## Level-1C Algorithm

Sentinel-2 MSI Technical Guide - Level-1C Algorithm Overview

Two successive operations are undertaken in order to obtain a Level-1C product from Level-1B products:

• Resampling of the Level-1B image to achieve an orthiimage in TOA reflectance.
• Calculations of cloud and land/water masks for a tile in the Level-1C geometry.

### Resampling

Resampling comprises five main steps:

1. Selection of tiles intersecting the image footprint
2. Projection (geographic coding)
3. Computation of resampling grids linking the image in native geometry to the target geometry (orthoimage)
4. Resampling of each spectral band in the geometry of the orthoimage using the resampling grids and an interpolation filter
5. Computation of TOA reflectance image in the target geometry

The masks of saturated areas, no-data and technical quality are also resampled in the target geometry. The resampling can process all or some spectral bands (all by default).

#### Tiling Module

The goal of this module is to select the list of predefined tiles which will be produced. The Earth's surface is split into several adjacent tiles in a given representation (UTM/WGS84). Some tiles may overlap between them. Each tile is defined by:
• an identifier
• a projection code (the default projection is the geographic coding, all EPSG projection shall be supported)
• an anchorage point (ground coordinates of the upper-left pixel of the tile)
• the pixel size in line and column
• the tile size in number of lines and of columns
• the tile bounding box coordinates in geographic representation

A list of tiles which intersect the footprint defined in the metadata is determined. If the intersection is void, the empty tiles are set to no-data by the resampling process.

The auxiliary data geometries are computed by this module.

#### Resampling function

The resampling function is intended to obtain radiometric information in the target geometry. This process is in two steps:

1. Geometric transformation.

#### Geometric Transformation

The geometric transformation allows linking of the points of the target image with the points of the initial image. For SENTINEL-2, a resampling grid is used and computed for each spectral band and each detector. For each tile, there are 13 by 12 resampling grids. Figure 1: Resampling Grid

The values of the resampling grid are computed for the footprint of the detector plus a small margin by extrapolation of the viewing directions. For each point of the orthoimage, the coordinates of the corresponding pixel in the native image are calculated by bi-linear interpolation of the four adjacent nodes. The grid computation is divided into three steps:

• Transformation of the native coordinates of the grid in coordinates expressed in the same reference system as the DEM
• Interpolation of the DEM at each grid point for obtaining the altitude
• Image location computation from each point to the source geometry of the band directly from the physical model of the band in question and detector (refined or not)

Also, the resampling grid provides complementary information:

• Altitude (DEM resampled in target geometry)
• quality flags of the DEM used

A point on the target image can have no homologous point in the initial image. To avoid this, the initial image is projected on the target geometry to determine its footprint. Only pixels included in the interest area of the target geometry are interpolated. The footprint of two detectors within the same spectral band may also overlap. The useful area of each detector is cropped at the column defined in the GIPP inter-detector of the overlapping area for each line (the middle column by default).

Interpolation estimates the radiance values of the target point, knowing the radiance of neighbouring pixels. A linear algorithm is used for this operation with B-spline functions.

#### TOA Reflectance Computation

The numeric digital counts (CN) of each pixel image (i,j) and each spectral band (k) are converted in TOA reflectance (ρ). This conversion takes into account the equivalent extra-terrestrial solar spectrum (Es), the incoming solar direction defined by its zenith angle (θs) for each pixel of the image and the absolute calibration (Ak) of the instrument MSI.

The conversion equation is: Equation 1: Top of Atmosphere conversion

where:

• CNk,NTDIis the equalized numeric digital count of the pixel (i,j) with NTDI, the number of SENTINEL-2 TDI lines
• Es is the equivalent extra-terrestrial solar spectrum and depends on the spectral response of the SENTINEL-2 bands
• The component d(t) is the correction for the sun-Earth distance variation (see Equation 2). It utilises the inverse square law of irradiance, under which, the intensity (or irradiance) of light radiating from a point source is inversely proportional to the square of the distance from the source. Equation 2: Earth Sun distance

t is the Julian Day corresponding to the acquisition date (reference day: 01/01/1950).

0.01673 is the Earth orbit eccentricity.

0.0172 is the Earth angular velocity (radians/day).

The parameters Ak and Es are provided by the GIPP and are also included in the ancillary data of the Level-1 products.

The sun zenith angles are determined at this level too. A sun angle grid is computed by regularly down-sampling the target geometry (Level-1C tile). The cosine of the zenith angle θs is defined at each point of the grid using the ground coordinates and the datation of the corresponding pixel acquisition. The azimuth angle is not processed here.

Reflectance, often between 0 and 1, is converted into integer values, in order to preserve the dynamic range of the data by applying a fixed coefficient (1000 by default).

For Level-1C products, the noise model is also adapted to the new range of TOA reflectance radiometric values. The parameters (Ak,Es) of the Level-1B noise model are corrected using Equation 1 by replacing CNk with the Level-1B parameters Ak1B and Es1B.