Atmospheric correction

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Atmospheric Correction

Remote sensing from satellite or airborne platforms of land or sea surfaces in the visible and near infrared is strongly affected by the presence of the atmosphere along the path from Sun to Target (surface) to Sensor (Vermote et al., 1997). Atmospheric correction (or compensation) of spectral imagery refers to the retrieval of surface reflectance spectra from measured radiances (Matthewa et al., 2000).

The necessary for atmospheric correction depends on the objectives of the analysis, for instance when multisensor or multidate images are bein classified, or where the aim of pattern recognition is to identify land cover change over time (Tso and Mather, 2009).

The magnitude of the electromagnetic energy in the visible and near-infrared region of the spectrum that is detected by a sensor above the atmosphere is dependent on the magnitude of incoming solar energy (irradiance), which is attenuated by the process of atmospheric absorption, and by the reflectance characteristics of the ground surface. For this reason, energy received by the sensor is a function of incident energy (path radiance), and atmospheric absorption (Tso and Mather, 2009). The value recorded for each pixel in a remotely sensed image is a function of the sensor-detected radiance, Tso and Mather (2009) give the fallowing approximation:

 \[\]            (eq.1)

Where: Lapp denotes the apparent radiance received by the sensor, Lp, is the path radiance, ρ is the target reflectance (%), T atmospheric transmittance (%), and E is the solar irradiance on the target.

Radiance is expressed in units of Wm-2sr-1μm-1 , and irradiance is expressed in th units of Wm-2μm-1. As these two terms are not expressed in equivalent units, solar irradiance is converted into equivalent solar radiance by introducing the term π.

Procedure for atmospheric correction

The procedure to obtain estimates of the ground target reflectance involves three steps. The first step is to converting the pixel value to radiance, in case of Rapideye images the equation is (RapidEye Standard Image Product Specifications , 2010):

(eq.2)

Where Ai is the radiometric scale factor of band i. The resulting value is the Top of Atmosphere (TOA) radiance of that pixel in Watts per steradina per square meter (Wm-2sr-1μm-1).

For Rapideye images Ai is 1/100 (RapidEye Standard Image Product Specifications, 2010, Haque et al., 2010).

The second step, conversion from apparent radiance Lapp to apparent reflectance ρ°, is based on the observation that in case of 100% reflectance, the radiance measured by the sensor is the result of multiplication of equivalent solar radiance (E/ π), the cosine of solar zenith angle (cos(θs)), and the Earth-to-sun distance multiplicative factor d (Kowalik and March, 1982 cited by Tso and Mather, 2009). The factor d is measured in astronomical units (au) and is described further below. One au is equal to the average Earth-to-sun distance. About January 3, at perihelion, the Earth-to-sun distance is approximately 0.983 au, and on July 5, at aphelion, the Earth-to-sun distance is about 1.0167 au. If the required coefficient are known, then the variation in sensor-detected apparent radiance Lapp is caused by the diffrence in reflectance as fallow (Tso and Mather, 2009)

          eq.3

or equivalently,

           eq.4

The value of the solar zenith angle can be retrieved form the image header file. The distance multiplicative factor d is used to compensate for the variation in solar irradiance E caused b y the change in distance between the sun and the Earth. It is obteined form:

  eq.5

However an alternative way to approximate d is given by (Tso and Mather, 2009):

    eq.6

where the term JD denotes the Julian day. The final step is to convert the apparent reflectance to ground target reflectance as fallow (Tso and Mather, 2009):

          eq.7

Where S is spherical albedo, A and B are coefficients obtained after running 5S or 6S model. The model 6S is described in Vermote et al. (1997). However, after Vermote et al. (1997) there are some applications where A, B and S have been obtained and evaluated. In the fallowing link a complete reference is presented: http://modis-sr.ltdri.org/code.html.

To be written and defined:

acquisition of A, B and S parameters

References

Md. Obaidul Haque, Aparajithan Sampath, G. C. 2010. Radiometric & Geometric Assessment of the Datafrom RapidEye Constellation of Satellites. Technical report, U.S. Geological Survey. 24p.m. SPIE Proceeding. Volume 4049 . 10p.

RapidEye AG. RapidEye Standard Image Product Specifications. 2010. RapidEye AG. 54p.

Vermote, Eric; Tan&ré, Didier; Deuzé. Jean Luc;. Herman, Maurice & Morcrette, Jean-Jacques. 1997. Second simulation of the satellite signal in the solar spectrum: An overview. IEEE Transactions on Geoscience and Remote Sensing 35, 675-686.

Tso, Brandt; Mather, Paul M. 2009. Classification Methods for Remotely Sensed Data. Second edition. CRC press. 356p.

Michael W. Matthewa; Steven M. Adler-Golden; Alexander, Berk; Steven C. Richtsmeier; Robert Y. Levine; Lawrence. S. Bernstein; Prabhat. K. Achrya; Gail P. Anderson; Gerriy W. Felde; Michael P. Hoke; Anthony Ratkowski; Hsiao-Hua. Burke; Robert D. Kaiser & David P. Miller. 2000. Status of atmospheric correction using a MODTRAN4-based algorithm.