# Coupling Modified Linear Spectral Mixture Analysis and Soil Conservation Service Curve Number (SCS-CN) Models to Simulate Surface Runoff: Application to the Main Urban Area of Guangzhou, China

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

#### 2.2. Remote Sensing Image

#### 2.3. Soil Data

## 3. Methods

#### 3.1. Linear Spectral Mixture Analysis

#### 3.1.1. Modified Linear Spectral Mixture Analysis

_{i}is the spectral reflectance of band i of a mixed pixel, f

_{k}is a proportion of endmember k within the mixed pixel, R

_{ik}is the known spectral reflectance of endmember k within a mixed pixel of band i, and ${\mathsf{\epsilon}}_{i}$ is the error of band i. The water body of the Landsat 8 OLI image is first masked by the Modified Normalized Difference Water Index (MNDWI) [50]. Four endmembers are then selected, including soil, vegetation, high-albedo, and low-albedo endmembers. The proportion f

_{k}of four endmembers is solved by the least square method with the following constraint:

#### 3.1.2. Accuracy Assessment

^{2}). The digitized proportions are considered as “ground” reference for validating results of the conventional and modified LSMA methods. Two assessment metrics are used in this study, including root mean square error (RMSE), and bias error (Bias):

#### 3.2. Surface Runoff Simulation

_{c}is the composite CN value; f

_{imp}, f

_{veg}, and f

_{soil}are the fraction of impervious surface, vegetation, and soil extracted by the modified LSMA, respectively; CN

_{imp}, CN

_{veg}, and CN

_{soil}are the initial CN values of impervious surface, vegetation, and soil, respectively.

_{5}) and the dormant/growing season, representing dry, normal, and wet conditions (AMC I, AMC II, and AMC III). The composite CN value in Equation (7) is calculated under the AMC II condition. The CN values for the AMC I and AMC III conditions are adjusted using the following conversion formulas, respectively [5,54]:

_{II}is the composite curve number calculated with Equation (3), and CN

_{I}and CN

_{III}are the adjusted curve numbers for the AMC I and AMC III condition, respectively.

_{IIα}is the adjusted CN for AMC II; CN

_{II}and CN

_{III}are the composite CN values for AMC II and AMC III condition, respectively; and α (%) is the basin average slope.

## 4. Results and Discussion

#### 4.1. Extraction Results of the Modified LSMA

^{2}). This indicates that the modified LSMA can enhance the accuracy of soil mapping. On the whole, the modified LSMA does make a significant contribution to the improvement of impervious surface, vegetation, and soil mapping accuracy.

#### 4.2. Calculation of the Composite CN

#### 4.3. Runoff Calculation

_{5}) is typically used to identify the soil moisture condition that shifts the soil from one AMC condition to another. The amount of antecedent precipitation varies from the dormant season to the growing season. Here, the antecedent soil moisture condition was categorized according to P

_{5}in the growing season as follows: AMC I (if P

_{5}< 35.56 mm), AMC II (if 35.56 mm ≤ P

_{5}≤ 53.34 mm), and AMC III (if P

_{5}> 53.34 mm) [53].

_{5}is found to be 105.5 mm, while the lowest P

_{5}is only 0.51 mm. Most of the study area has antecedent precipitation greater than 20 mm. Three centers of heavy precipitation of greater than 81 mm are formed and distributed in Liwan, southwest Huangpu, and west Baiyun. Figure 14b shows the adjusted CN map for different AMC conditions. By comparing with Figure 13b, we find that the CN values, adjusted based on the antecedent soil moisture condition are significantly increased under the AMC III condition. The CN values in centers of heavy precipitation are greater than 90, at times approaching 100. However, the CN values decrease under the AMC I condition. This indicates that soil moisture is an important parameter for setting CN. The accurate estimate of the soil moisture is crucial to improve the accuracy of CN estimation.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Flow chart for the surface runoff estimation in this study. LSMA: Linear Spectral Mixture Analysis; NDVI: Normalized Difference Vegetation Index; NDBI: Normalized Difference Built-up Index; CN: Curve Number; OLI: Operational Land Imager

**Figure 5.**(

**a**) Normalized Difference Built-up Index (NDBI); and (

**b**) Normalized Difference Vegetation Index (NDVI) maps.

**Figure 6.**Extracted results of the conventional (

**a**–

**c**); and modified LSMA (

**d**–

**f**) methods: (

**a**,

**d**) impervious surface; (

**b**,

**e**) vegetation; and (

**c**,

**f**) soil fractions.

**Figure 7.**Spectral curves of endmember selection of the conventional (

**a**); and modified (

**b**) LSMA methods.

**Figure 8.**Scatter plots of accuracy assessment results: (

**a**) impervious surface; (

**b**) vegetation; and (

**c**) soil. RMSE: root-mean-square error.

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## Share and Cite

**MDPI and ACS Style**

Xu, J.; Zhao, Y.; Zhong, K.; Ruan, H.; Liu, X.
Coupling Modified Linear Spectral Mixture Analysis and Soil Conservation Service Curve Number (SCS-CN) Models to Simulate Surface Runoff: Application to the Main Urban Area of Guangzhou, China. *Water* **2016**, *8*, 550.
https://doi.org/10.3390/w8120550

**AMA Style**

Xu J, Zhao Y, Zhong K, Ruan H, Liu X.
Coupling Modified Linear Spectral Mixture Analysis and Soil Conservation Service Curve Number (SCS-CN) Models to Simulate Surface Runoff: Application to the Main Urban Area of Guangzhou, China. *Water*. 2016; 8(12):550.
https://doi.org/10.3390/w8120550

**Chicago/Turabian Style**

Xu, Jianhui, Yi Zhao, Kaiwen Zhong, Huihua Ruan, and Xulong Liu.
2016. "Coupling Modified Linear Spectral Mixture Analysis and Soil Conservation Service Curve Number (SCS-CN) Models to Simulate Surface Runoff: Application to the Main Urban Area of Guangzhou, China" *Water* 8, no. 12: 550.
https://doi.org/10.3390/w8120550