Mesoscale dynamics and SWOT

R. M. Samelson

CEOAS, Oregon State University

rsamelson@coas.oregonstate.edu

Joint work with M. Schlax & D. Chelton (OSU)

Understanding the evolution and dynamics of “mesoscale” (currently resolvable ó wavelength 200 km or greater) features, including their generation, interaction, and decay, will require “submesoscale” information (smaller than currently resolvable, e.g., wavelengths down to 15-50 km). This will be the case whether or not the smaller scales are found to belong to a distinct or modified dynamical regime. SWOT has the exciting potential to provide these measurements, and thus to support a fundamental advance in understanding the dynamics of mesoscale variability (which is the primary agent of the lateral turbulent transports that must be parameterized in climate models…). Temporal resolution remains a challenge. A possible strategy is to combine deterministic analysis of fast-repeat data with statistical analysis of 22-day repeat data.

SWOT and the mesoscale

Randomness, symmetry and scaling of mesoscale eddy life cycles

R. M. Samelson, M. G. Schlax & D. B. Chelton

CEOAS, Oregon State University

rsamelson@coas.oregonstate.edu

OSTST Meeting, October 2013, Boulder

Cyclonic and Anticyclonic Eddies with Lifetimes ≥ 16 Weeks(35,891 total)

Average lifetime: 32 weeksAverage propagation distance: 550 kmAverage amplitude: 8 cmAverage horizontal radius scale: 90 km

Total number of observations: ~1.15 million

Observed amplitude life cycles: 3 examples

Normalized mean and std dev life cycles from altimeter eddy-tracking analysis

Universality, time-symmetry,…!!!

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

16 31 wks 32 47 wks 48 63 wks 64 80 wks

Mean

Std dev

dimensionless time

dim

ensi

onle

ss a

mpl

itude

and

std

dev b)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

16 31 wks 32 47 wks 48 63 wks 64 80 wks

Mean

Std dev

dimensionless time

dim

ensi

onle

ss a

mpl

itude

and

std

dev

r=0.06 ( =0.94), B0=0.6

c)

Subsequences of Gaussian random walk with linear damping:

Universal scaling: Normalized life cycle structure is essentially independent of lifetime (and is time-symmetric)!

Normalized mean and std dev life cycles from altimeter eddy-tracking analysis

Universality, time-symmetry,…!!!

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2 Mean Std dev

observations

stochastic model (r=0.06, B0=0.6)

simulation

dimensionless time

dim

ensi

onle

ss a

mpl

itude

and

std

dev d)

Mean amplitude and number of eddies vs. lifetime

0 50 100 1500

5

10

15

lifetime (wk)

ampl

itude

(cm

)

a)

0 50 100 150100

101

102

103

104

105

lifetime (wk)

num

ber o

f edd

ies

observations (20.5 yr record)stochastic model (r=0.06, B0=0.6)

simulation (7 yr record)

b)

Autocorrelation structure of altimeter SSH field (prior to eddy tracking) is consistent with stochastic model when viewed on long planetary (Rossby) wave characteristics

10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

Latitude (oN or oS)

ACF

at 5

wee

k la

g

The dynamics of random increments

How should the random increments be interpreted physically? Eddy-eddy interactions (vortex pairs)? Eddy-mean interactions (mean-flow instability)? Eddy-whatever interactions (everything and anything)? What are the implications for theories of mesoscale ocean dynamics (for example, the postulated inverse cascade)? Work in progress: Correlate observed eddy tracks and eddy amplitude variations to evaluate eddy-eddy interactions.

A candidate mechanism: gain or loss of material through eddy-eddy interaction

and filament generation or assimilation

4 2 0 2 46

4

2

0

2

4

6

x

y

t= 4t=0t=+4

4 2 0 2 46

4

2

0

2

4

6

x

y

t= 4

4 2 0 2 46

4

2

0

2

4

6

x

y

t=0

4 2 0 2 46

4

2

0

2

4

6

x

y

t=+4

4 2 0 2 46

4

2

0

2

4

6

x

y

t= 4t=0t=+4

4 2 0 2 46

4

2

0

2

4

6

x

y

t= 4

4 2 0 2 46

4

2

0

2

4

6

x

y

t=0

4 2 0 2 46

4

2

0

2

4

6

x

y

t=+4

Conclusions 1.  A simple Markov-based model reproduces many basic

aspects of observed mean eddy amplitude life cycles from altimeter-based identification and tracking, including time-reversal symmetry and lifetime-independence.

2.  Best fit of model results to observations requires inclusion of damping; difficult to reproduce relative magnitude of standard deviations.

3.  A “pure” noise model is inconsistent with observations.

4.  Physical interpretation of random increments – “forward” or “backward” filamentation?

5.  Underlying SSH field autocorrelation structure is

consistent with stochastic model when viewed on long planetary wave characteristics

Understanding the evolution and dynamics of “mesoscale” (currently resolvable ó wavelength 200 km or greater) features, including their generation, interaction, and decay, will require “submesoscale” information (smaller than currently resolvable, e.g., wavelengths down to 15-50 km). This will be the case whether or not the smaller scales are found to belong to a distinct or modified dynamical regime. SWOT has the exciting potential to provide these measurements, and thus to support a fundamental advance in understanding the dynamics of mesoscale variability (which is the primary agent of the lateral turbulent transports that must be parameterized in climate models…). Temporal resolution remains a challenge. A possible strategy is to combine deterministic analysis of fast-repeat data with statistical analysis of 22-day repeat data.

SWOT and the mesoscale