ESTIMATION OF PRECIPITABLE WATER AND 
SCALE HEIGHT 
If the absorption coefficient were constant, 
i.e. not dependent on pressure, temperature or 
humidity, then one could easily derive 
précipitable water P in the atmospheric path from 
the value for r, and T & ^ r would simply represent 
the weighted mean temperature of the water vapor. 
Thus if t. = k. P then P = r./k., and T . = 7: 
44 4' 4 air P 
/dr T(r). However in fact the absorption 
coefficient has a rather complicated dependence, 
e.g. as given by Kneizys et al., 1980. 
,T,p) = [ 4.18 +5578e' 78-7/X ]• 
e^OOd/T * V296) ( f + _ 002 p j 
(16) 
where p is pressure and e is vapor pressure in 
atmospheres and k^ has units km ^. 
Evidently it is not possible to use the inferred 
values of r, and T . to deduce the complete 
4 air r 
temperature and moisture distribution in the 
atmosphere. In fact we require a 
parameterization which contains at most two 
undetermined variables. Let e = (p - P t )/(P s 
- p p ), where e^ is the specific humidity at 
surface level, p g is the surface pressure, and p^_ 
is the pressure at some height at which the 
moisture content falls to zero, where a linear 
decrease has been assumed. Similarly let T(p) = 
T g [l - k (p^ - p)/p s ], where /c is the coefficent 
of adiabatic expansion k = 0.29. Finally, we 
simplify greatly the complicated dependence of k, 
because moisture is heavily concentrated in the 
lowest part of the atmosphere where air 
temperature does not vary greatly from 300K, and 
assume that the quadratic term in water vapor 
provides the dominant contribution to the 
respective integrals. Then the integrals may be 
approximated as follows, where we keep only first 
order terms in p - p . 
s r t 
r 4 
2 f P s 2 
0.0050€ q dp (p - p s ) /p g 
P t 
°- 0050e o 2 f P s ~ P t ) 
(17) 
and 
p tne pressure difference between the surface 
and the level at which moisture declines to zero, 
in terms of the satellite measured temperatures, 
by equating T g - T from equation 18 to the 
result from equation 15. Similarly, given 6p, we 
may solve equation 17 for e , the surface level 
humidity, in terms of r , which is given from 
equations 11 and 14. 
APPLICATION TO A SATELLITE DATA SET 
The data set used for this evaluation has been 
described previously (Price, 1984, 1990). 
Briefly, the central U.S. was imaged by NOAA-7 on 
July 20, 1981, under nearly cloud free conditions 
(fig 1). 
Figure 1. This image showing the central U.S. 
was acquired by the AVHRR onboard NOAA-7 on July 
20, 1981. The dark area at the bottom is the 
Gulf of Mexico. 
For this study the field of interest consisted of 
the major fraction of the AVHRR data acquisition, 
i.e. an area 2500 lines (2700 km) in the 
northwest-southeast direction, by 1920 picture 
elements, corresponding to a width of 
approximately 2700 km. Distortion is evident at 
the limbs of the images, where the atmospheric 
path length is much greater. The data were 
processed as described in sections II-III, except 
that a crude cloud filter was used in order to 
prevent unphysical values from clouds from 
destroying the statistical analysis. Subareas 
(40x40 picture elements) were eliminated, i.e. 
made black in the imagery, if more than 1/4 of 
the area was cloud contaminated. 
T . 
air 
0.0050 
0 2 J S dp (p - p s ) 
P t 
*(P S -P)/P S ]/P S 
2 
T 
s 
1 - 
(18) 
Figures 2, 3 and 4 illustrate derived values for 
optical depth, for the pressure height fraction 
6p/p at which moisture falls to zero, and for 
surface vapor pressure, all at 40x40 picture 
element scale. Most values are reasonable, but 
some areas show grossly incorrect values 
associated with residual cloud cover. 
where pressure and vapor pressure are in 
millibars. Finally we may solve for 6p = p - 
73