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D ATMOSPHER
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Radiative Transfer Modeling for SSMIS Upper-air Sounding Channels:
Doppler-shift Effect due to Earth Rotation
TRATION
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Yong Han
NOAA/NESDIS/Center for Satellite Applications and Research, Camp Springs, MD
Joint Center for Satellite Data Assimilation, Camp Springs, MD
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1. Introduction
Special Sensor Microwave Imager/Sounder (SSMIS) on board the DMSP F-16 satellite includes six upper atmosphere sounding (UAS) channels, channels 19 – 24. Because of the Zeeman-splitting of the O2
magnetic transition lines, the energy received in some of the UAS channels is partially polarized and depends strongly on the geomagnetic field and its orientation with respect to the propagation direction of the
electromagnetic wave. To assimilate measurements from the UAS channels, a fast radiative transfer (RT) model was developed for rapid radiance simulations and radiance derivative (Jacobian) calculations, in
which the Zeeman-splitting effect was taken into account (Han et al., 2007). However, the frequency shift of the radiation spectrum due to the Earth’s rotation is ignored in the model. The magnitude of the
Doppler shift may reach 80 KHz in some regions and scan pixels (Swadley et al., 2008). In this presentation ,we provide an analysis of the impact of the Doppler shift, which is the basis for the improvement of
the fast RT model, reported elsewhere.
2. Doppler shift due to Earth’s rotation
The frequency shift is given by (Swadley et al., 2008):
ν
Δν = − ΩRs cos(ψ )[cos(i) cos(ϕ ) ± sin(ϕ ) sin(i − λ) sin(i + λ) ]
c
ν
: Mean frequency of the received radiation spectrum
Ω : Earth’s angular velocity
ψ
i
Rs
λ
c
Figure 4. Simulated brightness temperature (BT) differences for channel 20 using the RT models with
and without the inclusion of the Doppler shift effect, for ascending (left) and descending (right)
observations on January 1, 2006. For the simulations, the temperature profiles are obtained from the
CIRA-88 model.
: nadir angle of scan (45o)
: spacecraft orbital inclination angle
: Earth radius + satellite altitude
4. Observations of the Doppler-shift effect
: spacecraft latitude
: speed of light
1 j −1
ϕ =( −
)Γ,
2 N −1
j = 1, N : azimuth angle of the scene (zero along the track & positive to the
right of the track)
To observe the Doppler-shift effect, two sets of data are selected, shown in Blocks 1 and 2,
respectively. The first set corresponds to the data with cos(θB) close to 1 or -1 and the second set
corresponds to the data with cos(θB) close to 0. According to the analysis in Section 3, the Dopplershift effect is large in data set 1 and small in set 2.
N : scan position, 1- 30
The positive and negative signs before the second term correspond to the ascending and
descending orbits, respectively.
Scan position 1 (72.0o)
Scan position 7 (42.2o)
Scan position 15 (2.5o)
Solid – ascending orbit; Dashed descending orbit
Block 1. Data selection: (1) latitudes are confined between 10oN and 40oN for the ascending orbits,
where the values of cos(θB) are about -0.7 and between -40oS and 0o for the descending orbits, where
the values of cos(θB) are about 0.7, (2) pixels at the edges of scans, where the Doppler-shifts are the
largest, and (3) data on the same scan are paired according to their smallest differences in cos(θB).
Table 1. Means and standard deviations of Be, cos(θB), Doppler frequency shift ∆ν and pixel position,
over the data set of n samples. The words “East” and “West” refer to the data pixel positions on the
east and west edges of the scans, which containing 30 pixel positions (1 – 30), numbered sequentially
from east to west for ascending orbits and west to east for descending orbits.
Be
(μT)
cos(θB)
East ∆ν
(KHz)
West ∆ν
(KHz)
East position
West position
Ascending (n=41772)
41.3, 4
-0.66, 0.05
-62.2, 3.2
65.3, 4.5
2, 1
26, 2
Descending (n=65476)
45.3, 7
0.68, 0.06
-63.0, 3.8
67.4, 4.7
29, 1
4, 2
Figure 1. Doppler frequency shift as a function of the
latitude at three scan positions.
Figure 5. The histograms of the differences of the
measured brightness temperature (BT) between the
paired data points on the east and west edges of the
scans, BT(west) – BT(east), with the solid curves from
the ascending observations (sample size = 41772) and
the dashed curves from the descending observations
(sample size = 65476).
3. The dependence of the Doppler-shift effect on Be and θB,
predicted from theory
Be : Earth magnetic field strength
ΘB : Angle between the magnetic field and wave propagation direction
Sensitivities of the brightness temperature to the Doppler frequency shift:
The positive mean BT differences in channels 19-21
are mainly due to the Doppler-shift effect.
Chan 19
Chan 20
Measured
2.54, 2.14
2.03, 2.40
-0.72, 1.38 -0.14, 1.49 -0.05, 1.01 -0.07, 0.68
Chan 21
Chan 22
Chan 23
Chan 24
Simulated
1.76, 0.38
1.65, 0.37
-0.61, 0.28
Table 2. Means and standard
deviations of the brightness
temperature (BT) differences between
the paired data points on the east and
west edges of the scans, BT(West) –
BT(East).
Ascending orbit (n=41772)
0.02, 0.22
0.04, 0.23
0.02, 0.14
Descending orbit (n=65476)
COS(θB) = -1.0, Be = 60 μT
COS(θB) = -0.5, Be = 60 μT
COS(θB) =
0, Be = 60 μT
COS(θB) = 0.5, Be = 60 μT
COS(θB) = 1.0, Be = 60 μT
COS(θB) = -1.0, Be = 30 μT
COS(θB) = -0.5, Be = 30 μT
COS(θB) =
0, Be = 30 μT
COS(θB) = 0.5, Be = 30 μT
COS(θB) = 1.0, Be = 30 μT
Figure 2. Simulated brightness temperature (BT) differences using the RT models with and
without the inclusion of the Doppler-shift effect for the US 76 Standard Atmosphere,
conditioned at different values of Be and θB.
The impact of the Doppler shift has a strong dependence on the angle θB, which may
reach 2K when θB = 0o or 180o, but becomes very small when θB = 90o.
Measured
-1.84, 2.08 -2.02, 2.32
0.01, 1.80
-0.26, 1.45 -0.14, 0.97 -0.05, 0.65
Simulated
-1.62, 0.41 -1.66, 0.43
0.95, 0.35
0.15, 0.35
Block 2. Data selection:
same as those in Block 1,
except that the latitudes are
confined between -40oS and 10oS for the ascending orbits
and between 15oN and 50oN
for the descending orbits.
The values of cos(θB) in both
zones are small about 0.15.
Images of the Be and cos(θB) fields and the simulated brightness temperature differences
using the RT model with and without the inclusion of the Doppler-shift effect:
0.14, 0.40
0.03, 0.25
Be
(μT)
cos(θB)
East ∆ν
(KHz)
West ∆ν
(KHz)
East
position
West
position
Ascending (n=36247)
36.9, 11.7
0.18, 0.07
-61.5, 2.5
64.4, 4.5
2, 1
27, 2
Descending
(n=36247)
38.5, 3.5
0.13, 0.07
-60.4, 1.9
65.6, 4.7
29, 1
3, 2
Chan 19
Chan 20
Chan 21
Chan 22
Chan 23
Chan 24
Ascending orbit (36247 samples)
Measured
0.05, 2.29
0.14, 2.47
0.26, 1.81
-0.11, 1.30
-0.15, 0.88
-0.05, 0.59
Simulated
-0.53, 0.50
-0.49, 0.41
0.15, 0.32
-0.03, 0.22
-0.06, 0.26
-0.01, 0.14
Descending orbit (57580 samples)
Measured
-0.39, 2.19
-0.83, 2.55
-0.71, 1.93
-0.87, 1.59
-0.50, 1.17
-0.26, 0.77
Simulated
-0.38, 0.39
-0.24, 0.44
-0.09, 0.33
-0.16, 0.36
-0.19, 0.39
-0.04, 0.23
The mean BT differences become small in channels 19-21 due to small cos(θB), although the
magnitudes of Doppler-shift are about the same as those in Block 1.
5. Summary and remark
Be
•
•
The Earth-Rotation Doppler shift can have an effect up to 2 K on SSMIS channels 19 – 21.
The effect depends on the Earth’s magnetic field strength and the angle between the
magnetic field and the wave propagation direction, as well as the scan positions.
•
Figure 3. The Earth’s magnetic field strength Be (left
figure) in μT at 00:00 Greenwich Mean Time on
January 1, 2006 at the height of 60 km, computed
using the IGRF model; the cosine of the angle, cos(θB),
between the magnetic field and wave propagation
direction for the ascending (right upper figure) and
descending (right lower figure) observations on
January 1, 2006. The data are used for the Brightness
temperature calculations shown in Figure 4.
Based on this work, the fast radiative transfer model has been improved to take the Doppler
shift into account.
Reference
Han, Y., F. Weng, Q. Liu, and P. van Delst (2007), A Fast Radiative Transfer Model for SSMIS Upperatmosphere Sounding Channels, J. Geophys. Res., 112(D11121), 1468, doi:10,1029/ 2006JD008208.
Swadley, S.D., G. A. Poe, W. Bell, Y. Hong, D. B. Kunkee, I. S. McDermid and T. Leblanc (2008)
Analysis and Characterization of the SSMIS Upper Atmosphere Sounding Channel Measurements,
IEEE Trans. Geosci. Remote Sensing, V 46, 962-983.