The rapid adjustment, or semi-direct effect, of marine stratocumulus clouds
to elevated layers of absorbing aerosols may enhance or dampen the radiative
effect of aerosol–radiation interactions. Here we use large-eddy
simulations to investigate the sensitivity of stratocumulus clouds to the
properties of an absorbing aerosol layer located above the inversion layer,
with a focus on the location, timing, and strength of the radiative heat
perturbation. The sign of the daily mean semi-direct effect depends on the
properties and duration of the aerosol layer, the properties of the boundary
layer, and the model setup. Our results suggest that the daily mean
semi-direct effect is more elusive than previously assessed. We find that
the daily mean semi-direct effect is dominated by the distance between the
cloud and absorbing aerosol layer. Within the first 24 h the
semi-direct effect is positive but remains under 2 W m-2 unless the
aerosol layer is directly above the cloud. For longer durations, the daily
mean semi-direct effect is consistently negative but weakens by 30 %,
60 %, and 95 % when the distance between the cloud and aerosol layer is
100, 250, and 500 m, respectively. Both the cloud response and semi-direct
effect increase for thinner and denser layers of absorbing aerosol.
Considerable diurnal variations in the cloud response mean that an
instantaneous semi-direct effect is unrepresentative of the daily mean and
that observational studies may underestimate or overestimate semi-direct
effects depending on the observed time of day. The cloud response is
particularly sensitive to the mixing state of the boundary layer: well-mixed
boundary layers generally result in a negative daily mean semi-direct
effect, and poorly mixed boundary layers result in a positive daily mean
semi-direct effect. The properties of the boundary layer and model setup,
particularly the sea surface temperature, precipitation, and properties of
the air entrained from the free troposphere, also impact the magnitude of
the semi-direct effect and the timescale of adjustment. These results
suggest that the semi-direct effect simulated by coarse-resolution models
may be erroneous because the cloud response is sensitive to small-scale
processes, especially the sources and sinks of buoyancy.
Introduction
Semi-permanent decks of marine stratocumulus clouds represent an important
negative radiative effect within the Earth's energy budget (Hartmann
et al., 1992; Hartmann and Short, 1980; Wood, 2012). In addition, the sharp
inversion layer and small-scale turbulent processes that characterize the
formation and maintenance of these clouds represent considerable uncertainty
in climate models, so stratocumulus clouds remain a key uncertainty in
future climate projections (Bony and Dufresne,
2005; Klein et al., 2017; Wood, 2012). Marine stratocumulus clouds are
sensitive to sea surface temperature (SST) and large-scale atmospheric
properties above the inversion, like the subsidence rate and thermodynamic
properties of the overlying air mass, and below the inversion, like cloud
condensation nuclei sinks and sources, that impact turbulent processes and
dynamics throughout the boundary layer (e.g. Bretherton
et al., 2013; Feingold et al., 2010; Sandu et al., 2010). Therefore, small
changes to these properties could result in large changes to the fluxes of
radiation in the atmosphere.
Perturbations to the aerosol distribution result in a radiative forcing
through both aerosol–radiation and aerosol–cloud interactions; this
distinction separates the radiative forcing caused by aerosol scattering and
absorption of longwave and shortwave radiation from that caused by the
availability of cloud condensation nuclei. Aerosol–cloud interactions lead
to changes in cloud albedo and subsequent rapid adjustments to the cloud
properties that include changes to precipitation and cloud evolution
(Sherwood et al., 2015). Aerosol–radiation
interactions result in instantaneous changes to the extinction profile (also
referred to as the direct radiative effect) and therefore the heating profile,
which lead to rapid adjustments in the physical and radiative properties of
the cloud (referred to in this paper as the semi-direct effect, SDE, for
convenience). Quantifying rapid adjustments is important as they may act to
dampen or strengthen the instantaneous forcing. Aerosol–radiation
interactions represent an important uncertainty in the anthropogenic
radiative forcing of the climate over the industrial era, especially from
absorbing aerosol species such as black carbon, which may result in
pronounced semi-direct effects (Boucher et al.,
2013). In a recent climate model intercomparison study Stjern et al. (2017) found that a tenfold increase in black carbon emissions resulted in
a strong positive direct effect that was partially offset by a negative
SDE. Although all models agree on the sign (negative) they disagree on the
size of that offset, from 12 % to 63 % for the models studied by Stjern et
al. (2017). High-resolution models that can sufficiently represent the
dominant processes within the boundary layer and cloud are a powerful
benchmark to test the realism of the response simulated by
climate-scale models.
During the African dry season, which lasts from August to October, plumes of
strongly absorbing biomass burning aerosol from central Africa are
transported westward over the semi-permanent marine stratocumulus deck of
the southeast Atlantic Ocean, where they eventually subside and mix into the
boundary layer (Das et al., 2017).
Observational and modelling studies suggest that elevated absorbing layers
result in thicker clouds and a negative SDE (Adebiyi
and Zuidema, 2018; Johnson et al., 2004; Wilcox, 2010), which may impact the
stratocumulus-to-cumulus transition process
(Yamaguchi et al., 2015; Zhou et
al., 2017). Once mixed into the cloud layer the absorbing aerosol exerts
aerosol–radiation interactions that enhance cloud evaporation (Hill
and Dobbie, 2008; Johnson et al., 2004) and aerosol–cloud interactions that
impact microphysical and dynamical processes (e.g. Feingold
et al., 2010; Gordon et al., 2018; Hill et al., 2009). Observational studies
have used satellite retrievals from the NASA A-Train to investigate the
interaction between clouds and absorbing aerosol over the southeast
Atlantic. Wilcox (2010) used
co-located CALIPSO, OMI, and AMSR-E retrievals and found that for all
overcast scenes liquid water path (LWP) increased for high aerosol loading.
This response was attributed to absorbing aerosol layers above the cloud top,
enhancing the heating rate and decreasing entrainment across the inversion.
However, satellites do not provide direct observations of entrainment and an
alternative explanation could be that the aerosol layers travel in
relatively moist layers (Adebiyi et
al., 2015), increasing moisture transport across the inversion layer, even
if entrainment remained unchanged. In a study with a similar methodology,
Costantino and Bréon (2013)
separated the CALIPSO-derived aerosol layer heights into cases when the
smoke was close to (<100 m) and well separated (<750 m)
from the cloud top. The authors found that when the aerosol layers are well
separated from the cloud top the LWP and cloud optical thickness showed no
statistically significant dependence on aerosol loading. These results are
supported by Adebiyi and Zuidema (2018), who
used satellite observations and reanalysis products to show evidence that
the sensitivity of low cloud cover to elevated aerosol layers increased for
small cloud–aerosol gaps. These observations suggest that the distance
between the elevated aerosol layer and cloud layer plays an important role
in the strength of the SDE. Additionally, a recent satellite study of
cloud–aerosol gaps by Rajapakshe et al. (2017) suggests that the elevated aerosol layers may be closer to the cloud
than previously thought, which demonstrates that elevated layers may have an
even more important impact on the clouds.
The observations hint at the potential importance of the extent of
cloud–aerosol gaps for the SDE. However, this complexity is not reflected
in the frameworks presented in current reviews (Bond
et al., 2013; Koch and Del Genio, 2010), and there is a lack of
high-resolution modelling studies investigating the SDE from elevated
layers of absorbing aerosol. Johnson et al. (2004) used large-eddy simulation (LES) to investigate the semi-direct effect of
absorbing aerosols on non-precipitating marine stratocumulus. In an
experiment in which a ∼1 km thick layer of absorbing aerosol,
with an aerosol optical depth (AOD) of 0.2 at 550 nm, was present above the
marine boundary layer throughout a 48 h simulation, the absorbing aerosol
enhanced the temperature inversion at the top of the boundary layer,
weakening the entrainment rate across the inversion and producing a
shallower, moister boundary layer and a higher LWP. The 48 h mean SDE was
estimated to be -9.5 W m-2, almost entirely cancelling a direct
effect of +10.2 W m-2. Yamaguchi et al. (2015) and Zhou et al. (2017) used LES
models to investigate the transition of marine stratocumulus to cumulus in
the presence of a smoke layer. As the marine boundary layer deepened, the
cloud–aerosol gap decreased until the smoke layer made contact with the
cloud layer. Both studies found little LWP response when the smoke layer was
separated by a no-aerosol gap. Yamaguchi et al. (2015) found that the elevated smoke layer reduced boundary layer turbulence
and cloud cover through a decrease in longwave cloud-top cooling. By
isolating the aerosol heating above and below the boundary layer top,
Zhou et al. (2017) found that when the layer
was directly above the inversion layer the elevated aerosol layer
strengthened the inversion, inhibiting entrainment, and increased LWP and
cloud cover, resulting in a negative SDE. Global models have also been used
to investigate the radiative impact of biomass burning aerosol in
stratocumulus regions (e.g. Lu et
al., 2018; Penner et al., 2003; Sakaeda et al., 2011); however,
Das et al. (2017) show that these coarser-resolution models may be unable to reproduce the observed vertical
distribution of absorbing aerosol layers over the southeast Atlantic,
resulting in an underrepresentation of elevated aerosol layers and
increased uncertainty in their radiative impact.
In summary, observation and modelling studies suggest that the diurnal cycle
and evolution of marine stratocumulus are strongly impacted by the presence
of absorbing aerosol layers at and above the top of the boundary layer. The
SDE may act to counteract or enhance the direct effect, resulting in either
a small or large net radiative effect from aerosol–radiation interactions.
Yet the sensitivity of the SDE to the properties of the elevated aerosol
layer has not been fully investigated. In this study the UK Met Office Large
Eddy Model (LEM) is used to investigate and quantify the impact that the
properties of a persistent elevated absorbing aerosol layer have on the
cloud and radiative response of marine stratocumulus, with a focus on the
role that the location, timing, and strength of the heat perturbation has in
the underlying cloud and boundary layer. Section 2 presents the LEM and its
configuration and introduces a set of experiments designed to assess the SDE
and its sensitivity to the aerosol layer properties. Section 3 focuses on a
single experiment to understand the processes that drive the cloud response
and SDE, then assesses the sensitivity of this response to the aerosol layer
properties. Section 3 also investigates the robustness of that assessment to
the processes that affect the maintenance of the cloud, namely
precipitation, sea surface temperature, and boundary layer depth. Section 4
summarizes the results by comparing to other modelling studies and
observations and discusses the limitations of this study in addition to identifying
remaining questions.
Model description and setupDescription of model
The LEM (Gray et al., 2001) is a non-hydrostatic
high-resolution numerical model that explicitly resolves the large-scale
turbulent motions responsible for the energy transport and flow. The LEM has
a long track record of being used to study cloud–precipitation–aerosol
interactions in several cloud regimes (e.g. Efstathiou
et al., 2016; Efstathiou and Beare, 2015; Hill et al., 2009, 2014) and has
been included in several LES intercomparison studies (e.g. Ackerman
et al., 2009; van der Dussen et al., 2013; Ovchinnikov et al., 2014; de
Roode et al., 2016). Sub-grid-scale turbulence responsible for the
dissipation of kinetic energy is parameterized. Prognostic variables are the
three-dimensional velocity fields (u,v,w), liquid water potential temperature
(θl), and mass mixing ratios of water vapour (qv), liquid
water (ql), and rain (qr). Liquid water mass is prognosed at every
grid point using a condensation–evaporation scheme in which excess
supersaturation is converted to liquid water and vice versa for
subsaturated air. Warm rain processes are represented by a single-moment
microphysics scheme that includes autoconversion and cloud droplet
collection following Lee (1989), sedimentation
of rain, and evaporation of rain into dry air. The influence of aerosol on
cloud droplet number concentration is not included in this study, and the cloud
droplet number is fixed to 240 cm-3 for microphysical processes.
Surface fluxes of moisture and heat are calculated using Monin–Obukhov
similarity theory (Monin and Obukhov, 1954), which
predicts the surface frictional stresses and heat fluxes using the local
gradients between the surface and the overlying model level. For these
experiments a prescribed constant sea surface temperature is used. A damping
layer that relaxes all prognostic variables to their horizontal mean is
present above an altitude of 775 m (∼150 m above the cloud
layer; see Sect. 2.2) with a height scale of 650 m
and a timescale of 30 s. This prevents the reflection of gravity waves at
the rigid top boundary and prevents the production of trapped buoyancy waves
above the inversion layer (Ackerman et al., 2009). The
subsidence rate ws is represented by a height-dependent function
ws(z)=-Dz for which large-scale divergence (D) is prescribed. The
model is run with a variable time step with a maximum of 0.5 s. The
LEM radiation scheme, described by
Edwards and Slingo (1996), is a
two-stream solver with six shortwave spectral bands and eight longwave
bands that calculates the vertical distribution of radiative fluxes and
heating rates. The scheme includes six aerosol species with wavelength- and
humidity-dependent mass absorption coefficients, mass scattering
coefficients, and asymmetry factors. A single value for the mean cloud
droplet effective radius of 10 µm is prescribed in the radiation
scheme.
Model setup
All simulations are three-dimensional with periodic lateral boundary
conditions. The model domain is 5200 m in the horizontal, with a horizontal
grid resolution of 40 m, and 2600 m in the vertical with a variable vertical
grid resolution: ∼6 m resolution at the cloud top and
inversion but less than 10 m throughout the boundary layer (BL). The LEM is
configured here to produce a stratocumulus with a consistent diurnal cycle
over an 8 d timescale. The initial profiles of θl and
qt were taken from Johnson et al. (2004) and based on subtropical marine stratocumulus observations from the
First International Satellite Cloud Climatology Project Regional Experiment
(FIRE) (Hignett, 1991) in the subtropical Pacific
Ocean. A series of 10 d simulations without absorbing aerosol were run
with varying subsidence rates to obtain steady-state profiles of θl and qt that would produce a consistent stratocumulus layer with
a maximum cloud-top height of 600 m. The resulting initialization profiles
are shown in Table 1; the BL is 0.6 g kg-1
drier than in Johnson et al. (2004) and Hill et al. (2008) due to
the inclusion of precipitation in our study and a cooler SST, which was
necessary in order to attain a similar cloud LWP to these studies. The
large-scale divergence D is set to 5.5×10-6 s-1,
giving a subsidence rate of ws=-3.3 mm s-1 at the cloud
top. D and ws are within the observed range for marine stratocumulus
regions (Zhang et al., 2009) and of similar
magnitude to other stratocumulus LES studies (e.g. Johnson
et al., 2004; De Roode et al., 2014). The initial profiles describe a
well-mixed moist BL capped by a sharp (10 K) inversion at 600 m with a warm
and dry free troposphere (FT) above the inversion. To account for a source
of large-scale heat divergence a cooling rate of 0.1 K d-1 is
applied. This value is lower than the 1.0 K d-1 used by
Johnson et al. (2004) and Hill et al. (2008) because
the greater cooling rates result in an unstable cloud-top height in our
simulations, which is undesirable as we require a consistent cloud layer to
isolate the cloud response due to the absorbing aerosol. A prescribed
surface pressure of 1012.5 hPa is used, and zonal and meridional geostrophic
winds are 6.0 and -1.0 m s-1, respectively. The radiation
scheme is set up for consistency with the FIRE campaign with a time-varying
solar zenith angle for mid-July at the coordinates 33∘ N,
123∘ W. Radiation calculations are performed for all grid points
within the domain every 30 s. Surface roughness is fixed at
2×10-4 m and SST at 287.2 K.
Initial profiles used in the control simulations.
Altitude (m)Liquid water potentialTotal water mixingtemperature (K)ratio (g kg-1)0287.59.0600287.59.0601297.05.5750300.05.51000301.75.51500303.25.52600304.05.5Setup of elevated–aerosol experiments
To simulate the effect of an elevated absorbing aerosol layer above the
cloud top, a layer of dry aerosol is prescribed, consisting of soot-like
and water-soluble-like aerosol, representing predominantly absorbing and
scattering species, respectively. The interaction of longwave and shortwave
radiation with the aerosol layer results in localized heating rates that are
coupled to the LEM. The prescribed aerosol layer properties include the
height of the layer base above the inversion layer (referred to as the
cloud–aerosol gap), geometric thickness, mean single-scattering albedo
(SSA), and AOD. These properties are set at the beginning of the experiment
and applied during each call to the radiation scheme. Using the prescribed
geometric thickness of the aerosol layer, a balance between the
mass mixing ratio of soot and water-soluble aerosol is used to achieve
the desired SSA and AOD throughout the simulation (see Appendix A for more
details on the method employed). In these experiments SSA is 0.9, which is
towards the higher end of the range of SSA for biomass burning aerosol
(Peers et al., 2016) and thus
represents a relatively conservative value for the absorption of the aerosol
layer.
Realistic cloud–aerosol gaps are needed for the elevated aerosol
experiments. They are taken from observations from the CALIPSO
Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) instrument (5 km
resolution, 532 nm Aerosol Layer Product and Cloud Layer Product, v4.10,
level 2 data) and the NASA Cloud–Aerosol Transport System (CATS) lidar (5 km resolution, V3-00, mode 7.2, level 2 Daytime Operational
Layer Data Product, 1064 nm wavelength) over the southeast Atlantic Ocean
(15∘ S to 2.5∘ N, 10∘ W to 10∘ E).
The distance Δz between the retrieved cloud-top and the aerosol base
heights is determined from scenes in which vertical profiles only include a
single layer of low cloud (cloud top below 2.5 km) and a single layer of
aerosol. Figure 1 shows the normalized frequency of
occurrence of Δz in 2.5∘ grids for all scenes within July,
August, and September between 2007 and 2016 for CALIOP data and between 2015
and 2017 for CATS data. Both datasets display considerable variation in
Δz at all locations, yet the CATS dataset has a higher percentage of
scenes in close proximity (within 360 m) to the cloud top compared to
CALIOP. This agrees well with the study of
Rajapakshe et al. (2017), who found that
the 532 nm wavelength used in the CALIOP retrieval often overestimates the
distance between the cloud top and aerosol base, whereas the longer 1064 nm
wavelength used by CATS provides a more reliable estimate. The CALIOP and
CATS analysis (Fig. 1) suggests that elevated
aerosol layers predominantly exist within 1500 m of the cloud top, with a
common occurrence of layers in close proximity (less than 360 m) to the
cloud. In line with this we focus on layers of absorbing aerosol that range
from directly above the cloud layer (Δz=0 m) to elevated layers
at Δz=500 m, and we additionally examine the role of the aerosol
layer depth, which, for a given AOD, will impact the vertical distribution
and strength of the localized heat perturbation.
Normalized frequency of occurrence of the gap distance between cloud
layer top and aerosol base heights from CALIOP (blue solid line) and CATS
(red dotted line) for single layer coincidences of aerosol and cloud in the
months of July, August, and September (2007–2016 for CALIOP; 2015–2017 for
CATS) over the southeast Atlantic (15∘ S to 2.5∘ N,
10∘ W to 10∘ E). Layer heights are binned from -1.5 to
5.5 km in 200 m increments, and data in each grid have been normalized to the
maximum frequency across the whole study area. The percentage of scenes
in which the aerosol layer base is less than 360 m above the cloud-top height
is shown in the top right of each subplot for each dataset.
A schematic of the experiments designed to investigate the sensitivity of
the SDE and cloud diurnal cycle to key layer properties, namely the AOD,
geometric thickness, and the cloud–aerosol gap, is shown in
Fig. 2. The first set investigates the sensitivity
of the SDE to the strength of the aerosol layer absorption. Following AOD
observations by Chand et al. (2009), the
AOD of the layer is varied from 0.1 to 0.5 while keeping the geometric
thickness constant at 200 m and the cloud–aerosol gap at 50 m. The second
set of experiments investigates the sensitivity of the cloud response to the
geometric thickness of the aerosol layer at constant AOD. This type of
experiment aims to understand the importance of correctly retrieving the
full geometric extent of the aerosol layer (altitudes of the layer top and
base) from a satellite retrieval when the AOD is known; these variables are often
provided in combined satellite products such as CCCM
(Kato et al., 2010, 2011). This is a known
deficiency with retrievals made using wavelengths that are strongly
attenuated by biomass burning aerosol such as the 532 nm channel currently
used in the CALIOP aerosol products (Rajapakshe et al., 2017). For these
experiments the geometric thickness of the aerosol layer is increased from
50 to 500 m with no cloud–aerosol gap and are effectively experiments with
variable density of aerosol particles, since with a fixed AOD the aerosol
layer mass mixing ratio decreases with the increasing geometric thickness of
the layer. The final set of experiments investigates the impact of the
cloud–aerosol gap by placing the aerosol layer base from 0 to 500 m above
the inversion layer while keeping the geometric thickness and AOD constant. A
full list of experiments performed is presented in
Table 2. We use one of the experiments, referred to
as the base experiment, to provide an initial in-depth analysis of the
cloud and radiative response. In the base experiment (hatched experiment in
Fig. 2) a 250 m thick absorbing aerosol layer with
an AOD of 0.2 is placed directly above the inversion layer.
Schematic showing the experiments performed for the
aerosol sensitivity simulations. The hatched experiment is named the base
experiment and is used to provide an initial analysis of the semi-direct
effect in Sect. 3.2. AOD stands for aerosol optical
depth and is given at a mid-band wavelength of 505 nm.
Breakdown of all experiments performed. AOD stands for aerosol
optical depth and is given at a mid-band wavelength of 505 nm. Bold text emphasizes the variable that is being tested in each set of experiments.
Type ofLayer properties experimentCloud–aerosolLayer thicknessLayergap (m)(m)AODVariable502000.1AOD502000.2502000.3502000.4502000.5Variable0500.2thickness01000.202500.205000.2Variable0*2500.2gap1002500.22502500.25002500.2
* Base experiment used for initial analysis.
The SDE is calculated following Johnson et al. (2004) as a residual of the difference in top-of-atmosphere net radiation
(FTOA) between the aerosol and no-aerosol simulations, minus the direct
radiative effect (DRE):
SDE=FTOA,aerosol-FTOA,no-aerosol-DRE,
where FTOA is calculated using the upward (↑) and downward
(↓) fluxes of longwave (LW) and shortwave (SW) radiation:
FTOA=FTOA,SW↓-FTOA,SW↑+FTOA,LW↑.
DRE is calculated as the difference between FTOA and that obtained in a
second diagnostic call to the radiation scheme with the same profiles of
liquid water, water vapour, and atmospheric gases but without aerosol. This
second call is only performed for the simulations with aerosol present.
ResultsNo-aerosol experiment
The no-aerosol experiment is initialized and then run for 15 d without
the presence of an aerosol layer. The first 5 d are used as a spin-up
period that allows the BL to reach a steady state; the following 3 d
(days 6, 7, and 8 of the simulation) are shown in
Fig. 3.
Evolution of domain averaged cloud properties in the no-aerosol
simulation including (a) cloud top and base (black lines; left axis),
liquid water path (blue line; right axis), and vertical profiles taken at
05:30 (dashed lines) and 13:00 (solid lines) on each day for (b) liquid water
potential temperature, (c) total water mass mixing ratio, (d) buoyancy flux,
and (e) the variance in vertical velocity w′w′.
The no-aerosol experiment produces a cloud-topped BL with strong diurnal
variations. During the daytime, cloud-top height decreases and cloud-base
height increases, thinning the cloud and producing a diurnal cycle of LWP
that reaches a maximum of 60 g m-2 at dawn and a minimum of 25 g m-2 just after midday (Fig. 3a). The
precipitation rate at the surface (not shown) ranges from a maximum of 0.2 mm d-1 at night to a minimum of 0.01 mm d-1 during the day.
For a cloud with an LWP of 60 g m-2 this is within the range of
observations presented by Abel et al. (2010). The diurnal cycle of the cloud layer can be separated into a growth
phase between 14:00 and 06:00 UTC and a decay phase between 07:00 and 13:00 UTC. The
growth phase is driven by pronounced buoyancy production during the night
(Fig. 3d) from longwave cloud-top cooling and
evaporative cooling of entrained air, which drives strong turbulent motion
throughout the BL (Fig. 3e). During the daytime,
solar heating reduces the buoyancy flux (Fig. 3d) through an offset in the
longwave cooling and reduces turbulence throughout the BL (Fig. 3e). This
weakens the BL circulation, prevents mixing throughout the BL, and
promotes a decoupled state in which the flux of moisture from the surface to
the cloud is insufficient to maintain the cloud-base height, as evident from
the non-constant BL profiles of θl
(Fig. 3b) and qt (Fig. 3c) at 13:00. The weakened flux and solar heating of the cloud drive
the lifting condensation level upwards and cause the cloud base to increase
with height, producing the decay phase. During the daytime weakened BL
eddies are unable to “push” against the subsidence at the BL top, which
decreases the BL depth and cloud-top height. Due to the different processes
that control the cloud-top and cloud-base diurnal variations, the cloud-top
height minimum occurs about 2 h after the cloud base reaches its
maximum. The cloud layer, LWP, and thermodynamic profiles in
Fig. 3a–e show very little change over the 3 d of the simulation and present a stratocumulus deck with a
consistent diurnal cycle in a steady state. This provides a suitable
simulation to use as a control for the elevated aerosol experiments.
Cloud response to elevated aerosol layer in the base experiment
We begin with the base experiment (hatched experiment in
Fig. 2) for which a 250 m thick absorbing aerosol layer
with an AOD of 0.2 is placed directly above the inversion layer. Following a
5 d spin-up period without aerosol, the simulation runs for a further
10 d with the aerosol layer present. The domain-averaged cloud response
following the introduction of aerosol is shown in
Fig. 4 and compared to the no-aerosol simulation.
10 d time series of domain-averaged cloud response to a layer
of aerosol directly above the boundary layer inversion with an aerosol
optical depth of 0.2 and geometric thickness of 250 m. Plots show the
difference between the no-aerosol simulation and the simulation with an
elevated aerosol layer for (a) cloud-top height (solid line) and cloud-base
height (dotted line), (b) cloud liquid water path (LWP), (c) albedo, and (d) the semi-direct effect. Solid lines in (b), (c), and (d) show the time series
of the response, and dashed lines in (b) and (d) show the daily mean.
The simulations show that the absorbing aerosol drives changes in the
diurnal cycle of cloud depth and LWP, predominantly through changes in the
cloud-base height. The presence of the absorbing aerosol drives a decrease
in cloud-top height (Fig. 4a), which occurs
predominantly in the afternoon and evening and is indicative of a decrease
in entrainment across the inversion layer. During the initial 2 d the
cloud base (Fig. 4a) decreases in altitude
∼10 m more than the cloud top, resulting in a thicker cloud;
however, from day 3 onwards there is less growth of the cloud throughout
the evening and early morning, followed by less thinning throughout the day.
Compared to the cloud in the presence of no aerosol, the introduction of the
absorbing aerosol layer results in relatively less LWP
(Fig. 4b) during the growth phase of the cloud and
more LWP during the decay phase.
The SDE (Fig. 4d) has a strong diurnal cycle that
is directly driven by modifications to the cloud albedo diurnal cycle
(Fig. 4c) and shows considerable sensitivity to the
LWP response during the cloud decay phase around midday. In the first 3 d the albedo response is positive from mid-morning to the late
afternoon. This drives an overall negative daily mean SDE. The length of
time with a positive albedo response gets shorter as the simulation
progresses, driving an increasingly positive SDE in the morning that cancels
out, on a daily mean, the negative SDE in the afternoon. Consequently, the
daily mean SDE is negative for the initial 3 d but almost net zero
SDE from the fourth day onwards.
The cloud response and SDE are therefore markedly different in the initial
phase compared to the steady state that is reached after 6 or 7 d
following the introduction of the absorbing aerosol layer. In that
steady-state phase the BL depth has decreased by ∼130 m
(∼20 %) and the diurnal cycle response in cloud thickness
has stabilized. This suggests there are timescales in the response to the
introduction of the aerosol layer: a short-term response that can be
interpreted as a rapid adjustment of the humidity profile and a longer-term
response that can be interpreted as a new equilibrium state for the BL
sources of moisture, turbulence, and heat.
This study focuses on the initial response because it is more relevant for real-world understanding as the aerosol perturbation is unlikely to remain
constant for several days, and the lifetime of stratocumulus decks is
generally on the order of a few days only. However, the steady-state
response provides insight into the key drivers behind the BL modifications.
Initial response in the base experiment
The domain-averaged time series of the response in the first 3 d
following the introduction of the aerosol layer (days 6, 7, and 8 of the
simulation) are shown in Fig. 5. The initial
response of the cloud to the elevated aerosol layer is driven by the
weakening of the entrainment rate
(we=dzcloudtopdt-ws) and subsequent increase
in the mean RH below cloud, which acts to produce a thicker cloud in the
first 2 d. Solar radiation heats the elevated absorbing aerosol layer
above the inversion layer. Strengthening of the temperature inversion at the
top of the BL drives a weakened we (Fig. 5b),
which causes the BL depth to decrease (Fig. 5a).
Simultaneously, there is an increase in mean RH below cloud
(Fig. 5d), which allows the cloud-base height to
decrease (Fig. 5a) and the LWP to increase
(Fig. 5c); this response continues for the first
2 d, after which the LWP starts to display a diurnal response with a
decrease in LWP during the night and an increase in the afternoon. The
increase in RH occurs due to the weakened we, which reduces the amount of
warm dry FT air that is mixed into the BL and allows the sub-cloud layer to
maintain a higher RH. The relatively small decrease in potential temperature
of ∼0.1 K (Fig. 5g) suggests that the RH response is driven
by an increase in available water vapour. There is little response of the
cloud before sunrise, which suggests a weak insulating effect of the aerosol
layer on longwave fluxes at the cloud top. This is supported by a lack of
systematically weakened cloud-top longwave cooling (Fig. S1 in the
Supplement), which would be expected for an increased
downwelling longwave flux from the aerosol layer.
3 d time series showing the initial domain-averaged cloud
response to a layer of absorbing aerosol in the base experiment (0 m
cloud–aerosol gap, 250 m thick layer, and AOD of 0.2). In the first column
the black dashed lines refer to the control experiment (no-aerosol) and
solid blue lines to the experiments with the aerosol layer present. The
second column shows the cloud response (red solid line). The plots show (a) the altitude of the cloud base and top, (b) the entrainment rate we, (c) the liquid water path (LWP), (d) the mean relative humidity (RH) between the
ocean surface and the cloud base, (e) the latent heat flux (LHF) from the
surface, (f) the total water path (TWP) of the boundary layer (BL), (g) the mean
liquid water potential temperature (θl) of the BL, (h) the mean
BL vertical velocity variance (w′w′), and (i) the semi-direct effect.
The thinner cloud (lower LWP; Fig. 5a) on the morning of the third day is
driven by changes to the supply of moisture to the cloud layer. The enhanced
RH below cloud and weakened vertical motions (Fig. 5h) drive a strong reduction in surface evaporation as demonstrated by the
decrease in latent heat flux (LHF; Fig. 5e),
especially during the night. By the end of day 3 the LHF at the surface
has been reduced by 20 % and the total water path (TWP) of the BL
(Fig. 5f) has been reduced by 10 %. During the night
when the BL is well mixed this reduction in TWP prevents the cloud from
developing to the same extent as in the no-aerosol simulation, resulting in
a thinner cloud when the sun rises. This process is amplified by the reduced
BL dynamics, which will weaken the flux of moisture from the sub-cloud
region to the cloud.
The thicker cloud (enhanced LWP; Fig. 5a) on the afternoon of the third day
is driven by relatively stronger coupling with the surface moisture fluxes
at midday, which produces a slightly thicker cloud and a negative SDE
(Fig. 5i). Under no-aerosol conditions, shortwave
absorption by the cloud stabilizes the cloud layer during the day, which
results in a degree of decoupling between the surface layer and cloud base
(Fig. 3). When an elevated absorbing aerosol layer
is present, the decrease in cloud layer height, following the BL depth
decrease, allows for better coupling to the surface (see Fig. S2 in the
Supplement), which becomes increasingly important around
midday when the BL dynamics are weakest (Fig. 5h). The
enhanced source of moisture to the cloud base, along with weakened entrainment
of dry FT air, prevents the cloud from thinning to the same extent. Although
the change in LWP is only 2–3 g m-2, this amounts to a 10 %
increase, which helps drive a strong negative SDE at midday and early
afternoon.
The analysis of the initial cloud response shows that the first 2 d are
characterized by a general thickening of the cloud driven by the reduction
in we across the temperature inversion and subsequent enhanced RH
profile below cloud via an increase in water vapour. The weakened we, BL
dynamics, and moisture flux from the surface begin to dry the BL, resulting
in less cloud growth overnight, whilst the lower cloud base enhances
coupling to the surface moisture fluxes during the middle of the day, and
less cloud decay.
Steady-state response in the base experiment
The final 3 d of the 15 d base experiment provide a mean diurnal
cycle of the cloud response. Although aerosol layers do not persist above
stratocumulus decks for so long in reality, the steady-state response
provides insight into the key drivers behind the BL modifications. The
steady-state response of the cloud to the elevated aerosol layer, shown in
Fig. 6, shows strong similarities to the third day
of the initial response: the growth phase of the cloud
(Fig. 6b) is weakened, producing a thinner cloud in
the morning, and the decay phase of the cloud (Fig. 6b) is weakened, producing a thicker cloud in the early afternoon. This
modification to the diurnal cycle of the cloud is driven by an increased
coupling between the surface moisture flux and cloud base during the daytime
(see Fig. S2 in the Supplement) and an overall decrease in
TWP of the BL with weakened dynamics overnight. The decrease in cloud layer
height allows for better mixing beneath the cloud base, which enhances the
evaporation of moisture from the surface between 09:00 and 15:00
(Fig. 6d); this is evident from the weakened diurnal
cycle in mean RH below cloud (Fig. 6c), which
usually occurs due to poor mixing, and the strengthened BL dynamics at
midday (Fig. 6g). The small response in the mean BL
potential temperature of -0.2 K (Fig. 6f) strengthens the hypothesis that
the RH response below cloud is driven by changes in available water vapour
rather than the decrease in temperature, although it is worth noting that
this decrease in temperature will act to slightly increase the RH.
Domain-averaged cloud response to a layer of absorbing aerosol
directly above the inversion in the base experiment (0 m cloud–aerosol gap,
250 m thick layer, and AOD of 0.2) for the mean diurnal cycle using the
final 3 d of the 15 d simulation. In the first column the black
dashed lines refer to the control experiment (no-aerosol) and solid blue
lines to the experiments with the aerosol layer present. The second column
shows the cloud response (red solid line). The plots show (a) the entrainment
rate we, (b) the liquid water path (LWP), (c) the mean relative humidity
(RH) between the ocean surface and cloud base, (d) the latent heat flux (LHF)
from the surface, (e) the total water path (TWP) of the boundary layer (BL),
(f) the mean liquid water potential temperature (θl) of the BL, (g) the mean BL vertical velocity variance (w′w′), and (h) the semi-direct effect.
The weakened cloud growth phase overnight occurs due to a 15 % reduction
in TWP of the BL (Fig. 6e) and a reduction in mean
BL vertical motions overnight of ∼20 %, indicated by the
mean BL vertical velocity variance (w′w′) in Fig. 6g.
The reduction in we (Fig. 6a) and subsequent
changes to below-cloud water vapour set up a positive feedback mechanism
with BL dynamics: vertical motions in the BL are considerably weakened
throughout the night and slightly strengthened at midday. Although there is
a decrease in LWP there is no systematic impact on the cloud-top longwave
cooling due to its weak sensitivity to LWP above 50 g m-2
(van der Dussen et al., 2013;
Garrett and Zhao, 2006). The weakened BL circulation is therefore due to a
reduction in entrainment. The mixing of dry air into the cloud layer results
in evaporation and a cooling that generates buoyancy; a reduction in
entrainment therefore weakens cloud-top buoyancy production. These combined
changes result in reduced vertical motions within the BL, which reduce
surface evaporation, cloud LWP, and buoyancy production from condensation at the
cloud base, which allow the reduced vertical motions to persist. A partial
offset to this process occurs during midday when stronger coupling to the
surface results in enhanced transport of water vapour to the cloud base.
The steady-state response establishes itself by the third day of the
simulation. The daily mean steady-state SDE (Fig. 6h) results from a balance between the degree to which the BL TWP has
decreased, producing a positive SDE in the morning, and the degree to which
the midday coupling is enhanced, producing a negative SDE in the afternoon.
In both cases modifications to BL depth, and thus we, play a significant
role in cloud response and SDE.
Sensitivity of initial response to aerosol layer properties
Figure 7 shows time series for the aerosol layer sensitivity experiments. In
this analysis the inversion strength Δθl is determined
between altitudes zupper and zlower. The value of zupper is the
topmost altitude at which the absolute gradient dθldz is 25 % of its maximum, and
zlower is the lowermost altitude at which dθldz is 2.5 % of its maximum. The upper
threshold is determined at a higher percentage of dθldz than the lower threshold to limit
spurious values occurring from aerosol layers close to the inversion layer
that impact θl.
3 d time series showing the sensitivity of the initial cloud
response (difference between the no-aerosol simulation and the simulation
with an elevated aerosol layer) to the properties of the elevated absorbing
aerosol layer. The three columns correspond to experiments in which systematic
changes have been made to the aerosol layer thickness (a–e),
cloud–aerosol gap (f–j), and aerosol layer AOD (k–o).
Cloud response
The majority of experiments show a positive spike in SDE
(Fig. 7d, i, and n) just before midday on the first
day. This occurs due to the lag time in response between the direct impact
on the cloud from changes to we and the increase in sub-cloud RH.
Figure S1 in the Supplement focuses on the response in the
initial 24 h. The positive SDE is driven by the decrease in LWP caused
by an increase in cloud-base height (Figs. 5a and S1a) without a
corresponding change in cloud-top height. The decrease in we weakens
buoyancy production throughout the cloud layer (Fig. S1c), which drives a
reduced moisture flux within the cloud and to the cloud base (Fig. S1d). As
the day progresses the continued reduction of we results in an increase
in mean below-cloud RH and a recovery of, or increase in, the LWP. This
explains why stronger perturbations to the entrainment rate on the first day
(such as when the layer is close to the cloud) result in a quicker recovery
of the LWP (Fig. 7c, h, and m). This result suggests that the specific timing of
the incoming aerosol plume may play a role in the cloud response and SDE on
the first day.
Geometrically thinner aerosol layers equate, for a given AOD, to a greater
aerosol mass mixing ratio and therefore stronger heating. This results in a
stronger inversion layer (Fig. 7a) and stronger
modification to the LWP response (Fig. 7c) and SDE
(Fig. 7d), especially on the first day. This
stronger inversion layer weakens we and decreases BL
depth (Fig. 7b). For the two thinnest layers the
cloud-top height decreases at a faster rate during the day than at night,
which correlates with the peak heat perturbation. For thicker layers the
heat perturbation extends further into the night; this corresponds with the
delay in time for the heating towards the top of the layer to reach the
inversion layer and drives a steadier reduction in BL depth when compared to
the thinner layers. By the third day the BL has started to adjust and less
dependence on aerosol layer thickness is apparent; however, the thinner
layers cause the BL to dry out at a quicker rate, thus producing a stronger
positive SDE on the morning of the third day.
Increasing the cloud–aerosol gap leads to a weaker and increasingly delayed
cloud-top height (Fig. 7g) and LWP response
(Fig. 7h) driven by changes in peak strengthening
of the inversion (Fig. 7f); this is most pronounced
in the first 2 d. Only aerosol layers directly above the inversion
trigger a considerable cloud response on the first day because of the
relatively rapid strengthening of the inversion layer and weakening of
we, which forces the cloud top downwards more rapidly than the RH profile
can adjust, resulting in a deeper cloud base. On the second day a cloud
response is seen with gaps up to 100 m, and by the third day all gaps lead to
a response in cloud LWP. The delay in response is driven by the delay in the
inversion layer strengthening. In the free troposphere the advection of the
heat perturbation is driven by subsidence; therefore, greater cloud–aerosol
gaps require more time for the heat perturbation to reach the cloud top.
Simultaneously, longwave cooling acts to weaken the heat perturbation
throughout its advection, which drives a relatively weaker strengthening of
the temperature inversion as the cloud–aerosol gap increases.
The initial cloud-top response (Fig. 7l) displays a
strong dependence on the AOD of the aerosol layer throughout the 3 d,
with greater AOD resulting in a greater response. As with geometric layer
thickness, larger AODs absorb more radiation and drive a stronger heat
perturbation and inversion strength (Fig. 7k). So
larger AODs result in a thicker cloud and a more negative SDE. On the third
day layers with the largest AODs, which have had the greatest impact on
cloud-top height and we, exhibit a considerably thinner cloud, driving
an increasingly positive SDE in the morning.
In summary, the layer sensitivity experiments show that on the first day
the initial response is for the cloud top to drop quicker than the cloud
base, resulting in a thinner cloud and a positive SDE in the morning, the
magnitude of which is primarily driven by the proximity of the aerosol layer
to the cloud top. With no gap between the inversion at the cloud top and
aerosol layer, the afternoon of the first day is characterized by a thicker
cloud and negative SDE, which increases in magnitude for stronger heat
perturbations. The second day is generally characterized by an increase in
the LWP at midday, which drives a negative SDE and is dependent on the
location and properties of the aerosol layer. By the third day a consistent
pattern occurs: the cloud is consistently thinner in the morning and thicker
at midday, the magnitude of which is dependent on the strength of the
perturbation.
Radiative response
Figure 8 shows time series of the daily mean radiative effects for the
layer sensitivity experiments. The immediate radiative response following
the introduction of the absorbing aerosol layer is primarily dependent on
the distance between the inversion layer and aerosol layer base. When there
is no cloud–aerosol gap the increase in LWP results in a negative SDE;
thinner layers and larger AODs increase the inversion layer strengthening
and drive a stronger negative SDE on the first day. When any cloud–aerosol
gap is present there is little LWP response on the first day due to the
delayed inversion layer strengthening; however, all experiments with a gap
present are characterized by a small positive SDE. For the experiments with
a 50 m gap (variable AOD experiments) the delay is short enough that there
is an increase in LWP in the evening of the first day
(Fig. 8i).
Daily mean radiative impact on the elevated aerosol layer
properties over the initial 3 d following the introduction of the
aerosol layer for systematic changes to (a–d) aerosol layer thickness, (e–h) cloud–aerosol gap, and (i–l) aerosol optical depth of layer.
On the second and third day the SDE is negative for all experiments; the
magnitude of the SDE increases for thinner layers closer to the inversion
layer. When a cloud–aerosol gap is present the AOD tends to have little
impact on the magnitude of the SDE. The rate at which the BL moisture
content decreases, itself a factor of how strongly we is perturbed,
results in variations in which day the peak SDE occurs. In experiments with
gaps smaller than 100 m the maximum SDE is reached on the second day,
whereas for gaps larger than or equal to 100 m the maximum occurs on the
third day. In all experiments the third day is characterized by a decrease
in the daily mean LWP response, which is primarily driven by less cloud
growth overnight and in the morning (see Fig. 7c, h,
and m) and becomes more pronounced as the temperature inversion strengthens.
The thinner cloud in the morning helps to shift the daily mean SDE towards
zero.
The properties of the aerosol layer have a considerable impact on the total
radiative effect, calculated as the sum of the DRE and SDE
(Fig. 8d, h, and l). Generally, the SDE acts to
counteract the positive DRE and in some cases results in an overall negative
total radiative effect. In all experiments the total radiative effect is
sensitive to the layer properties, whereas DRE is only sensitive to the
layer AOD. In many instances the SDE is greater in magnitude than the DRE,
with the second day constituting the period of time with the greatest
impact. The relative insensitivity of the SDE to changes in AOD suggests that
layers with a moderate AOD (∼0.2) may have the strongest
overall radiative impact due to the relatively low DRE; however, the
behaviour may change for increasing gaps.
The results of the experiments are summarized in
Table 3 with the daily mean SDE alongside the means
for the periods before and after midday. The daily mean SDE is only
consistently negative throughout the 3 d when there is no
cloud–aerosol gap. This result is consistent with Johnson et al. (2004), who similarly found a negative SDE for a ∼1000 m layer
of absorbing aerosol (AOD of 0.2, SSA of 0.88) directly above the inversion
layer. Johnson et
al. (2004) calculated a mean SDE of -9.5W m-2 and a mean DRE of
10 W m-2. These magnitudes are greater than in this study but similarly
show that the SDE is of approximately equal magnitude to the DRE and of opposite
signs. Our results also show that geometrically thin, but optically thick,
aerosol layers will have a stronger forcing than a thicker layer with the
same AOD due to a stronger localized heat perturbation; this effect is most
prominent on the first day. When a gap to the aerosol layer base is present,
as is predominantly observed (Fig. 1), our results show that the short-term
SDE is likely to be weakly positive but then becomes negative once the BL
has been mixed, which usually occurs during the first night when BL turbulence peaks, highlighting a sensitivity to the specific arrival timing of the
incoming plume. On the second and third day the magnitude of the SDE then
depends on the AOD, cloud–aerosol gap, and aerosol layer thickness.
Mean semi-direct effect (W m-2) for each of the aerosol
experiments shown in Fig. 2 and
Table 2. Mean values are presented for each day
(daily) between 00:00 and 12:00 (morning) and between 12:00 and 24:00 (afternoon). Bold text emphasizes the variable that is being tested in each set of experiments.
Type ofgapdzAODDay 1 Day 2 Day 3 experimentDailyMorningAfternoonDailyMorningAfternoonDailyMorningAfternoonVariable02500.2-21-5-7-6-7-5-4-6gap1002500.2240.4-5-5-4-5-5-52502500.2120.3-3-3-3-3-3-45002500.2212-0.41-1-2-3-0.5Variable0500.2-7-2-12-9-5-13-6-2-10thickness01000.2-4-1-8-8-5-11-6-2-1002500.2-21-5-7-6-7-5-4-605000.2-12-3-5-4-6-6-5-7Variable502000.10.32-1-3-3-3-3-2-4AOD502000.212-0.1-5-5-6-4-4-4502000.312-0.1-5-5-5-3-1-5502000.412-1-6-4-8-2-0.4-5502000.513-1-6-4-8-13-5
Table 3 highlights the diurnal variations in the
SDE. The SDE is generally more negative after midday but that contrast
varies with aerosol layer properties. Geometrically thin, optically thick
layers directly above the inversion layer display the strongest contrast
with the daily mean SDE dominated by the mean after midday. When a gap is
present there is less contrast and both time periods are generally
representative of the daily mean, until the BL begins to dry out
significantly in the high AOD experiments. These results demonstrate that
there are often strong diurnal variations in the SDE that are sensitive to
the aerosol layer properties and suggest that observations of the SDE made
within a small window of time, e.g. those from polar-orbiting satellites,
may be unrepresentative of the daily mean SDE.
Sensitivity to boundary layer and cloud properties
This section investigates the robustness of the results and conclusions from
Sect. 3.3. The parameter space considered in this
section includes previous LEM studies, such as
Hill and Dobbie (2008) and Johnson et al. (2004), and the range of environmental forcings observed within marine
stratocumulus regions.
The first set of sensitivities focuses on the model setup and includes no
precipitation from the cloud (noRain) and an enhanced large-scale advective heat
tendency of -0.5 K d-1 (05cool).
In the noRain setup the production of precipitation is switched off. Stratocumulus clouds
frequently produce precipitation in the form of drizzle (Leon
et al., 2009), yet studies often simplify simulations by focusing on
non-precipitating stratocumulus (e.g. Hill
and Dobbie, 2008; Johnson et al., 2004). Precipitation redistributes
moisture from the cloud layer to the sub-cloud layer, promoting BL
stability and acting to reduce BL dynamics and cloud LWP
(Ackerman et al., 2009).
In the 05cool sensitivity, the magnitude of the large-scale advective heat
tendency is increased from -0.1 to -0.5 K d-1. That parameter
accounts for the equatorward transport of the large-scale air mass and is
negative in subtropical marine regions. This value can be estimated using
large-scale reanalyses (e.g. Johnson et al., 2004) or used as a balancing
term to prevent subsidence heating and
represents a degree of variability in LES setups.
The second set of sensitivities focuses on properties of the BL that may
impact the diurnal cycle and maintenance of the cloud.
In the SST - 1K and SST+1K setups, SST is decreased and increased by 1 K, respectively,
while keeping the BL depth at 600 m. Stratocumulus decks in the Atlantic and
Pacific oceans are observed over a wide range of sea surface temperatures
(Sandu and Stevens, 2011;
Wood, 2012). As the SST increases the differential temperature across the
surface–air boundary increases, resulting in more pronounced surface
moisture and sensible heat fluxes.
The wetFT setup increases the mass mixing ratio of water vapour in the FT by
+0.4 g kg-1 to assess the impact of the water vapour content of
the entrained air on the SDE. Trajectory analyses from the Pacific and
Atlantic oceans by Sandu et al. (2010) show
that the mass mixing ratio of water vapour in the FT varies spatially and
temporally, ranging from 1.0 to 7.5 g kg-1 at 700 hPa; this result
is supported by in situ data summarized by Albrecht et al. (1995).
The 800 m and 1000 m setups increase the height of the temperature inversion by 200 and
400 m, respectively, by changing the large-scale divergence rate and
initial profiles of θl and qt, while keeping SST constant
at 287.2 K. Observations show that cloud-top heights in regions of
semi-permanent stratocumulus coverage (southeast Atlantic, southeast
Pacific, and northeast Pacific) typically range from ∼500 to
∼1500 m (Muhlbauer
et al., 2014; Painemal et al., 2014; Wyant et al., 2010) with variations
driven by SST and subsidence.
To isolate the cloud response due to the aerosol layer, the
cloud sensitivity experiments are initialized using profiles that produce
an approximately constant stratocumulus cloud layer at the top of the BL
following the method described in Sect. 2.2.
Table 4 shows the resulting initial profiles and
large-scale divergence rates for each setup. The same sets of experiments
from Sect. 3.3 are performed for each setup, along with a simulation without
aerosol to calculate the BL response to the aerosol perturbation. The daily
mean SDE on day 2 following the introduction of the absorbing aerosol layer
(day 7 of the simulation) is shown in Table 5 for
each setup and aerosol experiment. For the control setup the SDE values are the
same as shown in Fig. 8.
Initial profiles of liquid water potential temperature (θl; K) and total liquid mass mixing ratio (qt; g kg-1)
against altitude (z in metres) for each cloud sensitivity setup. Values in
parentheses indicate the large-scale divergence rate (D; s-1) used
for each setup. All setups result in a stable stratocumulus cloud deck at
the top of the boundary layer.
znoRain 05cool SST-1K SST+1K wetFT 800 m 1000 m (5.4×10-6) (6.2×10-6) (4.75×10-6) (5.75×10-6) (5.25×10-6) (4.0×10-6) (2.75×10-6) θlqtθlqtθlqtθlqtθlqtzθlqtzθlqt0287.59.0287.39.0286.58.6288.39.4287.39.00287.39.00287.39.0600287.59.0287.39.0286.58.6288.39.4287.39.0800287.39.01000287.39.0601297.05.5296.05.5296.05.5297.25.5297.05.9801297.05.91001297.05.9750300.05.5299.05.5300.05.5300.05.5299.55.9900299.55.91100299.55.91000301.75.5300.35.5301.75.5301.75.5301.55.91200301.55.91300301.55.91500303.25.5301.55.5303.25.5303.25.5302.65.91700302.65.91900302.65.92600304.05.5302.85.5304.05.5304.05.5303.85.92600303.85.92600303.85.9
Daily mean semi-direct radiative effect for the second day
following the introduction of the absorbing aerosol layer for control and
cloud sensitivity setups. All values are as a daily mean (W m-2). Layer
properties include the cloud–aerosol gap (“gap”, in metres), the geometric
thickness of the layer (“dz”, in metres), and the aerosol optical depth
(AOD) of the layer given at a mid-band wavelength of 505 nm. Bold text emphasizes the variable that is being tested in each set of experiments.
Type of experimentgapdzAODcontrolnoRain05coolSST-1KSST+1KwetFT800 m1000 mVariable gap02500.2-7-8-5-5-8-64171002500.2-5-6-5-3-7-36102502500.2-3-4-4-1-5-2665002500.20-1-210042Variable thickness0500.2-9-12-7-7-13-801801000.2-8-10-7-5-11-722002500.2-7-8-5-5-8-641705000.2-5-7-5-2-8-5511Variable AOD502000.1-3-5-3-1-3-367502000.2-5-7-4-3-6-5515502000.3-5-9-4-4-8-6522502000.4-6-9-5-4-10-5625502000.5-6-7-5-4-10-5526Sensitivity to model setup
Comparing the no-aerosol simulations, the removal of precipitation results
in stronger BL dynamics and a greater peak in LWP (+15 g m-2) than
the control setup. The noRain setup is characterized by a consistent increase in the
magnitude of the SDE by 1 W m-2 when a cloud–aerosol gap is present
and up to 3 W m-2 when there is no gap. In the control setup the presence of
the aerosol layer increases cloud LWP, which is partially offset by an
increase in precipitation. In the noRain setup that partial offset is not allowed,
resulting in a relatively enhanced LWP response and SDE.
When compared to the control setup, increasing the cooling rate of the large-scale
advective heat tendency results in stronger BL dynamics, enhanced cloud-top
entrainment of warm dry air, and enhanced surface LHF (which acts as a
feedback to enhanced entrainment). As the processes maintaining the cloud
layer become more important, they become more sensitive to perturbations.
Therefore, when the aerosol layer is present in the 05cool setup, the responses of
we, LHF, and below-cloud moisture flux are stronger than in the
control setup, and the simulations are characterized by a quicker decrease in the
TWP of the BL. However, this only becomes prominent on the third day and
results in little difference from the control setup over the first 2 d.
Sensitivity to BL properties
In the no-aerosol simulations warmer SST drives an enhanced below-cloud
moisture flux but a lower LWP due to an increase in BL temperature. The
warmer BL also leads to stronger in-cloud buoyancy production. When the
aerosol layer is present the LWP response increases with SST, driving a
stronger negative SDE in all experiments. The cloud response is particularly
sensitive to SST when the aerosol layer is near the cloud top. As discussed
in Sect. 3.2, the initial response from the
weakened we, and subsequently enhanced RH, occurs quicker than the
moisture source from the surface can readjust to. The reductions in we
and BL depth are equivalent for all SST, but the greater flux of moisture
from warmer SST results in a greater increase in mean qt and RH
perturbation, leading to a lower cloud base, thicker cloud, and tending to
push the SDE towards a more negative daily mean. The sensitivity of the
radiative response is driven by both the SST and the perturbation to
we; therefore, stronger heat perturbations closer to the cloud top result
in a more pronounced sensitivity to SST.
The no-aerosol simulation for the wetFT setup is characterized by an LWP +5 g m-2 greater than the control setup, with slightly weaker surface evaporation.
This increase in LWP is caused by entrainment of slightly moister FT air in
the wetFT setup, allowing the BL to maintain a greater mean RH. The mixing of
entrained air has a smaller impact on the cloud humidity, which then does
not need to be balanced as strongly from a source at the surface. When the
aerosol layer is present the weakened we therefore has a smaller impact
on the RH response of the BL, which results in a smaller SDE. This setup
shows that the degree to which the entrained air impacts the cloud plays an
important role in the strength of the SDE: very dry FT air will play a more
important role in reducing RH so that a perturbation to we will have a
greater impact on the cloud response.
Sensitivity to BL depth
As the BL depth increases its temperature increases and the TWP of the BL
decreases. Figure 9 shows the profiles of θl and qt for the three setups (control, 800 m, 1000 m) during the time of the strongest
(05:30) and weakest (13:00) BL dynamics. During the period with
the weakest dynamics the degree of coupling, or mixing, between the sub-cloud
and cloud layers is weakened. This reduces the flux of water vapour from the
surface layer to the cloud, resulting in an accumulation of water vapour
close to the surface (Fig. 9b). That redistribution
becomes more pronounced as the BL depth increases, increasing BL decoupling.
Vertical profiles of (a) liquid water potential temperature and (b) total water mass mixing ratio taken at 05:30 (dashed lines) and 13:00 (solid
lines) on day 1 (after spin-up) for the no-aerosol simulations.
Increasing the BL depth has a dramatic effect on the sign and magnitude of
the SDE shown in Table 5. The SDE switches sign
from negative for a 600 m deep BL in the control setup to positive in the 800 m and
1000 m setups. The SDE in the 800 m setup is roughly of equal magnitude to the
control, but the 1000 m setup is considerably greater in magnitude, peaking at
+26 W m-2. Responses for the base experiment shown in
Fig. 10 help to illustrate why the BL depth has
such a strong impact on the SDE. In all setups the cloud-top height
decreases by ∼100 m over the 3 d
(Fig. 10a, g, and m), driven by similar changes in
we (Fig. 10e, k, and q); however, the response
in cloud-base height depends on the simulation and accounts for the
variation in LWP response (Fig. 10b, h, and n). In
the 1000 m setup (Fig. 10m) the cloud base decreases less
than the cloud top throughout the time series, driving a consistently reduced
LWP.
3 d time series showing the initial response of the cloud to a
250 m thick layer of aerosol directly above the inversion with an aerosol
optical depth of 0.2 from the (a)–(f) control setup with a boundary layer
depth of 600 m, (g)–(l) 800 m setup, and (m)–(r) 1000 m setup. From the top to bottom
row, panels show the altitude of the cloud base and top, the liquid water
path (LWP), the mean boundary layer (BL) vertical velocity variance (w′w′),
the mean relative humidity (RH) between the ocean surface and the cloud
base, changes to the BL water content as the mean total water content
qt and the total water path (TWP), and the semi-direct effect.
As shown in Fig. 9 the degree of decoupling between
the sub-cloud and cloud layers increases with BL depth. The diurnal cycle
of the sub-cloud RH for the three setups (Fig. 10d, j, and p) shows that longer periods of decoupling occur as the BL
depth increases (elevated and prolonged mean sub-cloud RH corresponds to a
poorly mixed BL). In both the control and 800 m setups the BL is reasonably well mixed
throughout the day. The presence of the aerosol layer enhances the midday
coupling and weakens the cloud decay phase, producing a thicker cloud in the
afternoon. However, for the 1000 m setup the lowering of the cloud layer is not
sufficient to overcome the decoupling that occurs; therefore, there is no
additional flux of moisture at midday and the cloud does not thicken,
producing a positive SDE in the afternoon. As the BL deepens overnight, the
dynamics become increasingly sensitive to the elevated absorbing aerosol
layer (Fig. 10c, i, and o). The result is a more
pronounced decrease in the cloud growth phase overnight and a thinner cloud
in the morning. The 800 m and 1000 m setups produce a strong positive SDE in the
morning from day 2 onwards (Fig. 10l and r), which
dominates the daily mean SDE (Table 5). As
described in Sect. 3.2.2, reductions in we and
below-cloud moisture fluxes set up a feedback mechanism that decreases the
BL dynamics. As the BL deepens this mechanism occurs more rapidly and may be
further enhanced by reduced cloud-top longwave cooling that occurs when the
LWP is sufficiently reduced. The reduction by ∼30 g m-2
of the LWP in the 1000 m setup is a large enough perturbation to reduce the
longwave cloud-top cooling by ∼40 % and decrease buoyancy
production.
These results explain the different aerosol layer sensitivities shown in
Table 5. In all setups the enhanced temperature
inversion weakens we and the mixing of warm, dry FT air into the cloud
layer and enhances midday coupling. For the control setup there is little impact on
BL dynamics, so the cloud becomes thicker due to enhanced sources of
moisture; as the temperature inversion strengthens this response increases.
As the BL deepens the BL dynamics are increasingly weakened, driving a
reduction in sub-cloud sources of moisture and a thinner cloud; as the
temperature inversion strengthens this response also increases. The 1000 m setup
represents an extreme case of this scenario, whereas in the 800 m setup the
enhanced coupling is sufficient to produce an increase in sub-cloud
moisture flux during the afternoon, which acts to partially mitigate the
cloud thinning.
Discussion and conclusions
Figure 11 summarizes the findings of this study.
The SDE manifests itself as a modification to the processes that maintain
the supply of moisture to the cloud layer and are ultimately driven by the
strengthened inversion layer and weakened entrainment rate caused by an
absorbing aerosol layer above the inversion. The initial sequence of
responses to an elevated layer of absorbing aerosol is summarized below,
with numbers referring to each response labelled in
Fig. 11.
The absorbing aerosol layer produces a heat perturbation that results in a
strengthened temperature inversion.
Buoyant parcels of air in the BL require more energy in order to push
through the strengthened temperature inversion. This weakens the entrainment
rate (we) across the inversion layer.
Weakened entrainment results in a decrease in the cloud-top altitude and BL
depth.
The reduction in the entrainment of warm and dry air from the FT reduces the
amount of mixing, reducing the sink of qt in the cloud layer and
allowing the BL to maintain a greater RH. The result is an increase in
qt‾, a small decrease in BL temperature, and an increase in RH.
Weakened entrainment reduces the production of buoyancy from the evaporative
cooling of entrained air, causing a decrease in BL dynamics (w′w′‾),
especially overnight.
Cloud-top longwave cooling remains largely unchanged due to the weak
sensitivity to LWPs larger than 50 g m-2 overnight and the relatively
small changes in LWP during the daytime. The insulating effect of the
aerosol layer only weakly influences the net longwave fluxes and divergence
above the cloud.
Increased qt‾ in the BL and weakened BL dynamics reduce the
evaporation rate of water from the surface, as evidenced by the reduction in
latent heat flux (LHF).
According to the model sensitivity simulations presented, SDE is amplified
through the following mechanisms:
geometrically thinner aerosol layers of high aerosol density and low SSA,
which produce a stronger localized heat perturbation;
aerosol layers close to the inversion, while larger cloud–aerosol gaps
result in a delayed and weaker cloud response; and
warmer SSTs, which enhance the flux of moisture to the BL. As a secondary
response, the increased SST also drives a stronger reduction in LHF and
causes the BL to adjust at a quicker rate.
Conversely, SDE is reduced by the following:
precipitation that, as a sink of cloud liquid water, dampens the cloud
response (it follows that any feedbacks that result in an increase in
precipitation further weakens the SDE);
increases in the large-scale advective heat tendency (stronger cooling),
which are balanced by enhanced buoyancy production from we and a more
rapid BL adjustment; and
an increase in the moisture content of the FT, which increases the role that
entrainment plays in the supply of moisture to the BL.
Finally, an increase in the degree of decoupling in the BL increases the
sensitivity of the BL dynamics to changes in we, driving towards a
positive daily mean SDE. Extreme cases result in a strong positive SDE from
day 2 after applying the aerosol perturbation.
Summary of how the semi-direct effect manifests in a cross
section of a stratocumulus-topped boundary layer. Solid red lines refer to
the no-aerosol simulation and dashed red lines to the elevated absorbing
aerosol layer simulations. Key responses to the boundary layer profiles are
depicted in the blue boxes and include the strength of the inversion layer
(Δθl inversion), entrainment rate (we), boundary
layer depth (BL depth), cloud-top longwave cooling (LW cooling), mean
vertical motions in the boundary layer (w′w′‾), mean total water
content of the BL (qt‾), and the latent heat flux at the ocean
surface (LHF). Solid (dashed) arrows between boxes represent positive
(negative) feedbacks between responses. For each response we include
properties of the aerosol layer, boundary layer, or model setup that amplify
(denoted by +) or dampen (denoted by -) the response; this includes the
aerosol layer thickness (Layer thickness), cloud–aerosol gap (Proximity to
layer), the aerosol optical depth of the layer (AOD), the single-scattering
albedo of the aerosol layer (SSA), the sea surface temperature (SST), the
water content of the free troposphere (FTqt), precipitation (Rain),
large-scale advective heat tendency (LS cooling), and the degree of
boundary layer decoupling (Decoupling).
Several feedbacks between responses occur as the BL adjusts to the
perturbations. The key feedbacks occur in the sub-cloud layer and can work
together to greatly reduce the supply of moisture to the cloud layer.
Processes that act to decrease w′w′‾ also further decrease we
and the LHF; these changes weaken the response of qt‾ in the BL so
that there is a weaker flux of qv to the cloud layer. Reduced we
and a reduction in condensation at the base of the cloud layer weaken
buoyancy production in the cloud layer, which acts to further decrease
w′w′‾ and we. These feedbacks are most pronounced during the
cloud growth phase overnight when the diurnal cycles of we,
w′w′‾, and LHF peak, resulting in a weakened cloud growth phase and a
thinner cloud overnight and into the morning when the aerosol layer is
present, thus producing a positive SDE. Longwave cloud-top cooling is only
weakly sensitive to changes in LWP above 50 g m-2, and therefore we do
not see changes in the buoyancy production from this process unless the LWP
is significantly impacted, which occurs when the BL is decoupled. In this
case the reduced LWP further weakens the buoyancy production in the cloud
layer and consequently we and BL dynamics.
A second adjustment feedback on the cloud maintenance occurs through the
reduced depth of the BL, which acts to promote coupling of the cloud and
sub-cloud layers. In this case the feedback mechanism outlined previously
acts in reverse so that w′w′‾, LHF, and the supply of qv to the
cloud layer increase. This weaker feedback mechanism likely occurs
throughout the diurnal cycle but only becomes important at midday when BL
dynamics and sub-cloud moisture fluxes are at their weakest and most
sensitive to small changes. This adjustment results in reduced cloud decay
throughout the afternoon and a thicker cloud, and thus negative SDE, when
the elevated layer of absorbing aerosol is present. The strength of this
feedback mechanism decreases as the degree of BL decoupling increases until
the mechanism ceases to have any impact on the BL; in our study this occurs
when the BL is 1000 m deep.
The sign and magnitude of the SDE from elevated layers of absorbing aerosol
are sensitive to the layer properties and BL properties, especially the
diurnal variations in coupling between the cloud and sub-cloud layers. For
coupled BLs, the SDE on the first day after adding the absorbing aerosol
layer is slightly positive unless the aerosol layer is close to the
inversion layer. On the second and third day the SDE is strongly negative
and peaks on the second day. Generally, for coupled BLs the SDE is of
opposite sign to the DRE and often greater in magnitude, resulting in a
small or negative total radiative effect for aerosol–radiation interactions
from elevated absorbing aerosol layers. For BLs that show characteristics of
being decoupled for most of the diurnal cycle the SDE is positive for all
3 d and increases in magnitude throughout; as the BL becomes more
decoupled the magnitude of the SDE increases. For decoupled BLs the SDE acts
to enhance the DRE, resulting in a larger total radiative effect.
The increased LWP and negative SDE in the well-mixed coupled BL experiments
are consistent with satellite observations over the southeast Atlantic from
Adebiyi and Zuidema (2018) and Wilcox (2012). However, our LEM
simulations suggest a positive SDE in decoupled BL regions, such as near the
stratocumulus-to-cumulus transition region. In reality, the BL may not be
as decoupled as in the simulations. The deepening BL is usually accompanied
by an increasing SST (Sandu and Stevens, 2011), which was not represented in
our simulations; the increase in SST would provide a considerably larger
flux of moisture from the surface and enhance the production of buoyancy at
the surface, which may act to weaken the sensitivity of the BL to changes in
dynamics. The aerosol layer sensitivity experiments in Sect. 3.3 suggest
that the daily mean SDE strongly weakens as the distance of the gap between
the cloud top and aerosol layer increases. Table 3 shows that on the second
day of the simulation no gap results in a daily mean SDE of -7 W m-2
compared to -0.4 W m-2 for a 500 m gap. Additionally, even for a large
perturbation (AOD of 0.5) the daily mean SDE in the initial 24 h of the
50 m gap experiment is only 1 W m-2. These results are in general
agreement with the stratocumulus-to-cumulus transition LES studies by
Yamaguchi et al. (2015) and
Zhou et al. (2017), which suggest that only
those elevated smoke layers that are very close to, or in direct contact with,
the cloud layer impact the cloud properties. Combined with the satellite
observations in Fig. 1 these results suggest that the overall SDE from elevated
layers of aerosol over the southeast Atlantic is weak. However, it is worth
noting that Yamaguchi et al. (2015) and Zhou et al. (2017) used the same case study
(Sandu and Stevens, 2011) yet found opposing
results on whether the absorbing aerosol layer inhibits or hastens the
transition to cumulus. Yamaguchi et al. (2015)
state that throughout their simulations the BL is decoupled below 800 m,
whereas in Zhou et al. (2017) vertical mixing
within the BL continues until the inversion height exceeds ∼1.4 km (Zhou et al., 2017; Fig. 1b). Our
results highlight the fact that the cloud response is sensitive to the diurnal
variations in BL mixing, which may explain these opposing results.
Additionally, inconsistent responses between LES models can also arise
through differences in the representation of processes, including unresolved
sub-grid-scale turbulence (Stevens et al., 2005) and
microphysics (van der Dussen et al.,
2013). Our results show that the heat perturbation above the cloud layer
impacts all aspects of the BL profile; therefore, it would be beneficial to
repeat this study using other LES models to test our conclusions.
Satellite products provide an excellent opportunity to observe
aerosol–cloud and aerosol–radiation interactions in remote locations such
as the southeast Atlantic Ocean; however, most instruments are on polar-orbiting satellites that only provide observations from a limited window
within the diurnal cycle of the clouds. Our simulations suggest that the cloud
response to elevated absorbing aerosol layers and the SDE display important
diurnal variations, so a single observation is unlikely to be representative
of the daily mean response. Important changes to the cloud properties occur
overnight and play a considerable role in the SDE of the morning period, yet
little is known about the impact from absorbing aerosol layers overnight.
Future studies should use geostationary satellite observations to
investigate the full diurnal cycle of the SDE.
For a well-mixed coupled BL, the initial cloud and radiative responses
depend on small-scale processes, such as entrainment and turbulence, which
must be parameterized in climate models. Gordon et al. (2018) used a
nested regional model within the Hadley Centre Global Environment Model
(HadGEM) to investigate the impact of an incoming elevated plume of smoke in
the southeast Atlantic. They found that the elevated aerosol layer reduced
cloud-top height and enhanced LWP through a reduction in we driven by
localized heating at or just above the cloud layer of ∼6 K. The importance of the weakened we aligns well with the LES
results of the present study, but the magnitudes of the cloud and radiative
response are much greater in HadGEM, with an LWP increase of 90 %, an
increase in cloud fraction of 19 %, and a mean SDE of -30 W m-2. Gordon
et al. (2018) do not find a consistent longer-term (∼3 d)
reduction in LWP following BL adjustments. In the simulations presented
here, the cloud fraction remained ∼100 %, which may explain the
smaller SDE than that found by Gordon et al. (2018). Additionally, concurrent
aerosol-cloud interactions may modify the underlying cloud properties, which
may act to amplify the SDE. The lack of BL adjustment may be due to
processes that are not explicitly treated in HadGEM, such as BL turbulence
and subsequent missing feedbacks on surface fluxes, or due to aerosol–cloud
interactions not represented in the LES. Alternatively, differences may be
due to different simulated cases. The trajectory analysis of
Gordon et al. (2018) suggests
that their BL air mass traverses the study region more quickly than the
absorbing aerosol layer, which may prevent the BL adjustments from
occurring.
In our simulations the SST and subsidence rate are held constant for the
whole duration, whereas real stratocumulus decks tend to experience an
increasing SST and decreasing subsidence rate. An increasing SST increases
surface latent heat fluxes, cloud liquid water content, and the strength of
BL eddies; it also acts to deepen the BL through increased entrainment and
enhance decoupling of the sub-cloud layer
(Bretherton and Wyant, 1997). As the cloud
is advected over the warmer sea surface, the enhanced flux of moisture would
act to increase the magnitude of the SDE and prevent the BL from drying out
as quickly. Simultaneously, the enhanced decoupling of the sub-cloud layer
may result in BL dynamical feedbacks that result in a reduction in LWP (see
Fig. 10). Our model uses an Eulerian framework whereby
the absorbing aerosol layer remains at a constant height above the cloud,
whereas the heat perturbation is allowed to subside into the cloud. In
reality the aerosol layer may also subside. The sensitivity experiments in
Sect. 3.3 show that as the aerosol layer approaches the cloud layer, the SDE
increases; therefore, if we were to represent aerosol layer subsidence we
would expect an enhanced cloud response and SDE.
Changes to the aerosol distribution within the cloud or in the cloud droplet
distribution have not been considered in this study. A weakened we increases
condensate in the cloud and likely results in an increase in cloud droplet
effective radius (re). This would promote warm rain processes and enhance
precipitation, thus reducing the LWP and amplifying the reduction in BL
dynamics. These combined effects could lead to a decrease in LWP and shift
the SDE towards a positive sign at a quicker rate than suggested by the LES.
For the cases in which the aerosol layer is directly above the cloud layer an
enhanced flux of CCN into the BL would be expected and would act to reduce
re, suppress precipitation, and act to enhance buoyancy production.
However, in situ observations routinely find that the layers of smoke over
the southeast Atlantic are embedded in moist layers
(Adebiyi et al., 2015), which
could increase the flux of water from the free troposphere and act to
mitigate the changes that occur alongside an increased CCN. The
introduction of the absorbing aerosol into the cloud layer would
additionally enhance cloud evaporation and act to thin the cloud layer (Hill
and Dobbie, 2008; Johnson et al., 2004). Thus, although the experiments
in which the aerosol layer is directly above the inversion result in the most
strongly negative SDE, the response would be at least partially mitigated if
the aerosol distribution was represented explicitly, further decreasing the
role that SDE plays in the total radiative effect of elevated layers of
absorbing aerosol. Extending the present study using a binned microphysics
scheme would include the additional response of the droplet size
distribution, and using an aerosol scheme would include the additional
impacts the weakened we has on the availability of CCN and subsequent
cloud response.
This Appendix describes how the AOD and SSA are prescribed in elevated
aerosol layer experiments, along with the geometric thickness of the aerosol
layer and the distance between the inversion layer and the aerosol base. In
each call to the radiation scheme the desired AOD and SSA are used to
determine the mass mixing ratio of two aerosol species: water-soluble like
(WS) and biomass burning like (BB).
For a single wavelength, the AOD between the altitudes z0 and
z, corresponding to the base and top of the aerosol layer, respectively, is
calculated as
AOD=∑i=z0z∑j=WS,BBKscatj+Kabsj⋅qi,j⋅ρi⋅dzi,
where Kscat and Kabs are the specific scattering and absorption
coefficients, respectively, for the aerosol species j
(m2 kg-1), with a mass mixing ratio q (kg kgdry-1) at
each model level i of geometric thickness dz (in metres) and density of dry air
ρ (kg m-3). If the mass mixing ratio of each species is
assumed equal and constant with height (qWS=qBB and qi=q), Eq. (A1) becomes
q⋅∑i=z0zρi⋅dzi=AOD∑j=WS,BBKscatj+Kabsj.
We incorporate a factor XSSA into Eq. (A2) that can be used to
describe the relative ratio of WS mass to BB mass so that Eq. (A2) becomes
q⋅∑i=z0zρi⋅dzi=AODKscatWS+KabsWS+XSSA⋅KscatBB+KabsBB.
Equation (A3) can be rearranged to give q for a given AOD:
q=AODconstant∑i=z0zρi⋅dzi,
where
AODconstant=AODKscatWS+KabsWS+XSSA⋅KscatBB+KabsBB.
Therefore, for the two aerosol species
qj=q,j=WSXSSA⋅q,j=BB.
The overall SSA is calculated as
SSA=KscatWS+XSSA⋅KscatBBKscatWS+XSSA⋅KscatBB+KabsWS+XSSA⋅KabsBB.
Equation (A7) can be rearranged to solve for XSSA as
XSSA=KscatWS-SSA⋅KscatWS+KabsWSSSA⋅KscatBB+KabsBB-KscatBB.
At the beginning of the simulation XSSA and AODconstant are
calculated using Eqs. (A8) and (A5), respectively, using the shortwave
extinction coefficients of the aerosols for the wavelength band 320–690 nm and the prescribed AOD and SSA. At each horizontal grid point q is then
calculated using Eq. (A4) for the elevated aerosol layer, where z0 is the
base of the aerosol layer, and z is the top of the aerosol layer. The mass
mixing ratio of each species is calculated using Eq. (A6), and finally the mass
mixing ratio profiles of WS and BB are applied to the radiation scheme.
Data availability
Data and relevant information for reproducing Figs. 3–11 have been uploaded to Zenodo and can be accessed via: 10.5281/zenodo.3630557 (Herbert et al., 2020).
The supplement related to this article is available online at: https://doi.org/10.5194/acp-20-1317-2020-supplement.
Author contributions
RJH, NB, EJH, and AAH designed the methodology and experiments. AAH provided
model expertise and assistance. RJH set up, performed, and post-processed the
simulations. RJH, NB, EJH, and AAH analysed the results. RJH provided all
visualizations and wrote the initial paper draft. NB, EJH, and AAH
provided revisions and commentary on the paper.
Competing interests
The authors declare that they have no conflict of interest.
Special issue statement
This article is part of the special issue “New observations and related modelling studies of the aerosol–cloud–climate system in the Southeast Atlantic and southern Africa regions (ACP/AMT inter-journal SI)”. It is not associated with a conference.
Acknowledgements
This research was funded by the UK Natural Environment Research Council
(NERC) CLouds and Aerosol Radiative Impacts and Forcing: Year 2016
(CLARIFY-2016) project NE/L013479/1. We acknowledge use of the Monsoon
system, a collaborative facility supplied under the Joint Weather and
Climate Research Programme, a strategic partnership between the Met Office
and the Natural Environment Research Council. The CALIOP data were obtained
from the NASA Langley Research Center Atmospheric Science Data Center
https://eosweb.larc.nasa.gov/project/calipso/calipso_table (last access: 1 August 2017).
The CATS data were obtained from NASA Goddard Space Flight Center https://cats.gsfc.nasa.gov (last access: 31 July 2019).
Financial support
This research has been supported by NERC (grant no. NE/L013479/1).
Review statement
This paper was edited by Jérôme Riedi and reviewed by three anonymous referees.
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