superpressure balloon studies of atmospheric gravity waves

Gravity Wave Symposium

Superpressure Balloon Studies of Atmospheric Gravity Waves in the

Stratosphere

Robert Vincent Jennifer Haase, Albert Hertzog, Weixing Zhang

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Gravity Wave Symposium

Introduction• Super pressure balloons are a powerful way to derive

gravity wave momentum fluxes

• Problems occur at periods shorter than about 20 min

• High precision GPS measurements offer a way to derive momentum fluxes at short periods

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Gravity Wave Symposium

SPB Equation of Motion

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Following Nastrom (1980) the equation of motion in the vertical direction is:(MB + ηMa)

�2ζ �b

�t2 = �g(MB � Ma) � 12 ρaCdAB

��ζ �

b�t � w�

� ����ζ �b

�t � w���� +

(MB + ηMa)�w�

�ti.e. net force = buoyancy force + drag force + dynamic force

This can be simplified to�2ζ �

b�t2 = �ω2

Bζ�b + 2

3gR � A�

�ζ �b

�t � w�� ����ζ �

b�t � w�

��� + �w�

�t (1)where

ω2B = 2g

3T

��T�z + g

Ra

�

A = Cd4r

R = wave induced density perturbationωB = Buoyancy frequency

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For a gravity wave of intrinsic frequency ω and vertical velocity amplitude wothe instantaneous vertical velocity is w� = woe�iωt

R = ρ�

ρ = i N2

gωw�

N2 = gT

�gcp + �T

�z

�

(1) can be solved numerically

Example:Wave with 15 min intrinsic period, wo=1 ms�1

Red curve is numerical solution

Response contains only odd harmonics

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Wave packet τ = 15 min

Harmonic distortion increases as wave amplitude increases

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Quasi-Analytic Solution

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If the vertical displacement of air parcel is ζ � then let ζ �bζ � = Z = |Z|eiφ

(1) becomes:�ω2ζ �

b = �ω2Bζ

�b + 2

3N2ζ � � A(�iωζ �

b + iωζ �)| � iωζ �b + iωζ �| � ω2ζ �

Hence:

Z =23N

2�ω2�iAω2ζoYω2B�ω2�iAω2ζoY

(2)

where Y = |1 � Z|

Iterative solution for (2) with quick convergence.

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Note the limiting values of |Z| and φ when the balloon is on itsequilibrium density surface (EDS) - isopycnic balloon.

From (2) |ZEDS| � 2N2

3ω2B

=

�gcp

+ dTdz

�

( gRa

+ dTdz )

� 0.3

For referenceAntarctic:

N = 0.023 rad s�1 τN = 4.6 minωB = 0.034 rad s�1 τB = 3.1 minZEDS = 0.31

Equator:N = 0.025 rad s�1 τN = 4.2 minωB = 0.035 rad s�1 τB = 3.0 minZEDS = 0.34

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��� ζbζ���

��� ζbζ���

φ

φ

τ = 60 min

τ = 15 minNote significant phase shift, φ(ω),when τ � 20 min

Gravity Wave Symposium

SPB Measurements

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Horizontal position: x(t), y(t) � u(t), v(t)

Vertical position: ζb

Pressure: p�T = p� + dp

dz ζ�b

p� = p�T + ρgζ �

b

Temperature: T�T = T� + dT

dz ζ�b

Process observations in wavelet space as a function of (ω, t)

Im�pTu||

�= �ρHN2

ω Re�u�

||w�

Systematic errors in flux retrieval for τ � 20 min

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Characteristics of GW Generated by Convection

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Significant part of momentum flux spectrum at periods less than 20 min

Typical phase speeds c � 0 � 60 ms�1

Typical horizontal wavelengths λh � 10 � 100 km

Gravity Wave Symposium

High-Resolution GPS Observations

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Zhang et al., (2016) Improvement of stratospheric balloon GPS positioning andthe impact on gravity wave parameter estimation for the Concordiasi campaignin Antarctica, JGR, (under review).

�h � 0.1 m�u � 0.003 ms�1

��b � 0.2 m

Gravity Wave Symposium

I - Direct Computation of w′

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(Simple version)

1. In wavelet space find peak value of u2|| � tmax, �max

2. Estimate peak value of �b at this location

3. Find range of periods that are significant

4. Make an initial guess of �o = �b/ZEDS

5. Compute Z from (2), derive new guess of �o = �b/Re(Z)

6. Iterate until convergence � Zf � �(�, t) = �b(�, t)/Zf

7. Compute fluxes directly in wavelet space

Gravity Wave Symposium

II -Direct Computation of w′

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u�|| � �

b

Input

Output

� � before phase correction � � after phase correction

Notice distortion

τ = 12 minc = 25 ms�1

θ = 45�

u|| = 2 ms�1

Gravity Wave Symposium

III-Direct Computation of w′

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Flux Retrievals - Single Wave

τ = 10 minc = 26 ms�1

θ = 135�

Old Method New Method

With noise

Without noise

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Flux Retrievals - Multiple Waves

Up going

Down going

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Conclusions• Objective method for converting vertical SPB

displacements to vertical parcel displacements

• Requires high resolution GPS measurements of SPB position in horizontal and vertical

• Estimate fractional wave fluxes to ~2%

• Results important for flux retrievals over convection

• Easy to extend to derive temperature perturbations

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