From: Robert Millar To: Erik Mosselman ; Subject: Rivers-List: Regime Theory and Problems of the 21st Century Date: 06 July 2000 23:03 Dear All: The general discussion appears to have moved on to other matters related to eco-hydraulics. However, I'd like to respond to a couple of the major points raised recently by Dr Mosselman about regime theory. The two issues that I'd like to respond relate to regime as a single or multiple equlibrium state, and the application of "extremal hypotheses" to the study of river regime. (1) Single or Multiple Equilibrium States? Dr Mosselman raised a number of the excellent points that are valid if one views regime as a single-value equilibrium state defined only by discharge (Q), and sediment load and calibre (Qs). I would certainly agree that there are multiple equilibrium states for a given Q and Qs, and the anecdotal observations from the Bramaputra-Jamuna River support this view. My view is that for given Q and Qs, the bank stability determines an essentially unique, single-valued equilibrium state. Channels with the same Q and Qs, but different bank stability will each have different (but still single-valued) equilibrium geometry. I would interpret the differences between the growing and dying channels as reflecting the differences in erodibilty of the sediments making up the banks, that is consolidated floodplain sediment versus unconsolidated silts. I would expect that growing channels with banks composed of less erodible, consolidated floodplain sediment would indeed be narrower and deeper than dying channels with recently deposited and highly erodible silt banks. We find the same differences between gravel rivers with vegetated and non vegetated banks. (2) Application of Extremal Hypotheses (for want of a better term). I concur with Dr Mosselman that early fomulations such as those by Chang (in the 1980's) and White et al (1982) produce a single-valued equilibrium for given Q and Qs. However, when bank stability is added as an additional contraint on development of the optimum, then multiple solutions are possible, with each depending upon the stability of the banks (Millar and Quick, 1993, J Hydr. Eng., 119 (12), 1343-1363, and others). As an aside, Dr Mosselman's Discussion published in J. Hydr. Eng. (2000) critical of extremal hypotheses cites the "Illusion of Progress" paper by G. Griffiths (1984, Water Res Res., 20 (1), 113-118). This study is often used by critics of the approach. However, what is usually overlooked is that Griffiths' analysis is fundamentally flawed because the "wide channel approximation" that was used did not account for the effect of river bank resistance on transporting capacity (see discussion by H. Chang, 1984, WRR, 20 (11), 1767-1768). Thus, general dismissal of "extremal based" approaches based on Griffiths' analysis not justified. Best Regards Rob Millar *************************************************************************** Dr. Robert Millar Assistant Professor University of British Columbia Department of Civil Engineering 2324 Main Mall, Vancouver, BC, Canada, V6T 1Z4. Phone + (604) 822 2775 Fax + (604) 822 6901 email: millar@civil.ubc.ca Web Page: http://www.civil.ubc.ca ***************************************************************************