Review Three simple indicators of vulnerability to climate change on a Mediterranean beach: A modeling approach Philippe Larroudé a,1 , Thibault Oudart a , Mehdi Daou a , Nicolas Robin b , Raphaël Certain b a LEGI, BP 53, 38041 Grenoble, France b Univ. de Perpignan via Domitia, Centre de Formation et de Recherche sur les Environnements Méditerranéens, UMR 5110, 66860 Perpignan, France article info Article history: Received 8 November 2012 Accepted 30 October 2013 Available online 12 December 2013 Keywords: Coastal morphology evolution Numerical simulation Climate change Indictor of vulnerability abstract This study assesses three different approaches for evaluating coastal vulnerability using indicators. We began by establishing a procedure for binding three codes to simulate realistic or idealized climates. The procedure was validated in terms of hydrodynamics and beach morpho-dynamics. We then defined and studied the vulnerability of the coast on the basis of in situ observations and model results taken from a set of simulations based on different scenarios. We present three simple indicator methods developed to analyze the vulnerability of a sandy beach based on the results of simulations for different wave climate scenarios. The first method is based on the wave energy, and specifically how it differs as a function of climate change scenario. The second method consists of estimating the maximum grain size mobilized. Note that the calculation of stress at the sea bottom is routinely estimated solely on the basis of simulated velocity post-wave. Here, we calculate the maximum grain size potentially mobilized with a simpler approach, based on analysis in different points along the cross-shore profile. The third method presented is the analysis of the time-course evolution of cross-shore sea bed profiles in response to different climate change scenarios. & 2013 Elsevier Ltd. All rights reserved. Contents 1. Introduction ........................................................................................................ 172 2. Description of the Vulsaco program on sandy coast vulnerability ............................................................. 173 3. Field sites and measurement methodology ............................................................................... 174 4. Model and simulation methodology..................................................................................... 176 5. Results and discussions ............................................................................................... 177 5.1. The wave simulation ........................................................................................... 177 5.2. The current simulation ......................................................................................... 177 5.3. The morphology simulation ..................................................................................... 178 5.4. Vulnerability indicator taken from the numerical solution ............................................................. 178 6. Conclusions ........................................................................................................ 179 Acknowledgments ....................................................................................................... 181 References ............................................................................................................. 181 1. Introduction Hydrodynamic and morphodynamic processes in coastal envir- onments are recognized as important not only from a scientific point of view, but also for many aspects of human activities, including design of coastal protection structures or environmental risk assessments (Dally et al., 1984; Larson and Kraus, 1989; Nairn and Southgate, 1993; Bradford, 2000; Damgaard et al., 2002). Numer- ical modeling can run repeatable simulations that are extremely useful for testing the influence of morphogenic parameters, making it possible to predict the future evolution of coastal systems, notably in response to global climate change. To study these environmental problems numerically, the various approaches developed are based on beach models, including beach state models, profile evolution models, and beach evolution models. There are two kinds of beach state models: (1) equilibrium models, which predict the shape of near-shore features (e.g. bars and troughs), under constant incident wave conditions Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2013.10.017 1 Tel.: þ33 456528618; fax: þ33 476827022. E-mail address: philippe.larroude@legi.grenoble-inp.fr (P. Larroudé). Ocean Engineering 76 (2014) 172–182