Quantifying and correcting the effect of vertical penetration assumptions on droplet concentration retrievals from passive satellite instruments

Abstract. Droplet concentration (N d ) retrievals from passive satellite retrievals of cloud optical depth ( τ ) and effective radius ( r e ) usually assume the model of an idealised 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) with a constant N d profile. Generally it is assumed that the retrieved r e value is that at the top of the cloud. In reality, barring r e retrieval biases due to cloud heterogeneity, etc., the retrieved r e is representative of that lower down in the cloud due to the vertical penetration of photons at the shortwave infra-red wavelengths used to retrieve r e . This inconsistency will cause an overestimate of N d (referred to here as the penetration depth bias ), which this paper quantifies. Here we estimate penetration depths in terms of optical depth below cloud top ( dτ ) for a range of idealised modelled adiabatic clouds using bispectral retrievals and plane-parallel radiative transfer. We find a tight relationship between dτ and τ and that a 1-D relationship approximates the modelled data well. Using this relationship we find that dτ values and hence N d biases are higher for the 2.1 μm channel r e retrieval ( r e2.1 ) compared to the 3.7 μm one ( r e3.7 ). The theoretical bias in the retrieved N d is likely to be very large for optically thin clouds, nominally approaching infinity for clouds whose τ is close to the penetration depth. The relative N d bias rapidly reduces as cloud thickness increases, although still remains above 20 % for τ 19.8 and τ 7.7 for r e2.1 and r e3.7 , respectively. The magnitude of the N d bias upon climatological N d data sets is estimated globally using one year of daily MODIS (MODerate Imaging Spectroradiometer) data. Screening criteria are applied that are consistent with those required to help ensure accurate N d retrievals. The results show that the SE Atlantic, SE Pacific (where the VOCALS field campaign took place) and Californian stratocumulus regions produce fairly large overestimates due to the penetration depth bias with mean biases of 35–38 % for r e2.1 and 17–20 % for r e3.7 . For the other stratocumulus regions examined the errors are smaller (25–30 % for r e2.1 and 11–14 % for r e3.7 ). Significant time variability in the percentage errors is also found with regional mean standard deviations of 20–40 % of the regional mean percentage error for r e2.1 and 40–60 % for r e3.7 . This shows that it is important to apply a daily correction to N d 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, February (DJF) season. We show that this effect can be corrected for by simply removing dτ from the observed τ and provide a function to allow the calculation of dτ from τ . However, in reality this error will be combined with a number of other errors that affect both the r e and τ , which are potentially larger and may compensate or enhance the bias due to vertical penetration depth.