Entropy Spectral Analyses for Groundwater Forecasting
Publication: Journal of Hydrologic Engineering
Volume 22, Issue 7
Abstract
Forecasting of monthly and annual groundwater levels is important for water resources management, irrigation, and assessment of climate change. This study employs entropy spectral analysis for forecasting monthly groundwater levels. For spectral analysis, the domain of consideration for defining entropy is the frequency domain, in which three types of entropies are known: Burg entropy, configurational entropy, and relative entropy. These entropies lead to three types of spectral analysis: (1) Burg entropy spectral analysis (BESA), (2) configurational entropy spectral analysis (CESA), and (3) relative entropy spectral analysis (RESA). BESA, CESA, and RESA are employed to analyze spectra and forecast monthly groundwater levels, and then they are compared to determine which spectral analysis method better forecasts the monthly groundwater level. Monthly and annual groundwater data were obtained from South Carolina to verify the three methods. Both monthly and annual groundwater level data showed significant decreasing trends at almost all stations. It was found that relative entropy yielded the highest resolution in determining the spectral density, while for simulating groundwater levels, all three methods fitted the observed values well. This was indicated by the average value of Nash-Sutcliffe efficiency (NSE) for BESA, CESA, and RESA being 0.69, 0.70, and 0.70, respectively.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research is supported by the Key Research Program of the Chinese Academy of Sciences (ZDRW-ZS-2016-6-4).
References
Barbe, D. E., Cruise, J. F., and Singh, V. P. (1994). “Derivation of a distribution for the piezometric head in groundwater flow using entropy.” Stochastic and statistical methods in hydrology and environmental engineering, K. W. Hipel, ed., Kluwer Academic Publishers, Dordrecht, Netherlands.
Box, G. E. P., and Jenkins, G. M. (1970). “Time series analysis: Forecasting and control.” Holden-Day series in time series analysis, Holden-Day, San Francisco, 553.
Burg, J. P. (1967). “Maximum entropy spectral analysis.” Proc., 37th Meeting of Society Exploration Geophysics, Oklahoma City, 34–41.
Burg, J. P. (1975). “Maximum entropy spectral analysis.” Ph.D. thesis, Stanford Univ., Standford, CA, 123.
Cui, H., and Singh, V. P. (2015). “Configurational entropy theory for streamflow forecasting.” J. Hydrol., 521(0), 1–17.
Cui, H., and Singh, V. P. (2016). “Minimum relative entropy theory for streamflow forecasting with frequency as a random variable.” Stoch. Env. Res. Risk A, 30(6), 1545–1563.
Frieden, B. R. (1972). “Restoring with maximum likelihood and maximum entropy.” J. Opt. Soc. Am., 62(4), 511–518.
Gull, S. F., and Daniell, G. J. (1978). “Image-reconstruction from incomplete and noisy data.” Nature, 272(5655), 686–690.
Jaynes, E. T. (1957a). “Information theory and statistical mechanics.1.” Phys Rev, 106(4), 620–630.
Jaynes, E. T. (1957b). “Information theory and statistical mechanics. 2.” Phys Rev, 108(2), 171–190.
Krstanovic, P. F., and Singh, V. P. (1991a). “A univariate model for long-term streamflow forecasting. 1: Development.” Stoch. Hydrol. Hydraul., 5(3), 173–188.
Krstanovic, P. F., and Singh, V. P. (1991b). “A univariate model for long-term streamflow forecasting. 2: Application.” Stoch. Hydrol. Hydraul., 5(3), 189–205.
Liefhebber, F., and Boekee, D. E. (1987). “Minimum information spectral-analysis.” Signal Process., 12(3), 243–255.
Mogheir, Y., de Lima, J. L. M. P., and Singh, V. P. (2004). “Characterizing the spatial variability of groundwater quality using the entropy theory. II: Case study from Gaza Strip.” Hydrol. Process., 18(13), 2579–2590.
Mogheir, Y., de Lima, J. L. M. P., and Singh, V. P. (2009). “Entropy and multi-objective based approach for groundwater quality monitoring network assessment and redesign.” Water Resour. Manage., 23(8), 1603–1620.
Mogheir, Y., Singh, V. P., and de Lima, J. L. M. P. (2006). “Spatial assessment and redesign of a groundwater quality monitoring network using entropy theory, Gaza Strip, Palestine.” Hydrogeol. J., 14(5), 700–712.
Nadeu, C. (1992). “Finite length cepstrum modeling—A simple spectrum estimation technique.” Signal Process., 26(1), 49–59.
Papademetriou, R. C. (1998). “Experimental comparison of two information-theoretic spectral estimators.” Signal Processing Proc., 1998, ICSP ‘98, 4th Int. Conf., Beijing, 141–144.
Shore, J. E. (1979). Minimum cross-entropy spectral analysis, Naval Research Laboratory, Washington, DC.
Shore, J. E. (1981). “Minimum cross-entropy spectral-analysis.” IEEE Trans. Acoust. Speech, 29(2), 230–237.
Singh, V., and Cui, H. (2015). “Entropy theory for streamflow forecasting.” Environ. Process., 2(3), 1–12.
Singh, V. P. (1997). “The use of entropy in hydrology and water resources.” Hydrol. Process., 11(6), 587–626.
Singh, V. P. (2011). “Hydrologic synthesis using entropy theory: Review.” J. Hydrol Eng., 421–433.
Singh, V. P., Jain, S. K., and Tyagi, A. (2007). “Entropy theory and its applications in risk analysis.” Risk and reliability analysis, 356–391.
Tzannes, M. A., Politis, D., and Tzannes, N. S. (1985). “A general method of minimum cross-entropy spectral estimation.” IEEE T. Acoust. Speech, 33(3), 748–752.
Woodbury, A. D., and Ulrych, T. J. (1993). “Minimum relative entropy—Forward probabilistic modeling.” Water Resour. Res., 29(8), 2847–2860.
Woodbury, A. D., and Ulrych, T. J. (1996). “Minimum relative entropy inversion: Theory and application to recovering the release history of a groundwater contaminant.” Water Resour. Res, 32(9), 2671–2681.
Woodbury, A. D., and Ulrych, T. J. (1998). “Minimum relative entropy and probabilistic inversion in groundwater hydrology.” Stoch. Hydrol. Hydraul., 12(5), 317–358.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 22 • Issue 7 • July 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: May 5, 2016
Accepted: Dec 7, 2016
Published online: Mar 3, 2017
Published in print: Jul 1, 2017
Discussion open until: Aug 3, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.