Abstract
The design of optimal hydrometric networks is an important starting point in water resources planning and management. Redundant or inappropriate networks may require unnecessary monitoring costs, while a sparse network may cause a lack of understanding of the process being monitored. Many studies employ information theory, which uses the Shannon entropy, as a measure of the information to design optimal hydrometric networks measuring various hydrologic parameters, such as streamflow and precipitation. The majority of entropy application methods in hydrometric network design have had two common objectives, i.e., maximizing joint entropy and minimizing total correlation. However, it is still unclear what data lengths should be adequate to properly use the entropy approach to network design and how the data lengths affect the entropy values. In this study, four different data lengths (e.g., 5, 10, 15, and 20 years) of daily time series are used to determine the optimal streamflow and precipitation networks using entropy theory coupled with multiobjective optimization. The spatial distributions of the optimal monitoring locations appeared similarly for each data length. Specifically, the hot-spots where the selection likelihood from optimization results is high were not significantly changed; this is more obvious when the data length of daily time series was 10 years or greater. Additionally, the joint entropy and total correlation of the optimal networks were calculated from 10 days to 20 years with a 10-day increment. The joint entropy increased significantly during the first 5 years and then gradually increased without significant change after 10 years. Similarly, the total correlation stabilized after 5 years of daily time series lengths with no major change after 10 years. Therefore, it is recommended to use at least 10 years of data for information theory–based hydrometric network design when using daily time series.
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Acknowledgments
This research was supported by the Natural Science and Engineering Research Council (NSERC) of Canada, Water Survey of Canada, Environment Canada, BC-Hydro and Hydro-Quebec. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calcul Canada, and by datasets from Environment Canada, Water Survey Canada, BC-Hydro, and Credit Valley Conservation, Region of Peel. The authors acknowledge Dr. Joshua Kollat (Penn State University) who developed the , and provided the source codes.
References
Alfonso, L., He, L., Lobbrecht, A., and Price, R. (2013). “Information theory applied to evaluate the discharge monitoring network of the Magdalena River.” J. Hydroinf., 15(1), 211–228.
Alfonso, L., Lobbrecht, A., and Price, R. (2010a). “Information theory-based approach for location of monitoring water level gauges in polders.” Water Resour. Res., 46(3), 1–14.
Alfonso, L., Lobbrecht, A., and Price, R. (2010b). “Optimization of water level monitoring network in polder systems using information theory.” Water Resour. Res., 46(12), 1–13.
Alfonso, L., and Price, R. (2012). “Coupling hydrodynamic models and value of information for designing stage monitoring networks.” Water Resour. Res., 48(8), W08530.
Alfonso, L., Ridolfi, E., Gaytan-Aguilar, S., Napolitano, F., and Russo, F. (2014). “Ensemble entropy for monitoring network design.” Entropy, 16(3), 1365–1375.
Amorocho, J., and Espildora, B. (1973). “Entropy in the assessment of uncertainty in hydrologic systems and models.” Water Resour. Res., 9(6), 1511–1522.
Boiten, W. (2000). Hydrometry, A.A. Balkema, Rotterdam, Netherlands.
Davis, D. R., Duckstein, L., and Krzysztofowicz, R. (1979). “The worth of hydrologic data for nonoptimal decision making.” Water Resour. Res., 15(6), 1733–1742.
Environment Canada. (2015). “Water quantity monitoring, water survey of Canada.” ⟨https://www.ec.gc.ca/rhc-wsc/⟩ (Feb. 7, 2015).
Fahle, M., Hohenbrink, T. L., Dietrich, O., and Lischeid, G. (2015). “Temporal variability of the optimal monitoring setup assessed using information theory.” Water Resour. Res., 51(9), 7723–7743.
Glahn, H. R., and Lawrence, B. (2002). “GRIB2: The WMO standard for the transmission of gridded data—Current status and NWS plans.” Interactive Symp. on the Advanced Weather Interactive Processing System, American Meteor Society, Orlando, FL, 267–269.
Government of Canada. (2015a). “10km resolution numerical data of the regional deterministic prediction system (RDPS)—GRIB2 format.” ⟨http://weather.gc.ca/grib/grib2_reg_10km_e.html⟩ (Feb. 9, 2015).
Government of Canada. (2015b). “Climate.” ⟨http://climate.weather.gc.ca/⟩ (Feb. 8, 2015).
Harmancioglu, N. B., and Alpaslan, N. (1992). “Water quality monitoring network design: A problem of multi-objective decision making.” J. Am. Water Resour. Assoc., 28(1), 179–192.
Herschy, R. W. (1999). Hydrometry: Principles and practice, Wiley, West Sussex, U.K.
Husain, T. (1989). “Hydrologic uncertainty measure and network design.” J. Am. Water Resour. Assoc., 25(3), 527–534.
Jaynes, E. T. (1982). “On the rationale of maximum-entropy methods.” Proc. IEEE, 70(9), 939–952.
Kollat, J. B., Reed, P. M., and Kasprzyk, J. R. (2008). “A new epsilon-dominance hierarchical Bayesian optimization algorithm for large multiobjective monitoring network design problems.” Adv. Water Resour., 31(5), 828–845.
Kornelsen, K. C., and Coulibaly, P. (2015). “Design of an optimal soil moisture monitoring network using SMOS retrieved soil moisture.” IEEE Trans. Geosci. Remote Sens., 53(7), 3950–3959.
Kraskov, A., Stögbauer, H., Andrzejak, R. G., and Grassberger, P. (2005). “Hierarchical clustering using mutual information.” Europhys. Lett., 70(2), 278–284.
Krstanovic, P. F., and Singh, V. P. (1992). “Evaluation of rainfall networks using entropy. I: Theoretical development.” Water Resour. Manage., 6(4), 279–293.
Langbein, W. B. (1979). “Overview of conference on hydrologic data networks.” Water Resour. Res., 15(6), 1867–1871.
Laumanns, M., Thiele, L., Deb, K., and Zitzler, E. (2002). “Combining convergence and diversity in evolutionary multiobjective optimization.” Evol. Comput., 10(3), 263–282.
Leach, J. M., Kornelsen, K. C., Samuel, J., and Coulibaly, P. (2015). “Hydrometric network design using streamflow signatures and indicators of hydrologic alteration.” J. Hydrol., 529(3), 1350–1359.
McGill, W. J. (1954). “Multivariate information transmission.” Psychometrika, 19(2), 97–116.
Mishra, A. K., and Coulibaly, P. (2009). “Developments in hydrometric network design: A review.” Rev. Geophys., 47(2), RG2001.
Mishra, A. K., and Coulibaly, P. (2010). “Hydrometric network evaluation for Canadian watersheds.” J. Hydrol., 380(3–4), 420–437.
Moss, M. E. (1979). “Some basic considerations in the design of hydrologic data networks.” Water Resour. Res., 15(6), 1673–1676.
Moss, M. E., and Karlinger, M. R. (1974). “Surface water network design by regression analysis simulation.” Water Resour. Res., 10(3), 427–433.
Natural Resources Canada. (2015). “Regional, national and international climate modeling.” ⟨http://cfs.nrcan.gc.ca/projects/3⟩ (Jan. 14, 2015).
Pelikan, M. (2002). “Bayesian optimization algorithm: From single level to hierarchy.” Ph.D. thesis, Univ. of Illinois at Urbana-Champaign, Urbana, IL.
Pilon, P. J., Yuzyk, T. R., Hale, R. A., and Day, T. J. (1996). “Challenges facing surface water monitoring in Canada.” Can. Water Resour. J., 21(2), 157–164.
Samuel, J., Coulibaly, P., and Kollat, J. B. (2013). “CRDEMO: Combined regionalization and dual entropy-multiobjective optimization for hydrometric network design.” Water Resour. Res., 49(12), 8070–8089.
Samuel, J., Coulibaly, P., and Metcalfe, R. A. (2011). “Estimation of continuous streamflow in ontario ungauged basins: Comparison of regionalization methods.” J. Hydrol. Eng., 447–459.
Shannon, C. E. (1948). “A mathematical theory of communication.” Bell Syst. Tech. J., 27(3), 379–423.
Singh, V. P. (1997). “The use of entropy in hydrology and water resources.” Hydrol. Processes, 11(6), 587–626.
Stedinger, J. R., and Tasker, G. D. (1985). “Regional hydrologic analysis. 1: Ordinary, weighted, and generalized least squares compared.” Water Resour. Res., 21(9), 1421–1432.
U.S. Geological Survey. (1999). “Streamflow information for the next century: A plan for the national streamflow information program of the U.S. Geological Survey.”, Denver.
Watanabe, S. (1960). “Information theoretical analysis of multivariate correlation.” IBM J. Res. Dev., 4(1), 66–82.
Weijs, S. V., van de Giesen, N., and Parlange, M. B. (2013). “Data compression to define information content of hydrological time series.” Hydrol. Earth Syst. Sci., 17(8), 3171–3187.
Wilde, F. D. (2005). “Preparations for water sampling, version 2.0.” Chapter A1, National field manual for the collection of water-quality data: U.S. geological survey, techniques of water-resources investigations book 9, U.S. Geological Survey, Reston, VA.
World Meteorological Organization. (2003). “Introduction to GRIB edition 1 and GRIB edition 2.” Geneva.
World Meteorological Organization. (2008). “Guide to hydrological practices. Volume I: Hydrology—From measurement to hydrological information.”, Geneva.
Yang, Y., and Burn, D. H. (1994). “An entropy approach to data collection network design.” J. Hydrol., 157(1–4), 307–324.
Yoo, C., Jung, K., and Lee, J. (2008). “Evaluation of rain gauge network using entropy theory: Comparison of mixed and continuous distribution function applications.” J. Hydrol. Eng., 226–235.
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Published In
Journal of Hydrologic Engineering
Volume 22 • Issue 7 • July 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Aug 11, 2015
Accepted: Dec 1, 2016
Published online: Feb 22, 2017
Published in print: Jul 1, 2017
Discussion open until: Jul 22, 2017
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