Abstract
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.
Highlights
The estimation of runoff from a rainfall event is of primary importance in applied hydrology
The results show that using variable initial abstraction improved the accuracy of model predictions of runoff and heterogeneity (Table 3)
Larger events had greater influence on rNSEQ as well, but the values varied slightly between the models (Table 3). rNSEQ increased down the table whereas SEEQ decreased, with both indicating an improvement in model performance
Summary
The estimation of runoff from a rainfall event is of primary importance in applied hydrology. Curve number varies spatially due to watershed heterogeneity and temporally due to changes in soil moisture, land cover, temperature, and other processes (Hawkins et al, 2008; Ponce and Hawkins, 1996; Rallison and Miller, 1982). When heterogeneity is known at sufficient detail, CN variation can be accounted for by using a distributed parameter model, e.g., SWAT (Gassman et al, 2007). Otherwise this approach can introduce more parameters than can be reliably estimated from the available data (Soulis and Valiantzas, 2013) and can potentially cause large uncertainties in the predicted runoff. S is the total storage available for infiltration after the runoff begins
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