An Exploratory Model of Solar
Influence on Stratospheric
Dynamics
Alexander Ruzmaikin
John Lawrence & Cristina Cadavid
Approach
‹solar
UV variability (4-6% per cycle)
⇒ tropo-stratospheric dynamics
‹low-dimensional
North Annular Mode
⇒ low-dimensional modeling
Stratosphere Influences
Troposphere
NAM < 0
NAM > 0
Baldwin & Dunkerton (99)
Waves
Coupled Wind and Planetary Waves
Ψ
= F(ΨU,h,Λ)
-potential vorticity eq.
U
= G(ΨU,h,Λ)
-mean zonal wind eq
Ψ = X + iY - wave, u - mean zonal wind
Ψ0 = h - wave amplitude at source
Λ=
UR z - equilibrium gradient (UR = UB+ Λz)
Holton&Mass (74), Yoden (90), Christiansen (00),
Ruzmaikin, Lawrence & Cadavid (02)
Region of Integration and
Boundary Conditions
Latitudinal channel ∆y at 60˚N of 60˚ extent
Three levels z = 0, zT/2, zT
Top z = zT (=50 km): Ψ = 0,
Bottom z = 0 :
Sides y = 0, L:
U z =
U z|R = Λ
Ψ = /f0h, U = UR
Ψ = 0, U = 0
The Dynamical System
dX/dt = - X/ τ1 + qX- pY + sUY,
dY/dt = - Y/ τ1 + qY + pX - qUX - ζhU,
ηhY.
dU/dt = - (U - UR (0) - ΛzT)/ τ2 + qU -
τ1 = 122 days, τ2 = 30 days, X,Y = [L2/T]; L = a (Earth‘s radius).
p, s, ζ, η = 0.6, 2, 0.2, 87 [1/T, 1/L, L/T2, 1/T ,1/(L2T), L/T, L].
q = 4dy/dt/(∆y)3
QBO
(Ruzmaikin, Lawrence & Cadavid, 02)
Three Equilibrium Solutions
30
Λ = 0.8 m/s/km
Zonal Wind (m/s )
28
26
24
22
20
18
0
*
20
40
60
80
100
h (m)
120
140
160
180
200
X
o
stable
unstable
Annual and Solar Variability
Λ = Λ + δΛ sin(2πt/1y) + δΛs sin(2πt/11y)
Λ 0.75, δΛ

(R/fH)dT/dy
2.25 (m/s/km)
δΛs εΛ

--standard atmosphere

dU/dz = -
δΛs ≈ 4x104 δT/δy ≈ 0.1 m/s/km
--estimate
R = 3x106 cm2s-2, H = 7 km, f =10-4s-1, δy ≈ a, δT ≈ 2Κ

et al.

Zonal Wind Modulations
ε=0
Zonal Wind (m/s)
100
50
0
-50
ε = 0.03
100
0.03
50
0.02
0
0.01
-50
0
ε = 0.3
100
50
0
-50
0
5
10
15
20
25
time (years)
30
35
40
QBO Influence
∆y = ∆y0 [1 + q sin(2π/28)]
W and C winters (low and high U)
q
0
0.1
0.2
West QBO 30 25 11
16
6
21
East QBO
7
23
5
30 25 21
Holton&Tan
λο = 0.75, h = 62 m, t = 55 years
QBO and Solar
q = 0.1, εsol = 0.03
Sol Min
Sol Max
West QBO
31
38
23
60
East QBO
55
11
54
28
λο = 0.75, h = 62 m, t = 300 years
Observed States
High Flux West QBO at 20 hPa
60
60
40
40
U (m/s)
U (m/s)
Low Flux West QBO at 20 hPa
20
20
0
0
−20
−20
0
200
400
600
800
1000
0
60
60
40
40
20
0
−20
−20
200
400
600
800
400
600
1000
1000
0
200
400
600
A2 (m)
0
pdf(U,A2) pdf(U)pdf(A2)
at 60º lat
20 hPa
A2 (m)
−0.0007
800
20
0
0
200
A2 (m)
High Flux East QBO at 20 hPa
U (m/s)
U (m/s)
A2 (m)
Low Flux East QBO at 20 hPa
0.0007
800
1000
Model States
80
80
70
70
60
60
50
50
40
40
30
30
20
20
−200
−100
0
100
−200
0
X2
Solar Min East QBO
Solar Max East QBO
80
80
70
70
60
60
50
40
30
30
20
20
−100
0
100
−200
X2
−100
0
X2
−0.0001 0
100
50
40
−200
−100
X2
U
U
Solar Max West QBO
U
U
Solar Min West QBO
−0.0001
100
h = 62 m
q = 0.1
eps = 0.3
Discussion/Conclusions
‹
Solar variability influences stratosphere-troposphere
dynamics -- apparently through UV changes
‹
There are two stable major equilibrium states, possible
corresponding to two states of NAM
‹
Solar variability and QBO influence the occupation
frequency of the two states