Optical depths of semi-transparent cirrus clouds over oceans from CALIPSO infrared radiometer and lidar measurements , and an evaluation of the lidar multiple scattering factor

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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 Introduction

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Full 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 using different measurement techniques that have largely or wholly independent sources of uncertainty.While this multi-instrument 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 (i.e., 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 3-channel Imaging Infrared Radiometer (IIR) operating in the 8-12 µm thermal infrared spectral range (Corlay et al., 2000), and a Wide Field Camera (WFC) 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.The first method is the so-called "constrained retrieval", in which the "apparent" cloud optical depth is derived from the 2-way transmittance as measured from molecular scattering above and below the cloud layer.The cloud optical depth is then derived with an instrument-specific correction for multiple scattering effects.Direct measurements of apparent optical depth can also be obtained in the presence of some well-characterized 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., Introduction Conclusions References Tables Figures

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Full 2012) and opaque water clouds (Hu et al., 2007).In the second method, called "unconstrained retrievals" (Young and Vaughan, 2009), optical depth estimates are derived using a priori assumptions about the layer extinction-to-backscatter ratio, a quantity also known as the lidar ratio, S cal , and about the layer multiple scattering factor, η.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.
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).
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 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.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 op-Introduction

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Full tical 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 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) using a layer-constant multiple scattering factor of η = 0.6 (Young and Vaughan, 2009).Introduction

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Full In version 3 of the CALIPSO 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 %.The apparent twoway transmittance of these layers can then be obtained directly from the ratio of the mean attenuated scattering ratios in clear air regions above and below the cloud; i.e., T 2 apparent = R below / R above .The visible optical depth is simply where division by η represents the required correction of the measured transmittance for multiple scattering.Because solar background illumination injects large amounts of noise into the CALIOP daytime backscatter signal, the signal-to-noise ratios (SNR) 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 nighttime (Young and Vaughan, 2009).Uncertainties in CALIOP optical depth retrievals are described extensively in Young et al. (2013).

IIR
The IIR is a passive instrument providing calibrated radiances in 3 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 radiances are sensitive to absorbing clouds and to mineral dusts.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 foot-print, 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 Introduction

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Full 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 depolarizing aerosol layers such as mineral dust are discarded.Cloud absorption is characterized through its emissivity ε, where (Platt and Gambling, 1971;Platt, 1973;Garnier et al., 2012a) and cloud absorption optical depth τ a is subsequently derived using In Eq. ( 2), 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.Uncertainty in the emissivity includes 3 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.Similarly, the error dτ a on τ a is written where the quantity dR x is the error on the radiance R x weighted by the inverse of the radiative contrast, and where the subscript x refers to m, BB or BG.
In Eq. ( 4), each term dR x is related to the error on the equivalent brightness temperature dT x as Each term in Eq. ( 4) represents the sensitivity of τ a to each of the 3 quantities involved in the computation of τ a .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 /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).The value dT m = ±0.3K is based on the noise equivalent differential temperature and calibration accuracy as assessed by the Centre National d'Etudes Spatiales (CNES) and is taken as a random error in the final uncertainty assessment.
Both R BG and R BB in Eq. ( 2) 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.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).These two ensembles of retrievals will be evaluated separately as their sources of uncertainty are different.For the first ensemble, that is R BG measured in neighboring pixels, 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 0.3 to 0.5 K to account for possible differences between the studied area and the nearby non-cloudy area.Introduction

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Full The blackbody radiance R BB is computed from the FASRAD 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 random error of dT BB = 2 K is assumed to account for possible errors 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 et al., 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 Introduction

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Full 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. 2) 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 ultimately IIR retrievals can be corrected using Eqs.( 4) and (5).
CALIOP extinction profiles are reported at 5 km horizontal resolution 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 (ROI) 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 time period covers 12 months in 2008.Introduction

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Full 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. ( 3) is τ a (i ).By applying Eq. ( 2) 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 where τ a (n + 1) represents absorption above the cloud.
The denominator in Eq. ( 6) 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. ( 6) and from the FASRAD model.In Eq. ( 6), 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 zero.Assuming a ratio r between CALIOP visible optical depth τ vis and IIR absorption optical depth τ a , Eq. ( 6) can be re-written 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. ( 7).
The ratio r is taken equal to 2 based on the simulations shown in Sect.2.3, as well as Introduction

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Full 2 ± 20 % to evaluate the sensitivity of R BB to r.The vertical resolution δz is equal to 0.06 km in the CALIOP profiles products.
On the other hand, 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 ( 8) exhibits interesting similarities with Eq. ( 7).As radiance and altitude vary quasi-linearly with temperature within a few kilometer deep layer, Eqs. ( 7) and ( 8) 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. ( 8) 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. ( 7), or α(j )/2 if r = 2. Thus, the smaller transmittance term in Eq. ( 8) compared to the one in Eq. ( 7) 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. ( 8), the multiplying term is roughly proportional to the bin absorption optical depth τ a (i ) = α(i ) • δz/r, because the lidar ratio is taken constant in CALIOP extinction retrievals (Young and Vaughan, 2009).Therefore, the multiplying term in Eq. ( 8) can be seen as τ a (i ), which is larger than the multiplying term in Eq. ( 7), that is the emissivity ε(i ).
Overall, the temperature T r derived from Eq. ( 7) is found to be warmer than the temperature T c derived from Eq. ( 8) 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 2154 Introduction

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Full 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, with a slope close to zero for ∆z in 1-2 km and that increases up to 1.5 K per unit optical depth for ∆z between 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 covering 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 %.Therefore, the bias dT BB is estimated 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.Introduction

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Full 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 Level 2 products, are averaged to a 5 km horizontal resolution to match the resolution at which CALIOP optical depth is reported in the 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, defined as the 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. 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.On the other hand, 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.The fraction of type 2 clouds is larger at colder temperatures (see Fig. 5c, dashed lines), and the number of type 1 clouds is not significant at 193-203 K.In addition, 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 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 as 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.As 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.Introduction

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Full

Systematic errors: CALIOP
In the version 3 data products, CALIOP optical depth is retrieved using the constrained technique only when the estimated relative uncertainty in the derived lidar ratio is less than 40 %.This relative uncertainty increases rapidly for small optical depths (Young et al., 2013) and typically, optical depths smaller than 0.3 are retrieved using the unconstrained technique.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 do not satisfy the estimated relative uncertainty requirement and thus are excluded from the sample data set.This leads to an increasing high bias in constrained optical depths τ vis as optical decreases, which explains the sharp increase of the τ vis /τ a ratio as 2τ a decreases.
When the constrained technique is not selected, optical depth is retrieved using the unconstrained technique and a default lidar ratio.Nevertheless, whenever measurements of layer two-way transmittance can be made, this apparent transmittance is also reported in the CALIOP products.Optical depths for these layers can then be directly inferred, as is done for the standard constrained retrievals.An extended set of CALIOP optical depth measurements is thus obtained, still limited to nighttime data, which 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, distributions are again truncated, because non-physical negative optical depths due to random noise are discarded from the analysis.Standard deviations of the τ vis /τ a ra-Introduction

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Full tios 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 at any temperature in 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.Introduction

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Full 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 summary of in situ observations (Heymsfield et al., 2014).To go further in the discussion, ice crystal effective diameters retrieved from IIR measurements in the 3 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.These indices can be converted into an effective diameter through Look-Up 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 (PDF) 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 observations 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 Introduction

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Full 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 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 theoretical 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.On the other hand, even though CALIOP retrievals are robust because they are directly derived from the measured cloud layer two-way transmittance, the retrieved quantity is an apparent optical depth, τ apparent , which can be converted to the single-scattering optical depth only after applying a correction for the effect of multiple scattering on the signal measured below the cloud, which in the ver-Introduction

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Full sion 3 algorithm is taken constant and equal to η = 0.6 so that where η T is the "true" multiple scattering correction factor, and τ vis, T is the "true" singlescattering visible optical depth.It comes from Eq. ( 9) that variations of τ vis /τ a could be driven by τ vis and a correction factor η T , which increases as T c decreases.This tentative explanation is investigated in the following section.It is noted that a similar discussion can be found in Lamquin et al. (2008), which is based on infrared retrievals from Atmospheric Infrared Sounder (AIRS) and CALIOP co-located apparent optical depths retrieved by the authors, and where η T is found larger at temperatures colder than 210 K than for cloud temperatures between 230 and 240 K.

CALIOP multiple scattering factor
In case of cirrus clouds, composed of crystals that are very large compared to 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 2-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 introduced by Platt (Platt, 1973;Platt et al., 2002) is a convenient parameter to correct the apparent 2-way transmittance for contribution from multiple scattering (Nicolas et al., 1997;Eloranta, 1998).This correction factor is smaller than 1, which is the single-scattering limit.
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

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Full used to build Fig. 8a, we invoke the relationship given in Eq. ( 9) 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 are for the 12 months 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.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 departs from the single-scattering limit (η T = 1) and 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 alti-

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Full tude, the distance between the diffracting ice crystals and the top of the region where the 2-way transmittance is measured is the difference between Z c and the altitude Z b taken 2 km below the cloud base altitude in the CALIOP algorithm, to ensure that the measurement is through the entire cloud.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. ( 9) and of the estimated lateral displacement ld.The corresponding number of samples is shown in Fig. 10b.For most samples, optical depth is smaller than 1 and the estimated displacement 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 nicely increasing toward the single-scattering limit as the estimated value of ld increases (Fig. 10a), 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.

Discussion: implications for CALIOP retrievals
In this paper, CALIOP optical depths are derived from measurements of the apparent 2-way transmittance T 2 apparent .As seen in Eq. ( 9), the single-scattering optical depth is inversely proportional to the multiple scattering factor.According to the equation

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Full introduced by Platt (1973), the apparent lidar ratio S * can be derived as where γ is the cloud attenuated backscatter vertically integrated between layer bottom and top altitudes.The apparent lidar ratio S * is the product of the multiple scattering factor and of the lidar ratio and is written as where S cal and S cal, T are the lidar ratios retrieved by taking η = 0.6 and η T from this study, respectively.The equation introduced by Platt (1973) was established within the cloud, assuming that the multiple scattering correction factor is constant with range, which is only approximately true.In Eq. ( 12), a constant "bulk" correction factor η T is considered, which is assumed to be equal to the bulk factor within the cloud.This may not be fully correct according to simulations by Winker (2003), which showed that η T within and below the cloud could differ by about 15 %.The resulting relative error in S * due to this approximation can be derived from Eqs. ( 12) and (9) as As illustrated in Winker (2003), it is identical to dη T /η T when optical depth tends to zero and decreases as optical depth increases.Subsequently, the relative error in S cal, T derived from Eqs. ( 13) and ( 14) is

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Full Here, the relative error in S cal, T is null when optical depth tends to zero, and approaches progressively −dη T /η T as optical depth increases.
As seen in Eq. ( 12), the apparent lidar ratio S * is directly derived from measurements and does not require knowledge of the multiple scattering factor.When T 2 apparent cannot be measured, CALIOP optical depth is derived by using the unconstrained technique, and T 2 apparent is retrieved from a default apparent lidar ratio, which can be established from statistical analyses of S * retrieved from constrained retrievals (Garnier et al., 2012b).This ensures consistency between constrained and unconstrained retrievals, and in both cases, the conversion of apparent optical depth into single-scattering optical depth depends on an a priori specification of the multiple scattering factor.
Several ice crystal microphysical parameters are retrieved from the CALIPSO mission.Lidar ratios derived from measurements of the 2-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 significantly impacted by the multiple scattering factor (Reichardt and Reichardt, 2003).However, the derived lidar ratio is inversely proportional to the multiple scattering factor (see Eq. 13).
The changes in optical depth and lidar ratio resulting from taking η T derived in this study instead of η = 0.6 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.If this result is correct, then 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 de-Introduction

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Full rived from Eq. ( 9) (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 larger 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 will increase more rapidly with temperature than those retrieved using η = 0.6.This change will also be reflected in the ice water content estimates reported in the CALIOP data products, because ice water content is inferred from a non-linear parameterization based on extinction coefficients (Heymsfield andal., 2005, 2014).

Microphysics
Lidar ratios with constant and variable multiple scattering factors are shown in Fig. 12, which 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 likewise 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.
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 temperaturedependent 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 Introduction

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Full be essentially constant at T c larger than 228 K, and it is found to be increasing as T c gets colder.Furthermore, as seen in Fig. 13b, IIR retrievals indicate 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 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 ratios and depolarization ratios have been reported by numerous authors (e.g.Chen et al., 2002;Reichardt et al., 2002;Yorks et al., 2011), and correlations are expected.Overall, these observations show an apparent consistency between several independently retrieved microphysical 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 IIR absorption optical depth retrievals assume an isothermal cloud with a radiative temperature inferred from the centroid altitude of the CALIOP attenuated backscatter profile.It is shown that the cloud radiative temperature can be derived a posteriori from CALIOP cloud extinction profiles, leading to quantified estimates of biases in the IIR standard products.IIR standard absorption optical depths are found to be underestimated by 1 to 17 % with biases that increase with geometric thickness and optical depth and that can be corrected a posteriori.This analysis is restricted to semi-transparent clouds with visible optical depths smaller than 2.5.In addition, IIR absorption optical depths are retrieved after correcting the observed calibrated radiances for contributions from the background radiance, which is constrained by neighboring observations if possible or otherwise derived from computations using a radiative transfer model and ancillary data.These two distinct sets of retrievals are assessed separately through comparisons with CALIOP.A better agreement of their τ vis /τ a ratios is found after correction for the cloud radiative temperature.Differences are up to 7 % at 2τ a = 0.7 for the coldest clouds (203-213 K), which could be explained by biases of up to 1.1 K in the computations, even though actual differences cannot be ruled out.A specific assessment of background radiances computed in clear sky conditions is being conducted to aid in the development of future versions of the IIR data products.
Selection biases in CALIOP constrained retrievals are evidenced for visible optical depths smaller than about 0.6.The standard version 3 CALIOP constrained retrievals are conducted only when the relative uncertainty in the derived lidar ratio is estimated to be less than 40 %.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 %.Eliminating the 40 % relative uncertainty restriction substantially improves the comparisons with the IIR retrievals at small optical depths while at the same time substantially increasing the number of layers included in the study.
The retrieved τ vis /τ a ratios exhibit an unexpected quasi-linear dependence with temperature at layer centroid altitude T c .The observed values increase by about 10 % for Introduction

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Full 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 optical depth retrievals.This "bulk" multiple scattering factor derived by reconciling the observed and expected ratios of CALIOP visible to IIR infrared absorption optical depth is found to decrease from η T = 0.8 at T c = 200 K to η T = 0.5 at T c = 240 K for clouds of optical depth larger 0.3, and to be equal to 0.6 on average.The temperature-dependence of η T retrieved from this study is deemed plausible according to simplified estimates of key parameters driving the multiple scattering factor.The next steps in the assessment would be to perform detailed simulations in order to improve the accuracy of the current results.These findings imply that CALIOP optical depth and extinction coefficients 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 microphysical parameters, 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 from the CALIOP active lidar.Understanding and estimating biases, even for a limited data set, allows refining uncertainty Introduction

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Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 4 Comparison of IIR and CALIOP retrievals 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.4.1 Systematic errors: IIR 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 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 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. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | each 10 K decrease in temperature over a range from T c = 240 K down to T c = 200 K.