Learning / Height of ambiguity / Kirishima

The volcano grew. The map did not.

In 2011 lava filled the Shinmoedake crater on Kirishima, in southern Japan. An elevation model made in 2000 still shows the old, empty crater. Use that model to remove topography from an interferogram and the missing lava comes back as fringes. Here you can predict them, and then check the prediction against real Sentinel-1 data.

What changed on the volcano

Shinmoedake erupted in January 2011 and a lava dome grew until it filled most of the crater floor (Earth, Planets and Space, 2023). Two global elevation models sit on either side of that event. NASADEM comes from the Shuttle Radar Topography Mission of February 2000, before the dome. The Copernicus DEM comes from TanDEM-X data acquired between 2011 and 2015, after it. Subtract one from the other and the crater stands out: the newer model is higher by up to about 100 m.

Interferometry turns a height error into phase. If the model used to remove the topography is wrong by Δh, the interferogram keeps a residual

φ_DEM = 4π B_⊥ Δh / (λ R sin θ) = 2π Δh / h_a

so the error leaves Δh/h_a fringes. The residual grows with the perpendicular baseline B_⊥ and vanishes when B_⊥ is zero. That dependence on B_⊥ is how you tell a DEM error apart from ground motion, which does not depend on B_⊥ at all.

Explore

View Radar for your prediction Perpendicular baseline B_⊥

h_a

crater fringes

Move over the image to read a pixel.

Geocoded, north up. Sentinel-1 descending pass: flying south-southwest, looking west.

The real experiment

We took two pairs of Sentinel-1 images over Kirishima and processed each pair twice with the open-source ISCE2 software, changing only the elevation model used to remove the topography. The pair of 2 and 14 September 2026 has B_⊥ = −118 m. The pair of 16 and 28 July 2026 has B_⊥ = −1.4 m and serves as the control: at that baseline even a 100 m error should leave almost no phase. Subtracting the two runs of a pair cancels everything they share (ground motion, atmosphere, noise) and leaves only the phase of the DEM error. Open the three "Sep" tabs and the "Jul" tab above to see each step.

Dots: the measured phase difference between the two runs, averaged over all coherent pixels (coherence above 0.4) in 5 m bins of height error. Lines: the prediction 2πΔh/h_a from the processor's own geometry. The dashed gray line follows your baseline slider (Sentinel-1 geometry). The sign of the phase follows the sign of B_⊥, which is negative for both of these pairs; the slider line uses the same sign.

Try this

Before you open the September tabs, use "Your prediction" with Sentinel-1 at B_⊥ = 118 m. How many fringes should the crater show? Then open "Sep: difference" and compare.
Compare "Sep: NASADEM" with "Sep: Copernicus" in the crater view. Where do the two differ, and where do they look the same? The ring of color around the crater appears in both: what does that tell you about its cause?
Why does the July pair show nothing in the crater, even though the elevation model is just as wrong?
Switch your prediction to NISAR. What baseline would NISAR need to show the same crater signal as Sentinel-1 at 118 m? What does that mean for NISAR pairs processed with an old elevation model?
Look at the coherence. The crater stays coherent over 12 days while the forested flanks do not. Which part of the chart would be missing if the crater had decorrelated?

How it was made

Sentinel-1D, descending track 163, sub-swath IW2, bursts 348849 to 348851, VV polarization, assembled from ASF burst products with burst2safe. Precise orbits (POEORB) for 16 July, 28 July and 2 September; restituted orbits (RESORB) for 14 September, because precise orbits were not yet published. ISCE2 topsApp with 7 × 2 looks and enhanced spectral diversity; no unwrapping. Both elevation models were converted to heights above the WGS84 ellipsoid with the EGM96 (NASADEM) and EGM2008 (Copernicus) geoid models before processing. The difference images are the product of one run with the complex conjugate of the other, averaged over 5 × 5 pixels. Fitting the September difference against Δh gives h_a = 127 m against 131 m predicted.

Rosen, P.A., et al. (2000). Synthetic aperture radar interferometry. Proceedings of the IEEE 88(3), 333–382. doi:10.1109/5.838084
Farr, T.G., et al. (2007). The Shuttle Radar Topography Mission. Reviews of Geophysics 45, RG2004. doi:10.1029/2005RG000183
Rosen, P.A., Gurrola, E., Sacco, G.F., Zebker, H. (2012). The InSAR Scientific Computing Environment. EUSAR 2012. ISCE2 on GitHub
Companion page: Height of ambiguity simulator