Antecedent rainfall and heat extremes

# 4. Heat waves need dry soil

**Verdict: Supported as a moisture-limitation prediction; the feedback itself is not identified**

*Working test · not peer reviewed · AI-assisted · no clinical or safety advice*

## The hypothesis, as published

> Heat waves need dry soil: a dry surface cannot spend incoming radiation on
> evaporation, so the same forcing produces a higher temperature.

## What was tested

Soil moisture is not in this dataset. The reanalysis endpoints that serve it
were rate-limited throughout this run (see the note in test 1), so the test uses
the observable the mechanism requires: an antecedent precipitation deficit. Two
design choices narrow the gap between that proxy and the mechanism.

First, heat extremes are defined within station: a day counts if TMAX exceeds
that station's own summer 90th percentile, so a permanently hot climate cannot
produce the result. Second, a regional anomaly term — the mean temperature
anomaly of the other stations in the same 5-degree cell on the same day — absorbs
the synoptic forcing that drives both dry spells and heat waves. The test asks
whether a *local* moisture deficit adds information beyond the regional heat
wave.

GHCN-Daily TMAX and PRCP, 2014–2024, 1,305 stations poleward of
25°, 913,194 summer station-days.

## Results

| Quantity | Value |
|---|---|
| Stations | 1,305 |
| Summer station-days | 913,194 |
| Baseline heat-extreme rate | 9.4% |
| Antecedent-deficit coefficient | -0.0479 per percentile (cluster SE 0.0017) |
| Cluster-robust t (by station) | -28.5 |
| Effect across the full percentile range | -4.8 percentage points |
| Heat rate, driest decile | 15.6% |
| Heat rate, wettest decile | 5.2% |

Across the full range of antecedent moisture, moving from the driest to the
wettest percentile lowers the probability of a locally extreme hot day by
4.8 percentage points against a 9.4% baseline.
The raw decile curve is steeper still — 15.6% in the driest
decile against 5.2% in the wettest — because it also carries
the between-station climate differences that the fixed effects remove.

The regional anomaly coefficient is 0.041:
synoptic forcing dominates, as it should. The moisture term survives it.

## Sensitivity

- 30-day instead of 60-day antecedent window: the coefficient shrinks by about
  a fifth but keeps its sign and significance.
- Removing the regional-anomaly control roughly doubles the coefficient, which
  is the expected direction if regional forcing is a common cause of both
  dryness and heat.
- Dropping stations with fewer than eight summers of data leaves the estimate
  unchanged to two decimal places.

## What this test cannot see

This is the central limitation. Precipitation deficit is not soil moisture, and
dry spells and heat waves share an atmospheric cause: a blocking ridge produces
both. The regional-anomaly control absorbs the *shared* part of that forcing,
but a local subsidence anomaly that dries the soil and heats the boundary layer
would remain in the residual and would be attributed to moisture. The test
therefore shows that local moisture history carries information about local heat
extremes beyond the regional signal; it does not show that the information flows
through evaporation. A soil-moisture series would be needed to close that gap.

The 2014–2024 window is also short relative to the multi-decadal variability of
drought, and the station sample is weighted toward North America and Europe.

## Files

| File | What it is |
|---|---|
| `hypothesis.md` | the published entry, quoted verbatim |
| `run.py` | the analysis, runnable |
| `data.csv` | decile summary |
| `results.json` | every number quoted above |
| `figures/fig1.png` | decile curve and proxy distribution |
| `SOURCE.md` | row counts, URLs, hashes |

**Source.** GHCN-Daily TMAX and PRCP, NOAA NCEI. The soil-moisture version of
this test was not run; see test 1 for the failed fetch.