FA-70851 / Weather index computation / Open access

Heat index regression: humid adjustment sign · case 01

Saturated air at 80 to 86 degF reads cooler than the regression.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The high-humidity correction is subtracted instead of added.

VERIFIED REPAIR

Add ((RH - 85)/10)*((87 - T)/5) in the humid window.

Unsuccessful approach: Restoring the sign but dividing the temperature term by 10 halves the correction.

Case contract

Input dry-bulb temperature in degF and relative humidity in percent. Compute the simple Steadman estimate 0.5*(T+61+1.2*(T-68)+0.094*RH); if the mean of that estimate and T is below 80 return it, otherwise use the Rothfusz regression with the dry adjustment (RH<13, 80<=T<=112) or the humid adjustment (RH>85, 80<=T<=87). Round to 0.1 degF.

Why this case matters

Heat advisories are issued from this value; a wrong branch changes public warnings.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(t_f, rh):
    simple = 0.5 * (t_f + 61.0 + (t_f - 68.0) * 1.2 + rh * 0.094)
    if (simple + t_f) / 2 < 80:
        return round(simple, 1)
    hi = (-42.379 + 2.04901523 * t_f + 10.14333127 * rh - 0.22475541 * t_f * rh
          - 0.00683783 * t_f * t_f - 0.05481717 * rh * rh + 0.00122874 * t_f * t_f * rh
          + 0.00085282 * t_f * rh * rh - 0.00000199 * t_f * t_f * rh * rh)
    if rh < 13 and 80 <= t_f <= 112:
        hi -= ((13 - rh) / 4) * math.sqrt((17 - abs(t_f - 95)) / 17)
    elif rh > 85 and 80 <= t_f <= 87:
        hi -= ((rh - 85) / 10) * ((87 - t_f) / 5)
    return round(hi, 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['70F at 0% RH', [70, 0], 66.7], ['70F at 5% RH', [70, 5], 66.9], ['70F at 10% RH', [70, 10], 67.2], ['70F at 12% RH', [70, 12], 67.3], ['70F at 13% RH', [70, 13], 67.3], ['70F at 40% RH', [70, 40], 68.6], ['80F at 86% RH', [80, 86], 85.2], ['80F at 90% RH', [80, 90], 86.3]], [['70F at 85% RH', [70, 85], 70.7], ['70F at 86% RH', [70, 86], 70.7], ['70F at 90% RH', [70, 90], 70.9], ['70F at 95% RH', [70, 95], 71.2], ['70F at 100% RH', [70, 100], 71.4], ['76F at 0% RH', [76, 0], 73.3], ['80F at 100% RH', [80, 100], 89.3], ['81.5F at 95% RH', [81.5, 95], 92.4]], [['76F at 10% RH', [76, 10], 73.8], ['76F at 12% RH', [76, 12], 73.9], ['76F at 13% RH', [76, 13], 73.9], ['76F at 40% RH', [76, 40], 75.2], ['76F at 60% RH', [76, 60], 76.1], ['76F at 85% RH', [76, 85], 77.3], ['81.5F at 95% RH', [81.5, 95], 92.4], ['82F at 100% RH', [82, 100], 96.0]], [['76F at 90% RH', [76, 90], 77.5], ['76F at 95% RH', [76, 95], 77.8], ['76F at 100% RH', [76, 100], 78.0], ['79F at 0% RH', [79, 0], 76.6], ['79F at 5% RH', [79, 5], 76.8], ['79F at 10% RH', [79, 10], 77.1], ['82F at 90% RH', [82, 90], 92.0], ['85F at 95% RH', [85, 95], 104.6]], [['79F at 13% RH', [79, 13], 77.2], ['79F at 40% RH', [79, 40], 78.5], ['79F at 60% RH', [79, 60], 79.4], ['79F at 85% RH', [79, 85], 80.6], ['79F at 86% RH', [79, 86], 80.6], ['79F at 90% RH', [79, 90], 80.8], ['80F at 86% RH', [80, 86], 85.2], ['84F at 86% RH', [84, 86], 96.4]]]
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
70F at 0% RH	`66.7`	`66.7`	Passed
70F at 5% RH	`66.9`	`66.9`	Passed
70F at 10% RH	`67.2`	`67.2`	Passed
70F at 12% RH	`67.3`	`67.3`	Passed
70F at 13% RH	`67.3`	`67.3`	Passed
70F at 40% RH	`68.6`	`68.6`	Passed
80F at 86% RH	`84.9`	`85.2`	Failed
80F at 90% RH	`84.9`	`86.3`	Failed

SHA-256 / 90a7d066f8a2fc885746a65aca1801e642f40e22145167ceb57b3c458827236e

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(t_f, rh):
    simple = 0.5 * (t_f + 61.0 + (t_f - 68.0) * 1.2 + rh * 0.094)
    if (simple + t_f) / 2 < 80:
        return round(simple, 1)
    hi = (-42.379 + 2.04901523 * t_f + 10.14333127 * rh - 0.22475541 * t_f * rh
          - 0.00683783 * t_f * t_f - 0.05481717 * rh * rh + 0.00122874 * t_f * t_f * rh
          + 0.00085282 * t_f * rh * rh - 0.00000199 * t_f * t_f * rh * rh)
    if rh < 13 and 80 <= t_f <= 112:
        hi -= ((13 - rh) / 4) * math.sqrt((17 - abs(t_f - 95)) / 17)
    elif rh > 85 and 80 <= t_f <= 87:
        hi += ((rh - 85) / 10) * ((87 - t_f) / 10)
    return round(hi, 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['70F at 0% RH', [70, 0], 66.7], ['70F at 5% RH', [70, 5], 66.9], ['70F at 10% RH', [70, 10], 67.2], ['70F at 12% RH', [70, 12], 67.3], ['70F at 13% RH', [70, 13], 67.3], ['70F at 40% RH', [70, 40], 68.6], ['80F at 86% RH', [80, 86], 85.2], ['80F at 90% RH', [80, 90], 86.3]], [['70F at 85% RH', [70, 85], 70.7], ['70F at 86% RH', [70, 86], 70.7], ['70F at 90% RH', [70, 90], 70.9], ['70F at 95% RH', [70, 95], 71.2], ['70F at 100% RH', [70, 100], 71.4], ['76F at 0% RH', [76, 0], 73.3], ['80F at 100% RH', [80, 100], 89.3], ['81.5F at 95% RH', [81.5, 95], 92.4]], [['76F at 10% RH', [76, 10], 73.8], ['76F at 12% RH', [76, 12], 73.9], ['76F at 13% RH', [76, 13], 73.9], ['76F at 40% RH', [76, 40], 75.2], ['76F at 60% RH', [76, 60], 76.1], ['76F at 85% RH', [76, 85], 77.3], ['81.5F at 95% RH', [81.5, 95], 92.4], ['82F at 100% RH', [82, 100], 96.0]], [['76F at 90% RH', [76, 90], 77.5], ['76F at 95% RH', [76, 95], 77.8], ['76F at 100% RH', [76, 100], 78.0], ['79F at 0% RH', [79, 0], 76.6], ['79F at 5% RH', [79, 5], 76.8], ['79F at 10% RH', [79, 10], 77.1], ['82F at 90% RH', [82, 90], 92.0], ['85F at 95% RH', [85, 95], 104.6]], [['79F at 13% RH', [79, 13], 77.2], ['79F at 40% RH', [79, 40], 78.5], ['79F at 60% RH', [79, 60], 79.4], ['79F at 85% RH', [79, 85], 80.6], ['79F at 86% RH', [79, 86], 80.6], ['79F at 90% RH', [79, 90], 80.8], ['80F at 86% RH', [80, 86], 85.2], ['84F at 86% RH', [84, 86], 96.4]]]
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
70F at 0% RH	`66.7`	`66.7`	Passed
70F at 5% RH	`66.9`	`66.9`	Passed
70F at 10% RH	`67.2`	`67.2`	Passed
70F at 12% RH	`67.3`	`67.3`	Passed
70F at 13% RH	`67.3`	`67.3`	Passed
70F at 40% RH	`68.6`	`68.6`	Passed
80F at 86% RH	`85.1`	`85.2`	Failed
80F at 90% RH	`86.0`	`86.3`	Failed

SHA-256 / 17637c78851ced65d2419a665bd149f182714194431c85c875031a4458382d48

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(t_f, rh):
    simple = 0.5 * (t_f + 61.0 + (t_f - 68.0) * 1.2 + rh * 0.094)
    if (simple + t_f) / 2 < 80:
        return round(simple, 1)
    hi = (-42.379 + 2.04901523 * t_f + 10.14333127 * rh - 0.22475541 * t_f * rh
          - 0.00683783 * t_f * t_f - 0.05481717 * rh * rh + 0.00122874 * t_f * t_f * rh
          + 0.00085282 * t_f * rh * rh - 0.00000199 * t_f * t_f * rh * rh)
    if rh < 13 and 80 <= t_f <= 112:
        hi -= ((13 - rh) / 4) * math.sqrt((17 - abs(t_f - 95)) / 17)
    elif rh > 85 and 80 <= t_f <= 87:
        hi += ((rh - 85) / 10) * ((87 - t_f) / 5)
    return round(hi, 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['70F at 0% RH', [70, 0], 66.7], ['70F at 5% RH', [70, 5], 66.9], ['70F at 10% RH', [70, 10], 67.2], ['70F at 12% RH', [70, 12], 67.3], ['70F at 13% RH', [70, 13], 67.3], ['70F at 40% RH', [70, 40], 68.6], ['80F at 86% RH', [80, 86], 85.2], ['80F at 90% RH', [80, 90], 86.3]], [['70F at 85% RH', [70, 85], 70.7], ['70F at 86% RH', [70, 86], 70.7], ['70F at 90% RH', [70, 90], 70.9], ['70F at 95% RH', [70, 95], 71.2], ['70F at 100% RH', [70, 100], 71.4], ['76F at 0% RH', [76, 0], 73.3], ['80F at 100% RH', [80, 100], 89.3], ['81.5F at 95% RH', [81.5, 95], 92.4]], [['76F at 10% RH', [76, 10], 73.8], ['76F at 12% RH', [76, 12], 73.9], ['76F at 13% RH', [76, 13], 73.9], ['76F at 40% RH', [76, 40], 75.2], ['76F at 60% RH', [76, 60], 76.1], ['76F at 85% RH', [76, 85], 77.3], ['81.5F at 95% RH', [81.5, 95], 92.4], ['82F at 100% RH', [82, 100], 96.0]], [['76F at 90% RH', [76, 90], 77.5], ['76F at 95% RH', [76, 95], 77.8], ['76F at 100% RH', [76, 100], 78.0], ['79F at 0% RH', [79, 0], 76.6], ['79F at 5% RH', [79, 5], 76.8], ['79F at 10% RH', [79, 10], 77.1], ['82F at 90% RH', [82, 90], 92.0], ['85F at 95% RH', [85, 95], 104.6]], [['79F at 13% RH', [79, 13], 77.2], ['79F at 40% RH', [79, 40], 78.5], ['79F at 60% RH', [79, 60], 79.4], ['79F at 85% RH', [79, 85], 80.6], ['79F at 86% RH', [79, 86], 80.6], ['79F at 90% RH', [79, 90], 80.8], ['80F at 86% RH', [80, 86], 85.2], ['84F at 86% RH', [84, 86], 96.4]]]
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
70F at 0% RH	`66.7`	`66.7`	Passed
70F at 5% RH	`66.9`	`66.9`	Passed
70F at 10% RH	`67.2`	`67.2`	Passed
70F at 12% RH	`67.3`	`67.3`	Passed
70F at 13% RH	`67.3`	`67.3`	Passed
70F at 40% RH	`68.6`	`68.6`	Passed
80F at 86% RH	`85.2`	`85.2`	Passed
80F at 90% RH	`86.3`	`86.3`	Passed

SHA-256 / b675fa1f3fbe288cf863572af4de44cadb3476b3aa175cde201022506c2b95ab

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 2026-09-29T14:48:24.465823+00:00.

Case digest / c946f86fcd582f6982e2acc8cf70f1f289c24b44444a141924516f9188d060e7