Applicability Limits for Using 2D Shallow-Water Models to Predict Discharge over Fixed-Crest Weirs

Fixed-crest weirs are widely used hydraulic structures that control river discharge capacity and influence upstream water surface profiles. Accurate prediction of their rating curves is essential during flood events; however, two-dimensional (2D) shallow-water equation (SWE) models are often applied without clearly established criteria defining their range of reliable use. This study evaluates the performance of a 2D SWE model under varying submergence conditions using laboratory experiments, depth-averaged numerical simulations, theoretical analysis, and velocity measurements. Agreement between measured and simulated hydraulic characteristics met the adopted accuracy criterion only above a transition ratio of submergence depth to critical depth over the weir crest, estimated statistically as 0.70–0.77 for Case A and 0.97 for Case B (95% confidence interval 0.91–1.04). Below this transition, errors increase rapidly due to unresolved vertical contraction and non-hydrostatic effects. In both cases, the transition occurred at a lower relative submergence depth than that required by the classical parallel-flow criterion proposed by earlier researchers, and was closer to the theoretical force-balance estimate, which indicates approximately equal submergence and critical depths. These findings establish a physically supported range of reliable 2D SWE applications and provide practical guidance for hydraulic modelling of submerged weir flows.