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The processes of transport, diffusion and transformation of surface oil inseawater can be simulated using a Lagrangian model formalism coupled withEulerian circulation models. This paper describes the formalism and theconceptual assumptions of a Lagrangian marine surface oil slick numerical model andrewrites the constitutive equations in a modern mathematical framework. TheLagrangian numerical representation of the oil slick requires three differentstate variables: the slick, the particle and the structural state variables.Transformation processes (evaporation, spreading, dispersion and coastaladhesion) act on the slick state variables, while particle variables areused to model the transport and diffusion processes. The slick and particlevariables are recombined together to compute the oil concentration in water,a structural state variable. The mathematical and numerical formulation ofoil transport, diffusion and transformation processes described in thispaper, together with the many simplifying hypothesis and parameterizations,form the basis of a new, open source Lagrangian surface oil spill model,the so-called MEDSLIK-II, based on its precursor MEDSLIK (Lardner et al., 1998, 2006; Zodiatis et al., 2008a). Part 2 of this paper describes the applications ofthe model to oil spill simulations that allow the validation of the modelresults and the study of the sensitivity of the simulated oil slick todifferent model numerical parameterizations

MEDSLIK-II, a Lagrangian marine surface oil spill model for short-term forecasting – Part 1: Theory