling using ensemble Kalman filtering: evaluating the effect of ensemble size and localization on filter performance
Attribution of high resolution streamflow trends in Western Austria – an approach based on climate and discharge station data
Yongyong Zhang, Yongqiang Zhang, Xiaoyan Zhai, Jun Xia, Qiuhong Tang, Wei Wang, Jian Wu, Xiaoyu Niu, and Bing Han
Hydrol. Earth Syst. Sci., 29, 3257–3275, https://doi.org/10.5194/hess-29-3257-2025, https://doi.org/10.5194/hess-29-3257-2025, 2025
Short summary
Short summary
It is challenging to investigate flood variabilities and their formation mechanisms from massive event samples. This study explores spatiotemporal variabilities of 1446 flood events using hierarchical and partitional clustering methods. Control mechanisms of meteorological and physio-geographical factors are explored for individual flood event classes using constrained rank analysis. This gives insights into comprehensive changes in flood events and aids in flood prediction and control.
Wouter R. Berghuijs, Kate Hale, and Harsh Beria
Hydrol. Earth Syst. Sci., 29, 2851–2862, https://doi.org/10.5194/hess-29-2851-2025, https://doi.org/10.5194/hess-29-2851-2025, 2025
Short summary
Short summary
We present directional statistics to characterize seasonality, capturing the timing of streamflow (center of mass timing) and the strength of its seasonal cycle (concentration). Directional statistics are more robust than several widely used metrics to quantify streamflow seasonality. The introduced metrics can improve our understanding of streamflow seasonality and associated changes and can also be used to study the seasonality of other environmental fluxes within and beyond hydrology.
Julien Lerat
Hydrol. Earth Syst. Sci., 29, 2003–2021, https://doi.org/10.5194/hess-29-2003-2025, https://doi.org/10.5194/hess-29-2003-2025, 2025
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. The method, called the Quadratic Solution of the Approximate Reservoir Equation (QuaSoARe), is both fast and applicable to any equation of this kind regardless of its complexity. The method reduces runtime by a factor of 10 to 50 depending on the model.
Zahra Eslami, Hansjörg Seybold, and James W. Kirchner
EGUsphere, https://doi.org/10.5194/egusphere-2025-35, https://doi.org/10.5194/egusphere-2025-35, 2025
Short summary
Short summary
We used a new method to measure how streamflow responds to precipitation across a network of watersheds in Iran. Our analysis shows that streamflow is more sensitive to precipitation when groundwater levels are shallower, climates are more humid, topography is steeper, and drainage basins are smaller. These results are a step toward more sustainable water resource management and more effective flood risk mitigation.
Yixin Yang, Long Yang, Jinghan Zhang, and Qiang Wang
Hydrol. Earth Syst. Sci., 28, 4883–4902, https://doi.org/10.5194/hess-28-4883-2024, https://doi.org/10.5194/hess-28-4883-2024, 2024
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.
Giulia Bruno, Laurent Strohmenger, and Doris Duethmann
EGUsphere, https://doi.org/10.5194/egusphere-2024-2678, https://doi.org/10.5194/egusphere-2024-2678, 2024
Short summary
Short summary
Decreases in streamflow during dry periods threaten ecosystems and society, and increases in evapotranspiration may contribute to them. From data for small catchments in Germany, summer low flows decreased over 1970–2019 and increases in evapotranspiration relevantly contributed. Stronger-than-expected decreases in streamflow during the 1989–1993 drought occurred in catchments with increases in evapotranspiration. Increases in evapotranspiration need full consideration for streamflow prediction.
Jun Liu, Julian Koch, Simon Stisen, Lars Troldborg, and Raphael J. M. Schneider
Hydrol. Earth Syst. Sci., 28, 2871–2893, https://doi.org/10.5194/hess-28-2871-2024, https://doi.org/10.5194/hess-28-2871-2024, 2024
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
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.
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
Short summary
Short summary
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
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
The long-term study of precipitation, flows, flood or drought mechanisms, in the Réal Collobrier research Watershed, located in South-East France, in the Mediterranean forest, improves knowledge of the water cycle and is unique tool for understanding of how catchments function. This study shows a small decrease in rainfall and a marked tendency towards a decrease in the water resources of the catchment in response to climate trends, with a consistent increase in drought severity and duration.
Vazken Andréassian and Tewfik Sari
Hydrol. Earth Syst. Sci., 23, 2339–2350, https://doi.org/10.5194/hess-23-2339-2019, https://doi.org/10.5194/hess-23-2339-2019, 2019
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
Parameter optimization is necessary to improve the flood forecasting capability of physically based distributed hydrological model. A method for parameter optimization with particle swam optimization (PSO) algorithm has been proposed for physically based distributed hydrological model in catchment flood forecasting and validated in southern China. It has found that the appropriate particle number and maximum evolution number of PSO algorithm are 20 and 30 respectively.
D. Hawtree, J. P. Nunes, J. J. Keizer, R. Jacinto, J. Santos, M. E. Rial-Rivas, A.-K. Boulet, F. Tavares-Wahren, and K.-H. Feger
Hydrol. Earth Syst. Sci., 19, 3033–3045, https://doi.org/10.5194/hess-19-3033-2015, https://doi.org/10.5194/hess-19-3033-2015, 2015
J. Rasmussen, H. Madsen, K. H. Jensen, and J. C. Refsgaard
Hydrol. Earth Syst. Sci., 19, 2999–3013, https://doi.org/10.5194/hess-19-2999-2015, https://doi.org/10.5194/hess-19-2999-2015, 2015
C. Kormann, T. Francke, M. Renner, and A. Bronstert
Hydrol. Earth Syst. Sci., 19, 1225–1245, https://doi.org/10.5194/hess-19-1225-2015, https://doi.org/10.5194/hess-19-1225-2015, 2015
Cited articles
Anhui Provincial Department of Water Resources (APDWR): Anhui Water Information, http://yc.wswj.net/ahsxx/LOL/, last access: 9 August 2025.
Bates, P. D., Horritt, M. S., and Fewtrell, T. J.: A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling, J. Hydrol., 387, 33–45, https://doi.org/10.1016/j.jhydrol.2010.03.027, 2010.
Beven, K.: Towards an alternative blueprint for a physically based digitally simulated hydrologic response modelling system, Hydrol. Process., 16, 189–206, https://doi.org/10.1002/hyp.343, 2002.
Beven, K. J., Kirkby, M. J., Freer, J. E., and Lamb, R.: A history of TOPMODEL, Hydrol. Earth Syst. Sci., 25, 527–549, https://doi.org/10.5194/hess-25-527-2021, 2021.
Bisht, G. and Riley, W. J.: Development and verification of a numerical library for solving global terrestrial multiphysics problems, J. Adv. Model. Earth Sy., 11, 1516–1542, https://doi.org/10.1029/2018MS001560, 2019.
Chen, L., Deng, J., Yang, W., and Chen, H.: Hydrological modelling of large-scale karst-dominated basin using a grid-based distributed karst hydrological model, J. Hydrol., 628, 130459, https://doi.org/10.1016/j.jhydrol.2023.130459, 2024.
Chen, X., Zhang, K., Luo, Y., Zhang, Q., Zhou, J., Fan, Y., Huang, P., Yao, C., Chao, L., and Bao, H.: A distributed hydrological model for semi-humid watersheds with a thick unsaturated zone under strong anthropogenic impacts: a case study in Haihe river basin, J. Hydrol., 623, 129765, https://doi.org/10.1016/j.jhydrol.2023.129765, 2023.
Clark, M. P. and Kavetski, D.: Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes, Water Resour. Res., 46, W10510, https://doi.org/10.1029/2009WR008894, 2010.
Clark, M. P., Fan, Y., Lawrence, D. M., Adam, J. C., Bolster, D., Gochis, D. J., Hooper, R. P., Kumar, M., Leung, L. R., Mackay, D. S., Maxwell, R. M., Shen, C., Swenson, S. C., and Zeng, X.: Improving the representation of hydrologic processes in earth system models, Water Resour. Res., 51, 5929–5956, https://doi.org/10.1002/2015WR017096, 2015.
Clark, M. P., Schaefli, B., Schymanski, S. J., Samaniego, L., Luce, C. H., Jackson, B. M., Freer, J. E., Arnold, J. R., Moore, R. D., Istanbulluoglu, E., and Ceola, S.: Improving the theoretical underpinnings of process-based hydrologic models, Water Resour. Res., 52, 2350–2365, https://doi.org/10.1002/2015WR017910, 2016.
Computer Network Information Center of the Chinese Academy of Sciences (CNIC-CAS): SRTMDEMUTM 90 m resolution digital elevation product, Geospatial Data Cloud [data set], https://www.gscloud.cn/sources/details/306?pid=302, last access: 9 August 2025.
Di Giammarco, P., Todini, E., and Lamberti, P.: A conservative finite elements approach to overland flow: the control volume finite element formulation, J. Hydrol., 175, 267–291, https://doi.org/10.1016/S0022-1694(96)80014-X, 1996.
Dongarra, J. and Keyes, D.: The co-evolution of computational physics and high-performance computing, Nat. Rev. Phys., 6, 621–627, https://doi.org/10.1038/s42254-024-00750-z, 2024.
Fang, Y.-H., Zhang, X., Corbari, C., Mancini, M., Niu, G.-Y., and Zeng, W.: Improving the Xin'anjiang hydrological model based on mass–energy balance, Hydrol. Earth Syst. Sci., 21, 3359–3375, https://doi.org/10.5194/hess-21-3359-2017, 2017.
Fatichi, S., Vivoni, E. R., Ogden, F. L., Ivanov, V. Y., Mirus, B., Gochis, D., Downer, C. W., Camporese, M., Davison, J. H., Ebel, B., Jones, N., Kim, J., Mascaro, G., Niswonger, R., Restrepo, P., Rigon, R., Shen, C., Sulis, M., and Tarboton, D.: An overview of current applications, challenges, and future trends in distributed process-based models in hydrology, J. Hydrol., 537, 45–60, https://doi.org/10.1016/j.jhydrol.2016.03.026, 2016.
Freeze, R. A. and Harlan, R. L.: Blueprint for a physically-based, digitally-simulated hydrologic response model, J. Hydrol., 9, 237–258, https://doi.org/10.1016/0022-1694(69)90020-1, 1969.
Gong, W., Duan, Q., Li, J., Wang, C., Di, Z., Ye, A., Miao, C., and Dai, Y.: An intercomparison of sampling methods for uncertainty quantification of environmental dynamic models, J. Environ. Inform., 28, 11–24, https://doi.org/10.3808/jei.201500310, 2015.
Gottardi, G. and Venutelli, M.: An accurate time integration method for simplified overland flow models, Adv. Water Resour., 31, 173–180, https://doi.org/10.1016/j.advwatres.2007.08.004, 2008.
Gupta, H. V., Clark, M. P., Vrugt, J. A., Abramowitz, G., and Ye, M.: Towards a comprehensive assessment of model structural adequacy, Water Resour. Res., 48, W08301, https://doi.org/10.1029/2011WR011044, 2012.
He, C., Valayamkunnath, P., Barlage, M., Chen, F., Gochis, D., Cabell, R., Schneider, T., Rasmussen, R., Niu, G.-Y., Yang, Z.-L., Niyogi, D., and Ek, M.: Modernizing the open-source community Noah with multi-parameterization options (Noah-MP) land surface model (version 5.0) with enhanced modularity, interoperability, and applicability, Geosci. Model Dev., 16, 5131–5151, https://doi.org/10.5194/gmd-16-5131-2023, 2023.
Hodson, T. O.: Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not, Geosci. Model Dev., 15, 5481–5487, https://doi.org/10.5194/gmd-15-5481-2022, 2022.
Höge, M., Scheidegger, A., Baity-Jesi, M., Albert, C., and Fenicia, F.: Improving hydrologic models for predictions and process understanding using neural ODEs, Hydrol. Earth Syst. Sci., 26, 5085–5102, https://doi.org/10.5194/hess-26-5085-2022, 2022.
Hong, S. and Mostaghimi, S.: Comparison of 1-D and 2-D modeling of overland runoff and sediment transport, J. Am. Water Resour. As., 33, 1103–1116, https://doi.org/10.1111/j.1752-1688.1997.tb04128.x, 1997.
Jackson, E. K., Roberts, W., Nelsen, B., Williams, G. P., Nelson, E. J., and Ames, D. P.: Introductory overview: error metrics for hydrologic modelling – a review of common practices and an open source library to facilitate use and adoption, Environ. Modell. Softw., 119, 32–48, https://doi.org/10.1016/j.envsoft.2019.05.001, 2019.
Jain, M. K. and Singh, V. P.: DEM-based modelling of surface runoff using diffusion wave equation, J. Hydrol., 302, 107–126, https://doi.org/10.1016/j.jhydrol.2004.06.042, 2005.
Kampf, S. K. and Burges, S. J.: A framework for classifying and comparing distributed hillslope and catchment hydrologic models, Water Resour. Res., 43, W05423, https://doi.org/10.1029/2006WR005370, 2007.
Kavetski, D. and Clark, M. P.: Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction, Water Resour. Res., 46, W10511, https://doi.org/10.1029/2009WR008896, 2010.
Kazezyılmaz-Alhan, C. M. and Medina, M. A.: Kinematic and diffusion waves: analytical and numerical solutions to overland and channel flow, J. Hydraul. Eng., 133, 217–228, https://doi.org/10.1061/(ASCE)0733-9429(2007)133:2(217), 2007.
Knoben, W. J. M., Freer, J. E., Peel, M. C., Fowler, K. J. A., and Woods, R. A.: A brief analysis of conceptual model structure uncertainty using 36 models and 559 catchments, Water Resour. Res., 56, e2019WR025975, https://doi.org/10.1029/2019WR025975, 2020.
Kollet, S., Sulis, M., Maxwell, R. M., Paniconi, C., Putti, M., Bertoldi, G., Coon, E. T., Cordano, E., Endrizzi, S., Kikinzon, E., Mouche, E., Mügler, C., Park, Y., Refsgaard, J. C., Stisen, S., and Sudicky, E.: The integrated hydrologic model intercomparison project, IH-MIP2: a second set of benchmark results to diagnose integrated hydrology and feedbacks, Water Resour. Res., 53, 867–890, https://doi.org/10.1002/2016WR019191, 2017.
La Follette, P. T., Teuling, A. J., Addor, N., Clark, M., Jansen, K., and Melsen, L. A.: Numerical daemons of hydrological models are summoned by extreme precipitation, Hydrol. Earth Syst. Sci., 25, 5425–5446, https://doi.org/10.5194/hess-25-5425-2021, 2021.
Lam, S. K., Pitrou, A., and Seibert, S.: Numba: a LLVM-based Python JIT compiler, in: Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC, Austin, Texas, 15 November 2015, 7, https://doi.org/10.1145/2833157.2833162, 2015.
Li, B., Sun, T., Tian, F., Tudaji, M., Qin, L., and Ni, G.: Hybrid hydrological modeling for large alpine basins: a semi-distributed approach, Hydrol. Earth Syst. Sci., 28, 4521–4538, https://doi.org/10.5194/hess-28-4521-2024, 2024.
Liu, J., Chen, X., Zhang, J., and Flury, M.: Coupling the Xinanjiang model to a kinematic flow model based on digital drainage networks for flood forecasting, Hydrol. Process., 23, 1337–1348, https://doi.org/10.1002/hyp.7255, 2009.
Liu, Q. Q., Chen, L., Li, J. C., and Singh, V. P.: Two-dimensional kinematic wave model of overland-flow, J. Hydrol., 291, 28–41, https://doi.org/10.1016/j.jhydrol.2003.12.023, 2004.
Loritz, R., Hrachowitz, M., Neuper, M., and Zehe, E.: The role and value of distributed precipitation data in hydrological models, Hydrol. Earth Syst. Sci., 25, 147–167, https://doi.org/10.5194/hess-25-147-2021, 2021.
Lu, M., Kioke, T., and Hayakawa, N.: Distributed XinAnJiang model using radar measured rainfall data, in: Proceedings of International Conference on Water Resources & Environmental Research: Towards the 21st Century, Kyoto, Japan, 29–31 October 1996, 29–36, https://cir.nii.ac.jp/crid/1571417125513518464 (last access: 11 August 2025), 1996.
MacCormack, R. W.: A numerical method for solving the equations of compressible viscous flow, AIAA J., 20, 1275–1281, https://doi.org/10.2514/3.51188, 1982.
Maxwell, R. M., Putti, M., Meyerhoff, S., Delfs, J. O., Ferguson, I. M., Ivanov, V., Kim, J., Kolditz, O., Kollet, S. J., Kumar, M., Lopez, S., Niu, J., Paniconi, C., Park, Y. J., Phanikumar, M. S., Shen, C., Sudicky, E. A., and Sulis, M.: Surface-subsurface model intercomparison: a first set of benchmark results to diagnose integrated hydrology and feedbacks, Water Resour. Res., 50, 1531–1549, https://doi.org/10.1002/2013WR013725, 2014.
McGuire, K. J., Klaus, J., and Jackson, C. R.: Interflow, subsurface stormflow and throughflow: a synthesis of field work and modelling, Hydrol. Process., 38, e15263, https://doi.org/10.1002/hyp.15263, 2024.
Murphy, B., Yurchak, R., and Müller, S.: GeoStat-Framework/PyKrige (1.7.2), Zenodo [code], https://doi.org/10.5281/zenodo.11360184, 2024.
Nan, Y., Chen, C., Zhao, Y., Tian, F., and Mcdonnell, J.: A historical overview of experimental hydrology in China, Hydrol. Process., 38, e15233, https://doi.org/10.1002/hyp.15233, 2024.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I – a discussion of principles, J. Hydrol., 10, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6, 1970.
National Geomatics Center of China (NGCC): GlobeLand30–30 m resolution global land cover dataset, National Catalogue Service For Geographic Information [data set], https://www.webmap.cn/commres.do?method=globeIndex (last access: 9 August 2025), 2020.
National Meteorological Information Centre (NMIC): Daily surface climatological data for China (V3.0), China Meteorological Data Service Centre [data set], http://data.cma.cn/data/cdcdetail/dataCode/SURF_CLI_CHN_MUL_DAY_V3.0.html (last access: 13 February 2022), 2012.
Nippgen, F., Mcglynn, B. L., and Emanuel, R. E.: The spatial and temporal evolution of contributing areas, Water Resour. Res., 51, 4550–4573, https://doi.org/10.1002/2014WR016719, 2015.
O'Callaghan, J. F. and Mark, D. M.: The extraction of drainage networks from digital elevation data, Comput Vision Graph., 28, 323–344, https://doi.org/10.1016/S0734-189X(84)80011-0, 1984.
Ouyang, W., Ye, L., Chai, Y., Ma, H., Chu, J., Peng, Y., and Zhang, C.: A differentiable, physics-based hydrological model and its evaluation for data-limited basins, J. Hydrol., 649, 132471, https://doi.org/10.1016/j.jhydrol.2024.132471, 2025.
Overton, D. E. and Brakensiek, D. L.: A kinematic model of surface runoff response, in: Proceedings of the Wellington Symposium, Wellington, New Zealand, 1–8 December 1970, 100–112, https://unesdoc.unesco.org/ark:/48223/pf0000012503 (last access: 11 August 2025), 1970.
Panday, S. and Huyakorn, P. S.: A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow, Adv. Water Resour., 27, 361–382, https://doi.org/10.1016/j.advwatres.2004.02.016, 2004.
Paniconi, C. and Putti, M.: Physically based modeling in catchment hydrology at 50: survey and outlook, Water Resour. Res., 51, 7090–7129, https://doi.org/10.1002/2015WR017780, 2015.
Perrini, P., Cea, L., Chiaravalloti, F., Gabriele, S., Manfreda, S., Fiorentino, M., Gioia, A., and Iacobellis, V.: A runoff-on-grid approach to embed hydrological processes in shallow water models, Water Resour. Res., 60, e2023WR036421, https://doi.org/10.1029/2023WR036421, 2024.
Qu, Y. and Duffy, C. J.: A semidiscrete finite volume formulation for multiprocess watershed simulation, Water Resour. Res., 43, W08419, https://doi.org/10.1029/2006WR005752, 2007.
Reggiani, P., Sivapalan, M., and Majid Hassanizadeh, S.: A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics, Adv. Water Resour., 22, 367–398, https://doi.org/10.1016/S0309-1708(98)00012-8, 1998.
Santos, L., Thirel, G., and Perrin, C.: Continuous state-space representation of a bucket-type rainfall-runoff model: a case study with the GR4 model using state-space GR4 (version 1.0), Geosci. Model Dev., 11, 1591–1605, https://doi.org/10.5194/gmd-11-1591-2018, 2018.
Schoups, G., Vrugt, J. A., Fenicia, F., and van de Giesen, N. C.: Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models, Water Resour. Res., 46, W10530, https://doi.org/10.1029/2009WR008648, 2010.
Seibert, J. and Bergström, S.: A retrospective on hydrological catchment modelling based on half a century with the HBV model, Hydrol. Earth Syst. Sci., 26, 1371–1388, https://doi.org/10.5194/hess-26-1371-2022, 2022.
Shaw, J., Kesserwani, G., Neal, J., Bates, P., and Sharifian, M. K.: LISFLOOD-FP 8.0: the new discontinuous Galerkin shallow-water solver for multi-core CPUs and GPUs, Geosci. Model Dev., 14, 3577–3602, https://doi.org/10.5194/gmd-14-3577-2021, 2021.
Shen, C. and Phanikumar, M. S.: A process-based, distributed hydrologic model based on a large-scale method for surface–subsurface coupling, Adv. Water Resour., 33, 1524–1541, https://doi.org/10.1016/j.advwatres.2010.09.002, 2010.
Shu, L., Ullrich, P. A., and Duffy, C. J.: Simulator for Hydrologic Unstructured Domains (SHUD v1.0): numerical modeling of watershed hydrology with the finite volume method, Geosci. Model Dev., 13, 2743–2762, https://doi.org/10.5194/gmd-13-2743-2020, 2020.
Shu, L., Ullrich, P., Meng, X., Duffy, C., Chen, H., and Li, Z.: rSHUD v2.0: advancing the Simulator for Hydrologic Unstructured Domains and unstructured hydrological modeling in the R environment, Geosci. Model Dev., 17, 497–527, https://doi.org/10.5194/gmd-17-497-2024, 2024.
Song, Y., Knoben, W. J. M., Clark, M. P., Feng, D., Lawson, K., Sawadekar, K., and Shen, C.: When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling, Hydrol. Earth Syst. Sci., 28, 3051–3077, https://doi.org/10.5194/hess-28-3051-2024, 2024.
Stacke, T. and Hagemann, S.: HydroPy (v1.0): a new global hydrology model written in Python, Geosci. Model Dev., 14, 7795–7816, https://doi.org/10.5194/gmd-14-7795-2021, 2021.
Su, B., Kazama, S., Lu, M., and Sawamoto, M.: Development of a distributed hydrological model and its application to soil erosion simulation in a forested catchment during storm period, Hydrol. Process., 17, 2811–2823, https://doi.org/10.1002/hyp.1435, 2003.
Taheri, M., Ranjram, M., and Craig, J. R.: An upscaled model of fill-and-spill hydrological response, Water Resour. Res., 59, e2022WR033494, https://doi.org/10.1029/2022WR033494, 2023.
Todini, E.: A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach, Hydrol. Earth Syst. Sci., 11, 1645–1659, https://doi.org/10.5194/hess-11-1645-2007, 2007.
Tong, B.: Fine-scale rainfall-runoff processes simulation using grid Xinanjiang (grid-XAJ) modell, PhD thesis, Hohai University, LW223611, Hohai University Library, Nanjing, 153 pp., https://thesis.chaoxing.com/back/thesis/downLoadFile?thesisId=196936&fid=24578&sign=790ad94f-3e9a-4255-a4ef-0a7ec7259dd1&type=1&thesisId=196936 (last access: 11 August 2025), 2022.
Tran, Q. Q., De Niel, J., and Willems, P.: Spatially distributed conceptual hydrological model building: a generic top-down approach starting from lumped models, Water Resour. Res., 54, 8064–8085, https://doi.org/10.1029/2018WR023566, 2018.
Ul Hassan, Z., Jefferson, A. J., Avellaneda, P. M., and Bhaskar, A. S.: Assessment of hydrological parameter uncertainty versus climate projection spread on urban streamflow and floods, J. Hydrol., 638, 131546, https://doi.org/10.1016/j.jhydrol.2024.131546, 2024.
Wang, J., Lu, Z., Han, D. W., Liu, Y., and Rico Ramirez, M. A.: Hydrological model adaptability to rainfall inputs of varied quality, Water Resour. Res., 59, e2022WR032484, https://doi.org/10.1029/2022WR032484, 2023.
Woldegiorgis, B. T., Baulch, H., Wheater, H., Crossman, J., Clark, M., Stadnyk, T., and Bajracharya, A.: Impacts of uncontrolled operator splitting methods on parameter identification, prediction uncertainty, and subsurface flux representation in conceptual hydrological models, Water Resour. Res., 59, e2022WR033250, https://doi.org/10.1029/2022WR033250, 2023.
Wu, N., Zhang, K., Naghibi, A., Hashemi, H., Ning, Z., Zhang, Q., Yi, X., Wang, H., Liu, W., Gao, W., and Jarsjö, J.: Comparative Hydrological Modeling of Snow-Cover and Frozen Ground Impacts Under Topographically Complex Conditions, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2024-324, in review, 2024.
Yao, C., Li, Z., Bao, H., and Yu, Z.: Application of a developed Grid-Xinanjiang model to Chinese watersheds for flood forecasting purpose, J. Hydrol. Eng., 14, 923–934, https://doi.org/10.1061/(ASCE)HE.1943-5584.0000067, 2009.
Yao, C., Li, Z., Yu, Z., and Zhang, K.: A priori parameter estimates for a distributed, grid-based Xinanjiang model using geographically based information, J. Hydrol., 468–469, 47–62, https://doi.org/10.1016/j.jhydrol.2012.08.025, 2012.
Zhang, Q., Zhang, K., Chao, L., Chen, X., and Wu, N.: A unified runoff generation scheme for applicability across different hydrometeorological zones, Environ. Modell. Softw., 180, 106138, https://doi.org/10.1016/j.envsoft.2024.106138, 2024.
Zhao, J.: Code for TDD-XAJ, Zenodo [code], https://doi.org/10.5281/zenodo.14227068, 2024a.
Zhao, J.: Data for TDD-XAJ, Zenodo [data set], https://doi.org/10.5281/zenodo.14226969, 2024b.
Zhao, J., Duan, Y., Hu, Y., Li, B., and Liang, Z.: The numerical error of the Xinanjiang model, J. Hydrol., 619, 129324, https://doi.org/10.1016/j.jhydrol.2023.129324, 2023.
Zhao, R.: The Xinanjiang model applied in China, J. Hydrol., 135, 371–381, https://doi.org/10.1016/0022-1694(92)90096-E, 1992.
Zhao, R. and Zhuang, Y.: Regional patterns of rainfall-runoff relationship, Journal of Hohai University (Natural Sciences), S2, 53–68, 1963.
Zhao, R., Zhuang, Y., Fang, L., Liu, X., and Zhang, Q.: The Xinanjiang model, in: Proceedings of the Oxford Symposium, Oxford, England, 15–18 April 1980, 351–356, https://unesdoc.unesco.org/ark:/48223/pf0000043527 (last access: 11 August 2025), 1980.
Zhu, D., Ren, Q., Xuan, Y., Chen, Y., and Cluckie, I. D.: An effective depression filling algorithm for DEM-based 2-D surface flow modelling, Hydrol. Earth Syst. Sci., 17, 495–505, https://doi.org/10.5194/hess-17-495-2013, 2013.
Short summary
This paper reformulates the model equations of the distributed Xinanjiang hydrological model in fully differential form and incorporates two-dimensional slope runoff routing methods, which are solved using appropriate numerical techniques. The main contribution is to provide an approach for distributed hydrological models that have evolved from lumped counterparts to reduce inherited numerical errors and to improve terrain representation, thereby enhancing their physical realism and simulation accuracy.
This paper reformulates the model equations of the distributed Xinanjiang hydrological model in...
