SUPPLEMENTAL MATERIAL FOR

Engineers often use compound weirs in rivers and channels to control flow, reduce velocities, or direct water toward desired locations. When such structures operate under submerged conditions, they create additional flow resistance that affects upstream water levels. Representing these effects correctly in hydraulic models is important for reliable river and flood simulations. This study provides a simple analytical method that can be easily used in one- and two-dimensional river models to include the effects of submerged compound weirs. The method expresses the added resistance through a single correction factor that accounts for flow conditions and weir geometry. Because it is based on basic hydraulic principles, the approach can be applied without increasing model complexity or computational cost. The results help engineers and modelers improve the accuracy of large-scale hydraulic simulations involving compound or adjustable weirs used in flood management, river training, irrigation systems, and flow diversion structures.