Numerical and Assimilative Studies of the Equatorial Pacific: Impact of Assimilation on Tropical Instability Waves in a Biased GCM

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Numerical and Assimilative Studies of the
Equatorial Pacific Impact of Assimilation on
Tropical Instability Waves in a Biased GCM
Renellys C. Perez NRC Postdoctoral Research
Associate Robert N. Miller OSU/COAS
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Numerical and Assimilative Studies of the
Equatorial Pacific Impact of Assimilation on
Tropical Instability Waves in a Biased GCM

• Outline
• Introduction
• Assimilation scheme
• Optimality
• Impact on TIWs
• Temperature balance
• Summary and conclusions
• Current work

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Data Assimilation

• Convert a sparse set of observations into highly
  resolved estimate of a system using a numerical
  model to dynamically interpolate the observations

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The Kalman Filter

• Provides optimal estimate of the present state of
  the system when applied to a linear model
• Computational expense (size of model)3
• Natural choice for equatorial Pacific
• Large scale, low frequency equatorial dynamics
  simulated realistically with low-order numerical
  models (e.g., Cane and Patton 1984)
• 15 years of Kalman filtering studies (Miller and
  Cane 1989 Miller et al. 1995 Cane et al. 1996
  Keppenne et al. 2005)
• Assimilate anomalies!

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Cold Tongue

• Cold tongue of water seasonally extends
  westward from South America along equator to
  central Pacific (Mitchell and Wallace 1992)
• Strongest expression during La Niña and weakened
  during El Niño (Wallace et al. 1989 Deser and
  Wallace 1990)

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Cold Tongue

• Present models of the tropical Pacific have cold
  tongue biases and seasonal cycle errors in the
  equatorial upwelling region (Stockdale et al.
  1998)

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Tropical Instability Waves

• TIWs perturb the cold tongue boundaries
• Periods of 17 to 33 days, propagate westward with
  zonal wavelengths on the order of 1000 km (Qiao
  and Weisberg 1995 Lyman et al. 2005b)
• Most active during La Niña events (Baturin and
  Niiler 1997)

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Tropical Instability Waves

• Open question whether present models accurately
  simulate TIWs
• Amplitude
• Phase, westward propagation
• TIW-induced eddy advection

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Objective

• Examine extent to which assimilation of dynamic
  height anomalies from a sparse set of TAO
  moorings can improve the amplitude and phase of
  TIWs in a biased nonlinear GCM

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Numerical model

• Gent-Cane (1989) model coupled to advective
  atmospheric mixed layer (Seager et al. 1995)
• Nonlinear, reduced gravity, equatorial ?-plane
  model
• Hybrid mixing scheme (Chen et al. 1994)
• Lorenz 4-cycle time stepping ?t 1 hour
• Free slip at N/S boundaries, no slip at E/W
  boundaries
• Restoration to Levitus (1994) climatology at N/S
  boundaries
• Shapiro filter provides horizontal smoothing
• UNESCO equation of state
• Spun up from rest and Levitus initialization
• Dynamic height from model h, S, T

All runs driven by 5-day averaged QuikSCAT winds
during the period August 1999 to July 2004
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Vertical grid

• Model active region defined by
• 15 layers
• 1027.0 kg m-3 bottom density
• 9 ºC, 34.85 psu, 600 m
• Model dynamic height bias
• 10 - 20 dyn cm
• Low salinity in west
• Deep thermocline in east

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Vertical grid

• Model active region defined by
• 15 layers
• 1027.0 kg m-3 bottom density
• 9 ºC, 34.85 psu, 600 m

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Horizontal grid

• Horizontal grid resolves zonal currents TIWs

Need new fig!
Model domain 124 to 284 E, 30 S to 30 N (1
zonal x 0.33 stretched meridional grid) Size of
model (106) computationally expensive!
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Reduced State Space Kalman Filter (RKF)

• The Kalman machinery operates in reduced state
  space spanned by 44 Mutivariate Empirical
  Orthogonal Function (EOFs) which capture 80 of
  original variance
• Monte Carlo Markov Chain model used to obtain
  forecast error model with assumptions
• model errors dominated by wind errors
• white in time with spatial structure given by

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Reduced State Space Kalman Filter (RKF)

• The Kalman machinery operates in reduced state
  space spanned by 44 Mutivariate Empirical
  Orthogonal Function (EOFs) which capture 80 of
  original variance
• Monte Carlo Markov Chain model used to obtain
  forecast error model with assumptions
• model errors dominated by wind errors
• white in time with spatial structure given by
• QuikSCAT driven model (NODA)
• QuikSCAT driven assimilation run (ASSIM44)

Full Details of RKF in Perez (2005) Perez and
Miller (2006 in preparation)
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Autoregressive model

• To remove color from innovation sequence a 10-day
  autoregressive process is added to the RKF
• At each assimilated location, the innovation
  sequence is replaced by
• Run with autoregressive process named ASSIM44-AR

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Assimilated observations

• 5-day TAO dynamic height anomalies calculated
  from temperature and T-S relationships (Conkright
  et al. 2002)
• assimilated at 42 locations (?)
• 17 withheld locations used for validation (x)
• 8 locations with insufficient data (?)

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Assimilated observations

• 5-day TAO dynamic height anomalies calculated
  from temperature and T-S relationships (Conkright
  et al. 2002)
• assimilated at 42 locations (?)
• 17 withheld locations used for validation (x)
• 8 locations with insufficient data (?)
• Observations ordered from southwest corner to
  northeast corner

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Optimality
Lagged autocorrelations of innovation sequence
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Optimality

• Chi-squared test
• The scalar diT (HPfHT R)-1di should be a ?2M
  random variable
• Fall between the dashed lines 99 of the time
• In top 3 panels ASSIM44
• Bottom panel ASSIM44-AR

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Impact on TIWs (SST)
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Impact on TIWs (SSHA)
NODA ASSIM44 ASSIM44-AR
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SSHA spectra and westward propagation
1 yr
33d
17d
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SSHA spectra and westward propagation
1 yr
33d
17d
Description Cp (cm/s)
AVISO 39.2 2.2
NODA 46.5 1.3
ASSIM44 50.9 4.2
ASSIM44-AR 43.4 2.0
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Mixed layer temperature balance
T ? 60 d
T lt 60 d
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Mixed layer temperature balance
T ? 60 d
T lt 60 d
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SST comparison at TAO moorings
Reynolds et al. (2002) Satellite-in-situ SST
TAO-Reynolds NODA ASSIM44-AR
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LF horizontal advection at TAO moorings
Wang and McPhaden (1999 2000 2001) McPhaden
(2002)
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LF tendency horizontal material derivative
Wang and McPhaden (1999 2000 2001) McPhaden
(2002)
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Summary and conclusions

• Assimilation scheme passed the ?2-test between 8
  S and 2 N and adding autoregressive model
  whitened the innovation sequence
• Assimilation improved interannual and
  intraseasonal SSH variability
• Assimilation (without autoregressive model)
  reduced mean surface mixed layer temperature cold
  bias but increases phasing errors in seasonal
  cycle
• TIW x-t structure, spread of energy improved but
  amplitudes weakened
• Adding autoregressive model improved TIW westward
  propagation

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Summary and conclusions

• Assimilation decreases HF horizontal advection
  and LF horizontal advection (compensate)
• Amplitude of SST, tendency, horizontal material
  derivative annual cycle too weak in the model

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Recommendations

• Uncertainty in net surface flux tied
• mean DH and cold tongue cold bias
• errors in cold tongue seasonal cycle
• Forecast errors may no longer be dominated by
  wind errors
• Need to construct assimilation schemes that
• incorporate heat flux errors in the forecast
  error model
• introduce bias-correction algorithms (Keppenne et
  al. 2005)
• assimilate absolute fields rather than anomalies
  (Parent et al. 2003)
• Need cross-equatorial observations of 3-d
  circulation and fluxes

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Current Research ProjectSimulation Experiments
for Pacific Upwelling and Mixing Physics Study

• Renellys C. Perez
• NRC Postdoctoral Research Associate
• William S. Kessler
• NOAA/PMEL
• Paul S. Schopf
• George Mason University

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Simulation experiments

• Provide guidance for array design
• Estimate temporal and spatial scales of (u, v, T)
• Determine representativeness of w, heat and
  momentum budgets at diamond centers
• Suggest modifications to proposed array
• Study spin-up of 3-d cold tongue circulation in
  response to varying winds, remotely forced waves,
  and TIWs
• Vertical structure of poleward divergence
• Transition to Ekman dynamics
• Meridional structure of the zonal currents