Thermal expansion and contraction of urban ground and infrastructure from InSAR
Seasonal and diurnal temperature swings expand concrete and masonry by several millimetres, producing InSAR signals that mimic structural settlement. Separating thermoelastic deformation from genuine subsidence requires careful regression against surface temperature records.
Sensors
- COSMO-SkyMed (X-band SAR): 3 m spotlight and 15 m stripmap modes; X-band (9.6 GHz) produces dense persistent-scatterer networks on metal and concrete surfaces in cities, with revisit of 1–4 days from the four-satellite constellation. High coherence on man-made structures makes it the preferred sensor for urban thermoelastic studies.
- TerraSAR-X / TanDEM-X (X-band SAR): Spotlight mode achieves 1–3 m resolution; staring-spotlight reaches sub-metre. Revisit is approximately 11 days for a single satellite, shorter with TanDEM-X in tandem. Phase stability on corner reflectors and trihedral structures supports millimetre-level displacement time-series.
- Sentinel-1 (C-band SAR): 6-day repeat at mid-latitudes with two satellites; 5 × 20 m IW mode resolution. C-band (5.4 GHz) is more susceptible to vegetation and atmospheric decorrelation than X-band in dense urban cores, but free and systematic acquisition makes it practical for city-scale screening.
- Landsat 8 / 9 TIRS: Thermal infrared bands 10 and 11 at 100 m native resolution (resampled to 30 m in products); 16-day repeat per satellite, 8-day combined. Provides land surface temperature (LST) time-series used as the regression covariate to isolate thermoelastic displacement from secular trends.
- ECMWF ERA5 reanalysis (temperature): Hourly 2 m air temperature and surface skin temperature at approximately 31 km grid spacing globally. Fills temporal gaps between satellite thermal passes and enables diurnal thermoelastic modelling where Landsat revisit is insufficient.
What a concrete city does when the temperature changes
Steel-reinforced concrete has a linear thermal expansion coefficient of roughly 10–12 microstrain per degree Celsius. A bridge deck or rooftop slab experiencing a 30 °C seasonal swing will expand or contract by approximately 0.3–0.4 mm per metre of span. Across a large structure, that accumulates to several millimetres of apparent vertical displacement, which sits squarely within the detection range of spaceborne InSAR.
The signal is periodic. It follows the annual temperature cycle and, for structures with low thermal mass, even the diurnal cycle. In an InSAR time-series, this periodicity appears as a sinusoidal oscillation superimposed on whatever long-term trend the ground is actually following. If an analyst ignores it, a building that is thermally cycling but structurally sound can be misclassified as settling at several millimetres per year. That misclassification has consequences: unnecessary engineering inspections, false alarms to regulators, or, more dangerously, a genuine settlement signal masked by a dominant thermal component that was never removed.
Why X-band is the right tool, and where it falls short
X-band SAR at 9.6 GHz has a wavelength of roughly 3.1 cm. One full phase cycle corresponds to a line-of-sight displacement of about 1.55 cm, giving finer displacement sensitivity per fringe than C-band (5.6 cm wavelength) or L-band (23.6 cm). More importantly, X-band backscatter from metal fixtures, concrete edges and exposed rebar produces extremely stable persistent scatterers (PS) in urban environments. Studies using TerraSAR-X and COSMO-SkyMed have recovered PS densities exceeding 1,000 points per square kilometre in dense city centres, sufficient to resolve displacement gradients across individual structures.
The limits are real. X-band coherence degrades rapidly over vegetated surfaces, parks and unpaved ground, so the method works on built fabric and not on the green spaces between it. Atmospheric phase delay, particularly from water vapour, can introduce apparent displacements of several millimetres per acquisition and must be corrected using ERA5 or GNSS-derived zenith wet delay estimates before any thermoelastic regression is meaningful. X-band archives also tend to be shorter and less systematic than Sentinel-1, which constrains the length of the temperature time-series available for regression.
The regression method: separating heat from harm
The standard approach fits a linear model to the InSAR displacement time-series with two components: a secular trend (millimetres per year, representing genuine subsidence or uplift) and a thermal term proportional to land surface temperature or air temperature at the time of each acquisition. The thermal sensitivity coefficient, expressed in mm per °C, is estimated per persistent scatterer. Structures with high thermal sensitivity and low secular trend are flagged as thermoelastic; those with high secular trend and low thermal sensitivity are candidates for genuine ground motion investigation.
Landsat TIRS provides the temperature covariate at 16-day intervals, which aligns reasonably well with TerraSAR-X revisit. For denser time-series from COSMO-SkyMed, ERA5 hourly skin temperature interpolated to each SAR acquisition time is the practical alternative. The regression is not a single-pass calculation. Outlier acquisitions affected by unresolved atmospheric artefacts or snow cover on reflective surfaces must be identified and excluded, otherwise the thermal coefficient estimate is biased. Published studies on European cities have reported thermoelastic sensitivities of 0.1–0.5 mm per °C for reinforced concrete structures, consistent with the physical expansion coefficient applied over typical urban slab geometries.
One honest caveat: the regression assumes the thermal and secular components are separable and stationary. In a building undergoing active foundation settlement, the settlement rate itself may vary seasonally due to groundwater changes, producing a signal that correlates partly with temperature without being thermoelastic. Disentangling these cases requires ancillary data, typically piezometer records or groundwater-level time-series, and cannot be resolved from satellite data alone.
Where misclassification causes the most damage
The risk is asymmetric. Calling a thermoelastic signal genuine settlement wastes inspection budgets and can trigger unwarranted structural interventions. Missing genuine settlement because it is buried under a large thermal component is the more serious failure mode, particularly for infrastructure on compressible fill or in areas of known groundwater extraction.
Critical transport nodes are a particular concern. A railway viaduct or metro tunnel box in a city centre will show both thermoelastic cycling and, potentially, slow differential settlement from adjacent construction or dewatering. The two signals can be of similar amplitude. Without the temperature regression step, a time-series that looks like a clean 3 mm per year subsidence trend might actually be a 1.5 mm per year secular settlement plus a 1.5 mm amplitude annual thermal oscillation that happens to be sampled at a phase that mimics monotonic decline. The error is not obvious from the displacement plot alone.
Heritage structures present a related problem. Masonry and stone have lower thermal expansion coefficients than reinforced concrete, roughly 5–9 microstrain per °C, but they also have lower structural redundancy. A small genuine settlement signal matters more, which places higher demands on the quality of the thermal correction.
Practical limits and what the method cannot tell you
The minimum detectable secular displacement rate after thermoelastic correction depends on time-series length, PS density and atmospheric correction quality. With two or more years of X-band data and good atmospheric correction, rates below 1 mm per year can be estimated, but the uncertainty on individual PS points is typically 0.5–1 mm per year at one sigma. Shorter archives or noisier atmospheric conditions push that floor higher.
The method produces line-of-sight displacement, not vertical. Converting to vertical requires an assumption about the horizontal displacement component, which is usually small for thermoelastic effects on buildings but non-trivial for long linear infrastructure such as bridges, where horizontal expansion along the deck axis projects differently into ascending and descending geometries. Combining ascending and descending passes from the same sensor resolves this, at the cost of requiring two coherent acquisition stacks over the same area.
Satellize applies this regression workflow as part of its urban ground-motion analytics, combining open Sentinel-1 data for city-scale screening with commercial X-band tasking where structure-level resolution is required.
Typical figures
| SAR spatial resolution (X-band) | 1–3 m (TerraSAR-X/COSMO-SkyMed spotlight); 3–15 m stripmap |
| SAR spatial resolution (C-band, Sentinel-1) | 5 × 20 m (IW mode, range × azimuth) |
| Minimum detectable displacement rate (after thermoelastic correction) | Approximately 0.5–1 mm/yr at 1-sigma with 2+ years of X-band PS-InSAR |
| Thermoelastic sensitivity range (published studies) | 0.1–0.5 mm per °C for reinforced concrete urban structures |
| Temperature covariate: Landsat TIRS revisit | 8 days (Landsat 8 + 9 combined); 100 m native thermal resolution |
| Temperature covariate: ERA5 temporal resolution | Hourly; ~31 km spatial grid |
| X-band archive depth | COSMO-SkyMed from 2007; TerraSAR-X from 2007 (tasked, not systematic) |
| Sentinel-1 archive depth | From April 2014 (Sentinel-1A); systematic global acquisition |
| PS density (X-band, dense urban) | Typically 500–2,000 points/km² in built-up areas; near zero over vegetation |
| Delivery formats | GeoTIFF displacement maps, CSV/Shapefile PS point clouds, time-series JSON, PDF technical report |
Analytics Satellize can run
| Thermoelastic sensitivity map | Linear regression of PS-InSAR displacement time-series against LST (Landsat TIRS) or ERA5 skin temperature per scatterer point | GeoTIFF and Shapefile of thermal sensitivity coefficient (mm/°C) per PS point, city-wide |
| Secular subsidence rate map (thermally corrected) | Residual trend extraction after thermoelastic component removal from PS-InSAR time-series | GeoTIFF of annual displacement rate (mm/yr) with per-point uncertainty estimates |
| Structure-level displacement time-series | PS-InSAR with X-band (COSMO-SkyMed or TerraSAR-X) on individual buildings or bridge spans; ascending/descending decomposition for vertical/horizontal separation | CSV time-series per structure with fitted secular trend, thermal coefficient and residual; suitable for engineering review |
| Misclassification risk flag | Statistical test comparing amplitude of thermoelastic oscillation to secular trend; flags structures where thermal signal exceeds 50% of total displacement variance | Alert layer (GIS polygon or point) identifying structures requiring ancillary ground-truth before settlement classification |
| Atmospheric correction quality report | ERA5 zenith wet delay differencing between acquisition dates; comparison against available GNSS tropospheric estimates | Per-acquisition correction quality score appended to time-series metadata; PDF summary |
| City-scale screening (Sentinel-1 baseline) | SBAS or PS-InSAR on open Sentinel-1 IW stack; coarse thermoelastic regression using ERA5 for priority-area identification before commercial X-band tasking | Displacement rate GeoTIFF at 20 m posting; ranked list of anomalous zones for follow-on high-resolution analysis |
Who does the work
We can get this done for you. Satellize runs its own analyst desk and a strong science team. You do not buy a data feed and work out what it means; our people source the imagery, run the analysis described on this page, and hand you the answer with its confidence limits stated. Discuss this requirement.