Articles | Volume 15, issue 3
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Hydrologic similarity among catchments under variable flow conditions
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, USA
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, USA
School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA, USA
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Mathematical applicationsSpatial variability in Alpine reservoir regulation: deriving reservoir operations from streamflow using generalized additive modelsRegional significance of historical trends and step changes in Australian streamflowRiver flooding mechanisms and their changes in Europe revealed by explainable machine learningThe Wasserstein distance as a hydrological objective functionChanges in nonlinearity and stability of streamflow recession characteristics under climate warming in a large glaciated basin of the Tibetan PlateauA data-driven method for estimating the composition of end-members from stream water chemistry time seriesEvaporation loss estimation of the river-lake continuum of arid inland river: Evidence from stable isotopesTechnical note: PMR – a proxy metric to assess hydrological model robustness in a changing climateCausal effects of dams and land cover changes on flood changes in mainland ChinaCan 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 structureTechnical note: Calculation scripts for ensemble hydrograph separationSpecific climate classification for Mediterranean hydrology and future evolution under Med-CORDEX regional climate model scenariosA line-integral-based method to partition climate and catchment effects on runoffTechnical note: A two-sided affine power scaling relationship to represent the concentration–discharge relationshipOn the flood peak distributions over ChinaNew water fractions and transit time distributions at Plynlimon, Wales, estimated from stable water isotopes in precipitation and streamflowDoes 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 catchmentTechnical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–FuClimate or land cover variations: what is driving observed changes in river peak flows? A data-based attribution studyQuantifying new water fractions and transit time distributions using ensemble hydrograph separation: theory and benchmark testsLand cover effects on hydrologic services under a precipitation gradientTechnical note: Long-term persistence loss of urban streams as a metric for catchment classificationResponses of runoff to historical and future climate variability over ChinaCharacterization and evaluation of controls on post-fire streamflow response across western US watershedsAnalysis and modelling of a 9.3 kyr palaeoflood record: correlations, clustering, and cyclesClimate change impacts on Yangtze River discharge at the Three Gorges DamCan assimilation of crowdsourced data in hydrological modelling improve flood prediction?Delineation of homogenous regions using hydrological variables predicted by projection pursuit regressionMultivariate hydrological data assimilation of soil moisture and groundwater headOn the propagation of diel signals in river networks using analytic solutions of flow equationsDominant climatic factors driving annual runoff changes at the catchment scale across ChinaData assimilation in integrated hydrological modelling in the presence of observation biasRecent 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 hysteresisEstimating spatially distributed soil water content at small watershed scales based on decomposition of temporal anomaly and time stability analysisImproving flood forecasting capability of physically based distributed hydrological models by parameter optimizationTime series analysis of the long-term hydrologic impacts of afforestation in the Águeda watershed of north-central PortugalData assimilation in integrated hydrological modeling using ensemble Kalman filtering: evaluating the effect of ensemble size and localization on filter performanceAttribution of high resolution streamflow trends in Western Austria – an approach based on climate and discharge station dataA constraint-based search algorithm for parameter identification of environmental modelsHydrologic landscape classification evaluates streamflow vulnerability to climate change in Oregon, USATeleconnection analysis of runoff and soil moisture over the Pearl River basin in southern ChinaAssessing the predictive capability of randomized tree-based ensembles in streamflow modellingStreamflow input to Lake Athabasca, CanadaFlood-initiating catchment conditions: a spatio-temporal analysis of large-scale soil moisture patterns in the Elbe River basinMultivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimationImpact of climate change and anthropogenic activities on stream flow and sediment discharge in the Wei River basin, ChinaAn effective depression filling algorithm for DEM-based 2-D surface flow modelling
Manuela Irene Brunner and Philippe Naveau
Hydrol. Earth Syst. Sci., 27, 673–687,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,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,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.
Jared C. Magyar and Malcolm S. Sambridge
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 'work' required to rearrange one mass distribution into the other. We also use similar mathematical techniques for defining a type of 'average' between water distributions.
Jiarong Wang, Xi Chen, Man Gao, Qi Hu, and Jintao Liu
Hydrol. Earth Syst. Sci., 26, 3901–3920,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,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.,
Revised manuscript under review for HESSShort 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,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,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,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,
James W. Kirchner and Julia L. A. Knapp
Hydrol. Earth Syst. Sci., 24, 5539–5558,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,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.
Hydrol. Earth Syst. Sci., 24, 2365–2378,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,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,
Julia L. A. Knapp, Colin Neal, Alessandro Schlumpf, Margaret Neal, and James W. Kirchner
Hydrol. Earth Syst. Sci., 23, 4367–4388,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,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,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,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,
James W. Kirchner
Hydrol. Earth Syst. Sci., 23, 303–349,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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,
J. Rasmussen, H. Madsen, K. H. Jensen, and J. C. Refsgaard
Hydrol. Earth Syst. Sci., 19, 2999–3013,
C. Kormann, T. Francke, M. Renner, and A. Bronstert
Hydrol. Earth Syst. Sci., 19, 1225–1245,
S. Gharari, M. Shafiei, M. Hrachowitz, R. Kumar, F. Fenicia, H. V. Gupta, and H. H. G. Savenije
Hydrol. Earth Syst. Sci., 18, 4861–4870,
S. G. Leibowitz, R. L. Comeleo, P. J. Wigington Jr., C. P. Weaver, P. E. Morefield, E. A. Sproles, and J. L. Ebersole
Hydrol. Earth Syst. Sci., 18, 3367–3392,
J. Niu, J. Chen, and B. Sivakumar
Hydrol. Earth Syst. Sci., 18, 1475–1492,
S. Galelli and A. Castelletti
Hydrol. Earth Syst. Sci., 17, 2669–2684,
K. Rasouli, M. A. Hernández-Henríquez, and S. J. Déry
Hydrol. Earth Syst. Sci., 17, 1681–1691,
M. Nied, Y. Hundecha, and B. Merz
Hydrol. Earth Syst. Sci., 17, 1401–1414,
B. Gräler, M. J. van den Berg, S. Vandenberghe, A. Petroselli, S. Grimaldi, B. De Baets, and N. E. C. Verhoest
Hydrol. Earth Syst. Sci., 17, 1281–1296,
P. Gao, V. Geissen, C. J. Ritsema, X.-M. Mu, and F. Wang
Hydrol. Earth Syst. Sci., 17, 961–972,
D. Zhu, Q. Ren, Y. Xuan, Y. Chen, and I. D. Cluckie
Hydrol. Earth Syst. Sci., 17, 495–505,
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