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

Bo Qiu Dept of OceanographyUniversity of Hawaii

Contributors: D. Chelton, S. Chen, R. Scott

“A Workshop on Mesoscale and SubmesoscaleOceanic Processes: Explorations with Wide-

Swath Interferometry Radar Altimetry”28-30 April 2008

Scripps Institution of Oceanography

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?

Chelton et al. (2007, GRL)

Trajectories of cyclonic vs anticyclonic eddies with lifetimes > 4weeks

nonlinearity = u/c

Kuroshio Extension

South Pacific Subtropical Countercurrent

Schematic of NW Pacific Ocean Circulation

Chelton et al. (2007, GRL)

Semi-monthly Kuroshio Extension paths (1.7m SSH contours)

Stable yrs: 1993-94, 2002-04 Unstable yrs: 1996-2001, 2006-07

(a) Upstream KE path length (141-153°E)

(b) Eddy kinetic energy (141-153°E, 32-38°N)

Stable yrs: 1993-94, 2002-04 Unstable yrs: 1996-2001, 2006-07

PDO index

EKE level

Mesoscale EKE level in the KE region lags the PDO index by ~ 4 yrs

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)

Yearly SSH anomaly field in the North Pacific Ocean

+

-

+

center of PDO forcing

L

H

L

EKE level SSHA along 34°NSSH field PDO index

145E 165E155E135E

center of PDO forcing

L

H

L

SSHA along 34°N PDO indexSSHA along 34°N from wind-driven Rossby wave model

EKE modulations on interannual and longer timescales

atmosphere

WBC mean flow

mesoscale eddies

wind stresses

stability properties

feedback ?

Feedback of eddies to the modulating time-mean flow:

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:

• Surface ocean vorticity equation:

low eddy variability

high eddy variability

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 <0) works to increase the intensity of the northern/southern recirculating sub-gyres.

Are the eddy vorticity fluxes properly resolved?

SSH snapshot from the NLOM model for 04/10/2006

Right: from the original 1/32°-resolution outputLeft: reduced to 1/3°-resolution

(observable by current nadir-looking satellite altimeters)

(NLOM data provided by IPRC-APDRC)

SSH vs vorticity snapshot from the NLOM model for 04/10/2006

original 1/32°-resolution reduced 1/3°-resolution

reduced 1/3°-res. original 1/32°-res.

PDF of modeled vorticity as a function of intensity

anti-cyclonic

cyclonic

Ratio = anticyclonic/cyclonic

anticyclone-dominant

cyclone-dominant

reduced 1/3°-res. AVISO SSHA-derived original 1/32°-res.

PDF of modeled and observed vorticity as a function of intensity

anti-cyclonic

cyclonic

Chelton et al. (2007, GRL)

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)

Chelton et al. (2007, GRL)

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)

Chelton et al. (2007, GRL)

STCC band

September T(y,z) along 170°E

Eastward-flowing STCC overlying westward-flowing SEC

STCC-SEC shear ΔU vs regional EKE annual cycle

Eastward-flowing STCC overlying westward-flowing SEC

September T(y,z) along 170°E

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: 200~370 km; most unstable: 250 km (scaled well by f2|dU/dz|/βN2).

• Consider 2-d momentum eqs:

Quantifying eddy-eddy interaction

• Take discrete Fourier transform and form kinetic energy PSD eq:

wherespectral energy transfer term

PE to KE conversion term

dissipation term

• In a slowing-evolving eddy field:

Qiu, Scott and Chen (2008, JPO)

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

+: energy sink

: energy source

_

• In a slowing-evolving eddy field:

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

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

Bimonthly spectral energy transfers in the S Pacific STCC region

• In the quasi-equilibrium state, the spectral energy transfer is related to the convergence of spectral energy fluxes:

where

signifies spectral energy flux from k<K to k>K through eddy-eddy interactions

kK

Scott and Wang (2005, JPO)

Spectral energy flux ΠK in the S Pacific STCC region

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

+: forward cascade

: inverse cascade

_

Explaining Chelton’s 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

Is that all there is?

NLOM original 1/32°-res. vorticity

NLOM reduced 1/3°-res. vorticity

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

+: energy sink: energy source_

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_

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

+: forward cascade

: inverse cascade

_Spectral energy flux ΠK

n 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.

n 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.

Comments

Longitude-time plot of EKE along 21-29°S

OFES 1/10°-res. climatological run result

Longitude-time plot of EKE along 21-29°S

n 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.

n It further helps us explore the extent to which the mean circulation changes leads to the modulation in the mesoscale EKE field.

n 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).

Comments

Energy flow in a 2-layer baroclinic turbulent ocean

Rhines (1977) Vallis (2006)

NLOM field:

original 1/32°-res.

reduced 1/3°-res.

(note the different color scale)

NLOM field of S

original 1/32°-res.

reduced 1/3°-res.

+: anticyclonic forcing –: cyclonic forcing

Yearly-mean sea surface height field

Baroclinic instability growth rate based on upper ocean f/Ri1/2

Figure courtesy of D. Chelton