71 
ON THE POSSIBLE USE OF SPATIAL VARIABILITY IN AVHRR DATA 
TO ESTIMATE LOW LEVEL MOISTURE AND TEMPERATURE 
John C. Price 
Agricultural Research Service 
Beltsville, Maryland, USA 
Abstract 
The Advanced Very High Resolution Radiometers 
(AVHRR) onboard afternoon NOAA satellites (NOAA 
7,9,11) acquire data at 10.9 and 11.8 pm in the 
thermal infrared window. This permits estimation 
of surface temperature by derivation of a 
correction for the major atmospheric absorber, 
water vapor. Although two factors (total water 
vapor, and its mean temperature) combine to 
produce the atmospheric effect, it is possible to 
solve two equations in three unknowns due to the 
special form of the radiative transfer equation. 
Thus two thermal IR measurements yield surface 
temperature and the product of atmospheric 
moisture and low level temperature. The 
formalism developed here permits estimation of 
the separate atmospheric terms, assuming that 
ground temperatures are nonuniform. The method 
derives formulas for the variability of the 10.8 
pm measurements (channel 4) and the 11.9 pm 
measurements (channel 5), and thus does not apply 
in regions of uniform surface temperature, such 
as the oceans, where spatial variability is very 
small. 
Key Words: Atmospheric moisture, soundings, 
AVHRR, spatial variability 
INTRODUCTION 
The increasing interest in measuring long term 
weather and climate variability has prompted many 
studies of the exchange of energy and moisture 
between the earth and atmosphere. Although such 
studies have been routine in micrometeorology for 
many years, present interest is directed toward 
measuring this interaction over a substantial 
fraction of the surface to the globe. Almost by 
definition these efforts require the analysis of 
satellite data, with frequent and global coverage 
providing the essential perspective. The 
instrument of choice for analysis of Earth 
surface effects is the AVHRR onboard NOAA 
satellites. Five spectral channels in the 
visible (0.6-0.7 pm), near infrared (0.7-1.1 pm), 
mid infrared (3.6-3.9 pm) and thermal infrared 
(10.3-11.3, 11.5-12.5 pm) provide the key 
observations for assessing surface variability 
and its interaction with the atmosphere. In this 
paper we utilize principles applicable to regions 
of surface variability (Price, 1989, 1990), to 
the thermal infrared channels of AVHRR (called 
channels 4 and 5) to estimate of lower 
atmospheric moisture and temperature. As will 
become clear, uncertainties associated with the 
derived results for the atmospheric state are 
relatively large: the analysis should be linked 
to coincident data from the atmospheric sounder 
unit (HIRS) onboard the NOAA satellites. 
ESTIMATING OPTICAL DEPTH AND MEAN 
ATMOSPHERIC TEMPERATURE 
The discussion is based on earlier work by Price, 
1984, in which an estimate was obtained for the 
ratio of the absorption coefficients of channels 
4 and 5 of the AVHRR's. The ratio of absorption 
in channel 5 to that in channel 4, called R, 
stands out in the analysis of data from these 
thermal infrared channels. Through 
simplification of the radiative transfer equation 
by treating as small (first order) the 
atmospheric effect on satellite radiances, we 
obtain 
, T . ; 
4 air 
(1) 
Rr.T . 
4 air 
(2) 
where T. and T c are the satellite observed 
4 5 
radiance temperatures, T g is the surface radiance 
temperature, is the transmittance = Jdz 
k^q(z), and T^^ - Jdz k^q(z)T(z) . Also k^ is 
the absorption coefficient and q the density of 
atmospheric water vapor, and z is the path from 
surface to satellite through the atmosphere. At 
this level of approximation R is a constant, of 
order 1.35, so that one may solve the two 
equations (1, 2) for T g by multiplying the T^ 
equation by R and subtracting from the T<- 
equation. The result is 
T H ± — 
"4 (R-l) 
(T, 
(3) 
We 
may regard as fortuitous the fact that both 
and T ^ are eliminated by this process. 
One may produce a second result by eliminating T^ 
from equations 1 and 2: 
T. - r.T . 
4 4 air 
1 - r, 
T c - Rr. T . 
5 4 air 
1 - Rr, 
(4) 
In general a single equation in two unknowns 
(r. , T . ) is not useful. However IF surface 
4 air 
temperature is variable, this produces 
variability in T^ and T,.. Provided that a 
statistically valid correlation may be found over 
some limited area between T^ and T<_, e.g. by 
linear regression, then we may identify derived 
values of the slope and offset, i.e. T. - slope • 
T + offset, with the values of r, and T 
3 4 ai: 
Thus 
slope 
(1 - r 4 )/(l - Rr 4 ) 
(5)