[PPT] - A Data assimilation model for determining the mean state and PowerPoint Presentation

SLIDE 1

A Data assimilation model for determining the mean state and migrating tide structures in the mesosphere and lower thermosphere using satellite measurements of wind and temperature

David Ortland NorthWest Research Associates (ortland@nwra.com)

Contributions from: TIMED/TIDI and SABER science teams, University of Michigan, NCAR, Langely HRDI science team, University of Michigan Rolando Garcia, NCAR Ruth Lieberman, Co-RA

SLIDE 2

2

Introduction

Migrating tide and mean flow

components of the dynamic fields u,v, and T are almost perfectly aliased in satellite measurements.

Although satellite precession

provides local time sampling, tide and mean flow variability over the timer period required makes harmonic analysis problematic.

Information on tide and mean flow

is contained in data binned by track angle and altitude. This information can be extracted by using u, v and T and the distinct dynamical balance relations for diurnal, semi-diurnal and mean flow.

Satellite sampling pattern of mean+tide

60 120 180 240 300 360 Longitude 6 12 18 24 Time (hrs) Ascending node (Local midnight) Descending node (Local noon)

Analysis begins with separately averaging all data from ascending and descending nodes

At the equator

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3

Basic Idea behind the assimilation method

Track-altitude cross section of either v in a single node or difference
f T for ascending and descending nodes is mainly a superposition
f the migrating diurnal and semi-diurnal tides.
Diurnal and semi-diurnal tides have distinct vertical and horizontal

structural patterns that enable these two tides to be distinguished.

Once the tidal structures are known in one field they can be

determined in the other fields and subtracted from the data to determine the zonal mean flow.

Sums and differences of ascending and descending node data in all

three fields actually gives an over determined inverse problem and contributes to improved accuracy.

Almost enough information to solve the tide and mean separation

problem is contained in the T field alone. Only an additional lower boundary condition is required.

SLIDE 4

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SABER temperature and model fit

(Tascending-Tdescending)/2 on 15-sep-2004

80
60
40
20

20 40 70 80 90 100 110 Alt (km)

SABER asc-desc 15-Sep-2004

12

12 12 12 24 36

60
40
20

20 40 60 K

80
60
40
20

20 40 70 80 90 100 110

Model fit

12 12 2 4 3 6

80
60
40
20

20 40 Latitude 70 80 90 100 110 Alt (km)

Diurnal asc-desc

12

1 2

60
40
20

20 40 60 K

80
60
40
20

20 40 Latitude 70 80 90 100 110

Semi-diurnal asc-desc

12 2 4 36

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SABER temperature and model fit

(Tascending+Tdescending)/2 – Tmean

80
60
40
20

20 40 Latitude 70 80 90 100 110 Alt (km)

SABER-mean, asc+desc

10

1 10 20

40
20

20 40 K

80
60
40
20

20 40 70 80 90 100 110

Diur+Sdiur asc+desc

10

10 1 10 20

80
60
40
20

20 40 Latitude 70 80 90 100 110 Alt (km)

Diurnal asc+desc

40
20

20 40 K

80
60
40
20

20 40 Latitude 70 80 90 100 110

Semi-diurnal asc+desc

1

10 1 20

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SABER temperature and model fit

(Tascending+Tdescending)/2

80
60
40
20

20 40 70 80 90 100 110 Alt (km)

SABER asc+desc 15-Sep-2004

185 201 201 217 217 2 3 2 2 4 8 264

160 180 200 220 240 260 280 300 K

80
60
40
20

20 40 70 80 90 100 110

Model asc+desc

185 185 201 201 217 2 1 7 232 2 4 8 248 2 6 4

80
60
40
20

20 40 Latitude 70 80 90 100 110 Alt (km)

SABER-diur-sdiur, asc-desc

185 2 1 201 217 2 1 7 2 3 2 2 4 8 248 264

160 180 200 220 240 260 280 300 K

80
60
40
20

20 40 Latitude 70 80 90 100 110

Zonal mean T

1 8 5 201 201 217 217 232 2 4 8 2 4 8 264

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Assimilation model components

Tidal structures are determined using a time-dependent

primitive equation model forced by heating at various altitude levels that has Hough function structure and run to steady state.

Both the diurnal and semi diurnal tides are represented as

linear combinations of the mode-like responses determined in this way.

Tidal structure is also controlled by the background mean

flow, dissipation mechanisms and interaction with gravity

waves. The dissipation and GW effects are represented

by a small number of parameters that are determined via an off-line nonlinear least-squares fitting.

The zonal mean u and T are represented in terms of a

linear combination of geostrophic ‘modes’.

The assimilation is accomplished by fitting the coefficients
f these linear expansions to the data.

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8

Why GW forcing is necessary:

Model simulations of the tide reproduce the observed vertical wavelength only if gravity waves are included

60
40
20

20 40 60 80 85 90 95 100 105 110 Altitude (km)

HRDI v, March 94 at 12h

6
60
6
40
4
40
20
20
20

20 20 20 20 40 40 40 40 60 60 60 80 80

60
40
20

20 40 60 80 85 90 95 100 105 110

TIDI v, March 04 at 12h

80
60
40
4
2
20
20
20
20
2

2 20 40 6

60
40
20

20 40 60 Latitude 85 90 95 100 105 Altitude (km)

Model with no GW

6
40
4
40
2
20
20

20 20 20 4 40 60

60
40
20

20 40 60 Latitude 85 90 95 100 105

Model with GW

60
40
40
20
20
20

20 20 20 40 4 60 80

HRDI TIDI Model diurnal tide simulations: No GW force GW force included

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60
40
20

20 40 60 60 70 80 90 100 110 Altitude

60
40
20

20 40 60 60 70 80 90 100 110

60
40
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20 40 60 60 70 80 90 100 110

60
40
20

20 40 60 60 70 80 90 100 110 Altitude

60
40
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20 40 60 60 70 80 90 100 110

60
40
20

20 40 60 60 70 80 90 100 110

60
40
20

20 40 60 60 70 80 90 100 110 Altitude

60
40
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20 40 60 60 70 80 90 100 110

60
40
20

20 40 60 60 70 80 90 100 110

60
40
20

20 40 60 Latitude 60 70 80 90 100 110 Altitude

60
40
20

20 40 60 Latitude 60 70 80 90 100 110

60
40
20

20 40 60 Latitude 60 70 80 90 100 110

(1,1) (1,2) (1,3) (1,-2) Zonal wind Meridional wind Temperature

Forcing

Diurnal tide basis functions

Generated with a linear tidal model, GW forcing, eddy, molecular diffusion; URAP March wind/temperature background; Forced in a thin layer by heating with a Hough function horizontal structure

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10

Semi-diurnal tide basis functions

Tide patterns are distinct from each other and from the geostrophic modes (But maybe not distinct from terdiurnal tide?)

(2,1) (2,2) (2,3) (2,4)

Forcing

Zonal wind Meridional wind Temperature

60
40
20

20 40 60 60 70 80 90 100 110 Altitude

60
40
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20 40 60 60 70 80 90 100 110

60
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20 40 60 60 70 80 90 100 110

60
40
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20 40 60 60 70 80 90 100 110 Altitude

60
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20 40 60 60 70 80 90 100 110

60
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20 40 60 60 70 80 90 100 110

60
40
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20 40 60 60 70 80 90 100 110 Altitude

60
40
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20 40 60 60 70 80 90 100 110

60
40
20

20 40 60 60 70 80 90 100 110

60
40
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20 40 60 Latitude 60 70 80 90 100 110 Altitude

60
40
20

20 40 60 Latitude 60 70 80 90 100 110

60
40
20

20 40 60 Latitude 60 70 80 90 100 110

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Construction of geostrophic modes

used to represent zonal mean wind and temperatures

Vertical structure Geopotental and U

2
1

1 2 3 70 80 90 100 110 Altitude

50

50 Latitude 70 80 90 100 110 Altitude

Zonal wind Horizontal structure of U

20 40 60 Latitude

4
2

2 4

50

50 Latitude 70 80 90 100 110 Altitude

Geopotential Horizontal structure Geopotential and T

20 40 60 Latitude

3
2
1

1 2 3

50

50 Latitude 70 80 90 100 110 Altitude

Temperature Vertical structure of T

0.4
0.2

0.0 0.2 0.4 70 80 90 100 110 Altitude

d RT dz H Φ =

d fu dθ Φ = −

unm(θ,z) =dHn(θ) Vm(z) Tnm(θ,z) =Hn(θ) dVm(z) Vm(z) Hn(θ) dHn(θ) dVm(z)

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Validation experiment: proof of concept

Use WACCM 1b run for the month of January to

simulate a ‘real’ atmosphere sampled by TIMED TIDI and SABER tangent point locations.

Use Fourier analysis to determine WACCM tide,

mean flow and planetary waves structures.

Individual structures can be removed from the

WACCM fields to test the sensitivity of the assimilation method to their presence.

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13

WACCM fields binned by track angle and compared to the assimilation model fit

90

90 180 270 70 80 90 100 110 Alt (km)

WACCM T , Jan 21

195.0 2 1 . 2 1 . 2 2 5 . 225.0 240.0 255.0

160 180 200 220 240 260 280 300

90

90 180 270 70 80 90 100 110

Model T

195.0 1 9 5 . 210.0 2 1 . 225.0 225.0 240.0 255.0

90

90 180 270 80 90 100 110 Alt (km)

WACCM U

20

2 20 2 2 40 40

100
50

50 100

90

90 180 270 70 80 90 100 110

Model U

20

20 2 20

90

90 180 270 Track Angle 80 90 100 110 Alt (km)

WACCM V

24
24
1

2

12

12 12 1 2 24 24 2 4 36

60
40
20

20 40 60

90

90 180 270 Track Angle 70 80 90 100 110

Model V

1

2

12

12 1 2 1 2 12 24 24

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WACCM T components and model fit

reconstructed at fixed time=0 and longitude=0

40
20

20 40 60 80 70 80 90 100 110 Alt (km)

WACCM zonal mean T date=Jan 21

195.0 210.0 2 1 . 2 2 5 . 225.0 2 4 . 255.0

160 180 200 220 240 260 280 300

40
20

20 40 60 80 70 80 90 100 110

Model zonal mean T

195.0 210.0 210.0 2 2 5 . 2 2 5 . 2 4 . 255.0

40
20

20 40 60 80 70 80 90 100 110 Alt (km)

WACCM diurnal T time=0, lon=0

8
8
4
4
4

4 4 8

20
10

10 20

40
20

20 40 60 80 70 80 90 100 110

Model diurnal T

12
8
4
4

4

40
20

20 40 60 80 Latitude 70 80 90 100 110 Alt (km)

WACCM semi-diurnal T

8

8 8 16

40
20

20 40

40
20

20 40 60 80 Latitude 70 80 90 100 110

Model semi-diurnal T

8

8 8 1 6 24

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WACCM U and model fit

reconstructed at fixed time=0 and longitude=0

60
30

30 60 70 80 90 100 110 Alt (km)

WACCM zonal mean U date=Jan 21

4
20

20 40

100
50

50 100

60
30

30 60 70 80 90 100 110

Model zonal mean U

40
20

20 4

60
30

30 60 70 80 90 100 110 Alt (km)

WACCM diurnal U time=0, lon=0

12 12

60
40
20

20 40 60

60
30

30 60 70 80 90 100 110

Model diurnal U

60
30

30 60 Latitude 70 80 90 100 110 Alt (km)

WACCM semi-diurnal U

36
24
1

2

1

2

60
40
20

20 40 60

60
30

30 60 Latitude 70 80 90 100 110

Model semi-diurnal U

36
24
24
12
1

2

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WACCM V and model fit

reconstructed at fixed time=0 and longitude=0

It was necessary to include tide structures with a mesospheric source

60
30

30 60 70 80 90 100 110 Alt (km)

WACCM diurnal V Jan 21, time=0, lon=0

16 1 6 3 2

50

50

60
30

30 60 70 80 90 100 110

Model diurnal V

16 16 1 6 16 1 6 3 2 48

60
30

30 60 Latitude 70 80 90 100 110 Alt (km)

WACCM semi-diurnal V

3

6

24
12

12 12 1 2

60
40
20

20 40 60

60
30

30 60 Latitude 70 80 90 100 110

Model semi-diurnal V

4

8

3

6

24
1

2 1 2 1 2 12 2 4

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WACCM zonal mean U and model fit

day-latitude cross sections at 70,85 & 100 km

The assimilation model incorporates data in a 4-day window to smooth

ut 2-day wave effects

5 10 15 20 25 30

60
30

30 60 Latitude

WACCM zonal mean U alt=70 km

80
60
60
40
4
2
20

2 20 4 40 60 6 60

100
50

50 100 5 10 15 20 25 30

60
30

30 60 Latitude

Model zonal mean U alt=70 km

80
60
60
4
4
2
2

20 20 40 4 6

5 10 15 20 25 30

60
30

30 60 Latitude

WACCM zonal mean U alt=85 km

1
10

1 1 20

40
20

20 40 5 10 15 20 25 30

60
30

30 60 Latitude

Model zonal mean U alt=85 km

10

10 10 20

5 10 15 20 25 30 Day

60
30

30 60 Latitude

WACCM zonal mean U alt=100 km

1

2

12
6
6

6 6 12

30
20
10

10 20 30 5 10 15 20 25 30 Day

60
30

30 60 Latitude

Model zonal mean U alt=100 km

6
6
6
6
6

6 6 6 6 12

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WACCM tidal V amplitude and model fit

assimilation captures the WACCM tidal variability

presence of terdiurnal tide in WACCM, not accounted for in assimilation, causes underestimate of semi-diurnal tide amplitude

5 10 15 20 25 30

60
30

30 60 Latitude

WACCM diurnal V amplitude alt=95 km

4 4 4 4 4 8 8 8 8 12 12 12 12 12 1 2 16 16 16 20 20 2 2 4 2 4 2 8

10 20 30 40 5 10 15 20 25 30

60
30

30 60 Latitude

Model diurnal V alt=95 km

4 4 4 8 8 8 12 1 2 12 1 2 12 16 16 16 2 20 2 24

5 10 15 20 25 30 Day

60
30

30 60 Latitude

WACCM semi-diurnal V amplitude alt=110 km

8 8 8 8 8 8 8 1 6 16 1 6 16 16 1 6 16 24 24 24 24 32 32 32 3 2 40 40 48 48 5 6 64

20 40 60 80 5 10 15 20 25 30 Day

60
30

30 60 Latitude

Model semi-diurnal V alt=110 km

8 8 8 8 8 8 16 16 16 16 16 16 24 24 2 4 2 4 2 4 24 3 2 32 32 3 2 40 4 4 4 8 4 8 5 6

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Thermal wind equation solver:

given the zonal mean T field, solve for zonal mean U by fitting the geostrophic mode T patterns and then reconstructing U shows effect of not completely removing the tide

40
20

20 40 60 80 70 80 90 100 110 Alt (km)

WACCM Jan zonal mean U

60
40
20

20 4

100
50

50 100

40
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20 40 60 80 80 90 100 110

Model fit U

6
40
20

20 40

40
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20 40 60 80 90 100 110 Alt (km)

Gradient wind Model fit T

6
40
20
20

20 4

100
50

50 100

40
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20 40 60 80 80 90 100 110

Gradient wind Measured T binned over Jan

60
40
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20
2

2 20 40 4

40
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20 40 60 80 Latitude 70 80 90 100 110 Alt (km)

Gradient wind Measured T, asc node only

60
4
2
2

2 20 40 40 60

100
50

50 100

40
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20 40 60 80 Latitude 80 90 100 110

Gradient wind Measured T binned on Jan 1

60
40
40
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20

20 2 4 40 60

Obtained from Assimilation fit Obtained from assimilation using T only Fit to T data binned over whole month Fit to T data binned over whole month: ascending node only Fit to T binned on a single day

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Summary

The data assimilation method is able to reproduce the WACCM

mean flow and migrating tide fields to within 5-10 m/s for winds and 2-5K for T if only the WACCM mean flow and tide are used to generate the simulated data;

Larger errors are introduced above 100km due to the presence of

the terdiurnal tide, indicating that these modes should be included in the assimilation;

The 2-day wave causes a 2-day oscillation in both the mean flow

and tides, indicating that it does project onto these components. It is removed in both Fourier and assimilation analysis if a 4-day window is used;

Nonmigrating tides have virtually no effect on the assimilation;
The remaining geophysical ‘noise’ has effects less than 5 m/s for

winds and 2K for T.

SLIDE 21

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Results for HRDI data Zonal wind

21-Mar-1993

5 10 15 20 Local time

60
40
20

20 40 60 80 Latitude, 10 20 30 40 60 70 80 90 100 110

HRDI zonal wind

6
60
40
4
20
20

20 20 20 20 4 40 4 4 4 6 60 8 80

10 20 30 40 60 70 80 90 100 110 Altitude

Diurnal component

4
40
2
20
20

2 2 20

10 20 30 40 60 70 80 90 100 110

Mean component

6
40
2
20

20 20 20 2 20 40 4

10 20 30 40 Track position 60 70 80 90 100 110 Altitude

Semidiurnal component

20

2 20

10 20 30 40 Track position 60 70 80 90 100 110

Assimilation model fit

60
6
4
40
20
20
2

2 20 2 20 2 40 40 40 40 4 6 6 8

SLIDE 22

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Results for HRDI data meridional wind

10 20 30 40 50 60 70 80 90 100 110 Altitude

HRDI meridional wind

60
4
4
40
20
20
20

20 20 20 2 20 40 40 4 6 6 60

10 20 30 40 50 60 70 80 90 100 110

Assimilation model fit

4
40
40
2
2
20

20 2 2 2 40 40 40 40 60

10 20 30 40 Track position 50 60 70 80 90 100 110 Altitude

Diurnal component

4
4
40
2
20
2

20 20 2 2 40 4 4 6

10 20 30 40 Track position 50 60 70 80 90 100 110

Semidiurnal component

20

20 20

Note there is no evidence of the mesosphere diurnal source as in WACCM

SLIDE 23

23

HRDI and TIMED diurnal tide amplitude

meridional wind at 95 km and 23S 1993 and 2004 have a similar annual cycle

HRDI Diurnal tide meridional wind amplitude Alt=95 km, 23S

100 200 300 DOY 1993 20 40 60 80 100 m/s

TIMED Diurnal tide meridional wind amplitude Alt=95 km, 23S

100 200 300 DOY 2004 20 40 60 80 100 m/s

SLIDE 24

24

HRDI and TIMED semidiurnal tide

meridional wind at 110 km, reconstructed at local time 0h

reflects seasonal variability of amplitude and phase structure

100
50

50 100 m/s

semidiurnal tide meridional wind from HRDI Alt=110 km, local time=0h

100 200 300 DOY 1994

90
45

45 90 Latitude

100
50

50 100 m/s

semidiurnal tide meridional wind from TIMED Alt=110 km, local time=0h

100 200 300 DOY 2004

90
45

45 90 Latitude

SLIDE 25

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Mean zonal wind at the equator Evolution of the SAO

100
50

50 100 m/s

HRDI zonal wind at the equator, 1993

J F M A M J J A S O N D 50 60 70 80 90 100 110 Alt (km)

100
50

50 100 m/s

HRDI zonal wind at the equator, 1994

J F M A M J J A S O N D 50 60 70 80 90 100 110 Alt (km)

SLIDE 26

26

Assimilation monthly and zonal mean zonal wind compare to URAP wind climatology: tides removed

60
40
20

20 40 60 50 60 70 80 90 100 110 Altitude (km)

September 93 URAP

20 20 2 20 40 4

60
40
20

20 40 60 50 60 70 80 90 100 110

December 93 URAP

40
20

20 2 40 4

60
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20

20 40 60 50 60 70 80 90 100 110

March 94 URAP

20 20 20

60
40
20

20 40 60 Latitude 50 60 70 80 90 100 110 Altitude (km)

Assim

20 20 20 4

60
40
20

20 40 60 Latitude 50 60 70 80 90 100 110

Assim

4
2

20 20 40 40 60 6

60
40
20

20 40 60 Latitude 50 60 70 80 90 100 110

Assim

2 20 2