Including effects of watershed heterogeneity in the curve number method using variable initial abstraction

Abstract. The curve number (CN) method was developed more than half a century ago and is still used in many watershed and water-quality models to estimate direct runoff from a rainfall event. Despite its popularity, the method is plagued by a conceptual problem where CN is assumed to be constant for a given set of watershed conditions, but many field observations show that CN decreases with event rainfall (P). Recent studies indicate that heterogeneity within the watershed is the cause of this behavior, but the governing mechanism remains poorly understood. This study shows that heterogeneity in initial abstraction, I_a, can be used to explain how CN varies with P. By conventional definition, I_a is equal to the cumulative rainfall before the onset of runoff and is assumed to be constant for a given set of watershed conditions. Our analysis shows that the total storage in I_a (I_aT) is constant, but the effective I_a varies with P, and is equal to the filled portion ofI_aT, which we call I_aF. CN calculated using I_aF varies with P similar to published field observations. This motivated modifications to the CN method, called variable I_a models (VIMs), which replace I_a with I_aF. VIMs were evaluated against conventional models CM0.2 (λ  =  0.2) and CMλ (calibrated λ) in their ability to predict runoff data generated using a distributed parameter CN model. The performance of CM0.2 was the poorest, whereas those of the VIMs were the best in predicting overall runoff and watershed heterogeneity. VIMs also predicted the runoff from smaller events better than the CMs and eliminated the false prediction of zero-runoffs, which is a common shortcoming of the CMs. We conclude that including variable I_a accounts for heterogeneity and improves the performance of the CN method while retaining its simplicity.