Surface reflectance definitions of ATCOR outputs
Our definitions rely on the original paper by Nicodemus (1977) who compiled the relevant physical quantities systematically. The outputs of atmospheric correction can be described according to the principles below.
Surface Reflectance Outputs of ATCOR (and DROACOR)
Daniel Schläpfer, ReSe Applications LLC
The outputs of atmospheric correction is often simply called ‘surface reflectance’ which is an ambiguous term. Depending on the level of processing, various physical quantities are involved and are to be considered.
1) BRF and BRDF
BRF is defined as a reflectance factor, i.e. the factor you are getting if comparing what you see in a true bidirectional measurement if compared to a perfect 100% Lambertian target. BRDF is a true reflectance (distribution function) which is defined as the relation between reflected radiation to the incoming radiation at one angular configuration. The latter is the base quantity we use for modelling what is happening on the ground and is also the base quantity of atmospheric correction codes as we calculate/simulate the irradiance term to relate it with the measurement for getting a reflectance. In a fully model based physical correction, no white panels comparison is involved in the atmospheric compensation. Thus, the outputs of our software are better called ‘reflectance’ rather than ‘reflectance factors’.
2) Directionality vs. Conical
Theoretically, there are (almost) no directional measurements feasible as every measurement device measures in a cone of it’s FOV – but for practical reasons, the small IFOV of satellite is close to a infinitesimal angle of a directional measurement and in models it can be treated as such, ie. intra-conical variations are not considered. Therefore, using the ‘D’ for measurements seems to be appropriate – this has clearly to be distinguished from the field measurement situation where truly conical instruments are used for spectral data acquisition, what leads to ‘C’ type of quantities.
3) The HDRF
The term ‘HDRF’ is used by Nicodemus for a perfectly hemispheric diffusely illuminated target, and a directional observation. As such, the directional influence of the incident BRDF is to be corrected to get to a true HRDF. This is very hard to achieve and we use semi-empirical models such as the modified Minnaert approach to approximate a HDRF after atmospheric and terrain correction in ATCOR. Schaepman-Strub (1997) used the term differently than Nicodemus: the illumination of their ‘HDRF’ can be arbitrarily distributed due to the sun position and the atmospheric state (what leads to confusion in literature). Such a quantity is not a consistent surface characteristic; in the ATCOR we call that quantity a ‘bottom of atmosphere reflectance’ without referring to the physical definitions to avoid a misconception.
4) Correction or Compensation
The term ‘Atmospheric Correction’ is well established for what we do in our software. In close range remotes sensing, it is often used synonymously to ‘Reflectance Retrieval’. The latter is mostly used if a reference panel is used for reflectance normalization what leds to a reflectance factor as output. In principle, one should rather use the term ‘atmospheric compensation and spectral albedo normalization’ for ATCOR: we don’t do any correction because all inputs should be well calibrated radiances and are already physically correct. The process is rather compensating the correct inputs for atmospheric influences, but not only that – in topographic and BRDF correction, the directional measurements are normalized to a generic spectral albedo (see below).
5) BRDF-Correction
The most consistent quantity you can get after data processing is the BHR (bihemispherical reflectance), sometimes also called the spectral albedo as it is the relation between the hemispherically integrated reflected radiation to a perfectly diffuse irradiance – and it has no angular dependencies. The BHR can be modeled by integrating the true HDRF over the hemisphere under the use of a BRDF model. Nadir normalization is not consistent, as the nadir reflectance depends on the position of the sun and hinders comparability. So, the goal of a complete atmospheric correction for best comparability between data products is to derive BHR values for each pixel – that is what we try to achieve in our BREFCOR model.
NOTE: Bi-Directional has always two directions. Currently, we distinguish between incidence-BRDF (Topographic Cor.) and observer-BRDF correction (BREFCOR).
6) ATCOR outputs
“So, what physical quantiy do I get after ATCOR processing?”:
The result of first order atmospheric correction/compensation is best named ‘bottom of atmosphere reflectance’ and has lots of directional dependencies. If incidence BRDF is considered in topographic correction (ie. using the local solar incidence angle and diffuse irradiance models), the result is close to a true ‘HDRF’. If observer BRDF correction was done, the result would be a BHR (spectral albedo). The specrtral albedo is the only unambigous reflectance quantity to characterize the surface without directional influences; furthermore it equals the reflectance of a Lambertian target and could also be named a ‘Lambertian equivalent’. Only this quantity is well comparable amongst observation situations and to laboratory spectra without further directional adaptions.
Reflectance definitions
Definitions are often confused. Even the often cited main literature is not consistent about the definitions. We try to rely our surface reflectance definitions on the original paper by Nicodemus 1977 who compiled the relevant physical quantities systematically. The above mentioned definitions should be taken into account before starting and during the processing of remote sensing data with ATCOR®.
