Discretizing the Sphere for Multi-Scale Air Quality Simulations
using Variable-Resolution Finite-Volume Techniques
Martin J. Otte
U.S. EPA
Robert Walko
University of Miami
The Ocean-Land-Atmosphere Model (OLAM)
1. OLAM is based partly on RAMS, a limited area model specializing in
mesoscale and cloud scale simulations
2. The primary motivation for OLAM was to provide a global modeling
framework similar to RAMS in the following aspects:
•
•
•
•
•
•
Arakawa-C grid stagger
Mass- and momentum-conserving finite-volume discretization
Compressible equations with time-split solver
Local mesh refinement
Horizontal terrain-intersecting grid levels (an option in RAMS)
Same physical parameterizations (microphysics, land, etc.)
3. Other aspects of RAMS were abandoned:
•
•
•
Boussinesq  Full Navier Stokes
Polar stereographic projection  No projection
Squares  Triangles
4. A new dynamic core was developed to meet these requirements
Most common grid cell arrangement for global models:
Spherical coordinate system: latitude, longitude, height
Convenient: Grid is logically structured

Global spectral
model grid

Packs gridpoints
near poles

No nesting
capabilites
Polar stereographic projection used in RAMS:
Earth surface to planar surface
•
Map factors are used in
all horizontal derivative
terms
•
Spherical geometry
terms must be added
due to transformation
•
Limited to hemispheric
or smaller model
domain
..
.P
Global RAMS 1997: “Chimera Grid” approach
Lateral boundary values interpolated from interior of opposite grid
Not flux conservative
Global grid structure in OLAM version 1
Arakawa-C grid stagger in both square and triangular cells
The Ocean-Land-Atmosphere Model (OLAM):
An expansion of RAMS into an Earth System Model
Icosahedron
OLAM solves a finite-volume analog
of the full compressible NavierStokes equations in conservation
form, and exactly conserves mass,
momentum, and internal energy.
Unstructured Grid; No overlapping grid cell; No special nest communication;
Each cell communicates directly with its neighbor independently of resolution
(  )
 ( u )
 ( v )
 ( w )



 ...
t
x
y
z
Finite difference form:
 1
u
1
 2
u
2
 3
x
 1   2 1   2  2   3  2  3 
u1

u2

 (  2 2 )  2
2
2
2 

t
x
Finite volume form:
1
A1
u1
Vol 2
2
A2
u2
3
2 3 
1   2  2   3
 1   2
u1 A1

u2 A2

2
2
2
2 


Vol2
Vertical ADaptive APerture (ADAP) Grid
OLAM uses the Arakawa-C grid stagger
Control volumes for T, U, W
W
T
U
Large Eddy Simulation of Convective Boundary Layer
Grid Nesting Example:
Hurricane Wilma
8 km nest
Hurricane Wilma
observed
8km run
4km nest
Examine passage through 4 km nest
The Representation of Topography in GCMs
The
----
Andes mountains:
length of 7000 km
average height of 4 km
typical width of 200-300 km
Amazon Basin Precipitation Results (15S – 5N; 75W – 50W)
El Nino year
Improving representation of topography improves OLAM’s precipitation estimates
Higher resolution
gives correct
ENSO behavior
OLAM 200 km
OLAM 100 km
OLAM 25 km
Coarse GCMs do
not capture the
minimum during El
Nino years
(Medvigy et al., 2009, GRL)
Impact of Andes on global hydroclimate interannual variability
ENSO
400 km topography
50 km topography
Spurious large Amazon convection
realistic low Amazon convection
Different Walker/Hadley cells?
1998 Anomaly, precipitation [mm]
200 km topography



More drought in
Pacific Northwest
More drought in
Australia
Weaker North
Atlantic storm
tracks
(Medvigy et al., 2009, GRL)
25 km topography
Summary

OLAM has been developed as the advancement
of current regional forecast models to global
environmental modeling

The current grid structure is capable of
representing atmospheric processes from global
to turbulent timescales

Todo:




Integrated ocean model (ROMS)
Thermodynamic variable (enthalpy, total energy)
Hydraulic model for proper runoff modeling
Atmospheric chemistry transport and feedbacks using
CMAQ and RRTMg