The Curve Number Method in the 21st Century

The special collection on the Curve Number Method in the 21st Century is available in the ASCE Library (https://ascelibrary.org/jidedh/curve_number_method_21stcentury).

The curve number (CN) method is widely used to estimate the depth of runoff from the depth of rainfall in a given rainfall event. The attractiveness of the CN method is primarily due to two factors: (1) it is simple and easy to implement in that it only uses one parameter to characterize all influencing variables, and (2) it is endorsed by an agency of the US government, which gives the method legitimacy. The accuracy of the CN method is not usually cited as a reason to use the method, and the uncertainties of runoff predictions derived from the method are seldom stated. The method was developed in the 1950s, at a time when engineering hydrology was in its infancy and field data for validation were limited in quantity and quality. The method was intended for agricultural applications to give a broad measure of the impact of various land management and farming practices on runoff. The CN equation is actually formulated as a two-parameter heuristic model with the parameters being the initial abstraction, $I_a$, and the catchment storage, $S$. The CN equation takes on its one-parameter standard form by fixing the value of $I_a/S$ as 0.2, with this ratio commonly being denoted by $\lambda$. The appropriateness of specifying $\lambda$ as 0.2 has been a subject of debate for at least the past 20 years, with many asserting that actual $\lambda$ values are typically much less, and suggesting a revised standard value of 0.05. Nowadays, some 70 years on from the original development of the CN method, our knowledge of surface-water hydrology has markedly improved, and there is now a much wider database available to test the performance of the CN method, assess its assumptions, and identify improvements. With this perspective, this special collection takes a critical look at the fundamental formulation of the CN method, the validity of its implicit assumptions, its performance in the light of field measurements to date, and how it can be improved based on what we know now.

The CN method does not account for the temporal distribution of rainfall within a given event; it only accounts for the rainfall total. Chin (2021b) shows that if the rainfall amount and duration are fixed along with the catchment infiltration characteristics, and the intra-event temporal rainfall distribution is varied between distributions that are characteristic of different regions of the United States, then the applicable CN for given catchment characteristics can be substantially different. This implies that curve numbers are regional and not universal for given catchment characteristics as commonly assumed. Chin (2021b) also addresses the issue of incremental application of the CN method to determine incremental rainfall excesses that are subsequently used in unit-hydrograph models to calculate runoff hydrographs. It is demonstrated that this practice can lead to imposed incremental infiltration rates that exceed the infiltration capacities of the pervious areas of catchments, which then renders the incremental rainfall excess to be unrealistic and inconsistent with reality. With respect to the appropriate value of $\lambda$ that should be used in the CN model, it is demonstrated that a standard value much less than 0.2 is appropriate; however, it is recognized that $\lambda$ is fundamentally variable and is not a universal constant.

Chin (2021a) addresses the issue that the CN method is intended for application to “large” rainfall events and field measurements show that higher CNs are needed to reproduce the rainfall-runoff relation for “small” events. In this context, CN is more appropriately represented as ${\mathrm{CN}}_{\infty }$, where the $\infty$ subscript indicates that the CN is applicable to large rainfall events for which CN is independent of the rainfall amount. Chin (2021a) identifies an equation for calculating the minimum amount of rainfall for the predicted runoff to be within 10% of the runoff predicted when the curve number is taken as ${\mathrm{CN}}_{\infty }$. Whereas the required minimum rainfall amount can be substantial for some values of ${\mathrm{CN}}_{\infty }$, it is shown that using a CN base of $\lambda =0.05$ requires a minimum rainfall amount that is much less than using a CN base of $\lambda =0.2$.

Estimation of CN from field measurements generally requires data on the rainfall amount, $P$, and the resulting direct runoff, $Q$. Whereas $P$ can be obtained directly from rain-gauge measurements, runoff usually consists of a combination of base flow and direct runoff. Hence, it is commonly necessary to separate the direct runoff from the base flow. A convenient automated method for performing this partition is presented by Boughton (2021). This separation method is relatively simple in that it requires specification of only a single parameter to drive the separation model, and might be a useful alternative to more complex separation models.

Bertotto et al. (2021) studied the rainfall-runoff relation for a site in Brazil with clayey soil to determine the relation between CN and other variables. Rainfall distributions of varying durations were constructed from the local intensity-duration-frequency function using the alternating-block method, and runoff was calculated by imposing a Hortonian runoff process. Infiltration characteristics at the site were measured using a double-ring infiltrometer. The key findings of this study were that the representative CN of the site decreased as the rainfall duration increased, and the applicable CN was dependent on the rainfall amount. Lower rainfall amounts required the use of higher CNs to yield the measured runoff. Bertotto et al. (2021) also found that $\lambda$ was variable and dependent on the initial soil moisture at lower rainfall depths, and $\lambda$ tended to a constant of around 0.28 at higher rainfall depths.

Chin (2022a) addresses several of the core technical issues associated with the CN method by compiling results from 74 US Department of Agriculture experimental watersheds that have long records of high-quality measurements of rainfall and runoff. Key results from this study were as follows: (1) using CN values with a base of $\lambda =0.05$ leads to more accurate runoff predictions over the range of rainfall events experienced at these catchments; (2) the effective infiltration capacity of a catchment can be reliably estimated based on the CN of the catchment; and (3) CN dependence on event duration is relatively weak, and likely exists only for short durations and rainfall amounts; CN ultimately becomes independent of duration as it becomes independent of the rainfall amount. This study also shows that skewed probability distributions for CN are typically a result of investigators not taking into account the dependence of CN on the rainfall amount. It is also shown that the time lag in a catchment, defined as the time between the centroid of the rainfall excess and the corresponding peak in the runoff hydrograph, can be simply related to the catchment area, and including CN in the lag estimation does not bring any added value.

Chin (2022b) focuses on the minimum rainfall amount that is necessary for the applicable curve number to be independent of the rainfall amount. This is a particularly important consideration in stormwater management applications that involve calculating a water-quality treatment volume from a water-quality rainfall depth. It is shown that catchments with curve numbers of 50 and 70 require minimum rainfall amounts of 9 cm (3.5 in.) and 4 cm (1.5 in.), respectively.

Chin (2023) identifies an improvement of the CN method that addresses the technical issue of needing to adjust the initial abstraction ratio, $\lambda$, to better represent field measurements while maintaining the current standard values of ${\mathrm{CN}}_{\infty }$ that are found in engineering handbooks. The key to this improvement is incorporating the relation between CN and the rainfall amount into the standard CN equation. The improved CN equation would still relate the runoff to the rainfall amount with only a single parameter, ${\mathrm{CN}}_{\infty }$. However, the improved CN equation would not require specifying a new value for $\lambda$, and is much more accurate for lower rainfall amounts while preserving its accuracy for higher rainfall amounts.

Collectively, the investigations reported in this special collection coalesce around several key findings. Of particular interest are (1) CN can be substantially dependent on the intrastorm rainfall distribution for a given rainfall amount, and because characteristic rainfall distributions are regional, CN values for given catchment characteristics are also likely to be regional; (2) because CN depends on the rainfall amount for lower rainfall amounts, this dependence should be either accounted for in the CN method, or a threshold rainfall should be identified beyond which conventional curve numbers are applicable; and (3) when the CN equation is applied incrementally to determine incremental runoff amounts, the associated infiltration rate should be constrained by the infiltration capacity of the catchment to ensure the incremental runoff is realistic. As a culmination of these investigations, a modification of the existing CN equation is identified that addresses the shortcomings of the CN method that was developed some 70 years ago. Engineers and regulatory agencies are encouraged to build on the current state of knowledge as we move through the 21st century, and this special collection provides a road map for forward progress.