The impact of aerosols on cloud properties is one of the largest
uncertainties in the anthropogenic radiative forcing of the climate.
Significant progress has been made in constraining this forcing using
observations, but uncertainty remains, particularly in the magnitude
of cloud rapid adjustments to aerosol perturbations. Cloud liquid
water path (LWP) is the leading control on liquid-cloud albedo, making
it important to observationally constrain the aerosol impact on LWP.
Previous modelling and observational studies have shown that multiple
processes play a role in determining the LWP response to aerosol
perturbations, but that the aerosol effect can be difficult to isolate.
Following previous studies using mediating variables, this work investigates
use of the relationship between cloud droplet number concentration
(Nd) and LWP for constraining the role of aerosols. Using
joint-probability histograms to account for the non-linear relationship, this
work finds a relationship that is broadly consistent with previous studies.
There is significant geographical variation in the relationship, partly due
to role of meteorological factors (particularly relative humidity).
The Nd–LWP
relationship is negative in the majority of regions, suggesting that
aerosol-induced LWP reductions could offset a significant fraction of the
instantaneous radiative forcing from aerosol–cloud interactions (RFaci).
However, variations in the Nd–LWP relationship in response to
volcanic and shipping aerosol perturbations indicate that the
Nd–LWP relationship overestimates the causal Nd impact
on LWP due to the role of confounding factors. The weaker LWP reduction
implied by these “natural experiments” means that this work provides an
upper bound to the radiative forcing from aerosol-induced changes in the LWP.
Introduction
Atmospheric aerosols are known to affect the radiative balance of the
atmosphere, both through a direct interaction with radiation and via indirect
interactions with cloud properties . As almost all liquid
cloud droplets form on an aerosol particle, changing the number and
composition of aerosol particles can change the concentration of cloud
droplets (Nd) in a cloud, leading to changes in the cloud
brightness and possibly also leading to changes in the cloud
fraction (CF or fc) and possibly also to changes in
liquid water path (LWP or L) through an impact on precipitation
e.g.. Estimates of radiative forcing due to changes in
cloud properties vary significantly between different global climate models
, highlighting the need for observational
constraints on the impact of aerosol on cloud properties.
Unlike greenhouse gases, aerosol properties vary strongly in space and time.
The co-variation in aerosol and
cloud properties in the present-day atmosphere has been used to infer the
impact of aerosols on cloud properties e.g.. Such observed relationships have been used to estimate the
instantaneous radiative forcing (RFaci) from a change in Nde.g. and of the
aerosol-induced change in CF . As the leading order term for determining cloud albedo
, it is also vital to constrain aerosol effects on the
in-cloud LWP, separate from changes in the CF. Existing studies show a mixed
picture; while some models
and observational
studies suggest an increase in LWP with
increasing aerosol, other studies
find a
reduction in LWP as aerosol increases. Some studies find both an increase and
a decrease in LWP, depending on the meteorological conditions
, while other
studies suggest a very weak LWP response to aerosol
. The main aim of this work is to reconcile these
previous studies and develop a constraint on the aerosol impact on LWP.
Isolating an aerosol effect
The key difficulty in interpreting observed aerosol–cloud relationships is
separating the causal impact of aerosols (the change in LWP caused by an
aerosol perturbation) from the confounding role of local meteorology
e.g. and retrieval errors e.g..
Relative humidity in particular has been shown to obscure the causal
relationship between aerosol optical depth (AOD) and CF
. As many cloud properties are correlated to
CF, the factors that obscure the aerosol–CF relationship can also confound
other aerosol–cloud relationships, even those involving “intrinsic” cloud
properties , such as cloud top pressure
and LWP . Recent work
has suggested that the use of a mediating variable such as Nd can
be used to account for the confounding influence of relative humidity.
Following from this, the potential of the Nd–LWP relationship to
constrain the aerosol impact on LWP is investigated in this work.
Similar to the aerosol–LWP relationship, where both potential aerosol
effects and confounders can influence the strength of the relationship,
several effects may influence the observed Nd–LWP relationship.
Aerosol effects. An increased aerosol concentration is
likely to increase Nd. This increase in Nd may affect cloud
processes and in turn modify the LWP. There are several
hypothesised pathways for a causal effect of aerosol on LWP, varying
in relative strength with the local meteorological conditions and
aerosol environment:
Precipitation suppression – an increased
Nd at initially unchanged LWP implies reduced cloud droplet
sizes, suppressing the formation of precipitation. This reduction
in the cloud water loss to precipitation could subsequently
increase cloud depth and thus LWP. While it has
been demonstrated that a reduction in droplet size suppresses
precipitation , it is not clear how strongly this
impacts LWP.
The sedimentation–entrainment feedback –
the reduction in droplet radius from increased
Nd reduces the sedimentation flux in stratiform clouds,
concentrating liquid water in the entrainment zone at the cloud
top and increasing cloud-top evaporative and radiative cooling,
increasing the entrainment rate. This increases the evaporative
cooling in a positive feedback that depends on the above-cloud
relative humidity, with drier air above cloud tops implying a
larger LWP decrease. Negative Nd–LWP relationships in recent
observational studies were suggested to have been due to this
effect .
Evaporation–entrainment feedbacks –
smaller droplets have a faster
evaporation timescale, enhancing the cooling and hence the
negative buoyancy at the edge of cumulus clouds. This intensifies
the horizontal buoyancy gradient, increasing entrainment and hence
evaporation, reducing the LWP with an expected similar
meteorological dependency to E1b. Aircraft observations have
found increased horizontal buoyancy gradients and reductions in
cloud liquid water content (LWC) in polluted clouds
.
Warm cloud invigoration – when Nd is low, a
lack of droplet surface area slows the cloud LWC growth, increasing the local supersaturation. In this Nd-limited state, increasing the Nd in polluted clouds increases
the LWC and thus the latent heat release, allowing the cloud to
achieve a larger vertical extent, which may increase the LWP.
Retrieval errors. The MODIS LWP and Nd both depend on
the retrieved cloud top droplet effective radius (re) and cloud
optical depth (τc) and involve assumptions of varying
validity e.g..
Random errors in the retrieval of cloud properties (τc,
re) becoming correlated errors in Nd and LWP – using Nd
and LWP calculated using the adiabatic assumption, random errors
in τc will generate a positive Nd–LWP sensitivity
dlnLdlnNd=2, while errors in re
will generate a negative sensitivity dlnLdlnNd=-0.4; see Appendix A for details.
Sub-adiabatic clouds – both the LWP and the Nd retrieval
make assumptions about the adiabaticity of clouds. Variations in
the adiabaticity , even across a single cloud, can
therefore generate a positive Nd–LWP sensitivity dlnLdlnNd=2.
Other systematic retrieval errors – systematic biases in re
and τc (particularly in broken-cloud regions) may also
affect the Nd–LWP relationship. Other possibilities include
variations in the vertical distribution of cloud water,
assumptions about the droplet size spectrum, a dependence on
satellite and solar zenith angle ,
and non-linearities in the retrieval .
Feedbacks. A change to the LWP may affect Nd,
obscuring the causal impact of Nd on LWP. This feedback may
depend on other meteorological parameters, generating an apparent
dependence on local meteorology in the observed Nd–LWP
relationship. The existence of strong feedbacks can make using a
mediating variable to account for meteorological covariation
problematic .
Wet scavenging feedbacks – for a given Nd, precipitation preferentially occurs at high LWP. Precipitation scavenging of aerosol can reduce the amount of
aerosol available for future activation to cloud droplets,
reducing Nd. Conversely, if an increased Nd decreases the
precipitation rate, this could result in a further increase in
the Nd through a reduction in wet scavenging and an increase in
the available aerosol (a positive feedback).
The impact of entrainment on the retrieved Nd – the
retrieved Nd depends on the re and the impact of entrainment
on re depends on the mixing type. Extreme inhomogeneous mixing
leads to a reduction in Nd and LWP, but no
immediate change in the droplet size distribution and hence no
change in the re or the retrieved Nd. In contrast,
homogeneous mixing reduces the LWP and the re,
leading to an increase in the retrieved Nd. Increased dry air
entrainment would produce a larger change in retrieved Nd (and
LWP), generating a negative Nd–LWP relationship due to
fluctuations in entrainment where homogeneous mixing
dominates. This effect could decouple the cloud-top Nd (where
it is retrieved) from the activated Nd at cloud base.
Additional confounders. Although using Nd as a
mediating variable helps to account for the impact of RH on the
aerosol–LWP relationship, additional meteorological confounders,
impacting both Nd and LWP, may still impact the Nd–LWP
relationship, obscuring the causal impact of Nd on LWP. An
example case could be a convergence situation that leads to high
moisture values (high LWP) and high updraught values (high Nd, even at
constant aerosol). In addition, through the aerosol impact on Nd,
covariations between aerosol and LWP (due to changes in air mass)
could also create an Nd–LWP relationship, obscuring the causal
Nd impact on LWP.
These effects are depicted in Fig. . To constrain the causal
aerosol influence on LWP, the impact of E1 has to be identified and isolated
from that of E2–E4. This would allow the aerosol impact on LWP to be
constrained using the Nd–LWP relationship.
A simplified picture of the Nd–LWP system, showing
factors impacting the causal relationship (“E1”) – potential
meteorological confounders and retrieval errors (“E2”, “E4”), LWP
dependent controls on Nd (“E3”) and the impact of aerosols on
Nd (CCN).
It is necessary to understand the role of these different processes on the
Nd–LWP relationship in order to determine the impact of aerosols
on the LWP. Using a variety of different satellite retrievals along with
reanalysis data, the Nd–LWP relationship is investigated globally
and the impact of meteorology is explored. To understand the role of
feedbacks (E3) and additional confounders (E4), natural experiments are used
to examine the Nd–LWP relationship in regions where there is a
strong aerosol perturbation. Finally, the observed relationship is converted
to a radiative forcing, allowing it to be compared to other observational
studies and to be used for further analysis of the aerosol impact on clouds
and the climate.
Methods
This work is based on observational data from the Aqua satellite,
specifically the Moderate Resolution Imaging Spectroradiometer (MODIS), the
Advanced Microwave Scanning Radiometer for EOS (AMSR-E), and the Clouds And The
Earth'S Radiant Energy System (CERES) instruments for a 3 year period
(2007–2009 inclusive).
Nd is retrieved using the level-2 collection-6 MODIS cloud property
dataset (MYD06_L2) at a 1 km by 1 km resolution, making use of the
adiabatic assumption . Following the work of
and , the Nd is filtered to
include only liquid, single-layer clouds with a top warmer than 268 K at
1 km resolution. In addition, pixels with an optical depth smaller than 4 or an effective radius less than 4 µm are excluded due to
the uncertainty of these retrievals . Pixels with a 5 km
cloud fraction less than 0.9 are excluded to remove pixels close to cloud
edges, and only pixels with a solar zenith angle of less than 65∘ and
a sensor zenith angle of less than 41.4∘ are used to reduce the
impact of known biases . Finally,
only pixels with an inhomogeneity index (Cloud_Mask_SPI) of less than 30
are used to account for biases in the effective radius (re) in
inhomogeneous scenes . Trials using a more stringent upper
limit of 10 show little difference to the results presented here (not shown).
The Nd is gridded to a 1∘ by 1∘ resolution and,
finally, the condensation rate temperature correction from
is applied.
The MODIS LWP is gridded to a 1∘ by 1∘ resolution from
MYD06_L2, selecting only liquid, single-layer clouds with tops warmer than
268 K. The extra filtering applied to the Nd is not applied to the
LWP at the pixel resolution as the LWP is less sensitive to re
biases and this filtering would significantly bias the LWP against AMSR-E by
selecting primarily high LWP scenes. However, only 1∘ by 1∘
grid boxes with an Nd retrieval are retained for this analysis,
resulting in an implicit filtering by satellite and solar zenith angles.
As both the MODIS LWP and Nd rely on the adiabatic assumption and
the same retrieved cloud properties, there is a significant potential for
errors in these properties due to failures of the adiabatic assumption
and consequent correlated errors generating a
Nd–LWP relationship (E2b). The Nd retrieval is better
able to deal with non-adiabatic clouds than the effective radius retrieval
alone . For the majority of this work, the LWP is
determined using V6 of the AMSR-E Ocean product , a passive
microwave product that does not depend on the adiabatic assumption. Clear-sky
bias corrections are applied following at the pixel level.
As the wind speed and sea surface temperature retrievals are unreliable in
precipitating scenes, they are interpolated to precipitating locations by
fitting a cubic mesh . To determine the in-cloud LWP, the AMSR-E
LWP is divided by the MODIS cloud retrieval CF at the AMSR-E
pixel level (14 km), with pixels having a CF of less than 10 % being
excluded due to the large uncertainty in the resulting in-cloud LWP. Finally,
the AMSR-E data are gridded from the sensor footprint of 14 km to a
1∘ by 1∘ resolution.
As a linear sensitivity dlnLdlnNd is not able to fully describe the non-linear relationship
between Nd and LWP, a piecewise relationship of the form
(Eq. ) is used. Lp and Ndp are
the LWP and Nd values at the intersection between the two parts of
the curve, while ml and mh are the gradients of the fit
for the low- and high-Nd portions of the curve. This curve is fit
to the Nd–LWP joint-probability histogram (P(L|Nd)),
using the Levenberg–Marquardt algorithm in log–log space . By fitting to the joint-probability histogram, each
Nd bin is given equal weight, rather than the weighting by the
present-day Nd probability distribution implicit in the standard
linear regression. This leads to a clearer picture of the overall form of the
relationship, as the shape of the relationship does not change as the
Nd distribution changes as might happen due to anthropogenic
aerosol emissions;. Note that this method, using
“snapshots” of cloud fields, restricts the analysis to inferring
information about cloud development, rather than studying their evolution
directly e.g..
To convert a change in LWP to a change in top-of-atmosphere radiation, data
from the CERES 1∘ daily Single Scanner Footprint Edition 4 dataset are
used . The all-sky albedo from CERES (α) is
shown in a histogram as a function of the CF (fc), LWP and Nd,
creating a single, global, joint-probability histogram
(Pα|fc,L,Nd). Given the retrieved cloud
properties for a location (fc, LWP and Nd), this
histogram produces a distribution of consistent values of the all-sky albedo
(P(α)). This can be used to calculate the mean oceanic albedo to
within 1% in the tropics, with an RMS error in the tropics of 1 %,
increasing to around 5 % near the poles. These variations are primarily
due to differences in the mean solar zenith angle between the MODIS and CERES
datasets, such that they have a small effect when determining the albedo
sensitivities in this work.
Following Eq. (), the Nd–LWP and
Nd–fc relationships can be used to determine a change in
scene (all-sky) albedo as a function of an Nd change. The relationships
are treated as conditional probabilities P(L|Nd)=P(L,Nd)P(Nd), following . When
combined with the Nd sensitivity to aerosol (τa)
changes P(Nd|τa), this allows the scene albedo as a
function of aerosol (P(α|τa^)) to be calculated
for a given scene of liquid clouds (Eq. ), where the circumflex
indicates that a variable has been set to a certain value (the causal
relationship). Note that this is different from the observed relationship
P(α|τa), due to the confounding effects of local
meteorology . It also makes the assumption that
the observed conditional probabilities represent the causal relationship
(i.e. P(L|Nd)=P(L|Nd^), representing only E1), an
assumption that will be investigated in this work.
2P(α|Nd^)=∑fc∑LP(α|fc,L,Nd)P(fc|Nd)P(L|Nd)3P(α|τa^)=∑NdP(α|Nd^)P(Nd|τa)
The albedo sensitivity to aerosol through modifications of each of the
components of the albedo (Nd, L, fc) can be determined
by replacing probabilities conditioned on Nd with unconditional
probabilities. For example, the sensitivity due only to Nd
variations the Twomey effect; can be determined by
removing any dependence of CF and LWP on Nd
(P(fc|Nd)=P(fc) and P(L|Nd)=P(L)) in
Eq. (). The change in planetary albedo is then determined by
multiplying each grid box by 1-fcice (the ice cloud
fraction), making the implicit assumption that there is no change in the ice
cloud albedo or fcice. This is converted to a radiative
forcing by multiplying by the incoming solar flux and anthropogenic aerosol
fractions from and .
To avoid uncertainties associated with the aerosol anthropogenic fraction
inherent in estimates of the aerosol radiative forcing, the effective
radiative forcing (ERF) due to LWP changes is not reported directly, only as a fraction of the RFaci
calculated using the same dataset . The value for the
forcing due to LWP changes can be re-constructed using an appropriate
estimate of the RFaci if required
e.g..
The Nd–LWP relationshipGlobal relationships
(a, c, e) The sensitivity (linear regression coefficient in
log–log space) of Nd to LWP for a selection of different LWP
measures, using MODIS Nd for the period 2007–2009. The
sensitivities are calculated at a 1∘ by 1∘ resolution from
instantaneous (daily) data. (a) MODIS LWP, (b) AMSR-E
(all-sky) LWP and (c) AMSR-E (in-cloud) LWP. The right-hand column
shows the global joint Nd–LWP histogram, where each column is
normalised so that it sums to 1 (showing P(LWP|Nd)). The
black line is at an effective radius of 15 µm (assuming adiabatic
clouds), an approximate indicator of precipitation, with precipitating clouds
lying to the upper left of the line. The orange line is a linear regression
on the data, with the linear sensitivity shown in the top left of the subplot. The blue line is a fit of the form
Eq. (), with the gradients ml and mh
shown in the lower right of each subplot.
Similar to previous studies , a negative linear
Nd–LWP sensitivity (Fig. a, equivalent to the
slope of the orange line in Fig. b) is found globally
over oceans, with a particularly strong negative relationship in the
subtropical stratocumulus decks off the western coasts of continents.
Positive sensitivities are observed in some regions, particularly in the East
China Sea. The sensitivity becomes noisier close to the international
dateline, due to a mismatch between the MODIS and AMSR-E definitions of a
day.
A similar negative relationship is observed when using the AMSR-E LWP, both
the all-sky LWP (Fig. c) and the in-cloud LWP
(Fig. e). The relationship in
Fig. c, using the all-sky LWP, is much weaker than the
in-cloud LWP in Fig. e, which is the most strongly
negative linear sensitivity of the three relationships in
Fig. . A strong positive relationship remains in the
East China Sea.
The Nd–LWP joint histograms shown in the right-hand column of
Fig. show that the Nd–LWP relationship is
highly non-linear at a global scale. All of the histograms show an increase
in the LWP with increasing Nd at low Nd, followed by a
decrease in the LWP at high Nd. Despite global variations in
Nd and LWP retrieval biases e.g. and in
Nd, this non-linearity is not obvious in the global plots of the
linear sensitivity. However, a similar variation in the sensitivity simulated
in LES and in studies of ship tracks, where the
impact of the injection of aerosol from shipping depends on the background
cloud state . This non-linearity is consistent with the
action of at least two proposed aerosol effects in liquid clouds (E1). The
positive relationship at low Nd is consistent with precipitation
suppression, occurring only in the precipitating region of the
Nd–LWP space (left of the black line in
Fig. b, d, f). Warm cloud invigoration would also be
consistent with a positive Nd–LWP relationship. The negative
relationship at high Nd, in regions of Nd–LWP space
where the cloud is unlikely to be precipitating (right of the black line),
supports the model-based results of , and
, where increasing the Nd can result in a LWP
reduction in clouds in which
precipitation does not reach the surface.
The differences between the fits of Eq. () to the MODIS
(Fig. b) and the AMSR-E (Fig. f)
histograms demonstrate how a simple linear regression for calculating a
sensitivity does not capture the strength or nature of the relationship. The
AMSR-E relationship in Fig. f has a slightly weaker
negative relationship at high Nd (mh) than that found
using MODIS data (Fig. b), but a 50 % more strongly
negative sensitivity worldwide. This shows the importance of considering the
complete relationship and suggests that the linear sensitivity alone is not a
strict constraint on the aerosol impact on LWP. The MODIS Nd–LWP
relationship has an mh close to the value expected due to errors in
the re retrieval (-0.4). The mh values for the in-cloud
LWP from both MODIS and AMSR-E are larger than those from the LES simulations
of (mh≈-0.2 for the DYCOMS and dry ASTEX
cases), (equivalent mh≈-0.1) and
(mh<-0.2).
The non-linear behaviour of the Nd–LWP relationship is similar to
that expected due to correlated errors in the MODIS Nd and LWP
retrievals (E2, Appendix A). However, the similarity between the MODIS
(Fig. b) and the in-cloud AMSR-E
(Fig. f) relationships (unaffected by correlated errors
due to the independent LWP measurement) shows that although correlated errors
(E2) may play a role in determining the Nd–LWP relationship, they
do not dominate it. However, to avoid any further impact of E2, the AMSR-E
in-cloud LWP is used to characterise the Nd–LWP relationship for
the remainder of this work.
Regional relationships
(a) The location of the oceanic clusters for the
Nd–LWP relationship, determined using the k-POD clustering method,
using MODIS Nd and the AMSR-E in-cloud LWP. Panels (b) and
(c) show Nd–LWP joint histograms for the two clusters (as in
Fig. ) The line plot at the bottom shows the occurrence
of each Nd value for each cluster, and the number of retrievals
assigned to each cluster is displayed in the upper right of each histogram.
Due to the difficulty of visualising joint histograms globally, and the
sparse nature of the histograms in some regions making fitting
Eq. () prone to error, a clustering approach is used to select
regions with similar microphysics. A k-means clustering method
is used on the Nd–LWP joint-probability
histograms representing each 1∘ by 1∘ grid box. The algorithm
is modified to deal with missing data k-POD;, resulting in
two distinct clusters over ocean with each grid box being assigned to a single
cluster (Fig. ). The clustering algorithm fills in missing
data in the histograms with data interpolated from the clusters. This may
reduce the number of clusters, but it suffices for demonstrating global
variation. The first cluster (Fig. b) is found primarily in
the subtropical subsidence regions, particularly in the Pacific and South
Atlantic. This cluster is characterised by an increase in LWP with
Nd at low Nd, followed by a decrease in LWP at high
Nd, similar to the global relationships in
Fig. .
The second cluster (Fig. c) dominates in the tropics and in
the mid-latitudes, regions with a larger ice CF e.g..
The Nd distribution is less skewed towards lower values in this
cluster. This cluster only includes about half the number of retrievals of
the first cluster, occurring over a smaller area in regions that typically
have a higher ice CF. This lower frequency of occurrence explains the
similarity of the global results with the first cluster.
The primary difference between the clusters is in their behaviour at high
Nd. Whilst the subtropical cluster (Fig. b) shows
a decrease in LWP with increasing Nd (negative mh), the
second cluster is almost insensitive to Nd, even showing a slight
increase in the LWP at the highest Nd values. This may indicate a
difference in the processes that are important for forming precipitation in
the two different clusters and so a different
response to Nd perturbations. The weak sensitivity of LWP to
Nd (Fig. c) is similar to the results of
, who suggest a weak overall response of LWP to
Nd variations in a region where cluster two dominates. However, it
means that the mid-latitude response may be a poor constraint on the response
of the subtropical stratocumulus to Nd perturbations, an issue that
is of particular importance given the large role of the stratocumulus decks
for the global aerosol forcing .
Joint histograms (as in Fig. ) created for
meteorological conditions, separated by RH at 750 hPa and LTS. The
difference plots are shown at the end of each row and column, with red above blue
in each column, showing an increase in AMSR-E in-cloud LWP at high
LTS / RH750 for a given Nd. The histograms under each
joint histogram show P(Nd) for each set of meteorological
conditions.
The impact of meteorology
While the overall form of the relationship remains the same, there is some
variation in the Nd–LWP joint histogram as a function of the
meteorological state (Fig. ). Following previous studies
, the data are separated by low troposphere
stability (LTS) and relative humidity at 750 hPa (RH750; approximately
cloud top). Although the saturation deficit is more closely related to
evaporation rates, we use RH750 for consistency with previous work.
The response to LTS variations is small, occurring primarily in the part of
Nd–LWP space where precipitation is expected
(Fig. c, f). The weak response to LTS is different from previous
studies, which have shown a similar sized response to LTS and RH changes
. A comparison between Fig. a and b shows that this
variation in the linear sensitivity is partly due to variations in the
Nd distribution. At high LTS (Fig. b), the mean
Nd is larger than that found at low LTS (Fig. a),
resulting in a more negative linear sensitivity. However, the
high Nd sensitivity from the fitted relationship (mh) is
very similar at both high and low LTS. The difference in the precipitating
region sensitivity (ml) may be due to variations in the
precipitation processes or regime-dependent retrieval errors for shallow
cumulus (low LTS) and stratocumulus clouds (high LTS). However, the low
frequency of occurrence of these low-Nd conditions (the histograms
under each joint histogram in Fig. ) limits their impact on the
mean Nd–LWP sensitivity.
The difference in Nd–LWP histograms for the two RH750 classes
is much more pronounced, particularly for the high LTS cases
(Fig. b, e), where stratocumulus clouds are common. This may be
due to the dependence of the evaporation–entrainment feedback (E1c) on cloud
edge entrainment, where a weaker relationship to cloud top relative humidity
might be expected than in cases where the sedimentation–entrainment feedback
(E1b; and hence cloud top entrainment) dominates. At high Nd, there
is a significant shift in the LWP towards higher values with increasing
RH750, resulting in a decrease in the magnitude of mh as the
RH750 increases. A relative decrease in mh of around 20 %
is observed, slightly smaller than the 30 % decrease in the linear
sensitivity. Unlike the variations in the sensitivity with LTS, the increase
in Nd with increasing RH750 is accompanied by a decrease in
the linear sensitivity, showing that changes in the Nd distribution
are not the sole controller of the magnitude of the linear sensitivity and
that this measure of the relationship can provide information about
mh.
These changes in mh as a function of RH750 and LTS fit the
conclusions of previous studies ;
increased entrainment at higher Nd results in a reduction of the
LWP, with a stronger decrease at lower cloud top humidities. Results using
the saturation deficit are similar, but with an increased magnitude (see
Supplement). The resulting decrease in LWP with increasing Nd would
reduce cloud albedo, offsetting the RFaci (also due to an increase in
Nd) and reducing the overall ERFaci.
Feedbacks and additional confounders
The strong negative relationship observed in Sect. and in
previous observational studies is in
contrast to recent studies showing a weak or varied LWP response to aerosol
perturbations . While a
negative Nd–LWP relationship has been found in some modelling
studies with large-eddy simulations , the
strength of this negative relationship (mh≈-0.2) is weaker
than the sensitivities observed in Sect. . It is possible
that feedbacks (E3) or the existence of additional confounders (E4) could be
obscuring the causal relationship (Fig. ). This would reduce the
utility of the Nd–LWP relationship as a constraint on
aerosol–cloud interactions in climate models and for determining the aerosol
radiative forcing.
In situations where there is a loop or feedback in the causal graph (e.g.
Fig. ), an experiment is required to determine the strength of
the causal relationship. Although the capability to artificially alter
Nd over a large spatial and temporal scale does not exist, large
aerosol perturbations are able to alter the CCN environment and hence
Nd independently of any feedbacks or confounders (E2–E4;
Fig. ). The Nd–LWP relationship produced by these
“natural experiments” would therefore be expected to be closer to the
causal impact of aerosol on LWP than the relationship determined in
Sect. .
Nd–LWP relationships as in Fig. in
two regions around Hawai'i for 2 years, a low-emissions year (2007) and a
high-emissions year (2008). Panels (a) and (b) show the difference
in AI and LWP between the high and low emission years, with red indicating an
increase in 2008. Panels (c)–(f) show the Nd–LWP joint
histograms (as in Fig. ) for the two periods in the
regions from (a).
Volcanoes provide a possible natural experiment
e.g., as their SO2 emissions are
independent of the prevailing meteorological conditions
. Following . The Kilauea volcano on
the island of Hawai'i is used as an exogeneous aerosol perturbation. Previous
work has shown a stronger linear AOD–Nd sensitivity downwind of Kilauea than in surrounding regions, demonstrating the strong
impact the SO2 from Kilauea has on Nd.
There is significant variability in the SO2 emitted from the volcano.
Comparing a year with strong SO2 emissions (2008) with a
low-emissions year (2007) shows that the variation in aerosol index
AI; AOD times Ångström exponent; downwind from
the volcano comes primarily from the variation in aerosol
(Fig. a), rather than in meteorological conditions.
Despite the strong negative Nd–LWP relationship observed in
sub-tropical regions (Fig. b), there is no change in the
LWP (Fig. b) in the region with a strong change in AI
(region A). This lack of a LWP response to volcanic emissions is similar to
the results of but is within the area covered by the
more sensitive cluster (Fig. ). The weak LWP response to
aerosol variations suggests that the strong negative Nd–LWP
relationship (Figs. , ) is unlikely to
describe the impact of Nd variations on LWP.
This interpretation is supported by the variation in the Nd–LWP
relationships as a function of SO2 emissions. In 2007, volcanic
emissions were weak and the Nd–LWP relationship was very similar
between the regions downwind (region A; Fig. d) and upwind
(B; Fig. f) of the volcano, with a strongly negative
mh and negative linear sensitivity. However, in the high aerosol
environment of 2008 (Fig. c), this negative relationship
becomes much weaker in the volcanic plume (mh=-0.15), whilst little
change is observed upwind of the island (Fig. e). There is a
difference in the LTS between 2007 and 2008 of around 1 K in both regions.
However, the similarity of the Nd–LWP relationship in region B
indicates that variations in meteorological properties cannot explain the
changes in region A. This means that the inter-annual difference in region A
can be attributed primarily to aerosol variations (E1).
In the absence of feedbacks (E3), additional confounders (E4) and
meteorological variations, the Nd–LWP relationship should be
insensitive to the cause of the Nd variations. Given the similarity
in the meteorological conditions between the years, the difference in the
Nd–LWP relationship in region A therefore suggests that the
relationship is modified by feedbacks (E3) or additional confounders (E4).
Due to the high volcanic emissions, the 2008 Nd–LWP relationship
in region A is known to be strongly controlled by aerosol variations (E1) and
has a reduced impact of other processes (E2–E4), such that it is likely
closer to the causal Nd–LWP relationship. This indicates a
considerably weaker role for Nd than determined in
Sect. . With an mh of -0.15, the in-plume
results are much closer to the results from LES simulations
mh<-0.2 and in situ
observations of ship tracks, where decreases in LWP have been observed under
particularly polluted conditions
. The consequently weaker
LWP response to aerosol is in better agreement with the weak LWP changes
observed in Fig. b and .
The difference in the LWP between the ship track and surrounding
control regions as a function of the ship track Nd. The separate
lines are for different values of control LWP. The LWP and Nd
values are from MODIS, using the ship track dataset from
. The numbers in the legend are the number of ship tracks
that make up each line. Each line is characterised by a third-order
uncertainty-weighted polynomial fit (dashed), with the shaded area showing
the 2σ uncertainty on the fit.
The Kilauea volcano primarily affects shallow cumulus clouds
, which exert a weak control on the ERFaci from LWP
changes due to their low liquid CF. The processes responsible for a reduction
in LWP (E1c) may be different from those controlling stratocumulus clouds
(E1b). Shipping provides another source of exogeneous aerosol perturbations
, generating ship tracks that are primarily concentrated in the
high CF stratocumulus regions. Using a database of ship tracks from
, the relationship between the in-ship-track Nd
and LWP increase in the ship track compared to the control region around the
track (dLWP) indicates how the LWP responds to Nd perturbations. As
the Nd values always increase from the control region to the inside
the ship track, dLWP shares a sign with the gradient of the Nd–LWP
relationship. Note that due to the required spatial resolution, the LWP for
these ship tracks is retrieved using MODIS, rather than AMSR-E.
For low control values of the LWP (Fig. ), increases in
LWP (positive values of dLWP) are seen at lower in-ship-track values of
Nd, but as the ship track Nd gets higher, the dLWP reduces
to close to zero, with a negative dLWP for the most polluted cases. When the
control LWP is high, dLWP is consistently weakly negative, although this
likely is due to regression to the mean effects (the mean control LWP is
82 g m-2). This suggests that the LWP becomes insensitive to further
aerosol /Nd perturbations once the LWP reaches a sufficient
magnitude, consistent with an aerosol suppression of precipitation (E1a).
These small dLWP values at high Nd are consistent with the Kilauea
results, suggesting a weak LWP response at high Nd. If the LWP
response in ship tracks followed the relationships from
Sect. , a strong negative dLWP should be visible at high
Nd, in contrast to the weak negative response actually observed
(Fig. ).
By selecting situations where aerosol is known to be responsible for
Nd variations (so-called “natural experiments”), the impact of
feedbacks (E3) and additional covariations (E4) can be reduced (although not
completely removed). In these situations, the Nd variations are
driven by exogeneous aerosol perturbations, such that the LWP variations are
a response to (rather than a driver or indicator of) the change in
Nd (E1 only). This means that the Nd–LWP relationship
during these “natural experiments” provides better information on the LWP
response to Nd variations, such that the strong negative
Nd–LWP relationships observed in Sect. likely
overestimate the decrease in LWP in response to aerosol perturbations. While
the satellite-derived relationships may therefore be unsuitable as a direct
estimate on the aerosol impact on LWP, they could be used as a lower bound on
the LWP change (an upper bound on the radiative forcing) from aerosol-induced
LWP decreases.
The sensitivity of cloud albedo to lnAOD variations (a linear
sensitivity calculated from P(α|τa)) through
(a)Nd changes (Twomey only), (b) CF changes
(const. Nd and LWP) and (c) LWP changes.
Panel (d) shows the total sensitivity, which is calculated directly using
Eq. (), not as a linear sum of (a)–(c).
The implied ERFaci
The planetary albedo sensitivities to aerosol perturbations are shown in
Fig. following Eq. (). Due to the difficulty
of visualising joint histograms globally, linear sensitivities are determined
from the joint histograms (P(α|τa)) by weighting by the
present-day aerosol distribution see. The first three
subplots show the albedo sensitivity through modifying the Nd
(constant CF and LWP; Fig. a), CF (constant LWP;
Fig. b) and AMSR-E LWP (constant CF;
Fig. c). Both changes in Nd and CF increase the
scene albedo, which results in a negative radiative forcing. They have
somewhat different spatial patterns, with the albedo sensitivity to
Nd changes being concentrated in the centres of the stratocumulus
decks due to the high liquid cloud fraction. The sensitivity to CF changes is
highest at the edges of the stratocumulus decks, where the greatest potential
for modifying the cloud fraction exists, as found in previous studies
.
The sensitivity to LWP changes is also strongly dependent on the liquid CF
and so is strongest in the centres of the stratocumulus decks
(Fig. c). As a reduction in LWP with increasing Nd
is observed in these regions (Fig. ), this results in a
negative albedo sensitivity to aerosol through LWP changes, which would in
turn create a positive radiative forcing. Combining the albedo sensitivities
in Fig. with the anthropogenic aerosol fraction from
implies a positive radiative forcing from LWP changes that
offsets 62 % of the RFaci calculated using the same data, resulting in a
weakening of the RFaci. The offset is similar (59 %) when using the
anthropogenic fraction from . This is likely the upper bound
on the fraction of the RFaci offset by LWP reductions, following the results
of Sect. and supported by the weaker offsetting in
regions with larger aerosol perturbations (e.g. the East China Sea, the
tropical and North Atlantic). Despite the reduced albedo sensitivity due to
the LWP reduction, the overall albedo sensitivity to aerosols is still
positive (Fig. d), resulting in a negative ERFaci from
liquid clouds due to the strong implied forcing from the Nd–CF
relationship (approximately a 200 % increase above the RFaci).
There remains considerable uncertainty in the magnitudes of these effects.
The albedo change is only calculated over ocean. Observational studies
suggest the Nd change and RFaci over land are small, but it is
possible that the LWP adjustments could have a very different character and
relationship to the RFaci over land. The variation in the Nd–LWP
relationship in the Kilauea volcanic plume (Fig. ) and the
response of the LWP in ship tracks (Fig. ) suggest that
the LWP change determined in Fig. is overly strong. This
would then place a 62 % offset of the RFaci as the upper bound on the
radiative forcing from LWP changes (larger offsets are unlikely). This is
consistent with previous work, where an increase in cloud albedo is found in
response to a change in aerosol , such
that a LWP reduction cannot completely offset the RFaci.
Discussion
This work demonstrates that a non-linear relationship exists between
Nd and LWP (Fig. ). These results are in
agreement with previous studies, with an increase in LWP with Nd at
low Nd from precipitation suppression (E1a), but a decrease at high
Nd due to increased cloud top or lateral entrainment (E1b, c). The
similarity in the relationship when using different measures of LWP suggests
that this relationship is not primarily due to LWP retrieval errors (E2).
There are global variations in the Nd–LWP relationship and
significant changes accompany variations in meteorological factors,
particularly RH750 (Fig. ). The observed Nd–LWP
relationship implies a reduction in LWP with increasing aerosol and
Nd, resulting in a positive radiative forcing that offsets around
60 % of the RFaci.
The analysis in Sect. suggests that the negative
Nd–LWP relationship observed over much of the world may be
overestimated, resulting in too strong a corresponding positive radiative
forcing due to aerosol-induced LWP adjustments. A precipitation feedback
(E3a) would produce a positive Nd–LWP relationship and so is
unlikely to be responsible. An entrainment-based feedback on the Nd
(E3b) or an additional confounder (E4) could be responsible for the negative
Nd–LWP relationship.
The albedo sensitivity to aerosol via LWP changes is particularly strong in
the stratocumulus regions (Fig. ), due to the high liquid
cloud fraction. This implies an important role for the
sedimentation–entrainment feedback (E1b). With the entrainment of dry
environmental air at the cloud top, the assumptions in the Nd
retrieval of a linearly increasing liquid water content and vertically
constant Nd no longer hold as the cloud is no longer adiabatic,
such that the cloud top Nd is no longer representative of the cloud
base Nd. A reduction in the cloud top re by homogeneous
mixing during entrainment would produce an increase in Nd required
by E3b. Cloud top homogeneous mixing generating an apparent Nd–LWP
would also create the dependence of the Nd–LWP relationship on
RH750 observed in Fig. . A stronger impact on the retrieved
Nd would be found with the entrainment of drier air, resulting in a
more negative Nd–LWP relationship.
However, although some studies have found evidence of homogeneous mixing in
stratocumulus cloud , many studies have found that
inhomogeneous mixing dominates, particularly at cloud tops
. While inhomogeneous
mixing reduces the Nd, in extreme cases it does not result in an
re change and so may not be detected by satellite. As such, some
proportion of homogeneous mixing is required for E3b to generate a negative
Nd–LWP relationship in satellite data. A discrepancy between
satellite-retrieved and in situ Nd as a function of humidity or
entrainment rate might be one indicator of this process. Further
investigation into the mixing and behaviour of these retrievals at cloud tops
is necessary to establish the impact of E3b on the Nd retrievals
and the Nd–LWP relationship.
An additional, unknown confounder (E4) is also a possible explanation for the
results in Sect. . This effect would have to act on both
Nd and LWP together – a process that only affects one would not
generate the systematic bias required. Even if such an unknown, additional
confounding process exists, the conclusion drawn from
Sect. would still hold – that the implied aerosol impact
on LWP in Fig. is likely too strong.
By using 1∘ by 1∘ average values, this work ignores the
impact of sub-grid variability of the Nd and LWP retrievals
. Preliminary work indicates that this may modify the
relationship, with the strength of the relationship changing when it is
determined at smaller spatial and temporal scales. If the interpretation of
the results from natural experiments is followed, it implies that these small-scale Nd–LWP relationships are strongly influenced by E2–E4, due
to the lack of aerosol variation to drive the Nd variation
necessary to highlight the impact of E1. The cause of this scale dependence
will be investigated in future studies.
Although volcanic emissions (Fig. ) and ship tracks are
exogeneous sources of aerosol, the datasets linked to these sources are
limited. They occur in relatively restricted locations on the globe and there
are a small number of the high-Nd retrievals required to populate
the Nd–LWP histogram (Fig. ). While the
ship track dataset is concentrated in stratocumulus regions
, it is still possible that the effect on shallow
cumulus clouds could be large enough to overcome the relatively small CF in
this regime which has previously been shown to restrict the contribution of
shallow cumulus clouds to the RFaci . Given the
importance of the Nd to this work, an improved understanding of the
behaviour of the Nd retrieval through a comparison with in situ
data is particularly important. Future studies are planned to expand this
dataset of exogeneous aerosol perturbations in marine clouds such that a more
representative global study of this type can be performed. Process-resolving
simulations of these cases and a comparison to the global results are
necessary to fully understand the behaviour of the satellite retrievals and
how accurately they can represent the aerosol Nd–LWP system to
better constrain the aerosol impact on LWP.
Conclusions
Along with liquid cloud fraction (CF) and droplet number concentration
(Nd), the liquid water path (LWP) has a large impact on the albedo
of a scene containing liquid clouds. However, due to the nature of the
Nd–LWP relationship and the retrievals of these properties, global
constraints of the aerosol impact on LWP and the corresponding radiative
impact have been difficult to determine. Several possible mechanisms for
generating a relationship between Nd and LWP are described in
Sect. .
This work has demonstrated that although there is a clear relationship
between the satellite-retrieved Nd and LWP, this relationship is
highly non-linear. At low Nd values (where precipitation is
expected), there is an increase in LWP with increasing Nd
consistent with an aerosol suppression of precipitation (E1a). At high
Nd, the LWP decreases with increasing Nd, an effect which
has been previously suggested to be due to the droplet size impact on
entrainment (E1b/c, Fig. ). This non-linearity of the
Nd–LWP relationship restricts the ability of linear regressions to
characterise the relationship. The reduction in LWP with increasing
Nd is only slightly stronger when using MODIS LWP compared to the
in-cloud LWP from AMSR-E, suggesting that although correlated errors in the
MODIS LWP and Nd can play a role (E2), they do not dominate the
magnitude of the Nd–LWP relationship.
By clustering the Nd–LWP joint histograms, it is shown that the
primary variation in the histograms comes from variations in the LWP
behaviour at high Nd (Fig. ). In the subtropical
subsidence regions, there is a clear LWP reduction with increasing
Nd, whilst in other regions, LWP remains constant or even increases
with LWP even at high Nd. The global relationship is dominated by
the subtropical relationship due to the high liquid CF and higher
Nd variation in these regions, but the regional variations in the
Nd–LWP relationship make it difficult to use the results from one
region to constrain others.
Part of this variability come from regional differences in meteorological
conditions. Significant variations in the Nd–LWP relationship are
found with variations in RH750 and LTS (Fig. ). As with the
global relationships, linear regressions have difficulty fully characterising
these relationships. As noted by and ,
cloud top relative humidity plays an important role in determining the
strength of the relationship, with a more weakly negative Nd–LWP
relationship in humid regions.
However, results from natural experiments created by volcanic outgassing and
shipping suggest that the negative Nd–LWP relationship is likely
overestimated. In situations where the strong aerosol variability is the
leading control on Nd variations, the impact of feedbacks (E3) or
additional confounders (E4) on the Nd–LWP relationship is
significantly reduced. This suggests that the weaker Nd–LWP
relationship observed in response to ship and volcanic aerosol perturbations
better represents the impact of aerosols (E1) than the strong relationship
observed at a global scale (Sect. ), bringing the
observations into better agreement with LES simulations
.
The observed Nd–LWP relationship suggests that LWP adjustments
could offset up to 60 % of the RFaci (Twomey effect)
(Fig. ), as a positive radiative forcing. This represents an
upper bound on the positive radiative forcing expected from a LWP reduction.
The results from natural experiments suggest that the LWP response is likely
weaker than this (Figs. , ), as the
causal Nd–LWP relationship is obscured by feedbacks (E3) and
additional confounders (E4) in many cases. Further work is required to bound
the LWP response, but these results suggest that the overall ERFaci is likely
to be negative, supported by previous studies that have found that a complete
offset of the RFaci is unlikely .
Although it has been demonstrated in this work that the Nd–LWP
relationship has a substantial impact on the ERFaci, it is clear that
significant uncertainties remain. The satellite-retrieved Nd–LWP
relationship has several features that are similar to the relationship
predicted by high-resolution models , but the extent
to which these relationships represent the causal relationship (and so can be used to constrain aerosol–cloud interactions) is not clear
and so can be used to constrain aerosol–cloud interactions. A wider study of
the effect of aerosols on LWP due to exogenous aerosol perturbations in a
variety of cloud regimes would provide one avenue for progress, as would
finding a suitable mediating variable within the Nd–LWP
relationship.
Data availability
The MODIS data are from the NASA Goddard Space Flight
Center. The CERES data were obtained from the NASA Langley Research Center
Atmospheric Science Data Center. The AMSR-E were obtained from the National
Snow and Ice Data Center. The data products are referenced in Sect. 3.
Expected sensitivities
If the LWP and Nd are calculated from MODIS data using the
adiabatic assumption , they
take the form
A1Nd=1.67×10-8c(T)fadτc12re-52,A2L=59fadreτc,
where 0<fad≤1 is the adiabatic factor (fad=1 is
completely adiabatic) and c(T) is the temperature correction to the
condensation rate from . The linear sensitivity
dlnLdlnNd expected from re
variations, assuming a constant τc, is then
A3dLdNdτc=∂L∂reτc∂re∂Ndτc,A4dNddreτc=-52Ndre,A5dLdNdτc=Lre×-25reNd,A6dlnLdlnNdτc=-25.
By similar logic, the sensitivity expected at a constant re from
variations in τc is
dlnLdlnNdre=2.
Note that the cause of these variations is not specified. A variation in
re due to retrieval errors or Nd variations would produce
the same effect. As both the LWP and Nd relate to the adiabatic
factor in the same way as the optical depth, the expected sensitivity from
adiabatic factor variation is also 2.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-19-5331-2019-supplement.
Author contributions
All of the authors participated in the design of the study.
EG performed the analysis and wrote the paper. MC provided the ship track
dataset. All of the authors assisted in the interpretation of the results and
commented on the paper.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was supported by funding from the European Research Council under
the European Union's Seventh Framework Programme (FP7/2007-2013 and ERC grant
agreement no. FP7-306284 – QUAERERE). Edward Gryspeerdt is
supported by an Imperial College London Junior Research Fellowship. TG
received funding from the European Union Horizon 2020 research and innovation
program under the Marie Sklodowska-Curie grant agreement 703880. The authors
would like to thanks the reviewers for their helpful comments and
suggestions.
Review statement
This paper was edited by Graham Feingold and reviewed by two
anonymous referees.
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