Eddy-Mean Flow and Eddy-Eddy Interaction: Insights from Satellite Altimetry Measurements

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Eddy-Mean Flow and Eddy-Eddy Interaction
Insights from Satellite Altimetry Measurements
Bo Qiu Dept of Oceanography
University of Hawaii
Contributors D. Chelton, S. Chen, R. Scott
A Workshop on Mesoscale and Submesoscale Oceanic
Processes Explorations with Wide-Swath
Interferometry Radar Altimetry 28-30 April
2008 Scripps Institution of Oceanography
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Charges

• What have we learned from existing altimetry data
  and what are the limitations and challenges?
• What new dynamics can we study with an O(10) km
  resolution SSH dataset?

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Trajectories of cyclonic vs anticyclonic eddies
with lifetimes gt 4weeks
nonlinearity u/c
Kuroshio Extension
South Pacific Subtropical Countercurrent
Chelton et al. (2007, GRL)
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Schematic of NW Pacific Ocean Circulation
Chelton et al. (2007, GRL)
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Semi-monthly Kuroshio Extension paths (1.7m SSH
contours)
Stable yrs 1993-94, 2002-04
Unstable yrs 1996-2001, 2006-07
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(a) Upstream KE path length (141-153E)
(b) Eddy kinetic energy (141-153E, 32-38N)
Stable yrs 1993-94, 2002-04
Unstable yrs 1996-2001, 2006-07
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PDO index
EKE level
Mesoscale EKE level in the KE region lags the PDO
index by 4 yrs
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Pacific Decadal Oscillations (Mantua et al. 1997)

• Center of action of wind forcing is in the
  eastern half of the N Pacific basin
• Positive (negative) phase of PDO generates ()
  local SSH through Ekman divergence (convergence)

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Yearly SSH anomaly field in the North Pacific
Ocean


-
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EKE level
SSHA along 34N
SSH field
PDO index
L
H
L
center of PDO forcing
145E
165E
155E
135E
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SSHA along 34N
PDO index
SSHA along 34N from wind-driven Rossby wave
model
L
H
L
center of PDO forcing
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EKE modulations on interannual and longer
timescales
atmosphere
wind stresses
WBC mean flow
mesoscale eddies
stability properties
feedback ?
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Feedback of eddies to the modulating time-mean
flow

• Surface ocean vorticity equation

eddy-driven mean flow modulation

• Evaluate

mechanical feedback of eddies onto the
time-varying SSH field (e.g. Hoskins et al.
1983, JAS)

• Introduce the Kuroshio Extension index loading
  of the 1st EOF mode of the zonally-averaged SSHA
  field

low eddy variability
high eddy variability
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Eddy-forced S(x,y,T) field regressed to the KE
index

• anticyclonic forcing vs . cyclonic forcing
• In the upstream KE region, enhanced eddy
  variability (when KE index lt0) works to increase
  the intensity of the northern/southern
  recirculating sub-gyres.

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Are the eddy vorticity fluxes properly resolved?
SSH snapshot from the NLOM model for 04/10/2006
Right from the original 1/32-resolution output
Left reduced to 1/3-resolution
(observable by current nadir-looking satellite
altimeters)
(NLOM data provided by IPRC-APDRC)
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SSH vs vorticity snapshot from the NLOM model for
04/10/2006
original 1/32-resolution
reduced 1/3-resolution
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PDF of modeled vorticity as a function of
intensity
anti-cyclonic
cyclonic
Ratio anticyclonic/cyclonic
anticyclone-dominant
cyclone-dominant
reduced 1/3-res.
original 1/32-res.
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PDF of modeled and observed vorticity as a
function of intensity
anti-cyclonic
cyclonic
reduced 1/3-res.
AVISO SSHA-derived
original 1/32-res.
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Chelton et al. (2007, GRL)
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Statistics of eddy tracking in the South Pacific
STCC band

• maximum of eddies in October
• maximum average eddy amplitude in January
• maximum eddy diameters in March

(courtesy of D. Chelton)

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Chelton et al. (2007, GRL)
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Statistics of eddy tracking in the North Pacific
STCC band

• maximum of eddies in April
• maximum average eddy amplitude in August
• maximum eddy diameters in September

(courtesy of D. Chelton)

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Chelton et al. (2007, GRL)
STCC band
September T(y,z) along 170E
Eastward-flowing STCC overlying westward-flowing
SEC
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STCC-SEC shear ?U vs regional EKE annual cycle
September T(y,z) along 170E
Eastward-flowing STCC overlying westward-flowing
SEC
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Instability analysis for the 21/2-layer S Pacific
STCC/SEC system

• Stability condition depends on
  seasonally-varying STCC/SEC shear and upper ocean
  N2.
• Maximum Aug/Sept growth rate 50 days
• Unstable wavelengths 200370 km most unstable
  250 km (scaled well by f2dU/dz/ßN2).

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Quantifying eddy-eddy interaction

• Consider 2-d momentum eqs

• Take discrete Fourier transform and form
  kinetic energy PSD eq

where
spectral energy transfer term
PE to KE conversion term
dissipation term

• In a slowing-evolving eddy field

Qiu, Scott and Chen (2008, JPO)
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Spectral energy transfer T(kx, ky) in the S
Pacific STCC region
energy sink
_
energy source

• In a slowing-evolving eddy field

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Spectral energy transfer T(kx, ky) in the S
Pacific STCC region

• Baroclinic instability provides the energy
  source for the eddy-eddy interaction.
• At wavelengths gt 370km, nonlinear triad
  interactions serve as an EKE sink.

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Bimonthly spectral energy transfers in the S
Pacific STCC region
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• In the quasi-equilibrium state, the spectral
  energy transfer is related to the convergence of
  spectral energy fluxes

where
signifies spectral energy flux from kltK to kgtK
through eddy-eddy interactions
k
K
Scott and Wang (2005, JPO)
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Spectral energy flux ?K in the S Pacific STCC
region
forward cascade
_
inverse cascade

• Inverse energy cascade is seen in signals with
  wavelengths gt 230km
• There exists little preference in the x-y
  direction of the inverse energy cascade

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Explaining Cheltons eddy statistics in the S
Pacific STCC band

• maximum baroclinic shear of STCC-SEC in August
  baroclinic instability occurs, but with a weak
  growth rate O(months)
• maximum of eddies in October resulting from
  baroclinic instability
• maximum average eddy amplitude in January slow
  growth to reach full amplitude
• maximum eddy diameters in March due to inverse
  energy cascade from eddy-eddy interaction

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Is that all there is?
NLOM original 1/32-res. vorticity
NLOM reduced 1/3-res. vorticity
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Spectral energy transfer T(kx, ky) in the S
Pacific STCC region NLOM result
energy sink
_
energy source
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Spectral energy transfer T(kx, ky) in the S
Pacific STCC region NLOM result
primary baroclinic instability of STCC-SEC shear
secondary frontal instability of STCC (?) (what
determines its growth and scales?)
energy sink
_
energy source
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Spectral energy transfer T(kx, ky) in the S
Pacific STCC region NLOM result
forward cascade
Spectral energy flux ?K
_
inverse cascade
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Comments

• In addition to being a better tool for monitoring
  the global SSH signals, wide-swath satellite
  altimetry will help us discover new features of
  the turbulent ocean operating on different
  space/time scales.
• With enhanced coverage and accuracy, wide-swath
  altimeter data can be used to test dynamic
  hypotheses, leading to improved understanding of
  the ocean and climate system.

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Longitude-time plot of EKE along 21-29S
OFES 1/10-res. climatological run result
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Longitude-time plot of EKE along 21-29S
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(No Transcript)
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Comments

• High-quality SSH data of the past 15 yrs allows
  us to quantify changes in the mean circulation
  brought about by the basin-wide wind forcing.
• It further helps us explore the extent to which
  the mean circulation changes leads to the
  modulation in the mesoscale EKE field.
• Although there is evidence that time-modulating
  mesoscale eddies modify the mean circulation
  field, the presently available SSH data is
  insufficient to accurately evaluate the feedback
  processes (e.g., eddy vorticity flux divergence).

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Energy flow in a 2-layer baroclinic turbulent
ocean
Rhines (1977)
Vallis (2006)
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NLOM field
original 1/32-res.
reduced 1/3-res. (note the different color
scale)
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NLOM field of S
original 1/32-res.
reduced 1/3-res.
anticyclonic forcing cyclonic forcing
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Yearly-mean sea surface height field
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Baroclinic instability growth rate based on upper
ocean f/Ri1/2
Figure courtesy of D. Chelton