# Land Surface Temperature Retrieval Using Airborne Hyperspectral Scanner Daytime Mid-Infrared Data

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## Abstract

**:**

## 1. Introduction

## 2. Methodology and Data Simulation

#### 2.1. Basic Theory

_{i}is the Planck function. B

_{i}(T

_{i}) is the radiance measured at the top of the atmosphere (TOA) in channel i, and T

_{i}is the brightness temperature. ε

_{i}and T

_{s}are the surface emissivity and surface temperature, respectively. τ

_{i}is the transmittance of the atmosphere from the ground to the TOA along the viewing angle. ${R}_{atm\_i}^{\uparrow}$ and ${R}_{atm\_i}^{\downarrow}$ are the upward and downward atmospheric thermal radiances, respectively. ${R}_{atm\_i}^{s\uparrow}$ and ${R}_{atm\_i}^{s\downarrow}$ are the upward and downward solar diffusion radiances, respectively, which result from atmospheric scattering of the solar radiance. ρ

_{bi}is the surface bidirectional reflectivity. ${R}_{i}^{s}$ is solar radiance at ground level. In addition, ${R}_{i}^{s}={E}_{i}cos\left({\theta}_{s}\right){\tau}_{i}\left({\theta}_{s},{\phi}_{s}\right)/\pi $, where E

_{i}is the solar irradiance at TOA, ${\tau}_{i}\left({\theta}_{s},{\phi}_{s}\right)$ is the transmittance of the atmosphere from TOA to the ground along the solar angle, and ${\theta}_{s}$ and ${\phi}_{s}$ are the solar zenith and azimuth angle, respectively.

#### 2.2. Data

_{a}) of 250~310 K and the WVC of 0.06~5.39 g/cm

^{2}, extracted from the TOVS Initial Guess Retrieval (TIGR) database [28,29], are used to analyse atmospheric effects. The attenuation of the surface radiance has been considered by adding the uniformly mixed gases (CO

_{2}, N

_{2}O, CO and CH

_{4}) and ozone, included in the standard atmospheres of the MODTRAN 4.0 code, to the water vapor taken from profiles in the TIGR radiosoundings [30]. To accomplish this, a previous classification of the surface temperature is made with the rule that the surface temperatures are from T

_{a}− 5 K to T

_{a}+ 15 K with a step of 5 K. Furthermore, the VZAs are set to be 0°, 33.56°, 44.42°, 51.32°, 56.25°, and 60° (corresponding values of 1/cos(VZAs) are 1, 1.2, 1.4, 1.6, 1.8, and 2.0), respectively, so that 1/cos(VZAs) could be sampled with a step of 0.2. The SZAs are set as 0°, 25.84°, 36.87°, 45.57°, 53.13°, and 60° (cos(SZAs) are 1, 0.9, 0.8, 0.7, 0.6, and 0.5), respectively, so that the cos(SZAs) could be sampled with a step of 0.1. Also, 70 different emissivities obtained from the Johns Hopkins University (JHU) Spectral library (soils, vegetation, and water, etc.) are considered. Once the simulations are made, TOA radiance could be determined according to Equation (1). In total, for the TIGR database and the JHU Spectral library, 8,883,000 different situations are simulated for retrieval.

#### 2.3. LST Retrieval Method from Two AHS MIR Channels

#### 2.3.1. Estimation of Direct Solar Radiance

_{bi}), the solar radiance at ground level (${R}_{i}^{s}$), and the transmittance from ground to sensor (${\tau}_{i}$). As we all know, ${\tau}_{i}$ is related to WVC and VZA, while ${R}_{i}^{s}$ is related to WVC and SZA. Therefore, the relationship between direct solar radiance (${D}_{i}={\tau}_{i}\times {R}_{i}^{s}$) and WVC, VZA and SZA is investigated to estimate the direct solar radiance by assuming that the surface is Lambertian and the LSE is known.

#### Relationship between Direct Solar Radiance and WVC

_{i}and WVC with the aid of simulated data, a scatter plot between D

_{i}and ln(WVC) is shown in Figure 1. The data is shown for CH66 and CH68 with different VZAs and SZAs at the LST conditions of 250~310 K and WVC of 0~5.5 g/cm

^{2}. Figure 1a,b shows the relationships at the six different VZAs when SZA = 0°, while Figure 1c,d shows those at six different SZAs when VZA = 0°. It is noted that D

_{i}and ln(WVC) can be fitted using a quadratic polynomial with a formula as Equation (3) with a correlation coefficient of 0.985. Similar results also can be obtained for other combinations of SZAs and VZAs.

_{i}is the direct solar radiance.

**Figure 1.**Relationships between direct solar radiance (D

_{i}) and ln(WVC). (

**a**) AHS CH66 (SZA = 0°, VZA = 0~60°). (

**b**) AHS CH68 (SZA = 0°, VZA = 0~60°). (

**c**) AHS CH66 (VZA = 0°, SZA = 0~60°). (

**d**) AHS CH68 (VZA = 0°, SZA = 0~60°).

#### Direct Solar Radiance at Different VZAs

_{i}, Figure 2a,b express the relationships between coefficients a, b, c and 1/cos(VZA) at SZA = 0° and SZA = 60°, respectively. It is found that the coefficients a, b, and c can be fitted using the formulations of a = a

_{1}/cos(VZA) + a

_{2}, b = b

_{1}/cos(VZA) + b

_{2}, and c = c

_{1}/cos(VZA) + c

_{2}. The direct solar radiance can be described as a function of WVC and VZA as Equation (4) with a correlation coefficient of 0.992.

_{1}, a

_{2}, b

_{1}, b

_{2}, c

_{1}, and c

_{2}are unknown coefficients.

#### Direct Solar Radiance at Different SZAs

_{i}at other SZAs, Figure 3a,b shows the relationships between coefficients a

_{1}, a

_{2}, b

_{1}, b

_{2}, c

_{1}, c

_{2}and cos(SZA) in CH66 and CH68, respectively. It can be found that these coefficients a

_{1}, a

_{2}, b

_{1}, b

_{2}, c

_{1}, and c

_{2}can be expressed as a linear relationship of the cosine of SZA, i.e., a

_{1}= a

_{11}cos(SZA) + a

_{10}, a

_{2}= a

_{21}cos(SZA) + a

_{20}, b

_{1}= b

_{11}cos(SZA) + b

_{10}, b

_{2}= b

_{21}cos(SZA) + b

_{20}, c

_{1}= c

_{11}cos(SZA) + c

_{10}, and c

_{2}= c

_{21}cos(SZA) + c

_{20}. D

_{i}can be described as a function of WVC, VZA, and SZA as Equation (5) with a correlation coefficient of 0.994.

_{11}, a

_{10}, a

_{21}, a

_{20}, b

_{11}, b

_{10}, b

_{21}, b

_{20}, c

_{11}, c

_{10}, c

_{21}, and c

_{20}are fitting coefficients.

#### 2.3.2. Estimation of LST

_{i}and T

_{j}measured in the two adjacent TIR channels [14,15]. In consideration of the similar RTEs in MIR and TIR without the influence of solar direct radiance, this paper extends the split-window method to the MIR spectral region for LST retrieval after eliminating the effect of direct solar radiance. The new method is expressed as follows:

_{i}+ ε

_{j})/2, Δε = ε

_{i}− ε

_{j}, and k

_{0}, k

_{1}, k

_{2}, k

_{3}, k

_{4}, k

_{5}, and k6 are unknown coefficients, which can be derived from simulated AHS data. ${T}_{i}^{\prime}$ and ${T}_{j}^{\prime}$ are the TOA equivalent brightness temperatures in two MIR channels. ε

_{i}and ε

_{j}are the LSEs in channel i and j, respectively. ε is the averaged emissivity, and Δε is the emissivity difference between the two MIR channels.

**Figure 3.**Relationship between coefficients a

_{1}, a

_{2}, b

_{1}, b

_{2}, c

_{1}, c

_{2}and cos(SZA). (

**a**) AHS CH66. (

**b**) AHS CH68.

## 3. Results and Analysis

#### 3.1. Estimated Result of Direct Solar Radiance

_{i}can be expressed as a function of WVC, SZA and VZA, and the fitting coefficients can be obtained using the simulated data (see Table 1). To evaluate the accuracy of direct solar radiance retrieval, Figure 4a,b shows the histograms of the difference between the estimated and actual D

_{i}in CH66 and CH68, respectively. The root mean square errors (RMSEs) are 0.0123 W/(m

^{2}·sr·μm) for CH66 and 0.007 W/(m

^{2}·sr·μm) for CH68. The correlation coefficients (R) are 0.999 and 0.998, respectively.

Channel Coefficient | a_{11} | a_{10} | a_{21} | a_{20} | b_{11} | b_{10} | b_{21} | b_{20} | c_{11} | c_{10} | c_{21} | c_{20} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

AHS CH66 | 2.849 | −0.325 | −0.162 | 0.028 | −0.037 | −0.026 | −0.020 | 0.005 | −0.018 | −0.007 | −0.006 | 0.002 |

AHS CH68 | 0.709 | −0.163 | −0.086 | 0.026 | −0.080 | −0.001 | −0.010 | 0.004 | −0.024 | 0.002 | −0.001 | 0.001 |

**Figure 4.**Histogram of the difference between the estimated and actual direct solar radiance (D

_{i}) for CH66 (

**a**) and CH68 (

**b**).

#### 3.2. Coefficients of LST Retrieval Method

^{2}, and LSTs are divided into three sub-ranges: 265 K ≤ LST ≤ 295 K, 290 K ≤ LST ≤ 310 K, and 305 K ≤ LST ≤ 325 K [31]. Then, the coefficients in Equation (6) can be obtained through a statistical regression method for each sub-range under different VZAs. As an example, Figure 5 displays the coefficients as functions of the secant of VZAs at the sub-ranges of LSTs, which vary from 305 K to 325 K, for the two WVC groups. The coefficients k

_{0}~k

_{6}for other VZAs can be linearly interpolated as function of the secant of VZA. Similar results are obtained for the other sub-ranges.

**Figure 5.**Coefficients for the sub-range with LST varying from 305 K to 325 K. (

**a**) Dry atmosphere (WVC = 0~1.5 g/cm

^{2}). (

**b**) Humid atmosphere (WVC = 4~5.5 g/cm

^{2}).

#### 3.3. Result of LST Retrieval

_{0}~k

_{6}of the LST sub-range that is determined according to the approximate LST. Figure 6 gives the RMSEs between the actual and estimated LST as functions of the secant of VZA for different sub-ranges. The RMSEs are shown to increase with the increase of VZAs. The RMSEs are less than 1 K for all sub-ranges; the minimum value is 0.16 K (LST = 305~325 K, WVC = 4~5.5 g/cm

^{2}, and VZA = 0°).

**Figure 6.**RMSEs between the actual and estimated LST for different sub-ranges. (

**a**) 305 K ≤ LST ≤ 325 K. (

**b**) 290 K ≤ LST ≤ 310 K. (

**c**) 265 K ≤ LST ≤ 295 K. (

**d**) 265 K ≤ LST ≤ 325 K.

## 4. Sensitivity Analysis

#### 4.1. Sensitivity Analysis to Instrumental Noises

#### 4.2. Sensitivity Analysis to LSEs

_{i}and ε

_{j}in Equation (6). Table 2 shows the effect of emissivity on the accuracy of LST retrieval at the condition of VZA = 0°. It is worth noting the LST retrieval errors (the LSTs retrieved from LSE-uncertainty-added conditions minus those determined from no-LSE-uncertainty conditions) vary from 0.4 K to 2.83 K by assuming that the uncertainty of the emissivity is 0.01; errors increase with the decrease of LSTs. The reason may be that the proportion of direct solar radiance is larger in the total radiance when the LST is lower, and the same emissivity error may produce a larger effect on TOA radiance with lower LSTs. Meanwhile, the retrieval accuracy will be increasing with the increase of WVC. The possible reason is that the impact of the atmosphere on LST retrieval is more significant when the WVC increases; thus, the same emissivity error would produce smaller errors when the WVC is larger.

WVC (g/cm ^{2}) | 305~325 (K) Error | 290~310 (K) Error | 265~295 (K) Error | 265~325 (K) Error |
---|---|---|---|---|

0~1.5 | 0.50 | 1.04 | 2.83 | 2.71 |

1~2.5 | 0.49 | 0.94 | 1.68 | 1.31 |

2~3.5 | 0.44 | 0.84 | 1.37 | 0.92 |

3~4.5 | 0.40 | 0.76 | 1.40 | 0.81 |

4~5.5 | 0.40 | 0.74 | 1.26 | 0.73 |

#### 4.3. Sensitivity Analysis to WVC

^{2}(dry atmosphere) or 4~5.5 g/cm

^{2}(wet atmosphere). It can be seen from Figure 8 that RMSE and Bias are 0.21 K and 0.02 K under dry atmosphere, respectively, and 0.21 K and 0.047 K under wet atmosphere, respectively.

^{2}at VZA = 60°. The smallest RMSE is approximately 0.72 K for the sub-range of LST = 305~325 K and WVC = 4~5.5 g/cm

^{2}at VZA = 0°.

**Figure 8.**Histogram of the difference between the actual and estimated T

_{s}caused by a WVC uncertainty of 10%. (

**a**) WVC = 0~1.5 g/cm

^{2}. (

**b**) WVC = 4~5.5 g/cm

^{2}.

**Figure 9.**Total LST retrieval error caused by uncertainties of NEΔT, emissivity, and WVC. (

**a**) High LST conditions (LST = 305~325 K). (

**b**) Low LST conditions (LST = 265~295 K).

## 5. Preliminary Application to AHS data

#### 5.1. Data Processing

^{2}).

#### 5.2. Results and Validation

**Table 3.**Technical specifications of the thermal instruments [33].

Instrument | Spectral Range (um) | Temperature Range (°C) | Accuracy (K) | Resolution | FOV |
---|---|---|---|---|---|

Cimel CE312-1 | 8~13 | −80 to 50 | 0.1 | 8 mK | 10° |

11.5~12.5 | 50 mK | ||||

10.5~11.5 | 50 mK | ||||

8.2~9.2 | 50 mK | ||||

Cimel CE312-2 | 8~13 | −80 to 60 | 0.1 | 8 mK | 10° |

11~11.7 | 50 mK | ||||

10.3~11 | 50 mK | ||||

8.9~9.3 | 50 mK | ||||

8.5~8.9 | 50 mK | ||||

8.1~8.5 | 50 mK | ||||

Heitronics KT19 | 9.6~11.5 | −50 to 200 | 0.1 | 0.05 K | 2° |

NEC TH9100 | 8~14 | −40 to 120 | 2 | 0.1 K (320 × 240) | 22° × 16° |

**Figure 11.**Three areas with different covering types. (

**a**) Retiro Park (water). (

**b**) Soccer field (bare soil). (

**c**) Football field (grass) [33].

Coordinate | Surface Type | LSE | Retrieved LST | In situ Measurement | In situ Bias | |
---|---|---|---|---|---|---|

ε_{66} | ε_{68} | |||||

40°25′1.65″N, 3°41′2.65″W | Water | 0.976 | 0.979 | 297.6K | 298.3K | 0.3K |

40°32′52.44″N, 3°41′48.45″W | Bare soil | 0.769 | 0.799 | 314.8K | 313.9K | 0.6K |

40°32′51.71″N, 3°41′54.33″W | Grass | 0.984 | 0.987 | 306.3K | 304.0K | 2K |

**Figure 12.**Validation results over three areas. (

**a**) Retiro Park (water). (

**b**) Soccer field (bare soil). (

**c**) Football field (grass).

## 6. Conclusions

^{2}at VZA = 60°. The smallest one is approximately 0.72 K for the sub-range of LST = 305~325 K and WVC = 4~5.5 g/cm

^{2}at VZA = 0°.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Zhao, E.; Qian, Y.; Gao, C.; Huo, H.; Jiang, X.; Kong, X.
Land Surface Temperature Retrieval Using Airborne Hyperspectral Scanner Daytime Mid-Infrared Data. *Remote Sens.* **2014**, *6*, 12667-12685.
https://doi.org/10.3390/rs61212667

**AMA Style**

Zhao E, Qian Y, Gao C, Huo H, Jiang X, Kong X.
Land Surface Temperature Retrieval Using Airborne Hyperspectral Scanner Daytime Mid-Infrared Data. *Remote Sensing*. 2014; 6(12):12667-12685.
https://doi.org/10.3390/rs61212667

**Chicago/Turabian Style**

Zhao, Enyu, Yonggang Qian, Caixia Gao, Hongyuan Huo, Xiaoguang Jiang, and Xiangsheng Kong.
2014. "Land Surface Temperature Retrieval Using Airborne Hyperspectral Scanner Daytime Mid-Infrared Data" *Remote Sensing* 6, no. 12: 12667-12685.
https://doi.org/10.3390/rs61212667