Fields

WAVI.jl stores information relating to the solutions on fields, which are stored in the model. Fields are organised based according to the different grids (HGrid, CGrid etc – see Grids) on which quantities are stored. Note that all quantities here are set internally (i.e. they cannot be modified by the user). This page contains a full directory of the quantities defined on each of the Grids: HGrid, UGrid, VGrid, CGrid, SigmaGrid.

HGrid

The following quantities are stored in the HGrid structure within Fields (accessible via model.fields.gh.<field_name>):

h: Ice thickness
b: Bed elevation
s: Ice surface elevation ($s = b + h$)
dhdt: Time rate of change of surface elevation
accumulation: Ice accumulation rate (postive for mass added to the surface, negative for mass removed)
basal_melt: Melt rate applied to the base of the ice sheet (positive for mass removed from the base, negative for mass added).
grounded_fraction: Grid cell grounded fraction (zero in the shelf, one in the shelf and interpolated across the grounding line, see Seroussi et al. (2014))
u: Depth average ice velocity in the $x$ direction.
v: Depth average ice velocity in the $y$ direction.
av_speed: Depth averaged ice speed
us: Surface ice velocity in the $x$ direction.
vs: Surface ice velocity in the $y$ direction.
ub: Base ice velocity in the $x$ direction.
vb: Base ice velocity in the $y$ direction.
bed_speed: Ice speed at the base
weertman_c: Weertman C drag cofficient
haf: The height above floatation
dsdh: Rate of change of surface elevation with respect to thickness change
shelf_strain_rate: Strain rate computed using only longitudinal strain components
β: Raw multiplicative drag coefficient
βeff: Effective multiplicative drag coefficient
τbed: Ice stress at the bed.
ηav: Depth averaged viscosity
quad_f1: $F_1$ computed from numerical quadrature
quad_f2: $F_2$ computed from numerical quadrature
mask: boolean matrix that defines the solution space

For convenience, various utility matrices and rheological operators are also stored on the HGrid:

crop: diagonal matrix with mask entries on the diagonal
samp: boolean matrix that takes full domain to the model domain
spread: sparse form of the sampling matrix
dneghηav: $-h \times \bar{\eta}$
dimplicit: $-\rho_i \times g \times \mathrm{d}t \times \mathrm{d}h/\mathrm{d}s$

UGrid

The following quantities are stored on the UGrid structure within Fields (accessible via model.fields.gu.<field_name>):

nxu: Number of grid cells in x-direction in the UGrid (equals nx + 1, where nx is the number of grid cells in the x direction in the HGrid).
nyu: Number of grid cells in y-direction in the UGrid (equals ny, where ny is the number of grid cells in the x direction in the HGrid).
mask: Mask specifying model domain with respect to the UGrid.
n: Total number of cells in UGrid.
levels: Number of levels in the preconditioner
dwt: Wavelet matrix product at UGrid points
s: Ice surface elevation at UGrid points
h: Ice thickness at UGrid points
grounded_fraction: Grounded fraction at UGrid points
βeff: Effective sliding coefficient at UGrid points.
u: Ice velocities in the x-direction

For convenience, various utility matrices and rheological operators are also stored on the UGrid:

crop: diagonal matrix with mask entries on the diagonal
samp: boolean matrix that takes full domain to the model domain
spread: sparse form of the sampling matrix
cent: maps quantities from the UGrid to the HGrid
∂x: matrix representation of differentiation with respect to x
∂y: matrix representation of differentiation with respect to y

VGrid

The following quantities are stored on the VGrid structure within Fields (accessible via model.fields.gv.<field_name>):

nxv: Number of grid cells in x-direction in the VGrid (equals nx, where nx is the number of grid cells in the x direction in the HGrid).
nyu: Number of grid cells in y-direction in the VGrid (equals ny+1, where ny is the number of grid cells in the x direction in the HGrid).
mask: Mask specifying model domain with respect to the VGrid.
n: Total number of cells in VGrid.
levels: Number of levels in the preconditioner
dwt: Wavelet matrix product at VGrid points
s: Ice surface elevation at VGrid points
h: Ice thickness at VGrid points
grounded_fraction: Grounded fraction at VGrid points
βeff: Effective sliding coefficient at VGrid points.
u: Ice velocities in the x-direction

For convenience, various utility matrices and rheological operators are also stored on the VGrid:

crop: diagonal matrix with mask entries on the diagonal
samp: boolean matrix that takes full domain to the model domain
spread: sparse form of the sampling matrix
cent: maps quantities from the VGrid to the HGrid
∂x: matrix representation of differentiation with respect to x
∂y: matrix representation of differentiation with respect to y

CGrid

The following quantities are stored in the CGrid structure within Fields (accessible via model.fields.gc.<field_name>):

nxc: Number of grid cells in x-direction in the CGrid (equals nx-1, where nx is the number of grid cells in the x direction in the HGrid).
nyc: Number of grid cells in y-direction in the CGrid (equals ny-1, where ny is the number of grid cells in the x direction in the HGrid).
mask: Mask specifying model domain with respect to the CGrid.
n: Total number of cells in CGrid.

The following utility matrices are also stored on the CGrid

crop: diagonal matrix with mask entries on the diagonal
samp: boolean matrix that takes full domain to the model domain
spread: sparse form of the sampling matrix
cent: maps quantities from the CGrid to the HGrid

SigmaGrid

The following quantities are stored in the SigmaGrid structure within Fields (accessible via model.fields.g3d.<field_name>):

nxs: Number of grid cells in the x-direction in the SigmaGrid (equals nx, where nx is the number of grid cells in the x direction in the HGrid)
nvs: Number of grid cells in the y-direction in the SigmaGrid (equals ny, where ny is the number of grid cells in the x direction in the HGrid)
nxs: Number of levels in the vertical in the SigmaGrid
σ: Dimensionless levels in the vertical
ζ: Reverse dimensionless vertical levels
quadrature_weights: weights associated with sigma levels, used in computation of integrals over thickness
η: three dimensional viscosity field
θ: three dimensional temperature field
Φ: three dimensional damage field
glen_b: three dimensional field of glen_b values in viscosity calcluations