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 188.8.131.52, 184.108.40.206, 220.127.116.11 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 222, 230, 244, and 256. (The 0th order term is a constant or in this case the intercept value, and has a scale factor of 222. Similarly, the 3rd order term has a scale factor of 256.) 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 18.104.22.168.
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 Ci' 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 Li,3 C3 term in Equation 4.5-1). When the condition of Li,0 = 0, Li,1 = 1, Li,2 = 0, and Li,3 = 0 is met, then Ci' = Ci. 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/(m2-sr-cm-1), the 1st order coefficients (slope) are in units of mW/(m2-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 Ei is the radiance value, in mW/(m2-sr-cm-1), Ci' 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 Ai,2 Ci'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 C1 and C2, 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), C20' 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 (A20,2 C20'2) in Equation 4.5.2-1 can be dropped since A20,2 is usually 0.