FA-71101 / Weather index computation / Open access

Fosberg fire weather index: cubic damping term · case 01

Moist conditions show too much fire potential.

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

ROOT CAUSE

The cubic term in the moisture damping has the wrong sign.

VERIFIED REPAIR

Subtract 0.5x^3.

Unsuccessful approach: Using x squared instead of x cubed still mis-shapes the damping curve.

Case contract

Equilibrium moisture m: RH<10: 0.03229+0.281073RH-0.000578RH*T; 10<=RH<=50: 2.22749+0.160107RH-0.01478T; RH>50: 21.0606+0.005565RH^2-0.00035RH*T-0.483199RH. x=m/30; eta=1-2x+1.5x^2-0.5x^3; FFWI = eta*sqrt(1+U^2)/0.3002 clamped to [0,100] and rounded to 0.1.

Why this case matters

Red flag warnings and fire-weather dashboards chart FFWI.

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, wind_mph):
    if rh < 10:
        m = 0.03229 + 0.281073 * rh - 0.000578 * rh * t_f
    elif rh <= 50:
        m = 2.22749 + 0.160107 * rh - 0.01478 * t_f
    else:
        m = 21.0606 + 0.005565 * rh * rh - 0.00035 * rh * t_f - 0.483199 * rh
    x = m / 30.0
    eta = 1 - 2 * x + 1.5 * x * x + 0.5 * x ** 3
    f = eta * math.sqrt(1 + wind_mph ** 2) / 0.3002
    return round(min(max(f, 0.0), 100.0), 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['40F 5% RH wind 0 mph', [40, 5, 0], 3.0], ['40F 5% RH wind 10 mph', [40, 5, 10], 30.6], ['40F 5% RH wind 30 mph', [40, 5, 30], 91.5], ['40F 9% RH wind 0 mph', [40, 9, 0], 2.8], ['40F 9% RH wind 10 mph', [40, 9, 10], 28.5], ['40F 9% RH wind 30 mph', [40, 9, 30], 85.2], ['40F 10% RH wind 0 mph', [40, 10, 0], 2.7], ['40F 10% RH wind 10 mph', [40, 10, 10], 26.8]], [['40F 10% RH wind 10 mph', [40, 10, 10], 26.8], ['40F 10% RH wind 30 mph', [40, 10, 30], 80.1], ['40F 11% RH wind 0 mph', [40, 11, 0], 2.6], ['40F 11% RH wind 10 mph', [40, 11, 10], 26.5], ['40F 11% RH wind 30 mph', [40, 11, 30], 79.2], ['40F 30% RH wind 0 mph', [40, 30, 0], 2.1], ['40F 30% RH wind 10 mph', [40, 30, 10], 21.3], ['40F 30% RH wind 30 mph', [40, 30, 30], 63.5]], [['40F 30% RH wind 30 mph', [40, 30, 30], 63.5], ['40F 49% RH wind 0 mph', [40, 49, 0], 1.7], ['40F 49% RH wind 10 mph', [40, 49, 10], 16.8], ['40F 49% RH wind 30 mph', [40, 49, 30], 50.2], ['40F 50% RH wind 0 mph', [40, 50, 0], 1.7], ['40F 50% RH wind 10 mph', [40, 50, 10], 16.6], ['40F 50% RH wind 30 mph', [40, 50, 30], 49.6], ['40F 51% RH wind 0 mph', [40, 51, 0], 1.6]], [['40F 50% RH wind 0 mph', [40, 50, 0], 1.7], ['40F 51% RH wind 0 mph', [40, 51, 0], 1.6], ['40F 51% RH wind 10 mph', [40, 51, 10], 15.9], ['40F 51% RH wind 30 mph', [40, 51, 30], 47.5], ['40F 80% RH wind 0 mph', [40, 80, 0], 0.9], ['40F 80% RH wind 10 mph', [40, 80, 10], 8.7], ['40F 80% RH wind 30 mph', [40, 80, 30], 26.0], ['40F 100% RH wind 0 mph', [40, 100, 0], 0.2]], [['40F 51% RH wind 0 mph', [40, 51, 0], 1.6], ['40F 100% RH wind 0 mph', [40, 100, 0], 0.2], ['40F 100% RH wind 10 mph', [40, 100, 10], 1.7], ['40F 100% RH wind 30 mph', [40, 100, 30], 5.1], ['70F 5% RH wind 0 mph', [70, 5, 0], 3.1], ['70F 5% RH wind 10 mph', [70, 5, 10], 30.8], ['70F 5% RH wind 30 mph', [70, 5, 30], 92.0], ['70F 9% RH wind 0 mph', [70, 9, 0], 2.9]]]
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
40F 5% RH wind 0 mph	`3.0`	`3.0`	Passed
40F 5% RH wind 10 mph	`30.6`	`30.6`	Passed
40F 5% RH wind 30 mph	`91.5`	`91.5`	Passed
40F 9% RH wind 0 mph	`2.8`	`2.8`	Passed
40F 9% RH wind 10 mph	`28.5`	`28.5`	Passed
40F 9% RH wind 30 mph	`85.2`	`85.2`	Passed
40F 10% RH wind 0 mph	`2.7`	`2.7`	Passed
40F 10% RH wind 10 mph	`26.9`	`26.8`	Failed

SHA-256 / dec6418b91ee8a21dda95f7022cdd47c2f4f4a9c231fbbc54ec1a5ef7e7b21af

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, wind_mph):
    if rh < 10:
        m = 0.03229 + 0.281073 * rh - 0.000578 * rh * t_f
    elif rh <= 50:
        m = 2.22749 + 0.160107 * rh - 0.01478 * t_f
    else:
        m = 21.0606 + 0.005565 * rh * rh - 0.00035 * rh * t_f - 0.483199 * rh
    x = m / 30.0
    eta = 1 - 2 * x + 1.5 * x * x - 0.5 * x * x
    f = eta * math.sqrt(1 + wind_mph ** 2) / 0.3002
    return round(min(max(f, 0.0), 100.0), 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['40F 5% RH wind 0 mph', [40, 5, 0], 3.0], ['40F 5% RH wind 10 mph', [40, 5, 10], 30.6], ['40F 5% RH wind 30 mph', [40, 5, 30], 91.5], ['40F 9% RH wind 0 mph', [40, 9, 0], 2.8], ['40F 9% RH wind 10 mph', [40, 9, 10], 28.5], ['40F 9% RH wind 30 mph', [40, 9, 30], 85.2], ['40F 10% RH wind 0 mph', [40, 10, 0], 2.7], ['40F 10% RH wind 10 mph', [40, 10, 10], 26.8]], [['40F 10% RH wind 10 mph', [40, 10, 10], 26.8], ['40F 10% RH wind 30 mph', [40, 10, 30], 80.1], ['40F 11% RH wind 0 mph', [40, 11, 0], 2.6], ['40F 11% RH wind 10 mph', [40, 11, 10], 26.5], ['40F 11% RH wind 30 mph', [40, 11, 30], 79.2], ['40F 30% RH wind 0 mph', [40, 30, 0], 2.1], ['40F 30% RH wind 10 mph', [40, 30, 10], 21.3], ['40F 30% RH wind 30 mph', [40, 30, 30], 63.5]], [['40F 30% RH wind 30 mph', [40, 30, 30], 63.5], ['40F 49% RH wind 0 mph', [40, 49, 0], 1.7], ['40F 49% RH wind 10 mph', [40, 49, 10], 16.8], ['40F 49% RH wind 30 mph', [40, 49, 30], 50.2], ['40F 50% RH wind 0 mph', [40, 50, 0], 1.7], ['40F 50% RH wind 10 mph', [40, 50, 10], 16.6], ['40F 50% RH wind 30 mph', [40, 50, 30], 49.6], ['40F 51% RH wind 0 mph', [40, 51, 0], 1.6]], [['40F 50% RH wind 0 mph', [40, 50, 0], 1.7], ['40F 51% RH wind 0 mph', [40, 51, 0], 1.6], ['40F 51% RH wind 10 mph', [40, 51, 10], 15.9], ['40F 51% RH wind 30 mph', [40, 51, 30], 47.5], ['40F 80% RH wind 0 mph', [40, 80, 0], 0.9], ['40F 80% RH wind 10 mph', [40, 80, 10], 8.7], ['40F 80% RH wind 30 mph', [40, 80, 30], 26.0], ['40F 100% RH wind 0 mph', [40, 100, 0], 0.2]], [['40F 51% RH wind 0 mph', [40, 51, 0], 1.6], ['40F 100% RH wind 0 mph', [40, 100, 0], 0.2], ['40F 100% RH wind 10 mph', [40, 100, 10], 1.7], ['40F 100% RH wind 30 mph', [40, 100, 30], 5.1], ['70F 5% RH wind 0 mph', [70, 5, 0], 3.1], ['70F 5% RH wind 10 mph', [70, 5, 10], 30.8], ['70F 5% RH wind 30 mph', [70, 5, 30], 92.0], ['70F 9% RH wind 0 mph', [70, 9, 0], 2.9]]]
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
40F 5% RH wind 0 mph	`3.0`	`3.0`	Passed
40F 5% RH wind 10 mph	`30.6`	`30.6`	Passed
40F 5% RH wind 30 mph	`91.4`	`91.5`	Failed
40F 9% RH wind 0 mph	`2.8`	`2.8`	Passed
40F 9% RH wind 10 mph	`28.4`	`28.5`	Failed
40F 9% RH wind 30 mph	`84.9`	`85.2`	Failed
40F 10% RH wind 0 mph	`2.7`	`2.7`	Passed
40F 10% RH wind 10 mph	`26.6`	`26.8`	Failed

SHA-256 / 61d7f97cceb714d618f5466ef227b874a4c7145dc7df4c927ec86886ead321b3

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, wind_mph):
    if rh < 10:
        m = 0.03229 + 0.281073 * rh - 0.000578 * rh * t_f
    elif rh <= 50:
        m = 2.22749 + 0.160107 * rh - 0.01478 * t_f
    else:
        m = 21.0606 + 0.005565 * rh * rh - 0.00035 * rh * t_f - 0.483199 * rh
    x = m / 30.0
    eta = 1 - 2 * x + 1.5 * x * x - 0.5 * x ** 3
    f = eta * math.sqrt(1 + wind_mph ** 2) / 0.3002
    return round(min(max(f, 0.0), 100.0), 1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['40F 5% RH wind 0 mph', [40, 5, 0], 3.0], ['40F 5% RH wind 10 mph', [40, 5, 10], 30.6], ['40F 5% RH wind 30 mph', [40, 5, 30], 91.5], ['40F 9% RH wind 0 mph', [40, 9, 0], 2.8], ['40F 9% RH wind 10 mph', [40, 9, 10], 28.5], ['40F 9% RH wind 30 mph', [40, 9, 30], 85.2], ['40F 10% RH wind 0 mph', [40, 10, 0], 2.7], ['40F 10% RH wind 10 mph', [40, 10, 10], 26.8]], [['40F 10% RH wind 10 mph', [40, 10, 10], 26.8], ['40F 10% RH wind 30 mph', [40, 10, 30], 80.1], ['40F 11% RH wind 0 mph', [40, 11, 0], 2.6], ['40F 11% RH wind 10 mph', [40, 11, 10], 26.5], ['40F 11% RH wind 30 mph', [40, 11, 30], 79.2], ['40F 30% RH wind 0 mph', [40, 30, 0], 2.1], ['40F 30% RH wind 10 mph', [40, 30, 10], 21.3], ['40F 30% RH wind 30 mph', [40, 30, 30], 63.5]], [['40F 30% RH wind 30 mph', [40, 30, 30], 63.5], ['40F 49% RH wind 0 mph', [40, 49, 0], 1.7], ['40F 49% RH wind 10 mph', [40, 49, 10], 16.8], ['40F 49% RH wind 30 mph', [40, 49, 30], 50.2], ['40F 50% RH wind 0 mph', [40, 50, 0], 1.7], ['40F 50% RH wind 10 mph', [40, 50, 10], 16.6], ['40F 50% RH wind 30 mph', [40, 50, 30], 49.6], ['40F 51% RH wind 0 mph', [40, 51, 0], 1.6]], [['40F 50% RH wind 0 mph', [40, 50, 0], 1.7], ['40F 51% RH wind 0 mph', [40, 51, 0], 1.6], ['40F 51% RH wind 10 mph', [40, 51, 10], 15.9], ['40F 51% RH wind 30 mph', [40, 51, 30], 47.5], ['40F 80% RH wind 0 mph', [40, 80, 0], 0.9], ['40F 80% RH wind 10 mph', [40, 80, 10], 8.7], ['40F 80% RH wind 30 mph', [40, 80, 30], 26.0], ['40F 100% RH wind 0 mph', [40, 100, 0], 0.2]], [['40F 51% RH wind 0 mph', [40, 51, 0], 1.6], ['40F 100% RH wind 0 mph', [40, 100, 0], 0.2], ['40F 100% RH wind 10 mph', [40, 100, 10], 1.7], ['40F 100% RH wind 30 mph', [40, 100, 30], 5.1], ['70F 5% RH wind 0 mph', [70, 5, 0], 3.1], ['70F 5% RH wind 10 mph', [70, 5, 10], 30.8], ['70F 5% RH wind 30 mph', [70, 5, 30], 92.0], ['70F 9% RH wind 0 mph', [70, 9, 0], 2.9]]]
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
40F 5% RH wind 0 mph	`3.0`	`3.0`	Passed
40F 5% RH wind 10 mph	`30.6`	`30.6`	Passed
40F 5% RH wind 30 mph	`91.5`	`91.5`	Passed
40F 9% RH wind 0 mph	`2.8`	`2.8`	Passed
40F 9% RH wind 10 mph	`28.5`	`28.5`	Passed
40F 9% RH wind 30 mph	`85.2`	`85.2`	Passed
40F 10% RH wind 0 mph	`2.7`	`2.7`	Passed
40F 10% RH wind 10 mph	`26.8`	`26.8`	Passed

SHA-256 / 4dc46d0ca889cf12d9043546a2e172829e809eb56515a64e89ecd7e14b713bdc

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 2026-09-29T14:48:26.678755+00:00.

Case digest / c7fa0c980e8ebc80be340509bf31a78ec45c3cdc36493e2411ebd225e7685de9