Curve Numbers and Urban Runoff Modeling - Application Limitations Robert N. Eli1 and Samuel J. Lamont2 1
Associate Professor, Dept. of Civil and Environmental Engineering, West Virginia University, 395 Evansdale Drive, Box 6103, Morgantown, WV, 26506-6103; PH (304)-293-9932; email:
[email protected] 2 Postdoctoral Fellow, Natural Resource Analysis Center, West Virginia University, Morgantown, WV, 26506-6108;
[email protected] ABSTRACT The U.S.D.A. SCS (now the NRCS) Curve Number method has been in continuous use for about 50 years. As originally developed, the method yields a direct runoff depth from the accumulated 24 hour rainfall depth as function of the curve number CN. The method has since been extended to hydrograph generation and is found in commonly used hydrologic models applied to urban drainage design (e.g., WinTR55, SWMM and HEC-HMS). A number of recently published studies, including Curve Number Hydrology - State of the Practice, by the ASCE/EWRI Curve Number Hydrology Task Committee, have warned that it is inappropriate to use the method to generate runoff hydrographs, yet the practice continues with little awareness of this limitation by most users. A common misconception is that the CN method is an infiltration model, which can lead to significant errors in peak discharge predictions. CN values can be converted into equivalent physically based infiltration model parameters used in the Green-Ampt method in SWMM (or HEC-HMS), or in the infiltration component used in the PERLND module of EPA’s HSPF model, each of which can produce a more acceptable hydrograph that matches CN method direct runoff depth. INTRODUCTION The Curve Number method (CN method) was developed in response to the Small Watershed and Flood Control Act of 1954 that required the Soil Conservation Service (SCS), now the Natural Resource Conservation Service (NRCS), to develop a standard procedure for runoff volume estimation from small watersheds. The Agricultural Research Service (ARS) and the US Forest Service (USFS) also cooperated in the original development of the CN method (Hawkins et al, 2009). The primary source document outlining the method was the National Engineering Handbook, Section, Hydrology NEH4 (SCS, 1972), currently reprinted and updated as NEH 630 (NRCS, 2008). The method was intended for internal agency use and there was no outside peer review or involvement of the public scientific community in its development.
Initially, there was little outside attention paid to the CN method, but over the past 30 years a large volume of independent research work has been published on various aspects of the method, with some significant criticism. During this time the CN method found widespread use by other public agencies, local governments, engineering consultants, and other professionals who require rainfall/runoff predictions. The method was extended to urbanized lands with the publication of TR55 Urban Hydrology for Small Watersheds (NRCS, 1986). This publication was followed by development of the WinTR-55 computer program (NRCS, 2009) which automated the TR55 procedures. The WinTR-55 program also extended the TR55 manual procedures with addition of the WinTR-20 computational engine (NRCS, 2002). This replaced the TR55 graphical peak discharge method and the tabular hydrograph method with numerical unit hydrograph convolution and routing for determination of the design hydrograph and peak discharge. The original CN method had no pretentions of being a hydrograph generation technique. The CN runoff equation (Equation 1) gives the accumulated storm runoff depth Q as a function of the accumulated storm precipitation depth P and the parameters Ia (initial abstraction) and S (maximum potential retention) (NRCS, 2008). The equation is unit consistent in inches or mm, but we use inches here to preserve the original form of the CN to S relationship.
( P − Ia ) Q= ( P − Ia ) + S 2
1000 (S is in inches) (1) 10 + S It is important to note that Equation 1 is subject to the restriction P ≥ 0.2 S , Q = 0 otherwise . Further, S is interpreted to be the maximum potential difference between P-Ia (the effective storm depth Pe) and Q (Hawkins et al, 2009). It has no direct relationship to soil storage capacity, as is sometimes mistakenly assumed. The initial abstraction Ia is the accumulated rainfall depth required to begin to produce runoff. The CN definition in Equation 1 is arbitrary and was designed to conveniently limit the range of CN from 0 to 100 (Hawkins et al 2009). The magnitude of CN has no direct relationship to the infiltration capacity of the soil, which is also often mistakenly assumed. The CN method divides the storm depth P into losses and direct runoff depth Q for a particular storm event using a specified CN value. Many users of the method do not fully appreciate its limitations, thus creating opportunities for potential misapplication. It is commonly assumed that the method is fully investigated and documented, and peer reviewed, since the method has its source in a respected government agency (the NRCS). Unfortunately, such is not the case (Hawkins et al 2009). Many of the myths, misunderstandings, and misapplications of the CN method are summarized in Hawkins et al, 2009. The three most relevant difficulties with the method are listed below. 1) The tabulated CN values found in (NRCS 2008) and (NRCS, 1986), and reprinted in a wide variety of manuals and publications, are predominantly estimates or judgments based on soils and vegetation, to be used in absence of local data. Although there is some documentation that basic curve numbers have origins in small agricultural watersheds in humid regions, little source data has been found for deserts, forests, or urban watersheds. It is where I a = 0.2S and CN =
recommended that CN values be developed independently for local conditions. 2) CN values can be inverse-calculated using Equation 1 if watershed rainfall runoff data are available. Studies have shown that CN is a variable function of the storm depth P and storm rainfall distribution, in addition to soil characteristics (Lamont et al, 2008). Most watersheds have a decreasing CN that approaches a constant value as P increases (standard behavior in Figure 1), while others (including many urban watersheds) have increasing CN values for increasing P, approaching a steady state value (violent behavior in Figure 1). The third possibility features a continually declining CN value which never reaches a steady state (this watershed behavior is not applicable to the CN method). 3) The CN method is not an infiltration equation nor does it predict runoff peak discharges. Continuous simulation models such as WinTR-55, WinTR-20, HEC-HMS, EPA-SWMM, and many others, use Equation 1 to compute incremental direct runoff (rainfall excess) within the storm event to enable computation of a direct runoff hydrograph. This has been demonstrated to be incorrect since Equation 1 applies only to the total storm event depth P.
Figure 1. Sketch of typical behavioral trends in CN as a function of storm depth. In spite of the limitations listed above, plus others reported by Hawkins et al, 2009, the CN method is the most widely used technique to determine storm runoff volumes and peak discharges. Reasons for its popularity are apparent given its origins in a respected federal agency and its ease of use (plus the lack of any serious competition). It has been widely adopted and institutionalized by other authoritative bodies, including local and state agencies, and their consultants. Users are therefore supported by funding agencies whom approve of the use of the CN method and as result receive a degree of protection against any potential legal challenges that might result from its failure to perform.
CURVE NUMBERS AND DESIGN STORM EVENTS
The second difficulty listed in the previous section points out that the calculated values of CN for a given watershed, using measured values of rainfall and runoff depth, do not yield a fixed value. CN values have been shown to be a function of both the storm depth and storm rainfall distribution (Lamont et al, 2008). For a selected narrow range of storm depths on a specific watershed, computation of curve numbers from real watershed data results in a range of values scattered about a mean value. This scatter can be attributed to differences in rainfall distributions and antecedent runoff conditions (relative wetness, seasonal effects, etc.) Typically, urban watersheds exhibit standard or violent behavior (Figure 1) and the CN can be assumed to approach a stationary mean value at storm depths commonly used in design (> 2 year return period). These behaviors are consistent with watersheds having a mixture of pervious and impervious areas, and headwater drainage areas with little baseflow (groundwater outflow). Rainfall-Runoff models that use Equation 1 generate runoff hydrographs that are a direct function of the rate of rainfall accumulation (or equivalently, rainfall rate). It follows that the runoff hydrograph peak discharge will also be a direct function of the rate of rainfall accumulation, and therefore the storm rainfall distribution. If the CN method is to be used to generate runoff hydrographs, it is highly advisable that a standardized rainfall distribution be used to maintain consistency. It is logical to standardize using the SCS 24-hour rainfall distributions (Figure 2), since they have historically been an integral part of the CN method as applied in urban settings (NRCS, 1986). Both storm runoff depth Q and discharge peak Qp are typically needed for design of stormwater management infrastructure. From this point forward we will focus on the third limitation listed in the previous section, the questionable use of the CN method for computing peak discharges. We leave the issues of the appropriateness of CN application and the selection of its value for another forum.
Figure 2. SCS 24-hour rainfall distributions (NRCS, 1986).
CURVE NUMBERS AND INFILTRATION BEHAVIOR
Widely used rainfall-runoff models (WinTR-55, WinTR-20, HEC-HMS, EPA-SWMM, and others) compute incremental rainfall excess using Equation 1. This approach is not supported by the peer-reviewed literature (Ponce and Hawkins, 1996; Garen and Moore, 2005; Lamont et al, 2008) or the recently published ASCE state of practice (Hawkins et al, 2009). WinTR-55 and WinTR-20 use the CN method exclusively while HEC-HMS and EPA-SWMM offer other options. The Green-Ampt method is an alternative offered by both HMS and SWMM. The GreenAmpt method is a classic infiltration model based on Darcy’s law (Chow, Maidment, and Mays, 1988). Figure 3 illustrates the soil parameters of importance and the downward progression of a saturated wetting front that is the infiltration mechanism in the Green-Ampt method. The Green-Ampt equation is ⎡ψ Δθ ⎤ f (t ) = K ⎢ + 1⎥ (2) ⎣ F (t ) ⎦ where f(t) is the infiltration capacity at time t, K is the unsaturated hydraulic conductivity, ψ is the wetting front capillary pressure head, ∆θ is the change in soil moisture content across the wetting front (Figure 3), and F(t) is the accumulated infiltration at time t. Rawls, Brakensiek, and Miller (1983) evaluated 5000 soil horizons within the United States to determine average values of the Green-Ampt parameters associated with the standard USDA soil texture classifications. Table 2 lists 11 soil texture classifications used in this latter study (with additional data added by Eli and Lamont, 2005, also in Lamont et al 2008). The classifications range from Sand (coarse particles) to Clay (very fine particles). Brooks and Cory (1964) developed a relationship between soil water suction head ψ (cm of water) and effective saturation se , as a function of specific soil characteristics. λ
⎡ψ ⎤ se = ⎢ b ⎥ (3) ⎣ψ ⎦ ψb is the bubbling pressure corresponding to the soil water suction head at which air first enters the soil. λ is the pore size distribution index (a function of soil texture). The effective saturation is θ − θr se = (4) η − θr where θ is the moisture content of the soil (cm3/cm3), θr is the residual moisture content of the soil (equivalent to the wilting point), and η is the soil porosity (see Figure 3). Equations 3 and 4 can be solved for θ yielding Equation 5 (Eli and Lamont, 2005). λ
⎡ψ ⎤ (5) θ = θ r + (η − θ r ) ⎢ b ⎥ ⎣ψ ⎦ θ is therefore a function of soil water suction head ψ for a particular soil texture classification (for selected values of η, θr , ψb , and λ). Equation 5 is used to compute the value of the initial moisture content of the soil θi (Table 2) that is consistent with the antecedent runoff condition ARC II (formerly antecedent moisture condition AMC II) in the CN method (Lamont et al, 2008). Rawls and Brakensiek (1986)
concluded that ψ = 340 cm corresponded to AMC II, which is the basis for θi in Table 2.
Soil Moisture Content
0
θ
0 θi
Initial Moisture Content
Infiltration Wetting Front
D
η
Soil Porosity Soil Moisture Content
θ
Effective Soil Moisture Content
θe
Soil Depth, cm
Δθ Residual Moisture Content
θr
Depth
SCS Antecedent Moisture Condition II (AMCII)
Figure 3. Green-Ampt infiltration via a saturation wetting front (Eli and Lamont, 2005) The Green-Ampt infiltration capacity f(t) can be computed using Equation 2 with parameters values K, ψ, and Δθ given in Table 2. The parameter values in Table 2 should be considered mean values with considerable variation being possible within each of the soil texture classes listed. Brevnova (2001) conducted extensive experiments comparing the standard CN method of computing runoff hydrographs (using Equation 1) with equivalent runoff hydrographs produced using the GreenAmpt method (Equation 2). In order to conduct the comparison, it was assumed that the accumulative loss (P - Q) produced by CN method was due to infiltration plus initial abstraction Ia. Initial abstraction in the Green-Ampt method was assumed to be a component part of the infiltration process before direct runoff begins and was not treated as a separable loss component. Four soil texture classes were selected to represent the four hydrologic soil groups as listed in Table 1. Representative curve numbers were selected for each soil texture class and the corresponding Green-Ampt parameters K and ψ adjusted about their mean values by trial and error so that both methods produce the same accumulated losses. Four 24 hour storm accumulated depths (8, 16, 24, and 32 cm) were used to generate plots of accumulated loss as a function of time (the SCS type II rainfall distribution was used). Two examples of these plots are reproduced here as Figures 4 and 5. These plots were chosen to illustrate a principal result of the Brevnova (2001) study that concluded that the greatest difference in infiltration loss rates occur at low CN values, with less difference at high CN values. Figure 4 illustrates the difference for CN = 70, which shows a pronounced difference in the accumulated loss curves at the point where the
rainfall rate is the greatest. This characteristic feature of the CN accumulated loss rate is a direct result of the form of Equation 1. As can be observed in Figure 4, the rate of apparent infiltration loss rises abruptly at the onset of the highest rainfall rate in the central portion of the storm, while the Green-Ampt loss rate continues to rise in a smooth transitioning curve. It can be reasoned that the apparent CN infiltration loss rate is unrealistic since it far exceeds the maximum rate of infiltration that is possible based on soil physics theory (as used in the Green-Ampt method). Figure 5 illustrates the difference for CN = 90, which shows much less difference since the total loss is a much smaller fraction of the total rainfall depth. The conclusion is that infiltration loss rate differences may result in significant differences in runoff hydrograph peak discharges, especially for moderate values of CN. Table 1. CN versus Green-Ampt infiltration loss study parameters (Brevnova, 2001). GreenAmpt K
GreenAmpt ψ
cm/hr
cm
60
2.45
7.77
0.280
Silt Loam
70
1.27
9.64
0.169
C
Clay Loam
80
0.20
17.60
0.148
D
Silty Clay
90
0.027
33.70
0.158
Soil Group
Soil Texture
A
Sandy Loam
B
CN
GreenAmpt Δθ
INFILTRATION MODEL IMPACT ON PEAK DISCHARGE
In the Brevnova (2001) study a synthetic 1 km2 watershed with variable times of concentration was used to convert the rainfall excess computed by each method into a runoff hydrograph using the standard SCS nondimensional unit hydrograph (NRCS, 2008). The nondimensional unit hydrograph is scaled based on drainage area and time of concentration. Three values of time of concentration (37.5, 75, and 112.5 min) were used in the hydrograph generation portion of the study. The direct runoff hydrographs corresponding to the infiltration comparisons shown in Figures 4 and 5 (using the 75 min time of concentration) are included as Figures 6 and 7. These hydrograph comparisons show that for CN=70, the CN peak discharge is 60% of the Green-Ampt peak discharge while for CN=90, the CN peak discharge is 92% of the Green-Ampt value. Overall, the CN peak discharges were always less than the Green-Ampt, ranging from a low of 27% to a high of 98% of the Green-Ampt peak.
Silt Loam, B Soil, CN=70, P=16 cm Accumulated Rainfall and Infiltration, cm
16 14
Rainfall
12 10 CN model
8 6 Green-Ampt model
4 2 0 0
2
4
6
8
10
12
14
16
18
20
22
24
Time, hours
Figure 4. Accumulated rainfall and infiltration comparison for CN = 70. (Brevnova, 2001).
Silty Clay, D Soil, CN=90, P=16 cm Accumulated Rainfall and Infiltration, cm
16 Rainfall
14 12 10 8 6
CN model
4 2
Green-Ampt model
0 0
2
4
6
8
10
12
14
16
18
20
22
24
Time, hours
Figure 5. Accumulated rainfall and infiltration comparison for CN = 90. (Brevnova, 2001)
Silt Loam: Hydrologic Soil Group B 18.0
14.0
Wetting Front Hydraulic Conductivity = 0.394 cm/hr Wetting Front Capillary Pressure = 14.119 cm Total Porosity = 0.501 Initial Moisture Content = 0.332 SCS Type II 24 hr Depth = 16 cm ; SCS CN = 70 Time of Concentration = 75.0 min. ; Area = 1 sq-km
12.0
Green-Ampt Infiltration Model
Discharge, Cubic Meters per Second
16.0
SCS CN Infiltration Model
10.0 8.0 6.0 4.0 2.0 0.0 10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
26.0
Time from Beginning of Storm, Hours
Figure 6. Direct runoff hydrograph comparison for CN = 70. (Brevnova, 2001) Silty Clay: Hydrologic Soil Group D 28.0 Wetting Front Hydraulic Conductivity = 0.02746 cm/hr Wetting Front Capillary Pressure = 33.699 cm Total Porosity = 0.479 Initial Moisture Content = 0.320 SCS Type II 24 hr Depth = 16 cm ; SCS CN = 90 Time of Concentration = 37.5 min. ; Area = 1 sq-km
26.0
Discharge, Cubic Meters per Second
24.0 22.0 20.0 18.0
Green-Ampt Infiltration Model
16.0
SCS CN Infiltration Model
14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
26.0
Time from Beginning of Storm, Hours
Figure 7. Direct runoff hydrograph comparison for CN = 90. (Brevnova, 2001)
Table 2. Soil Texture Class Hydraulic Properties (Eli and Lamont, 2005) (also in Lamont et al, 2008). Soil Texture Class
Total Porosity η
Residual Moisture Content
Pore Size Distribution Index
θr
λ
Bubbling Pressure ψb (cm)
Initial Soil Moisture Content
Green-Ampt Soil Hydraulic Conductivity
θi at AMCII
K (cm/hr)
Wetting Front Cap. Pressure Head ψ (cm)
Green Ampt Δθ
Green-Ampt Infiltration Capacity at F(t) = 1 cm f(t) (cm/hr)
Hydrologic Soil Group1
INFILT Estimate2 (cm/hr)
Sand
0.437
0.020
0.546
17.340
0.102
11.78
4.95
0.335
31.309
A
2.50
Loamy Sand
0.437
0.036
0.449
9.078
0.117
2.99
6.13
0.320
8.850
A
1.45
Sandy Loam
0.453
0.041
0.378
16.777
0.173
1.09
11.01
0.280
4.450
A
1.00
Silt Loam
0.501
0.015
0.207
43.337
0.332
0.65
16.68
0.169
2.479
B
0.65
Loam
0.463
0.029
0.246
23.196
0.253
0.34
8.89
0.210
0.974
B
0.27
Sandy Clay Loam
0.398
0.068
0.345
25.868
0.204
0.15
21.85
0.194
0.786
C
0.24
Silty Clay Loam
0.471
0.039
0.164
36.855
0.339
0.10
27.30
0.132
0.460
C
0.19
Clay Loam
0.464
0.155
0.259
27.249
0.316
0.10
20.88
0.148
0.410
C
0.18
Silty Clay
0.479
0.056
0.186
27.167
0.320
0.05
29.22
0.158
0.282
C
0.14
Sandy Clay
0.430
0.109
*
*
0.2773
0.06
23.90
0.153
0.279
C
0.13
Clay
0.475
0.090
0.187
32.917
0.339
0.03
31.63
0.136
0.159
D
0.05
All values derived from Brakensiek, Engleman, and Rawls (1981) and Rawls, Brakensiek, and Miller (1983), unless otherwise noted. [1] Nearing, Liu, Risse, and Zhang (1996). [2] Figure 5 (Eli & Lamont, 2005). [3] Estimated using Rosetta (1999). [*] Unavailable.
CN AND GREEN-AMPT COMPARISION EXAMPLE IN EPA-SWMM
A simple example illustrates the difference in runoff peak discharge produced by the standard CN method of distributing rainfall excess on pervious surfaces as compared to the Green-Ampt infiltration method using the EPA-SWMM model. A portion of a golf course is to be developed into residential housing with a total area of 5.682 acres. The predeveloped condition has a B soil with CN = 61 with no impervious areas, and is modeled as a single subcatchment with a central 350 ft trapezoidal open channel draining the property. After development, the pervious surfaces are assumed to be unchanged (CN = 61), but the total area is divided into two subcatchments (Figure 8). Subcatchment 1 is a central 30 ft wide street (100% impervious) with an area of 0.492 acres, sloping from top to bottom at 1.19% slope (surface drainage only). Subcatchment 2 consists of the remaining area (5.19 acres) with 20 % impervious area (roofs and driveways), 20% of which is routed onto pervious surfaces (all of which drains to the street). A one hour design storm (2.05 inch depth) with 12 min increments was applied to the predeveloped and postdeveloped conditions for both the CN and Green-Ampt methods. The Green-Ampt parameters were first estimated using the information in Table 2 then adjusted so that the total infiltration loss matched the loss produced by the CN method at the end of the storm event (at the end of 1 hour). Although the simulation was allowed to continue for 4 hours, infiltration loss matching has to be done at the end of the storm event because the CN method losses are a function of rainfall accumulation, while infiltration continues with the Green-Ampt method as long as surface ponding remains.
Figure 8. 5.862 acre residential development used in SWMM example problem
The resulting runoff hydrographs for the above SWMM example are shown in Figure 9. In the predeveloped condition the CN method produces a runoff peak discharge that is 61% of that produced by the Green-Ampt method. In the postdeveloped condition the CN method is 80% of the Green-Ampt method.
10 Predeveloped - CN=61
9
Predeveloped - GA fitted Postdeveloped - CN
8
Postdeveloped - GA fitted
Discharge, cfs
7 Time series rainfall in 12 min increments, in/hr: Time: Rate: 0:00 0.757 0:12 1.363 0:24 4.952 0:36 2.200 0:48 0.976 1:00 0.000
6 5 4 3
GA Parameters: K = 0.98 in/hour ψ = 3.38 inches Δθ = 0.250
2 1 0 0:00:00
0:14:24
0:28:48
0:43:12
0:57:36
1:12:00
1:26:24
1:40:48
1:55:12
2:09:36
Time: hr:min:sec
Figure 9. Example runoff hydrograph comparison between CN and Green-Ampt using SWMM. DISCUSSION, CONCLUSIONS AND RECOMMENDATIONS
The CN method of separating direct runoff from losses was originally developed to separate total storm direct runoff depth from total accumulated losses. The method has been extended to compute the distribution of rainfall excess within storm events in order to adapt the method to distributed rainfall-runoff models. Many investigators, including Hawkins et al (2009), have concluded that this extension can not be justified. Other limitations have been discussed above. The CN distributed method is widely used and is an option in all of the most popular rainfallrunoff models with the exception of EPA-HSPF (Hydrological Simulation Program Fortran). Although space has not allowed a discussion of HSPF here, details of a method of relating HSPF parameters to CN is presented by Lamont et al (2008). As has been shown here, the CN method consistently results in an under prediction of runoff discharge peaks as compared to the Green-Ampt method. Since the CN method is well entrenched, and in many cases part of regulatory specifications, its replacement is not in sight. Its use for computation of total runoff volumes required for design is widely accepted, assuming that local CN values are accurately
determined. However, if discharge peaks are of critical importance in design, it is recommended that an alternate infiltration method be used. We have presented a loss volume method of matching Green-Ampt parameters to curve numbers. Other infiltration models can potentially be adapted in a similar manner. REFERENCES
Brakensiek, D.L., Engleman, R.L., and Rawls, W.J., 1981, “Variation within Texture Classes of Soil Water Parameters”, Transactions of the ASAE, Vol. 24, No. 2, 335-339. Brevnova, E.V., 2001, “Green-Ampt Infiltration Model Parameter Determination using SCS Curve Number (CN) and Soil Texture Class, and Application to the SCS Runoff Model”, Masters Thesis, Department of Civil and Environmental Engineering, West Virginia University, Morgantown, WV. Brooks, R.H. and Corey, A.T., 1964, “Hydraulic Properties of Porous Media”, Hydrology Paper No. 3, Colorado State University, Fort Collins, CO. Chow, V.T., Maidment, and Mays, 1988, Applied Hydrology, McGraw-Hill Book Co., NJ. Eli, R.N. and Lamont, S.J., 2005, “HSPF Mine Segment Modeling Concepts and Methodology”, Natural Resources Analysis Center, West Virginia University, Morgantown, WV, (unpublished manuscript dated 4/15/05 version 6) Garen, D.C. and Moore, D.S., 2005, “Curve Number Hydrology in Water Quality Modeling: Uses, Abuses, and Future Directions”, Journal of the American Water Resources Association, April, 2005, paper no. 03127. Hawkins, R.H., Ward, T.J., Woodward, D.E., and Van Mullem, J.A., 2009, “Curve Number Hydrology, State of the practice”, The ASCE/EWRI Curve Number Hydrology Task Committee, American Society of Civil Engineers, Reston, Va. Lamont, S.J., Eli, R.N., and Fletcher, J.J., 2008, “Continuous Hydrologic Models and Curve Numbers: A Path Forward”, Journal of Hydrologic Engineering, Vol. 13, No. 7, American Society of Civil Engineers. Natural Resource Conservation Service (NRCS), 1986, “Urban Hydrology for Small Watersheds”, Technical Release 55 (TR-55), 2nd edition, U.S. Department of Agriculture, Washington, D.C. Natural Resource Conservation Service (NRCS), 2002, WinTR-20 System: User Documentation, U.S. Department of Agriculture, Washington, D.C. Natural Resource Conservation Service (NRCS), 2008, Part 630 Hydrology, National Engineering Handbook, U.S. Department of Agriculture, Washington, D.C. Natural Resource Conservation Service (NRCS), 2009, Small Watershed Hydrology, WinTR-55 User Guide, U.S. Department of Agriculture, Washington, D.C. Nearing, M.A., Liu, B.Y., Risse, L.M., and Zhang, X., 1996, “Curve Numbers and Green-Ampt Effective Hydraulic Conductivities”, Water Resources Bulletin, American Water Resources Association, Vol. 32, No. 1. Ponce, V.M. and Hawkins, R.H., 1996, “Runoff Curve Number: Has It Reached Maturity?”, Journal of Hydrologic Engineering, Vol. 1, No. 1, 11-19, ASCE.
Rawls, W.J., Brakensiek, D.L., and Miller, N., 1983, “Green-Ampt Infiltration Parameters from Soils Data”, Journal of Hydraulic Engineering, Vol. 109, No. 1, American Society of Civil Engineers. Rosetta 1999, Version 1.0, Author: Marcel G. Schaap. http://www.ussl.usda.gov/models/rosetta/rosetta.HTM Soil Conservation Service (SCS), 1972,“National Engineering Handbook, Section 4, Hydrology,” (NEH-4), U.S. Department of Agriculture, Washington D. C.
