CURVE NUMBERS, RECENT DEVELOPMENTS

A. T. Hjelmfelt

USDA Agricultural Research Service, Agricultural Engineering Building,

University of Missouri, Columbia, MO, 65211 USA

573-882-1142 E-mail: hjelmfelta@missouri.edu

 D. A. Woodward, G. Conaway, A. Plummer, Q. D. Quan, J. Van Mullen

USDA Natural Resources Conservation Service

 R. H. Hawkins, P. D. Rietz

University of Arizona

Abstract: A joint work group was formed by the US Department of Agriculture to review the Curve Number procedure in terms of current field measurements.  As a result of this work group much of the National Engineering Handbook (USDA, 1993) has been rewritten to improve consistency and clarity.  A fuzzy set theory approach was used to establish a physical basis for classifying soils into Hydrologic Soil Groups.  An asymptotic method was developed for determining Curve Numbers from rainfall-runoff data and for determining quality of fit of data to the Curve Number runoff equation.

Keywords: rainfall-runoff, hydrologic losses, infiltration, surface water hydrology

1    INTRODUCTION

The Curve Number procedure of the U.S. Dept. of Agriculture, Natural Resources Conservation Service (NRCS) (formerly Soil Conservation Service, SCS) has elicited questions and concern since its conception.  This arises, for the most part, because users read into the procedure what they wish was covered. The actual intent of the procedure is often disregarded. Too, the basic reference for Curve Numbers, the National Engineering Handbook of the SCS, has been revised several times, not always by individuals or committees that understood the significance of their statements. The Natural Resources Conservation Service and the Agricultural Research Service,  both agencies of the U.S. Department of Agriculture, formed a joint work group to assess the state of the Curve Number procedure and to chart its future development.

The joint work group recognized three distinctly different modes of application for Curve Numbers: (1) determination of runoff volume of a given return period, given total event rainfall for that return period; (2) determine direct runoff for individual events, explaining the variability from event to event, as used in continuous simulation models; (3) determine infiltration rates for short time intervals as used with unit hydrograph development of  flood hydrographs.

The first mode of application represents the historical basis of the procedure, so receives the  most attention. Use as a surrogate for an infiltration is very common and follows from the historical basis, so must be considered. The application in continuous simulation models is an extension beyond the scope of the committee.

Discussions within the committee made it apparent that a portion of the difficulty surrounding the procedure was attributable to the presentation of the procedure in the National Engineering Handbook. The first task then was to rewrite those portions of the Handbook pertaining to the procedure. Problems identified ranged from incorrect and misleading statements to incomplete documentation. For example, it was incorrectly stated that S includes Ia, whereas it can be shown mathematically that S does not include Ia.  Fortunately, this is only significant for continuous simulation.  Another example was a table that related antecedent rainfall to antecedent moisture condition (AMC). This was not intended to have nationwide application, though it was treated as such. Folklore concerning Curve Numbers could also be attributed to problems with documentation. A folklore example is that the Curve Number Runoff Equation is an infiltration equation.

In rewriting the Curve Number portions of the Handbook, the work group agreed that: 1) Committee must Abelieve in@ concepts expressed;  2) references will be included if possible; and 3) results must be technically defensible. The results of the rewrite include such items as: ① Reference to Antecedent Moisture Condition (AMC) was removed.  Variability is incorporated by considering the curve number as a random variable and the AMC-I and AMC-III conditions as bounds on the distribution. ② Reiteration of desirability of locally determined curve numbers. This was part of the original documentation but tended to be neglected. ③ Explicit expression of Curve Number runoff equation as a transformation of  rainfall frequency distribution to runoff frequency distribution.  This was demonstrated in the original documentation but again was often neglected. ④ Expression of AMC-I and AMC-III as measures of dispersion about the central tendency (AMC II). This is a corollary of treating the CN as a random variable. ⑤ Mathematical proof showing that S does not include Ia. This is only significant because of the previous missunderstanding. ⑥ The chapters are posted on the World Wide Web as approved. http://www.wcc.nrcs.usda.gov/water/quality/wst.html.

As the work group progressed on the rewriting, they reached a level of agreement on principles allowing work to begin on two other areas of need.  These were to reconsider the hydrologic soils classifications recognizing the vastly expanded data base available today and the capabilities of modern computers, and to reconsider the tables of curve numbers in terms of the expanded rainfall-runoff database available.

2    HYDROLOGIC SOIL GROUPS

There has been a vast increase in basic soils property data since Musgrave (1955) first proposed the concept of  hydrologic soil groups in Handbook of Agriculture. The data are now available in an electronic database.  Modern tools of data mining were explored for analysis of this mass of data.  Both neural networks and fuzzy sets were tried with fuzzy sets being adopted. Originally, Soil Hydrologic Groups were assigned to soil series and phase of series by soil scientists based upon their interpretation of the published criteria (Soil Survey Staff, 1993). The soil scientist=s interpretation of the published criteria has varied across time and between states or regions. Thus, the hydrologic group criteria are  not applied consistently across the United States. This is most evident in the comparison of soils with similar soil hydrologic and physical properties and dissimilar hydrologic group placement.

The Hydrologic Soil Groups are A, B, C, D and dual groups A/D, B/D and C/D.   Soils in hydrologic group A have low runoff potential. Soils that have a moderate rate of infiltration when thoroughly wet are in hydrologic group B. Hydrologic group C soils that have a slow rate of infiltration rate when thoroughly wet. Soils in hydrologic group D have a high runoff potential. Dual Hydrologic Soil Groups (A/D, B/D, and C/D) are given for certain wet soils that could be adequately drained. The first letter applies to the drained and the second to the undrained condition. Soils are assigned to dual groups if the shallow depth to a permanent water table is the sole criteria for assigning a soil to hydrologic group D.

A model or rule based automated system that provides for objective placement of soils into Hydrologic Soil Groups was developed (Nielson and Hjelmfelt, 1998). The fuzzy system model for assigning soils to hydrologic soil groups is based on the published hydrologic group assumptions and criteria. The soil surface is taken to be bare and the soil is not permanently frozen. The soil physical and hydrologic characteristic which make up the hydrologic grouping criteria are the depth to permanent water, depth to a restrictive layer, minimum saturated hydraulic conductivity in the soil=s upper 100 cm, and the soil=s texture.

There are three components to the fuzzy systems model: the Property, the Evaluation, and the Rule. The Property is an SQL (Standard Query Language) statement that retrieves the needed soil data from the soil survey database. An example of a Property is the depth to a restrictive layer. The Evaluation=s function is to apply the data received from the SQL statement to a statement of the property=s relevance to the soil=s hydrologic grouping. In the case of the depth to a restrictive layer, the Evaluation determines the fit or truthfulness of the statement, AThe runoff characteristics of the soil increases as a soil=s depth a restrictive layer becomes shallower.@ At some depth, the restrictive layer in the soil has a maximum contribution to runoff and the Evaluation is true.  The result of an Evaluation is some number between 0 and 1. This number represents the truthfulness of the statement being evaluated. The closer the number is to 1 the closer the soil=s property fits the grouping criterion. Conversely, the closer the number is to 0 the less the soil property=s contribution to the hydrologic grouping of soils. In the restrictive layer example, an Evaluation output of 1 would mean that the soil=s restrictive layer is shallower than 50cm. Any output less than 1 would mean that the depth to any soil restrictive layer is greater than 50cm. This numeric output from the evaluation is passed to the Rule.  The Rule is the third component of the fuzzy system model. The Rule serves two functions that result in a soil=s Hydrologic Soil Group placement. The first function is to provide tools for the construction and implementation of the grouping system=s model and to bring the various hydrologic grouping criterion evaluations together into a single Hydrologic Soil Group model. The second is to convert the model=s numeric output into a Hydrologic Soil Group.

The model was applied to 1828 unique soil phases using data from Kansas, South Dakota, Missouri, Iowa, Wyoming, and Colorado and the correlation between these soils= assigned and modeled hydrologic grouping was analyzed. Table1 shows a detailed comparison by Hydrologic Soil Group between the currently assigned HSG and the modeled HSG. The correlation between the assigned and modeled HSG A and HSG D soils is higher than the correlation between the assigned and modeled HSG B and HSG C soils. There are several reasons for the poorer correlation between the assigned and modeled groups B and C.  The first is that of the boundary condition which occurs when a soil has properties that do not fit entirely into a single hydrologic group. In this case, the soil scientist may have placed the soil into one HSG while the model placed the soil into an adjacent group. Groups B and C are the most prone to this error because they are bounded by two groups whereas HSG A and D are only bounded by one group.  Another source of correlation inconsistency is that the assigned HSG may be relatively correct, but the data in the database may not support the corresponding HSG determination by the model. Finally, correlation inconsistencies can be attributed to the fuzzy modeling of the subjective Hydrologic Soil Group criteria.

Table 1    Correlation frequency between assigned and fuzzy modeled Hydrologic Soil Groups

3    CURVE NUMBERS FROM RAINFALL-RUNOFF DATA

The watershed research program of the USDA, Agricultural Research Service is a continuation of research initiated by the Soil Conservation Service. Much of the data collected should be directly applicable to the determination of curve numbers and to explaining the variation of curve number with the soil-cover complex. In addition, Prof. R. H. Hawkins of the University of Arizona had been developing the world=s largest event rainfall-runoff data base with software to analyze the data. Prof. Hawkins was added to the ARS/NRCS work group.  The ideal method of determining curve numbers from observed data is elusive due to the stochastic nature of the variable. Our decision to emphasize the concept that the runoff equation serves to transform a rainfall frequency distribution into a runoff frequency distribution led to use of frequency matching. That is, curve numbers were determined by use of rainfall of a given return period with runoff of the same return period. These data may or may not come from the same storm. That is, frequency transformation leads to treating ordered pairs (See Hjelmfelt, 1980).

In his analysis, Hawkins recognized that not all data sets are adequate to define a curve number and some watersheds do not even perform according to the Curve Number runoff equation. He developed a graphical procedure in which the calculated curve number is plotted versus the precipitation used in calculating that curve number. In part, this plot is in recognition that, due to the random nature of the curve number, for a watershed with a given Atrue@ curve number, the actual event curve number will range above and below that Atrue@ value. For small rainfall events the event Ia will vary above and below the Atrue@ Ia. Curve numbers can only be determined if there is runoff, so if the event Ia is low, runoff will occur and a CN computed.  If the Ia is high, no runoff occurs so no CN can be computed. Thus, the process of computing CN for small events biases the CN toward high values (low Ia). The CN vs. P plot displays this bias and the storm magnitude at which the bias becomes insignificant.

The concept of the CN method being a transformation between a rainfall-depth distribution and a runoff depth distribution is applied in treating rainfall and runoff data.  The rainfall depths and the runoff depths are sorted separately and then re-aligned on a rank order basis to form P:Q pairs of equal return period. The individual runoffs are not necessarily associated with the original causative rainfalls. When CNs are calculated from real storm data as outlined above, a secondary relationship almost always emerges between CN and storm rain­fall depth itself. In most of these cases, these calculated CNs approach a constant value with increasing rainfall.Three variations on this theme have been observed, however, and are described in the following:

  (1) Complacent behavior: Here the observed CN declines steadily with increasing rainfall depth, and with no appreciable tendency to achieve a stable value. An example of this is given in Figure 1. Curve Numbers cannot be safely determined from data which exhibit this pattern, because no constant value is clearly approached. This Curve Number behavior has been found to indicate a partial source area situation (Hawkins, 1979; Pankey and Hawkins, 1981), where the source area fraction may be quite small (i.e., 0.1-5 percent). In these cases the runoff is more properly modeled by the linear form Q=CP rather than by the Curve Number runoff

 equation.

(2) Standard behavior: This is the most common scenario. The observed CN declines with increasing storm size, as in the Complacent situation described above.  However, here the CNs approach and/or maintain a near-constant value with increasingly larger storms. The runoff itself may arise from a variety of source processes, including overland flow and rapid subsurface flow.  An example of this pattern is given in Figure 2.  

(3) Violent behavior: The distinguishing feature here is that the observed CNs rise suddenly and asymptotically approach an apparent constant value. There is often accompanying Complacent behavior at lower rainfalls.  From a source process standpoint, this could be a threshold phenomenon at some critical rainfall depth value.  An illustration of this is given in Figure 3.

Rietz and Hawkins (2000) used their large electronic database of rainfall-runoff data to determine data-defined CNs calculated from local rainfall-runoff data. Their study attempted to develop a better understanding of a watershed=s land use as manifested in its CN. The land use variable was isolated in a large data set of small watersheds, and land use CN=s were calculated and analyzed for each of these watersheds at a local, regional, and national scale. Data in this study contained detailed land use information on 177 watersheds covering 2,455 years of record and 32,891 events. The majority of data used here were retrieved from the Agricultural Research Service (ARS) Water Data Center web site or their compact disk (1995).  Only watersheds with a single land use were considered (e.g., no Amixed crops@) where one land use applied to at least 90% of a watershed=s total area was the criteria used to define single land use. Watershed land uses analyzed in this study were: alfalfa (close-seed legume), corn (row crop), cotton (row crop), desert shrub, fallow,  forest, grassland, meadow, oats (small grain), pasture, range, sage brush, sorghum (row crop), soy bean (row crop) and wheat (small grain).  Many of the cultivated watersheds had a different land use year to year due to crop rotation. When one watershed had several land uses throughout the period of  record, data were segregated by date of land use and CN calculated for each land use.  Curve Numbers for each land use on each watershed were determined using the Asym-ptotic data-derived procedure with ordered P:Q pairs (Hawkins, 1993).

Differences in land use CN at the local level can be attributed solely to a change in hydrological response of a watershed due to land use because all other input variables of the Curve Number model are constant. Soil type, climate, and morphology are fixed, and watershed land conditions are constant for that land use. Of the 177 watersheds used in this study, 53 were found to have more than one land use during their period of record. When ANOVA independent group tests were performed 96.23% of the watersheds (51 out of 53) were found to have significant differences among their land use Curve Numbers. The results were:

(1) Meadow Curve Numbers were almost always the lowest CN for a watershed. Of the 19 watersheds that had a meadow in their crop rotation, 13 had meadow Curve Numbers significantly lower than any other land use CN within that same watershed. Three others had meadow Curve Numbers that ranked second lowest.

(2) Pasture is a grassland watershed that is grazed. This CN was generally significantly higher (6 out of 8 times) than all other land use Curve Numbers on a given watershed.

(3) Watersheds that experienced a land conversion had a significant difference in their data-derived CN after the conversion. Two desert watersheds in the Boco Mountains of Colorado were converted from desert brush to grass and with both, the grass Curve Number was significantly lower than desert brush. Another land use conversion study was at Riesel, Texas watershed #42036. This ARS experimental watershed was 100% rangeland that was Ainfested@ with honey mesquite. In 1972 the watershed was treated, at which time the mesquites were killed and left standing. The Curve Number following mesquite killing was statistically higher than for live mesquites.

In order to compare land use Curve Numbers across all locations, a land use had to have been applied in more than one location, which was found to be the case with 11 single land uses. Seven of these 11 land uses (63.6%) exhibited a significant difference. The rank order of Curve Numbers was: forest and meadow were among the lowest average Curve Number, row crops or small grain were in mid-range, and desert brush exhibited the highest average Curve Number. Small grains (wheat and oats) were grouped together as were row crops (soybean, corn and sorghum). It was surprising however, that the average Curve Number for range was the third lowest average Curve Number and that row crops had a lower average CN than small grains.

4    CONCLUSIONS

The results of the work group are:

(1) The basic description of the Curve Number procedure is more clear, more consistent, and is in a more technically defensible state. 

(2) The  Hydrologic Soil Groups are associated with soil physical properties through fuzzy set procedures.

(3) Procedures for determining Curve Numbers from local data and interpretation of the results are much better established.

However, more work is needed.  For example, we still need to work at verifying, adjusting, and correcting the table of CN.  Regional variation in Curve Numbers should be explored.  Finally, the whole issue of the application of Curve Numbers in continuous simulation models (CREAMS, GLEAMS, EPIC, SWAT) may be quite different from the design storm Curve Numbers of NEH-4.  If there is a relation, that relation should be determined.

References

Agricultural Research Service Water Data Center. 1995. ARS Water Data: ARS/Access CD.

USDA-ARS Hydrology Lab, Beltsville, Maryland. Agricultural Research Service Water Data Center.  http://www.hydrolab.arsusda.gov/arswater.html.

Burford, J.B. and J.M. Clark. 1976. Hydrologic data for experimental agricultural watersheds in the United States, 1968. U.S. Department of Agriculture Miscellaneous Publication No. 1330, 542pp.

Hawkins, R. H. 1979. Runoff curve numbers from partial area watersheds.  Proc. American Society of Civil Engineering. 105(IR4).

Hawkins, R.H. 1993. Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering. 119(2):334-345.

Hjelmfelt, A.T. 1980. Empirical investigation of curve number technique.  Journal of the Hydraulics Division. 106 (HY9):1471-1476.

Musgrave, G. W. 1955 AHow much rain enters the soil,@ Water Yearbook of Agriculture, U.S. Department of Agriculture, Washington, D.C. pp. 151-159

Nielson, R. D. and A. T. Hjelmfelt. 1998 Hydrologic soil-group assignment. IN Water Resource Engineering 98, Am. Soc. Civil Engrs., Abt, Young-Pezeshk, Watson(eds), v2pp1297-1302

Pankey, J.M. and R.H. Hawkins. 1981. Stormflow as a function of watershed impervious area. Proceedings Arizona Section Amer. Water Resources Association, and Hydrology Section Arizona‑Nevada  Academy of Sciences. Tucson, Arizona.

Soil Survey Staff. 1993. National Soil Survey Handbook. USDA-SCS, Soil Survey Division. U.S. Gov. Printing Office, Washington, D.C. Section 618

Rietz, P.D. and R.H. Hawkins. 2000. Effects of land use on runoff curve numbers. Watershed Management 2000. Am. Soc. Civil Engineers (CD ROM).

U.S. Department of Agriculture, Soil Conservation Service. 1993. National Engineering Handbook, Section 4, Hydrology (NEH-4).