The angular distribution of the light reflected by the Earth's surface
influences top-of-atmosphere (TOA) reflectance values. This surface
reflectance anisotropy has implications for UV/Vis satellite retrievals of
albedo, clouds, and trace gases such as nitrogen dioxide (

Nitrogen dioxide (

Surfaces reflect light differently in each direction, and the angular
distribution of the reflected light influences top-of-atmosphere (TOA)
reflectance levels measured by satellite instruments that monitor atmospheric
composition. Therefore, surface reflectance anisotropy influences retrievals
of surface albedo, trace gases, aerosols, and clouds from satellite
instruments like the Global Ozone Monitoring Experiment 2 (GOME-2) and the
Ozone Monitoring Instrument (OMI). In surface albedo, cloud, aerosols, and
trace gas retrievals, the surface is often assumed to be Lambertian: an
idealised surface that reflects light isotropically

The Lambertian-equivalent reflectivity (LER) climatologies
represent the albedo of the Lambertian surface in the radiative transfer
simulations for cloud retrievals and trace gas retrievals. In constructing
such climatologies (e.g. monthly climatologies), a large ensemble of
measurements taken over a scene over multiple years is analysed
statistically, and based on the lower 1 % percentile reflectance, an
inversion is done to retrieve the surface reflectance

The angular distribution of the reflected light by a surface is represented
mathematically by the bidirectional reflectance distribution function (BRDF)

These studies show that surface BRDF effects depend on the specific geometry
(hence local time and season) and surface characteristics of the individual
measurements and that averaging over many pixels results in smaller
differences. They analysed mostly clear-sky scenes (i.e. no clouds present)
or scenes with very low cloud fractions (i.e. lower than 0.2), and they did
not consider how surface reflectance anisotropy affects the radiative
transfer in the atmosphere and TOA reflectances. The indirect effect of
biased cloud parameters on

Here we study the effect of surface reflectance anisotropy on surface LER
climatologies, on cloud fraction retrievals and on

Surface LER climatologies are commonly used as boundary conditions for cloud
and trace gas retrievals,

Figure

In Fig.

Box plot of cloud fractions retrieved with

Indeed, we find that cloud fractions retrieved with FRESCO cloud retrieval
from GOME-2 measurements are affected by the across-track bias in the surface
LER climatology. FRESCO retrieves cloud properties in the

This results in higher mean effective cloud fractions for the nadir
(

The OMCLDO2 cloud retrieval from the OMI retrieves cloud properties in the

OMI swath is divided into 60 different viewing directions; east corresponds to the 20 easternmost measurements and west to the 20 westernmost measurements

bias (Fig.We have shown that surface BRDF effects result in a distinct across-track
bias in surface LER climatologies and cloud fractions retrieved from
satellite instruments and that the effect is highly relevant in the NIR and
in the visible. Errors in cloud fraction and surface albedo are the most
important sources of tropospheric AMF errors

The amount of radiation reflected by a surface in a certain direction depends
on the direction of the incident irradiance and on the direction in which the
reflected radiance is observed. The surface bidirectional reflectance distribution function (BRDF) is a function that characterises the directional
reflecting properties of a surface. The surface BRDF mathematically describes
the angular distribution of the surface reflectance:

The albedo of a surface is generally defined as the ratio of the irradiance
reflected by a surface area into the whole hemisphere and the irradiance
incident on the surface with hemispherical angular extent (i.e. coming from
all directions)

Sketch of the surface to top-of-atmosphere system with zenith and
azimuth angles that define incident (

Several models have been developed to describe surface BRDF

Semi-empirical models are commonly used for global surface BRDF
characterisation using remote sensing instruments. In these models, surface
reflectance is represented as a linear combination of different terms (the
kernels) that characterise different types of scattering that lead to the
directional signatures on the reflectance

In the semi-empirical BRDF Ross Thick – Li Sparse (hereinafter Ross–Li)
kernel-driven model, the surface reflectance is expressed as the sum of an
isotropic term and two kernels (

The isotropy parameter (

The radiative transfer model DAK

After the implementation of the Ross–Li surface BRDF model in DAK, the
surface reflectance matrix

Surface reflectance modelled with the Ross–Li surface BRDF model
with parameters from MODIS band 3 (459–479 nm) representing a vegetated
surface over Amazonia

The coefficients of the Fourier expansion (Eq.

One of the disadvantages of empirical models is that they depend on
observations to derive the parameters

In radiative transfer modelling with the Doubling–Adding method, in order to
calculate the radiation field correctly, the reflectance and transmittance
values are needed for all

Figure

The surface reflectance dependence on geometry as shown in
Fig.

TOA reflectance at

To evaluate the surface BRDF implementation in DAK we compare TOA
reflectances with those simulated by other state-of-the-art radiative
transfer models that include a description of surface BRDF effects. Both
SCIATRAN

We select two combinations of the Ross–Li BRDF parameters to model surface reflectance of different surfaces. We simulate TOA reflectances at two different wavelengths: 469 and 645 nm. These wavelengths correspond to the middle of the MODIS band 3 (459–479 nm) and band 1 (620–670 nm) respectively.

Figure

We now compare TOA reflectance simulated with surface BRDF and TOA
reflectance simulated assuming a Lambertian surface at 469 nm
(Fig.

These results are consistent with those shown in Figs.

In Sect. 2 we showed that there is an east–west bias in the retrieved cloud
fractions from GOME-2 and OMI. Effective cloud fractions in FRESCO and
OMCLDO2 are retrieved as follows

Settings for Lambertian and BRDF

Simulated effective cloud fraction at

To improve our understanding of how surface reflectance anisotropy influences
the retrieval of cloud fractions, we use the forward model DAK to approximate

The settings of the simulations are summarised in
Table

We calculate cloud fractions using Eq. (

Figure

Surface BRDF effects are more important for small cloud fractions, and less
importance for large cloud fractions. For cloudy pixels the effect of surface
reflectance anisotropy vanishes because the scattering by the cloud dominates
in the measured reflectance. Figure

At 477 nm, surface BRDF effects on cloud fractions are less evident than at 758 nm. In the visible spectral region, surface BRDF effects are suppressed by Rayleigh scattering smoothing out the surface anisotropy effects on TOA reflectances. For lower geometric cloud fraction, Lambertian cloud fractions are moderately higher (by 0.05) in the backward-scattering direction than in the forward-scattering direction. These findings underscore the relevance of accounting for surface BRDF effects because measurements with small cloud fractions are most sensitive to pollution in the lower troposphere.

Differences in Lambertian cloud fractions between backward- and forward-scattering directions at 758 nm are on average 0.35. At 477 nm, the
differences amount to 0.1, depending on the surface and the geometry. This is
consistent with the observed bias in FRESCO and OMCLDO2 cloud fractions shown
in Fig.

We simulate Lambertian and BRDF cloud fractions for GOME-2A measurements over
Amazonia in March 2008. We use the exact illumination and viewing geometry
(

Figure

Geometric cloud fraction distributions for

Here we investigate the effects of accounting for surface reflectance
anisotropy on tropospheric

In satellite retrievals of trace gases, an air mass factor (

The AMF depends on the surface reflectance (

Here, tropospheric

Settings for the Lambertian and BRDF tropospheric

AMF is directly affected by the assumption of a Lambertian surface instead of
an anisotropic surface in the simulated TOA reflectance. In addition, AMFs are
indirectly affected by the cloud radiance fraction (

We calculate AMFs with Eq. (

Figure

Figure

Figure

For an unpolluted troposphere, surface BRDF effects on

Total tropospheric

Figure

Although this study does not address surface BRDF effects on cloud pressure, we did a preliminary analysis, applying a directional surface LER derived from GOME-2 in FRESCO+. The analysis shows that accounting for surface reflectance anisotropy effects reduces the cloud pressure by 40 hPa on average (with differences up to 120 hPa). This high bias in retrieved cloud pressure implies that the results shown for 850 hPa might be representative of the surface BRDF effects on AMFs for clouds currently retrieved at higher (biased) pressures.

Total tropospheric

We calculate Lambertian and BRDF

Figure

Relative differences between BRDF and Lambertian AMFs over Amazonia
for March 2008:

Figure

These results show that surface BRDF affects both clear-sky AMF and cloud
radiance fractions, which in combination significantly affect total

We analysed the effects of surface reflectance anisotropy on the OMI and
GOME-2 satellite retrievals of cloud parameters and tropospheric

An important finding is that the LER climatologies slightly overestimate surface albedo for forward-scattering satellite-viewing geometries (eastern part of GOME-2 orbit) and highly underestimate the surface albedo for backward scattering viewing geometries (western part). The underestimation is as large as a factor of 2 over forested scenes in the near-infrared (772 nm). They are weaker but still relevant in the visible (494 nm), where surfaces are darker and Rayleigh scattering effects are stronger. This across-track bias in surface LER propagates into the cloud fraction retrievals: we find biases in cloud fractions of up to 50 % between backward-scattering and forward-scattering geometries in the GOME-2 FRESCO and 26 % in the OMI OMCLDO2 cloud algorithms. Time of day does not drive the importance of surface BRDF effects but specific viewing geometry and spectral range do.

To interpret the above biases, we extended the description of surface
reflectance in DAK to include the geometrical surface reflecting properties
via the bidirectional reflectance distribution function (BRDF) from the
Ross–Li semi-empirical model. This allows DAK to simulate not only isotropic
reflection at the surface but also the anisotropic contributions from
volumetric (e.g. leaf scattering) and from geometric (e.g. shadow-casting)
effects. We evaluated DAK top-of-atmosphere (TOA) reflectance simulations
against other radiative transfer models and find agreement within 1 %
between DAK and SCIATRAN, even within the hotspot
backscatter reflectance peak. We
then simulated TOA reflectances over vegetated scenes using BRDF parameters
from a daily high-resolution database derived from 16-years of MODIS
measurements recently developed within the QA4ECV project

Subsequent sensitivity tests indicated that accounting for surface reflectance anisotropy in the FRESCO and OMCLDO2 retrieval framework removes the bias in cloud fractions. A correct physical description of surface anisotropy is essential for FRESCO, because cloud properties are retrieved in the NIR spectral range (760–790 nm) where surface BRDF effects are stronger and the atmosphere is virtually transparent. It is also of high relevance for scenes with low cloud fractions, where trace gas retrievals are still sensitive to pollution close to the ground. A discussion on the validity of the Lambertian cloud model is beyond the scope of this study. Nevertheless, the cloud fraction dependency with VZA for cloudy scenes suggests that the use of a more realistic cloud model should be considered in future improvements of cloud retrievals.

The implications for

An issue that was not addressed in this study is the role of aerosols.

We conclude that it is necessary to coherently account for surface
reflectance anisotropy effects in retrievals of cloud properties and trace
gases from UV/vis satellite sensors. Although this study does not apply
surface BRDF to a complete global cloud and

Radiative transfer model DAK is available upon request
(contact persons: Piet Stammes and Ping Wang). FRESCO and OMCLDO2 cloud
product and OMI DOMINO NO2 product are publicly available and the datasets
can be found at

We summarise here the expressions of the kernels implemented in DAK to model the surface reflectance anisotropy. We refer the reader to the original literature where these kernels were derived for more detailed information.

The expression of the Ross-Thick volumetric scattering kernel is

The term in the second pair of squared bracket in Eq. (A1) is the modified
part for the hotspot modelling, where

The expression of the Li–Sparse geometric scattering kernel is

The angles with a star are equivalent angles to convert spheroid-like object
to spheres:

The supplement related to this article is available online at:

The authors declare that they have no conflict of interest.

This research has been supported by the EU FP7 Project Quality Assurance for Essential Climate Variables (QA4ECV), grant no. 607405. We acknowledge the free use of the GOME-2 data provided by EUMETSAT. Edited by: Michel Van Roozendae Reviewed by: two anonymous referees