## NOAA Polar Orbiter Data User's Guide## Section 4.5 |

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TOVS thermal data values (HIRS/2 Channels 1-19, SSU Channels 1-3, and MSU Channels 1-4) may be converted to brightness temperatures, and TOVS visible data values (HIRS/2 Channel 20) may be converted to percent albedo, by the following calibration procedures. (Note: see Appendix M for an improved method of calibrating the HIRS data.)

The format and order of the calibration coefficients is
described in Sections
4.1.2.1, 4.2.2.1, 4.3.2.1 for HIRS/2, SSU, and
MSU data, respectively. Once the calibration coefficients have been
extracted they must be scaled and normalized in that order. The
scale factors for the coefficients from lowest to highest in order
are 2^{22}, 2^{30}, 2^{44}, and
2^{56}. (The 0th order term is a constant or in this case
the intercept value, and has a scale factor of 2^{22}.
Similarly, the 3rd order term has a scale factor of
2^{56}.) To scale the raw calibration values, they must be
divided by their respective scale factor. HIRS/2 users should refer
to adjustments necessary to obtain correct intercept values in Section 4.1.2.1.

Once the coefficients have been scaled, the raw data (in counts)
should be normalized or corrected for non-linearity by using the
normalization coefficients which are supplied with the calibration
coefficients. The equation for the normalized count value
C_{i}' is as follows:

where L is the normalization coefficient, C is the raw data in
counts, subscript i indicates the channel, and the subscripts 0, 1,
2, and 3 indicate the order of the normalization coefficient. This
is a generalized equation since the HIRS/2 calibration coefficients
do not contain a 3rd order normalization coefficient (i.e., drop
the L_{i,3} C^{3} term in Equation 4.5-1). When the
condition of L_{i,0} = 0, L_{i,1} = 1,
L_{i,2} = 0, and L_{i,3} = 0 is met, then
C_{i}' = C_{i}. This means that channel i is linear
and no non-linearity correction is necessary. At this time, the
normalization coefficients for HIRS/2 and SSU data have this
condition. The scaled calibration coefficients and normalized data
may now be used as described below.

The scaled thermal channel zero order coefficients (intercept)
are in units of mW/(m^{2}-sr-cm^{-1}), the 1st
order coefficients (slope) are in units of
mW/(m^{2}-sr-cm^{-1}) per count, etc.

The radiance measured by the sensor (Channel i) is computed as a function of the input data value as follows:

where E_{i} is the radiance value, in
mW/(m^{2}-sr-cm^{-1}), C_{i}' is the
normalized count value (computed from Equation 4.5-1), A is the
calibration coefficient (auto or manual), subscript i indicates the
channel, and subscripts 0, 1, and 2 indicate the order of the
calibration coefficients. The A_{i,2}
C_{i}'^{2} term in Equation 4.5.1-1 should be
dropped for SSU and MSU data.

For the SSU and MSU data, the conversion to "brightness"
temperature from energy is performed using the inverse of Planck's
radiation equation (which is
Equation 3.3.1-2 in Section
3.3.1). The same values should be used for the constants
C_{1} and C_{2}, and the central wave number values
can be found in Section 1.4 (see the
corresponding subsection for the desired satellite).

For the conversion to "brightness" temperatures for the HIRS/2
data, the same procedure is followed as with the MSU and SSU data,
except that a band correction algorithm must be applied to the
results of the inverse of Planck's equation. The inverse of
Planck's equation actually produces an apparent brightness
temperature, T^{*}, which is corrected using the following
equation:

where T is the corrected brightness temperature, and b and c are the band correction coefficients which are supplied in Section 1.4 (see the corresponding subsection for the desired satellite).

The scaled visible channel calibration values are in units of percent albedo for the zero order term (intercept), percent albedo/count for the 1st order term (slope), etc. The only visible channel for the TOVS is the HIRS/2 Channel 20, so the equation to compute the percent albedo, B, is as follows:

where A is the calibration coefficient (auto or manual),
C_{20}' is the normalized count value for Channel 20,
subscript 20 indicates Channel 20, and subscripts 0, 1, and 2
indicate the order of the calibration coefficients. At this time,
the second order term (A_{20,2}
C_{20}'^{2}) in Equation 4.5.2-1 can be dropped
since A_{20,2} is usually 0.

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Please see the NCDC Contact Page if you have questions or comments.