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Warning, /doc/algorithm/horiz-grid.rst is written in an unsupported language. File is not indexed.
view on githubraw file Latest commit ee406b47 on 2021-12-07 22:38:03 UTCbf89a37abc Phob*0001 .. _spatial_discrete_horizontal_grid: 4f2617d475 Jeff*0002 0003 Horizontal grid 0004 --------------- 0005 0006 The model domain is decomposed into tiles and within each tile a 0007 quasi-regular grid is used. A tile is the basic unit of domain 0008 decomposition for parallelization but may be used whether parallelized 0009 or not; see section [sec:domain\_decomposition] for more details. 0010 Although the tiles may be patched together in an unstructured manner 0011 (i.e. irregular or non-tessilating pattern), the interior of tiles is a 0012 structured grid of quadrilateral cells. The horizontal coordinate system 0013 is orthogonal curvilinear meaning we can not necessarily treat the two 0014 horizontal directions as separable. Instead, each cell in the horizontal** Warning **
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0015 grid is described by the length of it’s sides and it’s area. 0016 0017 The grid information is quite general and describes any of the available 0018 coordinates systems, cartesian, spherical-polar or curvilinear. All that 0019 is necessary to distinguish between the coordinate systems is to 0020 initialize the grid data (descriptors) appropriately. 0021 0022 In the following, we refer to the orientation of quantities on the 0023 computational grid using geographic terminology such as points of the 0024 compass. This is purely for convenience but should not be confused with 0025 the actual geographic orientation of model quantities. 0026 0027 .. figure:: figs/hgrid-abcd.* 0028 :width: 80% 0029 :align: center 0030 :alt: hgrid-abcd 0031 :name: hgrid-abcd ee406b477f Mart*0032 0033 Staggering of horizontal grid descriptors (lengths and areas). The grid 0034 lines indicate the tracer cell boundaries and are the reference grid for 0035 all panels. a) The area of a tracer cell, :math:`A_c`, is bordered by the 0036 lengths :math:`\Delta x_g` and :math:`\Delta y_g`. b) The area of a 0037 vorticity cell, :math:`A_\zeta`, is bordered by the lengths :math:`\Delta 0038 x_c` and :math:`\Delta y_c`. c) The area of a u cell, :math:`A_w`, is 0039 bordered by the lengths :math:`\Delta x_v` and :math:`\Delta y_f`. d) The 0040 area of a v cell, :math:`A_s`, is bordered by the lengths :math:`\Delta 0041 x_f` and :math:`\Delta y_u`. 4f2617d475 Jeff*0042 0043 :numref:`hgrid-abcd` (a) shows the tracer cell (synonymous with the continuity ee406b477f Mart*0044 cell). The length of the southern edge, :math:`\Delta x_g`, western edge, 0045 :math:`\Delta y_g` and surface area, :math:`A_c`, presented in the vertical are** Warning **
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0046 stored in arrays :varlink:`dxG`, :varlink:`dyG` and :varlink:`rA`. The “g” 0047 suffix indicates that the lengths are along the defining grid boundaries. The** Warning **
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0048 “c” suffix associates the quantity with the cell centers. The quantities are 0049 staggered in space and the indexing is such that **dxG(i,j)** is positioned to 0050 the south of **rA(i,j)** and **dyG(i,j)** positioned to the west. 0051 0052 :numref:`hgrid-abcd` (b) shows the vorticity cell. The length of the northern 0053 edge, :math:`\Delta x_c`, eastern edge, :math:`\Delta y_c` and surface area, 0054 :math:`A_\zeta`, presented in the vertical are stored in arrays :varlink:`dxC`,** Warning **
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0055 :varlink:`dyC` and :varlink:`rAz`. The “c” suffix indicates that the lengths** Warning **
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0056 are measured between the cell centers and the “:math:`\zeta`” suffix associates 0057 points with the vorticity points. The quantities are staggered in space and the 0058 indexing is such that **dxC(i,j)** is positioned to the north of **rAz(i,j)** 0059 and **dyC(i,j)** positioned to the east. 4f2617d475 Jeff*0060** Warning **
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0061 :numref:`hgrid-abcd` (c) shows the “u” or western (w) cell. The length of the ee406b477f Mart*0062 southern edge, :math:`\Delta x_v`, eastern edge, :math:`\Delta y_f` and surface 0063 area, :math:`A_w`, presented in the vertical are stored in arrays** Warning **
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0064 :varlink:`dxV`, :varlink:`dyF` and :varlink:`rAw`. The “v” suffix indicates** Warning **
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0065 that the length is measured between the v-points, the “f” suffix indicates that** Warning **
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0066 the length is measured between the (tracer) cell faces and the “w” suffix 0067 associates points with the u-points (w stands for west). The quantities are 0068 staggered in space and the indexing is such that **dxV(i,j)** is positioned to 0069 the south of **rAw(i,j)** and **dyF(i,j)** positioned to the east. 4f2617d475 Jeff*0070** Warning **
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0071 :numref:`hgrid-abcd` (d) shows the “v” or southern (s) cell. The length of the ee406b477f Mart*0072 northern edge, :math:`\Delta x_f`, western edge, :math:`\Delta y_u` and surface 0073 area, :math:`A_s`, presented in the vertical are stored in arrays** Warning **
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0074 :varlink:`dxF`, :varlink:`dyU` and :varlink:`rAs`. The “u” suffix indicates** Warning **
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0075 that the length is measured between the u-points, the “f” suffix indicates that** Warning **
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0076 the length is measured between the (tracer) cell faces and the “s” suffix 0077 associates points with the v-points (s stands for south). The quantities are 0078 staggered in space and the indexing is such that **dxF(i,j)** is positioned to 0079 the north of **rAs(i,j)** and **dyU(i,j)** positioned to the west. 0080 0081 .. admonition:: S/R :filelink:`INI_CARTESIAN_GRID 0082 <model/src/ini_cartesian_grid.F>` , 0083 :filelink:`INI_SPHERICAL_POLAR_GRID 0084 <model/src/ini_spherical_polar_grid.F>` , 0085 :filelink:`INI_CURVILINEAR_GRID 0086 <model/src/ini_curvilinear_grid.F>` 4f2617d475 Jeff*0087 :class: note 0088 0089 | :math:`A_c , A_\zeta , A_w , A_s` : :varlink:`rA`, :varlink:`rAz`, :varlink:`rAw`, :varlink:`rAs` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0090 | :math:`\Delta x_g , \Delta y_g` : :varlink:`dxG`, :varlink:`dyG` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0091 | :math:`\Delta x_c , \Delta y_c` : :varlink:`dxC`, :varlink:`dyC` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0092 | :math:`\Delta x_f , \Delta y_f` : :varlink:`dxF`, :varlink:`dyF` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0093 | :math:`\Delta x_v , \Delta y_u` : :varlink:`dxV`, :varlink:`dyU` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0094 0095 0096 Reciprocals of horizontal grid descriptors 0097 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0098 0099 Lengths and areas appear in the denominator of expressions as much as in 0100 the numerator. For efficiency and portability, we pre-calculate the 0101 reciprocal of the horizontal grid quantities so that in-line divisions 0102 can be avoided. 0103 ee406b477f Mart*0104 For each grid descriptor (array) there is a reciprocal named using the prefix 0105 ``recip_``. This doubles the amount of storage in :filelink:`GRID.h 0106 <model/inc/GRID.h>` but they are all only 2-D descriptors. 4f2617d475 Jeff*0107 0108 .. admonition:: S/R :filelink:`INI_MASKS_ETC <model/src/ini_masks_etc.F>` 0109 :class: note 0110 0111 | :math:`A_c^{-1} , A_\zeta^{-1} , A_w^{-1} , A_s^{-1}` : :varlink:`recip_rA`, :varlink:`recip_rAz`, :varlink:`recip_rAw`, :varlink:`recip_rAs` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0112 | :math:`\Delta x_g^{-1} , \Delta y_g^{-1}` : :varlink:`recip_dxG`, :varlink:`recip_dyG` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0113 | :math:`\Delta x_c^{-1} , \Delta y_c^{-1}` : :varlink:`recip_dxC`, :varlink:`recip_dyC` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0114 | :math:`\Delta x_f^{-1} , \Delta y_f^{-1}` : :varlink:`recip_dxF`, :varlink:`recip_dyF` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0115 | :math:`\Delta x_v^{-1} , \Delta y_u^{-1}` : :varlink:`recip_dxV`, :varlink:`recip_dyU` ( :filelink:`GRID.h <model/inc/GRID.h>` ) 0116 0117 Cartesian coordinates 0118 ~~~~~~~~~~~~~~~~~~~~~ 0119 0120 Cartesian coordinates are selected when the logical flag 0121 :varlink:`usingCartesianGrid` in namelist ``PARM04`` is set to true. The grid 0122 spacing can be set to uniform via scalars :varlink:`dXspacing` and 0123 :varlink:`dYspacing` in namelist ``PARM04`` or to variable resolution by the 0124 vectors :varlink:`DELX` and :varlink:`DELY`. Units are normally meters. 0125 Non-dimensional coordinates can be used by interpreting the 0126 gravitational constant as the Rayleigh number. 0127 0128 Spherical-polar coordinates 0129 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0130 0131 Spherical coordinates are selected when the logical flag 0132 :varlink:`usingSphericalPolarGrid` in namelist ``PARM04`` is set to true. The 0133 grid spacing can be set to uniform via scalars :varlink:`dXspacing` and 0134 :varlink:`dYspacing` in namelist ``PARM04`` or to variable resolution by the ee406b477f Mart*0135 vectors :varlink:`DELX` and :varlink:`DELY`. Units of these namelist variables 0136 are alway degrees. The horizontal grid descriptors are calculated from these 4f2617d475 Jeff*0137 namelist variables have units of meters. 0138 0139 Curvilinear coordinates 0140 ~~~~~~~~~~~~~~~~~~~~~~~ 0141 0142 Curvilinear coordinates are selected when the logical flag 0143 :varlink:`usingCurvilinearGrid` in namelist ``PARM04`` is set to true. The grid 0144 spacing can not be set via the namelist. Instead, the grid descriptors 0145 are read from data files, one for each descriptor. As for other grids, 0146 the horizontal grid descriptors have units of meters.
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