Digital images and reflectance
Chapter 3 of Remote sensing.
Pixels
A digital image is a raster: a grid of pixels (picture elements) in rows and columns. Each pixel covers an area on the ground and has a value and an address, its row and column. The value is the average for the whole area the pixel covers.
The geographic position of each pixel follows from its row and column, given the imaging geometry and the satellite’s orbit. Making that link is geometric correction and georeferencing: the image is corrected for distortions (from the Earth’s rotation, or a sensor not looking straight down) and fitted to a map projection, often with ground control points whose true coordinates are known. Satellite images are normally delivered already corrected and projected: Sentinel-2 in UTM, for Denmark zone 32N (EPSG:32632).
Digital numbers and radiometric resolution
The sensor records the radiation as a digital number (DN), an integer stored with a fixed number of bits. The number of bits is the radiometric resolution: 8 bits give values from 0 to 255 (2⁸ − 1), 12 bits from 0 to 4095. The measured radiation is scaled to fit that range.
From digital numbers to reflectance
A DN only means something together with the sensor’s calibration. In a radiometrically calibrated image the DN is converted to radiance with coefficients specific to the sensor:
Lλ = a × DN + b
where Lλ is the spectral radiance in W m⁻² sr⁻¹ µm⁻¹ (sr, the steradian, is the unit of solid angle: it is to the surface of a sphere what the radian is to the circumference of a circle).
Radiance depends on how much light there was. To compare images taken under different light, radiance is turned into reflectance, the fraction of the incoming sunlight that is reflected (as with a handheld spectrometer). That needs the sun’s irradiance in the band, Eλ (W m⁻² µm⁻¹), the sun’s zenith angle θs, and the Earth–sun distance d in astronomical units (close to 1, varying over the year):
r = π × Lλ × d² / (Eλ × cos θs)
Top-of-atmosphere and surface reflectance
- Top-of-atmosphere (TOA) reflectance uses only the sun’s position and the Earth–sun distance, from the image’s metadata. It still contains the atmosphere’s effects: haze, and absorption by gases. Sentinel-2 Level-1C products are TOA reflectance.
- Surface reflectance, also called bottom-of-atmosphere (BOA) reflectance or atmospherically corrected images, also removes the atmosphere’s effects, estimated from the image itself, weather data and terrain. It is the best estimate of what the surface reflects, and the right choice for comparing places and dates and for indices. Sentinel-2 Level-2A products are surface reflectance.
How reflectance is stored
Sentinel-2 stores reflectance as 16-bit integers, reflectance × 10,000, so 0.0323 is stored as 323. Since processing baseline 04.00 (January 2022) the products from ESA have an offset of 1000 added, so negative values from the correction can be stored:
reflectance = (DN − 1000) / 10,000
Where the data come from decides what has been done already:
- From the Copernicus Browser’s analytical download the values are already harmonised: as 32-bit floats they are reflectance (0–1), as 16-bit integers reflectance × 10,000, with no offset.
- From the original product (
.SAFE), the offset must be subtracted. - Other archives differ, and their metadata do not always match the values. Look at the values: summer vegetation has a red reflectance of about 0.02–0.05 and a NIR reflectance of about 0.3–0.5.
A wrong offset makes a vegetation index impossible: NDVI comes out above 1 (see Vegetation index from Sentinel-2 (Recipe - QGIS)).
Multispectral images
A multispectral radiometer measures in several wavelength bands (the name comes from bands of the spectrum). Each band is an image of its own, and together they form a multispectral image with one layer per band.
Sentinel-2 bands
| Band | Name | Centre (nm) | Pixel | Useful for |
|---|---|---|---|---|
| B1 | Coastal aerosol | 443 | 60 m | aerosols, coastal water |
| B2 | Blue | 490 | 10 m | water, soil and vegetation; true colour |
| B3 | Green | 560 | 10 m | the green peak of vegetation; true colour |
| B4 | Red | 665 | 10 m | chlorophyll absorption; true colour; NDVI |
| B5 | Red edge 1 | 705 | 20 m | the steep rise from red to NIR in vegetation: chlorophyll, stress |
| B6 | Red edge 2 | 740 | 20 m | as B5 |
| B7 | Red edge 3 | 783 | 20 m | as B5 |
| B8 | NIR | 842 | 10 m | biomass, leaf structure; NDVI |
| B8A | Narrow NIR | 865 | 20 m | as B8, narrower band |
| B9 | Water vapour | 945 | 60 m | atmospheric correction |
| B10 | SWIR cirrus | 1375 | 60 m | thin cirrus clouds (Level-1C only) |
| B11 | SWIR 1 | 1610 | 20 m | moisture of soil and vegetation; snow and cloud |
| B12 | SWIR 2 | 2190 | 20 m | moisture; minerals; burnt areas |
Level-2A products also contain a scene classification layer (SCL, 20 m), with a class per pixel from the atmospheric correction: 0 no data, 1 saturated or defective, 2 dark area, 3 cloud shadow, 4 vegetation, 5 not vegetated, 6 water, 7 unclassified, 8 cloud (medium probability), 9 cloud (high probability), 10 thin cirrus, 11 snow or ice. It is the simplest cloud mask.
Landsat 8 and 9 bands
Landsat’s OLI has bands 1 coastal aerosol, 2 blue, 3 green, 4 red, 5 NIR, 6 SWIR 1, 7 SWIR 2 (all 30 m), 8 panchromatic (15 m) and 9 cirrus; TIRS adds 10 and 11, thermal infrared (100 m). Band combinations written for Landsat translate to Sentinel-2 as 2→B2, 3→B3, 4→B4, 5→B8 (or B8A), 6→B11, 7→B12.