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Radiometric Correction Remote sensing signals are essentially the amount of energy received at the sensor from the target in a given spectral width. However, the signals we get directly the satellite are usually noisy. The noise is usually of two types: internal and external noise. Internal noise is from the sensor and external noise from the atmosphere and the areas adjacent to the target. What we received from satellite is DN values, not the amount of radiance directly. Why? 255 The number of DN values that a sensor can detect is called the sensor radiometric resolution. Why do the satellite send the DN values to the ground instead of radiance? The amount of energy was converted to DN value first on board the satellite as shown to the right. 0 the detector Gain and Offset (Bias) DN Gd L Bd Lmin Lmax Figure 1 where L Lmin L max DN Lmin 255 Spectral radiance measured over the spectral bandwidth of the channel. Gd: slope of response function Bd: Bias For Landsat 5, there are 16 detectors for each reflective band, and 4 detectors for the thermal band. For the convenience of users, the DN was calibrated (DNcal) as DN cal ( DN ref ) / ref or DN ref DN cal ref so that a single gain and bias can be used for each band. DN cal GL B For the remote sensing signals to be useful, the sensor must produce consistently the same DN at a given amount of energy received. Therefore, G and B must remain a constant for as long as the sensor is working. Each sensor on-board a satellite has been very carefully tested, and its gain and bias were accurately measured before it was put on the satellite. This is called pre-launch calibration. However, nothing is perfect, after the sensors is launched, the sensor gain and bias may change. In remote sensing, we called it sensor degradation. To trace the change of sensors on board, on-board calibration is needed. Landsat 5: on-board there are three tungsten lights whose intensity is very stable. Each light can be turned on/off. With three lights on board, we can calibrate the gains and offset frequently. How can we calibrate the gain and bias in Figure 1 with the three lights? Over the years, the sensors on-board Landsat five have been found to be drifting with time. In the meantime, scientists found that the Internal Calibration light was not constant, indicating the pre-launch sensor gain and bias do not apply with time. Scientists have been constantly monitoring the change in the gain and bias of Landsat 5 sensor. The most recent document recording the sensor gain and bias with is can be found in http://landsat.usgs.gov. In order to use the most recent sensor gain and bias, the sensor gain and bias produced earlier needs to be undone. L*new ( ref DN cal ref 3) / Gnew However, we may not have αref and βref. We will rely on a simple correction: L*new ( L*old )Gold / Gnew Where Gold is provided by USGS in a look-up-table and Gnew can be calculated based on Chander et al., 2007. Landsat 7: on-board there are two tungsten lights and a blackbody and a shutter flag. Shutter flag is used to block the external light source during internal calibration. Similar to the three tungsten lights for Landsat 5, they are used to calibrate the gains and offset frequently. The blackbody is set at temperature 30, 37 and 46oC to calibrate the thermal channels. Landsat 7 ETM+ sensors have been proven to be very stable since its launch. No sensor degradation has been found! Ground monitoring: In addition to the on-board calibration, there are a group of scientists who used some well defined ground feature whose surface reflectance is known and stable. These objects are used to monitor satellite performance. Atmosphere Correction: Remote Sensing Signals Figure 2 source of energy at the target surface and at the sensor Solar energy arrived on the target ground surface consists of two components: direct and diffuse solar radiation. The direct solar radiation on the ground is E 0 cos( z )T where E0 is solar constant, z is solar zenith angle, and Tz is the atmospheric transmissivity in the solar direction and can be estimated as Tz e cos( z ) Assuming the surface reflectance s, the amount of energy leaving the surface would be s [ E0 cos( z )Tz Edown ] The energy leaving the surface will be attenuated again before reaching the satellite sensor. In addition, the sensor will also receive path radiance that is scattered directly from the atmosphere to the sensor. Therefore, the radiance received at the satellite is Lsat s [ E0 cos( z )Tz Edown ]Tv L path where Lpath is the path radiance, and Tv is the atmosphere transmisssivity in the sensor direction, and can be estimated as Tv e cos( v ) Solving for the surface reflectance s, we have s ( Lsat Lpath ) Tv [ E0 cos( z )Tz Edown ] where Lsat=GL+B is at-satellite radiance (he sensor degradation effects gets in here). To correct for atmospheric effects, we need to know the path radiance, aerosol optical depth and the zenith angles from both sun and sensor directions. If we assume Tz=Tv=1.0, Lpath=0, Edown=0, the reflectance is called apparent reflectance (at satellite reflectance). * Lsat E0 cos( z ) The correct for the atmosphere effect, we need to understand how solar radiation interacts with the atmosphere. Scattering: Rayleigh Scattering: occurs when solar radiation interacts with atmospheric molecules and other tiny particles that are much smaller in diameter than the wavelength of the interacting radiation. It is strong in the blue region of the solar spectrum, thus the sky looks blue during clear days. Mie Scattering: occurs when solar radiation interacts with atmospheric particles whose diameters are essentially equal to the wavelength of solar radiation. Absorption: The spectral ranges of remote sensing are always carefully chosen to avoid atmospheric absorption. Therefore, it is less of a problem than scattering to remotely sensed imagery. Extinction Cross Section r 2Qext ( , r ) where Qext(, r) is nondimensional efficiency factor with values in [0,4]. Volume Extinction Coefficient (Ke) K e (r )n(r )dr 0 r r r Optical Depth (Thickness): TOA ( z ) K e ( z )dz z (z) z 0 Atmospheric Transmissivity T ( z ) e ( z ) / cos( z ) where z is the solar zenith angle.