Linear trends fitted to 1941-2005 annual flood peaks gave worse 2006-2025 forecasts than a stationary model at 1,187 unregulated US gauges; carrying 30-40% of the trend gave only a 1% gain

Question: does a linear trend fitted to past annual flood peaks forecast later peaks better than a stationary model? We used USGS annual peak discharges at 1,187 gauges with no regulation, diversion or urbanization code, at least 55 peaks in water years 1941-2005 and at least 16 peaks in 2006-2025 (264 are CAMELS reference basins). We fitted six models to ln(peak) in 1941-2005 and scored 2006-2025 forecasts with the continuous ranked probability score (CRPS). The plan was written before scoring. The at-site linear trend was worse than the stationary model: skill -2.9% (95% interval from test-year resampling -4.6% to -1.3%); -4.6% at CAMELS gauges. Its point estimate was negative in all eight regional groups. A trend used only when Mann-Kendall p<0.05 gave -1.1%, a regional median trend -0.3%, the 1976-2005 mean +0.8% and half of the trend +0.9%. Full trends also lost 5-10% at three other forecast origins (post hoc). Across gauges, the 2006-2025 anomaly increased by 0.38 (0.30-0.46) per unit of trend-predicted shift, below the 0.56-0.63 that estimation noise alone would give; so trends continued only in part. A post hoc scan found the best share of the trend at 30-40%, with about 1.1% gain. Stationary 10-year and 50-year floods were exceeded by 10.1% and 2.5% of 2006-2025 peaks. At CAMELS gauges, test-period anomalies followed annual precipitation anomalies, but precipitation explained only 7% of the variance of old trends. Limitations: lognormal predictive distributions, linear mean trends only, coding-based screening of human effects, 20 shared test years, and post hoc secondary analyses.

flood frequency · nonstationarity · annual peak flow · trend extrapolation · forecast verification · CRPS · USGS · CAMELS · updated stationarity · hydrology