The common radar and lidar ground-based observation data set obtained at Darwin is compiled for July 2005 to December 2009. Participants in this intercomparison applied their retrieval algorithm using this common data set. Here we examine the retrieved IWC, Re, and α from all algorithms. In addition, some algorithms also derive total number concentration (Nt), terminal fall velocity (Vf), and vertical air velocity (W). For the analysis, the entire time period is subdivided into subsamples in order to compare similar retrieval types:
 Radar-lidar subsample (called rali subsample) includes all data points when both radar and lidar instruments detect cloud. For these points, both radar-lidar algorithms (Varcloud and CombRet) and both radar-only Doppler moments algorithms (RadOn and Rad3mom) are applied. The purpose of applying the radar Doppler moments algorithms to the rali subsample is to examine how the two algorithm classes compare. The expectation here is that the radar-lidar methods should be more accurate than the Doppler moments methods, owing to a better extinction retrieval using the lidar measurements.
 Radar subsample includes all regions where only radar measurements are available for the retrieval of the cloud properties. For these data points, the Doppler radar methods are applied, as well as the radar-only components of the Varcloud and CombRet algorithms. The latter algorithms tend to be more empirically based than the Doppler moments methods. This subsample allows for a more direct comparison of these two classes of radar-only methods.
 Lidar subsample includes all regions where only lidar measurements are available, allowing for comparisons of the lidar-only part of the radar-lidar methods.
 The relative frequency of radar, lidar, and rali subsamples is given as a vertical profile in Figure 1. Overall, the important features of this vertical profile are that the radar subsample largely exceeds the lidar and rali subsamples up to 13 km, while the lidar subsample dominates above 14 km. It is noteworthy that the rali subsample, for which microphysical retrievals are presumably most accurate, represents at best 20–30% of the total sample (from 5 to 12 km height, see Figure 1). This important result highlights the fact that for ground-based remote-sensing measurements, the radiative effect of clouds is actually estimated most of the time from a single-instrument retrieval (lidar only for thin cirrus above 14 km height and radar only below 14 km height). This result may change in different climatic regimes where the tropopause height is lower and clouds are not as optically thin on average (i.e., midlatitudes) and when using satellite-borne radar-lidar instruments due to different viewing geometry.
4.1 Rali Subsample
 Figure 2 shows the probability density functions (PDFs) and height normalized PDFs (HPDFs) [Protat et al., 2009] of IWC, α, and Re retrieved by all algorithms for the rali subsample. Table 1 tabulates the first three moments of the PDFs displayed in Figure 2 (first row; mean, variance, and skewness) as well as the same comparisons for three selected heights of the HPDFs of Figure 2 (7, 11, and 15 km). Looking at the composite PDFs (Figure 2, first row), the radar-lidar methods produce very similar distributions for IWC and α, but very different PDFs of Re (see also values in Table 1). CombRet is characterized by a much larger variance in the Re distribution than the other methods (variance of 852 for the total PDF as compared with 167 for Varcloud; Table 1). RadOn is skewed toward smaller sizes, especially at 11 km (Table 1) where the mean value is half that of CombRet). Varcloud and Rad3mom have very similar distributions of Re (as judged by the PDF moments). Given the larger positive skewness of the Varcloud distribution when compared with CombRet, the mean values obtained from the two radar-lidar methods are 10 µm apart (Table 1), although the distribution peak for the two methods is the same value of about 40 µm. All algorithms exhibit a decrease in Re with altitude but RadOn clearly has the most altitude-dependent distribution and produces much smaller Re (<10 µm) at the highest altitudes. Rad3mom produces microphysical properties very similar to Varcloud (Table 1), although the Rad3mom distributions are systematically slightly broader (more frequent occurrence of smaller values for IWC and α, see first row in Figure 2 and Table 1). One possible reason for this general agreement is that Rad3mom and Varcloud use the same particle habit assumption for small particles (hexagonal columns).
Figure 2. Microphysical properties comparison in the radar-lidar cloud detection. (first row) PDFs of (left column) IWC, (middle column) α, and (right column) Re, respectively, from Varcloud (red), CombRet (blue), RadOn (green), and Rad3mom (yellow). Color contours of height normalized PDFs (HPDFs) of (second row) Varcloud, (third row) CombRet, (fourth row) RadOn, and (fifth row) Rad3mom, respectively. Overplotted in thin black lines are the corresponding results from CombRet for reference.
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Table 1. Moments of the PDFs of log(IWC), log(α), and Re for Each Retrieval Techniquea
|PDF at 7 km||Mean||−2.41||−2.34||−2.71||−2.36||−0.94||−0.88||−1.34||−0.88||75||81||81||77|
|PDF at 11 km||Mean||−2.09||−2.16||−2.07||−2.16||−0.50||−0.65||−0.27||−0.62||46||59||28||51|
|PDF at 15 km||Mean||−2.13||−2.08||−2.17||−2.44||−0.57||−0.40||+0.10||−1.15||74||76||54||76|
 In contrast to Re, the IWC and α HPDFs are similar among the algorithms with the exception that RadOn α increases more with altitude as expected from the previously described smaller Re. For IWC HPDFs, variance in the distributions with altitude is similar, though RadOn has a more pronounced decrease in IWC below 8 km and a larger variance up to 11 km (Table 1). One interesting feature in the HPDFs is that several algorithms exhibit a sharp decrease in IWC, α, and Re at ~15 km, which could distinguish the microphysical properties of anvil versus in situ generated cirrus. The differences exhibited by RadOn are in part due to the implicitly retrieved (and not assumed) particle habit produced by the algorithm (through a variable mass-maximum diameter and five possible cross-sectional area-maximum diameter relationships)., The implications of such large differences in terms of the radiative effect of clouds will be analyzed in section 5.
4.2 Radar Subsample
 The radar subsample, as shown in Figure 1, dominates the total sample at most heights. Recall that the radar-only part of the radar-lidar methods and the Doppler radar methods is actually compared here. Presumably, the use of an additional constraint (Vd) in the Doppler radar methods should be an advantage over the radar-lidar methods that apply more empirical approaches to retrieve cloud properties when only radar detects cloud. It must be noted that the Doppler radar methods (and Varcloud through the retrieval of the particle size distribution parameters) also provide additional information that can be compared: W, Vf, and Nt.
 Despite having different approaches to deriving microphysical properties when only radar detects cloud, Varcloud and CombRet produce very similar statistics for all microphysical quantities (Figure 3 and Table 2), including Re, which is quite different from the results for the rali cloud detections with these two retrievals (Figure 2, right column). The most notable difference is that the variance of the PDF produced by CombRet is systematically larger than that of Varcloud (Table 2), especially for the Re distribution. This general good agreement between the radar-lidar methods occurs because when only radar data are available, the two retrievals default to similar algorithms using radar reflectivity and temperature as inputs to the IWC and α retrieval.
Table 2. Same as Table 1 but for the Radar-Only Subsample
|PDF at 7 km||Mean||−2.16||−2.29||−2.21||−1.83||−0.72||−0.88||−0.78||−0.39||60||61||57||61|
|PDF at 11 km||Mean||−1.78||−1.81||−1.70||−1.81||−0.23||−0.29||+0.03||−0.31||48||57||29||54|
|PDF at 15 km||Mean||−1.71||−1.60||−2.10||−2.16||+0.01||+0.15||+0.08||−0.51||32||42||12||38|
 Comparisons of IWC produced by the four methods show that the PDFs produced by Varcloud, CombRet, and RadOn are similar, but corresponding HPDFs reveal different vertical distributions. The three methods agree fairly well up to 13 km, but do not agree at all above that height, where both radar-lidar methods produce an increasing IWC with height and both Doppler radar methods produce a constant IWC with height (Table 2 and Figure 3, left column). For the radar-lidar methods, this increase is caused by an increase in Ze with height above 13 km (not shown). Therefore, a retrieval method relying on radar reflectivity only must produce an increase in IWC and α by construction, while the Ze-Vd retrieval techniques rely on the characteristics of two or three Doppler moments. However, this result should be kept in perspective since the number of radar detections largely decreases above 13 km (Figure 1). Discrepancies between lidar and radar detections have been noted previously [Comstock et al., 2002] and can have significant impacts on derived TOA IR fluxes [Borg et al., 2011], which we will explore further in section 5. The IWC PDF produced by Rad3mom is characterized by a larger variance and peaks at smaller IWC than the three other methods. The HPDFs indicate that larger IWC values are produced by Rad3mom below 10 km height (see larger mean value and variance at 7 km, Table 2), while lower values are produced predominantly above 10 km height when compared with the other methods.
 PDFs of α show that RadOn produces larger extinction than the radar-lidar methods, primarily between 8 and 13 km (see mean values at 11 km, Table 2), for this radar subsample, while Rad3mom overall produces smaller α than the radar-lidar methods (Table 2 and Figure 3, middle column), which results from a compensation between larger values below 10 km and much smaller values above 11 km (Table 2). RadOn also has larger extinction values than the other methods above ~10 km in the rali subsample (Figure 2 and Table 1). The resulting comparison of Re (which is proportional to IWC/α, see ((1))) shows that owing to compensating effects of IWC and α, the Re produced by Rad3mom is slightly larger than Varcloud and CombRet at all heights above 6 km, with maximum differences around 8 km height and above 14 km height (Figure 3, right column). The larger extinctions produced by RadOn translate into much smaller Re compared to the other methods above 8 km (largest differences are found above 12 km height, see also Table 2). The HPDFs show that the Re distribution from CombRet is much narrower than the other methods due primarily to the temperature dependence of the Re retrieval used by CombRet for “radar only” clouds. The fact that the variance is actually much larger than other methods is due to the fact that the distribution is far from normal; hence, the variance calculation is more difficult to interpret in that case. Differences in Re between the two Doppler radar methods are very large, though the source of the discrepancies varies at different heights. Below 12 km, larger Re values produced by Rad3mom are predominantly due to IWCs larger than those from RadOn and the other methods. Above 12 km height, smaller Re values in RadOn are due to larger extinctions produced by RadOn (in agreement with CombRet) and IWCs similar to Rad3mom (but much smaller than Varcloud and CombRet). An assessment of the correct Re values will be performed using the surface shortwave flux comparisons, since clouds with smaller particles should reflect more incoming shortwave radiation than those with larger particles.
 Additional dynamical and microphysical properties are compared for the radar subsample for three of the algorithms (Figure 4 and Table 3). PDFs of Nt produced by Varcloud and RadOn are in reasonably good agreement in terms of mean values (less than 5% difference overall, Table 3); however, the Varcloud HPDF increases more distinctly with height and the RadOn Nt distribution is much broader and much less skewed at all heights (Table 3 and Figure 4, left column). This apparent agreement in mean values of Nt between Varcloud and RadOn is somewhat surprising, but is likely caused by offsetting uncertainties that are revealed in the HPDFs (Varcloud Nt is larger above 12 km, whereas RadOn is slightly larger below 12 km). Earlier comparisons between ground-based radar-lidar retrievals of Nt (using Varcloud) and space-borne radar-only retrievals from the CloudSat radar [Protat et al., 2010] have shown that reflectivity-only retrievals of Nt could not get the order of magnitude of total concentration correct. This is because the total concentration (which is the zeroth moment of the particle size distribution (PSD)) is indirectly related to the reflectivity measurements (the sixth moment of the PSD in the Rayleigh scattering regime), which is the main input to the radar-only methods. The differences observed between RadOn and Varcloud are much smaller than the differences reported in Protat et al. , at least below 12 km. Even if the two methods share the same assumption about the shape of the PSD, this comparison indicates that the two free parameters of the normalized PSD (the intercept parameter and the mean volume-weighted diameter), which are retrieved using the two methods, are in good agreement overall.
Figure 4. Comparison of total number concentration (Nt), particle fall velocity (Vf), and mean air motion (W) for radar-only cloud detections. (first row) PDFs of (left column) Nt, (middle column) Vf, and (right column) W, respectively, from Varcloud (red), RadOn (green), and Rad3mom (yellow). Color contours of HPDFs of (second row) Varcloud, (third row) RadOn, and (fourth row) Rad3mom, respectively. Overplotted in thin black lines are the corresponding results from RadOn for reference.
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Table 3. Same as Table 1 but for log(Nt), Vf, and W
|PDF at 7 km||Mean||1.08||1.08||0.82||1.06||0.61||0.05||−0.41|
|PDF at 11 km||Mean||1.97||2.31||0.59||0.66||0.50||0.02||−0.14|
|PDF at 15 km||Mean||2.89||2.37||0.29||0.38||0.29||0.06||−0.04|
 The terminal fall velocity PDF shows that the RadOn method retrieves slightly larger mean values of Vf compared to Rad3mom and Varcloud (Table 3 and Figure 4, middle column), though the latter two algorithms have a sharp peak at ~0.25 m s−1. The variance and skewness of the RadOn distribution are also larger than for the two other methods. The HPDFs and associated moments of Table 3 at three selected heights help characterize more clearly the differences in Vf. RadOn produces Vf that are almost twice as large as those retrieved by Rad3mom predominantly in the 5–10 km layer (see also mean values at 7 km in Table 3), while the agreement is better between RadOn and Rad3mom above 10 km height. Terminal fall speeds retrieved using the Varcloud algorithm fall between the two Doppler moments algorithms: Varcloud and Rad3mom agree very well in peak and width of the distributions above 10 km height, and Varcloud produces terminal fall speeds with values intermediate between RadOn and Rad3mom below 10 km height (Figure 4 and Table 3). Given the difference in Re for the three methods (Figure 3), we can infer that the particle fall speed-maximum diameter relationship retrieved on a case-by-case basis by RadOn and the assumption by Rad3mom of hexagonal columns for all cases produce very different results. In the Doppler moments retrievals, the measured Doppler velocity is split between the vertical air velocity component (W) and the terminal fall speed (Vf), using different methods (details can be found in Delanoë et al.  and Deng and Mace , respectively, for RadOn and Rad3mom). Varcloud uses a statistical fall speed-maximum dimension relationship approach for individual crystals by Mitchell and Heymsfield . Recent studies using multi-wavelength profiler observations over Darwin [Protat and Williams, 2011] suggest that the Vf-Ze approach used in RadOn tends to slightly underestimate terminal fall speed in tropical ice clouds, by 5–15 cm s−1 depending on height (their Figure 9). Protat and Williams  also caution against using a single particle habit assumption for all clouds and showed that assuming the hexagonal columns represents relatively well small terminal fall speeds associated with low reflectivities, but will strongly underestimate the larger terminal fall speeds associated with large Ze typically found in the lower portions of ice clouds [Protat and Williams, 2011] (Figure 5). Our comparison between RadOn and Rad3mom is fully consistent with the findings of Protat and Williams . The good agreement found between RadOn and Rad3mom above 10 km height is presumably due to the fact that hexagonal column habit assumption is relevant at these heights statistically, while it presumably underestimates terminal fall velocity below 10 km height. It also suggests that the RadOn retrieval of fall speed is reasonable, which was also a conclusion from Protat and Williams .
Figure 5. (top row) PDFs and HPDFs of (left column) IWC, (middle column) α, and (right column) Re, derived by (middle row) Varcloud and (bottom row) CombRet for the lidar sample.
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 RadOn and Rad3mom also retrieve vertical air velocity, W (defined as positive upward). Retrieved PDFs by RadOn and Rad3mom are symmetric centered on mean values of +2 and −18 cm s−1, respectively (Figure 4 and Table 3). The other moments of the two PDFs are similar (Table 3). The HPDFs of Figure 4 and the numbers in Table 3 show that RadOn W distributions are actually centered around 0, whereas Rad3mom is centered around a few cm s−1 downdraft (negative) except for below ~8 km where RadOn becomes more positive (+ 5 cm s−1) and Rad3mom more negative (mean value of −41 cms−1). This corresponds to the differences in the Vf between these two retrievals, which have been discussed previously.
4.3 Lidar Subsample
 Figure 5 shows the PDFs and HPDFs of IWC, α, and Re produced by Varcloud and CombRet. The PDF comparisons show that Varcloud has a slightly larger frequency of small IWC and α compared to CombRet, which translates into smaller mean values, larger variances, and slightly negative skewness of the Varcloud distributions at all heights (Table 4). For Re, the PDF produced by Varcloud is shifted toward slightly smaller values compared with CombRet (mean value of 29 versus 35 µm, Table 4). The HPDFs show that the Re differences are of similar magnitude at all heights, with Re produced by Varcloud being systematically 5 µm smaller than those produced by CombRet, with the notable exception of mean values from Varcloud being slightly larger at 7 km height (Table 4). Extinction results for CombRet show a somewhat artificial cutoff in the α PDF and HPDFs, which is likely caused by the forced max/min values for Sp, though a specific cutoff for α is not introduced into the algorithm. Recall from Figure 1 that the majority of lidar-only clouds occurs above 10 km; hence, the agreement above that altitude is somewhat constrained, particularly for α, which is primarily driven by the lidar ratio. PDFs of lidar ratio derived by the two methods exhibit significant differences for rali and lidar subsamples (Figure 6). Varcloud almost always retrieves a value of 33 sr because the a priori value of Sp is the center value, and the algorithm varies around that value. The CombRet algorithm begins the iteration at the largest allowed value of Sp rather than the center value, which results in a wider distribution, centered around 40 sr for the “lidar only” subsample. The range of allowed Sp is 10 to 66 sr. Sakai et al.  summarizes the available measurements of Sp in different climate regimes. While smaller values (5–25 sr) have been measured in midlatitude cirrus, larger values (39–79 sr) have been observed in tropical regimes. Theoretical calculations also presented in Sakai et al.  suggest that small crystals tend to have large values and hexagonal crystals tend to have small values. It is interesting that for the rali subsample the PDF of Sp is very broad compared to the “lidar only” sample, which has a peak near 38 sr. This could be indicative of a shift in the type of cirrus detected when radar does not detect the cloud (i.e., optically thin cirrus versus denser anvils). The small values of Sp (<20 sr) retrieved by CombRet likely indicate that the lidar profile is attenuation limited in some of the rali profiles, since the rali sample tends to have large optical depths than the “lidar only” sample. Despite these differences in the lidar ratio, the retrieved α agrees well, as shown in the HPDFs, which could be compensated for by the different multiple scattering treatments.
Table 4. Same as Table 1 but for the Lidar-Only Subsample
|PDF at 7 km||Mean||−2.84||−2.23||−1.34||−0.79||67||64|
|PDF at 11 km||Mean||−2.73||−2.47||−1.11||−0.93||42||49|
|PDF at 15 km||Mean||−2.87||−2.75||−1.06||−1.00||26||32|
Figure 6. Frequency distributions extinction-to-backscatter ratio (lidar ratio) retrieved by the CombRet and Varcloud algorithms for (top) rali and (bottom) lidar-only subsamples.
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