A

<figure><img src="image_22.png" /></figure>

B

<figure><img src="image_23.png" /><figcaption>FIGURE 18 | The AOD(560) retrieved by POLDER/GRASP (A) and MERIS/GRASP (B) for September 2008.</figcaption></figure>

(2017), for utilization with the ceilometers by Roman et al. (2018), for processing sun/sky aureole measurements by Torres and Fuertes (2020), etc.

It is important to note that the full compatibility of all retrievals inside of GRASP is fundamental base for the developments of diverse synergetic retrievals. Indeed, in a case if even very different observations of similar natural event are available then the interpretation of these observations by GRASP can be combined together in a single synergetic retrieval. It can be mentioned here that the DIVA (Demonstration of an Integrated approach for the Validation and exploitation of Atmospheric missions) platform has been developed to promote and simplify practical use of the GRASP synergetic capabilities (Fuertes et al., 2019). The system operates in computer cloud and contains loaded data from ground and space observation that can be easily used for the exploration of new retrieval possibilities such as the joint retrieval of the gas aerosol properties showed in *Ground-Based Passive Observations* or the joint inversion of ground-based radiometer and lidar observations discussed in *Ground-Based Active Observation and Synergy With Passive Observations* is only one example of such synergy. Similar approach is also being developed for synergetic processing of passive and active satellite observations. For example, GRASP based approach has been used in extensive numerical tests in frame of ongoing NASA Aerosol and Cloud, Convection and Precipitation (ACCP) study. The ACCP initiative considers deployment of coordinated observations by passive (polarimeter, spectrometer, microwave radiometer) and active (lidar and radar) sensors (https://science.nasa.gov/earth-science/decadal-accp). **Figure 22** illustrates the application of a GRASP-based testbed realized by Espinosa W. R. et al. (2019) for exploring the capabilities of synergistic passive and active remote sensing using a combination of multi-angular polarimeter and lidar observations considered in ACCP for future deployment. The aerosol retrieval displayed in **Figure 22** demonstrates that a retrieval using total and polarimetric radiances paired with HSRL lidar profiles can yield accurate, mode-resolved extinction profiles in relatively complex scenes. Retrievals of such quality are unachievable with just lidar or polarimeter data alone.

When only using lidar measurements for deriving aerosol properties, a different retrieval strategy can be adopted with GRASP. Instead of fully and independently retrieving particle microphysical and intensive optical properties, multichannel lidar measurements can be used to quantify the contribution of different aerosol components, that can be considered as aerosol “types”, to the vertical concentration profile of aerosols. The development of this approach in GRASP is also discussed in detailed by Lopatin et al. (2021). Each aerosol type may be assumed to be characterized by climatological size distributions and refractive indexes, which can also be used to infer effective aerosol properties for the mixture of aerosol types. This is the approach adopted by Cuesta (2021) to exploit the measurements of the future satellite mission ACCP that will deploy an advanced lidar payload providing for the first time multiwavelength, multipolarisation and high spectral resolution capabilities. This method is illustrated in **Figure 23** for an example of vertical distribution of five different aerosol types (the pseudo-reality in **Figure 23A**) and forward calculations of lidar measurements for 3 wavelengths (355 nm, 532 nm and 1,064 nm) with depolarization capabilities for each of them and HSRL-derived particle backscatter and extinction profiles measured in the UV and visible channels (**Figures 23B–E**). This numerical application also considers instrumental noise according to the ACCP lidar payload, a vertical resolution of 500 m and 50 km horizontal averaging, as well as perturbations of the size distributions and refractive indexes with respect to the climatological values of each aerosol type. The joint and simultaneous fit of the 8 lidar-derived profiles allows the retrieval of the profiles of the abundances of the 5 aerosol types (**Figure 23F**) with almost negligible error with respect to the supposed true (**Figure 23A**).

Also, it has been shown that multi-pixel approach realized in GRASP is eventually useful for enhanced synergetic processing of ground-based observations. It was demonstrated that this principle can be rather efficient for combining non-coinident but close in time observations, e.g., day- and night-ground-based measurements. For example, Lopatin et al. (2021) demonstrated that combining the
<figure><img src="image_24.png" /><figcaption>**FIGURE 19** | The illustration of MERIS/GRASP validation results globally. The upper panel: the correlations of MERIS/Models AOD(560) with AERONET globally for entire MERIS archive: Left - over land, Right - over ocean. The lower panel: The correlations of DHR (Direct Hemispheric Reflectance) retrieved by MERIS/GRASP and MODIS over land globally for September 2008, for several selected wavelengths (665 and 865 nm).</figcaption></figure>

daytime radiometric and photometric data with nighttime observations by elastic or inelastic lidars and radiosondes could be achieved. As illustrated in the scheme shown in **Figure 24** in such synergetic approach the aerosol information from the morning and evening observations

helps to constrain the retrieval during the night. The same approach was used by Parajuli et al. (2020) for generating aerosol climatology base on synergetic processing of daytime AERONET observation with day and night time observation by MPL lidar. Somewhat similar but simpler strategy was used
<figure><img src="image_25.png" /><figcaption>**FIGURE 20** | The correlations of S5P/GRASP AOD retrievals and their error estimates for the numerical tests, where the AOD was retrieved from synthetic observations of S5P/GRASP AOD simulated over Banizoumbou AERONET site (the random noise of ~3% was added to the simulations) for Summer 2019.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**FIGURE 21** | The diagram illustrating current application of GRASP code.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>**FIGURE 22** | The results of synthetic tests of aerosol retrieval using a combination of polarimeter and HSRL lidar satellite data from a simulated scene containing a bimodal smoke layer above a bimodal marine aerosol. Panel (A) illustrates GRASP's ability to retrieve the fine (f) and coarse (c) mode extinction contributions in each of the two layers over N = 85 tests under various polarimeter viewing geometries and instantiations of measurement noise. Panels (B) and (C) show the corresponding 1σ distribution of simulated measurements and the corresponding GRASP fits for total aerosol extinction and backscatter, respectively. Panels (D) and (E) show the simulated polarimeter measurements and fits for 3 of the 85 tested geometries: I ($\theta_s$ = 19°, $\phi$ = 85°), II ($\theta_s$ = 36°, $\phi$ = 35°) and III ($\theta_s$ = 58°, $\phi$ = 35°). Across all 85 tests, the retrieved AOD, AODF and SSA had RMS errors of 0.003, 0.005 and 0.003, respectively.</figcaption></figure>

by Benavent-Oltra et al. (2019) for combining sun-sky radiometric daytime measurements with nighttime lidar and lunar photometry observations.

In addition, GRASP can be applied for synergetic aerosol and surface properties retrieval from coordinated ground-based and satellite observations. Indeed, the set of observations containing both satellite and ground-based measurements has substantial sensitivity to both contributions from surface (especially over land) and aerosols that is not always a case for satellite only or ground-based only data. The advantages of such approach were already demonstrated by Sinyuk et al. (2007).

In these regards, GRASP has very high flexibility in synergistically processing diverse observations. First, GRASP can process satellite only or ground-based only data including both passive and active (lidar or radiosonde, etc.) observations as illustrated by **Figure 24**. Second, using multi-pixel concept GRASP can process not fully collocated or fully incident data that substantially increases the number of situations where synergetic retrieval can be used. In addition, GRASP supports processing both up- and down-looking airborne observations that can also be included into synergy processing as illustrated by **Figure 25**. The concept and application of synergy processing of airborne and ground-based observations has been introduced and demonstrated earlier by Gatebe et al. (2010).

It should be noted that synergetic processing of up- and down-looking observations from ground, airplane and satellite are useful not only for obtaining more accurate information about aerosol and surface reflectance properties but also for tuning different aspects of satellite retrieval algorithm. Indeed, in many cases satellite observations have significant limitation

in the information content and additional assumptions are needed in order to reduce the number of the retrieved parameters. In these regards the joint synergetic retrieval of aerosol and surface properties by simultaneous inversion of satellite and ground-based observations can be used for validating and tuning these assumptions. For example, Dubovik et al. (2011) has discussed the optimization of aerosol size distribution representation for observations with different information content. They suggested to use simplified aerosol model for POLDER like satellite retrieval with the size distribution approximated by 5 log-normal bins with fixed median sizes and standard deviations. Moreover, as discussed above even more constrained aerosol model was used for processing POLDER data, where aerosol was represented as external mixture (Eq 3.10-3.11) of several aerosol components with fixed particles sizes, refractive indices and shapes and only the concentration of the components to be retrieved (see Chen et al., 2020; Lopatin et al., 2021). The verification of the validity of the assumptions taken can be checked using joint processing of satellite and ground-based observations. For example, 5 bins size distribution model and a mixture of aerosol components were applied for processing Sentinel-S5P observations. **Figure 26** shows the results of joint inversion of collocated Sentinel-S5P and AERONET observations using 3 different models: 1) AERONET model with size distribution modeled using 22 triangle size bins, 2) model using 5 log-normal bins and 3) models representing aerosol by a mixture of predefined components. The joint retrievals showed that all three approaches allow rather accurate fitting of both AERONET and Sentinel-S5P with the best fit for the most detailed model and slightly degrading for the second and the third approaches.
<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /><figcaption>**FIGURE 23** | Multiwavelength high spectral resolution spaceborne lidar retrieval of the aerosol concentration profile as a function of aerosol type based on the GRASP approach. (A) Pseudo-reality of aerosol concentration profiles for 5 selected types. Lidar measurements calculated with the GRASP forward model and adding random noise for measured (crosses) and fitted (plain lines) profiles of (B) particle backscatter, (C) particle extinction, (D) attenuated total backscatter and (E) particle depolarization ratio. (F) Retrieved concentration profiles from GRASP inversion quantified for the 5 aerosol types. Forward calculations of lidar-derived profiles are provided for the available wavelengths (355 nm in blue, 532 nm in green and 1,064 nm in red) with noise equivalent to night-time conditions, vertical resolution of 500 m and horizontal resolution of 50 km, as well as adding perturbations in the size distribution and complex refractive index of each aerosol type with respect to the fixed aerosols properties used in the inversion.</figcaption></figure>

Moreover, the joint Sentinel-S5P and AERONET processing did not reveal neither evident limitations in fitting of the observations nor in agreement of the retrievals with available aerosol or surface. **Figure 26** demonstrates that all three approaches can rather adequately reproduce all aerosol properties that agree with standard AERONET aerosol results including total AOD, and more detailed properties such as AE (Angstrom Exponent) and SSA.

Finally, it should be emphasized that provided above examples of joint retrievals are only selected set of the most mature applications chosen to illustrate the broad possibilities in realizing synergetic processing of diverse remote sensing and *in situ* observations. The fact is that all data that currently can be processed by GRASP algorithm as those shown in diagram in **Figure 21** can, in principle, be

processed jointly in diverse combinations provided the observations were coordinated, i.e., taken in nearby location and in sufficiently close (for chosen application) moments of time. In future, the applicability of GRASP is expected to be further expanded.

# 5 CONCLUSION

The potential of utilizing Multi-term (Least Square Method) LSM approach for designing and improving retrieval algorithms in remote sensing has been discussed and illustrated in application. Both fundamental methodology of the approach and practical realizations were reviewed and discussed. The Multi-term LSM concept provides clear and efficient way of applying multiple a
Multi-temporal multi-instrumental retrievals concept

<figure><img src="image_34.png" /><figcaption>**FIGURE 24** | The illustration of synergy processing of collocated but not fully coincident ground-based observations using smoothness a priori constraints on temporal variability of aerosol in frame of multi-pixel retrieval approach by Dubovik et al. (2011).</figcaption></figure>

priori constraints that is not evident in the frame of Method Maximum Likelihood (MML) and LSM formulations. Indeed, the approach allows simultaneous application of diverse a priori constraints in the same retrieval and opens many potentially useful applications. For example, the AERONET retrieval of aerosol from ground-based observations by Dubovik and King (2000) used Multi-term LSM to apply several different a priori constraints simultaneously on several retrieved characteristics. As a result, AERONET retrieval uses a set of different smoothness a priori constraints allowing elimination of sharp variability in both retrieved aerosol size distributions and in spectral dependencies of real and imaginary part of refractive indices. Recently, Dubovik et al. (2011) and Dubovik et al. (2014) have designed algorithm called GRASP (Generalized Retrieval of Aerosol and Surface Properties) with an objective of more profound exploration of the Multi-term LSM approach in diverse remote sensing retrieval.

The following key methodological aspects of numerical Multi-term LSM inversion realized in GRASP were reviewed and discussed in the paper:

* It was outlined that the Multi-term LSM approach is fully based on MML and LSM developments and, therefore, the designed retrievals holds asymptotic optimality of the retrieved parameters, in sense of their error variances asymptotic approaching to the fundamental minimum accuracy boundaries related with Fisher information definition.

* It was shown that Multi-term LSM has the same base with Bayesian and Optimum Estimation (OE) (Rodgers 2000) approaches and can be considered as fundamentally equivalent methodology. At the same time, while Bayesian and OE methodologies rely on explicit representation of a priori constraints via a priori estimates of the state vector with known covariance matrix, Multi-term LSM in a contrast allows more flexible parameterization of a priori constraints, therefore providing more freedom in designing practical constrained inversion procedures.

<figure><img src="image_35.png" /><figcaption>**FIGURE 25** | The illustration of combined ground-based and satellite observations that can be processed synergistically by GRASP.</figcaption></figure>

* A possibility of including a priori knowledge about non-negativity of measurements or retrieved parameters was discussed and the statistical optimization of the inversion in the logarithmic space was recommended for positively defined values.

* Several details of realizing statistically optimized inversion for non-linear forward models were discussed and it was outlined that Levenberg-Marquardt non-linear inversion scheme can be optimized using Multi-term LSM optimization by considering linearization at each iteration as errors and as part of measurement uncertainties.

* An issue of possible domination in the retrieval by a rather similar and therefore possibly redundant observations was considered. For minimizing the possible negative effect of such domination, an assumption was adapted that the variance of error per measurement in data set increases proportionally to the total number of measurements in each data set. Such assumption is expected to reflect the general tendency of increasing overall uncertainty of a single observation related with an increase of the efforts in controlling more complex observation sets (with larger number of observation points).

* Multi-term LSM approach is aimed for the use of multiple a priori constraints assuming that different a priori assumptions come from the real knowledge and therefore consistent. The consistency of multiple a priori constraints can be verified based on the comparison of achieved value ("goodness of the fits") of minimized quadratic term corresponding to each a priori constraint with the value expected based on the used assumptions.

* The estimations of the retrieval errors obtained in frame of Multi-term LSM approach allows for evaluating the contribution of measurement and a priori uncertainties on the retrieval accuracy. The strategy for accounting for the contribution of possible biases in the initial data or forward model is also discussed.

The GRASP algorithm is a practical retrieval tool realized as an open source software (https://www.grasp-open.com/). This paper
<figure><img src="image_36.png" /><figcaption>**FIGURE 26** | The correlations of AOD obtained from combined S5P + AERONET observations using aerosol models of different complexity with AERONET data. Upper panel: the correlation of obtained from combined S5P + AERONET with AERONET AOD measurements; The middle and lower panels: the correlations of Angstrom Exponent (AE) and SSA obtained from combined S5P + AERONET observations using aerosol models of different complexity with AERONET only operational results.</figcaption></figure>

provided detailed description of GRASP structure, discussed the algorithm evolution and overviewed the key technical details and its main applications. GRASP has two main independent modules. The first, numerical inversion, includes mathematical operations not related to the particular physical nature of the inverted data (in this case, remote sensing observations). The second, the forward model, is developed to simulate diverse atmospheric remote sensing observations, laboratory and *in situ* observations of light scattering and absorption. The forward model unit of GRASP is designed to simulate the interaction of electromagnetic radiation with

atmospheric particles such as aerosol and clouds. The forward model of GRASP also accounts for gaseous absorption and for multiple interactions of light scattered by atmosphere and reflected by underlying surface using rigorous radiative transfer calculation in approximation of plane-parallel atmosphere. It allows the simulation of observations by diverse satellites, ground-based and airborne radiometers, spectrometers and lidars, *in situ* polar- and integrating-nephelometers, etc.

he independence of numerical inversion modules allows successful utilization of features realized in numerical inversion in many practical
applications. Moreover, the coordinated observations of different type
can be inverted simultaneously. This opens possibilities of exploring
diverse synergetic approaches. The possibilities of simultaneous
inversion of diverse combinations of multi-instrument observations
were discussed in the paper. For example, one of the most popular
GRASP synergetic retrieval is simultaneous inversion of passive
radiometric and active lidar observation acquired from ground,
satellite or airplane.

GRASP suggests using two rather distinct types of a priori
constraints. The a priori constraints for strictly coincident and
collocated observations are united in the group of “single-pixel”
constraints. These constraints include direct a priori estimates of
unknowns and smoothness constraints that can be applied for a
group of retrieved parameters representing continuous functions,
such as particle size or shape distributions, vertical profiles,
spectrally dependent index of refraction or parameters of
surface reflectance, etc. From the mathematic point of view, the
smoothness constraints are applied by using a priori estimates of
the first, second or third order derivatives of the retrieved function.
The second group includes a priori constraints for coordinated but
not fully coincident or/and not fully collocated observations are
called “multi-pixel” constraints. For example, if a large group of
satellite observations (“pixels” of the image) is inverted
simultaneously, the concept of multi-pixel constraints allows for
constraining the retrieval results by using known a priori limitation
of variability of the retrieved parameters in time and or space. For
example, in many satellite retrievals realized by GRASP the known
natural tendencies are used: variability of land surface reflectance is
quite limited in time while aerosol properties have an evident
horizontal continuity. The strength of all a priori constraints can be
different for each of the retrieved parameters. It should be noted
that a concept of multi-pixel retrieval opens extra possibilities for
synergetic processing of non-coincident or/and non-collocated
observations. For example, this concept was used for joint
processing of day- and night-time radiometric, photometric and
lidar observations. More complex constraints that currently are not
included neither in single- nor in multi-pixel constraints could also
be realized in GRASP with some extra efforts if the need is
identified or by request.

GRASP has been successfully adapted for a number of practical
applications demonstrated in the paper. For example, the algorithm
was used to generate an advanced aerosol product from series of multi-
angular POLDER polarimeters. POLDER/GRASP retrieval provided
the values of spectral AOD and other detailed aerosol parameters
including Angstrom parameter, spectral AOD for fine and coarse
aerosol modes, as well as spectral AAOD and SSA. The spectral values
of land and ocean surface BRDF and BPDF were retrieved
simultaneously with aerosol. GRASP is used in preparation of
operational aerosol algorithms for the future 3MI/EPS-SG and
CO2M polarimetric missions. It was shown to provide solid aerosol
retrieval for multi-angular MISR observations. In addition, aerosol
AOD product from single-view MERIS/Envisat radiometer was
generated using GRASP. Finally, the algorithm is also being
adapted for AOD and surface reflectance retrievals from
observations by more recent and future satellites including OLCI/
Sentinel-3, Sentinel-4, TROPOMI/Sentinel- 5P, HIMAWARI, MISR,
SGLI/GICOM-C, etc.

GRASP has been used quite extensively for retrieving aerosol from ground-based and *in situ* observations. For example, the algorithm was used for polar- and integrating-nephelometric measurements of angular aerosol scattering, total absorption and scattering for retrieving aerosol size, shape and information about the composition. One of the most popular GRASP applications, known as GRASP/GARRLiC, is retrieval of both columnar and vertical aerosol properties from a combination of collocated passive radiometric and active lidar observations. Such GRASP/ GARRLiC approach is adapted by ACTRIS pan-European research infrastructure as a part of operational data processing. Recently similar synergetic processing was extended in the frame of GRASP for joint inversion of active and passive satellite observations. As a result, such GRASP configuration was incorporated in a new aerosol retrieval testbed developed for exploring the capabilities of synergistic passive and active remote sensing in frame of NASA ACPP initiative.

Furthermore, in the frame of GRASP a new approach has been
developed for retrieval of aerosol chemical components directly
from satellite and ground-based measurements. The observed
aerosols are assumed to be mixtures of hydrated soluble particles
embedded with black carbon, brown carbon, iron oxide, and dust
or organic carbon insoluble inclusions and the volume fractions
of these components are derived along with aerosol size and
shape information. This component approach was successfully
applied to POLDER satellite and AERONET observations.

The paper also mentions other diverse less mature GRASP
applications that are under development or expected to be fully
realized in the near future. For example, GRASP is being
adapted for profound use of hyper spectral measurements
with an objective of using measurements of atmospheric
absorption for advanced retrieval of information about both
atmospheric aerosol and gases. In these regards, GRASP is being
expanded for retrieval of also atmospheric gases in addition to
aerosol and surface and, to reflect this development GRASP
should be renamed as Generalized Retrieval of Atmosphere and
Surface Properties.

DATA AVAILABILITY STATEMENT

The original contributions presented in the study are included in
the article/Supplementary Material, further inquiries can be
directed to the corresponding author.

AUTHOR CONTRIBUTIONS

OD - inversion theory, methodology, concept of GRASP, DF - GRASP applications, figures, PL - advancements of forward model, AL - methodology for active observations in GRASP, TL - software implementation of GRASP, ID - MML asymptotical properties, FX-inversion methodology, FD - implementation of POLDER applications, CC - diverse data analysis, BT - implementation of GRASP-AOD module, YD - scientific analysis, radiative forcing, LL - development of GRASP/Component approach, MH-G - hyperspectral and TIR applications, MH -
error estimations, YK - manuscript editing and polishing, CM - data analysis, GS - application of GRASP to nephelometrists editing, RE - application of GRASP to nephelometrs and for ACCP studies, AP - application of GRASP to HARP, ZL - discussion of GRASP concept and applications, JFr and RP - adaption to hyperspectral data, JC - using GRASP for ACCP lidar studies, AK, AC, and MA - application to real hyperspectral data, Aspetsberger, DM, LB, AH, VL, CH, and CF - software implementations.

## ACKNOWLEDGMENTS

The authors are grateful for the continuing support of GRASP developments: - from ESA in frame of multiple projects including IDEAS, CAWA, DIVA, QA4EO, aerosol retrieval developments for Sentinel-4, 5P and -7, etc., - from EUMETSAT in frame of multiple projects OLCI/Sentinel-3, 3MI/EPS-SG and MAP/S-7, - from CNES for POLDER-3/PARASOL, 3MI/EPS-SG, ACCP/EECLAT, etc., - from European Commission in frame of GRASP-ACE grant. The authors acknowledge the support from the Chemical and Physical

Properties of the Atmosphere Project funded by the French National Research Agency through the Programme d'Investissement d'Avenir under contract ANR-11-LABX-0 0 05-01, the Regional Council "Hauts-de-France", and the "European Funds for Regional Economic Development", from Research grant (no. URF/1/2180-01-01) "Combined Radiative and Air Quality Effects of Anthropogenic". Also, the authors acknowledge the support from the European Metrology Program for Innovation and Research (EMPIR) within the joint research project EMPIR 19ENV04 MAPP "Metrology for aerosol optical properties". The EMPIR is jointly funded by the EMPIR participating countries within EURAMET and the European Union. OD expresses personal thanks to B. Bojkov, formerly from ESA and currently from EUMETSAT, for his continuing support and encouragement of theoretical developments of Multi-term LSM inversion methodology and its applications in atmospheric remote sensing. Also, OD thanks G. Stenchikov for fruitful discussions and collaborations on optimizing GRASP application for ground-based and air-borne observations.

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**Conflict of Interest:** Authors DF, PL, AL, ID, CC, MH-G, YK, and CM were employed by the company GRASP-SAS. Authors AK and AC were employed by the company LuftBlick OG. Authors MA, DM, LB, AH, VL, CH, and CF were employed by the company Cloudflight GmbH. OD supported GRASP SAS with scientific consulting and held the actions of the company under "concours scientifique" convention of CNRS.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

**Publisher's Note:** All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Copyright © 2021 United States Government as represented by the Administrator of the National Aeronautics and Space Administration and Dr. Dubovik, Dr. Fuertes, Dr. Litvinov, Dr. Lopatin, Dr. Lapyonok, Dr. Doubovik, Dr. Xu, Dr. Ducos, Dr. Chen, Dr. Torres, Dr. Derimian, Dr. Li, Dr. Herreras-Giralda, Dr. Herrera, Dr. Karol, Dr. Matar, Dr. Puthukkudy, Dr. Li, Dr. Fischer, Dr. Preusker, Dr. Cuesta, Dr. Kreuter, Dr. Cede, Dr. Aspetsberger, Dr. Marth, Dr. Bindreiter, Dr. Hangler, Dr. Lanzinger, Dr. Holter and Dr. Federspiel. At least a portion of this work is authored by Gregory L. Schuster and Reed Espinosa on behalf of the U.S government and, as regards Dr. Schuster and Dr. Espinosa, U.S. copyright protection does not attach to separable portions of a Work authored solely by U.S. Government employees as part of their official duties. The U.S. Government is the owner of foreign copyrights in such separable portions of the Work and is a joint owner (with any non-U.S. Government author) of U.S. and foreign copyrights that may be asserted in inseparable portions of the Work. The U.S. Government retains the right to use, reproduce, distribute, create derivative works, perform, and display portions of the Work authored solely or co-authored by a U.S. Government employee. Non-U.S. copyrights also apply. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
GLOSSARY

**3MI** Multi-viewing Multi-channel Multi-polarization Imaging

**AAOD** Aerosol Absorption Optical Depth

**AATSR** Advanced Along-Track Scanning Radiometer

**ACCP** NASA Aerosol and Cloud, Convection and Precipitation

**ACEPOL** Aerosol Characterization from Polarimeter and Lidar

**ACTRIS** Aerosol, Clouds and Trace Gases Research Infrastructure

**AE** Ångström Exponent

**AERIS/ICARE** Data and Services for the Atmosphere/Cloud-Aerosol-Water-Radiation Interactions

**AERONET** Aerosol Robotic Network

**Aerosol-UA** Ukrainian space mission

**AGU** American Geophysical Union

**AirHARP** Airborne Hyper Angular Rainbow Polarimeter

**AOD** Aerosol Optical Depth

**AODC** Aerosol Optical Depth of Coarse aerosol mode

**AODF** Aerosol Optical Depth of Fine aerosol mode

**BRDF** Bidirectional Reflectance Distribution Function

**BPDF** Bidirectional Polarization Distribution Function

**BRDM** Bidirectional Reflectance Distribution Matrix

**CAWA** Advanced Synergy Aerosol products from MERIS and AATSR observations

**CGASA** Coefficient of Gas Absorption

**CLIMAT** Conveyable Low-noise Infrared radiometer for Measurements of Atmosphere and ground surface Targets

**CNES** Centre National d'Etudes Spatiales

**CNRS** Centre National de la Recherche Scientifique

**CO2M** Copernicus Carbon Dioxide Monitoring mission

**DHR** Direct Hemispheric Reflectance

**DIVA** Demonstration of an Integrated approach for the Validation and exploitation of Atmospheric missions

**DPC** Directional Polarimetric Camera

**ECMWF** European Centre for Medium-Range Weather Forecasts

**ENVISAT** ESA's Environmental Satellite

**ESA** European Space Agency

**EUMETSAT** The European Organisation for the Exploitation of Meteorological Satellites

**EPS-SG** EUMETSAT Polar System - Second Generation

**GARRLiC** Generalized Aerosol Retrieval from Radiometer and Lidar Combination

**GCOM-C** Global Change Observation Mission - Climate

**GRASP** Generalized Retrieval of Aerosol and Surface Properties; Generalized Retrieval of Atmosphere and Surface Properties (updated);

**GRASP-ACE** Development of GRASP radiative transfer code for the retrieval of aerosol-microphysics vertical profiles from space measurements and its impact in ACE-mission

**HIMAWARI** Geostationary satellites, operated by the Japan Meteorological Agency

**HARP** Hyper-Angular Rainbow Polarimeter

**HP** High Precision

**IDEAS** Instrument Data Quality Evaluation and Analysis Service

**LSM** Least Square Method

**MAP** Multi-Angular Polarimeter

**MAPP** Metrology for aerosol optical properties

**MERIS** Medium Resolution Imaging Spectrometer

**METEOSAT** Geostationary Meteorological Satellites operated by EUMETSAT

**METOP** European operational polar-orbiting meteorological satellite

**METOP-SG** METOP Second Generation

**MISR** Multi-angle Imaging SpectroRadiometer

**MML** Method of Maximum Likelihood

**MODIS** Moderate Resolution Imaging Spectro - Radiometer

**MPL** Micro Pulse Lidar

**NASA** National Aeronautics and Space Administration

**NIR** Near Infrared

**NRT** Near-Real-Time

**OE** Optimal Estimation

**OLCI** Ocean Land Colour Instrument

**PC** Principal Component

**PGN** Pandonia Global Network

**PARASOL** Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar

**PDF** Probability Density Function

**PM2.5** Fine particulate matter

**POLDER** POLarization and Directionality of the Earth's Reflectances

**PRISMA** PRecursore IperSpettrale della Missione Applicativa, Italian space mission

**RPV** Rahman-Pinty-Vestarte model

**RRI** Real part of Refractive Index

**RSP** Research Scanning Polarimeter

**S5P** Sentinel-5P

**SENTINEL** ESA family of Earth observation missions

**SGLI** Second Generation Global Imager

**SSA** Single Scattering Albedo

**TIR** Thermal Infrared

**TOA** Top of Atmosphere

**TROPOMI** TROPOspheric Monitoring Instrument

**UV** Ultra Violet

**VENµS** Vegetation and Environmental New micro Spacecraft

**VIS** Visible spectral range

**QA4EO** Quality Assurance framework for Earth Observation