# 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

Droplet concentration (inline-formulaNd) and liquid water path (LWP) retrievals from passive satellite retrievals of cloud optical depth (inline-formulaτ) and effective radius (inline-formulare) 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 inline-formulare value is that at the top of the cloud. In reality, barring inline-formulare retrieval biases due to cloud heterogeneity, the retrieved inline-formulare 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 inline-formulare. This inconsistency will cause an overestimate of inline-formulaNd and an underestimate of LWP (referred to here as the “penetration depth bias”), which this paper quantifies via a parameterization of the cloud top inline-formulare as a function of the retrieved inline-formulare and inline-formulaτ. Here we estimate the relative inline-formulare underestimate for a range of idealized modelled adiabatic clouds using bispectral retrievals and plane-parallel radiative transfer. We find a tight relationship between inline-formula $M13inlinescrollmathml{g}_{\text{re}}={r}_{\text{e}}^{\text{cloud top}}/{r}_{\text{e}}^{\text{retrieved}}$ 109pt17ptsvg-formulamathimge24e4ecccde638d47d7a9bab1ce9c575 amt-11-4273-2018-ie00001.svg109pt17ptamt-11-4273-2018-ie00001.png and inline-formulaτ and that a 1-D relationship approximates the modelled data well. Using this relationship we find that inline-formulagre values and hence inline-formulaNd and LWP biases are higher for the 2.1 inline-formulaµm channel inline-formulare retrieval (inline-formulare2.1) compared to the 3.7 inline-formulaµm one (inline-formulare3.7). The theoretical bias in the retrieved inline-formulaNd is very large for optically thin clouds, but rapidly reduces as cloud thickness increases. However, it remains above 20 % for inline-formulaτ<19.8 and inline-formulaτ<7.7 for inline-formulare2.1 and inline-formulare3.7, respectively. We also provide a parameterization of penetration depth in terms of the optical depth below cloud top (inline-formuladτ) for which the retrieved inline-formulare is likely to be representative.

The magnitude of the inline-formulaNd 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 inline-formulaNd 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 inline-formulare2.1 and 15–17 % for inline-formulare3.7. For the other stratocumulus regions examined the errors are smaller (24–28 % for inline-formulare2.1 and 10–12 % for inline-formulare3.7). 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 inline-formulare2.1 and 32–56 % for inline-formulare3.7. This shows that it is important to apply a daily correction to inline-formulaNd 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 inline-formulaNd (inline-formula−8 to inline-formula−11 % for inline-formulare2.1 and inline-formula−3.6 to inline-formula−6.1 % for inline-formulare3.7).

page4274In reality, and especially for more heterogeneous clouds, the vertical penetration error will be combined with a number of other errors that affect both the inline-formulare and inline-formulaτ, 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.

### Zitieren

Zitierform:

Grosvenor, Daniel P. / Sourdeval, Odran / Wood, Robert: 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. 2018. Copernicus Publications.

### Zugriffsstatistik

Gesamt:
Volltextzugriffe: