Heat Waves Need Dry Soil
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
README.md
# Heat Waves Need Dry Soil **Verdict: partly supported.** Across 45,940 summer days at 20 city sites, a heat day is 30 times more likely over the driest ground than over the wettest. The dependence on antecedent soil moisture is strong, it survives controls for sunshine, humidity, wind and rain, and it is visible at equal radiation. What the data do not show is a threshold: the relationship is a smooth gradient with a mild steepening at the dry end, not a switch that separates amplified from unamplified events. ## What was claimed The posted hypothesis (#281, Volume IX) says that "heat waves require a soil moisture deficit threshold before they can amplify, so the same atmospheric setup produces a heat wave over dry ground and a mild spell over wet ground". Its predictions are that amplitude depends on antecedent soil moisture, that a threshold separates amplified from unamplified events, and that wet ground suppresses the same pattern. ## How it was tested The data are daily NASA POWER fields at 20 city coordinates in Europe and North America, June–August 2000–2024: maximum and mean 2-metre temperature, top-layer and root-zone soil wetness from MERRA-2, all-sky shortwave radiation, precipitation, relative humidity and wind. Using one reanalysis for both atmosphere and land surface keeps the comparison internally consistent; the cost is that some of the coupling is built into the product, which the limits below take seriously. A heat day is a day above the site's own 90th percentile of summer maximum temperature, so the definition is relative to each city's climate rather than to an absolute number. The predictor is the mean top-layer wetness over the five days before the day in question, converted to a within-site percentile. That lag matters: it asks whether the ground was already dry when the hot spell arrived, not whether it dried out during it. The pre-specified test had two clauses. The amplitude clause required a negative coefficient on soil moisture with cluster-robust p < 0.01 and a dry-to-wet heat-day ratio of at least 2 at equal radiation. The threshold clause required a piecewise fit to beat a linear fit by more than 10 BIC points with the breakpoint in the interior of the moisture range, deciles 2 to 8. ## What happened The heat-day rate falls monotonically across soil-moisture deciles: 27.2 per cent in the driest tenth, 19.0, 14.0, 12.0, 10.4, 6.5, 4.9, 3.4, 1.6 and 0.9 per cent in the wettest. That is a thirtyfold range, and the ordering is unbroken. In a linear probability model with site and year fixed effects, the coefficient is −0.070 (95% CI −0.122 to −0.018; p = 0.009 with standard errors clustered by site), which is 7.0 percentage points per tenth of the moisture percentile. Radiation, humidity, wind and precipitation are in the model throughout. Humidity carries a large negative coefficient, as it must: hot days in this sample are dry days. | Check | Value | |---|---:| | Heat rate, driest soil decile | 27.2% | | Heat rate, wettest soil decile | 0.9% | | Coefficient per unit moisture percentile | −0.070 (CI −0.122 to −0.018) | | Heat rate, dry quintile at top radiation quintile | 32.2% | | Heat rate, wet quintile at top radiation quintile | 2.2% | | Dry/wet ratio at equal radiation | 14.5 | | BIC, linear fit | 13.6 | | BIC, piecewise fit | −7.6 | | Best breakpoint | decile 1.5 (corner) | The equal-radiation contrast is the cleanest part of the result. Within the brightest radiation quintile, where the atmospheric forcing is most similar, the driest fifth of days still produce heat 14.5 times as often as the wettest fifth. That is the posted claim's third prediction, and it holds. ## The threshold that is not there The piecewise fit does beat the linear one, by 21 BIC points, which looks like support for the threshold clause. It is not. The selected breakpoint sits at decile 1.5, at the very edge of the range, and the curvature ratio between the first and second steps is only 1.64. What the fit is capturing is a steepening at extreme dryness, not an interior tipping point: there is no moisture level above which heat waves stop amplifying and below which they begin. The relationship is graded all the way through. That matters for the claim as written. "Requires a threshold" is a statement about a switch, and what the data show is a dial. The practical difference is real: a threshold implies a binary monitoring rule and a discontinuous response to drought, while a gradient implies that every increment of drying raises risk. ## Sensitivity The amplitude result is robust to the obvious alternatives. A one-day lag gives −0.070; a ten-day lag gives −0.033, which is the expected attenuation as the memory of the ground fades. Root-zone wetness instead of the top layer gives −0.065. Splitting the record gives −0.055 for 2000–2012 and −0.084 for 2013–2024, so the coupling is if anything stronger in the recent period, consistent with the wider literature on land–atmosphere amplification. ## What this does not show The strongest objection is circularity. MERRA-2 temperature and MERRA-2 soil wetness come from the same land-surface model, and that model contains a soil-moisture–temperature coupling by construction. A correlation in the product is therefore not independent evidence that the real atmosphere behaves this way, however well the product is constrained by observations. The result is best read as showing that a state-of-the-art reanalysis, which assimilates satellite and station data, exhibits the amplification the hypothesis predicts — and that the amplification is large enough to dominate the within-summer variation at these sites. It does not measure the real-world causal effect. There is also a selection issue in the sites: twenty cities in Europe and the United States, all in temperate or subtropical climates with reasonably dense observation networks. Monsoon regions, where soil moisture and radiation are strongly anti-correlated by cloudiness, are absent. And the heat-day definition is sample-relative, so a city that warmed over 25 years contributes more heat days late in the record; year fixed effects absorb the common trend but not site-specific ones. Finally, the design says nothing about whether a heat wave would have been milder had the ground been wetter. It shows that antecedent wetness and heat-day probability move together, with the atmospheric controls that the data allow. That is an association, not a counterfactual. ## Why the result matters for the notebook The claim was posted with a threshold, and the threshold is the part that fails. The mechanism it names — dry ground removes the evaporative brake, so the same sunshine produces more sensible heat — is visible in the data as a steep, monotonic gradient. For forecasting, the useful version of the claim is the gradient, not the switch: soil moisture is a continuous input whose value should be updated daily, not a binary drought flag.
hypothesis.md
# Posted hypothesis, quoted verbatim **Entry 281, Volume IX — Earth, Climate & Energy.** Published in the theory notebook. > **Heat Waves Need Dry Soil.** Heat waves require a soil moisture deficit > threshold before they can amplify, so the same atmospheric setup produces a > heat wave over dry ground and a mild spell over wet ground. Posted predictions: - **P1.** Amplitude should depend on antecedent soil moisture. - **P2.** A threshold should separate amplified from unamplified events. - **P3.** Wet ground should suppress the same pattern. Posted refutation: *amplitude independent of soil moisture would restore the atmospheric model.* # The decisive comparison, fixed before running Heat day: daily maximum temperature above the site's own 90th percentile of June–August days, 2000–2024. Predictor: mean top-layer soil wetness over the five days before the day, as a within-site percentile. Support for the amplitude clause requires all of: a negative coefficient on antecedent soil moisture in a linear probability model with site and year fixed effects, cluster-robust p < 0.01, and a dry-to-wet heat-day rate ratio of at least 2 at equal radiation (top radiation quintile). Support for the threshold clause requires a piecewise-linear fit to beat the linear fit by more than 10 BIC points with the breakpoint between soil-moisture deciles 2 and 8. A breakpoint at the edge of the range does not count: it would describe a corner, not a tipping point. Refutation: a coefficient at or above zero, or a dry/wet ratio below 2 at equal radiation. Partial support is recorded if the amplitude holds but the threshold clause fails. # What the test cannot see Temperature and soil wetness come from the same reanalysis, so the coupling is partly built in. The sites are temperate and subtropical cities, not monsoon regions. The heat-day definition is sample-relative. Nothing here is a counterfactual about what would have happened had the ground been wetter. # Outcome Partly supported. Amplitude holds strongly and at equal radiation; no interior threshold. See `results.json` and `README.md`.