How to average curve numbers?

A representative curve number (CN) of a catchment is often calculated from the area-weighted average of CN values of unique land use and soil combinations. While convenient for implementation, this method is known to underestimate direct runoff depth. This paper investigates the mathematical mechanism of the expected underestimation and proposes alternative CN averaging methods, the quadratic and exact averaging methods, to handle the underestimation problem. Results suggest that the quadratic method could reduce the level of underestimation in direct runoff depth, and further the exact method could provide the same direct runoff depth as that of the area-weighted direct runoff depth averaging method. A representative CN is found to be a function of rainfall size as well as catchment landscape, and the underestimation is relatively large for small and mid-sized storm events. The improvement in runoff estimation with the newly proposed averaging methods is particularly beneficial to stormwater management, flood controls, and erosion controls upon small return-period events.