Source: ssd-api.jpl.nasa.gov/fireball.api, fields energy (radiated, kt) and
impact-e (estimated impact energy, kt), plus date, location, altitude and velocity. Saved
locally as data/fireballs.json (44 KB).
| Quantity | Value |
|---|---|
| Events | 602 |
| Radiated energy range | 1.24 – 37,500 kt |
| Impact energy range | 0.048 – 441 kt |
| Date coverage | 1997 – 2026 |
This is a real catalogue, and it is not volume-complete. Its lower cut-off is set by detection, so no statement here is about the true impact rate — only about what this catalogue contains.
The hub's H203 record concluded that the impact energy is a deterministic function of the radiated energy (reported r = −0.995), which is why the result was not promoted. That is confirmed here, and more sharply than reported.
| Statistic | Value |
|---|---|
| Pearson r, log₁₀ energy vs log₁₀ impact energy | 0.99992 |
| Spearman ρ | 0.99950 |
| Residual sd about a straight log–log line | 0.0064 dex |
| Median ratio impact/radiated | 0.03154 |
| Ratio range | 0.0118 – 0.0387 (3.29×) |
Interpretation. Over four and a half decades of energy, the two columns agree to 0.0064 dex — about 1.5%. The impact energy carries almost no information independent of the radiated energy. Any analysis that treats them as two measurements is using one measurement twice.
The 3.29× ratio spread is the one caveat: the relation is tight but not exactly proportional, so "deterministic" is right to a few per cent, not to machine precision. The hub's own conclusion — that this makes H203's tail result conditional rather than physical — stands and is strengthened.
Hill estimator of the tail index above several thresholds:
| Threshold (kt) | Exceedances | Hill α |
|---|---|---|
| 0.2 | 602 | 0.257 |
| 0.5 | 602 | 0.337 |
| 1.0 | 602 | 0.440 |
| 2.0 | 590 | 0.619 |
| 5.0 | 369 | 0.722 |
The hub reports b = 2.65–2.82 and α = 1.33–1.41 for thresholds 0.2–2 kt. This re-analysis gives α = 0.26–0.62 over the same thresholds — a factor of two to five lower, and in the opposite direction from the reported range.
A 40-point threshold sweep gives α from 0.24 to 0.69, median 0.37, a spread of 2.86×. The estimate is strongly threshold-dependent, which is the usual signature of a Hill estimator applied below its valid region.
Three explanations are possible, and I cannot separate them with this data alone:
The honest statement: the tail-index number in H203 does not reproduce from the current catalogue under a Hill estimator, and the discrepancy is large enough that the number should not be quoted until the estimator and the catalogue cut are both specified.
| H203 element | Status after re-analysis |
|---|---|
| Impact energy is a recalibration of radiated energy | Replicated, and sharper (r = 0.99992, 0.0064 dex) |
| "Not promoted until a second catalogue exists" | Correct call — the dependency is confirmed |
| b ≈ 2.65–2.82, α ≈ 1.33–1.41 | Not reproduced; α = 0.26–0.62 here |
| α = b/(3γ) with predicted 1.35 | Cannot be tested until b is re-derived consistently |
| # | Hypothesis | Disposition |
|---|---|---|
| N-20 | Published impact-loss tail indices are estimator-dependent, and the spread across estimators exceeds the difference between competing physical models. | test now — three estimators on this catalogue |
| N-21 | A catalogue whose impact energy is calibrated from radiated energy cannot test a hypothesis about impact energy, because the two are one measurement. This applies to any catalogue with a derived column. | test now — check other catalogues for derived columns |
| N-22 | The 3.29× ratio spread is not noise but encodes the velocity and altitude dependence, so the residual of the energy relation recovers the entry parameters. | test now — regress the residual on velocity and altitude |
If one sentence survives: the deterministic-recalibration objection to H203 is confirmed at 0.0064 dex, and the tail-index number does not reproduce from the current catalogue — so the record should keep the objection and withdraw the number until the estimator is specified.