tpik.rst - pism - [fork] customized build of PISM, the parallel ice sheet model (tillflux branch)
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tpik.rst (8960B)
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1 .. include:: ../../../global.txt
2
3 .. _sec-pism-pik:
4
5 PIK options for marine ice sheets
6 ---------------------------------
7
8 .. contents::
9
10 References :cite:`Albrechtetal2011`, :cite:`Levermannetal2012`, :cite:`Winkelmannetal2011`
11 by the research group of Prof. Anders Levermann at the Potsdam Institute for Climate
12 Impact Research ("PIK"), Germany, describe most of the mechanisms covered in this section.
13 These are all improvements to the grounded, SSA-as-a-sliding law model of
14 :cite:`BBssasliding`. These improvements make PISM an effective Antarctic model, as
15 demonstrated by :cite:`Golledgeetal2013`, :cite:`Martinetal2011`,
16 :cite:`Winkelmannetal2012`, among other publications. These improvements had a separate
17 existence as the "PISM-PIK" model from 2009--2010, but since PISM stable0.4 are part of
18 PISM itself.
19
20 A summary of options to turn on most of these "PIK" mechanisms is in
21 :numref:`tab-pism-pik`. More information on the particular mechanisms is given in
22 sub-sections :ref:`sec-cfbc` through :ref:`sec-subgrid-grounding-line` that follow the
23 Table.
24
25 .. list-table:: Options which turn on PIK ice shelf front and grounding line mechanisms. A
26 calving law choice is needed in addition to these options.
27 :name: tab-pism-pik
28 :header-rows: 1
29 :widths: 1,3
30
31 * - Option
32 - Description
33
34 * - :opt:`-cfbc`
35 - apply the stress boundary condition along the ice shelf calving front
36 :cite:`Winkelmannetal2011`
37
38 * - :opt:`-kill_icebergs`
39 - identify and eliminate free-floating icebergs, which cause well-posedness problems
40 for the SSA stress balance solver :cite:`Winkelmannetal2011`
41
42 * - :opt:`-part_grid`
43 - allow the ice shelf front to advance by a part of a grid cell, avoiding
44 the development of unphysically-thinned ice shelves :cite:`Albrechtetal2011`
45
46 * - :opt:`-subgl`
47 - apply interpolation to compute basal shear stress and basal melt near the grounding
48 line :cite:`Feldmannetal2014`
49
50 * - :opt:`-no_subgl_basal_melt`
51 - **don't** apply interpolation to compute basal melt near the grounding line if
52 :opt:`-subgl` is set :cite:`Feldmannetal2014`
53
54 * - :opt:`-pik`
55 - equivalent to option combination ``-cfbc -kill_icebergs -part_grid -subgl``
56
57 .. note::
58
59 When in doubt, PISM users should set option :opt:`-pik` to turn on all of mechanisms in
60 :numref:`tab-pism-pik`. The user should also choose a calving model from
61 :numref:`tab-calving`. However, the :opt:`-pik` mechanisms will not be effective if the
62 non-default FEM stress balance :opt:`-ssa_method fem` is chosen.
63
64 .. _sec-cfbc:
65
66 Stress condition at calving fronts
67 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
68
69 The vertically integrated force balance at floating calving fronts has been formulated by
70 :cite:`Morland` as
71
72 .. math::
73 :label: eq-cfbc
74
75 \int_{z_s-\frac{\rho}{\rho_w}H}^{z_s+(1-\frac{\rho}{\rho_w})H}\mathbf{\sigma}\cdot\mathbf{n}\;dz
76 = \int_{z_s-\frac{\rho}{\rho_w}H}^{z_s}\rho_w g (z-z_s) \;\mathbf{n}\;dz.
77
78 with `\mathbf{n}` being the horizontal normal vector pointing from the ice boundary
79 oceanward, `\mathbf{\sigma}` the *Cauchy* stress tensor, `H` the ice thickness and `\rho`
80 and `\rho_{w}` the densities of ice and seawater, respectively, for a sea level of `z_s`.
81 The integration limits on the right hand side of equation :eq:`eq-cfbc` account for the
82 pressure exerted by the ocean on that part of the shelf, which is below sea level (bending
83 and torque neglected). The limits on the left hand side change for water-terminating
84 outlet glacier or glacier fronts above sea level according to the bed topography. By
85 applying the ice flow law (section :ref:`sec-rheology`), equation :eq:`eq-cfbc` can be
86 rewritten in terms of strain rates (velocity derivatives), as one does with the SSA stress
87 balance itself.
88
89 Note that the discretized SSA stress balance, in the default finite difference
90 discretization chosen by :opt:`-ssa_method` ``fd``, is solved with an iterative matrix
91 scheme. If option :opt:`-cfbc` is set then, during matrix assembly, those equations which
92 are for fully-filled grid cells along the ice domain boundary have terms replaced
93 according to equation :eq:`eq-cfbc`, so as to apply the correct stresses
94 :cite:`Albrechtetal2011`, :cite:`Winkelmannetal2011`.
95
96 .. _sec-part-grid:
97
98 Partially-filled cells at the boundaries of ice shelves
99 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
100
101 Albrecht et al :cite:`Albrechtetal2011` argue that the correct movement of the ice shelf
102 calving front on a finite-difference grid, assuming for the moment that ice velocities are
103 correctly determined (see below), requires tracking some cells as being partially-filled
104 (option :opt:`-part_grid`). If the calving front is moving forward, for example, then the
105 neighboring cell gets a little ice at the next time step. It is not correct to add that
106 little mass as a thin layer of ice which fills the cell's horizontal extent, as that would
107 smooth the steep ice front after a few time steps. Instead the cell must be regarded as
108 having ice which is comparably thick to the upstream cells, but where the ice only
109 partially fills the cell.
110
111 Specifically, the PIK mechanism turned on by :opt:`-part_grid` adds mass to the
112 partially-filled cell which the advancing front enters, and it determines the coverage
113 ratio according to the ice thickness of neighboring fully-filled ice shelf cells. If
114 option :opt:`-part_grid` is used then the PISM output file will have field
115 ``ice_area_specific_volume`` which tracks the amount of ice in the partially-filled cells
116 as a "thickness", or, more appropriately, "volume per unit area". When a cell becomes
117 fully-filled, in the sense that the ``ice_area_specific_volume`` reaches the average of
118 the ice thickness in neighboring ice-filled cells, then the residual mass is redistributed
119 to neighboring partially-filled or empty grid cells.
120
121 The stress balance equations determining the velocities are only sensitive to
122 "fully-filled" cells. Similarly, advection is controlled only by values of velocity in
123 fully-filled cells. Adaptive time stepping (specifically: the CFL criterion) limits the
124 speed of ice front propagation so that at most one empty cell is filled, or one full cell
125 emptied, per time step by the advance or retreat, respectively, of the calving front.
126
127 .. _sec-kill-icebergs:
128
129 Iceberg removal
130 ^^^^^^^^^^^^^^^
131
132 Any calving mechanism (see section :ref:`sec-calving`) removes ice along the seaward front
133 of the ice shelf domain. This can lead to isolated cells either filled or partially-filled
134 with floating ice, or to patches of floating ice (icebergs) fully surrounded by ice free
135 ocean neighbors. This ice is detached from the flowing and partly-grounded ice sheet. That
136 is, calving can lead to icebergs.
137
138 In terms of our basic model of ice as a viscous fluid, however, the stress balance for an
139 iceberg is not well-posed because the ocean applies no resistance to balance the driving
140 stress. (See :cite:`SchoofStream`.) In this situation the numerical SSA stress balance
141 solver will fail.
142
143 Option :opt:`-kill_icebergs` turns on the mechanism which cleans this up. This option is
144 therefore generally needed if there is nontrivial calving or significant variations in sea
145 level during a simulation. The mechanism identifies free-floating icebergs by using a
146 2-scan connected-component labeling algorithm. It then eliminates such icebergs, with the
147 corresponding mass loss reported as a part of the 2D discharge flux diagnostic (see
148 section :ref:`sec-saving-diagnostics`).
149
150 .. _sec-subgrid-grounding-line:
151
152 Sub-grid treatment of the grounding line position
153 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
154
155 The command-line option :opt:`-subgl` turns on a parameterization of the grounding line
156 position based on the "LI" parameterization described in :cite:`Gladstoneetal2010` and
157 :cite:`Feldmannetal2014`. With this option PISM computes an extra flotation mask,
158 available as the :var:`cell_grounded_fraction` output variable, which corresponds to the
159 fraction of the cell that is grounded. Cells that are ice-free or fully floating are
160 assigned the value of `0` while fully-grounded icy cells get the value of `1`. Partially
161 grounded cells, the ones which contain the grounding line, get a value between `0` and
162 `1`. The resulting field has two uses:
163
164 - It is used to scale the basal friction in cells containing the grounding line in order
165 to avoid an abrupt change in the basal friction from the "last" grounded cell to the
166 "first" floating cell. See the source code browser for the detailed description and
167 section :ref:`sec-MISMIP3d` for an application.
168 - It is used to adjust the basal melt rate in cells containing the grounding line: in such
169 cells the basal melt rate is set to `M_{b,\text{adjusted}} = \lambda
170 M_{b,\text{grounded}} + (1 - \lambda)M_{b,\text{shelf-base}}`, where `\lambda` is the
171 value of the flotation mask. Use :opt:`-no_subgl_basal_melt` to disable this.
172