An Exploratory Model of Solar Influence on Stratospheric

Dynamics

Alexander RuzmaikinJohn 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 windΨ0 = 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, �U�z = �U �z|R = Λ

Bottom z = 0 : Ψ = �/f0h, U = UR

Sides y = 0, L: Ψ = 0, U = 0

The Dynamical SystemdX/dt = - X/ τ1 + qX- pY + sUY,

dY/dt = - Y/ τ1 + qY + pX - qUX - ζhU,

dU/dt = - (U - UR (0) - ΛzT)/ τ2 + qU -ηhY.

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

0 20 40 60 80 100 120 140 160 180 20018

20

22

24

26

28

30

h (m)

Zo

nal

Win

d (

m/s

)

Λ = 0.8 m/s/km

* o stableX unstable

Annual and Solar Variability

Λ = Λ + δΛ� sin(2πt/1y) + δΛs sin(2πt/11y)

Λ�0.75, δΛ� �2.25 (m/s/km) --standard atmosphere δΛs � εΛ

����������������������� dU/dz = -(R/fH)dT/dy

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

-50

0

50

100ε = 0

Zon

al W

ind

(m/s

)

-50

0

50

100

0

0.01

0.02

0.03ε = 0.03

0 5 10 15 20 25 30 35 40-50

0

50

100

time (years)

ε = 0.3

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 QBOHolton&Tan

30 25 21 7 23 5

λο = 0.75, h = 62 m, t = 55 years

QBO and Solarq = 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

0 200 400 600 800 1000

−20

0

20

40

60

Low Flux West QBO at 20 hPa

U (

m/s

)

A2 (m)0 200 400 600 800 1000

−20

0

20

40

60

High Flux West QBO at 20 hPa

U (

m/s

)

A2 (m)

0 200 400 600 800 1000

−20

0

20

40

60

Low Flux East QBO at 20 hPa

U (

m/s

)

A2 (m)0 200 400 600 800 1000

−20

0

20

40

60

High Flux East QBO at 20 hPa

U (

m/s

)

A2 (m)

−0.0007 0 0.0007

pdf(U,A2) -pdf(U)pdf(A2)

at 60º lat20 hPa

Model States

−200 −100 0 100

20

30

40

50

60

70

80

Solar Max East QBO

X2

U

−200 −100 0 100

20

30

40

50

60

70

80

Solar Min East QBO

X2

U

−200 −100 0 100

20

30

40

50

60

70

80

Solar Max West QBO

X2

U

−200 −100 0 100

20

30

40

50

60

70

80

Solar Min West QBO

X2

U

−0.0001 0 −0.0001

h = 62 mq = 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