The Aerosol and Cloud Experiments in ENA (ACE-ENA) project was “motivated by the need for comprehensive in situ characterizations of boundary-layer structure and associated vertical distributions and horizontal variabilities of low clouds and aerosol over the Azores” (Wang et al., 2016). The ARM Aerial Facility (AAF) Gulfstream-1 (G-1) aircraft was deployed during two intensive observation periods (IOPs), the summer 2017 IOP from 21 June to 20 July 2017 and the winter 2018 IOP from 15 January to 18 February 2018. Over 30 research flights (RFs) were carried out during the two IOPs around the ARM ENA site on Graciosa Island that sampled a large variety of cloud and aerosol properties along with the meteorological conditions.

Table 1 summarizes the in situ measurements from the ACE-ENA campaign used in this study. The location and velocity of G-1 aircraft and the environmental and meteorological conditions during the flight (temperature, humidity, and wind velocity) are taken from Aircraft-Integrated Meteorological Measurement System 20 Hz (AIMMS-20) dataset (Beswick et al., 2008). The size distribution of cloud droplets and the corresponding qc and Nc are obtained from the fast cloud droplet probe (FCDP) measurement. The FCDP measures the concentration and size of cloud droplets in the diameter size range from 1.5 to 50 µm in 20 size bins with an overall uncertainty of size around 3 µm (Lance et al., 2010; SPEC, 2019). Following previous studies (Wood, 2005a), we adopt r∗=20 µm as the threshold to separate cloud droplets from drizzle drops; i.e., drops with r<r∗ are considered cloud droplets. After the separation, the qc and Nc are derived from the FCDP droplet size distribution measurements. As an evaluation, we compared our FCDP-derived qc results with the direct measurements of qc from the multi-element water content system (WCM-2000; Matthews and Mei, 2017) also flown during the ACE-ENA and found a reasonable agreement (e.g., biases within 20 %). We also performed a few sensitivity tests in which we perturbed the value of r∗ from 15 up to 50 µm. The perturbation shows little impact on the results shown in Sects. 4 and 5. The cloud droplet spectrum from the FCDP is available at a frequency of 10 Hz, which is used in this study. We have also done a sensitivity study, in which we averaged the FCDP data to 1 Hz and got almost identical results. Since the typical horizontal speed of the G-1 aircraft during the in-cloud leg is about 100 m s-1, the spatial sampling rate these instruments is on the order of 10 m for the FCDP at 10 Hz.

In addition to the in situ measurements, ground measurements from the ARM ENA site are also used to provide ancillary data for our studies. In particular, we will use the Active Remote Sensing of Cloud Layers product (ARSCL; Clothiaux et al., 2000; Kollias et al., 2005) which blends radar observations from the Ka-band ARM zenith cloud radar (KAZR), the micropulse lidar (MPL), and the ceilometer to provide information on cloud boundaries and the mesoscale structure of cloud and precipitation. The ARSCL product is used to specify the vertical location of the G-1 aircraft and thereby the in situ measurements with respect to the cloud boundaries, i.e., cloud base and top (see example in Fig. 1). In addition, the radar reflectivity observations from KAZR, alone with in situ measurements, are used to select the precipitating cases for our study. Note that the ARSCL product is from the vertically pointing instruments, which sometimes are not collocated with the in situ measurements from G-1 aircraft. As explained later in the next section, only those cases with a reasonable collocation are selected for our study.

The section provides a brief overview of the G-1 aircraft flight patterns during the ACE-ENA and explains the method for case selections for our study using the 18 July 2017 RF as an example. As shown in Table 2, a variety of MBL conditions were sampled during the two IOPs of the ACE-ENA campaign, from mostly clear sky to thin stratus and drizzling stratocumulus. The basic flight patterns of G-1 aircraft in the ACE-ENA included spirals to obtain vertical profiles of aerosol and clouds, as well as legs at multiple altitudes, including below cloud, inside cloud, at the cloud top, and in the free troposphere. As an example, Fig. 1a shows the horizontal location of the G-1 aircraft during the 18 July 2017 RF, which is the “golden case” for our study as explained in the next section. The corresponding vertical track of the aircraft is shown in Fig. 1b overlaid on the reflectivity curtain of the ground-based KAZR. In this RF, the G-1 aircraft repeated the horizontal level runs multiple times in a V shape at different vertical levels inside, above, and below the MBL (see Fig. 1b). The lower tip of the V shape is located at the ENA site on Graciosa Island. The average wind in the upper MBL (i.e., 900 mbar) is approximately Northwest. So, the west side of the V-shape horizontal level runs is along the wind and the east side across the wind. Note that the horizontal velocity of the G-1 aircraft is approximately 100 m s-1. Since the duration of these selected V-shaped hlegs is between 580 and 700 s, their total horizontal length is roughly 60 km, with each side of the V shape ∼ 30 km. These V-shape horizontal level runs, with one side along and the other across the wind, are a common sampling strategy used in the ACE-ENA to observe the properties of aerosol and cloud at different vertical levels of the MBL. In our study we use the vertical location of the G-1 aircraft from the AIMMS to identify continuous horizontal flight tracks which are referred to as the “hlegs”. For the 18 July 2017 case, a total of 13 hlegs are identified as shown in Fig. 1b. Among them, hlegs 5, 6, 7, 8, 10, 11, and 12 are the seven V-shape horizontal level runs inside the MBL cloud. Together they provide an excellent set of samples of the MBL cloud properties at different vertical levels of a virtual GCM grid box of about 30 km. As previously mentioned, Boutle et al. (2014) found that the horizontal variance of qc increases with the horizontal scale L slowly when L is larger than about 20 km. Therefore, although the horizontal sampling of the selected hlegs is only about 30 km, the lessons learned here could yield useful insights for larger GCM grid sizes. In addition to the hlegs, we also identified the vertical penetration legs in each flight, referred to as the “vlegs”, from which we will obtain the vertical structure of the MBL, along with the properties of cloud and aerosol.

As illustrated in Fig. 1a and b for the 18 July 2017 RF, the criteria we used to select the RF cases and the hlegs within the RF can be summarized as follows:

The RF samples multiple continuous in-cloud hlegs at different vertical levels with the horizontal length of at least 10 km and cloud fraction larger than 10 % (i.e., the fraction of an hleg with qc > 0.01 g m-3must exceed 10 % of the total length of that hleg). It is important to note here that, unless otherwise specified, all the analyses of qc and Nc are based on in-cloud observations (i.e., in the regions with qc > 0.01 g m-3).

On 18 July 2017, the North Atlantic is controlled by the Icelandic low to the north and the Azores high to the south (see Fig. 2b), which is a common pattern of large-scale circulation during the summer season in this region (Wood et al., 2015). The Azores is at the southern tip of the cold air sector of a frontal system where the fair-weather low-level stratocumulus clouds are dominant (see satellite image in Fig. 2a). The RF on this day started around 08:30 UTC and ended around 12:00 UTC. As explained in the previous section, we selected seven hlegs from this RF that horizontally sampled the same region repeatedly in a similar V-shaped track but vertically at different levels. The radar reflectivity observation from the ground-based KAZR during the same period peaks around 10 dBZ, indicating the presence of significant drizzle inside the MBL clouds.

Among the seven selected hlegs, hlegs 5, 6, 7, and 8 constitute one set of four consecutive V-shaped tracks, with hlegs 5 close to cloud base and hleg 8 close to cloud top. The hlegs 10, 11, and 12 are another set of consecutive V-shaped tracks with hlegs 10 and 12 close to cloud base and top, respectively (see Fig. 1). Using qc>0.01 g m-3 as a threshold for cloud, the cloud fraction (fc) of all these hlegs is close to unity (i.e., overcast), except for the two hlegs close to cloud base (fc= 46 % for hleg 5 and fc= 51 % for hleg 10). The qc and Nc derived from the in situ FCDP measurements for these selected hlegs are plotted in Fig. 3 as a function of UTC time. It is evident from Fig. 3 that both qc and Nc have significant horizontal variations. At cloud base (see Fig. 3d for hleg 5 and Fig. 3g for hleg 10) the qc varies from 0.01 g m-3 (i.e., the lower threshold) up to about 0.4 g m-3 and the Nc from 25 up to 150 cm-3, with the mean in-cloud values around 0.08 g m-3 and 65 cm-3, respectively. Such strong variations of cloud microphysics could be contributed by a number of factors. One can see from the ground radar and lidar observations in Fig. 1b that the height of cloud base varies significantly. As a result, the horizonal legs may not really sample the cloud base. In addition, the variability in updraft at cloud base could lead to the variability in the activation and growth of cloud condensation nuclei (CCN). In the middle of the MBL cloud, i.e., hleg 6 (Fig. 3c), 7 (Fig. 3b) and 11 (Fig. 3f), the mean value of qc is significantly larger than that of cloud base hlegs while the variability is reduced. The mean value of qc keeps increasing toward cloud top to ∼ 0.73 g m-3 in hleg 8 (Fig. 3a) and to ∼ 0.53 g m-3 in hleg 12 (Fig. 3e), respectively. In contrast, the horizontal variability of qc seems to increase in comparison to those observed in mid-level hlegs.

To obtain a further understanding of the vertical variations of cloud microphysics, we analyzed the cloud microphysics observations from the two green-shaded vlegs 1 and 3 in Fig. 1b. The vertical profiles of the mean qc and Nc from these two vlegs are shown in Fig. 4a and b, respectively, with the mean and standard deviation of the qc and Nc derived from the seven selected hlegs overplotted. Overall, the vertical profiles of the qc and Nc are qualitatively aligned with the classic adiabatic MBL cloud structure (Brenguier et al., 2000; Martin et al., 1994). That is, the Nc remains relatively constant (see Fig. 4b), while the qc increases approximately linearly with height from cloud base upward as a result of condensation growth (see Fig. 4a,), except for the very top of the cloud, i.e., the entrainment zone where the dry air entrained from above mixes with the humid cloudy air in the MBL. In previous studies, a so-called inverse relative variance, ν, is often used to quantify the subgrid variations of cloud microphysics. It is defined as follows: 2νX=〈x〉2σX2, where X is either qc (i.e., νX=νqc) or Nc (i.e., νX=νNc) (Barker et al., 1996; Lebsock et al., 2013; Zhang et al., 2019). 〈x〉 and σX are the mean value and standard deviation of X, respectively. As such, the smaller the ν value, the larger the horizontal variation of X in comparison to the mean value. As shown in Fig. 4c, the νqc and νNc derived from the selected hlegs follow a similar vertical pattern: they both increase first from cloud base upward and then decrease in the entrainment zone, with the turning point somewhere around 1 km (i.e., around hleg 7 and 11). It indicates that both qc and Nc have significant horizontal variabilities at cloud base which may be a combined result of horizontal fluctuations of dynamics (e.g., updraft) and thermodynamics (e.g., temperature and dynamics), as well as horizontal variations of aerosols. The horizontal variabilities of both qc and Nc both decrease upward toward cloud top until the entrainment zone where both variabilities increase again.

So far, in all the analyses above, the variations of qc and Nc have been considered separately and independently. As pointed out in several previous studies, the covariation of qc and Nc could have an important impact on the EF for the autoconversion process in GCMs (Kogan and Mechem, 2016; Larson and Griffin, 2013; Zhang et al., 2019). This point will be further elucidated in detail in the next section. Figure 5 shows the joint distributions of qc and Nc for the seven selected hlegs, and the corresponding linear correlation coefficients as a function of height are shown in Fig. 4d. For the sake of reference, the linear correlation coefficient between ln⁡(qc) and ln⁡(Nc) , i.e., the ρL that will be introduced later in Eq. (4), is also plotted in Fig. 4d. Looking first at hlegs 10, 11, and 12, i.e., the second group of consecutive V-shaped legs, there is a clear increasing trend of the correlation between qc and Nc from cloud bottom (ρ=0.75 for hleg 10) to cloud top (ρ=0.95 for hleg 12). The picture based on hlegs 5, 6, 7, and 8 is more complex. As shown in Fig. 5, the joint distributions of qc and Nc of hleg 6 (Fig. 5b), hleg 7 (Fig. 5c), and, to a less extent, hleg 8 (Fig. 5d) all exhibit a clear bimodality. Further analysis reveals that each of the two modes in these bimodal distributions approximately corresponds to one side of the V-shaped track. To illustrate this, the east side (i.e., across wind) of the hleg is shaded in yellow in Fig. 3. It is intriguing to note that the Nc values from the east side of the hleg are systematically larger than those from the west side, while their qc values are largely similar. It is unlikely that the bimodality is caused by the along-wind and across-wind difference between the two sides of the V-shaped track. It is most likely just a coincidence. On the other hand, the bimodal joint distribution between qc and Nc is real, which could be a result of subgrid variations of updraft, precipitation, and/or aerosols.

As a result of the bimodality of Nc, the correlation coefficients between qc and Nc is significantly smaller for hlegs 6 (ρ=0.22) and 7 (ρ=0.31) in comparison to other hlegs. However, if the two sides of the V-shaped tracks are considered separately, then qc and Nc become more correlated, except for the east side of hleg 6, which still exhibits to some degree a bimodal joint distribution of qc and Nc. In spite of the bimodality, there is evidently a general increasing trend of the correlation between qc and Nc from cloud base toward cloud top. At the cloud top, the qc and Nc correlation coefficient can be as high as ρ=0.95 for hleg 12 (see Fig. 5e). As explained in the next section, this close correlation between qc and Nc has important implications for the simulation of the autoconversion enhancement factor.

As a summary, the above phenomenological analysis of the 18 July 2017 RF reveals the following features of the horizontal and vertical variations of cloud microphysics. Vertically, the mean values of qc and Nc qualitatively follow the adiabatic structure of MBL cloud; i.e., qc increases linearly with height and Nc remains largely invariant above cloud base. Even though the joint distribution of qc and Nc exhibits a bimodality in several hlegs, their correlation generally increases with height and can be as high as ρ=0.95 at cloud top. Horizontally, both qc and Nc have a significant variability at cloud base, which tends to first decrease upward and then increase in the uppermost part of cloud close to the entrainment zone. Finally, we have to point out a couple of important caveats in the above analysis. First, as seen from Fig. 1 the selected hlegs are sampled at different vertical locations and also at different times. For example, hleg 5 at cloud base is more than 1 h apart from hleg 8 at cloud top (Fig. 1a). As a result, the temporal evolution of clouds is a confounding factor and might be misinterpreted as vertical variations of clouds. On the other hand, as shown below, we also observed similar vertical structure of qc and Nc in other cases. It seems highly unlikely that the temporal evaluations of the clouds in all selected cases conspire to confound our results in the same way. Based on this consideration, we assume that the temporal evolution of clouds is an uncertainty that could lead to random errors but does not impact the overall vertical trend. The second caveat is that due to the very limited vertical sampling rate of hlegs (i.e., only 3–4 samples), we cannot possibly resolve the detailed vertical variation of νq, νN, and ρ. Although we have used the word “trend” in the above analysis, it should be noted that the vertical profile of these parameters may, but more likely may not, be linear. So, the word “trend” here indicates only the large pattern that can be resolved by the hlegs. Obviously these two caveats also apply to the analysis below the EF, which is also derived from the hlegs.

As explained in the introduction, in GCMs the autoconversion process is usually parameterized as a highly nonlinear function of qc and Nc, e.g., the KK scheme in Eq. (1). In such a parameterization, an EF is needed to account for the bias caused by the nonlinearity effect. A variety of methods have been proposed and used in the previous studies to estimate the EF (Larson and Griffin, 2013; Lebsock et al., 2013; Pincus and Klein, 2000; Zhang et al., 2019). The methods used in this study are based on Z19. Only the most relevant aspects are recapped here. Readers are referred to Z19 for detail.

If the subgrid variations of qc and Nc, as well as their covariation, are known, then the EF can be estimated based on its definition as follows: 3E=∫Nc,min∞∫qc,min∞qcβqNcβNPqc,NcdqcdNc〈qc〉βq〈Nc〉βN, where 〈qc〉 and 〈Nc〉 are the grid-mean value, P(qc,Nc) is the joint probability density function (PDF) of qc and Nc. qc,min and Nc,min are the lower limits of the in-cloud value (e.g., qc,min=0.01 g m-3). Some previous studies approximate the P(qc,Nc) as a bivariate lognormal distribution as follows: 4Pqc,Nc=12πqcNcσqcσNc1-ρL2exp⁡-ζ2ζ=11-ρL2ln⁡qc-μqcσqc2-2ρln⁡qc-μqcσqcln⁡Nc-μNcσNc+ln⁡Nc-μNcσNc2, where μX and σX are, respectively, the mean and standard deviation of ln⁡(X), where X is either qc or Nc. ρL is the linear correlation coefficient between ln⁡(qc) and ln⁡(Nc) (Larson and Griffin, 2013; Lebsock et al., 2013; Zhang et al., 2019). It should be noted here that ρL is fundamentally different from ρ (i.e., the linear correlation coefficient between qc and Nc). On the other hand, we found that for all the selected hlegs, ρ and ρL are in an excellent agreement (see Fig. 4d). In fact, ρ and ρL can be used interchangeably in the context of this study without any impact on the conclusions. Nevertheless, interested readers may find more detailed discussion of the relationship between ρ and ρL in Larson and Griffin (2013).

Substituting Pqc,Nc in Eq. (4) into Eq. (3) yields a formula for EF that consists of the following three terms: 5E=Eqνqc,βq⋅ENνNc,βN⋅ECOVρL,βq,βNνqc,νNc, where Eqνqc,βq corresponds to the enhancing effect of the subgrid variation of qc, if qc follows a marginal lognormal distribution, i.e., Px=12πxσexp⁡-ln⁡x-μ22σ2. It is a function of the inverse relative variance νq in Eq. (2) as follows: 6Eqνqc,βq=1+1νqcβq2-βq2. Similarly, the ENνNc,βN below corresponds to the enhancing effect of the subgrid variation of Nc, if Nc follows a marginal lognormal distribution: 7ENvNc,βN=1+1νNcβN2-βN2. The third term ECOVρL,βq,βNνqc,νNc in Eq. (5), 8ECOVρL,βq,βN,vqc,vNc=exp⁡ρLβqβNσqcσNc, corresponds to the impact of the covariation of qc and Nc on the EF. Because βq>0 and βN<0, if qc and Nc are negatively correlated (i.e., ρL<0), then the ECOV>1 and acts as an enhancing effect on the autoconversion rate computation. In contrast, if qc and Nc are positively correlated (i.e., ρL>0), then the ECOV<1, which becomes a suppressing effect on the autoconversion rate computation.

As previously mentioned, most previous studies of the EF consider only the impact of subgrid qc variation (i.e., only the Eq term). The impacts of subgrid Nc variation as well as its covariation with qc have been largely overlooked in observational studies, in which the Eq is often derived from the observed subgrid variation of qc based on the definition of EF, i.e., 9Eq=∫qc,min∞qcβqPqcdqc〈qc〉βq, where Pqc is the observed subgrid PDF of qc. Alternatively, Eq has also been estimated from the inverse relative variance νq by assuming the subgrid variation of qc follows the lognormal distribution, in which case Eq is given in Eq. (6).

Similar to EN, if only the effect of subgrid Nc is considered, the corresponding EN can be derived from the following two ways: one from the observed subgrid PDF PNc based on the definition of EF, i.e., 10EN=∫Nc,min∞NcβNPNcdNc〈Nc〉βN, and the other based on Eq. (7) from the relative variance νNc by assuming the subgrid Nc variation follows the lognormal distribution.

Now, we put the in situ qc and Nc observations from the selected hlegs in the theoretical framework of EF described above and investigate the following questions:

What is the (observation-based) EF derived based on Eq. (3) from the observed joint PDF P(qc,Nc)?

These questions are addressed in the rest of this section. Focusing first on the Eq in Fig. 6a, the Eq derived from observation based on Eq. (9) (solid circle) shows a clear decreasing trend with height between cloud base at around 700 m to about 1 km, with a value reduced from about 3 to about 1.2. Then, the value of Eq increases slightly in the cloud top hlegs 8 and 12. The Eq derived based on Eq. (6) by assuming lognormal distribution (open circle) has a very similar vertical pattern, although the value is slightly overestimated on average by 0.07 in comparison to the observation-based result. The vertical pattern of Eq can be readily explained by the subgrid variation of qc in Fig. 4c. The EN derived from observation (solid triangle) in Fig. 6b shows a similar vertical pattern as Eq, i.e., first decreasing with height from cloud base to about 1.2 km and then increasing with height in the uppermost part of cloud. The EN derived based on Eq. (7) by assuming a lognormal distribution (open triangle) significantly underestimates the observation-based values (mean bias of -4.3), especially at cloud base (i.e., hleg 5 and 10) and cloud top (i.e., hleg 8 and 12).

Using hleg 10 as an example, we further investigated the cause for the error in lognormal-based EFs in comparison to those diagnosed from the observation. As shown in Fig. 7a the observed qc is slightly negatively skewed in logarithmic space by the small values. Because the autoconversion rate is proportional to qc2.47, the negatively skewed qc also leads to a negatively skewed Eq in Fig. 7b. As a result, the leg-averaged Eq diagnosed from the observation is slightly smaller than that derived based on Eq. (6) by assuming a lognormal distribution. The negative skewness also explains the large error in EN for hleg 10 seen on Fig. 6b. As shown in Fig. 7c the observed Nc is also negatively skewed to a much larger extent in comparison to qc. Because the autoconversion rate is proportional to Nc-1.79, the highly negatively skewed Nc results in a highly positively skewed EN in Fig. 7d. As a result, the EN diagnosed from the observation is much larger than that derived based on Eq. (7) by assuming a lognormal distribution.

The Eq and EN reflect only the individual contributions of subgrid qc and Nc variations to the EF. The effect of the covariation of qc and Nc, i.e., the ECOV, is shown in Fig. 6c. Interestingly, the value of ECOV is smaller than unity for all the selected hlegs. As explained in Eq. (8), ECOV<1 is a result of a positive correlation between qc and Nc, as seen in Fig. 4d. Therefore, in these hlegs the covariation of the qc and Nc has a suppressing effect on the EF, in contrast to the enhancing effect of Eq and EN. This result is qualitatively consistent with Z19, who found that the vertically integrated liquid water path (LWP) of MBL clouds is in general positively correlated with the Nc estimated from the MODIS cloud retrieval product and, as a result, ECOV<1 over most of the tropical oceans. Because of the relationship in Eq. (8), the value ECOV is evidently negatively proportional to the correlation coefficient ρL in Fig. 4d. The largest value is seen in hleg 6 and 7, in which the bimodal joint distribution of qc and Nc results in a small ρL. A rather small value of ECOV∼0.45 is seen for cloud top hleg 8 and 12, as result of a strong correlation between qc and Nc (ρL>0.9) and moderate σq and σN.

Finally, the EF that accounts for all factors, including the individual variations of qc and Nc, as well as their covariation, is shown in Fig. 6d. Focusing first on the observation-based results (solid star), i.e., E in Eq. (3), evidently there is a decreasing trend from cloud base (e.g., E=2.2 for hleg 5 and E=1.59 for hleg 10) to cloud top (e.g., E=1.20 for hleg 8 and E=1.02 for hleg 12). The E values derived based on Eq. (5) by assuming the bivariate lognormal distribution between qc and Nc (i.e., open star in Fig. 6d) are in reasonable agreement with the observation-based results, with a mean bias of -0.09. It is intriguing to note that the value of E=Eq⋅EN⋅ECOV in Fig. 6d is comparable to Eq in Fig. 6a, which indicates that the enhancing effect of EN>1 in Fig. 6b is partially canceled by the suppressing effect of ECOV<1 in Fig. 6c. As previously mentioned, many previous studies of the EF consider only the effect of Eq but overlook the effect of EN and ECOV. The error in the studies would be quite large if it were not for a fortunate error cancellation.