Aerosol–cloud interactions are complex, including albedo and lifetime
effects that cause modifications to cloud characteristics. With most
cloud–aerosol interactions focused on the previously stated phenomena, there
have been no in situ studies that focus explicitly on how aerosols can affect
large-scale (centimeters to tens of meters) droplet inhomogeneities within
clouds. This research therefore aims to gain a better understanding of how
droplet inhomogeneities within cumulus clouds can be influenced by in-cloud
droplet location (cloud edge vs. center) and the surrounding environmental
aerosol number concentration. The pair-correlation function (PCF) is used to
identify the magnitude of droplet inhomogeneity from data collected on board
the Center for Interdisciplinary Remotely Piloted Aircraft Studies (CIRPAS)
Twin Otter aircraft, flown during the 2006 Gulf of Mexico Atmospheric
Composition and Climate Study (GoMACCS). Time stamps (at 10
The spatial inhomogeneity of cloud droplets at different spatial scales has impacts on multiple cloud processes, including precipitation formation on the smallest scales (millimeter to centimeter scale, from here on termed inertial clustering or just clustering) and radiative heating and cooling on the largest spatial scales. The work presented here deals with in situ measurements of the magnitude of cloud droplet spatial inhomogeneities at scales of centimeters to tens of meters (from here on termed droplet inhomogeneities or just inhomogeneities) to provide information on how the entrainment mixing present at cloud–clear air interfaces impacts inertial particles (i.e., cloud droplets).
This information is of interest due to the complex physical processes
controlling clouds, in particular the formation of precipitation and
aerosol–cloud interactions, both of which can affect cloud lifetime and
size. Along with these uncertainties, one of the main problems with cloud
microphysical research has been determining how turbulence and mixing
processes occurring on smaller scales affect the macroscopic evolution of
clouds (in particular the cloud droplet size distribution), along with
gathering in situ data to better understand these properties
Cloud droplets grow through the diffusion of water vapor up to sizes where
collision–coalescence occurs. However, the rapid onset of rain (typically 15
to 20 min observed through radar measurements;
Enhanced evaporation from smaller droplet sizes arises from aerosol
perturbations, resulting in a stronger horizontal buoyancy gradient and
increased entrainment (known as the evaporation–entrainment feedback
mechanism), as shown in both simulation
It is generally assumed that sub-saturated (droplet-free and laminar)
ambient air is entrained in “blobs” due to the turbulent motions of the
cloud. This results in a reduction in the total liquid water and directly
influences the droplet size distribution. As suggested by
After initial entrainment of the ambient, drop-free air into the cloud, the
subsequent turbulent mixing within the cloud acts to produce smaller and
smaller parcels of sub-saturated cloudy and ambient air until the Kolmogorov
length scale (approximately 1 mm for atmospheric conditions, depending on
the turbulent kinetic energy dissipation rate) is reached
Up until the late 1980s, it was mostly accepted that droplet spacing within
clouds was statistically homogeneous, or uniformly distributed according to
Poisson statistics
Analyses of droplet observations in adiabatic cores of cumulus clouds from
Specific questions in regards to droplet inhomogeneity in shallow, warm continental cumulus clouds to be answered include the following. (1) Does droplet inhomogeneity change as a function of location (cloud center vs. edge)? It is hypothesized that said inhomogeneities will be enhanced at cloud edge where entrainment of dry air is directly occurring. Turbulent mixing will reduce the large-scale inhomogeneities in the droplet population moving towards cloud center. (2) Does droplet inhomogeneity change as a function of cloud height? It is hypothesized that an increase in inhomogeneity will be present near cloud top due to the entrainment of dry air. (3) Does droplet inhomogeneity depend on aerosol number concentration? It is hypothesized that an increased aerosol load leads to enhanced inhomogeneities due to the resulting increased entrainment from smaller droplet sizes and evaporation.
This is a first step in developing a better understanding of droplet inhomogeneities as a result of entrainment mixing, in the hopes of eventually leading to better cloud microphysical parameterizations for modeling precipitation and the overall role of clouds in radiation models. Section 2 will provide a deeper introduction into droplet inhomogeneity along with the pair-correlation function (the statistical tool used to measure the magnitude of droplet inhomogeneities). Section 3 will discuss data collection and instrumentation along with environmental and flight characteristics. Results related to the three scientific questions proposed above are presented in Sect. 4. Finally, in Sect. 5 we discuss and summarize the work presented and provide suggestions for extending the analysis presented here.
As briefly introduced in Sect.
However, the mechanism responsible for inertial clustering is completely
unrelated to droplet inhomogeneities that result from entrainment mixing,
which is the focus of the work presented here. Inhomogeneous mixing (i.e.,
entrainment mixing) leads to the mixing of particles from one region of the
flow to another on a spatial scale comparable to the length scale of the
mixing eddies. The largest eddies are slightly smaller than the length scale
of the cloud itself
Entrainment is found to be governed by the large-scale parameters of the
flow.
The effect that gravity (i.e., droplet sedimentation) has on the droplet
response to the fluid must also be considered.
There are multiple tools that can be used to measure droplet clustering using
a time series of droplet detection times, but the 1-D temporal
pair-correlation function (PCF) will be used throughout this paper due to
the advantages of the PCF outlined in
The main advantage of the PCF is the fact that it is scale localized. The PCF
depends only on the presence or absence of particles separated by
When measuring data that are non-stationary (i.e., large-scale spatial
inhomogeneities are present), the PCF measures droplet spatial
heterogeneities that are a result of inertial clustering and entrainment
mixing
The PCF was calculated three times for each cloud penetration (120 m
section, representing roughly 2 s worth of data) at cloud edge (cloud entry
and exit) and cloud center. To calculate the
The PCF is calculated by binning the inter-arrival times of the droplets
into the vector sequence discussed in the previous paragraph. An
inter-arrival time is first determined between every subsequent droplet,
binned and summed (the sum of each inter-arrival time per bin). An
inter-arrival time is then determined for every other droplet, every third
droplet, every fourth droplet, and so on. The inter-arrival times are binned
and added to the previously summed binned inter-arrival times up until the
minimum inter-arrival time in the data is no longer less than
Figure
Panels
The Gulf of Mexico Atmospheric Composition and Climate Study (GoMACCS) was
conducted jointly with the 2006 Texas Air Quality Study (TexAQS) during
August and September of 2006 as a combined climate change and air quality
intensive field campaign. The Center for Interdisciplinary Remotely Piloted
Aircraft Studies (CIRPAS) Twin Otter aircraft (flight speed of about 60 m s
Shows the flight information for 20 of the 22 flights that occurred
during the GoMACCS campaign. Each flight corresponds to a RF number, date,
the number of clouds (after filtering; see text), the total aerosol number
concentration (
n/a – not applicable.
Table
Following the methods in
A summary of cloud, flight, and environmental properties from the
L1, L2, H1, H2, and case flights. Note that CDNC stands for cloud droplet
number concentration, LWC stands for liquid water content, and mean drops
(s
n/a – not applicable.
L1 and L2 are shown on the left and right, respectively. Flight altitude
(blue) as a function of time is displayed in
As in Fig.
Figures
It can be calculated from analyzing Table
Average values for low (L1, L2) and high (H1, H2) pollution clouds
for select variables from Table
PCF functions for L1, L2, H1, and H2 are given in Fig.
Shows cloud droplet diameter (
The mean PCF, 85th percent quantile, and 15th percent
quantile values for center data (on the left) and edge data (on the right)
for L1, L2, H1, and H2 in Fig.
The mean
The main takeaway from Fig.
PCF clustering signatures for L1
From analyzing Fig.
From analyzing L2 (Fig. 5c) and the corresponding tables, there are
significant differences from the other three cases. Although the mean edge
inhomogeneity is enhanced as compared to the center zone, the difference is
not statistically significant, with 0 % of the data having a
It is clear that there are enhanced inhomogeneities in the edge zone as
compared to the center zone, but one needs to understand how to define if the
overall inhomogeneities (both edge and center) are significant as compared to
a randomly distributed droplet population. This is done by analyzing the
range that the PCF can take on due to the random nature of the data. If the
physical inhomogeneities measured fall outside of this range, then the
conclusion can be made that the droplet spatial inhomogeneities being viewed
are indeed real and not perfectly homogeneous. This test was performed on
each of the four cases, following the methods outlined in
Percentage of inhomogeneities that are significant and
non-significant (as compared to a randomly distributed droplet population)
for center (
We can use the inter-arrival times used in calculating the PCF to develop a
better understanding of the overall droplet spatial distributions and the
largest inhomogeneities measured by directly analyzing the inter-arrival
time distribution (as is done in
Histogram distributions of the inter-arrival distance (IAD) for
droplet populations measured in flight L1, with edge data in blue and center
data in red. Note that the main histogram is zoomed in to a value of 60 on
the
Although the raw histograms of IAD data are not displayed for L2, H1, and H2
(they appear very similar in nature to that of L1), the resulting box plots of
the IAD data which are greater than or equal to the 0.998 quantile for each
of the four flights are presented in Fig.
Values for vertical velocity (m s
Figure
Box plots for the IAD data which are greater than or equal to the 0.998 quantile of the overall data sets for edge (blue) and center (red), with L1, L2, H1, and H2 shown moving from left to right, respectively. The median value for each data set is displayed within the plot. Tick marks occurring on the upper whiskers represent the raw data positions. Note that panel L1 represents the same box plot displayed in Fig. 6.
Shows the cloud droplet size distribution in panel
Figure
Figure
Panels
The larger mean inhomogeneity amount for the low-pollution clouds can be seen
well in Fig.
Low-pollution clouds have a non-statistically significant higher amount of
inhomogeneity than high-pollution clouds, with further analysis showing that
the higher amount of inhomogeneity in the low-pollution case is due entirely
to the L2 flight. Figure
The mean
An explanation for the statistically different inhomogeneity in L2 as
compared to the other three cases could be cloud age. A study by
As in panels
Figure
Median values of vertical velocity (m s
Box plots of L1, L2, H1, and H2, represented in that order on the
Figure
Figure
The
Aerosols can act as cloud condensation nuclei (CCN), increasing the number of
droplets in clouds and decreasing the mean droplet size
Other possible explanations for the increased inhomogeneity in L2 could be
due to flight path or the atmospheric environment for a given flight. The
flight path through the cumuli for L2 could have favored cloud edge or cloud
top instead of true cloud center. Favoring cloud edge would result in
measuring areas of cloud that favor a higher amount of inhomogeneity (as
displayed in Fig.
Comparing cloud width on different days can become complicated due to the
environmental factors that control cloud size. As is discussed in
The finding that droplet spacing is inhomogeneous agrees with the findings in
multiple other papers, including
PCF curves measuring inertial clustering in other literature
From the clouds measured, the conclusion can be made that droplet
inhomogeneity does change as a function of cloud center vs. cloud edge, with
the edge zone having a larger amount of inhomogeneity than the center of the
cloud, which is shown to be statistically significant. The decrease in
inhomogeneity in the center of the cloud as compared to the edge may be
attributed to several aspects, including (1) the mean entrainment rate
decreases from cloud edge to cloud center, as has been shown with in situ
measurements made by
Provides the median value and spectral width (10th to 90th percent quantile range) of the drop size distribution, the altitude at which measurements occurred, and the cloud droplet number concentration (CDNC) for both the center and edge zone of cloud passages for each of L1, L2, H1, and H2. Standard deviation values are given in parenthesis.
Along with enhanced inhomogeneity at cloud edge, enhanced inhomogeneity at
cloud top is also evident due to entrainment as is shown in Fig.
Although the conclusion in this paper is that aerosol number concentration
does not affect droplet inhomogeneity, this conclusion can only be made for
the range of
Flight data obtained from the CIRPAS Twin otter aircraft flown during the GoMACCS campaign near Houston, TX, from 2006 were used to investigate 81 non-precipitating cumulus clouds, and one vertically developed cumulus cloud, to better understand how droplet inhomogeneity changes as a function of cloud location (cloud edge vs. cloud center) and aerosol number concentration. Of the 22 flights flown, two low-pollution (L1, L2) and high-pollution (H1, H2) flights were selected to analyze how droplet inhomogeneity changed with aerosol number concentration.
It has been shown that (1) droplet inhomogeneity is enhanced at cloud edge as
compared to cloud center, with a statistically significant difference. Most
of the inhomogeneity measured is shown to be real, physical variability
(non-Poissonian). Statistically significant, enhanced inhomogeneity is also
shown at cloud top as compared to the lower portion of the cloud. (2) There
is no statistical difference at the 5 % level for droplet inhomogeneity
between low- and high-pollution clouds, at least for the range of
This work provides a good statistical base for analyzing how droplet inhomogeneity changes with cloud location and aerosol number concentration. The conclusions from this work are drawn only from 81 clouds whose properties are highly variable and influenced by environmental aspects that are not constrained by the observations, including the sub-cloud layer properties and the life cycle stage of the clouds. This study examined the cloud properties at instantaneous moments, resulting in a mean behavior averaged over each cloud and each flight. Further analysis and data from more clouds are required to confirm some of the ideas that have been presented here. For example, if a field campaign takes place in the future for the purposes of illuminating these results, constraints on the life cycle stage of the observed clouds must be considered, along with the proper instrumentation for turbulent analysis.
All cabin data from different aircraft platforms can be found on the NOAA Earth System Research Laboratory website for the TexAQS/GoMACCS at
DSD and JDSG contributed equally to both the analysis and the writing of this paper.
The authors declare that they have no conflict of interest.
We thank Haflidi Jonsson and Patrick Chuang for their support during the original field campaign. We also thank the CIRPAS Twin Otter crew and personnel for their effort and support during the field program and John Seinfeld and Rick Flagan (Caltech) and their research groups for assistance and discussions in the field regarding other GoMACCS data sets. Michael Larsen (College of Charleston) also deserves thanks for his suggestions and intellectual help which made this paper possible. This work was funded by NSF CAREERS grant 1255649.
This research has been supported by the National Science Foundation (grant no. 1255649).
This paper was edited by Armin Sorooshian and reviewed by Ewe-Wei Saw and one anonymous referee.