# Using FengYun-3C VSM Data and Multivariate Models to Estimate Land Surface Soil Moisture

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## Abstract

**:**

^{3}/cm

^{3}, ubRMSE = 0.130 cm

^{3}/cm

^{3}, and MAE = 0.120 cm

^{3}/cm

^{3}) than in the other months was found due to the impacts of vegetation and climate variations. To show a detailed relationship between SM and multiple factors, including vegetation coverage, location, and elevation, quantile regression (QR) models were used to calculate the correlations at different quantiles. Except for the elevation at the 0.9 quantile, the QR models of the measured SM with the FY-3C VSM, MODIS NDVI, latitude, and longitude at each quantile all passed the significance test at the 0.005 level. Thus, the MODIS NDVI, latitude, and longitude were selected for error correction during the surface SM retrieval process using FY-3C VSM. Multivariate linear regression (MLR) and multivariate back-propagation neural network (MBPNN) models with different numbers of input variables were built to improve the SM monitoring results. The MBPNN model with three inputs (MBPNN-3) achieved the highest R (0.871) and lowest RMSE (0.034 cm

^{3}/cm

^{3}), MAE (0.026 cm

^{3}/cm

^{3}), and mean relative error (MRE) (20.7%) values, which were better than those of the MLR models with one, two, or three independent variables (MLR-1, -2, -3) and those of the MBPNN models with one or two inputs (MBPNN-1, -2). Then, the MBPNN-3 model was applied to generate the regional SM in the United States from January 2019 to October 2019. The estimated SM images were more consistent with the measured SM than the FY-3C VSM. This work indicated that combining FY-3C VSM data with the MBPNN-3 model could provide precise and reliable SM monitoring results.

## 1. Introduction

## 2. Data and Methods

#### 2.1. Multisource Data

#### 2.1.1. Data from the ISMN

^{3}/cm

^{3}and 0.096 cm

^{3}/cm

^{3}, respectively, which indicated high accuracy between the ground-based and interpolated SM in the study area. According to Figure 2, the SM content in the midwestern part was significantly lower than that in the eastern and northwestern parts of this region, which is basically consistent with the patterns of rainfall variations and climate types.

#### 2.1.2. FY-3C VSM

_{p}model, which was built using advanced integral equation (AIE) model simulations of microwave emissions [14]. Compared with the single channel SM retrieval algorithm, both the vertical and horizontal polarizations of the X-band (10.65 GHz) were applied in the Q

_{p}model to decrease the effects of roughness and vegetation coverage [23]. Also, the pixels covered with snow, frozen soil, and coastal waters were removed from the FY-3C VSM retrievals. These products are classified into ascending (A) and descending (D) products at daily, 10-day, and monthly time intervals, and have been widely used to detect the global land surface soil volumetric water content (cm

^{3}/cm

^{3}) with a spatial resolution of 25 km. In this study, the monthly FY-3C VSM products (FY3C_MWRIX_GBAL_L3_VSM.HDF) data from January to October 2019 were downloaded from the website of the NSMC (satellite.nsmc.org.cn/) and reprojected from the equal-area scalable earth (EASE) grid 2.0 to the WGS-84 grid.

#### 2.1.3. MODIS NDVI

#### 2.2. Multivariate Models

#### 2.2.1. Quantile Regression Model

_{τ}(z) can be represented by

#### 2.2.2. Back-Propagation Neural Network Model

_{jk}and θ

_{k}(j = 1, 2, …, n; k = 1, 2, …, m), and the weights and thresholds from the hidden to output layer are w

_{k}(k = 1, 2, …, m) and θ, respectively. Then, the kth unit of the hidden layer (y

_{k}) and the output of the output layer (b) can be given as Equations (8) and (9), respectively.

#### 2.2.3. Linear Regression Model

_{0}+ β

_{1 × 1}+ β

_{2}x

_{2}+ … + β

_{n}x

_{n}+ ε

_{1}, x

_{2}, …, x

_{n}are independent variables, Y is the dependent variable, β

_{0}is a constant, β

_{i}(i = 1, 2, …, n) are coefficients of x

_{i}(i = 1, 2, …, n), and ε is the residual error.

#### 2.3. Statistical Indicators

_{i}represents the FY-3C VSM retrievals (cm

^{3}/cm

^{3}), SM

_{i}represents the SM measurements (cm

^{3}/cm

^{3}), $\overline{VSM\text{}}$ represents the average of FY-3C VSM retrievals (cm

^{3}/cm

^{3}) across all pixels in the study area, $\overline{SM}$ indicates the average of SM measurements (cm

^{3}/cm

^{3}), and N represents the total number of valid samples and varies for each month.

## 3. Results and Analysis

#### 3.1. Comparison between FY-3C VSM and Measured SM

^{3}/cm

^{3}and 0.45 cm

^{3}/cm

^{3}. In February 2019 (Figure 5b), the FY-3C VSM sample values from 10 to 50 were basically lower than the SM measurements, and the sample values from 70 to 130 were mainly higher than the measured SM values. It was obvious that the FY-3C satellite retrievals in July 2019 (Figure 5c) overestimated the SM in almost of the samples, and the estimation error was significantly greater than that in the other months, which was possibly due to the potential impacts caused by factors such as deep and widespread vegetation coverage in summer. The curves for October 2019 (Figure 5d) indicated a similar situation to that in July, although the proportion and degree of overestimation were slightly decreased compared with those in July. To further evaluate the vegetation impact on the FY-3C VSM retrieval accuracy in July, the SM deviations between the FY-3C VSM and the measured SM were calculated and compared to the MODIS NDVI by plotting the variation curves and evaluating the correlation between the two sources. The plot could be found in the Appendix A, where the curves of the MODIS NDVI (red line) and the SM deviations (green line) showed a similar variation pattern and the R value was 0.666, which indicated a strong correlation between the NDVI and SM deviation.

^{3}/cm

^{3}, ubRMSE = 0.113 cm

^{3}/cm

^{3}, and MAE = 0.092 cm

^{3}/cm

^{3}) and April (RMSE = 0.114 cm

^{3}/cm

^{3}, ubRMSE = 0.112 cm

^{3}/cm

^{3}, and MAE = 0.094 cm

^{3}/cm

^{3}) were significantly higher than those in July (RMSE = 0.164 cm

^{3}/cm

^{3}, ubRMSE = 0.130 cm

^{3}/cm

^{3}, and MAE = 0.120 cm

^{3}/cm

^{3}) and October (RMSE = 0.147 cm

^{3}/cm

^{3}, ubRMSE = 0.121 cm

^{3}/cm

^{3}, and MAE = 0.113 cm

^{3}/cm

^{3}). Among these months, despite the high correlation between the estimated and actual SM, the SM inversion in July yielded the worst accuracy due to overestimation.

#### 3.2. Relationship between Multiple Variables and SM Measurements

#### 3.3. SM Estimation Using Multivariate Models

#### 3.3.1. Multivariate Models for SM Estimation

^{3}/cm

^{3}, and MAE = 0.026 cm

^{3}/cm

^{3}, MRE = 20.7%) was the best among all of the models, followed by MLR-3 (R = 0.694, RMSE = 0.047 cm

^{3}/cm

^{3}, MAE = 0.035 cm

^{3}/cm

^{3}, and MRE = 27.3%).

^{3}/cm

^{3}) and relative (14.0%) errors than MLR-3. Additionally, the distribution ranges of the MLR-3 errors between the 25% (Q1) and 75% (Q3) quantiles, which were [−0.02, 0.02] for absolute errors and [11.0%, 28.0%] for relative errors, were both wider and overall larger than those for the MBPNN-3, whose absolute and relative errors between Q1 and Q3 were distributed between [−0.01, 0.02] and [7.5%, 25.0%], respectively. The results indicate that the multivariate nonlinear model is a suitable and promising approach for achieving SM estimation results with high accuracy.

#### 3.3.2. Regional SM Monitoring Results

^{3}/cm

^{3}were found in the southwestern part, and the proportion of dry areas gradually increased from January to July and slightly decreased from August to October. The wet areas with SM values greater than 0.30 cm

^{3}/cm

^{3}were mainly located in the mideastern region, and the proportions of wet area during January to July were slightly greater than those from July to October.

#### 3.3.3. Accuracy Assessment between the Estimated and Actual SM

^{3}/cm

^{3}, 0.054 cm

^{3}/cm

^{3}, and 46.7%, respectively, indicating that the SM estimation accuracy in the U.S. was generally high during all months. The SM estimation accuracy varied in different months. The highest SM estimation accuracy was found in February (R = 0.943, RMSE = 0.030 cm

^{3}/cm

^{3}, MAE = 0.022 cm

^{3}/cm

^{3}, and MRE = 10.4%), followed by January (R = 0.913, RMSE = 0.040 cm

^{3}/cm

^{3}, MAE = 0.031 cm

^{3}/cm

^{3}, and MRE = 15.4%). The worst accuracy was found in September (R = 0.862, RMSE = 0.063 cm

^{3}/cm

^{3}, MAE = 0.054 cm

^{3}/cm

^{3}, and MRE = 46.7%), followed by October and August. In conclusion, the established MBPNN-3 model yielded accurate and acceptable SM estimations in all seasons and can be employed to improve the monitoring accuracy of regional surface soil moisture.

## 4. Discussion

## 5. Conclusions

^{3}/cm

^{3}, 0.054 cm

^{3}/cm

^{3}, and 46.7%, respectively, which demonstrated the feasibility of using the MBPNN-3 model to improve the SM monitoring accuracy at the regional scale.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 5.**Comparison between the FY-3C VSM and measured soil moisture (SM) in different seasons. (

**a**)–(

**d**) show the comparison curves for January, April, July, and October 2019, respectively.

**Figure 7.**(

**a**) Absolute errors and (

**b**) relative errors between the measured and estimated SM using MLR-3 and MBPNN-3 models.

**Figure 8.**FY-3C VSM retrievals, estimated SM using MBPNN-3 and measured SM in the U.S. from January to October 2019. (

**a**)–(

**j**) are the SM monitoring results in January, February, March, April, May, June, July, August, September, and October 2019, respectively.

Frequency (GHz) | 10.65 | 18.7 | 23.8 | 36.5 | 89 |
---|---|---|---|---|---|

Polarization | V/H | V/H | V/H | V/H | V/H |

Band width (MHz) | 180 | 200 | 400 | 900 | 4600 |

Sensitivity (K) | 0.5 | 0.5 | 0.8 | 0.5 | 1.0 |

Calibration accuracy (K) | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |

IFOV (km × km) | 51 × 85 | 30 × 50 | 27 × 45 | 18 × 30 | 9 × 15 |

Pixel size (km × km) | 40 × 11.2 | 40 × 11.2 | 20 × 11.2 | 20 × 11.2 | 10 × 11.2 |

Dynamic range (K) | 3~340 | ||||

Sampling number | 240 | ||||

Beam efficiency | ≥90% | ||||

Beam error (°) | <0.1 | ||||

Scanning mode | Conical scanning | ||||

Orbit width (km) | 1400 | ||||

Viewing angle (°) | 45 ± 0.1 | ||||

Scanning period (s) | 1.7 ± 0.1 | ||||

Scanning period error (ms) | 0.34 ms (between scanning lines)/1 ms (in 30 min) |

**Table 2.**Independent/input variables of the multivariate linear regression (MLR) and multivariate back-propagation neural network (MBPNN) models.

Model | Independent/Input Variable |
---|---|

MLR-1, MBPNN-1 | FY-3C VSM |

MLR-2, MBPNN-2 | FY-3C VSM, MODIS NDVI |

MLR-3, MBPNN-3 | FY-3C VSM, MODIS NDVI, location |

**Table 3.**Root mean square error (RMSE), unbiased RMSE (ubRMSE), mean average error (MAE), and correlation coefficient (R) values between the measured SM and FY-3C VSM retrievals in different months.

Error Metrics | R | RMSE (cm^{3}/cm^{3}) | ubRMSE (cm^{3}/cm^{3}) | MAE (cm^{3}/cm^{3}) | |
---|---|---|---|---|---|

Month | |||||

January | 0.467 | 0.116 | 0.113 | 0.092 | |

April | 0.500 | 0.114 | 0.112 | 0.094 | |

July | 0.621 | 0.164 | 0.130 | 0.120 | |

October | 0.558 | 0.147 | 0.121 | 0.113 |

τ | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Variable | β(τ) | P | β(τ) | P | β(τ) | P | β(τ) | P | β(τ) | P | |

Intercept | 0.207 | <0.001 | 0.311 | <0.001 | 0.336 | <0.001 | 0.339 | <0.001 | 0.361 | <0.001 | |

FY-3C VSM | 0.024 | <0.001 | 0.070 | <0.001 | 0.094 | <0.001 | 0.125 | <0.001 | 0.201 | <0.001 | |

NDVI (×10 ^{−1}) | −0.136 | =0.005 | 0.116 | <0.001 | 0.304 | <0.001 | 0.523 | <0.001 | 0.470 | <0.001 | |

Latitude (×10 ^{−2}) | 0.568 | <0.001 | 0.318 | <0.001 | 0.235 | <0.001 | 0.077 | <0.001 | −0.207 | <0.001 | |

Longitude (×10 ^{−2}) | 0.323 | <0.001 | 0.321 | <0.001 | 0.310 | <0.001 | 0.248 | <0.001 | 0.135 | <0.001 | |

Elevation (×10 ^{−5}) | 0.891 | <0.001 | 0.667 | <0.001 | 0.591 | <0.001 | 0.399 | =0.001 | −0.001 | =0.992 |

**Table 5.**Correlation coefficient and error metrics between the estimated and actual SM values using the MLR and MBPNN models.

Error Metrics | R | RMSE (cm^{3}/cm^{3}) | MAE (cm^{3}/cm^{3}) | MRE (%) | |
---|---|---|---|---|---|

Model | |||||

MLR-1 | 0.640 | 0.050 | 0.039 | 32.0 | |

MBPNN-1 | 0.690 | 0.056 | 0.044 | 38.0 | |

MLR-2 | 0.661 | 0.049 | 0.038 | 30.4 | |

MBPNN-2 | 0.708 | 0.054 | 0.041 | 35.2 | |

MLR-3 | 0.694 | 0.047 | 0.035 | 27.3 | |

MBPNN-3 | 0.871 | 0.034 | 0.026 | 20.7 |

**Table 6.**Correlation coefficient and error metrics between the estimated and actual SM values from January to October 2019 using the MBPNN-3 model.

Error Metrics | R | RMSE (cm ^{3}/cm^{3}) | MAE (cm^{3}/cm^{3}) | MRE (%) | Number of Samples | |
---|---|---|---|---|---|---|

Month | ||||||

January | 0.913 | 0.040 | 0.031 | 15.4 | 4464 | |

February | 0.943 | 0.030 | 0.022 | 10.4 | 5501 | |

March | 0.787 | 0.056 | 0.043 | 21.7 | 6690 | |

April | 0.893 | 0.032 | 0.024 | 11.0 | 8870 | |

May | 0.824 | 0.047 | 0.039 | 18.1 | 8391 | |

June | 0.863 | 0.035 | 0.027 | 15.1 | 7701 | |

July | 0.871 | 0.034 | 0.026 | 20.7 | 7446 | |

August | 0.870 | 0.052 | 0.042 | 36.3 | 7366 | |

September | 0.862 | 0.063 | 0.054 | 46.7 | 8001 | |

October | 0.844 | 0.053 | 0.043 | 44.3 | 8852 |

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## Share and Cite

**MDPI and ACS Style**

Wang, L.; Fang, S.; Pei, Z.; Zhu, Y.; Khoi, D.N.; Han, W.
Using FengYun-3C VSM Data and Multivariate Models to Estimate Land Surface Soil Moisture. *Remote Sens.* **2020**, *12*, 1038.
https://doi.org/10.3390/rs12061038

**AMA Style**

Wang L, Fang S, Pei Z, Zhu Y, Khoi DN, Han W.
Using FengYun-3C VSM Data and Multivariate Models to Estimate Land Surface Soil Moisture. *Remote Sensing*. 2020; 12(6):1038.
https://doi.org/10.3390/rs12061038

**Chicago/Turabian Style**

Wang, Lei, Shibo Fang, Zhifang Pei, Yongchao Zhu, Dao Nguyen Khoi, and Wei Han.
2020. "Using FengYun-3C VSM Data and Multivariate Models to Estimate Land Surface Soil Moisture" *Remote Sensing* 12, no. 6: 1038.
https://doi.org/10.3390/rs12061038