A Comprehensive Description of Multi-Term LSM for Applying Multiple a Priori Constraints in Problems of Atmospheric Remote Sensing: GRASP Algorithm, Concept, and Applications

Date

2021-10-19

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Program

Citation of Original Publication

Dubovik, Oleg et al.; A Comprehensive Description of Multi-Term LSM for Applying Multiple a Priori Constraints in Problems of Atmospheric Remote Sensing: GRASP Algorithm, Concept, and Applications; Frontiers in Remote Sensing, 19 October, 2021; https://doi.org/10.3389/frsen.2021.706851

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Subjects

Abstract

Advanced inversion Multi-term approach utilizing multiple a priori constraints is proposed. The approach is used as a base for the first unified algorithm GRASP that is applicable to diverse remote sensing observations and retrieving a variety of atmospheric properties. The utilization of GRASP for diverse remote sensing observations is demonstrated. We describe an approach called the Multi-term Least Square Method (LSM) that has been used to develop complex aerosol inversion algorithms for a number of years and applied to retrievals of laboratory and ground-based measurements. Theoretically, it was shown how to unite the advantages of a variety of approaches and to provide transparency and flexibility in development of practically efficient retrievals. From a practical viewpoint, this approach provides a methodology for using multiple a priori constraints to atmospheric problems where rather different groups of parameters should be retrieved simultaneously. For example, Dubovik and King (J. Geophys. Res., 2000, 105, 673–696) used multi-term LSM for designing the algorithm that retrieves aerosol size distribution and spectrally dependent complex index of refraction from Sun/sky-radiometer ground-based observations. Furthermore, the significant potential of the multi-term LSM approach was demonstrated with the development of the GRASP (Generalized Retrieval of Aerosol and Surface Properties) algorithm. The GRASP algorithm is based on several generalization principles with the idea to develop a scientifically rigorous and versatile algorithm. It has significantly extended capabilities and areas of applicability and can be applied to diverse remote sensing observations. This paper also illustrates the practical applicability of GRASP and, therefore the multi-term LSM, in diverse situations. GRASP has two main independent modules. The first module is a numerical inversion that includes general mathematical operations not related to a particular physical nature of the inverted data. Numerical inversion is implemented as a statistically optimized fitting of observations following the multi-term LSM strategy. The presentation of the GRASP numerical inversion provides a profound description of the main methodological aspects used for establishing a multi-term LSM approach that is aimed at applying multiple a priori constraints in the retrieval. The foundation of this approach uses the fundamental frameworks of the Method of Maximum Likelihood (MML) and LSM statistical estimation concepts. We discuss the asymptotical optimal properties of MML and LSM estimates in order to emphasize the importance of statistical estimation methods in remote sensing. We also compare the multi-term LSM with other established statistical optimization approaches of numerical inversion that are constrained by a priori information, such as Bayesian concepts and the Optimal Estimation approach (Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, 2000). In addition, we discuss several other methodological inversion optimization aspects, including accounting for non-negativity of measured and retrieved characteristics, optimizing inversion in non-linear cases, accounting for measurement redundancy, estimating contributions of random measurement and systematic errors on the retrieval uncertainties, etc. All of these aspects are complimentary to multi-term LSM that need to be fully addressed in the development of practically efficient inversion algorithms. These methodological developments have already been applied to several remote sensing algorithms, such as the algorithm by Dubovik and King (J. Geophys. Res., 2000, 105, 673–696) that has been employed for more than two decades for operational processing of observations from AERONET ground-based Sun-sky radiometers, and the algorithm by Dubovik et al. (J. Geophys. Res., 2006, 111, D11208) developed for retrieval of aerosol particle refractive index together with size and shape distributions from full phase matrix measurements. The second main module of GRASP is the forward model. Similarly to the numerical inversion module, it has been developed in a universal way for simulating various atmospheric remote sensing observations with high accuracy. As a result, GRASP is a highly versatile algorithm that can be applied to diverse passive and active satellite and ground-based atmospheric observations and is inherently designed for synergetic retrievals when different observations are inverted simultaneously. Depending on the input data, GRASP can retrieve detailed columnar and vertical aerosol properties and surface reflectance. Diverse approaches for modeling aerosol and surface properties together with different a priori constraints can be used in GRASP retrievals. Thus, the GRASP package can be considered as a platform for developing, testing, and refining novel retrieval concepts and their utilization in operational processing environment. In addition, GRASP is designed as a practically efficient, transparent, and accessible community open source algorithm that can be used as an advanced tool for verifying different retrieval concepts and realizing those concepts in high-performance operational software. At present, GRASP is being adapted to reprocess the observations provided by several satellite instruments, ground-based networks, single instruments, aircraft and for various synergetic data sets that combine coordinated passive and active remote sensing observations. For example, GRASP has been adapted for operational reprocessing of observations from POLDER-1, -2, -3, MERIS, and AATSR/Envisat satellite missions. There are developments of operational retrievals of aerosol and surface properties from OLCI/Sentinel-3, Sentinel-5P, 3MI/Metop-SG, and Sentinel-4 geostationary observations. GRASP has also been used for synergetic aerosol retrievals by inverting a combination of ground-based lidar and radiometer data. GRASP has also been used for interpretation of airborne and laboratory nephelometer measurements, and it has been used for developing new approaches to derive diverse aerosol properties from ground-based direct sun and diffuse sky radiation measurements by radiometers and sky cameras. GRASP algorithm and software organization are described in detail, and an overview of GRASP applications and data products is provided.