Intraseasonal Variability
• Stochastic excitation of the equatorial
equatorial
waveguide
• WISHE
• Moisture-convection feedback
• Cloud-radiation feedback
• Ocean interaction
• Self-aggregation on the equator
1
Wind--Induced Surface Heat
Wind
Heat Exch
xchange ((WISHE)
(WISHE)
WISHE) 2
Add back WISHE term to linear und
damped
d equatiions:
u s

  yv
tt x

x
 ss

v
v
 
  yu 
t
 y

s
u v

  u

t
x y
3
First look for Kelvin-like modes with v=0:
u s


x
t

s
u

 u
t x
2
2
u u
u
 2  2 
t
x
x
ikx it
:
Let u  u0 e
 
k  i k
2
2
4
Note: α must be < 0 for ωr > 0 and ωi > 0
5
As k → ∞ ωi → -α/2
6
Effect of Stratosphere
Stratosphere
(Yano
(Yano and
and Emanuel
manuel, 1991)
1991)
7
Effect of finite convective response time:
s
1

t 1  p
 u v 
 M
 
 x y 
 p  u v 
M eq 
    u
1
1
  p  x y
y 
M M eq  M

t
c
8
9
10
11
12
Go back to dimensional, quasi-
linear QE equations on β plane
plane
13
Quasi--Linear  Plane System , Quasi
Neg
egllecti
ecting Barotrop
arotropiic Mode u
u
s *
 Ts  T 
  yv  ru
t
x
v
s *
 Ts  T 
  yu  rv
t
yy
sd
s *  d  


 p M  w 

 Qrad 

t
m 
z

sb
h
 Ck | V |  s0 * ssb    M  w  sb  sm 
t
14
u v w
  0
x y H
Define an equilibrum updraft mass flux from
from
boundary layer QE:
s0 * ssb
M eq  w  Ck | V |
sb  sm
Relax to equilibrium over a finite time scale:
M M eq  M


convective
t
and enforce
M 0
15
Numerical solution of β plane quas
quasii-lilinear
near equat
equatiions
ons
• Nonlinearity retained only in surface fluxes
• Zonally symmetric SST specified; also
symmetric about equator
• Background easterly wind of 2 ms-11
imposed
• Convectition relaxed
l
d to
t equilibrium
ilib i
over
time scale of 3 hours
16
17
18
19
20
21
22
Cloud
Cloud--Radiative Feedback
• Set OLR proportional to difference in θe
between boundary layer and mid
troposphere (Sandrine Bony)
23
24
25
26
Moisture
Moisture--Convection Feedback
Feedback
• Allow precipitation efficiency to depend on
on
relative humidity
• Greater heating/upward motion in moister
•
moister
air
upward motion moistens air
• Necessary for ttropiicall cycllones
• Appears to excite planetary Rossby waves
near equator
27
28
Possible effects of ocean response
response
29
Is tth
the
he MJO an example o
off self
lflf
lf
ggre
gg
reg
gated convection on the
the
agg
equatorial beta plane?
plane?
30
Explicitly Simulated
Radi
dia
diati
ttive
ive-C
-C
Convectti
tive
ive
Equilibrium
Equilibrium
31
Nolan et al., QJRMS, 2007
2007
32
Empirical Necessary Conditions for SelfSelf-Aggregation (after Held et al
al., 1993; Bretherton et al
al., 2005; Nolan et al
al.;
;
2007)
• Small vertical shear of horizontal wind
• Interaction of radiation with clouds
and/or water vapor
• Feedback
F db k off convective
ti d
downdraft
d ft surface winds on surface fluxes
• Sufficiently high surface temperature
33
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12.811 Tropical Meteorology
Spring 2011
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34