Characteristics of Vertical Air Motion in Convective Clouds

8 The vertical velocity and air mass flux in convective clouds are statistically analyzed using 9 aircraft in-situ data collected from three field campaigns: High-Plains Cumulus (HiCu) 10 conducted over the mid-latitude High Plains, COnvective Precipitation Experiment (COPE) 11 conducted in a mid-latitude coastal area, and Ice in Clouds Experiment-Tropical (ICE-T), 12 conducted over a tropical ocean. This study yields the following results. (1) Small-scale updrafts 13 and downdrafts (< 500 m in diameter) are frequently observed in the three field campaigns, and 14 they make important contributions to the total air mass flux. (2) The probability density functions 15 (PDFs) of the vertical velocity are exponentially distributed. For updrafts, the PDFs of the 16 vertical velocity are broader in ICE-T and COPE than in HiCu; for downdrafts, the PDFs of the 17 vertical velocity are broader in HiCu and COPE than in ICE-T. (3) Vertical velocity profiles 18 1 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-1021, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 4 February 2016 c © Author(s) 2016. CC-BY 3.0 License.


Introduction
Convective clouds are an important component of the global energy balance and water cycle because they dynamically couple the planetary boundary layer to the free troposphere through vertical heat, moisture and mass transport (Arakawa, 2004;Heymsfield et al., 2010;Wang and Geerts, 2013).The vertical velocity determines the vertical transport of cloud condensate, the cloud top height and the detrainment into anvils, which further impact the radiative balance (Del Genio et al., 2005).Vertical velocity also has significant impact on the aerosol activation, droplet condensation and ice nucleation in convective clouds, which control the cloud life cycle and precipitation efficiency.
In order to reasonably simulate convective clouds, the vertical air velocity must be parameterized reliably in numerical weather prediction models (NWPMs) and global circulation models (GCMs) (Donner et al., 2001;Tonttila et al., 2011;Wang and Zhang, 2014).However, the complexity of the vertical velocity structure in convective clouds makes the parameterization nonstraightforward (Wang and Zhang, 2014).Observations show that in most of the convective clouds the vertical velocity is highly variable, and consequently the detailed structure of convection cannot be resolved in many models (Kollias et al., 2001;Tonttila et al., 2011).and Australia (Lucas et al., 1994) showed a magnitude of vertical velocity similar to that in GATE.Although the results from the Thunderstorm Project are suspect, the significantly stronger drafts reveal the possible difference between continental and tropical maritime convective clouds.Lucas et al. (1994) suggested that the water loading and entrainment strongly reduce the strength of updrafts in maritime convections.However, this underestimation of the updraft intensity may be also due to the sampling issues, e.g.penetrations were made outside the strongest cores (Heymsfield et al., 2010).
There are a few more recent aircraft measurements (e.g.Igau et al, 1999;Anderson et al., 2005), but the data are still inadequate to fully characterize the vertical velocity in convective clouds.In most of these earlier papers, the defined draft or draft core required a diameter no smaller than 500 m; this threshold excluded many narrow drafts with strong vertical velocity and air mass flux.In addition, the earlier studies used 1-Hz resolution data, which can resolve only the vertical velocity structures larger than a few hundred meters, but the narrow drafts may be important to the total air mass flux exchange and cloud evolution.Furthermore, previous aircraft observations for continental convective clouds were based only on the Thunderstorm Project; thus, new data are needed to study the difference between continental and maritime convections.
Remote sensing by means of, for example, wind profilers and radars is another technique which has often been used in recent years for studying the vertical velocity in convective clouds (e.g.Kollias et al., 2001;Hogan et al., 2009;Schumacher et al., 2015).Using profiler data, May and Rajopadhyaya (1999) analyzed the vertical velocity in deep convections near Darwin, Australia.
They observed that the updraft intensified with height and that the maximum vertical velocity was greater than 15 m s -1 .Heymsfield et al. (2010) studied the vertical velocity in deep convection using an airborne nadir-viewing radar.Strong updrafts were observed over both continental and ocean areas, with the peak vertical velocity exceeding 15 m s -1 in most of the cases and exceeding 30 m s -1 in a few cases.Zipser et al. (2006) used satellite measurements to find the most intense thunderstorms around the world; they applied a threshold updraft velocity greater than 25 m s -1 to identify intense convection.Remote sensing has the advantage of being able to measure the vertically velocity at different heights simultaneously (Tonttila et al., 2011).
However, remote sensing measurements are not as accurate as aircraft measurements, because many assumptions are needed to account for the contribution of particle fall speed in the observed Doppler velocity in order to ultimately estimate air velocity.In addition, ground-based radars can rarely provide good measurements over oceans, and airborne cloud radars often suffer from the attenuation and non-Rayleigh scattering in convective clouds.Therefore, in-situ measurements are still necessary in order to characterize the dynamics in convective clouds and to develop parameterizations for models.
The present study provides aircraft data analysis of the updrafts and downdrafts in mid-latitude continental, mid-latitude coastal and tropical maritime convective clouds using the fast-response in-situ measurements collected from three field campaigns: the High-Plains Cumulus (HiCu), the COnvective Precipitation Experiment (COPE) and the Ice in Clouds Experiment-Tropical (ICE-T).All the clouds formed in isolation, but some of them merged as they evolved.Statistics of the vertical velocity and air mass flux are provided.The Wyoming Cloud Radar (WCR), onboard the aircraft, is used to identify the cloud top height, and high frequency (25-Hz) in-situ measurements of vertical velocity are used to generate the statistics.Section 2 describes the datasets and wind measuring systems.Section 3 presents the analysis method.Section 4 shows the results, and conclusions are given in Section 5.

2.
Dataset and instruments

Dataset
The data used in the present study were collected from three field campaigns: HiCu, COPE and ICE-T.Vigorous convective clouds were penetrated during the three field campaigns, including mid-latitude continental, mid-latitude coastal, and tropical maritime convective clouds.These penetrations provide good quality measurements for studying the microphysics and dynamics in the convective clouds, as well as the interactions between the clouds and the ambient air.The locations of the three field campaigns are shown in Fig. 1.Information regarding the penetrations used in this study is summarized in Table 1.
The HiCu project was conducted mainly in Arizona and Wyoming (Fig. 1 Fast-response in-situ instruments and the Wyoming Cloud Radar (WCR, Wang et al., 2012) were operated during the field campaign to measure the ambient environment, cloud dynamics and microphysics as well as two-dimensional (2D) cloud structure.As shown in Table 1, penetrations in HiCu were made between 2 km and 10 km MSL.The sample size is relatively good below 8 km and relatively small above 8 km.The aircraft flew about 2000 km in clouds.In-situ measurements and WCR worked well in these flights; however, the upward-pointing radar was operated in less than half of the research flights, and thus only a sub-set of the cloud tops can be estimated.Fig. 2a(1-3) shows an example of the clouds sampled in HiCu, including WCR reflectivity, Doppler velocity and 25-Hz in-situ measurement of the vertical velocity.In HiCu, both developing and mature convective clouds were penetrated; some penetrations were near cloud top, while most of them were more than 1 km below cloud top.From the Doppler velocity and the in-situ vertical velocity, we can see that, in both the developing and mature cloud, strong updrafts and downdrafts were observed, and multiple updrafts and downdrafts existed in the same cloud.
The COPE project was conducted from 03 July to 21 August, 2013 in Southwest England (Fig. 1).The UWKA was used to study the microphysics and entrainment in mid-latitude coastal convective clouds (Leon et al., 2015).Seventeen research flights were conducted; penetrations focused on regions near cloud top, which is verified based on the radar reflectivity from the onboard WCR.Since COPE was conducted in a coastal area, the convection initiation mechanism is different from that over a purely continental or ocean area.In addition, although the ambient air mainly came from the ocean, continental aerosols might be brought into clouds, since many of the convective clouds formed within the boundary layer, which further affects the microphysics and dynamics in the clouds.The measurements made in COPE include temperature, vertical velocity, liquid water content, and particle concentration and size distributions.The WCR provided excellent measurements of reflectivity and Doppler velocity.The downward Wyoming Cloud Lidar (WCL) was operated to investigate the liquid (or ice) dominated clouds.
Between 0 km and 6 km, about 800 penetrations were made.Flight distance in cloud totaled about 1000 km.The sample sizes are relatively good between 2 km and 6 km, but relatively small between 0 km and2 km.Examples of the penetrations are given in Fig. 2b(1-3).COPE has fewer penetrations than HiCu, and most of the penetrations are near the cloud top.Fig. 2b(2) reveals relatively simple structures of the updrafts and downdrafts in COPE compared to HiCu, but as shown by the 25-Hz in-situ vertical velocity measurement in Fig. 2b(3), there are still many complicated fine structures in the vertical velocity distribution.
The ICE-T project was conducted from July 1 to July 30, 2011 near St. Croix, U.S. Virgin Islands (Fig. 1), with state-of-the-art airborne in situ and remote sensing instrumentations, with the aim of studying the role of ice generation in tropical maritime convective clouds.The NSF/NCAR C-130 aircraft was used during ICE-T to penetrate convective clouds over the Caribbean Sea.Thirteen C-130 research flights were conducted during the field campaign, with vigorous convective clouds penetrated.In-situ measurements from ICE-T include the liquid and total condensed water contents, temperatures, vertical velocities, and cloud and precipitating particle concentrations and size distributions.The WCR was operated on seven research flights to measure the 2D reflectivity and Doppler velocity fields.The aircraft flew more than 1500 km in clouds, and more than 650 cloud penetrations were made between 0 km and 8 km.The sample sizes are good except between 2 km and4 km (Table 1).Examples of the penetrations are shown in Fig. 2c(1-3).During ICE-T, clouds in different stages were penetrated, including developing, mature and dissipating, some near cloud top and some considerably below cloud top.Strong updrafts were observed in the developing and mature clouds, but the downdrafts in ICE-T are typically weaker than those in HiCu and COPE.The vertical velocity structures are complicated, as confirmed by both the Doppler velocity and the 25-Hz in-situ measurement.Weak updrafts and downdrafts were also observed in the dissipating clouds.

Wind measuring system
On both C-130 and UWKA, A Radome Five-Hole Gust Probe is installed for three-dimensional (3D) wind measurement.A Radome Five-Hole Gust Probe is an aircraft radome probe with five pressure ports installed in a "cross" pattern.Relative wind components (e.g.true air speed and flow angles) are sensed by a combination of differential pressure sensors attached to the five holes (Wendisch and Brenguier, 2013).Detailed calculation of relative wind components is described in Kroonenberg et al. (2008) and Wendisch and Brenguier (2013).The time response and the accuracy of the pressure sensors is about 25 Hz and 0.1 mb.The 3D wind vectors can be derived by taking out the aircraft motions from the relative wind measurement.On both C-130 and UWKA, the aircraft motion is monitored by a Honeywell Laseref SM Inertial Reference System (IRS), with an accuracy of 0.15 m s -1 for vertical motion.Global Positioning System (GPS) was applied to remove the drift errors in the IRS position in all the three field campaigns (Khelif et al., 1998).The final vertical wind velocity product has an accuracy of about ±0.2 m s -1 , and a time response of 25 Hz.This uncertainty (±0.2 m s -1 ) is a mean bias.For each output, the uncertainty is related to the true air speed, aircraft pitch angle, roll angle and ambient conditions.
Therefore, the random error varies and could be larger than the mean bias.

Identifying cloud using in-situ measurements
The Particle Measuring Systems (PMS) Two-Dimensional Cloud (2D-C) Probe and the Forward Scattering Spectrometer Probe (FSSP) are often used to characterize cloud microphysics (e.g.Anderson et al., 2004), although different thresholds of 2D-C and FSSP concentrations are usually used to identify the edge of a cloud.In this paper, we also use FSSP and 2D-C probes to find the cloud edges.In order to find a reasonable threshold for identifying cloudy air, we first use the WCR reflectivity to identify the clouds and the cloud-free atmosphere; for those regions we then plot the particle concentrations measured by FSSP and 2D-C in order to determine the reasonable thresholds, and we apply the thresholds of particle concentrations to all the research flights without WCR.
To identify clouds using WCR, the six effective range gates nearest to the flight level (three above and three below) are chosen in each beam.Any beam in which the minimum reflectivity at the six gates exceeds the noise level 1 is identified as in cloud.
Fig. 3 shows the occurrence distribution as a function of the particle concentrations measured by FSSP versus the concentrations of the particles ≥ 50 μm in diameter measured by 2D-C in the clouds identified by WCR reflectivity.From the figure, we can see that the FSSP concentration ranges from 0.01 cm -3 to 1000 cm -3 , and the 2D-C concentration ranges from 0.1 L -1 to 10000 L -1 .
Generally, shallow clouds have relatively higher concentrations of small particles and lower 1 Based on the reflectivity measured in cloud-free air, the noise level of WCR reflectivity is -32 dBZ at a range of 500 m and -28 dBZ at a range of 1000 m.In this study, we choose -30 dBZ as the threshold to identify cloud.This threshold is examined for all three field campaigns.
concentration of particles larger than 50 μm.In deeper convective clouds, high concentrations can be seen for both small and large particles.The FSSP concentrations in cloud-free air are found to be 2 cm -3 at most, and the FSSP concentrations measured below the lifting condensation level (LCL), where precipitating particles dominated, are lower than 2 cm -3 , as well.Therefore, 2 cm -3 is selected as the concentration threshold to identify clouds based on the FSSP measurements, as shown by the dashed line in Fig. 3.However, in some clouds (e.g.pure ice clouds), the FSSP concentration could be lower than 2 cm -3 , and 2D-C concentrations are needed to identify these cold clouds.We chose a 1 L -1 2D-C concentration for particles ≥ 50 μm as the second threshold to identify cloud, as shown by the dotted line in Fig. 3.In order to avoid precipitating regions (below the LCL calculated from soundings), the second threshold is only applied to penetrations at temperatures colder than 0 º C; thus the cloud is defined as FSSP concentration ≥ 2 cm -3 or 2D-C concentration ≥ 1 L -1 .At temperatures warmer than 0 º C, the FSSP concentrations in most of the convective clouds are higher than 2 cm -3 , so only the first threshold is used.
Once a cloud is identified, the penetration details can be calculated, including the flight length, the flight height, the cloud top height if WCR is available, and the penetration diameter.The penetration diameter is calculated as the distance between the entrance and exit of a penetration.
In order to reject whirl penetrations and penetrations with significant turns, we require that the diameter of a penetration be at least 90% of the flight length.The penetration diameter can generally reveal the scale of a cloud, but since the aircraft may not penetrate exactly through the center of a cloud, the actual cloud diameter may be larger than the penetration diameter.Based on WCR reflectivity images, there are no isolated convective clouds larger than 20 km in diameter.There are a few penetrations longer than 20 km, but these clouds are more like mesoscale convective systems (MCS), and so they are excluded from this study.

Defining updraft and downdraft
In previous studies of the vertical velocity based on in-situ measurements, the updraft and downdraft are often defined as an ascending or subsiding air parcel with the vertical velocity continuously ≥ 0 m s -1 in magnitude and ≥ 500 m in diameter (e.g.LeMone and Zipser, 1980;Jorgensen and LeMone, 1989;Lucas et al., 1994;Igau et al., 1999).In this study, we use a vertical velocity threshold of 0.2 m s -1 , that is, the draft has a vertical velocity continuously ≥ 0.2 m s -1 in magnitude, because ±0.2 m s -1 is the accuracy of the instrument.Any very narrow and weak portion (diameter < 10 m and maximum vertical velocity < 0.2 m s -1 in magnitude) between two relatively strong portions is ignored, and the two strong portions are considered as one draft.
The diameter threshold (500 m) is not used in this paper, because drafts narrower than 500 m frequently occur and they make important contributions to the total air mass flux in the atmosphere and therefore they are necessarily to be considered in model simulations.Fig. 4 shows the PDFs of the diameters of all the updrafts and downdrafts sampled in HiCu, COPE and ICE-T.In all the panels, the diameters are exponentially distributed, the PDFs can be fitted using where f is the frequency and x is the diameter.The coefficients α, β and γ for each PDF is shown  , 1980), where ̅ is the mean air density at the measurement temperature,  ̅ is the mean vertical velocity and D is the diameter of each draft.Fig. 5b shows that the air mass flux in many drafts narrower than 500 m is actually larger than that in some of the broader drafts.The maximum value for these narrow updrafts reaches 4000 kg m -1 s -1 , and the minimum value for the downdrafts reaches -3000 kg m -1 s -1 .The normalized accumulated flux (red curves) reveals that the drafts narrower than 500 m (dotted horizontal lines) make very significant contributions to the total air mass flux.Calculations indicate that the updrafts narrower than 500 m contribute 20%-35% of the total upward flux, and that the downdrafts narrower than 500 m contribute 50%-65% of the total downward air mass flux.Drafts narrower than 50 m (dashed horizontal lines), which are excluded in this paper, contributes less than 5% of the total air mass flux.
In this study, we delineate three different groups of updraft and downdraft using three thresholds of air mass flux: 10 kg m -1 s -1 , 100 kg m -1 s -1 and 500 kg m -1 s -1 in magnitude.,The air mass flux is used here to delineate the draft intensity because (1) air mass flux contains the information of both vertical velocity and draft size; (2) air mass flux can reveal the vertical mass transport through convections; and (3) air mass flux is an important component in cumulus and convection parameterizations (e.g.Tiedtke, 1989;Bechtold et al., 2001).The first designated group, the "weak draft," with air mass flux 10-100 kg m -1 s -1 in magnitude, contributes 10% of the total upward air mass flux and 10% of the total downward air mass flux.The "moderate draft," with air mass flux 100-500 kg m -1 s -1 in magnitude, contributes 25% of the total upward air mass flux and 40% of the total downward air mass flux.The "strong draft," where the air mass flux ≥ 500 kg m -1 s -1 in magnitude contributes 60% of the total upward air mass flux and 20% of the total downward air mass flux.Drafts weaker than 10 kg m -1 s -1 are not analyzed because they are too weak and most of them are very narrow and can hardly be resolved in models (Fig. 5b).The numbers of weak, moderate and strong updrafts and downdrafts sampled at 0-2 km, 2-4 km, 4-6 km, 6-8 km and 8-10 km MSL are shown in Table 2. Generally, weak and moderate drafts are more often observed than strong drafts.At most of the height ranges, more updrafts are observed than downdrafts.
Some researchers have defined a "draft core" by selecting the strongest portion in a draft.For example, LeMone and Zipser (1980) define an updraft core as an ascending air motion with vertical velocity continuously ≥ 1 m s -1 and diameter ≥ 500 m.This definition of a "draft core" is followed in a few more recent studies (e.g.Jorgensen and LeMone, 1989;Lucas et al., 1994;Igau et al., 1999).We too analyzed the vertical air motion characteristics in the stronger portion of the drafts considered here.However, we found that in many updrafts the strong portion where the vertical velocity is continuously ≥ 1 m s -1 dominates and contributes 80% of the total air mass flux, so the statistics of the vertical air motion characteristics in the stronger portion are very similar to those in the draft as a whole.Therefore, the present study focuses on "drafts" in which both weak and strong portions are included.

Significance of drafts in different strengths
From the analysis above, we note that relatively small and weak updrafts are frequently observed in convective clouds.In this section, we provide further evidence to show the importance of the relatively weak updrafts in terms of air mass flux.As the diameter increases to 4 km, the contributions to total air mass flux from relatively weak updrafts (red bar) decrease, while those from stronger updrafts (blue bar) increase.For a penetration of 4 km, 80%-90% of the total upward mass flux is contributed by the strong updrafts with air mass flux ≥ 500 kg m -1 s -1 .However, for the penetrations with diameter larger than 4 km, the contribution from relatively weak updrafts increases, probably because more weak updrafts exist in wider clouds (Fig. 6).This is more obvious in Fig. 7b, in which only the penetrations with at least one strong updraft are included.As the diameter increases from 400 m to 20 km, the contribution from the weak and moderate updrafts (red bars and green bars) increases from 2% to 20%.This suggests that as the cloud evolves and becomes broader (e.g.mature or dissipating stage), the weak and moderate updrafts are also important and therefore necessary to be considered in model simulations.

PDFs of vertical velocity and air mass flux
Fig. 8 shows the PDFs of the vertical velocity in the drafts sampled at 0-2 km, 2-4 km, 4-6 km and higher than 6 km in the three field campaigns.Columns (a), (b) and (c) represent the drafts with air mass flux ≥ 10 kg m -1 s -1 , ≥ 100 kg m -1 s -1 and ≥ 500 kg m -1 s -1 in magnitude, respectively; in other words, column (a) includes all the weak, moderate and strong of drafts, column (b) includes moderate and strong updrafts, and column (c) includes strong updrafts only.
For statistical analysis, it is better to analyze different drafts together rather than separately.In all the panels, the vertical velocities are exponentially distributed for both updrafts and downdrafts; the PDFs can be fitted using Eq. ( 1).From Fig. 8 we can see that at 0-2 km, the PDFs for both COPE and ICE-T are narrow; the updrafts in COPE are slightly stronger than those in ICE-T, while the downdrafts are relatively weaker.At 2-4 km, stronger updrafts and broader PDFs are observed in both COPE and ICE-T compared to those at 0-2 km; the maximum vertical velocity is about 15 m s -1 .In COPE, the downdrafts are stronger than those in ICE-T, with the minimum vertical velocity as low as -10 m s -1 .For HiCu, the PDFs of the vertical velocity at 2-4 km are narrow, because the HiCu was conducted in the High Plains and the cloud bases are relatively high.At 4-6 km, the updrafts become stronger and the PDFs become broader in all the three field campaigns compared to those at lower levels, especially for COPE and ICE-T.Above 6 km, the PDFs for the updraft become broader in HiCu while they slightly narrow in ICE-T compared to those at 4-6 km.For the downdrafts, the PDFs broaden with height for all the three field campaigns.Generally, the PDFs of the vertical velocity are similar for the three columns.The main difference is found in the first bins of the vertical velocity (0-2 m s -1 and -2-0 m s -1 ): highest for column (a), which includes all the drafts with air mass flux ≥ 10 kg m -1 s -1 in magnitude, lowest for column (c), which only includes the strong drafts with air mass flux ≥ 500 kg m -1 s -1 in magnitude.
Generally, the updrafts are stronger in ICE-T or COPE (maritime or coastal convective clouds) than in HiCu (pure continental convective clouds), an observation that differs from earlier studies (e.g.LeMone and Zipser 1980), in which stronger drafts were observed in continental clouds.
This is probably because in the previous field campaigns over ocean (e.g.GATE), the aircraft did not penetrate the strongest cores due to safety concerns.Compared to GATE, the PDFs of the vertical velocity in ICE-T has a similar vertical dependence, broadening with height, but the PDFs are broader in ICE-T than those in GATE, and the maximum vertical velocity (25 m s -1 ) in ICE-T is greater than that observed in GATE (15 m s -1 ).In addition, convections in continental areas other than the High Plains (e.g.Great Plains) may be different from those in HiCu.
Recently, Heymsfield et al. (2010) observed strong updrafts in both maritime and continental convective clouds: most exceed 15 m s -1 and some exceed 30 m s -1 , but the measurements were made for mature deep convection using airborne Doppler radar.More in-situ measurements are needed to further evaluate the difference between maritime and continental convective clouds, including both developing and mature stages.
There are a few possible explanations for the stronger updrafts observed in ICE-T and COPE compared to those observed in HiCu.For example, the convective available potential energy (CAPE) is larger in ICE-T than that in HiCu.Typically, the CAPE in ICE-T is greater than 2000 J kg -1 , and the CAPE in HiCu was less than 100 J kg -1 .However, CAPE in COPE is also low (typically less than 100 J kg -1 ), which cannot explain the relatively strong vertical velocity.The strong vertical velocity in ICE-T and COPE maybe also be related to ice initiation.There are many more millimeter drops in the convective clouds observed in ICE-T (Lawson et al., 2015) and COPE (Leon et al., 2015) than that in HiCu; the millimeter drops can result in fast ice initiation (Lawson et al., 2015), and the significant latent heat released during the ice initiation process can strengthen the vertical velocity.In addition, high concentrations of millimeter drops in ICE-T and COPE can result in the quick formation of graupel and frozen rain drops.The falling graupel and frozen rain drops can strongly enhance the ice generation through ice multiplication processes (Heymsfield and Willis, 2014) and possibly strengthen the updraft.
Another difference among the three field campaigns is found in the downdrafts.The downdrafts in HiCu and COPE, which are sampled in mid-latitude convective clouds, are obviously stronger than those in ICE-T, which was conducted over tropical ocean.This may be because the ambient relative humidity is low in HiCu and COPE compared to ICE-T, resulting in a faster evaporation of cloud drops and a stronger cooling effect when ambient air mixes with cloud parcels through lateral entrainment (Heymsfield et al., 1978).But since the diameters of the downdrafts in ICE-T are relatively broader (Fig. 4), the air mass fluxes of the downdrafts are not obviously smaller than that in HiCu and COPE.
Fig. 9 shows the PDFs of the air mass flux for all the drafts sampled at 0-2 km, 2-4 km, 4-6 km and higher than 6 km.The PDFs are exponentially distributed for the three field campaigns at different heights, which can be fitted using Eq. ( 1).The coefficients for the fitted function are shown in each panel.At 0-2 km, the PDF of the air mass flux in the updrafts is relatively narrow in ICE-T compared to that in COPE.For the downdraft, the PDF is broader in ICE-T than those in COPE.As height increases up to 6 km, more updrafts with larger air mass flux are observed in ICE-T and the PDFs broadens, but in COPE the PDFs remain similar.In HiCu, the PDFs for updrafts broadens from 2-6 km then remain similar at altitudes higher than 6 km.For downdrafts, the PDFs are similar at different heights for all the three field campaigns.Among the three field campaigns, the differences of the PDFs are small for the weak and moderate drafts and are larger for the strong drafts., 1980;Lucus and Zipser, 1994).But

Profiles of vertical velocity and air mass flux
strong updrafts (downdrafts) in excess of 20 m s -1 (-10 m s -1 ) are also observed in this study, which are not shown in pervious aircraft observations.This finding is consistent with recent remote sensing observations (e.g.Heymsfield et al., 2009).The updrafts and downdrafts in convective clouds over land shown in this study (HiCu) are weaker than those shown by Byers and Braham (1949) and Heymsfield et al. (2009), possibly because HiCu was conducted over the High Plains.times smaller than those in the dotted boxed; for the 10%, 50%, 90% and the maximum absolute values, the differences among the three type of boxes become smaller.In HiCu, the air mass flux does not show an obvious trend with height.In the updraft, the 10%, 50% and 90% values remain similar at different height ranges.The maximum air mass flux increases from 2-6 km, then decreases with height.The peak value is about 1.3×10 4 kg m -1 s -1 , found at 4-6 km.The air mass flux in the downdrafts has relatively larger variability, especially for the minimum values.
The strongest downdraft in terms of air mass flux (about -1.2×10 4 kg m -1 s -1 ) is found at 4-6 km, but this is probably due to a specific case since the 50% and 90% values are similar to those at the other height ranges.In COPE, the 90% and the maximum air mass flux in the updraft tend to increase with height, while the 10% and 50% values are similar at different height ranges.For the downdraft, the minimum air mass flux decreases between 0-2 km and remains similar at 4-6 km.The 10%, 50% and 90% values are similar at different height ranges.The strongest updrafts and downdrafts in terms of air mass flux are observed at 4-6 km and 2-4 km, about 1.8×10 4 kg m -1 s -1 and -2.8×10 3 kg m -1 s -1 .In ICE-T, the maximum air mass flux in the updraft increases with height up to 6 km, then decreases at 6-8 km.The 10%, 50% and 90% values in the updraft and downdraft intensify from 0-4 km and decrease or remain similar at higher levels.The strongest updraft (3×10 4 kg m -1 s -1 ) and downdraft (-3.5×10 3 kg m -1 s -1 ) are observed at 4-6 km and 0-2 km, respectively.The minimum value is probably due to a specific case because the 10%, 50% and 90% values at 0-2 km are larger or similar to those at the other heights.
To summarize, the air mass flux varies with height differently for the three field campaigns.For updraft, the maximum air mass flux is of the order of 10 4 kg m -1 s -1 , and the median values for the three different types of boxes are typically ~100 kg m -1 s -1 , ~200 kg m -1 s -1 and ~1000 kg m -1 s -1 , respectively.The air mass flux in the downdrafts is a few times smaller in magnitude than those in the updrafts, but extreme strong downdraft on the order of 10 4 kg m -1 s -1 may be observed in some specific cases.Compared to previous studies, the air mass flux in this study shows similar magnitudes, but the vertical dependences are different.Lucas and Zipser (1994) show that the convection off tropical Australia intensifies with height from 0 to 3 km, then weakens with height in terms of air mass flux.Anderson et al. (2005) shows that updrafts and downdrafts over the tropical Pacific Ocean intensify with height up to 4 km, then weaken at higher levels in terms of air mass flux.In the present study, the strongest updrafts and downdrafts are observed at higher levels for all the three field campaigns.

Composite structure of vertical velocity
Fig. 11 shows the composite structure of the vertical velocity as a function of the normalized diameter for the updrafts and downdrafts with air mass flux ≥ 10 kg m -1 s -1 , 100 kg m -1 s -1 and 500 kg m -1 s -1 in magnitude.As expected, the draft as a whole is weaker if all the drafts are included in the calculation and becomes stronger if the drafts with small air mass flux are excluded.In HiCu, when all weak, moderate and strong updrafts are included (red curves), the vertical velocity near the center is about 1.7 m s -1 .When only moderate and strong updrafts are included (green curves), the vertical velocity near the center is ~2.4 m s -1 .When all the updrafts with air mass flux smaller than 500 kg m -1 s -1 in magnitude are excluded, the absolute values of the vertical velocity near the center increase to ~3.4 m s -1 .The vertical velocity in downdrafts is about 0.2 m s -1 smaller in magnitude than that in updrafts.The structures of the vertical velocity in COPE are quite similar to those in HiCu, in both shape and magnitude, especially for the red and green curves.The blue curves have relatively larger variations due to the small sample size.
These variations reveal the complicated structure in some drafts.In ICE-T, the shapes of the vertical velocity structures are similar to those in HiCu and COPE, but the magnitudes are smaller, which suggests that statistically more weak drafts are found in ICE-T, although the peak vertical velocity is observed in ICE-T.This is consistent with Fig. 10.In Fig. 11, if the magnitude of the vertical velocity is normalized, the structures of the three defined classes of updraft and downdraft among the three field campaigns will be very similar.
In this composite analysis based on in-situ measurements, the penetration direction has no obvious impact on the vertical velocity structure, whether the aircraft penetrates along or across the horizontal wind.For convective cloud, wind shear has a large impact on the cloud evolution (Weisman and Klemp 1982); however, aircraft data are insufficient to reveal the wind shear impact, because each penetration is made at a single level and the aircraft does not always penetrate through the center of the draft.Remote sensing data can be helpful to study the twodimensional or three-dimensional structures of the vertical velocity in convective clouds (e.g.Wang and Geerts, 2013).Thus, in-situ measurements as well as remote sensing measurements are needed to further analyze the wind shear impact.Generally, in HiCu and ICE-T the drafts intensify as the clouds evolve, but this is not found in COPE, maybe because most of the penetrations were made near the cloud top, rather than in the strongest portion of a draft.Since the vertical resolution of aircraft in-situ data is poor, more data, including remote sensing measurements, are needed to better understand the evolution of the vertical velocity in convective clouds as they go through the different stages..

Conclusions
The vertical velocity and air mass flux in convective clouds are statistically analyzed in this study using aircraft data collected from three field campaigns, HiCu, COPE and ICE-T, conducted over mid-latitude High Plains, mid-latitude coastal area and tropical ocean.Three thresholds of air mass flux are selected to delineate draft: 10 kg m -1 s -1 , 100 kg m -1 s -1 and 500 kg m -1 s -1 in magnitude.The main findings are as follows.
1) Small-scale updrafts and downdrafts in convective clouds are often observed in the three field campaigns.More than 85%, 90% and 74% of the updrafts are narrower than 500 m in HiCu, COPE and ICE-T, respectively, and more than 90 % of the downdrafts are narrower than 500 m in the three field campaigns combined.These small scale drafts make significant contributions to the total air mass flux.Updrafts narrower than 500 m contribute 20%-35% of the total upward flux, and downdrafts narrower than 500 m contribute 50%-65% of the total downward air mass flux.

2)
In terms of the air mass flux, the weak and moderate drafts make an important contribution to the total air mas flux exchange.Generally, the number of drafts increases with cloud diameter.For many narrow clouds, the weak and moderate drafts dominate and contribute most of the total air mass flux.For broader clouds, the stronger updrafts contribute most of the total air mass flux, but the contribution from weak and moderate drafts increases as the cloud evolves.
3) PDFs and profiles of the vertical velocity are provided for the three defined types of drafts.In all the height ranges, the PDFs are roughly exponentially distributed.At the lowest level, the PDFs of the vertical velocity are relatively narrow, and broaden with height.For the updrafts, the PDFs of the vertical velocity are broader in ICE-T and COPE, while for the

5)
The composite structures of the vertical velocity in the updrafts and downdrafts have similar shapes for the three field campaigns: the vertical velocity is the strongest near the center, and weakens towards the edges.On average, the updrafts have similar intensity across the three field campaigns, while for downdrafts the vertical velocity is the weakest in ICE-T and stronger in HiCu and COPE.

6)
The change of vertical air motion characteristics as the cloud evolves are briefly discussed.Generally, the strongest portion of a draft ascends with height as the cloud evolves.
The maximum vertical velocity is observed within 2 km below cloud top; the downdrafts are sometimes stronger at levels more than 2 km below cloud top.
Based on the aircraft observations from three field campaigns, this study provides quantitative analyses of the vertical air motion characteristics in isolated convective clouds, compares the differences of vertical velocity and air mass flux among the different field campaigns, and shows the importance of small-scale updrafts and downdrafts.The results are useful to evaluate model     s -1 and 500 kg m -1 s -1 in magnitude, respectively, which are the thresholds used to delineate the three different groups of draft.The result is a composite of HiCu, COPE and ICE-T.
) from 18 July to 05 August 2002 and from 07 July to 31 August 2003 to investigate the microphysics and dynamics in convective clouds over mid-latitude High Plains.The University of Wyoming King Air (UWKA) was operated as the platform.In 2002 and 2003, 10 and 30 research flights were made, respectively.In this study, the 2002 HiCu and 2003 HiCu are analyzed together because they were both conducted over the High Plains and the sample size of 2002 HiCu is relatively small.
Fig.5ashows the occurrence distributions as a function of the mean vertical velocity versus the diameter of the drafts with the vertical velocity continuously ≥ 0.2 m s -1 in magnitude.From the figure, it is noted that many drafts narrower than 500 m have quite strong vertical velocities.The maximum mean vertical velocity of these narrow drafts can reach 8 m s -1 , and the minimum mean vertical velocity in the downdrafts is -6 m s -1 .With such strong mean vertical velocity, narrow drafts could contribute noticeably to the total air mass flux.Fig.5bpresents the occurrence distributions as a function of the air mass flux versus the diameter of the drafts.The air mass flux is calculated as ̅  ̅ (LeMone andZipser, 1980), where ̅ is the mean air density

Fig. 6a shows
Fig.6ashows the average number of updrafts as a function air mass flux observed in the three field campaigns.The solid, dashed and dotted lines represent the penetrations with different diameters.As shown in Fig.6a, weak and moderate updrafts are more often observed than strong updrafts, and the numbers of updrafts are higher in longer penetrations.Since this is an average result, the number of updrafts could be smaller than 1 (e.g.many narrow penetrations do not have strong updrafts).Fig.6bis similar to Fig.6abut shows the occurrence frequency of updrafts with different air mass fluxes (i.e. the vertical axis in Fig.6a is normalized).For the penetrations < 1 km, many of the clouds only have weak or moderate updrafts, and strong updrafts are rarely observed.For penetrations of 1-10 km, the frequency of strong updrafts increases and the frequency of weak and moderate updrafts decreases.For even longer penetrations (>10 km), however, the frequency of weak updrafts increases again, indicating the increasing importance of weak updrafts.

Fig. 10
Fig. 10 is a Whisker-Box plot showing the profiles of the vertical velocity (a-c) and air mass flux (d-f) in the drafts based on the three defined thresholds of air mass flux.The solid box includes all the three different groups of drafts, the dashed boxes excludes the weak drafts, and the dotted boxes includes strong drafts only.The minimum, 10%, 50%, 90% and the maximum values areshown in each box.Notice that the vertical velocity and air mass flux in the downdraft is negative, so the minimum value represents the strongest subsiding parcel, the 10% value represents the strongest 10 th percentile subsiding parcel, and the 90% value represents the weakest 10 th percentile subsiding parcel.This is opposite to the updraft.In each panel, the absolute values of the vertical velocities and air mass flux (except the minimum and maximum ones) are relatively small for the solid boxes.

Fig. 10d -
Fig.10d-fshows the profiles the air mass flux statistics for the drafts sampled during the three field campaigns.As expected, the absolute values of the air mass flux are relatively small if all the drafts are included (dotted boxes), and become larger if the drafts with small air mass flux are excluded.However, the variations of the air mass flux with height are similar for the three

Fig. 12
Fig. 12 shows the profiles of the vertical velocity (a-c) and the air mass flux (d-f) for the updraft and downdraft in the convective clouds with different cloud top heights (CTH).Here, all weak, downdrafts the PDFs of the vertical velocity are broader in HiCu and COPE.The profiles show that updrafts are stronger in ICE-T and COPE than in HiCu, and downdrafts are stronger in HiCu and COPE compared to ICE-T.4)PDFs and profiles of the air mass flux are provided for the drafts.The PDFs are similarly exponentially distributed at different heights.For updrafts, the PDFs are broader in ICE-T than in HiCu and COPE, but for downdrafts the PDFs are broader in HiCu and COPE than in ICE-T.In the updrafts, the maximum air mass flux has an order of 10 4 kg m -1 s -1 .The air mass flux in the downdrafts are typically a few times smaller in magnitude than those in the updrafts.

Figure 1 .
Figure 1.Flight tracks for the three field campaigns: HiCu, COPE and ICE-T.

Figure 2 .
Figure 2. Examples of radar reflectivity, Doppler velocity and 25-Hz in-situ vertical velocity measurements for the convective clouds sampled in HiCu, COPE and ICE-T.The red dots in (a1), (b1) and (c1) are the cloud tops estimated by WCR.

Figure 3 .Figure 4 .
Figure 3. Occurrence distributions as a function of the particle concentrations measured by FSSP versus the concentrations of the particles ≥ 50 μm in diameter measured by 2D-C in the clouds identified by WCR reflectivity.The dashed and dotted lines indicate the FSSP concentration equal 2 cm -3 and the 2D-C concentration equal 1 L -1 , respectively.

Figure 5 .
Figure 5. Occurrence distributions as (a) a function of diameter and mean vertical velocity, and (b) a function of diameter and air mass flux for all updrafts and downdrafts.The normalized accumulation flux is also shown by the red curves.The horizontal dotted and dashed lines in (a) and (b) indicate the draft diameter equal 500 m and 50 m, which are used as the diameter thresholds to identify a "draft" in previous studies and in this study, respectively.The vertical dash-dotted, dashed and dotted lines in (b) indicate air mass flux equal 10 kg m -1 s -1 , 100 kg m -1

Figure 6 .
Figure 6.(a) Average number and (b) occurrence frequency of updrafts as a function of air mass flux observed in penetrations with length < 1 km (solid), 1-10 km (dashed) and >10 km (dotted).

Figure 7 .Figure 8 .
Figure 7. Average percentile contribution to total upward air mass flux by the weak (red), moderate (green) and strong (blue) updrafts delineated in this study.The result is a composite of HiCu, COPE and ICE-T.

Figure 9 .
Figure 9. PDFs of the air mass flux for the updrafts and downdrafts sampled at 0-2 km, 2-4 km, 4-6 km and higher than 6 km.The three thresholds of the air mass flux (±10 kg m -1 s -1 , ±100 kg m -1 s -1 and ±500 kg m -1 s -1 ) are shown by the solid (overlaps with the central y-axis in each panel), dashed and dotted lines.The numbers shown in each panel are the coefficients of the fitted exponential function (Eq.1).

Figure 11 .
Figure 11.Composite structure of the vertical velocity as a function of the normalized diameterfor the updrafts and downdrafts with air mass flux ≥ 10 kg m -1 s -1 , 100 kg m -1 s -1 and 500 kg m -1 s -1 in magnitude.The solid, dashed and dotted curves represent penetrations with the heading angles (HA) 0°-30°, 30°-60° and 60°-90° from the horizontal wind (HW) directions, respectively.The 0 and 1 coordinates on the x-axis indicate the upwind and downwind sides of the draft.

Figure 12 .
Figure 12.Profiles of (a-c) the vertical velocity and (d-f) the air mass flux for the updraft and downdraft with air mass flux ≥ 10 kg m -1 s -1 in magnitude.The red, orange, green and blue boxes represent clouds with cloud top heights of 0-4 km, 4-6 km, 6-8 km and higher than 8 km.