Aerosol effect on the distribution of solar radiation over the clear-sky
global oceans derived from four years of MODIS retrievals.

Lorraine A. Remer and Yoram J. Kaufman

Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt
MD

Re-Submitted for publication to

Atmospheric Chemistry and Physics (ACP)

May 31, 2005

[Corresponding author's address:]{.underline}

Lorraine Remer

Code 613.2

NASA/Goddard Space Flight Center

Greenbelt MD 20771

301-614-6194 (voice) 301-614-6307 (fax)

<Lorraine.A.Remer@nasa.gov>

**Abstract**

A four year record of MODIS spaceborne data provides a new measurement
tool to assess the aerosol direct radiative effect at the top of the
atmosphere. MODIS derives the aerosol optical thickness and
microphysical properties from the scattered sunlight at 0.55-2.1 µm. The
monthly MODIS data used here are accumulated measurements across a wide
range of view and scattering angles and represent the aerosol's
spectrally resolved angular properties. We use these data consistently
to compute with estimated accuracy of ± 0.3W m^-2^ the reflected
sunlight by the aerosol over global oceans in cloud free conditions. The
MODIS high spatial resolution (0.5 km) allows observation of the aerosol
impact between clouds that can be missed by other sensors with larger
footprints. We found that over the clear-sky global ocean the aerosol
reflected 5.0±0.3 W m^-2^ with an average radiative efficiency of 46±2 W
m^-2^ per unit optical thickness. The seasonal and regional distribution
of the aerosol radiative effects are discussed. The analysis adds a new
measurement perspective to a climate change problem dominated so far by
models.

**1.0 Introduction**

Traditionally, chemical transport and general circulation models enjoyed
a monopoly on estimating the role of aerosols in the Earth\'s climate.
Model results form the basis of almost every previous estimate of the
aerosol effect on climate (IPCC, 2001). Observations of aerosols from
ground-based, airborne or satellite instruments are used only to
validate these models. The prevailing strategy dictates that
measurements improve models, and then models, not measurements, answer
climate questions. However, there is a wide range of discrepancy in
model results because of the many inherent assumptions involved in
modeling the aerosol effect on climate. Models must properly estimate
the source terms of the many aerosol species, properly model the aerosol
sink terms, and simulate the transport. Even if the model properly
simulates the global distribution of aerosol concentration, assumptions
have to be made of the aerosol optical properties in order to convert
mass concentrations to the radiative fluxes. Because of the complexity
of the problem, it is no wonder that the uncertainties in estimating
aerosol effects on climate are growing, rather than shrinking.

To narrow the uncertainties associated with estimating aerosol effects
on climate, the time has come to include measurement-based estimates of
aerosol radiative effects and forcing. With the launch of EOS-Terra
carrying the Moderate resolution Imaging Spectroradiometer (MODIS),
Multi-angle Imaging (MISR) and Clouds and Radiant Energy System (CERES),
we are suddenly \"data rich\". These instruments, along with subsequent
instruments on EOS-Aqua, EOS-Aura, ICESat, and Parasol, are designed
specifically to observe aerosols and the Earth\'s radiation budget. They
provide global information in a way that previous ground-based or
airborne instruments could not, and they provide quantitative
information about aerosol that is not only more accurate than our
heritage instruments, but also more complete in terms of aerosol
characterization. With these increased capabilities, aerosol
observations from satellite can provide an independent measure of some
key climate parameters in parallel with model predictions.

One key measurement that satellites are able to provide is the direct
shortwave radiative effect of aerosols at the top of the atmosphere. By
aerosol direct shortwave radiative *effect* we mean the difference in
shortwave radiative flux between having aerosols present and having no
aerosols at all. This is different from aerosol shortwave direct
radiative *forcing*, which is the radiative effect of anthropogenic
aerosols only. Analysis suggests that by characterizing aerosol particle
size from space, there is information available to the satellites to
classify aerosol into natural and anthropogenic and therefore to
determine the anthropogenic portion of the aerosol loading and
subsequently determine aerosol forcing from the aerosol effect (Kaufman
et al. 2002; Kaufman et al. 2005). However, the focus of the present
study is the straightforward estimate of aerosol total direct radiative
effect.

In this study, we make global and regional estimates of the clear-sky
aerosol shortwave radiative effect over the oceans using an internally
consistent set of parameters from the MODIS aerosol retrieval. We first
put the present study in context with other measurement-based estimates
of aerosol effect. We then describe the MODIS aerosol retrieval over
ocean and the information available. The paper then describes the
radiative transfer model, how we adapt the MODIS data to be used as
inputs to the model, how we calculate the regional and global
instantaneous and 24 hour daily averages of the aerosol direct radiative
effect. The results include estimates of monthly mean direct aerosol
radiative effect over the oceans, globally and in 13 regional sections,
for both the Terra and Aqua satellites.

**2.0 Background**

There have been various approaches to using satellite data as the basis
for determining aerosol direct radiative effect. One approach is to
combine the satellite data with chemical transport model information (Yu
et al. 2004). This method allows apportionment of radiative effects to
chemical species, but requires assumption of aerosol optical properties.
Another approach is to use MODIS to measure aerosol loading in the form
of aerosol optical thickness and to use simultaneous observations of the
radiation field by CERES (Christopher and Zhang, 2002; Zhang et al.,
2005b). Using CERES eliminates the need to assume aerosol optical
properties, but does require aerosol dependent angular distribution
models (Loeb et al. 2003ab; Zhang et al. 2005a). Furthermore, the large
CERES footprint (20 km at nadir) biases results of clear sky direct
radiative effects to situations dominated by large high pressure
systems. Loeb and Manalo-Smith (2005) avoid this cloud-free sky bias by
basing their estimate on the finer resolution MODIS observations. They
first determine the relationship between MODIS narrowband radiances and
CERES broadband ones, and use the relationship to make a narrowband to
broadband conversion.

In this study we present an alternative method using MODIS data alone to
estimate direct aerosol radiative effect over the oceans. As mentioned
above, the 500 m spatial resolution of MODIS observations reduces any
unnatural bias to cloud-free conditions. Unlike the CERES studies,
above, we use an offline radiative transfer model (Chou et al., 1992) to
make the conversion between MODIS-measured narrowband angular radiances
and broadband hemispheric fluxes in one step. In this way we avoid the
empirical model that translates CERES angular measurements to
hemispheric flux. Unlike the other studies that use models we do not
have to go looking for outside sources for information to use as input
to the model. The MODIS aerosol retrieval provides a complete set of
aerosol optical properties that best match the spectral radiance at the
top of atmosphere. A similar method maintaining consistency between
retrieval and flux calculations was done using POLDER data (Boucher and
Tanré, 2000). By matching the measured spectral radiance, the influence
of errors in the MODIS assumptions on the derived flux are diminished.
For example, both the flux and the radiance are proportional to first
order to the single scattering albedo (ω~o~). An error in the ω~o~ will
cause an error in the derived aerosol optical thickness (τ~a~). However,
if the derived τ~a~ is used with the same assumed ω~o~ to derive the
flux, the errors in ω~o~ and τ~a~ will cancel, resulting in the correct
value of derived flux, at least in the single scattering approximation.

**3.0 The MODIS aerosol retrieval over ocean**

The MODIS satellite sensor has been observing and reporting on aerosol
characteristics since the beginning of the Terra satellite mission in
2000 (Ichoku et al., 2002; Chu et al., 2002; Remer et al. 2002). MODIS
measures radiance (W m^-2^ sr^-1^), denoted as L, in 36 channels.
Reflectance is calculated from these measurements according to the
definition ρ = πL/(µ~o~E~o~) where µ~o~ is the cosine of the solar
zenith angle and E~o~ is the extraterrestrial solar flux (W m^-2^) in
the given spectral band. Of the 36 MODIS channels 6 channels (0.55-2.13
µm) are directly used to retrieve aerosol information from scenes over
ocean (Tanré et al., 1997; Remer et al. 2005). While MODIS spatial
resolution ranges from 250 m to 1000 m depending on wavelength, the 6
channels used in the aerosol algorithm are all at resolution of 250 or
500 m. The 250 m bands are degraded to 500 m, and thus the basic
resolution of the MODIS aerosol retrieval input is uniformly 500 m. This
broad spectral range, coupled with the 500 m spatial resolution in these
bands, permits a unique view of aerosols that cannot be duplicated with
any other sensor. Because of the fine spatial resolution and specialized
cloud mask (Martins et al., 2002; Gao et al, 2002; Brennan et al.,
2005), MODIS retrieves aerosol properties closer to clouds than other
satellites such as AVHRR with its 1 km resolution or especially CERES
with its 20 km footprint. On the other hand, close proximity to clouds
may introduce "cloud contamination" into the aerosol optical thickness
retrieval. Recent studies have begun to estimate the proportion of the
retrieved aerosol optical thickness attributed to cloud effects (Kaufman
et al., 2005; Zhang et al., 2005).

The MODIS aerosol retrieval makes use of a LookUp Table (LUT) consisting
of calculated upwelling radiances (or when normalized as above, solar
reflectances) at top of atmosphere for each of the six wavelengths for a
rough ocean surface, a variety of geometries, aerosol amounts and
aerosol models (Remer et al. 2005). There are 9 aerosol models in the
LUT. Four of the models represent submicron (fine) mode aerosol
particles, and five of the models represent supermicron (coarse) mode
particles. Each of the nine models consists of a monomodal lognormal
size distribution, and real and imaginary refractive indices. Thus, a
unique spectral dependence of extinction, single scattering albedo
(ω~o~) and assymetry parameter (g) is defined for each model.

In the retrieval process, the algorithm is looking for a combination of
fine and coarse mode models to accurately represent the spectral
reflectances measured by MODIS at the top of atmosphere. The modes from
the LUT are combined using η as the weighting parameter,

ρ^LUT^~λ ~(τ~a~) =ηρ^f^~λ~(τ~a~)+\[1-η\]ρ^c^~λ~(τ~a~) (1)

The inversion finds the pair of fine and coarse modes and the τ~a~ and η
that minimizes the error (ε) defined as

![](media/image1.pct) (2)

where N~λ~ is the number of pixels at wavelength λ, ρ^m^~λ~ is the
measured MODIS reflectance at the wavelength λ and ρ^LUT^~λ~ is
calculated from the combination of modes in the Look Up Table, defined
by Eq. (1). The 0.01 prevents a division by zero for the longer
wavelengths under clean conditions. Typically solutions are found with ε
\< 3% (Remer et al., 2005).

The solution represents the best fit of the LUT reflectances to the
actual reflectances that MODIS measures. The combination of the two
chosen modes, τ~a~ and η represent a derived aerosol model from which a
variety of parameters including ω~o~ and g can be inferred. The
combination of τ~a~, ω~o~ and g represent the aerosol optical properties
that best fit the spectral reflectances at top of atmosphere. This is
not saying that the MODIS algorithm is retrieving ω~o~ or g with any
accuracy. There could be and are compensating errors associated with the
retrieval of any one of the parameters. For this reason we do not make
an attempt to estimate radiative effects at the surface, which are
particularly sensitive to the value of ω~o~. However, the combination of
MODIS retrieved τ~a~, ω~o~ and g, when used consistently has to produce
the best fit to the spectral reflectances at top of atmosphere.

**4.0 Estimating Aerosol Radiative Effect at Top of Atmosphere**

**4.1 The MODIS Aerosol Data**

We will use the results of the MODIS aerosol retrieval as a consistent
set of aerosol optical properties: τ~a~, ω~o~ and g, that will be input
into a column radiative transfer climate model (Chou et al, 1992; Chou
and Suarez, 1999) to calculate the upwelling hemispheric broadband
fluxes at the top of atmosphere. The MODIS data we use are the Level 3
monthly mean aerosol optical thickness by model, reported at 0.55 µm on
a 1 degree grid over oceans (King et al, 2003). This product gives us
the monthly statistics based on the original 500 m resolution data. Over
the course of a month, MODIS views the same 1 degree square with a wide
variety of view angles. This works to reduce the uncertainty in
calculating flux from the individual angular observations. The data from
the Terra satellite form a time series from September 2001 to October
2002, and additionally from June 2003 to October 2004. The 7 months of
data in 2002-03 are missing due to a reprocessing of the data occurring
during the time of this analysis. The data from the Aqua satellite form
a continuous time series from October 2002 to November 2004.

The MODIS-derived aerosol optical thickness product has been compared
extensively with AERONET observations (Holben et al., 1998). Comparisons
are made both in terms of individual observations collocated in space
and time (Ichoku et al., 2005; Remer et al., 2005) and also comparisons
of independently derived monthly mean values (Remer et al., 2005;
Kleidman et al. 2005). These evaluations suggest that the MODIS aerosol
optical thickness retrieval over oceans agrees with AERONET to within
±0.03±0.05 τ~a~. Even where the scatter from individual retrievals
exceeds expectations, the scatter is random, suggesting that long-term
statistics may be even more accurate (Remer et al., 2005).

When MODIS data are collocated in time with AERONET data, MODIS benefits
partially from AERONET\'s more aggressive cloud clearing algorithm.
Thus, uncertainty may be larger and biases may exist in MODIS retrievals
of aerosol optical thickness that has not been previously reported in
the validation studies. For example, MODIS may incorrectly make an
observation and report an optical thickness for a scene with cloud
contamination. AERONET would not make an observation in those
conditions. Therefore, that contaminated MODIS retrieval would never
make it to the validation scatter plots because there would be no
corresponding AERONET point. Because of these missing points, the
reported uncertainty of ±0.03±0.05 τ~a~ may be overly optimistic, and
MODIS retrievals could be biased high at all levels and scales. Recently
this potential problem has been addressed and quantitatively estimated.
We know that the cloud fraction, as measured by the MODIS satellite, is
about 50% of its global values in the validation data sets used to
collocate MODIS and AERONET. Also, recent analysis of MODIS-derived thin
cirrus reflectances and aerosol optical thickness retrievals suggests
that roughly 0.01-0.02 of the MODIS aerosol optical thickness at 0.55 µm
may be attributed to thin cirrus contamination and not aerosol at all
(Kaufman et al., 2005).

**4.2 The Radiative Transfer Model**

We use the radiative transfer model CLIRAD-SW (Chou et al., 1992; Chou
and Suarez 1999) to calculate the hemispherical flux at the top of the
atmosphere. CLIRAD-SW includes the absorption and/or scattering due to
water vapor, various gases, aerosols clouds and the surface. Fluxes are
integrated over the full solar spectrum, from 0.175 µm to 10 µm. The
reflection and transmission of clouds and aerosol layers are calculated
from the δ-Eddingtion approximation and the fluxes calculated using the
two-stream adding approximation. Note that we use the model only in
cloud free conditions.

CLIRAD-SW requires input of aerosol optical properties in 11 spectral
bands, 7 in the ultraviolet, 1 in the 0.40-0.70 µm visible range, 1 in
the near-infrared (0.70-1.22 µm), and 2 in the mid-infrared (1.22-10.0
µm). MODIS reports aerosol optical properties in 7 bands (0.47 -- 2.13
µm), none in the ultraviolet. We translate the MODIS values to the
wavelengths needed by the model by finding the wavelength of the
solar-weighted MODIS extinction in each of CLIRAD-SW\'s bands ,

![](media/image2.pct) (3)

with S(λ) the solar spectrum (Neckel and Labs, 1981), βex(λ,mode) the
spectral extinction for each of the MODIS modes, and
![](media/image3.pct) the weighted value used for the CLIRAD-SW input
for the band defined between λ1 and λ2. The representative wavelength is
![](media/image4.pct), and the MODIS optical properties are interpolated
or extrapolated to this value for each of the nine MODIS modes and each
CLIRAD-SW band.

The interpolation/extrapolation of MODIS values to CLIRAD-SW bands
introduces uncertainty in the final derivation of radiative effect.
However, Ichoku et al. (2003) discuss that the final results of flux
calculations, especially at top of the atmosphere are mostly insensitive
to the extrapolation to the UV or mid-IR bands. The main sensitivity of
translating input from the MODIS observations to the CLIRAD-SW bands is
to the interpolation in the only visible band, λ=0.40 µm to λ=0.70 µm,
corresponding closely to the MODIS primary channel (0.555 µm), and
making the interpolation more certain. The uncertainty in the final
results from many sources of error is fully discussed in Section 6.0.

We set the ocean surface albedo to be 0.07, and use the midlatitude
profiles for temperature and humidity for all model runs. The
sensitivity tests in Ichoku et al. (2003) show that the results at top
of atmosphere are insensitivity to choice of atmospheric profile, but
are sensitive to the choice of ocean albedo. A ∆albedo = 0.01 will
result in an uncertainty of radiative effect of \~2-4% depending on
solar zenith angle

We run CLIRAD-SW separately for each of the 9 sets of aerosol optical
properties corresponding to the 9 MODIS modes, for a range of aerosol
optical thickness values and for 9 solar zenith angles. From the model
output we subtract the net radiative flux at top of the atmosphere for
no aerosol optical thickness (τ~a~ = 0) from the values calculated at
each of the other values of aerosol optical thickness. This becomes a
Look Up Table (LUT) of aerosol effect at the top of the atmosphere. An
example of such results are displayed in Figure 1 averaged over the 24
hour period for a location at the equator at the equinox so that we are
simulating a 12 hour day with the solar zenith angle equal to 0 at noon.
We see that for a specific τ~a~, even for a moderate value such as 0.20,
the effect at top of the atmosphere can vary by approximately -5 W
m^-2^, depending on the type of aerosol present.

**4.3 The distribution of aerosol type**

The MODIS Level 3 monthly mean statistics include the product,
Optical_Depth_By_Models_Ocean, that provides the optical depth at
wavelength 0.55 µm attributed to each of the 9 modes in the MODIS
algorithm. This product provides the basis for determining the
distribution of aerosol properties over the world's oceans. As an
illustration we divide the global oceans into 13 sections defined in
Figure 2, and calculate the mean optical thickness attributed to each of
the MODIS modes for every month. Examples of the distribution of τ~a~
among the different modes observed from the Terra satellite for three
such sections and one section from the Aqua satellite are shown in
Figure 3.

Section 9 is the cleanest of the 13 sections in terms of aerosol loading
with an annual average τ~a~ =0.09. In this southern tropical Pacific
section the primary mode chosen by MODIS is mode=7, and to a lesser
extent mode =6, both corresponding to coarse marine sea salt aerosols.
Fine modes 1 and 4 also make a contribution, especially in the
non-summer months. The fine mode may represent dimethyl sulfide (DMS).
There is almost no contribution from fine modes 2 and 3, or coarse modes
5, 8 and 9. This is how Terra-MODIS interprets the background marine
aerosol, and Aqua-MODIS (not shown) is similar but with less coarse mode
6, slightly more in modes 1 and 9.

Section 6, off the coast of West Africa contains both transported
Saharan dust and biomass burning smoke with an annual average τ~a~
=0.20. In contrast to Section 9, we see that in Terra Section 6 modes 8
and 9 make a contribution to the total aerosol optical thickness. These
two modes correspond to mineral dust. In addition, mode 4 is much
stronger than in the purely background aerosol of Section 9. The broad
size distribution of mineral dust includes long tails into the submicron
region that the MODIS retrieval interprets as optical thickness in the
largest fine mode. The winter months tend to have a different
distribution of modes than the rest of the year, possibly due to a
greater contribution by biomass burning aerosol during that season. The
Aqua Section 6 distribution (not shown) is similar to Terra, but with
less contribution by mode 6, and more in the dust modes 8 and 9.

Section 4 is the region down stream from north and central Asia with an
annual mean τ~a~ =0.20. In Terra-MODIS we see a broad distribution of
aerosol modes, with the summer months exhibiting large increases in fine
modes 2 and 3. MODIS interprets smoke and pollution particles mostly as
an increase in modes 2 and 3. Although dust is prevalent in this region
in the Spring months only a slight elevation in mode 8 is noted. The
Aqua-MODIS representation in this section is quite different, showing
very little optical thickness due to mode 6, much more optical thickness
in the dust modes of 8 and 9, and very different distributions amongst
the fine modes. Annual mean fine mode fraction from Terra for Section 4
is 0.60, while for Aqua it is 0.70. Note that unlike annual mean values
of fine mode fraction published in other studies these mean values were
not weighted by τ~a~ and are used only to compare Terra and Aqua here.
Differences between Terra and Aqua arise from a combination of basic
calibration differences in the two instruments and also small changes to
the MODIS aerosol retrieval algorithms that may be implemented at
different times in the separate processing for Terra and Aqua. The MODIS
retrieval of aerosol size and choice of aerosol model are especially
sensitive to instrument calibration (Chu et al. 2005).

The examples in Figure 3 demonstrate two points. The first is that the
global distribution of aerosol optical properties is more complex than
simply the distribution of aerosol optical thickness, or even the
distribution of fine mode fraction. The second point is that differences
between Terra and Aqua demonstrate the sensitivity of the retrieval
algorithm to small perturbations in instrument calibration and software.

**4.4 Deriving regional and global daily average aerosol radiative
effect**

To calculate the aerosol radiative effect we combine the distribution of
aerosol modes from the MODIS retrieval (Figure 3) with the calculated
radiative effect as a function of mode (Figure 1). The MODIS-measured
aerosol optical thickness in each mode, τ~a~ (mode, lat, lon) and the
solar zenith angle are used as indices in the radiative effect look-up
table, F\[τ~a~ (mode, lat, lon),θ~o~\]. Then we sum the results over all
nine modes.

![](media/image5.pct) (4)

This is the monthly mean aerosol effect at top of atmosphere for a
particular 1 degree grid square, instantaneously at the time of
satellite overpass.

We estimate the 24 hour daily average radiative effect from the
instantaneous values calculated from the MODIS observations. To do so,
we return to the CLIRAD-SW model and simulate the diurnal cycle in
hourly increments of the aerosol effect for 7 latitudes and 12 months,
assuming that the aerosol AOT and properties do not vary systematically
through the day. We combine the results of the nine MODIS modes based on
the annual mean global aerosol optical thickness and distribution over
the nine modes. From this modeling effort we are able to calculate the
daily average and the ratio of the instantaneous at the time of
satellite overpass to the daily average. The Terra overpass is
considered to be 10:30 am, and the Aqua over pass 1:30 pm. An example of
these ratios is shown in Figure 4. Thus for any particular month,

![](media/image6.pct){width="3.067361111111111in"
height="0.5694444444444444in"} (5)

with F24(lat,lon) the 24 hour daily average radiative effect for the
grid square based on the MODIS observations, F(lat,lon) the
MODIS-derived instantaneous radiative effect from Eq. (4),
F*^calc^*24(lat,month) the model-derived daily average for month and
latitude and F*^calc^*I(lat,month) the model-derived value at the
instantaneous time of overpass.

The ratios of F*^calc^*24(lat,month)/F*^calc^*I(lat,month) are dependent
on aerosol optical thickness and type. There is a 10% uncertainty in
F24(lat,lon) introduced by the ratios due to uncertainty in aerosol
type, based on testing the differences in final F24 between using fine
mode 2 or coarse mode 7. There is an additional 8% uncertainty
introduced by varying the mean τ~a~ used in the calculation from global
mean values to ±σ, one standard deviation from global mean values.
Because of the symmetry around solar noon of the Terra and Aqua over
pass times, the ratios are the same for both satellites.

The Level 3 monthly mean MODIS data that we use will report a monthly
mean value in any grid square that has at least one retrieval in that
square during the month. Because the basic resolution of the MODIS
aerosol retrieval is 10 km, a grid square may have as many as 3000
retrievals in a 30 day month. Clouds, glint, geometry and orbital
considerations reduce that number considerably. However, there does
remain a significant difference between a grid square with just one 10
km retrieval in the entire month and another square with several hundred
retrievals. This difference would be minimal had we used daily data
instead of monthly. In order to reconstruct the statistics realized from
daily data as we calculate regional and global means, we simply weight
each monthly value by the number of MODIS aerosol observations for that
month and grid square, Nobs(lat,lon). We also weight by cosine of the
latitude to account for the decreasing surface area and corresponding
decreasing contribution to the total global or regional radiative effect
toward the poles.

![](media/image7.pct) (6)

![](media/image8.pct) (7)

where F24(sect) is the daily mean radiative effect at top of atmosphere
for one of the 13 sections defined in Figure 2 and F24_global is the
global value. F24(sect) and F24_global are calculated for every month of
available data.

**5.0 Results**

Figure 5 shows the 24 hour MODIS-derived aerosol radiative effect from
the Terra satellite at top of the atmosphere for four seasons, and
Figure 6 gives the numerical values for both the aerosol optical
thickness and the radiative effect. The locations noted for high aerosol
loading unsurprisingly also show prominent radiative effect from these
aerosols. Such locations as the Atlantic coast of Africa (Swap et al.,
2003; Tanré et al. 2003), the coasts of Asia (Huebert et al., 2003) and
the northern midlatitudes in spring (Chin et al. 2004) all report
radiative effect in excess of -15 W m^-2^. More surprising is the band
of strong effect that occurs in the southern midlatitudes during
Northern Fall and Winter.

Figure 7 shows time series of Terra-MODIS monthly mean aerosol optical
thickness, τ~a~, for each section and also the global value for both
Terra and Aqua satellites. These τ~a~ are weighted by the number of
retrievals in each grid box, analogous to Eqs. (6) and (7) for
F(lat,lon). These weighted τ~a~ are biased low when compared to
unweighted values, but better represent the clear-sky direct radiative
effect, which is the subject of the present study. Annual mean values of
the weighted τ~a~ over the global oceans for Terra-MODIS is 0.13, the
unweighted value is \~0.14. For Aqua-MODIS the weighted and unweighted
values are 0.12 and 0.13, respectively. The time series plots show a
great amount of variation in optical thickness between sections,
hemispheres and seasons. However the global mean value remains
remarkably constant. The sections of highest aerosol optical thickness
include the Asian outflow (section 4), the Saharan outflow (section 6)
and the Arabian Sea (section 7). Note that the cleanest region is the
south tropical Pacific, but that the midlatitude southern ocean also has
relatively little aerosol loading, despite the strong radiative effect
seen in Figure 5.

The center row of Figure 7 shows a time series of monthly mean aerosol
radiative effect from Terra-MODIS for each section, F24(sect), and also
F24_global for both Terra and Aqua. The same regional and seasonal
variations are seen in the radiative effect as in the optical thickness.
The bottom row of Figure 7 shows a time series for radiative efficiency
in units of W m^-2^ per unit τ~a,~ again from Terra-MODIS. Radiative
efficiency is defined as the slope of the linear regression equation
calculated from the relationship of F24 and τ~a~. In this work it is not
a simple ratio of F24/τ~a~. There is much more variability in the
radiative efficiency than in either τ~a~ or F24, not only regionally,
but globally as well. The higher the latitude the larger the solar
zenith angle and the greater the radiative efficiency. Section 13, the
midlatitude southern ocean, has a strong radiative efficiency,
explaining the apparent contradiction between low aerosol optical
thickness and relatively high F24.

Table 1 gives the annual mean global values of τ~a~, F24_global and the
radiative efficiency for 5 complete calendar years, 2 from Terra and 3
from Aqua. The global mean value of F24 for Terra is approximately -5.6
± 0.3 W m^-2^ and --5.9 ± 0.3 W m^-2^ for Aqua. The global mean value of
aerosol efficiency is approximately -43 W m^-2^ τ~a~^-1^ for Terra and
-48 W m^-2^ τ~a~^-1^ for Aqua.

The year to year variation of either platform is remarkably small.
However, even though the two platforms agree to within the given error
bars, Aqua does report higher values. This is not due to a global
diurnal variation of observed τ~a~, because Aqua \'s value of τ~a~ is
actually smaller than Terra\'s in this data set. The two platforms do
report different distributions of aerosol over the 9 modes (Figure 2),
suggesting either different aerosol types at the two overpass times, or
more likely, uncertainties in the two sensors\' calibrations or
properties that result in retrievals of different aerosol modes. For
example, the 1.6 µm channel on Aqua is not functional and the aerosol
retrieval is reduced to 5 channels of input. Retrieval of aerosol size
parameters strongly depend on instrument calibration.

A more detailed comparison between Terra and Aqua is shown in Figure 8.
Here monthly sectional means derived from the two sensors are plotted
against each other in scatter plots. Northern and southern hemispheres
are plotted separately, with midlatitude separated from tropical
sections by symbol. We use different scales on the axes in the two
hemispheres. Aqua aerosol optical thickness (τ~a~) is systematically
lower than Terra's for all sections and seasons, north and south of the
equator, both midlatitudes and tropics. However, Aqua's radiative effect
(F24) is similar to Terra's in the midlatitudes, while systematically
more negative in the tropics. The reason is the stronger efficiency
(F24/ τ~a~) observed by Aqua in all regions and seasons. The stronger
efficiency compensates for the lower τ~a~ in the midlatitudes, but
overcompensates in the tropics, causing the Aqua tropical F24 values to
be more negative than Terra's. For these matching monthly-sectional mean
values, Aqua τ~a~ are lower than Terra's by 8% in the midlatitudes and
3% in the tropics. The Aqua efficiencies are stronger by 6% in the
midlatitudes and 15% in the tropics, while the Aqua radiative effect
(F24) is 2% less negative than Terra's in the midlatitudes but 12% more
negative in the tropics.

**6.0 Random and Systematic Uncertainty**

The uncertainties appearing in Table 1 are based on the following
sources of unbiased uncertainty. The first source of error is the
uncertainty of the MODIS radiances themselves, \~2%. The second source
of error are the initial MODIS retrievals of the sets of parameters,
τ~a~, ω~o~ and g, which match the observed spectral radiances to within
3% (Eq. 2), and thus over an ensemble of measurements of various view
angles encountered during a month of MODIS observations should also
represent flux at top of atmosphere to within the same uncertainty. The
third source of error arrives from initialization of the CLIRAD-SW
model. Uncertainties in sea surface albedo of 0.01 will result in
uncertainty of flux of \~3%, uncertainties in extrapolation of aerosol
properties from MODIS wavelengths in the visible and near-infrared to
the ultraviolet and mid-infrared introduce less than 1% error, while the
choice of atmospheric profiles introduce negligible error. The last
source of error arises from converting instantaneous radiative effect to
24 hour daily averaged values. In making the conversion we model the
diurnal cycle of radiative effect based on assuming global mean aerosol
optical thickness and global mean distribution of aerosol type over the
9 MODIS modes. We determine uncertainty to these assumptions of aerosol
properties from sensitivity studies that deviated aerosol type from one
pure fine mode to one pure coarse mode, and then deviated aerosol amount
one standard deviation from global mean values. The uncertainty to the
conversion due to aerosol type adds a 10% error, while the uncertainty
due to aerosol amounts introduces an 8% error. We take these errors
originating in the conversion to 24 hour averages to be random, although
there could be systematic biases if assumptions underlying the original
aerosol optical models are not realistic. Combining all these sources of
uncertainty in a root mean square error sense results in an overall
*random* uncertainty of 5.5% or roughly 0.3 W m^-2^ for global values of
-5.5 W m^-2^.

The above error analysis assumes all uncertainties are random. Another
source of uncertainty concerns the issue of residual cloud contamination
in the retrievals, which introduce a biased error into the estimation of
aerosol radiative effect. Cloud contamination will always increase
aerosol optical thickness and therefore systematically introduce a high
bias to our estimates of radiative effect. As discussed above in Section
4.1, we estimate the potential increase of optical thickness due to
contamination may be as high as 0.015 to 0.020 optical thickness on a
global basis (Kaufman et al., 2005; Zhang et al. 2005). Clouds will also
modify the aerosol retrieval of the other two parameters of the solution
set, creating their own signature in the calculated fluxes and estimates
of radiative effect. It is unclear at this point, exactly how to
interpret the effect of cloud contamination on the final results.
However, if the global efficiencies in Table 1 remain the same with only
the global mean aerosol optical thickness affected then as an
approximation we can calculate a "cloud corrected" F24 by multiplying
the Table 1 efficiencies by their respective global values of (τ~a~ --
∆ τ~a~), where ∆ τ~a~ is the amount of optical thickness attributed to
cloud contamination (0.015 to 0.020). For the first row of Table 1 (τ~a~
-- ∆ τ~a~) is 0.11 to 0.115, which when multiplied by -43.1 W m^-2^ per
τ~a~ gives us a range of corrected F24 to be -4.7 to -5.0 W m^-2^.
Applying the same calculation to the other years and satellites listed
in Table 1 suggests that the Terra -5.5 W m^-2^ and the Aqua -5.9 W
m^-2^ listed in the table should be taken as an upper bound of the
estimate, and a cloud free number may be closer to -4.7 to -5.2 W m^-2^.

**7.0 Conclusions**

We have estimated the regional and global value of total clear-sky
aerosol shortwave radiative effect over the oceans in cloud free
conditions to be -5.5 ± 0.3 W m^-2^ to -5.9 ± 0.3 W m^-2^ using an
internally consistent set of MODIS retrieved aerosol parameters.
Correcting for estimated cloud contamination, these numbers become -4.7
± 0.3 W m^-2^ to -5.2 ± 0.3 W m^-2^ The global values of aerosol optical
thickness and radiative effect are remarkably consistent from season to
season and year to year.

Individual regions show greater variability, spatially, seasonally and
annually. For the most part, aerosol shortwave radiative effect is
directly proportional to aerosol optical thickness, with the regions and
seasons experiencing the highest optical thickness also experiencing the
greatest radiative effect. However, because of the increased solar
zenith angle at higher latitudes, the midlatitude and polar regions have
higher radiative efficiency and greater radiative effect for the same
optical thickness found in the tropics. There are also differences in
radiative efficiency due to different optical properties of aerosol in
different regions.

There is a systematic bias between the results from the Terra and Aqua
satellites with Terra showing 5% less effect and 11% weaker radiative
efficiency than Aqua, despite its consistently higher values of optical
thickness. Most of the differences between Terra and Aqua occur in the
tropics. Note that the 5% difference is slightly smaller, not larger and
in opposite direction than the difference in the AOT between the two
satellites. This is the result of the compensation effects between
errors made in the derivation of the AOT and in calculations of the
aerosol radiative effect. In summary, the MODIS analysis of the aerosol
effect on the raidative fluxes adds a new measurement perspective to a
climate change problem dominated so far by models.

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Table 1. Annual global mean aerosol optical thickness (~a~), radiative
effect at top of atmosphere (F24_global) and radiative efficiency
(F24/~a~) observed from Terra- and Aqua-MODIS during various calendar
years.

+----------------+--------+------------+--------------+--------------+
| year           | τ~a~   | F24_global | F24/τ~a~     | F24          |
|                |        | (W m^-2^)  |              | corrected    |
|                |        |            | (W m^-2^     |              |
|                |        |            | τ~a~^-1^)    | for clouds   |
+----------------+--------+------------+--------------+--------------+
| Terra Sep\'01  | 0.130  | -5.5±0.3   | -43.1        | -4.7 to -5.0 |
| to Aug\'02     |        |            |              |              |
+----------------+--------+------------+--------------+--------------+
| Terra Sep\'03  | 0.129  | -5.6±0.3   | -43.8        | -4.8 to -5.0 |
| to Aug\'04     |        |            |              |              |
+----------------+--------+------------+--------------+--------------+
| Aqua Sep\'03   | 0.122  | -5.8±0.3   | -47.8        | -4.9 to 5.1  |
| to Aug\'03     |        |            |              |              |
+----------------+--------+------------+--------------+--------------+
| Aqua Dec\'02   | 0.123  | -5.9±0.3   | -48.3        | -5.0 to 5.2  |
| to Nov\'03     |        |            |              |              |
+----------------+--------+------------+--------------+--------------+
| Aqua Dec\'03   | 0.123  | -5.9±0.3   | -48.1        | -5.0 to 5.2  |
| to Nov\'04     |        |            |              |              |
+----------------+--------+------------+--------------+--------------+

F24 corrected for clouds is an approximation based on estimates of cloud
contamination in the aerosol optical thickness product of 0.015 to 0.020
on a global basis, over the oceans. Discussion in Section 6.0.

**Figure Captions**

> Figure 1. Daily averaged aerosol radiative effect for a 12 hour day
> with the solar zenith angle equal to 0 at noon, a variety of aerosol
> optical thicknesses and the nine modes of the MODIS aerosol retrieval
> over ocean.
>
> Figure 2. Terra-MODIS observed seasonal mean aerosol optical thickness
> over oceans at 0.55 µm for the months June-July-August 2004. The 13
> regional sections are also identified.
>
> Figure 3. Fraction of aerosol optical thickness attributed to each of
> the 9 MODIS modes for four example sections of Figure 2 as functions
> of month. Months are composites of all available years of data. Three
> of the panels show distribution of mode optical thickness observed
> from the Terra satellite and the last panel (bottom right) shows
> observations from the Aqua satellite.
>
> Figure 4. Ratio of 24 hour daily average radiative effect
> (F*^calc^*24) to instantaneous radiative effect (F*^calc^*I) as a
> function of latitude and month. Shown are selected months. The same
> ratio applies for Terra and Aqua.
>
> Figure 5. Global distribution of MODIS-observed aerosol radiative
> effect at top of atmosphere from the Terra satellite for four seasons:
> Northern Winter 2003-2004 (upper left), Spring 2004 (upper right),
> Summer 2004 (lower left) and Fall 2003 (lower right).
>
> Figure 6. Seasonal values of aerosol optical thickness (top) and
> aerosol radiative effect at the top of the atmosphere (bottom) from
> the Terra satellite. The four numbers in each latitude-longitude
> section represents a seasonal mean for that section from all available
> monthly data. Starting from the upper left corner and proceeding
> clockwise the seasons are Northern Winter, Spring, Summer and Fall,
> respectively. Radiative effect values of the bottom panel are fluxes
> in units of W m^-2^.
>
> Figure 7. Time series of monthly mean aerosol optical thickness (top
> row), radiative effect (center row), and radiative efficiency (bottom
> row) from Terra-MODIS for each of the 13 sections defined in Figure 2
> (dots). Also shown are the global mean values from both Terra (black
> line) and Aqua (blue line). The left panels show the northern
> midlatitudes, the center panels the northern tropics and the right
> panels the southern hemisphere. Terra is missing 7 months of data
> (2002-2003) due to data unavailability during reprocessing.
>
> Figure 8. Scatter plots of quantities derived from Aqua data plotted
> against those derived from Terra data. Each point is a
> monthly-sectional mean from each of the 13 sections whenever both
> satellites reported values. The quantities shown are aerosol optical
> thickness- τ~a~ (top), radiative effect -- F24 (center) and radiative
> efficiency -- F24/ τ~a~ (bottom). The left column is for the northern
> hemisphere and the right column shows southern hemisphere results.
> Midlatitudes in both hemispheres are denoted by dots. Tropical
> sections in both hemispheres are denoted by open triangles.

![](media/image9.png){width="3.6819444444444445in"
height="3.2395833333333335in"}

Figure 1. Daily averaged aerosol radiative effect for a 12 hour day with
the solar zenith angle equal to 0 at noon, a variety of aerosol optical
thicknesses and the nine modes of the MODIS aerosol retrieval over
ocean.

![](media/image10.jpeg){width="4.929861111111111in"
height="2.879861111111111in"}

Figure 2. Terra-MODIS observed seasonal mean aerosol optical thickness
over oceans at 0.55 µm for the months June-July-August 2004. The 13
regional sections are also identified.

![](media/image11.pct){width="5.647222222222222in"
height="4.791666666666667in"}

Figure 3. Fraction of aerosol optical thickness attributed to each of
the 9 MODIS modes for four example sections of Figure 2 as functions of
month. Months are composites of all available years of data. Three of
the panels show distribution of mode optical thickness observed from the
Terra satellite and the last panel (bottom right) shows observations
from the Aqua satellite.

![](media/image12.pct){width="4.544444444444444in"
height="3.5770833333333334in"}

Figure 4. Ratio of instantaneous radiative effect (F*^calc^*I) to 24
hour daily average radiative effect (F*^calc^*24)as a function of
latitude and month. Shown are selected months. The same ratio applies
for Terra and Aqua.

![](media/image13.pct){width="5.80625in" height="4.879166666666666in"}

Figure 5. Global distribution of MODIS-observed aerosol radiative effect
at top of atmosphere from the Terra satellite for four seasons: Northern
Winter 2003-2004 (upper left), Spring 2004 (upper right), Summer 2004
(lower left) and Fall 2003 (lower right).

![](media/image14.pct){width="4.5in" height="3.182638888888889in"}

![](media/image15.pct){width="4.5in" height="3.1069444444444443in"}

Figure 6. Seasonal values of aerosol optical thickness (top) and aerosol
radiative effect at the top of the atmosphere (bottom) from the Terra
satellite. The four numbers in each latitude-longitude section
represents a seasonal mean for that section from all available monthly
data. Starting from the upper left corner and proceeding clockwise the
seasons are Northern Winter, Spring, Summer and Fall, respectively.
Radiative effect values of the bottom panel are fluxes in units of W
m^-2^.

![](media/image16.png){width="5.991666666666666in"
height="6.7555555555555555in"}

Figure 7. Time series of monthly mean aerosol optical thickness (top
row), radiative effect (center row), and radiative efficiency (bottom
row) from Terra-MODIS for each of the 13 sections defined in Figure 2
(dots). Also shown are the global mean values from both Terra (black
line) and Aqua (blue line). The left panels show the northern
midlatitudes, the center panels the northern tropics and the right
panels the southern hemisphere. Terra is missing 7 months of data
(2002-2003) due to data unavailability during reprocessing.

![](media/image17.png){width="5.704166666666667in"
height="7.019444444444445in"}

Figure 8. Scatter plots of quantities derived from Aqua data plotted
against those derived from Terra data. Each point is a monthly-sectional
mean from each of the 13 sections whenever both satellites reported
values. The quantities shown are aerosol optical thickness- τ~a~ (top),
radiative effect -- F24 (center) and radiative efficiency -- F24/ τ~a~
(bottom). The left column is for the northern hemisphere and the right
column shows southern hemisphere results. Midlatitudes in both
hemispheres are denoted by dots. Tropical sections in both hemispheres
are denoted by open triangles.