Due to the multilayer condition, a liquid water cloud layer is considered in the forward simulation of the cirrus case. The properties of the liquid water cloud are estimated by comparing measured and simulated spectral upward radiances, particularly in the absorp- tion bands of water vapor and oxygen-A. An optimal combination of cirrus and liquid τ results in a good fit in the absorption bands. Assuming an overestimated value of liquidτ , thereby an underestimated value of cirrusτ , reduces the upward radiance in the absorp- tion bands because a larger amount of radiation is transmitted by the cirrus and further absorbed by vater vapor and oxygen-A below the cirrus. An opposite condition is obtained when the liquid τ is underestimated, thus the cirrus τ is overestimated. However, please note that the estimation of liquidτ requires a precise knowledge on the geometrical alti- tudes (cloud top and base). Similarly, wavelengths with high absorption by cloud particles are applied to estimate the liquidreff.
In the retrieval, the cloud phase indexIpis applied to distinguish the cloud thermodynamic
phase. The retrieval can be run either in the ice or liquid water mode, depending on the information given byIp. Due to different absorption characteristics between ice and liquid
water particles atλ = 1550 and 1700 nm, measurements of upward radiances yield a positive slope (Ip> 0) for ice clouds and a negative slope (Ip< 0) for liquid water clouds. However,
the presence of low liquid water clouds might bias the resulting Ip if the cirrus is not
sufficiently thick (τ < 2), or when the measurements take place over an ocean surface. In these conditions, the information is misleading since Ip will result in a negative value,
indicating a liquid water cloud.
Based on the measurements of upward radiance, a radiance ratio retrieval is applied to retrieveτ and reff. Two combinations, C1 (I645↑ andℜ1240=I1240↑ /I
↑
645) and C2 (I ↑
645andℜ1640
=I1640↑ /I645↑ ), are applied in the retrieval algorithm. Due to different particle absorption atλ = 1240 and 1640 nm, the retrievals will result inreff from different cloud altitudes. Analyses
on the vertical weighting function have shown that forλ = 1240 nm, the lower cloud layers are more weighted compared to those forλ = 1640 nm. In this way, retrievals using C1 (λ = 1240 nm) will result in reff from a lower altitude. Because the upper layers are more
weighted, retrievals using C2 (λ = 1640 nm) produce reff from a higher altitude. Given that
cirrus particle sizes generally decrease with increasing altitude, retrievals ofreff using C1
result in larger values ofreffthan using C2. For liquid water clouds with increasing particle
sizes toward the cloud top, an opposite result is expected. To some degree, retrievals using those two combinations give a snapshot of the vertical variation ofreff in the cloud. The
vertical weighting function clearly shows that each cloud layer contributes the absorption imprinted in the upward radiance, where the weighting depends on the cloud profile itself and the applied wavelength. Thus, it must be kept in mind thatreff retrieved using this
technique does not represent a particle size at a single cloud layer. Instead, it represents a bulk property of the entire cloud layer.
Possible biases resulting from the assumption of the vertical profile ofreff in the retrieval is
investigated. A systematic deviation is found between assuming a vertically homogeneous and a realistic cloud profiles in the retrieval. For ice clouds with decreasing particle sizes towards the cloud top, retrievals assuming a vertically homogeneous cloud result in an underestimation ofreff by 1 µm. The deviation increases when the retrieval is performed
using a less absorbing wavelength (e.g.,λ = 1240 nm) because the lower layers contribute more strongly to the absorption. For a homogeneous profile, the weighting at the lower layers is smaller, while it is larger at the upper layers. However, for this type of retrieval, the assumption on the vertical profile ofreff does not give a significant impact, since both
profiles produce a similar total absorption at the applied wavelength.
With helps of the vertical weighting function, the vertical penetration depth of the radi- ation scattered into the view of the remote sensing instruments is quantified. Here, the penetration depth is defined as the distance between the cloud top and the location of weighting estimate of particle effective radiusr∗
terms, either by the optical thicknessτw or the geometrical thicknesshw. The penetration
depth atλ = 1000, 1240, 1500, 1550, 1640, 2130, and 3700 nm is analyzed. While it largely depends on τ , only at λ = 3700, the influence of cloud geometrical thickness h slightly enhances. For the other wavelengths, changes of h do not significantly alter the vertical weighting function, as long as the profile ofτ remains unchanged. The penetration depth decreases with increasingτ . For large τ , the weighting at the upper layers is strengthened, reducing the amount of radiation transmitted to the lower layers reduces. Thus, in this condition, the penetration depth is smaller. Compared to ice clouds, the penetration depth in liquid water clouds is generally higher due to smaller absorption given by liquid water droplets at the same particle size. Only atλ = 3700 nm, the penetration depth of liquid water clouds is lower due to higher absorption by liquid water droplets. In addition toτ , the penetration depth is highly affected by the solar zenith angleθ0. Increasingθ0results in
a lower penetration depth since the photons interact more strongly with the upper layers, reducing the contributions of the lower layers to the absorption.
Retrieval uncertainties due to the occurrence of multilayer condition and the assumptions of ice crystal habit and surface albedo are quantified. The presence of liquid water clouds below cirrus leads to an overestimation of the retrieved cirrusτ , when the low cloud is not considered in the forward simulation. This is because the upward radiance measured by the sensor located above cirrus is presumed to be reflected by the cirrus only, neglecting the role of the underlying cloud. An overestimation of liquidτ will artificially decrease the retrieved cirrusτ because the low liquid cloud contributes largely to the upward radiance, and vice versa. Given these facts, the liquidτ must be determined correctly since a wrong assumption almost directly propagates to the retrieved cirrusτ . The presence of low liquid water clouds also influences the retrieved cirrusreff, particularly when the cirrus layer is
not sufficiently thick (τ < 5). In this condition, multiple reflections between the two clouds alter the vertical weighting function at the lower layers of the cirrus. Consequently, for cirrus with decreasing particle size towards the cloud top, the retrievedreff becomes larger.
The impact vanishes when the cirrus layer is sufficiently thick withτ > 5.
The influence of surface albedoρ on the retrieval of reff is analyzed by the changes of the
vertical weighting function. It is found that its influence is similar with that given by the underlying liquid water cloud. Assuming a higher value ofρ enhances the weighting at the lower layers due to the multiple reflections between the surface and the cloud. For higher ρ, the retrieved reff is located at a lower altitude, and vice versa for lower ρ. Apart from
that, this study has shown that the impact of ice crystal habit on the retrieval uncertainties is considerably high. In general, assuming a habit with a lower asymmetry parameterg results in a smallerτ and a larger reff. The backward scattering is enhanced for a larger
g, resulting in a higher upward radiance measured by the sensor. For the range of τ (1- 8) and reff (10-45 µm) analyzed in this study, assuming general habit mixtures (GHM) in
the retrieval while in reality the habit is either aggregated plates or aggregated columns, results in uncertainties of up to 30 % forτ and 49 % for reff.