Flood Frequency Estimate for a Small Ungauged Culvert
A 26 km2 rural catchment needs a culvert sized for a 100-year flood. There is no gauge on the catchment. A nearby gauged catchment of 41 km2, 30 km away, has 28 years of record and an estimated 100-year flow of 38 m3/s. Regional regression gives 22 m3/s for the site, but the regression has a standard error of 45 percent. The site has 30 percent forest cover versus 12 percent at the gauged catchment, and soils at the site are noticeably more clay-rich. A landowner reports a 1998 flood that reached a well-known high-water mark on a bridge.
1. Evaluate the three available estimates (regional regression, transferred gauge estimate, and the historical high-water mark) and their limitations.
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Regional regression (22 m3/s) is the most transferable because it is built for the region, but a 45 percent standard error means the 100-year estimate is highly uncertain; the true value could plausibly range from about 12 to 32 m3/s at one standard error.
The gauged-catchment transfer (38 m3/s) requires scaling by drainage area and adjusting for land cover and soils. The site is smaller (26 vs 41 km2), more forested, and more clay-rich; more forest and clay typically increase runoff response and reduce infiltration, so simple area scaling would understate peak flow, but the magnitude of adjustment is uncertain and the 28-year record gives a weak 100-year estimate with wide confidence limits.
The 1998 high-water mark is a single point estimate of unknown return period and uncertain stage-to-discharge conversion; it is useful as a check but cannot define the 100-year flow.
2. Recommend a design flow and describe how you would document the uncertainty for the culvert decision.
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Recommend a design flow anchored on the regional regression but adjusted upward for the site's higher runoff potential, then bracketed by the other estimates. A reasonable working value is in the high 20s to low 30s m3/s, with the transferred gauge estimate treated as an upper bound and the regression as the central estimate.
Documentation should state: the regression estimate and its standard error, the transfer assumptions and the direction of land-cover and soil bias, and the historical mark as a consistency check. Where the historical mark converts to a discharge near the chosen value, confidence increases; if it exceeds it, the design flow should be raised.
For the culvert, size for the upper part of the range or provide freeboard and an overflow path, and record the uncertainty so the asset owner accepts the residual risk explicitly.