# Spatio-Temporal Estimation of Rice Height Using Time Series Sentinel-1 Images

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Datasets

## 3. Methodology

#### 3.1. Simplified Water Cloud Model

^{o}is the total backscattering coefficient; $\sigma $${}_{veg}$

^{o}and $\sigma $${}_{soil}$

^{o}are the backscatter coefficient of the vegetation cover and soil surface, respectively; $\theta $ is the angle of incidence; $\tau $${}^{2}$ is the two-way attenuation. In our study, A, B and $\sigma $${}_{soil}$

^{o}are regarded as constants. V${}_{1}$ and V${}_{2}$, as vegetation descriptors, describe the effect of canopy water content and its geometry on the backscatter [43,44]. Consequently, canopy height, as an important vegetation variable, was represented by both V${}_{1}$ and V${}_{2}$ in our study, and the Water Cloud Model was simplified as much as possible.

^{o}were determined by the minimization between the simulated and observed backscattering coefficient of rice [45]. (2) The look-up table (LUT), which was generated by SWCM with optimized parameters, contained rice height and the corresponding simulated backscattering coefficients. It was of great significance to rice height retrieval. (3) The nearest neighbor algorithm was used for rice height estimation based on LUT. Height estimation was obtained by finding the nearest $\sigma $${}^{o}$ in the LUT. Accuracy estimation was performed for test samples with R${}^{2}$ and RMSE.

#### 3.2. Particle Filter

## 4. Results

#### 4.1. Parameter Optimization

#### 4.2. Comparison of Rice Above-Ground Height Estimation by Two Methods

#### 4.3. The Spatio-Temporal Distribution of Above-Ground Height Estimation

## 5. Discussion

#### 5.1. Polarization Analysis

#### 5.2. Features for SWCM and PF

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The location of Guangdong Province in China; (

**b**) Location of the study area in Taishan County, Guangdong Province.

**Figure 2.**Acquisition dates of ground campaigns and Sentinel-1A images. Crosses denote a lack of images, and black circles denote acquired data. The backscattering coefficients of the missing image were the mean value of two adjacent images.

**Figure 4.**(

**a**) Relation between the age (days after transplanting) and the reference above-ground height (black circle); the model was obtained from the fitting of the Sigmoidal Richards model (red line). (

**b**) Relation between the reference above-ground height and VH backscatter (black circle); the model was obtained from the fitting of a polynomial curve (red line).

**Figure 5.**Flow diagram of the methodology for rice above-ground height estimation. Rice was harvested when the growing duration from transplanting to harvest was larger than 100 days.

**Figure 6.**RMSE and R${}^{2}$ of estimated rice above-ground height (

**a**) for SWCM with optimized parameters and (

**b**) for PF with initial height. The red line is a fitted line.

**Figure 7.**Estimation of rice above-ground height for field 9 by two methods. (

**A**) represents DoY and (

**B**) represents the ground truth of rice above-ground height. (

**C**,

**D**) are the results calculated using the SWCM and PF, respectively.

**Figure 9.**Relationships between the rice above-ground height and (

**a**) VV backscatter, (

**b**) backscattering coefficients for VH, (

**c**) the $\sigma $${}_{vh}$${}^{o}$/$\sigma $${}_{vv}$${}^{0}$ ratio and (

**d**) RVI.

Parameters | Sentinel-1A | Parameters | Sentinel-1A |
---|---|---|---|

Product type | GRD | Center frequency | 5.4 GHz |

Mode | IW | Look direction | Right |

Polarization | VV, VH | Pass direction | Ascending |

Incidence angle | 30.8°–46.2° | Range/Azimuth looks | 5/1 |

Band | C | Resolution | 10 m |

Model | Input Parameters | Output Parameters |
---|---|---|

SWCM | $\sigma $${}^{o}$, the observed height of rice | height estimation |

PF | $\sigma $${}^{o}$, the observed height of rice, days after transplanting | height estimation |

Polarization | A | B | ${\mathit{\sigma}}_{\mathit{soil}}$${}^{\mathit{o}}$ | RMSE | R${}^{2}$ |
---|---|---|---|---|---|

VH | 0.001 | −0.08 | 0.014 | 0.789488 | 0.824267 |

VV | 0.015 | −0.12 | 0.065 | 1.366691 | 0.229191 |

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**MDPI and ACS Style**

Yang, H.; Li, H.; Wang, W.; Li, N.; Zhao, J.; Pan, B.
Spatio-Temporal Estimation of Rice Height Using Time Series Sentinel-1 Images. *Remote Sens.* **2022**, *14*, 546.
https://doi.org/10.3390/rs14030546

**AMA Style**

Yang H, Li H, Wang W, Li N, Zhao J, Pan B.
Spatio-Temporal Estimation of Rice Height Using Time Series Sentinel-1 Images. *Remote Sensing*. 2022; 14(3):546.
https://doi.org/10.3390/rs14030546

**Chicago/Turabian Style**

Yang, Huijin, Heping Li, Wei Wang, Ning Li, Jianhui Zhao, and Bin Pan.
2022. "Spatio-Temporal Estimation of Rice Height Using Time Series Sentinel-1 Images" *Remote Sensing* 14, no. 3: 546.
https://doi.org/10.3390/rs14030546