FA-70936 / Weather index computation / Open access

Shade apparent temperature: humidity fraction · case 01

Humid weather feels hundreds of degrees hot.

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ROOT CAUSE

Relative humidity in percent multiplies the saturation vapour pressure without conversion to a fraction.

THE FAILURE

Relative humidity in percent multiplies the saturation vapour pressure without conversion to a fraction.

Unsuccessful approach: Using the humidity deficit (1 - RH/100) makes dry air feel hotter than humid air.

Case contract

Input air temperature degC, RH percent, wind in km/h measured at 10 m. e = RH/100*6.105*exp(17.27*Ta/(237.7+Ta)) hPa; wind in m/s = km/h / 3.6; AT = Ta + 0.33e - 0.70ws - 4.00 rounded to 0.1.

Why this case matters

Feels-like temperature on consumer forecasts uses this non-radiative apparent temperature.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ta, rh, wind_kmh):
    e = rh * 6.105 * math.exp(17.27 * ta / (237.7 + ta))
    ws = wind_kmh / 3.6
    at = ta + 0.33 * e - 0.70 * ws - 4.00
    return round(at, 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['-5 C 10% RH wind 0 km/h', [-5, 10, 0], -8.9], ['-5 C 10% RH wind 10 km/h', [-5, 10, 10], -10.8], ['-5 C 10% RH wind 36 km/h', [-5, 10, 36], -15.9], ['-5 C 10% RH wind 72 km/h', [-5, 10, 72], -22.9], ['-5 C 50% RH wind 0 km/h', [-5, 50, 0], -8.3], ['-5 C 50% RH wind 10 km/h', [-5, 50, 10], -10.2], ['-5 C 50% RH wind 36 km/h', [-5, 50, 36], -15.3], ['-5 C 50% RH wind 72 km/h', [-5, 50, 72], -22.3]], [['-5 C 10% RH wind 72 km/h', [-5, 10, 72], -22.9], ['-5 C 50% RH wind 72 km/h', [-5, 50, 72], -22.3], ['-5 C 90% RH wind 0 km/h', [-5, 90, 0], -7.7], ['-5 C 90% RH wind 10 km/h', [-5, 90, 10], -9.7], ['-5 C 90% RH wind 36 km/h', [-5, 90, 36], -14.7], ['-5 C 90% RH wind 72 km/h', [-5, 90, 72], -21.7], ['0 C 10% RH wind 0 km/h', [0, 10, 0], -3.8], ['0 C 10% RH wind 10 km/h', [0, 10, 10], -5.7]], [['-5 C 50% RH wind 36 km/h', [-5, 50, 36], -15.3], ['0 C 10% RH wind 36 km/h', [0, 10, 36], -10.8], ['0 C 10% RH wind 72 km/h', [0, 10, 72], -17.8], ['0 C 50% RH wind 0 km/h', [0, 50, 0], -3.0], ['0 C 50% RH wind 10 km/h', [0, 50, 10], -4.9], ['0 C 50% RH wind 36 km/h', [0, 50, 36], -10.0], ['0 C 50% RH wind 72 km/h', [0, 50, 72], -17.0], ['0 C 90% RH wind 0 km/h', [0, 90, 0], -2.2]], [['-5 C 90% RH wind 10 km/h', [-5, 90, 10], -9.7], ['0 C 90% RH wind 10 km/h', [0, 90, 10], -4.1], ['0 C 90% RH wind 36 km/h', [0, 90, 36], -9.2], ['0 C 90% RH wind 72 km/h', [0, 90, 72], -16.2], ['12 C 10% RH wind 0 km/h', [12, 10, 0], 8.5], ['12 C 10% RH wind 10 km/h', [12, 10, 10], 6.5], ['12 C 10% RH wind 36 km/h', [12, 10, 36], 1.5], ['12 C 10% RH wind 72 km/h', [12, 10, 72], -5.5]], [['0 C 10% RH wind 0 km/h', [0, 10, 0], -3.8], ['12 C 50% RH wind 0 km/h', [12, 50, 0], 10.3], ['12 C 50% RH wind 10 km/h', [12, 50, 10], 8.4], ['12 C 50% RH wind 36 km/h', [12, 50, 36], 3.3], ['12 C 50% RH wind 72 km/h', [12, 50, 72], -3.7], ['12 C 90% RH wind 0 km/h', [12, 90, 0], 12.2], ['12 C 90% RH wind 10 km/h', [12, 90, 10], 10.2], ['12 C 90% RH wind 36 km/h', [12, 90, 36], 5.2]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
-5 C 10% RH wind 0 km/h	`4.9`	`-8.9`	Failed
-5 C 10% RH wind 10 km/h	`3.0`	`-10.8`	Failed
-5 C 10% RH wind 36 km/h	`-2.1`	`-15.9`	Failed
-5 C 10% RH wind 72 km/h	`-9.1`	`-22.9`	Failed
-5 C 50% RH wind 0 km/h	`60.5`	`-8.3`	Failed
-5 C 50% RH wind 10 km/h	`58.6`	`-10.2`	Failed
-5 C 50% RH wind 36 km/h	`53.5`	`-15.3`	Failed
-5 C 50% RH wind 72 km/h	`46.5`	`-22.3`	Failed

SHA-256 / 52de357872548caa2ea3cccb0e02aee240fcd70cdf6ca81e52462e20bca0144f

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ta, rh, wind_kmh):
    e = (1 - rh / 100.0) * 6.105 * math.exp(17.27 * ta / (237.7 + ta))
    ws = wind_kmh / 3.6
    at = ta + 0.33 * e - 0.70 * ws - 4.00
    return round(at, 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['-5 C 10% RH wind 0 km/h', [-5, 10, 0], -8.9], ['-5 C 10% RH wind 10 km/h', [-5, 10, 10], -10.8], ['-5 C 10% RH wind 36 km/h', [-5, 10, 36], -15.9], ['-5 C 10% RH wind 72 km/h', [-5, 10, 72], -22.9], ['-5 C 50% RH wind 0 km/h', [-5, 50, 0], -8.3], ['-5 C 50% RH wind 10 km/h', [-5, 50, 10], -10.2], ['-5 C 50% RH wind 36 km/h', [-5, 50, 36], -15.3], ['-5 C 50% RH wind 72 km/h', [-5, 50, 72], -22.3]], [['-5 C 10% RH wind 72 km/h', [-5, 10, 72], -22.9], ['-5 C 50% RH wind 72 km/h', [-5, 50, 72], -22.3], ['-5 C 90% RH wind 0 km/h', [-5, 90, 0], -7.7], ['-5 C 90% RH wind 10 km/h', [-5, 90, 10], -9.7], ['-5 C 90% RH wind 36 km/h', [-5, 90, 36], -14.7], ['-5 C 90% RH wind 72 km/h', [-5, 90, 72], -21.7], ['0 C 10% RH wind 0 km/h', [0, 10, 0], -3.8], ['0 C 10% RH wind 10 km/h', [0, 10, 10], -5.7]], [['-5 C 50% RH wind 36 km/h', [-5, 50, 36], -15.3], ['0 C 10% RH wind 36 km/h', [0, 10, 36], -10.8], ['0 C 10% RH wind 72 km/h', [0, 10, 72], -17.8], ['0 C 50% RH wind 0 km/h', [0, 50, 0], -3.0], ['0 C 50% RH wind 10 km/h', [0, 50, 10], -4.9], ['0 C 50% RH wind 36 km/h', [0, 50, 36], -10.0], ['0 C 50% RH wind 72 km/h', [0, 50, 72], -17.0], ['0 C 90% RH wind 0 km/h', [0, 90, 0], -2.2]], [['-5 C 90% RH wind 10 km/h', [-5, 90, 10], -9.7], ['0 C 90% RH wind 10 km/h', [0, 90, 10], -4.1], ['0 C 90% RH wind 36 km/h', [0, 90, 36], -9.2], ['0 C 90% RH wind 72 km/h', [0, 90, 72], -16.2], ['12 C 10% RH wind 0 km/h', [12, 10, 0], 8.5], ['12 C 10% RH wind 10 km/h', [12, 10, 10], 6.5], ['12 C 10% RH wind 36 km/h', [12, 10, 36], 1.5], ['12 C 10% RH wind 72 km/h', [12, 10, 72], -5.5]], [['0 C 10% RH wind 0 km/h', [0, 10, 0], -3.8], ['12 C 50% RH wind 0 km/h', [12, 50, 0], 10.3], ['12 C 50% RH wind 10 km/h', [12, 50, 10], 8.4], ['12 C 50% RH wind 36 km/h', [12, 50, 36], 3.3], ['12 C 50% RH wind 72 km/h', [12, 50, 72], -3.7], ['12 C 90% RH wind 0 km/h', [12, 90, 0], 12.2], ['12 C 90% RH wind 10 km/h', [12, 90, 10], 10.2], ['12 C 90% RH wind 36 km/h', [12, 90, 36], 5.2]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
-5 C 10% RH wind 0 km/h	`-7.7`	`-8.9`	Failed
-5 C 10% RH wind 10 km/h	`-9.7`	`-10.8`	Failed
-5 C 10% RH wind 36 km/h	`-14.7`	`-15.9`	Failed
-5 C 10% RH wind 72 km/h	`-21.7`	`-22.9`	Failed
-5 C 50% RH wind 0 km/h	`-8.3`	`-8.3`	Passed
-5 C 50% RH wind 10 km/h	`-10.2`	`-10.2`	Passed
-5 C 50% RH wind 36 km/h	`-15.3`	`-15.3`	Passed
-5 C 50% RH wind 72 km/h	`-22.3`	`-22.3`	Passed

SHA-256 / 3249f60cf6637d4a050920d15e685772c01d103a1366375770aee6a8acfaa072

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Stipulated deterministic teaching model of an operational weather index; coefficients and thresholds are fixed by the contract and no claim of standards conformance is made. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:25.234900+00:00.

Case digest / e544a6a6589a044100a7ae85e33bda64a8c5c5742e356a240f98996e4532b315