Simulating river meandering processes using stochastic bank erosion coefficient Ari J. Posner a, ⁎, Jennifer G. Duan b a Department of Hydrology and Water Resources, University of Arizona, 1133 E James E. Rogers Way Rm 122, PO Box 210011, Tucson, AZ 85721, USA b Department of Civil Engineering and Engineering Mechanics, University of Arizona, CE Bldg, Room 206A-1, P.O. Box 210072, Tucson, AZ 85721, USA abstract article info Article history: Received 2 May 2011 Accepted 25 May 2011 Available online 17 June 2011 Keywords: Meander Monte Carlo Bank erosion Stochastic This study first compares the first order analytical solutions for flow field by Ikeda et. al. (1981) and Johanesson and Parker (1989b). Ikeda et. al.'s (1981) linear model of bank erosion was implemented to predict the rate of bank erosion in which the bank erosion coefficient is treated as a stochastic variable that varies with physical properties of the bank (e.g. cohesiveness, stratigraphy, vegetation density). The developed model was used to predict the evolution of meandering planforms. Then, the modeling results were analyzed and compared to the observed data. Because the migration of meandering channels consists of downstream translation, lateral expansion, and downstream or upstream rotations, several measures are formulated to determine which of the resulting planform is closest to the experimental measured one. Results from the deterministic model highly depend on the calibrated erosion coefficient. Because field measurements are always limited, the stochastic model yielded more realistic predictions of meandering planform evolutions. Because the coefficient of bank erosion is a random variable, the meandering planform evolution is a stochastic process that can only be accurately predicted by a stochastic model. © 2011 Elsevier B.V. All rights reserved. 1. Introduction One of the most perplexing and intriguing problems in open channel hydraulics is the phenomenon of river meandering. Motiva- tions for the continued research on a mathematical model to simulate this ubiquitous river planform are to advance our ability to explain complex natural phenomenon, to resolve issues associated with river ecological functions, to protect hydraulic structures such as bridges and levees, to mitigate erosion and flooding in valuable agricultural and urban lands, to understand the influence of sinuosity on surface/groundwater interaction, and to develop insight into the formation of oil reservoirs created by ancient meandering rivers (Sun et al., 1996). Research conducted under the Streambank Erosion Control Evaluation and Demonstration Act of 1974 (Sec 32, Public Law 32-251, submitted in December 1981), found that approximately 142,000 bank-miles of streams and waterways are in need of erosion protection. The cost to prevent or control this erosion by means of conventional bank protection methods was estimated to be in excess of $1 billion US annually. The Upper-Mississippi River alone, the cost estimate exceeded $21 million annually. Simulations of meandering rivers have been reported intensively in literature that includes three major approaches: 1) analytical solutions (Engelund, 1974; Ikeda et al., 1981; Johannesson and Parker, 1989a; Camporeale et al., 2007) 2) numerical solutions (Duan, 1998, 2001; Darby et al., 2002) 3) empirical solutions (Langbien and Leopold, 1966). Besides simulating the flow field to solve for flow velocity and shear stress, numerical and analytical models require the estimation of the rate of bank erosion to simulate the evolution of meandering planform from low to high sinuosities. The results of these models, however, are considerably different because of the differences in calculating the rate of bank erosion. Therefore, the goal of this study is to analyze the analytical method of bank erosion and modeling planform evolution by examining the available methods in literature, through developing metrics to measure error in modeling the evolution of meander planforms. The second goal of this effort is to represent this modeling method through a Monte Carlo simulation whose results we can compare to the usual deterministic representation. Bank erosion is a natural adjustment mechanism of channels of dynamic equilibrium and non-equilibrium. Alluvial channels adjust themselves to reach regime conditions through the degradation and aggradation of the river bed and also through width adjustment and planform evolution. The rate of bank erosion may depend on a variety of parameters including soil properties, the frequency of freeze-thaw, the stratigraphy of the bank, the type and density of vegetation, and sediment grain size at the toe of the bank (Micheli and Kirchner, 2002; Perucca et al., 2007). Bank erosion caused by hydraulic forces acting on bank surface and the failure of banks from geotechnical instability of the bank are the most commonly observed bank erosion phenomena in nature. In general, bank erosion of non-cohesive materials usually proceeds through the following sequence: firstly, bed scouring that steepens the side bank; secondly, bank collapse from instability of the scoured bank; thirdly, deposition of the collapsed bank materials at the Geomorphology 163–164 (2012) 26–36 ⁎ Corresponding author. Tel.: + 1 520 621 5082; fax: + 1 520 621 1422. E-mail addresses: aposner@email.arizona.edu (A.J. Posner), gduan@email.arizona.edu (J.G. Duan). 0169-555X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2011.05.025 Contents lists available at ScienceDirect Geomorphology journal homepage: www.elsevier.com/locate/geomorph