# Calving and front retreat¶

## Overview¶

All mechanisms described below fall into two categories:

mechanisms computing a

*retreat rate*due to calving and using it to update ice geometry (Eigen calving, von Mises stress calving, Hayhurst calving), andmechanisms removing ice at a grid point according to a certain criterion (Calving of thin floating ice, Calving of all floating ice, Prescribed front retreat).

To select several calving mechanisms, use a comma-separated list of corresponding keywords. For example,

```
-calving eigen_calving,thickness_calving
```

selects Eigen calving and Calving of thin floating ice.

If more than one retreat-rate-based mechanism is selected, the corresponded rates are
*added* and then used to update ice extent. (In other words: selected calving mechanisms
are applied *together* instead of applying their effects *in sequence*.)

The partially-filled grid cell formulation (section Partially-filled cells at the boundaries of ice shelves) provides a
framework suitable to relate calving rates to the mass transport scheme at the ice shelf
terminus. Ice shelf front advance and retreat due to calving are limited to a maximum of
one grid cell length per (adaptive) time step. The combined calving rate (velocity) can be
used to limit the overall timestep of PISM (thus slowing down all of PISM) by using
`geometry`

`.front_retreat`

`.use_cfl`

. This “CFL-type” time-step limitation is
definitely recommended in high-resolution runs which attempt to model calving position
accurately. Without this option, under certain conditions where PISM’s adaptive time step
happens to be long enough, dendritic structures can appear at the calving front because
the calving mechanism cannot “keep up” with the computed calving rate.

Setting the flag `geometry`

`.front_retreat`

`.wrap_around`

to `true`

allows the front
retreat to “wrap around” the computational domain. (This is appropriate in some regional
synthetic geometry setups.)

### Scaling calving rates¶

Set `calving`

`.rate_scaling`

`.file`

to scale the *total* (combined) calving rate from
all selected rate-based mechanisms, e.g. to introduce calving variability corresponding to
seasonal changes in ice melange. The file used with this option should contain the scalar
time-dependent variable `frac_calving_rate`

(units: \(1\)).

Parameters

Prefix: `calving.rate_scaling.`

## Eigen calving¶

PISM-PIK introduced a physically-based 2D-calving parameterization
[89]. This calving parameterization is turned on in PISM by option
`-calving eigen_calving`

. Average calving rates, \(c\), are proportional to the product
of principal components of the horizontal strain rates, \(\dot{\epsilon}_{_\pm}\), derived
from SSA-velocities

The rate \(c\) is in \(\text{m}\,\text{s}^{-1}\), and the principal strain rates
\(\dot\epsilon_\pm\) have units \(\text{s}^{-1}\), so \(K\) has units \(\text{m}\,\text{s}\). The
constant \(K\) incorporates material properties of the ice at the front. It can be set using
`calving`

`.eigen_calving`

`.K`

.

The actual strain rate pattern strongly depends on the geometry and boundary conditions along the confinements of an ice shelf (coast, ice rises, front position). The strain rate pattern provides information in which regions preexisting fractures are likely to propagate, forming rifts (in two directions). These rifts may ultimately intersect, leading to the release of icebergs. This (and other) ice shelf calving models are not intended to resolve individual rifts or calving events, but it produces structurally-stable calving front positions which agree well with observations. Calving rates balance calving-front ice flow velocities on average.

Parameters

Prefix: `calving.eigen_calving.`

## von Mises stress calving¶

While `eigen_calving`

(section Eigen calving) is appropriate for
Antartic ice shelves, it does not work for outlet glaciers that flow in narrow fjords.
Along valleys with nearly parallel walls the transverse component of the velocity is
close to zero and the transversal strain rate is therefore also close to zero and noisy.

Instead of the product of the eigen strain rates, [90] propose a calving law where the calving rate \(c\) is functionally related to tensile stresses:

where \(\tilde{\sigma}\) is the tensile von Mises stress and \(\sigma_{max}\) is a threshold
that has units \(Pa\) (see `calving`

`.vonmises_calving`

`.sigma_max`

). As the tensile
fracture strength is much smaller than the compressive fracture strength, the effective
tensile strain rate is defined as

Following [90], \(\tilde{\sigma}\) is given by

where \(B\) is the ice hardness.

Parameters

Prefix: `calving.vonmises_calving.`

`Glen_exponent`

(3) Glen exponent in ice flow law for von Mises calving`flow_law`

(`gpbld`

) The custom flow law for the von Mises stress computation`sigma_max`

(1e+06*Pa*) Set maximum tensile stress. Note references [90] use 1.0e6 Pa.`threshold_file`

Name of the file containing the spatially-variable`vonmises_calving_threshold`

.`use_custom_flow_law`

(no) Use custom flow law in the von Mises stress computation

## Hayhurst calving¶

The option `-calving hayhurst_calving`

implements the parameterization described in
[91] (equation 22).

Note

FIXME: not documented.

Parameters

Prefix: `calving.hayhurst_calving.`

`exponent_r`

(0.43) Damage law exponent [91]`sigma_threshold`

(0.17*MPa*) Damage threshold stress [91]

## Calving of thin floating ice¶

The option `-calving thickness_calving`

is based on the observation that ice shelf
calving fronts are commonly thicker than about 150–250 m (even though the physical
reasons are not clear yet). Accordingly, any floating ice thinner than \(H_{\textrm{cr}}\)
is removed along the front, at a rate at most one grid cell per time step. The value of
\(H_{\mathrm{cr}}\) can be set using the configuration parameter
`calving`

`.thickness_calving`

`.threshold`

.

To set a time-and-space dependent ice thickness threshold, set the parameter
`calving`

`.thickness_calving`

`.file`

. This file should contain the variable
`thickness_calving_threshold`

in meters.

Parameters

Prefix: `calving.thickness_calving.`

## Calving of all floating ice¶

The option `-calving float_kill`

removes (calves), at each time step of the run, any
ice that satisfies the flotation criterion. Use of this option implies that there are no
ice shelves in the model at all.

Set `calving`

`.float_kill`

`.margin_only`

to restrict this to cells at the ice margin.

Sometimes it is useful to preserve a one-cell-wide shelf near the grounding line. To do
this, set `calving`

`.float_kill`

`.calve_near_grounding_line`

to false.

Parameters

Prefix: `calving.float_kill.`

`calve_near_grounding_line`

(yes) Calve floating ice near the grounding line.`margin_only`

(no) Apply float_kill at ice margin cells only.

## Prescribed front retreat¶

Option `-front_retreat_file`

allows prescribing retreat of the ice front. The forcing
file specified using this option should contain `land_ice_area_fraction_retreat`

—
a 2D field, possibly time-dependent, that contains ones in areas that may be covered by
ice and zeros in areas that have to be ice-free. Values between \(0\) and \(1\) allow for a
“partial” retreat on coarser grids.

More precisely, `land_ice_area_fraction_retreat`

is a mask prescribing the *maximum
ice extent* at a given time throughout a simulation; a certain rate of retreat can be
prescribed by creating a field with an appropriately decreasing maximum extent.

Changes in ice mass resulting from using this mechanism are reported as a part of the
*discharge* (`tendency_of_ice_mass_due_to_discharge`

).

Note

This replaces the `ocean_kill`

mechanism available in previous PISM versions.

Parameters

Prefix: `geometry.front_retreat.prescribed.`

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