Convective Boundary Layer Clouds as Observed with Ground-Based Lidar at a Mid-Latitude Plain Site

: A total of 3047 individual shallow cumuli were identiﬁed from 9 years of polarization lidar measurements (2011–2019) at Wuhan, China (30.5 ◦ N, 114.4 ◦ E). These fair-weather shallow cumuli occurred at the top edge of the convective boundary layer between April and October with the maximum occurrence in July over the 30 ◦ N plain site. They persisted mostly (>92%) for a short period of ~1–10 min and had a geometrical thickness of ~50–600 m (a mean of 209 ± 138 m). The majority (>94%) of the cloud bases of these cumuli were found to appear ~50–560 m (a mean of 308 ± 254 m) above the lifting condensation level (LCL). In this height range from the LCL to the cloud base, the lidar volume depolarization ratio ( δ V ) slightly decreased with increasing height, showing gradually increasing condensation in this sub-cloud region due to penetrative thermals. Most of the observed shallow cumuli (79%) formed under the conditions of high near-surface air temperature (>30 ◦ C) and water vapor mixing ratio (>15 g kg − 1 ).


Introduction
The atmospheric boundary layer (ABL) is the lowest part of the troposphere that is directly influenced by the earth's surface. It can respond to surface forcing within hours or less [1][2][3]. In the daytime, the earth's surface is heated by solar radiation to produce rising warm air plumes so that the ABL is controlled by thermal convection and is designated a "convective boundary layer (CBL)" or "mixing layer (ML)" [1]. Clouds play a pivotal role in the weather, climate, and regional/global hydrological cycle on Earth [4][5][6]. The Earth's radiation budget largely depends on the cloud coverage, height, thickness, and composition [7][8][9]. The hydrological cycle can be driven by the radiation balance and, in turn, determines where clouds form [10][11][12]. This coupling of clouds, water circulation, and radiation budget composes the feedback process, and clouds, especially low clouds, are the main uncertainty in the system [13]. Under fair-weather conditions, convective clouds or shallow cumuli would form on the top of the plumes when moisture is sufficient [14]. The shallow cumuli are likely to have cloud bases at the lifting condensation levels (LCL) or above [15]. Although shallow cumuli have coverage of only~5% over land and~12% over ocean [16,17], they can significantly influence the solar radiation to the earth's surface [18], modify the structure of the CBL by affecting turbulent mixing [19], and play a significant role in the initiation of ice or precipitation [20,21].
Various measurements with ground-based lidar/radar and airborne and spaceborne sensors have revealed the cloud morphology and statistical properties of shallow cumuli. They can exist for several minutes with a typical horizontal scale of~1 km or less [14,22,23]. Their geometrical thickness is mostly less than 1 km [24]. The cloud top/base heights and their spatial/temporal distributions for shallow cumuli over the tropical belt and the Tibet Plateau have been characterized based on the spaceborne lidar measurements (the cloud-aerosol lidar and infrared pathfinder satellite observation, CALIPSO). Most shallow cumuli over the tropical ocean have cloud tops below 3 km, whereas those over tropical land tend to have higher cloud tops which are more strongly affected by diurnal variation in convection [25]. Cumulus clouds represent one of the dominant cloud types over the Tibet Plateau in the northern summer. The corresponding occurrence rate is much higher than that in the Tibet Plateau's surrounding regions [26]. Rodts et al. [27], using aircraft in situ measurements, found that the mass flux and buoyancy flux were dominated by intermediate-sized clouds (horizontal dimension of about 1 km) while the cloud fraction was by the smallest clouds (horizontal dimension less than 1 km), stating that the large-sized clouds contribute more to the dynamical properties, and the small-sized clouds largely outnumber the large-sized clouds. Based on the three-day observations of updraft and downdraft in the convective boundary layer with a ground-based Doppler lidar on a 51.4 • N flat terrain, the relationship between the draft occurrence frequency and the shallow cumulus formation has been examined [28]. In the case of cumulus formation, the draft is enhanced by~50% in frequency near the cloud base.
The atmospheric radiation measurement (ARM) climate research facility southern Great Plains (SGP) sites are located in north-central Oklahoma and south Kansas (36.5 • N), a flat area that is sparsely populated. Combined observations with remote and in situ sensors at the ARM SGP sites have yielded a comprehensive look into the characteristics of continental shallow cumulus clouds and corresponding CBL atmospheric conditions [14,23,[29][30][31]. The cloud properties show a clear-cut diurnal cycle [29]. The cloud fraction has a maximum value at around 14:00 local time (LT), which is sensitive to both the low-level moisture and the surface sensible heat flux. The average cloud-base height rises throughout the day, while the average cloud thickness falls with time. It is shown that the vertical velocity has increased variance during periods of medium cloud cover and larger skewness on shallow cumulus days than on clear-sky days [14]. The clouds with a positive cloud-based mass flux account for 63% of clouds and are linked to coherent updrafts extending over the entire CBL. In contrast, negative mass flux clouds lack coherent subcloud (the region below cloud base) drafts. Although many works have been reported, there is still a lack of research based on process-level observation that can present the detailed characterization of variation and structure of the cumulus.
The shallow cumuli remain, however, incompletely represented in general circulation models (GCMs) because of their small time (~10 min or less) and space (~1 km) scales, as well as behavior differences under different weather systems [14,32]. As a result, the GCMs suffer from errors in the location, timing, and extent of shallow clouds [33], which then affects the other components of the simulated system such as the structure of the ABL [34]. Moreover, the lifting mechanism varies on the distinct underlying surfaces (continent or ocean, mountain or plain, urban or rural area, forested or deforested surface) [30,[35][36][37][38]. To deepen our understanding relevant to the formation of the CBL cumuli, and enhance the performance of the GCMs, long-term, routine, and process-level lidar observations at more sites with different latitudes and underlying surfaces are required.
This work presents the long-term CBL cumulus observations using a ground-based polarization lidar. The polarization lidar has been operated routinely under fair weather conditions since October 2010 at Wuhan University atmospheric observatory, Wuhan, China (30.5 • N, 114.4 • E) [39]. The shallow cumuli were observed on 117 out of 848 observational days during 2011-2019. Each cumulus cloud day contains at least 6-hour lidar profiles in the period from 09:00 to 18:00 LT. Such abundant lidar data, together with simultaneously collected surface weather parameters, allow us to systematically investigate the continental cumulus cloud formation and relevant CBL atmospheric conditions over a megacity located on a mid-latitude plain. Here, this paper starts with instruments and methodology in Section 2. Then, Section 3 presents two examples and statistics on the observed shallow cumuli. The discussion and conclusions are finally given in Sections 4 and 5.

Instruments and Methodology
Cloud observations were made by a 532 nm polarization lidar deployed at Wuhan University atmospheric observatory. The observatory site (70 m above sea level) is located on a vegetation-covered small hill with a maximum peak height of 118 m which lies in the heart of the city of Wuhan. Wuhan is an industrialized megacity in central China. It is situated on the eastern Jianghan Plain, which has an area of~46,000 km 2 and a mean elevation of only 27 m above sea level. Wuhan has a humid subtropical climate with abundant rainfall and four distinctive seasons.

Polarization Lidar
During the period from October 2010 to the end of 2019, all of the polarization lidar observation sessions started under fair weather conditions and were terminated before extensive cloud cover or precipitation. The system parameters of our polarization lidar and its performance have been described in detail by Kong and Yi [39]. Here, we brief the technical improvement about its polarization measurement. A Brewster polarizer is used to increase the polarization purity of the output laser beam (up to 10,000:1). In the receiver optics, two additional polarizers are placed, respectively, on the two output sides of the polarization beam splitter prism (PBS) to reduce the crosstalk (probably occurring during cloud observation) between the two orthogonal polarization channels. The raw lidar data were stored with a vertical resolution of 3.75 m and a temporal resolution of 1 min. The lowest measurement height was 0.3 km due to an overlap factor effect caused by the off-axis lidar design.
The backscatter ratio (BSR) is defined as the ratio of the total (particulate and molecular) backscatter coefficient divided by the molecular one. It generally reflects the content of aerosols or clouds. For the standard lidar equation, two unknown variables (backscatter coefficient and extinction coefficient) are included in one equation. We need to make the following assumptions [40]: the molecular lidar ratio (molecular extinction coefficient divided by molecular backscatter coefficient) can be calculated from Rayleigh scattering theory, the lidar ratio (aerosol extinction coefficient divided by aerosol backscatter coefficient) is chosen according to the type of dominated aerosol, and the backscatter ratio BSR is known at a certain height. Once the assumptions are confirmed, there are two options to solve the lidar equation. The first is choosing the reference height without aerosols at a high altitude, assuming the BSR value, and making the backward integration (from the reference height to the surface). The result of this option is stable and this is the common choice for aerosol study. The other option is choosing the reference height at a low altitude, confirming the BSR value, and making the forward integration (from the low to the high altitude). The forward integration is unstable and may encounter the failure of retrieval.
Normally, for optically thin layers, the backscatter ratio BSR can be retrieved from the Mie signal (backscatter signal from aerosols or clouds) profile of lidar by assuming a constant lidar ratio and choosing an aerosol-free reference altitude. In the case of cloud, it is always difficult to find a reference altitude above the cloud base due to strong attenuation. In this study, the backward retrieval scheme with a lidar ratio of 50 sr and a reference altitude of~7 km was utilized for the cloud-free profiles [41], while the forward retrieval scheme with a lidar ratio of 18.6 sr and a reference altitude of~0.3 km was used for the cloud profiles [42]. The error of R comes from the noise of the signal, lidar ratio, and BSR at the reference height. In this study, the backward retrieval uncertainty of R is estimated as 15-20% (corresponding to the uncertainty of 10% and 4% for lidar ratio and BSR at the reference height, respectively) based on the error analysis by Comerón et al. [43]. As for the forward retrieval, the uncertainty of BSR at the reference height is larger due to the variation of aerosols at the low altitude. If we assume the uncertainty of the lidar ratio and BSR at the reference height is 10% and 50%, respectively, the uncertainty of BSR is estimated to be 45-55%.
Besides, the CBL height was calculated by using the variance method [39,44] based on 30 min cloud-free BSR profiles (if available). The foundation of the variance method is taking the aerosols as the tracer of the convective evolution of the boundary layer. The maximum in the vertical profile of the variance of BSR is taken as the CBL height. The height values in this article are all relative to sea level.
The volume depolarization ratio δ V is defined as the ratio of the perpendicular-to parallel-polarized backscatter coefficients. It can be calculated from the lidar signals of the two channels with the channel relative gain calibrated in advance using a method presented by Freudenthaler et al. [45]. The δ V could be used to investigate the particle shapes of clouds and aerosols [46], enabling us to obtain the sub-cloud liquid droplet layer properties due to condensation or hygroscopic growth [47].

Surface Weather Station
A surface weather station (CR800, made by Campbell Scientific, Inc., Logan, UT, USA) was installed near our 532 nm polarization lidar from March 2010. This allowed us to obtain the surface temperature, relative humidity, horizontal wind speed, and direction in 1 min time resolution, showing the surface meteorological parameters during the presence of shallow cumuli. Due to instrument breakdown, the data for the periods of August 2014, February-August 2015, and February-May 2016 are not available.

Cloud Camera
A fisheye lens camera was placed beside the lidar for taking all-sky images over our site from August 2018. The fisheye camera has a field-of-view (FOV) of 108 • . The all-sky images were captured every 2 min and stored automatically. The all-sky images were used to confirm that the formation or dissipation process of the cumulus occurred in the fieldof-view of our lidar. In this study, we only utilized the lidar data with the simultaneous all-sky images from August 2018 to December 2019 to present the case studies.

Cloud Information and Event Identification
In terms of the range-squared-corrected lidar signal (X) profile, the shallow cumulus clouds are characterized by large signal enhancement in a narrow height range (~300 m or less) at the top of the convective boundary layer (see Figure 1). The cloud base can be defined as a height above which the signal enhancement starts immediately. In the narrow height range, the cloud peak was determined as a height where the range-corrected lidar signal maximizes. The cloud base, peak, and top height were calculated using the method introduced by Platt et al. [48]. In detail, the cloud base was determined as the level at which the signal continued to increase for at least 5 height intervals. The cloud top (or effective top) was calculated as the level at which the signal continued to decrease for 5 height intervals. If the continuous decrease search failed, the height at which the signal drops to the background level was defined as the effective top. Then, the cloud peak height was the level at which the signal maximized. Following the criterion of the peak-to-base signal ratio for distinguishing cloud from aerosol layers [49], the signal profile was registered as a cumulus cloud profile when the ratio value was larger than 4.0. For identifying individual cumulus cloud events, we consecutively surveyed all the 117-day sequences of the 1-min lidar signal profiles according to the criterion of peak-to-base ratio value of 4.0. Figure 1 presents a typical cumulus lidar profile and the cloud information determined by the abovementioned method. The lifting condensation level (LCL), cloud base height, cloud peak height, and cloud top height are shown, respectively, by the black long dash, red long dash, red dash-dotted, and red short dash lines.
A cumulus cloud event was defined as follows. For sequences of the 1 min rangesquared-corrected lidar signal profiles, the event started with a cloud-free profile and ended with a cloud profile. The interval between the two events must be larger than 3 min (3 cloud-free profiles). A cumulus case day must contain at least 10 events. For a short-duration cumulus cloud event for which the lidar signal enhancement was visible in only one single profile, its parameters (cloud base/peak/top) were obtained simply from the 1 min profile. For a long-duration cumulus cloud event where the signal enhancement was discernible in several consecutive profiles (occurring in nearly the same height range), its parameters were from the average of the consecutive profiles. A cumulus cloud event was defined as follows. For sequences of the 1 min rangesquared-corrected lidar signal profiles, the event started with a cloud-free profile and ended with a cloud profile. The interval between the two events must be larger than 3 min (3 cloud-free profiles). A cumulus case day must contain at least 10 events. For a shortduration cumulus cloud event for which the lidar signal enhancement was visible in only one single profile, its parameters (cloud base/peak/top) were obtained simply from the 1 min profile. For a long-duration cumulus cloud event where the signal enhancement was discernible in several consecutive profiles (occurring in nearly the same height range), its parameters were from the average of the consecutive profiles.

Lifting Condensation Level
The lifting condensation level (LCL) is the height at which water vapor in an air parcel becomes saturated if the parcel is lifted adiabatically. It simplifies some actual physics processes (heat exchange, condensation) happening in the upward air parcel and can be used as a reasonable estimate of cloud base height when parcels experience forced ascent [50]. We present the CBL height evolution and LCL variation during the daytime to discuss the formation mechanism of cumulus in case studies. Besides, we compare the observed cloud base height with the calculated LCL and infer what causes the difference. The LCL ZLCL was computed from the surface temperature (T) and relative humidity (RH) Figure 1. A plot of 1 min polarization lidar range-squared-corrected signal X profile observed at 1125 LT on 9 August 2019. The lifting condensation level (LCL), cloud base height, cloud peak height, and cloud top height are shown, respectively, by the black long dash, red long dash, red dash-dotted, and red short dash lines. The LCL is calculated based on Equation (1) in Section 2.2.2.

Lifting Condensation Level
The lifting condensation level (LCL) is the height at which water vapor in an air parcel becomes saturated if the parcel is lifted adiabatically. It simplifies some actual physics processes (heat exchange, condensation) happening in the upward air parcel and can be used as a reasonable estimate of cloud base height when parcels experience forced ascent [50]. We present the CBL height evolution and LCL variation during the daytime to discuss the formation mechanism of cumulus in case studies. Besides, we compare the observed cloud base height with the calculated LCL and infer what causes the difference. The LCL Z LCL was computed from the surface temperature (T) and relative humidity (RH) using the approximation [51]: Remote Sens. 2021, 13, 1281 6 of 18

Results
The polarization lidar started routine operation under fair weather in October 2010, and a total of~20,000 hours of lidar data were collected till the 31st of December, 2019. Using the abovementioned method, 117 days with CBL cumulus occurrence are determined out of 848 observation days between the 1st of January, 2011 and the 31st of December, 2019. Benefitting from the 1 min time and 3.75 m range resolution of our lidar, the processes of cumulus formation, evolution, and dissipation could be captured. In this section, we start with two representative cases, followed by a series of statistics of the CBL cumulus from 117 case days. Meanwhile, the LCL was always above the CBL height, maintaining a state which was unsuited to the formation of cumuli. The surface T and water vapor mixing ratio (WVMR) generally kept growing, as seen from Figure 2c. However, after a rapid-rise phase, the CBL height jumped over and maintained above the LCL from 11:30 to 15:30 LT. During this period, it could be expected that the increasing surface moisture was transported upward (a decrease of surface WVMR could be found at~11:00 LT from Figure 2c) by convective lifting (surface T above 35 • C), filling the growing CBL. As air parcels with sufficient moisture were lifted across the LCL level, they could become oversaturated, which led to the formation of a series of clouds in a height range of 1.2-2.0 km. A total of 19 intermittent cumulus events were observed during this period, with each lasting less than 15 min. From Figure 2b, the region under the cumulus base presented relatively low δ V values during 13:00-16:00 LT, suggesting the existence of water droplets. The CBL height began decreasing rapidly from 15:00 LT, and was lower than the LCL after 15:30 LT; the accompanying surface T started a sharp decrease, indicating that the net radiation to the surface became negative starting from this period, and the thermal convection would weaken. The surface WVMR presented a sudden decrease starting from 15:25 LT, a short delay in contrast to the decrease in surface T. No other cumulus events were observed after 15:00 LT.

Case on 9 August 2019
To demonstrate the short time evolution of the cumulus cloud, a representative event was chosen and the corresponding sequences of the 1 min backscatter ratio BSR and δ V profiles during 11:24-11:29 LT on the 9th of August, 2019 are plotted in Figure 3a. The quasi-simultaneous all-sky images (captured every 2 min) are also shown in Figure 3b to confirm that the cumulus forms/dissipates in the lidar field-of-view (FOV). As seen from Figure 3a, no liquid water layer or cloud was observed above the LCL (~1.07 km) at 11:24 LT. One minute later, the initial stage of cumulus was observed, with a cloud base height of~1.27 km. The cumulus cloud peak was located at~1.3 km with a peak BSR of 84 and a corresponding δ V of~0.019. A height interval of~0.2 km for the sub-cloud zone (defined as the zone between the cloud base and LCL) suggests that strong updrafts from the air mass precipitate the phase transition from water vapor to liquid. The profiles at 11:26 and 11:27 LT showed a steady cloud base (~1.26 km and~1.25 km, respectively) and denser, broader cloud body (respective peak BSR of~135 and~504, more condensed liquid water) contrasting to the 11:24 LT profile. Then, at 11:28 LT, the peak BSR was~92 and the corresponding δ V~0 .018; the cumulus structure became similar to the initial stage, probably due to the high environmental temperature and lack of lifted water supply, then, that part of the condensed water evaporated. Up to 11:29 LT, the cumulus dissipated completely. The cloud thickness did not exceed 150 m for all of the four cumulus profiles. Note that the profile values of BSR in the sub-cloud zone showed an increment with height, while Remote Sens. 2021, 13, 1281 7 of 18 the corresponding δ V exhibited a slow decrement throughout the event. This suggests that the sub-cloud region is rich in aerosols lifted by convection and the water droplets, which form via the lifting condensation or convective condensation, supplying moisture for the cloud above.
Remote Sens. 2021, 13, x FOR PEER REVIEW 7 of 20 due to the high environmental temperature and lack of lifted water supply, then, that part of the condensed water evaporated. Up to 11:29 LT, the cumulus dissipated completely. The cloud thickness did not exceed 150 m for all of the four cumulus profiles. Note that the profile values of BSR in the sub-cloud zone showed an increment with height, while the corresponding δ exhibited a slow decrement throughout the event. This suggests that the sub-cloud region is rich in aerosols lifted by convection and the water droplets, which form via the lifting condensation or convective condensation, supplying moisture for the cloud above.   Figure 4 provides another case of a CBL cumulus observed on the 31st of July, 2019. As seen from Figure 4a, the CBL height started growing at 08:00 LT from ~0.38 km along with growing surface WVMR, and reached 1.09 km at 11:30 LT. Starting from 12:00 LT, the CBL height jumped over the LCL; meanwhile, the surface WVMR exhibited a sharp decrease, indicating abundant moisture had been transported upward around 12:00 LT. The CBL maintained higher than the LCL and the cumuli occurred in the height range of 1.1-2.0 km. A total of 10 cumulus events were observed from 12:00 to 16:30 LT. Similarly, the region under the cumulus presented relatively low δ values during 12:00-17:00 LT (Figure 4b). The CBL height turned to be lower than the LCL from 16:30 LT, while the surface WVMR experienced a decrease at ~17:00 LT. Henceforth, no more CBL cumulus events were observed after 16:30 LT. The clouds around ~1.8 km at 17:40 LT were inferred as cumulonimbus via the all-sky image (not shown here), and the weather turned from fair to rainy in about 30 min. It is interesting that the surface WVMR suddenly dropped to a relatively low value at ~18:30 LT, probably contributing to the coming precipitation. Figure 5a presents four sequential 1 min profiles of BSR and δ , displaying a quasicomplete CBL cumulus cloud event from 12:49 to 12:52 LT on the 31st of July, 2019. As seen from Figure 5b, the cumulus started forming at 12:47 LT, which could be recognized via the all-sky image (but not in the FOV of the lidar) at 12:49 LT, came into the FOV of the lidar at 12:51 LT and broke into dissipation at 12:53 LT. According to Figure 5a, the initial stage of the cumulus formation was not captured by our lidar at 12:49 LT. However, the evolution and dissipation processes from 12:50 to 12:52 LT were recorded. The cumulus cloud base was around 0.47 km (sub-cloud zone thickness) above the LCL (~1.05 km). Similar to the profile structure of the first event, an increment with height for the BSR and a slow decrement for the δ could be found from the profiles at 12:50 and 12:51 LT. In addition, the cumulus cloud base at 12:51 LT was ~1.62 km, about ~0.11 km higher than that at 12:50 LT. This height bias might be due to the sub-cloud air mass updraft during the two minutes. Note that a microlayer stratification structure could be found below the cloud base at 12:51 LT. The cloud peak BSR was ~326 (at ~1.68 km for 12:50 LT) and ~478  Figure 4 provides another case of a CBL cumulus observed on the 31st of July, 2019. As seen from Figure 4a, the CBL height started growing at 08:00 LT from~0.38 km along with growing surface WVMR, and reached 1.09 km at 11:30 LT. Starting from 12:00 LT, the CBL height jumped over the LCL; meanwhile, the surface WVMR exhibited a sharp decrease, indicating abundant moisture had been transported upward around 12:00 LT. The CBL maintained higher than the LCL and the cumuli occurred in the height range of 1.1-2.0 km. A total of 10 cumulus events were observed from 12:00 to 16:30 LT. Similarly, the region under the cumulus presented relatively low δ V values during 12:00-17:00 LT (Figure 4b). The CBL height turned to be lower than the LCL from 16:30 LT, while the surface WVMR experienced a decrease at~17:00 LT. Henceforth, no more CBL cumulus events were observed after 16:30 LT. The clouds around~1.8 km at 17:40 LT were inferred as cumulonimbus via the all-sky image (not shown here), and the weather turned from fair to rainy in about 30 min. It is interesting that the surface WVMR suddenly dropped to a relatively low value at~18:30 LT, probably contributing to the coming precipitation. Figure 5a presents four sequential 1 min profiles of BSR and δ V , displaying a quasicomplete CBL cumulus cloud event from 12:49 to 12:52 LT on the 31st of July, 2019. As seen from Figure 5b, the cumulus started forming at 12:47 LT, which could be recognized via the all-sky image (but not in the FOV of the lidar) at 12:49 LT, came into the FOV of the lidar at 12:51 LT and broke into dissipation at 12:53 LT. According to Figure 5a, the initial stage of the cumulus formation was not captured by our lidar at 12:49 LT. However, the evolution and dissipation processes from 12:50 to 12:52 LT were recorded. The cumulus cloud base was around 0.47 km (sub-cloud zone thickness) above the LCL (~1.05 km). Similar to the profile structure of the first event, an increment with height for the BSR and a slow decrement for the δ V could be found from the profiles at 12:50 and 12:51 LT. In addition, the cumulus cloud base at 12:51 LT was~1.62 km, about~0.11 km higher than that at 12:50 LT. This height bias might be due to the sub-cloud air mass updraft during the two minutes. Note that a microlayer stratification structure could be found below the cloud base at 12:51

Statistical Characteristics of the CBL Cumulus
The two cases along with two events in Sections 3.1 and 3.2 presented some similar features. Hereafter, statistics were made to explore whether these features are ubiquitous for CBL cumuli.

Statistical Characteristics of the CBL Cumulus
The two cases along with two events in Sections 3.1 and 3.2 presented some similar features. Hereafter, statistics were made to explore whether these features are ubiquitous for CBL cumuli.

Seasonal Distribution
Based on 848 day lidar observations from 2011 to 2019 at Wuhan, the monthly occurrence of the CBL cumulus is displayed in Figure 6. A total of 117 cumulus cloud days were identified. The observation days for each month are over 45, except for February when the lidar might stop operation due to the traditional Chinese Spring Festival vacation. The majority (~74%) of the cumulus days occur in summer, with corresponding occurrence frequency of~44% (July),~32% (August), and~24% (June), respectively. About 26% of the cumulus days occur in late spring (April, May) and early autumn (September, October). No cumulus events are observed in the period from November to March. Wuhan's climate is humid subtropical with abundant rainfall in summer and four distinctive seasons. The summer is humid along with strong solar radiation, providing moisture and lifting energy for the cumulus formation. Hence, the cumulus is more likely to form via convective lifting during summertime.   Figure 8 gives the statistical distributions of the CBL cumulus base height, top height, peak height, and geometrical thickness between 2011 and 2019. Figure 8a indicates that the CBL cumulus mostly (~72% out of all the events) occurs in a height range of 0.9-1.7 km. The average cloud base height is ~1.3 ± 0.38 km. According to Kong and Yi [39], the mean value of the maximum CBL height under fair weather conditions over our station is 1.24 km in spring and 1.27 km in summer, respectively. The average CBL cloud base height is slightly above the fair weather maximum CBL height, suggesting the cumuli are more likely to form at the top of the CBL. From Figure 8b, c, the cumulus top and peak are mostly located at the height range of 1.1-1.9 km (~70%) and 1.1-1.7 km (~70%), respectively. The average cumulus top height is ~1.51 ± 0.4 km and the peak height ~1.41 ± 0.14 km. Figure 8d shows that the CBL cumuli over Wuhan are dominated by shallow cumulus (70% of the events have a thickness of <250 m and the average is ~210 m). The seasonal difference is not apparent for cloud base/top/peak height, and thickness.

Cumulus Height Statistics
The LCL versus the cumulus base height pertinent to 2744 cumulus events from 2011 to 2019 is plotted in Figure 9. Unlike the results from [29] (a good agreement between the LCL and the cloud base height), the cloud base height over Wuhan is overwhelmingly higher than the pertinent LCL. 96% (2626 out of 2744) of the events present this situation and the average bias between the cloud base height and LCL is 308 ± 254 m. The possible explanation is as follows: the LCL is calculated based on surface temperature, and RH is the level where the updraft air mass becomes saturated; however, the air mass is likely to overshoot this level due to inertia. Therefore, it can be speculated that rapid condensation of updraft air mass will occur in the sub-cloud zone during the abovementioned process; accordingly, the will present a decreasing trend along the height. A similar structure could be found from the WVMR structure of the tropical atmosphere in Garstang and Betts [53]. The WVMR in the sub-cloud zone presented a decrease along height, meaning that water droplets formed increasingly along the height. The blue bar, yellow bar, and red bar represent, respectively, the number of events in summer (June, July, and August), autumn (September, October, and November), and spring (March, April, and May). Note that the cumulus clouds formed mostly (>95%) during the period of 09:00-18:00 LT, while their duration mostly (>92%) ranged from 1 to 10 min. Figure 8 gives the statistical distributions of the CBL cumulus base height, top height, peak height, and geometrical thickness between 2011 and 2019. Figure 8a indicates that the CBL cumulus mostly (~72% out of all the events) occurs in a height range of 0.9-1.7 km. The average cloud base height is~1.3 ± 0.38 km. According to Kong and Yi [39], the mean value of the maximum CBL height under fair weather conditions over our station is 1.24 km in spring and 1.27 km in summer, respectively. The average CBL cloud base height is slightly above the fair weather maximum CBL height, suggesting the cumuli are more likely to form at the top of the CBL. From Figure 8b, c, the cumulus top and peak are mostly located at the height range of 1.1-1.9 km (~70%) and 1.1-1.7 km (~70%), respectively. The average cumulus top height is~1.51 ± 0.4 km and the peak height~1.41 ± 0.14 km. Figure 8d shows that the CBL cumuli over Wuhan are dominated by shallow cumulus (70% of the events have a thickness of <250 m and the average is~210 m). The seasonal difference is not apparent for cloud base/top/peak height, and thickness.

Cumulus Height Statistics
The LCL versus the cumulus base height pertinent to 2744 cumulus events from 2011 to 2019 is plotted in Figure 9. Unlike the results from [29] (a good agreement between the LCL and the cloud base height), the cloud base height over Wuhan is overwhelmingly higher than the pertinent LCL. 96% (2626 out of 2744) of the events present this situation and the average bias between the cloud base height and LCL is 308 ± 254 m. The possible explanation is as follows: the LCL is calculated based on surface temperature, and RH is the level where the updraft air mass becomes saturated; however, the air mass is likely to overshoot this level due to inertia. Therefore, it can be speculated that rapid condensation of updraft air mass will occur in the sub-cloud zone during the abovementioned process; accordingly, the δ V will present a decreasing trend along the height. A similar structure could be found from the WVMR structure of the tropical atmosphere in Garstang and Betts [53]. The WVMR in the sub-cloud zone presented a decrease along height, meaning that water droplets formed increasingly along the height. Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 20  In order to verify the decreasing trend along with height in the sub-cloud zone, comparisons of at the LCL level and cloud base level are plotted in Figure 10. The LCL and cloud base were an average from eight height intervals which were above the LCL and below the cloud base, respectively. 1515 out of the 1941 (78%) counted events (803 events were excluded due to the low SNR) presented a decrease trend along In order to verify the δ V decreasing trend along with height in the sub-cloud zone, comparisons of δ V at the LCL level and cloud base level are plotted in Figure 10. The LCL δ V and cloud base δ V were an average from eight height intervals which were above the LCL and below the cloud base, respectively. 1515 out of the 1941 (78%) counted events (803 events were excluded due to the low SNR) presented a δ V decrease trend along height. The average δ V decrease between these two levels is 0.0045 ± 0.0058.  Figure 11, the majority (>79%) of the cumulus events occurred under the surface meteorological conditions of the near-surface temperature being higher than 30 °C and the WVMR larger than 15 g kg −1 . The cumulus day surface T versus WVMR presents a clustering pattern with a linear correlation coefficient of ~0.81. The average near-surface WVMR in Lareau, Zhang, and Klein [14] was lower than 15 g kg −1 , while the result at our site was 19.9 g kg −1 (a relatively large value). We infer that high near-surface temperature (mostly in summertime under fair-weather) is more likely to cause disturbances [55] and thus initiate thermal convection, promoting the formation of cumulus.

Surface Meteorological Parameters
The surface T versus WVMR for cumulus days during 2011-2019 are plotted in Figure 11. As seen from Figure 11, the majority (>79%) of the cumulus events occurred under the surface meteorological conditions of the near-surface temperature being higher than 30 • C and the WVMR larger than 15 g kg −1 . The cumulus day surface T versus WVMR presents a clustering pattern with a linear correlation coefficient of~0.81. The average near-surface WVMR in Lareau, Zhang, and Klein [14] was lower than 15 g kg −1 , while the result at our site was 19.9 g kg −1 (a relatively large value). We infer that high near-surface temperature (mostly in summertime under fair-weather) is more likely to cause disturbances [55] and thus initiate thermal convection, promoting the formation of cumulus. s. 2021, 13, x FOR PEER REVIEW 16 of 20 Figure 11. Scatterplot showing the relationship between surface air temperature (T) and water vapor mixing ratio (r) associated with 2744 shallow cumulus cloud events observed by our polarization lidar. Note that the shallow cumulus cloud events occurred mostly (>79%) when the near-surface temperature T was higher than 30° C and the WVMR larger than 15 g kg −1 .

Discussion
Fair-weather cumulus could be classified as "forced" and "active" cumulus [22]. The "forced" cumulus presents a thinner vertical extent or physical geometrical thickness and a shorter lifetime [56]. "Forced" cumulus forms via the convective lifting of surface thermals and locates at the top edge of the convective boundary layer. The two representative cumulus day cases in Section 3.1 and 3.2 exhibited the summer daytime occurrence of "forced" shallow cumulus. The two events were chosen to reflect a clear-cut process for a single shallow cumulus cloud evolving from formation to disappearance that could be simultaneously registered in both the lidar measurement and ground-based camera. Since many factors (e.g., small lidar FOV vs. quite large FOV for the ground camera, multiple shallow cumulus clouds in camera FOV, and wind advection) affect the availability of such cases, the two chosen cases actually represent the best examples in the simultaneous camera and lidar observations depicting the formation and vanishing of the single shallow cumuli. They provide the direct observation of the cloud physics process in the natural atmosphere. However, the temporal resolution of our lidar is 1 min while the cumulus formation and its variation could occur within 1 min. A higher temporal resolution lidar and cloud camera observation could investigate the short-time scale and fine vertical structure of the CBL clouds. A full-day operation polarization lidar with a tilted emitting laser and a much higher time resolution (10 s) has been built by Liu et al. [57], and the finer process-level observations can be expected in the future.
The cloud top determination is very sensitive to the cloud optical depth [58]. The CBL cumuli observed over Wuhan present mostly short duration and small size (according to Figure 7b and cloud images). In this study, the cloud top and cloud geometrical thickness should be underestimated slightly.
The GCMs suffer from errors in the location, timing, and extent of shallow clouds. The statistical study of cumulus can be a dataset from an urban area at a mid-latitude plain site, containing the location, onset time, and thickness information. Meanwhile, other researchers who are interested in using spaceborne instruments to explore the cumulus over different underlying surfaces can refer to our results [25]. Figure 11. Scatterplot showing the relationship between surface air temperature (T) and water vapor mixing ratio (r) associated with 2744 shallow cumulus cloud events observed by our polarization lidar. Note that the shallow cumulus cloud events occurred mostly (>79%) when the near-surface temperature T was higher than 30 • C and the WVMR larger than 15 g kg −1 .

Discussion
Fair-weather cumulus could be classified as "forced" and "active" cumulus [22]. The "forced" cumulus presents a thinner vertical extent or physical geometrical thickness and a shorter lifetime [56]. "Forced" cumulus forms via the convective lifting of surface thermals and locates at the top edge of the convective boundary layer. The two representative cumulus day cases in Sections 3.1 and 3.2 exhibited the summer daytime occurrence of "forced" shallow cumulus. The two events were chosen to reflect a clear-cut process for a single shallow cumulus cloud evolving from formation to disappearance that could be simultaneously registered in both the lidar measurement and ground-based camera. Since many factors (e.g., small lidar FOV vs. quite large FOV for the ground camera, multiple shallow cumulus clouds in camera FOV, and wind advection) affect the availability of such cases, the two chosen cases actually represent the best examples in the simultaneous camera and lidar observations depicting the formation and vanishing of the single shallow cumuli. They provide the direct observation of the cloud physics process in the natural atmosphere. However, the temporal resolution of our lidar is 1 min while the cumulus formation and its variation could occur within 1 min. A higher temporal resolution lidar and cloud camera observation could investigate the short-time scale and fine vertical structure of the CBL clouds. A full-day operation polarization lidar with a tilted emitting laser and a much higher time resolution (10 s) has been built by Liu et al. [57], and the finer process-level observations can be expected in the future.
The cloud top determination is very sensitive to the cloud optical depth [58]. The CBL cumuli observed over Wuhan present mostly short duration and small size (according to Figure 7b and cloud images). In this study, the cloud top and cloud geometrical thickness should be underestimated slightly.
The GCMs suffer from errors in the location, timing, and extent of shallow clouds. The statistical study of cumulus can be a dataset from an urban area at a mid-latitude plain site, containing the location, onset time, and thickness information. Meanwhile, other researchers who are interested in using spaceborne instruments to explore the cumulus over different underlying surfaces can refer to our results [25].

Conclusions
Two typical CBL cumulus occurrences in fair-weather summer over a megacity at a mid-latitude site was exhibited by polarization lidar, simultaneous surface weather station, and cloud camera measurements. The cumulus was most likely to form at the top of the CBL when the CBL height jumps over the LCL. The clear-cut process-level cumulus formation and its sub-cloud variation were displayed. This provides us a direct observation of the shallow convective cloud in the CBL and deepens our understanding of cloud physics in the low-level atmosphere.
Convective boundary layer clouds were statistically investigated based on extensive polarization lidar measurements on 848 different days from 2011 to 2019 at Wuhan, China (30.5 • N, 114.4 • E). A total of 3047 individual shallow cumulus events were identified from 117 different days out of the total 848 observational days. The 117 shallow cumulus days (each cumulus cloud day contained at least 10 cumulus cloud events) were distributed between April and October with the maximum occurrence in July. They formed mostly (>95%) in the period of 09:00-18:00 LT while surface air temperature and water vapor mixing ratio were generally larger than 30 • C and 15 g kg −1 , respectively.
These fair-weather shallow cumuli occurred at the top edge of the convective boundary layer with a duration of 1-10 min (79% having a duration of 1-5 min) and a geometrical thickness of~50-600 m (70% having a geometrical thickness less than 250 m). Their cloud base height ranged from 0.5 to 1.9 km. The lifting condensation level (LCL) was estimated to appear~50-560 m (a mean of 308 ± 254 m) below the cloud base. In the height range from the LCL to the cloud base, the lidar volume depolarization ratio (δ V ) slightly decreased with increasing altitude, showing a gradually increasing condensation in this sub-cloud region due to penetrative thermals.
The current study provides the statistical results of shallow cumulus cloud properties and formation conditions based on the polarization lidar and surface weather station observations at a 30 • N plain site. It supplements the existing data library of locally generated surface-forced shallow cumuli that has been established in terms of long-term continuous ground-based observational data at a couple of sites in the mid-latitude region [14,59,60]. Long-term observations at low-latitude sites are urgently required at present in order to efficiently develop and improve conventional global climate models. In addition, the cumulus cloud formation (mechanism and characteristics) also depends on underlying surface conditions [30,[35][36][37][38]. Thus, long-term observations for various underlying surface conditions are also needed. Our polarization lidar can be conveniently deployed in field conditions because of its robust configuration and unattended operation. It is actually a suitable sort of instrument for observing the shallow cumulus clouds over various underlying surfaces in the low-latitude region. In addition to a role in affecting large-scale dynamics, the presence of shallow cumulus clouds reflects a locally intensified vertical turbulent transport of heat, moisture, and momentum [61,62]. The present observations quantify statistically the local surface conditions for cumulus cloud formation that most of the observed cumuli are associated with: high air temperature (>30 • C) and mixing ratio (>15 g kg −1 ).