The evaluation of aerosol radiative effect on broadband hemispherical solar flux is often performed using simplified spectral and directional scattering characteristics of atmospheric aerosol and underlying surface reflectance. In this study we present a rigorous yet fast computational tool that accurately accounts for detailed variability of both spectral and angular scattering properties of aerosol and surface reflectance in calculation of direct aerosol radiative effect. The tool is developed as part of the GRASP (Generalized Retrieval of Aerosol and Surface Properties) project. We use the tool to evaluate instantaneous and daily average radiative efficiencies (radiative effect per unit aerosol optical thickness) of several key atmospheric aerosol models over different surface types. We then examine the differences due to neglect of surface reflectance anisotropy, nonsphericity of aerosol particle shape and accounting only for aerosol angular scattering asymmetry instead of using full phase function. For example, it is shown that neglecting aerosol particle nonsphericity causes mainly overestimation of the aerosol cooling effect and that magnitude of this overestimate changes significantly as a function of solar zenith angle (SZA) if the asymmetry parameter is used instead of detailed phase function. It was also found that the nonspherical–spherical differences in the calculated aerosol radiative effect are not modified significantly if detailed BRDF (bidirectional reflectance distribution function) is used instead of Lambertian approximation of surface reflectance. Additionally, calculations show that usage of only angular scattering asymmetry, even for the case of spherical aerosols, modifies the dependence of instantaneous aerosol radiative effect on SZA. This effect can be canceled for daily average values, but only if sun reaches the zenith; otherwise a systematic bias remains. Since the daily average radiative effect is obtained by integration over a range of SZAs, the errors vary with latitude and season. In summary, the present analysis showed that use of simplified assumptions causes systematic biases, rather than random uncertainties, in calculation of both instantaneous and daily average aerosol radiative effect. Finally, we illustrate application of the rigorous aerosol radiative effect calculations performed as part of GRASP aerosol retrieval from real POLDER/PARASOL satellite observations.

Direct atmospheric aerosol radiative forcing remains one of the most
uncertain components in evaluation of Earth's climate change (Andreae et al.,
2005; Hansen et al., 2011). Although aerosols are generally recognized as
having a negative radiative effect (cooling) on the surface–atmosphere
system, in some conditions aerosol can also have a positive radiative effect
(warming). The aerosol cooling effect is produced by reflecting solar
radiation back to space, i.e., scattering in the upward direction. Depending
on their composition, aerosol can also heat due to absorption of the incoming
solar radiation. However, not only properties of aerosol but also of the
undelaying surface are decisive for the sign of the aerosol radiative effect.
For example, the same particles can decrease (warming effect) or increase
(cooling effect) the planetary albedo depending on whether the underlying
surface is a bright desert or dark ocean. Regardless of warming or cooling
from the point of view of top-of-atmosphere albedo, aerosols always warm the
atmospheric layer if their absorption is not 0. In addition, the aerosols
generate a heating effect in thermal infrared spectrum, primary caused by large
mineral dust particles that strongly absorb outgoing terrestrial radiation
(e.g., Legrand et al., 2001). This aerosol heating effect in thermal infrared spectrum is similar to the effect of greenhouse gasses and thus counteracts the aerosol scattering effect in the solar spectrum. For clarity of the analysis performed in this study it is important
to recall that the term aerosol direct radiative forcing, which is defined as
perturbation of radiative fluxes due to human-induced components only, is
therefore different from the term radiative effect. Aerosol radiative effect
refers to the difference between radiative fluxes in aerosol-free and
aerosol-laden atmospheric conditions (e.g., Kaufman et al., 2005; Remer and
Kaufman, 2006). Using measurements, one can assess the aerosol radiative
effect by referring to aerosol-free conditions. In climate models, however,
it is feasible to evaluate forcing by referring to background or
pre-industrial aerosol. Therefore, because of the possibility to control numerous
aerosol emission and transport processes, evaluation of radiative forcing of
climate relies mostly on chemical transport and general circulation models.
In order to reduce dependence on assumptions that take place in the models,
important steps towards evaluation of aerosol direct radiative effect are
also taken using global aerosol and broadband flux observations from satellite
and ground-based remote sensing (Boucher and Tanré, 2000; Yu et al.,
2004; Bellouin et al., 2005; Zhou et al., 2005; Remer and Kaufman, 2006; Yu
et al., 2006; Su et al., 2013). The observation-based evaluations of aerosol
radiative effect create opportunities for intercomparison with models and
lead to improvement in the assessment of aerosol radiative effect on climate.
Therefore, there is an interest in continuing the measurement-based
evaluation of the aerosol radiative effect and examination of possible
sources of uncertainty. For example, descriptions of angular and spectral
features of scattering properties of aerosol and underling surface are often
simplified. The reasons for using these simplifications are usually the lack
of information regarding the details of these properties and the need for
substantial reduction of the computation time required for rigorous flux
computations. For instance, accurate modeling of scattering by nonspherical
particles and directional reflectance of surface is challenging and therefore
often neglected. Recent advancements in retrievals of aerosol optical
characteristics from ground and space remote sensing and from a combination of
sensors show capabilities to provide more detailed properties. For example,
aerosol size distribution, complex refractive index, single scattering albedo
and nonspherical fraction become available not only from ground-based
photometric observations (Dubovik et al., 2002b, 2006) but also from space
sensors (Dubovik et al., 2011, 2014), providing the advantage of large spatial
coverage. The retrievals from space also provide information about the
surface spectral albedo or bidirectional reflectance distribution
function (BRDF) parameters. In addition, the aerosol layer
height can be retrieved using even passive polarimetric sensors (Dubovik et
al., 2011; Tanré et al., 2011), while a combination of passive and active
sensors shows sensitivity to vertical profiles of extinction by aerosol in
fine and coarse mode fractions (Lopatin et al., 2013). These upcoming
enhanced remote sensing retrievals imply the possibility of more accurate aerosol
radiative effect computation that largely relies on the measurements and
reduced level of assumptions. For example, a close agreement is found in an
intercomparison of measured downward solar flux at the surface with fluxes
computed as part of the AERONET product. The studies conducted in the
framework of a field campaign (Derimian et al., 2008), on a global scale
(García et al., 2008) and in specific case studies (Derimian et al.,
2012) show that the computed broadband solar flux generally agrees with the
measured flux to within 5 to 10 %; note that accuracy of solar flux
measurements themselves is on the order of 5 %. The agreement between
simulated and measured flux is remarkable yet to be expected if the
computational approach employed here is understood. The main advantage of
the approach is that the retrieved aerosol and surface properties should fit
the measured radiances at given wavelengths within a few percent, as it
requires the inversion algorithm. Obviously, an interpolation or
extrapolation outside of the nominal wavelengths is needed and the errors may
accumulate during spectral radiances calculations and after radiances
integration into broadband flux. Essentially, it also implies that the
retrieved aerosol models that satisfy fit of simulated to measured radiances
in inversion algorithms should also accurately reproduce the spectral
variability of aerosol properties in the simulation of broadband flux.
Accurate and high spectral resolution computations of radiances that account
for spectral variability of gaseous absorption and detailed aerosol
characteristics, such as detailed phase function, which strongly depend on
particle sizes, shapes and index of refraction, should increase the accuracy
of the simulated flux. For example, the importance of accounting for particle
nonsphericity in calculation of desert dust radiative forcing is addressed in
several discussions (Mishchenko et al., 1995; Bellouin et al., 2004; Kahnert
and Kylling, 2004; Kahnert et al., 2005; Derimian et al., 2008; Yi et al.,
2011). Indeed, nonsphericity of the particles shape is often neglected in
aerosol radiative effect computations, mainly due to necessity to reduce
computational time. Hence, an assumption is made that the differences in
angular scattering by spherical and nonspherical particles are canceled when
all contributions of scattered light are summed up into the total
hemispherical flux. Also, the computation approach generally implies usage of
the asymmetry parameter, which is an integrated value, and therefore
differences in the aerosol phase function of spheres and spheroids are
expected be averaged out. However, Kahnert and Kylling (2004) and Kahnert et
al. (2005) conducted a detailed analysis of asymmetry parameter sensitivity
to particle shape and concluded that the use of spherical particles model
might be among the major error sources in broadband flux simulations. In the
work by Derimian et al. (2008) the effect of particles nonsphericity on
forcing was evaluated using detailed phase function in the flux calculations.
The nonsphericity effect was evaluated for cases of dust and mixed aerosol
type during biomass burning season in western Africa. The computations
revealed that neglecting particles' nonsphericity leads to a systematic
overestimation of the aerosol cooling effect by up to 10 %; the bias was
pronounced in instantaneous and daily average values. It was also noted that
the magnitude of the overestimation depends on the magnitude of aerosol
absorption and aerosol optical thickness (AOT or

In the current study we introduce a rigorous computational tool for broadband flux simulations and demonstrate the importance of detailed representation of aerosol and surface. We apply our simulation for (i) evaluating radiative effect of several key aerosol models; then (ii) we stress importance of diurnal dependence (dependence on SZA) of the aerosol radiative effect and (iii) examine the effects of assumptions using simplified representations of aerosol phase function, particle shape and directional properties of surface reflectance. It is often expected that the details of aerosol and surface optical properties are not really important because the flux is an integral product of spectral and angular properties of atmospheric radiation. Therefore we intend to clarify whether any cancelations of uncertainties appear in the integrated broadband hemispherical flux due to coexisting assumptions on aerosol and surface directional scattering.

Thus, the below paper is organized as follows. Section 2 provides a description of the flux computational tool. Section 3 contains a description of aerosol models used in the sensitivity tests. In Sects. 4 and 5 we analyze the importance of the diurnal dependence of the instantaneous aerosol radiative effect, which also varies as a function of aerosol characteristics and the surface albedo model. Section 6 provides the discussion about complexity of evaluation of the nonspherical–spherical difference in aerosol radiative effect due to a concurrent change in directional redistribution of scattering and spectral extinction cross sections of volume-equivalent spheres and spheroids. Section 7 discusses the errors appearing in radiative effect calculations due to the use of a simplified representation of aerosol directional scattering by asymmetry parameter. Finally, Sect. 8 includes an example of aerosol radiative effect computation for a part of Africa using the GRASP (Generalized Retrieval of Aerosol and Surface Properties) algorithm (Dubovik et al., 2014) applied to POLDER/PARASOL observations.

The initial version of this broadband solar flux computational tool was originally built in the AERONET operational code (Dubovik and King, 2000); the performances were studied and intercomparisons with the ground-based flux measurements conducted on a global scale (García et al., 2008) and in specific case studies (Derimian et al., 2008). As described below, the tool is significantly revised and integrated into the GRASP unified algorithm for characterizing atmosphere and surface. Thus, at present, the calculations can be performed as part of measurements processing and the radiative effect estimations can be provided in the framework of GRASP retrieval product. It is also possible to use the computational tool in various types of independent research calculations.

Computations of broadband solar flux in spectral interval from 0.2 to
4.0

General organization structure of computational code for broadband solar flux and aerosol radiative effect computations.

As mentioned above, several important revisions of the radiative effect
computation tool were done as part of GRASP project advancement
(Dubovik et al., 2011). The significant reduction of
computational time of spectral radiances was one of these advancements.
Another advantage, compared to the original tool, is that the radiative
transfer code implemented in the GRASP also accounts for polarization and
can account for both aerosol phase matrix and surface BPDF (bidirectional
polarization distribution function). Note that in the presented sensitivity
calculation the polarization effects were not considered, but they are
accounted for in application for POLDER/PARASOL observations. Finally, the
most important advancement is that all the aerosol and surface properties
that are necessary for the broadband solar flux calculation can be derived
simultaneously by GRASP as retrieval products, e.g., using POLDER/PARASOL
observations. In addition, there is an interest in interpreting new aerosol
retrievals produced by GRASP on the level of direct aerosol radiative
effect. The radiative effect calculation strategy described above is
therefore driven by this motivation and is tied to the retrieved
characteristics provided by GRASP. Spectral dependent properties, such as
aerosol complex refractive index, BRDF and BPDF parameters derived only at
the fixed instrumental channels, are used after interpolation or
extrapolation in the same manner as was done in initial version of the
computational tool. The gas absorptions calculations using the correlated

The results of calculations include instantaneous upward and downward
fluxes (with and without aerosol), instantaneous net radiative effect at the
bottom of atmosphere (BOA), TOA and in the atmospheric layer,
24 h average net radiative effects (BOA, TOA and atmospheric layer) and
vertical profiles of aerosol radiative effect for a given aerosol profile.
The aerosol net radiative effect is defined as the difference between
downwelling and upwelling fluxes at a given atmospheric layer in
aerosol-free and aerosol-laden conditions; that is, at the BOA the net
radiative effect is defined as

Complex refractive index for the employed aerosol models.

Several key aerosol models are selected in order to evaluate their radiative
effect under different assumptions. The average aerosol models are derived
from all available years of AERONET observations and include dust and
mixture of dust with biomass burning aerosol in the Dakar site (also known
as Mbour), biomass burning aerosol in the Mongu site, urban/industrial
pollution in the Paris site and mixture of dust with urban/industrial
aerosol in the Kanpur site. Except for Dakar, the AERONET sites and aerosol
models are selected pursuing the works of Dubovik et al. (2002a) and Giles et al. (2012). The Dakar
site was studied in the framework of the AMMA campaign
(Haywood et al., 2008) and is
characterized by a mixture of dust with biomass burning aerosol during the dry
season in January and February and by desert dust only starting from March (e.g., Derimian et al., 2008; Léon et al., 2009). The aerosol
characteristics are derived using version 2, level 2 almucantar AERONET
product and applying criteria recommended in Dubovik et al. (2002a). Additionally, a seasonal criterion is applied for the Mongu site in
southern Africa, where the biomass burning aerosol model is derived during
the summer period that is known as a peak of the biomass burning season. It
has to be mentioned that at this site the aerosol absorption was found as
varying within the biomass burning season (Eck et al., 2013); thus variability in the
biomass burning radiative efficiency is also expected. For the purpose of
our study, however, we take only an averaged characteristic and select
August and September as the months with highest aerosol optical thickness
and maximal number of observations. An additional criterion that was used to
distinguish the aerosol type is the value of Ångström exponent
(

Characteristics of the employed aerosol models:

Note that the computed

The calculated directional scattering of the employed aerosol models at 440, 1020 and 2100 nm.

A pronounced spectral dependence in the directional scattering can also be
seen in Fig. 3, which shows

Strong dependence of instantaneous aerosol radiative effect on SZA implies importance of (i) the proper intercomparison of instantaneous values assessed in different time and location and (ii) the evaluation of the daily average radiative effect, which is obtained by integration over corresponding range of SZAs in a given day and location. In order to examine dependence on SZA, diurnal radiative efficiencies are calculated for the above-presented aerosol models. The radiative efficiencies are calculated with respect to AOT at 550 nm and over Lambertian ocean surface albedo. The aerosol radiative efficiency is used in order to examine influence of different aerosol type and not of concentration, which is supposed to be ruled out because efficiency is defined as radiative effect per unit AOT. One should remember, however, that the aerosol radiative effect is not a linear function of AOT, e.g., as discussed by Markowicz et al. (2008). Thus, for a consistent intercomparison of radiative efficiencies calculated for different aerosol models, we choose to set all corresponding AOTs at 550 nm to unit.

Instantaneous aerosol radiative efficiencies with respect to 550 nm
at the

The first observation that can be drawn from the Fig. 4 is that not only
magnitude but also the shape of the curves of radiative efficiency vs.
cos(SZA) depends on the aerosol type. Note that cos(SZA) is used
hereafter since this variable appears in the radiative transfer equation.
This shape is essentially linked to the differences in aerosol phase
functions. Significant dependence of the instantaneous radiative effect on
SZA also implies that its accurate computation is important for the daily
average radiative effect. Hence, a proper analysis and intercomparison of
not only instantaneous but also of the daily average aerosol forcings
should respect the range of SZAs. Consistency in the daylight time duration
should also be taking into account if one intends to attribute the
differences in the daily average radiative effect to differences in aerosol
type or concentration. Strictly speaking, the same aerosol type and
concentration over the same surface and in same location, but at different
times
of the year or on the same day but in different latitudes, will give
different value of daily average forcing. Otherwise, for a consistent
intercomparison, a standard can be assumed; for example, the sun reaches
the zenith (SZA

It is known that the aerosol radiative impact on the Earth's albedo depends not
only on the aerosol properties but also on reflectance of the underlying
surface. In general, to describe surface reflectance accurately, the
BRDF is required. The BRDF
depends on illumination and scattering geometries (e.g., Litvinov et al.,
2011, 2012). Therefore, diurnal dependence of aerosol
radiative effect is also expected to vary with respect to SZA and
directional properties of the surface reflectance. As a first approximation
of surface reflectance description such characteristic as “black-sky”
albedo (also known as directional hemispherical reflection, DHR) is often
used. It can be defined through the integrals of BRDF
(Schaepman-Strub et al., 2006):

Figure 5a shows an example of surface black-sky albedo dependence on SZA at three AERONET sites employed in this study. These surface albedos are obtained for Ross–Li BRDF model, where the BRDF parameters are derived from MODIS climatology. As can be seen, the BRDF-based surface albedos significantly deviate from an isotropic Lambertian surface albedo that has no dependence on SZA. Stronger directional dependence for the desert sites than for a site in southern Africa can be also noted, which is consistent with a known general feature of soil vs. vegetation surfaces (e.g., Maignan et al., 2004; Litvinov et al., 2011, 2012). In Fig. 5b we show dependence on SZA of Lambertian to BRDF-based albedo ratio for three wavelengths over the solar spectrum. The ratio is equal to unity when the Lambertian albedo is equal to the BRDF-based albedo; thus it shows that underestimation (ratio below unity) or overestimation (ratio above unity) of the surface reflectance due to simplified Lambertian model is a function of SZA and wavelength. It therefore emphasizes the importance of the assumption on the surface albedo model of the diurnal dependence and absolute values of the aerosol radiative effect. However, if we consider the whole range of SZAs, the effect on the daily average aerosol effect can be partially canceled because the values below and above unity can be quasi-symmetric. For instance, for the monthly average TOA aerosol direct radiative effect over global land derived from MODIS, Yu et al. (2004) found an uncertainty due to neglecting of the angular dependence of the albedo of only about 5 %. However, the influence of the directional properties of the surface albedo is expected to vary depending on the range of SZAs over which the integration is done in order to obtain the daily average forcing. We therefore draw attention to the fact that the magnitude of the uncertainty will be a function of latitude and day of the year. Asymmetry of the ratio around unity in Fig. 5b is also a function of the wavelength; thus the uncertainty due to Lambertian assumption is dependent on spectral extinction of an aerosol model.

Instantaneous radiative efficiencies calculated using Lambertian and BRDF surface reflectance calculated for five employed aerosol models and three surface types.

Figure 6 shows calculations of diurnal aerosol radiative efficiency at the
top and bottom of atmosphere for Lambertian and BRDF surface reflectance for
different types of aerosol and surface. Several observations can be done from
this figure. First, diurnal radiative efficiencies can be intercompared for
key aerosol types over different surfaces. It can be observed, for example,
that over a bright desert surface, biomass burning and mixed aerosol type
produce mostly positive instantaneous radiative effects at TOA (Fig. 6c, g,
i). A mixture of dust and biomass burning over a Sahel type surface (Fig. 6g)
produces a positive instantaneous radiative effect when SZA is less than
53

Figure 7 shows the daily average values of aerosol radiative efficiency for
the same scenarios as in Fig. 6. The daily average values are calculated here
for the daylight fraction of 0.5 and for the minimal SZA of 0

Daily average aerosol radiative efficiencies at the

Phase function of spheres is known to differ from that of randomly oriented
spheroidal particles used for modeling optical properties of
nonspherical aerosol. Since spheres generally scatter stronger than
spheroids at backward scattering angles, it could be expected that the
upward hemispherical solar flux is also stronger for spheres. However, this
difference is not evident without conducting a rigorous calculation. First
of all, not at every scattering angle is the directional scattering of spheres
superior of spheroids. For example, for the dust aerosol model,
scattering by spheroids dominates between

Nonspherical–spherical differences in radiative efficiencies at the top
and bottom of atmosphere using detailed phase function of a dust aerosol model.
Calculations are done for different surface reflectance using a Lambertian
model. Panels

In order to evaluate uncertainties in aerosol radiative effect due to
assumption on spherical particles we calculate instantaneous radiative
effect for nonspherical and spherical dust aerosol models. The calculations
are conducted using detailed phase function or asymmetry parameter and over
different types of the underlying surface. The results show that, while
employing the detailed phase function (Fig. 9a, b), the spherical aerosol
model leads to overestimation of cooling at TOA and BOA over dark surfaces;
the relative differences in the instantaneous values range between

Relative differences in daily average aerosol radiative effect at
the

It should be mentioned, by consistently using the Mie calculation for the nonspherical aerosol retrievals and flux simulations, it is possible to achieve some reduction of the errors due to the nonspherical–spherical difference in aerosol scattering, as often expected when spherical aerosol model is used in remote sensing retrievals. Nonetheless, these differences cannot be fully eliminated and remain considerable, as shown in Derimian et al. (2008).

Another aspect for the analysis is the effect of surface reflectance anisotropy on the manifestation of particle nonsphericity in aerosol radiative effect. The question is how usage of BRDF-based surface reflectance model affects estimation of the nonspherical–spherical errors in aerosol radiative effect? In order to answer this question we re-calculated the nonspherical–spherical errors using BRDF surface models. The results show that depending on the SZA the calculated errors are partially reduced or increased. The errors variability also depends on the surface type. However, overall, the differences stay within a similar range to the Lambertian surface model. The conclusion is valid for the instantaneous (Fig. 11) and, as a consequence, for the daily average values (not shown here).

Relative differences in instantaneous radiative efficiencies due to
aerosol sphericity assumption at the

A comparison was conducted between calculations of radiative effect using
simplified representation of aerosol directional scattering, i.e., accounting
only for asymmetry parameter, and using accurate calculations with detailed
phase function. In this analysis two main questions were posed. How large is
the error in calculated radiative effect if only asymmetry of phase
function was accounted for? Also, what kind of uncertainly can be expected
for the nonspherical aerosol if this simplification is used in the
calculation of radiative effects? To seek the answers we compared the
calculation using only asymmetry parameter with accurate calculations where
the phase function features were accounted using a 12-moment expansion of
the Legendre polynomial. Figure 12 presents the calculated diurnal radiative
efficiencies of dust aerosol model over Lambertian surface using only the
asymmetry parameter. From a comparison with Fig. 9a and b showing the same, using
the detailed phase function, we can notice a significant change in the shape
of diurnal dependence of aerosol radiative efficiency at TOA as well as at
BOA. That is, the radiative efficiency varies much stronger with SZA
when the details of the directional scattering are neglected. At the SZA of

Same as in Fig. 9 but using calculations of only the asymmetry
parameter of the phase function. Note that the relative differences in
instantaneous radiative efficiencies at the top of atmosphere (panel

In this section we illustrate feasibility of rigorous direct aerosol
radiative effect calculations on a large scale using satellite observations. It
is done as part of the GRASP algorithm application for POLDER/PARASOL
observations. The product is of particular interest because it provides
detailed aerosol characteristics, including absorption, also over bright
surfaces where information about aerosol properties is rarely available. With
a goal to test the computational tool and assess an observation-based aerosol
radiative effect and its spatial variability, the calculations were conducted
for POLDER/PARASOL observations during summer 2008 (June, July, August) over
a part of Africa known as one of the major sources of the desert dust. It has
to be noted, however, that the GRASP algorithm is still in its completion phase
and that the quality of the aerosol properties retrievals is in a validation
process. In this work we therefore present an intercomparison of AOT
and

Intercomparison between GRASP retrievals applied for POLDER/PARASOL
observations and operational AERONET product during 2008 for ensemble of
observations at four sites (Banizoumbou, Agoufou, IER Cinzana and DMN Maine
Soroa). Panels

Three-month (JJA 2008) means of

Figure 14 presents the means for 3 months of (i) daily average top- and
bottom-of-atmosphere net aerosol radiative effects, (ii) radiative
efficiencies calculated with respect to AOT at 550 nm (interpolated from
nominal wavelength of POLDER), (iii) AOT at 565 nm, (iv) underlying surface
albedo at 565 nm and (v) spectral

(dashed lines) Dependence between calculated 24 h average aerosol
radiative effect and AOT at 550 nm; (solid lines) 24 h average aerosol
radiative efficiency calculated using AOT presented on the abscissa. Black
and red lines correspond, respectively, to “absorbing mixture” and
“absorbing dust” aerosol models described in Sect. 8; surface albedo at
550 nm is set to 0.43 for “absorbing mixture” and 0.34 for “absorbing
dust” scenarios; blue lines represent linear dependence between 24 h
average aerosol radiative effect and AOT. Panel

Noteworthy is also the obtained spectral

A rigorous yet fast computational tool for calculations of broadband solar flux and aerosol direct radiative effect was presented. The initial version of the tool developed for using AERONET results and employed in the AERONET operational code was significantly revised and integrated into the GRASP (Generalized Retrieval of Aerosol and Surface Properties) algorithm. Therefore, the GRASP retrieval product can include the estimations of radiative effect for interested users. The tool can also be used in research mode for various types of sensitivity analyses.

Using this tool we analyzed sensitivities of the diurnal and daily average
shortwave aerosol radiative effects to the details in aerosol and underlying
surface characteristics. Overall, the obtained results showed the importance of
accurately accounting for details in variability of atmospheric aerosol
characteristics, such as AOT,

We emphasize also that a proper intercomparison of radiative effects of volume-equivalent spherical and spheroidal aerosol particles models should account for alteration of geometrical cross section together with directional redistribution of scattering. In our study we apply a scaling of concentration in an attempt to compensate the geometrical and the corresponding extinction cross-section modification. The differences observed in this study between nonspherical and spherical models should be considered a worst-case scenario, but their importance should not be underestimated because they create a notable systematic bias. We also found that using BRDF of surface reflectance instead of Lambertian approximation does not influence significantly the nonspherical–spherical differences, although the diurnal dependence of the error is somewhat modified. The study showed that the nonspherical–spherical difference at the top of atmosphere is also pronouncedly dependent on the magnitude of surface brightness, while at the bottom of atmosphere this dependence practically does not exist. The differences also tend to be reduced with increase in AOT because the multiple scattering effects smooth out differences in the phase functions. It is also important to mention that strong variability of diurnal aerosol radiative effect signifies that the minimal SZA and daylight duration can overcome effects of aerosol type and concentration and thus should be taken into account in intercomparison of daily average aerosol radiative forcing in different time and locations.

Finally, application of rigorous aerosol radiative effect calculations was illustrated as feasible on a large-scale using GRASP algorithm for POLDER/PARASOL observations over Africa. Results of the observation-based calculations present quite a pronounced range of values and spatial variability of the aerosol radiative effect. The obtained values are generally in line with results of calculations for considered here climatological calculations. The effort presents one more step in the measurement-based estimate of the aerosol direct radiative effect on climate.

The work is supported by the CaPPA project. The CaPPA project (Chemical and Physical Properties of the Atmosphere) is funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissement d'Avenir) under contract “ANR-11-LABX-0005-01” and by the Regional Council “Nord-Pas de Calais” and the “European Funds for Regional Economic Development” (FEDER). This work was also supported, in part, by the NSF grant AGS-111916. Edited by: J.-Y. C. Chiu