When a surge crests at one gauge, these are the actual equations — coefficients and all — that predict its size and arrival downstream. Fit on every measured wave since December 2014, validated leave-one-year-out (each year predicted by a model that never saw it). Nothing here is hidden: transparency on public safety builds trust.
The moment a gauge starts a qualifying rise (25% and 30 cfs over its recent low), a provisional wave launches: the running peak is treated as a floor and the forecast grows with the river. When the gauge crests (drops back 8% from its peak), the wave is confirmed: inputs freeze, and the arrival window is pinned to the actual crest time. The prediction then lives until the water arrives downstream — it never disappears just because the upstream gauge started falling.
logU = the upstream crest (log); logB = this gauge's flow when the upstream rise began (log).
Band shown to users: ×0.84 to ×1.17 of the median (the middle half of out-of-sample errors); fit on 246 launches, median error 12.4% on waves ≥1,000 cfs.
| Wave size at Boxley | Travel time to Ponca |
|---|---|
| 0–1,000 cfs | 0.5–2.2 h (median 1.2) |
| 1,000–∞ cfs | 0.5–1.2 h (median 0.8) |
logU = the upstream crest (log); logB = this gauge's flow when the upstream rise began (log); rint = rain over the drainage between the two gauges (inches, storm max); ratio = how the storm's rain was split — in-between rain ÷ upstream rain.
Band shown to users: ×0.86 to ×1.15 of the median (the middle half of out-of-sample errors); fit on 296 launches, median error 12.0% on waves ≥1,000 cfs.
| Wave size at Ponca | Travel time to Pruitt |
|---|---|
| 0–1,000 cfs | 6.7–9.9 h (median 8.2) |
| 1,000–5,000 cfs | 4.8–6 h (median 5.2) |
| 5,000–∞ cfs | 4.8–5.5 h (median 5) |
logU = the upstream crest (log); logB = this gauge's flow when the upstream rise began (log); rint = rain over the drainage between the two gauges (inches, storm max); ratio = how the storm's rain was split — in-between rain ÷ upstream rain; ltrib = the tributary gauge's recent flow (log; Richland or Bear Creek).
Band shown to users: ×0.82 to ×1.16 of the median (the middle half of out-of-sample errors); fit on 302 launches, median error 14.5% on waves ≥1,000 cfs.
| Wave size at Pruitt | Travel time to St. Joe |
|---|---|
| 0–1,000 cfs | 6.3–19.2 h (median 12.9) |
| 1,000–5,000 cfs | 5.2–11 h (median 8.5) |
| 5,000–∞ cfs | 6.7–9.5 h (median 8.1) |
logU = the upstream crest (log); logB = this gauge's flow when the upstream rise began (log); rint = rain over the drainage between the two gauges (inches, storm max); ante = pre-storm 7-day rain over the in-between drainage (inches); ltrib = the tributary gauge's recent flow (log; Richland or Bear Creek).
Band shown to users: ×0.92 to ×1.06 of the median (the middle half of out-of-sample errors); fit on 319 launches, median error 6.3% on waves ≥1,000 cfs.
| Wave size at St. Joe | Travel time to Harriet |
|---|---|
| 0–1,000 cfs | 10.9–14.1 h (median 12.8) |
| 1,000–5,000 cfs | 5.5–8.2 h (median 6.5) |
| 5,000–∞ cfs | 4.8–6 h (median 5.5) |
logU = the upstream crest (log); logB = this gauge's flow when the upstream rise began (log); rint = rain over the drainage between the two gauges (inches, storm max); ante = pre-storm 7-day rain over the in-between drainage (inches); ltrib = the tributary gauge's recent flow (log; Richland or Bear Creek).
Band shown to users: ×0.81 to ×1.24 of the median (the middle half of out-of-sample errors); fit on 296 launches, median error 20.7% on waves ≥1,000 cfs.
| Wave size at Ponca | Travel time to St. Joe |
|---|---|
| 0–1,000 cfs | 10.3–25.2 h (median 18.2) |
| 1,000–5,000 cfs | 10.2–16.6 h (median 14) |
| 5,000–∞ cfs | 10.4–15.5 h (median 13.5) |
logU = the upstream crest (log); logB = this gauge's flow when the upstream rise began (log); rint = rain over the drainage between the two gauges (inches, storm max); ratio = how the storm's rain was split — in-between rain ÷ upstream rain; ltrib = the tributary gauge's recent flow (log; Richland or Bear Creek).
Band shown to users: ×0.83 to ×1.18 of the median (the middle half of out-of-sample errors); fit on 302 launches, median error 15.9% on waves ≥1,000 cfs.
| Wave size at Pruitt | Travel time to Harriet |
|---|---|
| 0–1,000 cfs | 10.3–28.9 h (median 19.8) |
| 1,000–5,000 cfs | 10.2–17.6 h (median 14) |
| 5,000–∞ cfs | 11.8–15.5 h (median 13.3) |
A watch fires when the median prediction reaches 60% of the destination gauge's flood threshold; a warning only when even the cautious low end of the band floods. And the tracker corrects itself: as the wave passes each gauge it is re-observed, and the freshest observation replaces the older, longer-range estimate. On 2026-06-22, the long-range model over-called St. Joe at ~14,000 cfs from Pruitt's crest; when the wave actually reached St. Joe at 7,890, Harriet's forecast snapped to ~8,300 against an actual 6,870.
Known limit: a wave riding onto bone-dry ground from upper-basin-only rain (roughly once a decade) over-predicts about 2× until re-observation corrects it — we chose not to tune the equations to a single event.
Every number on this page is generated from the deployed model files and an 11½-year hourly replay (2014-12 → 2026-06, baseline v6). Generated 2026-07-02T22:57:24+00:00. Experimental — never rely on a single number for safety decisions.