Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans

Cirrus cloud absorption optical depths retrieved at 12.05 μm are compared to extinction optical depths retrieved at 0.532 μm from perfectly co-located observations of single-layered semi-transparent cirrus over ocean made by the Imaging Infrared Radiometer (IIR) and the Cloud and Aerosol Lidar with Orthogonal Polarization (CALIOP) flying on board the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite. IIR infrared absorption optical depths are compared to CALIOP visible extinction optical depths when the latter can be directly derived from the measured apparent two-way transmittance through the cloud. An evaluation of the CALIOP multiple scattering factor is inferred from these comparisons after assessing and correcting biases in IIR and CALIOP optical depths reported in version 3 data products. In particular, the blackbody radiance taken in the IIR version 3 algorithm is evaluated, and IIR retrievals are corrected accordingly. Numerical simulations and IIR retrievals of ice crystal sizes suggest that the ratios of CALIOP extinction and IIR absorption optical depths should remain roughly constant with respect to temperature. Instead, these ratios are found to increase quasi-linearly by about 40 % as the temperature at the layer centroid altitude decreases from 240 to 200 K. It is discussed that this behavior can be explained by variations of the multiple scattering factor ηT applied to correct the measured apparent two-way transmittance for contribution of forwardscattering. While the CALIOP version 3 retrievals hold ηT fixed at 0.6, this study shows that ηT varies with temperature (and hence cloud particle size) from ηT = 0.8 at 200 K to ηT = 0.5 at 240 K for single-layered semi-transparent cirrus clouds with optical depth larger than 0.3. The revised parameterization of ηT introduces a concomitant temperature dependence in the simultaneously derived CALIOP lidar ratios that is consistent with observed changes in CALIOP depolarization ratios and particle habits derived from IIR measurements.


Introduction
Cirrus clouds are widely distributed over the globe.Most cirrus exhibit compensating thermal and solar radiative effects, with the net effect depending on optical depth and particle size (Berry and Mace, 2014).Thus, well-validated global measurements of cirrus optical depths and properties are required to reliably assess their radiative impacts (Sassen et al., 2008).Ideally, these measurements would be validated using wholly independent retrievals from different instruments that use different measurement techniques having largely or wholly independent sources of uncertainty.While this multiinstrument approach is conceptually straightforward, there are typically a number of practical difficulties (e.g., accurate spatial and temporal matching) that make full realization of the technique somewhat challenging.The sensor design and selection for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission (Winker et al., 2010) obviates most of these concerns.The instrumentation aboard the CALIPSO satellite includes CALIOP (the Cloud and Aerosol Lidar with Orthogonal Polarization), a two-wavelength (532 and 1064 nm) polarization-sensitive (at 532 nm) elastic backscatter lidar (Hunt et al., 2009), a threechannel Imaging Infrared Radiometer (IIR) operating in the 8-12 µm thermal infrared spectral range (Corlay et al., 2000), and a wide field camera operating in the visible domain (Pitts et al., 2007).These instruments are assembled in a staring and near-nadir-looking configuration.The cross-track swaths of the passive sensors are centered on the lidar footprint so that observations from all three instruments are almost perfectly collocated in both time and space.The combined measurements thus allow highly detailed comparison studies that are not subject to collocation uncertainties or concerns about view angle differences.
CALIOP cirrus visible optical depths are total extinction optical depths retrieved using one of two different and totally independent techniques (Young and Vaughan, 2009).The first method is the so-called "constrained retrieval", in which the cloud optical depth is derived from the apparent two-way transmittance as measured from molecular scattering above and below the cloud layer using an instrumentspecific correction for multiple scattering effects.Indeed, in case of cirrus clouds, composed of crystals that are very large compared to the CALIOP visible wavelength (λ = 532 nm), a significant fraction of the scattering energy is included in a small angle forward lobe and may stay in the lidar receiver field of view for an extended distance below the cloud base and hence contribute to an apparent increase of the measured two-way transmittance of the cloud.This fraction of energy varies with ice crystal phase function, ice crystal size, and lidar configuration (Nicolas et al., 1997;Chepfer et al., 1999;Hogan, 2008).The multiple scattering factor, η, introduced by Platt (Platt, 1973;Platt et al., 2002) is a convenient parameter to correct the apparent two-way transmittance for contribution from multiple scattering (Nicolas et al., 1997;Eloranta, 1998).In the single-scattering limit, η is equal to 1.In version 3 of the CALIOP algorithm, η is assumed constant throughout the layer, identical in cloud and below cloud, and equal to 0.6.The second method, called "unconstrained retrievals", is used when reliable measurements of the apparent two-way transmittance are not available.Optical depths derived using unconstrained retrievals use the same assumptions about η that are used in the constrained technique.In addition, a priori assumptions about the layer extinction-tobackscatter ratio, a quantity also known as the lidar ratio, S cal , are also required.The accuracy of the optical depth estimates obtained in this manner depends critically on the accuracy of the assumed apparent lidar ratio S * , which is defined as the product of S cal and η.
Direct measurements of apparent two-way transmittance can also be obtained in the presence of some wellcharacterized secondary scattering layer lying beneath the cirrus.Among the secondary scattering targets that have been recently identified for use in constrained retrievals are ocean surfaces (Josset et al., 2012) and opaque water clouds (Hu et al., 2007).However, the only constrained retrieval target currently implemented in the standard CALIOP analyses is clear air.It has long been recognized that when the scattering characteristics of the ambient molecular atmosphere are well known (e.g., from models or rawinsonde measurements), the apparent two-way transmittance of a layer can be measured directly whenever sufficiently clean air is found immediately above and below the layer (Young, 1995;Elouragini and Flamant, 1996;del Guasta, 1998;Chen et al., 2002;Yorks et al., 2011).The main advantage of the constrained retrieval technique is that it does not require an a priori assumption about the apparent lidar ratio.On the contrary, because the layer apparent optical depth has been measured, accurate estimates of S * can be retrieved by applying the constrained retrieval technique to suitable CALIOP data (Young and Vaughan, 2009;Young et al., 2013).Thus, the only assumed parameter in the constrained retrieval technique is the multiple scattering factor.
In order to extend the constrained approach, Platt (1973) proposed a combined radiometric and lidar retrieval to more fully characterize cirrus cloud properties.In this paper, the relationship between infrared absorption and visible extinction optical depth retrieved from CALIPSO is investigated in detail, based on heritage from the pioneering work of C. M. R. Platt in the 1970s, which is applied here to global space-borne observations.Previously, Lamquin et al. (2008) conducted a closely related study by combining infrared retrievals from Atmospheric Infrared Sounder (AIRS) with apparent optical depths retrieved by the authors from co-located CALIOP measurements.More recently, Josset et al. (2012) conducted a similar analysis using IIR data and apparent optical depth retrievals constrained by ocean surface measurements from both CALIOP and the CloudSat radar.Here, infrared absorption optical depths retrieved from IIR observations of single-layered cirrus clouds at 12.05 µm are compared to the visible optical depths derived by applying CALIOP's constrained retrieval technique to precisely collocated measurements of the same cloud.Based on a detailed analysis of these comparisons, a new relationship describing the temperature-dependent effect of multiple scattering in the CALIOP retrievals is derived and discussed.The technique used to retrieve cirrus emissivity and absorption optical depths from the CALIPSO IIR measurements is described in depth by Garnier et al. (2012a).A substantial review of this method is given below.These analyses use version 3 CALIOP Level 2 5 km cloud layer and profile products and the corresponding version 3 IIR Level 2 track products (Powell et al., 2013).The paper is constructed as follows.Retrieval techniques, sources of uncertainty, and expected ratios between retrievals in the visible and in the infrared are presented in Sect. 2. In the IIR algorithm, emissivity and absorption optical depth are retrieved assuming an isothermal cloud layer of equivalent temperature inferred from the CALIOP layer detection algorithm.This technique is assessed in Sect.3. CALIOP and IIR retrievals are then compared and discussed in Sect. 4. Using analyses organized around the specifics of each algorithm and cloud characteristics such as optical depth and temperature, the CALIOP multiple scattering factor derived from these comparisons is evaluated.Section 5 provides a summary of the work and presents our conclusions about the effectiveness of these multi-sensor analyses.

CALIOP
A detailed overview of CALIOP retrievals can be found in Winker et al. (2009) and the works cited therein.Here we provide only a brief synopsis.The CALIOP Level 1 calibrated 532 nm total attenuated backscatter profiles are used to detect scattering layers with horizontal resolutions of 5, 20, or 80 km, defined by the amount of averaging required to detect the layers (Vaughan et al., 2009).After discriminating between clouds and aerosols (Liu et al., 2009), cloud layers are further classified according to thermodynamic phase and crystal habit as water clouds, randomly oriented ice clouds, or horizontally oriented ice clouds (Hu et al., 2009).Cirrus cloud optical depths are then retrieved by CALIOP's Hybrid Extinction Retrieval Algorithms (HERA) (Young and Vaughan, 2009).Uncertainties in CALIOP optical depth retrievals are described extensively in Young et al. (2013).
When clear air is found immediately above and below a cirrus cloud layer, the apparent two-way transmittance can be obtained directly from the ratio of the mean attenuated scattering ratios, R , in clear air regions above and below the cloud; i.e., T 2 apparent = R below R above .The visible apparent optical depth is simply and the visible optical depth is where division by the multiple scattering factor η represents the required correction of the measured transmittance.These multiple scattering contributions are attributed solely to forward scattered photons that originate from in-cloud scattering events and subsequently propagate into the clear air below cloud base.
According to the equation introduced by Platt (1973), the apparent lidar ratio S * can be derived from this apparent twoway transmittance as where γ is the cloud attenuated backscatter vertically integrated between layer top and base altitudes.It is noted that Eq. ( 3) was established within cloud, so that η should be η c to represent the in-cloud multiple scattering factor that is supposed to be constant with range.As discussed in Winker (2003), deriving S * from Eq. (3) assumes that the multiple scattering factors within and below the cloud are identicali.e., that η = η c , whereas η below the cloud can be larger than η c in cloud (Nicolas et al., 1997).The difference between S * and the true in-cloud apparent lidar ratio, S c *, can be estimated analytically from Eqs. ( 2) and (3) as As illustrated in Winker (2003), (S * -S c *) / S * is identical to (η − η c ) / η when optical depth tends to 0 and decreases as optical depth increases.Similarly, the analyses in this study will rely on apparent optical depths derived from apparent two-way transmittances, so that the inferred multiple scattering factor will be η below cloud.The lidar ratio S cal will be derived from S * after correction for multiple scattering as whereas the true in-cloud lidar ratio, S cal,c , should be derived from Eq. ( 5), but using S * c and η c .The difference between S cal and S cal,c is estimated from Eqs. ( 4) and (5) as Here, the relative bias (S cal -S cal,c ) / S cal is 0 when optical depth tends to 0, and approaches progressively -(η −η c )/η as optical depth increases.As η − η c is ≥ 0, the lidar ratios derived from this technique can be too small, more notably for the largest optical depths.However, no information is available to us to quantify this bias.
In version 3 of the CALIOP data products, the HERA module identifies those layers for which constrained solutions are considered feasible by requiring that the estimated relative uncertainty in the derived lidar ratio be less than 40 % (Young and Vaughan, 2009).An initial estimate of S * is then derived from Eq. (3) and is refined iteratively until the integral of the retrieved extinction profile exactly matches the directly determined apparent optical depth (Young and Vaughan, 2009).This relative uncertainty increases rapidly for small optical depths (Young et al., 2013) and during nighttime, constrained solutions are generally deemed not possible for optical depths typically smaller than 0.3.Because solar background illumination injects large amounts of noise into the CALIOP daytime backscatter signal, the signal-to-noise ratios needed to satisfy this rather stringent requirement are almost never found in CALIOP daytime measurements.As a consequence, CALIOP version 3 constrained retrievals are available almost exclusively during www.atmos-meas-tech.net/8/2759/2015/nighttime for optical depths typically larger than 0.3.For consistency, optical depths reported in the CALIOP 5 km cloud layer product are derived from the measured apparent two-way transmittance using Eq. ( 2) only when the constrained technique is applied to retrieve the extinction profiles reported in the CALIOP cloud profile product.Otherwise, the optical depths reported in the version 3 layer product are retrieved using an initial lidar ratio set to S cal = 25 sr.Nevertheless, whenever the layer apparent two-way transmittance could be measured it is also reported, so that optical depth can also be computed a posteriori using Eq. ( 2), as for the constrained retrievals, hence extending the data set of measured apparent optical depths.In any case, the conversion of apparent optical depth into single-scattering optical depth depends on an a priori specification of the multiple scattering factor.

IIR
The IIR is a passive instrument providing calibrated radiances in three channels in the atmospheric window (8.65, 10.6, and 12.05 µm), with a medium spectral resolution of about 1 µm and a spatial resolution of 1 km per pixel over a 69 km swath.IIR channels are optimized for retrievals of cirrus optical and microphysical properties, such as ice crystals effective diameter (Garnier et al., 2012a(Garnier et al., , 2013)).The IIR 12.05 µm channel, which exhibits the largest absorption by cirrus clouds, is chosen for this analysis.The pixels located at the center of the 69 km swath are precisely collocated with CALIOP lidar footprint, and thus a vertically resolved description of the atmospheric column associated with passive IIR observations is obtained from CALIOP active measurements.IIR retrievals rely on cloud and aerosol detections from CALIOP, and as IIR observations are not vertically resolved the most suitable scenes are those containing only one single cloud layer in the column.Scenes containing low opaque water clouds, also analyzed by the IIR algorithm, are not included in this study.In addition, scenes containing dense depolarizing aerosol layers such as mineral dust are discarded.They represent less than 1 % of the total number of scenes.
Cloud absorption is characterized through its emissivity ε as (Platt and Gambling, 1971;Platt, 1973;Garnier et al., 2012a) where R m is the measured calibrated radiance, R BG is the background radiance at the top of the atmosphere that would be observed in the absence of the studied cloud, and R BB is the radiance of a blackbody source located at the cloud radiative altitude.Cloud absorption optical depth τ a is subsequently derived as Uncertainty in the emissivity includes three components associated with errors on R m , R BG , and R BB and is inversely proportional to the radiative contrast R BG -R BB (Garnier et al., 2012a).In other words, the colder the cloud with respect to the underlying scene, the smaller the uncertainty in the emissivity retrievals.It is convenient to introduce the error dR x on the radiance R x , where the subscript x refers to m, BB, or BG, further weighted by the inverse of the radiative contrast, so that where dT x is the error on the radiance R x converted in terms of equivalent brightness temperature.Thus, the sensitivity dτ a,x of τ a to an error dT x can be simply written for each component: Uncertainty estimates are derived after assessing the random and systematic errors dT m , dT BG , and dT BB .As an illustration, Fig. 1 shows the relative sensitivity dτ a,x / τ a to dT m = −0.3K, dT BG = +0.5 K, and dT BB = +2 K for cirrus clouds.The rationale for this choice of values is given below.The variation dτ a,BG due to a variation dR BG of the weighted background radiance does not depend on ε, and the relative variation dτ a,BG / τ a (dashed line) decreases with τ a , more rapidly for 2τ a smaller than 0.3.A similar behavior is seen for the measured radiance (dotted line).However, the relative variation of τ a due to a variation of dT BB increases steadily with τ a (solid line).
The on-board measured calibrated radiances have been validated by comparison with airborne observations (Sourdeval et al., 2012).Assuming that the measurement is not biased, a random noise dT m = ±0.3K is considered based on the noise equivalent differential temperature and calibration accuracy as assessed by the Centre National d'Etudes Spatiales (CNES).
Both R BG and R BB in Eq. ( 7) are inferred in synergy with CALIOP observations and so too are the respective uncertainty estimates dT BG and dT BB (Garnier et al., 2012a).
The background radiance, R BG , is preferably retrieved from cloud-free observations in neighboring pixels along track as identified by CALIOP at a distance chosen to be smaller than 100 km from the analyzed pixel.The cloud layers for which these conditions are fulfilled are identified as "type 1 clouds".If these conditions are not found, R BG is computed using the FASt RADiative (FASRAD) transfer model (Dubuisson et al., 2005) and ancillary atmospheric and surface data from the GEOS 5 model of the Global Modeling and Assimilation Office (Rienecker et al., 2008).This second ensemble of cloud layers is called "type 2 clouds".Type 1 and type 2 clouds will be evaluated separately as their sources of uncertainty are different.Indeed, for type 1 clouds, R BG is derived purely from observations and is expected to be unbiased with respect to measured radiances.A random error dT BG is assumed, which is arbitrarily augmented from the instrumental random noise dT m = ±0.3 to ±0.5 K to account for possible differences between the studied area and the nearby non-cloudy area.
The blackbody radiance R BB is computed from the FAS-RAD model and the thermodynamic temperature, T c , at the centroid altitude, Z c , of the CALIOP attenuated backscatter profile at 532 nm within the cloud layer (Vaughan et al., 2005).This parameter, derived from Level 1 CALIOP observations, is reported in the CALIOP 5 km layer product and is available as an input to the IIR Level 2 operational algorithm.In order to assess possible systematic errors dT BB , the cloud radiative temperature, T r , can be computed a posteriori from CALIOP extinction profiles and compared with the temperature T c .This analysis is detailed in Sect.3. Subsequent systematic errors on IIR optical depth and corrections will also be discussed.An additional error of dT BB = ± 2 K is assumed to account for possible biases in the atmospheric model.
Even though the IIR analyses take advantage of spatial information (e.g., cloud heights) derived from CALIOP collocated vertical profile observations, the IIR cloud optical properties retrievals are entirely independent from the CALIOP optical properties retrievals.The measurement techniques used by the two sensors rely on different physical principles and hence are subject to very different sources of uncertainty.The expected relationship between CALIOP and IIR optical depths is presented in the following section.

Simulated relationships between CALIOP and IIR optical depths
Ratios of CALIOP cirrus visible extinction optical depth τ vis to IIR absorption optical depth τ a at 12.05 µm are simulated using the FASDOM radiative transfer model (Dubuisson et al., 2005(Dubuisson et al., , 2008) ) for an isothermal cloud and ice crystal optical properties retrieved from pre-computed tables (Yang et al., 2005).Figure 2 shows simulated τ vis / τ a ratios for clouds composed of hexagonal solid columns and of aggregates by taking τ a = 0.25.Effective diameters (D e ) (x axis) are defined as 3/2 times the ratio of volume to projected area (Mitchell, 2002).As seen in Fig. 2, τ vis / τ a increases as D e increases for D e larger than 10-15 µm, from 1.7-1.9 at D e equal to 20 µm up to 2.07 at D e equal to 140 µm.These simplified simulations, which assume mono-disperse particle size distributions, are sufficient to assess the sensitivity of τ vis / τ a to ice crystal size and habit and to establish that τ vis / τ a is expected to be around 2. A more detailed discussion is given in Sect. 4. It is to be noted that τ a is not, strictly speaking, an absorption optical depth as it includes a small contribution from multiple scattering, which becomes more important as optical depth grows larger.Simulations show that τ a is increased by less than 3 % with respect to pure absorption optical depth at τ a equal to 1.25, or τ vis around 2.5, which is the maximum value attained by the semi-transparent cirrus clouds considered in this study.

Cloud radiative temperature
As seen in Sect.2, cloud effective emissivity and hence infrared absorption optical depth are retrieved through a simple relationship (see Eq. 7) by considering an isothermal cloud of blackbody radiance R BB computed using the centroid temperature T c at the centroid altitude Z c .In this section, systematic errors in the blackbody brightness temperature dT BB resulting from this assumption are quantified.To do so, the cloud radiative temperature T r is computed a posteriori from CALIOP extinction profiles and compared to T c , so that ul-timately IIR retrievals can be corrected using Eqs.( 9) and (10b).CALIOP extinction profiles are reported at 5 km horizontal resolution in the cloud profile products and are derived from the exact same attenuated backscatter profiles that are used to compute the centroid altitudes reported in the 5 km layer products.As the intent is to evaluate IIR retrievals, analyses are conducted for single-layered semi-transparent cirrus clouds over ocean.Data selection is further restricted to the subset of cirrus clouds composed of randomly oriented ice crystals for which the ice-water phase classification is reported with high confidence.In addition, possible contamination from mixed-phase clouds is minimized by restricting the analysis to clouds whose temperature at base altitude is colder than −20 • C (Hu et al., 2010).CALIOP optical depths and extinction profiles are retrieved from the constrained technique described previously.The chosen time period covers 12 months in 2008.
Each cloud is composed of a number, n, of vertical bins, i, of resolution δz, with i = 1 to i = n extending from base to top.Emissivity in bin i is noted ε(i) and absorption optical depth derived from Eq. ( 8) is τ a (i).By applying Eq. ( 7) successively to each of the bins, from cloud base to cloud top, it is found that the cloud blackbody radiance R BB can be expressed as where R BB (i) is the blackbody radiance of bin i of thermodynamic temperature T (i), and τ a (n + 1) represents absorption above the cloud.
The denominator in Eq. ( 11) represents the cloud emissivity.The cloud blackbody radiance can be seen as the centroid radiance of the attenuated emissivity profile, with the attenuation term corresponding to the infrared transmittance above the bin i.This expression has been validated by comparing R BB from Eq. ( 11) and from the FASRAD model.In Eq. ( 11), absorption by gases such as water vapor and ozone in the cirrus cloud is neglected, so that absorption is assumed to be purely due to the cloud.This simplification has no impact on the result for τ a larger than 0.2 and otherwise biases R BB by only 0.4 K of equivalent brightness temperature when τ a tends to 0. Assuming a ratio r between CALIOP visible optical depth τ vis and IIR absorption optical depth τ a , Eq. ( 11) can be rewritten as a function of the CALIOP cloud extinction coefficient α (in km −1 ) and r as The temperature T r is derived from the blackbody radiance R BB computed using Eq. ( 12).The ratio r is taken equal to 2 based on the simulations shown in Sect.2.3, as well as 2 ± 0.4 to evaluate the sensitivity of R BB to r.The vertical resolution δz is equal to 0.06 km in the CALIOP profiles products.
However, the centroid altitude Z c can be written as where Z(i) is the altitude of bin i, β part (i) and β mol (i) are, respectively, the particulate and molecular components of the total backscatter (in sr −1 km −1 ), α part (i) and α mol (i) are, respectively, the particulate and molecular extinction coefficients (in km −1 ), and η represents the required correction for multiple scattering introduced in Sect.2.1.Equation ( 13) exhibits interesting similarities with Eq. ( 12).As radiance and altitude vary quasi-linearly with temperature within a few kilometer deep layer, Eqs. ( 12) and ( 13) are effectively two different weighted averages of the cloud temperature profile.In both cases, the weight is composed of the product of a transmittance term and of a multiplying term.For cirrus clouds of sufficient optical depth, the molecular contribution is weak compared to the particulate one, and the transmittance term in Eq. ( 13) is driven by 2ηα(j ) or 1.2α(j ) assuming η = 0.6 for CALIOP observations, which is larger than α(j )/r in Eq. ( 12), or α(j )/2 if r = 2. Thus, the smaller transmittance term in Eq. ( 13) compared to that in Eq. ( 12) tends to provide Z c higher than the radiative cloud altitude for observations from the top of the atmosphere.However, this is partly compensated by the multiplying terms.Indeed, in Eq. ( 13) the multiplying term is roughly proportional to the bin absorption optical depth τ a (i)= α(i) • δz/r, because the lidar ratio is constant in CALIOP extinction retrievals (Young and Vaughan, 2009).Therefore, the multiplying term in Eq. ( 13) can be seen as τ a (i), which is larger than the multiplying term in Eq. ( 12), i.e., the emissivity ε(i).
Overall, the temperature T r derived from Eq. ( 12) is found to be warmer than the temperature T c derived from Eq. ( 13) as seen in Fig. 3a, where mean T r -T c differences are plotted against 2τ a for several ranges in cloud geometric thicknesses z from 1-2 km up to 7-8 km (colored lines) and for all observations (black line).The T r -T c differences represent systematic errors dT BB on the blackbody brightness temperature used in the IIR standard retrievals.They are primarily driven by the cloud geometric thickness z and increase quasi-linearly with optical depth (2τ a ) for a given z.The slope is close to 0 for the smallest thicknesses, z in 1-2 km, and increases up to 1.5 K per unit optical depth for z in 7-8 km.On average, the bias increases with 2τ a (black curve) from 0.5 to 3 K because optical depth and geometric thickness are not fully independent.Standard deviations are between 0.2 and 1.5 K (Fig. 3b) and include variability due to the fact that T r -T c varies with the shape of the extinction profile for a given optical depth and a given geometric thickness.
Biases shown in Fig. 3a have been retrieved assuming an a priori value r = 2. Sensitivity to this assumption is seen in Fig. 4, showing relative variations T r / (T r -T c ) of T r -T c when r is changed to 2.4 ( r = +20 %, solid lines) and to 1.6 ( r = −20 %, dashed lines), to cover a range of possible values according to the simulations (Fig. 2).As will be shown in Sect.4, assuming r between 1.6 and 2.4 also allows coverage of the range of retrieved values.Increasing the ratio r = τ vis / τ a does decrease τ a as τ vis is set from CALIOP retrievals, and the radiative temperature is increased ( T r / (T r -T c ) is positive).The opposite behavior is found when the ratio r is decreased.The estimated bias dT BB = T r -T c shown in Fig. 3a for r = 2 is found to vary by less than 16 % in the worst case, which is for 2τ a = 2.5 and r = −20 %, with small variations with respect to geometric thickness.Therefore, the bias dT BB is estimated and corrected in the following by taking r = 2.
Correcting for a bias dT BB ranging between 0.5 K at 2τ a ≈ 0 and 7 K at 2τ a = 2 as seen in Fig. 3a induces a relative increase of τ a between 0.5 and 17 % according to Fig. 1 and, on average, the largest increase is 7 % for dT BB = 3 K at 2τ a = 2.In the following, CALIOP and IIR retrievals will be compared before and after correcting IIR absorption optical depths for those biases in order to assess the impact on the comparisons.

Comparison of IIR and CALIOP retrievals
CALIOP and IIR cirrus retrievals are evaluated through ratios of CALIOP visible optical depth τ vis to IIR absorption optical depth τ a .Data selection is the same as in Sect.3. IIR absorption optical depths, reported at 1 km pixel resolution under the lidar track in the IIR Level 2 track products, are averaged to a 5 km horizontal resolution to match the resolution at which CALIOP optical depth is reported in the CALIOP 5 km cloud layer products.Median τ vis / τ a ratios during 2008 in the 25 • S-25 • N latitude band are plotted against 2τ a in Fig. 5. Figure 5a is from the standard products whereas Fig. 5b is obtained with τ a corrected by using the cloud blackbody radiance R BB derived from CALIOP extinction profiles as described in Sect.3. In order to simultaneously evaluate biases due to the background radiance R BG as presented in Sect.2, results are plotted by segregating type 1 clouds, for which a measured R BG is available and used to retrieve τ a (solid lines), from type 2 clouds, for which R BG is from computations (dashed lines).Furthermore, retrievals from computed R BG are also plotted for type 1 clouds (dotted lines) for comparison with the standard retrievals (solid line).Finally, the τ vis / τ a ratios are shown for several ranges in centroid temperature T c . Figure 5c shows the number of samples used to build the statistics.The standard deviation of the τ vis / τ a ratios plotted in Fig. 5d is found similar when τ a is from standard products or corrected for the cloud radiative temperature.Figure 5 shows that the median τ vis / τ a ratios are overall within the ranges of expected values according to the simulations shown in Fig. 2. Figure 5 also contains pieces of information about systematic errors on IIR and CALIOP retrievals, which are discussed first.The retrieved τ vis / τ a ratios and their variations with T c as seen in both Fig. 5a and b are discussed afterwards.Tropics are chosen for this discussion for simplicity, because biases due to computed R BG are known to vary with latitude (Garnier et al., 2012a), but this does not affect the representativeness of the results.

Systematic errors: IIR
The τ vis / τ a ratios derived for type 1 clouds from measured R BG (Fig. 5, solid lines) are expected to be the most accurate because they are the most constrained by IIR observations.For these exact same clouds, τ a from computed R BG (dotted lines) differs from τ a from measured R BG (solid line) by less than 2 % at 2τ a = 0.7.As, according to Fig. 1, an error dT BG = 0.5 K induces a relative error in τ a equal to 3.5 % at 2τ a = 0.7, this indicates a bias dT BG = 0.3 K in the computations.However, as seen in Sect.3, the correction of R BB increases τ a and as expected, the τ vis / τ a ratios in Fig. 5b are smaller than in Fig. 5a.For type 1 clouds, it is seen that the corrected R BB decreases the τ vis / τ a ratio by less than 5 % for the largest optical depths.
Type 1 and type 2 clouds are mutually exclusive and appear to have different properties.As seen in Fig. 5c, the fraction of type 2 clouds is larger at colder temperatures and the number of type 1 clouds is not significant at 193-203 K. Type 2 clouds are found to represent more than 85 % of the analyzed clouds in the western in the Ocean, and in the Atlantic Ocean and to represent 76 % overall in the tropics.Type 1 clouds are expected to be isolated cloud systems of small horizontal dimension or at the edge of large systems, whereas type 2 clouds are expected to be embedded in large cloudy areas.This is consistent with the fact that most of the type 1 clouds have a geometric thickness z between 1.5 and 3 km whereas type 2 clouds are deeper, with z mostly between 3 and 6 km and up to 8 km (not shown).Therefore, the blackbody correction is overall larger for type 2 clouds than for type 1 ones (Fig. 3a).As a result, a better agreement between τ vis / τ a from type 1 (dotted lines) and from type 2 (dashed) clouds is clearly noted after correction (Fig. 5b) than before correction (Fig. 5a) for the largest 2τ a between 1 and 1.5.After correction, the overall difference between τ vis / τ a from type 2 and from type 1 clouds is +1 to +5 % at 2τ a = 0.7, which is possibly due to additional biases of −0.2 to −0.8 K (Fig. 1) in the computed R BG , even though actual differences of the τ vis / τ a ratios cannot be ruled out because two distinct ensembles of clouds are compared.Further analyses of the differences between observations and computations are being conducted to help inform and improve future versions of the IIR science data products.
The τ vis / τ a ratio exhibits a sharp decrease of about 40 % from 2τ a = 0.3 to 2τ a = 0.5 for each temperature range and decreases slowly by about 10 % from 2τ a = 0.7 to 2τ a = 2.5.This behavior is observed for both type 1 and type 2 clouds.Because for type 1 clouds (solid lines) R BG is from neighboring observations, biases in IIR τ a retrievals do not seem to be a tenable explanation.As a consequence, possible biases in CALIOP retrievals are investigated in the following section.

Systematic errors: CALIOP
As seen in Sect.2.1, CALIOP optical depth is retrieved using the constrained technique only when the estimated relative uncertainty in the derived lidar ratio is less than 40 %, and this relative uncertainty increases rapidly for small optical depths.Because the signal is noisy, optical depth distributions derived from constrained retrievals are increasingly truncated as actual optical depth decreases, because a larger fraction of these small optical depths does not satisfy the estimated relative uncertainty requirement and thus is excluded from the sample data set.This leads to an increasing high bias in constrained optical depths τ vis as optical depth decreases, which explains the sharp increase of the τ vis / τ a ratio seen in Fig. 5 as 2τ a decreases.
In order to confirm this interpretation, the analysis is now applied to all the layers for which an apparent two-way transmittance could be measured, including those that do not satisfy the conditions required for the constrained technique, as introduced in Sect.2.1.An extended set of CALIOP optical depth measurements is thus obtained from Eqs. ( 1) and ( 2), still limited to nighttime data, and is compared to IIR τ a retrievals.Median τ vis / τ a ratios for the standard constrained retrievals (thin lines) and for the extended optical depth data set (thick lines) are shown in Fig. 6a for type 1 clouds only for more clarity, after correction of IIR τ a for the cloud radiative temperature, and again for several ranges in temperature T c .Associated standard deviations are plotted in Fig. 6b.For the extended data set (thick lines), the τ vis / τ a ratios now increase steadily from the largest optical depths down to 2τ a = 0.3, suggesting that the extended CALIOP optical depth distributions are not as biased for this data set.A sharp increase of the τ vis / τ a ratio is still seen for 2τ a smaller than 0.3, as this ratio of two small numbers becomes more sensitive to small residual biases.In addition, the τ vis distributions are still truncated, because non-physical negative optical depths due to random noise are discarded from the analysis.Standard deviations of the τ vis / τ a ratios are larger for the extended than for the standard constrained data set, suggesting larger random errors because CALIOP distributions are not as severely truncated in the former case.Implications are threefold.First, this confirms that IIR τ a retrievals are not biased by unidentified issues.Secondly, this highlights a systematic bias in all CALIOP standard constrained retrievals (thin lines) for optical depths smaller than about 0.6, which is of the order of +50 % at 2τ a = 0.3.This translates into similar relative biases in the retrieved lidar ratios, which is of importance when cirrus lidar ratios derived from constrained retrievals are used to evaluate the default lidar ratio used in unconstrained retrievals (Garnier et al., 2012b).Finally, this shows that the constrained technique could be improved, in the mean, by relaxing the threshold in the relative lidar ratio uncertainties used in version 3 of the CALIOP algorithm, notwithstanding the large dispersion.

Retrieved τ vis / τ a ratios
In the following, the retrieved median τ vis / τ a ratios are discussed.Results obtained after τ a is corrected for cloud radiative temperature are considered.As seen in Figs. 5 and 6, the ratios are found to increase by about 10 % as the temperature T c decreases by 10 K.The ratios derived from type 1 clouds are found between 1.6 at 233-243 K and 2.1 at 203-213 K, with a standard deviation of the order of 0.3 at 2τ a larger than 1.For type 2 clouds, the ratios are larger by 2 to 5 %, which could be partly explained by possible biases on IIR τ a retrievals.Nevertheless, as both type 1 and type 2 clouds exhibit the same behavior with respect to temperature, they will be combined in the following analyses.To reduce the impact of biases, subsequent analyses are limited to cases for which 2τ a is larger than 0.3.Also, CALIOP extended optical depth retrievals are chosen to avoid biases in CALIOP standard constrained retrievals.For a given temperature, the ratios decrease by about 10 % from 2τ a = 0.3 to 2τ a = 2, as seen in Fig. 6a.This may be due partly to an increasing contribution of multiple scattering in τ a , yet expected to not increase by more than 2 % according to simulations performed on numerous crystal habits.
The clear dependence of τ vis / τ a on temperature T c is interesting.According to the simulations shown in Fig. 2 for the 12.05 µm IIR channel, for effective diameters larger than 10-15 µm, the ratios are expected to increase as the effective diameter increases, with little sensitivity to effective diameters larger than 100 µm.Thus, the increase of the observed τ vis / τ a with decreasing T c could conceivably be caused by larger crystals, but this is in contradiction with the fact that mean crystal sizes and effective diameters are known to be generally decreasing with decreasing temperature for clouds of moderate optical depth smaller than 2.5 as considered in this study (see for example Heymsfield et al., 2014).Observations could also be explained by ice crystals effective diameters decreasing from 10-15 µm at T c = 240 K down to 5 µm at T c = 200 K, but this is very unlikely according to recent analyses of in situ observations (Heymsfield et al., 2014, and references herein).To go further in the discussion, ice crystal effective diameters retrieved from IIR measurements in the three available channels are investigated.The fundamental parameters are the so-called microphysical indices β 12/10 and β 12/08 , defined as the ratios of τ a from channel 12.05 µm to the absorption optical depths retrieved at 10.6 and at 08.65 µm, respectively (Garnier et al., 2013).These indices can be converted into an effective diameter through lookup tables, as illustrated in Fig. 7a, which shows the theoretical microphysical indices β 12/10 (solid lines) and β 12/08 (dashed lines) derived for hexagonal solid columns (blue) and aggregates (red) for τ a = 0.25.The effective diameter is derived from the crystal model for which the relationship between β 12/10 and β 12/08 agrees the best with the observations.More details about the IIR microphysical algorithm can be found in Garnier et al. (2013).Figure 7b shows the cumulative probability density function of the derived effective diameter D e .As discussed earlier, the analysis is applied to clouds exhibiting an optical depth 2τ a larger than 0.3, which allows minimizing possible biases in IIR retrievals at small optical depth.Still, as the IIR microphysical retrievals are the most robust for type 1 clouds with R BG derived from ob- servations as described in Garnier et al. (2013), the results are shown for type 1 clouds (green) only and by combining type 1 and type 2 clouds (black) in order to assess the impact of possible biases in the latter case.For both configurations, only 0.3 % of the retrieved diameters are smaller than 15 µm, which confirms that the observed behavior of the τ vis / τ a ratios with respect to T c cannot be explained by very small crystal sizes, especially because IIR retrievals are the most sensitive to small sizes, as evidenced in Fig. 7a.
IIR microphysical retrievals are representative of the small mode of the particle size distribution (Mitchell et al., 2010).Nonetheless, they indicate that IIR absorption optical depth is sensitive to the presence of ice crystals exhibiting these ranges in effective diameter, and the expected τ vis / τ a ratio can be estimated from the simulations shown in Fig. 2. The median expected ratios are plotted in Fig. 8a against the centroid temperature T c (thick lines), together with the median observed ratios (thin lines) to facilitate the discussion.The green curves are for type 1 clouds whereas the black curves show the results obtained by combining type 1 and type 2 clouds.As the black and green curves are very close in the overlapping region, the analysis is conducted by combining all clouds to take advantage of the larger number of samples, especially at the coldest temperatures (Fig. 8b).The expected τ vis / τ a ratio (thick lines) steadily increases from 1.8 ± 0.1 at T c = 195 K up to 1.95 ± 0.1 at T c larger than 230 K.This result is driven by the fact that effective diameters are found increasing as temperature increases from 195 up to 230 K, and with a decreasing occurrence of retrieved hexagonal solid columns, as will be shown in Sect.4.5.
There is an obvious disagreement between observed and expected variations with temperature of the τ vis / τ a ratios, which needs to be explained.The accuracy of the theoret- ical simulations is difficult to assess, but it is unlikely that they do not correctly reproduce the general behavior with respect to effective diameter.The expected τ vis / τ a ratios are weakly sensitive to the microphysical properties, so that the overall disagreement between observed and expected ratios is unlikely to be attributable to errors in IIR microphysical retrievals.However, even though CALIOP retrievals are robust because they are directly derived from the measured cloud layer two-way transmittance, the retrieved quantity is the apparent optical depth, which can be converted to the singlescattering optical depth only after applying a correction for the effect of multiple scattering.After rewriting Eq. ( 2) as where η T is the "true" multiple scattering correction factor and τ vis,T is the "true" single-scattering visible optical depth, it can be seen that variations of τ vis / τ a could be accounted for by a correction factor η T , which increases as T c decreases.This tentative explanation is investigated in the following section.

CALIOP multiple scattering factor
Following the approach introduced by Platt (1973), the "bulk" multiple scattering factors η T , derived by reconciling the observed and the expected ratios of visible optical depth to infrared absorption optical depth, are now examined.For every cloud sample used to build Fig. 8a, we invoke the relationship given in Eq. ( 14) to derive The 2-D histogram of η T (y axis) and T c (x axis) is shown in Fig. 9a for the same data set as in Fig. 8 and by combining type 1 and type 2 clouds.The mean multiple scattering factor is found to be decreasing from η T = 0.8 at T c = 200 K to η T = 0.6 at 220 K and then more slowly to η T = 0.5 at 240 K, which is the lower limit if scattering is only due to diffraction  (Hogan, 2008).The overall mean value of η T is 0.601, which is encouraging, since this is essentially identical to the constant value η = 0.6 used in the version 3 CALIOP operational algorithm.The results shown in Fig. 9  Variations of the multiple scattering factor reflect changes in the probability that a scattered photon will stay within the field of view and subsequently contribute to the measured signal.This probability becomes smaller as the lateral displacement of the photon in the clear region below the cloud increases and possibly exceeds the receiver footprint.The lateral displacement increases with the diffraction angle θ , which is inversely proportional to the ice crystal equivalent diameter D eq , defined as the diameter of a sphere of equivalent volume (Nicolas et al., 1997;Comstock and Sassen, 2001).For further evaluation, the 2-D histogram of η T and equivalent D eq derived from the IIR microphysical algorithm is shown in Fig. 9b.It is seen that, as expected, the mean value of η T progressively decreases as D eq increases or as the diffraction angle θ decreases.As the IIR effective diameter is sensitive to the small mode of the size distribution, it is a priori underestimated for many of these clouds, so that only qualitative conclusions can be drawn.Finally, the relation between η T and a simplified estimate of the lateral displacement resulting from forward diffraction only is examined.By taking the centroid altitude Z c as the "bulk" cloud altitude, the distance between the diffracting ice crystals and the region where the two-way transmittance is measured is the difference between Z c and the altitude Z b taken 2 km below the cloud base altitude.Thus, the lateral geometric displacement (ld) is roughly estimated as Figure 10a shows the mean value of the multiple scattering factor η T as a function of the "true" visible optical depth τ vis,T derived from Eq. ( 14) and of the estimated lateral displacement.The corresponding number of samples is shown in Fig. 10b.For most samples, optical depth is smaller than 1 and the estimated ld is found to be smaller than 60 m.For comparison, the radius of the CALIOP receiver footprint is about 50 m and the radius of the laser footprint is about 42 m (Hunt et al., 2009).The mean value of η T is found to be increasing toward the single-scattering limit (η T = 1) as the estimated value of ld increases (Fig. 10a) and increasing less rapidly as optical depth increases.It is recognized that ld is a crude estimate based on simplified geometric considerations and scattering due to diffraction only, and a quantified discussion would be hazardous.Nonetheless, these qualitative results indicate that the "bulk" multiple scattering factors η T derived by reconciling observed and expected τ vis / τ a ratios at cloud layer scale are a real measurement of the result of the complex journey of the photons within and below the layer due to diffraction and scattering.

Discussion: implications for CALIOP retrievals
Several parameters related to ice crystal microphysics are retrieved from the CALIPSO mission.Lidar ratios derived from measurements of the two-way transmittance provide insights into ice crystals scattering phase function at 180 • , and depolarization ratios at 532 nm are an indicator of ice crystal shape ratios (Noël et al., 2002).These measured parameters, available at global scale, have been compared with simulations for numerous ice crystal models (Baum et al., 2011).The depolarization ratio of semi-transparent cirrus clouds observed by CALIOP is not expected to be signif- icantly impacted by multiple scattering (Reichardt and Reichardt, 2003).However, the derived lidar ratio is inversely proportional to the multiple scattering factor (see Eq. 5).
The changes in optical depth and lidar ratio resulting from using η T as derived above, instead of η = 0.6 as used in the standard retrieval, are now examined.

Optical depth
The multiple scattering factor has been found to vary between η T = 0.8 and η T = 0.5 as temperature increases and to be equal to 0.6 on average.In this case, the CALIOP optical depth retrieved by using a constant value η = 0.6 is overestimated by 30 % on average at the coldest temperatures and underestimated by 15 % on average at the warmest ones.The resulting changes in optical depth histograms are shown in Fig. 11, which compares the 2-D histograms of τ vis (η = 0.6, Fig. 11a) and τ vis,T derived from Eq. ( 14) (η T , Fig. 11b) and centroid temperature, T c .Note that in Fig. 11b, τ vis,T is mostly larger than 0.3, because the analysis is conducted for 2τ a than 0.3.τ vis,T exhibits a general increase with increasing temperature (Fig. 11b), which is not seen in τ vis (Fig. 11a).This implies that on average, the extinction coefficients derived from CALIOP using η T would increase more rapidly with temperature than those retrieved using η = 0.6.This change would also be reflected in the ice water content estimates reported in the CALIOP data products, because ice water content is inferred from a parameterization based on extinction coefficients (Heymsfield et al., 2005(Heymsfield et al., , 2014)).

Parameters related to microphysics
Lidar ratios can be derived using Eqs.(3) and (5) with constant or variable multiple scattering factors.Figure 12 compares the 2-D histograms of S cal (η = 0.6, Fig. 12a) and S cal,T (η T , Fig. 12b) and centroid temperature, T c .When η is taken constant, the median lidar ratio S cal is found to be weakly varying with temperature, with a maximum S cal = 31 sr at T c = 225 K and minima at T c = 200 and 240 K that are smaller by only 10 % (S cal = 28 sr).Because η is taken constant, we can conclude that the apparent lidar ratio S * is like- wise only weakly varying with temperature.When the multiple scattering factor is taken from this study (η T ), the temperature dependence is increased, as the median lidar ratio S cal,T is found to increase by about 50 % from S cal,T = 21 sr at T c = 200 K up to S cal,T = 34 sr at T c = 228 K and to be roughly constant for T c warmer than 228 K These findings are qualitatively consistent with airborne observations over the Pacific Ocean as reported by Yorks et al. (2011).
Cirrus lidar ratio and depolarization are both expected to vary somewhat with crystal habit.Distributions of the integrated volume (blue) and particulate (red) depolarization ratios reported in the CALIOP products are shown in Fig. 13a.The particulate depolarization ratio is derived from the standard extinction solutions and thus according to this analysis should be expected to change slightly.Nevertheless, the temperature-dependent behavior of the particulate depolarization ratio is similar to the volume depolarization ratio, which indicates that contributions from molecular scattering is weak and therefore that the current particulate depolarization ratio provides sufficient accuracy for this discussion.As for the lidar ratio S cal,T , the depolarization ratio is found to be essentially constant at T c larger than 228 K, and it is found to be increasing as T c gets colder.This behavior is consistent with observations reported in Sassen and Benson (2001) based on profiles from ground-based ruby lidar located in Salt Lake City, Utah.Furthermore, as seen in Fig. 13b, IIR retrievals suggest a decrease in the occurrence of hexagonal solid columns as T c increases up to the same limit T c = 228 K, with no temperature dependence at warmer temperatures.Keeping in mind that this analysis is conducted for clouds dominated by randomly oriented ice crystals, both Fig. 13a and b suggest a progressive transition from solid columns-like crystals having large aspect shape ratios and depolarization ratios (Noël et al., 2002) at colder temperatures to more compact and less depolarizing crystals as temperatures increase.The inferred changes of crystal habit with temperature are in good agreement with in situ observations (Bailey and Hallett, 2009).Relationships between lidar ra- tios and depolarization ratios have been reported by numerous authors (e. g.Chen et al., 2002;Reichardt et al., 2002;Yorks et al., 2011), and a degree of correlation is expected.Overall, these observations show an apparent consistency between several independently retrieved parameters in terms of variations with layer centroid temperature.The improved correlation between depolarization ratio and lidar ratio when the latter is derived using η T rather than by assuming a constant value is noticeable and deemed another indication of the overall consistency of our analyses.

Conclusions
Infrared absorption optical depths (τ a ) retrieved from IIR observations of cirrus clouds at 12.05 µm are compared to visible extinction optical depths (τ vis ) derived from CALIOP observations of the same cloud when direct measurements of the apparent two-way transmittance are available.IIR absorption optical depths are derived for suitable scenes selected by taking advantage of the vertical information available from collocated CALIOP observations.In this paper, we focus on single-layered cirrus clouds over ocean, composed of randomly oriented ice according to CALIOP ice-water classification (high confidence) and with base temperatures colder than −20 • C.
The retrieved τ vis / τ a ratios exhibit an unexpected quasilinear dependence with temperature at layer centroid altitude T c .The observed values increase by about 10 % for each 10 K decrease in temperature over a range from T c = 240 K down to T c = 200 K.This behavior is not consistent with theoretical expectations inferred from simulations and IIR microphysical retrievals of ice crystal effective diameter D e and most probable crystal shape.The suggested explanation is a temperature-dependent multiple scattering factor η T , which is assumed constant and equal to 0.6 in CALIOP version 3 optical depth retrievals.
A "bulk" multiple scattering factor is derived by reconciling the retrieved and expected τ vis / τ a ratios after a detailed analysis of possible biases and after applying corrections, whenever relevant.For IIR, it is shown that the cloud radiative temperature can be derived a posteriori from CALIOP cloud extinction profiles.IIR standard version 3 absorption optical depths are corrected a posteriori and are augmented by 1 to 17 % with corrections that increase with geometric thickness and optical depth.Biases resulting from the background radiances computed using the radiative transfer model and GEOS 5 ancillary data are also evaluated by comparing retrievals for which τ a is from computed background radiances (type 2 clouds) with more accurate retrievals for which the background radiance could be measured in neighboring pixels (type 1 clouds).After correction for the cloud radiative temperature, the τ vis / τ a ratios for type 1 and type 2 clouds are found in satisfactory agreement.The multiple scattering factor is therefore derived by combining both types of clouds, which ensures a significant number of samples between 200 and 240 K.For CALIOP, selection biases in standard version 3 constrained retrievals are seen for visible optical depths smaller than about 0.6.When using only those optical depths originally accepted by the constrained retrieval algorithm, optical depth selection biases are seen to increase as optical depth decreases.For optical depths of 0.3, these biases introduce an overestimate of ∼ 50 %.For this analysis, all the layers for which an apparent two-way transmittance could be measured are considered, as using this extended data set substantially improves the τ vis / τ a ratios at small optical depths while at the same time substantially increasing the number of layers included in the study.However, because biases are still evidenced at 2τ a smaller than 0.3, the multiple scattering factor is only estimated for 2τ a larger than this limit.
The bulk multiple scattering factor is found to decrease from η T = 0.8 at T c = 200 K to η T = 0.5 at T c = 240 K and to be equal to 0.6 on average.The temperature dependence of η T retrieved from this study appears plausible according to simplified estimates of key parameters driving the multiple scattering factor.The next step in the assessment would be to perform detailed simulations in order to improve the accuracy of the current results.These findings, if confirmed, would imply that CALIOP optical depth and extinction coefficients from constrained retrievals are on average overestimated by about 30 % at T c = 200 K and underestimated by about 15 % at T c = 240 K for the data set selected in this study.This statement would need to be confirmed through comparisons with retrievals from other instruments.The apparent consistency between several independently retrieved parameters related to microphysics, namely the integrated depolarization ratio, the ice crystal shape occurrence derived from the IIR, and the lidar ratio is reinforced when the latter is derived from η T rather than by assuming a constant value.The increased correlation between lidar ratio and depolarization ratio is considered to be further evidence that the η T parameterization more accurately reflects the underlying microphysics of cirrus clouds.These results could contribute to a better characterization of optically thin cirrus clouds at night over ocean, with subsequent opportunities for improved understanding of possible formation mechanisms.
This paper illustrates the added value of synergetic analyses of perfectly collocated retrievals from the IIR passive radiometer and the CALIOP active lidar.Understanding and estimating biases, even for a limited data set, allows refining uncertainty estimates and improving the consistency of the retrievals and provides guidance for the development of future versions of the products.Continuous assessment and improvement of the CALIPSO data record, now spanning 9 years in both the visible and the thermal infrared spectral domains, are of importance for a better understanding of the radiative impact of cirrus clouds at global scale.

Figure 2 .
Figure 2. Simulations of the ratio between CALIOP optical depth at 532 nm (τ vis ) and IIR absorption optical depth at 12.05 µm (τ a ) at τ a = 0.25 against effective diameter D e for hexagonal solid columns (blue) and aggregates (red).Vertical dashed lines indicate D e smaller than 15 µm (see text).

Figure 3 .
Figure 3. (a) Mean value and (b) standard deviation of the difference T r -T c between cloud radiative temperature and temperature at centroid altitude of attenuated total backscatter against 2τ a assuming r = τ vis / τ a = 2. Colored lines are for several ranges in cloud geometric thickness.The black line is for all samples.The horizontal dotted lines indicate maximum values discussed in the text.Data set: single-layered cirrus randomly oriented ice with high confidence, base temperature < −20 • C, over ocean, 2008.

Figure 4 .
Figure 4. Relative sensitivity (in percentage) of the difference T r -T c to a variation of r = +20 % (solid lines) and r = −20 % (dashed lines) of the assumed τ vis / τ a ratio r = 2. Colored lines are for several ranges in cloud geometric thickness z .The black lines are for all samples.Same data set as in Fig. 3.

Figure 5 .
Figure 5. Median τ vis / τ a ratio against 2τ a (a) from IIR standard products and (b) after correction for cloud radiative temperature, (c) sample count, and (d) τ vis / τ a ratio standard deviation.Type 1 clouds: measured R BG available and τ a either from measured R BG (solid) or from computed R BG (dotted); type 2 clouds: no measured R BG available and R BG from computations (dashed).Colors are for temperature at centroid altitude T c in 193-203 K (purple), 203-213 K (navy blue), 213-223 K (light blue), 223-233 K (orange), and 233-243 K (red).The vertical dotted lines highlight the results for 2τ a between 0.3 and 0.7 (see text).Data set: single-layered cirrus randomly oriented ice with high confidence, base temperature < −20 • C, over ocean, 25 • S-25 • N, 2008.

Figure 6 .
Figure 6.(a) Median τ vis / τ a ratio and (b) standard deviation from standard CALIOP constrained retrievals (thin lines) and from extended CALIOP optical depth measurements (thick lines) for type 1 clouds retrieved from measured R BG after correction for cloud radiative temperature.The vertical dotted lines highlight the differences for 2τ a between 0.3 and 0.6 (see text).Same data set and color code as in Fig. 5.

Figure 7 .
Figure 7. (a) Theoretical microphysical indices β 12/10 (solid lines) and β 12/08 (dashed lines) against effective diameter D e for a cloud composed of hexagonal solid columns (blue) and of aggregates (red), with τ a = 0.25.The vertical dashed lines highlight the large sensitivity to D e smaller than 15 µm (see text).(b) Cumulative probability density function of D e retrieved from IIR microphysical indices for type 1 clouds (green, measured R BG ) and by combining type 1 and type 2 clouds (black).Data set: single-layered cirrus randomly oriented ice with high confidence, base temperature < −20 • C, extended CALIOP optical depth measurements, 2τ a > 0.3, over ocean, 2008.

Figure 8 .
Figure 8.(a) Median observed (thin lines) and expected (thick lines) τ vis / τ a ratio ± standard deviation and (b) associated samples count against temperature T c for type 1 clouds (green, measured R BG ) and combined type 1 and type 2 clouds (black).Same data set as in Fig. 7b.

Figure 9 .
Figure 9. Two-dimensional histogram of multiple scattering factor η T and (a) temperature T c and (b) equivalent diameter D eq .The color code is the number of samples.The median and mean values against T c are the black solid and dashed lines, respectively.In Fig. 9a, the horizontal red dotted dashed line shows the mean value of η T overall (0.601).The dotted lines indicate values discussed in the text.Same data set as in Fig. 8, all clouds combined.

Figure 10 .
Figure 10.(a) Mean value of the multiple scattering factor η T as a function of visible optical depth (τ vis,T ) and estimated lateral displacement (ld); (b) associated number of samples.Same data set as in Fig. 9.

Figure 11 .
Figure 11.Two-dimensional histogram of (a) τ vis (η = 0.6) and (b) τ vis,T (η T from this study), and centroid temperature T c .The color code is the number of samples.Same data set as in Fig. 9.

Figure 12 .
Figure 12.Two-dimensional histogram of lidar ratio (a) S cal (η = 0.6) and (b) S cal,T (η T from this study) and centroid temperature T c .The color code is the number of samples.The black solid line is the median value.The dotted lines indicate minimum and maximum values and associated temperatures (see text).Same data set as in Fig. 9.

Figure 13 .
Figure 13.(a) Mean ± standard deviation volume (blue) and particulate (red) depolarization ratio against T c ; (b) IIR retrieved shape occurrence against T c .The dotted lines indicate variations with T c discussed in the text.Same data set as in Fig. 9.
Lamquin et al. (2008) of 2008.The same analysis has been applied during 2010 and 2012, and very similar results within a few percents over the whole range of temperature are obtained (not shown), with overall mean values of η T equal to 0.604 and 0.602, respectively.Lamquin et al. (2008)also found larger values of η T at temperatures colder than 210 K than at 230-240 K.