Strides, steps and stumbles in the
march of the seasons
1.
2.
3.
4.
5.
Astronomical signal, processed by Earth
Earthly data sets, processed by computer
Strides: annual, semiannual
Steps: Asian monsoon onset, Americas MSD
Stumbles (a.k.a. “singularities”)
•
•
the US January Thaw
Brazil rain
•
Software demo (DVD available - ask)
High frequency aspects of the
mean seasonal cycle
Brian Mapes
University of Miami
Seasonality: the forcing
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Astronomical forcing
(spherical Earth, circular orbit)
solstice
equinox
equinox
solstice
Temporal Fourier spectrum
of annual insolation
sin(4pt/365d)
Semiannual
sin(2pt/365d)
Annual
no forcing, just
internal
nonlinearitites
Annual cycle signal processing
(by the Earth)
Cloud,
albedo
heating
Heat
capacity
temperature
gravity
pressure
rotation
wind
precip
microphysics
humidity
cloud
vertical
motion
evaporation,
advection
Annual cycle signal processing
(by the computer)
1. Form mean daily climatologies:
var (365 calendar days; lat, lon, level, dataset)
2. Compute mean, annual + semiannual harmonics
 mean, 2 amplitudes, 2 phases
3. Residual is called “HF”
HF = climatology - annual - semiannual
4. Wavelet analysis of HF
 {dates, periods, amplitudes, significances of HF
events}
Wavelet
example
Paul wavelet
•Sharp time localization
• broad in frequency
•Real part: max/min
•Imaginary part: rise/fall
(Torrence and Compo 1998 BAMS)
Signal processed. Now what??
Fourier and wavelet coefficients form a
supplement (index) to climatology.
This doubles the size of the data set.
?? What to do with all this information ??
interactive GUI visualization tool
Outline of examples
1. Annual
–
–
“Easy” (local, thermal): Tsfc
Nonlocal: Z250 (jet streams)
2. Semiannual
–
–
Nonlinear: angular momentum and u250
Statistical: 250mb eddy activity
3. Ter-annual and beyond
–
oceanic subtropical highs, monsoons
OBS
Simplest: annual
harmonic of
surface air T
GFDL
CSM
OBS
Cold winter 
low tropospheric
thickness?
GFDL
annual harmonic
of Z250
CSM
Temperature 
thickness?
Not so simple…
Local Hadley cells?
Jan 1
Annual
Harmonic
of u at
200 hPa
Apr 1
Annual
Harmonic
of atmos.
heating
Outline of examples
1. Annual
–
–
“Easy” (local, thermal): Tsfc
Nonlocal: Z250 (jet streams)
2. Semiannual
–
–
Nonlinear: angular momentum and u250
Statistical: 250mb eddy activity
3. Ter-annual and beyond
–
oceanic subtropical highs, monsoons
Semiannual
harmonic of
250 hPa zonal
wind
(Weickmann &
Chervin 1988)
Jan min
Jan max
Apr
Apr
Apr-Oct
Jan
OBS
Apr
Apr
May+Nov
Semiannual
harmonic of
250 hPa
zonal wind
HF
total
Apr-Oct
Jan
CSM
Apr
Apr
Jun+Dec
semiannual
harmonic of 250
hPa zonal wind
semiannual u in a
forced/damped
barotropic model
forced with annual
harmonic only of
200mb div (Huang
& Sardeshmukh
2000)
Apr-Oct
Jan-Jul
total
Apr-Oct
Jan-Jul
A nonlinear overtone
Semiannual eddy (storm) activity
Midwinter Suppression of Baroclinic Wave Activity in the Pacific
Nakamura 1992
ABSTRACT
Seasonal variations in baroclinic wave activity and jet stream structure in the Northern
Hemisphere are investigated based upon over 20 years of daily data. Baroclinic wave
activity at each grid point is represented for each day by an envelope function, the
lowpass-filtered time series of the squared highpass-filtered geopotential height.
Baroclinic wave activity over the Atlantic exhibits a single maximum in January,
whereas in the Pacific it exhibits peaks in late autumn and in early spring and a
significant weakening in midwinter, which is more evident at the tropopause level than
near the surface. This suppression occurs despite the fact that the low-level baroclinity
and the intensity of the jet stream are strongest in midwinter. Based on the analysis of
31-day running mean fields for individual winters, it is shown that over both the oceans
baroclinic wave activity is positively correlated with the strength of the uppertropospheric jet for wind speeds up to 45 m s 1. When the strength of the westerlies
exceeds this optimal value, as it usually does over the western Pacific during midwinter,
the correlation is negative: wave amplitude and the meridional fluxes of heat and zonal
momentum all decrease with increasing wind speed. The phase speed of the waves
increases with wind speed, while the steering level drops, which is indicative of the
increasing effects of the mean flow advection and the trapping of the waves near the
surface.
midwinter
eddy
minimum
NCEP 1969-96
Oct+Apr maxima
of eddy v variance
semiannual
amplitude (color) of
a climatology of
stdev of 9d sliding
window v250
Decently
simulated by
coupled model
CSM 1.3
Outline of examples
1. Annual
–
–
“Easy” (local, thermal): Tsfc
Nonlocal: Z250 (jet streams)
2. Semiannual
–
–
Nonlinear: angular momentum and u250
Statistical: 250mb eddy activity
3. Ter-annual and beyond
–
oceanic subtropical highs, monsoons
Ter-annual
variations of
sea-level
pressure
HF
total
10d
100d
CSM climate model
HF
total
Understanding
SLP
seasonality:
Zonal mean
total
HF
10d
100d
Pacific ter-annual SLP schematic
NH Winter High
Monsoon-related
~100d period high
Oceanic
(Aleutian)
~semiannual low
NH Summer Low
Outline of examples
1. Annual
–
–
“Easy” (local, thermal): Tsfc
Nonlocal: Z250 (jet streams)
2. Semiannual
–
–
Nonlinear: angular momentum and u250
Statistical: 250mb eddy activity
3. Ter-annual and beyond
–
oceanic subtropical highs, monsoons
Linho and
Wang 2002
wavelet
method
EASM
ISM
WNPM
EASM
ISM
WNPM
a model:
decent
ISM onset,
but poor at
oceanic
systems
EASM
ISM
WNPM
North
America at
same time
NAM
ENASM?
EASM
ISM
WNPM
EASM
ISM
WNPM
June onset in
southeast US
(from CPC .25deg 194898 gauge data set)
(mid-summer dip)
Jun
1
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Jul 1
5
Ter-annual
midsummer
structure
CMAP 23y mean obs. rain
1
dry
July Aug
high & dry in
tropical
Americas
NCEP 27 year (1969-96) SLP
Gulf of Mexico area
HF
Midsummer high in W. Atlantic
wet
dry
21 May10 June
3-27
July
SLP obs
G Mexico
IPRC/
ECHAM
model:
decent
Key features of Asian vs. American
monsoons : a model experiment
IPRC / ECHAM model: shown to have
decent Asian onset, American
midsummer drought
Enhance monsoons by allowing each
calendar day (solar declination) to last
5x24 hours. Summer continents get
hotter, atm has time to equilibrate.
(SST fixed to obs. for each calendar day)
April-Sept rainfall, exp-control:
S. Asia wetter, Americas drier
• S. Asia time series shows
earlier (May) onset in exp
• Stated regarding the control
run,
– Land-atm lags delay Asian
monsoon onset behind its
seasonal forcing by ~1mo.
– Onset is the main
disequilibrium of the Asian
monsoon wrt seasonal
forcing
total
May
April-Sept rainfall, exp-control:
S. Asia wetter, Americas drier
• Americas time series shows
mid-summer drought earlier
and drier in exp
• Stated regarding the control
run,
– Land-atm lags prevent
American midsummer
drought from developing
fully
– Midsummer drought is the
main disequilibrium of the
American summer
monsoon wrt seasonal
forcing
Jun July
Outline of examples
1. Ter-annual and beyond
–
–
oceanic subtropical highs
monsoons
•
•
•
Asian onset
American midsummer drought
These things are related
Chen, Hoerling and Dole 2001
Heating
Eddy Z1000
w/o shear
Eddy Z1000
July u(y,p)
u300, zonal mean
Jul-Aug time slice
60N
Westerlies retreat to >30N in midsummer
Qu i ck Ti me ™a nd a
T IF F (LZ W )d ec om pres so r
ne ed ed to s ee th i s pi c tu re.
<0
Eq
J F M A M J J A S O N D
time slice
easterlies protrude
to 30N suddenly
in mid summer
WHY, in terms of [u] budget?
• Not f[v]: ~barotropic; [v](t) wrong
• [u’v’]: Tilted TUTTs, Tibetan High, Transients?
Suggested story
timing as seen in
Key West data
Winter Wiggles
• Sub-ter-annual time scales: real ??
– ‘The January Thaw’
• a statistical phantom? (BAMS Jan 2001)
– Brazilian rainfall
January Thaw
lit. of 1919
Boston, 1872-1965
Entire debate centers
on this spike
missing this
Revisit, with
more spatial
averaging
3K
• 1969-96 NCEP
reanalysis surface
air temperature
• N. America mean
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Jul
• (think vdT/dy)
HF part
5K
10d
100d
Jan
Jun
CPC US
precip
1948-98
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Winter Wiggles
• Sub-ter-annual time scales: real ??
– ‘The January Thaw’
• a statistical phantom? (BAMS Jan 2001)
– Brazilian rainfall
Where are those boxes? W. subtropical oceans
High
igh
High
High
CMAP rainfall
climatologies:
TAIWAN 25N
May
CUBA 25N
May
SE BRAZIL 25S
Nov.
MADAGASCAR
25S
Nov.
East Brazil rain gauge data
?
Source: CPTEC Web site
SP &
Rio
clim.
?
Source: Hotel inter-continental Web site
Sub-ter-annual Wiggles
– Brazilian rainfall
Live software demo
mapes@miami.edu for a DVD copy
1. Semiannual jets: questions
• OK, it’s a nonlinear overtone driven by the annual
harmonic of divergence. What and where is the
nonlinearity?
• Superposition fails of course, but surely one could say
more than ann div everywhere -> semiann u
–
–
–
–
Tropical vs. extratropical divergence?
Advection of/by divergent vs. rotational wind, u vs v?
Zonal mean vs. longitudinal features (where)?
Spring/summer/fall/winter?
(HS2000 is really just a succession of steady states)
Does using obs. divergence presuppose too much?
East Asia
midsummer
drought
mechanism: the
Bonin High
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
upper level
(barotropic)
“Formation mechanism
of the Bonin High in
August”
(Enomoto, Hoskins, & Matsuda 2003)
u200 HF anomaly plot, July-Aug
HF anomalies
(total - annual - semiannual):
Yes, the Bonin
High and 2 other
stationary waves
are evident, but
also a zonally
elongated u
anomaly spanning
all Asia-WPAC
Japan
-4
-2
HF
0 m/s 2
time
slice
Jul Aug
10d
100d
HF wavelet analysis
Interannual consistency of the
Asian HF jet anomaly ~1 Aug
A hemispheric
adjustment?
• SLP 1969-96
from NCEP
reanalysis
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.