To compute scene radiance NE for NOAA KLM AVHRR channels 4 and 5 from the HRPT data stream:
Where:
NE is radiance
NLIN is linear radiance estimate
NCOR is nonlinear radiance correction
NS is non-zero radiance of space – constant
NBB is blackbody radiance
CBB is average blackbody count – we use the current line and 4 previous lines for a total of 50 counts
CS is average space count – we use the current line and 4 previous lines for a total of 50 counts
CE is 10-bit sensor count
The blackbody radiance NBB, is computed from the four PRT’s as follows:
Where:
TPRTi is the temperature of one PRT
d0i, d1i, d2i, d3i and d4i are constant coefficients one set for each PRT
CPRTi is the count value of each PRT
i goes from 1 to 4
Where:
TBB is the average internal blackbody temperature – a total of 50 prt measurements go into this average, current line plus previous 49 lines.
TBB* is the effective blackbody temperature
A, B, C1, C2 and nC are constants
We calculate the coefficients as follows:
The non-linear calibration coefficients: a0, a1 and a2 , are defined in a way such that:
Which means that:
Substituting the equations for NLIN and NCOR on the far right hand side; expanding these equations and collecting on terms of CE we determine that:
Thermal Calibration Constants from NOAA KLM User’s Guide Sec 7 and App. D |
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Constant |
NOAA 16 |
NOAA 17 |
||
|
Channel 4 |
Channel 5 |
Channel 4 |
Channel 5 |
Ns |
-2.467 |
-2.009 |
-8.55 |
-3.97 |
b0 |
2.96 |
2.25 |
8.22 |
4.31 |
b1 |
-0.05411 |
-0.03665 |
-0.15795 |
-0.07318 |
b2 |
2.4532E-4 |
1.4854E-4 |
7.5579E-4 |
3.0976E-4 |
A |
0.332380 |
0.674623 |
0.271683 |
0.309180 |
B |
0.998522 |
0.998363 |
0.998794 |
0.999012 |
C1 |
1.1910427E-5 |
|||
C2 |
1.4387752 |
|||
nc |
917.2289 |
838.1255 |
926.2947 |
839.8246 |
NOAA 16 |
NOAA 17 |
|||||||
PRT 1 |
PRT 2 |
PRT 3 |
PRT 4 |
PRT 1 |
PRT 2 |
PRT 3 |
PRT 4 |
|
d0 |
276.355 |
276.142 |
275.996 |
276.132 |
276.628 |
276.538 |
276.761 |
276.660 |
d1 |
5.562E-2 |
5.605E-2 |
5.486E-2 |
5.494E-2 |
5.098E-2 |
5.098E-2 |
5.097E-2 |
5.100E-2 |
d2 |
-1.590E-5 |
-1.707E-5 |
-1.223E-5 |
-1.344E-5 |
1.371E-6 |
1.371E-6 |
1.369E-6 |
1.348E-6 |
d3 |
2.486E-8 |
2.595E-8 |
1.862E-8 |
2.112E-8 |
0 |
0 |
0 |
0 |
d4 |
-1.199E-11 |
-1.224E-11 |
-0.853E-11 |
-1.001E-11 |
0 |
0 |
0 |
0 |