Grid Generation for OGCMs with Schwarz‐Christoffel ...€¦ · Grid Generation for OGCMs with Schwarz‐Christoffel Conformal Mappings Shiming Xu, YanluanLin, WenyuHuang, XiaomengHuang,

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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Conformal Mappings

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f

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

*

(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

Cell Sizes in Grid Index Space

Meridional Zonal

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15

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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New Medium‐Resolution Ocean/Ice Grid 

GX1V6 (320x384x60)

SX0.5V2 (720x560x46)

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Spin‐Up of OI w/ CORE‐2 Forcings (1)

• AMOC

• SST

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Spin‐Up of OI w/ CORE‐2 Forcings (2)

SST (yr 351~400) AMOC (yr 351~400)

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Spin‐up of OI w/ CORE‐2 Forcings (3)

Spin‐Up (yr 0400) Mean of Yr 351~400

24Sea ice

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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Surface net SW flux

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Preliminary Coupled Run (PI‐Control, 1870‐79)

New

Old

Diff

Double ITCZ problem alleviated

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New

Old

Diff

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Seasonal variation of P over the Pacific

Enhanced Walker circulation [10S‐5S]

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New

Old

Diff

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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Thanks. Any questions?

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Computational Infrastructure for CIESM

• TODO

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