Authors note: The equations are images from the journal printing. The web currently doesn't support greek characters so three substitutions have been made to the html text: 1)The HIRS channel number is greek eta in the equations while english "n" in the text, 2) The transmittance is greek Tau in the equations while english "t" in the text, and 3) the emittance is greek epsilon in the equations while capitol "E" in the text.
The HIRS radiometer senses infrared radiation in eighteen spectral bands that lie between 3.9 and 15 microns at 20 to 35 km resolution (depending upon viewing angle) in addition to visible reflections at the same resolution. The four bands in the CO2 absorption band at 15 microns are used to differentiate cloud altitudes and the longwave infrared window band identifies the effective emissivity of the cloud in the HIRS FOV.
The CO2 slicing technique is derived from the calculation of radiative transfer in an atmosphere with a single cloud layer. For a single level cloud element in a FOV the radiance observed at the satellite, R(n), in
spectral band n can be written
where t(n,P) is the transmittance through the atmosphere for band n, NE is the effective emissivity of the cloud in the FOV, and B(n,T(P)) is the Planck function for band n and temperature T at pressure level P.
Ps is the surface pressure while Pc is the cloud top pressure.
The four terms in Equation (A1) are the radiation emitted from the surface,
the contribution from the atmosphere below the cloud, the cloud contribution,
and the contribution from the atmosphere above the cloud.
For a clear FOV (NE = 0), the satellite measured radiance Rclr is
Subtracting the clear FOV radiance Rclr(n) from the cloudy FOV radiance R(n) yields the following result.
This is the cloud signal in the satellite measured radiances for
spectral band n; it is the radiance difference of the cloudy FOV
from neighboring clear FOVs. A simplified equation, after integration
by parts, is
Following the work of Smith and Platt (1978), the ratio of the
cloud signal for two spectral bands of frequency n1 and n2 viewing the same
FOV can be written as
If the frequencies are close enough together, then NE1 approximates NE2, and one has an expression by which the pressure of the cloud (Pc) within the FOV can be calculated without apriori knowledge of the emissivity.
The left side of Equation (A5) is determined from the satellite observed radiances in a given FOV and the clear air radiances inferred from spatial analyses of satellite clear radiance observations. The right side of Equation (A5) is calculated from a temperature profile T(p) and the profiles of atmospheric transmittance for the spectral bands t(n,P) as a function of Pc, the cloud top pressure. The calculation uses global analyses of temperature and moisture fields from the National Meteorological Center (NMC) and is performed at 50 hPa intervals from 1000 hPa to 100 hPa. For a given spectral band pair, the solution for Pc is the best match of observed and calculated ratios.
Once a cloud height has been determined, an effective emissivity (also
referred to as effective cloud amount in this paper) is evaluated from the
infrared window band data using the relation
Here NE is the effective cloud amount observed in the window band, w represents the window band frequency, and B[w, T(Pc)] is the opaque cloud radiance in the window band.
Using the ratios of radiances of the four CO2 spectral bands, four separate cloud top pressures can be determined (14.2/14.0, 14.0/13.7, 14.0/13.3, and 13.7/13.3). Whenever (R-Rclr) is within five times the noise response of the instrument (conservatively estimated at roughly 1 mW/m2/ster/cm-1), the resulting Pc is rejected. Using the measured infrared window radiance and the four cloud top pressures, four calculations of effective emissivity are also made. As described by Menzel et al. (1983), the most representative cloud height and effective emissivity are those that best satisfy the radiative transfer equation for the four CO2 spectral bands.
If no ratio of radiances can be reliably calculated because (R-Rclr) is within five times the instrument noise level, then a cloud top pressure is calculated directly from the comparison of the HIRS observed 11.1 micron infrared window band brightness temperature with an in situ temperature profile and the effective emissivity is assumed to be unity. In this way, all clouds are assigned a cloud top pressure either by CO2 or infrared window calculations.
Fields of view are determined to be clear or cloudy through inspection of the 11.1 micron brightness temperature with an 8.3 or 12.0 micron band correction for moisture absorption. The band differences (11.1 - 8.3 micron for NOAA 10 and 12, or 11.1 - 12.0 micron for NOAA 11) were used to lower the threshold for clear-cloudy decisions in areas were water vapor affected the window band. This threshold change varied from 0 C near the poles in dry air masses to as high as 7 C in the moist tropical atmospheres. If the moisture corrected 11.1 micron brightness temperature is within 2.5 C of the known surface temperature (over land this is inferred from the NMC Medium Range Forecast (MRF) model analysis; over the oceans this is the NOAA/NESDIS sea surface temperature analysis), then the FOV is assumed to be clear (Pc = 1000 hPa) and no cloud parameters are calculated.
The HIRS data are calibrated and navigated by NOAA/NESDIS. These data are transmitted daily to the Man computer Interactive Data Access System (McIDAS) at the University of Wisconsin-Madison. The HIRS data from NOAA 10, 11, and 12 are sampled to make the processing more manageable. Every third pixel on every third line is used. The data are also edited for zenith angle, eliminating data over 10 scan zenith angles to assure top down viewing of the clouds and to minimize any problems caused by the increased path length through the atmosphere of radiation upwelling to the satellite. The resulting coverage is restricted to approximately the center one third of the orbit swath. With two satellites, about one half of the Earth is sampled each day.
Morning orbits over land are not used because the surface temperature analysis over subtropical deserts is often warmer than the HIRS data; this causes cloud free areas to be mistaken as clouds. However, morning orbits over the oceans are used because no diurnal temperature change of the surface is assumed.
In the Arctic and Antarctic, the HIRS bands are inspected for the presence of surface temperature inversions. Over high altitude areas of Antarctica and Greenland, the HIRS 700 hPa band is often warmer than the window band. We assume that this indicates the presence of surface inversions from radiative cooling under clear skies. Surface inversions normally cannot be seen by the HIRS, but over polar high altitude continents the thermal contrast between 700 hPa and the elevated surface is often large enough to be detected. When the 700 hPa band is warmer than the window band, the observation is classified as cloud free. When the 700 hPa band is within 2.0 C of the window band, we assume that both bands saw the top of a cloud and the observation is classified as cloudy.