A BRDF–BPDF database for the analysis of Earth target reflectances

Land surface reflectance is not isotropic. It varies with the observation geometry that is defined by the sun, view zenith angles, and the relative azimuth. In addition, the reflectance is linearly polarized. The reflectance anisotropy is quantified by the bidirectional reflectance distribution function (BRDF), while its polarization properties are defined by the bidirectional polarization distribution function (BPDF). The POLDER radiometer that flew onboard the PARASOL microsatellite remains the only space instrument that measured numerous samples of the BRDF and BPDF of Earth targets. Here, we describe a database of representative BRDFs and BPDFs derived from the POLDER measurements. From the huge number of data acquired by the spaceborne instrument over a period of 7 years, we selected a set of targets with high-quality observations. The selection aimed for a large number of observations, free of significant cloud or aerosol contamination, acquired in diverse observation geometries with a focus on the backscatter direction that shows the specific hot spot signature. The targets are sorted according to the 16-class International Geosphere-Biosphere Programme (IGBP) land cover classification system, and the target selection aims at a spatial representativeness within the class. The database thus provides a set of high-quality BRDF and BPDF samples that can be used to assess the typical variability of natural surface reflectances or to evaluate models. It is available freely from the PANGAEA website (doi:10.1594/PANGAEA.864090). In addition to the database, we provide a visualization and analysis tool based on the Interactive Data Language (IDL). It allows an interactive analysis of the measurements and a comparison against various BRDF and BPDF analytical models. The present paper describes the input data, the selection principles, the database format, and the analysis tool.

analytical models. The present paper describes the input data, the selection principles, the database format and the analysis tool.

Introduction
The albedo of a target is the fraction of the incoming light that is reflected rather than absorbed by the surface (Schaepman-Strub et al., 2006). It varies between 0 (full absorption) and 1 (full reflection). 5 The albedo of natural Earth targets varies widely depending on the surface types: Vegetation absorbs most of the incoming visible light whereas the opposite is true for snow. In addition, the albedo varies with wavelength. Many land surface characteristics can be inferred from the spectral signature of their albedo. Spectral indices such as the Normalized Difference Vegetation Index (NDVI) have been developed to quantify the amount and state of vegetation or other properties (Carlson and Ripley, 10 1997;Asrar et al., 1984).
The albedo is a quantity that integrates the reflected light over all directions of the hemisphere. This quantity is difficult to measure as a typical radiometer measures the reflected light in a single direction. This is particularly true for spaceborne observations where a target is observed from a given direction.
As a direct consequence, the radiometer is not sensitive to the Albedo but rather to the reflectance 15 (solar) and view zenith and azimuth angles. In practice, and except for targets that show a preferential direction, such as crops planted along rows, the azimuths are only significant by their difference. Thus, the BRDF is most often described as a function of ! , ! , where θ s and θ v are the solar and view zenith angles and φ is the relative azimuth.
The goal of this paper is to describe a database of BRDF samples that has been developed based on 5 spaceborne measurements of the Earth reflectances. This database may be used to assess the variability of land surface BRDF, for the development and validation of BRDF models, and as a boundary condition for atmospheric radiative transfer studies.
Other characteristics of the land surface reflectance are its polarization properties. The incoming direct solar light is unpolarized. Conversely, the light scattered in the atmosphere by molecules and aerosols, 10 and the light reflected by the surface is partly polarized. Few optical instruments designed to monitor the Earth have polarization capabilities and much less efforts have been devoted to the polarization characterization of land surfaces than to the BRDF. However, polarization is a great tool to monitor anthropogenic aerosols and clouds from space, as demonstrated with the POLDER instrument (Waquet et al., 2009b;Deuze et al., 2001;Breon and Doutriaux-Boucher, 2005). This led to the development of 15 the Glory mission (Mishchenko et al., 2007) that was unfortunately lost at launch. The 3MI instrument, which is similar to POLDER but with advanced capabilities in terms of spatial resolution and spectral coverage, shall be onboard the forthcoming series of Eumetsat MetOp satellites (Marbach et al., 2015).
A primary objective of this space mission is the monitoring of atmospheric aerosols and clouds using the polarization characteristics of the reflected light. 20 Information about the land surface polarization characteristics is therefore needed. The database that is presented in this paper includes, in addition to the spectral reflectances, the polarization characteristics in one channel.
In the following, we describe the input data, the data processing and selection and the database format.
In addition, we have developed an interactive tool to allow a simple graphical analysis of the database 25 and a confrontation to analytical models. The tool is therefore described in the second part of the paper with a few examples of its outputs.

The POLDER instrument onboard the PARASOL mission
The POLDER-1 and POLDER-2 radiometers have been onboard the ADEOS 1 and 2 platforms in 1996-1997and 2003respectively (Deschamps et al., 1994. Unfortunately, the solar panel of both satellites failed after a few months of operations so that only 8 and 7 months of measurements were 5 available from these instruments. This limitation did not allow the monitoring of a full vegetation cycle, which strongly reduced the interest in the data. Fortunately, a new opportunity occurred with the development by CNES of a line of micro-satellite platforms. The POLDER instrument was selected to be installed onboard one of these platforms and became a member of the A-Train to complement the other instruments. The satellite was name PARASOL after Polarization and Anisotropy of Reflectances 10 for Atmospheric Sciences coupled with Observations from a Lidar (Tanre et al., 2011).
The experience gained with POLDER-1 and 2 was used and resulted in a few changes on the instrument, in particular regarding the choice of the spectral bands. There are eight spectral bands for the POLDER/PARASOL instrument with central wavelengths from 443 nm to 1020 nm. One main feature of POLDER is its capability to measure the linear polarization of the light in three channels 15 centred at 490, 670 and 865 nm. This is achieved through three successive measurements with identical spectral filters and three polarizers rotated by step of 60°. The processing of these measurements provides the radiance intensity, its polarization degree and the polarization direction or, alternatively, the Stokes vector components (I, Q and U).
The other main specificity of the POLDER instrument is its ability to provide multi-directional 20 measurements. This is possible thanks to its optical design that consists of a wide field of view lens associated with a bi-dimensional CCD matrix. This combination generates a bi-dimensional Field of View with forward/backward angles of ±51° and crosstrack angles of ±43°. The maximum view angle at the surface is close to 70°, and corresponds to measurements acquired around the corners of the CCD matrix. As the satellite flies over, up to 16 (average is 14) observations of the target are available. 25 These observations provide a sampling of the target BRDF. During the following days, the PARASOL satellite flies again over that target, albeit on a different orbit, which provides another set of BRDF samples. Depending on cloud cover, these successive measurements allow a very broad sampling of the Earth Syst. Sci. Data Discuss., doi:10.5194/essd-2016-46, 2016  BRDF for view angles up to ≈60°, assuming a stability of the target during the composition period.
Note however that PARASOL is on a helio-synchronous orbit so that the various acquisitions are made at a near constant solar time. As a consequence, there is little variation of the sun angle in the measurements of the target reflectance during a short period.

5
The Parasol satellite was launched in December 2004. Data acquisition started in early 2005 and was nearly continuous until October 2013. However, due to lack of fuel, the satellite left the A-Train and was on a slowly drifting orbit after December 2009. There have been some data acquisition interruptions during the lifetime of the satellite, mostly resulting from malfunctions of the stellar sensor.
The best year in term of data acquisition was 2008. As a consequence, we selected that year to build the 10 BRDF/BPDF database.
After the end of the on-orbit operations, POLDER/Parasol data benefited from further development in the calibration and data processing. Using several vicarious calibration techniques, all based on natural targets, it was possible to derive an accurate set of calibration parameters that account for the temporal evolution of the instrument sensitivity characterized by a mean decrease modulated by a variation 15 within the field-of-view (Fougnie, 2016). These progresses led to a full reprocessing of the POLDER/Parasol dataset at the end of 2015.

POLDER data processing
The POLDER instrument provides Top of the atmosphere Reflectances after calibration (Fougnie et al., 2007). These Level-1 measurements are processed into Level-2 products using several processing 20 chains. The reflectances are corrected for atmospheric absorption (H 2 O, O 3 , O 2 , NO 2 ). Over land, the atmospheric aerosol load is estimated from the polarized reflectance measurements using pre-computed tables (Deuze et al., 2001). The reflectance measurements are then corrected for atmospheric scattering for an estimate of the spectral surface reflectance. The polarized reflectances are corrected for the molecular scattering; they are not corrected for aerosol scattering. 25 The so-called Level-2-A official product contains an estimate of the directional surface reflectance for 6 spectral bands, and an estimate of the directional surface polarized reflectance at 865 nm. Only the Earth Syst. Sci. Data Discuss., doi:10.5194/essd-2016-46, 2016  longer wavelength channel is provided as (i) it is generally assumed (and the POLDER aerosol inversion does so) that the surface polarized reflectance is spectrally neutral (Waquet et al., 2009a) and (ii) the atmospheric contribution is dominant and more difficult to correct for the shorter wavelength channels. The product also includes a non-quantitative indication of the aerosol load.
Some explanation is needed on what we refer to as the "polarized reflectance". As said above, the 5 POLDER instrument measures the Stokes vector representation [I,Q,U] of the radiance. A reference plane is needed to define Q and U. Many studies use the vertical plane (that contains the view and local nadir directions) as a reference. Yet, it is more practical to use the scattering plane (that contains the sun and view direction). With this plane as a reference, U is most often very small with respect to both I and Q (Schutgens et al., 2004). This is because the polarization is either parallel or perpendicular to 10 the plane of scattering. Q is smaller than I but takes measurable values. In most cases, the polarization is perpendicular to the plane of scattering so that Q is negative. In rare cases, the polarisation is parallel to the plane of scattering in which case Q is positive. We thus define the polarized reflectance R p as: in a similar way as the reflectance definition: 15 where E 0 is the TOA solar irradiance. With such definition, R p is most often positive, but it nevertheless contains the information whether polarization is perpendicular or parallel to the plane of scattering.

Data selection
The objective is to sample the variability of land surface BRDF and BPDF while selecting only the 20 observations that are free from significant aerosol and cloud contamination and for which a large BRDFs as a function of the land surface cover. For this objective, we make use of the IGBP classification (Loveland et al., 1999). We used the official MODIS land cover product (MCD12Q1) for the year 2008 at 5 minute resolution (Liang et al., 2015). For each POLDER pixel (≈6.2x6.2 km 2 ) we analyse the land cover type for the 5x5 MODIS cells centred on the POLDER pixel. Only the POLDER 5 pixels for which there is a clear dominance of one land cover type (>75%) are kept for further processing. The POLDER pixels are assigned the IGBP land cover type as identified from the MODIS product and the relative fraction of the dominant type is kept for inclusion as ancillary information in the database.
For each POLDER pixel that passes this first step, and for each of the 12 months independently, we 10 retrieve all POLDER/Parasol directional observations that pass the cloud detection scheme. A BRDF model is fitted against the 670 nm surface reflectances and the Root Mean Squared Error (RMSE) between measurements and model is computed. The objective is to reject poorly corrected aerosol contamination, that increases the RMSE, and keep pixels with a large number of observation.
A score for the pixel-month is defined as: 15 where p identifies the POLDER pixel and m identifies the month; Nmes is the number of directional POLDER measurements that are available. In addition, as there is a particular interest in the analysis of the Hot-Spot directional signature, we increase the score by 20% if the set of directional measurements includes at least one with a phase angle of less than 1°. 20 We also compute a yearly score as the sum of the monthly scores: For each IGBP surface type and each month, we select the 50 "best" targets, i.e. those that have the highest score. On the other hand, we seek some diversity and thus want to avoid selecting pixels that are close to one another. We therefore select pixels iteratively: After a pixel with the highest score is 25 selected, that of all pixels is multiplied by 1 − /100 where d is the distance (in km) between each of these pixels and that selected at the previous step. The score of the nearby pixels is then reduced which insures that they are not selected subsequently.
As a result of this procedure, we select independently 50 targets for each of the 12 months and each of the 16 IGBP surface types. This procedure leads to the monthly database.

5
In addition, we generate a yearly database where the selection is based on the yearly score scoreY rather than the monthly scores. The procedure is very similar. In the yearly database, the same targets are selected for the 12 months. Conversely, the monthly database selects pixels independently for each month which results, in most cases, in different target sets. The monthly database is best to analyse targets of high quality for each month independently. The yearly database shall be used to assess the 10 variability of the BRDF and BPDF along the year, as shown in section 3.7 below, although some months may be poorly sampled.

Database structure
The two databases (monthly and yearly) are built around a large number of text files (≈16x12x50). Each file includes the surface reflectance and polarized reflectance acquired during the month. The files are 15 sorted by IGBP surface types (nn from 01 to 16) and then by month (mm from 01 to 12): The directory IGBP_nn contains the subdirectories 2008mm which contain the files. The file format is described in Appendix A.
In addition, the database includes a binary file map_IGBP.bin. It reproduces the IGBP classification used for the data selection on a 540 x 270 (lon x lat) grid. This file is used by the graphic analysis tool. 20

Visu_brdf tool set up
A graphical interface tool has been developed to analyse the BRDF/BPDF data file described above.
The code visu_brdf.pro is based on the IDL language and its use requires an IDL licence. Another option, that does not require an IDL licence, is to download the IDL Virtual Machine from the Harris 25 Geospatial web site (https://www.harris.com/what-we-do/geospatial-solutions). The virtual machine lets you run the compiled version of the analysis tool, provided in the visu_brdf.sav file.
The first step is to locate the database. Inside the code, you shall change the variable "HomePath" to the directory that contains the monthly and yearly databases. 5 When using IDL with a proper licence, one shall type: If the "HomePath" was not set properly, a warning message indicates that one must select the path for 10 the "POLDER BRDF" database and a window opens up for that purpose.
If one uses the IDL virtual Machine option, just double-click on the visu_brdf.sav icon. As described above, one must then select the path for the database. Figure 1 shows the Main Command Window of the BRDFs analysis tool. In the following, it is referred 15 to as MCW. One can select one of the IGBP surface type with the "BIOME" drop-down list or successive clicks on the "NEXT" button that is next to it. Similarly, one can select the time period with the "Month" drop-down list, and the NDVI range with the "NDVI" drop-down list.

The Main Command Window
The available targets are shown on the map. Note the lighter grey areas that indicate the Earth surface that corresponds to the selected IGBP surface type. The squares indicate the locations of the targets in 20 the BRDF database that correspond to the criteria (IGBP type, month and NDVI range). The colour of the squares is either from black to red (we use a rainbow palette) according to the NDVI if "ALL NDVI" is selected or red if a specific range of NDVI is selected.
The selected target is indicated by a red circle. There are several ways to choose a target for display of its measurements. The easiest one is to click on the map close to the desired square. The second is to 25 use the "Next_BRDF" button that selects the various targets in successive order. Finally, it is also possible to use the "Random" button that selects a target randomly among the ones shown on the map. Below the map are given some information on the selected target: latitude and longitude, surface type, fraction of this surface type, the number of orbits (satellite overpasses) and the total number of observations for this target.
When a target is selected, several windows are displayed and can be changed with various options.
They will be described below. 5 Below the BRDF and BPDF models selection is a box with check buttons that change the measurement model visualisation. The Meas / Surf / Isoc checkboxes affect the "Target BRDF" window and are described below. The "Polariz" checkbox controls the display, or not, of a specific window for the BPDF. The "PPlog" checkbox toggles between a linear and log scale for the "Principal plane" and 10 "Perpendicular plane" windows that are described below.
Further below, the checkboxes with the band central wavelengths make it possible to select three bands, from the 6 provided in the database, for display in the "Target BRDF", "Principal Plane" and "Perpendicular Plane" windows. been generated using that method.
The "SaveWindow" button makes a simple copy of the current window into another one. This is useful to compare the predictions of different models.
The "Clear" button erases all such windows.

BRDF/BPDF models within visu_brdf
The visu_brdf tool can be used to compare the BRDF and/or BPDF measurements to analytical models.
Several such models have been implemented within the tool and can be selected by the two drop-down lists "BRDF model" and "BPDF model".

1995)
• Maignan (linear, 1 parameter): developed from POLDER measurements (Maignan et al., 2009) • Litvinov (non-linear, 3 parameters) (Litvinov et al., 2011) 20 There are plans to develop a BPDF model for snow surfaces which may then become available for further releases of the visu_brdf tool. The reflectance shown in Figure 2 are typical for a surface with some vegetation. The reflectance is significantly larger in the near infrared (865 nm) than it is in the red (670 nm) or green (565 nm). For a given wavelength, the reflectance increases towards the backscatter direction. The model is able to 5 reproduce most of the directional variation, as shown on the scatter plot (right column), and the modelmeasurement correlation is more than 0.97. The central column shows the difference between measurement and modelled reflectances. In Figure 2, these differences appear mostly random and do not show a systematic variation within the directional space. This indicates that there is little hope for a BRDF model that fits the measurement better. Other targets show measurement-model differences with 10 more spatial structure, indicating a deficiency in the modelling that might be improved (not shown).

Analysis of a target BRDF
By default, the left column shows the reflectance measurements as shown on Figure 2. It is also possible to use other displays of the measurements as selected with the toggle buttons on the MCW. The option: • "Meas": shows the reflectance measurements (default), 15 • "Isoc": shows the isolines of the model outputs (after a best fit), • "Surf": shows the modelled reflectance as a coloured surface. This option disables the two others.  This correlation is small but are necessary to account for the variation of the sun angle within the 10 month, and the small variations of the reflectance between the observation geometry and the parallel/perpendicular plane.

Analysis of directional signatures in the principal and perpendicular planes
The Y-axis can be either on a linear or log scale depending on the "PPlog" option in the MCW.
Similarly, the 3 channels that are displayed can be modified among the 6 that are available in the database. These figures confirm the general observation made over Figure 2: The reflectance is 15 significantly larger in the near-infrared than it is in the visible; it increases markedly from forward scatter towards backscatter, while there is insignificant variations in the perpendicular plane; the model reproduces properly the observed variations. Figure 4 shows an example of the content of the Target BPDF window, which is very similar to the 20

Analysis of a BPDF target
Target BRDF except that it shows the surface polarized reflectance at a single wavelength (865 nm).
Although the POLDER instrument made polarized measurements in three channels, only the longer wavelength channel is provided in the database and, therefore, accessible through the visu_brdf tool.
Our experience is that the surface polarized reflectance is spectrally neutral, or that the spectral variations are smaller than the measurement noise. We thus provide the longer wavelength channel 25 estimates that are the least contaminated by atmospheric scattering. The left image shows the measurements; the middle image is the model-measurement difference, and the right figure is a scatter plot of the measurement and model. The same ancillary information as for the target BRDF window is provided on the bottom of the window.
The directional signature of the polarized reflectance is completely different than for the reflectance. At backscatter, the polarized reflectance is very small and even negative, indicating a polarization parallel 5 to the plane of scattering. The polarized reflectance tends to increase with the phase angle away from backscatter. Note that the polarized reflectance is much smaller than the reflectance, so that the polarisation ratio is only a few %. Although the model does a fairly good job, it does not reproduce the negative polarization close to backscatter. The scatter plot indicates two different regimes where the modelling is clearly larger or clearly smaller than the observation. The directional diagram (middle) 10 does not show any systematic feature. Positive and negative differences are observed in very similar observation geometry. This indicates a slight change in the target polarized reflectance within the period of synthesis.

Vegetation Indices time series
The Vegetation Indices window shows the time series of NDVI (in green) and 3*DVI (in blue) over the full year. 3*DVI is shown rather than DVI to get a range similar to that of NDVI. DVI is the simple difference of the 865 nm and 670 nm channels reflectances. NDVI is the normalized difference of these parameters. The reflectance is the nadir value derived from the selected BRDF model after a fit on the 5 measurements. The purpose of the Vegetation Indices window is mostly to provide some indication about the vegetation cover variations within the year for a better interpretation of the figures that are discussed below. On the example shown in Figure 6, there is a clear annual cycle of the vegetation cover with an increase of the vegetation indices during the spring and a dry down during the fall.

Model parameters time series 10
The Time Series window displays the annual time series of the three parameters of a linear BRDF model, referred to as k 0 , k 1 and k 2 . The model used is that selected in the MCW but, in the current version, the Time Series window only functions for the linear BRDF models (i.e. not Engelsen, RPV and Snow). If the TS Option checkbox is set, it displays, from top to bottom, the time series of the reflectance in a particular geometry (sun at 40° from zenith and view at nadir) and the ratio of model 15 parameters: k 1 /k 0 and k 2 /k 0 . An example is shown on the right side of Figure 7. When the checkbox is not set, the time series of k 0 , k 1 and k 2 are shown, as on the left side of Figure 7. The time series of the three selected channels are shown in color while the others channels are also displayed but in black.
Note that the parameters are displayed only if the coefficient of correlation between measurementmodel is larger than the "Time Series Min. Corr" threshold set in the MCW. Indeed, when the 20 correlation is low, the BRDF coefficients have little value and should not be displayed. The user can change the threshold and see its influence on the results.
The example of the Time Series window shown in Figure 7 indicates that the target BRDF changes with the vegetation growth and decay. Indeed, k 1 and k 2 (left), or their ratio with k 0 (right) vary concomitantly with the vegetation indices. Although it is not seen for all bands, k 1 tends to decrease 25 with an increase of the vegetation index while k 2 tends to increase. This behaviour is found over most targets (Breon and Vermote, 2012) and is somewhat expected as k 2 is associated with the RossThick Earth Syst. Sci. Data Discuss., doi:10.5194/essd-2016-46, 2016  kernel which aims at modelling the BRDF of a thick canopy. Note that the time series are often incomplete because of a lack of observations (because of cloud cover or sun angle issues). On the example of Figure 7, there are no parameter estimates for December.
The time series on this example are relatively clean. There are cases with more variable parameter retrievals. The blue (490 nm) band over the vegetation is particularly difficult because of the low 5 surface signal and the large atmospheric correction.

BRDF/BPDF seasonal evolution
Finally, when the All_BRDF checkbox is set, the All BRDF/BPDF window shows the BPDF (first line) and BRDF (following lines) for the 12 months. An example is shown in Figure 8. On each of the polar diagrams that are shown, one can identify the independent satellite overpasses, with up to 16 10 observation directions that are roughly aligned in the angular space. The general orientation of these observations vary along the year because the sun azimuth, at the local time observation, varies.
All polar plots show the main characteristics that have been described earlier, with a maximum reflectance and a minimum polarized reflectance close to backscatter. Figure 8 also shows a change in the general reflectance along the year. At 865 nm, the reflectance is the largest in August, when it 15 appears to be the lowest at 670 nm. This observation is fully consistent with the change of the vegetation index ( Figure 6) and the BRDF parameters (Figure 7) along the year. The All BRDF/BPDF window is appropriate to get a full view of the observation of a given target along the year, while the other windows are required for a more quantitative interpretation.

Conclusions 20
The main focus of the POLDER spaceborne instrument was for atmospheric studies, i.e. the monitoring of aerosols and clouds. It may be argued that the spatial resolution of 6x6 km 2 is not suitable for the analysis of land surface processes. However, we have here selected homogeneous targets, in which directional coverage of POLDER is better than that of MISR (Diner et al., 1998), the only other instrument that provides multi-directional sampling of the Earth reflectances (Lallart et al., 2008).
POLDER remains therefore, an up-to-date tool for the analysis of the directionality and polarization of land surface reflectances. We have developed a database for the remote sensing community that provides a description of representative Earth targets. A similar undertaking has been achieved based 5 on airborne measurements at a higher spatial resolution (Gatebe and King, 2016). Earlier version of the database had been developed based on the measurements from the POLDER instrument onboard the ADEOS and PARASOL satellites. Although these versions have not been properly described in the peer-reviewed literature, they have been used for several analysis of the surface directional (e.g. Kokhanovsky and Breon, 2012;Cui et al., 2009;Jiao et al., 2014;Bacour and Breon, 2005;Maignan et 10 al., 2004) andpolarization (e.g. Litvinov et al., 2012;Maignan et al., 2009) signatures. The new version, which is described in this paper, is of better quality. It benefits from improved calibration and data selection scheme; it provides the reflectance measurement over an extended spectral range (up to 1020 nm) and it is associated with an interactive analysis tool. These data can be used to develop new models and evaluate their ability to reproduce the observed spectral, directional and polarization 15 signatures. The database and the analysis tool are available free of charge for the scientific community

Acknowledgments
The work that led to this database was made possible thanks to the support from CNES and Eumetsat.
SZA is the sun zenith angle in degrees.
VZA is the view zenith angle in degrees.
RelAzi is the relative azimuth in degrees. 5 AziS is the sun azimuth with respect to the North direction, in degrees.
DVzC and DVzS can be used for slight corrections of the view geometry. Indeed, POLDER spectral measurements are not simultaneous so that each channel is acquired with a slightly different viewing geometry. The view angles that are given are for the 670 nm band. The view geometry for the other channels can vary by a few tenths of degrees. For applications that require a higher 10 accuracy, these parameters allow the correction that is described in appendix B.

15
Aero is a non-quantitative indication of the aerosol load retrieved from POLDER measurements. 0 is for minimal aerosol load, whereas 15 is for a high aerosol load.

Appendix B: Compute the exact view direction for all channels
With the POLDER/Parasol imaging concept, the 15 spectral/polarized measurements are acquired sequentially. Therefore, a given surface target is observed, for the various spectral bands, with slightly 20 different viewing angles. The differences are small, but can be significant for some applications that need a very high angular accuracy, such as the analysis of the Hot-Spot directional signature.
The view zenith angle (θ 0 ) and relative azimuth (φ 0 ) that are given in the BRDF database are for the central filter, i.e. 670P2. The two parameters DVzC=∆[θ v cos(φ)] and DVzS=∆[θ v sin(φ)], which are given for each viewing direction in the data file, are necessary to derive these angles for other spectral 25 bands θ j and ϕ j . The formulae are as follows: Earth Syst. Sci. Data Discuss., doi:10.5194/essd-2016-46, 2016 where Xj is given in the