Geodesic Modeling in Earth System Research Laboratory (ESRL)

OAR/NOAA

Jin Lee

Earth System Research Laboratory

Aeronomy Lab. Climate Diagnostic center

Climate Monitoring and Diagnostic Lab Environmental Technology Lab

Forecast Systems Lab

Chemical Sciences Div Global Monitoring Div Physical Sciences Div Global Systems Div

Modeling goal: to develop a non-hydrostatic global cloud resolving model for weather and intra-seasonal climate predictions.

GFDL,NSSL,ARL,AOML,GLERL,PMEL

ESRL f.-v. Icos- models (FIM and NIM)

1. Collab. with NCEP/EMC (Icos- for NCEP model ensemble)

•  FIM (flow-following finite- volume Icosahedral model): for weather fcsts.

model components: icosahedral grid, hydrostatic, 2-D f.-v. line integration, theta-sig hybrid coord,

2. Collab. among OAR and other labs.

•  NIM (Non-hydrostatic Icosahedral model) is GCRM for Wx/Clmt fcsts.

model components: Icosahedral grid,

non-hydrostatic, 3-D f.-v. surface integration,

…..

ESMF

Outline of the talk

•  Review FIM and NIM characteristics

•  FIM real-time medium-range weather forecast and performance

•  NIM preliminary results and future outlooks

•  Finite-Volume integrations on local coordinate Novel features of FIM/NIM:

Lee and MacDonald (MWR, 2009): A Finite-Volume Icosahedral Shallow Water Model on Local Coordinate.

spherical .vs. local coord. (ping pong .vs. golf ball)

Justification (i),

The 2-D operator applied to the straight lines, rather than the 3-D operator along the curved lines, e.g.,

Justification (ii): Reduce the number of basis functions in Vandermonde matrix.

Justification (iii): It requires only a few extra fast product operators

(~DWD MWR 2000: rotate with two great circles )

•  Finite-Volume integrations on local coordinate •  Conservative and monotonic Adams-Bashforth 3rd-order FCT scheme. - Lee, Bleck, and MacDonald (2010, JCP): A multistep flux-corrected transport

scheme (in review). AB3-MFCT extends Zalesak’s (1979) two-time level to multiple time levels.

“Slotted-Cylinder Advection over poles” (dx~120 km)

Cosine Bell Advection: (dx~120 km) Curve A: analytic Curve B: MFCT

Slotted cylinder: (dx~120 km) Curve A: analytic Curve B: MFCT

Cosine Bell Advection: (dx~120 km) Curve A: analytic Curve B: w/o two extra forcing terms

Slotted cylinder: (dx~120 km) Curve A: analytic Curve B: w/o two extra forcing terms

•  Finite-Volume integrations on local coordinate. •  Conservative and monotonic Adams-Bashforth 3rd-order FCT scheme. •  Grid optimization for efficiency and accuracy

- Wang and Lee (2010, SIAM): Geometric properties of icosahedral-hexagonal grid on sphere (minor revision).

Icosahedral Grid Generation

Recursive Grid Non-recursive Grid

SBiR, MBiR SGCL, MGCL

SBiR SPDN

MGCL

Comparisons of Icosa-grids

Uniformity Regularity

SBiR 1.195 1.476 MBiR 1.175 1.405 SGCL 1.476 1.194 MGCL 1.446 1.135

STD

SPN MGC

Williamson etal.(1992) Case V: Zonal flow over Mountain

SBiR (G8/dt=45 sec)

MBiR (G8/dt=45 sec)

SGCL (G8/dt=36 sec, blow up with dt=45)

MGCL (G8/dt=36 sec, blow up with dt=45)

•  Finite-Volume integrations on local coordinate. •  Conservative and monotonic Adams-Bashforth 3rd-order FCT scheme. •  Grid optimization for efficiency and accuracy •  Efficient indirect addressing scheme on irregular grid - MacDonald, Middlecoff, Henderson, and Lee (2010, IJHPC) : A general method for

modeling on irregular grids (in review).

•  Finite-Volume integrations on local coordinate •  Conservative and monotonic Adams-Bashforth 3rd-order FCT scheme. •  Grid optimization for efficiency and accuracy •  Efficient indirect addressing scheme on irregular grid •  FIM: hybrid σ-θ coordinate --Bleck, Benjamin, Lee and MacDonald (2010, MWR): On the use of an Arbitrary

Lagrangian-Eulerian vertical coordinate in global atmospheric modeling (in-press).

FIM model/ system

- Contributors

FIM DESIGN Jin Lee Sandy MacDonald Rainer Bleck Jian-Wen Bao John M. Brown Jacques Middlecoff Ning Wang Stan Benjamin

Tom Henderson

Chris Harrop

Bill Moninger Brian Jamison Susan Sahm Ed Szoke

Georg Grell

Jeff Whitaker,

SOS project: Bob Lipschutz David Himes Beth Russell Steve Albers Tom Kent + dozens more…

ESMF, Subversion

WorkFlow Manager, xml real-time scripts

Verification, Web page, Evaluation

FIM- chemistry, aerosols

EnKF data assimilation

Results of FIM medium-range weather forecasts

FIM real time forecasts initialized with GFS initial condition at 00 and 12 UTC

(comparisons of FIM and GFS 500 mb ACC)

•  Interpolate GFS initial data to Icosahedral grid.

•  Perform hydrostatic initialization.

•  Perform 7-day fcst with dx~30km.

•  Same initial condition, terrain & sfc parameters, physics package runing at similar model resolutions (dx~30 km)

Icosahedral Model Lat/Lon Model

• Near constant resolution over the globe

Same IC, terrain & sfc parameters, physics package, runing at similar model resolutions (dx~30 km)

Effect of different numerics, e.g., spectral v.s. finite-volume, on tracer transports.

•  Finite-Volume integrations on local coordinate. •  Conservative and monotonic Adams-Bashforth 3rd-order FCT scheme. •  Grid optimization for efficiency and accuracy. •  Efficient indirect addressing scheme on irregular grid. •  FIM: hybrid σ-θ coordinate •  Novel features of NIM:

-Use of three-dimensional control volume in height coordinate. 3-D control volume box

•  Finite-Volume integrations on local coordinate. •  Conservative and monotonic Adams-Bashforth 3rd-order FCT scheme. •  Grid optimization for efficiency and accuracy. •  Efficient indirect addressing scheme on irregular grid •  FIM: hybrid σ-θ coordinate •  Novel features of NIM:

-Use of three-dimensional control volume in height coordinate. -Dynamical design to utilize fast Graphic Processing Unit (GPU) to speed up 34 x on NIM model integration.

•  Finite-Volume integrations on local coordinate. •  Conservative and monotonic Adams-Bashforth 3rd-order FCT scheme. •  Grid optimization for efficiency and accuracy. •  Efficient indirect addressing scheme on irregular grid •  FIM: hybrid σ-θ coordinate •  Novel features of NIM:

-Use of three-dimensional control volume in height coordinate. -Dynamical design to utilize fast Graphic Processing Unit (GPU) to speed up 34 x on NIM model integration. -Implicit tri-diagonal solver .vs. Explicit characteristic solver in resolving vertically propagating acoustic waves.

NIM Non-hydrostatic analytic test cases:

Heat forced circulation warm bubble mountain waves

Comparison of N.H. vertical solvers in the warm bubble simulation. A rising thermal in an isentropic atmosphere. AB3 explicit characteristic .vs. RK4 implicit tri-diag solver

t= 0.0 min t= 0.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 1.0 min t= 1.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 2.0 min t= 2.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 3.0 min t= 3.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 4.0 min t= 4.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 5.0 min t= 5.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 6.0 min t= 6.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 7.0 min t= 7.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 8.0 min t= 8.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 9.0 min t= 9.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 10.0 min t= 10.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 11.0 min t= 11.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 12.0 min t= 12.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 13.0 min t= 13.0 min

Explicit Chs .vs. Implicit tri-diag solvers

t= 14.0 min t= 14.0 min

Explicit Chs .vs. Implicit tri-diag solvers

Final remarks and future outlook

•  A hydrostatic Flow-following Icosahderal Model, FIM, has been developed, tested and prepared for operational NCEP global model ensemble systems.

• A Non-hydrostatic Icosahderal Model, NIM, has been developed and tested w/ meso-scale benchmarks.

•  Incorporate physical packages (GFS, WRF) into NIM for Aqua-Planet simulations.

• Future NIM applications for intra-seasonal predictions, and hurricane intensity forecasts.