Fast RT Model for SSMIS Upperair Sounding Channels
Yong Han
NOAA/NESDIS/STAR
ITSC-15
Maratea, Italy
4-10 October 2006
Outline
• Radiometric characteristics of SSMIS channels 19-14
- Zeeman effect
- Channel passbands
- Weighting function variations with the Earth’s magnetic field
- Radiance variations with the Earth’s magnetic field
- A case study of Zeeman effect on channel 20
• Fast RT model
- Algorithm
- Model tests against line-by-line models
- Model results compared with measurements
• Summary and conclusions
Zeeman Effect
Energy level splitting:
In the presence of an external magnetic field, each energy
level associated with the total angular momentum quantum
number J is split into 2J+1 levels corresponding to the
azimuthal quantum number M = -J, …, 0, …,J
Lower energy level
Transition lines (Zeeman components) :
σ+
π
σ-
The selection rules permit transitions with ∆J = ±1 and ∆M = 0,
±1. For a change in J (i.g. J=3 to J=4, represented by 3+),
transitions with
∆M = 0 are called π components,
∆M = 1 are called σ+ components and
∆M = -1 are called σ- components.
Polarization:
The three groups of Zeeman components also exhibit
polarization effects with different characteristics. Radiation
from these components received by a circularly polarized
radiometer such as the SSMIS upper-air channels is a function
of the magnetic field strength |B|, the angle θB between B and
the wave propagation direction k as well as the state of
atmosphere, not dependent on the azimuthal angle of k
relative to B.
Zeeman spectral splitting of the 3+ O2 line
(unsplit frequency: 58.446590 GHz)
SSMIS upper-air channel parameters
Ch
#
Passband 1
Passband 2
F0
(GHz)
BW
(MHz)
F0
(GHz)
BW
(MHz)
19
62.9980
1.34
63.5685
1.36
20
60.4348
1.34
61.1506
1.37
21
60.4328
1.26
60.4368
22
60.4293
2.62
23
60.4188
24
60.3848
Passband 3
SSMIS channel 19 passbands
Passband 4
F0
(GHz)
BW
(MHz)
F0
(GHz)
BW
(MHz)
1.23
61.1486
1.33
61.1526
1.33
60.4403
2.61
61.1451
2.66
61.1561
2.67
7.01
60.4508
7.17
61.1346
7.40
61.1666
7.44
26.63
60.4848
26.33
61.1006
26.04
61.2006
26.88
F0=62.9980 GHz (15+)
-10
10
Frequency offset from F0(MHz)
All the six channels are left-circular polarization
F0=63.5685 GHz (17+)
-10
10
Frequency offset from F0(MHz)
SSMIS channel 20 – 24 passbands
F0=60.4348 GHz (7+)
-50
-16 -5.5 -2 0 2 5.5
16
Frequency offset from F0(MHz)
Channel 20
Channel 21
F0=61.1506 GHz (9+)
50
-50
Channel 22
-16 -5.5 -2 0 2 5.5
16
Frequency offset from F0(MHz)
Channel 23
50
Channel 24
• The passbands of channels 19 and 20 are centered at the O2 rotational transition line 7+, 9+, 15+ or 17+.
• The paired passbands of channels 21 – 24 are located with equal distances from the center of the transition line 7+ or 9+.
Variation of the Earth’s magnetic field
Field strength
Horizontal direction from North (east +)
Longitude = 180o
Lon = 90o
Lon =
0o
Lon = -90o
Field zenith angle
Field strength at different heights
Z = 40 km
Z = 80 km
The field may be treated as a constant with height
The magnetic field was computed with IGRF
Height (km)
Pressure (hPa)
Brightness Temperature (K)
Radiometric characteristics of channel 19 – 24 (1)
270
260
250
B=0
240
230
B = 0.63
COS(θB) = -0.5
220
210
B = 0.23
COS(θB) = -0.5
200
190
-4
Normalized weighting function
-3
B = 0.63 Gauss
COS(θB) = 0.5
B = 0.23
COS(θB) = 0.5
-2
-1
0
1
2
Frequency offset from 61150.560 MHz
9+ O2 line
3
• The weighting function peak heights of channels 19 and 20 decrease when the magnetic field
strength increases because the two channels are centered at the transition lines, where the
absorption decreases.
• The weighting function peak heights of channels 21 and 22 increase when the magnetic field
strength increases since the channels are located off the transition line centers, in the places
where the absorption increases.
• The channel brightness temperatures do not depend on the sign of COS(θB), if the central
frequencies of the passbands in channels 19 and 20 are centered at the transition lines and each
symmetric pair of the passbands in channels 21 – 24 have approximately the same bandwidth.
(see also slide 10)
4
8
14
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
7
channel 19
channel 19
6
channel 20
channel 21
channel 20
channel 21
5
BT - BT0 (K)
BT - BT0 (K)
Radiometric characteristics of channel 19 – 24 (2)
4
3
B = 0.6 Gauss
2
1
COS(θB) = 0.9
0
-1
0.2
0.3
0.4
0.5
0
0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
COS( θB)
Earth magnetic field strength (Gauss)
BT0 – brightness temperature offset, channel dependent
US Standard atmosphere (1976)
Height (km)
• The brightness temperatures increase
with the Earth’s magnetic filed strength in
channels 19 and 20 because the weighting
function peak heights decrease and move
into areas with warmer air temperature.
• Channel 21 is in a opposite situation.
• The variations of the brightness
temperature with COS(θB) can be
explained similarly.
Normalized weighting function
Temperature (K)
Radiance measurements plotted as functions of
magnetic field strength and COS(θB)
Channel 19
Channel 20
Channel 21
COS(θB)
0.8 < |COS(θB)| < 1.0
0.5 < B < 0.6 Gauss
Data were taken on February 15, 2006 within latitude range between 40S and 50S
Radiometric characteristics of channel 19 – 24 (3)
0.02
0.19
0
channel 22
0.165
channel 23
0.14
-0.04
channel 24
BT - BT0 (K)
BT - BT0 (K)
-0.02
0.115
0.09
COS(θB) = 0.9
0.065
0.04
B = 0.6 Gauss
-0.06
-0.08
-0.1
channel 22
-0.12
channel 23
-0.14
channel 24
-0.16
0.015
-0.18
-0.01
-0.2
0.2
0.3
0.4
0.5
0.6
0
0.1
0.2
0.3
Earth m agnetic field strength (Gauss)
Channel 24 is not affected by Zeeman-splitting
0.4
0.5
COS(θB )
0.6
0.7
0.8
0.9
1
Radiometric characteristics of channel 19 – 24 (4)
BT - BT0 (K)
The effect of shifting passbands by about 0.03 MHz in
channel 20: the channel shows a dependence on the sign
of the cosine angle between the Earth’s magnetic field
and wave propagation direction
2
1
0
-1
-2
-3
-4
-5
-6
-7
COS(0<θB<90o)
COS(90o<θB<180o)
0
0.2
0.4
0.6
|COS(θB)|
0.8
1
Zeeman effect case study: measurement simulations
along a track of channel-20 observations (1)
UTC = 22.21 h
February 15, 2006
Track of pixel 15
Channel 20
Earth’s magnetic field strength B
0.7
1
COS(θB)
0.6
0.5
0.5
0
0.4
-0.5
0.3
0.2
-1
0
0.2
0.4
0.6
0.8
1
1.2
UTC time (hour)
starting at 22 hours
1.4
1.6
1.8
2
COS(θ )
B field strength (Gauss)
UTC = 23.86
Zeeman effect case study: measurements and
simulations along a track of channel 20 (2)
Measurements (pixel 15)
Measured BT, channel 20
250
240
Ascending
230
Descending
220
210
200
190
180
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Simulated BT (K), channel 20
UTC time (hour)
starting at 22 hours
Simulation (pixel 15)
240
235
230
225
220
215
210
205
200
195
Ascending
Descending
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
UTC time (hour)
starting at 22 hours
The main features of the measurement time series are well captured by the simulations. The
differences are due mainly to the errors of the CIRA profiles used in the simulations.
CIRA profiles: monthly mean, 0 – 120 km, 80oN – 80oS every 5o latitude
CIRA: COSPAR International Reference Atmosphere 1986
Zeeman effect case study: measurements and
simulations along a track of channel 20 (3)
Weighting function peak height
Latitude (degree)
Equatorial latitude = 0o
Pressure (hPa)
Reference height (km)
Simulated BT (K), channel 20
Temperature contour (K)
240
235
230
225
220
215
210
205
200
195
Simulation
UTC time (hour)
Starting at 22 hours
Ascending
(pixel 15)
Descending
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
UTC time (hour)
starting at 22 hours
The radiance variation is due to both variations of the weighting function peak height and air temperature
Fast RT Model with inclusion of Zeeman Effect (1)
Algorithm:
(1)
Atmosphere is vertically divided into N fixed pressure layers from 0.000076 mb (about
110km) to 200 mb. (currently N=100, each layer about 1km thick).
(2)
The Earth’s magnetic field is assumed constant vertically
(3)
For each layer, the following regression is applied to derive channel optical depth with a leftcircular polarization:
m
ODlc ,i = ci ,0 + ∑ ci , j xi , j
j =1
xi,j – predictors; ci,j - constants
(4) Channel brightness temperature at zenith angle θ is computed as
n
Tb ,lc = ∑ (τ i −1 − τ i )Tair ,i
i =1
,
where τ i = τ i −1 exp( −ODlc ,i / COS (θ )), τ 0 = 1
Fast RT Model with inclusion of Zeeman Effect (2)
Training process:
(1)
Base line-by-line model: Rosenkranz (1988)
(2)
Atmospheric profile set: 48 UMBC profiles extended to 0.000076 mb (about 110
km) by merging them with standard atmospheric profiles
(3)
For each profile set, n x m radiances are calculated with n points on B and m
points on COS(θB)
(4)
Zenith angle variation range: 51 - 54
Model test:
(1)
Compared with line-by-line model
(a) independent test using 600 TIGR profiles extended to 110 km
(b) independent test using 204 CIRA model profiles
(c) independent test using 52 ECMWF profiles extended to 110 km
(2)
Compared with measurements
SSMIS Measurements: data taken on 10/25/2005, 11/15/2005, 2/15/2006,
3/15/2006 and 4/15/2006.
Collocated model input profiles: retrievals collected from the Sounding of the
Atmosphere using Broadband Emission Radiometry (SABER) experiment.
Predictors for fast-model layer optical depth
Channel
Predictor
19, 20
ψ, ψB-1, cos2(θB),ψcos2(θB), B-1, B-2, cos2(θB)B2
21, 22
ψ, cos2(θB), B, B3, cos2(θB)B, cos2(θB)B2
23
ψ, ψ2, cos2(θB), B
24
ψ, ψ2
ψ – 300/T; T – temperature
B – Earth magnetic field strength
θB – angle between magnetic field and propagation direction
Model test (the independent test set was
generated from CIRA profiles)
Brightness temperature error (K)
2
1.8
Fitting Errors
1.6
Independent Test
Measurement Error (NEDT)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
19
20
21
22
SSMIS channel number
23
24
Examples of Jacobian profiles computed with the
fast-model’s Jacobian routine
Blue – fast model
Green – finite-difference computed using the line-by-line model
Model results compared with measurements (1097 samples) (1)
Fast model
Chan 19
Chan 20
Chan 21
Rosenkranz LBL
Liebe93 LBL (line width
adjusted with a constant B)
Model results compared with measurements (1097 samples) (2)
Fast model
Chan 22
Chan 23
Chan 24
Rosenkranz LBL
Liebe93 LBL (line width
adjusted with a constant B)
Summary and Conclusions
•
A regression-based fast RT model has been developed for both forward and
Jacobian calculations; it is based on the Rosenkranz88 line-by-line model and the
UMBC 48 profile set.
•
The model was tested against the line-by-line model over various independent profile
data sets. The RMS differences over the CIRA data set (the worst among the test
sets) are 0.34, 0.63, 0.33, 0.053, 0.09 and 0.05 at channels 19 – 24, respectively.
•
The model was also compared with the measurements using matched SABER
profiles as inputs. Results show that the fast model has performances similar to the
line-by-line model in accuracy but a much faster computational speed.
•
The weighting function peak heights of the SSMIS channels 19 and 20 decrease with
the increase of the Earth’s magnetic field strength since the narrow channel
passbands are centered at the O2 transition lines and the Zeeman-splitting effect
reduces the absorption at the center of the absorption lines.
•
The weighting function peak heights of the channels 21 and 22 increase with the
increase of the Earth’s magnetic field strength since the channel passbands are off
the centers of the O2 transition lines and the Zeeman-splitting effect increases the
absorption in the wings of the absorption lines.
•
The channel radiance calculations are not sensitive to the sign of COS(θB) (radiances
at θB and π- θB have the same value). However, even a slight shift of the channel
passband frequencies may make the channel sensitive to the sign.