INITIAL ABSTRACTION REVISITED Victor M. Ponce and Luis Magallon 151025 ABSTRACT The concept of initial abstraction in the NRCS runoff curve number method is revisited, in light of the demonstrably different results obtained by current models (SWMM and HEC-HMS). The runoff curve number method is lumped in time, but it has been used by way of practice as a temporally distributed model, beyond the scope of its original development. This has led to various ways of accounting for the initial abstraction. There is an urgent need to revise the concept and to develop a new standard, so that the various models will lead to the same or similar results. 1.   INTRODUCTION The concept of initial abstraction has evolved since its introduction in the 1950s as part of the NRCS runoff curve number method (Ponce, 2014). Several interpretations are in current use, which has defied standarization. Hydrologic models such as SWMM and HEC-HMS apply the concept in different ways, resulting in different answers. Thus, it has become necesary to review and clarify the concept of initial abstraction in the runoff curve number method, in the hope that in the future, when the method is used in conjunction with SWMM and HEC-HMS, the calculated hydrograph will be essentially the same. 2.   INITIAL ABSTRACTION DEFINED The concept of initial abstraction originated with the NRCS runoff curve number (RCN) method, developed by the USDA Natural Resources Conservation Service (formerly Soil Conservation Service, or SCS) in the 1950s, and documented in National Engineering Handbook: Part 630 - Hydrology. For a given storm depth P and runoff curve number CN, the initial abstraction Ia is the initial fraction of the storm depth after which runoff begins. Victor Mockus, the lead developer of the RCN method, believed that for any one case, the amount of initial abstraction was, for all practical purposes, intractable. To circumvent the problem, Mockus proposed to plot P' = P - Ia, instead of P, in the abscissas, and runoff Q in the ordinates (Ponce, 1996). Had this procedure been adopted, it would have effectively separated the estimation of initial abstraction from the RCN method. As Mockus told Ponce in the now famous interview (Ponce, 1996), he was overruled by his superiors at SCS, who believed that an initial abstraction component had to be part of the nascent RCN method. For completeness, the original runoff curve number equation developed by Mockus is:  P - Q            Q _______  =  ______     S               P (1) in which S = potential storage, with all variables taken in depth units. The initial abstraction Ia was subtracted from the storm depth P to yield:  P - Ia - Q              Q ___________  =  _________        S                  P - Ia (2) To keep the method simple, Mockus expressed the potential retention S in terms of a more manageable runoff curve number CN:           1000 S = _________  -  10            CN (3) in which CN is a dimensionless number limited in the range 1 ≤ CN ≤ 100, and all other terms in Eq. 3 are depths, in inches. For the method to remain practical, featuring only one parameter (CN), the initial abstraction had to be related to the storage S. After much discussion, the following linear relation was adopted: Ia = λ S (4) in which λ = initial abstraction parameter. At the method's inception, the value of λ was fixed at λ = 0.2, because this value appeared to be at the center of the data. To this date, questions remain as to whether this value applies for all cases or, more so, whether it applies at all as a central and only value. In the past 20 years, much research has been reported on the subject. Hawkins et al. (2002) have argued persuasively for the use of λ = 0.05. At the present time (2020), no decision has been made by NRCS on whether to keep or to change the value of λ. Since the current set of CN's were developed in conjunction with λ = 0.2, it is readily seen that an official change of λ would effectively require a new CN set. In the time elapsed since its original development, the NRCS runoff curve number method has become a de facto standard in hydrologic engineering practice, with numerous applications in the U.S. and other countries (Ponce and Hawkins, 1996). Its popularity is based on its simplicity, although reasonable care is necessary in order to use the method correctly. In many instances, the method's capabilities have been stretched, largely for lack of an alternative. Mockus pointed out that the method was not intended to be a predictor of the rate of infiltration, but rather, of the total volume of infiltration for a given storm event (Ponce, 1996). Given P (in inches) and an estimate of CN, the runoff volume Q (in inches) is (Ponce, 2014):               [ CN ( P + 2 ) - 200 ] 2 Q =   ___________________________             CN [ CN ( P - 8 ) + 800 ] (5) As originally proposed, the NRCS RCN method is effectively lumped in time, providing an estimate of storm runoff Q (in), given storm rainfall P (in) and an appropriate CN value, independently of the storm duration, which is not explicitly accounted for. Mockus stated that the supporting data used in the method's development was daily rainfall, because this type of data was the only one available in large quantities (Ponce, 1996). In practice, this means that the RCN method ought to work best when the storm duration is close to one (1) day, although in many applications this has not been necessarily the case (NRCS, 1986). The correct definition of initial abstraction in the NRCS RCN method follows from the method's original development: "For a given storm depth P and runoff curve number CN, the initial abstraction Ia is the fraction of the storm depth after which runoff begins." Note that in the RCN method, the initial abstraction serves the avowed purpose of reducing the runoff Q below the value which would apply had the initial abstraction been zero. The emphasis is on the effect of initial abstraction in reducing total runoff Q (ordinate), and not on applying the initial abstraction to rainfall (abscissa). 3.   ANALYSIS According to the RCN method, runoff Q is a function of storm depth P and curve number CN, regardless of the storm duration. Therefore, for a given curve number CN, the storage S and initial abstraction Ia are constants. Like P, S, and Q, the initial abstraction Ia is a volume, interpreted as a fraction of storm depth evenly distributed for the given storm duration and watershed under consideration. It is argued here that if CN and S do not account for either the rate of infiltration or the storm duration, neither should the initial abstraction Ia. On this premise, it appears unwarranted to place the initial abstraction at the beginning of the storm. We observe that the RCN method is lumped in time, originally developed for storm durations of 24 hr, and subsequently extended by way of practice to storms of lesser duration. Given tr = storm duration, tc = time of concentration, and Pe = effective precipitation, distributing the total abstraction (P - Q) (i.e., the total losses) uniformly in time produces a constant effective rainfall intensity (Ie = Pe /tr). For tr ≥ tc, this procedure leads to runoff concentration, with peak flow Qp1 (Ponce, 2014): Qp1  =  Ie A (6) Conversely, if the initial abstraction is accounted for in the beginning of the storm, the total abstraction (P - Q) is not distributed uniformly in time. Thus, in order to conserve mass throughout the storm duration, runoff concentration must be attained at a peak flow Qp2, where: Qp2  >  Qp1 (7) with significant differences between the two approaches. Figure 1 shows a typical example of the difference in peak flows (Magallon and Ponce, 2015). The control model (Online_Overland) distributes the total abstraction uniformly in time, while SWMM and HEC-HMS do not. The question remains as to which of the approaches to rainfall abstraction using the runoff curve number method is more realistic or more appropriate. This results is significant differences in hydrograph properties (Magallon and Ponce, 2015). Fig. 1  Comparison of hydrographs for three overland flow models, using the NRCS runoff curve number as the abstraction method. 4.   CONCLUSIONS The concept of initial abstraction in the NRCS runoff curve number method is revisited, in light of the demonstrably different results obtained by hydrologic models in current use (SWMM and HEC-HMS). The runoff curve number method is lumped in time, but it has been used by way of practice as a temporally distributed model, beyond the scope of its original development. This has led to various ways of accounting for the initial abstraction. There is an urgent need to develop a new standard, so that the various models will lead to the same or similar results. REFERENCES Hawkins, R. H., R. Jiang, D. E. Woodward, A. T. Hjelmfelt, and J. E. VanMullen, 2002. Runoff curve number method: Examination of the initial abstraction ratio. Proceedings of the Second Federal Interagency Hydrologic Modeling Conference, Las Vegas, Nevada. Magallon, L., and V. M. Ponce. 2015. Comparison between overland flow models. Online publication. Ponce, V. M. 1996. Notes of my conversation with Vic Mockus. Online feature. Ponce, V. M. 2014. Engineering Hydrology, Principles and Practices. Online edition. Ponce, V. M., and R. H. Hawkins. 1996. Runoff curve number: Has it reached maturity? ASCE Journal of Hydrologic Engineering, Vol. 1, No. 1, January, 11-19. USDA Natural Resources Conservation Service. 1986. Urban Hydrology for Small Watersheds. USDA Natural Resources Conservation Service. 2015. National Engineering Handbook: Part 630 - Hydrology.

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