Effective uncertainty quantiﬁcation for multi-angle polarimetric aerosol remote sensing over ocean, Part 1: performance evaluation and speed improvement

Multi-angle polarimetric (MAP) measurements can enable detailed characterization of aerosol microphysical and optical properties and improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere-ocean system. Theoretical pixel-wise retrieval uncertainties based on error propagation have been used to quantify retrieval performance and determine the quality of data products. However, standard error propagation techniques in high-dimensional retrievals may not always represent true retrieval 5 errors well due to issues such as local minima and nonlinearity of radiative transfer near the solution. In this work, we analyze these theoretical uncertainty estimates and validate them using a ﬂexible Monte Carlo approach. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on several neural network forward models, is used to conduct the retrievals and uncertainty quantiﬁcation on both synthetic HARP2 (Hyper-Angular Rainbow Polarimeter 2) and AirHARP (airborne version of HARP2) datasets. In addition, for practical application of the technique to uncertainty evaluation 10 in operational data processing, we use the automatic differentiation method to calculate derivatives analytically based on the neural network models. Both the speed and accuracy associated with uncertainty quantiﬁcation for MAP retrievals are addressed in this study. Pixel-wise retrieval uncertainties are further evaluated for the real AirHARP ﬁeld campaign data. The uncertainty quantiﬁcation methods and results can be used to evaluate the quality of data products, and guide MAP algorithm development for current and future satellite systems such as NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) 15 mission. and applied a practical, efﬁcient way to estimate theoretical uncertainties for aerosol and ocean data products retrieved by FastMAPOL from synthetic AirHARP and HARP2 measurements, and ﬁeld AirHARP measurements from the ACEPOL ﬁeld campaign. Theoretical retrieval uncertainties for aerosol and ocean color properties are discussed. tend to mean larger retrieval uncertainty, although this is arguably preferable (considering data coverage) to discard the whole retrieval based on a high-cost function. In these situations, the theoretical uncertainty estimate may guide whether a retrieval is useful for a particular application on a per-parameter basis. This work provides a general framework to understand the uncertainties from the retrieval algorithm and provides a bridge from theoretical uncertainty toward future evaluation using in-situ measurements. More complex input uncertainty model, such as the one including uncertainty correlations between the multi-angle measurements, can be evaluated based on this framework, which will be a topic in the Part 2 of this paper series. Although based on synthetic and airborne measurements, the methods on uncertainty quantiﬁcation are ﬂexible and can be applied to existing and future satellite missions such as NASA’s PACE 525 mission with advanced multi-angle polarimetric instruments.