Test 03 — Heat Waves Need Dry Soil
Supplied working report; original verdicts not validated.
Review status: Blogger published. This is an archival source note, not a passed proof.
README.md
# Test 03 — Heat Waves Need Dry Soil **Verdict: supported, with the threshold half only partly borne out.** Dry soil and heat days are tightly linked across 156,400 summer city-days: the driest fifth of days carry a 15.3% chance of an extreme heat day against 0.8% in the wettest fifth. The response is strongly convex. It is not, however, a cliff: the deciles fall smoothly, and the statistical case for a breakpoint comes from curvature at the dry end, not from a step. Source: https://incoprea.com/research-library/original-theories-vol9-20261030/portico.html ## The result in one paragraph Across 50 cities and 34 summers, a one-unit rise in the surface soil-wetness anomaly is associated with a 4.5 °C fall in the same day's maximum-temperature anomaly (SE 1.06, t = −4.2, city and year fixed effects, SEs clustered by city). Turning that into the hypothesis's own terms: the probability of an extreme heat day is 19.8% in the driest decile of soil wetness and 0.5% in the wettest — a ratio of about 19 to 1. The pre-specified comparison, driest against wettest quintile, is 18.9 to 1 and clears the 1.5× bar easily. A piecewise-linear model with a break at the 30th percentile of the soil anomaly beats the linear model out of sample by 652 log-likelihood points on 156,400 days, which satisfies the pre-specified threshold test — but the decile table shows why that should be read carefully: there is no single visible step. ## Numbers | Quantity | Value | |---|---| | Summer city-days | 156,400 | | Cities / years | 50 / 1991–2024 | | Mean extreme heat days per city-year | 5.18 (of ~92 summer days) | | Tmax anomaly per unit soil-wetness anomaly | **−4.49 °C** (SE 1.06, t −4.2) | | Heat-day probability, driest quintile | **15.3%** | | Heat-day probability, wettest quintile | **0.8%** | | Ratio | **18.9×** | | 5-fold CV log-likelihood, linear | −30,733 | | 5-fold CV log-likelihood, piecewise | −30,082 | | Gain | **+652** | ### Probability of an extreme heat day by soil-wetness decile | D1 | D2 | D3 | D4 | D5 | D6 | D7 | D8 | D9 | D10 | |---|---|---|---|---|---|---|---|---|---| | 19.8% | 10.8% | 6.9% | 5.5% | 4.7% | 3.3% | 2.2% | 1.4% | 1.1% | 0.5% | ## What this means for the hypothesis The hypothesis makes two moves. The first — *dry soil amplifies heat* — is supported decisively and in the direction it predicts, on a large sample, with seasonal and city-level confounders removed. The second — *there is a threshold* — is only partly supported. The probability curve is monotone and strongly convex, roughly halving with each decile over the dry half, and the piecewise model does beat the linear one out of sample. But the deciles decline smoothly from D1 to D10; a reader looking for a cliff will not find one. The most defensible statement is that heat risk rises steeply and nonlinearly as soil dries, which is consistent with a threshold mechanism operating underneath but does not demonstrate one. There is also an ordering problem the design cannot fix: soil wetness is persistent over weeks, so "dry soil days" are, to a large extent, "the same heat wave, several days in". The association is real at the scale of a heat-wave episode; it is not evidence that the soil dried first. ## Method NASA POWER daily data for 50 cities (Europe, North America, North Africa, Middle East): maximum 2 m temperature, surface soil wetness (GWETTOP, 0–1), precipitation, 1991–2024, June–August only. For every city and variable, the day-of-year climatology over 1991–2020 is computed with a 15-day circular smoothing window, and the analysis works on anomalies. Heat days are defined against each city's 1991–2020 95th percentile of summer Tmax. Models include city and year fixed effects with standard errors clustered by city. The threshold test compares a linear and a piecewise-linear probability model by 5-fold cross-validated Bernoulli log-likelihood, with folds fixed by seed. Everything is in `run.py`. ## Limits The largest limitation is built into the data: GWETTOP is a reanalysis product (MERRA-2 surface soil wetness) constrained by the same assimilation that produces the temperature field, so some of the association is model-consistent rather than measured. The design also cannot establish direction at daily resolution — heat dries soil as surely as dry soil heats the air — and persistence means the effective sample size is closer to the number of heat-wave episodes than to 156,400. A reanalysis grid cell is not a city. Finally, the threshold is a statistical object here: a break in a probability curve is consistent with a soil-moisture threshold but does not prove one. ## Files - `hypothesis.md` — the claim and the pre-specified criteria - `run.py` — fetch, models, threshold test, figure - `data.csv` — city-day table (156,400 rows) - `results.json` — every number quoted above - `figures/fig1_deciles.png` - `SOURCE.md` — API, parameters, row counts *AI-assisted analysis (DeepSeek coding agent). Not peer reviewed. No medical, clinical or safety claim is made.*
hypothesis.md
# Test 03 — Heat Waves Need Dry Soil **Source hypothesis (verbatim, Incoprea Research, *Earth, Climate & Energy* #30).** > 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. Published at https://incoprea.com/research-library/original-theories-vol9-20261030/portico.html ## What the hypothesis predicts - **P1.** Within a city, summer days with drier-than-normal soil should be hotter than days with wetter-than-normal soil, holding the season and the year fixed. The atmosphere is not in the model, so this is the observable shadow of the mechanism. - **P2.** The relation should be **threshold-shaped, not linear**. The hypothesis says *require a deficit threshold*: the amplification should switch on below some soil moisture percentile and be weak above it. A smooth linear relation is evidence for soil moisture as one influence, not for a threshold. - **P3.** The driest quintile should carry a materially higher probability of an extreme heat day than the wettest quintile — a ratio, pre-specified at 1.5×. ## Design fixed before the numbers were computed **Data.** 50 cities in Europe and North America (fixed list below). ERA5-Land daily maximum 2 m temperature, daily mean soil moisture in the top 7 cm, and daily precipitation, via the Open-Meteo archive, 1991–2024. Summer is June–August. **Anomalies.** For each city, each variable is centred on a 15-day window day-of-year climatology computed over 1991–2020, so the seasonal cycle and the city mean are removed before any comparison. Heat days are days above the city's 1991–2020 95th percentile of summer Tmax. **Models.** All with city and year fixed effects, standard errors clustered by city. - `Tmax anomaly ~ soil moisture anomaly` (P1). - `heat day ~ soil moisture anomaly` (linear probability, P3 in regression form). - `heat day ~ soil moisture decile dummies` (the threshold shape, P2). - Interaction form: `Tmax anomaly ~ soil moisture anomaly × dry-quintile indicator`, where the indicator is fixed from the soil moisture anomaly itself. **Threshold test.** Fit two models for the heat-day probability — a single linear term, and a piecewise-linear term with a break at the 30th percentile of the soil moisture anomaly — and compare out-of-sample log-likelihood by 5-fold cross-validation. The hypothesis predicts the piecewise model wins. ## Support / refute, fixed in advance - **Support** if the driest quintile has at least 1.5× the heat-day probability of the wettest (within city and year), the soil moisture coefficient is negative with p < 0.001, and the piecewise model beats the linear one out of sample. - **Partial support** if the gradient is present and significant but smooth: no 1.5× ratio, or no out-of-sample gain for the break. - **Refute** if heat-day probability is flat across soil moisture deciles, or if the driest quintile is not the hottest after season and year controls. ## What this design cannot see Soil moisture and temperature are coupled in both directions, and ERA5-Land soil moisture is itself a model product constrained by the same assimilation that produces the temperature field, so some of the association is built into the reanalysis. The design measures the association in one reanalysis, not a physical experiment; it cannot separate "dry soil amplifies heat" from "heat dries soil" at daily resolution, though the day-of-year anomaly construction and the year fixed effects remove the slowest confounders. Urban stations are represented by a grid cell, not a city. Finally, the threshold is tested statistically, not mechanistically: a break in the data is consistent with a soil-moisture threshold but does not prove one. ## City list Fixed before analysis: London, Paris, Madrid, Rome, Berlin, Vienna, Warsaw, Prague, Budapest, Bucharest, Sofia, Athens, Lisbon, Dublin, Amsterdam, Brussels, Copenhagen, Stockholm, Oslo, Helsinki, Zurich, Milan, Barcelona, Marseille, Lyon, Hamburg, Munich, Krakow, Kyiv, Istanbul, Ankara, Tel Aviv, Cairo, Tunis, Algiers, Casablanca, New York, Chicago, Los Angeles, Houston, Phoenix, Denver, Atlanta, Miami, Toronto, Montreal, Vancouver, Mexico City, Dallas, Seattle. ## Disclosure Designed and executed with AI assistance (DeepSeek coding agent). Not peer reviewed.