Defending a Twenty-Year Urban Heat Island Claim

The direction is plausible; the number is not defensible.

Problems with top-of-atmosphere brightness temperature:

• It is not surface temperature. It excludes emissivity, and emissivity differs sharply between built-up, bare soil and vegetation. A surface turning from vegetation to concrete changes emissivity, so part of the apparent rise is a surface-type artefact.
• No atmospheric correction: water vapour and aerosol differences between the two dates propagate directly into the retrieved value.
• Cross-sensor mismatch: TM band 6 and TIRS band 10/11 differ in spectral response, calibration and noise; a raw difference mixes sensor change with climate signal.
• TIRS is 100 m and is commonly resampled to 30 m, creating false apparent detail that users then interpret as neighbourhood-scale variation.
• Footprint change is decisive: if the analysis window grew from 180 to 320 km2, the 2023 window contains more rural, cooler pixels, which would bias the comparison downward, or if the core was compared against a shifting background, the sign of the artefact is unpredictable. Either way the boundary must be fixed.

Verdict: report as "consistent with warming, magnitude unquantified" until reprocessed.

Processing chain:

1. Fix the analysis geometry. Define the 2003 municipal boundary as the core zone and keep it identical for both dates. Any change inside that fixed core is the trend; expansion is analysed separately.
2. Surface reflectance for reflective bands, with cloud and shadow masking at both dates.
3. Emissivity from a documented method (NDVI-threshold approach is acceptable if its failure over bare and built surfaces is acknowledged), then land surface temperature retrieval with atmospheric correction using scene-appropriate water vapour, or a single-channel algorithm with stated coefficients.
4. Analyse at 100 m support, not at resampled 30 m, so the reported unit matches the sensor.
5. Match acquisition conditions as closely as possible: same dry season, similar day-of-year and overpass time, similar antecedent rainfall.
6. Cross-sensor check on invariant targets (large water body, deep quarry, stable bare ground); if they differ beyond tolerance, the offset is a correction, not a finding.
7. Report uncertainty on the temperature difference, not just the point value.

Separate the two mechanisms by zoning:

• Core zone (2003 built extent): change here reflects densification, infill and green-cover loss without any change in what the zone contains.
• Expansion ring (2003 boundary to 2023 boundary): change here reflects conversion of rural to urban.
• Report the temperature change for each zone separately. A single city-wide number conflates two different physical processes and two different policy levers.

Remove the regional signal: compute an urban-minus-rural difference using stable rural reference pixels outside both boundaries, present on both dates. Regional warming and synoptic differences affect urban and rural alike; the difference isolates the local effect. Quote both the absolute and the differenced values, since they answer different questions.

Link to green cover honestly: derive vegetation fraction at the same 100 m support for both dates, then examine the change in LST as a function of change in vegetation fraction, ideally with other controls (impervious fraction, building height proxy). This yields an association with a slope and error bars, not proof of causation. State that clearly: attribution to green-cover loss is supported if the core zone shows loss of vegetation co-located with the strongest warming, but advection, albedo and anthropogenic heat are not excluded. Recommend the corporation quote a range and a confidence statement, not 4.2 degrees.