Kernels for Parсels simulator: Recovering particles and Convection mixing

Recovery_kernel.py and Convection_kernel.py contain the kernels RecoveryParticle and Vert_conv, respectively. These kernels are written in Python to be included in the particle tracking simulator Parcels V3. They are designed to meet the syntax requirements of Parcels V3. They do not function as standalone programs but only as an extension of Parcels.

RecoveryParticle is intended to recover particles that end up in an “out of boundary” position—for example, near the ice shelf front, where the vertical coordinates of neighboring grid nodes may differ by tens of meters in the sigma coordinate system used in the circulation model describing the cavity beneath the ice shelf. This discrepancy can cause a particle to disappear due to interpolation errors when the model algorithm cannot find enough grid nodes around it. The kernel restores the particle to its last valid position before it disappeared, adding a small random displacement in three dimensions: longitude (particle_dlon), latitude (particle_dlat), and depth (particle_ddepth). If the particle disappears again, the kernel is reapplied until the particle resumes movement within the current field.

Vert_conv describes additional vertical particle motion caused by convection, which is not explicitly represented in the surface mixed layer using the random Brownian motion parameterization. This mechanism is applied in the surface mixed layer, where the density difference between the surface and a given depth is less than 0.05 kg/m³. The mixed layer thickness should be calculated separately using potential temperature and absolute salinity. The maximum random vertical velocity is set to 0.1 m/s. No turbulent mixing is applied below the mixed layer or beneath the ice shelf.