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Mesoscale dynamics and SWOT
R. M. Samelson
CEOAS, Oregon State University
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
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