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

摘要

Droplet concentration ( Nsubd/sub ) and liquid water path (LWP) retrievals from passive satellite retrievals of cloud optical depth ( τ ) and effective radius ( rsube/sub ) 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 rsube/sub value is that at the top of the cloud. In reality, barring rsube/sub retrieval biases due to cloud heterogeneity, the retrieved rsube/sub 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 rsube/sub . This inconsistency will cause an overestimate of Nsubd/sub and an underestimate of LWP (referred to here as the “penetration depth bias”), which this paper quantifies via a parameterization of the cloud top rsube/sub as a function of the retrieved rsube/sub and τ . Here we estimate the relative rsube/sub 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 gsubre/sub values and hence Nsubd/sub and LWP biases are higher for the 2.1 μ m channel rsube/sub retrieval ( rsube2.1/sub ) compared to the 3.7 μ m one ( rsube3.7/sub ). The theoretical bias in the retrieved Nsubd/sub is very large for optically thin clouds, but rapidly reduces as cloud thickness increases. However, it remains above 20?% for ττrsube2.1/sub and rsube3.7/sub , respectively. We also provide a parameterization of penetration depth in terms of the optical depth below cloud top ( dτ ) for which the retrieved rsube/sub is likely to be representative. The magnitude of the Nsubd/sub 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 Nsubd/sub 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 rsube2.1/sub and 15–17?% for rsube3.7/sub . For the other stratocumulus regions examined the errors are smaller (24–28?% for rsube2.1/sub and 10–12?% for rsube3.7/sub ). 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 rsube2.1/sub and 32–56?% for rsube3.7/sub . This shows that it is important to apply a daily correction to Nsubd/sub 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 Nsubd/sub ( ?8 to ?11 % for rsube2.1/sub and ?3.6 to ?6.1 % for rsube3.7/sub ). 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 rsube/sub 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.