Articles | Volume 18, issue 5
https://doi.org/10.5194/hess-18-1793-2014
© Author(s) 2014. 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-18-1793-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
19 May 2014
Research article |
| 19 May 2014
A dual-inexact fuzzy stochastic model for water resources management and non-point source pollution mitigation under multiple uncertainties
C. Dong
MOE Key Laboratory of Regional Energy and Environmental Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China
Q. Tan
MOE Key Laboratory of Regional Energy and Environmental Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China
Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina S4S 7H9, Canada
G.-H. Huang
MOE Key Laboratory of Regional Energy and Environmental Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China
Y.-P. Cai
State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China
Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina S4S 7H9, Canada
Related subject area
Subject: Water Resources Management | Techniques and Approaches: Stochastic approaches
Check dam impact on sediment loads: example of the Guerbe River in the Swiss Alps – a catchment scale experiment
Controls on flood managed aquifer recharge through a heterogeneous vadose zone: hydrologic modeling at a site characterized with surface geophysics
Spatiotemporal responses of the crop water footprint and its associated benchmarks under different irrigation regimes to climate change scenarios in China
Bridging the scale gap: obtaining high-resolution stochastic simulations of gridded daily precipitation in a future climate
3D multiple-point geostatistical simulation of joint subsurface redox and geological architectures
News media coverage of conflict and cooperation dynamics of water events in the Lancang–Mekong River basin
Analysis of the effects of biases in ensemble streamflow prediction (ESP) forecasts on electricity production in hydropower reservoir management
Using paleoclimate reconstructions to analyse hydrological epochs associated with Pacific decadal variability
Bias correction of simulated historical daily streamflow at ungauged locations by using independently estimated flow duration curves
Season-ahead forecasting of water storage and irrigation requirements – an application to the southwest monsoon in India
Hydrostratigraphic modeling using multiple-point statistics and airborne transient electromagnetic methods
A risk assessment methodology to evaluate the risk failure of managed aquifer recharge in the Mediterranean Basin
A coupled stochastic rainfall–evapotranspiration model for hydrological impact analysis
Real-time updating of the flood frequency distribution through data assimilation
Estimating drought risk across Europe from reported drought impacts, drought indices, and vulnerability factors
The cost of ending groundwater overdraft on the North China Plain
Definition of efficient scarcity-based water pricing policies through stochastic programming
Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology
Determining spatial variability of dry spells: a Markov-based method, applied to the Makanya catchment, Tanzania
Streamflow droughts in the Iberian Peninsula between 1945 and 2005: spatial and temporal patterns
Estimating the flood frequency distribution at seasonal and annual time scales
Domestic wells have high probability of pumping septic tank leachate
Record extension for short-gauged water quality parameters using a newly proposed robust version of the Line of Organic Correlation technique
Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions
Trend analysis of extreme precipitation in the Northwestern Highlands of Ethiopia with a case study of Debre Markos
Ariel Henrique do Prado, David Mair, Philippos Garefalakis, Chantal Schmidt, Alexander Whittaker, Sebastien Castelltort, and Fritz Schlunegger
Hydrol. Earth Syst. Sci., 28, 1173–1190, https://doi.org/10.5194/hess-28-1173-2024, https://doi.org/10.5194/hess-28-1173-2024, 2024
Short summary
Short summary
Engineering structures known as check dams are built with the intention of managing streams. The effectiveness of such structures can be expressed by quantifying the reduction of the sediment flux after their implementation. In this contribution, we estimate and compare the volumes of sediment transported in a mountain stream for engineered and non-engineered conditions. We found that without check dams the mean sediment flux would be ca. 10 times larger in comparison with the current situation.
Zach Perzan, Gordon Osterman, and Kate Maher
Hydrol. Earth Syst. Sci., 27, 969–990, https://doi.org/10.5194/hess-27-969-2023, https://doi.org/10.5194/hess-27-969-2023, 2023
Short summary
Short summary
In this study, we simulate flood managed aquifer recharge – the process of intentionally inundating land to replenish depleted aquifers – at a site imaged with geophysical equipment. Results show that layers of clay and silt trap recharge water above the water table, where it is inaccessible to both plants and groundwater wells. Sensitivity analyses also identify the main sources of uncertainty when simulating managed aquifer recharge, helping to improve future forecasts of site performance.
Zhiwei Yue, Xiangxiang Ji, La Zhuo, Wei Wang, Zhibin Li, and Pute Wu
Hydrol. Earth Syst. Sci., 26, 4637–4656, https://doi.org/10.5194/hess-26-4637-2022, https://doi.org/10.5194/hess-26-4637-2022, 2022
Short summary
Short summary
Facing the increasing challenge of sustainable crop supply with limited water resources due to climate change, large-scale responses in the water footprint (WF) and WF benchmarks of crop production remain unclear. Here, we quantify the effects of future climate change scenarios on the WF and WF benchmarks of maize and wheat in time and space in China. Differences in crop growth between rain-fed and irrigated farms and among furrow-, sprinkler-, and micro-irrigated regimes are identified.
Qifen Yuan, Thordis L. Thorarinsdottir, Stein Beldring, Wai Kwok Wong, and Chong-Yu Xu
Hydrol. Earth Syst. Sci., 25, 5259–5275, https://doi.org/10.5194/hess-25-5259-2021, https://doi.org/10.5194/hess-25-5259-2021, 2021
Short summary
Short summary
Localized impacts of changing precipitation patterns on surface hydrology are often assessed at a high spatial resolution. Here we introduce a stochastic method that efficiently generates gridded daily precipitation in a future climate. The method works out a stochastic model that can describe a high-resolution data product in a reference period and form a realistic precipitation generator under a projected future climate. A case study of nine catchments in Norway shows that it works well.
Rasmus Bødker Madsen, Hyojin Kim, Anders Juhl Kallesøe, Peter B. E. Sandersen, Troels Norvin Vilhelmsen, Thomas Mejer Hansen, Anders Vest Christiansen, Ingelise Møller, and Birgitte Hansen
Hydrol. Earth Syst. Sci., 25, 2759–2787, https://doi.org/10.5194/hess-25-2759-2021, https://doi.org/10.5194/hess-25-2759-2021, 2021
Short summary
Short summary
The protection of subsurface aquifers from contamination is an ongoing environmental challenge. Some areas of the underground have a natural capacity for reducing contaminants. In this research these areas are mapped in 3D along with information about, e.g., sand and clay, which indicates whether contaminated water from the surface will travel through these areas. This mapping technique will be fundamental for more reliable risk assessment in water quality protection.
Jing Wei, Yongping Wei, Fuqiang Tian, Natalie Nott, Claire de Wit, Liying Guo, and You Lu
Hydrol. Earth Syst. Sci., 25, 1603–1615, https://doi.org/10.5194/hess-25-1603-2021, https://doi.org/10.5194/hess-25-1603-2021, 2021
Richard Arsenault and Pascal Côté
Hydrol. Earth Syst. Sci., 23, 2735–2750, https://doi.org/10.5194/hess-23-2735-2019, https://doi.org/10.5194/hess-23-2735-2019, 2019
Short summary
Short summary
Hydrological forecasting allows hydropower system operators to make the most efficient use of the available water as possible. Accordingly, hydrologists have been aiming at improving the quality of these forecasts. This work looks at the impacts of improving systematic errors in a forecasting scheme on the hydropower generation using a few decision-aiding tools that are used operationally by hydropower utilities. We find that the impacts differ according to the hydropower system characteristics.
Lanying Zhang, George Kuczera, Anthony S. Kiem, and Garry Willgoose
Hydrol. Earth Syst. Sci., 22, 6399–6414, https://doi.org/10.5194/hess-22-6399-2018, https://doi.org/10.5194/hess-22-6399-2018, 2018
Short summary
Short summary
Analyses of run lengths of Pacific decadal variability (PDV) suggest that there is no significant difference between run lengths in positive and negative phases of PDV and that it is more likely than not that the PDV run length has been non-stationary in the past millennium. This raises concerns about whether variability seen in the instrumental record (the last ~100 years), or even in the shorter 300–400 year paleoclimate reconstructions, is representative of the full range of variability.
William H. Farmer, Thomas M. Over, and Julie E. Kiang
Hydrol. Earth Syst. Sci., 22, 5741–5758, https://doi.org/10.5194/hess-22-5741-2018, https://doi.org/10.5194/hess-22-5741-2018, 2018
Short summary
Short summary
This work observes that the result of streamflow simulation is often biased, especially with regards to extreme events, and proposes a novel technique to reduce this bias. By using parallel simulations of relative streamflow timing (sequencing) and the distribution of streamflow (magnitude), severe biases can be mitigated. Reducing this bias allows for improved utility of streamflow simulation for water resources management.
Arun Ravindranath, Naresh Devineni, Upmanu Lall, and Paulina Concha Larrauri
Hydrol. Earth Syst. Sci., 22, 5125–5141, https://doi.org/10.5194/hess-22-5125-2018, https://doi.org/10.5194/hess-22-5125-2018, 2018
Short summary
Short summary
We present a framework for forecasting water storage requirements in the agricultural sector and an application of this framework to water risk assessment in India. Our framework involves defining a crop-specific water stress index and applying a particular statistical forecasting model to predict seasonal water stress for the crop of interest. The application focused on forecasting crop water stress for potatoes grown during the monsoon season in the Satara district of Maharashtra.
Adrian A. S. Barfod, Ingelise Møller, Anders V. Christiansen, Anne-Sophie Høyer, Júlio Hoffimann, Julien Straubhaar, and Jef Caers
Hydrol. Earth Syst. Sci., 22, 3351–3373, https://doi.org/10.5194/hess-22-3351-2018, https://doi.org/10.5194/hess-22-3351-2018, 2018
Short summary
Short summary
Three-dimensional geological models are important to securing and managing groundwater. Such models describe the geological architecture, which is used for modeling the flow of groundwater. Common geological modeling approaches result in one model, which does not quantify the architectural uncertainty of the geology.
We present a comparison of three different state-of-the-art stochastic multiple-point statistical methods for quantifying the geological uncertainty using real-world datasets.
Paula Rodríguez-Escales, Arnau Canelles, Xavier Sanchez-Vila, Albert Folch, Daniel Kurtzman, Rudy Rossetto, Enrique Fernández-Escalante, João-Paulo Lobo-Ferreira, Manuel Sapiano, Jon San-Sebastián, and Christoph Schüth
Hydrol. Earth Syst. Sci., 22, 3213–3227, https://doi.org/10.5194/hess-22-3213-2018, https://doi.org/10.5194/hess-22-3213-2018, 2018
Short summary
Short summary
In this work, we have developed a methodology to evaluate the failure risk of managed aquifer recharge, and we have applied it to six different facilities located in the Mediterranean Basin. The methodology was based on the development of a probabilistic risk assessment based on fault trees. We evaluated both technical and non-technical issues, the latter being more responsible for failure risk.
Minh Tu Pham, Hilde Vernieuwe, Bernard De Baets, and Niko E. C. Verhoest
Hydrol. Earth Syst. Sci., 22, 1263–1283, https://doi.org/10.5194/hess-22-1263-2018, https://doi.org/10.5194/hess-22-1263-2018, 2018
Short summary
Short summary
In this paper, stochastically generated rainfall and corresponding evapotranspiration time series, generated by means of vine copulas, are used to force a simple conceptual hydrological model. The results obtained are comparable to the modelled discharge using observed forcing data. Yet, uncertainties in the modelled discharge increase with an increasing number of stochastically generated time series used. Still, the developed model has great potential for hydrological impact analysis.
Cristina Aguilar, Alberto Montanari, and María-José Polo
Hydrol. Earth Syst. Sci., 21, 3687–3700, https://doi.org/10.5194/hess-21-3687-2017, https://doi.org/10.5194/hess-21-3687-2017, 2017
Short summary
Short summary
Assuming that floods are driven by both short- (meteorological forcing) and long-term perturbations (higher-than-usual moisture), we propose a technique for updating a season in advance the flood frequency distribution. Its application in the Po and Danube rivers helped to reduce the uncertainty in the estimation of floods and thus constitutes a promising tool for real-time management of flood risk mitigation. This study is the result of the stay of the first author at the University of Bologna.
Veit Blauhut, Kerstin Stahl, James Howard Stagge, Lena M. Tallaksen, Lucia De Stefano, and Jürgen Vogt
Hydrol. Earth Syst. Sci., 20, 2779–2800, https://doi.org/10.5194/hess-20-2779-2016, https://doi.org/10.5194/hess-20-2779-2016, 2016
Claus Davidsen, Suxia Liu, Xingguo Mo, Dan Rosbjerg, and Peter Bauer-Gottwein
Hydrol. Earth Syst. Sci., 20, 771–785, https://doi.org/10.5194/hess-20-771-2016, https://doi.org/10.5194/hess-20-771-2016, 2016
Short summary
Short summary
In northern China, rivers run dry and groundwater tables drop, causing economic losses for all water use sectors. We present a groundwater-surface water allocation decision support tool for cost-effective long-term recovery of an overpumped aquifer. The tool is demonstrated for a part of the North China Plain and can support the implementation of the recent China No. 1 Document in a rational and economically efficient way.
H. Macian-Sorribes, M. Pulido-Velazquez, and A. Tilmant
Hydrol. Earth Syst. Sci., 19, 3925–3935, https://doi.org/10.5194/hess-19-3925-2015, https://doi.org/10.5194/hess-19-3925-2015, 2015
Short summary
Short summary
One of the most promising alternatives to improve the efficiency in water usage is the implementation of scarcity-based pricing policies based on the opportunity cost of water at the basin scale. Time series of the marginal value of water at selected locations (reservoirs) are obtained using a stochastic hydro-economic model and then post-processed to define step water pricing policies.
F. Lombardo, E. Volpi, D. Koutsoyiannis, and S. M. Papalexiou
Hydrol. Earth Syst. Sci., 18, 243–255, https://doi.org/10.5194/hess-18-243-2014, https://doi.org/10.5194/hess-18-243-2014, 2014
B. M. C. Fischer, M. L. Mul, and H. H. G. Savenije
Hydrol. Earth Syst. Sci., 17, 2161–2170, https://doi.org/10.5194/hess-17-2161-2013, https://doi.org/10.5194/hess-17-2161-2013, 2013
J. Lorenzo-Lacruz, E. Morán-Tejeda, S. M. Vicente-Serrano, and J. I. López-Moreno
Hydrol. Earth Syst. Sci., 17, 119–134, https://doi.org/10.5194/hess-17-119-2013, https://doi.org/10.5194/hess-17-119-2013, 2013
E. Baratti, A. Montanari, A. Castellarin, J. L. Salinas, A. Viglione, and A. Bezzi
Hydrol. Earth Syst. Sci., 16, 4651–4660, https://doi.org/10.5194/hess-16-4651-2012, https://doi.org/10.5194/hess-16-4651-2012, 2012
J. E. Bremer and T. Harter
Hydrol. Earth Syst. Sci., 16, 2453–2467, https://doi.org/10.5194/hess-16-2453-2012, https://doi.org/10.5194/hess-16-2453-2012, 2012
B. Khalil and J. Adamowski
Hydrol. Earth Syst. Sci., 16, 2253–2266, https://doi.org/10.5194/hess-16-2253-2012, https://doi.org/10.5194/hess-16-2253-2012, 2012
W. J. Vanhaute, S. Vandenberghe, K. Scheerlinck, B. De Baets, and N. E. C. Verhoest
Hydrol. Earth Syst. Sci., 16, 873–891, https://doi.org/10.5194/hess-16-873-2012, https://doi.org/10.5194/hess-16-873-2012, 2012
H. Shang, J. Yan, M. Gebremichael, and S. M. Ayalew
Hydrol. Earth Syst. Sci., 15, 1937–1944, https://doi.org/10.5194/hess-15-1937-2011, https://doi.org/10.5194/hess-15-1937-2011, 2011
Cited articles
Azaiez, M. N., Hariga, M., and Al-Harkan, I.: A chance-constrained multi-period model for a special multi-reservoir system, Comput. Oper. Res., 32, 1337–1351, 2005.
Bender, M. J. and Simonovic, S. P.: A fuzzy compromise approach to water resource systems planning under uncertainty, Fuzzy Sets Syst., 115, 35–44, 2000.
Cai, Y. P., Huang, G. H., Nie, X. H., Li, Y. P., and Tan, Q.: Municipal Solid Waste Management Under Uncertainty: A Mixed Interval Parameter Fuzzy-Stochastic Robust Programming Approach, Environ. Eng. Sci., 24, 338–352, 2007.
Cai, Y. P., Huang, G. H., Yang, Z. F., Lin, Q. G., and Tan, Q.: Community–scale renewable energy systems planning under uncertainty – An interval chance–constrained programming approach, Renew. Sustain. Energy Rev., 13, 721–735, 2009a.
Cai, Y. P., Huang, G. H., Tan, Q., and Yang, Z. F.: Planning of community-scale renewable energy management systems in a mixed stochastic and fuzzy environment, Renew. Energy, 34, 1833–1847, 2009b.
Cai, Y. P., Huang, G. H., Tan, Q., and Chen, B.: Identification of optimal strategies for improving eco-resilience to floods in ecologically vulnerable regions of a wetland, Ecol. Model., 222, 360–369, 2011.
Cai, Y. P., Huang, G. H., Wang, X., Li, G. C., and Tan, Q.: An inexact programming approach for supporting ecologically sustainable water supply with the consideration of uncertain water demand by ecosystems, Stochast. Environ. Res. Risk Assess., 25, 721–735, 2012.
Canter, L. W., Chawla, M. K., and Swo, C. T.: Addressing trend-related changes within cumulative effects studies in water resources planning, Environ. Impact Assess. Rev., 44, 58–66, 2014.
Cao, M. F., Huang, G. H., Sun, Y., Xu, Y., and Yao, Y.: Dual inexact fuzzy chance-constrained programming for planning waste management systems, Stochast. Environ. Res. Risk Assess., 24, 1163–1174, 2010.
Castelletti, A., Pianosi, F., and Sessa, R. S.: Integration, participation and optimal control in water resources planning and management, Appl. Math. Comput., 206, 21–33, 2008.
Chen, C. H., Liu, W. L., Liaw, S. L., and Yu, C. H.: Development of a dynamic strategy planning theory and system for sustainable river basin land use management, Sci. Total Environ., 346, 17–37, 2005.
Chung, G., Lansey, K., Blowers, P., Brooks, P., Ela, W., Stewart, S., and Wilson P.: A general water supply planning model: Evaluation of decentralized treatment, Environ. Model. Softw., 23, 893–905, 2008.
Dessai, S. and Hulme, M.: Assessing the robustness of adaptation decisions to climate change uncertainties: A case study on water resources management in the East of England, Global Environ. Change, 17, 59–72, 2007.
Deviney Jr., F. A., Brown, D. E., and Rice, K. C.: Evaluation of Bayesian Estimation of a Hidden Continuous-Time Markov Chain Model with Application to Threshold Violation in Water-Quality Indicators, J. Environ. Inf., 19, 70–78, 2012.
Dong, C. L., Schoups, G., and van de Giesen, N.: Scenario development for water resource planning and management: A review, Tech. Forecast. Soc. Change, 80, 749–761, 2013.
Dong, C., Huang, G. H, Tan, Q., and Cai Y. P.: Coupled planning of water resources and agricultural land-use based on an inexact-stochastic programming model, Front. Earth Sci., 8, 70–80, 2014.
Gregory, R., Failing, L., and Higgins, P.: Adaptive management and environmental decision making: A case study application to water use planning, Ecol. Econ., 58, 434–447, 2006.
Gu, J. J., Huang, G. H., Guo, P., and Shen, N.: Interval multistage joint-probabilistic integer programming approach for water resources allocation and management, J. Environ. Manage., 128, 615–624, 2013.
Guo, P., Huang, G. H., and Li, Y. P.: An inexact fuzzy-chance-constrained two-stage mixed-integer linear programming approach for flood diversion planning under multiple uncertainties, Adv. Water Resour., 33, 81–91, 2010.
Huang, G. H., Batez, B. W., and Patry, G. G.: A grey linear programming approach for municipal solid waste management planning under uncertainty, Civ. Eng. Syst., 9, 319–335, 1992.
Huang, G. H., Batez, B. W., and Patry, G. G.: Grey integer programming: an application to waste management planning under uncertainty, Eur. J. Oper. Res., 83, 594–620, 1995.
Huang, Y., Li, Y. P., Chen, X., and Ma, Y. G.: Optimization of the irrigation water resources for agricultural sustainability in Tarim River Basin, China, Agric. Water Manage., 107, 74–85, 2012.
Khare, D., Jat, M. K., and Deva, J.: Sunder Assessment of water resources allocation options: Conjunctive use planning in a link canal command, Resour. Conserv. Recycling, 51, 487–506, 2007.
Kondilia, E. and Kaldellis, J. K.: Model development for the optimal water systems planning, Comput. Aided Chem. Eng., 21, 1851–1856, 2006.
Li, Z., Huang, G., Zhang, Y. M., and Li, Y.P.: Inexact two-stage stochastic credibility constrained programming for water quality management, Resour. Conserv. Recycling, 73, 122–132, 2013.
Lindenschmidt, K. E., Fleischbein, K., and Baborowski, M.: Structural uncertainty in a river water quality modelling system, Ecol. Model., 204, 289–300, 2007.
Lu, H .W., Huang, G. H., Zhang, Y. M., and He, L.: Strategic agricultural land-use planning in response to water-supplier variation in a China's rural region, Agric. Syst., 108, 19–28, 2012.
Mahmoud, M. I., Gupta, H. V., and Rajagopal, S.: Scenario development for water resources planning and watershed management: Methodology and semi-arid region case study, Environ. Model. Softw., 26, 873–885, 2011.
Mehta, V. K., Aslam, O., Dale, L., Miller, N., and Purkey, D. R.: Scenario-based water resources planning for utilities in the Lake Victoria region, Phys. Chem. Earth, 61–62, 22–31, 2013.
Qin, H. P., Su, Q., and Khu, S. T.: An integrated model for water management in a rapidly urbanizing catchment, Environ. Model. Softw., 26, 1502–1514, 2011.
Qin, X. S., Huang, G. H., Zeng, G. M., Chakma, A., and Huang, Y. F.: An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty, Eur. J. Oper. Res., 180, 1331–1357, 2007.
Ray, D. K., Pijanowski, B. C., Kendall, A. D., and Hyndman, D. W.: Coupling land use and groundwater models to map land use legacies: Assessment of model uncertainties relevant to land use planning, Appl. Geogr., 34, 356–370, 2012.
Riquelme, F. J. M. and Ramos, A. B.: Land and water use management in vine growing by using geographic information systems in Castilla-La Mancha, Spain, Agric. Water Manage., 77, 82–95, 2005.
Satti, S. R., Jacobs, J. M., and Irmak, S.: Agricultural water management in a humid region: sensitivity to climate, soil and crop parameters, Agric. Water Manage., 70, 51–65, 2004.
Sessa, R. S.: Modelling and control for participatory planning and managing water systems, Control Eng. Pract., 15, p. 985, 2007.
Sethi, L. N., Panda, S. N., and Nayak, M. K.: Optimal crop planning and water resources allocation in a coastal groundwater basin, Orissa, India, Agric. Water Manage., 83, 209–220, 2006.
Tan, Q., Huang, G. H., and Cai, Y. P.: Radial interval chance-constrained programming for agricultural non-point source water pollution control under uncertainty, Agric. Water Manage., 98, 1595–1606, 2011.
Victoria, F. B., Filho, J. S. V., Pereira, L. S., Teixeira, J. L., and Lanna, A. E.: Multi-scale modeling for water resources planning and management in rural basins, Agric. Water Manage., 77, 4–20, 2005.
Zarghami, M. and Hajykazemian, H.: Urban water resources planning by using a modified particle swarm optimization algorithm, Resour. Conserv. Recycling, 70, 1–8, 2013
Zhang, Y. M., Huang, G. H., and Zhang, X. D.: Inexact de Novo programming for water resources systems planning, Eur. J. Oper. Res., 199, 531–541, 2009.
