## 1. Introduction

Microphysical properties of ice clouds are important to radiation budget analysis but are still difficult to retrieve accurately because of their natural variability, their radiative properties, and the frequent multilayered cloud structure. Ice crystal effective diameters and ice water path retrievals have been performed from spaceborne passive instruments such as the Moderate Resolution Imaging Spectroradiometer (MODIS) on *Terra* and *Aqua* (Platnick et al. 2003), Meteosat Second Generation–Spinning Enhanced Visible and Infrared Imager (MSG-SEVIRI; Bugliaro et al. 2011), and Advanced Very High Resolution Radiometer (AVHRR; Roebeling et al. 2006), mostly using a combination of observations in the visible and near-infrared spectral domain (Nakajima and King 1990). Retrievals have also been performed in the 8–12-*μ*m atmospheric window from a number of spectral bands of various resolutions, using the split-window technique (Inoue 1985). The technique relies on the spectral signature of cirrus clouds in this domain, which is related to the varying absorption by ice (Warren 1984; Warren and Brandt 2008), the cirrus microphysical properties, and meteorological and surface parameters. The spectral signature has been analyzed in terms of interchannel brightness temperature differences (BTD) by using radiative transfer models to simulate the observations and ultimately retrieve the cloud optical and microphysical properties from daytime or nighttime operation (Ackerman et al. 1990, 1995; Duda et al. 1998; Chiriaco et al. 2004; Yue et al. 2007; Wang et al. 2011). The cirrus spectral signature can also be analyzed in terms of interchannel effective emissivity differences as applied to the high spectral resolution Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS; Stubenrauch et al. 1999; Rädel et al. 2003) and Atmospheric Infrared Sounder (AIRS; Guignard et al. 2012, hereinafter Gui12). A third approach based on the concept of microphysical index has also been proposed by Parol et al. (1991) to minimize the contribution of cloud optical depth in the ice cloud spectral signature analysis. The microphysical index was originally defined as the ratio of the effective optical depths in the AVHRR channels centered at 12 and 11 *μ*m. This concept, further tested by Giraud et al. (1997) using radiometric data only, has been applied to the analysis of our data for the *Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations* (*CALIPSO*) mission. It has also been considered for existing and future datasets (Heidinger and Pavolonis 2009; Heidinger et al. 2010; Pavolonis 2010). The representativeness and accuracy of the retrievals in the thermal infrared are conditioned by the scene identification. Using passive sensors, the cloud altitude is derived from multispectral analysis and most accurately by the CO_{2} slicing method (Stubenrauch et al. 1999; Rädel et al. 2003). Lidar and radar active sensors recently implemented in the A-Train offer improved cloud boundary retrievals (Stubenrauch et al. 2010).

This paper describes the operational retrieval of ice cloud particle effective diameter and cloud ice water path from the *CALIPSO* Imaging Infrared Radiometer (IIR) by taking advantage of the range-resolved inputs provided by the perfectly collocated *CALIPSO* lidar [Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP)] observations. The three IIR channels are centered at 8.65, 10.6, and 12.05 *μ*m, with medium spectral resolutions of 0.6–1 *μ*m (Corlay et al. 2000). The onboard calibrated radiances have been validated by comparison with airborne observations (Sourdeval et al. 2012). The IIR level-2 operational algorithm uses the concept of microphysical index applied to the pairs of channels (12.05, 10.6) and (12.05, 8.65). Those indices can be primarily related to the ice crystal effective diameter and shape through lookup tables (LUT) assuming that the ice crystals can be modeled. They are computed from the effective emissivity in each channel, as detailed in the first part of this paper (Garnier et al. 2012, hereinafter G1). This approach is being used for the first time to operationally derive ice crystal microphysical properties. An overview of the analysis is provided in section 2, followed by the presentation of the effective diameter retrievals in section 3. The sources of uncertainties are described and illustrated in section 4. Results are shown and discussed in section 5 before ending with conclusions in section 6.

## 2. Microphysical properties analysis

### a. Definitions

*z*) profile is obtained from the local volume distribution

*V*(

*D*,

*L*,

*z*) of the ice crystals of width

*D*and length

*L*, at a given altitude

*z*in the cloud as

*ρ*is the density of solid ice (approximately 9.17 × 10

_{i}^{2}kg m

^{−3}), and

*n*(

*D*,

*L*,

*z*) is the size distribution as a function of altitude. The effective diameter

*D*is defined from the ratio of the volume to the projected area over the whole size distribution, and for nonspherical particles, over the various shapes. Mitchell (2002) showed that by analogy with spheres, and by using the projected area-to-extinction relationship, IWC and the extinction coefficient

_{e}*α*can be linked through the effective diameter

*D*as

_{e}*Q*is the extinction efficiency representing the entire size distribution, which, assuming that the cirrus particle sizes are much larger than the wavelength at which the extinction is retrieved, is equal to 2. Retrieving the ice water content from the extinction only, as for example derived from the CALIOP lidar, is thus equivalent to using a formulation of the effective diameter as a function of extinction and ice water content. The observations by McFarquhar et al. (2003, hereinafter McF03) shown in section 5 are reported for

_{e}*D*defined from Eq. (2), which is proportional to the diameter

_{e}*D*

_{ge}defined in McF03 following Fu and Liou (1993) and Fu (1996), so that

*τ*, and

*D*is usually given by

_{e}*μ*m OD

_{eff}, and the integrated effective diameter 〈

*D*〉 is derived using Eq. (2), assuming

_{e}*Q*= 2, such as

_{e}*D*and IWP are in micrometers and grams per meter squared, respectively. It is to be noticed that the extinction efficiencies

_{e}*Q*derived by Fu et al. (1998) in the infrared using finite-difference time domain (FDTD) calculations are slightly larger than 2. In our simplified expression, the extinction optical depth at 12.05

_{e}*μ*m is taken equal to 2 times the effective optical depth inferred from the effective emissivity (see G1 for details), which assumes that OD

_{eff}is purely an absorption optical depth, with no contribution from multiple scattering, and that the scattering albedo is equal to 0.5 over the full range of sizes. This simplification biases the IWP by about +10% for

*D*= 20

_{e}*μ*m and ±5% for

*D*> 30

_{e}*μ*m. Comparisons with the expression given by Eq. (4) and used by Dubuisson et al. (2008) show that our IWP derived from Eq. (5) is overall larger by 15%–20%. On the other hand, it is by 10%–25% smaller than simulated by Gui12, who use different crystal optical properties.

### b. IIR data analysis

*ɛ*

_{eff,08},

*ɛ*

_{eff,10}, and

*ɛ*

_{eff,12}are the effective emissivities retrieved at 8.65, 10.6, and 12.05

*μ*m, respectively. Then, LUTs are screened to extract the effective diameters derived from the

_{e}12/08) and 12/10 (D

_{e}12/10) diameters is retained. The effective diameter

*D*is taken as the mean of D

_{e}_{e}12/08 and D

_{e}12/10, whereas the quantity defined as (D

_{e}12/08 − D

_{e}12/10)/2 represents the disagreement between both diameters. Finally, the algorithm provides an estimate for the cloud ice water path determined from its effective optical depth at 12.05

*μ*m and

*D*. The three parameters OD

_{e}_{eff},

*D*, and IWP are retrieved sequentially, first under the lidar track and then spread to the IIR swath using homogeneity criteria based on radiative equivalence as described in G1.

_{e}## 3. Retrieval of effective diameters

### a. The microphysical indices

The effective microphysical indices *ɛ*12–10 = *ɛ*_{eff,12} − *ɛ*_{eff,10} and Δ*ɛ*12–08 = *ɛ*_{eff,12} − *ɛ*_{eff,08}. As the emissivity approach is closer to the BTD analysis first used in the split-window and more familiar, both approaches are discussed in parallel. As an illustration, Fig. 1 shows the variation of Δ*ɛ*12–10 (Fig. 1a) and *ɛ*_{eff,12} computed using the FASDOM model for a cloud composed of solid columns of effective diameters between 11 and 80 *μ*m. Figures 2a and 2b show the same results for the 12/08 pair. The computations assume an isothermal cloud, simulating the cloud-layer equivalent temperature inferred from the CALIOP centroid altitude of the 532-nm attenuated backscatter coefficient in the operational algorithm (see G1). It is seen that the dependence on emissivity almost disappears in the microphysical index approach.

As in Fig. 1, but for Δɛ12−08 and β_{eff}12/08 and a different vertical scale.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

As in Fig. 1, but for Δɛ12−08 and β_{eff}12/08 and a different vertical scale.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

As in Fig. 1, but for Δɛ12−08 and β_{eff}12/08 and a different vertical scale.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

*ω*is the single-scattering albedo,

_{κ}*g*is the asymmetry factor, and

_{κ}*Q*is the extinction efficiency in the IIR channels 12.05

_{κ}*μ*m (noted

*k*= 12) and 10.6

*μ*m (

*k*= 10). Similarly, superimposed in Fig. 2b is

*μ*m and for the 12/08 pair. To account for the residual variation with the effective emissivity, the IIR analysis uses a set of LUTs chosen so that β

_{eff}12/

*k*is sampled with a step of the order of the expected random noise. Nevertheless, these simulations show that the approximate values, independent of the effective emissivity, are relevant for quick studies such as comparisons of crystal models.

The sensitivity of the split-window technique decreases for optically very thin and very thick cirrus clouds, with effective emissivity differences (Figs. 1a and 2a) tending to 0, allowing consistency checks, as shown in section 4. The varying sensitivity of the method with *ɛ*_{eff,12} propagates to the uncertainties in the microphysical indices, as discussed in section 4.

### b. Crystal models and size retrievals

The relationship between the microphysical indices β_{eff}12/10 and β_{eff}12/08 derived from the IIR analysis is used to determine the family of crystal models that agrees the best with the observations. The effective diameter *D _{e}* is then retrieved from a reference model chosen as representative of the selected family. The choice of the reference models used in the algorithm is presented and discussed in the following subsections.

#### 1) Crystal shape

The seven models available in the precomputed database have been compared in terms of microphysical indices using Eq. (7) and assuming a monodisperse distribution. Results are plotted in Figs. 3a and 3b showing β_{eff}12/10 against *D _{e}* and β

_{eff}12/08, respectively. Figure 3a shows more directly than Fig. 1b that the sensitivity of the method decreases as the effective diameter increases [the derivative of

*β*

_{eff}(

*D*) is about 10 times larger at 10

_{e}*μ*m than at 50

*μ*m]. It also shows that the sensitivity to the crystal model increases at large diameters. As seen in Fig. 3b, the models can be better distinguished through the relationship between β

_{eff}12/10 and β

_{eff}12/08. Keeping in mind the expected random error on the retrieved microphysical indices estimated at ±0.025 in the best conditions (see section 4), three main families of relationships can be identified, especially for β

_{eff}12/10 smaller than 1.2 (or

*D*larger than about 25

_{e}*μ*m), with differences in β

_{eff}12/08 of about 0.1. They are a) aggregates, hollow columns, and spheroids (blue); b) bullet rosettes and plates (red); and c) solid columns and droxtals (green). Values of

*D*associated with given values of β

_{e}_{eff}12/10 are listed in Table 1 for each model in each family (a, b, and c). One model per family is selected for the operational algorithm. Aggregates, chosen in family a, are similar to hollow columns in Table 1, and characterized by the largest β

_{eff}12/08 to β

_{eff}12/10 ratio for β

_{eff}12/10 larger than 1.3 (Fig. 3b). In family b, we choose plates, whose radiative signature in terms of

*β*

_{eff}is very close to bullet rosettes. In family c, solid columns are selected, as they exhibit the smallest values of

*β*

_{eff}at large diameter. We recognize that spheroids and droxtals are not well represented for β

_{eff}12/10 around 1.05, in a range of values where the sensitivity of the method is anyways limited when compared to the random errors. However, as emphasized in Dubuisson et al. (2008), the shape can be identified as a parameter with significant impact on the radiative signature. The crystal model selection within a family could be refined by accounting for temperature. For example, in family b, plates are more frequent at temperatures between −10° and −20°C than bullet rosettes (Pruppacher and Klett 1997).

The (a) β_{eff}12/10 vs effective diameter *D _{e}* and (b) β

_{eff}12/10 vs β

_{eff}12/08 for seven of P. Yang's crystal models.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The (a) β_{eff}12/10 vs effective diameter *D _{e}* and (b) β

_{eff}12/10 vs β

_{eff}12/08 for seven of P. Yang's crystal models.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The (a) β_{eff}12/10 vs effective diameter *D _{e}* and (b) β

_{eff}12/10 vs β

_{eff}12/08 for seven of P. Yang's crystal models.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Values of the effective diameters *D _{e}* (

*μ*m) associated with given values of β

_{eff}12/10 for each model in each family for a monodisperse size distribution.

#### 2) Size distribution

As the size distribution (and the crystal models) may vary between cloud types, a simple approach was chosen in this version of the operational analysis. Indeed, the primary focus has been given to the observations and to an unbiased retrieval of the microphysical indices (see section 4) required to correctly identify the crystal family. Thus, for each family, the microphysical indices are computed for the selected reference model assuming a monodisperse size distribution. They have been compared as in Dubuisson et al. (2008) with those obtained for two monomodal distributions simulating two extreme cases. These cases are small particles in young cirrus and large particles produced by aggregation. Computations show that the size distribution does not change the relationships between β_{eff}12/10 and β_{eff}12/08 and that consequently it does not impact the selection of the crystal family. Values of *D _{e}* associated with given values of β

_{eff}12/10 for the two monomodal distributions (small and large mode) are reported in Table 2 for the three models selected earlier. No significant differences are found for the small mode, whereas the spectral response is slightly different for the large mode. For solid columns and aggregates, effective diameters derived assuming a pure large mode are larger by 12%–15% at

*D*= 30

_{e}*μ*m and 20% at

*D*= 45

_{e}*μ*m, compatible with results reported from other work (Rädel et al. 2003). This is about the same order of magnitude as other error sources as shown in the next section, where the sources of uncertainties (random error and possible biases) and their impact on the microphysics retrievals are discussed.

Values of the effective diameters *D _{e}* (

*μ*m) associated with given values of β

_{eff}12/10 for two monomodal distributions (small and large mode) for aggregates, plates, and solid columns selected as representative of the families a, b, and c, respectively.

## 4. Sensitivity analysis and uncertainties

### a. Microphysical indices

The effective microphysical indices, β_{eff}12/*k*, are a function of the effective emissivities *ɛ*_{eff,12} and *ɛ*_{eff,k} at 12.05 *μ*m and in channel *k*. We discuss first the sources of uncertainties in the difference Δ*ɛ*12−*k* = *ɛ*_{eff,12} − *ɛ*_{eff,k}, and then present their impact on β_{eff}12/*k*.

*k*, the effective emissivity

*ɛ*

_{eff,k}is retrieved as described in G1:

*R*is the calibrated radiance measured in channel

_{k}*k*. The term

*R*

_{k}_{,BG}is the background radiance in channel

*k*, that is, the radiance which would be observed in the absence of the studied cloud. Finally,

*B*(

_{k}*T*,

_{c}*Z*) is the radiance of a blackbody source located at the reference altitude

_{c}*Z*of thermodynamic temperature

_{c}*T*retrieved from ancillary meteorological data. Upper-layer effective emissivities are retrieved for two main categories of background scenes, either the surface or an opaque layer. Furthermore, the background radiances are determined preferably from observations in neighboring pixels at a maximum distance of 100 km to minimize biases. If no suitable observations can be found, they are computed using the Fast-Calculation Radiative Transfer (FASRAD) model (Dubuisson et al. 2005) adapted to the IIR spectral functions and ancillary and atmospheric data. The FASRAD model is also used to compute the blackbody radiance assuming that the equivalent radiative altitude of the cloud

_{c}*Z*is located at the centroid altitude of the cloud layer as determined by the CALIOP algorithm (see G1 for more details).

_{c}*ɛ*12−

*k*in Δ

*ɛ*12−

*k*is composed of three terms associated with errors on the measurement, the background radiance, and the blackbody radiance for the channels 12 and

*k*, respectively, as

_{eff}12/

*k*on the microphysical index β

_{eff}12/

*k*is composed of three terms such as

*x*refers either to

*m*, BG, or BB as defined previously.

As in G1, the uncertainties are discussed in terms of equivalent brightness temperature uncertainties in the measured, background and blackbody radiances for the channels 12 and *k* named dT_{m,12} and dT_{m,k}, dT_{BG,12} and dT_{BG,k}, and dT_{BB,12} and dT_{BB,k}, respectively. The effective emissivity uncertainties per kelvin of brightness temperature error for each contributor shown in G1 at 12.05 *μ*m are similar for the other channels. The approach to compute dΔ*ɛ*12−*k*_*x* for each contributor *x* is detailed in the next three subsections, followed by the simulation of the overall uncertainty in dΔ*ɛ*12−*k* and β_{eff}12/*k*. The simulations are for background and blackbody radiances corresponding to 280 and 220 K, respectively. The radiative contrast of 60 K is chosen to simulate conditions typically observed for single-layered cirrus clouds, as discussed in G1. Finally, the β_{eff}12/10 and β_{eff}12/08 indices are taken equal to 1.1, simulating cirrus clouds composed of solid columns of 38-*μ*m effective diameter. Results are reported in Table 3.

Random uncertainty estimates assuming background and blackbody radiances equivalent to 280 and 220 K, respectively. See text for details.

#### 1) Error on the radiometric measurements

The error due to the measurement dΔ*ɛ*12−*k*_*m* [Eq. (9a)] is computed assuming that the uncertainties dT_{m,12} and dT_{m,k}, in the brightness temperatures measured at 12.05 *μ*m and in channel *k* are not correlated. It is computed using the radiometric performances of typically 0.15–0.3 K (see G1 for details) assessed by Centre National d'Études Spatiales (CNES).

#### 2) Errors on the background radiances

As seen in section 3, the difference in emissivity tends to zero (see Fig. 2a), and the microphysical index remains constant (see Fig. 2b), when the effective emissivity *ɛ*_{eff,12} tends to 0. This condition is fulfilled when the background radiance *R _{k}*

_{,BG}is correctly determined in each of the three IIR channels. This property is used to check for the existence of a bias in the determination of the background radiances by comparing the background brightness temperatures (BTs) determined from neighboring observations with those derived from the radiative transfer model, also reported in the IIR products.

The BT distributions of the differences between computations and observations are shown in Fig. 4 for the 12.05-*μ*m channel (Fig. 4a), and for the 12–10 (Fig. 4b) and 12–08 (Fig. 4c) interchannel differences. The median value and standard deviation of the computed minus observed differences at 12.05 *μ*m are −0.05 and 1.7 K, respectively, showing no major bias in the retrieval at this wavelength. A small bias is however observed in the interchannel difference for 12–10 (−0.3 ± 0.4) K, slightly larger for 12–08 (−0.8 ± 0.6) K. This case study is for high-altitude (>7 km) single-layered cirrus clouds with no aerosols (type 21 and 40; see G1) of temperature *T _{c}* at the centroid altitude

*Z*smaller than 233 K, over ocean during January 2011. The impact of these differences is clearly seen in Fig. 5 showing the median value of Δ

_{c}*ɛ*12−

*k*(Fig. 5a) and β

_{eff}12/

*k*(Fig. 5b) versus

*ɛ*

_{eff,12}for the background radiances retrieved from the neighboring observations (solid lines) and from the computations (dashed lines). For observed background radiances and

*ɛ*

_{eff,12}tending to 0, the median values of Δ

*ɛ*12–08 and Δ

*ɛ*12–10 are −0.002 corresponding to residual biases of about −0.1 K. One can still see the existence of a small bias with a change of slope for

*ɛ*

_{eff,12}smaller than 0.02, behavior that is better evidenced in the microphysical index approach (Fig. 5b). These residual biases are smaller than the radiometric measurement error of 0.14–0.18 K expected at warm brightness temperatures (see G1) for clear scenes over the ocean and are barely significant. As for computed background radiances, we find negative effective emissivity differences dΔ

*ɛ*12/10_BG = −0.003 and dΔ

*ɛ*12/08_BG = −0.015 for

*ɛ*

_{eff,12}tending to 0 because of the biases shown in Figs. 4b and 4c. The difference between β

_{eff}12/

*k*derived from computed and observed radiances shown in Fig. 5b is significant. As expected from Eq. (9b), the difference decreases with increasing

*ɛ*

_{eff,12}. In this example, it is 0.02 or more when

*ɛ*

_{eff,12}is smaller than 0.4 for β

_{eff}12/10, and

*ɛ*

_{eff,12}smaller than 0.8 for β

_{eff}12/08. We find that for

*ɛ*

_{eff,12}from 0 to 0.1 (from 0.1 to 0.2), 100%–60% (60%–25%) of the values of β

_{eff}12/

*k*derived from computations do not fall in the range of values expected from the LUTs (see Fig. 3), preventing the algorithm from attempting microphysics retrievals. Still, the algorithm is able to perform retrievals at larger emissivity, but the errors on β

_{eff}12/

*k*bias the crystal model selection and the effective diameter retrievals toward too-large values in this case. On the contrary, when observed background radiances are used, microphysics retrievals are obtained in 50% of the cases for

*ɛ*

_{eff,12}~ 0, with this percentage increasing to 75% for

*ɛ*

_{eff,12}= 0.1 and 90% for

*ɛ*

_{eff,12}= 0.3 as the random noise decreases, as discussed at the end of this section. The products derived when a clear-air observed reference is available are thus more accurate and should be considered preferentially in the analyses.

Distribution of differences between computed and observed background brightness temperatures over ocean at (a) 12.05 *μ*m and for the (b) 12–10 and (c) 12–08 interchannel differences. Note that the horizontal scale in (a) is 2 times that of (b) and (c).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Distribution of differences between computed and observed background brightness temperatures over ocean at (a) 12.05 *μ*m and for the (b) 12–10 and (c) 12–08 interchannel differences. Note that the horizontal scale in (a) is 2 times that of (b) and (c).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Distribution of differences between computed and observed background brightness temperatures over ocean at (a) 12.05 *μ*m and for the (b) 12–10 and (c) 12–08 interchannel differences. Note that the horizontal scale in (a) is 2 times that of (b) and (c).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

(a) Median Δɛ12−*k* and (b) median β_{eff}12/*k* (black: 12–10; gray: 12–08) against *ɛ*_{eff,12} for single-layer high-altitude (>7 km) ice cirrus (*T _{c}* < 233 K) clouds (no aerosols), over ocean during January 2011. Background radiances are from neighboring observations (solid lines) or from computations (dashed lines).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

(a) Median Δɛ12−*k* and (b) median β_{eff}12/*k* (black: 12–10; gray: 12–08) against *ɛ*_{eff,12} for single-layer high-altitude (>7 km) ice cirrus (*T _{c}* < 233 K) clouds (no aerosols), over ocean during January 2011. Background radiances are from neighboring observations (solid lines) or from computations (dashed lines).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

(a) Median Δɛ12−*k* and (b) median β_{eff}12/*k* (black: 12–10; gray: 12–08) against *ɛ*_{eff,12} for single-layer high-altitude (>7 km) ice cirrus (*T _{c}* < 233 K) clouds (no aerosols), over ocean during January 2011. Background radiances are from neighboring observations (solid lines) or from computations (dashed lines).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Similar studies have been performed to assess the relevance of the microphysical indices retrieved in case of semitransparent high-altitude (>7 km) single-layered cirrus (*T _{c}* < 233 K) clouds overlying a low (<7 km) opaque cloud (type 31; see G1). The results are shown in Figs. 6 and 7 similarly as in Figs. 4 and 5, respectively. The only difference is that the background radiance is not taken as corresponding to the surface, but to the underlying low opaque cloud. Here, the median value of the computed minus observed BT differences seen in Fig. 6 is rather large (2.1 ± 2.2) K at 12.05

*μ*m, consistent with results discussed in G1. By contrast, the interchannel differences remain comparable to the clear-air case, with even smaller discrepancies in absolute value equal to (0.2 ± 0.6) K for 12–10 and (−0.3 ± 0.6) K for 12–08. We observe a 0.5-K difference between both interchannel BTDs as for clear air. For computed background radiances, the combination of the errors on

*ɛ*

_{eff,12}and

*ɛ*

_{eff,k}leads to the unrealistic interchannel effective emissivity differences seen in Fig. 7a (dashed lines). However, for observed background radiances (solid lines), the median values of Δ

*ɛ*12–10 and Δ

*ɛ*12–08 show the expected behavior versus

*ɛ*

_{eff,12}, even though a residual bias of −0.004 at

*ɛ*

_{eff,12}= 0 is still present, inducing the rapid decrease of β

_{eff}12/

*k*seen in Fig. 7b for

*ɛ*

_{eff,12}< 0.05. We can see that the impact on the microphysical index 12–8 is very strong, which precludes any accurate retrieval using computed background radiances. This is possibly due to the scattering contribution not accounted for in the determination of the low cloud background radiance using FASRAD. Second-order corrections should be considered in the next version of the algorithm using tabulated values to maintain a short processing time.

As in Fig. 4, but for low opaque clouds.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

As in Fig. 4, but for low opaque clouds.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

As in Fig. 4, but for low opaque clouds.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

As in Fig. 5, but for cirrus overlying a low (<7 km) opaque cloud.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

As in Fig. 5, but for cirrus overlying a low (<7 km) opaque cloud.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

As in Fig. 5, but for cirrus overlying a low (<7 km) opaque cloud.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

In the following, the discussion is limited to the cases for which the background radiance could be derived from observations rather than from computations. This makes it possible to attempt the microphysical retrievals for clouds of very small emissivity over ocean, as well as over land, and in the case of a semitransparent overlying a low opaque cloud. Consequently, the error dΔ*ɛ*12−*k*_BG is simulated assuming that the uncertainties dT_{BG,12} and dT_{BG,k} in the brightness temperatures measured at 12.05 *μ*m and in channel *k* are due to the radiometric noise and are not correlated. As expected, the error dΔ*ɛ*12−*k*_BG (see Table 3) decreases as *ɛ*_{eff,12} increases. Further studies are needed to improve the accuracy of the computed background radiances for future versions of the algorithm.

#### 3) Errors on the blackbody radiances

The blackbody radiance *B _{k}*(

*T*,

_{c}*Z*) is computed using FASRAD assuming that the equivalent radiative altitude of the cloud

_{c}*Z*is located at the centroid altitude of the cloud layer as determined by the CALIOP algorithm. The error dΔ

_{c}*ɛ*12−

*k*_BB [Eq. (9c)] is simulated knowing that the uncertainties dT

_{BB,12}and dT

_{BB,k}in the blackbody brightness temperatures are not independent, as they are retrieved from FASRAD using the same meteorological data. The interchannel differences mostly depend on the amount of water vapor above the high-altitude cloud derived from the meteorological data and are typically equal to a few tenths of a kelvin (depending on altitude and latitude, and typically less than 0.3 K for high clouds above 7 km). Also, as mentioned earlier, the computations of the blackbody temperatures with FASRAD do not include multiple scattering. Comparisons with FASDOM, which accounts for multiple scattering, show a good agreement within 0.3 K for effective diameters larger than 10

*μ*m at both 12.05 and 10.6

*μ*m, and for crystal sizes larger than 30

*μ*m at 8.65

*μ*m. However, FASRAD overestimates the 08.65-

*μ*m blackbody temperature by about 1 K for sizes of the order of 10

*μ*m. As a result, the microphysical index β

_{eff}12/08 is in those cases underestimated by about 0.05 at

*ɛ*

_{eff,12}= 0.9 and by 0.10 at

*ɛ*

_{eff,12}= 0.95. Nevertheless, because of the very large sensitivity of the method for sizes of 10

*μ*m (Fig. 3a), the error on

*D*would not exceed a few micrometers. To more extensively quantify this error, calculations have been performed assuming dT

_{e}_{BB,12}= ±1 K to include an error on

*T*inferred from the equivalent radiative altitude, and with dT

_{c}_{BB,12}− dT

_{BB,k}= ±0.1 K assuming an error of 30% due to the relative humidity. The resulting error dΔ

*ɛ*12−

*k*_BB reported in Table 3 increases with

*ɛ*

_{eff,12}, as expected. As the error is further increasing beyond acceptable values at larger emissivities, we will have to limit the analysis domain in the upper range, as will be discussed in next subsection.

#### 4) Overall uncertainty

*ɛ*12−

*k*is computed assuming that the three sources of uncertainty previously discussed are independent, so that the overall error is written

*ɛ*12−

*k*derived from Eq. (10) and corresponding errors on β

_{eff}12/

*k*are reported in Table 3 and shown in Figs. 8a and 8b, respectively. These estimates are for retrievals at the IIR pixel resolution of 1 km. Even though dΔ

*ɛ*12−

*k*vary by less than 40% with

*ɛ*

_{eff,12}, dβ

_{eff}12/

*k*is 3 times larger at small (

*ɛ*

_{eff,12}= 0.1) and large (

*ɛ*

_{eff,12}= 0.96) effective emissivity than in the medium range (

*ɛ*

_{eff,12}from 0.3 to 0.85), where the estimated random error is ±0.025. Indeed, the microphysical index β

_{eff}12/

*k*is primarily a measure of the microphysical properties, whereas the variation with

*ɛ*

_{eff,12}of its uncertainty reflects the varying sensitivity of the technique. Nevertheless, the retrievals will be attempted down to

*ɛ*

_{eff,12}~ 0.0, using measured references, which allows for reducing the errors as discussed earlier. For the largest emissivities, the main unknowns in the error estimates are possible biases in the computation of the blackbody radiances. Indeed, Fig. 5a shows that Δ

*ɛ*12–08 and Δ

*ɛ*12–10 do not tend to 0 when

*ɛ*

_{eff,12}tends to 1 but to a residual value of 0.003–0.005. On the other hand, we observe that Δ

*ɛ*12−

*k*steadily decreases with increasing

*ɛ*

_{eff,12}as expected, showing a minimum at

*ɛ*

_{eff,12}= 0.95. This suggests that

*ɛ*

_{eff,12}is underestimated and should be closer to 1 for this population of clouds. As these clouds typically fully attenuate the CALIOP beam, the centroid altitude

*Z*can be too high,

_{c}*T*too small, and consequently

_{c}*ɛ*

_{eff,12}can be underestimated. There is unfortunately no straightforward consistency check available to the IIR algorithm to accurately assess the errors at very large emissivity. Therefore, we choose to limit the retrievals to

*ɛ*

_{eff,12}smaller than 0.95 where the error on the microphysical indices stays within ±0.05 according to the simulations.

Overall uncertainty estimates for (a) dΔɛ12−*k* and (b) dβ_{eff}12/*k* against *ɛ*_{eff,12} for β_{eff}12/*k* = 1.1.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Overall uncertainty estimates for (a) dΔɛ12−*k* and (b) dβ_{eff}12/*k* against *ɛ*_{eff,12} for β_{eff}12/*k* = 1.1.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Overall uncertainty estimates for (a) dΔɛ12−*k* and (b) dβ_{eff}12/*k* against *ɛ*_{eff,12} for β_{eff}12/*k* = 1.1.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

### b. Effective diameter

In this subsection, we present the uncertainty in the retrievals of *D _{e}* directly driven by the errors on the microphysical indices and assume that the LUTs have been correctly determined (see discussions in section 3). The IIR algorithm is presently designed to constrain the retrieval by selecting the crystal family that minimizes the difference between D

_{e}12/10 and D

_{e}12/08 on a 1-km pixel basis. Random errors on the microphysical indices can direct the algorithm to the wrong crystal family and ultimately to a wrong

*D*. Simulations have been performed to assess the errors induced by this artifact for the cases for which the background reference is retrieved from neighboring observations with no bias as discussed in section 4a and with a random noise as shown in Fig. 8. Figure 9 shows the fraction of each crystal family selected for a cloud composed entirely of aggregates (a, left-hand column), plates (b, center), and solid columns (c, right-hand column). The results are shown against the effective emissivity

_{e}*ɛ*

_{eff,12}and for “true”

*D*equal to 20

_{e}*μ*m (top), 50

*μ*m (middle), and 80

*μ*m (bottom). As expected, the selection is the most accurate when the error on the microphysical indices is the smallest, that is, for

*ɛ*

_{eff,12}typically between 0.3 and 0.9. The best scores are obtained for

*D*= 50

_{e}*μ*m because this range of diameters is where the relationship between β

_{eff}12/10 and β

_{eff}12/08 differs the most from one model to another, as seen in Fig. 3b. Families b (plates and bullet rosettes) and c (solid columns, droxtals) can be here identified with up to 100% accuracy, whereas a lower score of 80% is obtained for family a (aggregates, hollow columns, and spheroids) whose LUT is located “between” its companions. The best scores are between 60% and 85% for

*D*= 20

_{e}*μ*m and between 50% and 95% for 80

*μ*m.

Impact of a random error on the crystal family selection (a: cross; b: star; and c: plus sign) as a function of the effective emissivity *ɛ*_{eff,12} in case of families (left) a (aggregates), (center) b (plates), and (right) c (solid columns) for *D _{e}* = (top) 20, (middle) 50, and (bottom) 80

*μ*m.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Impact of a random error on the crystal family selection (a: cross; b: star; and c: plus sign) as a function of the effective emissivity *ɛ*_{eff,12} in case of families (left) a (aggregates), (center) b (plates), and (right) c (solid columns) for *D _{e}* = (top) 20, (middle) 50, and (bottom) 80

*μ*m.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Impact of a random error on the crystal family selection (a: cross; b: star; and c: plus sign) as a function of the effective emissivity *ɛ*_{eff,12} in case of families (left) a (aggregates), (center) b (plates), and (right) c (solid columns) for *D _{e}* = (top) 20, (middle) 50, and (bottom) 80

*μ*m.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Figure 10 shows the impact on the median *D _{e}* (

*y*axis) of the random error and resulting crystal model selection for a simulated cloud composed entirely of aggregates (a, left), plates (b, center), and solid columns (c, right) of specified

*D*(

_{e}*x*axis). The results are shown for

*ɛ*

_{eff,12}equal to 0.1, 0.5, and 0.9. The simulations show that

*D*is correctly retrieved for

_{e}*D*smaller than 40

_{e}*μ*m over the full range of effective emissivity and for the three families thanks to the large sensitivity of the method, which outscores the random errors on the microphysical indices and the erroneous crystal selections. The ability to well classify family b even for large diameters allows a bias smaller than 6% up to

*D*= 100

_{e}*μ*m. For a cloud supposedly composed of solid columns (respectively aggregates), the misclassifications induce a positive (respectively negative) bias. The bias is the largest at

*ɛ*

_{eff,12}= 0.1, representing up to 30% (respectively −20%) at

*D*= 80

_{e}*μ*m for solid columns (respectively aggregates). For

*ɛ*

_{eff,12}= 0.5 (respectively 0.9), the bias remains smaller than 10% (respectively 25%) up to

*D*= 80

_{e}*μ*m. The standard deviations associated with the median values shown in Fig. 10 are plotted in Fig. 11. They increase with

*D*, as the sensitivity of the method weakens and are much larger at

_{e}*ɛ*

_{eff,12}= 0.1 than at

*ɛ*

_{eff,12}= 0.5 or 0.9 because of the larger errors on the microphysical indices. These results are summarized in Table 4.

Impact of the random error and crystal family selection on the median value of *D _{e}* (

*y*axis) for a specified

*D*(

_{e}*x*axis) in family (left) a, (center) b, and (right) c for

*ɛ*

_{eff,12}= 0.1 (plus sign), 0.5 (cross), and 0.9 (star).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Impact of the random error and crystal family selection on the median value of *D _{e}* (

*y*axis) for a specified

*D*(

_{e}*x*axis) in family (left) a, (center) b, and (right) c for

*ɛ*

_{eff,12}= 0.1 (plus sign), 0.5 (cross), and 0.9 (star).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Impact of the random error and crystal family selection on the median value of *D _{e}* (

*y*axis) for a specified

*D*(

_{e}*x*axis) in family (left) a, (center) b, and (right) c for

*ɛ*

_{eff,12}= 0.1 (plus sign), 0.5 (cross), and 0.9 (star).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Simulation of the standard deviation of *D _{e}* (%) in case of family (left) a, (center) b, and (right) c for

*ɛ*

_{eff,12}= 0.1 (plus sign), 0.5 (cross), and 0.9 (star).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Simulation of the standard deviation of *D _{e}* (%) in case of family (left) a, (center) b, and (right) c for

*ɛ*

_{eff,12}= 0.1 (plus sign), 0.5 (cross), and 0.9 (star).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Simulation of the standard deviation of *D _{e}* (%) in case of family (left) a, (center) b, and (right) c for

*ɛ*

_{eff,12}= 0.1 (plus sign), 0.5 (cross), and 0.9 (star).

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Values in percent of the effective diameters *D _{e}* biases and standard deviations (in parentheses) for given values of

*D*and three effective emissivities (0.1, 0.5, and 0.9) for aggregates, plates, and solid columns selected as representative of the families a, b, and c, respectively.

_{e}## 5. Results and discussions

### a. Effective diameter

The data have been first analyzed for high-altitude (>7 km) semitransparent (ST) single-layered ice cirrus (*T _{c}* < 233 K) clouds (from type 21 and 30; see G1) over ocean between 60°S and 60°N during January 2011, after selecting the pixels for which the background radiance could be determined from observations, as discussed previously. Figure 12a shows the 2D histogram of the effective diameter

*D*= (D

_{e}_{e}12/08 + D

_{e}12/10)/2 as a function of the effective emissivity

*ɛ*

_{eff,12}. The differential in

*D*due to the averaging of D

_{e}_{e}12/08 and D

_{e}12/10 is defined as D

_{e}_u = (D

_{e}12/08 − D

_{e}12/10)/2. The 2D histogram of D

_{e}_u and

*ɛ*

_{eff,12}is shown in Fig. 12b. The black dots in Figs. 12a and 12b are the median values in each bin of effective emissivity. Figure 12b shows that a good agreement between the two pairs of channels is obtained on average with a median value of D

_{e}_u smaller than 1.5

*μ*m, and a standard deviation of about 8

*μ*m. The median

*D*(Fig. 12a) increases rapidly from 18 to 34

_{e}*μ*m between

*ɛ*

_{eff,12}= 0 and 0.1, then up to 45

*μ*m at

*ɛ*

_{eff,12}= 0.7. The observed standard deviation is about 17

*μ*m at all emissivities. It includes the contribution of the random errors, whose estimates are 10–13

*μ*m for

*ɛ*

_{eff,12}= 0.1 and

*D*= 30

_{e}*μ*m, decreasing to 4

*μ*m for

*ɛ*

_{eff,12}= 0.5 and

*D*= 40

_{e}*μ*m (Fig. 11). The observed standard deviation appears to be larger but consistent with our simulations. This is a fair agreement, keeping in mind the unknown contribution of the natural variability of the cloud microphysical properties, and the limited sampling causing the number of points to decrease as the effective diameter increases. Figure 13 shows the crystal model occurrence corresponding to Fig. 12. The fraction of family c (solid columns and droxtals) is seen to be preponderant. It, however, decreases from 65% at

*ɛ*

_{eff,12}= 0.1 to 50% at

*ɛ*

_{eff,12}= 0.6, whereas the fraction of family a (aggregates, hollow columns or spheroids) steadily increases from about 15% to 30%. The fraction of family b crystals (plates or bullet rosettes) stays almost constant between 15% and 20%. Comparison of aggregate occurrence as a function of emissivity to results previously reported by Gui12 shows that family a (aggregates and hollow columns) exhibits behavior similar to a 6-yr climatology from AIRS (Gui12, their Fig. 4). However, the occurrence fractions obtained in our analysis are about half as large. Note that while Gui12 use 6 channels in the 8–12-

*μ*m region and more elaborated crystal model assumptions, their cloud detection scheme relies on passive radiometry, leading them to consider only clouds with emissivities larger than 0.2. According to the simulations in Fig. 9 for aggregates and

*D*= 20 or 50

_{e}*μ*m, random errors could introduce a low bias in the aggregate-like shape occurrence as

*ɛ*

_{eff,12}decreases. Nevertheless, no significant bias of the median

*D*is to be expected because of erroneous aggregate shape detection as

_{e}*D*is in the range of 20–40

_{e}*μ*m where simulations indicate a limited impact of the crystal model selected (Fig. 10).

The 2D histogram of (a) the effective diameter *D _{e}* and (b) D

_{e}_u = (D

_{e}12/08 − D

_{e}12/10)/2, and the effective emissivity

*ɛ*

_{eff,12}for high-altitude (>7 km) semitransparent single-layered ice cirrus (

*T*< 233 K) clouds over ocean between 60°S and 60°N during January 2011. The color code represents the decimal logarithm of the number of points. The superimposed small black dots are the median values in each bin of effective emissivity.

_{c}Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The 2D histogram of (a) the effective diameter *D _{e}* and (b) D

_{e}_u = (D

_{e}12/08 − D

_{e}12/10)/2, and the effective emissivity

*ɛ*

_{eff,12}for high-altitude (>7 km) semitransparent single-layered ice cirrus (

*T*< 233 K) clouds over ocean between 60°S and 60°N during January 2011. The color code represents the decimal logarithm of the number of points. The superimposed small black dots are the median values in each bin of effective emissivity.

_{c}Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The 2D histogram of (a) the effective diameter *D _{e}* and (b) D

_{e}_u = (D

_{e}12/08 − D

_{e}12/10)/2, and the effective emissivity

*ɛ*

_{eff,12}for high-altitude (>7 km) semitransparent single-layered ice cirrus (

*T*< 233 K) clouds over ocean between 60°S and 60°N during January 2011. The color code represents the decimal logarithm of the number of points. The superimposed small black dots are the median values in each bin of effective emissivity.

_{c}Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Occurrence of the crystal families associated with Fig. 12.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Occurrence of the crystal families associated with Fig. 12.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Occurrence of the crystal families associated with Fig. 12.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The previous analysis for January 2011 over ocean has been extended over land, and for cirrus clouds overlying a low opaque cloud, to analyze cirrus clouds associated with different categories of background radiances. The results are reported in Fig. 14a for the effective diameter and Fig. 14b for the crystal type occurrence of families a and c. In addition, clouds classified as ST (thin lines) and opaque (thick lines) by CALIOP are distinguished. The crystal model occurrence is remarkably close for the three families of ST clouds with differences of less than 10% at low emissivity. For the opaque clouds fully attenuating the CALIOP laser beam (type 40 in G1), the solid columns occurrence increases from 0.6 to 0.8 for *ɛ*_{eff,12} greater than 0.8 both over sea and over land. The median effective diameters are similar for the three families of ST clouds, within 2–3 *μ*m for medium emissivities *ɛ*_{eff,12} ~ 0.5–0.6. We observe an excellent agreement between opaque and ST clouds over sea in the overlapping range of *ɛ*_{eff,12} between 0.5 and 0.7. For opaque clouds, *D _{e}* increases rapidly by 10

*μ*m from

*ɛ*

_{eff,12}= 0.8 up to about 60

*μ*m at

*ɛ*

_{eff,12}= 0.95

_{,}

*D*being lower over land than over sea, by about 5

_{e}*μ*m at

*ɛ*

_{eff,12}= 0.95, whereas the crystal model occurrences are identical. As these differences are seen in the larger range of emissivity, they cannot be attributed to an artifact linked to the background radiance retrievals (see section 4) and can be considered as real, notwithstanding the standard deviation of the order of 20

*μ*m. Gui12 also observe a similar increase of

*D*with

_{e}*ɛ*

_{eff,12}(see their Fig. 4), but with a larger slope at middle emissivity, for example +10%–30% (50–60

*μ*m) at

*ɛ*

_{eff,12}~ 0.6, and with

*D*rapidly decreasing for emissivities larger than 0.85, behavior that is not observed here. Wang et al. (2011) find crystal diameters in the same range of values as in our study by using a new fast radiative transfer model applied to similar MODIS channels.

_{e}(a) Median effective diameter ±1 standard deviation and (b) crystal model occurrence vs *ɛ*_{eff,12} for high-altitude (>7 km) single-layered ice cirrus (*T _{c}* < 233 K) clouds between 60°S and 60°N over ocean (black), land (red), and low opaque clouds (blue) during January 2011. Thin and thick lines are for ST and opaque clouds, respectively.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

(a) Median effective diameter ±1 standard deviation and (b) crystal model occurrence vs *ɛ*_{eff,12} for high-altitude (>7 km) single-layered ice cirrus (*T _{c}* < 233 K) clouds between 60°S and 60°N over ocean (black), land (red), and low opaque clouds (blue) during January 2011. Thin and thick lines are for ST and opaque clouds, respectively.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

(a) Median effective diameter ±1 standard deviation and (b) crystal model occurrence vs *ɛ*_{eff,12} for high-altitude (>7 km) single-layered ice cirrus (*T _{c}* < 233 K) clouds between 60°S and 60°N over ocean (black), land (red), and low opaque clouds (blue) during January 2011. Thin and thick lines are for ST and opaque clouds, respectively.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

### b. Ice water path and ice water content

*α*, which can be estimated from 2 × OD

_{eff}divided by the cloud thickness. As given in section 2, the effective diameter can be expressed as the ratio between the mean IWC and the mean extinction coefficient. Equation (2) can thus be rewritten

*D*is in micrometers, IWC is in grams per meter cubed, and

_{e}*α*is in inverse meters. We choose to analyze our retrievals in terms of relationship between

*D*and extinction, and the resulting relationship between IWC and extinction. The median

_{e}*D*is shown in Fig. 15 against α inferred from the IIR for high-altitude (>7 km) single-layered ST (thin lines) and opaque (thick line) ice cirrus clouds over ocean during January 2011. The results are shown for various temperature ranges:

_{e}*T*< 203 K (navy blue),

_{c}*T*in 203–213 K (light blue), 213–223 K (green), and 223–233 K (red), for which the fraction of ST clouds is 11%, 17%, 35%, and 37%, respectively. Opaque clouds are found mostly at 213–223 K (34%) and 223–233 K (60%). The standard deviation (not shown) is 15–20

_{c}*μ*m. The geometrical thickness is prevailingly between 0.5 and 2 km for the ST clouds with extinctions smaller than 0.001 m

^{−1}. For opaque clouds, the thickness is found to be mainly between 1 and 3 km, but these values are likely underestimated as such clouds totally attenuate the laser beam. It is seen in Fig. 15 that

*D*increases with α and temperature, between 16 and 45

_{e}*μ*m for ST clouds, and is larger for opaque clouds, up to 60

*μ*m at 223–233 K, with a fairly good overlap. A more rapid increase of

*D*with

_{e}*α*cannot be ruled out for opaque clouds, as

*α*could be overestimated. The 2D histogram of IWC and α corresponding to Fig. 15 is shown in Fig. 16, for all temperatures and extinction coefficients larger than 10

^{−4}m

^{−1}. The median IWC/

*α*ratio is between 5 ± 4.6 and 14 ± 7 g m

^{−2}for ST clouds, up to 18 ± 7 g m

^{−2}for opaque clouds. The IIR

*D*retrievals can be further compared with in situ measurements of the IWC/

_{e}*α*ratio available in the literature. The squares in Figs. 15 and 16 show the relationship derived from in situ measurements at midlatitude by Mioche et al. (2010, hereinafter M10) who proposed a relationship between IWC and

*α*of

*α*can also be obtained from the IIR for the four ranges of temperature using the coefficients reported in Table 5 (dash–dotted colored lines in Fig. 15). The IIR median

*D*increases more rapidly with

_{e}*α*than in M10, more in agreement with McF03. Considering that tropical latitudes have more cirrus than midlatitudes and that the largest extinction coefficients in opaque clouds may be overestimated reconciles these results. Average coefficients characterizing the whole global cloud population (solid curve in Fig. 16) derived using the same power-law relationship are

*a*= 75 and

*b*= 1.23.

Median effective diameter vs extinction coefficient for high-altitude (>7 km) single-layered ST (thin line) and opaque (thick line) ice cirrus clouds over ocean during January 2011 for *T _{c}* < 203K (navy blue),

*T*between 203–213 K (light blue), 213–223 K (green), and 223–233 K (red). The squares are from M10 and the triangles are from McF03. The dash–dotted color lines are best fits derived from this study.

_{c}Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Median effective diameter vs extinction coefficient for high-altitude (>7 km) single-layered ST (thin line) and opaque (thick line) ice cirrus clouds over ocean during January 2011 for *T _{c}* < 203K (navy blue),

*T*between 203–213 K (light blue), 213–223 K (green), and 223–233 K (red). The squares are from M10 and the triangles are from McF03. The dash–dotted color lines are best fits derived from this study.

_{c}Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Median effective diameter vs extinction coefficient for high-altitude (>7 km) single-layered ST (thin line) and opaque (thick line) ice cirrus clouds over ocean during January 2011 for *T _{c}* < 203K (navy blue),

*T*between 203–213 K (light blue), 213–223 K (green), and 223–233 K (red). The squares are from M10 and the triangles are from McF03. The dash–dotted color lines are best fits derived from this study.

_{c}Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The 2D histogram of ice water content and extinction coefficient for high-altitude (>7 km) single-layered ST and opaque ice cirrus clouds over sea during January 2011 for *T _{c}* < 233 K. The color code represents the decimal logarithm of the number of points. Superimposed in black and red are the median values in each bin of extinction for the ST and opaque clouds, respectively. The squares are from M10 and the triangles from McF03. The gray solid line is the best fit derived from this study.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The 2D histogram of ice water content and extinction coefficient for high-altitude (>7 km) single-layered ST and opaque ice cirrus clouds over sea during January 2011 for *T _{c}* < 233 K. The color code represents the decimal logarithm of the number of points. Superimposed in black and red are the median values in each bin of extinction for the ST and opaque clouds, respectively. The squares are from M10 and the triangles from McF03. The gray solid line is the best fit derived from this study.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

The 2D histogram of ice water content and extinction coefficient for high-altitude (>7 km) single-layered ST and opaque ice cirrus clouds over sea during January 2011 for *T _{c}* < 233 K. The color code represents the decimal logarithm of the number of points. Superimposed in black and red are the median values in each bin of extinction for the ST and opaque clouds, respectively. The squares are from M10 and the triangles from McF03. The gray solid line is the best fit derived from this study.

Citation: Journal of Applied Meteorology and Climatology 52, 11; 10.1175/JAMC-D-12-0328.1

Coefficients *a* and *b* used to link IWC (g m^{−3}) and extinction coefficient *α* (m^{−1}) through the power-law relationship IWC = *aα ^{b}*.

Overall, these results show a good consistency between the IIR microphysics retrievals and knowledge established from in situ observations only (M10) or including remote sensing measurements from the Atmospheric Radiation Measurement sites (McF03). However, the effective diameters and IWC reported in this study are lower by about 40% than those reported by Heymsfield et al. (2005).

## 6. Conclusions

The results presented in this paper have been obtained with the version-3 IIR level-2 operational algorithm for the retrieval of cirrus clouds' effective diameters and ice water path, whose definitions are presented and discussed. The analysis relies on two effective microphysical indices defined as the ratio of the effective optical depths for the pairs of channels (12.05, 10.6) and (12.05, 08.65) and uses a series of LUTs computed offline by using the FASDOM model. Three crystal families representative of main relationships between the microphysical indices are chosen from a precomputed database. The effective diameter is inferred from the crystal family that best simulates the pair of retrieved microphysical indices, assuming a monodisperse size distribution. Errors of about 15%–20% on the effective diameters due to these simplifications have been discussed. The impact of the microphysical index random error on the crystal model selection and the effective diameters retrievals has been simulated. The possible biases have been assessed through consistency checks based on effective emissivity differences. It has been shown that the retrievals of single-layered cirrus clouds can be attempted, for the first time, down to effective emissivities close to 0.05 when accurate measured background radiances can be used to reduce biases due to ancillary parameters and radiative calculations, and up to 0.95 where errors due to blackbody radiance become significant. An excellent consistency between retrievals over ocean, over land, and in the case of clouds overlying a low opaque cloud, as well as between ST and opaque clouds, has been found in terms of both crystal model selection and effective diameter. For high-altitude single-layered cirrus clouds with centroid temperature smaller than 233 K during January 2011, solid columns (family c) are selected in 60% of the cases on average for ST clouds, increasing up to 80% in opaque clouds. The median effective diameters increase with effective emissivity between 18 and 60 *μ*m for effective emissivities from 0.05 to 0.95. The standard deviations are ±17 *μ*m on average, larger but still compatible with the simulations, since they include the natural variability. The relation between median effective diameter or IWC and mean extinction shows a good agreement with the relationship established by in situ observations at midlatitudes (M10) and tropical latitudes (McF03). An IIR power-law relationship between IWC and extinction was established for four temperature ranges for the dataset presented in this paper. An average global relationship is also given that presents a simpler approach for large-scale models.

Overall, these results indicate accurate retrievals of the microphysical indices down to very small and up to rather large effective emissivity, notwithstanding the random noise, because this is partly compensated by the sensitivity of the method to particles with small diameters of several tens of micrometers. The perfectly collocated vertical information provided by the CALIOP lidar and the resulting accurate knowledge of the background conditions in each IIR channel are the main drivers of these performances. Future work will include an improved modeling of the background computed radiances for both clear and cloudy cases and an improved determination of blackbody radiance to improve retrievals at large emissivity, and thus increase the range in cloudy conditions of the data. Studies will be conducted for a refined selection of the LUTs and for the use of temperature and depolarization ratio from CALIOP as an additional constraint to better identify the relevant crystal model.

## Acknowledgments

The authors thank F. Parol, C. Stubenrauch, and S. Ackerman for fruitful discussions, the ICARE data center, and the *CALIPSO* team at NASA Langley Research Center for their help with the IIR level-2 algorithm. The products are processed at NASA/LaRC and are publicly available at NASA/LaRC (https://eosweb.larc.nasa.gov/) and ICARE (http://www.icare.univ-lille1.fr/) data centers. The authors are thankful to CNES, Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences de l'Univers (INSU), and NASA for their support.

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