Quantification of Curve Numbers for Arid Watersheds

Although the curve number (CN) method has been widely used in rainfall and runoff models, the physical interpretation of the CN method is still challenging, for instance how to estimate the potential maximum retention. This paper analyzed the historical rainfall and runoff event data from 1975 to 2021 for two arid to semiarid watersheds, the Santa Rita and the Lucky Hills experimental watersheds in Tucson, Arizona. As is well known, a constant CN for a watershed can be back-calculated by fitting the observed rainfall and runoff. This study found this constant CN increase with the ratio of initial abstraction. On the other hand, CN can also be back-calculated for each event using the observed rainfall and runoff. The event-based CN depends on precipitation, land use, types and density of vegetation, as well as soil properties. If assuming the potential maximum retention is equal to the cumulative infiltrated water in each rainfall event, we applied the Green–Ampt infiltration model to estimate the CN for each historical event and compared with the back-calculated event-based CN. We found that 71% of the calculated CNs fell in the 10% margin of error, and 88% were within the 20% margin of error compared with the observed data. This indicated that the retention in CN can be considered as the cumulative infiltrated water in each event and calculated using the soil properties and rainfall duration. This is the first physical-based quantitative interpretation of retention in CN that will enable the determination of CN for ungauged watersheds in remote areas.