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where R is radiance (mW/[m2-sr-cm-1]) and X is the GVAR count value. The coefficients m and b are the scaling slope and intercept, respectively. The values of m and b are listed in Table 1. They depend on the channel selected, but for a given channel they are constant for all time and are the same for all satellites of the series. Table 1-1. GOES-8 through -11 Imager Scaling Coefficients
Table 1-2. GOES-12 and -13 Imager Scaling Coefficients
II. Conversion of Imager GVAR count to TemperatureThere are three steps to convert a 10-bit GVAR count value (0-1023) to temperature. Step 1: Convert the GVAR count value to a radiance using the way described in part I. Step 2: Convert radiance to effective temperature using the inverse of the Planck function as follows:
where Teff is effective temperature (K), ln stands for natural logarithm, and R is radiance. The coefficients n, c1, and c2 are the central wavenumber of the channel and the two radiation constants, respectively. The constants c1 and c2 are invariant, but n depends on the spectral characteristics of the channel and will vary from instrument to instrument. Step 3: Convert effective temperature Teff to actual temperature T (K) using the following equation:
where a and b are two conversion coefficients. Note in the conversions that:
Table 2-1. GOES-8 Imager (Side 1) Coefficients
Table 2-2. GOES-9 Imager (Side 1) Coefficients
Table 2-3. GOES-10 Imager (Side 2) Coefficients
Table 2-4. GOES-11 Imager (Side 1) Coefficients
Table 2-5. GOES-12 Imager (Side 1) Coefficients
Table 2-6. GOES-13 Imager (Side 1) Coefficients
III. Precision of the Conversion of Imager GVAR Count to TemperatureThe use of Teff accounts
for the variation of the Planck function across the spectral
passband
of the channel. The differences between the values of T and
Teff increase with decreasing temperature. They are
usually of the order of 0.1 K. In the worst case, near
180 K, they are approximately 0.3
K. The errors resulting from the above approximations can be reduced by a factor of 10 if the following second-order polynomial is adopted:
This yields errors under 0.001 K, even at temperatures above 310 K or under 210 K. The a, b, and g coefficients and centroid wavenumber n for all detectors are listed in the tables 3-1a through 3-5a below: IV. Conversion of Sounder GVAR Count to Scene Radiance or TemperatureAs mentioned at the beginning of this memorandum, the methods described here to convert imager GVAR data to scene radiance or temperature are also applicable to GOES sounders. The GOES sounder scaling coefficients are listed in Table A2 of the above-mentioned NOAA Technical Memorandum - Operational Calibration of the Imagers and Sounders on the GOES-8 and -9 Satellites.. As described in the memorandum, infrared sounder data in GVAR are scaled radiances packaged in 16-bit words. The conversion of the raw data from the instruments to 16-bit scaled radiances is carried out in real time in the SPS at the CDA facility at Wallops, VA. The related coefficients (n, a, b, and g) of GOES sounders for the first- and second-order polynomials (Equations [3] and [4]) - are included in the following tables:
Coefficients (n, a and b) for the first-order polynomial:
Coefficients (n, a, b, and g) for the second-order polynomial:
V. Look-Up Tables of GOES radiances, Brightness Temperatures vs. GVAR CountsThe GOES-8, GOES-9, GOES-10 GOES-11 and GOES-M Imager and Sounder look-up tables of radiances, brightness temperatures vs. GVAR counts are listed below. The look-up tables for the Imagers cover all the detectors, while the look-up tables for the Sounders only cover detector 1 for each infrared channel. This arrangement intends to avoid huge disk space the Sounder look-up tables might have occupied. Sounder look-up tables are arranged according to their channels and are also compressed.
The mode - A count value Xa is derived from the temperature with the following equations3: For 163K <= T <= 242K, Xa = 418 - T.
Mode - A count values are on an eight-bit scale and range in value from 0 to 255, with high counts representative of low temperatures. Beyond the difference in precision, there is a fundamental difference between GVAR counts and mode-A counts--their units. GVAR counts are scaled radiances, whereas mode-A counts are temperatures. REFERENCES [1] Weinreb, M.P., M. Jamieson, N. Fulton, Y. Chen, J.X. Johnson, J. Bremer, C. Smith, and J. Baucom, "Operational calibration of Geostationary Operational Environmental Satellite-8 and -9 imagers and sounders," Applied Optics, 36, pp. 6895-6904, 1997. [2] Johnson, J.X., GOES-8 radiance to brightness-temperature conversions, internal memorandum, Sept. 20, 1996. [3] Bristor, C.L. (ed.), "Central processing and analysis of geostationary satellite data," NOAA Tech. Memo. NESS 64, U.S. Dep't. Commerce, National Oceanic and Atmospheric Administration, Washington, DC, 155 pp. (1975) GOES | POES | DMSP | Contact Us | Webmaster Privacy Policy |
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