Articles | Volume 22, issue 9
Research article
10 Sep 2018
Research article |  | 10 Sep 2018

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

Vijay P. Santikari and Lawrence C. Murdoch

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, Ia, can be used to explain how CN varies with P. By conventional definition, Ia 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 Ia (IaT) is constant, but the effective Ia varies with P, and is equal to the filled portion ofIaT, which we call IaF. CN calculated using IaF varies with P similar to published field observations. This motivated modifications to the CN method, called variable Ia models (VIMs), which replace Ia with IaF. 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 Ia accounts for heterogeneity and improves the performance of the CN method while retaining its simplicity.

Short summary
The curve number (CN) method is the most widely used approach for estimating runoff from rainfall. Despite its popularity, there is a conceptual flaw where CN varies with rainfall although it is assumed to be constant. In this paper, we describe theoretical analyses that show how this behavior is due to watershed heterogeneity, and we then provide simple modifications to the method to improve its runoff predictions. The findings will benefit hydrologists and watershed models that use CN method.