pygetm.vertical_coordinates module

class pygetm.vertical_coordinates.Adaptive(nz: int, *, ddu: float = 0.0, ddl: float = 0.0, gamma_surf: bool = True, Dgamma: float = 0.0, csigma: float = 0.0, cgvc: float = 1.0, chsurf: float = 0.0, hsurf: float = 0.5, chmidd: float = 0.0, hmidd: float = -4.0, chbott: float = 0.0, hbott: float = -0.25, decay: float = 0.6666666666666666, hpow: int = 3, cneigh: float = 0.0, rneigh: float = 0.25, cNN: float = 0.0, drho: float = 0.3, cSS: float = 0.0, dvel: float = 0.1, chmin: float = 0.0, hmin: float = 0.3, nvfilter: int = 1, vfilter: float = 0.3, nhfilter: int = 1, hfilter: float = 0.4, timescale: float = 14400.0)

Bases: FromTGrid

Adaptive vertical coordinates based on Hofmeister et al. (2010) and their GETM implementation

Initial layer thicknesses are based on Generalized Vertical Coordinates (GVC), parameterized by ddu, ddl, gamma_surf, and Dgamma. This is equivalent to uniform sigma coordinates when both ddu and ddl, are zero, and to zoomed sigma coordinates when Dgamma is zero.

Parameters:

• nz – number of layers

• ddu – zoom factor at surface (0: no zooming, 2: strong zooming)

• ddl – zoom factor at bottom (0: no zooming, 2: strong zooming)

• gamma_surf – use layers of constant thickness Dgamma/nz at surface (otherwise, at bottom)

• Dgamma – water depth below which to use equal layer thicknesses

• csigma – tendency towards equal layer thicknesses (uniform sigma) DEPRECATED: for (zoomed) sigma background, use cgvc>0.0 with Dgamma=0 instead

• cgvc – tendency towards Generalized Vertical Coordinates (GVC), as parameterized by ddu, ddl, gamma_surf, Dgamma. LEAVE AT 1, so that all other tendencies are relative to this background, and tune timescale to adjust the rate of convergence

• chsurf – tendency to zoom in (prefer thinner layers) towards the surface

• hsurf – reference thickness for surface layer (absolute thickness in m if >0, relative to average thickness D/nz if <0)

• chmidd – tendency to keep all layers bounded

• hmidd – reference thickness for other layers (absolute thickness in m if >0, relative to average thickness D/nz if <0)

• chbott – tendency to zoom in (prefer thinner layers) towards the bottom

• hbott – reference thickness for bottom layer (absolute thickness in m if >0, relative to average thickness D/nz if <0)

• decay – fraction of surface/bottom zooming tendencies (controlled by chsurf, chbott) to preserve for each additional layer away from surface/bottom. It must range between 0 (only apply tendency in targeted layer) and 1 (apply same tendency in all layers)

• hpow – exponent for ramp of tendencies focused on reference thicknesses, that is, the tendencies controlled by chsurf, chbott, chmidd.

• cneigh – tendency to keep neighbors of similar size

• rneigh – relative difference with the thinnest neighbor where size-ratio-limiting tendency reaches its maximum value cneigh

• cNN – tendency to zoom in on stable density gradients

• drho – local density difference over distance D/nz (average layer thickness) where to stop zooming in further on stable density gradients. There the tendency reaches its maximum value of cNN

• cSS – tendency to zoom in on horizontal velocity gradients (shear)

• dvel – local difference in horizontal velocity over distance D/nz (average layer thickness) where to stop zooming in further on velocity gradients. There the tendency reaches its maximum value of cSS

• chmin – tendency towards equal layer thicknesses in shallow-water regions, maximized when average layer thickness D/nz drops below 2/3 hmin, and reduced to zero when average layer thickness exceeds hmin

• hmin – minimum layer thickness (m)

• nvfilter – number of vertical filter iterations

• vfilter – strength of vertical filter-of-Dgrid [0:~0.5]

• nhfilter – number of horizontal filter iterations

• hfilter – strength of horizontal filter-of-Dgrid [0:~0.5]

• timescale – time scale of grid adaptation (s)

initialize(tgrid: Grid, *other_grids: Grid, logger: Logger)

update_T_grid(timestep: float)

Update thicknesses hn for T grid

class pygetm.vertical_coordinates.Base(nz: int)

Bases: object

Base class. It is responsible for updating layer thicknesses hn for all grids provided to initialize

initialize(tgrid: Grid, *other_grids: Grid, logger: Logger)

logger: Logger

update(timestep: float)

Update layer thicknesses hn for all grids

class pygetm.vertical_coordinates.FromTGrid(nz: int)

Bases: Base

update(timestep: float = 0.0)

Update layer thicknesses hn for all grids

update_T_grid(timestep: float)

Update thicknesses hn for T grid

class pygetm.vertical_coordinates.GVC(nz: int, *, ddl: float = 0.0, ddu: float = 0.0, gamma_surf: bool = True, Dgamma: float = 0.0)

Bases: PerGrid

Generalized Vertical Coordinates

This blends equidistant and surface/bottom-zoomed coordinates as described in Burchard & Petersen (1997). It is designed to keep the thickness of either the surface or bottom layer at a constant value, except in shallow water where all layers are assigned equal thickness.

Parameters:

• nz – number of layers

• ddl – zoom factor at bottom (0: no zooming, 2: strong zooming)

• ddu – zoom factor at surface (0: no zooming, 2: strong zooming)

• gamma_surf – use layers of constant thickness Dgamma/nz at surface (otherwise, at bottom)

• Dgamma – water depth below which to use equal layer thicknesses

initialize(*grids: Grid, logger: Logger)

class pygetm.vertical_coordinates.PerGrid(nz: int)

Bases: Base

Base class for vertical coordinate types that apply the same operation to every grid.

__call__(D: ndarray, out: ndarray | None = None, where: bool | ArrayLike = True)

Calculate layer thicknesses

Parameters:

• D – water depths (m)

• out – array to hold layer thicknesses. It must have shape (nz,) + D.shape

• where – locations where to compute thicknesses (typically: water points). It must be broadcastable to the shape of D

initialize(*grids: Grid, logger: Logger)

prepare_update_args(grid: Grid)

Prepare grid-specific information that will be passed as arguments to __call__

update(timestep: float)

Update all grids

class pygetm.vertical_coordinates.Sigma(nz: int, *, ddl: float = 0.0, ddu: float = 0.0)

Bases: PerGrid

Sigma coordinates with optional zooming towards bottom and surface

Parameters:

• nz – number of layers

• ddl – zoom factor at bottom (0: no zooming, 2: strong zooming)

• ddu – zoom factor at surface (0: no zooming, 2: strong zooming)

pygetm.vertical_coordinates.calculate_sigma(nz: int, ddl: float = 0.0, ddu: float = 0.0) → ndarray

Return sigma thicknesses (fraction of column depth) of all layers, using a formulation that allows zooming towards the surface and bottom.

Parameters:

• nz – number of layers

• ddl – zoom factor at bottom (0: no zooming, 2: strong zooming)

• ddu – zoom factor at surface (0: no zooming, 2: strong zooming)