The curve number and phi (φ)-index models each provide a simple one-parameter relationship between storm-event rainfall and runoff. It is shown that the curve number and φ-index models can both be used to segregate the rainfall hyetograph into initial abstraction, retention, and runoff amounts. However, the principal advantages of the φ-index model are that both rainfall distribution and duration can be explicitly taken into account in calculating runoff, and the φ index is more physically based than the curve number. The quantitative relationship between the curve number and the φ index is presented and validated with field measurements. Knowing the relationship between the curve number and the φ index is useful in that it facilitates using the extensive database of curve numbers in the more realistic φ-index model in calculating a runoff hydrograph from a given rainfall hyetograph. It is demonstrated that conventional adjustments to curve numbers can be largely explained by variations in storm duration, which suggests that variable rainfall duration can possibly be an essential factor in accounting for deviations from the median curve number of a catchment.
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