Observational Relationship Between Entrainment Rate andEnvironmental Relative Humidity and Implicationsfor Convection ParameterizationChunsong Lu1,2 , Cheng Sun1, Yangang Liu2 , Guang J. Zhang3 , Yanluan Lin4 ,Wenhua Gao5 , Shengjie Niu1, Yan Yin1, Yujun Qiu1, and Lianji Jin1

1Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, and Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, Nanjing University of Information Science and Technology,Nanjing, China, 2Environmental and Climate Sciences Department, Brookhaven National Laboratory, Upton, NY, USA,3Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, USA, 4Key Laboratory for Earth SystemModeling, Ministry of Education, Department of Earth System Science, and Joint Center for Global Change Studies,Tsinghua University, Beijing, China, 5State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences,Beijing, China

Abstract Entrainment rate is a critical but highly uncertain quantity in convective parameterizations;especially, the effects of environmental relative humidity on entrainment rate are controversial, or evenopposite, in different studies. Analysis of aircraft observations of cumuli from the Routine AAF (AtmosphericRadiation Measurement [ARM] Aerial Facility) Clouds with Low Optical Water Depths (CLOWD) OpticalRadiative Observations (RACORO) and Rain in Cumulus over the Ocean (RICO) field campaigns shows thatentrainment rate is positively correlated with relative humidity. Physical analysis shows that higher relativehumidity promotes entrainment by reducing buoyancy in the cloud cores and by weakening downdraftsnear the cloud cores. The reduced buoyancy in the cloud cores and weakened downdrafts surrounding thecores further reduce updrafts in the cloud cores; the cloud cores with smaller updrafts are more significantlyaffected by their environment, resulting in larger entrainment rate. The relationship between entrainmentrate and relative humidity is consistent with the buoyancy sorting concept widely used in convectionparameterizations. The results provide reliable in situ observations to improve parameterizations ofentrainment rate.

Plain Language Summary Cumulus clouds affect vertical distributions of atmospheric energy andmass and further affect weather and climate. Near cloud edges, environmental air can be entrained intoclouds. Entrainment rate describes how fast environmental air is entrained, which affects the growth anddissipation of clouds. However, our understanding of the factors affecting entrainment rate is far fromestablished. Especially, different studies found that the effects of environmental relative humidity onentrainment rate could be opposite. Based on in situ observations of cumulus clouds, it is found that higherrelative humidity causes larger entrainment rate. Physical analysis shows that relative humidity affectsentrainment rate through its effects on thermodynamic and dynamical structures in and outside cumulusclouds. Mathematical artifacts in the calculation of entrainment rate are ruled out.

1. Introduction

Clouds cover around two thirds of the Earth’s surface and are important for radiative transfer and global cli-mate (Chiu et al., 2009; Lin et al., 2015; Yang et al., 2016; Zhang et al., 2018). Cumulus clouds play importantroles in vertical transport of energy and mass (Heiblum et al., 2016); convective parameterizations are criticalto simulations of precipitation, Madden-Julian Oscillation, etc (Del Genio & Wu, 2010; Lu & Ren, 2016; Su et al.,1999; Wu et al., 2007; Zhang & McFarlane, 1995). Many studies have focused on entrainment-mixing nearcloud edges (Kumar et al., 2013, 2017; Lu et al., 2018; Malinowski et al., 2013; Small et al., 2013; Xue &Feingold, 2006). Entrainment rate (λ) is a key quantity in convective parameterizations (Blyth, 1993; Donneret al., 2016; Luo et al., 2010; Moser & Lasher-Trapp, 2017; Nie & Kuang, 2012). However, its parameterizationhas large uncertainties (Romps, 2010). Many parameterizations relate λ to different quantities, such as buoy-ancy (B) and vertical velocity (w; Dawe & Austin, 2013; de Rooy & Siebesma, 2010; Grant & Brown, 1999;

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Geophysical Research Letters

RESEARCH LETTER10.1029/2018GL080264

Key Points:• Entrainment rate is found to be

positively correlated with relativehumidity based on in situobservations for the first time

• Physical mechanisms underlying therelationship between entrainmentrate and relative humidity areexamined

• Mathematical artifacts affecting therelationship between the twoquantities are ruled out

Supporting Information:• Supporting Information S1

Correspondence to:C. Lu,clu@nuist.edu.cn;luchunsong110@gmail.com

Citation:Lu, C., Sun, C., Liu, Y., Zhang, G. J., Lin, Y.,Gao, W., et al. (2018). Observationalrelationship between entrainment rateand environmental relative humidityand implications for convectionparameterization. Geophysical ResearchLetters, 45, 13,495–13,504. https://doi.org/10.1029/2018GL080264

Received 1 SEP 2018Accepted 20 NOV 2018Accepted article online 26 NOV 2018Published online 18 DEC 2018

©2018. American Geophysical Union.All Rights Reserved.

BNL-209495-2018-JAAM

Gregory, 2001; Lin, 1999; Neggers et al., 2002; Squires & Turner, 1962; von Salzen & McFarlane, 2002; Zhanget al., 2015). Environmental relative humidity (RH) is also expected to have a significant impact on convectionthrough entrainment (Axelsen, 2005; Böing et al., 2014; Jensen & Del Genio, 2006; Stirling & Stratton, 2012). Itis interesting to find that different studies have reached different or even opposite conclusions on the rela-tionship between λ and RH.

Using the Met Office Large-Eddy Model, Stirling and Stratton (2012) found that λ was higher for higher RH.Using a large eddy simulation model, Axelsen (2005) carried out sensitivity simulations and found that thedriest simulations had the lowest λ. Jensen and Del Genio (2006) analyzed ground-based remote sensingdata and found that λ was positively correlated with RH.

However, Bechtold et al. (2008) and Zhao et al. (2018) argued that λwas negatively correlated with RH in deepconvection, and they implemented such relationships in climate models, respectively. Based on large eddysimulation results, Böing et al. (2012) found that the sensitivity of λ to RH was quite weak, although thetwo quantities were still negatively correlated. In a cloud-resolving model, Derbyshire et al. (2011) set RHto 80% between 1 and 2 km and different RH above 2 km. The λ did not show any consistent trend withRH above 2 km; in the layer 1–2 km, λ was found to be smaller in a wetter environment.

Based on the above literature review, it is still not clear how RH affects λ. Stirling and Stratton (2012) pointedout “that caution should be applied about the universality of the relationship we find between entrainmentand RH.” Derbyshire et al. (2011) claimed that the adaptive entrainment to RH raised big questions andrequired further research. de Rooy et al. (2016) concluded that “the influence of environmental RH on λwas yet far from established.”

There are three deficiencies in the previous studies on the relationship between λ and RH. First, to theauthors’ knowledge, the relationship between λ and RH is mostly studied by numerical simulations, and thereare no analyses based on in situ cloud observations. Second, physical mechanisms underlying the relation-ship between λ and RH are still not clear. Third, in many studies, λ was estimated with conserved quantitiesrelated to RH, and thus, it is possible that the relationship could be due to mathematical artifacts.

To address these problems, this study examines the relationship between λ and RH with in situ aircraft obser-vations for the first time. The data were collected during the Routine AAF (Atmospheric RadiationMeasurement [ARM] Aerial Facility) Clouds with Low Optical Water Depths (CLOWD) Optical RadiativeObservations (RACORO) field campaign (Vogelmann et al., 2012) and during the Rain in Cumulus over theOcean (RICO) project (Rauber et al., 2007). The underlying physical mechanisms are examined after eliminat-ing the possible mathematical artifacts for the relationship. Note that this work only focuses on shallowcumulus clouds with the cloud thickness in the range of 200–500 m (Vogelmann et al., 2012).

2. Data and Approaches2.1. Data

During RACORO from 22 January to 30 June 2009, measurements were carried out with the Center forInterdisciplinary Remotely-Piloted Aircraft Studies Twin Otter aircraft over the ARM Southern Great Plains site.Cloud microphysics was observed by the Cloud and Aerosol Spectrometer and Cloud Imaging Probe. ARosemount probe was used to measure temperature (T), and the Diode Laser Hygrometer was used to mea-sure water vapor mixing ratio (qv; Podolske et al., 2003). Temperature is empirically corrected using liquidwater content (LWC; Lu et al., 2016). Several microphysical, thermodynamic, and dynamical criteria are usedto select nondrizzling growing cumulus clouds (Lu et al., 2016); one important criterion is that

B ¼ Tvc � TveTve

g > 0:005 m=s2; (1)

where g is the acceleration of gravity and Tv is virtual temperature (Wallace & Hobbs, 2006):

Tv ¼ T 1þ 0:608qvð Þ: (2)

The subscripts c and e in equation (1) indicate cloud cores and environments, respectively. The cloud coreedge is the point where updraft changes to downdraft (Lu, Liu, Niu et al., 2012). In total, 102 clouds satisfythe criteria.

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During RICO, cumulus clouds were observed with the National Center for Atmospheric Research C-130research aircraft over Eastern Atlantic and Western Caribbean from 24 November 2004 to 24 January 2005.The Particle Volume Monitor probe was used to observe LWC, and the Lyman-Alpha hygrometer was usedto observe qv. T, measured by a Rosemount sensor, is empirically corrected, the same as in RACORO.Gerber et al. (2008) selected 28 growing cumulus clouds in Flight RF12 with the criteria that at least 80%of vertical velocity is positive, cloud tops are visible, etc. Gerber et al. (2008) and Lu, Liu, Yum et al. (2012)estimated λ in these clouds. Here another criterion in equation (1) is applied. Eleven clouds are selected.

2.2. Approaches

Two approaches are used and compared in this study. The first approach (Lu, Liu, Yum et al., 2012) is themixing fraction approach, and λ estimated from this approach is labeled as λmix. Briefly, both qt (equal toqv plus liquid water mixing ratio [ql]) and liquid water potential temperature (θl) are conserved. λmix is calcu-lated with the conservation of them:

qtc ¼ qtaχa þ qte 1� χað Þ; (3a)

θlc ¼ θlaχa þ θle 1� χað Þ; (3b)

λmix ¼ � lnχah

; (3c)

where the subscripts c, a, and e indicate cloud cores, adiabatic clouds, and environments, respectively; χa ismixing fraction of adiabatic cloud; and h is the aircraft penetration height above cloud base. θl is defined as(Betts, 1973)

θl ¼ θ � θTLcp

� �ql; (4)

where cp is specific heat capacity at constant pressure, L is evaporative latent heat, and θ is potential tempera-ture. One advantage of the mixing fraction approach is that there is no need to measure temperature incloud, which is often problematic (Lu, Liu, Yum et al., 2012). Therefore, both equations ((3a)) and ((3b)) areused to calculate χa without using temperature as an input. The temperature after correction with LWC is onlyused to calculate buoyancy in equations ((1)) and ((2)) to select clouds in RACORO. See more details in Lu, Liu,Yum et al. (2012), Lu et al. (2016).

The second approach is the bulk-plume approach (Betts, 1975), and λ estimated is labeled as λbulk:

λbulk ¼ ∂ϕc

∂z1

ϕe � ϕc; (5)

where ϕ is a conserved quantity and z is height; the subscripts c and e indicate cloud cores and environ-ments, respectively.

As tested in Lu, Liu, Yum et al. (2012), the two approaches produced similar vertical profiles of λ, but theresults from the mixing fraction approach had smaller uncertainties. Only the mixing fraction approach isused for RACORO to study the relationship between λ and RH. Both approaches are used for RICO to ruleout the mathematical artifact, which is detailed in section 3.

3. Results3.1. Relationships Between λmix and Environmental RH in RACORO

In RACORO, λmix is estimated. As illustrated in Figure 1 of Lu, Liu, Niu et al. (2012), the environmental T and qvare from near the cloud core edges; the distance between the environmental air and the cloud core edge is D-2D, where D is equal to 10, 20, 30, 40, 50, 100, 300, and 500 m. Cloud base heights and h in equations ((3a))and ((3b)) are estimated for each cloud by assuming that adiabatic LWC (LWCa) equals the observed maxi-mum LWC (LWCmax; Lu, Liu, Niu et al., 2012).

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As shown in Figure 1, λmix is positively correlated with environmental RH and the relationships between themcan be well fitted with

λmix ¼ fRHg; (6)

where f and g are two empirical parameters. The correlation coefficient (R) is high, between 0.71 and 0.81 fordifferent D values with p < 0.01.

3.2. Removing the Effect of RH in Calculation of Entrainment Rate

A first glance at the equations for estimating λmix suggests that the positive correlations between λmix and RHmight be due to the conservation of qt, that is, a result of a mathematical artifact without any physical mean-ing. Rewriting equation (3a) yields

χa ¼qtc-qteqta-qte

: (7)

Everything else being equal, qtc-qte in equation (7) is larger for lower RH (and thus qte). Therefore, χa is larger.As a result, λmix is smaller according to equation (3c). Conservation of qt dictates that less dry air from outsidecloud is needed to reduce LWCa to the observed value when environmental RH is lower; less dry air enteringcloudmeans smaller λmix. The positive correlation between λmix and RH could bemathematical artifacts, evenwithout physical mechanisms.

It should be emphasized that the bulk-plume approach also suffers from such potential mathematical arti-facts if qt is used in equation (5). However, it does not have such a problem if θl is used as the conserved quan-tity, because RH is not included in the calculations of θl. To rule out the possible mathematical artifact, 11clouds observed in RICO are used to estimate λbulk using θl in the bulk-plume approach. The definitions ofcloud cores and environmental air are the same as those in RACORO, respectively. D is equal to 10, 20, 30,40, 50, and 100m. The distance between two neighboring cloud core edges should be larger than 3D tomakesure that the selected dry air with D to 2D away from one cloud core edge is also far away (≥D) from its neigh-boring cloud core edge (Lu, Liu, Niu et al., 2012). For D = 300 or 500 m, the distance between the edges ofsome clouds is even smaller than 2D. If we use D = 300 or 500 m and abandon these clouds, there will betoo few clouds to analyze. Therefore, D = 300 or 500 m is not used. In addition, the purpose to analyze theRICO data is to verify that λ is positively correlated with RH, not to study the dependence of λ on D. UsingD ≤ 100 m is good enough for this purpose.

Measurements at two levels are needed to calculate λbulk. Here we use the cloud base height and a horizontalpenetration of aircraft. The cloud base heights of the 11 clouds were supposed to be similar because theywere marine cumulus clouds (Gerber et al., 2008). Figure 2a shows that λbulk is positively correlated withRH with D = 50m as well. The positive correlation between λbulk and RH indicates that the positive correlationis due to physical mechanisms, not mathematical artifacts. The relationships between λbulk and RH for otherenvironmental air sources with different D values are similar.

The reason why the bulk-plume approach is not used in RACORO is that cloud base heights for differentclouds change even in the same flight (Vogelmann et al., 2012). In the mixing fraction approach, cloud baseheights are estimated assuming that LWCmax is equal to LWCa. As discussed in Lu, Liu, Niu et al. (2012), theassumed LWCmax might be less than LWCa, because LWCmax could already be affected by entrainment.However, the effects of uncertainties in LWCa on the calculations of χa and h are canceled to some extent.Assuming that LWCa is 1.25 times of LWCmax causes relative difference of λmix estimation within the rangeof 10%–16% for different D values. However, the uncertainties in LWCa and cloud base estimation could sig-nificantly affect λbulk, because there is no cancellation in the bulk-plume approach. In RICO, the cloud baseheights of different clouds are similar because of the marine environment. The cloud base height estimatedby Gerber et al. (2008) should be quite accurate. Both mixing fraction and bulk-plume approaches are applic-able in RICO. Figure 2b shows that λbulk and λmix are positively correlated. This further confirms that even if λin RACORO is estimated with the bulk-plume approach instead of the mixing fraction approach, the sign ofthe correlation between λ and RH remains unchanged.

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Figure 1. Entrainment rate (λmix) versus environmental relative humidity (RH) for different D values in the 102 clouds dur-ing Routine AAF (Atmospheric Radiation Measurement [ARM] Aerial Facility) Clouds with Low Optical Water Depths(CLOWD) Optical Radiative Observations (RACORO). See text for more details on D. R and p are correlation coefficients andsignificant levels, respectively.

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4. Physical Mechanisms for the Positive CorrelationsBetween λmix and RH

After ruling out the possibility of implicit mathematics being the reasonsfor the positive correlations between λmix and RH, here we perform in-depth inspection to reveal the underlying physical mechanisms—a chainof thermodynamic, dynamical, and microphysical interactions betweencloudy and environmental air.

4.1. Mechanism Related to Buoyancy

As shown in Figure 3a, w in the cloud cores (wc) is negatively correlatedwith RH. As discussed in Neggers et al. (2002) and Lu et al. (2016), entrain-ment rate is larger for smaller wc. Therefore, higher RH corresponds tosmaller wc, and then larger λmix. Note that wc is driven by B and B has sig-nificant impacts on cumulus lifecycle and entrainment (e.g., Luo et al.,2010). Figure 3b shows that B is also negatively correlated with RH. Thenthe question boils down to how RH affects B. Substituting Tvc and Tve inequation (2) to equation (1) yields

B ¼ 0:608 Tcqc � Teqeð Þ þ Tc � Teð ÞTve

g: (8)

In 62 out of 102 clouds, the humidity term, 0.608(Tcqc� Teqe), is larger thanthe thermal term, (Tc � Te). Others being equal, smaller qe and RH causelarger B. Furthermore, Tcqc = Teqc + (Tc � Te)qc; (Tc � Te)qc is much smallerthan Teqc; therefore, Tcqc ≈ Teqc and the humidity term becomes0.608(Teqc � Teqe), eliminating the effect of temperature. Again, thereare also 62 clouds, which have the humidity term larger than the thermalterm. This analysis suggests that water vapor plays a bigger role than tem-perature in determining B in the cloud cores, and further affects wc. Thedependence of λmix on RH arises through the effects of RH on B and wc.Telford and Chai (1984) also found that convection was driven by watervapor instead of temperature. Yang (2018) found that the horizontal scaleof convective self-aggregation decreased if the effect of water vapor wasnot considered. Seeley and Romps (2016) showed that the effect of watervapor on buoyancy was larger than that of temperature in low levels, andsmaller in high levels. Seeley and Romps (2015) found that smaller RHleads to larger B and wc.

4.2. Mechanism Related to Humid Shells

In addition to B, wc is also affected by humid shells; the shells are subsiding air surrounding cloud cores(Becker et al., 2018; Heus & Jonker, 2008; Jonas, 1990; Katzwinkel et al., 2014). As shown in Table 1,wc is nega-tively correlated with w in the environment (we) in all the 102 clouds with p < 0.05 for D < 100 m. A largerdowndraft (more negative we) corresponds to a larger updraft (more positive wc). The negative correlationbetween wc and we may be related to the coherent structure or internal circulation between updraft anddowndraft (Park et al., 2016; Sherwood et al., 2013; Zhao & Austin, 2005). When D is equal to 100, 300, and500 m, the correlations are still negative though with p > 0.05. The reason could be that the coherent struc-ture between wc and we becomes weak for D ≥ 100 m. Note that not all the 102 clouds have negative we fordifferent D values. When the clouds with positive we are excluded, the absolute values of R increase forD < 100 m (Table 1).

Sincewc is related towe, it is interesting to analyze whetherwe is affected by RH. As shown in Table 1, positivecorrelations between we and RH are found for different D values. Therefore, lower RH corresponds to morenegative we. The reason is that when RH is lower, more cloud droplets near cloud edge evaporate and eva-porate faster, which results in faster and stronger evaporative cooling. The lower temperature in environment

Figure 2. Entrainment rate (λbulk) (a) versus environmental relative humidity(RH) with D = 50 m and (b) versus entrainment rate (λmix) in the 11 cloudsduring Rain in Cumulus over the Ocean (RICO). See text for more details on D.R and p are correlation coefficients and significant levels, respectively.

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increases the downdraft convective available potential energy, whichfurther causes more negative we, because the maximum downdraft is pro-portional to square root of downdraft convective available potentialenergy (Emanuel, 1994). More negative we corresponds to more positivewc due to the coherent structure as discussed above. Because evaporationoccurs near the cloud core edges, the correlations are not significant forD> 100 m (Table 1). In addition, R increases when the clouds with positivewe are excluded for small D. Therefore, RH affects λmix through its effectson the evaporation rate of cloud droplets, and then we, wc.

5. Further Discussions

The positive correlation between λ and RH is also supported by the con-cept of buoyancy sorting (Bretherton et al., 2004; de Rooy & Siebesma,2008; Emanuel, 1991; Kain & Fritsch, 1990). Buoyancy sorting refers to aconcept of lateral mixing across the interface of cloud cores and environ-ments. Different mixtures around cloud edges have different proportionsof cloudy and dry air. The positively buoyant mixtures with mixing fractionof dry air (χd) smaller than its critical value (χdc) are entrained into cloudcores, and the negatively buoyant ones with χd > χdc are detrained. Thisconcept is supported by observations and high-resolution simulationsand is widely used in cumulus parameterizations (Bretherton et al., 2004;de Rooy & Siebesma, 2008; Emanuel, 1991; Kain & Fritsch, 1990) and sto-chastic cloud models (Raymond & Blyth, 1986). Although the methods todetermine χdc and λ could be different in different studies, the conceptsare similar. de Rooy and Siebesma (2008) derived χdc as a function of RH:

χdc ¼A

B� RH; (9a)

where A and B are two parameters. Bretherton et al. (2004) derived that

λ ¼ ε0χdc2; (9b)

where ε0 is a parameter related to height above ground. Equations (9a)and (9b) indicate that χdc and λ are larger when RH is higher, that is, a posi-tive correlation between λ and RH. Figure S1 shows that regression of theobservational data conforms well with equations (9a) and (9b).

As discussed in de Rooy et al. (2016), the buoyancy sorting concept standsin contrast with the negative relationship between λ and RH assumed inthe parameterization developed by Bechtold et al. (2008) and Zhao et al.

(2018). Derbyshire et al. (2011) suggested two competing mechanisms regarding cloud size and naturalselection from a diverse population of clouds to discuss the different relationships between λ and RH. Thepositive correlation between λ and RH in RACORO supports natural selection that when RH is high, a cloudwith large λ can still exist; when RH is low, only a cloud with small λ can survive. No significant correlationbetween λ and cloud size is found in RACORO (not shown). Stirling and Stratton (2012) tried to compromisethe different relationships and stated that Bechtold et al.’s (2008) parameterization might be “an alternativeway of inhibiting the convection in low-RH environments, (where our CRM results achieve this through higherdetrainment rates).” Stirling and Stratton’s (2012) CRM results are consistent with the conclusion based on theequation derived by Bretherton et al. (2004)

δ ¼ ε0 1� χdcð Þ2; (10)

where δ is detrainment rate. Lower RH corresponds to smaller χdc (equation (9a)) and further causes larger δ(equation(10)), inhibiting convection. Further observational studies between δ and RH are needed toconfirm this.

Figure 3. (a) Cloud cores’ vertical velocity (wc) and (b) buoyancy (B) versusenvironmental relative humidity (RH) with D = 50 m in the 102 cloudsduring Routine AAF (Atmospheric Radiation Measurement [ARM] AerialFacility) Clouds with Low Optical Water Depths (CLOWD) Optical RadiativeObservations (RACORO). See text for more details on D. R and p arecorrelation coefficients and significant levels, respectively.

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6. Concluding Remarks

The relationship between λ and RH is examined by use of in situ observational data collected during theRACORO and RICO aircraft campaigns. The λ in the cumulus clouds during RACORO is estimated using themixing fraction approach and is found to be positively correlated with RH. Because RH is implicitly embeddedin the mixing fraction approach, the positive correlation between λ and RH could be due to mathematicalartifacts: more dry air is needed to reduce LWCa to observed LWCwhen the RH is higher. To rule out themath-ematical artifacts, λ in the clouds during RICO is estimated using both the bulk-plume approach with θl that isnot related to RH and the mixing fraction approach. The λ from the bulk-plume approach is still positively cor-related with RH, and λ from the two approaches are positively correlated. Therefore, the positive correlation isnot due to mathematical artifacts, but due to physical mechanisms, as summarized below.

First, higher RH promotes λ through its effects on B. In 62 out of 102 clouds, water vapor plays a more impor-tant role than temperature in determining B. Higher RH causes smaller B. Since wc is driven by B, higher RHcorresponds to smaller wc. Smaller wc means that a cloud has more time to interact with environmentalair, causing larger λ (Neggers et al., 2002; Zhang et al., 2015). The effects of RH on B and/or wc are likelythe primary reasons for the dependence of λ on RH. Second, higher RH promotes λ through its effects onwe. It is found that we is positively correlated with RH; that is, lower RH corresponds to stronger downdraftnear the cloud cores, which further causes larger wc in the cloud cores and smaller λ.

Two points are noteworthy. First, the relationship between λ and RH agrees with the buoyancy sorting con-cept that has been used in previous studies (Bretherton et al., 2004; de Rooy & Siebesma, 2008; Emanuel,1991; Kain, 2004) but is at odds with Bechtold et al.’s (2008) and Zhao et al.’s (2018) parameterization for deepconvection. This study focuses only on shallow cumulus clouds; aircraft observations from deep cumulusclouds are needed to further examine the relationship between the two quantities. Second, this study isfocused on entrainment rate; it is also needed to extend the current approaches to calculate detrainment rateusing aircraft observations and further examine the effects of RH on detrainment rate.

ReferencesAxelsen, S. L. (2005). The role of relative humidity on shallow cumulus dynamics; results from a large eddy simulation model. Utrecht,

Netherlands: Utrecht University.Bechtold, P., Köhler, M., Jung, T., Doblas-Reyes, F., Leutbecher, M., Rodwell, M. J., Vitart, F., et al. (2008). Advances in simulating atmospheric

variability with the ECMWF model: From synoptic to decadal time-scales. Quarterly Journal of the Royal Meteorological Society, 134(634),1337–1351. https://doi.org/10.1002/qj.289

Becker, T., Bretherton, C. S., Hohenegger, C., & Stevens, B. (2018). Estimating bulk entrainment with unaggregated and aggregated con-vection. Geophysical Research Letters, 45, 455–462. https://doi.org/10.1002/2017GL076640

Betts, A. K. (1973). Non-precipitating cumulus convection and its parameterization. Quarterly Journal of the Royal Meteorological Society,99(419), 178–196. https://doi.org/10.1002/qj.49709941915

Betts, A. K. (1975). Parametric interpretation of trade-wind cumulus budget studies. Journal of the Atmospheric Sciences, 32(10), 1934–1945.https://doi.org/10.1175/1520-0469(1975)032<1934:piotwc>2.0.co;2

Blyth, A. M. (1993). Entrainment in cumulus clouds. Journal of Applied Meteorology, 32(4), 626–641. https://doi.org/10.1175/1520-0450(1993)032<0626:eicc>2.0.co;2

Böing, S. J., Jonker, H. J. J., Nawara, W. A., & Siebesma, A. P. (2014). On the deceiving aspects of mixing diagrams of deep cumulus convection.Journal of the Atmospheric Sciences, 71(1), 56–68. https://doi.org/10.1175/JAS-D-13-0127.1

Table 1Correlation Coefficients (R) and Significant Levels (P Values) of the Correlations Between Environmental Vertical Velocity (we) and Cloud Cores’ Vertical Velocity (wc), andBetween we and Relative Humidity in Environment (RH), respectively, in the 102 Clouds During RACORO

wc in cloud cores RH for corresponding D Cloud number

we, D = 10 m R = �0.31, p < 0.01 (R = �0.48, p < 0.01) R = 0.25, p = 0.01 (R = 0.53, p < 0.01) 102 (55)we, D = 20 m R = �0.24, p = 0.01 (R = �0.37, p < 0.01) R = 0.24, p = 0.01 R = 0.30, p = 0.02) 102 (61)we, D = 30 m R = �0.32, p < 0.01 (R = �0.52, p < 0.01) R = 0.32, p < 0.01 (R = 0.39, p < 0.01) 102 (65)we, D = 40 m R = �0.25, p = 0.01 (R = �0.34, p = 0.01) R = 0.34, p < 0.01 (R = 0.36, p < 0.01) 102 (65)we, D = 50 m R = �0.27, p = 0.01 (R = �0.34, p = 0.01) R = 0.37, p < 0.01 (R = 0.32, p = 0.01) 102 (67)we, D = 100 m R = �0.16, p = 0.12 (R = �0.20, p = 0.13) R = 0.26, p = 0.01 (R = 0.19, p = 0.15) 102 (60)we, D = 300 m R = �0.16, p = 0.10 (R = �0.15, p = 0.24) R = 0.13, p = 0.18 (R = 0.12, p = 0.33) 102 (67)we, D = 500 m R = �0.15, p = 0.12 (R = �0.11, p = 0.46) R = 0.03, p = 0.78 (R = 0.03, p = 0.82) 102 (50)

Note. The R, p, and cloud numbers in the parentheses are for the clouds with only negative we. See text for more details on D.

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AcknowledgmentsThis research is supported by theNational Key Research andDevelopment Program of China(2017YFA0604000), the National NaturalScience Foundation of China andJiangsu Province (91537108, 91437101,BK20160041, 41822504, 41475035, and41505119), the Qinlan Project, the SixTalent Peak Project in Jiangsu (2015-JY-011), and the 333 High-level TalentsTraining Project in Jiangsu(BRA2016424). Liu is supported by theU.S. Department of Energy’s BERAtmospheric System Research Program(DE-SC00112704). The RACORO andRICO data are available from https://www.arm.gov/ and https://www.eol.ucar.edu/, respectively.

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