Articles | Volume 19, issue 4
https://doi.org/10.5194/hess-19-1977-2015
© Author(s) 2015. 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-19-1977-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
24 Apr 2015
Research article |
| 24 Apr 2015
Effects of snow ratio on annual runoff within the Budyko framework
D. Zhang
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 10084, China
Z. Cong
CORRESPONDING AUTHOR
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 10084, China
G. Ni
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 10084, China
D. Yang
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 10084, China
S. Hu
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 10084, China
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Wencong Yang, Hanbo Yang, Changming Li, Taihua Wang, Ziwei Liu, Qingfang Hu, and Dawen Yang
Hydrol. Earth Syst. Sci., 26, 6427–6441, https://doi.org/10.5194/hess-26-6427-2022, https://doi.org/10.5194/hess-26-6427-2022, 2022
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We produced a daily 0.1° dataset of precipitation, soil moisture, and snow water equivalent in 1981–2017 across China via reconstructions. The dataset used global background data and local on-site data as forcing input and satellite-based data as reconstruction benchmarks. This long-term high-resolution national hydrological dataset is valuable for national investigations of hydrological processes.
Changming Li, Hanbo Yang, Wencong Yang, Ziwei Liu, Yao Jia, Sien Li, and Dawen Yang
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2021-456, https://doi.org/10.5194/essd-2021-456, 2022
Revised manuscript not accepted
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A long-term (1980–2020) global ET product is generated based on a collocation-based merging method. The produced Collocation-Analyzed Multi-source Ensembled Land Evapotranspiration Data (CAMELE) performed well over different vegetation coverage against in-situ data. For global comparison, the spatial distribution of multi-year average and annual variation were in consistent with inputs.The CAMELE products is freely available at https://doi.org/10.5281/zenodo.6283239 (Li et al., 2021).
Yuting Yang, Tim R. McVicar, Dawen Yang, Yongqiang Zhang, Shilong Piao, Shushi Peng, and Hylke E. Beck
Hydrol. Earth Syst. Sci., 25, 3411–3427, https://doi.org/10.5194/hess-25-3411-2021, https://doi.org/10.5194/hess-25-3411-2021, 2021
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This study developed an analytical ecohydrological model that considers three aspects of vegetation response to eCO2 (i.e., stomatal response, LAI response, and rooting depth response) to detect the impact of eCO2 on continental runoff over the past 3 decades globally. Our findings suggest a minor role of eCO2 on the global runoff changes, yet highlight the negative runoff–eCO2 response in semiarid and arid regions which may further threaten the limited water resource there.
Wencong Yang, Hanbo Yang, Dawen Yang, and Aizhong Hou
Hydrol. Earth Syst. Sci., 25, 2705–2720, https://doi.org/10.5194/hess-25-2705-2021, https://doi.org/10.5194/hess-25-2705-2021, 2021
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This study quantified the causal effects of land cover changes and dams on the changes in annual maximum discharges (Q) in 757 catchments of China using panel regressions. We found that a 1 % point increase in urban areas causes a 3.9 % increase in Q, and a 1 unit increase in reservoir index causes a 21.4 % decrease in Q for catchments with no dam before. This study takes the first step to explain the human-caused flood changes on a national scale in China.
Yuting Yang, Shulei Zhang, Michael L. Roderick, Tim R. McVicar, Dawen Yang, Wenbin Liu, and Xiaoyan Li
Hydrol. Earth Syst. Sci., 24, 2921–2930, https://doi.org/10.5194/hess-24-2921-2020, https://doi.org/10.5194/hess-24-2921-2020, 2020
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Many previous studies using offline drought indices report that future warming will increase worldwide drought. However, this contradicts observations/projections of vegetation greening and increased runoff. We resolved this paradox by re-calculating the same drought indices using direct climate model outputs and find no increase in future drought as the climate warms. We also find that accounting for the impact of CO2 on plant transpiration avoids the previous overestimation of drought.
Quan Zhang, Huimin Lei, Dawen Yang, Lihua Xiong, Pan Liu, and Beijing Fang
Biogeosciences, 17, 2245–2262, https://doi.org/10.5194/bg-17-2245-2020, https://doi.org/10.5194/bg-17-2245-2020, 2020
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Research into climate change has been popular over the past few decades. Greenhouse gas emissions are found to be responsible for climate change. Among all the ecosystems, cropland is the main food source for mankind, therefore its carbon cycle and contribution to the global carbon balance interest us. Our evaluation of the typical wheat–maize rotation cropland over the North China Plain shows it is a net CO2 emission to the atmosphere and that emissions will continue to rise in the future.
Bing Gao, Dawen Yang, Yue Qin, Yuhan Wang, Hongyi Li, Yanlin Zhang, and Tingjun Zhang
The Cryosphere, 12, 657–673, https://doi.org/10.5194/tc-12-657-2018, https://doi.org/10.5194/tc-12-657-2018, 2018
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This study developed a distributed hydrological model coupled with cryospherical processes and applied it in order to simulate the long-term change of frozen ground and its effect on hydrology in the upper Heihe basin. Results showed that the permafrost area shrank by 8.8%, and the frozen depth of seasonally frozen ground decreased. Runoff in cold seasons and annual liquid soil moisture increased due to frozen soils change. Groundwater recharge was enhanced due to the degradation of permafrost.
Zhentao Cong, Qinshu Li, Kangle Mo, Lexin Zhang, and Hong Shen
Hydrol. Earth Syst. Sci., 21, 2449–2462, https://doi.org/10.5194/hess-21-2449-2017, https://doi.org/10.5194/hess-21-2449-2017, 2017
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It is interesting to understand vegetation distribution and dynamics under water limitation in this transect. We apply Eagleson's ecohydrological optimality method in the NECT based on data from 2000 to 2013 to get M*, then compare with M from NDVI, furthermore to discuss the sensitivity of M* to vegetation properties and climate factors. The result indicates that the average M* fits the actual M well. The sensitivity analyses show how M* changes with vegetation characteristics and climates.
Zhongwang Chen, Huimin Lei, Hanbo Yang, Dawen Yang, and Yongqiang Cao
Hydrol. Earth Syst. Sci., 21, 2233–2248, https://doi.org/10.5194/hess-21-2233-2017, https://doi.org/10.5194/hess-21-2233-2017, 2017
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The significant climate changes remind us to characterize the hydrological response to it. Based on the long-term observed hydrological and meteorological data in 291 catchments across China, we find a pattern of the response stating that
drier regions are more likely to become drier, whereas wetter regions are more likely to become wetter. We also reveal that the precipitation changes play the most significant role in this process.
Xing Zhou, Guang-Heng Ni, Chen Shen, and Ting Sun
Hydrol. Earth Syst. Sci., 21, 999–1015, https://doi.org/10.5194/hess-21-999-2017, https://doi.org/10.5194/hess-21-999-2017, 2017
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We develop a fusion framework to improve precipitation estimation by jointly utilizing the gauge precipitation and vegetation index and then applying them to mountainous areas of the Nu River basin. The results demonstrate the reliability of the framework in reproducing the high-resolution precipitation regime and capturing its high spatial variability in the Nu River basin. The framework can significantly reduce the errors in precipitation estimates as compared with the IDW and TRMM methods.
Tingting Gong, Huimin Lei, Dawen Yang, Yang Jiao, and Hanbo Yang
Hydrol. Earth Syst. Sci., 21, 863–877, https://doi.org/10.5194/hess-21-863-2017, https://doi.org/10.5194/hess-21-863-2017, 2017
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Seasonal and inter-annual features of ET were analyzed over four periods. A normalization method was adopted to exclude the effects of potential evapotranspiration and soil water stress on ET. During the land degradation process, when natural vegetation (including leaves and branches), sand dunes, dry sand layers, and BSCs were all bulldozed, ET was observed to increase at a mild rate. In a vegetation rehabilitation process with sufficient groundwater, ET also increased at a faster rate.
Bing Gao, Dawen Yang, Yue Qin, Yuhan Wang, Hongyi Li, Yanlin Zhang, and Tingjun Zhang
The Cryosphere Discuss., https://doi.org/10.5194/tc-2016-289, https://doi.org/10.5194/tc-2016-289, 2017
Revised manuscript not accepted
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This study developed a distributed hydrological model coupled with cryospherical processes and used it to simulate the long-term change of frozen ground and hydrological impacts in the upper Heihe basin. Results showed that the permafrost area shrank by 9.5 %, and frozen depth of seasonally frozen ground decreased at a rate of 4.1 cm/10 yr. Runoff increased in cold season due to the increase in liquid soil moisture. Groundwater recharge was enhanced due to the degradation of permafrost.
Wen-Yu Yang, Guang-Heng Ni, You-Cun Qi, Yang Hong, and Ting Sun
Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2016-388, https://doi.org/10.5194/amt-2016-388, 2016
Revised manuscript has not been submitted
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Using a dataset consisting of one-year measurements by an X-band radar and distrometer, we found that error corrections greatly improve X-band-radar-based rainfall estimation. Specifically, the greatest improvement is realized by the beam integration. Derivation of localized Z-R relationships for specific rainfall systems is also of great importance. Moreover, wind drift correction improves quantitative estimates and temporal consistency.
Quan Zhang, Hui-Min Lei, Da-Wen Yang, Lihua Xiong, and Beijing Fang
Biogeosciences Discuss., https://doi.org/10.5194/bg-2016-484, https://doi.org/10.5194/bg-2016-484, 2016
Revised manuscript not accepted
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With the increasing concern about global warming, investigating carbon cycle becomes imperative to predict future climate trend. As cropland has great potentials in mitigating carbon emissions, therefore we designed a comprehensive carbon budget assessment in a typical cropland in North China Plain, the results indicate the high groundwater table contributes to carbon sink of this cropland. The conclusion confirms that field management has profound effect on cropland carbon cycle.
Zhongwei Huang, Hanbo Yang, and Dawen Yang
Hydrol. Earth Syst. Sci., 20, 2573–2587, https://doi.org/10.5194/hess-20-2573-2016, https://doi.org/10.5194/hess-20-2573-2016, 2016
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The hydrologic processes have been influenced by different climatic factors. However, the dominant climatic factor driving annual runoff change is still unknown in many catchments in China. By using the climate elasticity method proposed by Yang and Yang (2011), the elasticity of runoff to climatic factors was estimated, and the dominant climatic factors driving annual runoff change were detected at catchment scale over China.
Qinshu Li, Zhentao Cong, Kangle Mo, and Lexin Zhang
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-235, https://doi.org/10.5194/hess-2016-235, 2016
Revised manuscript has not been submitted
T. T. Gong, H. M. Lei, D. W. Yang, Y. Jiao, and H. B. Yang
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-11-13571-2014, https://doi.org/10.5194/hessd-11-13571-2014, 2014
Revised manuscript not accepted
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Modelling approaches
Comment on “Are soils overrated in hydrology?” by Gao et al. (2023)
Multi-decadal fluctuations in root zone storage capacity through vegetation adaptation to hydro-climatic variability have minor effects on the hydrological response in the Neckar River basin, Germany
Projected future changes in the cryosphere and hydrology of a mountainous catchment in the upper Heihe River, China
On the importance of plant phenology in the evaporative process of a semi-arid woodland: could it be why satellite-based evaporation estimates in the miombo differ?
Regionalization of GR4J model parameters for river flow prediction in Paraná, Brazil
Evolution of river regimes in the Mekong River basin over 8 decades and the role of dams in recent hydrological extremes
Skill of seasonal flow forecasts at catchment scale: an assessment across South Korea
To what extent do flood-inducing storm events change future flood hazards?
When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling
Assessing the impact of climate change on high return levels of peak flows in Bavaria applying the CRCM5 large ensemble
Impacts of climate and land surface change on catchment evapotranspiration and runoff from 1951 to 2020 in Saxony, Germany
Quantifying and reducing flood forecast uncertainty by the CHUP-BMA method
Developing a tile drainage module for the Cold Regions Hydrological Model: lessons from a farm in southern Ontario, Canada
To bucket or not to bucket? Analyzing the performance and interpretability of hybrid hydrological models with dynamic parameterization
Widespread flooding dynamics under climate change: characterising floods using grid-based hydrological modelling and regional climate projections
HESS Opinions: The sword of Damocles of the impossible flood
Metamorphic testing of machine learning and conceptual hydrologic models
The influence of human activities on streamflow reductions during the megadrought in central Chile
Elevational control of isotopic composition and application in understanding hydrologic processes in the mid Merced River catchment, Sierra Nevada, California, USA
Enhancing long short-term memory (LSTM)-based streamflow prediction with a spatially distributed approach
Broadleaf afforestation impacts on terrestrial hydrology insignificant compared to climate change in Great Britain
Hybrid Hydrological Modeling for Large Alpine Basins: A Distributed Approach
Impacts of spatiotemporal resolutions of precipitation on flood event simulation based on multimodel structures – a case study over the Xiang River basin in China
A network approach for multiscale catchment classification using traits
Multi-model approach in a variable spatial framework for streamflow simulation
Advancing understanding of lake–watershed hydrology: a fully coupled numerical model illustrated by Qinghai Lake
HESS Opinions: A few camels or a whole caravan?
Technical note: Testing the connection between hillslope-scale runoff fluctuations and streamflow hydrographs at the outlet of large river basins
Empirical stream thermal sensitivity cluster on the landscape according to geology and climate
Karst aquifer discharge response to rainfall interpreted as anomalous transport
Multi-scale soil moisture data and process-based modeling reveal the importance of lateral groundwater flow in a subarctic catchment
Deep learning for monthly rainfall–runoff modelling: a large-sample comparison with conceptual models across Australia
On optimization of calibrations of a distributed hydrological model with spatially distributed information on snow
Toward interpretable LSTM-based modeling of hydrological systems
Vegetation Response to Climatic Variability: Implications for Root Zone Storage and Streamflow Predictions
Flow intermittence prediction using a hybrid hydrological modelling approach: influence of observed intermittence data on the training of a random forest model
What controls the tail behaviour of flood series: rainfall or runoff generation?
Seasonal prediction of end-of-dry-season watershed behavior in a highly interconnected alluvial watershed in northern California
Glaciers determine the sensitivity of hydrological processes to perturbed climate in a large mountainous basin on the Tibetan Plateau
Leveraging gauge networks and strategic discharge measurements to aid the development of continuous streamflow records
On the need for physical constraints in deep learning rainfall–runoff projections under climate change: a sensitivity analysis to warming and shifts in potential evapotranspiration
Evaluation of hydrological models on small mountainous catchments: impact of the meteorological forcings
HESS Opinions: Never train an LSTM on a single basin
Projecting sediment export from two highly glacierized alpine catchments under climate change: exploring non-parametric regression as an analysis tool
Simulation-Based Inference for Parameter Estimation of Complex Watershed Simulators
A framework for parameter estimation, sensitivity analysis, and uncertainty analysis for holistic hydrologic modeling using SWAT+
On understanding mountainous carbonate basins of the Mediterranean using parsimonious modeling solutions
Comparing quantile regression forest and mixture density long short-term memory models for probabilistic post-processing of satellite precipitation-driven streamflow simulations
Recent ground thermo-hydrological changes in a southern Tibetan endorheic catchment and implications for lake level changes
Towards robust seasonal streamflow forecasts in mountainous catchments: impact of calibration metric selection in hydrological modeling
Ying Zhao, Mehdi Rahmati, Harry Vereecken, and Dani Or
Hydrol. Earth Syst. Sci., 28, 4059–4063, https://doi.org/10.5194/hess-28-4059-2024, https://doi.org/10.5194/hess-28-4059-2024, 2024
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Gao et al. (2023) question the importance of soil in hydrology, sparking debate. We acknowledge some valid points but critique their broad, unsubstantiated views on soil's role. Our response highlights three key areas: (1) the false divide between ecosystem-centric and soil-centric approaches, (2) the vital yet varied impact of soil properties, and (3) the call for a scale-aware framework. We aim to unify these perspectives, enhancing hydrology's comprehensive understanding.
Siyuan Wang, Markus Hrachowitz, and Gerrit Schoups
Hydrol. Earth Syst. Sci., 28, 4011–4033, https://doi.org/10.5194/hess-28-4011-2024, https://doi.org/10.5194/hess-28-4011-2024, 2024
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Root zone storage capacity (Sumax) changes significantly over multiple decades, reflecting vegetation adaptation to climatic variability. However, this temporal evolution of Sumax cannot explain long-term fluctuations in the partitioning of water fluxes as expressed by deviations ΔIE from the parametric Budyko curve over time with different climatic conditions, and it does not have any significant effects on shorter-term hydrological response characteristics of the upper Neckar catchment.
Zehua Chang, Hongkai Gao, Leilei Yong, Kang Wang, Rensheng Chen, Chuntan Han, Otgonbayar Demberel, Batsuren Dorjsuren, Shugui Hou, and Zheng Duan
Hydrol. Earth Syst. Sci., 28, 3897–3917, https://doi.org/10.5194/hess-28-3897-2024, https://doi.org/10.5194/hess-28-3897-2024, 2024
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An integrated cryospheric–hydrologic model, FLEX-Cryo, was developed that considers glaciers, snow cover, and frozen soil and their dynamic impacts on hydrology. We utilized it to simulate future changes in cryosphere and hydrology in the Hulu catchment. Our projections showed the two glaciers will melt completely around 2050, snow cover will reduce, and permafrost will degrade. For hydrology, runoff will decrease after the glacier has melted, and permafrost degradation will increase baseflow.
Henry M. Zimba, Miriam Coenders-Gerrits, Kawawa E. Banda, Petra Hulsman, Nick van de Giesen, Imasiku A. Nyambe, and Hubert H. G. Savenije
Hydrol. Earth Syst. Sci., 28, 3633–3663, https://doi.org/10.5194/hess-28-3633-2024, https://doi.org/10.5194/hess-28-3633-2024, 2024
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The fall and flushing of new leaves in the miombo woodlands co-occur in the dry season before the commencement of seasonal rainfall. The miombo species are also said to have access to soil moisture in deep soils, including groundwater in the dry season. Satellite-based evaporation estimates, temporal trends, and magnitudes differ the most in the dry season, most likely due to inadequate understanding and representation of the highlighted miombo species attributes in simulations.
Louise Akemi Kuana, Arlan Scortegagna Almeida, Emílio Graciliano Ferreira Mercuri, and Steffen Manfred Noe
Hydrol. Earth Syst. Sci., 28, 3367–3390, https://doi.org/10.5194/hess-28-3367-2024, https://doi.org/10.5194/hess-28-3367-2024, 2024
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The authors compared regionalization methods for river flow prediction in 126 catchments from the south of Brazil, a region with humid subtropical and hot temperate climate. The regionalization method based on physiographic–climatic similarity had the best performance for predicting daily and Q95 reference flow. We showed that basins without flow monitoring can have a good approximation of streamflow using machine learning and physiographic–climatic information as inputs.
Huy Dang and Yadu Pokhrel
Hydrol. Earth Syst. Sci., 28, 3347–3365, https://doi.org/10.5194/hess-28-3347-2024, https://doi.org/10.5194/hess-28-3347-2024, 2024
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By examining basin-wide simulations of a river regime over 83 years with and without dams, we present evidence that climate variation was a key driver of hydrologic variabilities in the Mekong River basin (MRB) over the long term; however, dams have largely altered the seasonality of the Mekong’s flow regime and annual flooding patterns in major downstream areas in recent years. These findings could help us rethink the planning of future dams and water resource management in the MRB.
Yongshin Lee, Francesca Pianosi, Andres Peñuela, and Miguel Angel Rico-Ramirez
Hydrol. Earth Syst. Sci., 28, 3261–3279, https://doi.org/10.5194/hess-28-3261-2024, https://doi.org/10.5194/hess-28-3261-2024, 2024
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Following recent advancements in weather prediction technology, we explored how seasonal weather forecasts (1 or more months ahead) could benefit practical water management in South Korea. Our findings highlight that using seasonal weather forecasts for predicting flow patterns 1 to 3 months ahead is effective, especially during dry years. This suggest that seasonal weather forecasts can be helpful in improving the management of water resources.
Mariam Khanam, Giulia Sofia, and Emmanouil N. Anagnostou
Hydrol. Earth Syst. Sci., 28, 3161–3190, https://doi.org/10.5194/hess-28-3161-2024, https://doi.org/10.5194/hess-28-3161-2024, 2024
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Flooding worsens due to climate change, with river dynamics being a key in local flood control. Predicting post-storm geomorphic changes is challenging. Using self-organizing maps and machine learning, this study forecasts post-storm alterations in stage–discharge relationships across 3101 US stream gages. The provided framework can aid in updating hazard assessments by identifying rivers prone to change, integrating channel adjustments into flood hazard assessment.
Yalan Song, Wouter J. M. Knoben, Martyn P. Clark, Dapeng Feng, Kathryn Lawson, Kamlesh Sawadekar, and Chaopeng Shen
Hydrol. Earth Syst. Sci., 28, 3051–3077, https://doi.org/10.5194/hess-28-3051-2024, https://doi.org/10.5194/hess-28-3051-2024, 2024
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Differentiable models (DMs) integrate neural networks and physical equations for accuracy, interpretability, and knowledge discovery. We developed an adjoint-based DM for ordinary differential equations (ODEs) for hydrological modeling, reducing distorted fluxes and physical parameters from errors in models that use explicit and operation-splitting schemes. With a better numerical scheme and improved structure, the adjoint-based DM matches or surpasses long short-term memory (LSTM) performance.
Florian Willkofer, Raul R. Wood, and Ralf Ludwig
Hydrol. Earth Syst. Sci., 28, 2969–2989, https://doi.org/10.5194/hess-28-2969-2024, https://doi.org/10.5194/hess-28-2969-2024, 2024
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Severe flood events pose a threat to riverine areas, yet robust estimates of the dynamics of these events in the future due to climate change are rarely available. Hence, this study uses data from a regional climate model, SMILE, to drive a high-resolution hydrological model for 98 catchments of hydrological Bavaria and exploits the large database to derive robust values for the 100-year flood events. Results indicate an increase in frequency and intensity for most catchments in the future.
Maik Renner and Corina Hauffe
Hydrol. Earth Syst. Sci., 28, 2849–2869, https://doi.org/10.5194/hess-28-2849-2024, https://doi.org/10.5194/hess-28-2849-2024, 2024
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Climate and land surface changes influence the partitioning of water balance components decisively. Their impact is quantified for 71 catchments in Saxony. Germany. Distinct signatures in the joint water and energy budgets are found: (i) past forest dieback caused a decrease in and subsequent recovery of evapotranspiration in the affected regions, and (ii) the recent shift towards higher aridity imposed a large decline in runoff that has not been seen in the observation records before.
Zhen Cui, Shenglian Guo, Hua Chen, Dedi Liu, Yanlai Zhou, and Chong-Yu Xu
Hydrol. Earth Syst. Sci., 28, 2809–2829, https://doi.org/10.5194/hess-28-2809-2024, https://doi.org/10.5194/hess-28-2809-2024, 2024
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Ensemble forecasting facilitates reliable flood forecasting and warning. This study couples the copula-based hydrologic uncertainty processor (CHUP) with Bayesian model averaging (BMA) and proposes the novel CHUP-BMA method of reducing inflow forecasting uncertainty of the Three Gorges Reservoir. The CHUP-BMA avoids the normal distribution assumption in the HUP-BMA and considers the constraint of initial conditions, which can improve the deterministic and probabilistic forecast performance.
Mazda Kompanizare, Diogo Costa, Merrin L. Macrae, John W. Pomeroy, and Richard M. Petrone
Hydrol. Earth Syst. Sci., 28, 2785–2807, https://doi.org/10.5194/hess-28-2785-2024, https://doi.org/10.5194/hess-28-2785-2024, 2024
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A new agricultural tile drainage module was developed in the Cold Region Hydrological Model platform. Tile flow and water levels are simulated by considering the effect of capillary fringe thickness, drainable water and seasonal regional groundwater dynamics. The model was applied to a small well-instrumented farm in southern Ontario, Canada, where there are concerns about the impacts of agricultural drainage into Lake Erie.
Eduardo Acuña Espinoza, Ralf Loritz, Manuel Álvarez Chaves, Nicole Bäuerle, and Uwe Ehret
Hydrol. Earth Syst. Sci., 28, 2705–2719, https://doi.org/10.5194/hess-28-2705-2024, https://doi.org/10.5194/hess-28-2705-2024, 2024
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Hydrological hybrid models promise to merge the performance of deep learning methods with the interpretability of process-based models. One hybrid approach is the dynamic parameterization of conceptual models using long short-term memory (LSTM) networks. We explored this method to evaluate the effect of the flexibility given by LSTMs on the process-based part.
Adam Griffin, Alison L. Kay, Paul Sayers, Victoria Bell, Elizabeth Stewart, and Sam Carr
Hydrol. Earth Syst. Sci., 28, 2635–2650, https://doi.org/10.5194/hess-28-2635-2024, https://doi.org/10.5194/hess-28-2635-2024, 2024
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Widespread flooding is a major problem in the UK and is greatly affected by climate change and land-use change. To look at how widespread flooding changes in the future, climate model data (UKCP18) were used with a hydrological model (Grid-to-Grid) across the UK, and 14 400 events were identified between two time slices: 1980–2010 and 2050–2080. There was a strong increase in the number of winter events in the future time slice and in the peak return periods.
Alberto Montanari, Bruno Merz, and Günter Blöschl
Hydrol. Earth Syst. Sci., 28, 2603–2615, https://doi.org/10.5194/hess-28-2603-2024, https://doi.org/10.5194/hess-28-2603-2024, 2024
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Floods often take communities by surprise, as they are often considered virtually
impossibleyet are an ever-present threat similar to the sword suspended over the head of Damocles in the classical Greek anecdote. We discuss four reasons why extremely large floods carry a risk that is often larger than expected. We provide suggestions for managing the risk of megafloods by calling for a creative exploration of hazard scenarios and communicating the unknown corners of the reality of floods.
Peter Reichert, Kai Ma, Marvin Höge, Fabrizio Fenicia, Marco Baity-Jesi, Dapeng Feng, and Chaopeng Shen
Hydrol. Earth Syst. Sci., 28, 2505–2529, https://doi.org/10.5194/hess-28-2505-2024, https://doi.org/10.5194/hess-28-2505-2024, 2024
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We compared the predicted change in catchment outlet discharge to precipitation and temperature change for conceptual and machine learning hydrological models. We found that machine learning models, despite providing excellent fit and prediction capabilities, can be unreliable regarding the prediction of the effect of temperature change for low-elevation catchments. This indicates the need for caution when applying them for the prediction of the effect of climate change.
Nicolás Álamos, Camila Alvarez-Garreton, Ariel Muñoz, and Álvaro González-Reyes
Hydrol. Earth Syst. Sci., 28, 2483–2503, https://doi.org/10.5194/hess-28-2483-2024, https://doi.org/10.5194/hess-28-2483-2024, 2024
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In this study, we assess the effects of climate and water use on streamflow reductions and drought intensification during the last 3 decades in central Chile. We address this by contrasting streamflow observations with near-natural streamflow simulations. We conclude that while the lack of precipitation dominates streamflow reductions in the megadrought, water uses have not diminished during this time, causing a worsening of the hydrological drought conditions and maladaptation conditions.
Fengjing Liu, Martha H. Conklin, and Glenn D. Shaw
Hydrol. Earth Syst. Sci., 28, 2239–2258, https://doi.org/10.5194/hess-28-2239-2024, https://doi.org/10.5194/hess-28-2239-2024, 2024
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Mountain snowpack has been declining and more precipitation falls as rain than snow. Using stable isotopes, we found flows and flow duration in Yosemite Creek are most sensitive to climate warming due to strong evaporation of waterfalls, potentially lengthening the dry-up period of waterfalls in summer and negatively affecting tourism. Groundwater recharge in Yosemite Valley is primarily from the upper snow–rain transition (2000–2500 m) and very vulnerable to a reduction in the snow–rain ratio.
Qiutong Yu, Bryan A. Tolson, Hongren Shen, Ming Han, Juliane Mai, and Jimmy Lin
Hydrol. Earth Syst. Sci., 28, 2107–2122, https://doi.org/10.5194/hess-28-2107-2024, https://doi.org/10.5194/hess-28-2107-2024, 2024
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It is challenging to incorporate input variables' spatial distribution information when implementing long short-term memory (LSTM) models for streamflow prediction. This work presents a novel hybrid modelling approach to predict streamflow while accounting for spatial variability. We evaluated the performance against lumped LSTM predictions in 224 basins across the Great Lakes region in North America. This approach shows promise for predicting streamflow in large, ungauged basin.
Marcus Buechel, Louise Slater, and Simon Dadson
Hydrol. Earth Syst. Sci., 28, 2081–2105, https://doi.org/10.5194/hess-28-2081-2024, https://doi.org/10.5194/hess-28-2081-2024, 2024
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Afforestation has been proposed internationally, but the hydrological implications of such large increases in the spatial extent of woodland are not fully understood. In this study, we use a land surface model to simulate hydrology across Great Britain with realistic afforestation scenarios and potential climate changes. Countrywide afforestation minimally influences hydrology, when compared to climate change, and reduces low streamflow whilst not lowering the highest flows.
Bu Li, Ting Sun, Fuqiang Tian, Mahmut Tudaji, Li Qin, and Guangheng Ni
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-54, https://doi.org/10.5194/hess-2024-54, 2024
Revised manuscript accepted for HESS
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This paper developed hybrid distributed hydrological models by employing a distributed 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 improves understanding about the hydrological sensitivities to climate change in large alpine basins.
Qian Zhu, Xiaodong Qin, Dongyang Zhou, Tiantian Yang, and Xinyi Song
Hydrol. Earth Syst. Sci., 28, 1665–1686, https://doi.org/10.5194/hess-28-1665-2024, https://doi.org/10.5194/hess-28-1665-2024, 2024
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Input data, model and calibration strategy can affect the accuracy of flood event simulation and prediction. Satellite-based precipitation with different spatiotemporal resolutions is an important input source. Data-driven models are sometimes proven to be more accurate than hydrological models. Event-based calibration and conventional strategy are two options adopted for flood simulation. This study targets the three concerns for accurate flood event simulation and prediction.
Fabio Ciulla and Charuleka Varadharajan
Hydrol. Earth Syst. Sci., 28, 1617–1651, https://doi.org/10.5194/hess-28-1617-2024, https://doi.org/10.5194/hess-28-1617-2024, 2024
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We present a new method based on network science for unsupervised classification of large datasets and apply it to classify 9067 US catchments and 274 biophysical traits at multiple scales. We find that our trait-based approach produces catchment classes with distinct streamflow behavior and that spatial patterns emerge amongst pristine and human-impacted catchments. This method can be widely used beyond hydrology to identify patterns, reduce trait redundancy, and select representative sites.
Cyril Thébault, Charles Perrin, Vazken Andréassian, Guillaume Thirel, Sébastien Legrand, and Olivier Delaigue
Hydrol. Earth Syst. Sci., 28, 1539–1566, https://doi.org/10.5194/hess-28-1539-2024, https://doi.org/10.5194/hess-28-1539-2024, 2024
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Streamflow forecasting is useful for many applications, ranging from population safety (e.g. floods) to water resource management (e.g. agriculture or hydropower). To this end, hydrological models must be optimized. However, a model is inherently wrong. This study aims to analyse the contribution of a multi-model approach within a variable spatial framework to improve streamflow simulations. The underlying idea is to take advantage of the strength of each modelling framework tested.
Lele Shu, Xiaodong Li, Yan Chang, Xianhong Meng, Hao Chen, Yuan Qi, Hongwei Wang, Zhaoguo Li, and Shihua Lyu
Hydrol. Earth Syst. Sci., 28, 1477–1491, https://doi.org/10.5194/hess-28-1477-2024, https://doi.org/10.5194/hess-28-1477-2024, 2024
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We developed a new model to better understand how water moves in a lake basin. Our model improves upon previous methods by accurately capturing the complexity of water movement, both on the surface and subsurface. Our model, tested using data from China's Qinghai Lake, accurately replicates complex water movements and identifies contributing factors of the lake's water balance. The findings provide a robust tool for predicting hydrological processes, aiding water resource planning.
Franziska Maria Clerc-Schwarzenbach, Giovanni Selleri, Mattia Neri, Elena Toth, Ilja van Meerveld, and Jan Seibert
EGUsphere, https://doi.org/10.5194/egusphere-2024-864, https://doi.org/10.5194/egusphere-2024-864, 2024
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We compare the catchment forcing data provided in large-sample datasets, namely the Caravan dataset and three of the original CAMELS datasets (US, BR, GB). We show that the differences affect hydrological model performance and that the data quality in the Caravan dataset is lower than the one in the CAMELS datasets, both for precipitation and potential evapotranspiration. We want to raise awareness of the lower data quality in Caravan and we suggest possible improvements for the Caravan dataset.
Ricardo Mantilla, Morgan Fonley, and Nicolás Velásquez
Hydrol. Earth Syst. Sci., 28, 1373–1382, https://doi.org/10.5194/hess-28-1373-2024, https://doi.org/10.5194/hess-28-1373-2024, 2024
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Hydrologists strive to “Be right for the right reasons” when modeling the hydrologic cycle; however, the datasets available to validate hydrological models are sparse, and in many cases, they comprise streamflow observations at the outlets of large catchments. In this work, we show that matching streamflow observations at the outlet of a large basin is not a reliable indicator of a correct description of the small-scale runoff processes.
Lillian M. McGill, E. Ashley Steel, and Aimee H. Fullerton
Hydrol. Earth Syst. Sci., 28, 1351–1371, https://doi.org/10.5194/hess-28-1351-2024, https://doi.org/10.5194/hess-28-1351-2024, 2024
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This study examines the relationship between air and river temperatures in Washington's Snoqualmie and Wenatchee basins. We used classification and regression approaches to show that the sensitivity of river temperature to air temperature is variable across basins and controlled largely by geology and snowmelt. Findings can be used to inform strategies for river basin restoration and conservation, such as identifying climate-insensitive areas of the basin that should be preserved and protected.
Dan Elhanati, Nadine Goeppert, and Brian Berkowitz
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-46, https://doi.org/10.5194/hess-2024-46, 2024
Revised manuscript accepted for HESS
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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 karst systems.
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. Discuss., https://doi.org/10.5194/hess-2024-81, https://doi.org/10.5194/hess-2024-81, 2024
Revised manuscript accepted for HESS
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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.
Stephanie R. Clark, Julien Lerat, Jean-Michel Perraud, and Peter Fitch
Hydrol. Earth Syst. Sci., 28, 1191–1213, https://doi.org/10.5194/hess-28-1191-2024, https://doi.org/10.5194/hess-28-1191-2024, 2024
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To determine if deep learning models are in general a viable alternative to traditional hydrologic modelling techniques in Australian catchments, a comparison of river–runoff predictions is made between traditional conceptual models and deep learning models in almost 500 catchments spread over the continent. It is found that the deep learning models match or outperform the traditional models in over two-thirds of the river catchments, indicating feasibility in a wide variety of conditions.
Dipti Tiwari, Mélanie Trudel, and Robert Leconte
Hydrol. Earth Syst. Sci., 28, 1127–1146, https://doi.org/10.5194/hess-28-1127-2024, https://doi.org/10.5194/hess-28-1127-2024, 2024
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Calibrating hydrological models with multi-objective functions enhances model robustness. By using spatially distributed snow information in the calibration, the model performance can be enhanced without compromising the outputs. In this study the HYDROTEL model was calibrated in seven different experiments, incorporating the SPAEF (spatial efficiency) metric alongside Nash–Sutcliffe efficiency (NSE) and root-mean-square error (RMSE), with the aim of identifying the optimal calibration strategy.
Luis Andres De la Fuente, Mohammad Reza Ehsani, Hoshin Vijai Gupta, and Laura Elizabeth Condon
Hydrol. Earth Syst. Sci., 28, 945–971, https://doi.org/10.5194/hess-28-945-2024, https://doi.org/10.5194/hess-28-945-2024, 2024
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Long short-term memory (LSTM) is a widely used machine-learning model in hydrology, but it is difficult to extract knowledge from it. We propose HydroLSTM, which represents processes like a hydrological reservoir. Models based on HydroLSTM perform similarly to LSTM while requiring fewer cell states. The learned parameters are informative about the dominant hydrology of a catchment. Our results show how parsimony and hydrological knowledge extraction can be achieved by using the new structure.
Nienke Tessa Tempel, Laurene Bouaziz, Riccardo Taormina, Ellis van Noppen, Jasper Stam, Eric Sprokkereef, and Markus Hrachowitz
EGUsphere, https://doi.org/10.5194/egusphere-2024-115, https://doi.org/10.5194/egusphere-2024-115, 2024
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This study explores the impact of climatic variability on root zone water storage capacities 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.
Louise Mimeau, Annika Künne, Flora Branger, Sven Kralisch, Alexandre Devers, and Jean-Philippe Vidal
Hydrol. Earth Syst. Sci., 28, 851–871, https://doi.org/10.5194/hess-28-851-2024, https://doi.org/10.5194/hess-28-851-2024, 2024
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Modelling flow intermittence is essential for predicting the future evolution of drying in river networks and better understanding the ecological and socio-economic impacts. However, modelling flow intermittence is challenging, and observed data on temporary rivers are scarce. This study presents a new modelling approach for predicting flow intermittence in river networks and shows that combining different sources of observed data reduces the model uncertainty.
Elena Macdonald, Bruno Merz, Björn Guse, Viet Dung Nguyen, Xiaoxiang Guan, and Sergiy Vorogushyn
Hydrol. Earth Syst. Sci., 28, 833–850, https://doi.org/10.5194/hess-28-833-2024, https://doi.org/10.5194/hess-28-833-2024, 2024
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In some rivers, the occurrence of extreme flood events is more likely than in other rivers – they have heavy-tailed distributions. We find that threshold processes in the runoff generation lead to such a relatively high occurrence probability of extremes. Further, we find that beyond a certain return period, i.e. for rare events, rainfall is often the dominant control compared to runoff generation. Our results can help to improve the estimation of the occurrence probability of extreme floods.
Claire Kouba and Thomas Harter
Hydrol. Earth Syst. Sci., 28, 691–718, https://doi.org/10.5194/hess-28-691-2024, https://doi.org/10.5194/hess-28-691-2024, 2024
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In some watersheds, the severity of the dry season has a large impact on aquatic ecosystems. In this study, we design a way to predict, 5–6 months in advance, how severe the dry season will be in a rural watershed in northern California. This early warning can support seasonal adaptive management. To predict these two values, we assess data about snow, rain, groundwater, and river flows. We find that maximum snowpack and total wet season rainfall best predict dry season severity.
Yi Nan and Fuqiang Tian
Hydrol. Earth Syst. Sci., 28, 669–689, https://doi.org/10.5194/hess-28-669-2024, https://doi.org/10.5194/hess-28-669-2024, 2024
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This paper utilized a tracer-aided model validated by multiple datasets in a large mountainous basin on the Tibetan Plateau to analyze hydrological sensitivity to climate change. The spatial pattern of the local hydrological sensitivities and the influence factors were analyzed in particular. The main finding of this paper is that the local hydrological sensitivity in mountainous basins is determined by the relationship between the glacier area ratio and the mean annual precipitation.
Michael J. Vlah, Matthew R. V. Ross, Spencer Rhea, and Emily S. Bernhardt
Hydrol. Earth Syst. Sci., 28, 545–573, https://doi.org/10.5194/hess-28-545-2024, https://doi.org/10.5194/hess-28-545-2024, 2024
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Virtual stream gauging enables continuous streamflow estimation where a gauge might be difficult or impractical to install. We reconstructed flow at 27 gauges of the National Ecological Observatory Network (NEON), informing ~199 site-months of missing data in the official record and improving that accuracy of official estimates at 11 sites. This study shows that machine learning, but also routine regression methods, can be used to supplement existing gauge networks and reduce monitoring costs.
Sungwook Wi and Scott Steinschneider
Hydrol. Earth Syst. Sci., 28, 479–503, https://doi.org/10.5194/hess-28-479-2024, https://doi.org/10.5194/hess-28-479-2024, 2024
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We investigate whether deep learning (DL) models can produce physically plausible streamflow projections under climate change. We address this question by focusing on modeled responses to increases in temperature and potential evapotranspiration and by employing three DL and three process-based hydrological models. The results suggest that physical constraints regarding model architecture and input are necessary to promote the physical realism of DL hydrological projections under climate change.
Guillaume Evin, Matthieu Le Lay, Catherine Fouchier, David Penot, Francois Colleoni, Alexandre Mas, Pierre-André Garambois, and Olivier Laurantin
Hydrol. Earth Syst. Sci., 28, 261–281, https://doi.org/10.5194/hess-28-261-2024, https://doi.org/10.5194/hess-28-261-2024, 2024
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Hydrological modelling of mountainous catchments is challenging for many reasons, the main one being the temporal and spatial representation of precipitation forcings. This study presents an evaluation of the hydrological modelling of 55 small mountainous catchments of the northern French Alps, focusing on the influence of the type of precipitation reanalyses used as inputs. These evaluations emphasize the added value of radar measurements, in particular for the reproduction of flood events.
Frederik Kratzert, Martin Gauch, Daniel Klotz, and Grey Nearing
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2023-275, https://doi.org/10.5194/hess-2023-275, 2024
Revised manuscript accepted for HESS
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Recently, a special type of neural network architecture became increasingly popular in hydrology literature. However, in most applications, this model was applied as a one-to-one replacement for hydrology models without adapting or rethinking the experimental setup. In this opinion paper, we show how this is almost always a bad decision and how using these kinds of models require the use of large-sample hydrology datasets.
Lena Katharina Schmidt, Till Francke, Peter Martin Grosse, and Axel Bronstert
Hydrol. Earth Syst. Sci., 28, 139–161, https://doi.org/10.5194/hess-28-139-2024, https://doi.org/10.5194/hess-28-139-2024, 2024
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How suspended sediment export from glacierized high-alpine areas responds to future climate change is hardly assessable as many interacting processes are involved, and appropriate physical models are lacking. We present the first study, to our knowledge, exploring machine learning to project sediment export until 2100 in two high-alpine catchments. We find that uncertainties due to methodological limitations are small until 2070. Negative trends imply that peak sediment may have already passed.
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. Discuss., https://doi.org/10.5194/hess-2023-264, https://doi.org/10.5194/hess-2023-264, 2024
Revised manuscript accepted for HESS
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Large-scale hydrologic a needed tool to explore complex watershed processes and how they may evolve under 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 with a set of experiments in the Upper Colorado River Basin.
Salam A. Abbas, Ryan T. Bailey, Jeremy T. White, Jeffrey G. Arnold, Michael J. White, Natalja Čerkasova, and Jungang Gao
Hydrol. Earth Syst. Sci., 28, 21–48, https://doi.org/10.5194/hess-28-21-2024, https://doi.org/10.5194/hess-28-21-2024, 2024
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Research highlights.
1. Implemented groundwater module (gwflow) into SWAT+ for four watersheds with different unique hydrologic features across the United States.
2. Presented methods for sensitivity analysis, uncertainty analysis and parameter estimation for coupled models.
3. Sensitivity analysis for streamflow and groundwater head conducted using Morris method.
4. Uncertainty analysis and parameter estimation performed using an iterative ensemble smoother within the PEST framework.
Shima Azimi, Christian Massari, Giuseppe Formetta, Silvia Barbetta, Alberto Tazioli, Davide Fronzi, Sara Modanesi, Angelica Tarpanelli, and Riccardo Rigon
Hydrol. Earth Syst. Sci., 27, 4485–4503, https://doi.org/10.5194/hess-27-4485-2023, https://doi.org/10.5194/hess-27-4485-2023, 2023
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We analyzed the water budget of nested karst catchments using simple methods and modeling. By utilizing the available data on precipitation and discharge, we were able to determine the response lag-time by adopting new techniques. Additionally, we modeled snow cover dynamics and evapotranspiration with the use of Earth observations, providing a concise overview of the water budget for the basin and its subbasins. We have made the data, models, and workflows accessible for further study.
Yuhang Zhang, Aizhong Ye, Bita Analui, Phu Nguyen, Soroosh Sorooshian, Kuolin Hsu, and Yuxuan Wang
Hydrol. Earth Syst. Sci., 27, 4529–4550, https://doi.org/10.5194/hess-27-4529-2023, https://doi.org/10.5194/hess-27-4529-2023, 2023
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Our study shows that while the quantile regression forest (QRF) and countable mixtures of asymmetric Laplacians long short-term memory (CMAL-LSTM) models demonstrate similar proficiency in multipoint probabilistic predictions, QRF excels in smaller watersheds and CMAL-LSTM in larger ones. CMAL-LSTM performs better in single-point deterministic predictions, whereas QRF model is more efficient overall.
Léo C. P. Martin, Sebastian Westermann, Michele Magni, Fanny Brun, Joel Fiddes, Yanbin Lei, Philip Kraaijenbrink, Tamara Mathys, Moritz Langer, Simon Allen, and Walter W. Immerzeel
Hydrol. Earth Syst. Sci., 27, 4409–4436, https://doi.org/10.5194/hess-27-4409-2023, https://doi.org/10.5194/hess-27-4409-2023, 2023
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Across the Tibetan Plateau, many large lakes have been changing level during the last decades as a response to climate change. In high-mountain environments, water fluxes from the land to the lakes are linked to the ground temperature of the land and to the energy fluxes between the ground and the atmosphere, which are modified by climate change. With a numerical model, we test how these water and energy fluxes have changed over the last decades and how they influence the lake level variations.
Diego Araya, Pablo A. Mendoza, Eduardo Muñoz-Castro, and James McPhee
Hydrol. Earth Syst. Sci., 27, 4385–4408, https://doi.org/10.5194/hess-27-4385-2023, https://doi.org/10.5194/hess-27-4385-2023, 2023
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Dynamical systems are used by many agencies worldwide to produce seasonal streamflow forecasts, which are critical for decision-making. Such systems rely on hydrology models, which contain parameters that are typically estimated using a target performance metric (i.e., objective function). This study explores the effects of this decision across mountainous basins in Chile, illustrating tradeoffs between seasonal forecast quality and the models' capability to simulate streamflow characteristics.
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Short summary
1. Catchments with higher snow ratio tend to have larger runoff index.
2. A modified Budyko method is proposed to illustrate the snow effect on runoff.
3. Snow ratio change has a significant contribution to runoff change, according to historical observations and projected future climate scenarios, especially in northwestern mountainous and northern high-latitude areas of China.
1. Catchments with higher snow ratio tend to have larger runoff index.
2. A modified Budyko...
