Curve Number Conversion Equations for Adjusting Initial Abstraction Ratios

The curve number (CN) method is widely used for rainfall-runoff estimation, yet its performance depends strongly on the assumed initial abstraction ratio (λ). Although λ=0.20 remains the standard assumption, recent national studies demonstrate that λ≈0.05 better represents runoff initiation in many US watersheds. This study develops new CNλ conversion equations to translate CN values calibrated under λ=0.20 (CN0.2) to values representative of λ=0.05 (CN0.05), using daily rainfall-runoff data from 1,358 watersheds across the contiguous United States. CN values were calibrated using the least-squares error method under two rainfall thresholds (P>0 mm and P≥25.4 mm). Sixteen conversion equations were formulated by combining linear and power forms, weighting schemes, and full and outlier-cleaned datasets, and compared with existing literature equations. Across all scenarios, power-type equations outperformed linear formulations, reflecting the inherent nonlinearity relationship between CN and potential maximum storage. The weighted power relations derived from outlier-cleaned datasets provided the strongest performance, yielding the lowest error, minimal bias, and exclusive retention in the 95% model confidence set. These equations reveal a consistent functional structure, including an overlap zone (CN0.2≈50–75) where λ-adjusted CN values are largely insensitive to model choice. Spatial patterns in calibration uncertainty and hydrologic inconsistency indicate that CNλ behavior varies across major hydroclimatic regions, highlighting the potential benefits of region-specific adjustments. While the weighted-outlier-cleaned power equations offer reliable national-scale CNλ conversions suitable for hydrologic design and modeling applications, the findings support future work integrating seasonality, antecedent runoff, and physiographic descriptors to refine regional CNλ relationships. Overall, the weighted-outlier-cleaned equations offer a defensible, practitioner-ready framework supporting the ongoing transition toward λ≈0.05 in CN-based hydrologic analysis.