Reliability of Prediction Intervals for Local Pier Scour under Distribution Shift: A Comparison of Split Conformal and Conformalized Quantile Regression

Point-estimate accuracy for local pier scour has improved; however, bridge-foundation design also requires prediction intervals that achieve nominal coverage.Conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee may fail when evaluation conditions extend beyond the training range.This study analyzed 1,152 field records from the U.S. Geological Survey pier-scour database, partitioned at the 70% quantile of flow intensity to create a controlled covariate shift.Split conformal, which produces fixed-width intervals, and conformalized quantile regression (CQR), which produces input-dependent intervals, were compared using an extreme gradient boosting model configured for quantile regression over five random seeds.Both methods achieved coverage close to the target levels in the in-distribution region.In the shifted region, at the 90% target, the coverage of split conformal fell to 0.783 (11.7 percentage points below the target), whereas CQR maintained 0.898.The mean CQR interval width increased from 1.116 to 1.432 because of a larger base quantile spread rather than the calibration term.The higher shifted-region coverage of CQR remained consistent across split ratios of 0.6-0.9.Because neither method retains a theoretical guarantee under distribution shift, CQR's higher coverage is empirical and reflects wider intervals rather than improved physical extrapolation.