Abstract
Regional flood frequency (RFF) equations are statistical characterizations that, in their simplest form, show how peak discharge quantiles scale with drainage area. They remain separated from the physical processes that occur during flood-generating rainfall-runoff events. A physical understanding of RFF equations is a long-standing unsolved problem in hydrology. This study addresses this problem using a scaling framework. Two hypotheses are introduced that collectively state that scaling slopes of event peak discharges are on average equivalent to the mean scaling slope of annual peak quantiles; the later quantity refers to an average taken over a set of exceedance probabilities under consideration. To test these hypotheses, a nested mixed-effects linear (NMEL) model was developed that characterizes event-to-event variability in scaling relationships between stream discharge peaks and drainage area. The model leads to scaling relationships for event peak discharge quantiles and annual peak quantiles that are the basis for RFF equations. Because event-based scaling relationships can be connected to physical processes, the model provides a way of investigating whether quantile-based scaling relationships can be connected as well. The model was tested against data for 148 rainfall-runoff events from the Goodwin Creek Experimental Watershed (GCEW) located in the state of Mississippi. Test results support the NMEL model and the two hypotheses, but raise new questions that need to be addressed in future research.
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Acknowledgments
The authors are grateful to Radoslaw Goska of the Iowa Flood Center (IFC) for his help with figures. The lead author is also grateful to IIHR and IFC for providing support to work on this project. The National Science Foundation partially supported this research through grant EAR-1005311 to the University of Colorado and EAR-10007324 to NorthWest Research Associates. We thank the referees, Salvatore Grimaldi and William Farmer, for their insightful inputs that helped to improve this paper.
References
Ayalew, T. B., Krajewski, W. F., and Mantilla, R. (2014a). “Connecting the power-law scaling structure of peak-discharges to spatially variable rainfall and catchment physical properties.” Adv. Water Resour., 71, 32–43.
Ayalew, T. B., Krajewski, W. F., Mantilla, R., and Small, S. J. (2014b). “Exploring the effects of hillslope-channel link dynamics and excess rainfall properties on the scaling structure of peak-discharge.” Adv. Water Resour., 64(1), 9–20.
Benson, M. A. (1962). “Factors influencing the occurrence of floods in a humid region of diverse terrain.” U.S. Geological Survey, Washington, DC.
Benson, M. A. (1964). “Factors influencing the occurrence of floods in the southwest.” U.S. Geological Survey, Washington, DC.
Berman, S. M. (1964). “Limit theorems for the maximum term in stationary sequences.” Ann. Math. Stat., 35(2), 502–516.
Blackmarr, W. M. and the Channel and Watershed Processes Research Unit. (1995). “Documentation of hydrologic, geomorphic, and sediment transport measurements on the Goodwin Creek experimental watershed, northern Mississippi, for the period 1982–1993—Preliminary release.”, National Sedimentation Laboratory, Agricultural Research Service, U.S. Dept. of Agriculture, Oxford, MS.
Dawdy, D. R., Griffis, V. W., and Gupta, V. K. (2012). “Regional flood-frequency analysis: How we got here and where we are going.” J. Hydrol. Eng., 953–959.
Furey, P. R., and Gupta, V. K. (2007). “Diagnosing peak-discharge power laws observed in rainfall-runoff events in Goodwin Creek experimental watershed.” Adv. Water Resour., 30(11), 2387–2399.
Furey, P. R., Gupta, V. K., and Troutman, B. M. (2013). “A top-down model to generate ensembles of runoff from a large number of hillslopes.” Nonlinear Processes Geophys., 20(5), 683–704.
Gupta, V. K., Castro, S., and Over, T. M. (1996). “On scaling exponents of spatial peak flows from rainfall and river network geometry.” J. Hydrol., 187(1–2), 81–104.
Gupta, V. K., Troutman, B. M., and Dawdy, D. R. (2007). “Towards a non-linear geophysical theory of floods in river networks: an overview of 20 years of progress.” Nonlinear dynamics in geosciences, A. A. Tsonis and J. B. Elsner, eds., Springer, New York, 121–151.
Gupta, V. K., and Waymire, E. C. (1998). “Spatial variability and scale invariance in hydrologic regionalization.” Scale dependence and scale invariance in hydrology, G. Sposito, ed., Cambridge University Press, Cambridge, U.K., 88–135.
Menabde, M., and Sivapalan, M. (2001). “Linking space-time variability of river runoff and rainfall fields: A dynamic approach.” Adv. Wat. Resour., 24(9-10), 1001–1014.
Ogden, F. L., and Dawdy, D. R. (2003). “Peak discharge scaling in small Hortonian watershed.” J. Hydrol. Eng., 64–73.
Pielke, R., Sr., et al. (2009). “Climate change: The need to consider human forcings besides greenhouse gases.” EOS, 90(45), 413.
R Core Team. (2014). “R: A language and environment for statistical computing, version 3.1.2.” R Foundation for Statistical Computing, Vienna, Austria.
Soong, D. T., Audrey, L. I., Sharpe, J. B., and Avery, C. F. (2004). “Estimating flood-peak discharge magnitudes and frequencies for rural streams in Illinois.”, U.S. Geological Survey, Washington, DC.
Tasker, G. D., and Stedinger, J. R. (1989). “An operational GLS model for hydrologic regression.” J. Hydrol., 111(1–4), 361–375.
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© 2016 American Society of Civil Engineers.
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Received: Jan 24, 2015
Accepted: Mar 21, 2016
Published online: Jun 14, 2016
Published in print: Oct 1, 2016
Discussion open until: Nov 14, 2016
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