(1)
The InfraRed Sea Surface Emissivity (IRSSE) model was developed for use in the Global Data Assimilation System (GDAS) at NCEP/EMC. Previously, the GDAS used an IRSSE model based on Masuda et al (1988). The Masuda model doesn't account for the effect of enhanced emission due to reflection from the sea surface (only an issue for larger view angles) and the implementation was based on coarse spectral resolution emissivity data making its application to high resolution instruments, such as AIRS, problematic.
The old IRSSE model has been upgraded to use sea surface emissivities derived via the Wu and Smith (1997) methodology as described in van Delst and Wu (2000). The emissivity spectra are computed assuming the infrared sensors are not polarised and using the data of Hale and Querry (1973) for the refractive index of water, Segelstein (1981) for the extinction coefficient, and Friedman (1969) for the salinitiy/chlorinity corrections. Instrument spectral response functions (SRFs) are used to reduce the emissivity spectra to instrument resolution. These are the quantities predicted by the IRSSE model.
A starting point was the sea surface infrared emissivity model, SSIREM, described in Sherlock (1999),
(1)
where
is the normalised view angle, and
and
are integers.
The coefficients
, 
, and 
for a set of
and
are determied by regression with a maximum residual cutoff of
=0.0002 only for wind speeds of 0m/s.
In generating the sensor emissivities, it was noticed that the emissivity
variation with wind speed was much larger than the 0.0002 residual tolerance
used in SSIREM and so the exponents
and
of the emissivity model were also allowed to vary in the fitting process. For integral
values of
and
their variation with wind speed suggested inverse relationships for both. When the
exponents were changed to floating point values and the fitting exercise
repeated, the result showed a smoother relationship. These two cases are shown below
for NOAA-17 HIRS channel 8. Click on a figure for a larger view.
| Wind speed dependence of integral exponents | Wind speed dependence at floating point exponents |
|---|---|
|
|
Based on the smooth variation of the exponents with wind speed shown above, the emissivity model was changed to,
(2)
where
is the wind speed in m/s. In generating the model coefficients, for a series of wind
speeds 0-15m/s, the coefficients
were obtained using Levenberg-Marquardt least-squares minimization. Interpolating
coefficients for each
as a function of wind speed were then determined. In using the model, the
are computed for a given wind speed and these computed coefficients are used in
equation 2 to calculate the view angle dependent emissivity.
The emissivity fit RMS residuals for an independent data set were computed for all wind speeds For the NOAA-17 HIRS and the Aqua AIRS instruments, the maximum emissivity fit error was at the 0.00002 level. For instruments that scan out to higher view angles, e.g. GOES instruments, the maximum errors were around 0.0001 at 65°.
To determine the impact of emissivity fit errors on the top-of-atmosphere (TOA) brightness temperatures (Tb), the fitted emissivities were used in radiative transfer calculations. Two tests were run; one determining the impact of emissivity fit errors on the TOA Tb values for all wind speeds, and another to determine the impact when emissivities at only 0.0m/s are predicted.
The TOA Tb RMS residuals for HIRS and AIRS where emissivities at all wind speeds are predicted are shown below. The maximum residuals for either instrument never exceeded 0.001K. Click on a figure for a larger view.
| RMS residual for NOAA-17 HIRS | RMS residual for Aqua AIRS 281 subset |
|---|---|
|
|
The brightness temperature residuals when only emissivities at 0.0m/s wind speed are predicted are shown below. The increase in the RMS residuals compared to the plots above is about two orders of magnitude. The maximum errors are about the same magnitude. Click on a figure for a larger view.
| RMS residual for NOAA-17 HIRS | RMS residual for Aqua AIRS 281 subset |
|---|---|
|
|
When wind speed is taken into account, the fit residuals are relatively independent of view angle and channel with magnitudes (average, RMS, and maximum) of around 10^-4 to 10^-3K. For those instruments with maximum scan angles <50-55° (e.g. HIRS, AIRS), ignoring the wind speed effect does increase the errors, but to much less than the instrument noise in most cases. When large view angles are used, however, the wind speed dependence of the emissivity must be included to avoid large errors in the result. Given the relative simplicity of the model (see eqn.(2)) and how it was implemented, there is no speed of execution impact in including the wind speed as a predictor.
Friedman, D. 1969. Infrared characteristics of ocean water. Appl. Opt., 8, 2073-2078