www.sciencemag.org/cgi/content/full/321/5891/946/DC1
Supporting Online Material for
Smoke Invigoration Versus Inhibition of Clouds over the Amazon
Ilan Koren, J. Vanderlei Martins, Lorraine A. Remer, Hila Afargan
Published 15 August 2008, Science 321, 946 (2008)
DOI: 10.1126/science.1159185
This PDF file includes:
SOM Text
Figs. S1 to S5
References
Smoke invigoration vs. inhibition of clouds over the Amazon
Ilan Koren1, J. Vanderlei Martins2,3, Lorraine A. Remer3 and Hila Afargan1
1. Department of Environmental Sciences Weizmann Institute, Rehovot 76100, Israel
2. Department of Physics and Joint Center for Earth Systems Technology, University of Maryland Baltimore County
3. Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA
Supporting Online Material
This supplement contains:
1) Logarithmic parameterization of the microphysical effect
2) More on the superposition of the microphysical and the radiation processes
3) Radiative transfer of a smoky layer
4) The Amazon basin
5) Observations of aerosol effect on cloud cover over the Amazon Basin
6) Cloud aerosol data analysis per pressure level
1. Logarithmic parameterization of the microphysical effect
As stated in the paper the logarithmic response of the cloud fraction (8,9,10) to
microphysical effects is simulated empirically by:

 1 
C fm = C fs 1 − exp − τ  
 b 

(5).
Where τ is a measure for the amount of cloud condensation nuclei (CCN) and b and
Cfs are the two free parameters that determine the properties of the dependence. Cfs the
saturation cloud fraction determines the maximum level that the cloud fraction will
reach and b controls how fast the cloud fraction will reach Cfs. Figure S1 shows two
sets of simulated cloud fractions. The blue set Cfs=0.8, b=0.05 and the red Cfs=0.5,
b=0.2.
1
0.9
0.8
cloud fraction
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
τ
Figure S1. Microphysical simulations of the cloud fraction as function of the aerosol
loading. The blue set Cfs=0.8, b=0.05 and the red Cfs=0.5, b=0.2.
2. More on the superposition of the microphysical and the radiation processes
Equation 6 in the paper:
C ft = 1 − (1 − C fm ) exp(aτQt )
(6),
describes the combined processes of the microphysical and the radiative effects. The
logarithmic dependence of the microphysical processes is empirically simulated (eq.
5) and the dependence of the cloud fraction on the aerosol absorption was analytically
developed into the absorption–fraction feedback (eq 4). The two processes are
coupled in eq. 6. We assume that the saturation cloud fraction of the microphysical is
a faster process compared with the radiative time scale and therefore Cfm can be used
as the initial cloud fraction of the radiative process. We would like to approximate the
overall cloud fraction dependence (in eq. 6) by a set of two independent equations,
one per each process. Inputting eq 5 as Cfm into eq. 6 yields:
C ft = 1 − exp(aτQt ) + C fs exp(aτQt ) − C fs exp(aτQt ) exp(
−τ
)
b
(S1).
The first 3 terms is the exact solution of the AFF equation (4) with the saturation
cloud fraction Cfs serving as the initial cloud fraction. The last term can be
approximate by C fm − C fs using eq. 5 in the following way:

 1 
C fm − C fs = C fs 1 − exp − τ   − C fs =
 b 

1
 1 
− C fs exp(− τ ) ≈ −C fs exp − τ  exp(aτQt )
b
 b 
(S2).
This approximation is applicable because the term exp(aτQt ) is close to one for small
τ and exp(−τ / b) approach zero when the microphysical system reaches the saturation
level. Therefore the cloud fraction dependence on both processes (eq. 6) can be
approximated by:
C ft ≈ C f + C fm − C fs
(S3)
with C 0 = C fs for the Cf calculations.
The quality of the approximation depends on b. As b get larger (larger τ for
saturation) the error increases. When the microphysical process reaches the saturation
level eq. S3 becomes identical to eq. 6. The maximum differences between the
analytical solution to the approximation, for the values used in the paper, were <1%.
Figure 1 in the paper shows the separated two processes and how the exact solution of
the combined effect (eq 6, the dotted lines) is close to a linear super position of the
separated effects as in eq. S3.
3. Radiative transfer of a smoky layer
The atmospheric temperature (and relative-humidity) profile changes naturally
due to turbulent heat and moisture fluxes from the surface, lateral advection,
variations in the solar geometry and the column composition of absorbents (such as
water vapor). Here we define the baseline atmospheric profile as the theoretical one
without the presence of smoke and we investigate how the smoke causes deviation
from this profile.
Cloud fraction depends on temperature and humidity profiles. Warming in the
aerosol layer reduces relative humidity and stabilizes the lower atmosphere below the
roof of the smoke layer. The stabilization blocks local moisture fluxes from reaching
the cloud layer (S1, S2). Thus, warming in the aerosol layer will reduce cloud fraction.
To simplify the physical presentation, we neglect many slower processes (such as the
changes in geometry) and possible feedbacks (such as changes in the surface heat
flux). Therefore our analysis is a perturbation analysis of the natural (clean) profile.
3.1 Linearity of the absorption of solar radiation in the atmosphere as a function
of the aerosol optical thickness
The heating rate of the aerosol layer will be proportional to the amount of energy
trapped in the layer due to the aerosol absorption. In this section we will show why a
linear approximation of the heating rate to the (absorbing) aerosol optical thickness is
appropriate.
This description intends to show that the change in temperature of an air parcel
due to aerosol absorption of solar radiation is proportionally linear to the aerosol
optical thickness, as stated in equation 2 of the manuscript. As the paper only assumes
an arbitrary proportionality constant (Q), the main purpose here is to state the linearity
of this relationship. Nevertheless a simplified model will also be used to estimate the
constant Q within a given range of uncertainty and aerosol optical thickness.
Figure S2 shows a graphic representation of an aerosol layer above a given
surface and the radiative fluxes entering and leaving the layer.
z1
z2
Asurf
F -(τ1)
F+(τ1)
F -(τ2)
F+(τ2)
τ1
(2
Figure S2 – Graphic representation of the solar fluxes entering and leaving the aerosol layer with
optical thickness τ, aloft above a surface with albedo Asurf.
The radiative heating of the atmospheric layer by aerosols is caused by the
difference between the radiative fluxes going into and leaving the layer. The total
radiative flux absorbed by the layer per unit volume or the heating rate (H in W/m3)
can be written as:
F − (τ 1 ) − F + (τ 1 ) − F − (τ 2 ) + F + (τ 2 )
H=
z1 − z 2
(S4)
In the absence of other sources, the rate of change of temperature of a parcel at
constant pressure can be written as:
∂T
H
=−
∂t
Cpρ
where Cp is the heat capacity of
the air at constant pressure, and the ρ is the air density.
The discrete points in figures S3a and S3b show results of radiative transfer
calculations (using SBDART; S3) for the total amount of monochromatic solar
radiation (λ=0.55µm) absorbed by a smoke layer illuminated at two solar zenith
angles (0 and 60dg). The thick solid lines show linear fits to the calculated points
attesting for the linearity of the relationship. The intercept of the fit was forced to zero
and the fitted slope and correlation coefficient is shown besides every line. These
results per-se show that the atmospheric absorption is linearly proportional to the
aerosol optical thickness of the layer (as assumed the manuscript equation 2).
Single scattering approximation - The dashed lines in the plots represent an
extension of this interpretation by attempting to model the value of the slope of the
linear relationship using a single scattering approximation. For a surface with albedo
equal to zero, the flux F+(τ2) also equals zero. Assuming an optically thin aerosol
layer aloft over a surface with albedo equal to zero, with an upscatter fraction β(µo),
and solar zenith angle µo we can write the other fluxes as:
F + (τ 1 ) = Fo
ω oτ
β (µ o )
µo


ωτ
τ
F − (τ 2 ) = Fo 1 −
(1 − ω o ) − o β ( µ o ) 
µo
 µo

(S5)
(S6)
Where Fo is the solar flux at the top of the atmosphere, τ is the aerosol optical
depth at a particular wavelength, and ωo is the aerosol single scattering albedo.
Substituting equations (S5) and (S6) into equation (S4) we obtain:
H = Fo
τ
τ
1
1
(1 − ω o )
= Fo abs
µo
z1 − z 2
µ o z1 − z 2
(S7)
Linear Approximation X SBDART Calculations for Biomass Burning
Aerosols (SZA=0, wavelength=0.55um)
Atmospheric Absorption (W/m2/um)
450
y = 406.25x
2
R =1
400
350
300
y = 226.05x
2
R = 0.9994
250
wo = 0.9
wo = 0.8
200
wo = 0.95
y = 123.04x
2
R = 0.9987
150
100
50
0
0
0.2
0.4
0.6
0.8
1
1.2
AOT
Linear Approximation X SBDART Calculations for Biomass Burning
Aerosols (SZA=0.5, wavelength=0.55um)
400
Atmospheric Absorption (W/m2/um)
y = 326.1x
350
2
R = 0.996
300
250
y = 189.1x
2
R = 0.999
200
wo = 0.9
wo = 0.8
wo = 0.95
150
y = 107.0x
2
R = 0.999
100
50
0
0
0.2
0.4
0.6
0.8
1
1.2
AOT
Figure S3a and S3b: Comparison between the atmospheric absorption from biomass burning
aerosols as calculated from the approximation described in the text versus calculations from a full
radiative transfer code. The dashed line for wo=0.9 in figure 2b is in perfect agreement with the solid
line and cannot be seen in the plot.
Eq. S7 shows how H in these circumstances is proportional to the aerosol
absorption optical thickness. The dashed lines in figures S3a and S3b show the
comparison between the result of this linear model and the full radiative transfer
calculation. The results shows that the simple linear approximation holds within 25%
difference for relatively large τ up to 1.0, and ω0 values about 0.95. Smaller τ or
smaller ω0 values produced much better results down to single digit differences.
Similar arguments apply to the cases with surface albedo different than zero, and
taking into account the multiple reflections between the surface and the atmosphere.
In this case, the atmospheric absorption is also proportional to the aerosol absorption
optical thickness with increasingly more absorption for higher surface albedos.
3.2 Total flux radiation transfer
To see the heating rates for the whole profile with no assumptions, we simulated it
using a full solar flux radiative transfer model (S4,S5). The model was initialized with
profiles of temperature, humidity, and atmospheric gases of a tropical atmosphere.
The smoke is distributed from the surface up to a pressure level of 750mb (~2500m)
with a single scattering albedo of 0.91 in the mid-visible range (a moderate value for
the Amazon smoke absorption, S6). We can see in figure S4 that the upper smoke
layer (concentrated around 775mb) has the maximum heating rate while the rate
decreases for the layers below mostly due to extinction of the solar flux. Figure S5
shows the rate of temperature change as a function of τ for few smoke layers.
Figure S4 - Heating profiles showing the rate of temperature changes as a function of the pressure
level of each layer for total smoke optical depth of 0.1, 0.2, 0.4, and 0.8.
Figure S4 – Rates of temperature change as a function of the aerosol optical depth for few pressure
levels.
Figure S4 shows that the slopes (of the rates of temperature change vs. τ) decrease
for the lower atmosphere (stabilizing the profile by heating more on the upper part). It
is also shown that the linear approximation is excellent (R=1) for the uppermost
smoke layer (780mb~2200m) and it slightly deviates from linear to slower heating
rates for larger τ in the lower atmosphere (920mb~800m) which makes the
stabilization of the atmosphere even stronger.
4. The Amazon Basin
During the dry season the Amazon basin is under the influence of a regional highpressure system, resulting in relatively stable meteorological conditions and lower
precipitation, facilitating human-induced biomass burning of existing pasture and
cultivated areas, and new land clearing (S7). Biomass burning supplies significant
amounts of aerosol particles from smoke to the atmosphere (S8). Over the Amazon
rainforest, there are two major sources of moisture for cloud formation and
precipitation. Roughly 50% of the moisture is carried by easterly winds from the
Atlantic Ocean over the basin until they reach the barrier of the Andes (S9). The other
source for 50% of the moisture is water vapor produced locally through vegetative
evapotranspiration (S10). These conditions make this region ideal for studying the
effect of manmade aerosols on clouds through both pathways.
5. Observations of aerosol effect on cloud cover over the Amazon Basin
MODIS retrievals of cloud and aerosol properties (S11,S12) over the Amazon
were collected for two months (August-September) of the dry season of 2005. The
study area, bounded by 5N–14S and 46W-72W, is restricted to be over the rainforest
region and away from the Andes. This region experiences consistent meteorological
conditions during the dry season, with little day to day variation (S13). The data
(Level 3) used here is averaged at one degree resolution from higher resolution
retrievals (10km for aerosols and 1km for clouds) (S14). The satellite products include
cloud fraction, and mean cloud optical thickness, droplet effective radius, cloud top
pressure and temperature (S11), and aerosol optical depth (t) at 550 nm in each 1
degree grid square (S12).
6. Cloud aerosol data analysis per pressure level
To see the effect separately for low, medium and high clouds, the data was
divided into 3 pressure levels: low level (water clouds) 1000>P>800, medium clouds
800>P>600, and high clouds P<600. The same analysis as for the whole data was
performed for each level showing that there are similar relationships between cloud
fraction and cloud top pressure to τ for all cloud levels. The results are noisier due to
smaller data sets.
Figure S5. Correlations between cloud properties and aerosol loading (estimated by τ). Left – cloud
top pressure (P) vs. τ. Right – cloud fraction vs. τ. Upper, first row – shallow clouds P>800, second
row 800>P>600 and third row P<600.
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