Comparison between Deseasonalized Models for Monthly Streamflow Generation in a Hurst–Kolmogorov Process Framework
Publication: Journal of Hydrologic Engineering
Volume 22, Issue 4
Abstract
The Hurst–Kolmogorov (HK) behavior in geophysical series is the product of fluctuations occurring simultaneously at several time scales. In streamflow time series, the clustering of similar events characterizes this behavior and brings forth the peculiarly persistent structure of such series. Because the Hurst exponent expresses the intensity of the HK behavior in time series, it is essential to preserve it in modeling hydrological series. This paper addresses an approach for multisite monthly streamflow generation in a HK framework. A deseasonalized symmetric moving average (SMAD) model is proposed, in which the seasonal components are removed from the streamflow series prior to their submission to the model. A case study applied at six gauging stations in the Iguazu River Basin, southern Brazil, is presented. SMAD synthetic series are compared with a multisite contemporaneous autoregressive integrated moving average (CARIMA) model. The results show that both models exhibited similar performance regarding marginal distribution statistics. However, the SMAD model provided a more precise reproduction of the individual persistence structures and cross-correlations among sites. It also generated estimates with higher uncertainty.
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Acknowledgments
The authors would like to kindly thank the editor and the anonymous reviewers for the invaluable criticism, suggestions, and further contributions.
References
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. Contr., 19(6), 716–723.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (2008). Time series analysis forecasting and control, 4th Ed., Wiley, Hoboken, NJ.
Camacho, F., McLeod, A. I., and Hipel, K. W. (1987). “Multivariate contemporaneous ARMA model with hydrological applications.” Stochastic Hydrol. Hydraul., 1(2), 141–154.
Detzel, D. H. M., and Mine, M. R. M. (2014). “Trends in hydrological series: Methods and application.” Proc., 11th Int. Conf. on Hydroscience and Engineering, Bundesanstalt für Wasserbau, Lehfeldt & Kopmann, Hamburg, Germany.
Eichner, J. F., Kantelhardt, J. W., Bunde, A., and Havlin, S. (2011). “The statistics of return intervals, maxima, and centennial events under the influence of long-term correlations.” Extremis: Disruptive events and trends in climate and hydrology, J. Kropp and H. J. Schellnhuber, eds., Springer, Berlin.
Fatichi, S., Barbosa, S. M., Caporali, E., and Silva, M. E. (2009). “Deterministic versus stochastic trends: Detection and challenges.” J. Geophys. Res., 114, D18121.
Ghanbarpour, M. R., Abbaspour, K. C., Jalalvand, G., and Moghaddam, G. A. (2010). “Stochastic modeling of surface stream flow at different time scales: Sangsoorakh karst basin, Iran.” J. Cave Karst Stud., 72(1), 1–10.
Grimm, A. M., Ferraz, S. E. T., and Gomes, J. (1998). “Precipitation anomalies in southern Brazil associated with El Niño and La Niña events.” J. Clim, 11(11), 2863–2880.
Guimarães, R. C., and Santos, E. G. (2011). “Principles of stochastic generation of hydrologic time series for reservoir planning and design: Case study.” J. Hydrol. Eng., 891–898.
Haltiner, J. P., and Salas, J. D. (1988). “Development and testing of a multivariate, seasonal ARMA(1, 1) model.” J. Hydrol., 104(1–4), 247–272.
Hamed, K. H. (2009). “Enhancing the effectiveness of prewhitening in trend analysis of hydrologic data.” J. Hydrol., 368(1-4), 143–155.
Hao, Z., and Singh, V. P. (2011). “Single-site monthly streamflow simulation using entropy theory.” Water Resour. Res., 47(9), W09528.
Hipel, K. W., and McLeod, A. I. (1994). “Contemporaneous autoregressive moving-average models.” Time series modelling of water resources and environmental systems, Elsevier, Amsterdam, Netherlands.
Kirsch, B. R., Characklis, G. W., and Zeff, H. B. (2013). “Evaluating the impact of alternative hydro-climate scenarios on transfer agreements: A practical improvement for generating synthetic streamflows.” J. Water Resour. Plan. Manag., 396–406.
Kleiber, W., Katz, R. W., and Rajagopalan, B. (2012). “Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes.” Water Resour. Res., 48(1), W01523.
Klemeš, V. (1974). “The Hurst phenomenon: A puzzle?” Water Resour. Res., 10(4), 675–688.
Koutsoyiannis, D. (2000). “A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series.” Water Resour. Res., 36(6), 1519–1533.
Koutsoyiannis, D. (2002). “The Hurst phenomenon and fractional Gaussian noise made easy.” Hydrol. Sci., 47(4), 573–595.
Koutsoyiannis, D. (2003). “Climate change, the Hurst phenomenon, and hydrological statistics.” Hydrol. Sci., 48(1), 3–24.
Koutsoyiannis, D. (2006). “Nonstationarity versus scaling in hydrology.” J. Hydrol., 324(1–4), 239–254.
Koutsoyiannis, D. (2011). “Hurst-Kolmogorov dynamics and uncertainty.” J. Am. Water Resour. Assoc., 47(3), 481–495.
Koutsoyiannis, D. (2013). “Hydrology and change.” Hydrol. Sci. J., 58(6), 1177–1197.
Koutsoyiannis, D. (2016). “Generic and parsimonious stochastic modelling for hydrology and beyond.” Hydrol. Sci. J., 61(2), 225–244.
Koutsoyiannis, D., and Montanari, A. (2007). “Statistical analysis of hydroclimatic time series: Uncertainty and insights.” Water Resour. Res., 43(5), 1–9.
Koutsoyiannis, D., and Montanari, A. (2015). “Negligent killing of scientific concepts: The stationarity case.” Hydrol. Sci. J., 60(7-8), 1174–1183.
Lall, U., and Sharma, A. (1996). “A nearest neighbor bootstrap for resampling hydrologic time series.” Water Resour. Res., 32(3), 679–693.
Langousis, A., and Koutsoyiannis, D. (2006). “A stochastic methodology for generation of seasonal time series reproducing overyear scaling behaviour.” J. Hydrol., 322(1-4), 138–154.
Li, W., and McLeod, A. (1981). “Distribution of the residual autocorrelations in multivariate ARMA time series models.” J. R. Stat. Soc., 43(2), 231–239.
Mandelbrot, B. B., and Wallis, J. R. (1968). “Noah, Joseph, and operational hydrology.” Water Resour. Res. 4(5), 909–918.
Mandelbrot, B. B., and Wallis, J. R. (1969a). “Computer experiments with fractional Gaussian noises: Part 1, averages and variances.” Water Resour. Res., 5(1), 228–241.
Mandelbrot, B. B., and Wallis, J. R. (1969b). “Computer experiments with fractional Gaussian noises. Part 2: Rescaled ranges and spectra.” Water Resour. Res., 5(1), 242–259.
Mandelbrot, B. B., and Wallis, J. R. (1969c). “Computer experiments with fractional Gaussian noises. Part 3: Mathematical appendix.” Water Resour. Res., 5(1), 260–267.
Matalas, N. C. (1967). “Mathematical assessment of synthetic hydrology.” Water Resour. Res., 3(4), 937–945.
Mondal, M. S., and Wasimi, S. A. (2006). “Generating and forecasting monthly flows of the Ganges River with PAR model.” J. Hydrol., 323(1–4), 41–56.
Ndiritu, J. (2011). “A variable-length block bootstrap method for multi-site synthetic streamflow generation.” Hydrol. Sci. J., 56(3), 362–379.
Peel, M. C., Finlayson, B. L., and McMahon, T. A. (2007). “Updated world map of the Köppen-Geiger climate classification.” Hydrol. Earth Syst. Sci., 11(5), 1633–1644.
Salas, J. D., and Lee, T. (2010). “Nonparametric simulation of single-site seasonal streamflows.” J. Hydrol. Eng., 284–296.
Schwartz, G. (1978). “Estimating the dimension of a model.” Ann. Math. Stat., 6(2), 461–464.
Şengül, S., and Can, I. (2011). “Stochastic modelling of mean monthly flows of Karasu River, in Turkey.” Water Environ. J., 25(1), 31–39.
Serinaldi, F., and Kilsby, C. G. (2014). “Simulating daily rainfall fields over large areas for collective risk estimation.” J. Hydrol., 512, 285–302.
Serinaldi, F., and Kilsby, C. G. (2015). “Stationarity is undead: Uncertainty dominates the distribution of extremes.” Adv. Water Resour., 77, 17–36.
Serinaldi, F., and Kilsby, C. G. (2016a). “Irreversibility and complex network behavior of stream flow fluctuations.” Phys. A Stat. Mech. Appl., 450, 585–600.
Serinaldi, F., and Kilsby, C. G. (2016b). “Understanding persistence to avoid under-estimation of collective regional flood risk.” Water, 8(4), 152.
Shapiro, S. S., and Wilk, M. B. (1965). “An analysis of variance test for normality (complete samples).” Biometrika, 52(3-4), 591–611.
Shittu, O. I., and Asemota, M. J. (2009). “Comparison of criteria for estimating the order of autoregressive process: A Monte Carlo approach.” Eur. J. Oper. Res., 30(3), 409–416.
Srivastav, R. K., and Simonovic, S. P. (2014). “An analytical procedure for multi-site, multi-season streamflow generation using maximum entropy bootstrapping.” Environ. Model. Soft., 59, 59–75.
Srivastav, R. K., Srinivasan, K., and Sudheer, K. P. (2011). “Simulation-optimization framework for multi-season hybrid stochastic models.” J. Hydrol., 404(3–4), 209–225.
Stedinger, J. R., Lettenmaier, D. P., and Vogel, R. M. (1985). “Multisite ARMA(1, 1) and disaggregation models for annual streamflow generation.” Water Resour. Res., 21(4), 497–509.
Thomas, H. A., and Fiering, M. B. (1962). “Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation.” Design of water resources systems, A. Maass, ed., Harvard University Press, Cambridge, MA.
Tyralis, H., and Koutsoyiannis, D. (2011). “Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process.” Stochastic Environ. Res. Risk Assess., 25(1), 21–33.
Villarini, G., Seo, B. C., Serinaldi, F., and Krajewski, W. F. (2014). “Spatial and temporal modeling of radar rainfall uncertainties.” Atmos. Res., 135-136, 91–101.
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Published In
Journal of Hydrologic Engineering
Volume 22 • Issue 4 • April 2017
Copyright
©2016 American Society of Civil Engineers.
History
Received: May 16, 2016
Accepted: Sep 20, 2016
Published online: Nov 30, 2016
Published in print: Apr 1, 2017
Discussion open until: Apr 30, 2017
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