Articles | Volume 16, issue 3
https://doi.org/10.5194/hess-16-873-2012
© Author(s) 2012. 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-16-873-2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions
W. J. Vanhaute
Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, 9000 Ghent, Belgium
S. Vandenberghe
Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, 9000 Ghent, Belgium
K. Scheerlinck
Department of Mathematical modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, 9000 Ghent, Belgium
B. De Baets
Department of Mathematical modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, 9000 Ghent, Belgium
N. E. C. Verhoest
Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, 9000 Ghent, Belgium
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
A dual-inexact fuzzy stochastic model for water resources management and non-point source pollution mitigation under multiple uncertainties
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
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
C. Dong, Q. Tan, G.-H. Huang, and Y.-P. Cai
Hydrol. Earth Syst. Sci., 18, 1793–1803, https://doi.org/10.5194/hess-18-1793-2014, https://doi.org/10.5194/hess-18-1793-2014, 2014
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
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
Aarts, E. H. L. and Van Laarhoven, P. J. M.: Statistical cooling – A general-approach to combinatorial optimization problems, Philips J. Res., 40, 193–226, 1985.
Aarts, E. H. L. and Van Laarhoven, P. J. M.: Simulated {A}nnealing: {T}heory and {A}pplications, D. Reidel, Dordrecht, 1987.
Boughton, W. and Droop, O.: Continuous simulation for design flood estimation – a review, Environ. Modell. Softw., 18, 309–318, 2003.
Box, M. J.: A new method of constrained optimization and a comparison with other methods, Comput. J., 8, 42–52, 1965.
Burton, A., Kilsby, C., Fowler, H., Cowpertwait, P., and O'Connell, P.: RainSim: A spatial-temporal stochastic rainfall modelling system, Environ. Modell. Softw., 23, 1356–1369, 2008.
Cameron, D., Beven, K., and Tawn, J.: An evaluation of three stochastic rainfall models, J. Hydrol., 228, 130–149, 2000.
Cameron, D., Beven, K., and Tawn, J.: Modelling extreme rainfall using a modified random pulse {B}artlett-{L}ewis stochastic rainfall model (with uncertainty), Adv. Water Resour., 24, 203–211, 2001.
Cardoso, M. F., Salcedo, R. L., and De Azevedo, S. F.: The {S}implex-{S}imulated {A}nnealing approach to continuous non-linear optimization, Comput. Chem. Eng., 20, 1065–1080, 1996.
Chandler, R.: Moment-based inference for stochastic-mechanistic models, internal report no. 7, DEFRA project: Improved methods for national spatial-temporal rainfall and evaporation modelling for BSM, 2004.
Cowpertwait, P. S. P.: Further developments of the {N}eyman-{S}cott clustered point process for modeling rainfall, Water Resour. Res., 27, 1431–1438, 1991.
Cowpertwait, P. S. P.: A generalized point process model for rainfall, P. Roy. Soc. Lond. A Mat., 447, 23–37, 1994.
Cowpertwait, P. S. P.: A {P}oisson-cluster model of rainfall : high-order moments and extreme values, P. Roy. Soc. Lond. A Mat., 454, 885–898, 1998.
Cowpertwait, P. S. P.: Mixed rectangular pulses models of rainfall, Hydrol. Earth Syst. Sci., 8, 993–1000, https://doi.org/10.5194/hess-8-993-2004, 2004.
Cowpertwait, P. S. P., Isham, V., and Onof, C.: Point process models of rainfall: developments for fine-scale structure, P. Roy. Soc. Lond. A Mat., 463, 2569–2587, 2007.
De Jongh, I. L. M., Verhoest, N. E. C., and De Troch, F. P.: Analysis of a 105-year time series of precipitation observed at {U}ccle, {B}elgium, Int. J. Climatol., 26, 2023–2039, 2006.
Duan, Q., Sorooshian, S., and Gupta, V. K.: Optimal use of the SCE-UA global optimization method for calibrating watershed models, J. Hydrol., 158, 265–284, 1994.
Engelbrecht, A.: Fundamentals of Computational Swarm Intelligence, John Wiley, London, 2006.
Entekhabi, D., Rodriguez-Iturbe, I., and Eagleson, P. S.: Probabilistic representation of the temporal rainfall process by a {M}odified {N}eyman-{S}cott {R}ectangular {P}ulses {M}odel: {P}arameter estimation and validation, Water Resour. Res., 25, 295–302, 1989.
Gibbons, J. D.: Nonparametric statistical inference, Marcel Dekker, New York, 1985.
Gyasi-Agyei, Y. and Willgoose, G.: Generalisation of a hybrid model for point rainfall, J. Hydrol., 219, 218–224, 1999.
Hansen, L. P.: Large properties of generalized method of moments estimators, Econometrica, 50, 1029–1054, as cited by \citet{kaczmarska11}, 1982.
Hartig, F., Calabrese, J. M., Reineking, B., Wiegand, T., and Huth, A.: Statistical inference for stochastic simulation models - theory and application, Ecol. Lett., 14, 816–827, 2011.
Heneker, T. M., Lambert, M. F., and Kuczera, G.: A point rainfall model for risk-based design, J. Hydrol., 247, 54–71, 2001.
Jiang, M., Luo, Y. P., and Yang, S. Y.: Stochastic convergence analysis and parameter selection of the standard {P}article {S}warm {O}ptimization algorithm, Inform. Process. Lett., 102, 8–16, https://doi.org/10.1016/j.ipl.2006.10.005, 2007.
Kaczmarska, J.: Further development of {B}artlett-{L}ewis models for fine-resolution rainfall, Tech. Rep., Department of Statistical Science, University College London, 2011.
Kavvas, M. L. and Delleur, J. W.: A stochastic cluster model of daily rainfall sequences, Water Resour. Res., 17, 1151–1160, 1981.
Kennedy, J. and Eberhart, R.: Particle swarm optimization, in: Proceedings of the IEEE International conference on neural networks, IV, 1942–1948, Piscataway, NJ: IEEE Service Center, 1995.
Khaliq, M. N. and Cunnane, C.: Modelling point rainfall occurences with the {M}odified {B}artlett-{L}ewis {R}ectangular {P}ulses {M}odel, J. Hydrol., 180, 109–138, 1996.
Kirkpatrick, S.: Optimization by simulated annealing – {Q}uantitative studies, J. Stat. Phys., 34, 975–986, 1984.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P.: Optimization by {S}imulated {A}nnealing, Science, 220, 671–680, 1983.
Kruskal, W. H. and Wallis, W. A.: Use of ranks in one-criterion variance analysis, J. Am. Stat. Assoc., 47, 584–621, 1952.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E.: Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087–1092, 1953.
Nelder, J. A. and Mead, R.: A simplex-method for function minimization, Comput. J., 7, 308–313, 1965.
Obeysekera, J. T. B., Tabios III, G. Q., and Salas, J. D.: On parameter estimation of temporal rainfall models, Water Resour. Res., 23, 1837–1850, 1987.
Onof, C. and Wheater, H. S.: Modelling of {B}ritish rainfall using a random parameter {B}artlett-{L}ewis {R}ectangular {P}ulse {M}odel, J. Hydrol., 149, 67–95, 1993.
Onof, C. and Wheater, H. S.: Improved fitting of the B}artlett-{L}ewis {R}ectangular {P}ulse {M}odel for hourly rainfall, Hydrolog. Sci., 39, 663–680, 1994{a.
Onof, C. and Wheater, H. S.: Improvements to the modeling of B}ritish rainfall using a modified random parameter {B}artlett-{L}ewis rectangular pulse model, J. Hydrol., 157, 177–195, 1994{b.
Press, W. H. and Teukolsky, S. A.: Simulated Annealing over continuous spaces, Computers in Physics, 5, 426, 1991.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes - The Art of Scientific Computing, Cambridge University Press, New York, 1986.
Rodriguez-Iturbe, I., Cox, D. R., and Isham, V.: Some models for rainfall based on stochastic point processes, P. Roy. Soc. Lond. A Mat., 410, 269–288, 1987{a}.
Rodriguez-Iturbe, I., Febres de Power, B., and Valdés, J. B.: Rectangular pulses point process models for rainfall: analysis of empirical data, J. Geophys. Res., 92, 9645–9656, 1987{b}.
Rodriguez-Iturbe, I., Cox, D. R., and Isham, V.: A point process model for rainfall: further developments, P. Roy. Soc. Lond. A Mat., 417, 283–298, 1988.
Scheerlinck, K., Pauwels, V. R. N., Vernieuwe, H., and De Baets, B.: Calibration of a water and energy balance model: {R}ecursive parameter estimation versus particle swarm optimization, Water Resour. Res., 45, W10422, https://doi.org/10.1029/2009WR008051, 2009.
Shi, Y. and Eberhart, R.: A modified particle swarm optimizer, in: Proceedings of the IEEE International Conference on Evolutionary Computation, 69–73, Piscataway, NJ: IEEE Press, 1998.
Smithers, J. C., Pegram, G. G. S., and Schulze, R. E.: Design rainfall in {S}outh {A}frica using {B}artlett-{L}ewis rectangular pulse rainfall models, J. Hydrol., 258, 83–99, 2002.
Spendley, W., Hext, G. R., and Himsworth, F. R.: Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation, Technometrics, 4, 441–461, 1962.
Trelea, I.: The {P}article {S}warm {O}ptimization algorithm: convergence analysis and parameter selection, Inform. Process. Lett., 85, 317–325, 2003.
Vandenberghe, S., Verhoest, N. E. C., Onof, C., and De Baets, B.: A comparative copula-based bivariate frequency analysis of observed and simulated storm events: A case study on Bartlett-Lewis modeled rainfall, Water Resour. Res., 47, W07529, https://doi.org/10.1029/2009WR008388, 2011.
Velghe, P. A., Troch, P. A., De Troch, F. P., and Van de Velde, J.: Evaluation of cluster-based rectangular pulses point process models for rainfall, Water Resour. Res., 30, 2847–2857, 1994.
Verhoest, N. E. C., Troch, P. A., and De Troch, F. P.: On the applicability of {B}artlett-{L}ewis rectangular pulses models in the modeling of design storms at a point, J. Hydrol., 202, 108–120, 1997.
Verhoest, N. E. C., Vandenberghe, S., Cabus, P., Onof, C., Meca-Figueras, T., and Jameleddine, S.: Are stochastic point rainfall models able to preserve extreme flood statistics?, Hydrol. Process., 24, 3439–3445, 2010.
Waymire, E. and Gupta, V.: The mathematical structure of rainfall representations. 1. A review of stochastic rainfall models, Water Resour. Res., 17, 1261–1272, 1981.
Wheater, H. S., Isham, V. S., Chandler, R. E., Onof, C. J., and Stewart, E. J.: Improved methods for national spatial-temporal rainfall and evaporation modelling for BSM, Tech. Rep. F2105/TR, Department for Environment, Food and Rural Affairs, London, 2006.
Wheater, H. S., Chandler, R. E., J., O. C., Isham, V. S., Bellone, E., Yang, C., Lekkas, D., Lourmas, G., and Segond, M.-L.: Spatial-temporal rainfall modelling for flood risk estimation, Stoch. Env. Res. Risk A., 19, 403–416, 2005.