Solar Cycle Induced Ozone Perturbations
and the Reflection of Tropospherically
Forced Planetary Waves
Terry Nathan
Atmospheric Science Program
University of California, Davis
Eugene Cordero
Department of Meteorology
San Jose State University
SORCE 2004
WAVE REFLECTION - SOLAR ACTIVITY
• “… planetary waves, which may be subjected to
variable reflection in the upper atmosphere and so
may induce variable interference patterns in the lower
atmosphere, constitute a potential candidate [for sunweather correlations] …” Hines (1974)
• “Stratospheric ozone feedback plays a crucial role in
the amplification process whereby solar heating
variations modify the zonal wind, altering wave
propagation, which then alters the lower atmosphere’s
temperature response.” Shindell et al. (1999)
UNRESOLVED ISSUES
What is the importance of wave-ozone feedbacks to
solar-induced changes in planetary wave reflection?
WAVE-OZONE FEEDBACKS
Inertio-gravity waves
(Zhu and Holton, 1986)
Free Rossby waves
(Nathan 1989; Nathan and Li 1991; Nathan et al. 1994)
Kelvin, Rossby-gravity waves
(Echols and Nathan 1996; Nathan and Cordero 2003)
QBO
(Cordero, Nathan, Echols 1998;Cordero and Nathan 2000)
GOAL
Determine how the background wind, radiativephotochemical processes and solar-induced
changes in zonal-mean ozone affect planetary wave
reflection and climate.
PLANETARY WAVE REFLECTION
CONCEPTUAL BASIS
d2A
2
+
m
A=0
2
dz
m 2 ( z; u , T , O 3 , ...)
m2<0
Evanescent Region
m2=0
Transition Region
m2>0
Propagating Region
MODEL AND GOVERNING EQUATIONS
Extratropical model that couples radiative transfer, ozone advection,
and ozone photochemistry with the quasi-geostrophic circulation
QGPV
2
fo 1 ∂ ⎛ ρ
∂φ ′
∂ ⎡ 2
1 ∂ ⎛⎜ ρ f o ∂φ ′ ⎞⎟⎤
⎞
′
u ⎢∇ φ ′ +
+
=
Q
κ
β
⎜
⎟
⎥
e
2
2
⎟
⎜
∂x ⎢⎣
∂x
ρ ∂z ⎝ N ∂z ⎠⎥⎦
ρ H ∂z ⎝ N
⎠
O3 Continuity Eqn.
∂
∂φ ' ∂γ
∂γ
u γ '+
+ w'
= S'
∂x
∂x ∂y
∂z
∞
O3 Source/Sink
ρ (ζ )
f0 H
∂φ '
γ ' dζ −
ξT
S ' = −ξ1γ '+ξ 2 ∫
ρ0
R
∂z
z
Vertical Motion
fo ⎡
∂ ∂ φ ′ d u ∂φ ′ κ Q ⎤
+
w′ = 2 ⎢- u
+
⎥
∂
∂
∂
dz
x
H
x
z
f
N ⎢⎣
o ⎥⎦
∞
Diabatic Heating
Q ' = Γ1γ '−Γ2 ∫
z
ρ (ζ )
H
∂φ '
γ ' dζ − f 0 ΓT
ρ0
κ
∂z
WKB (ANALYTICAL) SOLUTION
Evanescent Region, m2<0
⎡ ∞
⎤
C
ϕ ( x, y , z ; ε ) =
exp ⎢− ∫ m( z )dz ⎥ exp[i (kx + ly ]
m0
⎣ z
⎦
Transition Region, m2≈0 (Airy Functions)
ϕ ( x, y, z; ε ) = [ Ai ( z; m, u , γ , ...) + Bi ( z; m, u , γ , ...)] exp i (kx + ly )
Propagating Region, m2>0
⎧
⎫
⎛ zt
⎞⎪⎪
⎞
⎤ ⎪⎪ ⎛ zt
⎡ zt
hm
π
ϕ ( x, y , z ; ε ) = D
exp ⎢− i ∫ m( z )dz ⎥ ⎨exp⎜ i ∫ m( z )dz ⎟ + B exp⎜ − i ∫ m( z )dz + ⎟⎬ exp[i (kx + ly )]
⎜
⎟
2 ⎟⎠⎪
m0
⎥⎦ ⎪ ⎜⎝ z
⎢⎣ 0
z
⎝
⎠
1444
424444
3 1442443 1444424444
3
⎪⎩
⎪⎭
Amplitude
Downward Wave
Upward Wave
Refractive Index, m(z)
m( z ) = (m0 + εm1 )
Classic
Ozone Feedbacks
MEAN ZONAL WIND
REFRACTIVE INDEX SQUARED
Zonal Wind
Sept
July
Refractive Index Squared
March
March
Dec
m2
NUMERICAL RESULTS
wave-ozone
feedbacks
CONCLUSIONS
Wave-ozone interactions in the stratosphere can
directly alter planetary wave reflection and change
the mid-tropospheric heat flux by as much as 25%.
The importance of wave-ozone interactions to
planetary wave reflection has been overlooked in
previous studies examining the effects of the 11-year
solar cycle on planetary wave dynamics.
ONGOING WORK
• Examination of the effects of solar induced changes
on wave-ozone feedbacks in realistic two
dimensional background flows.
• Examination of the effects of solar-induced changes
on wave-ozone feedbacks and the interaction
between the planetary waves and QBO.
REFRACTIVE INDEX
m( z ) = (m0 + εm1 )
⎡⎛ β
1 ⎤
2
2 ⎞ N
m0 ( z ) = ⎢⎜⎜
− (k + l ) ⎟⎟ 2 −
2 ⎥
4 H ⎥⎦
⎢⎣⎝ u ( z )
⎠ f0
2
1/ 2
m1 ( z ) = f (u , T , γ , γ y , γ z , NC , rad − photochem coeff )
OUTLINE
• Wave reflection and solar activity
• Unresolved issues and goals
• Planetary wave reflection – conceptual basis
• Model and solution procedure
• Results (analytical and numerical)
• Conclusions and ongoing work