Umbra X-band · COP30 topography · slant-range simulation
A SAR image is not a map of the ground. It is a map of range, and a GEC product converts range to position by pretending the whole scene sits at one height. Everything that is not at that height lands somewhere it isn't.
The product is geocoded onto an ellipsoid, not onto the terrain.
Umbra's sar:product_type = GEC means Geocoded Ellipsoid Corrected:
every pixel is placed as though the ground were a single constant-height surface above
the ellipsoid. You can see the assumption in the metadata — each scene's footprint
polygon carries one elevation for all four corners, and that is the height the
geocoding assumed.
Click anywhere on the image. The tool reads the COP30 height there and works out where that point appears in this GEC product.
A radar measures the time for an echo to return, which gives slant range.
For a point at ground-range g and height h, seen at
incidence θ:
Height shortens the range. Two points at the same range are indistinguishable to the radar, however far apart they are on the ground.
To turn range back into a map position, the GEC processor must assume a height.
It assumes one constant value, h_ref, for the whole scene, and solves
Subtract the two and the error falls out. This single line is the whole exercise:
Ground above the reference plane is pushed toward the sensor; ground below is pushed away. Nothing about the radar is wrong — the range is exact. The map position is wrong because the height was guessed.
Push the same idea further. If a slope facing the radar is steeper than the incidence angle, the top of it reaches a shorter range than the bottom, so it images before the bottom does — the slope appears inside out. That is layover:
On the far side, ground that falls away faster than the grazing angle never gets illuminated at all — shadow:
Both thresholds depend only on the acquisition, which is why the same mountain changes character completely between the passes in the strip above.
SAR is the real amplitude, already geocoded the flawed way. Simulated is what the geometry predicts from COP30 alone — no radar involved, just the terrain pushed through this acquisition's look vector. Hillshade is the topography lit from exactly the direction and elevation the radar illuminated it, which is the fairest optical-style comparison.
Flip between SAR and Simulated on a steep scene and the bright folds and dark shadows should fall in the same places. Where they don't, you are looking at something the terrain model doesn't know about — vegetation, buildings, or change since COP30 was made.
The simulation uses 30 m COP30, so it cannot resolve anything finer than about 60 m. It is a geometry model, not a backscatter model.