A geometry-dependent surface Lambertian-equivalent reflectivity product at 466 nm for UV / Vis retrievals : Part I . Evaluation over land surfaces using measurements from OMI

The anisotropy of the Earth’s surface reflection has implications for satellite-based retrieval algorithms that utilize climatological surface reflectivity databases that do not depend upon the observation geometry. This is the case for most of the current ultraviolet and visible (UV/Vis) cloud, aerosol, and trace-gas algorithms. The illumination-observation dependence of surface reflection is described by the bidirectional reflectance distribution function (BRDF). To account for the 5 BRDF effect, we use the concept of geometry-dependent surface Lambertian-equivalent reflectivity (GLER), which is derived from the top-of-atmosphere (TOA) radiance computed with Rayleigh scattering and surface BRDF for the exact geometry of a satellite-based pixel. We present details on the implementation of land and water surface BRDF models. : , ::: and : We evaluate our GLER product over land surfaces using observed and computed sun-normalized radiances at 466 nm. The 10 input surface BRDF parameters for computing TOA radiance are derived from MODerate-resolution Imaging Spectroradiometer (MODIS) satellite observations. The observed TOA radiance for comparison is from the Ozone Monitoring Instrument (OMI). The comparison shows good agreement between observed and calculated OMI radiances in ::::::::: reflectivity :: in ::::: 2006 :: in typical geographical regions, with correlation coefficients greater than 0.9 for a majority of the selected regionsin the year 15 of 2006. ::: 0.8 ::: for :::: some ::::::: regions. : Seasonal variations of clear-sky OMI radiances ::::::::: reflectivity (i.e., with minimum clouds and aerosols) closely follow those computed using MODIS-derived GLER over land. GLER also captures the cross-track dependence of OMI radiances, although the observations are ::::::::::: OMI-derived ::::: LER, :::::: though ::: the ::::: latter :: is : slightly higher than those computed using GLER ::: the ::::: former : presumably owing to residual cloud and aerosol (non-absorbing) contamination, particu20 larly over dark surfaces (heavily vegetated regions such as mixed forest, croplands and grasslands).


Introduction
It is well-known that reflection of the incident sunlight by the Earth's surface is generally anisotropic in the optical wavelength range (Rencz and Ryerson, 1999).Rough surfaces (vegetated landscapes, urban and built-up, bare soils, etc) usually exhibit marked backward scattering, whereas smooth surfaces (e.g., water, snow/ice) tend to have a strong forward scattering peak (specular reflection).
Two well-known phenomena related to surface reflection anisotropy are the hot-spot effect over land and the sunglint over ocean.The hot-spot effect occurs when the viewing direction coincides with the illumination direction, such that all shadows are invisible.This results in a reflectance peak in backward scattering directions (e.g., Qin et al., 1996).Sunglint, however, is a peak in forward scattering caused by Fresnel reflection over a smooth surface such as calm water, when sunlight reflects off the surface at the same angle that the surface is viewed (e.g., Kay et al., 2009).
The dependence of surface reflection on illumination and observation directions is mathematically described by the bidirectional reflectance distribution function (BRDF), an intrinsic property of the surface (Nicodemus, 1965;Martonchik et al., 2000;Schaepman-Strub et al., 2006).Since BRDF is defined in terms of differential solid angles, in theory it cannot be measured (Nicodemus, 1977).
Therefore, another quantity which can be retrieved from remote sensing data, the bidirectional reflectance factor (BRF), has been widely used ever since.BRF is defined as the ratio of the reflected radiance from the surface to that from a perfect Lambertian surface under the same geometry (illumination and observation) and ambient conditions.Since an ideal diffuse surface reflects the same radiance in all viewing directions, the BRDF for a Lambertian surface is 1/π.Because of this, the BRF for any surface is equal to its BRDF times π.However, unlike the BRDF, BRF is a unitless quantity.
The effect of surface anisotropy on satellite-observed radiances propagates through the atmosphere and may :: in ::: the ::::: visible :: is :::::: notable :::: and :::::: neglect :: of :: it :: in ::::::: retrievals ::: can : produce complex errors.The influence of surface anisotropy on the top of the atmosphere (TOA) radiance increases with wavelength for a Rayleigh atmosphere (no aerosols or clouds) because atmospheric transmittance increases with wavelength in the ultraviolet and visible (UV/Vis) spectral regions.Under natural conditions for
Global characterization of BRDF from satellite measurements for surfaces covered by snow and ice is an area of active research.Though recent improvements in the MODIS Collection 6 MCD43 BRDF data (Wang et al., 2018) may enable the use of the MCD43 data for seasonal and variable short-term snow cover in GLER product, the first version of the GLER product uses the gap filled (GF) Collection 5 product (MCD43GF) which is intended to provide BRDF parameters using the RTLS model for land surfaces free of seasonal snow and those covered by permanent snow or ice.
Top panel: region of Lakes Superior and Michigan; Bottom panel: Chesapeake Bay.
The above kernel coefficients depend on wavelength.For the present study we selected MODIS band 3, the shortest wavelength in the MCD43GF product, with a center wavelength of 470 nm (ranging from 459 to 479 nm) to represent 466 nm, which is the wavelength used in our cloud algorithm to retrieve effective cloud fraction (ECF) (Yang et al., 2015).Observations at this wavelength are relatively free of atmospheric rotational-Raman scattering (RRS) and trace gas absorption.OMI collection 3 data are used in this study.Specifically, we use LERs :::: LER : retrieved from TOA reflectances :::::::: radiances at 466 nm that are computed by normalizing the OMI radiances to the OMI day-1 solar irradiance spectrum ::::::: measured ::: on ::: 21 ::::::::: December ::::: 2004 ::::: along :::: with :: a :::::::: correction ::: for :::: the :::::::: Earth-Sun ::::::: distance ::::: when ::::::::: calculating :::::::::::: OMI-derived :::: LER.The GLER product is designed to characterize the magnitude and the angular variability of the Earth's surface reflectance under :: in a Rayleigh atmosphere, so in the context of GLER product validation, absolute radiometric response and consistency across the measurement swath are the two most critical aspects of instrument calibration to consider.For this study we ignore spectral dependence in the calibration, because our focus is strictly on the 466 nm channel.Spectral calibration will be important for validation of future versions of the GLER product that are planned to report data at several other wavelengths.
The OMI calibration has been detailed in previous work.Dobber et al. (2008) estimated that the uncertainty in viewing angle dependence of OMI collection 3 sun-normalized radiances is less than 2% .Their estimate follows the application of calibration adjustments based on the evaluation of TOA measurements over a target region of Antarctic ice, using a surface model that accounts for non-Lambertian effects in a radiative transfer model of the atmosphere as described by Jaross and Warner (2008).
In that work, the authors used the same technique to establish the absolute radiometric calibration of OMI at nadir within an estimated model uncertainty of 1 ::: and ::: Since only clear sky measurements are used for our comparison, we apply the UV aerosol index (AI) from OMAERUV product (Torres et al., 2007) to detect and screen out absorbing aerosol contaminated OMI measurements.This aerosol index is defined as the ratio of radiances measured at 354 and 388 nm compared to the ratio calculated for a pure Rayleigh-scattering atmosphere.
It is sensitive to the presence of absorbing aerosols that reduce LER retrieved from OMI data.
We plan to examine aerosol effects on GLER in a future work.

Results
First, we examine the overall performance of GLER by comparison with the OMI-derived LER.

Seasonal variations
months.
Throughout the year, both GLER and OMI-derived LER vary as much as 0.03-0.04 at 466 nm .

Sub-region case study
To further assess the anisotropy in GLER, we performed a small case study on a sub-region in western Australia (see Figure ?? :: 10) with very homogeneous land type and elevation.Figure ?? :: 11b shows that for this sub-region f iso , which is a measure of the surface albedo, is very consistent for all rows due to the homogeneity of the surface.tropospheric air-mass factor (AMF).The results presented in Section 3 are therefore important as they demonstrate that the GLER concept as implemented with MODIS data is able to capture reliably the complex angular, seasonal, and inter-annual variations in OMI reflectances over different regions on the Earth with diverse land cover types.
A significant issue related to the GLER evaluation is the presence of thin clouds and non-absorbing aerosols over land surfaces.Both effectively result in the OMI-retrieved LERs data ::: LER : being larger than the calculated GLERs ::::: GLER, since neither was included in the radiative transfer simulations.Here, we excluded data with elevated cloud fractions to mitigate cloud and aerosol effects.
Our results suggest that GLERs ::::: GLER : may be used with confidence in OMI trace gas retrievals, many of which presently utilize climatological OMI LER data.However, it should also be understood that use of GLERs ::::: GLER : calculated from aerosol-corrected MODIS BRDF data removes the effects of non-absorbing aerosols that are known to exist in the climatological LER data derived from UV/Vis sensors; this is supported by the slightly elevated OMI-derived LERs :::: LER : we find compared with GLERs ::::: GLER.The effects of aerosols are partially accounted for indirectly through the current cloud algorithms that do not distinguish between clouds and non-absorbing aerosol.It is therefore important that the same approach to account of surface effects, whether it be the use of climatological LERs or GLERs, be used for both cloud and trace-gas retrievals.
There are other issues to be considered with the MODIS BRDF model and the Collection 5 gapfilled BRDF parameters (MCD43GF) over seasonal snow cover or permanent ice.The fact that MCD43GF only provides snow-free land BRDF parameters usually leads to either data gaps or too small GLER values for snow-covered OMI pixels.The current temporary fix to this issue is to use OMI-derived LER but capped by a constant snow albedo of 0.6 as suggested in the KNMI's daily OMI NO 2 (DOMINO) product (Boersma et al., 2011;McLinden et al., 2014) based on the Nearreal-time Ice and Snow Extent (NISE) flags (Nolin et al., 2005) in the OMI L1b data set.The second issue is that the current MODIS kernel model lacks a mechanism to deal with strong forward reflection over snow/ice.Finally, since the shortest wavelength in the MODIS BRDF product MCD43GF is 466 nm, it does not cover the shorter range of OMI blue and UV wavelengths.We plan to explore other BRDF products in the future that have more wavelengths and fewer data gaps.A good candidate is the Multi-Angle Implementation of Atmospheric Correction (MAIAC) data (Lyapustin et al., 2012).Compared to MCD43GF, MAIAC includes a shorter wavelength (412 nm) and provides pixel snow fraction that can be used for snow and ice covered regions.
We have focused here on evaluation of land GLERs ::::: GLER, because the GLER product is primarily targeted towards improvement of retrievals of trace gas pollutants such as NO 2 that are concentrated over land.We recognize that our evaluation in this paper excludes several important land types, such as compact and dense urban areas, land that is close to water, and a combination of the two.
It can be a challenge to collect substantial amounts of data over cities, due to their relatively small size in comparison to the large regions that are the subject of this study.Particulate pollution is also common in urban regions, where non-absorbing sulfate aerosols can interfere with the derivation of LERs, thus making it difficult to validate GLERs with satellite data.These regions require further careful study using data from days when these regions are exceptionally clear.Given the importance of understanding the influence of surface reflectance on AMF calculations in highly polluted regions, we believe this work should be carried out in the future.
The validation results reported in this study apply to OMI and other sensors in similar low-Earth orbits that collect measurements with similar geometries, such as TropOMI ::::::::: TROPOMI, which has higher spatial resolution than OMI (7 km at nadir).In theory, the smaller pixel size of TropOMI ::::::::: TROPOMI : and other future sensors should enhance the ability to validate the GLER approach by enabling more complete cloud and aerosol clearing for regions with widespread but broken clouds that were specifically avoided in the present work.
Since MCD43 product is not recommended for solar zenith angles beyond 70 • (Schaaf et al., 2011), it may not be applicable for some geostationary (GEO) satellite observations, for which such high solar angles will certainly occur.Instead, GEO instruments such as the Geostationary Operational Environmental Satellite (GOES) imagers may be needed to provide BRDF coefficients that apply to the different range of observing conditions relevant to the planned GEO UV/Vis spectrometers.

Fig. 3 :
Fig.3: Pixel-based simulated TOA radiance over land (left) when the pixel land fraction is larger than 5%, water (middle) when the pixel water fraction is larger than 5%, and the merged scene using Eq. 3 (right).Top panel: North America; Bottom panel: SE Asia.

Figure ? ?Fig. 7 :Fig. 8 :
Figure ?? : 9 : shows LER dependence on the cross-track position across several regions with varying land types.There are two main factors that contribute to the cross-track anisotropy of LER.First and foremost is the BRDF effect.The second factor is the spatial heterogeneity of land coverage within a selected region (box) that causes a nonuniform distribution of the surface reflectivity.This effect

Table 1 :
Spatial and temporal resolutions of ancillary data used for land GLER calculation

Table 4 :
LUT structures for input parameters