Impact of horizontal eddy diffusivity on Lagrangian statistics for coastal pollution from a major marine fairway Bert Viikmäe & Tomas Torsvik & Tarmo Soomere Received: 30 November 2012 / Accepted: 2 April 2013 / Published online: 26 April 2013 # Springer-Verlag Berlin Heidelberg 2013 Abstract Lagrangian trajectory methods are often applied as deterministic transport models, where transport is due strictly to advection without taking into account stochastic elements of particle dispersion, which raises questions about validity of the model results. The present work investigates the impact of horizontal eddy diffusivity for a case study of coastal pollution in the Gulf of Finland, where the pollutants are assumed to originate from a major fairway and are transported to the coast by surface currents. Lagrangian trajectories are calculated using the TRACMASS model from velocity fields calculated by the Rossby Centre circu- lation model for 1982 to 2001. Three cases are investigated: (1) trajectory calculation without eddy diffusivity, (2) sto- chastic modelling of eddy diffusivity with a constant diffu- sion coefficient and (3) stochastic modelling of eddy diffusivity with a time- and space-variable diffusion coeffi- cient. It is found that the eddy diffusivity effect increases the spreading rate of initially closely packed trajectories and the number of trajectories that eventually reach the coast. The pattern of most frequently hit coastal sections, the probabil- ity of hit to each such section and the time the pollution spends offshore are virtually invariant with respect to inclu- sion of eddy diffusivity. Keywords Hydrodynamic modelling . Lagrangian transport . Statistics of currents . Baltic Sea . Pollution transport . Pollution control . Ship routing . Smagorinsky diffusion 1 Introduction Lagrangian trajectory methods offer a convenient, and in- creasingly popular, framework for the study of flow-driven transport problems in the marine environment. They are used for applications such as the transport of fish eggs and larvae (Mariani et al. 2010), toxic algae (Havens et al. 2010), suspended particulate matter (Gräwe and Wolff 2010), oil pollution (Korotenko et al. 2004; Chrastansky and Callies 2009), or marine litter (Yoon et al. 2010), among others. Analysing transport by tracking individual particles over time provides several advantages compared to Eulerian tracer con- centration methods, including the ability to backtrack particle trajectories to a specific place of origin and to easily extract measures depending on time integrated properties of individ- ual agents. In many cases, perhaps in particular for simulations of ocean drift (de Vries and Döös 2001; Döös 1995), Lagrangian trajectories are calculated as a pure advection process which implicitly assumes that the velocity field gives a true representation of the flow at all relevant spatial and temporal scales. However, in practical applications, the veloc- ity vectors represent the average flow characteristics over some spatial and temporal scales, in which case the disregard for subgrid-scale processes in the Lagrangian trajectory cal- culations is a controversial issue. It is well known that the horizontal dispersion of sub- stances floating on the sea surface is not only the result of molecular processes, but is enhanced by the effects of shear- ing and straining on length scales ranging from millimetres to kilometres and also normally involves the direct wind and Responsible Editor: Martin Verlaan Based on the presentation “Spatial Pattern of Hits to the Nearshore from a Major Marine Highway in the Gulf of Finland” to the 16th Biennial Workshop of the Joint Numerical Sea Modelling Group (JONSMOD) This article is part of the Topical Collection on the 16th biennial workshop of the Joint Numerical Sea Modelling Group (JONSMOD) in Brest, France 21-23 May 2012 B. Viikmäe (*) : T. Torsvik : T. Soomere Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia e-mail: bert@ioc.ee Ocean Dynamics (2013) 63:589–597 DOI 10.1007/s10236-013-0615-3