Equations Used in ENVI to Calculate Sea Surface Temperature from AVHRR Data
The equations used to calculate sea surface temperature (SST) from AVHRR images in ENVI are available from a NOAA web site referenced in the ENVI documentation (
http://noaasis.noaa.gov/NOAASIS). Nevertheless, it takes a bit of effort to find on this web site all of the information necessary to put together the SST equations which ENVI uses. This article provides the equations and coefficients in an easier format.
The following URL is for a NOAA web page which provides links to documents describing the AVHRR SST Equations:
http://noaasis.noaa.gov/NOAASIS/ml/sst.html
This URL is slightly more direct than the URL cited in the ENVI documentation. ENVI uses the Multi-Channel Sea Surface Tempera (MCSST) equations mentioned in the NOAA documents. The non-linear SST algorithms that are also available from NOAA are not used because they require ground truth data.
SST Equations for NOAA-12, -14, and -15 used in ENVI
Night (split): Ts = a0 + a1*band4 + a2(band4 - band5) + a3(band4 - band5)(sec(theta) - 1)
Night (dual): Ts = a0 + a1*band4 + a2(band3 - band4) + a3(sec(theta) - 1)
Night (triple): Ts = a0 + a1*band4 + a2(band3 - band5) + a3(sec(theta) - 1)
Day (split): Ts = a0 + a1*band4 + a2(band4 - band5) + a3(band4 - band5)(sec(theta) - 1)
SST Equations for NOAA-16 and -17 used in ENVI
Night (split): Ts = a0 + a1*band4 + a2*band5 + a3(band4 - band5)(sec(theta) - 1)
Night (dual): Ts = a0 + a1*band4 + a2(band3 - band4) + a3(sec(theta) - 1)
Night (triple): Ts = a0 + a1*band3 + a2*band4 + a3*band5 + a4(band3 - band5)(sec(theta) - 1)
Day (split): Ts = a0 + a1*band4 + a2*b5 + a3(band4 - band5)(sec(theta) - 1)
Sec(theta) is the secant of the satellite zenith angle, and band 3, band 4, and band 5 are the calibrated brightness temperatures of NOAA AVHRR bands (in Kelvin). The "a" coefficients used in the above equations are derived from a regression model based on global drifting buoy and tropical Pacific fixed buoy data. The coefficient values depend on which NOAA satellite was used to collect the AVHRR image. The following table shows the "a" coefficients for NOAA-12, -14, -15, and -16.
Satellite a0 a1 a2 a3 a4
MCSST triple night
NOAA-12 -271.971 1.000281 0.911173 1.710028
NOAA-14 -275.364 1.010037 0.920822 1.760411
NOAA-15 -276.7558563 1.015354 1.0635723508 1.294955
NOAA-16 -271.763 0.733532 1.01684 0.344182 -0.753123
NOAA-17 -274.622 1.00903 0.913248 0.440015
NOAA-18 -274.398 1.00820 0.841674 0.377061
MCSST dual night
NOAA-12 -279.846 1.031355 1.288548 2.265075
NOAA-14 -273.914 1.008751 1.409936 1.975581
NOAA-15 -283.5117285 1.041037 1.5875819344 1.67743
NOAA-16 -273.082 1.50825 1.00413 1.52452
NOAA-17 -276.603 1.01805 1.49789 1.96181
NOAA-18 -279.755 1.02958 0.0502887 1.78302
MCSST split night
NOAA-12 -263.94 0.967077 2.384376 0.480788
NOAA-14 -282.24 1.029088 2.275385 0.752567
NOAA-15 -271.3969724 0.993892 2.7523466369 0.662999
NOAA-16 -273.15 3.5316 -2.53655 0.753291
NOAA-17 -276.590 1.01015 2.58150 1.000541
NOAA-18 -276.075 1.00841 2.23459 0.736946
MCSST split day
NOAA-12 -263.006 0.963563 2.579211 0.242598
NOAA-14 -278.43 1.017342 2.139588 0.779706
NOAA-15 -261.029735 0.959456 2.663579879 0.570613
NOAA-16 -273.77 3.301267 -2.30195 0.628966
NOAA-17 -271.206 0.992818 2.49916 0.915103
NOAA-18 -280.43 1.02453 2.10044 0.0784059