# PELETS-2D: Particle tracking and drift climatologies

The Fortran 90 program PELETS-2D is a toolbox that allows for offline Lagrangian transport calculations (i.e. particle tracking) based on 2D current fields stored on at least an hourly basis. The toolbox was developed for its use in connection with model based re-analyses of past atmospheric and sea state conditions in the data base coastDat. Depending on a study's objective, drift simulations may be performed either forward or backward in time. For substances drifting at the water surface an extra wind drift may be taken into account. A recent application of this type is the analysis of trends in chronic oil pollution of the German coast and the interpretation of related beached bird survey data.

Example: Chronic Oil Pollution in the German Bight

Two main components of PELETS-2D deal with a) particle tracking based on pre-calculated hydrodynamic fields and b) the setup and evaluation of large ensembles of such simulations.

### Particle tracking algorithm

The PELETS-2D algorithm is adapted to two-dimensional current fields on unstructured triangular grids. Transport velocities for particles are updated by linear interpolation between two nodes each time a particle crosses an edge of the underlying triangular grid. As a result of this approach time steps used in PELETS-2D are not constant. Times between velocity updates implicitly shrink as soon as particles enter regions with higher spatial resolution. In regions where spatial resolution is very poor, however, an upper limit for the time step may become effective.

In the case of velocity fields that originated from hydrodynamic simulations on a rectangular grid, the grid topology must be pre-processed in such a way that diagonals are added in each grid cell. This simple approach to the emulation of a triangular grid does not change the information content of the hydrodynamic fields. The only practical implication of the additional edges is that updates of particle velocities are triggered each time particles cross them.

In the case of velocity fields that originated from hydrodynamic simulations on a rectangular grid, the grid topology must be pre-processed in such a way that diagonals are added in each grid cell. This simple approach to the emulation of a triangular grid does not change the information content of the hydrodynamic fields. The only practical implication of the additional edges is that updates of particle velocities are triggered each time particles cross them.

### Ensemble simulations

PELETS-2D supports dealing with large ensembles of particle cloud simulations. Simulations may be initialized, for instance, with constant time lags so as to properly cover different atmospheric conditions with an implicit weighting according to the frequency of their occurrence in the coastDat re-analyses. Alternatively, simulations may be scheduled to meet special requirements of biological studies (e.g. the selection of specific seasons), for instance. PELETS-2D provides a couple of general tools for the evaluation of such large ensembles.

Each simulation of an individual particle cloud involves integration of a certain number of trajectories, initialized at random within one or a couple of source regions. These user defined source regions are delimited by arbitrarily shaped polygons. Optional weighting of initial local particle densities with water depth should be applied when particles are meant to represent water volumes. For material drifting on the surface (e.g. oil slicks), a depth weighted initialization is not meaningful. Initial partitioning of particles between different source regions can either be uniform or weighted with each subregion's area.

Similar to the set of source regions, users may define a set of target or receptor regions. Then the basic type of information stored (on an hourly basis) will be the number of particles from each source region that a) presently reside within a given receptor region and b) have visited this receptor region at any time since particle tracking was started. In addition the distribution of travel times is described in terms of ten percentiles. In PELETS-2D travel time is specified as the time of first arrival in a given receptor region. Ensemble simulations provide detailed information that can be either averaged to obtain composite presentations or subjected to Principal Component Analysis (PCA) to obtain dominant patterns of variability.

Details of each particle's trajectory may be stored for the purpose of graphical visualization. For large applications (particle clouds consisting of many particles, large numbers of particle clouds, long integration times), however, storing trajectories will require too many resources.

Each simulation of an individual particle cloud involves integration of a certain number of trajectories, initialized at random within one or a couple of source regions. These user defined source regions are delimited by arbitrarily shaped polygons. Optional weighting of initial local particle densities with water depth should be applied when particles are meant to represent water volumes. For material drifting on the surface (e.g. oil slicks), a depth weighted initialization is not meaningful. Initial partitioning of particles between different source regions can either be uniform or weighted with each subregion's area.

Similar to the set of source regions, users may define a set of target or receptor regions. Then the basic type of information stored (on an hourly basis) will be the number of particles from each source region that a) presently reside within a given receptor region and b) have visited this receptor region at any time since particle tracking was started. In addition the distribution of travel times is described in terms of ten percentiles. In PELETS-2D travel time is specified as the time of first arrival in a given receptor region. Ensemble simulations provide detailed information that can be either averaged to obtain composite presentations or subjected to Principal Component Analysis (PCA) to obtain dominant patterns of variability.

Details of each particle's trajectory may be stored for the purpose of graphical visualization. For large applications (particle clouds consisting of many particles, large numbers of particle clouds, long integration times), however, storing trajectories will require too many resources.