tbox.rst - pism - [fork] customized build of PISM, the parallel ice sheet model (tillflux branch)
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       tbox.rst (3128B)
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            1 .. include:: ../../../global.txt
            2 
            3 .. _sec-coords:
            4 
            5 Computational box
            6 -----------------
            7 
            8 PISM performs all simulations in a computational box which is rectangular in the PISM
            9 coordinates. The coordinate system has horizontal coordinates `x,y` and a vertical
           10 coordinate `z`. The `z` coordinate is measured positive upward from the base of the ice.\
           11 [#]_ The vector of gravity is in the negative `z` direction. The surface `z=0` is the base
           12 of the ice, however, and thus is usually not horizontal in the sense of being parallel to
           13 the geoid.
           14 
           15 The surface `z=0` is the base of the ice both when the ice is grounded and when the ice is
           16 floating.
           17 
           18 When the ice is grounded, the true physical vertical coordinate `z'`, namely the
           19 coordinate measured relative to a reference geoid, is given by
           20 
           21 .. math::
           22    z' = z + b(x,y),
           23 
           24 where `b(x,y)` is the bed topography. The top surface of the ice `h(x,y)` is described by
           25 `h(x,y) = H(x,y) + b(x,y)`, where `H(x,y)` is the ice thickness.
           26 
           27 In the floating case, the physical vertical coordinate is
           28 
           29 .. math::
           30    :label: eq-vertical-coordinate
           31 
           32    z' = z + z_{sl} - \frac{\rho_i}{\rho_w} H(x,y)
           33 
           34 where `\rho_i` is the density of ice, `\rho_w` the density of sea water, and `z_{sl}` is
           35 the sea level elevation. Again, the physical elevation of the bottom (top) surface of the
           36 ice relative to the geoid can be computed by substituting `z = 0` (`z = H(x,y)`) in
           37 :eq:`eq-vertical-coordinate`.
           38 
           39 Here the *flotation criterion* `z_{sl} - \frac{\rho_i}{\rho_w} H(x,y) > b(x,y)` applies.
           40 
           41 The computational box can extend downward into the bedrock. As `z=0` is the base of
           42 the ice, the bedrock corresponds to negative `z` values regardless of its true (i.e.
           43 `z'`) elevation.
           44 
           45 The extent of the computational box, along with its bedrock extension downward, is
           46 determined by four numbers ``Lx``, ``Ly``, ``Lz``, and ``Lbz`` (see
           47 :numref:`fig-rectilinearbox` and :numref:`tab-compbox`). The first two of these are
           48 half-widths and have units of kilometers when set by command-line options or displayed.
           49 
           50 .. figure:: figures/rectilinearbox.png
           51    :name: fig-rectilinearbox
           52 
           53    PISM's computational box
           54 
           55 .. list-table:: Options defining the extent of PISM's computational box
           56    :name: tab-compbox
           57    :header-rows: 1
           58    :widths: 20, 80
           59 
           60    * - Option
           61      - Description
           62    * - :opt:`-Lx` (km)
           63      - Half-width of the computational domain (in the `x`\-direction)
           64    * - :opt:`-Ly` (km)
           65      - Half-width of the computational domain (in the `y`\-direction)
           66    * - :opt:`-Lz` (meters)
           67      - Height of the computational domain; must exceed maximum ice thickness
           68    * - :opt:`-Lbz` (meters)
           69      - Depth of the computational domain in the bedrock thermal layer
           70    * - :opt:`-x_range A,B` (meters)
           71      - Specify the range of `x` coordinates. Use this to select a subset of an input grid
           72        that isn't in the center of a domain.
           73    * - :opt:`-y_range A,B` (meters)
           74      - Specify the range of `y` coordinates.
           75 
           76 See :ref:`sec-grid-registration` for details about the interpretation of `L_x`, `L_y`, and
           77 the way the grid spacing is computed.
           78 
           79 .. rubric:: Footnotes
           80 
           81 .. [#] See :ref:`sec-vertchange` for details.