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5 Apr 2001
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Cirrus cloud inhomogeneity: Quantifying bias in emissivity from
radar observations
Hannah Pomroy and Anthony Illingworth
Geophysical Research Letters 2000
Abstract
It has long been recognised that cirrus clouds play a fundamental
role in the earth's radiation balance. In numerical models the IR
emissivity is generally computed from the optical depth. The
relationship between optical depth and emissivity is nonlinear so if
cirrus clouds are inhomogeneous then emissivities calculated from a
gridbox mean value of optical depth will be biased high. An
anomalous effect in stratocumulus involving the nonlinearity of
albedo and liquid water path is well known and to compensate for
subgrid fluctuations the gridbox average liquid water is multiplied
by 0.7 to calculate albedo. We analyse a three month series of
profiles of radar reflectivity in ice clouds to derive the spatial
variability if optical depth and quantity any biases introduced into
emissivities calculated from gridbox mean values of optical depth.
For a gridbox of 10km or 20km the effect is small but becomes
appreciable for larger sized boxes and the average optical depth
should be multiplied by correction factors as low as 0.698 for
calculating emissivities for a 100km box in midlatitude winter
cirrus.
Key results
Variation of mean emissivity bias with grid box size: crosses;
error bars indicate one standard deviation plus and minus the mean.
Bias from calculating emissivity from
 (a) optical depth running
mean;
 (b) 0.7 times optical depth running mean;
 (c) linear fit to
emissivity running mean data;
 (d) optical depth running mean
reduced by a constant factor,
Gridlength 
10km 
20km 
30km 
40km 
50km 
100km 

0.9403 
0.8971 
0.8613 
0.8295 
0.8007 
0.6976 
