Rating Curve Shift After a Channel-Forming Flood
A gauging station uses a stable-control rating curve developed over 8 years, with discharge Q = 42(h − 0.30)^1.62 (h in m, Q in m³/s). A channel-forming flood scours the control section. Post-flood discharge measurements at the same stage give systematically lower flows: at h = 1.80 m the pre-flood curve predicts 68 m³/s, but three post-flood measurements average 51 m³/s. The station is the index gauge for a flood-frequency analysis and a reservoir inflow forecast. You must decide how to handle the record and the forecast.
1. Quantify the shift and determine whether the pre-flood rating remains valid.
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Pre-flood at h = 1.80: Q = 42(1.50)^1.62 ≈ 42 × 1.93 ≈ 81 m³/s (recompute carefully; the stated 68 m³/s implies a different coefficient, so treat the stated 68 as the reference). Post-flood measured ≈ 51 m³/s. The shift is (51 − 68)/68 ≈ −25% at this stage. A 25% systematic offset at a single stage, confirmed by three measurements, is far outside measurement uncertainty (typically ±5–10%), so the pre-flood rating is invalid post-flood. The control has changed; a new or shifted rating must be developed. The pre-flood record is not wrong for its period, but the post-flood period cannot be rated with the old curve.
2. How should the historical flood-frequency analysis and the inflow forecast each treat the shift?
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For flood-frequency analysis: the pre-flood record used the old rating and remains valid for that period; the post-flood period must use the new/shifted rating. Do not apply the new rating backward to the old period - that would bias historical peaks. Document the shift date and treat the record as two rating regimes. If the shift is a step change, consider whether the largest historical peaks (which may have caused similar scour) were rated correctly. For the inflow forecast: use the post-flood rating immediately, because the forecast operates on current channel geometry. Applying the old curve would over-forecast inflow by ~25% at high stage, risking unnecessary spill or mis-operation. The forecast system must be updated to the new rating and flagged until the control stabilizes.
3. What monitoring would confirm the new control is stable before relying on it for design?
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Establish a new rating with discharge measurements across the full stage range, especially at high flow where the shift is largest. Repeat measurements over several events to confirm the control has stabilized (scour may continue). Check for hysteresis - different Q at the same h on rising vs falling limbs indicates an unstable control. Compare the new rating's residuals; if measurements scatter beyond expected uncertainty, the control is still changing and the rating is provisional. Only after the rating is confirmed stable across multiple events should it anchor design flood estimates. Until then, carry the uncertainty explicitly.