The author is with the United Kingdom Meteorological Office, Building Y70 Defense Research Agency (Aerospace), Farnborough, Hants, GU14 6TD, United Kingdom.
Through the use of new line-by-line spectral calculations in both the infrared and microwave regions, coefficients have been generated for the transmittance stage of the fast radiative transfer model used by the United Kingdom Meteorological Office. These permit the fast model to calculate the transmittance for the high-resolution infrared sounder and the microwave sounding unit instruments aboard the National Oceanic and Atmospheric Administration polar-orbiting satellite for a given atmospheric profile, simply by taking these coefficients in linear combination with a set of predictors. These are expressed in terms of the deviation of the profile from a reference. However, the method can be applied to any instrument within the range of the spectral calculations, thereby permitting new coefficients to be calculated as soon as the spectral response details for the instrument become available. It also permits effective consideration to be given in the longer term to new line data or improvements in line-shape theory. The process by which these coefficients have been obtained is described, along with a discussion of some of the tests carried out on their installation into the fast model; these tests show that they are suitable for operational use. The predictors employed by the fast model are discussed, and changes are proposed for those that relate to the water-vapor transmittance. In this respect it was found that the inclusion of predictors that depend primarily on the zenith angle of the radiation path leads to improvements in the transmittance calculation.
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Each model run calculated transmittances for 40 levels at five viewing angles, for 32 profiles, combining the mixed and variable gases in several ways. The spectral resolutions used for the computations and the archiving are also shown.
Table 2
Regression Predictors used by the Fast Model rttov for Mixed Gases and for Water Vapora
Predictor
Mixed Gases
Water Vapor
Original
Modified
X1
δT sec θ
δT(u sec θ)1/2
no change
X2
δT2 sec θ
(u sec θ)1/2
no change
X3
sec θ
δq(u sec θ)1/2
no change
X4
sec θ
(u sec θ)1/2
no change
X5
(sec θ − 1)
δT(u sec θ)
no change
X6
(sec θ − 1)2
δT2(u sec θ)
no change
X7
(sec θ − 1)
δq(u sec θ)
no change
X8
(sec θ − 1
δq2(u sec θ)
(sec θ − 1)(u sec θ)
X9
δT(sec θ − 1)
δTδq(u sec θ)
(sec θ − 1)2(u sec θ)
X10
1
(u sec θ)1/2
no change
Here δ’s indicate deviations from the reference profile, and quantities shown with overbars are explained in Subsection 3.A of the text. Note that the water predictors are scaled by the layer water amount, some linearly, some to half-power.
Table 3
Positions of the Infrared and Microwave Channels of HIRS and MSU for NOAA-11 and NOAA-12
NOAA-11: Means and Standard Deviations of Statistic [τji(R) − τji(G)] × 100 Taken over 160 Casesa
Level (hPa)
HIRS 8
HIRS 11
HIRS 12
MSU 1
Means
115
0.00
0.03
0.09
0.00
150
0.00
0.07
0.26
0.00
200
0.00
0.09
0.24
0.00
300
0.00
0.02
−0.28
0.00
400
0.00
0.09
−0.06
0.00
500
0.00
0.07
−0.11
0.00
700
0.02
−0.12
−0.14
0.01
850
0.04
−0.19
−0.05
0.02
950
0.09
−0.15
0.19
0.02
1000
0.10
−0.14
0.44
0.02
Standard Deviations
115
0.00
0.04
0.17
0.00
150
0.00
0.15
0.66
0.00
200
0.00
0.25
1.07
0.00
300
0.00
0.40
1.33
0.00
400
0.01
0.89
1.52
0.01
500
0.03
1.15
1.42
0.02
700
0.21
1.16
1.16
0.12
850
0.55
1.11
0.41
0.25
950
0.89
1.11
0.66
0.38
1000
1.07
1.09
1.21
0.46
There are 32 dependent profiles and five angles, where τji(R) and τji(G) are the rttov and genln2 transmittances, respectively, from the jth level to space in the ith channel.
Table 5
NOAA-11: Means and Standard Deviations of Statistic [τji(R) − τji(G)] × 100, for Cross-Validation Test Taken over 155 Casesa
Level (hPa)
HIRS 8
HIRS 11
HIRS 12
MSU 1
Means
115
0.00
0.04
0.10
0.00
150
0.00
0.11
0.41
0.00
200
0.00
0.22
0.75
0.00
300
0.00
0.12
0.00
0.01
400
0.00
0.22
0.29
0.01
500
0.01
0.22
0.11
0.02
700
0.04
−0.08
−0.06
0.05
850
0.11
−0.27
−0.11
0.07
950
0.24
−0.30
0.04
0.12
1000
0.29
−0.29
0.19
0.16
Standard Deviations
115
0.00
0.05
0.21
0.01
150
0.00
0.25
1.19
0.01
200
0.00
0.61
2.71
0.01
300
0.00
0.72
2.54
0.02
400
0.02
1.43
1.97
0.03
500
0.06
1.38
1.65
0.06
700
0.32
1.37
0.97
0.19
850
0.76
1.24
0.47
0.35
950
1.28
1.21
0.35
0.56
1000
1.58
1.17
0.57
0.78
There are 31 independent profiles and five angles, where τji(R) and τji(G) are the rttov and genln2 transmittances, respectively, from the jth level to space in the ith channel.
Table 6
NOAA-11: Difference in the Standard Deviations of Statistic [τji(R) − τji(G)] × 100 for the Original and Modified Predictorsa
Level (hPa)
HIRS 8
HIRS 11
HIRS 12
MSU 1
115
0.00
0.02
0.05
0.00
150
0.00
0.05
0.16
0.00
200
0.00
0.04
0.10
0.00
300
0.00
0.04
−0.02
0.00
400
0.00
0.21
0.28
0.01
500
0.01
0.20
−0.02
0.01
700
0.12
0.14
−0.08
0.07
850
0.24
0.11
−0.01
0.16
950
0.50
0.16
0.15
0.25
1000
0.61
0.17
0.15
0.31
A positive value indicates improvement. The averages are taken over 160 cases (32 dependent profiles, five angles), where, respectively, τji(R) and τji(G) are the rttov and genln2 transmittances from the jth level to space in the ith channel.
Each model run calculated transmittances for 40 levels at five viewing angles, for 32 profiles, combining the mixed and variable gases in several ways. The spectral resolutions used for the computations and the archiving are also shown.
Table 2
Regression Predictors used by the Fast Model rttov for Mixed Gases and for Water Vapora
Predictor
Mixed Gases
Water Vapor
Original
Modified
X1
δT sec θ
δT(u sec θ)1/2
no change
X2
δT2 sec θ
(u sec θ)1/2
no change
X3
sec θ
δq(u sec θ)1/2
no change
X4
sec θ
(u sec θ)1/2
no change
X5
(sec θ − 1)
δT(u sec θ)
no change
X6
(sec θ − 1)2
δT2(u sec θ)
no change
X7
(sec θ − 1)
δq(u sec θ)
no change
X8
(sec θ − 1
δq2(u sec θ)
(sec θ − 1)(u sec θ)
X9
δT(sec θ − 1)
δTδq(u sec θ)
(sec θ − 1)2(u sec θ)
X10
1
(u sec θ)1/2
no change
Here δ’s indicate deviations from the reference profile, and quantities shown with overbars are explained in Subsection 3.A of the text. Note that the water predictors are scaled by the layer water amount, some linearly, some to half-power.
Table 3
Positions of the Infrared and Microwave Channels of HIRS and MSU for NOAA-11 and NOAA-12
NOAA-11: Means and Standard Deviations of Statistic [τji(R) − τji(G)] × 100 Taken over 160 Casesa
Level (hPa)
HIRS 8
HIRS 11
HIRS 12
MSU 1
Means
115
0.00
0.03
0.09
0.00
150
0.00
0.07
0.26
0.00
200
0.00
0.09
0.24
0.00
300
0.00
0.02
−0.28
0.00
400
0.00
0.09
−0.06
0.00
500
0.00
0.07
−0.11
0.00
700
0.02
−0.12
−0.14
0.01
850
0.04
−0.19
−0.05
0.02
950
0.09
−0.15
0.19
0.02
1000
0.10
−0.14
0.44
0.02
Standard Deviations
115
0.00
0.04
0.17
0.00
150
0.00
0.15
0.66
0.00
200
0.00
0.25
1.07
0.00
300
0.00
0.40
1.33
0.00
400
0.01
0.89
1.52
0.01
500
0.03
1.15
1.42
0.02
700
0.21
1.16
1.16
0.12
850
0.55
1.11
0.41
0.25
950
0.89
1.11
0.66
0.38
1000
1.07
1.09
1.21
0.46
There are 32 dependent profiles and five angles, where τji(R) and τji(G) are the rttov and genln2 transmittances, respectively, from the jth level to space in the ith channel.
Table 5
NOAA-11: Means and Standard Deviations of Statistic [τji(R) − τji(G)] × 100, for Cross-Validation Test Taken over 155 Casesa
Level (hPa)
HIRS 8
HIRS 11
HIRS 12
MSU 1
Means
115
0.00
0.04
0.10
0.00
150
0.00
0.11
0.41
0.00
200
0.00
0.22
0.75
0.00
300
0.00
0.12
0.00
0.01
400
0.00
0.22
0.29
0.01
500
0.01
0.22
0.11
0.02
700
0.04
−0.08
−0.06
0.05
850
0.11
−0.27
−0.11
0.07
950
0.24
−0.30
0.04
0.12
1000
0.29
−0.29
0.19
0.16
Standard Deviations
115
0.00
0.05
0.21
0.01
150
0.00
0.25
1.19
0.01
200
0.00
0.61
2.71
0.01
300
0.00
0.72
2.54
0.02
400
0.02
1.43
1.97
0.03
500
0.06
1.38
1.65
0.06
700
0.32
1.37
0.97
0.19
850
0.76
1.24
0.47
0.35
950
1.28
1.21
0.35
0.56
1000
1.58
1.17
0.57
0.78
There are 31 independent profiles and five angles, where τji(R) and τji(G) are the rttov and genln2 transmittances, respectively, from the jth level to space in the ith channel.
Table 6
NOAA-11: Difference in the Standard Deviations of Statistic [τji(R) − τji(G)] × 100 for the Original and Modified Predictorsa
Level (hPa)
HIRS 8
HIRS 11
HIRS 12
MSU 1
115
0.00
0.02
0.05
0.00
150
0.00
0.05
0.16
0.00
200
0.00
0.04
0.10
0.00
300
0.00
0.04
−0.02
0.00
400
0.00
0.21
0.28
0.01
500
0.01
0.20
−0.02
0.01
700
0.12
0.14
−0.08
0.07
850
0.24
0.11
−0.01
0.16
950
0.50
0.16
0.15
0.25
1000
0.61
0.17
0.15
0.31
A positive value indicates improvement. The averages are taken over 160 cases (32 dependent profiles, five angles), where, respectively, τji(R) and τji(G) are the rttov and genln2 transmittances from the jth level to space in the ith channel.