{"generated":"2026-09-15T02:40:57Z","headline":"Drawn to scale, the heat a data centre adds to its surroundings falls below what any instrument can see about 1.3 km from a 130 MW site, and about 3.5 km from a gigawatt-scale one \u2014 and that is the physically impossible best case, before wind or evaporation take most of the heat away.","law":{"expression":"dT(r) = 0.079 K x (4.5 km / r)^2 x (P / 130 MW)","anchor":{"delta_k":0.079,"km":4.5,"mw":130.0},"second_anchor":{"delta_k":0.016,"km":10.0},"inverse_square_agreement_pct":0.02,"assumptions":"Every watt released at ground level, no wind carrying heat away, nothing leaving as water vapour. None of these is true; all of them make the number LARGER. This is a ceiling, not an estimate.","valid_from_km":1.0,"validity_note":"A campus is roughly 250 m across, so treating it as a point is only fair beyond about a kilometre. Closer in the formula runs away \u2014 it would claim 6.4 K at 500 m \u2014 so those distances are marked invalid and not published rather than printed in our own favour."},"rings_130mw":[{"km":1,"delta_k":1.5998,"valid":true,"detectable_by_any":true},{"km":1.5,"delta_k":0.711,"valid":true,"detectable_by_any":true},{"km":2,"delta_k":0.3999,"valid":true,"detectable_by_any":false},{"km":3,"delta_k":0.1777,"valid":true,"detectable_by_any":false},{"km":4.5,"delta_k":0.079,"valid":true,"detectable_by_any":false},{"km":6,"delta_k":0.0444,"valid":true,"detectable_by_any":false},{"km":8,"delta_k":0.025,"valid":true,"detectable_by_any":false},{"km":10,"delta_k":0.016,"valid":true,"detectable_by_any":false},{"km":15,"delta_k":0.0071,"valid":true,"detectable_by_any":false},{"km":20,"delta_k":0.004,"valid":true,"detectable_by_any":false}],"rings_1000mw":[{"km":1,"delta_k":12.3058,"valid":true},{"km":1.5,"delta_k":5.4692,"valid":true},{"km":2,"delta_k":3.0764,"valid":true},{"km":3,"delta_k":1.3673,"valid":true},{"km":4.5,"delta_k":0.6077,"valid":true},{"km":6,"delta_k":0.3418,"valid":true},{"km":8,"delta_k":0.1923,"valid":true},{"km":10,"delta_k":0.1231,"valid":true},{"km":15,"delta_k":0.0547,"valid":true},{"km":20,"delta_k":0.0308,"valid":true}],"instruments":[{"name":"Satellite land-surface temperature (MODIS, Landsat, ECOSTRESS)","floor_k":1.0,"why":"Per-pixel retrieval accuracy is about a kelvin at best, before any question of how often the sky is clear.","crossover_km_130mw":1.26,"crossover_km_1000mw":3.51},{"name":"Repeated satellite comparison of one campus against its surroundings","floor_k":0.5,"why":"WAPR's own environmental review found a per-campus systematic offset of roughly half a kelvin to one and a half, and that offset does NOT shrink by averaging more observations \u2014 it is a property of the site, not of the sample.","crossover_km_130mw":1.79,"crossover_km_1000mw":4.96},{"name":"Weather station or reanalysis cell","floor_k":0.5,"why":"A thermometer resolves far finer than this, but the nearest station is rarely the right place and a reanalysis cell is 9 to 28 km across \u2014 bigger than the whole effect it would be asked to find.","crossover_km_130mw":1.79,"crossover_km_1000mw":4.96}],"plain":"People expect a data centre to warm the land around it, and to see that heat spreading out on a map. It does add heat \u2014 but spread over the distances a map would show, it is a few hundredths of a degree. Even granting the physically impossible best case, the warming drops below what satellites or weather stations can detect a kilometre or so from a mid-sized site, and a few kilometres from the very largest. So there is no plume to draw. This picture is the honest version of that question: the effect at true size, next to the instruments that would have to find it.","what_survives":"Two real measurements sit either side of this dead end. Inside the fence, a site's own night-time temperature can be compared with its own past, using ordinary warehouses as a control \u2014 that is a genuine instrument. And water, not heat, is where the measurable effect lives: a 100 MW campus evaporates roughly 1.5 to 2 million litres a day, and that comes from permits and utility records rather than pixels.","caveats":["This is a physical bound computed from stated assumptions, not a measurement of any particular site. It says what the effect CANNOT exceed.","A published paper reporting +1.0 C at 4.5 km is about thirteen times this ceiling. The measurement is not the problem; the attribution is, because the surrounding land was developing too and the study carried no spatial controls.","None of this concerns power stations. A generating station's cooling water is a real, permitted and metered thermal discharge \u2014 a different object with a different mechanism, which is why WAPR keeps plants and campuses in separate layers.","Nothing here rules out local effects at the fence line, where the formula is not published: hot exhaust, roof surfaces and cooling yards are real and are exactly what the within-site night-time comparison is for."],"source":"WAPR environmental research synthesis (datacenter-environmental-layer): ground-level release bound, 0.079 K at 4.5 km and 0.016 K at 10 km for a 130 MW campus; per-campus systematic offset that does not shrink with sample size. Computed here, not asserted."}