ROMS Embedded Gridding,

1
ROMS Embedded Gridding, Test and Application for
the Simulation of the Central Upwelling of the
Pacific Coast of the United States
Aim to obtain high resolution local coastal
solutions, at reasonable computational cost,
while preserving the large scale circulation
Contributors James C Mc Williams, Institute of
Geophysics and Planetary Physics, UCLA,
USA Laurent Debreu, Institut dInformatique et
Mathematiques Appliquees de Grenoble,
France Patrick Marchesiello, Institute of
Geophysics and Planetary Physics, UCLA,
USA Pierrick Penven, Institute of Geophysics and
Planetary Physics, UCLA, USA
Approach Local refinement via nested grids
family of fixed high resolution local models
embedded in larger coarse-grid models.
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Plan

• Embedding method
• The 1 way, 15 5, Central Upwelling model
• 1 way nesting evaluation comparisons with
  other models
• Another application the Southern California
  Bight
• Conclusion

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1 - Embedding method

• AGRIF (Adaptive Grid Refinement in Fortran)
  package Debreu Blayo 1999
• Fortran 90 library for the integration of
  adaptive mesh refinement (AMR) features in a
  finite difference model.
• Arbitrary number of embedded levels.
• Solution-adaptive grid refinement (not used).
• Based on the use of pointers ? minimizes the
  changes in the original model

• CFL criterion child time step equal the parent
  time step divided by the coefficient of
  refinement
• (3 for 5 km resolution grid embedded in a 15
  km resolution grid)
• Recursive procedure for the temporal coupling
  between parent and child grids
• Advance parent by one parent time step
• Interpole parent variables in space and time to
  get the boundary conditions for the child grid
• Advance the child grid
• Update point by point the parent model by the
  child model variables

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Embedding in ROMS

• Time splitting for barotropic and baroclinic
  modes
• Parent-child coupling only at each baroclinic
  time step.
• Local preservation of the volume fluxes across
  the parent-child boundaries via the use of the
  parent volume fluxes to get the child barotropic
  boundary conditions.
• Parallelization
• S-coordinate difference of topography between
  the parent and child grid. Can create
  inconsistencies when updating parent variables
  (2-way nesting).

Positions of the parent (o) and child (.)
rho-points for refinement coefficient of 3
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2 The 1 way, 15 5, Central Upwelling model

• Central Upwelling of the Pacific Coast
• From Point Conception to Cape Mendocino
• Year long upwelling favorable winds
• Maximum eddy energy in Northern California
• Topographic particularities Cape Mendocino
  Point Arena Monterey Bay Canyon

• 1 Level embedding
• 1-way nesting
• Parent model
• 15 km resolution
• 84 X 169 X 20 grid points
• dt 40 min
• Derived from the US-West Coast model
  Marchesiello et al., 2001b
• 3 open boundaries Marchesiello et al., 2001a
  oblique radiation condition if direction
  inward nudging towards Levitus (1994) monthly
  climatology sponge layers (width 150 km ,
  ?max 300 m2.s-1) global volume conservation
  enforcement
• Child model
• 5 km resolution
• From north of Cape Mendocino to Point Conception
• 94 X 190 X 20 grid points ( 500 km cross shore
  X 1000 km along shore)
• dt 15 min
• weak sponge layers (width 50 km , ?max 30
  m2.s-1)
• Both models same forcing (COADS) same initial
  condition (Levitus) same topography

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Results of the 155 model

• Solution stable (10 years) statistical
  equilibrium
• No discontinuities at the parent child
  boundary
• Vigorous eddy activity in the child grid

SST (C) and surface currents 6 August 10
SST (C) 15 July 6
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Parent Child comparison SST 15 July 6 (C)
Parent
Child

• Similitude of the solutions filament general
  location does not appear to be affected by the
  resolution
• Child grid
• longer filaments
• stronger upwelling
• intrusion of off shore warm water closer to the
  shore
• narrower upwelling front

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Illustration of the parent-child boundary
behavior SSH time series (m)
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Annual Mean SSH (m)
Parent
Child
Preservation of the large scale mean circulation,
but stronger meanders for the child model
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RMS SSH (m)
Parent
Child
RMS of SSH off shore in the child model more than
2 times stronger than the parent Effects of eddy
variability or variations induced by the boundary
?
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Summer mean EKE (cm2.s-2)
Parent
Child
More than 2 times more eddy activity in the child
model
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3 1 way nesting evaluation comparisons with
other models

• 3 other simulations used to evaluate the
  capabilities of 1 way nesting
• Whole pacific coast model at 5 km resolution
  Marchesiello et al, 2001 used as a reference
  (WPC) .
• 2 models using the child grid alone and active
  open boundaries
• 1 using the Levitus (1994) monthly climatology
  to force the boundaries (LEV).
• 1 using a monthly climatology derived from the
  solution of the whole pacific at 5 km resolution
  (MCLM).

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SST 15 July 6 for the 4 experiments (C)

• Strong similarities in the upwelling structure.
• Filaments at approximately the same location and
  with the same lengths.
• Smoother field offshore for LEV.

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Mean SSH for the 4 experiments (m)

• Stronger differences
• Stronger gradient for LEV
• The 155 model is very close to WPC (3 meanders
  with the correct values at the correct locations)

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Annual RMS SSH for the 4 experiments (m)

• LEV and MCLM around 2 times smaller than WPC.
• Few differences between LEV and MCLM the mean
  state does not affect much the variance of SSH.
• 155 close to WPC SSH variance appears to be
  forced by the large scale.
• Stronger values ( 10) in the north-west
  corner sign of blocking.

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Annual Surface EKE for the 4 experiments (cm2.s-2
)

• LEV 2 time smaller than WPC
• MCLM perform well away from the boundaries
• The eddy kinetic energy is locally produced and
  is controlled by the mean large scale.

• 155 is slightly lower to MCLM near the coast
  (mean state induced by the parent less accurate
  than the climatology used in MCLM).
• Better values in the middle of the domain.
• Blocking at the offshore boundary and in the
  north-west corner

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Summer intra-seasonal surface EKE for the 4
experiments (cm2.s-2 )

• During the period of strongest eddy activity
• 155 closest to WPC
• Good off shore
• 25 lower in the coastal transition zone
• Some eddy activity, coming from North, is not
  resolved by the 155 (extension of the child
  domain a bit North ?)

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4 Another application the Southern California
Bight

• From Point Conception to the US-Mexico border
• Complex bathymetric region (Islands, shallow
  banks, basins and trough)
• Sheltered from the upwelling favorable winds
• ? Circulation driven by interactions between
  bathymetry and remotely forced currents

• 2 levels of embedding parent 20 km resolution
  1st child 6 km resolution 2nd child 2
  km resolution
• Bottom topography different between the parent
  and the Childs (connection at the boundaries)

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Southern California Bight - SST - 1 October 3 (C)

• New type of instabilities at high resolution

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Southern California Bight Chlorophyll-a - 1
October 3 (mg.m-3)
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5 -Conclusion

• Using the 1-way embedding method, we obtained a
  high resolution local solution, at reasonable
  computational cost, while preserving the large
  scale circulation.
• (It requires about 19 wall-clock hours on 16
  processors of SGI Origin 2000 to compute 1 year
  of simulation, against 16 hours for the child
  grid alone and 120 hours for the whole pacific
  coast at high resolution)
• The solution compares well to the whole pacific
  coast model, but
• there are some blocking near the off shore
  boundary
• the level of EKE is slightly smaller at the
  coast.
• In the near future, we propose to radiate the
  variables at the child boundaries, to develop and
  test the 2-way nesting, and to extend the child
  grid of the 155 slightly to the North.
• The new pressure gradient scheme will allow the
  use of closer topographies between parent and
  child grids.
• For the Central Upwelling of California, in case
  of smooth climatological atmospheric forcing, the
  variance in SSH is mostly produced by variations
  in the large scale circulation, while most of the
  eddy activity is locally generated (a part is
  also coming from the north).