Stability and Bifurcation Analysis of Reservoir Sedimentation Management

Abstract

The alarming loss of water storage capacity to sedimentation in reservoirs worldwide is prompting a paradigm shift toward sustainable management. Previous research has investigated the physical capability of various technologies to control reservoir sediment, and formulated economic rules governing their optimal sustainable use. We ask the next rele- vant questions: Is sustainable reservoir management structurally stable for particular technologies, or do thresholds exist such that small perturbations in key management parameters abruptly unleash dynamics driving the reservoir toward ex- tinction? What are the dynamic properties of reservoirs in transition? We uncover a saddle-node bifurcation for the par- ticular case of a multi-purpose public reservoir manager who adopts the environmentally friendly 'hydrosuction-dredging' sediment removal technology. Beyond the bifurcation threshold, sustainable management abruptly gives way to eventual loss of storage capacity to sedimentation. Reservoirs throughout the world suffer from sedimenta- tion. Examples include estimated annual storage capacity losses of 2.3% in China (2), 0.5% in India (2), and 1% worldwide (3). Specific examples are catalogued by Batuca and Jordaan (4). These include the Cir-lurtsk Reservoir on the Sulak River (Russia) which was 95% sedimented in 7 years; the Gumati Reservoir on the Vakhs River (Georgia) which was 90% sedimented in 11 years; and the Zemo Af- char Reservoir at the confluence of the Kura and Aragi Riv- ers (Russia) which lost 44% of its initial storage capacity in the first 2 years, 32% in the next 8 years, and 3.5% up to 1967. Other examples include the Tarbela Dam on the Indus River—the most important facility of its kind in Pakistan— which lost 20% of its storage capacity after 23 years of op- eration (5); and the Matilija Dam in California whose storage capacity decreased from 7,000 acre feet in 1947 to less than 500 acre feet by 2005 (6).