Addressing the Ques.on of Large-­‐Scale Nonlinear Wave Coupling in the Space-­‐
Atmosphere Interac.on Region 1*
1
2
1
3 Vu Nguyen , Sco/ Palo , Ruth Lieberman , Jeffrey Forbes , and David Ortland *Author contact: [email protected] 1University of Colorado, Department of Aerospace Engineering Sciences 2GATS, Inc., 3NWRA 60
55
50
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40
35
30
25
20
15
10
5
0
100
Altitude [km]
90
Problem Statement Although there has been evidence of secondary waves generated from wave-­‐wave interac.on in the atmosphere, the forcing and manifesta.on of these waves are poorly understood due to the difficulty of obtaining short term .dal/wave es.mates on a global scale. This research focuses on the secondary waves arising from an interac.on between the migra.ng diurnal .de (DW1) and quasi two-­‐day wave (2dayW3), two of the largest waves in the MLT region. The main ques.ons to be answered in this study are: Al.tude 6
2dayE2 5
4
2
1
-5
0
Wavenumber
5
Altitude [km]
Altitude [km]
Altitude [km]
7
50
0
-50
0
Latitude [deg]
50
42.0
DW1 V Amp. 1/ 21/ 2006 [m/s]
100
36.0
90
30.0
80
24.0
70
60
55
50
45
40
35
30
25
20
15
10
5
0
18.0
60
12.0
50
40
12-50
11
10
9
8
7
6
5
4
3
2
1
0
f)
0
DW1 T Amp. 1/ 21/ 2006 [K]
0
50
Latitude
100
6.00
50
0.00
12
11
10
9
8
7
6
5
4
3
2
1
0
90
80
70
60
50
40
-50
16.0hrW4 U Amp. 1/ 21/ 2006 [m/s]
12
11
10
9
8
7
6
5
4
3
2
1
0
Altitude [km]
160
140
120
100
60
b)
0
0
Latitude [deg]
12
11
10
9
8
7
6
5
4
3
2
1
0
Altitude [km]
180
160
140
120
100
80
60
c)
12
11
10
9
8
7
6
5
4
3
2
1
0
160
140
120
100
80
60
-50
0
Latitude [deg]
160
140
120
100
80
60
e)
50
0
50
48.0hrE2 V Amp. 1/ 21/ 2006 [m/s]
200
12
11
10
9
8
7
6
5
4
3
2
1
0
180
160
140
120
100
80
60
-50
16.0hrW4 T Amp. 1/ 21/ 2006 [K]
180
12
11
10
9
8
7
6
5
4
3
2
1
0
180
50
200
48.0hrE2 U Amp. 1/ 21/ 2006 [m/s]
-50
16.0hrW4 V Amp. 1/ 21/ 2006 [m/s]
0
d)
f)
0
50
48.0hrE2 T Amp. 1/ 21/ 2006 [K]
200
12
11
10
9
8
7
6
5
4
3
2
1
0
180
160
140
120
100
80
60
-50
0
Latitude [deg]
90
80
70
60
50
40
-50
b)
0
The author would like to thank Prof. Sco[ Palo and Dr. Ruth Lieberman for their guidance on the project. The author also thanks Prof. Jeffrey Forbes (CU) for his advice on the Global Scale Wave Model and Dr. David Ortland for providing es.mates of the DW1. This research was supported by JPL subcontract 1483557. 60
50
40
-50
90
80
70
60
50
40
c)
0
30.0
27.5
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
90
80
70
60
50
40
-50
f)
12
11
10
9
8
7
6
5
4
3
2
1
0
100
90
80
70
60
50
2dayE2 V Forcing Amp. 1/ 21/ 2006 [1e-5 m/s2]
50
0
Latitude [deg]
0
100
16hrW4 T Forcing Amp. 1/ 21/ 2006 [1e-5 K/s]
0
50
2dayE2 T Forcing Amp. 1/ 21/ 2006 [1e-5 K/s]
12
11
10
9
8
7
6
5
4
3
2
1
0
100
90
80
70
60
50
40
50
-50
Forcing Projec.on on 1st Mode (40-­‐105 km) 0
Latitude [deg]
Key Points • Forcing amplitude is largest between 80-­‐100 km where primary waves are largest • 16hrW4 forcing is mainly concentrated at lower la.tudes • 2day forcing extends to higher southern la.tudes • Differences between 16hrW4 and 2dayE2 forcing is determined by the phase of primary waves 50
Response to 1st Mode Forcing (50-­‐200 km) 16hrW4 1st Mode T Forcing Amp. [1e-5 K/s]
16hrW4 T Response Amp. to 1st Mode Forcing [K]
200
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
100
90
80
70
60
50
40
-50
0
140
120
100
60
50
100
90
80
70
60
50
40
0
Lattiude [deg]
160
80
-50
0
50
2dayE2 T Response Amp. to 1st Mode Forcing [K]
200
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-50
12
11
10
9
8
7
6
5
4
3
2
1
0
180
48hrE2 1st Mode T Forcing Amp. [1e-5 K/s]
12
11
10
9
8
7
6
5
4
3
2
1
0
180
160
140
120
100
80
60
50
-50
0
Latitude [deg]
50
Secondary Wave Response vs. Forcing Loca.on a)
Independent Var.: Φ = la.tude λ = longitude z = al.tude t = .me Secondary Waves: Numerical Experiments 16hrW4 Maximum Amp. vs. Forcing Location
100
90
80
70
T [K]
U [m/s]
60
V [m/s]
50
40
0
2
50
Acknowledgements 70
30.0
27.5
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
4. Key Points • 16hrW4 is the larger secondary wave reaching maximum amplitudes of 12 K in the lower thermosphere. Significant throughout the thermosphere. • 16hrW4 amplitude structure is mainly composed of its 1st propaga.ng Hough mode (43 ver.cal wavelength). Longer ver.cal wavelength implies more effec.ve propaga.on. • 2dayE2 amplitude structure is composed of its 1st propaga.ng Hough mode (38 km ver.cal wavelength) at the equator, but contains higher modes at higher la.tudes in the MLT region 80
50
100
-50
30.0
27.5
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
90
e)
Field Variables: u = zonal wind v = meridional wind w = ver.cal wind T = temperature 2dayE2 U Forcing Amp. 1/ 21/ 2006 [1e-5 m/s2]
100
16hrW4 V Forcing Amp. 1/ 21/ 2006 [1e-5 m/s2]
-50
50
d)
30.0
27.5
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
100
40
CompuFng Secondary Wave Response in Tidal Model • Nonlinear momentum and thermal forcing (Panel 2) is input into Global Scale Wave Model (Hagan, 1995) to produce secondary wave amplitude and phase • Effects of background winds and la.tudinal temperature gradients are not included in order to assess the rela.onship to the forcing 2dayE2 Forcing (40-­‐105 km) 16hrW4 U Forcing Amp. 1/ 21/ 2006 [1e-5 m/s2]
50
200
50
200
-50
a)
50
Secondary Waves: 16hrW4 and 2dayE2 -50
16hrW4 Forcing (40-­‐105 km) Nonlinear Forcing Region 50
80
Altitude [deg]
% of Input Amplitude
Altitude [km]
Frequency [cycles per day]
8
70
0
Latitude [deg]
180
9
60
0.0
60
200
10
80
e)
0
-50
70
3. 48.0
40
50
80
a)
2dayE2 Temperature Amp. 1/ 21/2006 [K]
2dayW3 (QTDW) 50
Key Points • Quasi two-­‐day wave (2dayW3) reaches peak amplitude in S. Hemisphere MLT region during late-­‐
January • DW1 is concentrated near the equator • Both waves dissipate in the lower thermosphere around 100 km due to molecular dissipa.on 16hrW4 Amplitude (50-­‐200 km) 2dayE2 Amplitude (50-­‐200 km) 3
0.2
0
2dayW3 T Amp. 1/ 21/ 2006 [K] 40
-50
90
2dayE2 50
40
100
0.4
60
60
50
11
0.6
70
70
90
12
2dayW3 80
-50
Quasi two-­‐day wave (2dayW3) 70
60
55
50
45
40
35
30
25
20
15
10
5
0
100
Migra.ng Diurnal Tide (DW1) 80
-50
80
40
Nonlinear Forcing Region 90
50
100
c)
1.0
0.8
0
50
Extrac.ng Evidence of Secondary Waves 2dayE2 Aliasing from 2dayW3
100
•  Apply the Fast Fourier Synop.c Mapping (FFSM) method Least Squares
80
(Salby, 1982) to SABER temperatures. FFSM
•  FFSM eliminates aliasing between 2dayW3 (primary 60
wave) and 2dayE2 (secondary wave) unlike commonly-­‐
40
used least squares methods 20
•  2dayE2 may contain aliasing from other secondary wave 0
(16hrW4) and thus, represents secondary wave ac.vity. -40
-20
0
20
40
Latitude [deg]
Secondary Waves Observed in TIMED-­‐SABER Satellite Temperatures •  FFSM-­‐derived wavenumber-­‐frequency spectrum shows dominate peaks at 2dayW3 and 2dayE2 in the MLT region during January 2006 •  DW1-­‐QTDW secondary waves are significant above 80 km and largest at low la.tudes in the southern hemisphere. b)
100
90
Secondary Wave Response (2dayE2, 16hrW4) 60
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10
5
0
100
90
2dayW3 V Amp. 1/ 21/ 2006 [m/s]
b)
DW1 U Amp. 1/ 21/ 2006 [m/s]
DW1 HME Merdional
Wind Amp. [m/s], 1/ 21/ 2011
60
60
-50
ObservaFons of Secondary Waves FFSM Spectrum (90 km, 30S) 1/21/2006
70
40
•  Where in the atmosphere are DW1 and QTDW interacFng to force secondary waves and where do significant responses occur? •  How does the nonlinear forcing region determine the secondary wave response? a)
80
50
Impacts on MLT Region and Above d)
2dayW3 U Amp. 1/ 21/ 2006 [m/s]
Thermal Forcing Altitude [km]
a)
Meridional Forcing Altitude [km]
Primary Wave 2 Zonal Forcing 4
6
Maximum Amplitude
b)
Center Altitude of Nonlinear Forcing [km]
Primary Wave 1 2dayW3 Amplitude (40-­‐105 km) DW1 Amplitude (40-­‐105 km) Nonlinear Forcing Region Secondary wave forcing arises from the nonlinear terms in the conservaFon equaFons, which contain products of primary waves in u, v and T (assuming w is small) Generalized Hough Modes • Generalized Hough modes developed by Ortland [2005] describes classical Hough modes for .des in a realis.c atmosphere • Generalized Hough modes are fit to SABER temperatures to obtain daily DW1 defini.ons Center Altitude of Nonlinear Forcing [km]
•  Nonlinear interac.ons are a fundamental source of global scale variability in the atmosphere. •  Secondary waves may propagate ver.cally away from their forcing region and thus, couple space-­‐
atmosphere regions through currently unknown pathways. Nonlinear Forcing cos(s1λ − σ 1t) cos(s2 λ − σ 2 t)
NOGAPS-­‐ALPHA TIMED Satellite ObservaFons • Naval Research Laboratory • SABER is used to extract reanalysis model assimila.ng 2dayW3 temperature Aura-­‐MLS and TIMED-­‐SABER es.mates above 88 km satellite temperatures • TIDI is used to extrapolate • Used for 2dayW3 es.mates NOGAPS 2dayW3 winds from 30 to 88 km above 88 km Altitude [km]
cos((s1 + s2 )λ − (σ 1 + σ 2 )t)
2. Primary Waves: 2dayW3 and DW1 Altitude [km]
Secondary Wave 2 Al.tude Impacts on the Space-­‐Atmosphere Coupling Secondary Wave 1 cos((s1 − s2 )λ − (σ 1 − σ 2 )t)
1. Altitude [km]
Nonlinear InteracFon Scenario •  Past research has primarily focused on atmospheric .des and planetary waves that are excited by solar-­‐driven processes. •  However, theory and evidence suggests that waves may nonlinearly interact to produce secondary waves. Altitude [km]
Global scale wave-­‐wave interac.ons Understanding the Process of Secondary Wave ManifestaFon Altitude [km]
IntroducFon 8
2dayE2 Maximum Amp. vs. Forcing Location
100
90
80
70
60
50
40
0
2
4
6
Maximum Amplitude
8
Key Points • Nonlinear momentum and thermal forcing (Panel 2) is projected onto the 1st propaga.ng mode of each secondary wave and used to compute the model response • Greater 1st mode projected forcing causes larger 16hrW4 response than 2dayE2 • 16hrW4 response to 1st mode forcing captures the majority of the overall 16hrW4 response Key Points • Nonlinear momentum and thermal forcing (Panel 2) is divided into 15 km al.tude subsec.ons and used to compute individual model responses • Majority of 16hrW4/2dayE2 response is determined from forcing in the lower mesosphere due to exponen.al wave growth. • 2dayE2 response is also determined from forcing in the lower thermosphere Conclusions Ø  Significant DW1-­‐2dayW3 secondary wave ac.vity is only observed above 80 km. Ø  16hrW4 is larger than 2dayE2 response due to more efficient excita.on of the 1st Ø  16hrW4 and 2dayE2 secondary waves are predicted to maximize in the lower thermosphere. propaga.ng mode, which has the longest ver.cal wavelength. The 16hrW4 is significant in the middle thermosphere as well, highligh.ng implica.ons for Ø  The majority of both secondary wave responses is determined by the nonlinear forcing driving the E-­‐region dynamo in the space-­‐atmosphere interac.on region. contained in the lower mesosphere due to exponen.al wave growth with height. Higher Ø  Largest secondary wave amplitudes are NOT coincident with the largest primary wave or order modes of the 2dayE2 are also excited from in-­‐situ forcing in the lower nonlinear forcing amplitudes. thermosphere.