Uncertainty quantification in predictive models for NLIW

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Uncertainty quantification in predictive models
for NLIW

• Overview
• Models and uncertainty
• Example of high-resolution NLIW simulation and
  comparison to observations
• Generation mechanism
• Nonhydrostatic effects
• Effects of rotation

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Phase ? /- 10 Amplitude ?
Modeling and prediction
NLIW models Hydrostatic circulation models
(POM/ROMS) Regional nonhydrostatic models
(MITgcm,SUNTANS) 2D (xz) nonhydrostatic models
(spectral/finite difference) 3D DNS Strongly
nonlinear IW models (2Dmultilayer) Weakly
nonlinear IW models (KdV, eKdV)
Acoustic models
Empirical models
Surface currents UIW UBG O(100 m)
Surface wave models Wave action equation ? O(1
m) Model for the small scales ? O(1 cm)
Backscatter models Remote sensing
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Recommendations
NLIW models Hydrostatic circulation models
(POM/ROMS) Regional nonhydrostatic models
(MITgcm,SUNTANS) 2D (xz) nonhydrostatic models
(spectral/finite difference) DNS Strongly
nonlinear IW models Weakly nonlinear models
(KdV, eKdV)

• Development of nonlinear (2D or layered)
  internal wave model to satisfy O(100 m)
  resolution requirements
• Assimilation/integration of remote
  sensing/in-situ data and high-resolution models
  to develop parameterization of nonhydrostatic
  effects and other uncertainties not accounted
  for in 2D model.
• Examples
• 2D model simulates deep-basin propagation well
• 2D model probably has trouble capturing
  transformation is it possible to develop
  parameterizations of dissipation and higher-order
  nonhydrostatic effects to improve the 2D model?

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Quantification of uncertainty

• Study basic generation problem under the overall
  motivation to quantify uncertainty
• Uncertainty depends a great deal on location and
  process
• NLIW
• Arrival time (phase) /- 10
• Greatest uncertainty u, du/dx, amplitude, of
  waves in packet
• RESOLUTION lt 100 m SCS, lt 20 m NJS
• Bathymetry?
• Stratification/Currents due to seasonal and
  mesoscale variability
• Coriolis
• Surface wave models
• Initial spectra
• Surface currents
• Greatest uncertainty Wind-forcing/dissipation/wav
  e-wave interaction
• Remote Sensing
• Development/implementation of test problems to
  quantify uncertainty by comparing in-situ and
  remote sensing data to models

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Comparison to observations
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SPRING TIDE JUNE 2005
Observations (S. Ramp, NPS)
SUNTANS
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SSH, 25 June 2005
SAR image from internalwaveatlas.com
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28 June 2005, 1220
27 June 2005, 1130
28 June 2005
30 June 2005, 1401
29 June 2005, 1311
Generation is strongly influenced by
three- dimensional topography.
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2D simulations with SUNTANS
Levitus stratification
28 C
Depth at sill DS 200 m
3 C
Ocean depth D0 3500 m
Barotropic forcing at diurnal frequency
Radiation of first-mode baroclinic wave. Sponge
layers are also employed to damp internal waves
at the boundaries.
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Case with Frsill0.27
Isotherms 16, 20, 24, 28 degrees C
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Case with Frsill1.60
Isotherms 16, 20, 24, 28 degrees C
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Beginning of ebb tide
t10
End of ebb tide
t2T/2
LT/2c1
Beginning of flood Lee wave release
t3T/2
Arrival at B1
t4t3LB1/c1
DtLB1/c1
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Nonhydrostatic effects (Frsill1.60)
Nonhydrostatic code
Isotherms 16, 20, 24, 28 degrees C
Hydrostatic code
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Nonhydrostatic-Hydrostatic Comparison
Dispersion in the hydrostatic model is purely
numerical. The numerical dispersion is much
smaller than the physical, nonhydrostatic
dispersion, which leads to excessive steepening
of the front. The oversteepened front is
diffused due to grid-scale numerical diffusion,
and this causes a reduction in the wave
amplitude. Reduction in the wave
amplitude reduces the amplitude dispersion and
thereby reduces the speed of propagation of the
wavetrain.
15o C isotherm after 3 tidal periods.
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Using the KdV equation as a model
Initial wave Half-sine wave (first-mode internal
tidal wavelength) with amplitude 70 m.
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Computed vs. Modeled (KdV) Results
SUNTANS
KdV
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Effects of rotation
16 oC isotherm after 2 K1 tides
(1) Reduction of along-sill tidal excursion
distance in the ebb direction causing wave with
rotation to appear much faster. (2) Larger
amplitude wave without rotation eventually
overtakes wave with rotation due to
amplitude dispersion.
(2)
(1)