ABSTRACT - DRUM - University of Maryland

horizontal error bars in Fig. 3.5 are calculated from the propagation of these errors in
the same way discussed above.
Third, an uncertainty arises because clouds are not solid bodies, and the different
wavelengths “see” slightly different clouds because the cloud attenuates radiation of
various wavelengths differently [Hunt, 1973]. To estimate the magnitude of this
uncertainty on our estimation of the overshooting height, a simple sensitivity test was
performed.
Figure 3.6 is a schematic of this problem. The 10.8-µm channel measures the
temperature at one optical depth. The shadow, on the other hand, is determined by
height at which the solar slant path at 0.63 µm is one optical depth. In the case shown
in Fig. 3.6, the 10.8-µm channel reads the temperature at h IR , but the shadow length is
defined by a cloud of height h VIS . Thus, in calculating the lapse rate, there is a
mismatch between the temperature difference and the height. One can consider this an
error in either the length of the shadow or in the temperature of the overshoot - which
one we choose is arbitrary. I will ascribe the error to the length of the shadow.
A simple calculation will help quantify this error. First, assuming values for the
effective radius and ice water content, the distances corresponding to one optical depth
in both channels is estimated [Fu and Liou, 1993]. One further assumes that the
cloud’s shape can be described by a Gaussian distribution (A*exp(-x 2 /(2s 2 )), with its
height and width defined by the parameters A and s. Assuming a homogeneous
extinction coefficient (i.e. constant particle size and ice water content) [Ou et al., 1993],
one can estimate the height difference caused by the error in the shadow length. For
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