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In WRF application, nested domain has always been used for weather/air quality modeling for the place of interest in a better resolution. The figure below illustrates this:

enter image description here

I have noticed that the ratio of grid resolution between outer (coarser) domain and inner (finer) domain are always set at 3:1 ratio.

Is there any reason in the aspects of physical process or computation? Is the ratio of 3:1 helpful for the interaction between the boundary?

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    $\begingroup$ You mean why it is 3:1 and not 2:1 or 4:1? $\endgroup$ – daniel.neumann May 26 '16 at 6:55
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    $\begingroup$ @Han Zhengzu - take a look at Milan Curcic's answer from this question - About the parent_grid_ratio parameter. This is an integer factor of child grid refinement relative to the parent grid. For example, if set to 3, and parent grid resolution is 12 km, the child grid resolution will be 4 km. Odd values for parent_grid_ratio (3, 5, etc.) are recommended because for even values, interpolation errors arise due to the nature of Arakawa C-grid staggering. parent_grid_ratio = 3 is the most commonly used value, and recommended by myself $\endgroup$ – gansub May 26 '16 at 8:41
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    $\begingroup$ earthscience.stackexchange.com/questions/2732/… $\endgroup$ – gansub May 26 '16 at 8:42
  • $\begingroup$ @daniel.neumann. Yes, I always find out the grid resolution were set in 3:1 not 2:1 or 4:1. $\endgroup$ – Han Zhengzu May 26 '16 at 8:46
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To understand why the nesting ratio of 3 is preferred to the nesting ratio of 2, it is important to understand the following two features of WRF:

1) Grids are Arakawa C-staggered: mass points are at cell centers, u-velocities are at east-west cell edges, v-velocities are at north-south cell edges. See Mesinger and Arakawa 1976, Chapter 4 for a good description and explanation of Arakawa staggering. WRF's grid in computer memory looks like this:

   +-------+-------+-------+
   |     v |     v |     v |
j=3|       |       |       |
   | u   p | u   p | u   p |
   +-------+-------+-------+
   |     v |     v |     v |
j=2|       |       |       |
   | u   p | u   p | u   p |
   +-------+-------+-------+
   |     v |     v |     v |
j=1|       |       |       |
   | u   p | u   p | u   p |
   +-------+-------+-------+
      i=1     i=2     i=3

Thus, p(1,1) is geographically located $\Delta x /2$ East of u(1,1) and $\Delta x /2$ south of v(1,1).

2) For computational efficiency and accuracy, the data from the child (nested) domain is copied to the parent domain. This is opposite from the data going from parent to child, which is interpolated. For more specifics, see the WRF Registry documentation by Michalakes and Schaffer.

As a consequence of the above two, it is more computationally efficient and accurate to use a nesting ratio of 3, rather than 2. In the example below, for 2:1 nesting ratio and 1-d case for simplicity, u values are simply copied from child to parent array because these points are guaranteed to overlap between two grids. Notice that the p points do not overlap and child p values must be interpolated to the parent. This induces computational overhead and numerical damping of the $2\Delta x$ wavelength in mass:

child  u   p   u   p   u   p   u
       +-------+-------+-------+
       |    \     /    |
       |     \   /     |
       |      \ /      |
       v       v       v

parent U       P       U
       +---------------+

In a 3:1 nesting ratio however, both the velocity and mass points overlap, and a simple copy is feasible:

child  u   p   u   p   u   p   u
       +-------+-------+-------+
       |           |           |
       |           |           |
       v           v           v

parent U           P           U
       +-----------------------+
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    $\begingroup$ Did you make those diagrams? Nicely done $\endgroup$ – jgadoury Sep 13 '16 at 19:17

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