Risk analysis in the coastal zone using reverse-time ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Risk analysis in the coastal zone using reverse-time diffusion
Paper
Author:Daria Spivakovskaya <d.spivakovskaya@ewi.tudelft.nl> (Department of Applied Mathematical Analysis, Faculty of EEMCS, Delft University of Technology)
Arnold W. Heemink <a.w.heemink@ewi.tudelft.nl> (Department of Applied Mathematical Analysis, Faculty of EEMCS, Delft University of Technology)
John G. M. Schoenmakers <schoenma@wias-berlin.de> (Weierstrass Institute for Applied Analysis and Stochastics)
Presenter:Daria Spivakovskaya <d.spivakovskaya@ewi.tudelft.nl> (Department of Applied Mathematical Analysis, Faculty of EEMCS, Delft University of Technology)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000616
DOI:10.4122/1.1000000617

Recently we have been faced with serious ecological problems due to calamities at sea. For prediction the spreading of pollutants accurate methods must be available. There are two main concepts for the simulation of the diffusion processes. One can use the Eulerian approach and solve the advection-diffusion equation numerically. However, numerical methods often have problems with mass conservation or positiveness in case of high concentration gradients of the pollutant. Using a Lagrangian approach the advection-diffusion equation is interpreted as a Fokker-Planck equation and a system of underlying stochastic differential equations for the behavior of the position of the individual particle of the pollutant can be derived. By numerically simulating the positions of many different particles of the pollutant the diffusion process can be described. This method is mass conserving and the concentration can never become negative. Particle models are very attractive from the computational point of view. Because of the independence of the movements of all particles, particle models can be easily parallelized. In this paper we investigate the risk of very high concentrations of the pollutant. Suppose that for some locations a high concentration of the pollutant can be dangerous or even fatal for life of some species. To prevent ecological disasters we need to determine which areas in the sea are potentially dangerous and which areas are safe, in other words we need to construct a risk map. By the risk map for a given location of interest along the coast we mean the concentration of the pollutant in this area for any locations (x,y) where the pollutant may be released. From a risk map we can immediately determine the most dangerous as well as the safe location of the pollutant release. In this paper we develop an efficient method to construct the risk map based on the concept of the reverse time diffusion. Using the reverse time model, which can be derived from the original one, we can simulate backward particle trajectories. By averaging the results of many independent realizations of the reverse time model we can build the risk map. Comparing with the direct Monte-Carlo method based on the original random walk models, the proposed method is more attractive from the computational point of view. In this paper we apply the reverse time method to investigate the several critical locations along Dutch seaside and construct the risk map for the Dutch coastal zone.