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 Sentinel-2 is a set of two satellites - a "constellation". While this constellation consists of sensor platforms that are similar, they are not identical in exactly what wavelengths they measure (see table below as an example for the difference between the two satellites in the sentinel 2 constellation). Sentinel-2 is a set of two satellites - a "constellation". While this constellation consists of sensor platforms that are similar, they are not identical in exactly what wavelengths they measure (see table below as an example for the difference between the two satellites in the sentinel 2 constellation).
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 +<html>
 +</p><!--kg-card-begin: html--><table xmlns="http://www.w3.org/1999/xhtml" dir="ltr" style="table-layout:fixed;font-size:10pt;font-family:Arial;width:0px;border-collapse:collapse;border:none" cellspacing="0" cellpadding="0" border="1"><colgroup><col width="157"><col width="110"><col width="138"><col width="147"></colgroup><tbody><tr style="height:21px;"><td style="border-top:1px solid #000000;border-right:1px solid #000000;border-bottom:1px solid #000000;border-left:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;font-weight:bold;text-align:center;" rowspan="2" colspan="1" data-sheets-value="{&quot;1&quot;:2,&quot;2&quot;:&quot;Spatial Resolution\n (m)&quot;}"><span><div style="max-height:42px">Spatial Resolution<br> (m)</div></span></td><td style="border-top:1px solid #000000;border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;font-weight:bold;text-align:center;" rowspan="2" colspan="1" data-sheets-value="{&quot;1&quot;:2,&quot;2&quot;:&quot;Band Number&quot;}"><span><div style="max-height:42px">Band Number</div></span></td><td style="border-top:1px solid #000000;border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;font-weight:bold;text-align:center;" rowspan="1" colspan="2" data-sheets-value="{&quot;1&quot;:2,&quot;2&quot;:&quot;S2A, S2B difference (abs)&quot;}">S2A, S2B difference (abs)</td></tr><tr style="height:21px;"><td style="border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;font-weight:bold;text-align:center;" data-sheets-value="{&quot;1&quot;:2,&quot;2&quot;:&quot;Central Wavelength\n (nm)&quot;}">Central Wavelength<br> (nm)</td><td style="border-right:1px solid #000000;border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;font-weight:bold;text-align:center;" data-sheets-value="{&quot;1&quot;:2,&quot;2&quot;:&quot;Bandwidth\n (nm)&quot;}">Bandwidth<br> (nm)</td></tr><tr style="height:21px;"><td style="border-right:1px solid #000000;border-bottom:1px solid #000000;border-left:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" rowspan="4" colspan="1" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:10}"><span><div style="max-height:84px">10</div></span></td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:2}">2</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0.2999999999999545}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0.3</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0</td></tr><tr style="height:21px;"><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:3}">3</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0.7999999999999545}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0.8</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0</td></tr><tr style="height:21px;"><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:4}">4</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0.2999999999999545}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0.3</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0</td></tr><tr style="height:21px;"><td style="border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:8}">8</td><td style="border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0.10000000000002274}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0.1</td><td style="border-right:1px solid #000000;border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0</td></tr><tr style="height:21px;"><td style="border-right:1px solid #000000;border-bottom:1px solid #000000;border-left:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" rowspan="6" colspan="1" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:20}"><span><div style="max-height:126px">20</div></span></td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:5}">5</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0.3000000000000682}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0.3</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:1}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">1</td></tr><tr style="height:21px;"><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:6}">6</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:1.3999999999999773}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">1.4</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0</td></tr><tr style="height:21px;"><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:7}">7</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:3.099999999999909}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">3.1</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0</td></tr><tr style="height:21px;"><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:2,&quot;2&quot;:&quot;8a&quot;}">8a</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0.7000000000000455}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0.7</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:1}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">1</td></tr><tr style="height:21px;"><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:11}">11</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:3.2999999999999545}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">3.3</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:3}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">3</td></tr><tr style="height:21px;"><td style="border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:12}">12</td><td style="border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:16.700000000000273}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">16.7</td><td style="border-right:1px solid #000000;border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:10}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">10</td></tr><tr style="height:21px;"><td style="border-right:1px solid #000000;border-bottom:1px solid #000000;border-left:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" rowspan="3" colspan="1" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:60}"><span><div style="max-height:63px">60</div></span></td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:1}">1</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0.5}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0.5</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:0}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">0</td></tr><tr style="height:21px;"><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:9}">9</td><td style="overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:1.8999999999999773}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">1.9</td><td style="border-right:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:1}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">1</td></tr><tr style="height:21px;"><td style="border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:center;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:10}">10</td><td style="border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:3.400000000000091}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">3.4</td><td style="border-right:1px solid #000000;border-bottom:1px solid #000000;overflow:hidden;padding:2px 3px 2px 3px;vertical-align:bottom;text-align:right;" data-sheets-value="{&quot;1&quot;:3,&quot;3&quot;:1}" data-sheets-formula="=abs(R[-19]C[0]-R[-19]C[2])">1</td></tr></tbody></table><!--kg-card-end: html--><p>
 +</html>
 +
 +We can observe that the difference in both central wavelength and bandwidth varies between bands, and band 12 at 2190 nm shows a larger deviation. However, since we are already in the short wave infrared part of the spectrum, this deviation is relatively small (about 0.8%). Having a precise measure of the central wavelength gives the ground segment a number to correct for in calculating the radiance values. More on that in the processing section, and the below section on units.
 +
 +Note that certain bands are processed only to a certain spatial resolution. We will return to this in later sections where we talk about requesting specific spatial resultions to be produced by sen2cor.
 +
 +Finally, there is [[https://sentinels.copernicus.eu/web/sentinel/user-guides/Sentinel-2-msi/resolutions/radiometric|radiometric resolution]], which measures the range of brightness values that can be recorded by the satellite and is bounded by the interger type - 12 bit in the case of Sentinel-2 - used to store the data which limits it to integers between 0 to 4095. This can be thought of as the "dynamic range" in photography terms.
 +
 +== Units ==
 +
 +As hinted at in the resolution section above, the radiance values (energy flux) recorded at the sensor are rescaled into a digital representation from a unit often measured in watt/(steradian/square meter). Steradian, or "square radian" here being the SI unit for volumetric angles compared to the radian being the unit for planar angles.
 +
 +To make this perfectly clear: one radian unit of angle represents the angle in planar section of a circle where the circumference cut of the circle is equal to its radius. Correspondingly, the one steradian represents the volumetric element where the surface area of a cone is a circle of area radius^2. So nothing more exotic than a radian in three dimensions (how can we genereralize the radian to four, or five dimensions?).
 +
 +Note that the digital number resulting in a derived radiance value is taken at sensor level - there is no separation of radiance sources (atmosphere, land objects, etc) in the recording of the data. Any diffuse medium between the land object and the sensor (a cloud for instance) will  diminish the radiance contribution from that object and render it more diffusely. More on this, and other correction steps, in later sections where we discuss data processing.
 +
 +Reflectance should not be confused with Radiance, in that it is the ratio of the quantity of radiation reflected from a target to the radiation incident on the target. Therefore it is unitless and depends directly on the material being observed.
 +
 +These two terms - reflectance and radiance - are sometimes used interchangebly and in others with minor variations depending on the physics of the system being observed. In both cases it is worth remembering that the sensor doesnt measure either of them but rather the energy flux incident on the sensor, which can then be converted (or re-scaled) to an unsigned interger that represents the physical variable.
 +
 +==== Sentinel 2 data processing ====
 +
 +The sections below detail the different steps or processing levels that the raw data from the satellite is subject to after having been recieved at the ground station.
 +
 +There is always error in physical measurements, and we will start by considering the sources of error or image distortion that apply to satellite data. In general terms there are four categories of sources for satellite image distortion, and they are briefly described below.
 +
 +=== The Sensor ===
 +
 +The digital output from the sensor deployed on the satellite is subject to degradation, as well as minute mechanical differences for a type of sensor in a production series. Therefore, it is not suitable to use the raw output from them as spectral measures. Instead they must be scaled into a number of a certain bit depth by using suitable calibration coefficients. This process converts digital sensor numbers to what is typically refered to in the litterature as at-sensor radiance. This is different from sensor calibration, which is the process of modelling sensor degradation and deriving calibrations coefficients as a function of sensor usage over time.
 +
 +=== The Sun ===
 +
 +Once the at-sensor radiance values are obtained, the next step would account for solar radiation interference and earth-sun geometry, which is dependent on latitude and datum, to obtain values of top-of-atmosphere (TOA) reflectance. The effect of this source of distortions depend on solar power (which varies over time), the solar elevation angle (determining the amount of light reflected) and the Earth-Sun distance (which also varies over time).
 +
 +Thankfully, while solar flux can be a complicated process to model depending on the need for detail, the Earth and the Sun are reasonably well-behaved celestial bodies and the geometric relationships between them are easily calculated. It is worth noting that in some literature, correcting for this is sometimes grouped together with the sensor correction step.
 +
 +=== The atmosphere ===
 +
 +== Top of Atmosphere Radiance ==
 +
 +Radiation, both from terrestrial and interstellar sources, has varying probability of scattering in parts of the volume segment from the surface of the earth to the sensor platform of the satellite. As such, the observed radiation is a superposition of all of those scattering processes distributed over space and wavelength. What that mix of scattered radiation consists of depends on a great variety of physical processes - Rayleigh scattering in the atmosphere, for instance, results in a large part of the blue region of the visible spectrum scattering in the atmosphere.
 +
 +Knowing what processes and types of radiation yield what type of scattering allows us to selectively correct for certain regions. Removing the scattered light in the atmosphere and only preserving the surface contribution provides a bottom of atmosphere (BOA) corrected product, and the inverse is true for the top of atmopshere (TOA) variation. However, simply knowing that a data product has been TOA or BOA corrected is no enough since there are many ways of caluculating those values. The user is adviced to read up on what kind of correction has been applied, before using the data in their analysis.
 +
 +Reflectance is dimensionless because radiance is divided by irradiance so the units cancel. However (and this confuses many people) reflectance is not constrained to fall between 0-1; sometimes it is stored in integer format (e.g. 12-bit or 16- bit) because floating point format (0-1) takes up too much disk space. If you have pixel values of 1000 then the data can certainly be in top-of-atmosphere or surface reflectance. However, you need to look at the metadata and/or read the data description to be certain what level of processing the data had. Do not look at the data and try to make guesses about the processing - the level of processing is explained in the data documentation.If you are using Landsat climate data record (CDR) data then it is mostly in surface reflectance but it needs to be slightly rescaled as well as have a sun angle correction applied. If the data was distributed as TOA reflectance then the radiance at the Landsat sensor was divided by the exo-atmospheric irradiance and this is better than nothing but there will be band-specific biases (according to Rayleigh scattering).
 +
 +The energy that is captured by Landsat sensors is influ- enced by the Earth’s atmosphere. These effects include scattering and absorption due to interactions of the elec- tromagnetic radiation with atmospheric particles (i.e.,gases, water vapor, and aerosols)
 +
 +However, some atmospheric effects are highly variable over the Earth’s surface and can be difficult to correct in Landsat imagery. While it is not always necessary to atmospherically correct Landsat data to surface values, there are instances where this level of correction is needed. In general, absolute atmospheric corrections are needed when (1) an empirical model is being created for application beyond the data used to develop it, (2) there is a comparison being made to ground reflectance data such as a field-based spectroradi- ometer, or (3) as an alternative to relative correction when comparisons are being made across multiple images. All atmospheric correction methods have associated assump- tions about the target and the nature of the atmospheric particles or emissivity (for land surface temperature). There are numerous atmospheric correction methods available, ranging from simple approaches that use only within-image information such as dark object subtraction (Chavez 1988), to more complex and data-intensive approaches such as the method used for the Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) products (Masek et al. 2006)