In this study, the main observation instruments are a zenith-pointing micropulse lidar (MPL) and a collocated 15° off-zenith-pointing AVORS lidar (manufactured by AVORS Technology Company). Both lidars operate at 532 nm wavelength, have depolarization capabilities and a range resolution of 15 m. The raw temporal resolutions are 15 s for the MPL and either 10 or 60 s for the AVORS lidar. Additionally, a 33.44 GHz Ka-band zenith-pointing cloud Doppler radar at the same site is used to further investigate the HOIC events, with its quality control following Ding et al. (2022). The vertical and temporal resolutions of the cloud radar are 30 m and 13 s, respectively. Environmental variables, including relative humidity, temperature, and horizontal wind speed and direction, are provided by ERA5 reanalysis data extracted at the Peking University Physics Building grid (116.3° E, 40.0° N) and radiosonde profiles from the Beijing Nanjiao Observatory (116.37° E, 39.80° N; WMO no. 54511). Further details are provided in Sect. 2 of our previous publication (Wu et al., 2025). The total observation period covers 354 d in 2022. The time used in the paper is local time (China Standard Time, UTC+8).

The specialized classification algorithm detailed in our previous study (Fig. 2 in Wu et al., 2025) is applied to classify cloud phase for the identified cloud range bins. In our previous study, the cloud bins identified by both the zenith-pointing and off-zenith-pointing lidars are used. Here we refer to it as the “rigorous” cloud mask.

In general, the off-zenith-pointing lidar shows a lower signal-to-noise ratio (SNR) than the zenith-pointing MPL at the same altitude bin. First, the off-zenith-pointing lidar was deployed outdoors without a container and was therefore more susceptible to solar background noise, whereas the MPL was housed inside a container with a lens hood to reduce such contamination. Second, for a given altitude, the off-zenith geometry leads to a longer atmospheric path length and hence stronger attenuation. Moreover, HOICs can produce mirror-like specular reflection. For the zenith-pointing lidar, the incident laser beam is nearly perpendicular to the main facets of the HOICs, so a strong specular reflection component is returned to the receiver. At 15° off zenith, the incident laser beam is no longer close to normal incidence, and most of the specular reflection component is reflected away from the receiver, resulting in much weaker backscatter (Wu et al., 2025). Because the cloud-layer detection algorithm identifies cloud bins when the backscatter-related quantity exceeds a predefined threshold, HOIC-containing cloud bins are more readily detected in the zenith observations (Zhao et al., 2014). Consequently, the zenith-pointing lidar often detects more HOIC range bins in many cases.

In this way, we find that using a rigorous cloud mask underestimates some of the topmost cloud range bins. To make up for this, we only use the zenith-pointing lidar's cloud mask, which we refer to as the “relaxed” cloud mask. Furthermore, to reduce possible missing HOIC data points, the non-typed cloud range bins are subjected to further HOIC classification evaluation (i.e., evaluating the ratios of attenuated backscatter and depolarization ratio between the two lidars).

We have carefully tested the dependency of the results to both the relaxed and rigorous cloud masks and found that most findings are robust under both schemes. The main exceptions are the HOIC fraction and the macrophysical characteristics, which will be discussed in detail in the relevant sections below. Since attenuation is common in lidar-based cloud research (Zhao et al., 2014), the relaxed cloud mask better represents the actual cloud structure. Therefore, the relaxed cloud mask is used in this study.

With height-resolved, high-spatiotemporal-resolution cloud phase categorization, the duration and horizontal extent of HOIC events can be estimated. Two HOIC range bins (in the time-height domain) are considered to belong to the same HOIC event if their temporal separation is less than 60 min and their vertical separation is less than 2 km (Δt<60 min, Δh<2 km). A depth-first search (DFS) algorithm (Cormen et al., 2022) is then applied to group all connected HOIC range bins into individual events.

For each identified HOIC event, the set of unique time indices occupied by the event is extracted. The HOIC event duration is calculated as the number of distinct time steps multiplied by the temporal resolution of 5 min. Following the approach of Westbrook et al. (2010), the advection-based horizontal extent of the HOIC event is estimated using horizontal wind speeds interpolated from ERA5 reanalysis data. This quantity should be interpreted as a proxy for horizontal scale rather than a direct geometric cloud width. For each time step belonging to the event, the horizontal displacement is calculated as the wind speed multiplied by the 5 min time interval. The total geometric extent of the event is obtained by summing these displacements over all time steps of the event. This provides an estimate of the overall horizontal distance over which the HOIC event has been advected during its lifetime.

Turbulent eddy dissipation rate (EDR) is retrieved using the cloud radar Doppler velocity together with ERA5 horizontal wind speed. The retrieval method used was compared with the approach proposed by Griesche et al. (2020), showing good agreement in the field experiment on SWC seeding organised by Zhang et al. (2026a). Griesche et al. (2020) retrieved turbulent dissipation rates from cloud radar observations, which has been validated using tethered-balloon in situ measurements. For HOIC diameter and Reynolds-number estimates, the radar Doppler velocity is treated as the terminal fall velocity, and hexagonal plate assumptions with corresponding mass and area-ratio relationships are used in an aerodynamic model. The technical details are provided in the Appendix of Wu et al. (2025).

To quantitatively compare cloud-property distributions for HOICs and ROICs, this study used non-parametric statistical tests. The two-sample Kolmogorov–Smirnov (K-S) test (Massey, 1951) was used to assess whether the two orientation groups originated from the same cumulative distribution, while the Mann–Whitney U test (Mann and Whitney, 1947) was used to evaluate differences in the central tendency (or distribution ranks) of the two groups. Let X=xii=1m and Y=yjj=1n denote the cloud-property samples for HOICs and ROICs, respectively. The Mann–Whitney U statistic corresponding to the HOIC sample was calculated from the pooled ranks as: 1Uobs=RX-mm+12 where RX is the sum of the pooled average ranks assigned to the m HOIC observations. A one-sided alternative, assuming that the HOIC values are stochastically smaller than the ROIC values, was used, and its p value was defined as 2pMW=PrH0U≤Uobs where Uobs is the observed Mann–Whitney statistic, U denotes the corresponding random statistic under the null hypothesis H0, and PrH0 denotes probability under the null hypothesis H0 that the HOIC and ROIC samples originate from the same underlying distribution. Given the large sample sizes, the Mann–Whitney p value was evaluated using the asymptotic implementation in SciPy (scipy.stats.mannwhitneyu; Virtanen et al., 2020), with correction for ties and the default continuity correction.

For the two-sided two-sample Kolmogorov–Smirnov test, the observed statistic was defined as: 3Dobs=supzFmz-Gnz with the corresponding p value 4pKS=PrH0Dm,n≥Dobs where Fm and Gn are the empirical cumulative distribution functions of the HOIC and ROIC samples, respectively; supz denotes the supremum over all possible z; Dm,n denotes the random two-sample Kolmogorov–Smirnov statistic for sample sizes m and n under H0; and H0 denotes that the two underlying distributions are identical. The p value was evaluated via the asymptotic Kolmogorov–Smirnov test in SciPy (scipy.stats.ks_2samp; Virtanen et al., 2020).

Given the exceptionally large sample size in this study, which tends to yield extremely small p values even for minor physical differences, we further calculated Cliff's Delta (d) to measure the effect size (Cliff, 1993). Cliff's Delta was calculated directly from the Mann–Whitney statistic returned for the HOIC sample: 5d=2Uobsmn-1 where m and n are the HOIC and ROIC sample sizes, respectively. Effect-size magnitudes follow Romano et al. (2006): negligible for |d|<0.147, small for 0.147≤|d|<0.330, medium for 0.330≤|d|<0.474, and large for |d|≥0.474. All statistical analyses were conducted using the SciPy library in Python (Virtanen et al., 2020).

Figure 1 shows a mid-level cloud case on 14 December 2022, during which strong specular reflections were observed, along with a collocated sun dog photograph. In the zenith-pointing lidar data, the attenuated backscatter is highly enhanced (see the red part in Fig. 1a, from 11:00 to 23:30 local time at the height of 2–4 km). The corresponding volume depolarization ratio approaches near-zero values (blue part in Fig. 1b), which alone would suggest SWCs for those parts of cloud. However, simultaneous observations from the 15° off-zenith-pointing lidar reveal a different scenario: in the same region, the attenuated backscatter is notably weaker (in yellow, green and blue of Fig. 1c), and the corresponding volume depolarization ratio is much larger compared to the zenith-pointing lidar (orange and yellow part in Fig. 1d). Consequently, the ratio of attenuated backscatter is quite large (see Fig. 1e) and the ratio of depolarization ratio rather low (see Fig. 1f), meeting the criteria for specular reflection induced by HOICs, instead of SWCs, as introduced in Wu et al. (2025). The categorization result of the cloud phase is shown in Fig. 1g, with HOIC in an orange flag.

A sun dog (parhelion) photograph was captured simultaneously at 16:09 local time on 14 December 2022 at the Summer Palace in Beijing, approximately 3 km from our lidar station at Peking University (see Fig. 1h). A sun dog is one kind of common atmospheric halo, which requires the existence of horizontally oriented hexagonal plate crystals (Greenler, 1980; Tape, 1994). It exists when the solar elevation angle is low, such as near sunset in this case. Sunlight is refracted twice within the prism facets of these horizontally oriented hexagonal plates to the observer, creating two bright spots besides the sun (Takano and Liou, 1989). In the provided photograph, only the bright spot on the left side of the sun is visible, as the sun itself is outside the frame. A schematic diagram illustrating the formation mechanism of a sun dog is provided in Appendix A.

Given the low solar elevation angle, the exact atmospheric volume producing the observed sun dog may be located at some horizontal distance from our lidar station. Nevertheless, the consecutive orange HOIC label in Fig. 1g means that the horizontal extent of HOIC is very large, likely filling the whole sky. The sun dog photograph serves as independent qualitative evidence to support the validity of our HOIC categorization.

Figure 2 presents the cloud phase classification results for representative HOIC cases under various cloud-top temperature (CTT) regimes in 2022. The selected CTTs, ranging from around -15, -25 to -20, -30 to -25, -40 to -25, to <-40 °C, are specifically chosen because they dictate distinct ice crystal growth habits (Bailey and Hallett, 2009). By analyzing these cases, which are primarily stratiform mixed-phase clouds characterized by SWC at the cloud top and ice crystals below, this section aims to elucidate a potential relationship between HOICs, crystal growth regime, and the presence of SWCs. SWC, specifically, is a potential candidate to foster the formation of HOIC, because it promotes the growth of simple plate-like crystals rather than irregular polycrystals (Westbrook et al., 2010). Note that while HOIC events with CTTs between -10 and -5 °C were also observed in 2022, their vertical structures were overly complex and are therefore not shown here. The corresponding direct observables from the lidars and radar for these cases (e.g., attenuated backscatter, volume depolarization ratio, radar reflectivity, Doppler velocity, spectral width, and EDR) are detailed in Appendix B.

It is important to note that the temperatures discussed here refer specifically to the cloud-top temperatures. As ice crystals sediment after formation, their altitude decreases, and the ambient temperature they experience rises accordingly unless an inversion layer exists within clouds. Consequently, the actual temperatures where these ice clouds reside are typically higher than the cloud-top temperatures stated here.

Figure 2a corresponds to a CTT of approximately -15 °C, which is a typical temperature regime for the formation of plate or dendritic ice crystal habits. From 02:00 to 05:00 on 26 June 2022, a stable layer of SWC existed at the cloud top at an altitude of about 7 km. In this case, HOICs were consistently present at 6–8 km from 00:00 to 06:00. The horizontal orientation of these ice crystals was well maintained between 03:00 and 06:00, with no obvious ROICs appearing at the cloud base.

Figure 2b corresponds to a CTT of approximately -25 to -20 °C, a regime favorable for the plate-like ice crystal formation. On 29 August 2022, between 17:00 and 18:00, an SWC layer was present at the cloud top at an altitude of about 8 km. In this case, stable HOICs were consistently present at 7–9 km from 15:00 to 21:00, corresponding to ambient temperatures of -20 to -15 °C. Between 15:00 and 18:00, the horizontal orientation of ice crystals at 6–7 km could not be maintained in the lower portions, resulting in the appearance of a massive amount of ROIC forming a layer up to 1 km thick.

Figure 2c corresponds to a CTT of approximately -30 to -25 °C, a regime favorable for polycrystalline plate ice-crystal formation. On 6 August 2022, from 03:00 to 05:00, a stable SWC layer existed at the cloud top at approximately 9 km. In this case, stable HOICs were consistently present at 7–9 km from 03:00 to 07:00, corresponding to temperatures of -20 to -10 °C. At the cloud base, the horizontal orientation was not fully maintained, and ROICs occurred.

Figure 2d presents a typical case illustrating the relationship between supercooled liquid water and HOIC. On 12 October 2022, a cloud layer was observed around 08:00. Initially, the cloud-top temperature was low, with values below -40 °C. Subsequently, the cloud layer's altitude gradually decreased, and its temperature gradually increased. As the cloud-top temperature reached approximately -30 °C (around 12:00), a distinct region of HOIC became evident. When the cloud-top altitude further decreased, with the cloud-top temperature rising to approximately -25 °C (around 18:00), supercooled liquid water (marked in light blue) appeared at the cloud top, and the number of HOIC range bins began to multiply. After 21:00, the cloud-top temperature was around -25 °C, and a stable SWC top emerged; the HOIC increased significantly and began to dominate the entire cloud layer. The presence of SWCs led to a rapid increase in HOIC occurrence. This case illustrates that the presence of SWCs is a favorable condition for the occurrence of HOICs.

Figure 2e presents a case of a pure cirrus cloud without the presence of SWCs. On 19 May 2022, the CTT was below -55 °C, which is significantly lower than the homogeneous freezing threshold (-38 °C). At this temperature, supercooled liquid water cannot exist, and the cloud must be entirely composed of ice crystals. From 03:00 to 05:00, significant signals of HOICs were observed at the cloud top at an altitude of 11 km, persisting for nearly 2 h. This case demonstrates that HOICs can also occur in cirrus clouds without supercooled liquid water above.

Note that the corresponding raw observational quantities from the lidar and cloud radar for the aforementioned cases shown in Fig. 2, including attenuated backscatter, volume depolarization ratio, radar reflectivity factor, Doppler velocity, spectral width, and EDR, are detailed in Appendix B.

Figure 3 shows the temperature dependence of the statistical characteristics of the volume depolarization ratio and attenuated backscatter for cloud data points observed by the lidars in 2022. In Fig. 3a, the volume depolarization ratio distributions from the zenith-pointing (blue) and 15° off-zenith-pointing (gray) lidars are compared by temperature bin. The figure marks the median and interquartile range for each temperature interval. Below -38 °C and above 0 °C, the two lidars give broadly consistent depolarization ratios. However, in the mixed-phase cloud temperature range from -38 to 0 °C, the off-zenith depolarization ratios are distinctly higher than the zenith-pointing values. The largest median difference, about 0.18, occurs between -15 and -10 °C. The -20 to -15 °C interval exhibits the second-highest difference, with values reaching 0.15. These pronounced discrepancies are a clear signature of HOICs, which cause a strong reduction in the zenith-pointing lidar depolarization ratio due to specular reflection.

Note that in liquid water clouds at temperatures above 0 °C, the off-zenith lidar depolarization ratio is slightly higher. This difference is primarily explained by the different fields of view (FOV) of the two instruments. The off-zenith AVORS lidar has a larger FOV (0.2 mrad) than the zenith lidar (0.1 mrad), making it more sensitive to multiple scattering effects, which in turn increase the measured depolarization ratio (Jimenez et al., 2020a). At temperatures below -38 °C, the off-zenith lidar depolarization ratio is slightly higher likely due to a small presence of HOICs.

Figure 3b presents a density scatter plot showing the ratio of the depolarization ratios (δzenith/δoff-zenith) from the two lidars against temperature. The vast majority of data points, corresponding to ROICs and to liquid-water droplets, cluster around a ratio of 1 (the red, yellow, and green high-density areas). However, between -20 and -10 °C, a distinct yellow-green data cluster emerges, indicating the presence of HOICs, corresponding to a ratio close to 0.

The vertical red dashed line in the figure marks the threshold of 0.6 used in the identification algorithm of this study (Wu et al., 2025). The density scatter distribution confirms the physical validity of this threshold: it effectively isolates data where the zenith-pointing depolarization ratio is significantly lower than the off-zenith one (i.e., HOIC-dominated regions), while successfully excluding the majority of conventional cloud data (with a ratio near 1) from being misidentified.

The attenuated-backscatter statistics in Fig. 3c show a complementary pattern. In most temperature ranges, the two lidars measure similar attenuated backscatter values. Between -20 and 0 °C, however, zenith-pointing attenuated backscatter is enhanced relative to the off-zenith signal, again indicating specular reflection. In the -15 to -10 °C temperature interval, the zenith median attenuated backscatter is nearly half an order of magnitude larger than the off-zenith median, representing a substantial discrepancy.

Figure 3d is a density scatter plot showing the base-10 logarithmic ratio of the attenuated backscatter from the two lidars as a function of temperature. The vast majority of data points in the figure are concentrated around 0 (i.e., a linear ratio of approximately 1), indicating that for most cloud data points, the backscatter intensities received by the two lidars are comparable, with no significant specular reflection. However, between -20 and 0 °C, a “spike-like” dense cluster of data points clearly extends to the right. This represents a strong specular reflection region where the signal intensity of the zenith-pointing lidar far exceeds that of the off-zenith lidar. Particularly in the -15 to -10 °C interval, the difference between the two reaches its maximum; the attenuated backscatter coefficient of the zenith-pointing lidar can be up to 3 orders of magnitude higher than that of the off-zenith-pointing lidar (i.e., the base-10 logarithmic ratio reaches 3).

The vertical red dashed line in the figure marks the threshold used in the identification algorithm, corresponding to a linear ratio of 2. The density scatter distribution confirms the physical validity of this threshold selection: the algorithm selectively isolates data where the zenith-pointing scattering intensity is significantly higher than the off-zenith one (ratio >2), while successfully excluding the conventional scattering cloud data points where the ratio is close to 1 (indicated by the red, yellow, and green colors).

Figure 4 displays the joint two-dimensional frequency distributions of the volume depolarization ratio (δ) and the logarithmic attenuated backscatter for both the zenith-pointing and off-zenith-pointing lidars across different temperature intervals, along with the characteristics of their density differences. This figure compiles valid cloud data points for the entire year of 2022. Distinct cloud microphysical phases occupy different regions in the joint distribution diagrams. Liquid water clouds, consisting of high concentrations of spherical water droplets, exhibit low (near-zero) depolarization ratios and high attenuated backscatter coefficients (Hamel et al., 2026). Conventional ice clouds (ROICs), dominated by non-spherical ice crystals with relatively lower number concentrations, show high depolarization ratios and low-to-moderate attenuated backscatter. The black dashed boxes in the lower right corners of Fig. 4a and b indicate the threshold range to identify liquid water clouds introduced by Wu et al. (2025): δv<0.1 and β′>5 Mm⁻¹ sr⁻¹ (attenuated backscatter coefficient).

It should be noted that the algorithm used in this study requires the depolarization ratio of HOICs observed by the zenith-pointing lidar to be below 0.1. However, in practice, this study selected only the most representative HOICs. Some range bins contain HOICs at relatively low concentrations, resulting in depolarization ratios with values that are lower than those of ROICs but may still exceed the 0.1 threshold.

First, the warm cloud regime with T>0 °C is evaluated. When the temperature exceeds 0 °C (Fig. 4a1 and b1), clouds consist primarily of warm liquid water. The high-density data points from both lidars fall precisely into the dashed box in the lower right corner, confirming the physical validity of the liquid water cloud thresholds defined in this study. The few data points scattered outside the box mainly arise from large, falling ice crystals that have not fully melted or from aerosol particles misidentified as clouds. When the temperature exceeds 3–5 °C (not shown), the remaining ice-phase particles melt, and nearly all cloud data points become concentrated within the dashed box in the lower right corner.

A careful comparison between Fig. 4a1 and b1 reveals that the data points from the zenith-pointing lidar lie closer to the x axis (where the depolarization ratio is near zero). This difference arises from the larger field of view of the off-zenith lidar, which enhances multiple-scattering effects and slightly increases depolarization in dense water clouds (Jimenez et al., 2020b).

Second, the pure ice cloud regime of temperatures ≤-38 °C is discussed in detail. When the temperature drops below the homogeneous nucleation threshold of -38 °C, the clouds are composed entirely of the ice phase. All supercooled liquid water freezes, and no SWCs can exist within this temperature regime (Pruppacher and Klett, 2010). Figure 4b4 shows that all cloud data points observed by the off-zenith lidar exhibit high depolarization ratios and low backscatter, perfectly clustering in the upper-left ice cloud region outside the dashed box. This further proves the robustness of the liquid water threshold established in Wu et al. (2025). Conversely, in the zenith-pointing observations (Fig. 4a4), a small number of data points still fall within the dashed box, suggesting some presence of HOICs even at these low temperatures.

Third, the mixed-phase cloud regime (-38 °C < T≤0 °C) is discussed. This temperature regime is an active zone for ice-water phase transitions and the frequent occurrence of HOICs. In the -20 to 0 °C interval, the cloud parameter space clearly splits into two distinct extremes: a conventional ice cloud region in the upper-left part and a liquid-water-like cloud cluster in the lower-right part. Comparing of Fig. 4a2 and b2 indicates that the zenith-pointing lidar accumulates a very large cluster of data points in the lower-right part. This difference is more intuitively illustrated in Fig. 4c2 (off-zenith minus zenith density), where negative values prevail in the lower-right part (zenith density > off-zenith density), whereas positive values prevail in the upper-left part (off-zenith density > zenith density). In other words, when the lidar observation switches from zenith to off-zenith probing, a large number of data points originally concentrated in the low-depolarization-ratio, high-backscatter region migrate in the parameter space and return to their background ice cloud location, which is characterised by a high depolarization ratio and lower backscatter. These particles, which thus reveal their true non-spherical morphology, are precisely the HOICs responsible for the strong zenith reflections.

In the -38 to -20 °C interval (Fig. 4a3–b3), the bimodal distribution persists. The difference map (Fig. 4c3) shows that the low-depolarization region (δ between 0 and 0.3) is dominated by negative values (higher frequency in zenith observations), whereas the high-depolarization region centred near δ≈0.4 is dominated by positive values (higher frequency in off-zenith observations). This indicates that within this temperature regime, some range bins are still mixed with HOICs, and their presence biases the depolarization ratio observed by the zenith lidar towards lower values. However, compared with the -20 to 0 °C interval, the frequency difference within the dashed box is no longer significant. The primary difference area is located in the upper left part of the dashed box, indicating that the occurrence frequency of HOICs decreases markedly in this temperature regime.

While Sect. 4.1 focuses on the direct optical signatures measured by the lidars, this subsection examines the statistical characteristics of the retrieved cloud-phase products. We begin with the occurrence frequency and cloud-phase fractions, followed by the macrophysical and spatiotemporal characteristics of HOIC events.

Figure 8 shows the two-dimensional local-time-temperature distributions of cloud mean attenuated backscatter coefficient (β′) and depolarization ratio (δ) measured by the lidars at different pointing angles. The sampling intervals for time and temperature are 0.5 h and 1 °C, respectively. Overall, the spatiotemporal distributions of both lidar parameters exhibit significant temperature and temporal dependencies.

One of the most prominent features in Fig. 8 is the presence of a distinct low-δ layer near -15 °C, which is generally attributed to signals originating from HOICs. This low-δ layer is particularly pronounced in the zenith-pointing lidar observations (Fig. 8a1), where the corresponding β′ values are anomalously high (>10 Mm⁻¹ sr⁻¹; see Fig. 8b1, note that the figure uses a log₁₀ scale). This is caused by specular reflection during zenith pointing. In the warm cloud regime with temperatures above 0 °C, extremely high backscatter and extremely low depolarization ratios are also observed. However, these features arise from the high number concentration and spherical shape of liquid water droplets, a mechanism fundamentally different from the specular reflection of ice crystals.

When observing with an off-zenith-pointing lidar (Fig. 8a2), the δ values detected near -15 °C are higher because the specular reflection angle of HOIC is avoided. Simultaneously, the corresponding β′ values drop noticeably (Fig. 8b2). Figure 8a3 shows the difference in depolarization ratio between the zenith-pointing and off-zenith-pointing lidars. A substantial difference between the two occurs in the temperature interval of -30 to -10 °C, peaking around -15 °C. Figure 8b3 shows the difference in attenuated backscatter between the zenith-pointing and off-zenith-pointing lidars, again revealing a substantial difference between -20 and -10 °C.

Regarding diurnal variations, observations show that at temperatures below -20 °C, the cloud backscatter detected during the daytime is generally stronger than that at night, with correspondingly higher depolarization ratios. As seen in Fig. 8a3, the diurnal variation of the depolarization ratio difference is generally weak, with minimum values at 10:00–11:00 and 16:00–20:00 (which correspond to higher differences in attenuated backscatter). However, the lidar cloud detection algorithm can be affected by solar background noise during daytime (Zhao et al., 2014), resulting in a lower SNR that may cause only optically thick clouds with sufficiently strong signals to trigger the cloud identification algorithm. The conclusions of this study may be subject to such lidar instrument-related limitations. We have attempted to remove cloud data points detected at nighttime whose attenuated backscatter was lower than the minimum attenuated backscatter of clouds detected during the daytime by using the daytime minimum as a threshold. A figure with a similar pattern to Fig. 8 was generated based on this approach (figure not shown), and the resulting day-night distribution showed no significant difference. Finally, we present the current diurnal variations here.

It is worth noting that Kikuchi et al. (2021) utilized data from the spaceborne CALIOP lidar at different pointing angles, finding a similar latitude-temperature distribution (see Fig. 2 in their paper). However, constrained by the fixed local overpass times of sun-synchronous orbit satellites, spaceborne CALIOP data cannot be used to investigate the cloud diurnal cycles. Furthermore, due to the large receiver FOV of the CALIOP lidar telescope, strong multiple scattering effects occur when detecting liquid water clouds. Consequently, the liquid-cloud signals observed by CALIOP do not exhibit depolarization ratios approaching zero, unlike those from ground-based lidars, but instead exhibit high backscatter and high depolarization. In contrast, the ground-based dual-angle lidar configuration employed in this study not only captures HOIC signals with extremely low depolarization ratios approaching 0, but also finely characterizes their full diurnal evolution.

While Fig. 8 presents the distribution of mean values, the median distributions were also calculated during data processing. The two distributions exhibit consistent features with similar conclusions and are therefore not shown. Figure 9 illustrates the daily evolution of the abundance of HOICs obtained using the relaxed cloud mask scheme. The cloud abundance here is defined as the ratio of the number of identified HOIC data points to the total number of valid lidar detections within a specific time-temperature grid cell. The temporal and temperature resolutions for the gridding process are set to 30 min and 2 K, respectively. The red dashed lines in the figure indicate the typical formation temperature regime for plate-like ice crystals (-22 to -8 °C). It can be observed that most of the HOIC data points are concentrated within this interval, whereas they seldom appear in environments colder than -40 °C.

The diurnal evolution of HOIC exhibits some variations, with larger occurrences in the periods: 02:00–09:00 and 16:00–22:00. To quantitatively evaluate the diurnal discrepancy, this study utilized the Python Astral library (Kennedy, 2023) to precisely calculate the daily sunrise and sunset times in Beijing, thereby strictly categorizing the HOIC data into daytime and nighttime. Statistical results indicate a slightly higher occurrence proportion of HOIC at night (54.3 %) compared to the daytime (45.7 %), further corroborating its characteristic of weak diurnal variability.

Next, this study further investigates the dependence of HOICs and ROICs on macroscopic environmental variables, such as horizontal wind speed and temperature. The analytical approach in this section is similar to that described in Sect. 4.2 of Wu et al. (2025), but it utilizes observational data from the entire year of 2022. By significantly expanding the sample size to over 300 000 HOIC data points and over 1.4 million ROIC data points, the statistical results in this section are more representative and statistically significant in terms of climatological characteristics.

From a dynamical perspective, Fig. 10a reveals a significant difference in the horizontal wind speed distributions between HOIC and ROIC. Compared to ROIC, HOIC tends to form in environments with lower horizontal wind speeds, with most of the HOIC samples exhibiting wind speeds below 40 m s⁻¹. Conversely, the wind speed distribution for ROIC is much broader, with a substantial presence even in high wind speed regions exceeding 40 m s⁻¹. From an aerodynamic standpoint, higher horizontal wind speeds are typically accompanied by stronger environmental wind shear and atmospheric turbulence. These perturbations disrupt the stable aerodynamic falling posture of ice crystals, causing them to tumble and thus exhibit random orientations. In contrast, a weaker wind field provides a stable dynamical background for ice crystals to maintain a horizontal orientation. This observation also corroborates the results of Garrett et al. (2025), which concluded that the mean horizontal wind field plays a key role in modulating the spatial orientation and fall velocity of hydrometeor particles.

From a thermodynamic perspective, Fig. 10b shows that the two types of ice crystals are distinctly separated in temperature space. The ambient temperatures where HOICs exist are significantly higher than those for ROICs, exhibiting an extremely sharp distribution peak between -22 and -8 °C. Specifically, the median and mean temperatures of HOIC occurrences are -13.8 and -14.0 °C, respectively. This temperature regime is of critical significance in cloud microphysics: according to classical ice crystal growth theory, -22 to -8 °C is precisely the core temperature zone for the growth of plate and dendrite ice crystals. During their descent, aerodynamic drag tends to stabilize these flat ice crystals with their broad faces nearly normal to the direction of motion, thereby resulting in horizontal alignment. In contrast, the overall temperature distribution of ROIC is significantly lower (median -36.8 °C, mean -34.7 °C). Ice crystals generated in such cold environments are predominantly columnar or irregular polyhedra; furthermore, they are more susceptible to aggregation, making them much more likely to exhibit random orientations.

Figure 10c further presents the joint density distribution of HOIC in the two-dimensional space of horizontal wind speed and temperature. The high-frequency concentration region of HOIC (the dark green core) is clearly confined within an envelope characterized by relatively high temperatures (-5 to -25 °C) and low wind speeds (3 to 30 m s⁻¹). Notably, within the dense regions of HOIC occurrence, environment temperature and horizontal wind speed show a distinct negative correlation (i.e., lower temperatures correspond to higher wind speeds). This not only conforms to the general meteorological rule of the mid-to-upper troposphere – where temperature decreases and wind speed increases with altitude – but also clearly delineates the “composite temperature-wind threshold boundary” required to maintain the horizontal alignment of ice crystals.

The temperature range where HOICs occur largely coincides with that in which SWCs are typically observed. To characterize the spatial association between HOICs and SWC, we consider the Euclidean distance from each ice-crystal-phase data point to the nearest overlying SWCs, as defined in Sect. 4.5 of our previous study (Wu et al., 2025): the root-sum-square of its horizontal and vertical offsets from that SWC. Here the vertical offset is the height gap between the two bins, whereas the horizontal offset equals the ERA5 horizontal wind multiplied by their time gap. This distance provides a quantitative measure of the proximity between HOICs and SWCs. The following presents the statistical results for the full year of 2022. The requirement to find the corresponding overlying SWC is that it precedes the ice crystals temporally and is located spatially above them, ice-crystal bins without such an overlying SWC are excluded. This requirement is consistent with the physical mechanism of ice crystal sedimentation. After this filtering, more than 200 000 valid HOIC and ROIC data points satisfied these criteria.

Figure 11 visually compares the Euclidean distance distributions from HOICs and ROICs to the overlying SWCs. The median distance from HOICs to SWCs is only 12.7 km, whereas the median for ROICs reaches 58.3 km, with mean distances exhibiting a similarly pronounced contrast (83.0 vs. 176.5 km). To rigorously verify this distinction, two-sample Kolmogorov–Smirnov and Mann–Whitney U tests were performed, both confirming a statistically significant difference (p≪0.001). Furthermore, Cliff's delta (d) was calculated to quantify the effect size without relying solely on p value significance. The resulting value of d=-0.32 indicates a substantial systematic shift approaching a medium effect size (Romano et al., 2006). Together, these quantitative results provide strong evidence that HOICs typically exist in much closer physical proximity to SWCs than ROICs.

This phenomenon is physically consistent with a potential cloud microphysical mechanism. Building on the case analyses of different cloud-top temperatures presented in Sect. 3.2, we propose that the formation of HOICs may be closely linked to microphysical processes involving supercooled liquid water layers, particularly Wegener–Bergeron–Findeisen growth. Ice crystals existing within or immediately below SWCs are typically pristine ice crystals newly formed (Radenz et al., 2021; Zhang et al., 2026b). Growing in a water-vapour-rich environment, these ice crystals often develop intact, large planar geometries (e.g., plate or dendritic shapes, Bailey and Hallett, 2009). Their small aspect ratios make them highly susceptible to aerodynamic drag during the initial stage of descent, enabling them to form and maintain a horizontal orientation.

As the ice crystals continue to fall, their Euclidean distance from the overlying SWC continuously increases. During this prolonged descent and evolution, the probability of ice crystals undergoing aggregation or riming increases significantly. These processes destroy the original flat and regular structure of the ice crystals and increase their asymmetry, which destabilizes their aerodynamic posture and ultimately causes them to transition from a horizontal to a random orientation.

Furthermore, SWCs typically exist in stable atmospheric stratification (Pruppacher and Klett, 2010). SWCs are in a highly sensitive metastable state, and unstable airflows can easily trigger their freezing (Yang et al., 2018). Conversely, HOICs also require a relatively stable stratification to be maintained (Garrett et al., 2015). This shared requirement for stability may be another reason why the Euclidean distance between HOICs and SWCs is short.

Moreover, the statistical results of this study provide additional observational support for previous research. Ross et al. (2017) reported a close relationship between HOICs and surface precipitation in midlatitude marine low clouds using CALIPSO and CloudSat satellite products, while previous studies (French et al., 2018; Silber et al., 2021) identified SWCs as key components of cold-cloud precipitation processes. The quantitative statistics of Euclidean distance in this study establish a direct spatial link between SWCs and HOICs, thereby supporting an observationally consistent link between HOIC occurrence and SWC-related precipitation.

It is worth emphasizing that, constrained by observational methods, Ross et al. (2017) noted that polar-orbiting satellites, including the Moderate Resolution Imaging Spectroradiometer (MODIS), CALIPSO, and CloudSat, cannot provide a sufficient temporal sampling rate to investigate the continuous dynamical processes underlying the phenomena related to HOIC and precipitation. Spaceborne active remote sensing platforms move extremely fast, typically acquiring only “snapshot” profiles of a certain region. Passive satellite sensors have limited penetration capabilities, making it difficult to resolve the vertical cloud-phase structure. In contrast, the dual-angle ground-based polarization lidar configuration employed in this study boasts the advantages of high temporal continuity and vertical resolution. Through continuous fixed-point observations from an Eulerian perspective, this study achieves high-resolution discrimination of supercooled water layers and ice crystals with different orientations, and precisely captures their relative positions and spatiotemporal evolution. These capabilities provide valuable insight for the investigation of cloud and precipitation microphysical mechanisms.

In the previous section we found a link between ice orientation and horizontal wind, within this section, we further examine how turbulence is associated with HOIC occurrence on the analysis of EDR that was retrieved from the zenith-pointing Doppler cloud radar. To avoid contamination from melting ice particles, this section only includes HOIC samples colder than -2.5 °C, following the temperature criterion used by Westbrook et al. (2010). Figure 12 illustrates the frequency distributions (Fig. 12a) and two-dimensional temperature dependencies (Fig. 12b, c) of the EDR in environments containing differently oriented ice crystals, based on the relaxed cloud mask scheme. Overall, as the ambient temperature increases (approaching 0 °C), the EDR within the ice-containing cloud layers exhibits a gradual upward trend for both HOIC and ROIC (Fig. 12b, c).

Under conditions of low EDR (i.e., relatively stable and laminar atmospheric environments), both HOICs and ROICs can exist extensively. However, as the EDR increases to 10-2 m² s⁻³ (i.e., >-2 on a log₁₀ scale), the occurrence frequency of HOIC begins to decrease sharply (Fig. 12a). From an aerodynamic perspective, a high EDR implies the presence of intense microscale turbulent eddies and wind shear within the cloud. When the overturning torque generated by these fluid perturbations exceeds the aerodynamic restoring torque of the ice crystal, the crystal's stable falling posture is disrupted. This causes the crystal to tumble and transition to a random orientation.

An EDR of approximately 10-2 m² s⁻³ can be considered one of the approximate empirical dynamical thresholds for maintaining large-scale horizontal alignment of ice crystals. In Appendix C, statistical results based on the rigorous cloud mask scheme (Fig. C1) highlight this turbulence cutoff characteristic even more clearly.

A further comparison of the two-dimensional density scatter plots in Fig. 12b and c reveals that the EDRs in HOIC environments are significantly biased toward lower values. To quantitatively evaluate this, non-parametric tests (Mann–Whitney U and Kolmogorov–Smirnov) were applied, both confirming a statistically significant difference in their overall EDR distributions (p≪0.001). Interestingly, the calculated Cliff's Delta yields a small overall effect size (d=-0.060). This seemingly modest effect size reflects the aforementioned microphysical reality: under weak turbulence, both ice crystal types extensively coexist, resulting in heavily overlapping distributions. The true physical distinction driving the statistical difference lies in the high-turbulence right tail. While ROICs maintain a certain density of data points even in extremely turbulent environments (EDR >10-2 m² s⁻³), HOICs exhibit a dynamical cutoff and are almost entirely absent.

This identified contrast in HOIC occurrence at EDR >10-2 m² s⁻³ is further demonstrated in Fig. 13, which comprehensively shows the statistical distribution characteristics of direct millimeter-wave cloud radar observations (Doppler velocity, spectral width, and reflectivity factor) as well as retrieved physical quantities (EDR) across different temperature intervals, which will be described as follows in detail.

The following reports on the radar-based parameters. Figure 13a compares the Doppler velocities of the falling ice crystals with different orientations. Overall, as the temperature increases (approaching 0 °C), ice particles gradually grow, and their fall velocities increase accordingly. Notably, across all temperature intervals, the Doppler velocities of HOICs are systematically lower than those of ROICs. This difference is particularly prominent in the -20 to -10 °C range, where HOIC frequently occurs. In the -30 to -20 °C range, although there is some overlap, a clear difference in the medians persists.

This phenomenon has a profound aerodynamic basis. As noted by Heymsfield and Iaquinta (2000), the horizontal orientation of an ice crystal causes its maximum cross-section to face the airflow, thereby significantly increasing the aerodynamic drag force and effectively slowing its terminal settling velocity. According to the fluid dynamic derivations by Pruppacher and Klett (2010), small ice crystals that have not undergone significant aggregation tend to maintain this quasi-horizontal stable posture, which maximizes drag, when the environmental Reynolds number is between 1 and 100. In contrast, ROICs often experience a sudden increase in mass due to aggregation or riming, or undergo tumbling caused by strong turbulent perturbations. This results in a reduction of their time-averaged drag coefficient, leading to larger terminal velocities under the influence of gravity.

Furthermore, the Doppler velocities observed here are slightly larger than those reported by Westbrook et al. (2010). For example, at -35 °C, they observed mean Doppler velocities of 0.25 and 0.3 m s⁻¹ for HOIC and ROIC, while the corresponding values in this study are approximately 0.5 and 0.6 m s⁻¹. This discrepancy likely reflects differences in observation instrument sensitivity: the backscattering cross-section of a millimeter-wave cloud radar scales with the sixth power of diameter (D6). Consequently, the cloud radar volume scattering signal is naturally dominated by larger (and faster-falling) particles (Donovan and Van Lammeren, 2001; Bühl et al., 2015). Consistent with our estimates, He et al. (2021) observed 32 HOIC events in Wuhan using polarization lidar and estimated fall velocities of 0.28 to 1.0 m s⁻¹ from depolarization ratio profiles.

Figure 13b and c reveal the dependence of ice crystal orientation on atmospheric turbulence from the perspectives of both retrievals and direct observations. Figure 13b shows the variation in retrieved EDR for different ice crystal orientations across various temperature intervals. This figure can be considered an alternative representation of Fig. 12b and c. Figure 13 further quantifies the conclusions drawn from Fig. 12: across all temperature intervals, the EDR in environments containing HOICs is significantly lower than that of ROICs, by nearly an order of magnitude on average. This is a novel finding with significant microphysical implications, providing valuable observational evidence for the parameterization of cloud microphysics schemes in numerical models, such as establishing turbulence cutoff thresholds for ice crystal orientation.

This conclusion is cross-validated by the Doppler spectral width distribution in Fig. 13c. Doppler spectral width, corresponding to the second moment of the radar Doppler spectrum, is directly measured by cloud radar without additional retrieval. High spectral width directly reflects a large dispersion in the fall velocities of the particle population within the sampling volume, strong wind shear, beam broadening, and high atmospheric turbulence intensity (Shupe et al., 2012; Li et al., 2021). The statistical results show that HOICs are associated with lower spectral widths, indicating their existence in environments with weak turbulence. Only under such dynamically stable conditions can ice crystals steadily maintain a horizontal posture. Once ambient turbulence intensifies (characterized by increased spectral width and EDR), not only is the stable posture of the ice crystals disrupted (transitioning to ROIC), but the intense turbulent mixing may also increase the collision probability among particles (Chellini and Kneifel, 2024).

Figure 13d shows that the radar reflectivity factor (dBZ) for HOIC is systematically lower than that for ROIC across all temperatures. Because radar reflectivity is strongly weighted toward larger particles, approximately following a sixth-power dependence on the particle diameter (D6) under the Rayleigh approximation, this further corroborates the inference of this study: HOICs represent relatively small, pristine ice crystals in stable environments that have not undergone significant aggregational growth. In contrast, ROICs contain abundant complex ice crystal aggregates with larger equivalent diameters resulting from aggregation, riming, or other intricate growth processes.

The single-profile case shown in Fig. 5 of Wu et al. (2025) reported that the reflectivity of ROIC at the cloud base was lower than that of the HOIC above it. This is likely not a contradiction, but rather a distinction between macro-statistics and micro-evolutionary stages. Actual observations indicate that the radar reflectivity factor of cloud radar is often smaller at cloud boundaries and larger in the middle of the cloud profile; cloud boundaries are typically on the verge of dissipation. In a single cloud profile, the cloud base is usually located within the dissipation zone of the cloud boundary. After falling out of the cloud base, ice crystals undergo intense sublimation, leading to a sharp decrease in particle size and number concentration, which in turn causes a steep drop in radar reflectivity. In contrast, the statistics in this section – based on a large sample size from the entire year of 2022 – cover HOIC and ROIC samples at various developmental stages within the cloud body. This filters out the interference from the edge dissipation effects of a single profile, thereby more accurately reflecting the microphysical size differences between the two orientation types of ice crystals throughout their entire life cycles.

Westbrook et al. (2010) pointed out that the distribution of cloud radar reflectivity factors in specular regions (HOIC) is almost identical to that in non-specular regions (ROIC). However, a closer inspection of their Fig. 19 reveals that HOICs may exhibit slightly lower dBZ values, particularly at temperatures below -20 °C.

Wu et al. (2025) presented the retrieval results of the microphysical characteristics of HOICs based on a single case study on 13 October 2022. To obtain statistical laws with greater climatological representativeness, Fig. 14, in conjunction with Table 1, further illustrates the distributions of the lidar-cloud radar retrieved particle Reynolds number and model-equivalent diameter of HOICs during the entire year of 2022. This retrieval utilized the same aerodynamic model as in Wu et al. (2025), assuming HOICs as hexagonal plates, and the resulting values should therefore be interpreted as first-order estimates rather than exact particle properties. The statistical analysis comprises over 150 000 valid retrieval points, covering a diverse range of macro- and micro-environmental cloud characteristics, thereby ensuring statistical significance. The retrieval was not applied to ROICs because their particle habits and orientations are not independently constrained, preventing unique estimates of Reynolds number and diameter from Doppler velocity alone.

As shown in Fig. 14a and Table 1, the annual statistics for HOIC diameters are primarily concentrated from 700 to 2000 µm, with median and mean values 1187 and 1249 µm, respectively. Compared to the single case (Wu et al., 2025), the annual scale distribution is broader, which reasonably reflects the complex and diverse microphysical evolutionary stages of cloud bodies in nature. It should be specifically noted that the HOIC scales retrieved in this study are overall larger compared to typical ice crystal populations. This is primarily limited by the inherent detection mechanism of millimeter-wave cloud radar: under the Rayleigh scattering approximation, the particle backscattering cross-section scales with the sixth power of diameter (D6) (Li, 2021). For the large HOIC particles retrieved here, however, this should be regarded as an approximate size-weighting argument rather than a strict Rayleigh-regime relationship. Consequently, the mean Doppler velocity observed by the cloud radar is actually a reflectivity-weighted fall velocity (Bühl et al., 2015), which is naturally dominated by the larger, faster-falling ice crystals within the cloud volume. In contrast, lidar backscattering is typically proportional only to the cross-sectional area (D2) (Stephens, 1994; Bohren and Huffman, 1998; Donovan and Van Lammeren, 2001). While retrievals based on lidar Doppler velocities would theoretically be biased toward smaller ice crystals, this study utilizes cloud radar data, which are inherently more sensitive to the “larger ice crystal population” that maintains a horizontal orientation. Consequently, the samples in this study likely miss small-scale HOICs. For instance, in Fig. B5 of Appendix B, the ground-based lidars identified HOIC in high-altitude cirrus (approximately 11 km), but the millimeter-wave cloud radar did not actually detect this cloud layer. Due to the lack of Doppler velocity observations, the scale retrieval for HOIC in that case could not be implemented. Since high-altitude cirrus clouds form at extremely low temperatures with limited water vapor supply, they typically consist of smaller ice particles (Heymsfield et al., 2017; Krämer et al., 2020).

Figure 14b presents another critical fluid dynamic parameter governing ice crystal orientation, the Reynolds number (Re), which characterizes how the surrounding air responds to the motion of sedimenting ice crystals. The histogram reveals that HOICs (with a third quartile of 59) mostly have Reynolds numbers distributed between 0 and 100, with cases exceeding 200 being rare. This implies that Re must remain relatively small to maintain the stable horizontal alignment of ice crystals.

Here, Re quantifies the relative importance of inertial and viscous effects during the ice crystal's descent, directly determining the wake instability of the microscopic flow field around the crystal. From an aerodynamic perspective, at low Re, the fluid maintains a stable laminar state over the ice crystal surface, and the forces on the crystal are uniform, allowing it to stably maintain a horizontal orientation that maximizes drag. Once Re exceeds a critical threshold, boundary layer separation occurs behind the crystal, generating periodic vortex shedding. These asymmetric aerodynamic lift forces and torques induce pitching and fluttering motions, eventually disrupting the horizontal posture (Pruppacher and Klett, 2010).

These retrieval results are consistent with laboratory fluid dynamic experiments. For example, List and Schemenauer (1971) observed the fall of solid snowflake particle analogs in salt solutions and glycerin-water mixtures and found that for five types of planar ice crystal geometries, stable descent was maintained when Re<100. When Re≈200, discs, broad-branched analogs and hexagonal plates began to exhibit small oscillations. Recently, sedimentation experiments by Stout et al. (2024) using 3D-printed plate analogs in a water-glycerin mixture further confirmed that solid hexagonal plates begin to undergo significant rocking and vibration when Re reaches 237.