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The stereoscopic approach:

Fundamental assumptions : Lambertian reflection from the surface. The stereoscopic approach: . The difference between measured radiances at two view-angles can be used as a proxy for relative surface roughness. (1). (3). Fundamentals: .

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The stereoscopic approach:

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  1. Fundamental assumptions: Lambertian reflection from the surface The stereoscopic approach: The difference between measured radiances at two view-angles can be used as a proxy for relative surface roughness

  2. (1) (3) Fundamentals: • For a given pixel, surface-reflected solar irradiance L (Wm-2sr-1) at a given view angle  can be approximated as: • The ratio between L at 1 and L at 2 is then: (2) Isol – incident solar irradiation (Wm-2) Re- surface reflectivity S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction

  3. Can be removed using ‘dark object subtract’ Becomes a multiplicative scaling actor Assuming a laterally ~homogeneous atmosphere at the image scale t(a1) / t(a2) can be regarded as constant for the whole image. (5) Atmospheric effects: • Per pixel, the ratio between at-sensor surface-reflected solar irradiance values L(Wm-2sr-1) at view angles 1 and 2 can be approximated as: (4) Isol – incident solar irradiation (Wm-2) Re- surface reflectivity S- path radiance (Wm-2sr-1) S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction t(a) – atmospheric transmissivity

  4. - can be regarded as a proxy for relative surface roughness between similarly sloping pixels within a single image. • incorporates roughness variations at all sub-pixel scales • is independent of surface composition • fairly insensitive to atmospheric effects 30° Atmospheric transmissivity is a function of path length atmosphere surface Atmospheric effects: Isol – incident solar irradiation (Wm-2) Re- surface reflectivity S- path radiance (Wm-2sr-1) S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction t(a) – atmospheric transmissivity

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