Introduction
Tropical deep convective clouds (DCCs) constitute an important source of
precipitation (Liu, 2011) and they interact with atmospheric solar and
terrestrial radiation, dynamical processes, and the hydrological cycle
(Arakawa, 2004). Deep tropical convection is responsible for transporting
energy upwards and thus sustaining the Hadley circulation that redistributes
heat to higher latitudes (Riehl and Malkus, 1958; Riehl and Simpson, 1979;
Fierro et al., 2009, 2012). Therefore, understanding the processes that
impact the characteristics of tropical DCCs is crucial in order to
comprehend and model the Earth's climate.
The DCCs over the Amazon are of particular interest. Given the relative
homogeneity of the surface (as compared to urbanized regions) and the
pristine air over undisturbed portions of the rainforest, Amazonian DCCs can
have similar properties to maritime systems (Andreae et al., 2004). At the
same time, their daily persistence and the considerable latent heat release
have a noticeable impact on the South America climate by, for instance,
maintaining the Bolivian High, which is a key component of the South
American monsoon system (Zhou and Lau, 1998; Vera et al., 2006).
Clouds and aerosol particles interact in a unique way in the Amazon. Low
concentrations of natural aerosols derived from the forest are the major
source of natural cloud condensation nuclei (CCN) and ice-nucleating
particle (INP) populations under undisturbed conditions (Pöschl et
al., 2010; Prenni et al., 2009; Pöhlker et al., 2012, 2016). Other
sources of aerosol particles over the Amazon include long-range Saharan dust
and sea salt transport, biomass burning (either naturally occurring or
human-induced), and urban pollution downwind from cities and settlements
(Talbot et al., 1988, 1990; Cecchini et al., 2016; Martin et al., 2010; Kuhn
et al., 2010).
Human-emitted pollution can significantly alter cloud properties by
enhancing CCN number concentrations (NCCN). Since the work of
Twomey (1974) analyzing the effects of enhanced NCCN on cloud albedo, much
attention has been given to aerosol–cloud–precipitation interactions. The
effects of aerosol particles on warm-phase precipitation formation is fairly
well understood, with enhanced CCN concentrations leading to the formation of
more numerous but smaller droplets delaying the onset of rain (Albrecht,
1989; Seifert and Beheng, 2006; van den Heever et al., 2006; Rosenfeld et al.,
2008). However, in mixed-phase clouds, the rain suppression by pollution can
enhance ice formation, leading to stronger updrafts and convective
invigoration (Andreae et al., 2004; Khain et al., 2005; van den Heever et
al., 2006; Fan et al., 2007; van den Heever and Cotton, 2007; Lee et al., 2008;
Rosenfeld et al., 2008; Koren et al., 2010; Li et al., 2012; Gonçalves et
al., 2015). Aerosol effects on clouds have been reviewed by Tao et al. (2012),
Rosenfeld et al. (2014), and Fan et al. (2016). By changing cloud
properties, aerosol particles have an indirect impact on the thermodynamics
of local cloud fields through, for instance, the suppression of cold pools
and the enhancement of atmospheric instability (Heiblum et al., 2016b).
Clouds that develop above the freezing level are more difficult to model
given the complexity of the processes involving ice particles. One aspect of
the aerosol effects on clouds is their ability to alter the way in which ice
is formed in the mixed phase of convective clouds. Contact freezing is
possibly the dominant process by which the first ice is formed (Cooper,
1974; Young, 1974; Lamb et al., 1981; Hobbs and Rangno, 1985). As pointed
out by Lohmann and Hoose (2009), anthropogenic aerosol particles can either
enhance or hinder cloud glaciation due to primary aerosol emission
(increasing INP concentrations) and aerosol particle coating (decreasing
INP effectiveness), respectively. After the initial ice formation,
secondary ice generation can be triggered by the release of ice splinters
from freezing droplets (Hallett and Mossop, 1974; Huang et al., 2008; Sun et
al., 2012; Lawson et al., 2015). Rather big (larger than 23 µm) cloud
and drizzle droplets favor secondary ice generation (Mossop, 1978; Saunders
and Hosseini, 2001; Heymsfield and Willis, 2014). Consequently, the smaller
droplets found in polluted Amazonian clouds (Andreae et al., 2004; Cecchini
et al., 2016; Wendisch et al., 2016) may slow down secondary ice generation.
In order to model aerosol effects on clouds and the thermodynamic feedback
processes involved, it is crucial to understand their effects on hydrometeor
size distributions. The first step is the study of aerosol impacts on liquid
droplet size distributions (DSDs) in the cloud's warm phase. Operational
models that require fast computations usually adopt a gamma function
(Ulbrich, 1983) to parameterize the DSDs:
N(D)=N0Dμexp(-ΛD),
where N0 (cm-3 µm-1), μ (dimensionless), and
Λ (µm-1) are the intercept, shape, and curvature
parameters, respectively. N(D) is the concentration of droplets per cubic centimeter of air and
diameter (D) bin interval. Even though the gamma function is widely adopted in models
(Khain et al., 2015), there is almost no study regarding its phase space for
checking DSD predictions between parameterization schemes.
The phase space of cloud micro- and macrophysical properties has received
recent attention because of the considerable gain of information accessible
using relatively simple analysis tools. Heiblum et al. (2016a, b) studied
cumulus fields in a two-dimensional (2-D) phase space consisting of the cloud
center of gravity versus water mass. The authors were able to evaluate
several processes in this subspace, including the aerosol effect.
McFarquhar et al. (2015) studied the gamma phase space for improving ice
particle size distribution (PSD) fitting and parameterization. They showed
that the inherent uncertainty of gamma fittings results in multiple
solutions for a single ice PSD, corresponding to ellipsoids rather than
points in the phase space. However, there is no study regarding the
representation of warm-phase cloud DSDs in the gamma phase space and its evolution.
For the representation of hydrometeor size distributions in two-moment bulk
schemes, one of the three gamma parameters is either fixed or diagnosed
based on thermodynamic or DSD properties (Thompson et al., 2004; Milbrandt
and Yau, 2005; Formenton et al., 2013a, b). This process may produce
artificial trajectories in the phase space by limiting the parameter
variability. This study analyzes cloud DSD data collected during the
ACRIDICON–CHUVA campaign (Wendisch et al., 2016) in the gamma phase space.
ACRIDICON is the acronym for Aerosol, Cloud, Precipitation, and Radiation
Interactions and Dynamics of Convective Cloud Systems, while CHUVA stands
for Cloud Processes of the Main Precipitation Systems in Brazil: A
Contribution to Cloud Resolving Modeling and to the GPM (Global
Precipitation Measurement). The gamma phase space and its potential use
for understanding cloud processes is introduced and explored. A specific
focus is on the aerosol effect on the trajectories in the warm-layer phase
space and potential consequences for the mixed-phase formation.
General characteristics of the cloud profiling missions of interest
to this study: condensation nuclei (NCN) and CCN concentrations
(NCCN, with S = 0.48 ± 0.033 %), cloud base and
0 ∘C isotherm altitude (Hbase and H0∘C,
respectively), start and end time, and total number of DSDs collected. The
data are limited to the lower 6 km of the clouds. The unit for NCN and
NCCN is per cubic centimeter and the unit for altitude is meters. Profile start and
end are given in local time. The names in the third column have the following
meaning: M1 – Maritime 1; RA1 and RA2 – Remote Amazon 1 and Remote Amazon 2;
AD1, AD2, and AD3 – Arc of Deforestation 1, Arc of Deforestation 2, and Arc of Deforestation 3.
Region
Flight
Name
NCN
NCCN
Hbase
H0∘C
Start
End
No. of DSDs
(this
(cm-3)
(cm-3)
(m)
(m)
study)
Atlantic coast
AC19
M1
465
119
550
4651
13:17
14:57
630
Remote
AC09
RA1
821
372
1125
4823
11:30
14:21
665
Amazon
AC18
RA2
744
408
1650
4757
12:32
14:14
397
Arc of deforestation
AC07
AD1
2498
1579
1850
4848
13:49
17:16
674
AC12
AD2
3057
2017
2140
4938
12:55
15:16
381
AC13
AD3
4093
2263
2135
4865
12:46
15:36
204
Profile locations and trajectories of interest to this study. The
ACRIDICON–CHUVA research flights were labeled chronologically from AC07 to AC20.
The labels in the figure reflect the respective flights where the cloud profiling
section took place. The colors represent the different regions: green for remote
Amazon, blue for near the Atlantic coast, and red for the arc of deforestation
(different shades for clarity).
Section 2 describes the instrumentation and methodology. The results are
presented in Sect. 3, followed by concluding remarks in Sect. 4.
Methodology
Flight characterization
During September–October 2014, the German HALO (High Altitude and Long Range
Research Aircraft) performed a total of 96 h of research flights over the
Amazon. The 14 flights were part of the ACRIDICON–CHUVA campaign (Machado et
al., 2014; Wendisch et al., 2016) that took place in cooperation with the
second intensive operation period (IOP2) of the GoAmazon2014/5 experiment
(Martin et al., 2016). Here we focus on cloud profiling sections during six
flights that occurred in different regions in the Amazon (Fig. 1). The
research flights of ACRIDICON–CHUVA were named chronologically from AC07 to
AC20; the six flights selected (AC07, AC09, AC12, AC13, AC18, and AC19)
accumulated 16.8 h of data (in or out of clouds), of which 50 min were
inside the lower 6 km of the clouds. We concentrate primarily on the first
6 km for the DSD analysis in order to capture both warm-phase characteristics
and early mixed-layer formation. There were other flights with cloud
penetrations, but they are not considered in this study because of higher
aerosol variability below clouds. The flights chosen for analysis presented
relatively low aerosol variability, meaning that the clouds probed in the
same flight were likely subject to similar aerosol conditions. The time
frame of the campaign corresponds to the local dry-to-wet season transition,
when biomass burning is active in the southern Amazon (Artaxo et al., 2002;
Andreae et al., 2015). For clarity, the flights of interest are renamed in
this study according to the region probed. Flight AC19 will be referred as
M1 (Maritime 1), flights AC09 and AC18 as RA1 and RA2 (Remote Amazon 1 and
Remote Amazon 2, respectively), and flights AC07, AC12, and AC13 as AD1,
AD2, and AD3 (Arc of Deforestation 1, Arc of Deforestation 2, and Arc of
Deforestation 3, respectively). Those definitions are listed in Table 1.
The flight paths followed a regular three-stage pattern: (i) sampling of the
air below clouds for aerosol characterization, (ii) measurements of DSDs at
cloud base, and (iii) sampling of growing convective cloud tops (Braga et
al., 2017; Wendisch et al., 2016). The latter step was deployed as follows.
After the cloud base penetration, the aircraft performed several
penetrations in vertical steps of several hundred meters. In each step, the
aircraft penetrated the cloud tops available, thus avoiding precipitation
from above. In this way, different clouds can be penetrated in the same
altitude level and the vertical steps followed the growing cumuli field
overall. Surface and thermodynamic conditions were different for the various
flights (see Figs. 1 and 3) with high contrasts in the north–south
direction. Logging, agriculture, and livestock activity management involves
burning extended vegetated areas in the region, which emits large quantities
of particles that serve as CCN in the atmosphere (Artaxo et al., 2002;
Roberts et al., 2003). Because of this, this region is known as the “arc of
deforestation,” and its thermodynamic properties tend toward pasture-like
characteristics. The energy partitioning over pasture-like areas is
different compared to regions over the rainforest (Fisch et al., 2004),
favoring sensible heat flux and higher cloud base heights (see Table 1).
Contrasting with the arc of deforestation, the region named Remote Amazon in
this study has much lower background aerosol concentrations, producing
cleaner clouds. Clouds over the Atlantic Ocean developed under cleaner
conditions as compared to the continental counterparts, and also had lower
cloud bases (Table 1).
The cloud profiling missions were mostly characterized by cumulus fields,
with some developed convection in two flights over the arc of deforestation
(Fig. 2d and f). For flight AD1 some precipitation-sized droplets were
observed (not shown); the clouds sampled during AD2 and AD3 presented almost
no droplets with D > 100 µm. The precipitation during AD1
might be explained by the lower aerosol particle number concentrations
compared to flights AD2 and AD3, later start time of the profile, and the
presence of deep convection nearby (Table 1 and Fig. 2).
GOES-13 visible images for flights (a) M1, (b) RA1,
(c) RA2, (d) AD1, (e) AD2, and (f) AD3.
Images are approximately 1 h after the profile start time.
Data handling and filtering
The results to be presented here are based on five sensors carried by HALO.
A comprehensive description of the airborne instrumentation introduced below
can be found in Wendisch and Brenguier (2013). Aerosol particle number
concentrations (NCN) were measured using a butanol-based condensation
particle counter (CPC). The flow rate was set to 0.6 L min-1, with a
nominal cutoff particle size of 10 nm. NCCN at a given supersaturation
(S, averaging 0.48 % ± 0.033 % for the data used here, with 10 %
error) was measured using a cloud condensation nuclei counter (CCN-200; Roberts
and Nenes, 2005). This instrument contains two columns and was connected to
two different inlet systems for aerosol sampling: the HALO Submicrometer Aerosol
Inlet (HASI) for the aerosol particles and the Counterflow
Virtual Impactor (CVI) inlet to sample cloud droplets, evaporate the cloud
water, and analyze the residual particles. The aerosol measurements reported
in this study refer to the HASI inlet.
Cloud DSDs were measured using a cloud droplet probe (CDP; Lance et al., 2010;
Molleker et al., 2014) that is part of the cloud combination probe (CCP). The
CCP also contained a grayscale cloud imaging probe (CIPgs; Korolev, 2007),
but we focus on CDP measurements in which D < 50 µm. The intent
is to focus on cloud droplet growth processes and bringing the analysis
closer to modeling scenarios. Additionally, the percentage of data with
significant liquid water content (LWC) for D > 50 µm is
relatively small. The number of data with LWCD>50 > 0.1 g m-3
is only 12 % of the number of DSDs with LWCD<50 > 0.1 g m-3,
meaning that drizzle and precipitation are relatively
infrequent in the dataset. This observation combined with the possibility of
higher uncertainty (especially on the lower CIPgs bins) when combining two
different instruments with distinct measurement principles further justifies
the exclusive focus on CDP. The CDP counted and sized the droplets based
on their forward scattering characteristics, sorting them into 15 droplet
size bins between 3 and 50 µm. The sample volume had an
optical cross section of 0.278 mm2 (±15 %). Uncertainties in
the cross-section area, the sampling volume, and counting statistics were
the major sources of uncertainty for the DSD measurements (Weigel et al.,
2016). According to Molleker et al. (2014), the CDP uncertainty is about
10 %. Additionally, Braga et al. (2017) performed an intercomparison
between HALO probes, as well as hot-wire measurements, and concluded that
they agree well within instrumental uncertainties. We excluded all cloud
DSDs with droplet number concentrations (Nd) less than 1 cm-3
from further analysis.
The DSDs measured using the CDP were fitted to gamma distributions (Eq. 1) by
matching the zeroth, second, and third moments. These moments were chosen in
order to favor the study of the DSD properties of interest to this study
(i.e., droplet number concentration, LWC, and effective
diameter), but they also coincide with the properties usually predicted using
bulk microphysics models (zeroth and third moments in two-moment schemes).
The complete gamma function is used to be consistent with modeling
scenarios, in which the gamma parameters are calculated by
μ=6G-3+1+8G2(1-G)Λ=(μ+3)M2M3N0=Λμ+1M0Γ(μ+1),
where Mp is the pth moment of the DSD. The symbol G is a nondimensional
ratio, given as follows:
G=M23M32M0.
The three parameters N0, μ, and Λ define the gamma
distribution in Eq. (1); they are used to construct the phase space
described in the next section. Previous studies comparing the complete and
incomplete (or truncated) gamma fits suggest that, while there are
differences in the resulting parameters, the relation between them remains
similar. The first indication of that comes from the study of Ulbrich (1985)
that analyzed the relation between rainfall DSD moments in the empirical
form Mp = αMqβ, where p and q are the two distinct moment
orders and α and β are fit parameters. The author notes that
β is relatively insensitive to DSD truncation, meaning that the
relation between the moments remains similar while their overall values
change. Brandes et al. (2003) also note that the μ–Λ relation
introduced by Zhang et al. (2001) is relatively insensitive to DSD truncation.
In order to confirm that both the complete and incomplete gamma fits result
in similar correlations among the DSD parameters, a method similar to the
one presented in Vivekanandan et al. (2004) was applied. This method aims to
find the incomplete gamma parameters by using an iterative method to
adjust μ and Λ. Here the moments of order zero, two, and three will
be used instead of two, four, and six as in Vivekanandan et al. (2004). The
first step is to calculate the ratio G using the incomplete gamma as
Ginc=[γΛDmax,μ+3-γΛDmin,μ+3]3γΛDmax,μ+1-γΛDmin,μ+1γΛDmax,μ+4-γΛDmin,μ+42,
where γ is the incomplete gamma function and ΛDmin and
ΛDmax are its integration range. Dmin and Dmax were
calculated from the measured DSDs as the lowest and highest diameter bins
associated to drop concentrations higher than 10-6 cm-3
(considering both CDP and CIPgs for testing purposes). This ratio is found
to be greater than or equal to its counterpart in Eq. (5). Therefore, μ and
Λ should be lowered until Ginc is sufficiently close to G (the
threshold of 0.001 is used here). For that purpose, μ was lowered in
0.01 steps, where the respective Λ is calculated using Eq. (3) until
Ginc - G ≤ 0.001. When this condition is met, N0 is
recalculated from Eq. (4).
For the incomplete gamma fit, the adjustment described above was needed in
64 % of the data used here. In the other cases, the ratios G and
Ginc were similar and resulted in the same gamma parameters. For the
64% of the dataset, median relative differences in log(N0), μ, and
Λ ranged from 10 to 20 % towards higher N0 and lower
μ and Λ. However, regardless of their different values, the relation
among the gamma parameters remains unchanged in the incomplete fit because
they are based on the same underlying equations. As will be shown later, the
main interest of this study is in the relation among the gamma parameters
and not in their values themselves. Therefore, we will focus on the complete
gamma, noting that the results can be slightly shifted if truncation were to be considered.
The DSD bulk properties, such as droplet number concentration (Nd),
LWC, effective droplet diameter (Deff), and relative
dispersion (ε), can be derived from the gamma parameters
N0, μ, and Λ by taking into account the complete gamma
function integral properties. In the units considered here, the equations are given by
Nd=∫0∞N(D)dD=N0Γ(μ+1)Λμ+1LWC=10-9π6ρw∫0∞N(D)D3dD=10-9π6ρwN0Γ(μ+4)Λμ+4Deff=∫0∞N(D)D3dD∫0∞N(D)D2dD=μ+3Λε=σDg=1μ+1,
where ρw = 1000 g m-3 represents the density of liquid
water and σ and Dg are the DSD standard deviation and mean
geometric diameter, respectively. Nd, LWC, and Deff are given in
per cubic centimeter, gram per cubic meter, and micrometer, respectively. Given the choice of the
conserved moments, they exactly match the respective characteristics of the
observed DSDs. The parameter ε is described in detail in Tas et
al. (2015). The relative dispersion of the gamma DSD may differ from the
observations, given the differences between the parameterized and observed
DSDs. However, our measurements show that the gamma and observed
ε values are closely related by εGamma = 0.95εObserved (R2 = 0.93), showing that the
gamma DSDs are slightly narrower on average. We focus on ε as
obtained using the gamma parameters and do not use subscripts.
Cloud hydrometeor sphericity was analyzed with the NIXE-CAPS probe (New Ice
eXpEriment – Cloud and Aerosol Particle Spectrometer; Luebke et al., 2016;
Costa et al., 2017). NIXE-CAPS also contains two instruments, a CIPgs as the
CCP and the CAS-Depol for particle measurements in the size range 0.6 to
50 µm. The sizing principle of CAS-Depol is similar to the CDP; the
difference is the particle probing: while CAS-Depol has an inlet tube
(optimized with respect to shattering), CDP is equipped with an open path
inlet. In addition to the sizing, CAS-Depol is equipped with a detector to
discriminate between spherical and aspherical particles by measuring the
change of the polarized components of the incident light. Spherical
particles do not strongly alter the polarization state, in contrast to
nonspherical ice crystals. The cloud particle phase of the whole cloud
particle size spectrum was analyzed from the combination of phase
determination in the size ranges < 50 µm (from the CAS-Depol
polarization signal) and > 50 µm (from visual inspection of
the CIPgs images) (for details, see Costa et al., 2017). Here, the phase
states are defined as follows: “Sph (liquid)” stands for many only
spherical (D < 50 µm) and predominantly spherical
(D > 50 µm) hydrometeors, “Asph small (mixed phase)” for many
predominantly spherical (D < 50 µm) and only aspherical
(D > 50 µm) hydrometeors, “Asph large (ice)” for only very few aspherical
(D < 50 µm) and only aspherical (D > 50 µm) hydrometeors.
The NIXE-CAPS classification is a separate analysis and will not be
considered as a filter to apply the gamma fits to the CDP measurements. The
CDP data fits are primarily focused on the warm phase and the transition to
the mixed layer, where liquid droplets predominate.
Meteorological conditions, including three-dimensional (3-D) winds, were
obtained with the Basic HALO Measurement and Sensor System (BAHAMAS) located
at the nose of the aircraft (Wendisch et al., 2016). The wind components
were calibrated according to Mallaun et al. (2015), with an uncertainty of
0.2 and 0.3 m s-1 for the horizontal and vertical directions, respectively.
All probes were synchronized with BAHAMAS and operated at a frequency of 1 Hz.
All HALO instruments are listed in Wendisch et al. (2016).
Introducing the gamma phase space
The gamma fit parameters can be plotted in a 3-D subspace where each
parameter (N0, μ, and Λ) represents one dimension. Each
point in this 3-D gamma phase space is defined by one (N0, μ, and
Λ) triplet and thus represents one fitted DSD. This space includes
all possible combinations of gamma parameters of the theoretical variability
in the DSDs.
The 3-D gamma phase space is illustrated in Fig. 3. There are two points in
this figure defined by two location vectors P1 and P2, each one
representing a fit to a specific DSD (see the insert in the left side of
Fig. 3) at different times (t1 and t2 for t2 > t1).
If we consider that P1 and P2
represent the same population of droplets evolving in time (i.e., a
Lagrangian case), we can link the two points by a displacement vector
P = P2 - P1, which can be associated with a pseudo-force
F (blue arrow in Fig. 3). We use the term pseudo-force in order to
illustrate that the growth processes produce displacements in the phase
space. Alternatively, displacements in the phase space can also be
understood as phase state transitions, in which case each phase-state is
related to a DSD. The pseudo-force F can be decomposed into two
components, one related to condensational growth and the other to the
collision–coalescence (collection) process. The respective pseudo-forces are
illustrated as Fcd and Fcl in Fig. 3, respectively.
This approach can be applied to multiple points, defining a trajectory
through the phase space (gray dotted line). The change of the DSD results in
modified gamma parameters, which determine the trajectory through the gamma
phase space. The direction and speed of the displacements forming the
trajectory are determined by the direction and intensity of the underlying
physical processes that modify the DSD (condensation and collection). These
pseudo-forces are defined by properties such as the initial DSD, CCN,
updraft speed, and supersaturation. Of course, this generalization considers
only condensation and collision–coalescence. The pseudo-forces can be
represented with more sophistication in models, including the several
processes involved in DSD changes, such as evaporation, turbulence, melting
from the layer above, breakup, sedimentation, etc. Therefore, these two
processes can be replaced by a number of pseudo-forces as a function of the
level of sophistication of the model. We should remember that this approach
does not consider contributions from other levels because advection is not
directly addressed. To describe the whole process of DSD evolution during
the entire cloud life cycle, the contribution from other layers should be considered.
Conceptual drawing of the properties of the gamma phase space in the
warm layer of the clouds. The dotted gray line represents one trajectory through
the phase space, representing the DSD evolution. P1 is one DSD that grows
by condensation and collision–coalescence to reach P2. The displacement
represented by the pseudo-force F is decomposed into two components – Fcd
(condensational pseudo-force) and Fcl (collisional pseudo-force).
Also shown are the two DSDs representative of points P1 and P2.
Average vertical profiles of potential temperature (a) and
relative humidity (b) for flights over the Atlantic coast, remote
Amazon, and arc of deforestation. The markers in the left vertical axis in (a)
represent the altitude of the 0 ∘C isotherm for the different flights.
Altitudes are relative to cloud base (H, negative values are below clouds).
θ and RH are calculated as averages of level flight legs outside clouds.
The direction of the Fcd pseudo-force in Fig. 3 represents the
transition of the DSD during the condensation process, which favors high
values of μ and slightly increasing Λ. This induces both the
narrowing of and a slight increase in the effective droplet diameter (see
equations in Sect. 2.2) of the DSD, which is expected from conventional
condensation growth theory. Because of the DSD narrowing, the intercept
parameter (N0) is also reduced. Condensational growth may cause a
broadening of the DSD in specific situations such as at the cloud base of
polluted systems. However, this is an exception and most of the time
condensational growth leads to DSD narrowing. The collision–coalescence
pseudo-force acts in a significantly different way in the phase space. From
theory and precise numerical simulations that solve the stochastic
collection equation, it is known that this process leads to DSD broadening
(given the collection of small droplets and breakup of bigger ones) and
faster droplet growth in size (compared to condensation). In the gamma phase
space, it should be reflected in lower values of Λ and μ, the
former decreasing at a faster pace. The intercept parameter N0 can
remain relatively constant or increase because the effects of increased
mean diameter and DSD broadening balance each other. If N0 remains
constant, lower values of Λ and μ result in reduced droplet
number concentration, which is consistent with theory (see Fig. 7).
Gamma phase space for flight M1 over the coastal region. Small markers
represent 1 Hz data, while bigger ones are averages for 200 m vertical intervals.
The continuous black line represents a cubic spline fit for the averaged DSDs
to illustrate its mean evolution. Altitudes are relative to cloud base (H).
Similar to Fig. 5, but for flights RA1 and RA2 over the remote Amazon.
To confirm the overall directions of the pseudo-forces and the
characteristics of the gamma phase space, we performed some calculations
with the Lagrangian model described in Feingold et al. (1999) – see their
Section 3c and references therein. Basically, the model solves CCN
activation (only at cloud base), condensation and collision–coalescence
growth, and the effects of giant CCN on the DSDs (the latter process was
turned off in our runs). The DSDs are sorted into 35 mass-doubling bins from
∼ 3 µm to ∼ 9 mm; thus, the condensation and
collision–coalescence processes are not parameterized as in bulk approaches.
The model was initialized with conditions that mimic flight RA1 (Table 1,
Fig. 4). By performing two runs, one with exclusively condensational
growth and the other with both growth processes, it was possible to isolate
their effects on the DSDs. In the run with both processes active, by the
time the collection was significant the droplets were big enough
(Deff > 25 µm) to grow very slowly by condensation.
Similar to Fig. 5, but for flights AD1, AD2, and AD3 over the arc of deforestation.
From the Lagrangian model runs it was possible to calculate the direction
of the displacements caused by condensation and collision–coalescence growth
in spherical coordinates. For this first introduction of the phase space, we
will focus on the elevation angle φ (from the plane
N0 × μ to the Λ axis) and azimuth angle θ (calculated from the
N0 to the μ axes), when N0, μ, and Λ are in logarithm
(base 10) scale (as in Figs. 5–8). The angles vary depending on the relative
values of N0, μ, and Λ, but the following numbers are provided
as a first estimate. For condensational growth, φ averaged
0.26 ∘ and θ averaged 179.6∘, while they were
-4.23 and -13.7 ∘ for collision–coalescence, respectively.
Note that the angles have opposite signs for the two processes and their
overall direction is the same as exemplified in Fig. 3. The direction of
the displacements remains consistent even when other moments are chosen to
fit the gamma DSDs. For more details on the model runs, refer to the Supplement.
Note that, given the relation between the gamma parameters, the phase space
is non-orthogonal and it is not trivial to mathematically represent the
pseudo-forces. The mathematical treatment of such forces is beyond the scope
of this paper, which intends to illustrate microphysical processes in the
phase space. But this aspect should be considered in potential future
implementations of this methodology in practical applications.
Observed trajectories for the clouds measured over the remote Amazon
during flight RA1 (continuous line) and over the arc of deforestation during
flight AD2 (dashed line). The numbers shown close to the observed trajectories
start at 1 at cloud base and grow with altitude (the respective markers are
colored according to altitude above cloud base, H). Their respective properties
are presented in Tables 2 and 3.
In Sect. 3.2, we show gamma parameters fitted to real DSD observations. As
it is not feasible to follow fixed populations of droplets in a Lagrangian
way with an aircraft, the evolutions we analyze in the gamma space are not
strictly over time. As a compromise, we use the altitude above cloud base (H)
of the measurements instead of time evolution, given the conditions of
the measurements and our data handling. The cloud profiling missions were
planned to capture growing convective elements before reaching their mature
state, which is the reason why they usually started at around 12:00 LT (local
time). Additionally, we only consider DSD measurements in which updraft speed
w > 0 in order to focus on the ascending part of the growing clouds.
Another point to take into consideration are the ellipsoids discussed in
McFarquhar et al. (2015). Basically, by considering the instrument and gamma
fitting uncertainties, it is possible to define volumes (with ellipsoid
shapes) rather than individual points in the gamma phase space. Inside each
ellipsoid, all DSDs are equally realizable and therefore the movements
within it have no particular physical meaning and are statistically the
same. In this study, however, we estimate that the results evolve beyond
individual ellipsoids and the patterns are associated with physical processes.
The results shown in the next sections will not consider the ellipsoid
approach, but the points shown can be considered to be the central points of such volumes.
Results
Aerosol and thermodynamic conditions in different Amazonian regions
The HALO flights are classified according to the region they covered and the
respective aerosol and CCN number concentrations (Table 1). Note the close
link between region of the measurements and the aerosol concentrations. From
the most pristine clouds at the coast to the most polluted cases in the arc
of deforestation, there is a 10-fold increase in NCN. Remote regions in
the Amazon have aerosol particle concentrations slightly higher than over
the coast, which is one of the reasons for the term “Green Ocean” used for
the unpolluted Amazon regions (Williams et al., 2002). Flights AD1, AD2, and AD3
present flight paths progressively shifted to the south, which are
accompanied by increasing values of NCN and NCCN. The farther away
the flights take place from the forest, and consequently closer to developed
regions, the higher the pollution levels.
Cloud profiles started at the end of the morning or beginning of the
afternoon. The flights were specifically planned for this time period
because the convective systems are usually in their developing stages at
this time. The freezing level varied between 4500 and 5000 m, while cloud
base altitudes were more variable (500 to 2000 m), which resulted from the
regional meteorological conditions (Fig. 4), and which affects the
characteristics of the cloud layers. Clouds in the arc of deforestation grow
from drier air, given the diminished evapotranspiration rate, and form
higher in the atmosphere. As a result, there are thinner warm layers in the
polluted clouds, which reduces the time available for droplets to grow by
collision–coalescence. Flight RA2 was characterized by a just slightly
higher depth of the warm layer compared to the polluted clouds, partly due
to the lower altitude of the freezing level. Nevertheless, cleaner clouds
can present warm layers 1000 m thicker than clouds affected by pollution.
The vertical profile of the relative humidity (RH) should also be taken into
account when comparing clouds formed over different regions. Figure 4b shows
that all clouds measured formed in a surrounding environment with a RH between
60 and 90 % for their lower 2500 m layer, with RH being higher for forested
areas compared to the arc of deforestation. For 2500 m and above, there was
a significant drying of the atmosphere for flights M1, RA2, and AD2. It is
not clear if the other flights presented similar behavior given the
relatively low data coverage for this layer. Regardless, surrounding dry air
can significantly enhance the entrainment mixing process (Korolev et al.,
2016). As pointed out by Freud et al. (2008), the mixing in Amazonian
convective clouds (and also in other regions – Freud et al., 2011) tends
toward the extreme inhomogeneous mixing case, in which the effective droplet
diameter Deff presents almost no sensitivity to the entrainment. Our
result largely corroborates this finding (see Fig. 11). It should be
pointed out, however, that the recent studies by Korolev et al. (2016) and
Pinsky et al. (2016a, b) show that homogeneous and
inhomogeneous mixing can be indistinguishable depending on meteorological
conditions and DSD characteristics when considering the time-dependent
characteristics of the entrainment process. Mixing processes may have an
impact on the shape of the DSDs measured, thus affecting displacements in
the gamma phase space. The specific type of mixing responsible for it,
however, is beyond the scope of this work.
Observed trajectories in the gamma phase space
In this study, we use the gamma phase space as a means to study DSD
variability. As described in Sect. 2.3, this space is obtained when the
DSD measurements are fitted to Eq. (1), and N0, μ, and Λ are used
as the dimensions of the 3-D subspace. In this space, each point represents
one DSD. As the different DSDs were obtained close to the cloud top at the
time of the cloud development, the ensemble of positions in the gamma phase
space can be hypothesized as the evolution of the DSDs of a typical cloud
through stages of its life cycle. The sequential connection of points (here
we use cubic spline fits for illustrating purposes) can be considered as
trajectories describing multiple processes responsible for the DSD
variability observed. The advantage of using this space is that this
variability can be readily observed and compared between different cloud
life cycles with different properties. Given the relations between gamma
parameters and DSD properties (Sect. 2.2), the variability in all cloud
microphysical properties can also be inferred from the points in the
trajectories. We limited the analysis regarding cloud DSDs and the gamma
phase space to the regions in which w > 0 in order to capture the
developing parts of the growing convective elements.
Figures 5 to 7 show the gamma phase space for all profiles considered in
this study, grouped by region. The coloring represents the altitude above
cloud base (H), with the 1 Hz measurements shown as small markers. Bigger
markers represent averages at every 200 m vertical interval with available
information. Curves (or trajectories) represent cubic spline fits to the
averaged points. At first glance, it is possible to see stronger differences
between the trajectories in the different regions, while internal variations
are much weaker. Aerosol concentrations seem to be a key factor controlling
warm-phase properties in the Amazon; thus, the internal similarities can be
attributed to similar pollution conditions. Conversely, differences
between the regions stem from the different weights of growth processes.
Pristine clouds, like the ones found over the remote Amazon and the coast of
the Atlantic Ocean, are characterized by faster droplet growth with altitude
associated with enhanced collisional growth. In the gamma space, this is
seen as diagonally tilted trajectories in Figs. 5 and 6, contrasting with
the more vertical trajectories found in polluted clouds (Fig. 7).
Properties of the points highlighted in Fig. 8 for flight RA1. H is
shown as the average of each of the 200 m vertical bins. The adiabatic fraction
is defined as the ratio between the observed and adiabatic LWC.
Point
H
Nd
LWC
ε
Deff
T
UR
w
Adiabatic
(m)
(cm-3)
(g m-3)
(µm)
(∘C)
(%)
(m s-1)
fraction
1c
100
214
0.079
0.19
9.2
19.9
81
0.84
0.31
2c
300
238
0.15
0.22
11.1
18.6
82
0.91
0.22
3c
500
218
0.25
0.24
13.8
17.5
83
1.43
0.30
4c
700
227
0.34
0.28
15.2
16.6
77
1.41
0.28
5c
1100
245
0.61
0.27
18.0
13.6
85
1.13
0.31
6c
1300
284
0.79
0.29
18.9
12.0
80
1.03
0.34
7c
1700
231
0.79
0.28
20.1
10.6
71
1.49
0.28
8c
2300
187
1.21
0.27
24.7
7.1
78
1.66
0.34
9c
3100
233
1.95
0.22
26.4
3.5
64
2.79
0.47
10c
3900
54
0.61
0.34
30.9
-1.2
39
1.08
0.13
11c
4100
49
0.31
0.36
25.6
-1.8
61
0.31
0.065
12c
4700
36
0.26
0.47
28.6
-4.8
67
1.30
0.053
13c
5300
39
0.42
0.40
31.4
-8.1
26
2.39
0.083
14c
5900
30
0.16
0.48
26.4
-11.4
33
3.27
0.032
Properties of the points highlighted in Fig. 8 for flight AD2. H is
shown as the average of each of the 200 m vertical bins. The adiabatic fraction
is defined as the ratio between the observed and adiabatic LWC.
Point
H
Nd
LWC
ε
Deff
T
UR
w
Adiabatic
(m)
(cm-3)
(g m-3)
(µm)
(∘C)
(%)
(m s-1)
fraction
1p
100
528
0.11
0.37
8.4
16.3
72
1.17
0.59
2p
300
960
0.27
0.31
8.8
15.5
64
1.02
0.72
3p
500
634
0.21
0.28
9.2
14.7
58
1.28
0.29
4p
700
597
0.29
0.27
10.4
12.4
59
0.57
0.24
5p
1300
543
0.34
0.29
11.5
6.9
65
1.13
0.15
6p
1900
1066
1.12
0.29
13.7
2.6
69
0.74
0.38
7p
2100
874
0.75
0.31
12.8
2.4
62
2.89
0.26
8p
2700
477
0.62
0.32
14.8
0.4
8
1.62
0.17
9p
2900
1271
1.95
0.32
15.7
0.2
5
9.36
0.52
10p
3300
1024
1.78
0.24
15.7
-1.5
3
5.68
0.44
11p
3700
137
0.25
0.24
16.0
-3.6
4
0.26
0.06
The differences in the DSD variability in each region highlight the relation
of growth processes and trajectories in the gamma phase space. From the
theory described in Sect. 2.3, it is expected that collisional growth
results in diagonal trajectories where the droplets get progressively bigger
with DSD broadening. Pristine clouds over the coast and remote Amazon show
such tilting (Figs. 5 and 6), indicating that this process is effective in
these systems. The more vertically oriented trajectories of polluted clouds
(Fig. 7) show that there is a different balance between condensational and
collisional growth. In terms of the gamma phase space characteristics, this
can be understood as weaker Fcl as a result of smaller droplets
and narrower DSDs. This highlights that the interaction between aerosols and
collisional growth occurs mainly through changes in the initial DSD (i.e.,
P1 in Fig. 3). For each point in the gamma phase space the collisional
pseudo-forces have different intensities and directions, suggesting that a
vector field can be constructed. This could only be achieved with idealized
model experiments, however, where the updraft speeds can also be prescribed.
Condensational growth can also be illustrated by some points in Figs. 6
and 7. Under polluted conditions, this type of growth is expected to be
dominant close to cloud base where the droplets are too small to trigger
collision–coalescence. In Fig. 7, this is seen in the first two or three points
in the trajectories (dark blue colors), where the points evolve to higher
μ values with altitude. This results in DSD narrowing and almost opposite
displacement in the gamma space compared to collisional growth. This trend
is shifted when the altitude at which collection processes start to
become relevant is reached. Another example of condensational growth can be seen in
Fig. 6 at 3000 m. At this point, which is close to the freezing level,
there is a sudden increase in the updrafts (see Tables 2 and 3) and
consequently increased condensation rates. The rapid increase in
condensational growth, with no significant changes in collision–coalescence,
tilts the trajectories to a direction similar to that observed close to
cloud base in polluted systems. The displacement is closer to the horizontal
direction (i.e., the plane N0 × μ), because droplets grow
concomitantly by collision–coalescence in the cleaner clouds.
The magnitude of the condensational pseudo-force (Fcd in
Fig. 3) also depends on the initial DSD characteristics (P1). Condensational
growth rates are inversely proportional to droplet size, meaning that they
get weaker higher in the cloud. The different dependences of Fcd
and Fcl on P1 and their balance throughout the warm-phase
life cycle ultimately define the cloud trajectory in the phase space. If
they can be mapped with sufficient resolution, covering different updraft
and supersaturation conditions, trajectories may be forecast from a single
DSD at cloud base and the evolving thermodynamic conditions. Aerosols are a
key aspect in this regard because they significantly change the
cloud base DSD in the gamma space (Figs. 5–7) and also affect cloud
thermodynamics, impacting condensation rates and consequently latent heat
release. Note that clouds subject to similar aerosol conditions have
similarities in their trajectories represented by small variability along
the trajectories of the respective flights (Figs. 6 and 7).
The Fcd and Fcl tabulation over the gamma space can
potentially be achieved with the help of Lagrangian large-eddy-simulation
bin-microphysics models that precisely solve the condensation and collection
equations for varying input DSDs and updraft conditions. Initial DSDs can be
obtained from observations and analytical considerations. For instance,
Pinsky et al. (2012) show an analytical way to obtain the maximum
supersaturation (which is usually a few meters above cloud base) and the
relative droplet concentration. If Deff behaves adiabatically (Freud et
al., 2008; Freud et al., 2011) and is linearly correlated to the mean
volumetric diameter (Freud and Rosenfeld, 2012), it is possible to estimate
the initial DSD based on gamma DSD equations and adiabatic theory given that
the aerosol population is known. The advantage of such an approach is that all
DSD characteristics, most notably the shape, would be realistically
represented and there would be no need for fixing or diagnosing (Thompson et
al., 2004; Milbrandt and Yau, 2005; Formenton et al., 2013a, b) gamma
parameters for various hydrometeor types – which works for specific
applications but may be lacking the physical representation of the
processes. This study focuses on introducing the gamma phase space and its
characteristics, and further work is needed if new parameterizations are to be developed.
Contrasts between clean and polluted trajectories
In this section, we focus on flights RA1 and AD2 in order to study the
differences between natural and human-affected clouds in the gamma space.
Figure 8 shows the trajectories of the clouds measured during these flights,
where the points related to the averaged DSDs are numbered and the
corresponding properties are shown in Tables 2 and 3. The numbers start at
1 close to cloud base and grow with altitude (“p” stands for polluted,
while “c” is for clean). Also presented in Tables 2 and 3 are the
adiabatic fractions that correspond to the ratio between the observed and
adiabatic LWC. Some observed DSDs and their corresponding gamma DSDs are
shown in Fig. 9, highlighting different growth processes.
Averaged DSDs and their respective gamma fittings for some points in
the trajectories of clouds measured over (a) the remote Amazon (flight RA1)
and (b) the arc of deforestation (flight AD2).
It is clear from Fig. 8 that clean and polluted clouds cover different
regions of the gamma phase space. Nevertheless, it is possible to see that
the trajectories can evolve almost in parallel depending on the dominant
growth process. Polluted clouds have wider DSDs at cloud base because of the
tail to lower diameters (Fig. 9), which brings down the value of μ
(see Eq. 9). Given the lower droplet size (Table 3), condensation is
efficient and the trajectories evolve in the overall direction of
Fcd illustrated in Fig. 3. From points 1p to 2p, Nd and
LWC are approximately doubled. Condensational growth seems to be the dominant
growth process in the polluted clouds up to the point 3p, corresponding to a
cloud depth of 600 m. A similar layer does not exist in cleaner clouds,
where there are enough big droplets to readily activate the
collision–coalescence growth. Collisional growth dominates the DSD shape
evolution between points 1c and 6c for flight RA1 and between 4p and 7p for
AD2. Note that the trajectories are almost parallel in this region.
Condensation is still active in this period given the increasing LWC, but
collision–coalescence has a comparatively bigger impact on the overall DSD
shape. Both sections of the trajectories represent 1400 m thick layers, but
droplet growth and DSD broadening is more efficient in the cleaner clouds
(Fig. 9). This explains the pronounced tilting of its trajectory,
consistent with a stronger Fcl pseudo-force.
Eventually, the trajectories reach a point close to the 0 ∘C
isotherm where the updrafts are enhanced given the continued latent heat
release. This w-enhanced layer can be several hundred meters thick and
culminates in narrower DSDs. This is exemplified between points 7c and 9c
and between 8p and 10p. Although droplets still grow by
collision–coalescence, the enhanced updrafts increase condensational growth
sufficiently to produce observable effects on the DSDs. Both trajectories
evolve in the condensational growth direction, but with slightly different
tilting. The tilting is less pronounced in the cleaner clouds given the
stronger Fcl component. The way in which the DSDs evolve in this
region is important for the mixed-phase initiation, given that both primary
and secondary ice generation depend on the characteristics of the liquid
droplets. The different properties of the polluted and clean DSDs (see
Tables 2 and 3, Figs. 8 and 9) indicate that ice formation may follow distinct pathways.
Previous studies suggest that droplets bigger than 23 µm at
concentrations higher than 1 cm-3 favor secondary ice generation, which
was identified as the main mechanism for cloud glaciation (Mossop, 1978;
Saunders and Hosseini, 2001; Heymsfield and Willis, 2014; Lawson et al., 2015).
In order to visualize these conditions in the gamma phase space, it is
interesting to consider constant Nd surfaces. These surfaces are defined
when Nd is fixed in Eq. (6), resulting in a relation of the form
Λ = f(N0μ) when inverted. Examples are shown in Fig. 10,
where Nd = {10, 100, 1000} cm-3
(axes are rotated for clarity). The surfaces are evidently parallel and are
stacked in relatively close proximity (on the scale used here). The
trajectories evolve through the surfaces depending on their Nd, where
polluted clouds tend toward higher droplet concentration (i.e., closer to
the red surface). These surfaces can be used to delimit specific regions of
interest. Additionally, further DSD properties can be analyzed along these
surfaces. Figure 10 highlights the region of 23 µm < Deff < 50 µm with black lines along the surface of
Nd = 10 cm-3. The purple ellipse represents an estimate of the
size of the ellipsoids introduced by McFarquhar et al. (2015). For the
calculation of the ellipse, we considered that the 10 % error in the CDP
measurements translates to 10 % error in Nd, Deff, and
ε. Under those conditions, the size of the ellipsoids can be
represented by the purple ellipse in Fig. 10. Note that its dimension in
the normal direction from the Nd surfaces is very small (1/100 of the
distance between the surfaces shown); that is why we only show an ellipse
rather than an ellipsoid. This simple estimate is meant to find the order of
magnitude of the ellipsoids of McFarquhar et al. (2015) and it shows that
the trajectories are not just random displacement inside one ellipsoid (the
trajectories evolve beyond them).
Regarding cloud DSDs (drizzle droplets are not analyzed here, although they
also contribute to ice formation), the region delimited by the black lines
for the different surfaces of constant Nd can be interpreted as the most
favorable for secondary ice generation, thus indicating a quick glaciation
process. Note that the trajectory of the cleaner clouds enters this region
while in the w-enhanced layer mentioned previously, which corresponds to the
transition to temperatures below 0 ∘C. Polluted clouds are able
to produce high droplet number concentrations, but their smaller droplet
size means that they are out of the delimited region. More details about the
transition to the mixed phase are given in the next section.
Surfaces of constant Nd as calculated by the inversion of
Eq. (6). The trajectories for the clouds measured during flights RA1 (blue)
and AD2 (red) are also shown. Note that the axes are rotated for clarity. The
purple ellipse represents an estimation of the size of the ellipsoids introduced
by McFarquhar et al. (2015) – see text for more details.
The observation of constant Nd surfaces poses an interesting question
for parameterizations. In existing two-moment schemes, both Nd and LWC are
predicted. For each pair of such properties, it is possible to define two
surfaces (with constant Nd and LWC) based on Eqs. (6) and (7).
These surfaces intersect, defining a curve where both properties are
conserved. In this curve, the mean volumetric diameter (proportional to the
ratio between LWC and Nd) is also constant. Based on the limited
information provided by the model (only two moments for three gamma
parameters), this curve represents the infinite DSD solutions for the
undetermined equation system. A good parameterization scheme should be able
to choose one of the DSDs that best fits observations. Given the
undetermined equation system, other considerations have to be made.
One parameter that varies along the infinite DSD solution curve is the
relative dispersion ε. If ε can be constrained in
the model, it should be possible to obtain the full gamma DSD – which is
the point in the intersection curve that presents the given ε.
The advantage of relying on ε is that it has low variability
between clean and polluted clouds and its average is almost constant with
altitude. Tas et al. (2015) studied the relative dispersion parameter in
detail, noting that averaged values for ε were independent of
Nd, LWC, or height, but its variability is significantly lower for the most
adiabatic portions of the cloud (notably its updraft core). For precise
parameterizations, ε variability should be taken into account
in regions with relatively low Nd and LWC, but averaged values may be
considered for the updraft cores. Our observations show that ε is
slightly higher in polluted Amazonian clouds compared to the ones
measured over remote regions mainly because of their reduced droplet size
(Tables 2 and 3). This can be considered to produce slight corrections to
ε based on CCN number concentrations.
Observations of the mixed-phase formation
The gamma phase space provides an insightful way to study the formation of
the mixed phase by providing the history of the warm-phase development as a
trajectory. Liquid cloud droplet properties are important for the glaciation
process because they determine the probability of contacting INPs and the conditions for secondary generation. As shown in
the previous sections, different aerosol and thermodynamic conditions alter
warm-phase characteristics and can thus impact the early formation of ice in the clouds.
Figure 11 shows vertical profiles of Nd, LWC, Deff, and
ε for clouds subject to background and polluted conditions
(flights RA1 and AD2, respectively). It shows the different microphysical
properties (1 Hz) of the clouds associated with the trajectories presented
in Figs. 8 to 10 (w > 0). It shows that droplet concentrations
are much higher in polluted clouds, which are not depleted with altitude as
much as cleaner clouds (Fig. 11a and b). The lower effective diameter for
clouds over the arc of deforestation may contribute to enhanced evaporation,
leading to lower adiabatic fractions. As commented in the previous section,
ε shows small variations between the flights and does not change
much with altitude.
The properties of the DSDs around the 0 ∘C level in Fig. 11 are
a significant feature regarding the mixed-phase formation. Note that cleaner
clouds have a sudden change in behavior right above the freezing level. At
this point, there is a fast decrease in LWC, with higher variability in both
Deff and ε. This suggests that ice processes have been
triggered, disrupting the smooth evolution observed in the warm phase. In
polluted clouds, this transition takes place at considerably different DSD
properties. Averaged Nd reaches values above 1000 cm-3 (compared to
50 cm-3 in cleaner clouds) with very strong updrafts, bringing LWC
closer to adiabaticity. However, no significant variability was observed for
Deff, suggesting that most of the water is still in a condensed state.
Vertical profiles of the 1 Hz measurements of Nd, LWC,
Deff, and ε for background clouds over the remote
Amazon (a, c, e, g) and polluted clouds over the arc of deforestation (b, d, f, h).
Updraft speeds are colored in log scale, corresponding to 0.1 ≤ w ≤ 5 m s-1.
Horizontal black lines mark the 0 ∘C level. Magenta curves in (c)
and (d) are the adiabatic water content profiles. H is relative to
cloud base altitude.
In order to further detail the characteristics of the hydrometeors in the
transition from warm to mixed phase, we analyzed the sphericity criteria
obtained with the NIXE-CAPS probe (Costa et al., 2017). The methodology
developed by Costa et al. (2017) indicates whether each individual 1 Hz
measurement contained some aspherical hydrometeors or not. This criterion
can be used to indicate whether the hydrometeors are liquid (spherical),
mixed (spherical and aspherical), or frozen (aspherical). By combining all
measurements for clouds over the remote Amazon (RA1 and RA2) and the arc of
deforestation (AD1, AD2, and AD3), we obtained the results shown in Fig. 12.
Frequency of occurrence of NIXE-CAPS sphericity classifications for
(a) the remote Amazon and (b) the arc of deforestation.
“Sph (liquid)” stands for many only spherical (D < 0 µm) and
predominantly spherical (D > 50 µm) hydrometeors, “Asph small
(mixed phase)” for many predominantly spherical (D < 50 µm)
and only aspherical (D > 50 µm) hydrometeors, and “Asph large
(ice)” for only very few aspherical (D < 50 µm) and only
aspherical (D > 50 µm) hydrometeors. Temperatures shown on the
x axis are the center for 6 ∘C intervals, which corresponds to roughly
1 km thick layers.
The classifications shown in Fig. 12 separate the volumes probed as
containing only spherical hydrometeors (Sph (liquid)) or if there are
also aspherical particles too. In that case, the data are further divided
into containing both small (D < 50 µm) spherical and large
aspherical particles (D > 50 µm) – Asph small (mixed phase) – or
if there are only large (D > 50 µm) aspherical
particles – Asph large (ice). It is possible to observe that close to
cloud base most of the hydrometeors were detected as spherical for both
regions, which is expected given that it is the warmest layer of the cloud.
However, higher in the clouds the distribution of the classifications becomes
different. The number of measurements with aspherical particles increases
relatively fast for the cleaner clouds, being higher than 90 % at the
layer around 0 ∘C. For polluted clouds, however, almost
half of the measurements contained exclusively spherical hydrometeors at
this level. Exclusively spherical hydrometeors persisted with a frequency of
∼ 20 % down to temperatures of -15 ∘C. This is in line
with previous studies that found supercooled droplets high into continental
convective systems (Rosenfeld and Woodley, 2000; Rosenfeld et al., 2008).
Our results show that the persistence of supercooled droplets in Amazonian
clouds is more likely under polluted conditions.
The characteristics of the cloud warm layer determine the properties of the
liquid DSDs close to the 0 ∘C level and should have a determining
role in the glaciation initiation. Our measurements show that clean clouds
can produce droplets roughly twice the size of the ones found in polluted
systems at this layer, at 95 % lower droplet concentrations (Tables 2 and 3).
Bigger droplets are not only more likely to interact with INPs and
glaciate by immersion or contact freezing, but may also trigger a cascading
effect through secondary ice generation (Heymsfield and Willis, 2014; Lawson
et al., 2015). This process is able to quickly glaciate the cloud, which
fits the results shown in Fig. 12. Beyond the DSD bulk properties, the
gamma phase space can also provide more information regarding the kind of
DSD that enables or inhibits the glaciation process. In the present study,
we have only a few examples to compare warm- and mixed-phase
characteristics, but it is clear that it is possible to correlate some
regions of the phase space with the characteristics of the ice initiation.
Detailed model experiments would greatly enrich this discussion by providing
control over the liquid DSD properties and the resulting formation of the
mixed layer. More specifically, it would be invaluable to study the impacts
of the properties of DSDs at cloud base and at the 0 ∘C isotherm
on the primary and secondary ice production.
Concluding remarks
Despite being widely adopted in many modeling and remote sensing
applications, there is almost no study analyzing the evolution of cloud
droplet size distributions in gamma phase space. Here, we introduce this
visualization, defined by the intercept, shape, and curvature of the gamma
curve, which is parameterized by obtaining the moments of the orders zero, two,
and three. We show that trajectories in the space are related to DSD
evolution and are linked to microphysical processes taking place inside the
cloud. These processes can be understood as pseudo-forces in the phase space.
Measurements over the Amazon during the ACRIDICON–CHUVA and GoAmazon2014/5
campaigns show that it is possible to relate the direction of the
pseudo-forces to different DSD growth processes. Cloud layers with strong
updrafts and consequently relatively strong condensational growth showed
that this process induces displacements in the direction of high shape and
curvature parameters. This tendency is accompanied by DSD narrowing,
consistent with condensational growth theory. Conversely,
collision–coalescence, observable in clean clouds over the Amazon, favors
displacements in roughly the opposite direction. Observed displacements in
the warm phase may be interpreted as a combination of both pseudo-forces.
The gamma phase space can also be used as a diagnostic tool for cloud
evolution. By studying the displacements in the warm phase, it is possible
to determine regions that favor, for instance, cloud glaciation. Previous
studies have identified cloud conditions that favor rapid secondary ice
generation, which can be translated into the phase space. We show that clean
clouds over the Amazon evolve into the region that favors secondary ice
generation because of the enhanced collisional growth. Droplets in polluted
clouds take much longer to grow by warm processes and they cross
0 ∘C long before reaching the region favorable for glaciation. This
leads to the persistence of supercooled droplets higher in the clouds, which
interact with other ice processes including sublimation to produce big ice
particles through the Wegener–Bergeron–Findeisen mechanism. In this regard,
the gamma phase space approach proves to be an interesting tool to analyze
the relation between warm microphysics and the evolution of the mixed phase.
More studies are encouraged in that direction, especially in modeling
scenarios given the difficulties in the prediction of mixed-phase processes.
We propose that the gamma space can be used to both evaluate current
parameterization and steer the development of new ones. The results
presented here show that different types of clouds have different
trajectories through the gamma phase space. The aerosol effect seems to play
a major role in the trajectories of the warm layer. The ability of current
parameterizations to reproduce such aspects can be tested in the phase
space, where artificially produced DSDs would be apparent. For new
two-moment parameterizations, the gamma space can be used to constrain the
DSD from the given droplet concentration and liquid water content. For each
pair of these properties, the possible DSD solutions lie on a curve in the
gamma space where the main differentiating factor is the distribution
relative dispersion. Observations such as the ones shown here and in
previous studies can be used to find the appropriate relative dispersion
value to find the optimal solution. Additionally, precise bin microphysics
simulations can be used in order to produce full condensational and
collisional pseudo-force fields in the space. The fields would be dependent
on the evolution of properties such as aerosol concentration, updraft speed,
and supersaturation conditions. With such a tabulation, bulk microphysical
models would only need to predict the initial DSD close to cloud base and
the rest would be determined with the pseudo-force fields.
This paper shows just an initial view of potential applications of the gamma
space. Future efforts are encouraged in order to test its efficiency and
adequacy. Currently, we are performing bin microphysics simulations in a
column model to compare different closures in bulk schemes. Additionally, we
are in the process of testing the use of the gamma space in a nowcasting
scenario based on dual-polarization radar retrievals.