Journal of Geographical Sciences >
Two universal runoff yield models: SCS vs. LCM
^{*}Corresponding author: Liu Changming, Professor, specialized in hydrology and water resources. Email:liucm@igsnrr. ac.cn
Author: Li Jun (1968), PhD Candidate, specialized in hydrology and water resources. Email:lijun.12b@igsnrr.ac.cn
Received date: 20140505
Accepted date: 20140610
Online published: 20150315
Supported by
National Natural Science Foundation of China, No.41271048
The Key Program of National Natural Science Foundation of China, No.41330529
Copyright
Runoff calculation is one of the key components in the hydrological modeling. For a certain spatial scale, runoff is a very complex nonlinear process. Currently, the runoff yield model in different hydrological models is not unique. The Chinese LCM model and the American SCS model describe runoff at the macroscopic scale, taking into account the relationship between total actual retention and total rainfall and having a certain similarity. In this study, by comparing the two runoff yield models using theoretical analyses and numerical simulations, we have found that: (1) the SCS model is a simple linear representation of the LCM model, and the LCM model reflects more significantly the nonlinearity of catchment runoff. (2) There are strict mathematical relationships between parameters (R, r) of the LCM model and between parameters (S) of the SCS model, respectively. Parameters (R, r) of the LCM can be determined using the research results of the SCS model parameters. (3) LCM model parameters (R, r) can be easily obtained by field experiments, while SCS parameters (S) are difficult to measure. Therefore, parameters (R, r) of the LCM model also can provide the foundation for the SCS model. (4) The SCS model has a linear relationship between the reciprocal of total actual retention and the reciprocal of total rainfall during runoff period. The oneorder terms of a Taylor series expansion of the LCM model describe the same relationship, which is worth further study.
LI Jun , LIU Changming , WANG Zhonggen , LIANG Kang . Two universal runoff yield models: SCS vs. LCM[J]. Journal of Geographical Sciences, 2015 , 25(3) : 311 318 . DOI: 10.1007/s1144201511702
Figure 1 Solution of runoff equation (Cronshey, 1986) 
Table 1 Values of parameters R and r for LCM model 
Antecedent soil moisture  Classification of the losses  

II  III  IV  V  VI  
Wet  R  0.83  0.95  0.98  1.10  1.22 
r  0.56  0.63  0.66  0.76  0.87  
General  R  0.93  1.02  1.10  1.18  1.25 
r  0.63  0.69  0.76  0.83  0.90  
Dry  R  1.00  1.08  1.16  1.22  1.27 
r  0.68  0.75  0.81  0.87  0.92 
Note: Description of the terrain condition, i.e. II: clay, saline clay, thin layer of soil, and poor vegetation; III: sand clay and poor silt loam and poor vegetation, Gobi, vegetation, earth and rock hill regions with thin layer of soil; IV: silt loam and poor vegetation, earth and rock hill regions with thick layer of soil, the hill regions with thicket, grass land; V: silt and well vegetated forest; VI: sand, original forest with thick forest floor. 
Figure 2 Linear regression analysis of the LCM model (t=1 h; a = [30, 210] mm/h; 1/μ vs. 1/α) 
Figure 3 Coefficient of determination of the LCM and SCS models for different values of r (α= [30, 210] mm/h, step = 1; r = [0.05, 0.95], step= 0.001) 
Figure 4 Relationship of R (LCM model) to CN (SCS model) (α=[30, 210] mm/h, step=1; r=[0.05, 0.95], step= 0.001) 
Figure 5 Relationship of r (LCM model) to CN (SCS model) (α= [30, 210] mm/h, step=1; r=[0.05, 0.95], step= 0.001). 
Figure 6 Relationship of R to r (LCM model) (α= [30, 210] mm/h, step=1; r=[0.05, 0.95], step= 0.001) 
The authors have declared that no competing interests exist.
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