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Analogy Between SCS-CN and Muskingum Methods

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Abstract

Soil Conservation Service Curve Number (SCS-CN) method is one of the most widely used, popular, stable, reliable, and attractive rainfall-runoff methods, initially designed for direct surface runoff estimation in small and medium agricultural watersheds. It, in various forms, is now being employed to several areas other than the intended one, such as infiltration, sediment yield, pollutant transport and so on. In this study, the proportionality concept of the SCS-CN method is further extended to the field of flood routing and is shown to either parallel or be analogous to the Muskingum routing method, which is a simplified variant of St. Venant equations. When employed to various real (typical) flood events of four different river reaches available in literature from different sources, and thus, of varying flow and channel settings, the results of SCS-CN concept compare well with those due to Muskingum method in terms of their evaluation for performance through root mean square error (RMSE) for overall hydrograph, and relative error (RE) for peak discharge (Qp) and time to peak (Tp) of all four flood events. It thus underscores not only the efficacy but also the versatility of the SCS-CN concept in application to one more field of flood/flow routing, which forms to be an element of paramount importance in distributed hydrologic modeling.

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Abbreviations

A:

Surface area of the system (watershed, canal or reservoir) [L2]

B:

Channel width [L]

CN:

Curve number (nondimensional)

C0, C1, C2 :

Dimensionless parameters of SCS-CN and Muskingum routing procedures (nondimensional)

DA :

Actual detention storage [L]

DP :

Potential maximum detention storage [L]

F:

Actual retention storage [L]

F0 :

Cumulative dynamic retention [L]

f0 :

Initial infiltration capacity [LT−1]

fc :

Constant minimum infiltration capacity [LT−1]

I:

Rate of inflow to the system [L3T−1]

Ip :

Peak rate of inflow to the system [L3T−1]

Ia :

Initial abstraction or rainfall losses [L]

Is :

Initial storage depth or condition in routing [L]

i 0 :

Uniform rainfall intensity [LT−1]

i e :

Uniform effective rainfall intensity [LT−1]

k:

Horton’s decay coefficient [T−1]

K:

Storage coefficient [T]

m:

A nondimensional parameter defined as: m = θK/Δt

N:

Number of ordinates of outflow hydrograph (nondimensional)

Oai :

Ordinates of actual outflow [L3T−1]

Ori :

Ordinates of routed outflow [L3T−1]

Opa :

Actual peak outflow [L3T−1]

Opr :

Routed peak outflow [L3T−1]

O :

Rate of outflow from the system [L3T−1]

Ob :

Base flow [L3T−1]

P:

Total rainfall [L]

Pe :

Effective rainfall [L]

Q :

Direct surface runoff [L]

Sa :

Actual detention storage of a canal reach excluding initial storage (Si) [L3]

Sb :

Channel bed slope [LL−1]

Si :

Initial storage in canal reach [L3]

SSCS :

Potential maximum retention storage [L]

S0 :

Potential storage space prior to rainfall [L]

Sp :

Potential detention storage of a canal reach excluding initial storage (Si) [L3]

tp :

Time to ponding [T]

Tpa :

Actual time to peak [T]

Tpr :

Routed time to peak [T]

X:

Outflow depth [L]

Y:

Inflow depth [L]

ΔF0 :

Change in retention storage of the system [L]

ΔSMusk :

Change in Muskingum storage in channel routing [L3]

Δt:

Time interval [T]

β:

Initial abstraction coefficient (nondimensional)

λ:

Initial abstraction coefficient (nondimensional)

θ:

Weighting factor (nondimensional)

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Acknowledgements

The authors are thankful to Department of Water Resource Development and Management, Indian Institute of Technology Roorkee, Roorkee-247667, India, for providing all necessary facilities to carry out this study.

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Authors and Affiliations

  1. Department of WRD&M, Indian Institute of Technology Roorkee, Roorkee, 247 667, Uttarakhand, India

    Esmatullah Sangin & S. K. Mishra

  2. Department of Water Resources and Environmental Engineering, Helmand University, Helmand, Afghanistan

    Esmatullah Sangin

  3. Centre for Flood Management Studies, National Institute of Hydrology, Patna, 801 505, India

    Pravin R. Patil

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  1. Esmatullah Sangin
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All authors contributed to the preparation of the manuscript in the present form. Conceptualization, writing original draft, formal analysis, methodology, and interpreting results was done by S.K. Mishra. Material preparation, review and editing, and formal analyzing was performed by Esmatullah Sangin. Data curation, writing-review & editing and visualization of the manuscript was performed by P.R. Patil.

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Correspondence to Esmatullah Sangin.

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Sangin, E., Mishra, S.K. & Patil, P.R. Analogy Between SCS-CN and Muskingum Methods. Water Resour Manage 38, 153–171 (2024). https://doi.org/10.1007/s11269-023-03660-4

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