IPEZHAT

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• IPEZ-HAT
• (High Accuracy Tides or is it Harmonically
  Analyzed Tides)
• Motivation, progress report
• A more general IOM issue interface between a
  multi-purpose modeling system and the IOM

• Definition of model and adjoint states
• Flexibility in defining boundary conditions

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Surface expression of internal tides Elevation
of a few cm can be seen in harmonically analyzed
TOPEX/POSEIDON data
Hawaiian Ridge (Ray Mitchum, 1997)
75-150 km wavelength modulations in M2 amplitude
and phase are consistent with phase-locked
internal tides propagating away from many
mid-ocean ridges
But energy flux away from ridge inferred from
altimetry is about half that seen in model studies
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• Possible explanations
• Low-mode energy flux inferred from altimetry
  corresponds to phase-locked component only there
  is significant phase/amplitude modulation due to
  propagation of internal waves through variable
  background mesoscale current and density fields
• Poor sampling of altimetry have missed some of
  the areas of most intense flux
• There really is more dissipation near the ridge
  than the models predict

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• PEZ-HAT Primitive-Equation Z-coordinate --
  Harmonically Analyzed Tides
• Adapt Bennett and Chua's PEZ (Primitive-Equation
  Z-coordinate) model for application to regional
  internal tide modeling and data-assimilation,
  particularly in the open ocean, using altimetry
  data
• Use this to study energetics, temporal
  intermittency and dissipation of low-mode
  internal tides around major generations sites
  such as Hawaii
• Preserve the previous functionality in the
  time-domain while using code as kernel for a
  frequency-domain solver.

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• Some Recent Developments
• Most PEZ compile-time arguments are now set at
  run-time.
• Program execution is driven with an XML
  document, which includes
• a) Grid/Geometry information
• b) Solver parameters
• c) State variable definition
• Beginning to interface with IOM I/O via netCDF

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• Modifications to solver kernel
• Variety of averaging kernels for split-explicit
  time stepping (Shchepetkin and McWilliams)
• "Ghost-cell immersed boundary" method for rigid
• boundaries (Tseng and Ferzinger)
• Radiation open-boundary conditions modified for
  improved computational efficiency

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• Experiments
• Assess model accuracy (How well does it solve
  the equations?)
• -- an ongoing concern --
• Assess model validity (How well does it compare
  with data?)
• -- Pretty well in some places
• not so well in others.

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Modeled and observed harmonic constants for T/P
altimetry (high-pass filtered along track)
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Propagation of internal tide through realistic
spatially varying density and mesoscale current
fields Use tangent linear of PEZ with
background currents defined from other ocean model
SODApop (J. Carton optimal interpolation,
climatology)
HYCOM from NRL (forward modeling only)
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Mode 1 baroclinic energy flux PEZ-HAT forward
model, horizontally uniform stratification
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Experience developing PEZ-HAT from Classic PEZ
raise some more general issues

• Useful community modeling codes have to be
  flexible, and adaptable Grids, BCs, Forcing,
  Outputs
• ROMS, POM, etc., have been developed with this
  flexibility in mind
• Interfacing a model to the IOM takes some effort

How do we develop the interface of a modeling
system to the IOM to maximize generality,
flexibility and code reusability?
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• Key Points
• (1) Clear definition of the state or TRAJ as
  seen by the IOM is required

• This is generally distinct from the internal
  state definition of the modeling code
• State definition is central to defining the
  interface between the IOM and the modeling system
• also need to be clear about the adjoint state

(2) Definition of the state (and adjoint state)
are closely tide to inputs and outputs for TL and
Adjoint codes
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• Key Points (cont)
• (3) Allowing for flexibility in choice of BCs is
  important, challenging

• If BC of the forward problem are changed, how
  do BC change for TL, Adjoint?
• Can modeling systems be devised to
  facilitate/simplify needed coding? E.g., can we
  isolate code in FWD, TL, ADJ that is relevant to
  BC choice?
• As modules for multiple applications develop for
  a modeling and assimilation system, how do users
  ensure consistency (e.g., of TL and ADJT BC
  modules)?

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Example Definition of the model state (TRAJ)
for IPEZ-HAT Initial approach/assumption Tides
are harmonic in time (at least over some time
window). Thus, the model state consists of
complex harmonic constants (for constituents k
1, Nc) for currents, elevation and tracers (or
density)
The harmonic constants are then related to the
time dependent state via
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Internal to the time-stepping model, the state is
essentially not
(actually the internal state generally involves a
complicated discrete representation!)
From the point of view of interaction with the
IOM, the TRAJ is the frequency domain
representation
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Backward Problem
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Classic PEZ tropical ocean application of
Bennett and Chua Impulsive forcing once/day .
Sample solution once/day
Forward Problem
Backward Problem
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A different scheme (standard for ROMS?) Input
forcing/BC once every n time steps, linearly
interpolate to BT/C time steps Sample results
every n time steps
Forward Problem
Backward Problem
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Adjoint of Linear Interpolation
Filter with triangular averaging window,
subsample
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Implementation in IPEZ-HAT
IPEZ-HAT for internal tides
Classic IPEZ for tropical ocean
By switching routines, different modeling
problems can be readily accomodated
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Related Issue a clear and well documented
definition of the boundaries of the modeling
black box is required Inputs and outputs must
be clearly defined.
Example modeling in a periodic domain One way to
implement dummy nodes at domain edges
Does the input state for a time stepping routine
include the dummy nodes, or just the live
interior nodes? This has a huge impact on what
the adjoint of the time stepping routine is!
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Another modularity feature being implemented in
IPEZ-HAT flexibility in specification of
boundary conditions

• BCs implemented through separate routines
• Structure of PEZ time stepping code makes
  implementation of adjoint BCs fairly
  straightforward (for many cases)

FWD explicit in time update of interior nodes
then update boundary nodes w/ new interior
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Adjoint explicit in (backwards) time update of
boundaries
Then update interior nodes
Two parts of the code are specific to choice of
BC
By keeping these parts of the update stencil as
separate modules, coding for adjoints of
different BCs is simplified