[MITgcm-devel] problems with llc grid?

[Ed Hill]

On Wed, 23 May 2007 11:33:21 +0200 Martin Losch <Martin.Losch at awi.de>
wrote:

> Hi,
> I am moving this to the development list, as it seems to me that
> this should not only affect me, but everyone using an llc grid.
> 
> I include a plot of dyC (taken from the  
> llc45x45x180_lonshift_correctededgeval_?.mitgcm) along the face edge  
> between face 2 (tile8) and 3 (tile9). The last northern-most row of  
> dyC in tile8 is the same as the first row in tile9, which is exactly  
> what we want, BUT the value of this row is larger than both the next  
> rows away from the edge, so that you have a "spike" in dyC when you  
> go across this edge. All dy? fields have this problem, dyU is exacly  
> like dyC, dyF and dyG do not have the "spike" in both face2 and 3,  
> but only in 3 because ny is only 45 for them. It's also visible in
> rAs. Also the corresponding thing is visible in dxC, (between face3
> and face4) etc.
> I assume that the problem (if it is one) is somewhere in  
> compute_grid_perface_nX.m because I don't see this in the 1deg  
> version of the llc grid?
> 
> Ed, maybe you can have a quick look at compute_grid_perface_nX.m and  
> tell my what's wrong so we can correct that.


Hi Martin,

OK, I think I understand.  Please bear with me as I re-state your
observation:

The dyC values match at the edges (as they should!) but these edge
values are higher than they "ought to be" based on a smoothness
argument.  That is, the adjacent dyC lengths within each tile are
appreciably smaller than the dyC values right at the edges.

That's the problem, right?

If so, then there is a way to "fix" it or to at least strike a slightly
different balance between un-even grid lengths and un-even grid cell
areas.  The thing to do is to manually adjust the relative grid spacing
by adjusting where the grid lines "start" on each logically rectangular
region during the initial grid generation stage.  I did exactly that
when I generated the llc grids.  I spent a fair amount of time tuning
these parameters as I tried to produce grids with relatively "smooth"
transitions.  Please understand that these were all "eyeball norms".  I
tried to produce grids with approximately equal-areas and similarly
shaped cells -- especially along the transition from the lat-long
region to the cap and at the connections between the top (northern-most
edge) of the four equator-containing faces and the north-pole-containing
face.

And I'm certain that there are other ways to approach this smooothness
issue.  Jean-Michel has written routines that adjust grid cell areas
and/or grid cell lengths in the vicinity of, for instance, cube corners.
One can probably apply similar adjustments here.  So that would be
another way to increase or enforce some measure of smoothness.

Ed

ps - I can show someone how to adjust these things.  Its all there 
     in the scripts and code that generate the llc grids.  It just 
     takes some time to (iteratively) make the adjustments and
     decide what is/isn't better.

pps - If one could pose a comprehensive norm for "grid goodness"
      then the entire process could be treated as an optimization 
      problem.


-- 
Edward H. Hill III, PhD  |  ed at eh3.com  |  http://eh3.com/
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