Post on 27-Aug-2018
Grid Generation for OGCMs with Schwarz‐ChristoffelConformal Mappings
Shiming Xu, Yanluan Lin, Wenyu Huang, Xiaomeng Huang, Fanghua Xu
Department of Earth System Sciences Tsinghua University
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23rd CESM Annual Meeting, Boulder, CO, June 2017
Outline
• Motivation• Schwarz‐Christoffel mapping based grid generation• Sample grid & applications• Updates on new ocean grid in CIESM development
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State‐of‐the‐Art OGCM Grids
Global Models Regional Models Models w/ Irregular Meshes
Grid Analytical Forms Coastline Following Coastline Fitting
Precision of Bathemetry Effects* BAD GOOD ACHIEVABLE
Land Occupation HIGH LOW NONE
Computational Efficiency LOW HIGH HIGH
Multi‐Scale Modeling NONE NONE ACHIEVABLE
Friendliness w/ Existing Models GOOD GOOD BAD
3* isobath alignment, river discharge & plumes, etc.
V.S.
Tripolar Dipolar
&
POP, MOM, NEMO … POM, ROMS, … FVCOM, ICOM, …
Lateral Boundaries As Key Regions in (High‐Resolution) Ocean Models
• Smaller Rossby radii due to shallower bathymetry• Strong model biases, due to complex air‐sea processes• A key area of kinematic energy cascading of mesoscale eddies• Biogeochemistry processes• Closely related to human activities
4[Zhai et al, 2010] [Wang et al, 2014]
Coastal Kelvin Waves – A Case Study
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[Griffith, JCP, 2013]
[Frischknecht et al, JGR, 2015]
10 2 10 1 10010 2
10 1
tan
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Motivations
• Computation: remove continents from grid index space • Science‐I: aligning (large‐scale) continental boundaries & isobaths to grid lines
• Science‐II: multi‐scale simulation support with higher spatial resolution on continental boundaries
• Practicality: compatible with existing Bryan‐Cox‐Semtner type OGCMs
• POP, MOM, NEMO | POM, ROMS
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Geophysical Fluid Dynamics
Models & Algorithms
Parallel Computers
Outline
• Motivation• Schwarz‐Christoffel mapping based grid generation• Sample grid & applications• Updates on new grid in CIESM development
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Schwarz‐Christoffel Mapping Deals with Irregular Boundaries …
• Riemann Mapping Theorem for the existence of a conformal mapping between:
• Schwarz‐Christoffel mapping• User‐specified boundary information and SC Mapping
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[Driscoll and Trefethen, 2002]
Schwarz‐Christoffel Conformal Mapping for Multiply Connected Regions
** *
(c) Canonical slits I - parallel lines
(d) Canonical slits II -radial lines
(e) Canonical slits III -circular lines
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(a) A sample region (connectivity=5)
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(b) Canonical circles
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• Canonical forms• Construction of maps:
• Reflection principle [DeLillo and Kropf, 2011]
• Laurent series expansion [DeLillo et al, 2013]
SCC‐Grid – Multiply‐Connected Schwarz‐ChristoffelConformal Mapping based OGCM Grid
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Shiming Xu, Bin Wang and Jiping Liu, On the use of Schwarz–Christoffel conformal mappings to the grid generation for global ocean models, Geoscientific Model Development, 8, 3471‐3485, doi:10.5194/gmd‐8‐3471‐2015, 2015.
Outline
• Motivation• Schwarz‐Christoffel mapping based grid generation• Sample grid & applications• Updates on new grid in CIESM development
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180oW 135oW 90oW 45oW 0o 45oE 90oE 135oE 180oW
75oS
30oS
0o
30oN
75oN
Sample Global Grid (1/4 deg.)
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* 1 in every 10 points shown
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135
o W
90 oW
45oW
0o
45o E
60
o N
160 oW 150oW 140oW 130oW 120oW
110o W
25 oN
35 oN
45 oN
55 oN
65 oN
100oE 110oE 120oE
15oN
25oN
35oN
10 oW 0o
10oE 20oE 30oE 40o E
30 oN
40 oN
50 oN
Spin‐Up Run with POP model
• Idealized forcings• Actions needed: replacement of grid files• 50‐yrs spin‐up run• Climate simulations w/ CESM underway
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Outline
• Motivation• Schwarz‐Christoffel mapping based grid generation• Sample grid & applications• Updates on new grid in model development
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Ocean Model for CMIP6
•New 0.5 deg. dipolar SCCGrid (720x560)•Canuto vertical mixing scheme•A scalable barotropic solver (already in POP2)•dT‐dependent wind stress scheme
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New Medium‐Resolution Ocean/Ice Grid
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• Schwarz‐Christoffel mapping for the North Atlantic‐Arctic region• Up to 94% of the ocean is pure Lat.‐Lon.
• Higher than any other global model grid
Comparisons
Grid Model Type Turning Lat.
Non. Lat-Lon (Oceanic Area)
Scaling FactorTransition
(Oceanic Area)
ORCA025 NEMO Tripolar 20.31 24.5% 3.21
HYCOM HYCOM Tripolar 46.99 8.8% 2.09
GX1V6POP -CESM
Dipolar 0 42.9% 1.02
TX0.1V2 Tripolar 28.55 18.7% 1.23
SX0.5V3 POP -CESM Dipolar Non-
Uniform 6.2% 1.10
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Atmosphere model for CMIP6
• MG1.5 single ice scheme
• Park‐RH/Zhang condensation a diagnostic PDF cloud scheme
• ZM new ZM
• Four stream shortwave radiation
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Summary & Conclusion
• New grid generation for current OGCMs• Alignment of grid lines w/ large‐scale coastlines• Removal of continental areas, free computational load balancing• Better coastal spatial resolution, enabling easier spatial refinement
• Application as easy as replacing grid files• No need to modify the model
• Preliminary application shows reasonable results• Coupled runs underway
• Future work includes high‐resolution (0.1‐deg, tripolar) grid generation and simulation
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