TRACMASS—A Lagrangian Trajectory Model
A detailed description of the Lagrangian trajectory model TRACMASS is presented. The theory behind the original scheme for steady state velocities is derived for rectangular and curvilinear grids with different vertical coordinates for the oceanic and atmospheric circulation models. Two different ways to integrate the trajectories in time in TRACMASS are presented. These different time schemes are compared by simulating inertial oscillations, which show that both schemes are sufficiently accurate not to deviate from the analytical solution.
The TRACMASS are exact solutions to differential equations and can hence be integrated both forward and backward with unique solutions. Two low-order trajectory subgrid parameterizations, which are available in TRACMASS, are explained. They both enable an increase of the Lagrangian dispersion, but are, however, too simple to simulate some of the Lagrangian properties that are desirable. The mass conservation properties of TRACMASS are shown to make it possible to follow the water or air masses both forward and backward in time, which also opens up for all sorts of calculations of water/air mass exchanges as well as Lagrangian stream functions.
The authors wish to thank Tarmo Soomere and Ewald Quak for constructive comments. This work was originally motivated by the BONUS+ project BalticWay that was supported by the funding from the European Community’s Seventh Framework Programme (FP7 2007–2013) under grant agreement No. 217246 made with the joint Baltic Sea research and development programme BONUS+ and by the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (Formas, Ref. No. 2008–1900).
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