Stochastic Generation of Streamflow Time Series
Publication: Journal of Hydrologic Engineering
Volume 23, Issue 10
Abstract
This paper proposes, systematizes, and validates a methodology for stochastically generating streamflow time series at virtually any time scale. Starting from deseasonalized data (i.e., observed series removed of their periodicity), the proposed methodology works by sequentially sampling each new streamflow value from a joint probability density function (PDF) conditioned by the previously generated values. This joint PDF is obtained directly from the observed data, and it represents the probability distribution and probabilistic dependency between consecutive streamflow values. An example application of the series generation methodology was developed based on daily streamflow data from Portugal. The proposed methodology’s results showed good agreement between the observed and generated PDFs. Generated series display less than 10% and 25% deviation, respectively, in terms of the means and standard deviation (for the 0th, 1st, and 2nd order) and the serial autocorrelation, from the observed series. This provides strong evidence for the methodology’s capability for reproducing the streamflow’s autocorrelation structure.
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Acknowledgments
The present work has been developed under a scholarship funded by the Fundação para a Ciência e Tecnologia, of Portugal, with the scholarship reference number PD/BI/113799/2015.
References
Beckers, F., M. Noack, and S. Wieprecht. 2016. “Reliability analysis of a 2D sediment transport model: An example of the lower river Salzach.” In Proc., 13th Int. Symp. on River Sedimentation. London: Taylor & Francis.
Chatfield, C. 2016. The analysis of time series: An introduction. Boca Raton, FL: CRC Press.
Chen, X. Y., K. W. Chau, and A. O. Busari. 2015. “A comparative study of population-based optimization algorithms for downstream river flow forecasting by a hybrid neural network model.” Eng. Appl. Artif. Intell. 46 (Oct): 258–268. https://doi.org/10.1016/j.engappai.2015.09.010.
Dolgos, D., H. Meier, A. Schenk, and B. Witzigmann. 2012. “Full-band Monte Carlo simulation of high-energy carrier transport in single photon avalanche diodes with multiplication layers made of InP, InAIAs and GaAs.” J. Appl. Phys. 111 (10): 104508. https://doi.org/10.1063/1.4717729.
Fisher, N. I., and P. Switzer. 2001. “Graphical assessment of dependence.” Am. Stat. 55 (3): 233–239. https://doi.org/10.1198/000313001317098248.
Genest, C., and J.-C. Boies. 2003. “Detecting dependence with Kendall plots.” Am. Stat. 57 (4): 275–284. https://doi.org/10.1198/0003130032431.
Gentle, J. E. 2003. Random number generation and Monte Carlo methods. 2nd ed. New York: Springer.
Geweke, J. 1989. “Bayesian inference in econometric models using Monte Carlo integration.” Econometrica 57 (6): 1317–1339. https://doi.org/10.2307/191371010.2307/1913710.
Grimaldi, S. 2004. “Linear parametric models applied to daily hydrological series.” J. Hydrol. Eng. 9 (5): 383–391. https://doi.org/10.1061/(ASCE)1084-0699(2004)9:5(383).
Jia, Y., and T. B. Culver. 2006. “Bootstrapped artificial neural networks for synthetic flow generation with a small data sample.” J. Hydrol. 331 (3–4): 580–590. https://doi.org/10.1016/j.jhydrol.2006.06.005.
Kalra, A., and S. Ahmad. 2011. “Evaluating changes and estimating seasonal precipitation for the Colorado River Basin using a stochastic nonparametric disaggregation technique.” Water Resour. Res. 47 (5): W05555. https://doi.org/10.1029/2010WR009118.
Lall, U., and A. Sharma. 1996. “A nearest neighbor bootstrap for resampling hydrologic time series.” Water Resour. Res. 32 (3): 679–693. https://doi.org/10.1029/95WR02966.
Lee, T., and J. D. Salas. 2011. “Copula-based stochastic simulation of hydrological data applied to the Nile River flows.” Hydrol. Res. 42 (4): 318–330. https://doi.org/10.2166/nh.2011.085.
Lettenmaier, D. P. 1984. “Synthetic streamflow forecast generation.” J. Hydraul. Eng. 110 (3): 277–289. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:3(277).
Loucks, D. P., and E. Van Beek. 2005. Water resources systems planning and management: An introduction to methods, models and applications. Paris: UNESCO.
McNeil, B. J. 1985. “Probabilistic sensitivity analysis using Monte Carlo simulation: A practical approach.” Med. Decis. Making 5 (2): 157–177. https://doi.org/10.1177/0272989X8500500205.
Morway, E. D., R. G. Niswonger, and E. Triana. 2016. “Toward improved simulation of river operations through integration with a hydrologic model.” Environ. Modell. Software 82 (May): 255–274. https://doi.org/10.1016/j.envsoft.2016.04.018.
Musa, J. J. 2013. “Stochastic modelling of Shiroro river stream flow process.” Am. J. Eng. Res. 2 (6): 49–54.
Niederreiter, H. 2010. “Quasi-Monte Carlo methods.” In Encyclopedia of quantitative finance, edited by R. Cont. New York: Wiley.
Nowak, K., J. Prairie, and B. Rajagopalan. 2008. Development of stochastic flow sequences based on observed data. Washington, DC: Allen Institute.
Papadrakakis, M., V. Papadopoulos, and N. D. Lagaros. 1996. “Structural reliability of elastic-plastic structures using neural networks and Monte Carlo simulation.” Comput. Methods Appl. Mech. Eng. 136 (1–2): 145–163. https://doi.org/10.1016/0045-7825(96)01011-0.
Portela, M. M., M. Zeleñákpvá, A. T. Silva, and A. C. Santos. 2017. Obtenção de Séries Sintéticas de Escoamentos Diários por Desagregação Direta de Escoamentos Anuais. Silusba: Porto, Portugal.
Prairie, J., B. Rajagopalan, U. Lall, and T. Fulp. 2007. “A stochastic nonparametric technique for space-time disaggregation of streamflows.” Water Resour. Res. 43 (3): W03432. https://doi.org/10.1029/2005WR004721.
Scott, D. W. 2015. Multivariate density estimation: Theory, practice, and visualization. 2nd ed. New York: Wiley.
Sirangelo, B., T. Caloiero, R. Coscarelli, and E. Ferrari. 2017. “A stochastic model for the analysis of maximum daily temperature.” Theor. Appl. Climatol. 130 (1–2): 275–289. https://doi.org/10.1007/s00704-016-1879-6.
Smith, R. E., and R. H. B. Hebbert. 1979. “A Monte Carlo analysis of the hydrologic effects of spatial variability of infiltration.” Water Resour. Res. 15 (2): 419–429. https://doi.org/10.1029/WR015i002p00419.
Srinivas, V. V., and K. Srinivasan. 2001. “Post-blackening approach for modeling periodic streamflows.” J. Hydrol. 241 (3–4): 221–269. https://doi.org/10.1016/S0022-1694(00)00363-2.
Srinivas, V. V., and K. Srinivasan. 2005. “Hybrid moving block bootstrap for stochastic simulation of multi-site multi-season streamflows.” J. Hydrol. 302 (1–4): 307–330. https://doi.org/10.1016/j.jhydrol.2004.07.011.
Tiwari, K. M., and C. Chatterjee. 2010. “Development of an accurate and reliable hourly flood forecasting model using wavelet–bootstrap–ANN (WBANN) hybrid approach.” J. Hydrol. 394 (3–4): 458–470. https://doi.org/10.1016/j.jhydrol.2010.10.001.
Trivedi, P. K., and D. M. Zimmer. 2007. “Copula modelling: An introduction for practitioners.” Found. Trends Econometrics 1 (1): 1–111. https://doi.org/10.1561/0800000005.
Wang, W., Y. Li, and S. Hu. 2011. “Wavelet transform method for synthetic generation of daily streamflow.” Water Resour. Manage. 25 (1): 41–57. https://doi.org/10.1007/s11269-010-9686-9.
Wang, W. C., K. W. Chau, D. M. Xu, L. Qiu, and C. C. Liu. 2017. “The annual maximum flood peak discharge forecasting using Hermite projection pursuit regression with SSO and LS method.” Water Resour. Manage. 31 (1): 461–477. https://doi.org/10.1007/s11269-016-1538-9.
You, G. J.-Y., B.-H. Thum, and F.-H. Lin. 2014. “The examination of reproducibility in hydro-ecological characteristics by daily synthetic flow models.” J. Hydrol. 511: 904–919. https://doi.org/10.1016/j.jhydrol.2014.02.047.
Yurekli, K., and A. Kurunc. 2005. “Performance of stochastic approaches in generating low streamflow data for drought analysis.” J. Spatial Hydrol. 5 (1): 20–32.
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©2018 American Society of Civil Engineers.
History
Received: Dec 6, 2017
Accepted: Apr 25, 2018
Published online: Aug 1, 2018
Published in print: Oct 1, 2018
Discussion open until: Jan 1, 2019
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