The observed backscatter can deviate from the expected theoretical backscatter because of the topography of the Earth's surface.
Topographical mechanisms modulating the backscatter with respect to the azimuth angle are:
Incidence angle $\theta$ vs. local incidence angle $\theta_{L}$:
Although the $\sigma^0$ measurement is recorded at the nominal incidence angle $\theta$, the angle determining the backscatter is actually the local incidence angle $\theta_{L}$ because of the local slope of the surface.
possibility of double or multiple "bounce" interaction
backscatter in certain viewing directions from a few point-like targets becomes so high that it can affect the backscatter response over the entire footprint!
e.g. urban areas laid out along a rectangular grid
size of the sloping targets ≈ footprint size
backscattered waves are subject to constructive interference at certain incidence angles
e.g. reflections from surface ripples on sand dunes
Mean of the differences between fore- and aft-beam taken for ascending overpass (top) and descending overpass (bottom)
method developed by Bartalis et al. (2006)
statistically expected backscatter value of a target is derived from historically recorded data
azimuthal anisotropy can vary depending on the incidence angle and with the season of the years
number of possible azimuth-incidence combinations:
6 possible azimuth directions
19 possible incidence angles
⇒ 114 possible combinations
Enough data must be available
$\delta$ = expected backscatter - measured backscatter
Backscatter measurements can be normalized by adding/subtracting the bias $\delta$
Including seasonal changes: $114\;*\;n$ azimuth-incidence-time combinations ($n$...number of chosen periods)
Second order polynomial fitted to the backscatter versus incidence angle relationship, separately for each of the six azimuth angles
Polynomial irrespective of azimuth fitted to all measurements, respresenting the expected backscatter of a target as a function of the incidence angle
⇒ the required azimuthal normalisation biases can be calculated at any incidence angle as the difference between each of the six azimuth polynomials and the seventh, cumulative polynomial