The optical signals detected on multiple satellite platforms over snow surfaces are determined by the optical properties of snow surface and atmosphere. The solution of both direct and inverse problems of an atmosphere – underlying snow system requires simple relationships between top-of-atmosphere (TOA) reflectance R and microphysical/optical characteristics of both snow and atmosphere. The task of this paper is to present a simple analytical relationship between the value of R as detected on a satellite with atmosphere/snow properties. Such a relationship can be established using a numerical solution of integro - differential radiative transfer equation (RTE) (Liou, 2022). However, this path is quite complicated and time consuming. The analytical solutions of RTE are needed for the solution of various applied atmospheric and snow optics problems (Cachorro et al., 2022; Mei et al., 2020, 2022; Kokhanovsky, 2021). This is the main driver of this work. To simplify the problem under study we consider the case of Antarctica, where both snow and atmosphere are almost free of pollutants. This work is focused on the simulation of the moderate spectral resolution TOA measurements (1nm or so) and the spectral range 400-1000nm.

This document describes the theoretical basis of the algorithms used to determine properties of snow and ice from the measurements of the Ocean and Land Color Instrument (OLCI) onboard Sentinel-3 satellites within the Pre-operational Sentinel-3 snow and ice products (SICE) project: http://snow.geus.dk/. The code used for the SICE retrieval and its documentation can be found at https://github.com/GEUS-SICE/pySICE. The algorithms were developed after the work from Kokhanovsky et al. (2018, 2019, 2020).

In this work, we propose simple and robust technique for the retrieval of underlying surface spectral albedo using spaceborne observations. It can be used to process both multispectral moderate resolution satellite data and also multi - zone high spatial resolution data. The technique can work automatically for different types of land surfaces without using huge databases accumulated in advance. The new cloud discrimination and retrieval of the water vapor content in atmosphere procedures are presented. The key point of the proposed atmospheric correction technique is the suggested single-wavelength method for determining the atmospheric aerosol optical thickness without reference to a specific type of underlying surface spectrum. The retrievals of spectral albedo for various land surfaces with developed technique, performed using computer simulation and experimental data, have demonstrated a high retrieval accuracy.

We have proposed a simple algorithm to retrieve the total ozone column and snow properties (spectral albedo and effective light absorption path) using the high spatial resolution single – view MSI/S-2 measurements over Antarctica.

Atmospheric correction is a necessary step in image processing data and spectra recorded by spaceborne sensors for pure cloudless atmosphere, primarily in the visible and near-IR spectral range. We have present a fast and sufficiently accurate method of atmospheric correction based on the proposed analytical solutions describing with high accuracy the spectrum of outgoing radiation at the top boundary of the cloudless atmosphere. This technique includes the model of the atmosphere and its optical parameters that are important in terms of radiation transfer. The solution of the inverse problem for finding unknown parameters of the model is carried out by the method of non-linear least squares (Levenberg-Marquardt algorithm) for an individual selected pixel of the image (its spectrum), taking into account the adjacency effects. Using the found parameters of the atmosphere and the average surface albedo, assuming homogeneity of the atmosphere within a certain area of the hyperspectral image (or the whole frame), the spectral albedo at the Earth's surface is calculated for all other pixels. It is essential that the procedure of the numerical simulation with non-linear least squares of the direct transfer problem is based on using analytical solutions, which provides a very short calculation time of the atmospheric parameters (seconds or less) and the ability to perform atmospheric correction "on-fly." Testing methods of atmospheric correction was performed using the synthetic outgoing radiation spectra at the top of the atmosphere (TOA), obtained by numerical simulation in the LibRadTran code, as well as spectra of real space images of the Hyperion hyperspectrometer. A comparison with the results of atmospheric correction in module FLAASH of ENVI package has been performed. Finally, to validate our data obtained by the SHARK method, a comparative analysis with ground-based measurements of Radiometric Calibration Network (RadCalNet) was carried out.

We present the update of the Snow and Ice (SICE) property retrieval algorithm proposed initially by Kokhanovsky et al. (2019). The algorithm is based on the spectral measurements of Ocean and Land Color Instrument (OLCI) onboard Sentinel-3 satellites combined with the asymptotic radiative transfer theory valid for weakly absorbing turbid media. The main improvements include the introduction of a new atmospheric correction, retrieval of snow impurity load and properties, retrievals for partially snow-covered ground and also accounting for various thresholds to be used to assess the retrieval quality. The algorithm is available as python and Fortran packages at https://github.com/GEUS-SICE/pySICE. The technique can be applied to various optical sensors (satellite and ground-based) operated in the visible and near infrared regions of electromagnetic spectra.

We present a simplified atmospheric correction algorithm for the snow/ice albedo retrieval using single view satellite measurements. The validation of the technique is performed using Ocean and Land Colour Instrument (OLCI) on board Copernicus Sentinel - 3 satellite and ground spectral or broadband albedo measurements from locations on the Greenland ice sheet and in the French Alps. Through comparison with independent ground observations, the technique is shown to perform accurately in a range of conditions from a 2100 m elevation mid-latitude location in the French Alps to a network of 15 locations across a 2390 m elevation range in seven regions across the Greenland ice sheet. Retrieved broadband albedo is accurate within 5% over a wide (0.5) broadband albedo range of the (N = 4,155) Greenland observations and with no apparent bias.

The Sentinel Application Platform (SNAP) architecture facilitates Earth Observation data processing (http://step.esa.int/main/toolboxes/snap/). In this work we present results from a new Snow Processor for SNAP. We also describe physical principles behind the developed snow property retrieval technique based on the analysis of Ocean and Land Colour Instrument (OLCI) onboard Sentinel-3A/B measurements over clean and polluted snow fields. Using OLCI spectral reflectance measurements in the range 400-1020nm, we derive important snow properties such as spectral and broadband albedo, snow specific surface area, snow extent and grain size on the spatial grid of 300m. The algorithm also incorporates cloud screening and atmospheric correction procedures over snow surfaces. We present validation results using ground measurements from Antarctica, the Greenland ice sheet and the French Alps. We find the spectral albedo retrieved with accuracy of better than 3% on average, making our retrievals sufficient for a variety of applications. Broadband albedo is retrieved with the average accuracy of about 5% over snow. Therefore, the uncertainties of satellite retrievals are close to experimental errors of ground measurements. The retrieved surface grain size shows good agreement with ground observations. Snow specific surface area observations are also consistent with our OLCI retrievals. We present snow albedo and grain size mapping over the inland ice sheet of Greenland for areas including dry snow, melted/melting snow and impurity rich bare ice. The algorithm can be applied to OLCI Sentinel-3 measurements providing an opportunity for creation of long – term snow property records essential for climate monitoring and data assimilation studies - especially in the Arctic region, where we face rapid environmental changes including reduction of snow/ice extent and, therefore, planetary albedo.