Towards direct assimilation of
SSM/I radiances in 4D-Var
P Bauer, G Kelly, E Andersson
European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, RG2 9AX, UK
E-mail: peter.bauer@ecmwf.int
SPECIAL SENSOR MICROWAVE / IMAGER (SSM/I) DATA has been incorporated in the assimilation system of the European Centre for Medium-Range
Weather Forecasts (ECMWF) through a one-dimensional variational retrieval (1D-Var) of water vapour path (WVP) since 1997 [1,2] and near-surface
wind speed (SWS) since 1999. For the preparation of direct radiance assimilation, research experiments with the operational ECMWF four-dimensional
variational assimilation (4D-Var) have been carried out employing the (NWP SAF) radiative transfer package RTTOV-6 [3] and the fast sea-surface
emissivity model FASTEM-2 [4].
Radiative Transfer Modelling
RTSSMI
Radiance statistics – 1
Two 4D-Var experiments have been set up: (1) a control experiment with the assimilation of water vapour path and near-surface
wind speed from SSM/I data and (2) an SSM/I radiance assimilation experiment with the RTTOV package. Figures 1 and 2 show the
brightness temperature (TB) departures between model first-guess (FG; bias corrected), analysis (AN), model FG (uncorrected)
and the observations (OBS) over 4 days (July 1–4, 2001). The table lists departure averages and standard deviations per SSM/I
channel in the order 19v, h, 22v, 37v, h, 85v, h, respectively:
• RTTOV produces much better FGs, i.e. smaller FG departures (except at 37.0(v) GHz).
In the framework of the 1D-Var assimilation, the radiative-transfer modelling package of [5] was implemented. Atmospheric absorption is calculated from regression fits to explicit calculations with a line-by-line model. Surface emission is calculated explicitly
through a two-scale geometric optics model. Non-precipitating cloud liquid-water path (LWP) is included.
RTTOV
The main generic difference between RTSSMI and RTTOV is the explicit treatment of multi-angular radiance reflection by RTSSMI vs.
the methodology of FASTEM-2 which integrates specular and non-specular contributions to an effective emissivity [6]. In extension
to the standard RTTOV version, cloud emission was implemented at ECMWF [7].
• The spread of the distributions is much smaller for RTTOV at all frequencies.
• The better agreement at lower frequencies indicates a better sea-water permittivity model in RTTOV.
• The good performance of RTTOV at 37.0 GHz and comparing vertical and horizontal polarizations at the same frequency shows a
good quality of the surface roughness parametrization.
RTTOV-6
1.0
1.0
0.8
0.8
0.8
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 19.35 GHz (h)
10
8
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 19.35 GHz (v)
1.0
10
8
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 19.35 GHz (h)
10
0.4
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 22.235 GHz (v)
1.0
8
10
0.8
0.8
σ∆TB [K]
FGC
3.6
6.5
5.0
5.0
9.3
5.1
11.0
AN
0.9
0.7
0.8
1.2
0.8
1.4
1.3
FGU
3.7
6.4
4.8
5.2
9.6
4.9
11.0
n / nmax
n / nmax
<∆TB> [K]
FGC AN FGU
0.0
0.2
2.4
0.0
0.0
2.5
0.0
0.1
2.3
–0.8 –0.2 –1.1
–0.4
0.2 –0.6
–0.8 –0.5 –2.9
–0.5 –0.1 –3.7
0.6
10
F–13
F–13
0.8
8
<∆TB> [K]
FGC AN FGU
0.6
0.0
0.9
1.0
0.0
0.1
0.7
0.0 –0.4
0.9
0.1
2.7
1.0
0.0 –0.7
0.8
0.0
1.4
1.5
0.0 –0.9
0.6
0.4
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 22.235 GHz (v)
8
10
1.0
1.0
1.0
0.8
0.8
0.8
σ∆TB [K]
FGC
3.0
4.6
3.8
3.3
3.9
3.7
5.9
AN
1.0
1.1
1.1
1.1
1.2
1.4
1.4
FGU
3.0
4.5
4.1
3.1
4.1
3.6
6.3
• Again, RTTOV has little problems to properly account for increasing surface roughness with wind speed. However, vertically polarized TBs show a worse match than those horizontally polarized. There, RTTOV seems to overestimate roughness contributions.
• RTSSMI performs well for vertically polarized TB but shows a strong increasing negative bias with increasing wind speed at all
frequencies for horizontally polarized TBs.
RTSSMI
19.35 GHz (v)
0.6
0.4
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 37.0 GHz (v)
1.0
8
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 37.0 GHz (h)
1.0
10
0.8
8
0.8
5
0.4
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 37.0 GHz (v)
1.0
10
8
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 37.0 GHz (h)
1.0
10
0.8
5
0
–5
8
0.4
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 85.5 GHz (v)
8
10
n / nmax
0.4
0.6
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 85.5 GHz (h)
8
–10
8
10
20
30
40
50
60
70
0
10
20
30
40
50
60
10
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 85.5 GHz (h)
F–13
–5
8
–10
10
20
30
40
50
60
0
20
30
40
50
60
70
0
85.5 GHz (v)
∆TBFG [K]
–5
30
40
50
60
–10
0
20
30 40 50
WVP [kg m–2]
60
70
0
10
20
30 40 50
WVP [kg m–2]
60
∆TBFG [K]
∆TBFG [K]
0
5
0
10
15
20
0
5
10
15
–30
–25
latitude (deg)
–20
–15
50
60
70
30 40 50
SWS [ms–1]
60
70
∆TBFG [K]
0
–5
–10
10
20
30
40
50
60
70
0
10
20
30
40
85.5 GHz (h)
10
10
5
5
0
0
–5
–10
10
20
30 40 50
SWS [ms–1]
60
70
0
10
20
19.35 GHz (h)
10
10
5
5
0
0
–5
0
5
10
15
–10
20
0
5
10
15
20
15
20
15
20
5
0
F–13
F–13
0
–5
5
10
15
–10
20
37.0 GHz (v)
∆TBFG [K]
∆TBFG [K]
5
0
0
5
10
15
20
37.0 GHz (v)
37.0 GHz (h)
10
0
–5
37.0 GHz (h)
10
10
5
5
0
0
–5
–5
–10
–10
0
0
5
10
15
20
0
85.5 GHz (v)
10
5
10
15
–10
20
0
5
10
15
–10
20
0
5
85.5 GHz (v)
85.5 GHz (h)
10
10
85.5 GHz (h)
10
10
–40
–35
–30
–25
latitude (deg)
–20
–15
5
5
19.35 GHz (h)
–45
–10
∆TB 22v
0
–5
0
5
5
–5
0
–5
0
–5
15
∆TB [K] (FG-OBS)
WVP [kg m–2]
∆TBFG [K]
5
–5
20
30
20
10
–10
10
–10
0
5
5
10
SWS [ms–1]
15
20
0
5
10
SWS [ms–1]
15
20
–10
0
5
10
SWS [ms–1]
15
20
–10
0
5
10
SWS [ms–1]
0
–5
–10
–15
22.235 GHz (v)
–20
SWS
0
22.235 GHz (v)
–5
25
40
0
–50
5
–10
–25
–50
–10
70
10
∆TBFG [K]
–35
60
37.0 GHz (h)
10
–10
20
5
∆TBFG [K]
–40
50
70
–5
2.235 GHz (v)
∆TBFG [K]
∆TB [K] (FG-OBS)
LWP [kg m–2]
WVP
–45
40
10
–20
0
–50
50
30
RTTOV-6
–10
0
10
60
19.35 GHz (v)
–5
–10
–15
0.1
20
Figure 4 As Figure 3 for RTTOV.
5
5
∆TB 19h
50
5
0
19.35 GHz (h)
10
–5
Moist windy
RTTOV
RTSSMI
40
RTSSMI
19.35 GHz (v)
0
25
30
–10
70
Figure 3 FG-OBS departures (black: FG bias corrected; green: analysis) as a function of
WVP for F-13 SSM/I and RTSSMI.
10
Dry calm
20
–5
–10
0.2
10
85.5 GHz (v)
–10
10
10
10
0
–5
0.3
0
F–13
–10
70
85.5 GHz (h)
–5
5
B
20
5
0
10
To increase the number of observations to be used for the assimilation of SSM/I radiances, the inclusion of clouds is of utmost
importance. The treatment of clouds requires their inclusion in the forward modelling of the radiative transfer and the updating of the FG
cloud-model liquid-water path along with those parameters being part
of the control vector (wind speed, water vapour).
10
10
Figure 7 1D-Var WVP retrievals SE Indian Ocean on July 1, 2001 (note A-B
cross-section).
15
–10
70
–5
–10
10
A
Perspectives
0
–5
0
Generally, the largest departures occur where model clouds strongly differ from the observed ones. FG and retrieved WVP and SWS
are fairly similar. RTTOV shows similar or better performance under all conditions at 19.35 GHz (h) due to the better permittivity
model. At 22.235 GHz (v) and 37.0 GHz (v) both models produce almost identical results for all combinations of dry/moist and
calm/windy environments.
20
60
37.0 GHz (v)
5
∆TBFG [K]
∆TBFG [K]
∆TBFG [K]
Cross-sections of LWP, WVP, and SWS (Figure 8) and 19h, 22v, and 37v FG-OBS TB departures (Figure 9) along A-B were extracted
where a strong gradient of both WVP and SWS was observed in North-South direction.
0.4
50
0
0
37.0 GHz (h)
10
5
Finally, Figure 7 shows an example of WVP retrievals from 1D-Var in the south-eastern Indian Ocean on July 1, 2001.
FIRST GUESS
OBSERVATIONS
40
–10
70
37.0 GHz (v)
5
Case Study
0.5
30
–5
10
0.6
20
10
0
LWP
10
5
0
–10
Dry windy
0
22.235 GHz (v)
5
0.4
Figure 2 FG-OBS departures from global F-13 SSM/I
observations using RTTOV
Moist windy
0
–5
10
–5
Dry calm
0
0.6
0
Dry windy
5
–10
70
22.235 GHz (v)
10
Figure 1 FG-OBS departures from global F-13 SSM/I
observations using RTSSMI.
10
5
–5
–10
0
0.2
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 85.5 GHz (v)
10
0
–5
0.8
∆TBFG [K]
0.2
n / nmax
n / nmax
n / nmax
0.4
0.6
19.35 GHz (h)
10
10
10
0.6
19.35 GHz (v)
19.35 GHz (h)
10
0.6
∆TBFG [K]
0.4
∆TBFG [K]
0.2
0.6
n / nmax
0.4
n / nmax
n / nmax
n / nmax
10
0.6
RTTOV-6
∆TBFG [K]
8
Figures 5 and 6 show a similar comparison for wind speed:
0.4
∆TBFG [K]
0
–10 –8 –6 –4 –2 0 2 4 6
∆TB [K] @ 19.35 GHz (v)
1.0
0.2
∆TBFG [K]
0.2
0.6
∆TBFG [K]
0.4
∆TBFG [K]
0.6
∆TBFG [K]
0.4
• RTSSMI seems to underestimate the reflection of radiation indicated by too small FG TBs; a trend that increases with frequency
and is stronger at horizontal than vertical polarization.
∆TBFG [K]
0.2
0.6
FG departure (bias)
∆TBFG [K]
0.4
n / nmax
1.0
0.8
n / nmax
1.0
0.6
• RTTOV shows little dependence on atmospheric transmission.
AN departure
∆TBFG [K]
FG departure
∆TBFG [K]
FG departure (bias)
∆TBFG [K]
AN departure
n / nmax
n / nmax
FG departure
Figures 3 and 4 show the FG departures as a function of integrated water vapour path to analyse their dependence on atmospheric
transmission. The transmission is used differently in both codes to account for the reflection of downwelling radiances which are
integrated over the hemisphere. First-order linear fits are superimposed to illustrate systematic trends:
∆TBFG [K]
RTSSMI
Radiance statistics – 2
–45
–40
–35
–25
–30
latitude (deg)
–20
–15
–25
–50
–10
–45
–40
–35
–30
–25
latitude (deg)
–20
–15
Figure 5 As Figure 3 for SWS.
–10
25
20
Figure 6 As Figure 5 for RTTOV.
∆TB 37v
20
15
∆TB [K] (FG-OBS)
SWS [m/s]
15
10
5
10
References
5
0
[1] Phalippou, L., 1996: Variational retrieval of humidity profile, wind speed, and
cloud liquid-water path with the SSM/I: Potential for numerical weather prediction.
Q. J. R. Meteorol. Soc., 122, 327-355.
–5
–10
–15
37.0 GHz (v)
–20
0
–50
A
–45
–40
–35
–25
–30
latitude (deg)
–20
–15
–10
–25
–50
B
A
Figure 8 Cross-section (see A-B, Figure 7) of FG (blue)
and retrieved (red) LWP, WVP, and SWS.
–45
–40
–35
–25
–30
latitude (deg)
–20
–15
–10
B
Figure 9 See Figure 8 for FG-OBS TB departures (blue:
RTTOV, red: RTSSMI).
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Special Sensor Microwave / Imager total column water vapour in the ECMWF model.
Q. J. R. Meteorol. Soc., 125, 3077-3101.
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for assimilation of satellite radiance observations - RTTOV-5.
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T. Hayasaka, D.L. Wu,Y.-Q. Jin, J.-S. Jiang (Eds.), 3503, 22-30.
[5] Phalippou, L., 1993: A microwave radiative transfer model.
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[6] Deblonde, G., 2000: Evaluation of FASTEM and FASTEM-2. NWP-SAF report. Available
from NWP Division, Satellite Appl. Group, Met Office, Bracknell, UK, 53 pp.
[7] Chevallier, F., P. Bauer, G. Kelly, C. Jakob, and T. McNally, 2001: Model clouds over
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J. Climate, 14, 4216-4229.