Case Studies of the Vertical Structure of the Direct Shortwave Aerosol
Radiative Forcing During TARFOX

Redemann^1^, J., R.P. Turco^2^, K.N. Liou^2^, P.V. Hobbs^3^, W.S.
Hartley^3^, R.W.Bergstrom^1^, E.V. Browell^4^ and P.B. Russell^5^

^1^ Bay Area Environmental Research Institute, San Francisco, CA

^2^ Department of Atmospheric Sciences, UCLA, Los Angeles, CA

^3^ Department of Atmospheric Sciences, University of Washington,
Seattle, WA

^4^ NASA Langley Research Center, Hampton, VA

^5^ NASA Ames Research Center, Moffett Field, CA

(Revised manuscript submitted for consideration to be included

in the 2^nd^ *[TARFOX JGR Special Issue]{.underline}*)

11/14/2023

**Abstract**. The vertical structure of aerosol-induced radiative flux
changes in the Earth's troposphere affects local heating rates and
thereby convective processes, the formation and lifetime of clouds, and
hence the distribution of chemical constituents. We present
observationally-based estimates of the vertical structure of direct
shortwave aerosol radiative forcing for two case studies from the
Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX)
which took place on the US East coast in July 1996.

The aerosol radiative forcings are computed using the Fu-Liou broadband
radiative transfer model. The aerosol optical properties used in the
radiative transfer simulations are calculated from independent
vertically-resolved estimates of the complex aerosol indices of
refraction in two to three distinct vertical layers, using profiles of
*in situ* particle size distributions measured aboard the University of
Washington research aircraft. Aerosol single-scattering albedos at 450
nm thus determined range from 0.9 to 0.985, while the asymmetry factor
varies from 0.6 to 0.8. The instantaneous shortwave aerosol radiative
forcings derived from the optical properties of the aerosols are of the
order of ‑36 W m^-2^ at the top of the atmosphere and about --56 W m^-2^
at the surface for both case studies.

1\. Introduction

Current interest in atmospheric aerosols derives in part from the
assessments of the Intergovernmental Panel on Climate Change (IPCC)
regarding the potential importance of radiative forcing of climate by
tropospheric aerosols \[*IPCC*, 1995\]. For the purpose of this paper,
"radiative forcing" due to a radiatively active species is defined as
the change in net radiative flux (shortwave + longwave) at a given level
in the atmosphere due to the presence of this species in the
earth-atmosphere system. The total aerosol radiative forcing can be
broken down into the *direct* effect due to the actual interaction of
the aerosols with radiation, and the *indirect* effect due to aerosol
induced changes in the radiative properties of clouds. The IPCC
estimates the globally-averaged *direct* and *indirect* aerosol
radiative forcings forcings due to changes in atmospheric composition
over the last few decades are both on the order of -1 W m^-2^, with
larger uncertainties in the estimates of the indirect effect. If in fact
the total anomalous aerosol forcing amounts to -2 W m^-2^, it attains a
magnitude comparable to the positive radiative forcing anomaly
attributed to the greenhouse gases, CO~2~, N~2~O and CH~4~. However, the
IPCC 1995 assigns a low confidence to the estimate of the direct aerosol
effect, and a very low confidence to the estimate of the indirect
effect. In reality, there is very little scientific basis for making
such estimates, especially given the uncertainty in the radiative
forcing associated with background aerosols and their natural
variations.

The low confidence in the estimates of aerosol radiative perturbations
is caused by the highly non-uniform compositional, spatial and temporal
distributions of tropospheric aerosols on a global scale owing to their
heterogeneous sources and short lifetimes. Nevertheless, recent studies
have shown that the inclusion of aerosol effects in climate model
calculations can improve agreement with observed spatial and temporal
temperature distributions \[*Hansen et al*., 1995; *Tett et al*., 1996,
*Haywood and Ramaswamy*, 1998\]. Accordingly, it is crucial to establish
a sound observational basis for estimating the magnitude of the
absolute, and perturbed, global aerosol forcing, as well as its
geographical distribution.

*Hansen et al.* \[1997\] studied the sensitivity of climate to the
vertical distribution of a globally-uniform "ghost" forcing of 4 W m^-2^
(for example due to aerosols). They found that global surface
temperature changes associated with this forcing are quite sensitive to
the altitude at which the forcing occurs. Hence, it is important to
devise techniques that can not only determine a column-averaged aerosol
radiative forcing, but methods that provide estimates of the
vertically-resolved radiative forcing.

In this paper we present vertically-resolved estimates of the direct
shortwave aerosol radiative forcing based on: (1) the determination of
the effective aerosol complex index of refraction in distinct horizontal
layers obtained from a combination of lidar-derived aerosol backscatter,
sunphotometer-derived aerosol optical depths and *in situ* particle size
distribution measurements \[*Redemann et al.*, this issue\]; (2)
vertical profiles of aerosol particle size distributions measured aboard
the University of Washington research aircraft \[*Hobbs*, 1999\]; (3)
vertical profiles of lidar-derived water vapor obtained form the LASE
(Lidar Atmospheric Sensing Experiment) instrument \[*Ferrare et al*.,
this issue; *Browell et al*., 1996\]; and (4) radiative flux simulations
with the Fu-Liou radiative transfer model \[*Fu and Liou*, 1992; *Fu and
Liou*, 1993\].

2\. Data sources

One of the main goals of TARFOX is to reduce uncertainties in estimates
of tropospheric aerosol radiative forcing of climate \[*Russell et al*.,
1999a\]. To calculate solar radiative fluxes with the Fu-Liou radiative
transfer model, a quantification of the amounts of radiatively active
gases and the aerosol single-scattering parameters including the
extinction coefficient, asymmetry factor and single-scattering albedo is
necessary. For the determination of aerosol scattering parameters the
following approach was used. Estimates of the aerosol refractive indices
at 815 nm derived by *Redemann et al*. \[this issue\] were utilized for
the first two bands of the Fu-Liou radiative transfer model (0.2 -- 1.3
µm*).* These estimates are obtained by comparing vertically resolved *in
situ* particle size distribution measurements (0.05\<*r*\<\~11.8 µm)
with lidar-derived aerosol backscatter and sunphotometer-derived aerosol
optical depths and determining which aerosol complex index of refraction
best reproduces the remote sensing measurements when assumed in a Mie
calculation based on the particle size distribution measurements in a
given vertical layer of the atmosphere. The results of the study by
*Redemann et al.* \[this issue\] are particle size distribution
measurements and estimates of the effective aerosol refractive indices
in distinct vertical layers which result in closure with the
lidar-derived aerosol backscatter and the sunphotometer-derived aerosol
optical depth, respectively.

*Redemann et al.* \[this issue\] also validated the assumption that the
aerosol refractive index is constant in the sunphotometer wavelength
range (0.38 -- 1.02 µm). For wavelengths beyond 1.3 µm, the aerosol
refractive indices modeled by *Hignett *\[private communication\] were
incorporated. These refractive indices are obtained using the ELSIE
model \[*Lowenthal et al.*, 1995\] based on average TARFOX aerosol
chemical composition measurements by *Novakov et al*. \[1997\] and *Hegg
et al*. \[1997\].

Figure 1 shows the ELSIE-derived average TARFOX aerosol complex index of
refraction for three relative humidities of 0%, 80% and 90%. It is
noteworthy that there is no difference in the refractive indices at 80%
and 90% RH for wavelengths greater than about 2.9 µm. Therefore, for
wavelengths greater than 2.9 µm, the 80% RH TARFOX average refractive
were used in this study. For wavelengths between 1.3 and 2.9 µm, the
refractive indices were calculated by gradually decreasing the
difference between the refractive index derived by *Redemann et al*.
\[this issue\] and the 80% RH TARFOX refractive index at 1.3 µm as a
function of wavelength, so that the difference vanishes at a wavelength
of 2.9 µm.

This process was used for both the real and the imaginary part of the
aerosol complex index of refraction. It is schematically illustrated in
Figure 1 for a hypothetical case study in which the technique by
*Redemann et al.* \[this issue\] obtained a best-fit backscatter aerosol
refractive index of 1.44 -- 0.01i at 815 nm. The resulting curve (black
dotted lines in Figure 1, labeled 'synthesized refractive index') is
constant in the region 0.2 µm\<\< 1.3 µm, asymptotically approaches the
80% RH refractive index in the region between 1.3 and 2.9 µm, and is
identical with the 80% RH refractive index for wavelengths greater than
2.9 µm. In this way, the TARFOX-average compositional analysis supplied
the aerosol index of refraction in the part of the spectrum where no
optical measurements were available to help constrain the choice of the
aerosol refractive index.

Based on the wavelength-dependent aerosol refractive indices in distinct
horizontal layers, and the profiles of *in situ* particle size
distributions measured aboard the UW C-131A aircraft, the vertical
profiles of aerosol single-scattering properties (i.e. the aerosol
extinction coefficient, single-scattering albedo and asymmetry factor)
can be calculated as a function of altitude.

Since the 18 bands in the Fu-Liou radiative transfer model are
relatively broad, the aerosol radiative properties for a given band and
altitude were obtained by integrating over the band width. For instance,
the average aerosol single-scattering albedo,
![](media/image1.pct){width="13.0in" height="13.0in"}, in the first band
(0.2 µm \< \< 0.7 µm) can be obtained from:

> $\overline{w} = \int_{0\text{.}2}^{0\text{.}7}{w(\lambda)d\lambda}/\int_{0\text{.}2}^{0\text{.}7}{d\lambda}$
> (1)

Similarly, the aerosol extinction coefficient and asymmetry factor can
be calculated. After the aerosol optical properties for the 18 bands of
the Fu-Liou model have been calculated as a function of altitude, we can
obtain the direct shortwave aerosol radiative forcing by subtracting the
net irradiances (downward minus upward) in the radiative transfer model
runs with aerosols from those without aerosols as follows:

$D_{a}F(z) = F_{a}(z) - F_{\text{na}}(z)$. (2)

In this study we present only computations of the shortwave aerosol
forcing, covering the first six bands of the Fu-Liou model (0.2 to
4.0 µm). This choice is based on the fact that the estimates of aerosol
refractive indices by *Redemann et al*. \[this issue\] are obtained from
measurements of aerosol optical properties in the visible to near
infrared part of the spectrum, where most of the solar energy resides.
Therefore, an extrapolation of these refractive indices into the IR part
of the spectrum cannot be justified and should only be performed when
additional optical measurements in that part of the spectrum are
available. Moreover, due to their sizes, aerosols are usually considered
to be more important for their influence on solar radiation.

The most important gaseous atmospheric constituent affecting the aerosol
radiative forcing is water vapor, since it potentially alters the amount
of solar flux incident on the aerosol layers. For the TARFOX radiative
flux calculations the profiles of water vapor were provided by the LASE
differential absorption lidar (DIAL) system aboard the ER-2 aircraft.
This system has been intercompared with *in situ* sensors and has been
shown to measure water vapor concentrations across the entire
troposphere to an accuracy of better than 6% or 0.01 g/kg, whichever is
greater \[*Browell et al*, 1996; *Ferrare et al*., this issue\].

Ozone profiles for the radiative transfer calculations were taken from
mid-latitude summer standard atmosphere data, while the CO~2~ mixing
ratio was fixed at 350 ppm. Profiles of pressure and temperature were
measured *in situ* aboard the UW C-131A aircraft. For altitudes above
the aircraft ceiling, data from balloon-sondes launched from Wallops
Island, Virginia, during TARFOX were utilized.

Aerosol induced radiative flux changes are a strong function of the
solar zenith angle and the albedo of the underlying surface. Estimates
of the ocean surface albedo, *A~s~*, were taken from a parameterization
developed by *Taylor et al*.\[1996\] and *Glew et al*.\[1998\] who used
a large set of over-ocean measurements to derive the following
expression for the wavelength-independent surface albedo \[*Briegleb and
Ramanathan*, 1982\]:

$A_{s} = \frac{0\text{.}\text{037}}{1\text{.}1m_{0}^{1\text{.}4} + 0\text{.}\text{15}}$
, (3)

where *µ~0~* is the cosine of the solar zenith angle.

Table 1 summarizes the data sources for the radiative flux calculations
in this work.

3\. Radiative transfer simulations

3.1 Radiative flux calculations for July 17, 1996

For this case study, equation 1 (and its analogs for extinction
coefficient and asymmetry factor) yields the vertical profile of the
single-scattering albedo shown in Figure 2 and extinction and asymmetry
factor in Figure 3 (for the first band of the Fu-Liou model). The
aerosol refractive indices obtained from the retrieval technique
developed by *Redemann et al*. \[this issue\] were 1.33 - 0.00117i for
the surface layer (0-250 m), 1.378 ‑ 0.00428i for the layer between 250
and 1650 m, and 1.451 - 0.00224i for the layer extending from 1650 to
4030 m. A number of investigators \[e.g., *Ackerman and Toon,* 1981;
*Bohren and Huffman*, 1983\] have pointed out that an effective
refractive index as derived from an optical scattering measurement may
lead to erroneous estimates of the aerosol absorption coefficient and
thereby the single-scattering albedo. To validate our single-scattering
albedo profiles, Figure 2 shows a comparison of our data to values
derived from in situ measurements of aerosol extinction and absorption
using nephelometers and aerosol soot absorption photometers,
respectively \[*Hartley et al*., this issue\]. The gray-shaded area in
Figure 2 represents error estimates by *Hartley et al*. \[this issue\],
comprised of one-standard deviation plus instrumental errors. In
general, the two entirely different methods show good agreement within
the error bars, and yield very good agreement for the data below 2000 m
where most of the aerosol optical depth occurs. The single-scattering
albedo is lowest for the middle layer with a value of about 0.96 and
shows values between 0.97 and 0.985 for the other two layers.

The asymmetry factor (shown in Figure 3) on the other hand is largest
for the surface layer, where the *in situ*-measured particle size
distributions contained large particles.

For the time and location of this case study, the parameterization of
the surface albedo by *Glew et al.* \[1998\] (cf. equation 3) yields a
value of 3.8% for *µ~0~* = 0.81. Figure 4 shows the results for the
vertical profile of the instantaneous shortwave aerosol radiative
forcing. The top of the atmosphere (TOA) aerosol radiative forcing
calculations for this case yield a value of -36 W m^-2^, while the
forcing at the surface is -56 W m^-2^. Most of the forcing occurs in the
aerosol layer between 250 and 1650 m, which accounts for most of the
aerosol optical depth (mid-visible optical depth of \~0.35). However,
the relatively shallow surface layer beneath 250 m also contributes
significantly.

Since the aerosol radiative forcing is a strong function of the solar
zenith angle and the surface albedo, the diurnal variation of the
aerosol radiative forcing needs to be estimated in order to compare the
instantaneous forcing values at a certain time of the day to other case
studies under different conditions. However, there is no information on
the temporal evolution of the aerosol layers detected in case study 1.
Accordingly, a time dependence of the forcing results presented here can
only be introduced by varying the solar zenith angle and the surface
albedo. The diurnal dependence of the shortwave aerosol radiative
forcing resulting from this variation is shown in Figure 5.

Figure 5 shows the distinct noon-time minimum of the aerosol radiative
forcing and maxima in the mid-morning and mid-afternoon, which have been
reported previously (e.g., *Russell et al*.\[1999b\]). Since the case
study on this day took place at \~14:30 GLT (870 minutes, genuine local
time), Figure 5 shows that a value of approximately --36 W m^‑2^ for the
TOA radiative forcing is representative for the forcing throughout this
day in that it is a fairly good average value between the noon-time
minimum of about --31 W m^-2^ and the afternoon maximum of some -43 W
m^-2^.

3.2 Radiative flux calculations for July 24, 1996

Figures 6 and 7 show the derived aerosol optical parameters in the first
band of the Fu-Liou radiative transfer model for the July 24 1996 case
study at 15:00 GLT (900 minutes, genuine local time). The aerosol
refractive indices for this case study were estimated to be 1.451 -
0.00345i for the lower layer (150 to 1280 m) and 1.451 - 0.00819i for
the layer extending from 1280 to 1980 m \[*Redemann et al*., this
issue\]. The single-scattering albedo in Figure 6 clearly shows the
aerosol layer structure, with values ranging from approximately 0.975 in
the lower layer to values between 0.90 and 0.94 in the layer above 1280
m. Theses values are again in good agreement with independently
determined single-scattering albedos by *Hartley et al*. \[this issue\]
(see Figure 6).

Aerosol refractive indices retrieved for the layer above 150 m were used
for the calculations of the optical properties of the two aerosol size
distributions below 150 m. The aerosol asymmetry factor and extinction
thus determined are shown in Figure 7.

Figure 8 shows the vertical profile of the instantaneous shortwave
aerosol radiative forcing for this case study. The ocean surface albedo
and the cosine of the solar zenith angle at this time and location are
4.3% and 0.74, respectively. The aerosol radiative forcing at the top of
the atmosphere amounts to -37 Wm^‑2^ and the forcing at the surface is
again of the order of -56 W m^‑2^.

As in the first case study, we can place these results in perspective by
calculating the diurnal variations of the shortwave aerosol radiative
forcings at the top of the atmosphere (TOA) and at the top of the
aerosol layer (TOL). Again, this simulation does not include any time
evolution of the aerosol but merely the changes in the solar zenith
angle and the surface albedo for this case study as a function of the
genuine local time (GLT). Figure 9 shows the distinct noon-time minimum
of the aerosol radiative forcing and maxima in the mid-morning and
mid-afternoon. For this case study however, the absolute difference
between the TOA radiative forcing at local noon and at the mid-afternoon
maximum is only of the order of 6 W m^‑2^. This implies that the
instantaneous value for the TOA forcing of -37 W m^‑2^ in Figure 6 (at
15:00 GLT) is very close to the afternoon maximum of ‑39.5 W m^‑2^.

4\. Error propagation in the radiative transfer modeling results

The radiative forcing calculations presented here are the result of
simulations using the Fu-Liou radiative transfer model. Therefore, an
analysis of the error propagation from the model input parameters into
the radiative flux results must be performed by means of a sensitivity
study, as opposed to an error estimate based on analytical expressions.
For legibility, let *F* be the aerosol-induced radiative forcing at the
top of the atmosphere and let us assume that *F* is a function of the
aerosol optical depth, , the single-scattering albedo, , the aerosol
asymmetry parameter, *g*, the surface albedo, *A~S~*, and the cosine of
the solar zenith angle, *~0~=cos~0~*, hence *F=F( , , g, A~S~, ~0~).*
Assuming that the error in the forcing is proportional to the errors in
the input parameters we can write the absolute error in the forcing,
*F*, as follows (cf. *Bevington* \[1969\] ):

$DF@Dt\left( \frac{¶F}{\text{¶t}} \right) + Dw\left( \frac{¶F}{\text{¶w}} \right) + Dg\left( \frac{¶F}{¶g} \right) + {DA}_{S}\left( \frac{¶F}{¶A_{S}} \right) + {Dm}_{0}\left( \frac{¶F}{\text{¶m}_{0}} \right)$
(4)

The terms on the right hand side of (4) were estimated by calculating
the model response to realistic errors in the input parameters. Table 2
summarizes the results from this type of sensitivity analysis for the
two TARFOX case studies presented in this paper. Errors in the aerosol
optical depth were estimated to be of the order of 10%, the
single-scattering albedo was also varied by 10%, and the asymmetry
parameter was varied by only 5%, based on the fact that it usually
exhibited less variability than the other two aerosol parameters. The
surface albedo, *A~S~*, was changed by 20% from its central value, while
the solar zenith angle was varied by 1. We believe that the above
uncertainties represent the maximum range of possible errors, rather
than a 1-standard deviation from the mean values. The 10% error in the
single-scattering albedo may appear large, but is well within the range
of values determined during the TARFOX experiment \[*Hegg et al.*, 1997;
*Hartley et al*., this issue\]. However, by using relatively large
values for the uncertainties in the aerosol single-scattering
properties, we intended to quantify the maximum error in our aerosol
radiative forcing results.

The results in Table 2 show that the TARFOX radiative forcing estimates
are most sensitive to the 10% change in the aerosol single-scattering
albedo, and somewhat less sensitive to changes in the aerosol optical
depth and the asymmetry parameter. The change in the single-scattering
albedo reduces the magnitude of the negative radiative forcings by about
30%, while the variations in the aerosol optical depth and asymmetry
factor result in \~10% changes in the TOA forcing. Thus, the changes in
the aerosol parameters have the largest impact on the aerosol radiative
forcing, while moderate errors in the estimates of the surface albedo
and the solar zenith angle have negligible effects on the accuracy of
the radiative forcing results, likely because of the large magnitude of
the TOA radiative forcing. The results in Table 2 further suggest that
the sensitivity of the radiative forcing to changes in all of the input
parameters is fairly linear in the range of parameters considered here.

Table 2 shows that equation (4) is not likely to produce an accurate
value for the absolute error in the aerosol radiative forcing at TOA for
the following reason. Equation (4) assumes that the errors in the
variables are small and, more importantly, that they are independent of
each other. However, errors in the aerosol parameters (extinction,
single-scattering parameter and asymmetry parameter) are necessarily a
consequence of errors in the fundamental aerosol properties (i.e., the
aerosol size distribution and/or complex index of refraction). For
example, an increase in the imaginary part of the aerosol index of
refraction will increase the aerosol optical depth and, at the same
time, decrease the single-scattering albedo. According to Table 2, these
two circumstances (increased aerosol optical depth and decreased
single-scattering albedo) have opposite effects on the TOA aerosol
radiative forcing for both of the TARFOX case studies presented here.

From the above considerations, we can conclude that the error in TOA
aerosol radiative forcing can be assessed more realistically by carrying
out a sensitivity analysis with respect to the complex aerosol
refractive indices and the aerosol particle size distributions. In the
technique for estimating the refractive index developed by *Redemann et
al*. \[this issue\], the *in situ* particle size distributions were
adjusted to yield closure with the sunphotometer-derived aerosol optical
depths. This adjustment was performed because the aerosol refractive
indices retrieved from the lidar backscatter profiles and the original
particle size distributions did not reproduce the independent
sunphotometer aerosol optical depths. Hence, the study by *Redemann et
al*. \[this issue\] produced two sets of particle size distribution and
aerosol refractive index data. The first one reproduces the lidar
derived aerosol backscatter on the basis of the original particle size
distributions, but does not yield closure with the sunphotometer-derived
aerosol optical depths. The second one yields aerosol refractive indices
and adjusted particle size distributions, which are in accord with both
the lidar-derived aerosol backscatter and the sunphotometer-derived
aerosol optical depths (for details on the required adjustment to the
particle size distribution measurements, see *Redemann et al.* \[this
issue\]). Surprisingly, the aerosol radiative forcings calculated on the
basis of the original aerosol size distributions, and the corresponding
retrieved aerosol refractive indices, did not vary by more than 15% from
the values calculated based on the adjusted size distributions and their
corresponding retrieved refractive indices (cf. Table 3).

The reason for this lack of sensitivity in the aerosol radiative forcing
calculations is that the retrieved aerosol refractive indices are based
on a certain set of particle size distributions, and that, in some
sense, the retrieved refractive indices compensate for errors in the *in
situ* particle size distributions in order to reproduce the lidar
backscatter measurements. This sensitivity study shows that a TOA
aerosol radiative forcing estimate can be accurate, provided the set of
particle size distributions and refractive index data properly represent
the aerosol backscattering. This result is not surprising, considering
that in simplified analytical expressions, the aerosol radiative forcing
is proportional to the hemispheric aerosol upscattering (i.e. the
scattering integrated over the backward hemisphere \[e.g., *Russell et
al*., 1997\]).

Finally, to assess the uncertainties in the radiative forcing
calculations caused by independent errors in the retrieved aerosol
refractive indices, Table 4 shows the sensitivity of the TARFOX
radiative forcing results to a 20% error in the imaginary part and a 5%
error in the real part of the retrieved aerosol refractive indices
(without any adjustments to the *in situ* particle size distributions).
These errors were selected based on a sensitivity study for the TARFOX
refractive index retrieval technique \[cf., *Redemann et al*., this
issue\], which approximately yielded the above errors in aerosol
refractive indices as a consequence of 30%-random errors in the input
lidar backscatter data.

Summarizing Table 4, the TARFOX TOA radiative forcings show a strong
sensitivity to errors in the real part of the aerosol refractive indices
(on the order of 30% to a 5% change in *m~r~*), and are less sensitive
to errors in the imaginary part. Undoubtedly, this is caused by the
small absolute values of the imaginary parts of the retrieved refractive
indices, for which a 20% change does not produce major changes in the
derived aerosol properties (extinction, single-scattering albedo and
asymmetry parameter). However, the sensitivity of the aerosol radiative
forcing estimates to the imaginary refractive indices is likely greater
for aerosols with imaginary refractive indices above 0.01.

In conclusion, the TARFOX TOA aerosol radiative forcing estimates are
likely to have maximum uncertainties of the order of 12 W m^-2^
corresponding to relative errors of 30%.

5\. Discussion

The shortwave aerosol radiative forcing calculations for the two TARFOX
case studies discussed here yield very comparable top of the atmosphere
forcings of -36 and ‑37 W m^‑2^. This similarity can be attributed to
the comparable aerosol optical depths for the two cases (about 0.5 in
the midvisible), and the fact that the case studies took place at about
the same time of the day. The aerosol-induced flux changes at the
surface are about ‑56 W m^‑2^ implying a strong cooling effect in the
surface layers. These calculations are based on effective aerosol
refractive index estimates obtained from a combination of lidar-derived
aerosol backscatter, sunphotometer-derived aerosol extinction and *in
situ* particle size distributions \[*Redemann et al*., this issue\].
Since a number of investigators \[e.g., *Ackerman and Toon,* 1981;
*Bohren and Huffman*, 1983\] have pointed out that an effective
refractive index as derived from an optical scattering measurement may
lead to erroneous estimates of the aerosol absorption coefficient (and
the single-scattering albedo), we intercompared our single-scattering
albedo profiles to independent measurements by *Hartley et al*. \[this
issue\]. In general the data sets agreed within the measurement
uncertainties and showed very good agreement in those parts of the
profiles where most of the extinction occurs. Therefore, we conclude
that our single-scattering albedo estimates are valid and hence
appropriate for radiative forcing calculations as carried out here.

*Russell et al*.\[1999b\] calculated the aerosol induced changes in the
upward and downward irradiances for several TARFOX flights and showed
generally good agreement between their theoretical values and values
obtained from pyranometer measurements aboard the UK Meteorological
Office C‑130 aircraft \[*Hignett et al*., 1999\]. In particular, they
investigated the aerosol radiative effects for a case study on July 17,
which took place only three hours before the case study 1 of the present
study. The diurnal variation in the aerosol-induced changes in the
upward irradiance for July 17 given by *Russell et al*. \[1999b\] (their
Figure 7) is similar to the diurnal forcing calculations given here (see
Figure 4), suggesting the validity of their simplified flux calculation
method.

It is noteworthy that both TARFOX cases studied here yield only a small
difference (approximately 2 W m^‑2^) between the forcing at the top of
the aerosol layer (TOL) and the top of the atmosphere (TOA), see Figures
5 and 9. If the forcing at the TOL was caused solely by the aerosol
induced change in the upward irradiance, one would expect that the TOA
forcing is simply the product of the TOL forcing and the transmission of
the overlying atmosphere. Assuming for example a TOL forcing of --35 W
m^‑2^, and a transmission of 0.8, one would derive a TOA forcing of ‑28
W m^‑2^ and hence a difference between the two forcings of the order of
7 W m^‑2^, rather than 2 W m^‑2^ obtained from the detailed radiative
transfer model calculations. The explanation for this apparent
discrepancy lies in the aerosol induced changes in the downward
irradiance at TOL. Table 5 gives the detailed flux results at TOL and
TOA for our July 17, 1996 case study .

Table 5 confirms that the TOA aerosol radiative forcing is caused by the
aerosol induced change in the upward irradiance only. However, the TOL
aerosol radiative forcing caused by an increase in the upwelling
component (![](media/image2.pct){width="29.0in" height="14.0in"}) of the
net flux by 41.51 W m^‑2^ is reduced by a simultaneously increased
downwelling irradiance. The change in the downwelling flux at TOL is
only 4.3 W m^‑2^, but is large enough to reduce the difference between
the TOL and the TOA radiative forcings to 1.3 W m^‑2^.

6\. Conclusions

The finding of an aerosol induced change in the downwelling component of
the net flux at the top of an aerosol layer is an important result which
shows that, while the dominant factor in the aerosol radiative forcing
at a given level in the atmosphere is the change in the upwelling
component, the downwelling can also be significant. Thus, for the
determination of aerosol induced flux changes in the atmosphere, both
the upwelling and the downwelling components of the net flux need to be
measured. Importantly, these conclusions can only be drawn from detailed
radiative transfer calculations that consider the vertical structure of
the aerosol radiative forcing based on vertically-resolved information
regarding the aerosol optical and microphysical properties (obtained
here through synthesis of lidar, sunphotometer and *in situ* particle
size distribution data). The vertical distribution of the aerosol
radiative forcing is relevant to climate studies since it affects
convection and the formation and lifetime of clouds. An application of
the multi-instrument approach, as outlined here, to different aerosol
data sets will likely provide a comprehensive picture of the vertical
structure of tropospheric aerosol radiative forcing and hence improve
our understanding of climate responses to aerosol-induced changes in
Earth's radiation balance.

**Acknowledgements.** TARFOX is a contribution to the International
Global Atmospheric Chemistry (IGAC) core project of the International
Geosphere-Biosphere Programme (IGBP). The authors would like to thank
D. McIntosh (Symtech) for support during the preparation of this
manuscript. This work was funded under NSF grants ATM-96-18425 and
ATM-94-12082. Support through NASA radiation science program, codes
622-44-10-10 and 622-44-75-10, and NASA grant NAGS-7675 is also
gratefully acknowledged.

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> **Table 1.** Summary of the data sources from TARFOX used for the
> aerosol radiative forcing calculations described in this paper.

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**Figure 1.** Example of synthesis of the complex aerosol index of
refraction for input into the Fu-Liou radiative transfer model. The 80%
relative humidity TARFOX average aerosol refractive index from the ELSIE
model is used to extrapolate the refractive indices estimated by
*Redemann et al.* \[this issue\].

**Figure 2.** Single-scattering albedo (solid line) for the first band
of the Fu-Liou radiative transfer model (0.2 µm \< \< 0.7 µm) for TARFOX
case study 1, July 17, 1996 derived using *in situ* particle size
distributions and effective aerosol refractive index estimates from
*Redemann et al.* \[this issue\]. For comparison, independently measured
single-scattering albedos at 450 nm from *Hartley et al*. \[this issue\]
are shown (dotted line). The gray-shaded area represents their error
estimates based on one standard deviation plus instrumental error.

**Figure 3.** Aerosol extinction coefficient and asymmetry factor for
the first band of the Fu-Liou radiative transfer model (0.2 µm \< \< 0.7
µm) for TARFOX case study 1, July 17, 1996.

**Figure 4.** Vertical profile of the instantaneous shortwave aerosol
radiative forcing, as calculated by the Fu-Liou radiative transfer model
for TARFOX case study 1, July 17, 1996, 14:30 GLT (genuine local time)
for a surface albedo *A~S~* of 3.8% and *µ~0~* of 0.81. The forcing at
the top of the atmosphere (TOA) is --35.91 W m^-2^.

**Figure 5.** Estimate of the diurnal variation of the instantaneous
shortwave aerosol radiative forcing, as calculated by the Fu-Liou
radiative transfer model for TARFOX case study 1, July 17, 1996 for the
top of the atmosphere (TOA: solid line) and the top of the aerosol layer
(TOL: short-dashed line) by varying only the solar zenith angle and the
ocean surface albedo with time. The diurnal variation of ocean surface
albedo and *µ~0\ ~*are indicated.

**Figure 6.** Single-scattering albedo (solid line) for the first band
of the Fu-Liou radiative transfer model (0.2 µm \< \< 0.7 µm) for TARFOX
case study 2, July 24, 1996 derived using *in situ* particle size
distributions and effective aerosol refractive index estimates from
*Redemann et al.* \[this issue\]. For comparison, independently measured
single-scattering albedos at 450 nm from *Hartley et al*. \[this issue\]
are shown (dotted line). The gray-shaded area represents their error
estimates based on one standard deviation plus instrumental error.

**Figure 7.** Aerosol extinction coefficient and asymmetry factor for
the first band of the Fu-Liou radiative transfer model (0.2 µm \< \< 0.7
µm) for TARFOX case study 2, July 24, 1996.

**Figure 8.** Vertical profile of the instantaneous shortwave aerosol
radiative forcing, as calculated by the Fu-Liou radiative transfer model
for TARFOX case study 2, July 24, 1996, 15:00 GLT (genuine local time)
for a surface albedo *A~S~* of 4.3% and *µ~0~* of 0.74. The forcing at
the top of the atmosphere (TOA) is --36.87 W m^-2^.

**Figure 9.** Estimate of the diurnal variation of the instantaneous
shortwave aerosol radiative forcing, as calculated by the Fu-Liou
radiative transfer model for TARFOX case study 2, July 24 1996 for the
top of the atmosphere (TOA: solid line) and the top of the aerosol layer
(TOL: short-dashed line) by varying only the solar zenith angle and the
ocean surface albedo with time. Ocean surface albedo and *µ~0\ ~*are
indicated.