Constrained Bias Correction for Satellite Radiance
Assimilation in Limited Area Model
Wei HAN
NWPC/CMA,Beijing,China Email : hanwei@cma.gov.cn
ABSTRACT
Radiance bias correction is crucial to the successful assimilation of satellite radiance observations which are typically affected by biases that arise from uncertainties in the
absolute calibration, the radiative transfer modeling, or other aspects. These biases have to be removed for the successful assimilation of the data in NWP systems. There are
several issues in the implementation of the bias correction method in limited area models (LAMs) which was originally developed for global models. One of these important
issues is how to separate the observation bias from the innovations if there are obvious model diurnal biases in LAMs using adaptive bias correction in 3D-Var. In this study, the
constrained bias correction scheme is proposed and tested considering the estimate of radiometric uncertainties and the relative model diurnal bias. Enhanced cooperation
between NWP and other ITWG groups are recommended for the validation and characterization of satellite radiance bias estimation.
1. Motivation
4. Validation of Bias Correction
Bias correction is essential for successful use of satellite radiance
δJ =
-FSO view: BC could change the impact sign[1]
H ( xb − ε b ) = o − o b
∂J
, y − Hxb − b
∂y
− Hε b = o − Hxb − ob
-No absolute calibration in radiance
Collocated independent unbiased obs.
-Bias dependence on scene temperature
-map the background error to radiance space
Bias correction issues in LAMs[6]
Tobin et al,2013,
Fig8:On-orbit RU estimates for a
typical warm Earth view spectrum
collected on 24 February 2013.
-Limit samples
-Model diurnal bias
AA917A
Using observation operater H
Dropsonde observations at 00Z Oct. 27,2012
Progress in RT and calibration uncertainty estimation[7]
18
Pressure[hPa]
Before_BC
After_BC
−H(Te+Qe)
−H(Qe)
2. Methodology
16
Constrained Bias Correction[4]
Channel
-Background term for bias estimation
-Use of uncertaity information of RT and calibration
2J (x, β) = (xb − x)T B−x1 (xb − x)
+ (β − βb )T B−β1 (β − βb )
14
200
Pressure[hPa]
200
500
700
700
1000
1000
0
12
500
5
10
15
Humidity[g/Kg]
20
−6
−4
−2
0
Humidity O−B [g/Kg]
2
10
O-B of F16 SSMIS CH14(22GHz,V) passed QC
+ [y − H (x) − b(x, β)] T R−1 [y − H (x) − b(x, β)]
8
−10
+ γ 2[b(x, β) − b0 ]T Rb−1[b(x, β) − b0 ]
−5
0
O−B
5
10
15
Constraints
-Physical based bias model
-Priori uncertainty estimate of observation bias
-The time evolution of bias (cycle period of bias coefficients)
-Consideration of model bias [2,5]
5. Results and Discussion
-Background term for observation bias estimation
3. Case Study: Bias correction of SSMIS imager channels[3]
Black: before bias correction
Red: after bias correction
Bias model for SSMIS imager channels
-Scan bias (Ascending and Descending)
All the data passed QC over the
period 23-29 October 2012
-Bias predicor: LWP (liquid water contribution)
CH01
1.5
0.6
1.0
0.5
0.0
−0.5
0
20
40
Scan Position
60
CH03
0.4
CH02
4
0.4
3
0.3
2
0.2
1
0.1
0
0.0
0
0.4
20
40
Scan Position
2
1
−0.2
−0.4
0
20
40
Scan Position
60
CH05
0.5
−0.4
0
0.8
20
40
Scan Position
60
−0.4
0
-Validation of bias estimation and correction
60
CH15
-collocated independent unbiased observations
-inter-comparison among operational NWP centers
1
0
20
40
Scan Position
60
−1
0
20
40
Scan Position
60
CH16
Ascending: black
Descending:Blue
Solid: O-B before bias correction
Time evolution of LWP coefficients Dotted: bias correction
in Hurricane Sandy Experiments. Dashed: O-B aftre bias correction
Grey bar: assimilated obs. number
0.5
USING ALL
0.0
−0.2
0.0
0
(β − β b )T B −β1 (β − β b )
20
40
Scan Position
2
1.0
0.0
0.1
5
1.5
0.2
0.2
0
−1
0
3
2.0
0.4
0.3
60
4
CH06
0.6
0.4
20
40
Scan Position
CH14
−1
0
60
-Adaptive update of the bias correction coefficients
1
0
20
40
Scan Position
- pre-lauch and on-orbit
CH13
2
3
0.0
20
40
Scan Position
−0.5
0
60
20
40
Scan Position
Spin-up of the bias coefficients
60
1st loop
3.5
4000
2.5
26/10
Time
27/10
28/10
NWP+CLIMATE
3.Han W. and Weng F.,2013: Impact of SSMIS imager channels on hurricane analyses and forecasts, 2013 EUMETSAT
Meteorological Satellite Conference, 16-20 Sept., Vienna
5.McNally, A.P. (2007), The assimilation of uncorrected AMSU-A channel 14 to anchor the VarBC system in the stratosphere.
Research Department Memorandum, ECMWF, R43.8/AM/0715.
29/10
The background variance of coefficient of LWP predictor for F16
SSMIS channel 12 during the spin-up.
REGIONAL +GLOBAL
4.Han W., 2014: Constrained variational bias correction for satellite radiance assimilation, 19th International TOVS Study Conference,
6 March - 1 April 2014,Jeju Island, South Korea.
1.0
0
12 00 12 00 12 00 12 00 12 00 12 00 12 00 12
25/10
- physical based observation bias model
Bias Correction + RT + Calibration
2.Han W. and McNally AP. 2010: The 4D-Var assimilation of ozone-sensitive infrared radiances measured by IASI. Q. J. R. Meteorol.
Soc. 136: 2025–2037. DOI:10.1002/qj.708
2nd loop
1000
1.5
- characterize the uncertainties of the bias correction
1.Cardinali, C., 2009: Monitoring the observation impact on the short-range forecast. Q. J. R. Meteorol.Soc., 135, 239-250
2000
2.0
-NWP,CLIMATE, RT and Calibration GROUP
Reference
3000
Observation Number
Variance
3.0
24/10
AVAILABLE
INFORMATION
B x = α B x , α = 0.1
23/10
- channel, scene temperature
3
CH04
0.2
0.0
6
5
4
−1
0
60
0.2
−0.2
CH12
5
0.5
γ 2 [b( x, β) − b 0 ]T R b−1[b(x, β) − b 0 ]
-Uncertainty of observation operator and calibration
Spin-up of the bias coefficients
6.Randriamampianina R, et al., 2014:Radiance data assimilation in HIRLAM and ALADIN consortia -Recent developments, 19th
International TOVS Study Conference, 6 March - 1 April 2014,Jeju Island, South Korea.
7.Tobin, D., et al. (2013), Suomi-NPP CrIS radiometric calibration uncertainty, J. Geophys. Res. Atmos., 118, 10,589–10,600,
doi:10.1002/jgrd.50809.
Acknowledgements This study was supported by funding from the International
S&T Cooperation Program of China(ISTCP) under Grant no. 2011DFG23210.
8. Zhu Y.Q. et al.,2014, Enhanced radiance bias correction in the National Centers for Environmental Prediction’s Gridpoint Statistical
Interpolation data assimilation systemQ. J. R. Meteorol. Soc. 140: 1479–1492, July 2014 A DOI:10.1002/qj.2233