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?
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.
the detector Gain and Offset (Bias)
where
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
or
so that a single gain and bias can be used for each band.
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.
However, we may not have αref and βref. We will rely on a simple correction:
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:
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
where E0 is solar constant, qz is solar zenith angle, and Tz is the atmospheric transmissivity in the solar direction and can be estimated as
Assuming the surface reflectance rs, the amount of energy leaving the surface would be
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
where Lpath is the path radiance, and Tv is the atmosphere transmisssivity in the sensor direction, and can be estimated as
Solving for the surface reflectance rs, we have
where Lsat=G´L+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).
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
where Qext(l, r) is nondimensional
efficiency factor with values in [0,4].
Volume Extinction Coefficient (Ke)
Optical Depth (Thickness):
0
Atmospheric Transmissivity
where qz is the solar zenith angle.