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J. Indian Water Resour. Soc., Vol. 34, No.4, October, 2014

30

Engineering Handbook (NEH) Section 4 (NEH-4): Hydrology (SCS, 1985).

The origin of the method was based on the proposal of Sherman (1949) on plotting direct runoff versus storm rainfall. The subsequent work of Mockus (1949) focused on estimating surface runoff for ungauged watersheds using information on soil, land use, antecedent rainfall, storm duration and average annual temperature. Andrews (1954) also developed a graphical procedure for estimating runoff from rainfall for combinations of soil texture and type, the amount of vegetative cover and conservation practices. The association was referred to as the soil-cover complex (Miller and Cronshey, 1989). Thus, the empirical rainfall-runoff relation of Mockus (1949) and the soil cover complex of Andrews (1954) constituted the basis for the SCS-CN method described in the SCS, NEH- 4 (USDA-SCS, 1985).

The method has been structurally diagnosed and critically reviewed by several researchers worldwide for its enhanced performance without disfiguring its inherent simplicity. The diagnostic works of Rallison (1982), Chen (1982), Ponce and Hawkins (1996), Mishra and Singh (1999; 2002a&b; 2003a&b; 2004a&b), Michel et al. (2005), and Chung et al. (2010) are noteworthy. Based on the works of Ponce and Hawkins (1996) and Mishra & Singh (2003a), it was concluded that the SCS-CN method is a conceptual model of hydrologic abstraction of storm rainfall supported by empirical data dedicated to estimate direct runoff volume based on a single numeric parameter CN.

ADVANTAGES AND DISADVANTAGES OF SCS-CN METHODOLOGY Well established in hydrologic, agriculture, and environmental engineering, its popularity is rooted in its convenience, simplicity, authoritative origins, and responsiveness to four readily available catchment properties: soil type, land use/treatment, surface condition, and antecedent moisture condition. The method though appealing to many practicing hydrologists and watershed managers by its overwhelming simplicity, contains some unknowns and inconsistencies (Chen, 1982). Due to its origin and evolution as agency methodology, which effectively isolated it from rigors of peer review, other than the information contained in NEH-4, which was not intended to be exhaustive no complete account of the methods foundation is available to date.

Though the technique is versatile in its conceptual as well as application domain, the ultimate

success is often governed by the precision with which the values of CN and Ia are assigned, which indeed are most sensitive but typically assumed constant over space and time. Previous researches have well established that even for the same location these values are highly changeable during a year owing to factors like changes in land use, crop cover, crop growth, land treatment etc. Recently the method has been critically reviewed and diagnosed by various researchers for its structural inconsistencies by Mishra et al. (2004a), Michel et al. (2005), and Sahu et al. (2007) and uses and limitations by Ponce and Hawkins (1996) and Garen and Moore (2005).

DEVELOPMENTS IN CN ESTIMATION Before dealing with recent developments in CN estimation and various watershed characteristics that affect its estimation, it would be appropriate here to quote Hawkins (1975) that the errors in CN may have much more consequences on runoff estimation than errors of similar magnitude in storm rainfall P. This reflects the importance of accurate CN estimation for modeling rainfall-runoff process. Major watershed characteristics such as soil type, land use/treatment classes, hydrologic soil group, hydrologic condition and the most important one antecedent moisture condition (AMC) play a significant role in accurate CN estimation.

The CN is a hydrologic parameter that relies implicitly on the assumptions of extreme runoff events and represents a convenient representation of the potential maximum soil retention, S (Ponce and Hawkins, 1996). The Curve Number (CN) is used in the determination of S and values for the CN for different landuse, soil types and soil moisture conditions can be found in table (NEH-4). It has been observed that CN will be the highest for the Poor, average for the Fair, and lowest for the Good hydrologic condition. Similarly, the hydrologic soil group of a watershed significantly affects the CN or the runoff potential of the watershed, and it increases as the soil group changes from group A to group D, and vice

Fig.1. Determination of CN for AMC I to AMC III using existing SCS-CN method


31

versa. Hawkins et al. (1985) found that the antecedent moisture condition (AMC) is one of the most influential watershed characteristics in determining curve number (CN).

Despite widespread use of SCS-CN methodology, the accurate estimation of CN is a topic of much discussion among hydrologists (Hawkins, 1978; Chen, 1982; Hjelmfelt, 1980; McCuen, 2002; Bonta, 1997; Ponce and Hawkins, 1996; Mishra and Singh, 1999; Mishra and Singh, 2002a; and Mishra and Singh, 2006). Originally CNs were developed using daily rainfall-runoff records corresponding to the maximum annual flows from gauged watersheds for which information on their soils, cover, and hydrologic condition was available (SCS, 1972). The rainfall (P)-runoff (Q) data were plotted on the arithmetic paper having a grid of plotted curve number, as shown in Fig. 1.

The CN corresponding to the curve that separated half of the plotted data from the other half was taken as the median curve number for the watershed. Thus the developed cure numbers represented the averages or median site values for soil groups, cover, and hydrologic condition and corresponds to AMC II (CNII). The upper enveloping curve was taken to correspond to AMC III (CNIII) and the lower curve to AMC I (CNI). The average condition was taken to mean average response, which was later extended to imply average soil moisture condition (Miller and Cronshey, 1989).

Depending on 5-day antecedent rainfall, CNII is convertible to CNI and CNIII using the relationships given by Sobhani (1975), Hawkins et al. (1985), Chow et al. (1988), Neitsch et al. (2002), and Mishra et al. (2008) as given in Table 1 and directly from the NEH-4 Tables (SCS, 1972 and Mishra & Singh, 2003a) and these are applicable to ungauged watersheds. However, to estimate the CNII mathematically from the observed rainfall (P)-runoff (Q) data of a gauged watershed, Hawkins (1993) suggested the following expression for S (or CN) computation as:

[ ])P5Q4(QQ2P5S +−+= (1)

Schneider & McCuen (2005) developed a new Log-normal frequency method to estimate curve numbers from observed P-Q data. The developed method was found to be more accurate

than the rank-order method (Hjelmfelt, 1980) and the method suggested by Hawkins (1993). Recently, Mishra and Singh (2006) investigated the variation of CN with AMC and developed a new power relationship between the S (or CN) and the 5-day antecedent rainfall. The developed CN-AMC relationship is applicable to gauged as well as ungauged watershed and eliminates the problem of sudden jump from one AMC level to other.

In recent past few researchers have also considered watershed slope in CN computations. The works of Sharpley & Williams (1990) and Huang et al. (2006) are noteworthy. Sharpley & Williams (1990) incorporated slope factor in CN estimation assuming that CN2 obtained from the NEH Handbook (SCS 1972) corresponds to a slope of 5%. The slope adjusted CN2 (CN2α) were represented as:

( )( ) II86.13

IIIIIII CNe21CNCN31CN +−−= α−

α (2)

where α is the soil slope in m/m. However, Huang et al. (2006) explored the applicability of the above equation and found that the equation has limited applications and, as an improvement, they developed another set of equations for climatic and steep slope conditions observed in Loess Plateau of China. The modified CN2α can be expressed as:

( ) ⎥⎦

⎤⎢⎣

⎡+α

α+=α 52.323

63.1579.322CNCN IIII (3)

However, the credibility of the above models needs to be validated for other regions having similar climatic and slope conditions. From the above discussions, it can be concluded that there is still ample future scope of research for improvements in CN estimation methods.

DEVELOPMENTS IN IA-S RELATIONSHIP The relationship between Ia-S has always been a topic of discussions among researchers worldwide. Initially, Ia was not a part of the SCS-CN model in its initial formulation, however, as the developmental stages continued, it was included as a fixed ratio of Ia to S (Plummer & Woodward, 2002). Because of the larger variability, the Ia = 0.2S relationship has been the focus of discussion and modification since its very inception.

Table 1: AMC Dependent CN Conversion Formulae

CN Conversion Formulae AMC I AMC III

Sobhani (1975) II

III CN01334.0334.2

CNCN

−=

II

IIIII 0.005964CN0.4036

CNCN+

=

Hawkins et al. (1985) II

III CN01281.0281.2

CNCN

−=

II

IIIII 0.00573CN0.427

CNCN+

=

Chow et al. (1988) II

III CN058.010

CN2.4CN−

= II

IIIII CN13.010

CN23CN+

=

Neitsch et al. (2002) )]}CN0.0636(100exp[2.533CN{100)CN20(100CNCN

IIII

IIIII −−+−

−−= )}CN3(100 exp{0.0067CNCN IIIIIII −=

Mishra et al. (2008) II

IIIII 0.012754CN2.274

)CN20(100CNCN

−−

−= II

IIIII 0.0057CN0.430

CNCN+

=


32

As an example, Aron et al. (1977) suggested λ ≤ 0.1 and Golding (1979) provided λ values for urban watersheds depending on CN as λ = 0.075 for CN ≤ 70, λ = 0.1 for 70 < CN ≤ 80, and λ = 0.15 for 80 < CN ≤ 90. Ponce & Hawkins (1996) suggest that the fixing of the initial abstraction ratio at 0.2 may not be the most appropriate number, and that it should be interpreted as a regional parameter. Hawkins et al. (2001) found that a value of λ = 0.05 gives a better fit to data and would be more appropriate for use in runoff calculations.

Mishra & Singh (1999) suggested that the initial abstraction component accounts for the short-term losses such as interception, surface storage and infiltration before runoff begins, and therefore, λ can take any non-negative value. Mishra & Singh (2004b) developed criterion for applicability of SCS-CN method based on runoff coefficient (C) and λ variation. They defined the applicability bounds for the SCS-CN method as: λ ≤ 0.3; Ia* (=Ia/P) ≤ 0.35 and C ≥ 0.23. Considering the fact that P is an implicit function of climatic/meteorological characteristics, a more general non-linear Ia-S relation was developed by Jain et al. (2006a), expressed as:

( )

α

⎟⎟⎠

⎞⎜⎜⎝

⎛+

λ=SP

PSIa (4)

where α is a constant. Since Eq. (4) reduces to Ia = 0.2S for λ = 0.2 and α = 0, and hence could be taken as a generalized form of Ia-S relationship. The model resulting from the coupling of Eq. (4) with Eq. (6) (general form of SCS-CN method) for λ = 0.3 and α = 1.5 were found to perform much better than the existing SCS-CN method (Eq. 13) for λ = 0.2.

Mishra et al. (2006a) developed a modified non-linear Ia-S relationship based on the hypothesis that Ia largely depends on initial soil moisture M, as:

( )MSSI

2

a +λ

= (5)

The generalized nature of the above equation can be seen as, for M = 0 or a completely dry condition, Eq. (5) reduces to Eq. (7), which is the basic Ia and S relationship. Therefore, it can be concluded that the Ia-S relationship can be further refined for an enhanced performance of the SCS-CN methodology.

HYDROLOGICAL APPLICATIONS OF SCS-CN METHODOLOGY The SCS-CN method has witnessed myriad and variety of applications to the fields not originally intended, due to the reason of its simplicity, stability and accountability for most runoff producing watershed characteristics: Soil type, land use treatment, surface condition, and antecedent moisture condition. Some of its critics suggest it to be obsolete, a remnant of outdated technology, and needs overhaul or outright replacement (Smith & Eggert, 1978 and Van-Mullem, 1989). However, recently Singh and Frevert (2002) edited a book titled “Mathematical Models of Small Watershed Hydrology and Applications”, in which at least 6 of the 22 chapters have mathematical models of watershed hydrology based on SCS-CN approach. This reflects the robustness and lasting popularity of SCS-CN methodology. Recently, the

SCS-CN method has also been successfully applied in some of the newer fields like water quality, metal partitioning, erosion and sedimentation, and irrigation scheduling.

A considerable amount of literature on the method has been published and the method has undergone through various stages of critical reviews several times (Rallison, 1980; Chen, 1982; Ponce and Hawkins, 1996; and Mishra & Singh, 2003a). Rallison (1980) provided detailed information about the origin and evaluation of the methodology and highlighted major concerns to its application to the hydrology and water resources problems it was designed to solve and suggested future research areas. Chen (1982) evaluated the mathematical and physical significance of methodology for estimating the runoff volume.

Though primarily intended for event-based rainfall-runoff modeling of the ungauged watersheds, the SCS-CN method has been applied successfully in the realm of hydrology and watershed management and environmental engineering, such as long-term hydrologic simulation (LTHS) (Williams and LaSeur, 1976; Hawkins, 1978; Knisel, 1980; Woodward and Gburek, 1992; Pandit and Gopalakrishnan, 1996; Mishra and Singh, 2004a; Michel et al., 2005; Jain et al., 2006a&b; Sahu et al., 2007; Kannan et al., 2008; Durbude et al., 2010; Sahu et al., 2010; and Babu & Mishra, 2012), sediment yield modeling (SYM) (Mishra and Singh, 2003a; Mishra et al., 2006b; Tyagi et al., 2008; and Singh et al., 2008; and Bhunya et al., 2010), metal partitioning (Mishra et al., 2004b&c), determination of subsurface flow (Yuan et al., 2001), urban hydrology (Pandit & Gopalakrishnan, 1996 and Singh et al., 2013), water quality (Ojha, 2012), rainwater harvesting (Kadam et al., 2012 and Singh et al., 2013). The method has also been successfully applied in distributed watershed modeling (White, 1988; Moglen, 2000; and Mishra and Singh, 2003a). A brief description on few of these applications is being discussed here as follows.

SCS-CN BASED LONG-TERM HYDROLOGIC SIMULATION (LTHS) MODELS This section discusses some of the important and widely used LTHS models based on SCS-CN method.

Water Yield Model (Wym) Williams & LaSeur (1976) were probably the first to introduce the concept of Soil Moisture Accounting (SMA) procedure to develop a Water Yield Model (WYM) based on the existing SCS-CN methodology. The model is based on the notion that CN varied continuously with soil moisture, and thus considering many values of CN instead of only three (CNI, CNII, CNIII). The model computes a soil moisture index depletion parameter that forces an agreement between the measured and predicted average annual runoff. The model eliminates sudden jump in the CN-values while changing from one AMC to the other and requires simple inputs as: (i) CNII estimate for the study watershed; (ii) measured monthly runoff; (iii) daily rainfall; and (iv) average monthly lake evaporation, and only outputs runoff volume. It can also be applied to the nearby ungauged watershed by adjusting the curve number for the ungauged watershed in proportion to ratio of the AMC II curve number to the average predicted curve number for the gauged watershed. However, the model


33

utilizes an arbitrary assigned value of 20 inches for absolute potential maximum retention Sb. The general expression of the model is given in Table 2.

Hawkins Model Hawkins (1978) developed continuous soil moisture accounting (SMA) procedure by linking evapo-transpiration (ET) and CN for use in continuous hydrologic simulation model. The model uses the volumetric concept for accounting the site moisture on a continuous basis. The general expression of the model is given in Table 2. Hence, if (i) CNt for the first time step and (ii) P, Q, and ET for the next time step (∆t) are known, then Eq. (12) can be used to compute CNt+∆t for the next time step and sequentially the daily Q from Eq. (10). The model accounts for the site moisture on continuous basis and thus eliminates the problem of sudden jump in CN. The model is easier to apply and the SMA procedure followed in model development is hydrologically sounder than WYM.

Annual Storm Runoff Coefficient (ASRC) Model Pandit and Gopalakrishnan (1996) developed a continuous simulation technique, for computing annual pollutant loads using annual storm runoff coefficient (ASRC) and degree of perviousness/ imperviousness of watershed, using existing SCS-CN method. The model is very simple and specifically useful for small urban watersheds characterized by the percent imperviousness. The technique is cost-effective since the continuous simulations can be performed on spread sheets, and requires easily available daily rainfall data from a nearby climatological station. However, it allows sudden jumps in CN values, ignores evapo-transpiration, drainage contribution, and watershed routing. The general expression of the model is given in Table 2. It involves the following steps (Mishra and Singh, 2004a):

1. Determine the pervious curve number for AMC II,

2. Determine the directly connected impervious area of the urban watershed according to SCS (1956),

3. Estimate the daily runoff depth for both pervious and impervious areas separately using Eq. (13),

4. Determine the actual AMC based on the previous 5-day rainfall and modify CN using Eqs. (14 and (15) such that it does not exceed 98, and

5. Calculate the yearly storm runoff depth by summing the runoff for each day.

Versatile MS-SCS-CN (VMS-SCS-CN) Model Mishra & Singh (2004a) developed a four parameter VMS-SCS-CN model to remove the inconsistencies and complexities associated with the existing models of long term hydrologic simulation such as Water Yield Model (WYM) (William and LaSeur, 1976), Hawkins model (Hawkins, 1978), ASRC model (Pandit and Gopalakrishnan, 1996), Mishra et al. (1998) model, and MS model (Mishra and Singh, 2002a). They described the water balance equation of Mishra and Singh (2002) by discretizing them for time (t) using Eq. (22) and modified the SCS-CN runoff equation of Mishra and Singh (2002) as in Eq. (23).

The dynamic infiltration (Fd), occurred during ∆t period was computed using Eq. (24), which represents an increase in the

amount of soil moisture in the soil profile during ∆t period. The soil moisture budgeting was expressed as given in Eq. (25) which yields the antecedent moisture amount for the next storm to modify S(t) for the next storm. The model obviates the sudden jumps in CN values, exclusively considers the soil moisture budgeting on continuous basis, evapotranspiration, and watershed routing procedures. These characteristics make the model versatile. The developed model has been given in Table 2. They also expressed the evapo-transpiration ET(t), in terms of pan coefficient (PANC) and absolute maximum potential retention (Sabs) using Eq. (27).

SCS-CN based Time Distributed Runoff Model Mishra & Singh (2004b) established the criterion for the applicability of SCS-CN method and extended the SCS-CN concept to derivation of a time distributed runoff model. Further, they attempted to develop SCS-CN based infiltration model. The governing equations (Eqs. 28 a&b) of the developed models are given in Table 2.

Michel SCS-CN (MSCS-CN) Model Michel et al. (2005) reviewed SMA procedure that lies behind SCS-CN method and pointed out severe inconsistencies in the treatment of antecedent moisture conditions in SCS-CN procedure and proposed a sounder methodology. They hypothesized that the SCS-CN model is valid not only at the end of the storm but at any instant along a storm. Their findings are based on an analysis of the continuous soil moisture accounting (SMA) procedure implied by the SCS-CN equation. Their SMA procedure is based on the notion that higher the moisture store level, higher the fraction of rainfall will be converted into runoff.

They developed a procedure that is more consistent from SMA viewpoint, by introducing the term V0, the initial soil moisture store level. MSCS-CN model eliminates initial abstraction (Ia) and introduces a new parameter Sa (Sa=Ia+V0) to compute the direct runoff. The developed MSCS-CN model with new insight in SMA procedure is given in Table 2.

Enhanced SCS-CN (ESCS-CN) Model Jain et al. (2006b) developed ESCS-CN model for long-term hydrologic simulation by incorporating the storm duration and a non-linear relation for initial abstraction (Ia). They also proposed a continuous moisture content using a 5-day antecedent rainfall (P5) relation instead of the existing discrete relationship. The expression of ESCS-CN model is given in Table 2.

Sahu et al. Model Sahu et al. (2007) developed a continuous hydrologic simulation model for long-term hydrologic simulation using SCS-CN method. They found that the antecedent or initial soil moisture (V0) depends not only on P5 but also on S. The dependency on S is based on the fact that the watershed with larger retention capacity S must retain higher moisture compared to the watershed with lesser S for a given P5. V0 depends not only on the antecedent 5-day precipitation (P5), which is the basis for three AMCs in the SCS-CN method, but also on S. Considering Sa = α S in consistence with the MSCS-CN model and using other suitable assumptions, they derived Eqs. (35) to (38) for different conditions. These expressions are given in Table 2.


34

Table 2: SCS-CN Based Hydrologic Simulation (LTHS) Models

Model Name Governing Equation SMA accounting Water Yield Model (Williams and LaSeur, 1976) SIP

)IP(Qa

2a

+−−

= ; if P>Ia, Q = 0, otherwise

(6)

SIa λ=

(7)

SSM abs −= (8)

Sabs = absolute potential maximum

retention equal to 20.

( )( )∑ =

+= T

1t tc

tEMb1

MM (9)

where t = time; bc = depletion coefficient; M = soil moisture index at the beginning of the first storm; M(t) = soil moisture index at any time t; E(t) = average monthly lake evaporation for day t and T = number of days between storms.

Hawkins (1978) model ( )⎟⎟⎠

⎞⎜⎜⎝

⎛+

−−=S8.0P

S2.1SPQ for P≥0.2S

(10)

( ) ( ) ( )[ ]( )tt,tttt QPETSS ∆+∆+ −−+= (11)

(t, t+∆t) = the ∆t duration between time t and (t+∆t)

( )

( )( )[ ]( )tt.,t

t

ttQPETCN

12001200CN

∆+

∆+−−+

= (12)

Pandit and Gopalakrishnan (1996) model S8.0P

)S2.0P(Q2

+−

= for P≥0.2S

(13)

II

III CN01281.0281.2

CNCN−

= for AMC I (14)

II

IIIII CN00573.0427.0

CNCN

+= for AMC III (15)

Mishra et al. (1998) model

SPSPQ

8.0)2.0( 2

+−

=,for P≥0.2S

.......23121 +++= −− tttt ROdROdROdDO

(16)

DO= direct runoff at the outlet,

RO – direct surface runoff at any time t,

d1, d2, d3,... = non-dimensional regression

coefficients.

t

ttt CN01281.0281.2

CNCN

−=∆+

for AMC I (17)

t

ttt CN00573.0427.0

CNCN

+=∆+

for AMC III (18)

Mishra-Singh (2002) model

( )( )SMIPMIPIPQ

a

aa

++−+−−

= , if P>Ia,

(19) Q = 0, otherwise (20)

SI a λ=

( ) ( ) ⎥⎦⎤

⎢⎣⎡ +λ−+λ+−= SP4S1S15.0M 5

22 (21)

λ = 0.2 [ ]SP4S64.0S2.15.0M 5

2 ++−=λ = 0 [ ]SP4SS5.0M 5

2 ++−= where, P5= amount of antecedent 5-day rainfall.

Versatile SCS-CN Model (Mishra & Singh, 2004a)

Q)tt(F)tt(F)t(I)tt(P dca +∆++∆++=∆+ (22)

( ) ( ) ( ) ( )[ ] ( ) ( ) ( )[( ) ( ) ( ) ( ) ( ttsttMttFtIttP

ttFtIttPttFtIttPttQ

ca

caca

∆++∆++∆+−−∆++∆+−−∆+∆+−−∆+

=∆+

(23) where Fd and Fc represent the dynamic and static portion of infiltration during ∆t period; St, potential maximum retention at time t; Sabs absolute potential maximum retention; PANC, pan coefficient; M, the antecedent moisture content prior to the beginning of the storm; PET, ET and E represent the potential evapotranspiration, evapotranspiration and pan evaporation at time t, respectively.

( ) ( ) ( ) ( )tt,tRO)tt,t(FtItt,tPtt,tF cad ∆+−∆+−−∆+=∆+ (24)

( ) ( ) ( )tt,tETtt,tMStttS ∆++∆+−=∆+ (25) ( ) ( )tt,tPANCxEtt,tPET ∆+=∆+

(26)

abs

t

SSPANC= (27)

SCS-CN based Time distributed runoff and Infiltration models Mishra & Singh (2004b)

( )we2 Ai

kt111)t(Q

⎭⎬⎫

⎩⎨⎧

λ−+−=

(28a) where Q(t) is the rainfall-excess rate (L3T-1); ie is the effective rainfall intensity (LT-1); Aw is the catchment area (L2); and k and λ are the infiltration decay constant and initial abstraction coefficient, respectively.

SCS-CN based Infiltration model:

( )2

c0c kt1

fiff

+λ−

−+= (28b)

where f is the infiltration rate (LT-1) at any time t ; fc is the final infiltration rate (LT-1); i0 is the uniform rainfall intensity; λ is the initial abstraction coefficient; and k is the decay parameter (T-1).

Mi h l t l If V ≤ S P th Q 0


35

SME Model Sahu et al. (2010) developed a revised version of MS model (Mishra & Singh, 2002) by incorporating a hydrologically more sound procedure for accounting antecedent moisture and designated as Sahu-Mishra-Eldho (SME) model. The governing equations of the model are given in Table 2. The SME model has several advantages over the existing SCS-CN based models.

Babu and Mishra Model Babu & Mishra (2012) modified ESCS-CN model by including a new parameter, Sabs, to overcome most of the limitations existing in the SCS-CN method and proposed a new model consisting of five parameters as given in Table 2. It was assumed that Sabs as the sum of potential retention (S) and moisture content (M), where S is a variable quantity from storm to storm and inversely varies with moisture content (M). Further, to make the model more realistic, M was modified as

a function of P5 as well as Sabs. The expression of the developed model is given in Table 2.

SCS-CN Based Rain Water Harvesting Model Singh et al. (2013) explored applicability of SCS-CN method and its variants, i.e., Hawkins SCS-CN (HSCS-CN) model (Hawkins et al., 2001), Michel SCS-CN (MSCS-CN) model (Michel et al., 2005), and Storm Water Management Model-Annual Storm Runoff Coefficient (SWMM-ASRC) (Heaney et al., 1976) and compared their performance with Central Ground Board (CGWB) (CGWB, 2000) approach. It was found that for the same amount of rainfall and same rooftop catchment area, the MSCS-CN model yields highest rooftop runoff followed by SWMM-ASRC>HSCS-CN>SCS-CN>CGWB. The versatility of SCS-CN based models for rainwater harvesting studies can be attributed to the fact that the model implicitly incorporates major runoff producing catchment characteristics and have sound hydrological foundation and therefore, these models could be a better

Michel et al. (2005) model

If V0 ≤ Sa–P, then Q=0 (29)

QPVV 0 −+= (32) where; V = soil moisture store level at time when the accumulated rainfall is equal to P. If Sa–P < V0<Sa, then ( )

SSVPVSPQa0

20a

+−+−+

=

(30) If Sa ≤ V0≤ Sa+S, then,

( )( ) ⎥

⎦

⎤⎢⎣

⎡

−++−+

−=PVSSS

VSS1PQ0a

2

20a

(31)

Jain et al. (2006b) model

( )( )SMIP

MIP)IP(Qadc

adcadc

++−+−−

= ; Pc>Iad,

Q=0, otherwise (33) α

⎟⎟⎠

⎞⎜⎜⎝

⎛+

λ=SP

PSIc

cad ;

β

⎟⎟⎠

⎞⎜⎜⎝

⎛=

P

Poc t

tPP

5PM γ= (34)

where; γ = coefficient; P5=antecedent 5-day precipitation amount; Po=

observed rainfall; Pc=adjusted rainfall, Iad=adjusted initial abstraction; Pt=mean storm duration, tP = storm duration, α, β=coefficients.

Sahu et al. (2007) Model

For 5a00 PSV −≤ , 5000 PVV β+= (35)

SV00 γ= (38)

V00 - old moisture level available on 5 days before the onset of rainfall, and

γ - model parameters ranging from 0 to 1. β - model parameters ranging from 0 to 1.

For Sa-P5<V00<Sa,

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−+−+

−β+=SSVP

SVPPVV

a005

2a005

5000

(36) For Sa ≤ V00 ≤ Sa+S, then,

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

−++−+

β+=500a

2

200a

5000 P)VSS(SVSS

PVV

(37) Sahu-Mishra-Eldho (2010) model

( )( )0a

aa

SIP)MIP(IP

Q+−

+−−= , if P>Ia, Q=0,

otherwise (39)

( )MSI 0a −λ=

(40)

( )⎥⎦

⎤⎢⎣

⎡+λ−

λ−β=

005

005

S)SP(SSP

M , for P5 > λS0 (41)

and M = 0, for P ≤ λS0

Babu & Mishra (2012) model

( )( )SMIP

MIP)IP(Qa

aa

++−+−−

= , Pc>Ia, Q=0,

otherwise (42)

( )MSI absa −λ=

(43)

MSSabs += (44)

where, Sabs = constant quantity for a watershed irrespective of storms.

abs5SPM γ= (45)

where, γ = proportionality coefficient.


36

alternative to the empirical coefficients/constant based method used for the purpose. Recently, Kadam et al. (2012) identified the potential sites to construct rainwater harvesting structures coupling SCS-CN method with GIS and remote sensing. It was found that that the SCS-CN method adopted deciphers the more precise, accurate and ability to process large catchment area than other methods.

SCS-CN Based Erosion, Sedimentation and Water Quality Models Sediment yield is defined as the total sediment outflow from a watershed or a drainage basin, measurable at a point of reference and in a specific period of time (ASCE, 1970). This section briefly discusses some of the recently developed models based on SCS-CN method for erosion, sedimentation and metal partitioning in hydrological and environmental engineering. As discussed previously, most of the computer based sedimentation simulation models such as AGNPS (Young et al., 1989), CREAMS (Knisel, 1980), SWRRB (Arnold et al., 1990), SWAT (Neitsch et al., 2002), EPIC (Sharpley & Williams, 1990) and GWLF (Haith & Shoemaker, 1987) use the SCS-CN method as a component model for runoff estimation, however, the SCS-CN method has not witnessed many applications in the field of erosion & sediment yield and environmental engineering, despite some noteworthy works of Mishra and Singh (2003a), Mishra et al. (2006b), Tyagi et al. (2008), Singh et al. (2008), and Bhunya et al. (2010). In the recent past, an interesting review paper by Garen & Moore (2005) titled ‘Curve Number Hydrology in Water Quality Modeling: Uses, Abuses, and Future Directions’ was widely appreciated by the water quality modelers. Hence, it can be stated that the SCS-CN method is still a central tool available to the scientific community with its broad applicability.

Metal Partitioning Analog (MPA) Models Mishra et al. (2004b) employed the basic proportionality concept of the SCS-CN method for partitioning 12 metal elements, Zn, Cd, Pb, Ni, Mn, Fe, Cr, Mg, Al, Cu, and Na between dissolved and particulate bound form. In order to apply this metal partitioning analogy, two parameters, the potential maximum desorption (Ψ ) (Eq. 47) and the partitioning curve number (PCN) (Eq. 48) are postulated as analogous to the SCS-CN parameters S and CN, respectively.

These parameters were introduced, along with Ψ -PCN and Ψ -ADP, where ADP is the antecedent dry period similar to the AMC. Based on these parameters analogous relationships were developed as given Table 3. In an another attempt, Mishra et al. (2004c) further suggested a new partitioning curve number (PCN) approach for partitioning heavy metals into dissolved and particulate bound forms in urban snow melt, rainfall/runoff, and river flow environments on the basis of an analogy between SCS-CN method based infiltration and metal sorption processes.

USLE-SCS-CN Model For the first time, Mishra et al. (2006b) coupled the popular and widely used models of SCS-CN method and universal soil loss equation (USLE) for modeling rain-storm generated sediment yield from a watershed. The coupling is based on three hypotheses: (i) the runoff coefficient (C) is equal to the degree of saturation (Sr); (ii) the potential maximum retention (S) can be expressed in terms of the USLE parameters, and (iii) the sediment delivery ratio (DR) is equal to the runoff coefficient (C). The expressions of the model for various conditions are given in Table 3.

Time Distributed Sediment Yield Model A time distributed sediment yield model was developed by Tyagi et al. (2008) utilizing the SCS-CN based infiltration model for computation of rainfall-excess rate, and the SCS-CN-inspired proportionality concept for computation of sediment-excess. Finally, for computation of time distributed sediment yield (sediment graphs), the sediment-excess was routed to the watershed outlet using a single linear reservoir technique. The general expression of the model is given in Table 3.

Conceptual Sediment Graph Model New conceptual sediment graph models were developed by Singh et al. (2008) based on coupling of popular and extensively used methods, viz., Nash model (Nash, 1957) based instantaneous unit sediment graph (IUSG), SCS-CN method, and Power law (Novotny and Olem, 1994). The models for different conditions are given in Table 3. The proposed models are useful in computation of sediment graph as well as total sediment yield and can be successfully applied for ungauged conditions as well. The models can be very useful for computing dynamic pollutant loads in water quality

Table 3: SCS-CN Based Erosion, Sedimentation and Water Quality Models

Model Name Governing Equations PCN Metal Partitioning Analog Model (Mishra et al. 2004b&c)

PCN method ( )

ψ+−−

=fT

2fT

p iCiCC ; for fT iC ≥

(46)

if-Ψ hypothesis ψλ= tfi

(47)

Ψ –CN mapping ψ+

=1000

1000PCN

(48)

where CP = particulate-bound metal; CT = total metal; Cd = dissolved metal; Ψ = potential maximum desorption; if = initial flush

USLE SCS CN M d l (i) I i f I ( λS)


37

modelling if the sediment transports the pollutants that are toxic at high concentrations, requiring determination of peak, rather than average sediment flow rate. The expressions of the model for various conditions are given in Table 3.

Modified Long-Term Hydrologic Simulation Advance Soil Moisture Accounting (MLTHS ASMA) Model Jain et al. (2012) proposed modified long-term hydrologic simulation advance soil moisture accounting (MLTHS ASMA) model by suitably amalgamating the advanced soil moisture

USLE-SCS-CN Model (Mishra et al., 2006b)

(i) Incorporation of Ia (=λ S)

( )( )SIP

AIPYa

a

+−−

=

(49)

Taking Ia = 0.2S which is a standard practice:

( )S8.0PAS2.0PY

+−

=

(ii) Incorporation of antecedent moisture (V0)

( )( )0a

0a

VSIPAVIPY

++−+−

=

(50)

Taking Ia = 0.2S which is a standard practice: ( )( )0

0

VS8.0PAVS2.0PY

+−+−

=

(iii) Incorporation of initial flush (If = λ1A)

( )( )( ) ⎥

⎦

⎤⎢⎣

⎡λ+

++−+−λ−

= 1VSIP

AVIP1Y0a

0a1

(51)

for Ia = 0.2S

( )( )( ) ⎥

⎦

⎤⎢⎣

⎡λ+

+−+−λ−

= 1VS8.0P

AVS2.0P1Y0

01

where Y = sediment yield; A =the potential maximum erosion; P =total rainfall; S = potential maximum retention; V0 = initial soil moisture; Ia = initial abstraction coefficient; and If = initial flush coefficient.

SCS-CN Time Distributed Sediment Yield (Tyagi et al., 2006) ( )

( )c2

2

tt fi

SSPS1

PAY −⎥

⎦

⎤⎢⎣

⎡

λ−+−=

∆

(52) where A is the potential maximum erosion of the watershed dependent on the soil properties and storage capacity (S); and P∆t is the rainfall amount during time interval ∆t; i is the rainfall intensity and fc is the final infiltration rate.

SCS-CN Based Sediment Graph Model (SGM) (Singh et al., 2008)

The sediment graph models (SGM) for four different cases, depending on the number of model parameters, and these are designated as SGM1 through SGM4, respectively. For SGM1, both the initial soil moisture V0 and initial abstraction Ia are assumed to be zero, i.e. V0 = 0 and Ia = 0. For SGM2, V0 = 0, but Ia ≠ 0. For SGM3, V0 ≠ 0 and Ia = 0. Finally, for SGM4, V0 ≠ 0 and Ia ≠ 0. The governing general expression of the above models is given as:

( )⎥⎦⎤

⎢⎣⎡ −Γ−+λ−++λ−α= −β 1n])t/t(e)t/t)[(n(t/n)1n()]S/Vkt1/()S/Vkt[(AAtQ sps

psspss

s00ws

(53)

where Qs(t) = sediment yield rate (Ton/h); A = potential maximum erosion; Aw = watershed area; � and � =coefficient and exponent of power law; k = infiltration decay coefficient; and ns is the number of reservoirs.

SCS-CN Based Water Quality Model for RBF (Ojha, 2012)

CN 1000 R10 R 1 R input

; (54) where R = output/input = input/(input+S)

Finally the filtrate quality can be computed using the following expression as: R Ce

C0 vf C0 CN

1000 10CN vfC0 CN;

(55) where Ce = filtrate (effluent) quality, C0 = influent quality and vf = flow velocity


38

accounting (ASMA) procedure, the modified subsurface drainage flow concept, and curve number (CN)–based model for simulating daily flows. The proposed model uses the ASMA procedure both for surface and sub-surface flows. In this model, the direct surface runoff is computed using the modified formulations of SCS-CN method given by Michel et al. (2005) and Durbude et al. (2011). The sub-surface drainage flow is modeled using a new formulation on the basis of the concept of Yuan et al. (2001).

Water Quality Model for River Bank Filtration Ojha (2012) explored the potential of the SCS-CN approach in water quality modeling of the river bank filtration (RBF) process using a theoretical framework through relating the curve number (CN) with the filtration/kinetic coefficient (K) and the input applied to the system. The CN was found to be dependent on travel time between source water and the abstraction well in addition to the influent concentration. For very low or very high values of influent concentration, the curve number exhibits an asymptotic variation approaching 100 and 0, respectively. The governing equations of the postulated theory are given in Table 3. The salient features of the study were found as:

(i) CN is related with the performance (output to input ratio, R) of a water quality system. The simulation of filtrate quality (R) using filtration coefficient (λ), kinetic coefficient, and CN is equivalent to each other as these are all interrelated.

(ii) For flow through porous media, CN is dependent on the filtration coefficient/kinetic coefficient. Therefore, CN is dependent on all the parameters that influence the filtration/kinetic coefficient such as filtration velocity, medium properties and the distance between source water and abstraction point, and the source water quality.

CONCLUSION Within the tremendous literature available on applications of SCS-CN methodology in surface water hydrology, a relevant work dealing with its origin, theoretical and historical background, nature, advantages and limitations, issues pertaining to structural foundation, including the CN vs AMC variation, Ia vs S and storm duration dependence, CN vs SMA procedure, and advanced applications of methodology including the areas other than originally intended was presented and discussed critically for their merits and demerits.

Following explorative and diagnostic discussions, it can be stated that the SCS-CN methodology has been applied through the spectrum of hydrology ranging from runoff and flood estimation to water quality and erosion & sedimentation. It is observed that the methodology has gone under rigors of the peer review and modifications by incorporating soil moisture accounting (SMA) procedures, storm duration (t), non- linear Ia-S relation, slope factors, etc. Looking into current trends of advanced applications as well as sound hydrological re-structuring of the SCS-CN methodology, there is always ample scope for further refinements to enhance its wider applicability in the field of erosion & sedimentation, groundwater, environmental engineering, urban hydrological studies, and

water resources assessment related studies through coupling with the latest GIS and remote sensing techniques

REFERENCES 1. Andrews, R. G. (1954). The use of relative infiltration

indices in computing runoff (unpublished). Soil Conservation Service, Fort Worth, Texas, p. 6.

2. Arnold, J. G., Williams, J. R., Griggs, R. H. & Sammons, N. B. (1990). SWRRB—A Basin Scale Simulation Model for Soil and Water Resources Management. A&M Press, Texas.

3. Arnold, J.G., Williams, J.R., Srinivasan, R., King, K.W., 1996. SWAT: Soil and Water Assessment Tool. USDA-ARS, Grassland, Soil andWater Research Laboratory, Temple, TX. Aron G, Miller A C and Lakatos D F. (1977). Infiltration formula based on SCS curve numbers. Journal of Irrigation and Drainage Division. ASCE. 103(4): 419-427.

4. ASCE (1970). Sediment sources and sediment yields. J. Hydraulics Division, ASCE, 96 (HY6), 1283– 1329.

5. Babu, P. S. and Mishra, S.K. (2012). Improved SCS-CN–Inspired Model. J. Hydrologic Engg., 17(11), pp. 1164–1172.

6. Bhunya, P. K., Jain, S. K., Singh, P. K. & Mishra, S. K. (2010). A simple conceptual model of sediment yield. Water Resources Management, 24(8) 1697–1716.

7. Bonta, J. V. 1997 Determination of watershed curve number using derived distributions. J. Irrigation & Drainage Engg., 123 (1), 234–238.

8. Boszany, M. (1989). Generalization of SCS curve number method. J. Irrigation & Drainage Engg., 115 (1), 139–144.

9. Central Ground Water Board (2000). Guide on artificial recharge to ground water prepared by central ground water board. Ministry of Water Resources, Government of India, New Delhi.

10. Chen C L. (1982). Infiltration formulas by curve number procedure. Journal of Hydraulic Division, ASCE, 108(7): 828-829.

11. Chow V T, Maidment D R and Mays L W. (1988). Applied Hydrology. New York. Mc-Graw-Hill.

12. Chung, W., Wang, I., and Wang, R. (2010). Theory based SCS-CN method and its applications. J. Hydrologic Engg., 15(12), 1045-1058.

13. Durbude, D. G., Jain, M. K. and Mishra, S. K. (2011). Long-term hydrologic simulation using SCS-CN based improved soil moisture accounting procedure. Hydrological Processes, 25, 561-579.

14. Garen, D. and Moore, D. S. (2005). Curve number hydrology in water quality modeling: use, abuse, and future directions. J. American Water Resources Association, 41 (2), 377–388.


39

15. Golding, B. L. (1979). Discussion of runoff curve numbers with varying soil moisture. J. Irrig. Drain. Div. ASCE 105 (IR4), 441–442.

16. Grayson, R.B., Moore, I.D., McMahon, T.A. (1992). Physically based hydrologic modelling 2. Is the concept realistic? Water Resources Research 28, 2659–2666.

17. Haith, D. A. & Shoemaker, L. L. (1987). Generalized watershed loading functions for streamflow nutrients, J. American Water Resources Association, 23, 471–478.

18. Hawkins R H. (1978). Runoff curve number with varying site moisture. J. Irrigation and Drainage Engg., 104(4): 389-398.

19. Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. J. Irrigation and Drainage Engg. 119 (2), 334–345.

20. Hawkins, R. H. 1978 Runoff curve numbers with varying site moisture. J. Irrig. Drain. Div. ASCE 104 (IR4), 389–398.

21. Hawkins, R. H., Hjelmfelt, A. T., Jr. & Zevenbergen, A. W. (1985). Runoff probability, storm depth and curve numbers. J. Irrigation and Drainage Engg., 111 (4), 330–340.

22. Hawkins, R. H., Woodward, D. E. & Jiang, R. (2001). Investigation of the runoff curve number abstraction ratio. Paper presented at USDA-NRCS Hydraulic Engineering Workshop, Tucson, Arizona.

23. Heaney, J.P., Huber, W.C., Nix, S.J. (1976). Storm water management model: level I-preliminary screening procedures, EPA Rep. No. 66/2-76-275. U.S. Environ. Protection Agency (U.S. EPA), Cincinnati, Ohio

24. Hjelmfelt, A. T., Jr. (1980). Empirical investigation of curve number technique. J. Hydraul. Div. ASCE 106 (9), 1471–1477.

25. Huang, M., Gallichand, J., Wang, Z. & Goulet, M. (2006). A modification to the soil conservation service curve number method for steep slopes in the Loess Plateau of China. Hydrological Processes, 20, 579–589.

26. Jain, M. K., Mishra, S. K., Babu, S. & Singh, V. P. (2006b). Enhanced runoff curve number model incorporating storm duration and a nonlinear Ia–S relation. J. Hydrologic Engg. 11 (6), 631–635.

27. Jain, M. K., Mishra, S. K., Babu, S. & Venugopal, K. (2006a). On the Ia–S relation of the SCS-CN method. Nord. Hydrol. 37 (3), 261–275.

28. Jain, M.K., Durbude, D.G., and Mishra, S.K. (2012). Improved CN-Based Long-Term Hydrologic Simulation Model. J. Hydrologic Engg. 17 (11), 1204–1220.

29. Kadam, A.K., Kale, S.S., Pande, N.N., Pawar, N.J., and Sankhua, R.N. (2012). Identifying potential rainwater harvesting sites of a semi-arid, basaltic region of western India, using SCS-CN method, Water Resources Management, 26, pp. 2537-2554.

30. Kannan N, Santhi C, Williams J R and Arnold J G. (2008). Development of a continuous soil moisture accounting procedure for curve number methodology and its behavior with different evapotranspiration methods. Hydrological Processes, 22, 2114-2121.

31. Knisel, W. G. 1980 CREAMS: a field-scale model for chemical, runoff and erosion from agricultural management systems. Conservation Research Report No. 26, South East Area, US Department of Agriculture, Washington, DC

32. McCuen, R. H. (2002). Approach to confidence interval estimation for curve numbers. J. Hydrologic Engg. 7 (1), 43–48.

33. Michel C, Vazken A and Charles P. (2005). Soil conservation service curve number method: how to mend among soil moisture accounting procedure? Water Resources Research, 41(2), 1-6.

34. Miller, N. & Cronshey, R. (1989). Runoff curve numbers, the next step, Proc. Int. Conf. on Channel Flow and Catchment Runoff. University of Virginia, Charlottesville, VA.

35. Mishra S K and Singh V P. (2004b). Validity and extension of the SCS-CN method for computing infiltration and rainfall-excess rates. Hydrological Processes, 18, 3323–3345.

36. Mishra S K and Singh VP. (1999). Another look at the SCS-CN method. J. Hydrologic Engineering, 4(3): 257–264.

37. Mishra, S. K. & Singh, V. P. 2006 A re-look at NEH-4 curve number data and antecedent moisture condition criteria. Hydrol. Process. 20, 2755–2768.

38. Mishra, S. K. and Singh, V. P. (2002a). SCS-CN method: Part-I: Derivation of SCS-CN based models. Acta Geophysica Polonica, 50(3): 457–477.

39. Mishra, S. K. and Singh, V. P. (2002b). SCS-CN-based hydrologic simulation package in V. P. Singh and D. K. Frevert (eds), Mathematical Models in Small Watershed Hydrology, Water Resources Publications, Littleton, Colo., Chap.13, 391–464.

40. Mishra, S. K. and Singh, V. P. (2003a). Soil conservation service curve number (SCS-CN) methodology. Kluwer, Dordrecht, The Netherlands. ISBN: 1-4020-1132-6.

41. Mishra, S. K. and Singh, V. P. (2003b). SCS-CN method: Part-II: Analytical treatment. Acta Geophysica Polonica, 51(1), 107–123.

42. Mishra, S. K. and Singh, V. P. (2004a). Long-term hydrological simulation based on soil conservation service curve number. Hydrological Processes, 18(7), 1291–1313.

43. Mishra, S. K., Jain, M. K., and Singh, V. P. (2004a). Evaluation of SCS-CN based models incorporating antecedent moisture. J. Water Resources Management, 18, 567-589.


40

44. Mishra, S. K., Jain, M. K., Babu, P. S., Venugopal, K. & Kaliappan, S. 2008 Comparison of AMC-dependent CN-conversion formulae. Water Resour. Manage. 22, 1409–1420.

45. Mishra, S. K., Sahu, R. K., Eldho, T. I. & Jain, M. K. (2006a). An improved Ia–S relation incorporating antecedent moisture in SCS-CN methodology. Water Resources Management, 20, 643–660.

46. Mishra, S. K., Sansalone, J. J. & Singh, V. P. (2004b). Partitioning analog for metal elements in urban rainfall-runoff overland flow using the soil conservation service curve number concept. J. Environmental Engg., 130 (2), 145–154.

47. Mishra, S. K., Sansalone, J. J., Glenn, D. W., III & Singh, V. P. (2004c). PCN based metal partitioning in urban snow melt, rainfall/runoff, and river flow systems. J. American Water Resources Association, 40 (5), 1315–1337.

48. Mishra, S. K., Tyagi, J. V., Singh, V. P., and Singh, R. (2006b). SCS-CN based modeling of sediment yield. J. Hydrology, 324, 301-322.

49. Mishra, S.K., Singh, R.D., and Nema, R.K., (1998). A modified SCS-CN method for watershed modeling, Proc., Int. Conf. on Watershed Management and Conservation, Central Board of Irrigation and Power, New Delhi, India, Dec. 8–10

50. Mockus, V. (1949). Estimation of total (peak rates of) surface runoff for individual storms. Exhibit A of Appendix B, Interim Survey Report Grand (Neosho) River Watershed, USDA, Dec. 1.

51. Moglen, G. E. (2000). Effect of orientation of spatially distributed curve number in runoff calculations. Journal of American Water Resource Association, 36, 1391-1400.

52. Neitsch, S. L., Arnold, J. G., Kiniry, J. R., Williams, J. R. & King, K. W. (2002). Soil and Water Assessment Tool (SWAT): Theoretical Documentation, Version 2000. Texas Water Resources Institute, College Station, Texas, TWRI Report TR-191.

53. Ojha C.S.P. (2012). Simulating turbidity removal at a river bank filtration site in India using SCS-CN approach. J. Hydrologic Engg., 17(11), 1240-1244.

54. Pandit, A. and Gopalakrishnan, G. (1996). Estimation of annual storm runoff coefficients by continuous simulation. J. Irrigation and Drainage Engg., 122(4): 211-220.

55. Plummer, A. & Woodward, D. E. (2002). The origin and derivation of Ia/S in the runoff curve number system. Available at the NRCS website: http://www.wcc.nrcs.usda.gov/water/quality/common/techpaper/don1.pdf

56. Ponce, V. M. and Hawkins, R. H. (1996). Runoff curve number: Has it reached maturity? J. Hydrological Engg., 1(1): 11–19.

57. Rallison, R. E. & Miller, N. (1982). Past, present, and future. In Proc. Int. Symp. Rainfall-Runoff Relationship

(ed. V. P. Singh). Water Resources Pub., P.O. Box 2841, Littleton, CO.

58. Rallison, R. E. (1980). Origin and evaluation of the SCS runoff equation. Proc. Symp. Watershed Management, ASCE, Idaho, 912–924.

59. Ramasastry, K. S. & Seth, S. M. (1985). Rainfall-runoff Relationships. Rep. RN-20, National Institute of Hydrology, Roorkee, India.

60. Reshmidevia, T.V., Janab, R., Eldho, T.I. (2008). Geospatial estimation of soil moisture in rain-fed paddy fields using SCS-CN-based model. Agricultural Water Management, 95, 447–457.

61. Sahu, R. K., Mishra, S. K. and Eldho, T. I. (2010). An improved AMC-coupled runoff curve number model. Hydrological Processes, 21(21): 2834-2839.

62. Sahu, R. K., Mishra, S. K., Eldho, T. I. and Jain, M. K. (2007).An advanced soil moisture accounting procedure for SCS curve number method. Hydrological Processes, 21, 2827-2881.

63. Schneider, L. E. & McCuen, R. H. (2005). Statistical guidelines for curve number generation. J. Irrigation & Drainage Engg., 131 (3), 282–290.

64. SCS (1972). Hydrology National Engineering Handbook, Supplement A, Section 4, Chapter 10, Soil Conservation Service, USDA, Washington, DC.

65. SCS 1985 National Engineering Handbook. Supplement A, Section 4, Chapter 10, Soil Conservation Service, USDA, Washington, DC.

66. Sharpley, A. N. & Williams, J. R. (1990). EPIC—Erosion/Productivity Impact Calculator: 1. Model Documentation. US Department of Agriculture Technical Bulletin No. 1768. US Government Printing Office, Washington, DC.

67. Sherman, L. K. (1949). The unit hydrograph method. In Physics of the Earth (ed. O. E. Meinzer), 514–525. Dover Publications, Inc., New York, NY.

68. Shi, Zhi-Hua, Chen, Li-Ding, Fang, Nu-Fang, Qin, De-Fu, and Cai, Chong-Fa (2009). Research on the SCS-CN initial abstraction ratio using rainfall-runoff event analysis in the Three Gorges Area, China. Catena, pp. 1-7.

69. Singh, P. K., Bhunya, P. K., Mishra, S. K. & Chaube, U. C. (2008). A sediment graph model based on SCS-CN method. J. Hydrology, 349, 244–255.

70. Singh, P.K., Yaduwanshi, B.K., Patel, S, and Ray, S. (2013). SCS-CN based quantification of potential of rooftop catchments and computation of ASRC for rainwater harvesting. Water Resources Management, 27 (7), 2001-2012.

71. Singh, V. P. & Frevert, D. K. (2002). Mathematical Models of Small Watershed Hydrology and Applications. Water Resources Publications, Highlands Ranch, CO.


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72. Smith, R.E., and Eggert, K.G. (1978). Discussion to infiltration formula based on SCS cure number by G. Aron, A.C. Miller, and D.F. Lakatos. J. Irrig. And Drain. Div., ASCE, 104(4), 462-463.

73. Sobhani, G. (1975). A review of selected small watershed design methods for possible adoption to Iranian conditions. MS Thesis, Utah State University, Logan, Utah.

74. Tyagi, J. V., Mishra, S. K., Singh, R. & Singh, V. P. (2008). SCS-CN based time distributed sediment yield model. J. Hydrology, 352, 388–403.

75. Van-Mullem, J. A. (1989). Runoff and peak discharges using Green-Ampt model. J. Hydraul. Eng. ASCE 117 (3), 354–370.

76. White, D. (1988). Grid-based application of runoff curve numbers. J. Water Resources Planning and Management, 114(6), 601-612.

77. Williams, J. R. and LaSeur, V. (1976). Water yield model using SCS curve numbers. J. Hydraulic Engg., 102(9), 1241-1253.

78. Woodward, D. E. and Gbuerek, W. J. (1992). Progress report ARS/SCS curve number work group. Proceedings of ASCE Water Forum. ASCE, New York, 378-382.

79. Young, R. A., Onstad, C. A., Bosch, D. D. & Anderson, W. P. (1989). AGNPS: a nonpoint-source pollution model for evaluating agricultural watersheds. J. Soil & Water Conservation, 44 (2), 168–173.

80. Yuan, Y., Mitchell, J. K., Hirschi, M. C. and Cooke, R. A. C. (2001). Modified SCS Curve Number Method for predicting sub surface drainage flow. Transaction of the ASAE. 44(6): 1673-1682.

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