pik.rst (8960B)
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