Abstract

Contiguous time–height cloud objects at the Department of Energy Atmospheric Radiation Measurement Southern Great Plains (SGP) site are matched with surface condensation nuclei (CN) concentrations and retrieved thermodynamic and kinematic vertical profiles for warm-cloud-base, cold-cloud-top systems in convectively unstable environments. Statistical analyses show that previously published conclusions that increasing CN concentrations cause a decrease in minimum cloud-top temperature (CTT) at the SGP site through the aerosol convective invigoration effect are unfounded. The CN–CTT relationship is statistically insignificant, while correlations between convective available potential energy (CAPE), level of neutral buoyancy (LNB), and CN concentration account for most of the change in the CN–CTT positive correlation. Removal of clouds with minimum CTTs > −36°C from the analysis eliminates the CN–CTT correlation. Composited dirty conditions at the SGP have ~1°C-warmer low levels and ~1°C-cooler upper levels than clean conditions. This correlation between aerosol concentrations and thermodynamic profiles may be caused by an increase in regional rainfall preceding deep convective conditions as CN concentration decreases. Increased rainfall can be expected to increase wet deposition of aerosols, cool low-level temperatures, and warm upper-level temperatures. The masking of a potential aerosol effect by such small thermodynamic changes implies that the strategy of analyzing subsets of aerosol data by binned meteorological factor values is not a valid method for discerning an aerosol effect in some situations. These findings highlight the need for more careful, detailed, and strategic observations to confidently isolate and quantify an aerosol deep convective invigoration effect.

1. Introduction

Deep convection is driven by buoyancy with cloud tops that are determined by the level of neutral buoyancy (LNB) associated with the convecting air. The LNB is also commonly referred to as the equilibrium level. It corresponds to a nonmixing parcel of air lifted from low levels that follows a moist adiabatic temperature lapse rate after reaching saturation. The altitude at which the moist adiabat’s temperature equals the environmental temperature defines the LNB altitude, while the associated temperature at this altitude is the LNB temperature. Air within real-world deep convection does not typically follow a moist adiabat because of mixing with cooler or drier environmental air. This has the effect of reducing buoyancy, but additional latent heating from fusion can partially offset this effect (e.g., Zipser 2003). Additionally, deep convection typically overshoots the LNB because of inertia. The magnitude of the vertical overshoot is determined by both the stability above the LNB and the vertical velocity at the LNB. This vertical velocity is related to the convective available potential energy (CAPE), which is the theoretical potential energy (assuming air parcel ascent along a moist adiabat) that is converted to kinetic energy to fuel the convection. Again, in reality, the actual energy available to an air parcel depends on the degree that CAPE is modified by entraining environmental air and fusional heating.

The cloud-top temperature (CTT), extent, and thickness of deep convective anvil clouds are climatically important because of their latent heating and radiative effects (Houze 1982; Ackerman et al. 1988; Randall et al. 1989). Additionally, overshooting convection is a key mechanism for troposphere–stratosphere exchange (e.g., Fischer et al. 2003; Corti et al. 2008). Therefore, potential anthropogenic effects on deep convection are important to consider in predicting future climate. Cloud condensation nuclei (CCN) concentration has been proposed to impact deep convective strength through its control on the size of liquid droplets, which can impact buoyancy through alteration of the amount of liquid lofted to altitudes where it freezes and impacts latent heat release. A greater CCN concentration causes more numerous, smaller droplets (e.g., Gunn and Phillips 1957; Borys et al. 1998; Rosenfeld 1999) that are more easily lofted into the mixed phase region than larger droplets, thus increasing the latent heat release and buoyancy aloft through increased fusion. This has the potential to increase cloud-top height and decrease CTT through warmer, stronger updrafts that reach higher altitudes. This process is termed “aerosol convective invigoration” and has many theoretical (e.g., Rosenfeld et al. 2008; Stevens and Feingold 2009), modeling (e.g., Khain et al. 2005; van den Heever et al. 2006; Tao et al. 2007; Lebo and Seinfeld 2011; Storer and van den Heever 2013), and observational (e.g., Andreae et al. 2004; Koren et al. 2005, 2010, 2012; Lin et al. 2006; Bell et al. 2008; Li et al. 2011; Rosenfeld and Bell 2011; Yuan et al. 2011; Storer et al. 2014; Yan et al. 2014; Igel and van den Heever 2015; Chen et al. 2016; Peng et al. 2016) studies that support its viability. Additional studies indicate that the aerosol convective invigoration effect varies as a function of environmental conditions (e.g., Fan et al. 2007, 2009; van den Heever and Cotton 2007; Khain et al. 2008; Khain 2009; Lebo and Morrison 2014), and fairly comprehensive literature reviews are provided by Tao et al. (2012) and Altaratz et al. (2014).

However, there are modeling (e.g., Morrison and Grabowski 2011; Morrison 2012; Boucher and Quaas 2013; Grabowski 2015; Grabowski and Morrison 2016; White et al. 2017) and observational (e.g., Zhang et al. 2005; Mauger and Norris 2007; Chew et al. 2011; Chand et al. 2012; Altaratz et al. 2013; Omar et al. 2013; Yuter et al. 2013; Gryspeerdt et al. 2014a,b; Wall et al. 2014) studies that point out understated uncertainties or flaws in many of the studies that claim to conclusively show invigoration of convection by increased CCN concentrations. For example, CCN concentrations are often replaced by imperfect proxies such as condensation nuclei (CN) or aerosol optical depth (AOD). Additionally, negative buoyancy from increased condensate loading is often neglected along with uncertainties or biases in AOD, CN, or CCN observations. The effects of aerosols on a single, isolated convective cell may also be different than cumulative effects over a mesoscale or synoptic region for a period of days or longer because of meteorological buffering responses that minimize the overall impact of aerosol perturbations on cloud populations (e.g., Stevens and Feingold 2009; van den Heever et al. 2011).

This paper focuses on the ability to observe dynamical invigoration of convection by increases in aerosol concentration. This differs from aerosol effects on surface rainfall, cloud coverage, riming, radar reflectivity, or lightning. These effects, while also climatically important, do not necessarily imply changes in convective intensity that lead to increased cloud-top heights. Many observationally based studies that are critical of claims of observed aerosol invigoration of deep convection have focused on problems in satellite retrievals of AOD, which depends on cloud fraction and relative humidity in addition to aerosol loading. This study differs from previous studies in that thermodynamic variables most relevant to deep convective CTTs are analyzed, dependent cloud statistics are removed, and aerosol and meteorological properties are evaluated in a statistically consistent manner, which have not been collectively done in some previous studies in a satisfactory manner. It is only through proper accounting of key meteorological variables that an aerosol indirect effect on convective depth can be isolated and accurately quantified. It will be shown that for the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site in north-central Oklahoma, 14 years of observations are not sufficient for concluding that increased aerosol concentrations cause an increase in cloud-top height and decrease in CTT because of strong correlations between CN concentration and meteorological factors (LNB and CAPE), which contradicts the results of Li et al. (2011) and Yan et al. (2014). Additionally, it will be shown that only slight changes in thermodynamic conditions are capable of creating the illusion of an aerosol indirect effect on deep convection. Therefore, greater care than has been exhibited in many previous studies needs to be taken in attempting to statistically isolate a potential aerosol effect from meteorological effects.

The rest of this study is organized into five sections. Section 2 describes datasets and methodology. Section 3 discusses aerosol–meteorology correlations. Aerosol–CTT correlations after accounting for aerosol–meteorology correlations are discussed in section 4. Section 5 examines causes for aerosol–meteorology correlations, and section 6 presents the conclusions.

2. Datasets and methodology

All data used are from the ARM SGP site in north-central Oklahoma between 1997 and 2010 between the warm-season months of April and October. The Active Remotely-Sensed Cloud Location (ARSCL) value-added product [ARM (Climate Research Facility) ARM CRF 1996a; Clothiaux et al. 2000, 2001] is used to define cloud boundaries. This product includes a cloud boundary vertical profile at discrete times generated from a combination of millimeter cloud radar (MMCR), micropulse lidar, and ceilometer data. It includes times with precipitation, although heavy precipitation can attenuate the MMCR signal before it reaches cloud top. Contiguous time–height cloud objects are constructed and subsampled to only include objects with a maximum cloud-base temperature (CBT) > 15°C and a minimum CTT < −4°C to ensure that sufficient warm cloud depth and cold CTTs exist such that an aerosol indirect effect on convective strength can potentially operate. This follows Li et al. (2011) with the caveat that a minimum CTT of −4°C does not ensure the presence of ice, a topic that is revisited in the results. The maximum CBT and minimum CTT are found by matching the minimum cloud-base and maximum cloud-top heights to temperatures in the MERGESONDE value-added product (ARM CRF 1996b; Troyan 2012). MERGESONDE provides nearly continuous estimates of temperature, humidity, and wind vertical profiles by combining four-times-daily radiosonde observations with microwave radiometer data, surface meteorological data, and European Centre for Medium-Range Weather Forecasts (ECMWF) model output.

An example ARSCL cloud object is shown in Fig. 1 with other relevant measurements. The MERGESONDE profile used to match temperature, humidity, and wind profiles to each cloud object is shown with a purple arrow at the start time of the cloud object. Additionally, lifted condensation level (LCL), level of free convection (LFC), LNB, CAPE, and convective inhibition (CIN) for lifted parcels that have the most unstable CAPE value in the MERGESONDE profile are computed for each of these profiles and matched to each cloud object. The maximum cloud-top height corresponds with the minimum CTT shown in green, while the minimum cloud-base height corresponds with the maximum CBT located just off of the surface in the Fig. 1 example. Last, surface CN concentrations measured by a condensation particle counter (ARM CRF 1995; Kuang 2016) are matched to each cloud object. Because precipitation lowers CN concentrations and CN can be noisy over short time intervals, the CN concentration matched to each cloud object is computed as the median value between the start of the cloud object and the first time when the cloud base warms to at least 15°C. CN concentrations are used to remain consistent with the Li et al. (2011) methodology. Additionally, CCN concentration datasets are not available for all 14 years and require adjustments to estimate CCN for a constant supersaturation. Correlation between CN and CCN for specific deep convective cases is left for future work.

Fig. 1.

An example time–height ARSCL cloud object shaded in blue with cloud base warmer than 15°C and cloud top colder than −4°C. The minimum CTT is shown in green. CN and CCN concentrations are shown as solid and dashed black lines, respectively, with CCN concentrations shown for a ~0.4% supersaturation. CN is matched to the cloud object using a median value over the time period shown in red between the start of the cloud and the time when the cloud base first warms to 15°C. The MERGESONDE sounding matched to the object is taken at the time shown in purple at the start of the cloud object.

Fig. 1.

An example time–height ARSCL cloud object shaded in blue with cloud base warmer than 15°C and cloud top colder than −4°C. The minimum CTT is shown in green. CN and CCN concentrations are shown as solid and dashed black lines, respectively, with CCN concentrations shown for a ~0.4% supersaturation. CN is matched to the cloud object using a median value over the time period shown in red between the start of the cloud and the time when the cloud base first warms to 15°C. The MERGESONDE sounding matched to the object is taken at the time shown in purple at the start of the cloud object.

This methodology is similar to that in Li et al. (2011) but differs in several key aspects. First, a contiguous time–height cloud object is counted as a single sample rather than every ARSCL profile in the object to avoid sampling dependency and erroneous robustness of results. Second, meteorological variables are only accumulated for each cloud object at the start time of the object rather than at all times when CN measurements exist. This eliminates irrelevant times without convective clouds detected. Third, meteorological variables that are most relevant to the convective CTT, namely, LNB and CAPE, are analyzed. Other meteorological variables such as lapse rates, relative humidity, vertical wind shear, and boundary layer properties affect CTT through alterations to LNB or CAPE or through dilution of convecting air. This methodology still has significant limitations because of the point and profile nature of the measurements that may not be representative for any given case. However, it is used here to remain consistent with Li et al. (2011) so that results can be effectively compared between the studies.

Conclusions drawn from correlations between MERGESONDE, CN, and minimum CTT data are evaluated using radiosonde measurements. CAPE and LNB are computed from 6-hourly radiosonde measurements (ARM CRF 2013) between 1997 and 2010 during the months of April–October. They are then matched with MERGESONDE temperature, humidity, and wind profiles at the same times and correlated with CN data averaged over the hour centered on the radiosonde time for all soundings with CAPE > 0, LCL > 15°C, and LNB < −4°C. ERA-Interim data (Dee et al. 2011) from 1997 to 2010 is used to composite synoptic meteorological conditions in relatively clean and dirty conditions with identical CAPE, LCL, and LNB thresholds at the same times as the radiosonde observations to provide context for correlations between meteorological variables and CN concentrations. Last, Arkansas–Red Basin River Forecast Center (ABRFC) hourly estimated rainfall at 4-km grid spacing (ARM CRF 1994) is used to accumulate 6-h rainfall prior to convectively unstable radiosonde times with warm-LCL and cold-LNB conditions to examine the possible impact of previous rainfall on CN concentrations and meteorological conditions. This product combines radar estimates of rainfall with hourly rain gauge data over the Arkansas–Red River basin.

3. Aerosol–meteorology correlations

Following Li et al. (2011), variables are separated into six CN concentration categories separated by 1000 cm−3 each with category 1 having less than 1000 cm−3 and category 6 having between 5000 and 6000 cm−3. A minimum CN concentration of 500 cm−3 is implemented to remove situations that are likely heavily affected by recent precipitation, although this rarely occurs and has minimal impact on results. Figure 2 shows distributions of minimum CTT as a function of CN category for ARSCL cloud objects with CBTs > 15°C and CTTs < −4°C. For all CN conditions, a bimodal distribution exists. For the four best-sampled CN categories between 1000 and 5000 cm−3, there are slight changes in the peak and width of these two modes. The warmer CTT mode centered on 5°–10°C likely contains a significant number of clouds without ice or clouds with minimum CTTs that are not well characterized by ARSCL. Analyses will focus on the full distribution of minimum CTTs so that comparisons can be made with Li et al. (2011), but also the cold CTT mode with minimum CTTs < −36°C, which contains clouds almost certainly containing ice.

Fig. 2.

ARSCL minimum CTT probability density functions for different surface CN concentration ranges. Colors are defined in the legend.

Fig. 2.

ARSCL minimum CTT probability density functions for different surface CN concentration ranges. Colors are defined in the legend.

Figure 3a shows minimum CTT as a function of CN category. Mean CTT minimum decreases from −34° to −40°C as CN increases from less than 1000 cm−3 to between 4000 and 5000 cm−3 for ARSCL cloud objects with CBTs > 15°C and CTTs < −4°C (diamonds). An exception to this trend is CN > 5000 cm−3, although sample sizes are less than 140 in categories 1 and 6. Sample sizes for categories 2–5 range from 229 to 309, which leads to standard errors of the mean CTT minimum that overlap with one another, indicating a potentially nonrobust trend. Confining minimum CTTs to less than −36°C mostly eliminates the cooling CTTs as a function of CN (squares). Introducing additional constraints of MERGESONDE CAPE > 0 and LCL > 15°C removes uncertainty in the ARSCL cloud-base height and ensures that a convectively unstable, warm-cloud-base environment exists. However, this reduces sample sizes by 30%–50% depending on CN category, increasing the overlap of standard error bars (Fig. 3b) and limiting the decreasing CTT trend with increasing CN concentration. Mean CTT minimum decreases by less than 2°C as CN concentration increases from 1000–2000 to 4000–5000 cm−3 (diamonds), and standard error bars overlap for categories 1–5 (Fig. 3b). A Mann–Whitney U test confirms that the minimum CTT differences between CN categories 2 and 5 is not statistically significant at the 0.05 level. Limiting the CTT to temperatures colder than −36°C produces even less of a correlation (squares). Despite the lack of statistical significance, the trend of cooling cloud tops with increasing CN concentrations is similar to that shown in Li et al. (2011), and the potential causes for it are explored further.

Fig. 3.

(a) Minimum CTT as a function of CN category for warm-cloud-base, cold-cloud-top systems; (b) as in (a), but with additional constraints of CAPE > 0, LCL > 15°C, and LNB < LCL; (c) CAPE as a function of CN category; and (d) LNB as a function of CN category. Both (c) and (d) use the same samples used in (b). Mean values for all minimum CTTs < −4°C are shown with diamonds, mean values for minimum CTTs < −36°C are shown with squares, and standard errors of the mean are shown with vertical lines.

Fig. 3.

(a) Minimum CTT as a function of CN category for warm-cloud-base, cold-cloud-top systems; (b) as in (a), but with additional constraints of CAPE > 0, LCL > 15°C, and LNB < LCL; (c) CAPE as a function of CN category; and (d) LNB as a function of CN category. Both (c) and (d) use the same samples used in (b). Mean values for all minimum CTTs < −4°C are shown with diamonds, mean values for minimum CTTs < −36°C are shown with squares, and standard errors of the mean are shown with vertical lines.

Li et al. (2011) concluded that increasing CN concentrations cause cooler cloud-top temperatures through the aforementioned aerosol invigoration effect because meteorology does not correlate with minimum CTT. However, Figs. 3c and 3d show that this may not be the case and that further analysis is warranted. For the MERGESONDE profiles that were matched to each ARSCL cloud object, the mean of the most unstable CAPE (i.e., MUCAPE) increases from just over 1000 to greater than 1500 J kg−1 between CN categories 1 and 4. The mean LNB temperature associated with the lifted parcel corresponding to the MUCAPE decreases from approximately −45° to −54°C (diamonds) with standard errors of the mean CTT minimum that do not overlap. Mann–Whitney U tests confirm that the CAPE and LNB distributions for CN categories 2 and 5 are statistically significantly different at the 0.05 level. Limiting the CAPE and LNB statistics to CTTs colder than −36°C produces similar CAPE–CN and LNB–CN correlations (squares). Therefore, increasing CN concentrations are correlated with increasing CAPE and decreasing LNB temperature. This does not mean that CN concentration does not impact CTT, but it does imply that much of the correlation between CN concentration and CTT could result from correlations between CN concentration and LNB or CAPE.

Keeping the constraints of CBT > 15°C, CTT < −4°C, LCL > 15°C, and LNB < LCL, Fig. 4 shows mean vertical profiles of the size of ARSCL cloud objects along with MERGESONDE temperature anomaly and relative humidity as functions of CN concentration categories. With the exception of CN category 1, which has a very limited sample size, mean anvil size steadily increases and mean anvil CTT steadily decreases as CN concentration increases from 1000–2000 to 4000–5000 cm−3 (categories 2–5). This is consistent with the decrease of minimum CTTs as a function of CN concentration in Figs. 3a and 3b, although it is worth noting that the vertical profile measurements may not be representative of system areal coverage for any given case. Figure 4b shows that mean temperature lapse rates increasingly steepen and destabilize as CN concentrations increase, with CN category-1 upper-tropospheric mean temperatures approximately 4°C warmer than CN category-6 temperatures. Relatively low CN concentrations are also correlated with slightly cooler-than-average lower-tropospheric temperatures while relatively high CN concentrations are correlated with slightly warmer-than-average low-level temperatures. Mean relative humidity in Fig. 4c decreases at many altitudes as CN concentration increases, most notably in the low to midtroposphere.

Fig. 4.

Mean (a) ARSCL cloud size (number of ARSCL profile times in the object), (b) MERGESONDE temperature anomaly, and (c) MERGESONDE relative humidity as functions of CN category for warm-cloud-base (CBT > 15°C), cold-cloud-top (CTT < −4°C) systems in conditions of CAPE > 0 and LCL > 15°C. Colors are defined in the legend in (c).

Fig. 4.

Mean (a) ARSCL cloud size (number of ARSCL profile times in the object), (b) MERGESONDE temperature anomaly, and (c) MERGESONDE relative humidity as functions of CN category for warm-cloud-base (CBT > 15°C), cold-cloud-top (CTT < −4°C) systems in conditions of CAPE > 0 and LCL > 15°C. Colors are defined in the legend in (c).

These results are supported by Fig. 5, which shows correlations between CN concentrations and MERGESONDE profiles at times of radiosonde launches (0000, 0600, 1200, and 1800 UTC) during April–October 1997–2010 for conditions of LCL > 15°C and LNB < −4°C. Sample sizes are larger in this dataset (3198 vs 770) since it does not require an ARSCL cloud object to be present. Profiles in Figs. 5a and 5b confirm that mean temperature lapse rate steepens and mean relative humidity decreases with increasing CN concentration. Additionally, mean zonal and meridional wind profiles in Figs. 5c and 5d change as a function of CN concentration. Mean low-level zonal and meridional winds increase as CN concentration increases. Mean upper-level meridional winds also steadily shift from southerly to northerly as CN concentrations increase. Figure 6 shows that mean radiosonde LNB temperature decreases as a function of CN concentration from approximately −45° to −48°C, while mean CAPE increases from just below 950 to 1300 J kg−1. The distributions of LNB and CAPE for CN categories 2 and 5 are statistically significantly different at the 0.05 level using a Mann–Whitney U test. Median CAPE and LNB values have correlations with CN concentration (Fig. 6) that are similar to mean CAPE and LNB values but offset to different values because of nonnormal CAPE and LNB distributions (Fig. 7). CAPE and LNB distributions for ARSCL objects (Figs. 7a,b) and sounding times (Figs. 7c,d) both indicate a shift to slightly higher CAPE values and slightly colder LNB values as CN concentration increases. Both datasets confirm that CN concentration is correlated with LNB and CAPE, which are perhaps the two most relevant environmental thermodynamic variables in determining deep convective cloud-top temperatures.

Fig. 5.

Mean MERGESONDE (a) temperature anomaly, (b) relative humidity, (c) zonal wind, and (d) meridional wind at all radiosonde times (0000, 0600, 1200, and 1800 UTC) as functions of CN category for conditions of CAPE > 0, LCL > 15°C, and LNB < −4°C. Colors are defined in the legend in (d).

Fig. 5.

Mean MERGESONDE (a) temperature anomaly, (b) relative humidity, (c) zonal wind, and (d) meridional wind at all radiosonde times (0000, 0600, 1200, and 1800 UTC) as functions of CN category for conditions of CAPE > 0, LCL > 15°C, and LNB < −4°C. Colors are defined in the legend in (d).

Fig. 6.

The 6-hourly radiosonde (a) CAPE and (b) LNB temperature as functions of CN category for conditions of CAPE > 0, LCL > 15°C, and LNB < −4°C. Mean values are shown with diamonds, standard errors with vertical lines, and median values with crosses.

Fig. 6.

The 6-hourly radiosonde (a) CAPE and (b) LNB temperature as functions of CN category for conditions of CAPE > 0, LCL > 15°C, and LNB < −4°C. Mean values are shown with diamonds, standard errors with vertical lines, and median values with crosses.

Fig. 7.

Probability density functions of (a),(c) CAPE and (b),(d) LNB temperature as functions of CN category for (a),(b) ARSCL cloud object times and (c),(d) sounding times. Only times with convective instability, LCL > 15°C, and LNB < −4°C are included.

Fig. 7.

Probability density functions of (a),(c) CAPE and (b),(d) LNB temperature as functions of CN category for (a),(b) ARSCL cloud object times and (c),(d) sounding times. Only times with convective instability, LCL > 15°C, and LNB < −4°C are included.

4. Accounting for CN–meteorology correlations

The correlations between CN concentrations and thermodynamic variables (CAPE and LNB) need to be taken into account in order to isolate the potential impact of aerosols on deep convective cloud tops. This is done in Fig. 8 by computing ARSCL cloud object sample size, mean CTT minimum, and standard error of mean CTT minimum within CN–LNB and CN–CAPE bins. As LNB temperature decreases and CAPE increases within individual CN categories, mean CTT minimum generally decreases. However, mean CTT minimum does not generally decrease with increasing CN concentration within LNB or CAPE bins. In fact, mean CTT minimum warms with increasing CN concentration in six of the eight LNB and CAPE bins. Sample size within each bin ranges from 12 to 42, producing standard errors that are of the same magnitude as the overall changes in mean CTT minima across the CN categories. These small sample sizes are a result of counting each cloud system only once to avoid dependent samples. Uncertainty is also introduced by the limited representativeness of point and vertical profile measurements for each individual system. Future measurements covering a larger domain would aid in reducing this uncertainty, while additional sites would increase independent sample sizes. In particular, locations with more frequent isolated deep convection, less meteorological variability, and greater susceptibility to changes in aerosol concentrations than the SGP site would increase the chances for isolating an aerosol effect signal. However, the relative occurrence of situations in which aerosols have a measureable impact on deep convection should also be considered in determining the overall importance of a possible aerosol indirect effect.

Fig. 8.

The mean of the minimum CTT (shaded) for warm-cloud-base, cold-cloud-top systems as a function of (left) LNB and CN bins and (right) CAPE and CN bins. The number of samples (#), mean CTT minimum value (μ), and standard error of the mean CTT minimum (SE) in each bin are written in black.

Fig. 8.

The mean of the minimum CTT (shaded) for warm-cloud-base, cold-cloud-top systems as a function of (left) LNB and CN bins and (right) CAPE and CN bins. The number of samples (#), mean CTT minimum value (μ), and standard error of the mean CTT minimum (SE) in each bin are written in black.

Linear regression slopes, slope 95% confidence intervals, and constants for relationships between CN, CAPE, LNB, and minimum CTT are shown in Table 1. Although these relationships are not necessarily linear, the regressions aid in quantitatively comparing CN, CAPE, and LNB as predictors for minimum CTT. Minimum CTT is significantly correlated at the 0.05 level with LNB and CAPE, but not significantly correlated with CN. Additionally, CAPE and LNB are both significantly correlated with CN for minimum CTTs < −4°C. The significance of minimum CTT correlations remains the same for minimum CTTs that are confined to less than −36°C; however, CAPE and LNB become no longer significantly correlated with CN using this CTT restriction.

Table 1.

Linear regression statistics for several fitted relationships including slopes, slope 95% confidence intervals, constants, and Pearson linear correlation coefficients. Regressions are shown for conditions with convective instability, LCL > 15°C, and LNB < −4°C. Statistics are shown separately for minimum CTT < −4°C and minimum CTT < −36°C. Units are °C for CTT and LNB, cm−3 for CN concentration, and J kg−1 for CAPE.

Linear regression statistics for several fitted relationships including slopes, slope 95% confidence intervals, constants, and Pearson linear correlation coefficients. Regressions are shown for conditions with convective instability, LCL > 15°C, and LNB < −4°C. Statistics are shown separately for minimum CTT < −4°C and minimum CTT < −36°C. Units are °C for CTT and LNB, cm−3 for CN concentration, and J kg−1 for CAPE.
Linear regression statistics for several fitted relationships including slopes, slope 95% confidence intervals, constants, and Pearson linear correlation coefficients. Regressions are shown for conditions with convective instability, LCL > 15°C, and LNB < −4°C. Statistics are shown separately for minimum CTT < −4°C and minimum CTT < −36°C. Units are °C for CTT and LNB, cm−3 for CN concentration, and J kg−1 for CAPE.

Approximately 65% of the decrease in minimum CTT with increasing CN concentration between 1000 and 5000 cm−3 can be predicted by changes in LNB with CN concentration. A total of 70% can be predicted by changes in CAPE with CN concentration. This is further supported by linear Pearson correlation coefficients between minimum CTT and CAPE (−0.249), minimum CTT and LNB temperature (0.216), CN concentration and CAPE (0.128), and CN concentration and LNB temperature (−0.141) that are all significantly higher than between minimum CTT and CN concentration (−0.046). When minimum CTTs are confined to temperatures less than −36°C, correlation coefficients increase between CTT and LNB (0.433), CTT and CAPE (−0.317), and CTT and CN (−0.066), again highlighting the far stronger relationships between minimum CTT and thermodynamic conditions than between minimum CTT and CN conditions. The relatively low correlation coefficient values are partly caused by measurements being limited to a single location and profile. The much lower correlation between CTT and CN than between any other two variables indicates that very large sample sizes and/or more comprehensive measurement strategies are needed to isolate a potential aerosol impact on deep convective cloud tops from first-order thermodynamic effects at the SGP site.

A multiple linear regression of minimum CTT using CN, CAPE, and LNB as predictors is also performed with predictor slopes and slope 95% confidence intervals given in Table 2. This regression again shows that the minimum CTT relationship with CN is not statistically significant at the 0.05 level, whereas relationships between minimum CTT and thermodynamic variables (CAPE and LNB) are significant. Standardizing the predictors to a standard deviation scale makes the coefficient magnitudes comparable. Table 2 shows that the CAPE coefficient is more than 18 times as large as the CN coefficient while the LNB coefficient is over 25 times as large. This indicates much stronger relationships of CAPE and LNB with minimum CTT than CN concentration with minimum CTT. Conclusions remain largely unchanged for minimum CTTs < −36°C with an insignificant relationship between CN and CTT, although the relationship between minimum CTT and CAPE weakens and the relationship between minimum CTT and LNB strengthens. To visualize these results, predicted minimum CTT using this regression is plotted against observed minimum CTT in Fig. 9, showing that the regression does a poor job for CTTs < −4°C because of the bimodal nature of the minimum CTT distribution and the limited dependence of the warmer CTT mode on the predictors (Fig. 9a). The regression for CTTs < −36°C does a better job (Fig. 9b) but significant spread remains. Removing the CN term from the multiple linear regression produces the results shown in Figs. 9c and 9d, which are largely unchanged from the results including CN in Figs. 9a and 9b.

Table 2.

Multiple linear regression statistics for minimum CTT as a function of CN concentration, CAPE, and LNB including the regression coefficients, coefficient 95% confidence intervals, and constants. Standardized regressions use CN, CAPE, and LNB values in terms of standard deviation units of each variable. Regressions are shown for conditions with convective instability, LCL > 15°C, and LNB < −4°C. Statistics are shown separately for minimum CTT < −4°C and minimum CTT < −36°C. Units are °C for CTT and LNB, cm−3 for CN concentration, and J kg−1 for CAPE for nonstandardized regressions. Units are inverse standard deviation for standardized regressions.

Multiple linear regression statistics for minimum CTT as a function of CN concentration, CAPE, and LNB including the regression coefficients, coefficient 95% confidence intervals, and constants. Standardized regressions use CN, CAPE, and LNB values in terms of standard deviation units of each variable. Regressions are shown for conditions with convective instability, LCL > 15°C, and LNB < −4°C. Statistics are shown separately for minimum CTT < −4°C and minimum CTT < −36°C. Units are °C for CTT and LNB, cm−3 for CN concentration, and J kg−1 for CAPE for nonstandardized regressions. Units are inverse standard deviation for standardized regressions.
Multiple linear regression statistics for minimum CTT as a function of CN concentration, CAPE, and LNB including the regression coefficients, coefficient 95% confidence intervals, and constants. Standardized regressions use CN, CAPE, and LNB values in terms of standard deviation units of each variable. Regressions are shown for conditions with convective instability, LCL > 15°C, and LNB < −4°C. Statistics are shown separately for minimum CTT < −4°C and minimum CTT < −36°C. Units are °C for CTT and LNB, cm−3 for CN concentration, and J kg−1 for CAPE for nonstandardized regressions. Units are inverse standard deviation for standardized regressions.
Fig. 9.

Multiple linear regression predicted minimum CTT vs observed minimum CTT for (a) all ARSCL convective cloud objects and (b) ARSCL convective cloud objects with minimum CTTs colder than −36°C. (c),(d) As in (a) and (b), respectively, but with CN concentration removed as a predictor.

Fig. 9.

Multiple linear regression predicted minimum CTT vs observed minimum CTT for (a) all ARSCL convective cloud objects and (b) ARSCL convective cloud objects with minimum CTTs colder than −36°C. (c),(d) As in (a) and (b), respectively, but with CN concentration removed as a predictor.

5. Cause of aerosol–meteorology correlations

In an attempt to understand the cause of the correlations between CN concentration and meteorology, mean synoptic conditions between relatively clean (1000 < CN < 2000 cm−3) and dirty (4000 < CN < 5000 cm−3) conditions are plotted in Fig. 10. Geopotential heights at 200 and 850 hPa show broadly the same pattern in clean and dirty conditions. A ridge aloft is centered just east of central Oklahoma, low-level south-southwesterly flow over the Southern Great Plains is induced by high pressure centered over the southeastern United States, and low pressure is observed over the western United States. These are very typical synoptic conditions from late spring to summertime. Despite the similarity in patterns, it is clear that 200-hPa temperatures are cooler over the central Great Plains in dirty conditions by ~1°C while 850-hPa temperatures are warmer by ~1°C. This is clear in Figs. 10e and 10f, which show mean clean conditions subtracted from mean dirty conditions. These panels indicate that dirty conditions have anomalous upper-level northerly flow caused by slightly higher geopotential heights to the west and slightly lower geopotential heights to the east of Oklahoma relative to clean conditions. At 850 hPa, the geopotential height gradient is greater in dirty conditions than in clean conditions, causing stronger south-southwesterly flow in dirty conditions than in clean conditions. The cooler air aloft and warmer air at low levels in dirty conditions creates conditions with colder LNB temperatures and greater CAPE than in clean conditions. Temperature differences in Figs. 10e and 10f are ~1°C and wind differences are ~2–4 m s−1, producing mean conditions in Figs. 10a–d that are largely similar with differences that may be small enough to be of the same magnitude as errors in any single weather analysis.

Fig. 10.

ERA-Interim (left) 200- and (right) 850-hPa analyses of (a),(b) CN category-2 (1000–2000 cm−3) mean “clean” conditions; (c),(d) CN category-5 (4000–5000 cm−3) mean “dirty” conditions; and (e),(f) dirty minus clean conditions. Temperature is color filled, wind vectors are in black, and geopotential heights are contoured every 50 m (mean) and 4 m (anomaly) in the left column and every 10 m (mean) and 2 m (anomaly) in the right column with greater values in red and lesser values in blue. Only times with CN-matched sounding CAPE > 0, LCL > 15°C, and LNB < −4°C are included. The 6-hourly ERA-Interim data are only included if they are within 3 h of a CN-matched sounding, which is used to assign each analysis to a CN category and sounding.

Fig. 10.

ERA-Interim (left) 200- and (right) 850-hPa analyses of (a),(b) CN category-2 (1000–2000 cm−3) mean “clean” conditions; (c),(d) CN category-5 (4000–5000 cm−3) mean “dirty” conditions; and (e),(f) dirty minus clean conditions. Temperature is color filled, wind vectors are in black, and geopotential heights are contoured every 50 m (mean) and 4 m (anomaly) in the left column and every 10 m (mean) and 2 m (anomaly) in the right column with greater values in red and lesser values in blue. Only times with CN-matched sounding CAPE > 0, LCL > 15°C, and LNB < −4°C are included. The 6-hourly ERA-Interim data are only included if they are within 3 h of a CN-matched sounding, which is used to assign each analysis to a CN category and sounding.

What causes this correlation between meteorology and surface CN concentrations? Table 3 explores the possible role of seasonality by separating ARSCL cloud objects and their environmental conditions by month. Minimum CTTs are coldest in the spring and warmest in the fall, while CAPE and LNB decrease between spring and fall. CN concentration has less of a seasonal trend but is perhaps slightly higher in the spring and fall than in the summer. The fraction of CN category samples within each month show some monthly differences, although clear trends between the categories are difficult to discern. To estimate the role of seasonality on the CN–meteorology correlations, the CN category fractions are multiplied by the monthly mean CTT minimum and accumulated to yield a predicted minimum CTT for each CN category. Doing so yields a slight decrease (0.6°C) in minimum CTT with increasing CN concentration, but this falls short of the 2°C differences shown in Fig. 3.

Table 3.

Monthly mean minimum CTT, CAPE, LNB, and CN with the fraction of CN category samples within each month. The CN category fractions are multiplied by the monthly mean CTT minimums to yield a predicted minimum CTT for each CN category in the right column.

Monthly mean minimum CTT, CAPE, LNB, and CN with the fraction of CN category samples within each month. The CN category fractions are multiplied by the monthly mean CTT minimums to yield a predicted minimum CTT for each CN category in the right column.
Monthly mean minimum CTT, CAPE, LNB, and CN with the fraction of CN category samples within each month. The CN category fractions are multiplied by the monthly mean CTT minimums to yield a predicted minimum CTT for each CN category in the right column.

Table 4 explores the possible role of the diurnal cycle in the correlation between meteorology and CN concentration. There is a strong diurnal cycle in minimum CTT and CAPE with the coldest cloud tops and highest CAPE values in the evening (0000–0300 UTC). The coldest LNB temperature is also in the evening, but the mean CN concentration peaks in the late morning to early afternoon (1500–1800 UTC). As is the case for seasonality, it is difficult to discern consistent trends in the fraction of CN category samples within each 3-h period of the diurnal cycle. When minimum CTT is predicted based on these fractions multiplied by the mean CTT minimum in each 3-h period, minimum CTTs actually warm by 0.4°C with increasing CN concentration, largely canceling out the effect of seasonal correlations. Therefore, the diurnal and seasonal cycles collectively fail to explain the correlations between CAPE, LNB, and CN.

Table 4.

The 3-hourly mean minimum CTT, CAPE, LNB, and CN with the fraction of CN category samples within each 3-h period of the diurnal cycle. The CN category fractions are multiplied by the 3-hourly mean CTT minima to yield a predicted minimum CTT for each CN category in the right column.

The 3-hourly mean minimum CTT, CAPE, LNB, and CN with the fraction of CN category samples within each 3-h period of the diurnal cycle. The CN category fractions are multiplied by the 3-hourly mean CTT minima to yield a predicted minimum CTT for each CN category in the right column.
The 3-hourly mean minimum CTT, CAPE, LNB, and CN with the fraction of CN category samples within each 3-h period of the diurnal cycle. The CN category fractions are multiplied by the 3-hourly mean CTT minima to yield a predicted minimum CTT for each CN category in the right column.

Although not shown, soil moisture also does not vary significantly with CN concentration. However, Fig. 11 shows that 6-h regional ABRFC-estimated rainfall preceding soundings with convective instability, LCL > 15°C, and LNB < −4°C varies significantly with CN concentration. Although near-surface flow directions are extremely variable for each CN category, the mean direction is from the southeast. Both around the SGP site and to the south and east, there is a clear decrease in rainfall preceding a sounding time as CN concentration increases between category 2 (1000–2000 cm−3) and category 5 (4000–5000 cm−3). It is plausible that rainfall would be correlated with both surface CN concentration and thermodynamic profiles. Rainfall decreases aerosol concentrations through wet deposition. It also cools and moistens low levels through evaporation while warming upper levels through latent heating. The situation in Fig. 11 will not be representative of every case just as CAPE is not always greater and LNB temperature is not always colder as CN concentration increases. As already highlighted, a significant spread exists for relationships between these variables. However, a correlation between mean rainfall preceding a deep convective situation and surface CN concentration represents a plausible explanation for the statistically significant correlation between CN concentration, CAPE, LNB, and temperature profiles.

Fig. 11.

Arkansas–Red Basin River Forecast Center mean 6-hourly rainfall accumulations preceding soundings with convective instability, LCL > 15°C, and LNB < −4°C for (a) CN category 2 (1000–2000 cm−3), (b) CN category 3 (2000–3000 cm−3), (c) CN category 4 (3000–4000 cm−3), and (d) CN category 5 (4000–5000 cm−3).

Fig. 11.

Arkansas–Red Basin River Forecast Center mean 6-hourly rainfall accumulations preceding soundings with convective instability, LCL > 15°C, and LNB < −4°C for (a) CN category 2 (1000–2000 cm−3), (b) CN category 3 (2000–3000 cm−3), (c) CN category 4 (3000–4000 cm−3), and (d) CN category 5 (4000–5000 cm−3).

6. Conclusions

The results shown in sections 35 refute those drawn in Li et al. (2011) and Yan et al. (2014). Correlation between surface CN concentration and minimum CTT for warm-cloud-base, cold-cloud-top systems at the SGP site in north-central Oklahoma nearly disappears when the correlations between CN concentration and meteorological factors (LNB and CAPE) are taken into account. Both CAPE and LNB are statistically significantly related to CN concentration. MERGESONDE retrievals matched to ARSCL cloud objects and radiosondes show that the temperature lapse rate steepens and relative humidity decreases as CN concentration increases in convectively unstable, warm-cloud-base, cold-cloud-top conditions. Additionally, southwesterly winds increase at low levels and upper-level meridional winds become more northerly as CN concentration increases. Composite ERA-Interim synoptic analyses show warmer low-level temperatures and colder upper-level temperatures in dirty conditions relative to clean conditions. Seasonal and diurnal variations in meteorological and CN conditions fail to explain this correlation. However, the regional rainfall amount preceding the time of a warm-cloud-base, cold-cloud-top deep convective sounding is highly correlated with CN concentration. Increased rainfall may decrease CN concentrations through wet deposition, cool low levels through evaporation, and warm upper levels through latent heating. This is a potential explanation for the correlation between thermodynamic profiles and surface CN concentrations.

After accounting for dependencies of minimum CTT on LNB and CAPE through linear regressions, the number of independent deep convective events at the SGP site over 14 years is insufficient given vertical profile measurement limitations for making any conclusions regarding impacts of aerosol concentrations on deep convective cloud depth. This is especially true when minimum CTTs are confined to temperatures less than −36°C, which should be done to eliminate a relatively warm cloud-top mode peaking between −5° and −10°C that may not contain ice in most conditions. CN–CTT correlations largely disappear when this temperature threshold is applied.

There is a larger lesson to be gleaned from this analysis that is confined to the ARM SGP site. The effect on a cloud property by large changes in one variable (e.g., CN concentration) can be canceled out by small changes in a more controlling variable (e.g., LNB). This means that analyzing subsets of aerosol data in bins of similar meteorological conditions, as done by numerous previously cited studies, is not a valid method for discerning an aerosol effect in many situations. Individual meteorological variables are not isolated from one another in nature, and small changes in the thermodynamic or kinematic environment within a relatively larger meteorological variable bin may be correlated with large changes in the aerosol concentration within that bin. As an example, with the typically large meteorological bins that are often chosen for “controlling meteorology,” the mean dirty and mean clean conditions in Fig. 10 would likely be included in the same meteorological bin, where higher CN concentrations have colder minimum CTTs and lower CN concentrations have warmer minimum CTTs on average. However, it would be incorrect to assume that this implies that aerosols cause this change in CTT rather than meteorological factors. Temperature changes of ~1°–2°C create a change in LNB and CAPE that explain the change in CTT between CN concentrations of 1000–2000 and 4000–5000 cm−3. These relatively small anomalies imply that correlations between aerosol concentration and meteorological factors in deep convective conditions may be quite limited yet explain correlations between cloud-top temperature and aerosol concentration. Therefore, the role of meteorological factors in altering cloud-top height and temperature cannot be neglected simply because the change in meteorological values with aerosol concentration is limited.

These results do not draw into question the validity of the well-reasoned aerosol convective invigoration hypothesis for certain environmental conditions. Rather, they highlight the need for more careful, detailed, and strategic observational analyses so that this potentially climatically important aerosol indirect effect can be more confidently isolated and quantified for a range of deep convective morphologies, life cycle stages, and large-scale environmental conditions around the world. As stated in Tao et al. (2012), “Disentangling meteorological and aerosol effects remains a daunting task,” and it needs to be treated as such. The SGP site is characterized by high aerosol concentrations in even relatively clean conditions, meaning collision–coalescence suppression that forms the basis for theorized aerosol invigoration of deep convection may not substantially increase between clean and dirty periods. Locations experiencing much cleaner and less meteorologically variable deep convective environments may allow for better isolation and quantification of aerosol convective invigoration. However, the recommendation that correlations between aerosol concentration and deep convective meteorological parameters such as LNB and CAPE requires careful and detailed analysis with proper usage of statistical sampling also applies to environments that are cleaner than the SGP.

Carefully analyzed correlations between convective meteorological parameters and aerosol concentrations in other regions of the world are required for determining the number of independent convective systems that need to be observed to confidently isolate a potential second-order aerosol invigoration effect from first-order thermodynamic and kinematic controls on deep convective strength and depth. Furthermore, CN concentration and AOD are not perfect proxies for CCN because their correlations can differ as a function of the diurnal cycle, aerosol size and composition, and relative humidity (e.g., Sheridan et al. 2001; Burkart et al. 2011; Sihto et al. 2011). The vertical location of aerosols also impacts deep convective cloud properties (Lebo 2014). More research is needed to determine uncertainties caused by CCN proxies and limited environmental measurements. Last, deep convective activity is relatively infrequent in most regions of the world with potentially differing effects of aerosols on different mesoscale convective organizational morphologies and life cycle stages, further making the robust quantification of an aerosol indirect effect on deep convection difficult in any one location given currently available observational datasets. Despite the climatic importance of complex mesoscale convective systems, isolated deep convective cells where the three-dimensional structural evolution of kinematic, thermodynamic, and aerosol properties around the convection can be well characterized should likely be targeted first for attempting to isolate an aerosol indirect effect on convective intensity. These cells should occur frequently with fairly predictable forcing (e.g., an isolated orographic feature or island) in a location with minimal spread in meteorological conditions, a range of aerosol loadings, and relatively clean conditions on average. An example of this methodology is the study by Nugent et al. (2016) that used Dominica Experiment (DOMEX) measurements to analyze the impact of aerosols on precipitation in orographic cumulus clouds. From such observations, model microphysics parameterizations can be evaluated, made more realistic and trustworthy, and then used to study more complex aerosol interactions within mesoscale convective systems.

Acknowledgments

This study was supported by the Department of Energy (DOE) Atmospheric System Research program under Grant DE-SC0008678. The author thanks Edward J. Zipser and three anonymous reviewers for helpful comments. The author also thanks DOE ARM, ECMWF, and NOAA ABRFC for providing datasets. ARSCL, MERGESONDE, CN, radiosonde, and Arkansas–Red Basin River Forecast Center hourly rainfall datasets can be freely downloaded from the DOE ARM archive (www.arm.gov/data). ERA-Interim data was accessed in January 2013 and can be freely downloaded (http://apps.ecmwf.int/datasets/data/interim-full-daily/).

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