-
Atmos. Chem. Phys., 20, 15079–15099,
2020https://doi.org/10.5194/acp-20-15079-2020© Author(s) 2020. This
work is distributed underthe Creative Commons Attribution 4.0
License.
Constraining the Twomey effect from satellite
observations:issues and perspectivesJohannes Quaas1, Antti Arola2,
Brian Cairns3, Matthew Christensen4, Hartwig Deneke5, Annica M. L.
Ekman6,Graham Feingold7, Ann Fridlind3, Edward Gryspeerdt8, Otto
Hasekamp9, Zhanqing Li10, Antti Lipponen2,Po-Lun Ma11, Johannes
Mülmenstädt11, Athanasios Nenes12,13, Joyce E. Penner14, Daniel
Rosenfeld15,Roland Schrödner5, Kenneth Sinclair3,16, Odran
Sourdeval17, Philip Stier4, Matthias Tesche1,Bastiaan van
Diedenhoven3, and Manfred Wendisch11Leipzig Institute for
Meteorology, Universität Leipzig, Leipzig, Germany2Finnish
Meteorological Institute, Kuopio,Finland3NASA Goddard Institute for
Space Studies, New York, USA4Department of Physics, University of
Oxford, Oxford, UK5Leibniz Institute for Tropospheric Research,
Leipzig, Germany6Department of Meteorology and Bolin Centre for
Climate Research, Stockholm University, Stockholm, Sweden7NOAA
Earth System Laboratories, Chemical Science Laboratory, Boulder,
USA8Space and Atmospheric Physics Group, Imperial College London,
UK9SRON Netherlands Institute for Space Research, Utrecht, the
Netherlands10Earth System Science Interdisciplinary Center and
Department of Atmospheric and Oceanic Science,University of
Maryland, College Park, USA11Pacific Northwest National Laboratory,
Richland, USA12School of Architecture, Civil & Environmental
Engineering, École Polytechnique Fédéralede Lausanne, Lausanne,
Switzerland13Institute of Chemical Engineering Sciences, Foundation
for Research and Technology Hellas, Patras, Greece14Department of
Climate and Space Sciences and Engineering, University of Michigan,
Ann Arbor, USA15Institute of Earth Sciences, Hebrew University of
Jerusalem, Jerusalem, Israel16Department of Earth and Environmental
Engineering, Universities Space Research Association
(USRA),Columbia, MD 21046, USA17Université de Lille, CNRS, UMR 8518
– LOA – Laboratoire d’Optique Atmosphérique, Lille, France
Correspondence: Johannes Quaas
([email protected])
Received: 24 March 2020 – Discussion started: 15 May
2020Revised: 24 September 2020 – Accepted: 8 October 2020 –
Published: 4 December 2020
Abstract. The Twomey effect describes the radiative
forcingassociated with a change in cloud albedo due to an
increasein anthropogenic aerosol emissions. It is driven by the
per-turbation in cloud droplet number concentration (1Nd, ant)in
liquid-water clouds and is currently understood to exerta cooling
effect on climate. The Twomey effect is the keydriver in the
effective radiative forcing due to aerosol–cloudinteractions, but
rapid adjustments also contribute. Theseadjustments are essentially
the responses of cloud fractionand liquid water path to 1Nd, ant
and thus scale approxi-
mately with it. While the fundamental physics of the influ-ence
of added aerosol particles on the droplet concentration(Nd) is well
described by established theory at the particlescale (micrometres),
how this relationship is expressed at thelarge-scale (hundreds of
kilometres) perturbation, 1Nd, ant,remains uncertain. The
discrepancy between process under-standing at particle scale and
insufficient quantification atthe climate-relevant large scale is
caused by co-variability ofaerosol particles and updraught velocity
and by droplet sinkprocesses. These operate at scales on the order
of tens of me-
Published by Copernicus Publications on behalf of the European
Geosciences Union.
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15080 J. Quaas et al.: Twomey from satellite
tres at which only localised observations are available and
atwhich no approach yet exists to quantify the
anthropogenicperturbation. Different atmospheric models suggest
diversemagnitudes of the Twomey effect even when applying thesame
anthropogenic aerosol emission perturbation. Thus, ob-servational
data are needed to quantify and constrain theTwomey effect. At the
global scale, this means satellite data.There are four key
uncertainties in determining 1Nd, ant,namely the quantification of
(i) the cloud-active aerosol – thecloud condensation nuclei (CCN)
concentrations at or abovecloud base, (ii) Nd, (iii) the
statistical approach for inferringthe sensitivity of Nd to aerosol
particles from the satellitedata and (iv) uncertainty in the
anthropogenic perturbationto CCN concentrations, which is not
easily accessible fromobservational data. This review discusses
deficiencies of cur-rent approaches for the different aspects of
the problem andproposes several ways forward: in terms of CCN,
retrievalsof optical quantities such as aerosol optical depth
suffer froma lack of vertical resolution, size and hygroscopicity
infor-mation, non-direct relation to the concentration of
aerosols,difficulty to quantify it within or below clouds, and the
prob-lem of insufficient sensitivity at low concentrations, in
ad-dition to retrieval errors. A future path forward can
includeutilising co-located polarimeter and lidar instruments,
ide-ally including high-spectral-resolution lidar capability at
twowavelengths to maximise vertically resolved size
distributioninformation content. In terms ofNd, a key problem is
the lackof operational retrievals of this quantity and the
inaccuracy ofthe retrieval especially in broken-cloud regimes. As
for theNd-to-CCN sensitivity, key issues are the updraught
distribu-tions and the role of Nd sink processes, for which
empiricalassessments for specific cloud regimes are currently the
bestsolutions. These considerations point to the conclusion
thatpast studies using existing approaches have likely
underesti-mated the true sensitivity and, thus, the radiative
forcing dueto the Twomey effect.
1 Introduction
Cloud droplets in liquid-water clouds form on cloud
con-densation nuclei (Aitken, 1880), a subset of the atmo-spheric
aerosol particle population. The formation of clouddroplets in
thermodynamic equilibrium is established text-book knowledge
(Köhler, 1936). Whether an aerosol parti-cle acts as cloud
condensation nuclei (CCN) at a given su-persaturation depends on
its size and chemical composition,which determine the particle
hygroscopicity (Dusek et al.,2006; Ma et al., 2013). If CCN
concentrations at one su-persaturation level are known, CCN
concentrations at othersupersaturation levels approximately scale
with it accordingto the Twomey (1959) parameterisation. Here, we
implic-itly consider a supersaturation level of 0.2 % unless
other-wise stated. Supersaturation is generated in the large
majority
of clouds by updraughts. The rare exceptions are formationdue to
radiative cooling (mainly fog events) or the mixing ofcold and dry
with warm and moist air masses. Cloud-scaleupdraughts originate in
most cases from turbulence, con-vection or gravity waves. Updraught
velocity, w, exhibits alarge heterogeneity across temporal and
spatial scales (Tont-tila et al., 2011; Moeng and Arakawa, 2012).
For a givenprobability density function (PDF) of updraughts, in an
adia-batic air parcel with no active collision and coalescence,
theaddition of extra CCN will generally lead to a monotonic
in-crease in cloud droplet number concentration, Nd (Twomeyand
Warner, 1967). The approximate functional form of thedependence of
Nd on CCN concentration is then logarith-mic, since the increase in
Nd associated with activation ofadditional aerosol leads to a
depletion of the maximum su-persaturation (Twomey, 1959).
The CCN concentration in the atmosphere is increasedby
anthropogenic emission of aerosols and aerosol precursorgases
(Boucher et al., 2013). This leads to enhanced Nd, un-less aerosol
particle concentrations are high and updraughtsweak (Ghan et al.,
1998; Feingold et al., 2001; Reutter et al.,2009). In turn, cloud
albedo (αc, the fraction of solar radiativeenergy reflected back to
space by clouds in relation to thatincident at the cloud top)
increases, as it is a monotonicallyincreasing function of Nd.
Following Platnick and Twomey(1994) and Ackerman et al. (2000),
∂αc
∂ lnNd=
13αc (1−αc) , (1)
a formulation which relies on (i) a two-stream radiative
trans-fer approximation and (ii) the assumption that clouds
obeyvertical stratification that scales with an adiabatic one
andthat is horizontally homogeneous. Equation (1) is expressedas a
partial derivative: other quantities – notably cloud waterpath –
are considered constant.
These two facts – Nd is a monotonic function of CCN andαc in the
partial-derivative sense is a monotonic function ofNd – imply that
the anthropogenic increase in CCN concen-trations causes a negative
(cooling) radiative forcing due toaerosol–cloud interactions, RFaci
(Boucher et al., 2013), de-noted as Faci (Bellouin et al., 2020b).
It can be approximately(neglecting absorption in the column above
the cloud afterscattering at cloud top) written as (Quaas et al.,
2008; Bel-louin et al., 2020b)
Faci = F↓s ·∂αc
∂ lnNd·∂ lnNd∂ lna
·1 lnaant, (2)
with the downward solar radiative flux density (irradiance)above
clouds, F↓s , and a quantitative description of CCN de-noted here
as a. The relative anthropogenic perturbation toa is denoted 1
lnaant. This formulation assumes (i) that onlythe solar spectrum is
relevant, which is well justified for theoptically thick, liquid
water clouds considered here, since anNd perturbation only
marginally changes the cloud radiative
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J. Quaas et al.: Twomey from satellite 15081
effect in the terrestrial spectrum of an optically thick
cloudand (ii) that there is one liquid water cloud layer that
deter-mines the effect so that the problem can be considered
purelyhorizontal in space. In contrast to the formulation by
Bellouinet al. (2020b), we consider the problem as horizontally
vari-able in space (x, y) and in time (t), i.e. Faci = Faci(x, y,
t).If Eq. (2) is assessed from temporally sparse satellite data,a
proper integration over temporally varying solar zenith an-gles and
cloud diurnal cycles is necessary.
RFaci is often referred to as the “Twomey effect”(Twomey, 1974)
and also called the “(first) aerosol indi-rect effect” or “cloud
albedo effect” (Lohmann and Feichter,2001). Atmospheric models
simulate a large range for RFaci(Gryspeerdt et al., 2020; Smith et
al., 2020). It is, thus, nec-essary to constrain the Twomey effect
quantitatively basedon observations. Only satellites can provide
global observa-tional data that could be used to quantify the
global RFaci(Stephens et al., 2019).
The Twomey effect has been assessed in many studies(starting
with Bréon et al., 2002) in terms of cloud dropleteffective radius,
re, rather than using Nd. This is plausibleas, for idealised
vertical profiles of droplet size distributions(e.g. vertically
constant or adiabatically increasing profiles),cloud optical depth
and cloud albedo are easily expressedin terms of re (Hansen and
Travis, 1974; Stephens, 1978).Given that re is closely related to
light-scattering proper-ties of clouds in the visible and
near-infrared, this quantityis operationally retrieved from
remote-sensing observations(Nakajima and King, 1990). However, re
is not just a func-tion of Nd but also varies with cloud liquid
water path, L(Brenguier et al., 2000). It is thus necessary to
formulate theproblem for constant L, which is difficult to realise
in dataanalysis from observations that are limited in time and
space,or for selected cloud scenarios, so that datasets stratified
byL become too small for meaningful analysis (Quaas et al.,2006;
McComiskey and Feingold, 2012; Liu and Li, 2019).Specifically, in
Eq. (2), the middle term, ∂ lnNd
∂ lna , would be for-mulated as ∂ lnre
∂ lna , in which case the evaluation of the partialderivative
requires stratification by L, in addition to the up-draught regime,
which adds substantial complexity.
Among the four factors on the right-hand side of Eq. (2),the
first one, F↓s , is well quantified for each given
latitude,longitude and time. The second one, ∂αc/∂ lnNd, can
beevaluated using Eq. (1) (Bellouin et al., 2020b; Hasekampet al.,
2019a), or alternatively by radiative-transfer simula-tions
(Mülmenstädt et al., 2019). This implies that the twokey problems
in determining RFaci are the quantificationof the anthropogenic
perturbation of CCN, 1 lnaant, andthe sensitivity of Nd to CCN
perturbations, β = ∂Nd/∂ lna(Feingold et al., 2001). Taken
together, this is the distribu-tion of the anthropogenic
perturbation of Nd (here expressedin absolute, not relative,
terms):
1Nd, ant =∂Nd
∂ lna
∣∣∣∣w
·1 lnaant = β(w) ·1 lnaant. (3)
The plausible range of the sensitivity is 0≤ β ≤ 1, except
forheavily polluted situations (where it may become
negative;Feingold et al., 2001), or when giant CCN play an
importantrole (Ghan et al., 1998; Morales Betancourt and Nenes,
2014;Gryspeerdt et al., 2016; McCoy et al., 2017) where
com-petition for water vapour during droplet formation is at
itsstrongest. Such conditions represent a significant challengeto
models and parameterisations of the process (Morales Be-tancourt
and Nenes, 2014).
The aerosol forcing has to be evaluated at a scale muchlarger
than an individual cloud. One of the key reasons forthis is that
there is currently no way to use satellite data todetermine the
anthropogenic fraction of the CCN populationfor a single air
parcel. Methods applying model information,or data-tied approaches
such as Bellouin et al. (2013) insteaduse the scale of model
resolution or aggregate data resolutionwhich is typically of the
order of 1◦ × 1◦ (or about 100×100 km2). The problem formulated in
Eq. (3) then has to bereformulated, using an overbar to denote the
averaging overa 1◦× 1◦ grid box as
1Nd, ant =
∞∫w=−∞
∂Nd
∂ lna
∣∣∣∣w
P(w)P(a)dw
1 lnaant= β ·1 lnaant, (4)
which considers the mean sensitivity of Nd to CCN, β, giventhe
probability density function (PDF) of cloud base up-draught
velocity, w in the grid box, P(w); the PDF of CCNat cloud base
within the scene, P(a); and the anthropogenicperturbation of the
CCN concentration at the grid-box scale,1 lnaant. Note in the above
equation, β is assumed indepen-dent of lnaant, which assumes that
P(w) is independent ofcloud properties (primarily, liquid water
content), which ap-plies to stratus clouds (Morales and Nenes,
2010) but not ingeneral. Similarly, the covariance of P(w) and
P(a)may notbe zero (e.g. Kacarab et al., 2020 – in addition to
Bougiatiotiet al., 2020). All of the above suggest that observation
of β ata cloud parcel scale is not directly transferrable to the
largescale for an assessment of the Twomey effect. Rather, β hasto
be estimated.
Beyond RFaci, aerosol–cloud interactions also lead torapid
adjustments: once cloud droplet size distributions arealtered due
to anthropogenic CCN, cloud microphysical anddynamical processes
are modified as well (Albrecht, 1989;Ackerman et al., 2000; Wang et
al., 2003; Heyn et al., 2017;Mülmenstädt and Feingold, 2018).
Aerosols can induce tran-sitions between cloud regimes, for
instance by changing driz-zle behaviour (Rosenfeld et al., 2006;
Feingold et al., 2010;Wood et al., 2011). The direction and
magnitude of thesechanges depends on the cloud state and regime,
because re-sponses to aerosol changes occur due to processes
spanning arange from microphysics to the mesoscale (Christensen
andStephens, 2012; Kazil et al., 2011; Wang et al., 2011).
Theseprocesses include precipitation suppression (Albrecht,
1989),
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15082 J. Quaas et al.: Twomey from satellite
rapid feedbacks involving cloud-top entrainment (Ackermanet al.,
2004; Bretherton et al., 2007; Hill et al., 2009; Bula-tovic et
al., 2019) and rapid feedbacks involving cloud lateralentrainment
(Xue and Feingold, 2006; Small et al., 2009) aswell as responses in
dynamics (Xue et al., 2008; Stevens andFeingold, 2009; Wang and
Feingold, 2009). If one also con-siders deep clouds, further
intricate cloud adjustments mayoccur that are not considered here
(e.g. Ekman et al., 2011;Fan et al., 2013; Yan et al., 2014). As a
result of these adjust-ment processes, cloud horizontal extent
(Gryspeerdt et al.,2016) and liquid water path (Gryspeerdt et al.,
2019) re-spond to perturbations in Nd. The sum of RFaci and the
ra-diative effects of these adjustments is the effective
radiativeforcing due to aerosol–cloud interactions, ERFaci
(Boucheret al., 2013). Based on modelling and data analysis, it is
ev-ident that the adjustments and, thus, also ERFaci scale with1Nd,
ant (Bellouin et al., 2020b; Gryspeerdt et al., 2020; Mül-menstädt
et al., 2019). Analysis of model data shows thatthe rapid
adjustments due to other contributions (small-scaleto mesoscale
circulation changes, thermodynamic changes)are small (Heyn et al.,
2017; Mülmenstädt et al., 2019).Even so, thermodynamic and dynamic
adjustments to aerosolchanges can still have an important impact on
droplet forma-tion – especially under conditions where droplet
formationis largely velocity-limited (Kacarab et al., 2020;
Bougiatiotiet al., 2020).
Despite the fact that the activation of an individual CCNto form
a droplet is well understood in thermodynamic equi-librium (Köhler,
1936), it is not clear how Nd responds toperturbations of CCN at
the scale of a cloudy air parcel, anentire cloud or of a cloud
field up to the large scale of theorder of 1◦× 1◦ as used in Eq.
(4). A one-to-one relation-ship between CCN in the updraught below
cumulus and Ndabove the cloud base within the cumulus has been
observed(Werner et al., 2014); although even at the cloud
updraughtscale, this relationship could be a convolution of the
effect ofCCN on droplet number, vertical velocity variability and
lat-eral entrainment (Morales et al., 2011). At a larger scale,
thisrelation is less pronounced (Boucher and Lohmann,
1995),consistent with the expectation from Eq. (4). In turn,
theremay be co-variability of updraughts and aerosol
concentra-tions that lead to larger β compared to situations with
con-stant w (Kacarab et al., 2020; Bougiatioti et al., 2017,
2020).
Ground-based remote-sensing methods provide data to in-fer the
sensitivity term β from long-term observations (Fein-gold et al.,
2003; McComiskey et al., 2009; Schmidt et al.,2015; Liu and Li,
2018). However, this approach is limitedto individual sites and
cloud regimes. In consequence, wheninvestigating the global
radiative forcing relevant for climatestudies, the sensitivity term
necessarily is derived from satel-lite remote sensing (Nakajima and
Schulz, 2009).
This leads to a number of problems and challenges dis-cussed in
more detail in the following sections.
- Retrieval of CCN. The first issue is the missing co-incidence
of cloud and aerosol retrievals. Usually, noaerosol is retrieved
below or within clouds. It is thusquestionable how representative
aerosol in cloudlessscenes is for (neighbouring) cloud base CCN.
The sec-ond issue is the imperfect nature of proxies for CCN.Often
the aerosol optical depth (AOD; see below) or avariant thereof is
used, which can only imperfectly berelated to CCN due to
differences in sensitivity and thelack of vertical resolution.
- Retrieval of Nd . There are (i) retrieval errors and biasesin
Nd, which depend on cloud regimes, and (ii) oneneeds to consider
the link between Nd as formed byCCN activation at cloud base and
the retrieved cloud-topNd. Cloud-topNd (Nd, top) is the one that
determinesthe scattering of sunlight and, thus, is relevant for
thetop-of-atmosphere cloud radiative effect. It differs fromcloud
base Nd (Nd, base) in conditions where Nd sinkssuch as
precipitation or mixing play a role. When usingre rather thanNd the
additional problem of stratificationby retrieved L arises.
- Cloud-regime dependence. Cloud base droplet concen-tration,
Nd, base, is a function of both CCN and up-draught, and Nd, top is
further a function of Nd sinkssuch as precipitation formation and
entrainment mixing.Thus, one needs to understand how the
characteristics ofw and its PDF, as well as precipitation and
mixing pro-cesses, depend on cloud regime and how this may beused
for an empirical estimation of β.
- Aggregation scale. The relation of aggregate quantitiesis not
the same as the aggregate relation, and, thus,one needs to
determine how to derive β optimally fromremote-sensing data
(Grandey and Stier, 2010; Mc-Comiskey and Feingold, 2012).
In practical terms, one further needs to assess to which ex-tent
a simple scalar sensitivity metric is sufficient, or whethera
joint-PDF approach is preferable (McComiskey and Fein-gold, 2012;
Gryspeerdt et al., 2017).
Beyond these questions which are discussed in the follow-ing
sections, it is necessary to quantify the anthropogenicperturbation
to CCN, 1 lnaant, which is not easily quanti-fied from
observations. The key problem is that there is lit-tle potential to
observe an atmosphere unperturbed by an-thropogenic emissions
(Carslaw et al., 2013, 2017). Somestudies attempt to quantify the
anthropogenic perturbation tothe column aerosol light extinction,
or aerosol optical depth(AOD; τa), in a data-tied approach (Kaufman
et al., 2005;Bellouin et al., 2005, 2013; Kinne, 2019). Such
approachesrely on simplifying parameterisations, such as the
assump-tion that small-mode aerosol particles are predominantly
an-thropogenic. The other option is to estimate it from
simula-tions (Quaas et al., 2009b; Gryspeerdt et al., 2017). There
are
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J. Quaas et al.: Twomey from satellite 15083
some indirect ways to infer the anthropogenic impacts on
Nd(Quaas, 2015), such as from trends (Krüger and Graßl,
2002;Bennartz et al., 2011) or periodicity in anthropogenic
emis-sions such as the weekly cycle (Quaas et al., 2009a).
Hence,models are involved in determining an anthropogenic
pertur-bation of CCN concentrations, which can even be attemptedfor
individual weather events (Schwartz et al., 2002). In anycase, it
seems impossible to know the anthropogenic pertur-bation to the
aerosol at the scale of an air parcel; rather it ispossible only at
larger, aggregate scales. The remainder ofthis review will focus on
the sensitivity term β.
2 Remote sensing of CCN concentrations
The aerosol quantity most accessible to passive satellite
re-mote sensing is AOD (Kaufman et al., 2002). It is derivedfrom
the multi-spectral reflectance of the Earth–atmospheresystem using
the incident solar radiation and retrieving or as-suming surface
albedo characteristics as well as aerosol ab-sorption coefficient
and scattering phase functions. There arefour key issues with using
the retrieved AOD for estimatingtheNd to CCN sensitivity, which
will be discussed in the fol-lowing subsections.
- AOD is the vertical integral of the extinction coefficient.For
the sensitivity of Nd to the aerosol, one needs toknow the vertical
distribution of the CCN concentration,most importantly the CCN at
cloud base.
- AOD is an optical integral and does not provide infor-mation
on the aerosol size distribution and its hygro-scopicity. The use
of AOD does not isolate aerosol par-ticles that have the size and
chemical composition toserve as CCN. It is also affected by aerosol
swelling dueto hygroscopic growth.
- AOD can be derived only for pixels determined to becloud-free.
The degree to which this correlates withthe CCN at the base of
(neighbouring) clouds is ques-tionable. In addition, retrieved AOD
can show a posi-tive bias due to enhanced reflectance from
neighbouringcloudy pixels or due to the lack of detecting
spuriousclouds in a retrieval scene.
- The optical signal is very weak at low
concentrations.Therefore, retrievals become more and more
uncertainbelow a certain aerosol load, especially over land and
insituations with variable or uncertain surface albedo.
At aggregate scales, i.e. for monthly averages over re-gions,
AOD from ground-based remote-sensing retrievals(AERONET; Holben et
al., 2001) correlates well with CCNsurface measurements (Andreae,
2009; Shen et al., 2019).Similar results were also reported for
aircraft measurements(Clarke and Kapustin, 2010; Shinozuka et al.,
2015). How-ever, at shorter timescales or less spatial aggregation,
there
are significant deviations from a perfect correlation (Liu
andLi, 2014). AOD due to aerosol light extinction is determinedby
the vertical integral of the extinction cross section,
pro-portional to the vertical integral of the second moment of
theaerosol size distribution. In turn, for a given chemical
com-position of aerosol particles, the CCN concentration is
thezeroth moment of the size distribution for particles exceed-ing
a size threshold that depends on supersaturation. In thefollowing,
the different problems are discussed in more de-tail, together with
options for a better proxy for CCN fromsatellite remote
sensing.
2.1 Vertical co-location
Stier (2016) investigated the correlation between AOD andCCN as
represented in a climate model. He confirmed amostly positive
correlation of the temporal variability of thetwo quantities,
although in some regions the correlation islow or even negative. A
key reason for the partly low cor-relation is the fact that AOD is
a vertically integrated quan-tity and may include aerosol layers
that are not interactingwith clouds. A similar result was reported
from a statisti-cal analysis of satellite data: cloud microphysical
parame-ters correlate well with aerosol properties only if the
verticalalignment of the aerosol and cloud layers is accounted
for(Costantino and Bréon, 2010, 2013). More recently, Paine-mal et
al. (2020) demonstrate a much higher correlation be-tween Nd and
aerosol extinction coefficients below cloudtop sampled from
satellite lidar compared to Nd vs. AOD.Ship measurements of CCN and
microwave-retrieved Nd atcloud base between Los Angeles and Hawaii
show a weakerβ metric as the boundary layer deepens, thus
indicating thatsurface aerosol measurements become less
representative foraerosol variability at cloud base as the boundary
layer deep-ens (Painemal et al., 2017), or that the updraughts
becomehigh enough to activate smaller aerosols than the
accumula-tion mode. In situ observations suggest that AOD may
evenbe anticorrelated with CCN at cloud base (Kacarab et
al.,2020).
A way forward is the use of spaceborne vertically
resolvedobservations such as lidar measurements (Shinozuka et
al.,2015; Stier, 2016). The Cloud-Aerosol Lidar and
InfraredPathfinder Satellite Observations (CALIPSO; Winker et
al.,2009) lidar retrieves aerosol backscatter profiles and thus
iscapable of identifying aerosol layers (Costantino and
Bréon,2010). Profiles of aerosol particle extinction are
inferredfrom these backscatter profiles by using typical
extinction-to-backscatter ratios based on aerosol type. However,
the signalis not sensitive to smaller aerosol concentrations, which
ham-pers a quantitative analysis at the large scale
(Watson-Parriset al., 2018; Ma et al., 2018). For situations with
sufficientaerosol loading for reliable CALIPSO aerosol profile
ob-servations, methods for retrieving CCN concentrations
fromground-based lidar measurements can be adapted (Feingoldand
Grund, 1994; Lv et al., 2018; Haarig et al., 2019). These
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15084 J. Quaas et al.: Twomey from satellite
methods apply empirical
extinction-to-particle-concentrationrelationships to obtain input
for CCN concentrations for dif-ferent aerosol types (Mamouri and
Ansmann, 2016). In thefuture, the EarthCARE satellite mission
currently scheduledfor launch in 2022 (Illingworth et al., 2015;
Hélière et al.,2017) shows promise to extend and improve upon the
successof the CALIPSO mission. Its Atmospheric Lidar (ATLID)is a
linearly polarised high-spectral-resolution lidar (HSRL)operating
at a wavelength of 355 nm. The instrument allowsthe direct
inference of profiles of aerosol backscatter andextinction
coefficients, thereby substantially increasing theretrieval
accuracy. The direct retrieval of the extinction-to-backscatter
(lidar) ratio (Müller et al., 2007) with ATLID(compared to the use
of pre-set values in the CALIPSO re-trieval; Kim et al., 2018) and
the large difference betweenlidar ratios of aerosols (20–80 sr) and
clouds (20–30 sr) arealso expected to provide better distinction
between opticallythin cirrus clouds and aerosols than CALIPSO
(Reverdyet al., 2015). While a similar sensitivity to aerosol load
is ex-pected for ATLID and CALIOP observations during night-time,
ATLID promises a better daytime sensitivity. Earth-CARE is also
expected to provide better distinction betweenoptically thin clouds
and aerosols than CALIPSO (Reverdyet al., 2015). Airborne
measurements have shown that furtherutilising HSRL at more than one
wavelength (extending be-yond ATLID) would provide substantial
additional informa-tion content for retrieving vertically resolved
aerosol param-eters, especially when combined with polarimeter
measure-ments (Burton et al., 2016). From the
passive-remote-sensingperspective, promising results have been
obtained for re-trievals of aerosol vertical information from
near-ultravioletpolarimetry (Wu et al., 2016), although the quality
degradesfor small aerosol concentrations. Passive observations
withhigh spectral resolution within the oxygen A absorption
bandaround 760 nm can also be used to infer aerosol layer
height(Hollstein and Fischer, 2014; Geddes and Bösch, 2015).In
particular, an operational aerosol layer height productis now
available from the Tropospheric Monitoring Instru-ment (TROPOMI)
flown on the Sentinel-5p mission (Sanderset al., 2015). Also, a
recent study presents promising re-sults based on Orbiting Carbon
Observatory 2 (OCO-2) ob-servations (Zeng et al., 2020). In
particular, a combinationof such approaches, e.g. passive
polarimetry and active lidarobservations (Stamnes et al., 2018) or
multi-angle polarime-try and oxygen A band observations as planned
for NASA’sPlankton, Aerosol, Cloud, ocean Ecosystem (PACE)
mission(Remer et al., 2019), shows potential. Retrievals could
alsocombine observations and model adjoints to constrain
below-cloud aerosol number, which is directly relevant for
aerosol–cloud interactions (Saide et al., 2012).
In summary, the lack of vertical co-location between re-trieved
CCN proxy and clouds leads to an underestimate inNd–CCN sensitivity
(Costantino and Bréon, 2010). Modelstudies suggest that this bias
may be approximately cancelledby a corresponding bias in the
anthropogenic component of
the cloud base CCN (Gryspeerdt et al., 2017). However, theextent
of this cancellation in current observational studies isunknown and
requires further investigation. For an accurateestimation of β, the
use of lidar retrievals seems to be thebest way forward, while
additional information on the ver-tical distribution of aerosol can
also be gained from presentand upcoming passive satellite
instruments.
2.2 Horizontal co-location
In studies examining β from satellite data, spatial
aggregatesare considered (i.e. β as in Eq. 4), in which the aerosol
re-trievals in the cloud-free pixels are averaged at a coarse
res-olution (such as 1◦) and taken to define the relation with
Ndretrievals in the same grid box (Quaas et al., 2008). Thisassumes
that the aerosol population is horizontally homo-geneous at such
large scales. According to Anderson et al.(2003), this is often the
case. It has been confirmed from air-craft data for the
stratocumulus cases investigated by Shi-nozuka et al. (2020).
However, CCN is consumed whendroplets activate, and aerosol is
scavenged when clouds pre-cipitate. Hence, the assumption of
aerosol concentration hor-izontal homogeneity is questionable, at
least in precipitatingclouds.
It is the aerosol in air masses before cloud particlesform that
is relevant to compute the aerosol impact on Nd(Gryspeerdt et al.,
2015). In one of the early aerosol–cloudinteraction studies from
satellite data Bréon et al. (2002) usedtrajectories to identify
cloudless situations in which aerosolretrievals were possible for
air masses that later formedclouds. This is a promising solution
but it requires muchmore effort than the simpler co-location
assumptions. It alsorequires reliable, high-resolution information
about atmo-spheric trajectories. Another complication is that the
forma-tion rate of secondary aerosol is enhanced by aqueous
phasereactions, potentially enhancing aerosol concentrations in
thevicinity of clouds (Jeong and Li, 2010). Such trajectory
ap-proaches are particularly useful when they exploit the
hightemporal resolution that is available from geostationary
satel-lites. Aerosol retrievals from geostationary satellites may
becombined using trajectory modelling to link these to cloudsthat
form in these air masses (Kikuchi et al., 2018), or alsothe aerosol
retrieval from a polar orbiter could be related toclouds retrieved
from geostationary satellites that form in thesame air masses
(Christensen et al., 2020).
Altogether, the lack of horizontal co-location may implysomewhat
too low β due to the potential de-correlation ofCCN concentrations
and Nd in situations with spatially het-erogeneous aerosol. The
consideration of backward trajec-tory analysis seems the best
option to address the issue sincethere is no solution yet to
retrieve aerosols below or withinclouds from satellite.
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2.3 Hygroscopic growth of aerosol particles
The extinction of solar radiation by aerosol particles is
astrong function of the hygroscopic growth of the particles.Haze
particles attenuate much more sunlight compared tothe same aerosol
particle ensemble in dry conditions. AODis thus heavily influenced
by the variability of relative hu-midity. The light extinction
caused by dry particles (at rel-ative humidities below 30 %) is
much better correlated toCCN concentrations than the extinction of
particles at am-bient relative humidity (Shinozuka et al., 2015).
Liu and Li(2018) showed that using total AOD compared to dry AODas
a CCN proxy when estimating β from measurements atdifferent
Atmospheric Radiation Measurements (ARM) sitesresulted in a 23 %
underestimate. A way forward is to ap-ply parameterisations in
terms of retrievals of relative hu-midity to account for the
aerosol swelling. These need infor-mation about aerosol
hygroscopicity and relative humidityat the appropriate scale.
Hygroscopicity information couldrely on the kappa-Köhler
parameterisation approach (Pettersand Kreidenweis, 2007; Pringle et
al., 2010), and a param-eterisation of small-scale to mesoscale
humidity variabilitycould make use of approaches exploited in
general circula-tion models (GCMs) (Quaas, 2012; Petersik et al.,
2018). An-other alternative would be to retrieve the amount of
aerosolwater, making use of the real part of the refractive
index(Schuster et al., 2009). This would allow the translation
ofthe size distribution of humidified aerosol particles to
thecorresponding dry size distribution. In the near future,
accu-rate refractive index retrievals are expected from
polarime-ters such as the SPEXone instrument on the NASA
PACEmission (Hasekamp et al., 2019b; Werdell et al., 2019), to
belaunched in 2022.
Summarising, using AOD as a proxy for CCN resultsin low-biased
estimates of β due to aerosol swelling. Ap-proaches to parameterise
the dry aerosol properties on thebasis of the humidified one can
help alleviate the problem.
2.4 Approaches using aerosol index, column-CCN,reanalysis or
cloud base updraught
The aerosol index (AI1) is defined as the product of AODand the
Ångström exponent (Deuzé et al., 2001). This latterquantity is the
slope of the spectral variation in AOD and istypically larger for
smaller particles (Ångström, 1929). AIis more weighted towards
smaller particles, which makesit better suited as a proxy for CCN
concentration at typi-cal supersaturations than AOD. For log-normal
size distribu-tions, AI is approximately proportional to the column
aerosolnumber concentration (Nakajima et al., 2001). Studies us-ing
models concluded that AI is a better predictor for CCN
1The difference in the measured radiance in the ultraviolet
spec-tral range from a purely Rayleigh-scattering atmosphere is
alsocalled the UV-AI (Torres et al., 1998), but the UV-AI is
differentfrom the AI as used in this review.
(Stier, 2016) and that AI–Nd relationships are better suited
topredict 1Nd, ant than AOD–Nd relationships (Penner et al.,2011;
Gryspeerdt et al., 2017). However, retrievals of theÅngström
exponent, and thus of AI, over land are not re-ported in
operational products such as the MODIS dark tar-get algorithm and
are in general not as reliable as they areover ocean (Lee and
Chung, 2013; Sayer et al., 2013).
Further refining this idea, Hasekamp et al. (2019a) aimedto
retrieve the column CCN concentrations over oceans. Theanalysis of
polarimetric observations allowed us to accountfor some aspects of
the aerosol particle size distribution, andfor particle sphericity,
which is related to particle hygroscop-icity. This column-CCN
retrieval implied larger β, increasingthe resulting RFaci by almost
50 %. It is an example of howadditional information from
polarimetry is useful for study-ing the CCN-to-Nd relationship.
However, neither the approach of Hasekamp et al. (2019a)nor the
use of AI overcomes the problem of lack of hori-zontal and vertical
coincidence of CCN and Nd retrievals.An option to overcome this
problem is to make use of ad-ditional model information.
Satellite-retrieved AOD is as-similated into aerosol models, e.g.
in the Copernicus Atmo-sphere Monitoring Service (CAMS, Benedetti
et al., 2009;Inness et al., 2019) or the Modern-Era Retrospective
Anal-ysis for Research and Applications (version 2; MERRA-2Gelaro
et al., 2017). The model predictions are applied toobtain aerosol
information beneath clouds. Such aerosol re-analysis information
has been used for assessing RFaci inseveral studies (Bellouin et
al., 2013; McCoy et al., 2017;Bellouin et al., 2020a). However,
assessing the validity ofmodel results requires extensive and
rigorous evaluation, es-pecially for coarsely resolved models with
regard to aerosolscavenging below clouds. For this, independent
data are re-quired such as from ground-based observations or
satelliteobservations from sensors other than those that are
assimi-lated.
Yet another solution initially proposed by Feingold et al.(1998)
and applied to satellite retrievals by Rosenfeld et al.(2016) is to
parameterise the cloud base updraught, w, on thebasis of cloud
retrievals, rather than to retrieve the aerosol.For convective
clouds, Zheng et al. (2015) suggested thatw scales with cloud base
altitude, which can be retrievedfrom satellites. For stratocumulus
clouds, Zheng et al. (2016)proposed that updraught is a function of
cloud-top radiativecooling, and that this can be computed by
radiative trans-fer modelling on the basis of cloud quantities
retrieved frompassive sensors and thermodynamic profiles from
meteoro-logical re-analyses. The retrieved profiles of re together
withderivations of supersaturation as a function of w and
Nd(Rosenfeld et al., 2016) then allow the parameterisation ofthe
CCN concentration at any given supersaturation. This ap-proach does
not suffer from the problem of a lower detec-tion limit. However,
it has not yet been used to quantify theTwomey effect.
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Concluding, all four approaches alleviate many
problemsencountered when using AOD. An ideal solution may be
thecombination of several of these by also assimilating, in
ad-dition to AOD, polarimetric satellite observations, as well
aslidar measurements, into the analysis of the atmospheric statein
high-resolution models.
3 Remote sensing of cloud droplet concentrations
The problem of the remotely sensed Nd as used to estimateβ has
three different facets to it, which will be discussed inthis
section, namely the following.
- Consideration of re rather than Nd in aerosol–cloud
in-teraction studies. In many studies, the droplet effectiveradius,
re, is used, and the datasets are stratified with re-spect to L in
order to estimate β. This is very difficultto perform adequately
and leads to biases.
- Biases in the retrieved Nd . For the assessment of
sen-sitivity, systematic (rather than random) errors in
re-trievedNd are relevant. Also,Nd is not retrieved in stan-dard
operational procedures, so that inconsistencies be-tween the
retrieval of standard components and in thecomputation of Nd on the
basis of retrievals can lead toadditional errors.
- Relationship of Nd formed at activation with retrievedand
radiation-relevant Nd, top. Retrieved Nd, top refersto the drop
concentration within the top one to two opti-cal depths of the
clouds, and it is Nd, top that is relevantfor determining the cloud
radiative effect. Nd sink pro-cesses such as coagulation imply that
Nd, top is smallerthan the one resulting from activation above
cloud base,Nd, base.
Nd is vertically constant for single-layer, purely
liquid-waterclouds with (i) a vertically homogeneous droplet size
spec-trum, (ii) for adiabatically stratified clouds or (iii) for
sub-adiabatic clouds in which mixing is homogeneous. However,in
many situations, precipitation formation or entrainmentcan lead to
reduction of Nd above cloud base. In such sit-uations, it is Nd,
top that is relevant to determine the cloudradiative effect (cloud
albedo in Eq. 2). Building on Eq. (4)thus gives
1Nd, top,ant
=dNd, topdNd, base
·
∞∫w=−∞
∂Nd, base
∂ lna
∣∣∣∣w
P(w)P(a)dw
·1 lnaant = β̂ ·1 lnaant . (5)
When estimating β as a regression coefficient from, for
ex-ample, satellite-retrieved Nd and a proxy for CCN such asAOD, it
is thus this β̂ that is inferred.
3.1 Considering re rather than Nd
Many past studies have used operationally retrieved re
ratherthan Nd in aerosol–cloud interaction studies. However, re isa
function of bothNd and L. This introduces the requirementfor
stratifying the data with respect to L in order to estimateβ̂. To
further complicate matters, Nd and L have been foundto be
correlated (e.g. Michibata et al., 2016; Gryspeerdt et al.,2019). A
precise estimation of β̂ is thus only possible fora large amount of
data combined with suitable binning byL. Errors in this approach
that are related to a lack of dataincrease at aggregated scales
(McComiskey and Feingold,2012). Using derived Nd is therefore
preferable to avoid un-necessary complications.
3.2 Biases in the Nd retrieval
Satellite retrievals of Nd were extensively reviewed byGrosvenor
et al. (2018). Since Nd currently is not retrievedby operational
algorithms and new developments to retrieveNd (e.g. from
polarimetry) are still in their infancy, the mostfrequently used
method is to infer Nd from retrieved re andcloud optical depth, τc,
using the relationship
Nd = γ · τ12
c · r−
52
e , (6)
where γ ≈ 1.37× 10−5 m−0.5 is a parameter provided as aconstant
here but more realistically depending on cloud basetemperature and
pressure, the adiabatic fraction, and the dropsize distribution
breadth (Boers et al., 2006; Quaas et al.,2006; Grosvenor et al.,
2018). The relationship in Eq. (6) as-sumes that clouds are
adiabatic or nearly adiabatic (i.e. adia-batic clouds or
sub-adiabatic clouds with homogeneous mix-ing only; Brenguier et
al., 2000). The most common methoduses a bispectral approach to
retrieve re and τc (Nakajimaand King, 1990). Various error sources
lead to an overall re-trieval error forNd (Grosvenor et al., 2018;
Wolf et al., 2019).As can be deduced form Eq. (6), the most
important contri-butions are from retrieval errors in re. Other
error sourcesare the uncertainty in sub-adiabatic factor, the cloud
modelused in the retrieval, and the droplet size distribution
width.Satellite retrievals of the vertical profile of cloud droplet
sizemay help to improve the retrieval (Chang and Li, 2002; Chenet
al., 2008). Grosvenor et al. (2018) identified biases of
re-trievedNd in particular for broken cloud regimes and at
largesolar zenith angles. In stratocumulus, it was suggested
thatthe retrieval yields the most trustworthy results when
con-sidering only the brightest pixels (Zhu et al., 2018). For
theideal case of homogeneous, low-latitude stratiform
clouds,relative errors in the Nd retrieval at pixel scale are
quanti-fied as 78 % (Grosvenor et al., 2018). In such cases, the
errorwas assumed to be random. However, systematic errors oc-cur in
particular in broken cloud regimes and for large solarzenith
angles, leading to an underestimation (broken cloudi-ness) and
overestimation (large solar zenith angles), respec-tively, ofNd.
Painemal et al. (2020) addressed theNd bias for
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broken clouds by only samplingNd retrieved for large
clouds(larger than 5 km× 5 km) to find that the relation
betweenNdand aerosols is substantially enhanced.
For improvements in estimates of Nd, it would be bene-ficial to
formulate a retrieval in terms of Nd directly ratherthan in terms
of re and τc. It is also possible to reduce un-certainties in
retrievals of re and τc, or to reduce uncertain-ties related to
assumptions of the vertical structure of thecloud and particle size
distribution shape. Approaches toquantify and partly correct for
retrieval biases as discussedin Grosvenor et al. (2018) include
accounting for cloud het-erogeneity by using those channels in
passive imagers thatprovide spatial resolution that exceeds the one
at which thestandard retrieval products are provided (Zhang et al.,
2016).The combination of passive observations with radar may
fur-ther improve the retrieval (Posselt et al., 2017).
Substan-tially more accurate retrievals of re and additional
relevantinformation about droplet size distributions may also
comefrom multi-angular polarimetric measurements (Alexandrovet al.,
2012a, b; Shang et al., 2019), which will be possi-ble from orbit
at pixel level from the Hyper-Angular Rain-bow Polarimeter-2
(HARP-2) on the NASA PACE mission(Martins et al., 2018; McBride et
al., 2019). Polarimetricretrievals allow the inference of the
spectral width or gen-eral shape of the droplet size distribution
at cloud top (Huet al., 2007). This approach is not substantially
sensitive tosub-pixel cloudiness, mixed-phase conditions and 3D
radia-tive effects (Alexandrov et al., 2012b). The sensitivity of
de-rived Nd to uncertainties in re from polarimetric retrievalsmay
further be reduced by additionally inferring cloud phys-ical
thickness. In this case, Nd can be inferred to be linearin τc and
inversely linear in geometrical thickness and meandroplet
extinction cross section at cloud top (Sinclair et al.,2019). The
geometrical thickness may also be inferred fromtotal and/or
polarised reflectances measured in oxygen or wa-ter vapour
absorption bands (Desmons et al., 2013; Sanghaviet al., 2015;
Richardson et al., 2019; Sinclair et al., 2019)or by retrieving
cloud base using lidar (Mülmenstädt et al.,2018) or using
multi-angle observations (Böhm et al., 2019).When exploiting
passive observations together with lidar,Ndat cloud top can be
robustly inferred as the ratio of in-cloudextinction (lidar) and
extinction cross section (passive). Aslightly less direct approach
using depolarisation to estimateextinction and effective radius to
estimate extinction crosssection has been presented by Hu et al.
(2007).
3.3 Relationship between Nd formed at CCN activationand
retrieved radiation-relevant Nd
In stratiform clouds, droplets form in updraughts near cloudbase
which is where Nd most closely relates to CCN. Inconvective clouds,
updraught in some cases increases withheight above cloud base.
Hence, additional CCN may acti-vate above cloud base and lead to
vertically increasing Nd inthe lower third of the cloud with a
decrease further up (Endo
et al., 2015). However, in most cumulus clouds, and in
strat-iform clouds, Nd is found to be largest at cloud base and
toslightly decrease above it (Jiang et al., 2008; Small et
al.,2009; vanZanten et al., 2011). In the approach discussed
byGrosvenor et al. (2018), the retrieved Nd is representative ofthe
cloud-top reflectance, and thus the relevant proxy for theNd that
matters for cloud albedo and RFaci (Platnick, 2000).To which extent
the microphysical structure of lower partsof a cloud exactly
impacts radiation (weighting function)depends on the multiple
scattering and thus on the verticalstructure of Nd itself
(Platnick, 2000; Krisna et al., 2018).For vertically constant Nd,
the retrieved Nd represents thedroplet concentration formed by CCN
activation. However,there are Nd sinks, in particular due to
collision and coales-cence (in liquid clouds, the autoconversion
and accretion, or“warm rain” processes) that lead to droplet
depletion. Wood(2006) demonstrated that the depletion is
exponential in pre-cipitation rate and estimated a loss in Nd of
100 cm−3 d−1
for precipitation rates of 1 mm d−1. There may also be lat-eral
and vertical mixing (of heterogeneous type; Lehmannet al., 2009) of
cloud air with environmental cloud-free airthat can lead to the
full evaporation of droplets. In both sinksfor Nd, the one due to
precipitation formation and the onedue to mixing, the retrievedNd
is expected to be smaller thanthe Nd formed at activation of CCN.
In an aged cloud, how-ever, updraughts may have decayed such that
no additionaldroplets are formed, while existing droplets persist,
or maybe advected from elsewhere. Also, in case they are very
large,raindrops may break up into droplets, in which case Nd is
in-creased. Arguably, it is the right choice to relate the
retrievedNd, as the radiation-relevant one, to CCN, i.e. to use β̂,
whencomputing the Nd-to-CCN sensitivity with the aim to con-strain
RFaci.
Cloud-resolving models are a good tool to investigatethese
interpretations (McComiskey and Feingold, 2012). Fig-ure 1 shows an
analysis of a large-domain large-eddy sim-ulation with the ICON-LEM
model (Heinze et al., 2017;Costa-Surós et al., 2020). CCN
concentrations in these simu-lations are relaxed towards
pre-computed spatially and tem-porally varying fields and are
consumed at activation. In the22 million grid columns, the droplet
concentration at cloudtop (what is retrieved from satellites) is
compared to themaximum droplet concentration (approximately the
concen-tration of activated CCN divided by formed droplets).
Thisdemonstrates that there is a link between the droplet
concen-tration formed at activation and Nd determining the cloud
ra-diative effect at its top. These two quantities correlate
ratherwell in the joint histogram, though that link is far from one
toone. The second plot (Fig. 1b) assesses the possibility to in-fer
cloud-top Nd from cloud-top re and τc (Grosvenor et al.,2018). For
this, the MODIS simulator (Pincus et al., 2012)that is part of the
Cloud Feedback Model IntercomparisonProject (CFMIP) Observational
Simulator Package (COSP;Bodas-Salcedo et al., 2011) is applied to
the model outputto compute cloud-top re and τc. From these, Nd is
computed
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15088 J. Quaas et al.: Twomey from satellite
as in Eq. (6). This approach mimics the satellite retrieval
butassumes no retrieval errors; i.e. the comparison is a lowerbound
on the accuracy of the retrievedNd in representing theactual Nd at
cloud top. There is a meaningful co-variationin the two quantities,
but it is far from perfect. In particu-lar, there is a systematic
overestimation of Nd in the retrievalapproach, especially at low
Nd. The relative error even is afunction of Nd, with larger
relative errors at low Nd.
In conclusion, the fact that cloud-topNd is in general lowerthan
Nd at activation height implies that β̂ is indeed some-what smaller
than unity. This is not a problem but rather a de-sired analysis
result when studying the Twomey effect. How-ever, Nd obtained from
retrieval products is biased high forlow values of Nd, top. This
relative error, which is a functionof Nd, implies that the
regression between satellite-derivedNd and CCN yields a sensitivity
that is too weak.
4 Cloud-regime dependence
Aerosol–cloud interactions depend on cloud regime (Stevensand
Feingold, 2009; Mülmenstädt and Feingold, 2018).When it comes to
RFaci, there are three reasons for this:(i) the radiative
sensitivity (Oreopoulos and Platnick, 2008;Alterskjær et al.,
2012), i.e. the first two terms on the right-hand-side of Eq. (2)
(in particular the sensitivity expressedin Eq. 1); (ii) the
updraught dependence of β̂; and (iii) thedependence of the relation
of cloud-top to cloud base Ndto characteristics of turbulence and
rain. The latter two areof interest here. “Cloud regime” thus here
means, a clus-
ter of clouds with similar P(w) and similar dNd, topdNd,
base
inEq. (5). When considering CCN at a certain
supersaturationlevel, β̂ is larger at larger updraught, w
(MacDonald et al.,2020). Broadly, cumulus clouds have largerw than
stratiformclouds. In addition, clouds over land usually have larger
wthan clouds over ocean. Building on Eq. (5), this suggests
aregime-based analysis expressed as
1Nd, top,ant =dNd, top
dlna
∣∣∣∣∣regime
·1 lnaant . (7)
Figure 2 shows the spatial distribution of the Nd – AI
regres-sion coefficient from its temporal variability within 1◦×
1◦
grid boxes. The large spatial heterogeneity is not
straightfor-ward to interpret. Some problems may be due to the lack
ofaerosol retrieval sensitivity (e.g. in regions with low
CCNconcentrations such as the southern oceans) or lack of ver-tical
or horizontal co-incidence (e.g. in regions with het-erogeneous
aerosol and large cloud coverage such as mid-latitude storm
tracks). However, aspects of the geographicalheterogeneity may
indeed be attributable to physical and rel-evant reasons. However,
it is difficult to determine any at-tributable factors in the
spatial and cloud-regime variationsin β̂ (Gryspeerdt and Stier,
2012) before retrieval errors areremedied.
In precipitating situations, the two-way interactions canlead to
large challenges in determining the β̂ term (Ekmanet al., 2011).
Precipitation scavenges aerosol and, in certainsituations, the
interplay between aerosol, droplet concentra-tions and
precipitation determines both aerosol and dropletconcentrations.
This may yield bifurcations between situa-tions with large Nd in
which no drizzle forms and very lowNd and cloud dissolution when
precipitation forms (e.g. Ya-maguchi et al., 2017). In such
situations, it is particularlychallenging to identify the Nd–CCN
concentration sensitiv-ity.
5 Aggregation scale
The impact of aggregation scale on estimates of β has
beendiscussed in detail by McComiskey and Feingold (2012).Their key
conclusion is that at scales larger than the cloudvariability scale
of about 1 to 10 km, aerosol and cloud databecome de-correlated so
that the diagnosed β becomes lessand less representative for
individual cloud parcels. In turn,Sekiguchi et al. (2003) computed
β̂ for different aggregationscales and demonstrated that it
actually increases with largerscales. An analysis of
spatio-temporal vs. temporal-only co-variability of Nd and AOD by
Grandey and Stier (2010)found that β̂ is larger when considering
spatio-temporal vari-ability over entire regions compared to only
temporal vari-ability at individual 1◦× 1◦ grid boxes. These
results areopposite to those expected from the process-based
conclu-sions of McComiskey and Feingold (2012). A possible prob-lem
in the Sekiguchi et al. (2003) study is their use of rerather than
Nd, and the subsequent need to stratify by L.McComiskey and
Feingold (2012) demonstrated that this ap-proach becomes more
problematic with increasing aggrega-tion scale. However, their
analysis suggested a low-bias inβ at coarser scales due to
stratification by L. Reduced β̂ atsmall scales could occur if
aerosol conditions become too ho-mogeneous to diagnose the full
range of co-variability due tosmaller sample sizes at smaller
scales.
Concluding, from a process point of view, aggregationover larger
scales is expected to lead to a decrease in esti-mated β̂. In turn,
to study the large-scale Twomey effect, anaggregate Nd–CCN
relationship is desired as it is the large-scale 1Nd, ant that
matters for the radiation perturbation andbecause the anthropogenic
aerosol perturbation can only beinferred at a large scale. The
often adopted choice of a 1◦×1◦
gridding is somewhat motivated by the suggestion that this isa
scale at which aerosol concentrations are considered ho-mogeneous
(Anderson et al., 2003) and loosely (to withina factor of about 2
in each horizontal direction; re-analysesare to closer ∼ 50 km
scales, and many general circulationmodels still are as coarse as
200 km) related to the scale atwhich models infer the anthropogenic
perturbation of CCN.A rigorous study on the scale dependency of β̂
and the con-sequences thereof for RFaci would be desirable.
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Figure 1. Analysis of Nd in the “virtual reality” of a
cloud-resolving simulation: droplet number concentration (cm−3)
from the ICONlarge-eddy simulation (156 m horizontal resolution)
over the domain of Germany for 2 May 2013 (Heinze et al., 2017),
for the overpasstimes of the Terra and Aqua satellites for which
the swath of the MODIS instrument covered the domain (twice around
10:30 local solartime for Terra, twice around 13:30 for Aqua) even
if no actual data are used in this analysis (Costa-Surós et al.,
2020). Joint histograms,normalised along the y axis as in
Gryspeerdt et al. (2016) for (a) column-maximum (proxy for
activated CCN) vs. cloud-top Nd (taken atτc = 1 integrated from
cloud top) and (b) Nd derived from re and τc as in Grosvenor et al.
(2018) vs. cloud-top Nd, where both quantitiesare computed as seen
from a satellite using the Cloud Feedback Model Intercomparison
project (CFMIP) Observational Simulator PackageCOSP (Bodas-Salcedo
et al., 2011). The blue line is the mean in each bin for cloud-top
Nd.
Figure 2. Regression coefficients ofNd computed on the basis of
retrievals of the MODerate Resolution Imaging Spectroradiometer
(MODIS;Platnick et al., 2017) as in Grosvenor et al. (2018) and AI
from MODIS (Levy et al., 2013) from the daily temporal variability
in grid boxesof 1◦× 1◦.
6 Quantification for the regression coefficient
When sensitivities are approximated by linear regression
co-efficients from an ordinary least-squares (OLS) line
fittingmethod, rather than derived in the form of joint
histograms,the problem of regression dilution arises to the extent
thatthe aerosol quantity shows errors: the regression
coefficientbecomes gradually smaller as the stochastic error
increases(Cantrell, 2008; Pitkänen et al., 2016; Wu and Yu,
2018).Regression dilution, also known as regression attenuation,
isa problem if the independent variable (x axis) in the regres-sion
is subject to a statistical error. If the regression methoddoes not
take the statistical error into account, which is oftenthe case
(for example in OLS), the regression coefficient isalways
systematically biased low. In turn, statistical error on
the dependent variable (y axis) only causes uncertainty in
theregression coefficient but no systematic bias. This is
quanti-fied for the column-CCN vs. Nd sensitivity evaluated as
aregression coefficient in Fig. 3. Due to the regression dilu-tion,
the sensitivity decreases by factors of 2 to 3 as the errorin
column CCN increases when considering relative errorsof 50 %. This
can to a large extent be remedied by ignor-ing data points at low
CCN concentrations from the regres-sion (Fig. 3b). However, this
solution is limited to regionsnot dominated by low aerosol
concentrations. Figure 3 alsoillustrates that an absolute bias in
the data translates to rela-tive bias in logarithmic scale.
Therefore, if no bias correctionis applied, an absolute bias in the
data will cause a bias inthe sensitivity estimates. As shown by
Pitkänen et al. (2016),the regression dilution in turn becomes
weaker at coarser ag-
https://doi.org/10.5194/acp-20-15079-2020 Atmos. Chem. Phys.,
20, 15079–15099, 2020
-
15090 J. Quaas et al.: Twomey from satellite
Figure 3. Nd–column CCN sensitivity as a function of the
stochastic error in column CCN (absolute additive error) in an
emulated analysisas in Hasekamp et al. (2019a), for different
relative (multiplicative) errors, for (a) the full range of data,
including low NCCN values and(b) excluding NCCN < 107 cm−2.
Hasekamp et al. (2019a) suggest a realistic error is about 0.2
·NCCN+ 4× 106 cm−2.
gregation scales in cases of auto-correlated data, which isthe
case for aerosol concentrations. This is of relevance inthe case of
both temporal and spatial aggregation. In otherwords, the
systematic low-bias in the sensitivity is reduced ifdata are
aggregated. This could partly explain some previousfindings of
increasing sensitivity with decreasing resolution(see discussion in
the previous section), in addition to the ac-tual bias due to the
aggregation over a smaller scale of cloudprocesses. These
considerations imply that it is necessary toeither analyse the full
variability of aerosol–cloud interac-tions, e.g. in the form of
joint histograms, or to account forthe regression dilution using
established mathematical ap-proaches that properly consider
measurement uncertainties,as discussed in Mikkonen et al. (2019),
for instance.
7 Conclusions
The radiative forcing due to aerosol–cloud interactions, orthe
Twomey effect, requires quantification based on observa-tional
data, since models are associated with large uncertain-ties. At a
large scale, this calls for satellite retrievals. Thereare,
however, large challenges when using satellite data andthis review
summarises these challenges and suggests somepotential ways
forward. The key data-related question isthe sensitivity of droplet
concentration, Nd, to perturbationsin the cloud-active aerosol,
i.e. the cloud condensation nu-clei (CCN) concentration at or above
cloud base. The mostwidely used proxy of the cloud base CCN
concentration isthe aerosol optical depth (AOD), or alternatively
the aerosolindex (AI), taken from cloud-free pixels in the vicinity
ofthe locations of the cloud retrievals. The four main caveatswith
AOD are the lack of vertical resolution, the additionalinfluence of
hygroscopic swelling, the fact that the detectedaerosol might be
not active as CCN nd the impossibility toretrieve it below clouds.
In terms of the vertical resolution,satellite-based lidar offers
help. However, current lidar re-trievals are even more constrained
to large aerosol concentra-tions than passive AOD retrievals.
EarthCARE’s ATLID lidarwill allow direct inference of the ratio of
backscatter to ex-
tinction, enabling greatly improved retrievals of aerosol
ex-tinction profile. Adding a second wavelength with ATLID
ca-pabilities and combining it with polarimetric measurementswould
substantially extend vertically resolved aerosol infor-mation
content. In terms of horizontal co-location, trajectorycomputations
may help to identify the aerosol representativeof that affecting
specific clouds. However, this requires extraeffort and reliable
information about trajectories. The hygro-scopic swelling can be
addressed by parameterisations thatuse retrievals and ancillary
data to compute the swelling. Fur-ther relevant information is
possible from polarimetric mea-surements.
Cloud droplet number concentration, Nd, is only indi-rectly
available from current operational satellite retrievals.It is
generally computed from retrieved cloud-top droplet ef-fective
radius, re, and cloud optical thickness, τc, leadingto substantial
biases in comparison to the cloud-top dropletnumber concentration,
especially in inhomogeneous, brokenand/or precipitating cloud
regimes. Sink processes for Ndand variability due to atmospheric
dynamics, including tur-bulent mixing, imply that the radiatively
relevant cloud-topNd relates imperfectly to the Nd formed by CCN
activation.In addition, at a given CCN concentration, the
updraughtvariability also leads to sensitivities of Nd to CCN that
aremuch less than 1. These latter two facts are not problematicwhen
assessing the Nd to aerosol sensitivity from data forthe estimation
of the Twomey effect. In fact, it is desirable toquantify at a
large scale the net impact of aerosol perturba-tions of the
(radiatively relevant) cloud-top Nd that accountsfor updraught and
Nd sink variability. However, it is neces-sary to operationally
retrieve Nd, rather than to indirectlycompute it from re and τc
retrievals. It is also necessary toimprove these retrievals in
particular for low droplet concen-trations and broken cloud
conditions. In addition, these re-trievals should take into account
additional information, e.g.about the onset of drizzle.
Regression dilution influences the statistically
inferredsensitivity as a result of stochastic retrieval errors in
CCNconcentration. On the one hand, at aggregate scales, this
Atmos. Chem. Phys., 20, 15079–15099, 2020
https://doi.org/10.5194/acp-20-15079-2020
-
J. Quaas et al.: Twomey from satellite 15091
problem becomes less relevant due to the autocorrelationof the
aerosol concentrations. The relationship between Nd,which varies at
cloud-dynamics scales, and CCN proxies be-comes weaker at aggregate
scales. Relative retrieval errors inNd that depend on actual Nd
(with larger high-biases at lowtrue Nd) lead to a further reduction
in the estimated sensi-tivity. It is thus necessary to account for
the impact of CCNerrors in the statistics and to optimise the
resolution of Ndand CCN retrievals towards cloud-scale
resolutions.
The recent study by Hasekamp et al. (2019a) made useof
polarimetric satellite measurements to suggest a global-ocean
average Nd-to-CCN sensitivity of 0.66. This, com-bined with
anthropogenic column-CCN concentrations andradiative sensitivities,
translates into a global Twomey ef-fect of −1.1 W m−2. The net
effect of the remaining prob-lems laid out above suggests that this
likely is still too lowan estimate for the Nd–CCN sensitivity,
implying a strongerTwomey effect. However, the estimate is in line
with an inde-pendent observation-based estimate of McCoy et al.
(2020)that used differences in Nd between pristine and polluted
re-gions in combination with GCM results as an emergent
con-straint. In any case, it is desirable to add the extra steps
toimprove the quantification supported by data for process
un-derstanding as well as for evaluating and improving
climatemodels.
In situ and ground-based observations, as well as analysisof
cloud-resolving dynamical models, may be a path forwardfor the
evaluation of critical aspects in the satellite-basedanalysis.
Important steps would be the quantification of up-draught PDFs for
different cloud regimes and the assessmentof horizontal homogeneity
of aerosol concentrations.
Data availability. The data used in Fig. 1 are the simulation
data asdescribed in Costa-Surós et al. (2020,
https://doi.org/10.5194/acp-20-5657-2020) and available upon
request due to the largeamount of data; it is securely saved in
tape archives at theDeutsches Klimarechenzentrum (DKRZ), which will
be accessi-ble for 10 years. The MODIS data used in Fig. 2 was
down-loaded from the Level-1 and Atmosphere Archive &
DistributionSystem (LAADS) Distributed Active Archive Center
(DAAC), lo-cated in the Goddard Space Flight Center in Greenbelt,
Maryland(https://ladsweb.nascom.nasa.gov/, last access: 19 November
2020,LAADS DAAC, 2020). The data used for Fig. 3 are archived
andavailable at
https://cera-www.dkrz.de/WDCC/ui/cerasearch/entry?acronym=DKRZ_LTA_1002_ds00001
(last access: 19 November2020, Hasekamp and Quaas, 2020).
Author contributions. JQ led the writing of the manuscript with
sig-nificant contributions from all authors.
Competing interests. The authors declare there are no
competinginterests.
Acknowledgements. The work of Johannes Quaas, Annica M. L.Ekman,
Athanasios Nenes and Philip Stier was supported by theEuropean
Union via its Horizon 2020 project FORCeS. The work ofAthanasios
Nenes was further supported by the European ResearchCouncil via the
project PyroTRACH. Philip Stier was also sup-ported by the European
Research Council (ERC) project constRain-ing the EffeCts of
Aerosols on Precipitation (RECAP). This revieworiginated from
discussions at the 2019 Nanjing workshop of
theAerosols-clouds-precipitation and climate (ACPC) initiative
(http://acpcinitiative.org/, last access: 13 November 2020) and
benefitedfrom discussions within the group “Study of aerosol–cloud
inter-actions based on satellite observations of the terrestrial
underlyingsurface–atmosphere system: a new frontier of atmospheric
science”,hosted by the International Space Science Institute
(ISSI). We thankthe German Climate Computing Centre (Deutsches
Klimarechen-zentrum, DRKZ) and the German Federal Ministry of
Educationand Research (BMBF) within the framework programme
“Researchfor Sustainable Development (FONA)”, https://www.fona.de/
(lastaccess: 13 November 2020) for making the ICON-LEM simula-tions
available. Po-Lun Ma and Johannes Mülmenstädt were sup-ported by
the U.S. Department of Energy, Office of Science, Of-fice of
Biological and Environmental Research, Earth System Mod-eling
program. Johannes Quaas is grateful to the NASA GoddardInstitute
for Space Studies, New York, for hospitality during a re-search
stay. We thank Andrew Ackerman and Patrick Chuang forconstructive
discussions. We thank the three anonymous reviewersand David
Painemal for helpful comments on the earlier version ofthe
manuscript. We acknowledge support from Leipzig Universityfor Open
Access Publishing.
Financial support. This research has been supported by the
Euro-pean Union’s Horizon 2020 research and innovation programmevia
H2020-EU.3.5.1. – Fighting and adapting to climate change(FORCeS
(grant agreement no. 821205)), the European ResearchCouncil (ERC)
via H2020-EU.1.1. – Excellent Science program(PyroTRACH (grant
agreement no. 726165) and RECAP (grantagreement no. 724602)), the
U.S. Department of Energy, Office ofScience, Office of Biological
and Environmental Research, EarthSystem Modeling program by the
“Enabling Aerosol-cloud interac-tions at GLobal
convection-permitting scalES (EAGLES) (projectno. 74358), and the
Pacific Northwest National Laboratory is oper-ated for the U.S.
Department of Energy by Battelle Memorial Insti-tute (contract no.
DE-AC05-76RL01830).
Review statement. This paper was edited by Frank Dentener
andreviewed by three anonymous referees.
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