The signature of aerosols and meteorology on the development of precipitation from shallow cumuli in the trades is investigated with ground-based lidar and radar remote sensing. The measurements are taken from a cloud observatory recently established on the windward shore of Barbados. Cloud microphysical development is explored through an analysis of the radar echo of shallow cumuli before the development of active precipitation. The increase of reflectivity with height (Z gradient) depends on the amount of cloud water, which varies with meteorology, and cloud droplet number concentration N, which varies with the aerosol. Clouds with a large Z gradient have a higher tendency to form precipitation than clouds with a small Z gradient. Under similar meteorological conditions, the Z gradient is expected to be large in an environment with few aerosols and small in an environment with many aerosols. The aerosol environment is defined using three methods, but only one (based on the Raman lidar linear-depolarization ratio) to measure dusty conditions correlates significantly with the Z gradient. On average, nondusty days are characterized by a larger Z gradient. However, the dust concentration varies seasonally and covaries with relative humidity. Large-eddy simulations show that small changes in the relative humidity can have as much influence on the development of precipitation within the cloud layer as large changes in N. When clouds are conditioned on their ambient relative humidity, the sensitivity of the Z gradient to dust vanishes.
Whether variations in cloud condensation nuclei (CCN) (and hence the aerosol more generally) meaningfully affect precipitation development in warm clouds remains an open and controversial question (Stevens and Brenguier 2009). Observations from satellites (Kaufman et al. 2005) suggest that cloud amount covaries with aerosol amount, which is consistent with the idea that increasing aerosol amounts suppress warm rain formation and hence increase cloudiness (e.g., Albrecht 1989; Liou and Ou 1989). However, this covariability could also be explained by other factors (e.g., changes in relative humidity). In this study, simultaneous measurements from advanced ground-based lidar and radar remote sensing are employed to explore to what extent the variability in the ambient aerosol can explain variability in the propensity of shallow trade wind clouds to form rain.
Cumulus clouds with tops below the freezing level are ubiquitous in the trades (Nuijens et al. 2014). The formation of rain in these shallow trade wind cumuli occurs through the collision and coalescence of water droplets on short time scales (Byers and Hall 1955). As discussed by Rauber et al. (2007), the relatively rapid onset of warm rain is still not well understood. As warm rain constitutes a significant fraction of precipitation in the tropics (e.g., Short and Nakamura 2000; Burdanowitz et al. 2015; Takayabu et al. 2010) and the cloud amount may ultimately depend on the precipitation efficiency of clouds, as hypothesized by Albrecht (1989), precipitation controlling factors within trade wind clouds are important to understand. One of these factors is thought to be changes in aerosol concentration. For example, an observational study by Knight et al. (2002) discussed that giant aerosols could have an impact on the presence of large rain drops.
Already in the early 1970s it was recognized that changes in aerosol concentration might influence the microphysical structure of clouds. Twomey (1974) suggested that variations in the concentration of CCN may influence cloud radiative properties and, hence, planetary albedo. Even though the physics behind what has come to be known as the Twomey effect are now well established, the extent to which these microphysical changes help explain variability in the propensity of clouds to form rain and the degree to which changes in precipitation efficiency affect cloud amount is much less clear (Stevens and Feingold 2009). There is no question that, all other things being equal, changes in CCN concentrations will change cloud microphysical properties. The question remains open as to whether it is reasonable to assume that all other things will remain equal. To address this issue, a better understanding of the susceptibility of clouds to their meteorological environment is required. In a warming climate this meteorological susceptibility may become even more important, as changes in the cloud environment (e.g., changes in humidity, stability, or surface wind speeds) are expected. Many of those changes have a large potential to influence cloudiness (Nuijens et al. 2009) but are much less studied than is the effect of aerosols (e.g., Stevens and Boucher 2012).
To better quantify the relative role of the aerosol as compared to meteorological changes in regulating precipitation from shallow convection, we have begun a program of surface-based remote sensing from an upwind observatory on the island of Barbados (Stevens et al. 2015). Aerosols from pollution sources over Europe or dust sources over North Africa may imprint themselves on air masses far upstream of Barbados. But because these sources are far away, and because aerosols adjust to changes in their environment on time scales of days (e.g., Warneck 1988), while thermodynamic conditions in the boundary layer adjust on time scales of hours (Schubert et al. 1979), meteorological differences between air masses of different origins are not expected over Barbados. In other words, the meteorological and chemical properties of air masses may decorrelate, which makes measurements from Barbados well suited to study the aerosol signal on trade wind cumuli.
Previous studies (e.g., Snodgrass et al. 2009; Zuidema et al. 2012) have investigated the main characteristics of precipitating trade wind cumuli and their environment using about 2 months of data. In contrast, this study analyzes long-term measurements from advanced remote sensing measurements to explore to what extent changes in the propensity of trade wind cumuli to form rain during aerosol-rich days can be attributed to changes in the aerosol or whether subtle variations in other factors may be more important.
The manuscript is organized as follows. In section 2 the main question of the manuscript is framed by analyzing how strongly the radar reflectivity increases with height (i.e., the vertical gradient of Z, which we denote by ), depending on the cloud microphysical properties (e.g., droplet number concentration N) and cloud bulk properties (e.g., how cloud water varies with height). Section 3 gives a short overview of the Barbados Cloud Observatory and the instruments used, along with the data treatment. In section 4, the change in the propensity of shallow clouds to form rain is investigated as a function of the observed . The change in this is discussed for aerosol-rich and aerosol-poor days in section 5 and for relative humidity effects in section 6. Conclusions are presented in section 7.
2. Background and theoretical framing
The radar reflectivity factor Z, or simply “reflectivity,” is the sixth moment of the droplet number distribution , with D being the droplet diameter and measuring the number of droplets whose diameters are between and :
Assume that the droplet number distribution is distributed:
with scale parameter B and the shape parameter p. A different distribution (e.g., bimodal distribution) may have to be considered when clouds start to form precipitation because collision and coalescence of cloud droplets lead to the formation of drizzle drops, which broadens the droplet spectrum and forms a second mode. However, the focus of this study is on developing clouds that do not yet rain; hence, the distribution is believed to be a reasonable assumption for . To test the appropriateness of the assumed distribution, results obtained from the simple semianalytic analysis are compared to those obtained from a bin microphysical model coupled to a 1D kinematic cloud draft at the end of this section. It is shown that allowing more degrees of freedom for the shape of the droplet distribution does not appreciably affect the conclusions that we draw.
The reflectivity and the liquid water content are related to each other, as is proportional to the third moment of the droplet number distribution. By inserting Eq. (2) into Eq. (1), B vanishes and Z can be expressed as
where N is the zeroth moment. For simplicity, it is assumed that N is constant with height. It is not entirely clear why this should be the case (as mixing processes can be expected to change the droplet number concentrations), but measurements from airborne platforms (Gerber et al. 2008; Siebert et al. 2013) have shown this to be a relatively good assumption. This assumption implies that the droplet size changes follow the changes.
The parameter appearing in Eq. (3) depends on the shape parameter of the droplet number distribution:
Equation (4) thus describes the sensitivity of the reflectivity to the choice of . A difference in reflectivity of 2.5 dBZ can be explained by a rather large increase of p from 8.7 to 34.3 (equivalent to a decrease of from 2.25 to 1.13) or a factor of 2 increase in N under relatively steady thermodynamic conditions. Here the question arises: How realistic is this increase in p? In situ measurements at cloud top show large variations in the shape parameter (Siebert et al. 2013) between shallow cumuli with different CCN concentration. However, at cloud top the formation of rain has often already initiated and this modifies the distribution and thus the shape parameter. Model studies of nonprecipitating clouds show very small variations in the shape parameter (Beheng 1994), being a result of opposing effects by autoconversion, which tends to narrow the spectrum, and self-collection, which broadens the spectrum (Beheng and Doms 1990).
In the literature values such as p = 7 (Deirmendjian 1969) and p = 8.7 ± 6.8 (Brandau et al. 2010) can be found resulting in k2 = 2.62 and 2.25, respectively. In contrast, if the distribution in is assumed to be monodisperse, then k2 equals unity. In this study, k2 = 2.25 is assumed for aerosol-rich and aerosol-poor days. Hence, most of the analysis should be interpreted bearing in mind that k is constant, the effects of which can be assessed in reference to the detailed bin microphysical calculations which relax this assumption. As such, the microphysical influence on Z may be parameterized by variations in N and , only.
It is further assumed that variations in height can be represented through a subadiabatic factor β, such that
with the adiabatic liquid water lapse rate , which is a function of temperature. Here, the temperature is assumed to be constant resulting in (cf. Albrecht et al. 1990), which equals when assuming the density of air with 1.29 kg m−3.
The subadiabatic factor is defined as the ratio of the actual cloud liquid water to its adiabatic value. It ranges from 0 to 1 for , with cloud base and cloud top . For cloudy air rising reversibly (i.e., without mixing and with radiative effects being negligible), the liquid water will increase adiabatically (i.e., ). Shallow cumuli are known to be very subadiabatic (Zhang et al. 2011; Blyth and Latham 1993) because they continuously mix with their environment. Based on measurements (Kim et al. 2008; Boers et al. 2006) and large-eddy simulations (Zhang et al. 2011), a range in β can be found with 0.1 < β < 0.9. Especially near cloud tops of cumulus clouds, β is often much less than 1.
In light of these assumptions,
For Z in , dBZ is defined as
Hereafter, Z and dBZ are used interchangeably to describe reflectivity.
The factor in Eq. (6) determines how rapidly the reflectivity increases with height and is referred to as (the vertical) Z gradient in this study. The variable is sensitive to (or ) but inversely proportional to only the first power of N. Hence, β has a stronger impact on than N, if assuming N and β to be invariant with height. Even if we were to allow for N to vary, the height variations in β would likely dominate for this very reason, in part justifying our earlier assumptions.
One of the premises of this study was that, if the cloud water can be controlled by sampling clouds in sufficiently homogeneous thermodynamic conditions, variations in N may dominate variations in . Because the trades are a steady region in terms of their meteorological environment it may be possible to isolate the role of N and the underlying CCN concentration, by assuming that β does not vary, or relative humidity would be constant in the cloud layer. During a field campaign in Barbados, Siebert et al. (2013) measured large variations in N (almost by a factor of 10) but proportionally much smaller (or in other words, subtle) differences in the thermodynamic environment (e.g., temperature) and cloud-base height.
Nonetheless, the assumption that β is constant is a strong one, particularly given the choice to measure the microphysical trajectory of clouds in terms of their radar reflectivity, which, compared to a lower moment, emphasizes the role of β. Unfortunately, long-term measurements from a microwave radiometer were not available. These would have allowed us to stratify clouds by their liquid water content, which is equivalent to setting β constant. For this reason, additional measurements are employed in an attempt to better control β, for instance, through the use of coincident and high-frequency relative humidity profiles derived from a Raman lidar.
Figure 1 illustrates how the reflectivity would change with height as a function of a single parameter, , which is assumed to be constant (black lines), or linearly decreasing in height (gray line), for instance, as might happen if the subadiabatic factor decreases with height in the cloud. If N stays constant with height, a decrease in can be interpreted as a decrease in β. For example, for and β = 0.2, one obtains (long dashed line in Fig. 1), and for and β = 0.1 one obtains (solid line).
To test our assumptions that a single distribution is valid to describe the cloud number distribution, the 1D kinematic bin microphysics model by Seifert and Stevens (2010) with the setup illustrated in their Fig. 1 is used. Clouds with three different CCN concentrations and w0 = 2 m s−1 (cf. Seifert and Stevens 2010) are used to explore the validity of Eqs. (3) and (6). Note that effects of underestimating the broadening of the cloud droplet size distribution cannot be excluded. However, the growth of large cloud droplets and hence their effect on the magnitude of the increase in reflectivity works well (not shown) and offers a good explanatory model. Very good agreement between the theoretical behavior of reflectivity with height (gray lines) and its modeled counterpart (black lines) for the developing stage of the cloud (15 min into the simulation just before first rain drops are produced) is achieved, as seen in Fig. 2. The values derived using Eq. (6) are rather large from the 1D model simply because , which assumes a smaller amount of mixing. However, this does not influence the validity of using a single distribution to describe the cloud number distribution of a developing cloud.
3. Data and methodology
Here, the Barbados Cloud Observatory (BCO) is introduced along with the instruments used in this study. Furthermore, three methods that have been employed to identify different aerosol environments are described. Last, the algorithm of identifying cloud objects and the treatment of the data are explained.
a. Barbados Cloud Observatory
The BCO is located on the eastern coast of Barbados (Deebles Point), where it faces easterly trade winds that prevail during most of the year and occupy a layer of up to 3 km deep, although the marine layer itself is usually somewhat shallower. The dominant cloud type is cumulus mediocris and cumulus fractus, although at times cumulus congestus occurs (see Fig. 3). The observatory has been developed by our institute in cooperation with the Caribbean Institute for Meteorology and Hydrology in Barbados and began continuous operations in April 2010. A full description of the site can be found in Stevens et al. (2015). Here, only a brief overview of the instruments, of which the first 2 years of data (January 2011–March 2012) are used, is presented. With the unique long-term dataset from BCO, we are able to simultaneously measure the thermodynamic properties of the marine layer as well as the aerosol and clouds within the layer. In this study, we take measurements from a cloud radar (KATRIN), a Raman lidar, and a Micro Rain Radar.
1) KATRIN cloud radar
Measurements by the KATRIN1 cloud radar are used to investigate how and why microphysical properties of trade wind cumuli change, in particular with regard to their development of precipitation. The KATRIN cloud radar is a fully scanning linearly polarized Ka-band Doppler radar with a frequency of 35.5 GHz (λ = 8.6 mm). This wavelength ensures a high sensitivity to small hydrometeors, like cloud droplets. Further, the measured Doppler velocity υ depends on the droplet fall velocities and the vertical velocity of the airstream in the measurement volume. Hence, if the cloud radar is pointing vertically upward and the Doppler velocity can be used as an indicator of the formation of precipitation for clouds characterized by low reflectivities. For a more general overview on cloud radars, see Kollias et al. (2007).
KATRIN measures through a range of 15 km with a range resolution of 30 m and an averaging time of 10 s. More background information of a second nearly identical radar can be found in Grenzhäuser (2012) and further specifications of KATRIN are listed in Table 1.
A comparison of profiles from different elevation angles by KATRIN shows no evidence of an island effect; that is, the statistics of radar retrievals were difficult to distinguish from the vertical-pointing mode with those several kilometers offshore. Based on this, measurements have predominantly been collected in the vertical-pointing mode. Hence, the remainder of this study is restricted to an investigation of measurements taken in this mode of operation.
Individual radar retrievals of KATRIN were evaluated by eye to look for signs of spurious signals from ground clutter and clear-air echoes. A comparison to a second radar (Grenzhäuser 2012) that was collocated on the site for a period of some weeks enabled to identify these spurious signals. To distinguish weak but real signals from clutter and clear-air echoes, the cloud radar’s high sensitivity and polarization information is often used. In this study, however, where very low reflectivity returns are not necessary, a conservative filter of dBZ ≥ −35 for the KATRIN cloud radar was deemed sufficient, thereby avoiding any question of possible contamination from spurious signals.
2) Raman lidar
The Raman lidar is useful in providing information of the vertically resolved aerosol as well as temperature and humidity (whereby for thermodynamic parameters, our system is limited by signal to noise considerations to nighttime retrievals only). The lidar measures the energy backscattered by particulate matter and molecules at three different wavelengths (355, 532, and 1064 nm). The particle depolarization ratio (at 532 nm) is used to characterize the aerosol as a vertical profile with a range resolution of 60 m up to 15 km. For all quantities, single Raman profiles are averaged over a time of 2 min. The Raman lidar hatch stays closed during times when the sun is directly overhead (1130–1330 local time during April and August) or when rain is measured at any height below 3 km by the Micro Rain Radar. Clouds are able to modify lidar measurements of aerosols and relative humidity. To avoid cloud contamination, only profiles under clear-sky (cloud free) conditions are considered in this study.
Because the Raman lidar only provides relative humidity data at night, evidence of a diurnal cycle in humidity was searched for both in cloud radar data and through measurements with a coincident differential absorption lidar system, which provided daytime humidity profiles over a few weeks of coincident operation. However, a pronounced diurnal cycle, such as seen over and downwind of the island, is not evident at the site, which is only tens of meters from the upwind edge of the island. This shows that the BCO measurements are representative of the open ocean, where diurnal variations are generally small (Stevens et al. 2015).
b. Identifying cloud entities
One aim of this study is to look at the development of trade wind cumuli in different aerosol and meteorological environments. For this purpose, a segmentation algorithm has been developed to identify echo objects (named “cloud entities”) representative of typical trade wind cumuli. This algorithm allows us to treat the properties of trade wind cumuli independent of their cloud size by averaging over each individual entity and to relate to bulk cloud properties, like cloud depth.
Before applying the algorithm, the radar data is regridded on to a time–equidistant grid. Following the initial screening of the data, radar echoes are defined as pixels with dBZ ≥ −35. Then the segmentation algorithm identifies conterminous radar echoes as cloud entities, having common edges and vertices (Fig. 4). Only cloud entities consisting of more than three pixels with a width and height of at least two pixels (20 s and 60 m, respectively) and with bases below 1 km (named “shallow cloud entities” and highlighted in black in Fig. 4b) are considered so as to exclude cloud fragments and stratiform clouds. The minimum base and the maximum top of echo objects is hereafter named cloud base and cloud top, respectively. Because only retrievals with reflectivities larger than dBZ = −35 are retained, the first radar echoes near cloud base and very small, cumulus humulis are not well sampled and the actual base of the cloud will in most instances be somewhat below the level of the first radar echo. Because our interest is in the properties of cumulus clouds toward their tops, this is not an issue for our present purposes.
To identify nonprecipitating active clouds, hereafter referred to as developing cumulus clouds, a combined velocity–reflectivity threshold is applied to every cloud entity. Such a combined threshold is necessary to filter out precipitation embryos trapped in updrafts, which can be as large as 8 m s−1 (Siebert et al. 2013). Other techniques in separating cloud and drizzle make use of the whole spectra (e.g., Luke and Kollias 2013).
To pass the reflectivity threshold, at least 95% of all pixels of a cloud entity have to be below −18 dBZ. This threshold is similar to the threshold used by Frisch et al. (1995) in order to avoid any contamination by rain drops characterized by high reflectivities. Additionally, only clouds with a mean updraft greater than 0.5 m s−1 at all heights are considered. For this purpose, the mean Doppler velocity at every height level is calculated. Thus, we consider mean properties of a cloud rather than individual updrafts and downdrafts inside the cloud. By concentrating on shallow clouds with a mean upward motion, a higher susceptibility toward changes in environmental air properties is expected, as shown in numerical simulations by Zhao and Austin (2005). Most importantly, the strict criterion used here to identify developing clouds ensures that clouds with falling hydrometeors (i.e., drizzle and rain) are excluded, because, for these, the assumptions that are made in section 2 regarding the drop size distribution are not valid.
c. Different aerosol environments
Three different methods for identifying the aerosol environment are explored: (i) a back-trajectory analysis that identifies the airmass origin as continental or maritime, (ii) the particle backscatter in the subcloud layer as measured by the Raman lidar, (iii) the integrated linear-depolarization ratio δ up to 4-km height as measured by the Raman lidar, which identifies dust. In general, dust is not thought to be a good CCN, but, by the time the dust aerosol reaches Barbados, it has aged considerably, and organic coatings or salt accumulation can increase its solubility (Savoie and Prospero 1980). So associating dusty days with higher CCN concentration is not unreasonable.
The first method defines air masses as continental if during a period of 5–10 days before arriving at the measurement site the air mass was estimated to have been over any of the continental areas north of 10°N. Air masses are defined as maritime if the air mass never crossed land during the 10 days prior to arriving at the measurement site. Here, 10-day back trajectories are estimated using HYSPLIT (e.g., Draxler and Hess 1997) forced by 6-hourly ERA-Interim data. The cloud radar data is then segregated according to the airmass origin at an altitude of 3 km, where Saharan dust typically resides (Prospero and Carlson 1972).
For the second method, the mean aerosol backscatter distribution in the subcloud layer (between 140 and 260 m) is calculated and low backscatter samples are defined within the 5th–30th-percentile range and high backscatter samples within the 70th–95th-percentile range. The first and last 5% in the probability distribution of aerosol backscatter are excluded to omit outliers or extreme values.
The third method uses the property of dust particles being nonspherical and therefore having higher values of δ. For each Raman lidar profile up to 4 km, the height-averaged δ is used to differentiate into a nondusty and a dusty profile. The chosen threshold of δ = 0.04 roughly separates two different probability distributions of δ that appear when sampled over 2 years between April 2010 and March 2012.
A radar profile is classified as nondusty when the coincident lidar signal has and as dusty when . Here, the closest Raman profile in time up to 60 s before and after the radar echo is considered. Each developing shallow cloud entity is associated with a number of radar profiles (described in section 3b). If more nondusty profiles exist over the duration time of a cloud than dusty profiles, then the developing shallow cloud is labeled “nondusty” (vice versa for dusty conditions). Consequently, a day is labeled nondusty when there are more developing shallow cloud entities during this day that are classified as nondusty than dusty.
A different classification, using the average of all lidar profiles to identify a day as dusty, has also been tested; however, no significant difference was seen. That the chosen classification works reasonably well can be seen in the aerosol optical depth (AOD) at 500 nm, product level 2.0, measured at Ragged Point using the Aerosol Robotic Network (AERONET) (Smirnov et al. 2000). For dusty days, the daily AOD values are nearly a factor of 3 larger, with a mean of 0.25 as compared to 0.09 for nondusty days, which is consistent with a higher aerosol concentration on dusty compared to nondusty days.
d. Data treatment
Section 2 postulates that reflectivity increases with height. Here, we investigate if this theory applies to the measured reflectivity values. Figure 5a displays the histogram of Z for all data (523 616 profiles). The most frequent reflectivity increases with height up to 3 km, but the spread is large and the signal is weak, because retrievals of rain and drizzle with dBZ ≥ −15 distort the signal. By focusing on radar retrievals within shallow cloud entities with υ ≥ 0.5 m s−1, rain is most likely excluded at every height level; however, updrafts may still include some raindrop-sized particles. Here, reflectivity increases as postulated in section 2, with a rather small spread (Fig. 5b) and a sample size of 42 260 profiles. The few detections with small reflectivities below 700 m can be explained by a few raindrops caught in an updraft, by cloud fragments (smaller than three pixels, not excluded in Fig. 5b), or by clutter (caused by side lobes of radar antenna) that was not excluded by the threshold of dBZ ≥ −35. In conclusion, the displayed behaves according to the theoretical (see different dashed lines in Fig. 1), confirming that the postulated hypothesis on (section 2) reasonably explains the development of radar echoes of trade wind cumuli.
The value of , more precisely , is derived by performing a nonlinear regression of the median reflectivity of a single developing cloud entity or from an average of of all developing cloud entities , as done in section 5. In this context, and are given per height level, . Values of the lower quartile of the distribution in are defined as clouds with low and values in the upper quartile are defined as clouds with high . A day is labeled “large- day” when there are more developing shallow cloud entities measured during this day having a high (larger ) than low (and similarly for “small- day”).
4. Precipitation characteristics
To better understand precipitation of shallow cumuli and their dependencies we first explore if large- days are different from small- days in terms of their precipitation behavior before investigating what factors control the variation in . The aim is to understand whether (equivalently ) is a good proxy for the tendency of macrophysically similar clouds to develop precipitation and if the subsequent statistics of these clouds are consistent with a more rapid development of precipitation on large- days.
In general, clouds can have a negative velocity at cloud top because of two reasons: the development of raindrops large enough to fall through the updraft and the evaporative collapse of an updraft. As clouds penetrate deeper into dry air, updrafts mix with evaporatively unstable air and collapse. Assuming that a small subset of large cloud droplets at cloud top can be considered as precipitation embryos, which start to fall through the cloud layer (Wood et al. 2009), the development of precipitation can also be associated with the collapse of the cloud-top echo. Because the liquid water content increases with height in shallow cumulus clouds (e.g., Gerber et al. 2008), precipitation tends to form first at cloud top (cf. Fig. 6 in Seifert et al. 2010). Hence, cloud entities with a negative Doppler velocity also have higher values in reflectivity (not shown).
The propensity of clouds to form precipitation can be measured by the frequency with which the cloud-top echo collapses, for a cloud with a given cloud top. This type of analysis can be performed by calculating the ratio of the number of clouds that have a downward-moving cloud top to the number of all clouds present during a day. As mentioned, however, not all clouds with collapsing tops can be associated with the formation of precipitation. Therefore, only clouds that have a downward motion at cloud base, in the middle of the cloud, and at cloud top are considered first. Figure 6 shows the fraction of days on which a certain portion of clouds have downward motion, only considering clouds with tops between 720 and 1140 m. Here, a cloud with downward motion has hydrometeors, if a mean Doppler velocity at cloud base, at cloud middle, and at cloud top of or less is found. Figure 6 shows that clouds on large- days have more frequent downward motion than on small- days, consistent with clouds having a higher tendency to form rain on large- days. As this result does not change when considering only clouds with downward-moving cloud tops (not shown), clouds with collapsing tops can be associated with having a higher tendency to form rain.
In addition to more readily forming rain, we expect that clouds on large- days, which rain, start to form rain drops large enough to sediment at a lower height. To test this, we show the distribution in daily mean Doppler velocity at cloud top (Fig. 7). Because cloud base is confined to 700 ± 200 m (Nuijens et al. 2014), trade wind cumuli having high cloud tops are assumed to be deeper. In general, the most frequently observed decreases with an increase in cloud-top height, starting from about 0.75 m s−1 at zt = 0.8 km to about −0.25 m s−1 at zt = 2.1 km. On large- days the tendency to sample a downward-moving echo (which we interpret as the effect of precipitation) at lower heights (zt ≈ 1.0 km and above) is enhanced relative to small- days (zt ≈ 1.5 km).
By excluding all cloud entities with negative velocities and large reflectivities (i.e., presence of rain), one would expect lower cloud tops for large- days, because we exclude clouds that rain, which are usually deep clouds with high cloud tops. Figure 8 shows the distribution of cloud tops for developing cumulus clouds. As expected, developing cumulus clouds on a large- day have lower cloud tops with a peak at 0.85 km compared to clouds on a small- day, which have a peak at 1.05 km. This is also consistent with the hypothesis that trade wind cumuli with a large have a higher propensity to form rain, because clouds do not have to grow that deep before developing precipitation, compared to clouds with a small .
In summary, although one could find fault with any one of the measures used to establish a connection between and the propensity toward rain development, combined, they paint a consistent picture. On large- days more clouds develop cloud-top signatures indicative of rain (Fig. 6), the emergence of a precipitation shaft happens lower in the cloud (Fig. 7), and nonprecipitating clouds do not become as deep (Fig. 8). Additionally, the mean cloud reflectivity is higher on large- days compared to small- days (not shown). Thus, appears to be a useful proxy for the propensity of clouds to form rain. To study this propensity with ground-based measurements (e.g., surface precipitation) is difficult because cloud droplets and evaporating rain drops cannot be detected on the ground.
Based on the above, the next section investigates how N influences . Assuming, initially, that β is likely to be constant given the homogeneity of the thermodynamic conditions. We use different indicators of the aerosol to investigate how different CCN concentrations and hence different cloud droplet number concentrations affect .
5. for different aerosol environments
How does change in an environment with many or few CCN? And what is the variability in , when the liquid water content is similar? According to the theory (section 2) we would expect a larger for clouds with low droplet number concentration N compared to clouds with high N, under the influence of similar meteorological conditions that can be measured by the subadiabatic factor β.
Although a back-trajectory analysis was successful in discriminating between aerosol-rich and aerosol-poor days during a 6-week period of intensive field measurements (Siebert et al. 2013) and backscatter is commonly used as an indicator of aerosol amount, surprisingly only the third method using the depolarization ratio δ for discriminating between dusty and nondusty days was associated with statistically significant differences in the radar retrievals. In detail, for maritime conditions, is found to be , and for continental conditions, it is . For both conditions of low and high backscatter, a value of was derived, not showing any difference. Hence, both the back-trajectory and backscatter analysis only yield very small differences, which are not significant as determined by a Kolmogorov–Smirnov test of the distribution of average reflectivities between the regimes.
There are many possible reasons for similar values in despite differences in airmass history and differences in aerosol backscatter. One reason could be that the airmass history correlates with thermodynamic properties of the air masses, depending on wind being southeasterly or northeasterly. These differences in the meteorology might dominate the aerosol signal. High values in backscatter may not solely be a signal of a high number of particles but also of larger-sized particles—for example, swollen particles—in a more humid environment. Then again, it may simply be that the aerosol plays less of a role in echo development than is commonly assumed. Certainly, our analysis does not support a strong aerosol influence on the onset of precipitation, even if it is difficult to rule out an influence entirely.
Using the lidar depolarization as a measure of the aerosol amount does, however, indicate a difference in on dusty versus nondusty days (Fig. 9). Here, only average reflectivities of nondusty and dusty conditions are considered for which the two-sided Kolmogorov–Smirnov test proves a significant difference in the distribution of between the regimes. The dotted colored lines in Fig. 9 are nonlinear fits for following Eq. (3) with k2 = 2.25 and zb = 0.5 km. A slightly larger can be seen during nondusty conditions with compared to dusty conditions with . These calculated numbers are in the range of the proposed , consistent with a change in the dust load impacting the behavior of radar reflectivities. How much β and N contribute to a change in is discussed in section 6.
Assuming a fixed cloud base of zb = 0.5 km may introduce uncertainties in . During winter, cloud bases are about 200 m higher than during summer (Nuijens et al. 2014). Table 2 presents the number of days on which we find certain regimes. In general, we sample more days during nondusty conditions than during dusty conditions, but the nondusty regime is sampled relatively more often during winter (December–May) than during summer (June–November), consistent with our understanding of dust transport from Africa (Prospero and Lamb 2003). Therefore, the mean cloud base during nondusty conditions could be higher than during dusty conditions, which would shift the Z profile toward the right (higher ). For example, assuming a cloud base of zb = 0.7 km yields . This could be interpreted as an uncertainty of for the derived values of . Thus, by considering zb = 0.5 km it is even further supported that nondusty conditions are different than dusty conditions. However, the difference in is still rather small ().
The postulated behavior of how differs between nondusty and dusty conditions holds true for the derived from the average reflectivities of all height levels calculated from all developing cumulus clouds. To test if this holds true for derived from individual developing cumulus clouds, a nonlinear fit of the median reflectivity is performed for each cloud entity separately. The distribution of the derived is shown in Fig. 10 for all and for dusty conditions. The majority of all cloud entities are sampled during nondusty conditions; hence the distribution of during all conditions resembles the distribution during nondusty conditions. The average of over all cloud entities differs from the derived in Fig. 9 during nondusty and dusty days. This is because the measured reflectivities of fewer deeper clouds contribute more strongly to the derived in the first case. Therefore, it is crucial to investigate how the distribution of from individual developing cloud entities behaves during nondusty and dusty conditions.
In Fig. 10, slightly more low values of are seen on dusty days than on nondusty days. However, many of the cloud entities on nondusty and dusty days do not behave differently in terms of their values. This and the large spread in for all samples imply that changes in the number of CCN, and hence N, cannot solely explain the variability in (or ) for shallow cumuli, even under quite-steady meteorological conditions. In the next section, the dependence of on subtle changes in the meteorological conditions (here, expressed by β) is investigated.
6. Meteorological factors influencing echo development
Our analysis suggests that indicators of the aerosol environment can, at best, explain relatively small systematic differences in . The weakness of the signal motivates us to revisit an underlying assumption of our analysis. At the outset, we hypothesized that the different time scales at which the thermodynamic and chemical environment of the marine boundary layer evolve, combined with the distance between the measurement site and the places where the aerosol properties are imprinted on the air mass, would reduce (and hopefully eliminate) the influence of covarying meteorological factors on echo development. Certainly there is a strong meteorological influence on echo development, which in our theoretical framework is captured by the influence of the large-scale environment on the subadiabatic factor (e.g., Blyth 1993; Burnet and Brenguier 2007; Holloway and Neelin 2009; Nuijens et al. 2009; Stevens and Seifert 2008). Whether this may confound a possible signature of the aerosol depends on the strength of the meteorological signal on the one hand and the extent to which it correlates with a possible aerosol signal on the other. This question is explored in further depth in the two subsections below, first through an analysis of the Barbados data, and second using large-eddy simulation.
a. Humidity–reflectivity relationships in the data
For this analysis we explore the relationship between echo development, as measured by and the relative humidity of the cloud environment. We are motivated to do so because both observations and modeling (e.g., Nuijens et al. 2009; Stevens and Seifert 2008) have shown that rain formation in shallow cumulus depends on the ambient relative humidity in the lower troposphere and because simple physical arguments would seem to imply that the amount of condensate within a cloud depends on the humidity of the environment with which it mixes. A high relative humidity might be expected to lead to less dilution of the cloud, making it more adiabatic (i.e., higher β). It may also cause cloud elements to live longer, thereby giving the initial stages of the coalescence process more time to develop. To assess the impact of relative humidity on (), the variability in daily median relative humidity on dusty and nondusty days is studied. In light of these results, we analyze the sensitivity of large-eddy simulations to changes in the relative humidity commensurate to what is observed.
Somewhat surprisingly, dusty days are, on average, more humid than nondusty days. This is illustrated with the help of Fig. 11, which compares the average and interquartile range of daily median relative humidity through the lower troposphere. Daily data are used because the Raman humidity retrievals are only available during the night and because the autocorrelation time scale of the radar reflectivity is about 6 h, so that sampling on shorter time scales is not warranted. The higher relative humidity (Fig. 11a) for dusty days encapsulates a seasonal signal, as dust events are more frequent during summer when low-level winds are more easterly, or even southeasterly. That means that during dusty days, an aerosol effect on through an increase in N may be systematically offset by an increase in arising from an increase in This would explain why the distribution of (Fig. 10) is so similar on dusty versus nondusty days.
To look at this another way, we also compare the humidity between large- versus small- days. As might be expected, large- days have a more humid cloud layer (Fig. 11b). The factor describing the average of the daily median relative humidity is similar up to 0.8 km and then decreases less with height for large- days. This makes it difficult to attribute a large value of to the effect of as on days when is larger than average η is also larger, which would appear to also favor a larger The higher relative humidity on large- days is also consistent with the stronger signal in precipitation. This enhanced sensitivity of developing clouds to form rain (not shown) on large- as compared to small- days is stronger than the precipitation signal on nondusty compared to dusty days (Fig. 7).
In terms of the full distribution, dusty samples, which on average have a high η (and presumably a larger β), in addition to a high dust load (and presumably a high N), are more likely to have a low than do nondusty days (Fig. 10). Arguments based on the evaluation of the mean humidity on dusty versus nondusty days cannot explain this difference. So, instead, we construct the full distribution of η for both dusty and nondusty days (Fig. 12). On nondusty days, the distribution in relative humidity is rather unimodal, whereas on dusty days the distribution is bimodal with a low peak at 70%–75% and a high peak at 85%–90%. The latter peak is associated with dust events during the more humid summer season.
This analysis raises the question as to whether differs if one controls for the humidity during the dusty days. Differences between on dusty versus nondusty days exist when = 70%–75% but vanish in the case of higher humidities, = 85%–90% (not shown). Hence, the low during dusty conditions may predominantly arise from a low relative humidity, < 75%, rather than a high . A two-sided Kolmogorov–Smirnov test, however, fails to disprove the null hypothesis for a significance level of 10% that nondusty and dusty samples are drawn from the same distribution. To put it differently, if we condition our analysis on humidity, then we can no longer detect an aerosol influence, even for the dust indicator of aerosol, on .
b. Large-eddy simulation
To explore the role small changes in the meteorological conditions might play in the development of precipitation size drops, we analyze large-eddy simulations. The simulations we analyze, described more fully by Seifert et al. (2015), are for trade wind conditions similar to what one observes over Barbados. The simulations are computationally intensive, spanning large domains (50 km) with a relatively fine grid (25 m uniform), thus enabling the resolution of individual clouds, but enabling reasonable statistics of the cloud layer. The simulations differ in terms of their adiabatic droplet population density N and the environmental humidity. The differences in the humidity between the moist and default simulations are illustrated with the help of Figs. 13a and 13b and consist only of a moistening of the cloud layer and free troposphere at the initial time. The humidity differences specified in the initial data are similar to the observed differences between large- and small- days (e.g., Fig. 11). All simulations are 60 h of simulated time, a time period over which they come into equilibrium with precipitation rates of about 1 mm day−1 irrespective of the assumed droplet population density. The present analysis focuses on the initial development of the simulations before the onset of precipitation. During this time period, the cumulus layer deepens, but at a rate that is relatively independent of microphysical changes in the cloud, as surface fluxes are about the same in the simulations during this period. The humidity at the time of the analysis (8–10 h) is also shown in Fig. 13b. As the cumulus layer develops, humidity differences tend to be reduced within the cloud layer and enhanced near cloud top.
The simulations demonstrate that relatively small changes in humidity can have as much influence on the development of the cloud layer as do large differences in the droplet population densities N. This can be quantified by comparing the time it takes for precipitation to develop as a function of the specified humidity or cloud microphysical properties [for times, please refer to in Table 1 in Seifert et al. (2015)]. In the dry (default) simulation, precipitation begins developing after 38.5 h for . Reducing N by a factor of 2 allows precipitation to form in shallower clouds, and precipitation develops after only 13.5 h. For the moister case, with , precipitation also develops after 13.5 h. This suggests that slight (10% or less) changes in the ambient humidity have as much influence on the rain development as a factor 2 change in the droplet concentration. A comparison of simulations with droplet population densities of 35 and 70 cm−3 show that, for the dry (default) condition, rain develops after 9 and 20 h, respectively. For a moist simulation with , precipitation again develops as rapidly (9.9 h) as for the case with a twofold reduction in .
The simulations show a more pronounced peak in the cloud water layer (also associated with a larger cloud fraction) near cloud top (between 1.6 and 1.8 km above the surface) at times before the onset of precipitation, as shown in Fig. 13c. Cloud water is about 50% larger in the moist simulations and the deepest clouds penetrate somewhat more deeply than they do for the dry (default) case. This is consistent with the more rapid development of precipitation in the simulations with the slightly moister cloud layer and free troposphere. A 50% increase in liquid water within an individual cloud would imply that increases more than large enough to offset a doubling of the droplet population density, consistent with the idea that small changes in the cloud environment mask any possible influence of the aerosol on cloud microphysical development. The interpretation of the large-eddy simulation in light of the observations is, however, not without ambiguity. Because cloud fraction increases with cloud water the average cloud is not more condensate laden. Although it seems reasonable to assume that the most condensate-laden clouds would be more condensate laden as relative humidity increases, to follow this line of thought more quantitatively, it would be helpful to have a radar simulator in the LES domain.
7. Summary and conclusions
In this study, simultaneous advanced ground-based lidar and radar remote sensing measurements of aerosol, clouds, and meteorological factors are exploited to investigate what controls the formation of rain in trade wind cumuli.
Before shallow clouds form precipitation (developing clouds), the cloud droplet number distribution n is assumed to be gamma distributed. This allows us to calculate the increase of radar reflectivity with height as a function of a fixed subadiabatic fraction of liquid water β and a height-constant droplet number concentration N. For each developing cloud, a best estimate of (equivalently ) is derived by regressing the profile of reflectivity following theory. Thermodynamical conditions, which allow the clouds to have a higher adiabatic liquid water content, would increase β. Simultaneously, a decrease in aerosol concentration would decrease N. Both changes lead to an increase in .
The assumption of the shape parameter of the gamma-distributed cloud droplet number concentration might appear to be inappropriate as the development of precipitation is accompanied by the development of a larger mode in the droplet distribution. To some degree, this can be expressed through a change of the distribution shape parameter . Various observational (e.g., Siebert et al. 2013) and modeling studies (e.g., Beheng 1994) show large and small variations of p. However, calculations show that an increase of the shape parameter from 8.7 to a rather large value of as much as 34.2 is necessary to explain the difference in reflectivity between a nondusty and a dusty day at 1.4-km height. Thus, it seems unlikely that our findings can be explained by systematic variations in the shape of the droplet distribution. Although this merits further study, the null hypothesis that humidity fluctuations play a much stronger role in affecting cloud properties and the development of precipitation appears to be a more plausible explanation for the lack of a discernible aerosol effect on the development of precipitation.
Applying all mentioned assumptions, is derived only for clouds that have not yet developed precipitating shafts with negative velocities. Days on which is larger than normal are marked by clouds that develop precipitation more readily at lower heights, as measured by the fraction of nonprecipitating clouds that reach a given height. This suggests that is a good proxy for conditions that favor a more rapid onset of precipitation of shallow cumulus.
Factors influencing are explored in terms of the relative role of the environmental humidity and aerosol. Aerosol-rich and aerosol-poor days are identified using three measures. Only the depolarization measure, which is a good indicator of dust amount, shows small but statistically significant differences in and hence precipitation development. On average, nondusty days have larger () than dusty days () plus or minus 10% uncertainty, but the difference is limited. Furthermore, the spread in for individual developing shallow cumuli is large. Clouds with high values of are more plentiful on dusty days, which would mean that those clouds have a lower cloud droplet number concentration, assuming β is constant. However, this would contradict the assumption that on a dusty day the number of CCN, and hence the number of cloud droplets N is enhanced. This leads to the question of the relative role of environmental factors such as the relative humidity in controlling β as compared to changes in the aerosol which may influence N on the echo development, as measured by . This question gains weight through the observation that only one of the three measures of the aerosol here investigated (i.e., the dust signal) appears to explain variability in the echo development of shallow clouds.
Over Barbados, dust is most prevalent during summer, which aliases small thermodynamic differences from seasonality onto the signal from dust. The low-level flow during the summer tends to be more easterly or even southeasterly and somewhat more humid. Such differences in the relative humidity may influence the adiabaticity or lifetime of cloud elements and its initial echo development and, hence, . To further investigate this effect, Raman lidar measurements are used to provide relative humidity profiles through the cloud layer (but not through clouds) during nighttime. Dusty days, which are more frequent in summer, are on average moister (through the depth of the marine layer) than nondusty days. When conditioning on a given range of cloud-layer relative humidity, in fact no statistically significant differences in are found between dusty and nondusty days.
To further understand the role of humidity variations in explaining the variability in , large-eddy simulations are analyzed. These simulations show that small differences in the humidity (from a few percent to 10%) within the cloud layer and above the cloud top have an effect on precipitation development (and presumably the reflectivity structure) in shallow cumulus that is commensurate to a twofold change in the aerosol. The simulations do not enable us to discern exactly how and where differences in the ambient humidity influence echo development. But they do point to the fact that even in a relatively homogeneous environment, subtle variations in the relative humidity within the cloud layer have a pronounced influence on the adiabaticity of clouds (or ), an effect that increases with the mean humidity.
The results of this study lead us to conclude that aerosol effects on the formation of precipitation are likely very difficult to separate from covarying meteorological effects, even though aerosol changes might be externally imposed. It also serves to highlight that factors such as a small change in relative humidity, which may also accompany a changing climate, can have a profound influence on the development of shallow cumulus. These factors remind us that the largest microphysical responses to a changing climate may have nothing to do with changes in the atmospheric aerosol.
The authors thank Ilya Serikov, Friedhelm Jansen, Björn Brügmann, Holger Linné, and Monika Pfeiffer for their contributions to the maintenance of the BCO and providing its dataset. We thank Christian Jacob for encouraging the cloud entity analysis. Furthermore, we thank Daniel Büttner for providing the information about the integrated linear-depolarization ratio from the Raman lidar. Special thanks to Matthias Bauer-Pfundstein for discussions on cloud radar retrievals and Jan Handwerker for letting the cloud radar from the Karlsruhe Institute of Technology, Karlsruhe, Germany, operate at the BCO until January 2011. The three anonymous reviewers are thanked for the valuable comments that improved the final version of the manuscript. In particular, we thank one reviewer for his/her insistence that an earlier dynamical framework we had adopted was flawed, which encouraged us to analyze the large-eddy simulations instead, something that we believe strengthened the paper. We acknowledge the NOAA/Air Resources Laboratory (ARL) for the provision of the HYSPLIT transport and dispersion model using the READY website (http://www.arl.noaa.gov/ready.php). ECMWF ERA-Interim data used in this study have been provided by ECMWF and have been obtained from the ECMWF Data Server. Norbert Noreiks is thanked for graphical support.
Denotes Chemistry/Aerosol content
The KATRIN cloud radar was named in memory of Katrin Lehmann, whose untimely and premature death prevented her from joining the project.