NOAA KLM Thermal Channel Radiance Computation

 

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

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

Constant

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