tcalving.rst - pism - [fork] customized build of PISM, the parallel ice sheet model (tillflux branch)
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---
tcalving.rst (8865B)
---
1 .. include:: ../../../global.txt
2
3 .. _sec-calving:
4
5 Calving and front retreat
6 -------------------------
7
8 .. contents::
9
10 The :numref:`tab-calving` summarizes options controlling calving parameterizations
11 implemented in PISM.
12
13 .. list-table:: Options for the calving models in PISM.
14 :name: tab-calving
15 :header-rows: 1
16 :widths: 1,1
17
18 * - Option
19 - Description
20
21 * - :opt:`-front_retreat_cfl`
22 - Apply CFL-type criterion to reduce (limit) PISM's time step using the horizontal
23 calving rate computed by ``eigen_calving`` or ``vonmises_calving``.
24
25 * - :opt:`-calving eigen_calving`
26 - Physically-based calving parameterization :cite:`Levermannetal2012`,
27 :cite:`Winkelmannetal2011`. Whereever the product of principal strain rates is positive,
28 the calving rate is proportional to this product.
29
30 * - :opt:`-eigen_calving_K` (`m s`)
31 - Sets the proportionality parameter `K` in `\text{m}\,\text{s}`.
32
33 * - :opt:`-calving vonmises_calving`
34 - Physically-based calving parameterization :cite:`Morlighem2016` that uses the tensile
35 von Mises stresses.
36
37 * - :opt:`-vonmises_calving_sigma_max` (`Pa`)
38 - Sets the maximum tensile stress `\tilde{\sigma}` in `\text{Pa}`.
39
40 * - :opt:`-calving thickness_calving`
41 - Calve all near-terminus ice which is thinner than ice threshold thickness
42 `H_{\textrm{cr}}`.
43
44 * - :opt:`-thickness_calving_threshold` (m)
45 - Sets the thickness threshold `H_{\textrm{cr}}` in meters.
46
47 * - :opt:`-thickness_calving_threshold_file`
48 - Specifies the file containing the variable :opt:`calving_threshold` to be used as
49 the spetially-variable thickness threshold
50
51 * - :opt:`-calving float_kill`
52 - All floating ice is calved off immediately.
53
54 * - :opt:`-float_kill_margin_only`
55 - At each time step, calve cells at the ice margin only instead of removing all
56 floating ice.
57
58 * - :opt:`-float_kill_calve_near_grounding_line`
59 - Calve floating ice near the grounding line (this is the default). Disable using
60 :opt:`-float_kill_calve_near_grounding_line off`.
61
62 To select several calving mechanisms, use a comma-separated list of keywords mentioned in
63 :numref:`tab-calving`:
64
65 .. code-block:: none
66
67 -calving eigen_calving,thickness_calving,ocean_kill,vonmises_calving
68
69 .. _sec-eigen-calving:
70
71 Eigen calving
72 ^^^^^^^^^^^^^
73
74 PISM-PIK introduced a physically-based 2D-calving parameterization
75 :cite:`Levermannetal2012`. This calving parameterization is turned on in PISM by option
76 :opt:`-calving eigen_calving`. Average calving rates, `c`, are proportional to the product
77 of principal components of the horizontal strain rates, `\dot{\epsilon}_{_\pm}`, derived
78 from SSA-velocities
79
80 .. math::
81 :label: eq-calv2
82
83 c = K\; \dot{\epsilon}_{_+}\; \dot{\epsilon}_{_-}\quad\text{and}\quad\dot{\epsilon}_{_\pm}>0\:.
84
85 The rate `c` is in `\text{m}\,\text{s}^{-1}`, and the principal strain rates
86 `\dot\epsilon_\pm` have units `\text{s}^{-1}`, so `K` has units `\text{m}\,\text{s}`. The
87 constant `K` incorporates material properties of the ice at the front. It can be set using
88 the :opt:`-eigen_calving_K` option or a configuration parameter
89 (:config:`calving.eigen_calving.K` in |config-cdl|).
90
91 The actual strain rate pattern strongly depends on the geometry and boundary conditions
92 along the confinements of an ice shelf (coast, ice rises, front position). The strain rate
93 pattern provides information in which regions preexisting fractures are likely to
94 propagate, forming rifts (in two directions). These rifts may ultimately intersect,
95 leading to the release of icebergs. This (and other) ice shelf calving models are not
96 intended to resolve individual rifts or calving events, but it produces
97 structurally-stable calving front positions which agree well with observations. Calving
98 rates balance calving-front ice flow velocities on average.
99
100 The partially-filled grid cell formulation (section :ref:`sec-part-grid`) provides a
101 framework suitable to relate the calving rate produced by ``eigen_calving`` to the mass
102 transport scheme at the ice shelf terminus. Ice shelf front advance and retreat due to
103 calving are limited to a maximum of one grid cell length per (adaptive) time step. The
104 calving rate (velocity) from ``eigen_calving`` can be used to limit the overall timestep
105 of PISM--thus slowing down all of PISM--by using :opt:`-front_retreat_cfl`. This "CFL"-type
106 time-step limitation is definitely recommended in high-resolution runs which attempt to
107 model calving position accurately. Without this option, under certain conditions where
108 PISM's adaptive time step happens to be long enough, dendritic structures can appear at
109 the calving front because the calving mechanism cannot "keep up" with the computed calving
110 rate.
111
112 .. _sec-stress-calving:
113
114 Von Mises stress calving
115 ^^^^^^^^^^^^^^^^^^^^^^^^
116
117 .. warning::
118
119 This code is experimental and has not yet been thoroughly tested, use at your own risk.
120
121 While eigen-calving (section :ref:`sec-eigen-calving`) is appropriate for Antartic ice
122 shelves, it does not work for outlet glaciers that flow in narrow fjords. Along valleys
123 with nearly parallel walls, the transverse component of the velocity is close to zero, and
124 the transversal strain rate is therefore also close to zero and noisy.
125
126 Instead of the product of the eigen strain rates, :cite:`Morlighem2016` proposes a calving
127 law where the calving rate `c` is a functionally related to tensile stresses:
128
129 .. math::
130 :label: eq-calv3
131
132 c = |\mathbf{u}| \frac{\tilde{\sigma}}{\sigma_{max}},
133
134 where `\tilde{\sigma}` is the tensile von Mises stress and `\sigma_{max}` is a threshold
135 that has units `Pa`. It can be set as a configuration parameter
136 (:config:`calving.vonmises.sigma_max` in |config-cdl|). As the tensile fracture strength
137 is much smaller than the compressive fracture strenth, the effective tensile strain rate
138 is defined as
139
140 .. math::
141 :label: eq-calv4
142
143 \tilde{\dot{\epsilon}}_e = \left(\frac{1}{2}\left(\max(0,\dot{\epsilon}_{_+})^2 +
144 \max(0,\dot{\epsilon}_{_-})^2\right)\right)^{1/2}.
145
146 Following :cite:`Morlighem2016` `\tilde{\sigma}` is given by
147
148 .. math::
149 :label: eq-calv5
150
151 \tilde{\sigma} = \sqrt{3} B \tilde{\dot{{\epsilon}}}_e^{1/n},
152
153 where `B` is the ice hardness.
154
155 Similar to ``eigen_calving``, the calving rate from ``vonmises_calving`` can be used to
156 limit the overall timestep of PISM --- thus slowing down all of PISM --- by using
157 :opt:`-front_retreat_cfl`.
158
159 .. _sec-additional-calving:
160
161 Additional calving methods
162 ^^^^^^^^^^^^^^^^^^^^^^^^^^
163
164 PISM also includes three more basic calving mechanisms (:numref:`tab-calving`). The
165 option :opt:`-calving thickness_calving` is based on the observation that ice shelf
166 calving fronts are commonly thicker than about 150--250 m (even though the physical
167 reasons are not clear yet). Accordingly, any floating ice thinner than `H_{\textrm{cr}}`
168 is removed along the front, at a rate at most one grid cell per time step. The value of
169 `H_{\mathrm{cr}}` can be set using the :opt:`-thickness_calving_threshold` option or the
170 :config:`calving.thickness_calving.threshold` configuration parameter.
171
172 To set a spatially-variable ice thickness threshold, use the option
173 :opt:`-thickness_calving_threshold_file` or the parameter
174 :config:`calving.thickness_calving.threshold_file`. This file should contain the variable
175 :var:`calving_threshold` in meters (or other compatible units).
176
177 Option :opt:`-calving float_kill` removes (calves), at each time step of the run, any ice
178 that satisfies the flotation criterion. Use of this option implies that there are no ice
179 shelves in the model at all.
180
181 Use the option :opt:`-float_kill_margin_only` to restrict this to cells at the ice margin.
182
183 Sometimes it is useful to preserve a one-cell-wide shelf near the grounding line. To do
184 this, set :config:`calving.float_kill.calve_near_grounding_line` to false.
185
186 .. _sec-prescribed-retreat:
187
188 Prescribed front retreat
189 ^^^^^^^^^^^^^^^^^^^^^^^^
190
191 Option :opt:`-front_retreat_file` allows prescribing retreat of the ice front. The forcing
192 file specified using this option should contain :var:`land_ice_area_fraction_retreat` ---
193 a 2D field, possibly time-dependent, that contains ones in areas that may be covered by
194 ice and zeros in areas that have to be ice-free. Values between `0` and `1` allow for a
195 "partial" retreat on coarser grids.
196
197 More precisely, :var:`land_ice_area_fraction_retreat` is a mask prescribing the *maximum
198 ice extent* at a given time throughout a simulation; a certain rate of retreat can be
199 prescribed by creating a field with an appropriately decreasing maximum extent.
200
201 Changes in ice mass resulting from using this mechanism are reported as a part of the
202 *discharge* (:var:`tendency_of_ice_mass_due_to_discharge`).
203
204 .. note::
205
206 This replaces the :literal:`ocean_kill` mechanism available in previous PISM versions.