Uncertainty Quantification of Discharge Prediction in Sharp‐Crested Power‐Law Weirs Under Fixed and Uncertain Geometries

Abstract

ABSTRACT Accurate discharge measurement is essential for irrigation water allocation, billing and operational control. Sharp‐crested power‐law weirs provide a flexible framework because rectangular, parabolic and triangular geometries can be represented by the exponent n . However, existing stage‐discharge equations are commonly applied deterministically, without explicitly propagating measurement and geometric uncertainties. This study develops a Monte Carlo uncertainty‐propagation framework using 502 free‐flow experimental runs. Two discharge formulations were evaluated: an analytical weir‐theory model and an empirical critical‐flow‐based model. Three uncertainty cases were considered: fixed nominal geometry, bounded exponent uncertainty with 0 ≤ ns ≤ 1, and a boundary‐relaxed robustness case with ns ≤ 1.05. For fixed geometries, the mean 95% relative uncertainty bandwidth ranged from 4% for rectangular weirs to 7% for triangular weirs. Under bounded exponent uncertainty, the bandwidth increased to 6%–9%. The boundary‐relaxed analysis showed that the triangular geometry becomes comparably sensitive when small deviations above n = 1 are allowed, indicating that sensitivity rankings depend on how geometric uncertainty is represented. The framework provides a probabilistic complement to deterministic discharge equations for uncertainty‐aware irrigation flow measurement.