In Parcels v3.1.0, we implemented support for CROCO sigma grids. We assumed that the conversion from the depth-coordinate (z) to the terrain-following coordinate (sigma) was simply sigma(t, y, x) = z(t, y, x) / H(y, x), where H is the local seafloor depth.
However, following the discussion in https://github.com/OceanParcels/Parcels/discussions/1752, we now realise that this conversion is a bit more complex, and requires not only the free-surface field (eta), but also a a critical depth controlling the stretching depth_c , and a dimensionless vertical coordinate stretching function C[zi] as a function of vertical grid
It would be good to implement this conversion under the hood in Parcels too, so that the mapping between sigma and z is more in line with CROCO numerics
In Parcels v3.1.0, we implemented support for CROCO sigma grids. We assumed that the conversion from the depth-coordinate (z) to the terrain-following coordinate (sigma) was simply
sigma(t, y, x) = z(t, y, x) / H(y, x), whereHis the local seafloor depth.However, following the discussion in https://github.com/OceanParcels/Parcels/discussions/1752, we now realise that this conversion is a bit more complex, and requires not only the free-surface field (
eta), but also a a critical depth controlling the stretchingdepth_c, and a dimensionless vertical coordinate stretching functionC[zi]as a function of vertical gridSee http://cfconventions.org/cf-conventions/cf-conventions.html#_ocean_s_coordinate_generic_form_1 for detailed information about this conversion
It would be good to implement this conversion under the hood in Parcels too, so that the mapping between
sigmaandzis more in line with CROCO numerics