GOLD STANDARD · REMOTE SENSING · HOW X WORKS
Find the decision hidden inside the model
A shaded mountain pixel can still be lit by bright snow, rock or vegetation on the opposite slope. Terrain-reflected irradiance travels sideways through the valley, so local slope and sky view alone cannot close the radiative budget.
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Orient terrain interreflection
Calculate a first-order contribution
Audit view factors and assumptions
Transfer across scenes
Use evidence and next routes
CHAPTER 1 OF 12 · ORIENT THE RADIATION
1. A neighboring slope can become a light source
Direct sunlight reaches a target from the Sun. Diffuse skylight arrives after atmospheric scattering. Terrain-reflected irradiance reaches the target after radiation strikes another surface and is reflected across the landscape.
This third component can matter in deep valleys, snow-covered mountains and shadowed slopes. It changes with the illumination and reflectance of visible neighbors, not only the target’s local slope. Treating every shaded pixel as if it receives the same diffuse fraction misses that geometry.
CHAPTER 2 OF 12 · ORIENT THE RADIATION
2. Separate sky view from terrain view
The sky-view factor measures the weighted fraction of the overlying hemisphere open to the sky. The terrain-view factor is the complementary weighted fraction occupied by surrounding land under a compatible definition. Direction and surface tilt matter.
A terrain-view factor does not specify how bright the terrain is. It is geometric coupling. The radiative contribution also needs neighboring irradiance, reflectance and angular scattering. A dark forest and bright snowfield can occupy the same solid angle but illuminate the target very differently.
CHAPTER 3 OF 12 · CALCULATE INTERREFLECTION
3. Write a first-order irradiance model
For an illustrative Lambertian neighbor, approximate terrain-reflected irradiance at target i as Eterr,i≈Σj Fij ρj Ej, where Fij is a view factor from target i to terrain element j, ρj is its reflectance and Ej is irradiance incident on j.
The sum represents one reflection. A physically careful implementation also handles distance, orientation, occlusion, projected area and reciprocity consistently. Atmosphere between slopes may matter over long paths.
CHAPTER 4 OF 12 · CALCULATE INTERREFLECTION
4. Work a two-slope valley example
Suppose a shaded target sees an opposite bright slope with view factor F=0.25. That slope receives 600 W m−2 in the band-integrated illustration and has reflectance 0.50. The first-order contribution is 0.25×0.50×600=75 W m−2.
If diffuse sky contributes 90 W m−2 and direct beam is zero, terrain reflection supplies 45% of the target’s 165 W m−2 first-order total. Ignoring it would make retrieved reflectance too high because too little incident energy was assumed.
| Component | Worked value | Reason |
|---|---|---|
| Direct beam | 0 W m−2 | Target is cast-shadowed |
| Diffuse sky | 90 W m−2 | Visible sky contribution |
| Terrain-reflected | 75 W m−2 | FρE from opposite slope |
| First-order total | 165 W m−2 | Incident energy estimate |
CHAPTER 5 OF 12 · CALCULATE INTERREFLECTION
5. Extend the model to several terrain classes
Let the target view three classes: snow, rock and forest with factors 0.10, 0.20 and 0.15. Their contributions must be evaluated with band-specific reflectance and incident irradiance; the remaining hemisphere may be sky or occluded under the chosen discretisation.
A single average adjacent reflectance can be useful for a first pass but hides spectral mixing. Bright snow may dominate visible wavelengths, while vegetation and rock change differently across near-infrared and shortwave infrared bands.
CHAPTER 6 OF 12 · AUDIT THE GEOMETRY
6. Know when multiple reflections matter
Radiation reflected from a neighbor can strike another slope and return again. In a high-albedo enclosed valley, this coupling can require an iterative radiosity or three-dimensional radiative-transfer solution rather than one reflection.
A matrix form writes outgoing flux as emitted or directly reflected input plus reflectance times view-factor coupling. Iteration should conserve energy under the model. If reflectance and enclosure make the series converge slowly, a first-order correction is not an uncertainty-free shortcut.
| Approximation | Keeps | Main limit |
|---|---|---|
| Local cosine | Direct beam only | No shadow or neighbor light |
| Sky-view model | Diffuse sky fraction | No terrain brightness |
| First-order terrain term | One neighbor reflection | No repeated coupling |
| 3-D/radiosity model | Multiple reflections | Higher data and computation needs |
CHAPTER 7 OF 12 · AUDIT THE GEOMETRY
7. Treat the DEM and land-cover map as coupled inputs
View factors depend on elevation, resolution, surface orientation and occlusion. Neighbor reflectance depends on classification, season, snow state and atmospheric correction. Misregistration between the DEM and image can pair the wrong slope geometry with the wrong material.
Run sensitivity checks for DEM resolution, search radius, land-cover reflectance and shadow boundaries. Report whether the surface is bare-earth terrain or a digital surface including vegetation and buildings.
CHAPTER 8 OF 12 · TRANSFER AND VALIDATE
8. Transfer from optical reflectance to snow energy balance
For snowmelt modelling, terrain-reflected shortwave radiation can add energy to shaded snow. The stable mechanism is visible neighboring terrain redirecting radiation. The changing output is energy balance rather than satellite surface reflectance.
The changed-context check includes spectral albedo, solar path, changing snow cover and thermal longwave exchange. A broadband shortwave view factor cannot simply substitute for longwave temperature-dependent emission.
CHAPTER 9 OF 12 · TRANSFER AND VALIDATE
9. Separate terrain interreflection from atmospheric adjacency
Atmospheric adjacency occurs when photons from nearby bright surfaces scatter in the atmosphere into the sensor’s line of sight. Terrain-reflected irradiance first changes the light incident on the target surface. Both are neighbor effects, but they occur on different path segments.
A correction can need both mechanisms. Diagnose them with geometry, atmosphere and scale: terrain interreflection follows mutual visibility and slope illumination, while atmospheric adjacency depends strongly on aerosol scattering and sensor point-spread behavior.
CHAPTER 10 OF 12 · TRANSFER AND VALIDATE
10. Validate in more than one valley and Sun position
Compare modeled irradiance with field radiometers, three-dimensional simulations or high-quality reference retrievals across sunlit and shadowed targets. One valley can hide compensating errors in albedo and view factors.
Repeat across solar elevation, azimuth and surface state. Preserve uncertainty by component. A visually smooth corrected image is not validation if class reflectance or spectral shape becomes implausible.
CHAPTER 11 OF 12 · CHECK AND CONTINUE
11. Questions readers often ask
Is terrain-view factor always one minus sky-view factor?
Only under compatible hemispheric definitions and complete partitioning. Different weighting, horizons, surface tilt or discretisation can make a casual subtraction inconsistent.
Can a dark target receive strong terrain-reflected irradiance?
Yes. Incident energy depends on visible neighbors and their illumination. The target’s own reflectance controls how much of that energy it later reflects toward the sensor.
CHAPTER 12 OF 12 · CHECK AND CONTINUE
12. Evidence, connected routes and the next check
Schulmann, Katurji and Zawar-Reza’s surface-irradiance modelling study separates diffuse and terrain-reflected light in topographic correction. Dozier and Frew’s terrain-parameter paper develops rapid sky and terrain view-factor calculations from elevation data.
Continue through terrain shadows and sky-view correction, topographic normalisation and C-correction, and atmospheric correction and adjacency effects. The next check is to map which bright terrain cells are mutually visible from each shaded validation target.
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