1. Aug. 24, 2010 Shin-ichi Iga NICAM group, JAMSTEC, Japan
Tropically or locally fine triangular grids on a sphere based on conformal projections
Aug. 24, 2010
Shin-ichi Iga
NICAM group, JAMSTEC, Japan

2. Introduction Global simulation: Regional simulation:
quasi-uniform (icosahedral, cubic, Yin-Yang, … etc)
Most convection occurs in the tropics. Is quasi-uniform most cost-effective?
We proposed tropically enhancing as an alternative method.
Regional simulation:
Grid nesting  noise around the boundary
Grid stretching
cubic, octagonal  corner problem
Stretched icosahedral
In this study, the other type of stretched triangular mesh is proposed. ( Iga 2010, submitted to MWR)

3. Newly proposed icosahedral grid different topology quasi-uniform
Non-uniform resolution
Stretched (Tomita2008)

4. Benefit of the tropically fine mesh
High resolution is needed to represent cloud convection.
Most deep convections occurs in the tropics. The new grid represents them cost-effectively.
Fine mesh in
convective
region

5. Benefit of the locally fine mesh
Uniform resolution inside the target region.
No wave-reflection problem which is seen in nesting grid.
Non-uniform
uniform
Resolution varies
continuously
New grid
Stretched Icosahedral (Tomita2008)

6. PSP(polar stereo)
１、two hexagon are projected on two Polar Stereographic map.
They can be connected at an arbitrary latitudes.
( above example is 50S).
2, same alphabets are connected
3, smooth using spring grid of Tomita et al(2001）
Equatorial resolution is twice
Than that of pole

7. PSP (regional model) Connection latitude is 60N Quasi uniform
1, use PSP.
2, connected latitude is 60N
・half of grid points are inside the target region (red circle)

8. LCP (Lambert’s conformal conic)
1, use 2 Lambert conformal conic map.
2, angle of the map can be > 360
3, almost same to PSP
Larger resolution contrast

9. MLCP (Mercator + LCP) LCP (low latitudes) + Mercator (high latitudes)
Tropical belt of uniform resolution

10. resolution We can generate various kind of Resolution distribution
Tropically fine cases
Normalized by maximum
We can generate various kind of
Resolution distribution
Regionally fine cases
S(1/3) is NICAM Stretch Model

11. Topology Hereafter, GPn: grid point which shares n lines
Euler’s formula:
Vertex – Edge + Face = 2
For the triangular grid:
∑n (6-n)Vn = 12
Where Vn is number of GPn (grid points which shares n lines).
Icosahedral mesh have 12 GP5

12. Relocate twelve GP5 GP5 Icosahedral grid New grid (locally fine)
Located
Around
The
Target
region
12 GP5 are
uniformly
distributed
GP5
Stretched icosahedral
New grid (PSP)
Located
Around
The
equator
Located
Inside and
Outside
The
Target
region

13. 24 GP5 and 2 GP12 GP12 GP5 Quasi uniform
Locate GP5 around high resolution area
Locate GP(n>6) at or around low resolution area.

14. Shallow-water experiment
The new grid is implemented on NICAM Shallow-water model (Tomita et al 2001)
Williamson et al.(1992) test case 1 and 2　are performed.
Test case 1: cosine-bell type passive tracer on solid body rotation. 12days.
Test case 2: solid body rotation. 5days
We will show only grid cases (MLCP, PSP-region)

15. Time series MLCP12 pole-passing case Dx_min=53km t=0 t=3day t=4day
Grid interval around poles is near the size of cosbel. But original bell shape is remain

16. Resolution dependency 1
Initial
MLCP12 equator passing case
After 12 days
Dx_min=53km
Dx_min=108km
Dx_min=212km
MLCP after 12days
As resolution increase, original cosbel shape kept

17. Resolution dependency 2
PSP-region dx=102km
PSP-region dx=51km
PSP regional model. After 12 days. As resolution increases, error decreases
PSP-region dx=25km
Icosahedral-stretched dx=27km

18. error case1 PSP regional model Pole massing MLCP pole passing
MLCP equator passing
They are reasonable

19. error
case2
They are reasonable

20. summary
Tropically or locally fine triangular grids are proposed using a new topology.
Shallow water tests were performed on NICAM
Future works:
Now we are implementing the new grid to NICAM-3d model (maybe soon).