Southern Hemispheric mean spectra
Eddy kinetic energy
Precipitation
ERA-Interim
~20-25 days
Normalized Power
AMSR-E
0
0.05
0.1
0.15
Cycles/day
0.2
0.25
0
0.05
0.1
0.15
Cycles/day
0.2
0.25
Thompson/Woodworth 2014; Thompson/Barnes 2014
Exploring periodicity in the extratropical
circulation on synoptic scales …
David W J Thompson
Dept of Atmospheric Science, CSU
Spectrum of EKE at 300 hPa averaged 40-60S
power
a) zonal-mean
0
0.1
0.2
0.3
0.4
cpd
wer
b) 180 deg longitude windows
0.5
Projection
onto of
regional
Spectrum
EKE atscales
300 hPa averaged 40-60S
0
0.1
0.2
0.3
0.4
0.5
cpd
power
b) 180 deg longitude windows
0
0.1
0.2
0.3
cpd
wer
c) 90 deg windows
0.4
0.5
Projection
onto of
regional
Spectrum
EKE atscales
300 hPa averaged 40-60S
0
0.1
0.2
0.3
0.4
0.5
0.4
0.5
cpd
power
c) 90 deg windows
0
0.1
0.2
0.3
cpd
er
d) 30 deg windows
Projection
onto of
regional
Spectrum
EKE atscales
300 hPa averaged 40-60S
0
0.1
0.2
0.3
0.4
0.5
0.4
0.5
cpd
power
d) 30 deg windows
0
0.1
0.2
0.3
cpd
periodicity is largely absent on
scales less than <180 degrees
Longitude/time lag regression plots
1. Average EKE at 300 hPa over latitudes 40-60S.
2. Form the longitude/time lag regression map for
EKE40-60 at a base longitude of 0E.
3. Repeat 2), but for EKE40-60 at all base longitudes.
4. Average 3) over all base longitudes to generate a
mean lag regression plot.
Lag regression plot of EKE. Starting at lag 0.
EKE regressed on itself at lag 0
−10
Lag in time
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
Lag in longitude
−90
0
−10
Lag (days)
−5
0
5
wave packet propagates to the east at ~25 m/s
10
180
−90
0
90
180
Longitude
−90
0
−10
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
−90
0
−10
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
−90
0
note the development of EKE anomalies in wake of wave packet
−10
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
−90
0
−10
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
−90
0
Negative EKE anomalies emerge at lags ~5-10 days.
zooming in on positive lags
−10
0
Lag (days)
−5
0
5
5
10
−90
0
90
180
Longitude
−90
10
0
Lag (days)
180
15
20
25
30
0
90
180
−90
0
Longitude
Positive EKE anomalies emerge at lags ~25 days.
90
180
How does the periodicity appear along the path of
individual wave packets?
−10
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
−90
0
weak periodicity along path
of wave packet
Does the periodicity in storm amplitudes project onto
regional weather?
−10
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
weak periodicity at fixed location
−90
0
−10
Lag (days)
−5
0
5
10
180
−90
0
90
180
Longitude
−90
0
varying periodicity
depending on the flow rate sampled
along the latitude circle
periodicity in a “hierarchy” of models…
Normalized Power
Spectra of SH-mean EKE
observations (solid) and GFDL CM3 (dashed)
0
0.05
0.1
0.15
Cycles/day
0.2
0.25
Thompson/Barnes 2014
Normalized Power
Spectra of SH-mean EKE
observations (solid)
GFDL dry dynamical core in HS framework (dashed)
0
0.05
0.1
0.15
Cycles/day
0.2
0.25
Thompson et al. 2017
−10
−10
−5
−5
Lag (days)
Lag (days)
Spectra of SH-mean EKE
observations (solid)
0
0
5
5
10
10
180
−90
0
90
180
Longitude
−90
Observations
0
−180
−90
0
+90
+180
Relative longitude
−180
Dry dynamical core
−90
Simple(st?) model of the periodicity
Upper layer
EKE anomalies are driven by heat fluxes in lower layer
Lower layer
Two way interactions between heat fluxes and baroclinicity
Lower layer
H denotes heat fluxes; B denotes baroclinicity.
∂
∂
B
B + U lower
B = α BH −
∂t
∂x
τB
Anomalously poleward heat fluxes => decreases in baroclinicity
∂
∂
H
H + U lower
H = αH B −
∂t
∂x
τH
Anomalously high baroclinicity => poleward heat fluxes
Upper layer
H denotes heat fluxes; E denotes EKE.
∂
∂
E
E + U upper
E = αEH −
∂t
∂x
τE
Anomalously poleward heat fluxes => increases in EKE
We will consider 3 cases:
U lower = U upper = 0
U lower = U upper = 25 m/s
U lower = 10 m/s; U upper = 25 m/s
power
Power spectrum of zonal mean EKE
0
0.1
0.2
0.3
cpd
0.4
0.5
Lag (days)
U lower = U upper = 0
−1
−3
−5
−7
−9
−11
−13
90
180
−90
0
Longitude
90
180
−90
EKE anomalies decay and grow at fixed location.
Lag (days)
U lower = U upper = 25 m/s
−1
−3
−5
−7
−9
−11
−13
90
180
−90
0
Longitude
90
180
−90
anomalies decay and grow following wave packet
U lower = 10 m/s
Lag (days)
U upper = 25 m/s
−1
−3
−5
−7
−9
−11
−13
90
180
−90
0
Longitude
90
180
−90
EKE anomalies develop in wake of existing packets
Take home messages
Analyses of increasingly simple models suggest that:
1. The periodicity in SH wave activity derives from (dry)
feedbacks between the heat fluxes and baroclinicity in the lower
troposphere.
2. The structure of the periodicity on synoptic scales derives
from the contrasting eastward speeds of the source of the
periodicity in the lower troposphere (~10 m/s) and wave packets
in the upper troposphere (~25 m/s).
How does the periodicity appear in the context of
individual wave packets?
Power spectra of EKE following the flow
25
Rate (m/s)
20
15
10
5
0
0
0.1
0.2
0.3
cpd
25 days
0.4
0.5
eddy kinetic energy at 300 hPa
spectrum
ofoffield
30-70S
Power
spectra
fieldsaveraged
averaged 30-70
deg. S
Spatial
signatures
the BAM
spatial
signature
ofofBAM
a) EKE 300
b) EKE 300
100
80
60
0
−20
m2/s2
20
Normalized Power
40
−40
−60
−80
0
−100
0.05
0.1
0.15
Cycles/day
0.2
0.25
Thompson/Woodworth 2014