# An Improved SCS-CN Method Incorporating Slope, Soil Moisture, and Storm Duration Factors for Runoff Prediction

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}value and three introduced factors (slope gradient, soil moisture, and storm duration). The proposed method was tested for calibration and validation with a dataset from three runoff plots in a watershed of the Loess Plateau. The results showed the model efficiencies of the proposed method were improved to 80.58% and 80.44% during the calibration and validation period, respectively, which was better than the standard SCS-CN and the other two modified SCS-CN methods where only a single factor of soil moisture or slope gradient was considered, respectively. Using the parameters calibrated and validated by dataset of the initial three runoff plots, the proposed method was then applied to runoff estimation of the remaining three runoff plots in another watershed. The proposed method reduced the root-mean-square error between the observed and estimated runoff values from 5.53 to 2.01 mm. Furthermore, the parameters of soil moisture (b

_{1}and b

_{2}) is the most sensitive, followed by parameters in storm duration (c) and slope equations (a

_{1}and a

_{2}), and the least sensitive parameter is the initial abstraction ratio λ on the basis of the proposed method sensitivity analysis. Conclusions can be drawn from the above results that the proposed method incorporating the three factors in the SCS method may estimate runoff more accurately in the Loess Plateau of China.

## 1. Introduction

_{c}), which is a product of the minimum infiltration rate and rainfall duration; Shi et al. [25] introduced the static infiltration into the soil moisture accounting (SMA)-based SCS-CN method to improve runoff predictions on the Loess Plateau. However, all these methods have no contact with the CN value of the original SCS-CN method, which has limited the application of the models.

_{2}in the calculation of the runoff volume, but it has not been tested in the field. Based on the data of experimental plots with slopes varying from 14% to 140% on the Loess Plateau of China, Huang et al. [15] proposed an equation for considering the influence of slope on CN value. However, there is no study that couples these factors (storm duration, soil moisture, and slope) in the SCS-CN method for predicting runoff, which would be the focus of this study.

_{2}value, slope gradient, soil moisture, and storm duration in the conventional SCS-CN method; (2) to compare the performance of the standard SCS-CN method, those from Huang et al. [15] and Huang et al. [34], and the proposed method by observing three experimental plots in the Loess Plateau region; (3) to apply the proposed method to predict runoff from three runoff plots in the other watershed.

## 2. Methods

#### 2.1. The Original SCS-CN Method

_{a}and λ are the initial abstraction (mm) and coefficient of initial abstraction (dimensionless), respectively; F is the cumulative amount of infiltration (mm); and S is the maximum potential retention (mm), which can be calculated by

_{2}) of the average moisture condition (AMC 2), which depends on land cover, soil group, and hydrologic conditions using a table from the SCS handbook [2], and is then converted to AMC 1 or AMC 3 based on the five-day-prior precipitation.

#### 2.2. The Proposed Method

_{2}, and the function of slope, soil moisture, and storm duration:

^{−1}), θ is soil moisture (cm

^{3}cm

^{−3}), and t is storm duration (h). f(α), f(θ), and f(t) are functions of α, θ, and t, respectively.

_{2}value. They used the modified SCS-CN method to evaluate runoff prediction in runoff plots with an 11-year observation experiment and a slope range of 14–140% in Xifeng City of the Loess Plateau. It is adopted in this study:

_{0}value prior to each storm event can be expressed by the water storage in the upper 15 cm soil. It is also adopted and can be expressed as follows:

_{1}, a

_{2}, b

_{1}, b

_{2}, and c are the empirical coefficients.

#### 2.3. Performance of the Methods

^{th}observed and estimated runoff, respectively; $\overline{Q}$ is the average measured runoff of events; and N is the total events. Higher NSE and lower RMSE values indicate that the model has better agreement with the observations.

## 3. Study Area and Data

#### 3.1. Study Area

^{2}) is located in Suide County. The average annual temperature is 8 °C and the mean annual precipitation is 470 mm, mostly between June and September. The soil type of the XDG watershed is mainly silty loam. The characteristics of soil physical and particle size distribution are homogeneous in the top 30 cm soil [37].

^{2}) is located in Zizhou County. The mean temperature is also 8 °C and the average annual precipitation is 450 mm. The precipitation from July to August accounts for more than 70%, most of which are heavy and short-term rainstorms. The main soil in CBG watershed is Malan loess soil, in which the content of clay particles is less than 40%, leading to the large porosity of soil and the vulnerability to erosion [38].

#### 3.2. Data Collection

#### 3.3. Parameter Estimation

_{1}and a

_{2}) obtained from Huang et al. [15] were also used for Huang et al. [15] and the proposed method (Method 1). Moreover, the effect of initial abstraction and slope on the proposed method was tested with the optimized λ (Method 2) and both optimized λ and slope parameters (Method 3).

## 4. Results

#### 4.1. Model Calibration and Validation

#### 4.1.1. The Original SCS-CN Method

#### 4.1.2. The Huang et al. and Huang et al. Methods

#### 4.1.3. The Proposed Method (Methods 1–3)

^{2}increasing to 0.79 from 0.21 (the SCS-CN method), and the regression line of which is closer to the perfect line, where the regression line slope and intercept is 0.90 and 0.30, respectively (Table 3). Moreover, the prediction results of Method 1 are satisfactory because most of the values are closer to the perfect prediction line, and in good agreement with observed runoff even for large runoff events (Figure 5a). Method 1 yielded a larger NSE value of 75.84% and a smaller RMSE value of 3.26 mm in the calibration case, whereas the NSE value of Method 1 increases from −182.60% (the traditional SCS-CN method) to 77.45%, and the RMSE value decreased from 13.18 to 3.72 mm in the validation case (Table 3). Thus, we can conclude that Method 1 performed the best of the four methods for both the calibration and validation cases.

_{1}and a

_{2}) (Method 3) based on Method 2 to test the slope factor on the proposed method as compared with the fixed values obtained from Huang et al. [15].

_{1}= 213.99 and a

_{2}= 25.38), as compared with Method 2, with NSE values of 80.73% vs. 80.44% in calibration and 81.21% vs. 80.58% in validation. The results indicated that the proposed methods with optimized λ (Methods 2 and 3) could further improve the SCS-CN method for runoff prediction in this study area.

#### 4.2. Model Application

#### 4.3. Sensitivity Analyses

_{1}, where the value of NSE sharply decreases from 80.58% to 47.83% as the b

_{1}value changes in a small range of 130–80% of the calibrated value. However, the initial ratio λ appears to be the least sensitive. In general, the parameters of soil moisture (b

_{1}and b

_{2}) are the most sensitive, followed by parameters in storm duration (c) and slope equations (a

_{1}and a

_{2}), and the least sensitive parameter is the initial abstraction ratio λ.

## 5. Discussion

#### 5.1. The Effect of Rainfall Duration

#### 5.2. The Effect of Slope

_{2}of the standard SCS-CN method obtained from the handbook table [2] are based on 5% slope. Therefore, a slope equation (Equation (6)) was developed that incorporated the slope in the standard SCS-CN method for steep slope conditions.

#### 5.3. The Effect of Soil Moisture

_{2}occurring before a rainfall-runoff event was only 7%, rather than 50% [54], which indicated that the AMC value was underestimated and thereby resulted in runoff underprediction by the original SCS method. Huang et al. [34] indicated that there was no correlation between the CN value and the five-day AMC, and the tabulated CN values were less than the measured ones in most cases, which further confirmed the runoff underprediction. Therefore, the five-day AMC used in the original CN method is unreasonable.

_{1}and a

_{2}) are less sensitive, so Method 2 can be applied to similar sub-humid, semi-arid, and arid regions with the optimized parameters, but may need adjustment for humid regions because the soil moisture and rainfall may differ from the tested results in this study.

## 6. Conclusions

_{2}value and three introduced factors (slope gradient, soil moisture, and storm duration). Six models including the original SCS-CN method, Huang et al. [15], Huang et al. [34], and the proposed method with different optimized parameters (Methods 1–3) were used to test the reliability of the data from three runoff plots in the XDG watersheds of Loess Plateau. Subsequently, using the parameters calibrated and validated by dataset of the initial three runoff plots, the proposed method was then applied to runoff estimation of the remaining three runoff plots in CBG watershed. High NSE and low RMSE values during the calibration, validation, and application period indicated the proposed method can estimate runoff accurately for six plots in two watersheds and had greater reliability than the standard SCS-CN, Huang et al. [15], and Huang et al. [34] methods. Moreover, Method 2 with an initial abstraction ratio of λ = 0.001 rather than the standard value of 0.2 and slope parameters obtained from Huang et al. [15] with data from slopes ranging from 14% to 140% seems to be the most promising SCS method for runoff estimation in the experimental plots of the Loess Plateau. Furthermore, the parameters of soil moisture (b

_{1}and b

_{2}) are the most sensitive, followed by parameters in storm duration (c) and slope equations (a

_{1}and a

_{2}), and the least parameter is the initial abstraction ratio λ on the basis of the proposed method sensitivity analysis.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Data Availability Statement

## References

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**Figure 5.**Measured versus estimated runoff depths for (

**a**) Method 1, (

**b**) Method 2, and (

**c**) Method 3 for calibration and validation for three runoff plots of the XDG watersheds.

**Figure 6.**Measured versus estimated runoff depths for (

**a**) original SCS-CN method, (

**b**) Method 1, (

**c**) Method 2, and (

**d**) Method 3 for the three experimental plots located in the CBG watershed.

**Figure 8.**Measured versus estimated runoff depths for (

**a**) the original SCS-CN method and (

**b**) Method 2 of the three rainfall regimes.

Watershed | XDG | CBG | ||||
---|---|---|---|---|---|---|

Plot | 1 | 2 | 3 | 1 | 2 | 3 |

Land use | Grassland | Grassland | Cropland | Grassland | Cropland | Cropland |

Vegetation | Alfalfa | Sweet clover | Millet | Pasture | Millet | Potato |

Length (m) | 20 | 20 | 20 | 40 | 20 | 20 |

Width (m) | 5 | 5 | 5 | 10 | 10 | 10 |

Slope gradient (°) | 35 | 33 | 15 | 30 | 25 | 22 |

Soil moisture (%) | 18.54 ± 5.93 | 18.08 ± 5.92 | 19.68 ± 5.89 | 15.82 ± 4.50 | 16.80 ± 5.64 | 16.79 ± 4.30 |

Rainfall (mm) | 23.59 ± 14.43 | 23.90 ± 22.76 | 25.97 ± 22.08 | 22.31 ± 24.31 | 24.81 ± 28.24 | 23.93 ± 17.88 |

Runoff (mm) | 4.52 ± 8.54 ^{#} | 4.60 ± 7.97 | 4.09 ± 4.52 | 2.07 ± 2.12 | 2.02 ± 1.95 | 6.61 ± 8.16 |

Strom duration (h) | 4.53 ± 6.08 | 4.88 ± 6.53 | 5.84 ± 6.95 | 4.65 ± 6.74 | 5.82 ± 7.75 | 2.46 ± 2.59 |

Observation period | 1956–1959 | 1956–1959 | 1954–1959 | 1959–1961 | 1959–1962 | 1964–1965 |

^{#}: Mean ± standard deviation.

Model | Parameter | |||||
---|---|---|---|---|---|---|

λ | a_{1} | a_{2} | b_{1} | b_{2} | c | |

Original SCS-CN | 0.2 | - | - | - | - | - |

Huang et al. [15] | 0.2 | 323.57 | 15.63 | - | - | - |

Huang et al. [34] | 0.2 | - | - | 0.01 | 1.12 | - |

Method 1 | 0.2 | 323.57 | 15.63 | 0.05 | 0.61 | 0.020 |

Method 2 | 0.001 | 323.57 | 15.63 | 0.13 | 0.31 | 0.035 |

Method 3 | 0.001 | 213.99 | 25.38 | 0.15 | 0.24 | 0.035 |

Model | Linear Regression | NSE | RMSE | Performance Rating [40] | ||
---|---|---|---|---|---|---|

Slope | Interception | R^{2} | (%) | (mm) | ||

Calibration | ||||||

Original SCS-CN | 0.83 | 0.07 | 0.24 | −118.64 | 9.83 | Unsatisfactory |

Huang et al. [15] | 0.92 | 0.10 | 0.27 | −133.00 | 10.14 | Unsatisfactory |

Huang et al. [34] | 0.27 | 0.41 | 0.15 | −9.80 | 6.96 | Unsatisfactory |

Method 1 | 0.88 | −0.48 | 0.79 | 75.84 | 3.26 | Acceptable |

Method 2 | 0.80 | 0.95 | 0.80 | 80.58 | 2.94 | Good |

Method 3 | 0.82 | 0.72 | 0.81 | 80.73 | 2.91 | Good |

Validation | ||||||

Original SCS-CN | 0.77 | 1.33 | 0.18 | −182.60 | 13.18 | Unsatisfactory |

Huang et al. [15] | 0.87 | 1.58 | 0.19 | −229.67 | 14.23 | Unsatisfactory |

Huang et al. [34] | 0.21 | 1.14 | 0.07 | −32.27 | 9.02 | Unsatisfactory |

Method 1 | 0.92 | 0.04 | 0.80 | 77.45 | 3.72 | Acceptable |

Method 2 | 0.81 | 0.87 | 0.81 | 80.44 | 3.46 | Good |

Method 3 | 0.84 | 0.71 | 0.81 | 81.21 | 3.40 | Good |

Full data | ||||||

Original SCS-CN | 0.80 | 0.56 | 0.21 | −148.17 | 11.23 | Unsatisfactory |

Huang et al. [15] | 0.90 | 0.67 | 0.23 | −177.64 | 11.87 | Unsatisfactory |

Huang et al. [34] | 0.24 | 0.70 | 0.11 | −20.18 | 7.81 | Unsatisfactory |

Method 1 | 0.90 | −0.30 | 0.79 | 76.58 | 3.45 | Acceptable |

Method 2 | 0.80 | 0.92 | 0.81 | 80.50 | 3.15 | Good |

Method 3 | 0.83 | 0.71 | 0.81 | 80.95 | 3.11 | Good |

^{2}: coefficient of determination; NSE: model efficiency; RMSE: root-mean-square error; Performance rating: very good (NSE > 90%), good (80% < NSE < 90%), acceptable (65% < NSE < 80%), and unsatisfactory (NSE < 65%).

Rainfall Regime | Eigenvalue | Mean | Standard Deviation | Variation Coefficient | Frequency (%) |
---|---|---|---|---|---|

Regime 1 | P (mm) | 14.92 | 6.95 | 0.47 | 79.73 |

D (h) | 2.43 | 2.55 | 1.05 | ||

Regime 2 | P (mm) | 50.49 | 11.06 | 0.22 | 16.89 |

D (h) | 12.61 | 7.94 | 0.63 | ||

Regime 3 | P (mm) | 109.36 | 7.68 | 0.07 | 3.38 |

D (h) | 22.93 | 1.31 | 0.06 |

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**MDPI and ACS Style**

Shi, W.; Wang, N.
An Improved SCS-CN Method Incorporating Slope, Soil Moisture, and Storm Duration Factors for Runoff Prediction. *Water* **2020**, *12*, 1335.
https://doi.org/10.3390/w12051335

**AMA Style**

Shi W, Wang N.
An Improved SCS-CN Method Incorporating Slope, Soil Moisture, and Storm Duration Factors for Runoff Prediction. *Water*. 2020; 12(5):1335.
https://doi.org/10.3390/w12051335

**Chicago/Turabian Style**

Shi, Wenhai, and Ni Wang.
2020. "An Improved SCS-CN Method Incorporating Slope, Soil Moisture, and Storm Duration Factors for Runoff Prediction" *Water* 12, no. 5: 1335.
https://doi.org/10.3390/w12051335