Vertical Coordinate

Overview

Omega uses pseudo height, \(\tilde{z} = \frac{p}{\rho_0 g}\), as the vertical coordinate (V1 governing equation document). In practice, \(\tilde{z}\) is not computed directly. Instead, the model tracks and evolves the pseudo-thickness, \(\tilde{h} = \Delta \tilde{z}\), defined as the difference between adjacent layer interfaces. The pseudo height is essentially a normalized pressure coordinate, with the advantage that it has units of meters. The VertCoord class contains variables and functions relevant to keeping track of:

• the maximum possible number of layers in a cell, i.e. the extent of the vertical dimension (read in from the mesh file)

• the bottom depth of each cell (read in from the mesh file)

• the location of active vertical layers (used to set extents of vertical loop bounds):

  • the max and min indices of active layers in each cell (read in from the mesh file)

  • the max and min indices of active layers for edges and vertices at the bottom and top of the water column (computed from min/max cell layers)

• pressure (computed from the layer thickness and surface pressure)

• \(z\) height (computed from the bottom depth, specific volume, and layer thickness)

• geopotential (computed from the z height and tidal forcing)

• desired vertical interface locations (computed from pressure, reference layer pseudo thickness, and user-specified weights)

Multiple instances of the vertical coordinate class can be created and accessed by a unique name.

Variables

Variable Name	Description	Units
NVertLayers	maximum number of vertical layers	-
NVertLayersP1	maximum number of vertical layers plus 1	-
PressureInterface	pressure at layer interfaces	force per unit area at layer interfaces
PressureMid	pressure at layer mid points	force per unit area at layer mid point
ZInterface	z height of layer interfaces	m
ZMid	z height of layer midpoint	m
GeopotentialMid	geopotential at layer mid points	m\(^2\)/s\(^2\)
LayerThicknessPStar	desired layer thickness based on total perturbation from the reference thickness	-
MinLayerCell	first active layer for cell	-
MaxLayerCell	last active layer for cell	-
MinLayerEdgeTop	min of the first active layers for cells on edge	-
MaxLayerEdgeTop	min of the last active layer for cells on edge	-
MinLayerEdgeBot	max of the first active layer for cells on edge	-
MaxLayerEdgeBot	max of the last active layer for cells on edge	-
MinLayerVertexTop	min of the first active layer for cells on vertex	-
MaxLayerVertexTop	min of the last active layer for cells on vertex	-
MinLayerVertexBot	max of the first active layer for cells on vertex	-
MaxLayerVertexBot	max of the last active layer for cells on vertex	-
VertCoordMovementWeights	weights to specify how total column thickness changes are distributed across layers	-
RefLayerThickness	reference layer thickness used to distribute total column thickness changes	m
BottomDepth	positive down distance from the reference geoid to the bottom	m

Configuration options

The vertical coordinate movement can be specified by the MovementWeightType option in the configuration file.

omega:
   VertCoord:
      MovementWeightType: [Fixed,Uniform]

The option Uniform specifies that perturbations to the total pseudo-thickness of the water column is distributed evenly to all vertical layers. This is similar to the standard “z-star” coordinate in Boussinesq models. The option Fixed means that total pseudo-thickness perturbations are confined to the top layer, while all others remain constant. This is similar to the traditional “z” coordinate in Boussinesq models.