Calving and front retreat

Overview

All mechanisms described below fall into two categories:

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.

  1. file File containing the scaling factor applied to calving rates from eigen_calving, vonmises_calving, and hayhurst_calving (variable name: frac_calving_rate)

  2. periodic (no) If true, interpret forcing data as periodic in time

Eigen calving

PISM-PIK introduced a physically-based 2D-calving parameterization [94]. 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

(33)\[ \begin{align}\begin{aligned}c &= K\; \dot{\epsilon}_{_+}\; \dot{\epsilon}_{_-},\\\dot{\epsilon}_{_\pm} &> 0.\end{aligned}\end{align} \]

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.

  1. K (0 meter second) Set proportionality constant to determine calving rate from strain rates. Note references [94], [52] use K in range \(10^{9}\) to \(3 \times 10^{11}\) m a, that is, \(3 \times 10^{16}\) to \(10^{19}\) m s.

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, [98] propose a calving law where the calving rate \(c\) is functionally related to tensile stresses:

(34)\[c = |\mathbf{u}| \frac{\tilde{\sigma}}{\sigma_{max}},\]

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

(35)\[\tilde{\dot{\epsilon}}_e = \left(\frac{1}{2}\left(\max(0,\dot{\epsilon}_{_+})^2 + \max(0,\dot{\epsilon}_{_-})^2\right)\right)^{1/2}.\]

Following [98], \(\tilde{\sigma}\) is given by

(36)\[\tilde{\sigma} = \sqrt{3} B \tilde{\dot{{\epsilon}}}_e^{1/n},\]

where \(B\) is the ice hardness.

Parameters

Prefix: calving.vonmises_calving.

  1. Glen_exponent (3) Glen exponent in ice flow law for von Mises calving

  2. flow_law (gpbld) The custom flow law for the von Mises stress computation

  3. sigma_max (1e+06 Pa) Set maximum tensile stress. Note references [98] use 1.0e6 Pa.

  4. threshold_file Name of the file containing the spatially-variable vonmises_calving_threshold.

  5. 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 [99] (equation 22).

Note

FIXME: not documented.

Parameters

Prefix: calving.hayhurst_calving.

  1. B_tilde (65 (MPa)^r / year) Effective damage rate [99]

  2. exponent_r (0.43) Damage law exponent [99]

  3. sigma_threshold (0.17 MPa) Damage threshold stress [99]

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.

  1. file Name of the file containing the spatially-variable thickness calving threshold.

  2. periodic (no) If true, interpret forcing data as periodic in time

  3. threshold (50 meters) When terminal ice thickness of floating ice shelf is less than this threshold, it will be calved off.

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.

  1. calve_near_grounding_line (yes) Calve floating ice near the grounding line.

  2. 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.

  1. file Name of the file containing the maximum ice extent mask land_ice_area_fraction_retreat

  2. periodic (no) If true, interpret forcing data as periodic in time


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