Parameterizing cloud top effective radii from satellite retrieved values, accounting for vertical photon transport: quantification and correction of the resulting bias in droplet concentration and liquid water path retrievals
Abstract. Droplet concentration ( Nd ) and liquid water path (LWP)
retrievals from passive satellite retrievals of cloud optical depth ( τ )
and effective radius ( re ) usually assume the model of an idealized
cloud in which the liquid water content (LWC) increases linearly between
cloud base and cloud top (i.e. at a fixed fraction of the adiabatic LWC).
Generally it is assumed that the retrieved re value is that at the
top of the cloud. In reality, barring re retrieval biases due to
cloud heterogeneity, the retrieved re is representative of
smaller values that occur lower down in the cloud due to the vertical
penetration of photons at the shortwave-infrared wavelengths used to
retrieve re . This inconsistency will cause an overestimate of
 Nd and an underestimate of LWP (referred to here as the
“penetration depth bias”), which this paper quantifies via a
parameterization of the cloud top re as a function of the retrieved
 re and τ . Here we estimate the relative re 
underestimate for a range of idealized modelled adiabatic clouds using
bispectral retrievals and plane-parallel radiative transfer. We find a tight
relationship between g re = r e cloud
top / r e retrieved and τ and that a 1-D relationship
approximates the modelled data well. Using this relationship we find that
 gre values and hence Nd and LWP biases are higher for the
2.1  µ m channel re retrieval ( re2.1 ) compared to
the 3.7  µ m one ( re3.7 ). The theoretical bias in the
retrieved Nd is very large for optically thin clouds, but rapidly
reduces as cloud thickness increases. However, it remains above 20 % for
 τ and τ for re2.1 and re3.7 ,
respectively. We also provide a parameterization of penetration depth in
terms of the optical depth below cloud top ( dτ ) for which the retrieved
 re is likely to be representative. The magnitude of the Nd and LWP biases for climatological data sets
is estimated globally using 1 year of daily MODIS (MODerate Imaging
Spectroradiometer) data. Screening criteria are applied that are consistent
with those required to help ensure accurate Nd and LWP retrievals.
The results show that the SE Atlantic, SE Pacific and Californian
stratocumulus regions produce fairly large overestimates due to the
penetration depth bias with mean biases of 32–35 % for re2.1 
and 15–17 % for re3.7 . For the other stratocumulus regions
examined the errors are smaller (24–28 % for re2.1 and
10–12 % for re3.7 ). Significant time variability in the
percentage errors is also found with regional mean standard deviations of
19–37 % of the regional mean percentage error for re2.1 and
32–56 % for re3.7 . This shows that it is important to apply a
daily correction to Nd for the penetration depth error rather than
a time–mean correction when examining daily data. We also examine the
seasonal variation of the bias and find that the biases in the SE Atlantic,
SE Pacific and Californian stratocumulus regions exhibit the most
seasonality,
with the largest errors occurring in the December, January and February (DJF)
season. LWP biases are smaller in magnitude than those for Nd ( −8 
to −11  % for re2.1 and −3.6 to −6.1  % for
 re3.7 ). In reality, and especially for more heterogeneous clouds, the vertical
penetration error will be combined with a number of other errors that affect
both the re and τ , which are potentially larger and may
compensate or enhance the bias due to vertical penetration depth. Therefore
caution is required when applying the bias corrections; we suggest that they
are only used for more homogeneous clouds.