# Optimization of the Local Split-Window Algorithm for FY-4A Land Surface Temperature Retrieval

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. Ground Sites Introduction

#### 2.1.2. Ground In-Situ Data

^{-1}and a calibrated aperture lens (field of view angle was 4.8°) were selected. The temperature of warm and cold blackbody was set to 40 °C and 10 °C, respectively. Each scan was set to 8 times of spectral superposition and was always ensured that the Dewar bottle was filled with liquid nitrogen. The measurements were carried out in the following order: Cold blackbody–warm blackbody–gold plate-sample. Finally, the sample emissivity curve was obtained by automatically setting Planck function (setting 7–7.5µm emissivity to 1.0), as shown in Figure 2. According to the spectral response function of AGRI (as shown in Figure 3), the emissivity values corresponding to AGRI channels 12th and 13th are calculated as follows:

#### 2.1.3. Remote Sensing Data

**March 12**, March 13, March 14,

**April 16**,

**April 17**, April 19,

**May 2**, May 6,

**May 12**, May 13,

**May 14**, May 15, May 22,

**May 31**,

**June 12**,

**July 13**, July 16,

**July 17**, 2018 and

**May 20**,

**May 24**,

**June 3**, 2019), only 1 for Kangle Station (June 12, 2019), and 4 for Qifeng Station (June 7, June 12, June 16, June 17, 2019), only 1 for the Kangle station (12 June 2019), and 4 for the Qifeng station (7 Jun, 12 June, 16 June, 17 June, 2019). The dates in bold represent dates used for algorithm optimization among the 328 LST research samples and 33 surface emissivity samples, and the remainder are the dates of test samples. The bands’ characteristics of AGRI onboard FY-4A are all shown in Table 1.

#### 2.2. Methods

#### 2.2.1. Local Split-Window Algorithms

_{veg}and T

_{soil}are vegetation and bare soil temperatures, respectively; LST_K is the LST estimated by the Kerr algorithm; the unit is K; TB

_{12}and TB

_{13}are the brightness temperatures of the 12th and 13th thermal infrared channels of AGRI, respectively; fv is the vegetation coverage; NDVIs and NDVIv are the normalized vegetation index (NDVI) values of the soil and vegetation conditions (NDVIs = 0.2 and NDVIv =0.5); and b

_{1}–b

_{6}are coefficients used in the Kerr and optimized Kerr algorithms as shown in Table 2.

_{1}–a

_{7}are constants. The values of the B&L algorithm and the constants optimized by the particle swarm optimization (PSO) algorithm on the basis of different emissivity models are shown in Table 3.

#### 2.2.2. Measured Emissivity Models

#### 2.2.3. PSO Algorithm

_{1}and c

_{2}correspond to acceleration constants; r

_{1}and r

_{2}are random numbers between 0 and 1; and L

_{i}and G

_{n}refer to the local and global optimal locations searched by i particles, respectively.

_{x}refers to the value after parameter mapping; R

_{o}denotes the actual parameter value; and R

_{max}and R

_{min}represent the actual maximum and minimum parameter values, respectively. In this paper, the maximum and minimum values of parameters were set to ±100 times of the parameter values used in the B&L algorithm.

#### 2.2.4. Accuracy Evaluation of Estimation Results

_{i}refers to the estimate sequence; $\overline{\mathrm{E}}$ represents the mean value of the estimate sequence; O

_{i}denotes the measured sequence; $\overline{\mathrm{O}}$ corresponds to the mean value of the measured sequence; and N denotes the number of samples participating in the calculation.

## 3. Results

#### 3.1. Diurnal Variation of Emissivity

#### 3.2. LST Retrieved by Local Split-Window Algorithms

#### 3.3. Kerr Algorithm Optimization

#### 3.4. B&L Algorithm Optimization

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Overview of observation stations and emissivity observation instrument 102F, where (

**a**) is the Dingxi station, (

**b**) is the emissivity observation instrument 102f, (

**c**) is the Kangle station, and (

**d**) is the Qifeng station.

**Figure 4.**Correlation analysis between measured channel emissivity and reflectance, where (

**a**) is the correlation analysis between e12 and ref2, (

**b**) is the correlation analysis between e12 and ref3, (

**c**) is the correlation analysis between e13 and ref2, and (

**d**) is the correlation analysis between e13 and ref3.

**Figure 5.**Correlation analysis between average channel emissivity and channel reflectance and its combined parameters, where (

**a**) is the correlation analysis between e and ref2, (

**b**) is the correlation analysis between e and ref3, (

**c**) is the correlation analysis between de and ref2, (

**d**) is the correlation analysis between de and ref3, (

**e**) is the correlation analysis between e and “ref3–ref2”, and (

**f**) is the correlation analysis between de and normalized vegetation index (NDVI).

**Figure 6.**The diurnal variations of measured emissivity, where (

**a**) is the band emissivity corresponding to the 12th and 13th channels of FY-4A (referred to as e12 and e13), and (

**b**) is the variations of mean and differences of emissivity (referred to as e and de) of the 12th and 13th channels of FY-4A.

**Figure 7.**The comparison of LST retrieved by different split-window algorithms and measured values, (

**a**) is the time series, (

**b**) is the LST retrieved by B&L algorithm, (

**c**) is the LST retrieved by Kerr algorithm.

**Figure 8.**The comparison of LST retrieved by the optimized Kerr algorithm and measured values; (

**a**) is the time series, (

**b**) is the scatters.

**Figure 9.**Comparison of LST retrieved by different emissivity models and measured values; (

**a**) is the time series, (

**b**) is the LST results based on the DX1 emissivity model, and (

**c**) is the LST results based on the DX2 emissivity model.

**Figure 10.**The comparison of LST retrieved by the optimized split-window algorithm and measured values; (

**a**) is the time series, (

**b**) is the LST results based on the SB emissivity model, (

**c**) is the LST results based on the DX1 emissivity model, and (

**d**) is the LST results based on the DX2 emissivity model.

**Figure 11.**Distribution of the correlation coefficient and RMSE between the estimated LST and the measured values. The colors represent the correlation coefficients, and the isoline and numbers represent the RMSE values; (

**a**) is the estimated LST by the Kerr algorithm and (

**b**) is the LST estimated by the B&L algorithm.

Channel | Band (µm) | Spatial Resolution (km) | Sensitivity | Main Application |
---|---|---|---|---|

Visible Near Infrared | 0.45–0.49 | 1 | Signal to Noise Ratio(S/N) ≥ 90 (ρ = 100%) | Aerosol |

0.55–0.75 | 0.5–1 | S/N ≥ 200 (ρ = 100%) S/N ≥ 5 (ρ = 1%) @ 0.5 Km | Fog, Cloud | |

0.75–0.90 | 1 | Vegetation | ||

Short- Wave Infrared | 1.36–1.39 | 2 | S/N ≥ 200 (ρ = 100%) S/N ≥ 200 (ρ = 100%) | Cirrus |

1.58–1.64 | 2 | Cloud, Snow | ||

2.1–2.35 | 2–4 | Cirrus, Aerosol | ||

Mid-wave Infrared | 3.5–4.0(High) | 2 | Noise Equivalent Temperature Difference(NEΔT) ≤ 0.7 K(300 K) | Fire |

3.5–4.0(Low) | 4 | NEΔT ≤ 0.2 K(300 K) | Land surface | |

Water Vapor | 5.8–6.7 | 4 | NEΔT ≤ 0.3 K(260 K) | Water Vapor (WV) |

6.9–7.3 | 4 | NEΔT ≤ 0.3 K(260 K) | WV | |

Long- Wave Infrared | 8.0–9.0 | 4 | NEΔT ≤ 0.2 K(300 K) | WV, Cloud |

10.3–11.3 | 4 | NEΔT ≤ 0.2 K(300 K) | Sea Surface Temperature | |

11.5–12.5 | 4 | NEΔT ≤ 0.2 K(300 K) | Sea Surface Temperature | |

13.2–13.8 | 4 | NEΔT ≤ 0.5 K(300 K) | Cloud, WV |

Coefficients | b_{1} | b_{2} | b_{3} | b_{4} | b_{5} | b_{6} | RMSE (K) |
---|---|---|---|---|---|---|---|

Kerr | −2.4 | 3.6 | −2.6 | 3.1 | 3.1 | −2.1 | 5.47 |

Kerr_PSO ^{1} | −4.47 | 5.26 | −4.24 | 5.59 | 2.94 | −1.96 | 4.02 |

^{1}Kerr_PSO is the optimized Kerr algorithm. PSO, particle swarm optimization.

Coefficients | a_{1} | a_{2} | a_{3} | a_{4} | a_{5} | a_{6} | a_{7} | RMSE (K) |
---|---|---|---|---|---|---|---|---|

B&L | 1.274 | 1.0 | 0.15616 | −0.482 | 6.26 | 3.98 | 38.33 | 6.75 |

B&L _SB_PSO ^{2} | 0.83 | 0.98 | 0.01 | 0.0 | 8.01 | 5.67 | 178.45 | 4.08 |

B&L _DX1_PSO ^{3} | 0.68 | 0.95 | 1.65 | −1.71 | 9.61 | 156.95 | 69.35 | 3.23 |

B&L _DX2_PSO ^{4} | 0.65 | 0.98 | 0.79 | −0.07 | 12.2 | 118.34 | 246.19 | 3.22 |

^{2}B&L_SB_PSO is the optimized B&L algorithm based on the SB emissivity model.

^{3}B&L_DX1_PSO is the optimized B&L algorithm based on the DX1 emissivity model.

^{4}B&L_DX2_PSO is the optimized B&L algorithm based on the DX2 emissivity model.

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**MDPI and ACS Style**

Wang, L.; Guo, N.; Wang, W.; Zuo, H.
Optimization of the Local Split-Window Algorithm for FY-4A Land Surface Temperature Retrieval. *Remote Sens.* **2019**, *11*, 2016.
https://doi.org/10.3390/rs11172016

**AMA Style**

Wang L, Guo N, Wang W, Zuo H.
Optimization of the Local Split-Window Algorithm for FY-4A Land Surface Temperature Retrieval. *Remote Sensing*. 2019; 11(17):2016.
https://doi.org/10.3390/rs11172016

**Chicago/Turabian Style**

Wang, Lijuan, Ni Guo, Wei Wang, and Hongchao Zuo.
2019. "Optimization of the Local Split-Window Algorithm for FY-4A Land Surface Temperature Retrieval" *Remote Sensing* 11, no. 17: 2016.
https://doi.org/10.3390/rs11172016