MSU channel 2 brightness temperature trend when calibrated using simultaneous nadir overpasses
Cheng-Zhi Zou, Mitch Goldberg, Zhaohui Cheng*, Norman Grody, Jerry Sullivan, Changyong Cao, and Dan Tarpley
NOAA/NESDIS/Office of Research and Applications, NOAA Science Center, 5200 Auth Road, Camp Springs, MD 20746
* QSS Group Inc., Lanham, MD 20706
3. Calibration algorithm
1. Purpose
• To re-calibrate MSU observations at level 0 using simultaneous nadir overpasses
• To generate well-calibrated and well-merged multi-satellite MSU 1B data for
use by the climate community
• To investigate the MSU trend derived from the well-merged 1B dataset
• To compare with previous trend studies and identify problems with previous use of
the MSU data
• To provide a guidance on the future use of MSU data
• To provide the climate community an observed reference on the tropospheric
temperature trend
5. Results
Rl = Rc + S (Ce − Cc )
(1) Æ Linear calibration equation;
254
-1
N12 = 0.16 K Dec ,
254
-1
N14 = 0.58 K Dec
NOAA10
-1
Rc Æ Cold Space Radiance, fixed value; Cc
Æ cold space raw counts;
252
Ce Æ Earth-view raw counts;
n12
251
Linear (NOAA12)
Rw − Rc
C w − Cc
Linear (NOAA14)
(2) Æ slope;
Rw
Æ Blackbody target radiance;
Cw
250
1987
Re = Rl − δR + u S 2 (Ce − Cc )(Ce − Cw ) = Rl − δR + uZ
1989
1991
1993
1995
1997
1999
(3) Æ nonlinear calibration equation;
Five-day averages of ascending and descending
orbits for NOAA 11 for the period of October 1-5,
1988. Pixels 5, 6, and 7 are used in generating the
pentad data
Æ observed radiance R by satellite j at time and location
(t j , X j )
16
Rk (t k , X k ) = Rk' (t k , X k ) + ε k
8812
9012
9212
9412
9612
9812
0012
Schematic viewing the overpasses between two NOAA satellites
-7
∆Rl − ∆δR + uk Z k − u j Z j = ε k − ε j + ∆R(∆X)
NOAA14
1989
∆δR and ∆u = uk − u j
regression method. Therefore,
(4) Æ Error equation for any SNO data pairs
1991
1993
1995
Linear (NOAA11)
1997
1999
2001
Linear (NOAA14)
2003
= 0 and u = 5
252
Linear (NOAA11)
Linear (NOAA12)
251
Linear (NOAA14)
250
1987
1989
1991
1993
1995
1997
1999
2001
250
1987
2003
using regression method; however, colinearity between
Z k and Z j
Scatterplot showing relationships of
the Z factor between NOAA 10 and
NOAA 11 for their SNO data pairs.
Unit for Z and ζ is 10-6 (mW)2 (sr m2
cm-1)-2. The regression
coefficients for the fitting line
is expressed as
Z j = β Zk + α
for reference satellite NOAA 10.
1.4
(b)
N10 and N12
N11 and N12
0.8
Ntn and N6
0.6
N7 and N8
N8 and N9
0.4
N6 and N9
N11 and N14
0.2
Number of Points
STD (K)
S TD (K )
N10 and N11
0.2
N12 and N14
NOAA12
NOAA14
Linear (NOAA10)
Linear (NOAA11)
249
-1
Trend: N10 = -1.10 K Dec , N11 = 0.88 K Dec
-1
N12 = 0.22 K Dec ,
248
1987
1989
1991
N14 = 0.37 K Dec
1993
1995
Linear (NOAA12)
-1
-1
Linear (NOAA14)
1997
1999
2001
2003
Time series and trend for the pentad dataset of the global
ocean-averaged MSU channel 2 brightness temperature for
NOAA 10, 11, 12 and 14 with NESDIS operational calibration
algorithm.
244
20
40
60
80
100
120
Distance (km)
(a)
140
160
180
200
220
-1
N12 = 0.33 K Dec ,
253
N14 = 0.18 K Dec
-1
NOAA10
-1
NOAA11
-1
Trend: N10 = -0.39 K Dec , N11 = -1.31 K Dec
-1
N12 = 0.62 K Dec ,
NOAA10
-1
N14 = 0.46 K Dec
NOAA11
243
NOAA12
NOAA12
NOAA14
252
NOAA14
242
Linear (NOAA10)
Linear (NOAA10)
Linear (NOAA11)
Linear (NOAA11)
251
241
Linear (NOAA12)
Linear (NOAA12)
Linear (NOAA14)
Linear (NOAA14)
250
1987
1989
1991
1993
1995
1997
1999
2001
2003
Pentad time series and trend for the global ocean-averaged MSU
channel 2 brightness temperature for NOAA 10, 11, 12 and 14
calibrated by Grody et al. (2004) calibration algorithm. The
nonlinear adjustment is directly on the global ocean-averaged
pentad time series with linear calibration at level 0. Combined
trend is 0.19 K/Decade.
240
1987
1989
1991
1993
1995
1997
1999
2001
2003
Pentad time series of the global ocean-averaged MSU channel 2 brightness
temperature for NOAA 10, 11, 12 and 14 with Christy et al. (2004)
empirical calibration algorithm. The adjustment is directly on the global
ocean-averaged pentad time series with linear calibration at level 0.
Combined trend is 0.02 K/Decade.
• Use new nonlinear calibration equation to convert raw counts to radiance. Coefficients for reference satellite
N7 and N8
1000
N8 and N9
N6 and N9
100
N9 and N10
N10 and N11
N10 and N12
10
N11 and N12
N9 and N10
N11 and N14
N12 and N14
1
0
0
2003
Ntn and N6
N6 and N7
1
0.4
2001
6. Summary and Future work
10000
1.2
0.6
1999
NOAA11
-1
Latitudinal difference vs longitudinal difference for the SNO pairs for some satellite overlaps. Unit is in degree
N6 and N7
1997
251
Trend: N10 = -0.41 K Dec , N11 = 0.52 K Dec
Brightness temperature of nonlinear calibrated (Tb), offset and u are included.
1
1995
(b)
-1
0.8
1993
Time series and trend for the pentad dataset of the global ocean-averaged MSU channel 2
brightness temperature for NOAA 10, 11, 12 and 14 with nonlinear calibration algorithm. (a)
Individual time series and trends for NOAA 10, 11, 12 and 14. (b) Combined time series and
trend for NOAA 10, 11, 12 and 14. The mean biases between different satellites as shown in
Table 6 have been removed with NOAA 10 as the reference satellite
254
Scatter plots showing effects of the nonlinear
calibration on the error statistics and distribution of the
brightness temperature difference between NOAA 10
and NOAA 11. (a) SNO data between Tl (N10) and Tl
(N11 ); (b) SNO data between Tl (N10) and Tl
(N11 )-Tl (N10). (c) SNO data between Tb(N10) and
Tb(N11); (d) SNO data between Tb(N10) and
Tb(N11)- Tb(N10); (e) SNO data of versus ∆Tb-∆Tl
versus Tl (N10).
(a)
1991
Time series of NOAA 10, 11, 12, and 14 before correction (ocean averages)
253
250
for reference satellite
Scatterplot of the brightness temperature difference versus the center distance between two nadir pixels of the overpass satellites for some selected
overlaps. The pixel center distance has been extended to 222 km from 111km and the time window is still set to be 100 sec. The brightness
temperature is computed using the linear calibration equation.
1989
(a)
NOAA10
can be reliably obtained from
δR and u
Combined
-1
Linear (Combined)
Linear (NOAA10)
251
Global ocean-averaged pentad time series
and trend of the nonlinear Z term for
NOAA 10, 11, 12, and 14. Unit for Z is 106 (mW)2 (sr m2 cm-1)-2 .
Brightness temperature of linear calibrated (Tl)
1.2
2003
253
Æ noise;
have to be determined a priori from pre-launch calibration.
1.4
2001
Year
has to be considered (see figure). With colinearity, only
Here δR
1999
NOAA14
Linear (NOAA10)
Trend: N10 = -0.13, N11 = -1.67
N12 = 1.18 , N14 = -2.15
252
∆δR = δRk − δR j , uk , and u j
Trend = 0.17 K Dec
NOAA11
252
Using (3)
Relationship of the Channel 2 Tb differences between
NOAA 10 and 11of the nadir pixels versus time window
for the SNO dataset. The maximum spatial distance for
the SNOs is set to be 111 km. Note that when the time
difference is larger than about 100 seconds, not many
SNO data pairs can be found.
1997
NOAA12
-10
1987
∆R = Rk' (t j , X j ) − R 'j (t j , X j ) + ε k − ε j + ∆R (∆t , ∆X)
We solve
1995
NOAA10
-1
Linear (NOAA12)
(tk , X k )
Taking differences
The local equator crossing time (LECT) of the ascending orbit
of NOAA satellites
N14 = 0.31 K Dec
253
NOAA12
-9
Æ observed radiance R by satellite k at time and location
R ' Æ error free measurement; ε
0301
Time
1993
254
-1
N12 = 0.43 K Dec ,
NOAA11
-1
Trend: N10 = -0.39 K Dec , N11 = 0.58 K Dec
NOAA10
-8
12
8612
1991
(b)
254
Ch 2 Z Time Series and Trend for NOAA 10, 11, 12, and 14 (ocean averages)
-5
Z
R j (t j , X j ) = R (t j , X j ) + ε j
14
1989
Æ constant offset; u Æ nonlinear calibration coefficient
'
j
18
250
1987
2003
Time series and trend for the pentad dataset of the global ocean-averaged MSU channel 2
brightness temperature for NOAA 10, 11, 12 and 14 with linear calibration algorithm. (a)
Individual time series and trend for NOAA 10, 11, 12 and 14. (b) Combined time series and
trend for NOAA 10, 11, 12 and 14. The mean biases between different satellites has been
removed with NOAA 10 as the reference satellite.
Re Æ Earth-view radiance by nonlinear calibration;
-6
20
2001
(a)
Æ Blackbody target raw counts
4. Calibration with SNO dataset
n14
Linear (Combined)
252
Linear (NOAA11)
-1
n11
Combined
Linear (NOAA10)
-4
n10
22
-1
253
NOAA12
251
S=
δR
24
Trend=0.32 K Dec
NOAA11
253
NOAA14
2. SNO dataset
Hour
-1
Trend: N10 = -0.35 K Dec , N11 = 1.05 K Dec
Æ Earth-view radiance by linear calibration
Rl
20
40
60
80
100
120
Distance (km)
(b)
140
160
180
200
220
20
40
60
80
100 120 140 160 180 200 220
Distance (km)
(c)
STD of channel 2 brightness temperature differences between satellite pairs versus center distance of the nadir overpass pixels.
(a) Satellite pairs that have a well defined relationship, (b) satellite pairs that do not show well defined SDT-distance relationship
for smaller distance due to sampling size problems, and (c) SNO numbers used in the STD computation for a corresponding
distance.
(c)
(d)
(e)
are determined by pre-launch calibration but non-reference satellites are determined by post-launch SNO data.
• Very-well calibrated and merged MSU channel 2 data are generated. Biases for pentad global ocean-averages
are on the order of 0.05 to 0.1 K between satellite pairs, compared to 0.5 to 1 K with NESDIS operational
algorithm.
• Global ocean trend with this merged dataset is 0.17-0.20 K/Decade, consistent with surface temperature trend.
Reference: Zou,C.-Z., M. Goldberg, Z. Cheng, N. Grody, J. Sullivan, C. Cao, and D. Tarpley, 2005:MSU
channel 2 brightness temperature trend when calibrated using simultaneous nadir overpasses, to be submitted
as NOAA Technical Report. Email: Cheng-Zhi.Zou@noaa.gov