# Land Surface Temperature Derivation under All Sky Conditions through Integrating AMSR-E/AMSR-2 and MODIS/GOES Observations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{MODIS}) has a very good relationship with the GOES LST difference (ΔT

_{GOES}) between two times at 1 to 1.5 h after sunrise and before local noon. Therefore, MODIS LST can also be implemented into the ALEX model to estimate ET at MODIS spatial resolution of 1 km.

## 2. Data and Methods

#### 2.1. Data Used

#### 2.1.1. Satellite Data

- The MODIS daily Aqua LST product (MYD11C1) in version 5.1, with a spatial resolution of 5 km is used in this study. Only good quality LST data with an accuracy of less than 1 K is selected.
- The MODIS land covers Climate Modeling Grid (CMG) product in version 5.1 (Short Name: MCD12C1) provides the dominant land cover types at a spatial resolution of 0.05°.
- The Normalized Difference Vegetation Index (NDVI) data that were used in the microwave algorithm development is extracted from the MODIS 16-days NDVI composite (short name: MYD13C1), with a resolution of 0.05° [46]. The daily NDVI data used in the downscaling process were derived from the MODIS/Aqua surface reflectance product at 0.05° grid (short name: MYD09CMG) [47]. The gaps in the daily NDVI data are filled with the previously available data.
- The Geostationary Operational Environmental Satellite (GOES) monitors the weather conditions in the Unites States (U.S.). The GOES LST data used in this study, which is available at half-hour temporal resolution and 4 km spatial resolution, are derived from the GOES-13 imager observations at 3.9 µm and 11 µm channels while using the algorithms that Sun and Pinker [24] and Sun et al. [26] developed.
- The digital elevation model (DEM) data are derived from the National Elevation Dataset (NED) data [48] at a resolution of 100 m.

#### 2.1.2. In-Situ Data

^{↑}is the surface upwelling longwave radiation, F

^{↓}is the surface downwelling longwave radiation, ε

_{b}is the surface broadband emissivity, and σ is the Stefan–Boltzmann constant.

_{b}) in Equation (1) can be estimated from the MODIS spectral emissivity while using narrowband to broadband conversion method [50], as follows:

_{29}, ε

_{31}, and ε

_{32}are the spectral emissivity of MODIS bands 29, 31, and 32, respectively.

#### 2.2. Methods

#### 2.2.1. Physical Basis for Remote Sensing of LST from Passive Microwave

_{a}

^{↓}is the downward atmospheric brightness temperature, and T

_{a}

^{↑}is the upward atmospheric brightness temperature, T

_{f}is the brightness temperature of frequency f, τ

_{f}is the atmospheric transmittance in frequency f at viewing direction θ (zenith angle from nadir), and ε

_{f}is the ground emissivity. B

_{f}(LST) is the ground radiance, and B

_{f}(T

_{a}

^{↓}) and B

_{f}(T

_{a}

^{↑}) are the downwelling and upwelling path radiances, respectively.

_{V}= aε

_{H}+ b, where ε

_{V/H}stands for surface emissivity at vertical/horizontal polarization, respectively, and a and b are the linear regression coefficients. Therefore, LST can be derived:

_{b}is for brightness temperature and subscripts V and H represent vertical and horizontal polarization, respectively. Several algorithms were selected here for comparison in order to develop good LST algorithms for passive microwave sensors AMSR-E and AMSR-2.

#### 2.2.2. Algorithms for Retrieving LST from Passive Microwave Data

_{m}) by utilizing the AMSR-2 five channels at 6.9, 18.7, 23.8, 36.5, and 89 GHz in both the vertical and horizontal polarizations. The new proposed five-channel algorithm is also compared with the two previously published microwave LST algorithms:

#### The Single-Channel Algorithm with the 36.5 V GHz

#### The Four-Channel Algorithm

_{36.5V}is the primary channel to retrieve LST; (2) The brightness temperature difference at the 36.5 GHz and 23.8 GHz channels in vertical polarization (T

_{36.5V}–T

_{23.8V}) is utilized to attenuate the influence of atmospheric water vapor; (3) T

_{36.5V}–T

_{18.7H}can compensate for the influence of surface water, and, (4) T

_{89V}can decrease the average influence of atmosphere. They used the following equation:

_{m}= B

_{0}+ B

_{1}T

_{36.5V}+ B

_{2}(T

_{36.5V}–T

_{23.8V}) + B

_{3}(T

_{36.5V}–T

_{18.7H}) + B

_{4}T

_{89V}

_{0}, B

_{1}…B

_{4}are the regression coefficients.

#### A Proposed New Five-Channel Algorithm

_{m}= C

_{0}+ C

_{1}(T

_{6.9V}–c

_{1}T

_{6.9H}) + C

_{2}(T

_{36.5V}–c

_{2}T

_{36.5H}) + C

_{3}(T

_{23.8V}–c

_{3}T

_{23.8H}) + C

_{4}(T

_{18.7V}–c

_{4}T

_{18.7H}) + C

_{5}(T

_{89V}–c

_{5}T

_{89H}) + C

_{6}UTC

_{0}, C

_{1}…C

_{6}, c

_{1}…c

_{5}are the regression coefficients.

#### 2.3. Regression Tree Algorithm

#### 2.4. Gap Filling and Downscaling Method

- (1)
- Aggregate NDVI and DEM to microwave resolution (25 km for AMSR-E and 10 km for AMSR-2). Here, we take the AMSR-E and MODIS as an example, NDVI
^{5km}and DEM^{5km}denote the auxiliary variables at the MODIS pixel resolution, whereas NDVI^{25km}and DEM^{25km}represent the aggregated auxiliary variables at the AMSR-E pixel resolution. - (2)
- Establish the non-stationary relationship between the AMSR-E 25 km LST with the same spatial resolution auxiliary data:LST
^{25km}= a_{0}^{25km}(x,y) + a_{1}^{25km}(x,y) NDVI^{25km}+ a_{2}^{25km}(x,y) DEM^{25km}+ ε^{25km}

- (3)
- Estimate the regression coefficients a
_{0}(x,y), a_{1}(x,y), a_{2}(x,y), and the error term ε via Gaussian distance weighting at the coarse microwave resolution. - (4)
- Apply the regular gap-filling algorithm to both MODIS LST and AMSR-E LST, so that the first gap-free observations can be obtained.
- (5)
- The bi-cubic interpolation is used to interpolate the regression coefficients and the residual at coarse microwave resolution to MODIS 5km resolution a
_{0}^{5km}(x,y), a_{1}^{5km}(x,y), a_{2}^{5km}(x,y), and error term ε^{5km}. - (6)
- The final downscaled LST at 5 km resolution can be calculated while using the auxiliary variables (NDVI and DEM) at 5 km resolution in conjunction with the regression coefficients and the residual term at 5 km m resolution:LST
^{5km}= a_{0}^{5km}(x,y) + a_{1}^{5km}(x,y) NDVI^{5km}+ a_{2}^{5km}(x,y) DEM^{5km}+ ε^{5km}

## 3. Results

#### 3.1. Results from the Calibrations

#### 3.1.1. Results from the AMSR-E to MODIS Calibration

#### Implementation of the Single-Channel Algorithm

#### Implementation of the Four-Channel Algorithm

#### Implementation of the Proposed Five-Channel Algorithm

#### 3.1.2. Results from the AMSR-2 to GOES Calibration

#### 3.2. Results from the Validation against Ground Observations

#### 3.3. Results from the Implementation to the Real Observations

## 4. Discussion

## 5. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Cloud free MODIS LST, (

**b**) the merged MODIS and AMSR-E LST, (

**c**) the original MODIS LST in the zoomed area (inside the gold square of Figure 1a), (

**d**) the original merged LST in the zoomed region (inside the gold square of Figure 1b), (

**e**) the merged LST with the regular gap-filling method, and (

**f**) the integrated LST with the GWR-based filling algorithm applied to fill the gaps and also downscale to the same resolution of the MODIS LST, during nighttime on 15 December 2008.

**Figure 2.**Scatter plots of MODIS ascending (

**a**) and descending (

**b**), and AMSR-E ascending (

**c**) and descending (

**d**) LST against the SURFRAD observations. The RMS is the Root Mean Square (RMS) error, and R represents Pearson correlation coefficient, N stands for sample number. The black diagonal refers to 1:1 line and the pink line is the least square fit line.

**Figure 3.**Scatter plots of GOES LST products at 1.5 h before noon (

**a**) and 1.5 h after sunrise (

**b**), and the retrieved AMSR-2 ascending (

**c**) and descending (

**d**) LST vs. the SURFRAD observations in 2015. The RMS and R are the same as in Figure 2. The black diagonal refers to 1:1 line, the pink line is the least square fit line.

**Figure 4.**(

**a**) Cloud free MODIS LST at 5 km resolution, (

**b**) the derived AMSR-E LST at 25 km resolution, (

**c**) the merged MODIS and AMSR-E LST at 25 km resolution, and (

**d**) the integrated LST from MODIS and AMSR-E with the GWR-based method applied to fill the gaps and also downscale to the same 5 km resolution as the MODIS LST, during daytime on 5 December 2008.

**Figure 5.**(

**a**) Cloud free MODIS LST at 5 km resolution, (

**b**) the AMSR-E LST at 25 km resolution, (

**c**) the merged MODIS and AMSR-E LST at 25 km resolution, and (

**d**) the integrated LST from MODIS and AMSR-E with the GWR-based method applied to fill the gaps and also downscale to the same 5 km resolution as the MODIS LST, during nighttime on 2 June 2008.

**Figure 6.**(

**a**) Cloud free GOES LST with 4 km resolution at 1.5 h before noon, (

**b**) the AMSR-2 ascending LST at 10 km resolution, (

**c**) the merged GOES and AMSR-2 LST at 10 km resolution, and (

**d**) the integrated GOES and AMSR-2 LST with the GWR-based method applied to fill the gaps and also downscale to the same 4 km resolution as the GOES LST, on 19 July 2013.

**Figure 7.**(

**a**) Cloud free GOES LST with 4 km resolution at 1.5 h after sunrise, (

**b**) the AMSR-2 descending LST at 10 km resolution, (

**c**) the merged GOES and AMSR-2 LST at 10 km resolution, and (

**d**) the integrated LST from GOES and AMSR-2 with the GWR-based method applied to fill the gaps and also downscale to the same 4 km resolution as the GOES LST, on 27 September 2013.

**Figure 8.**An example of daily proxy ESI with the integrated MODIS and AMSR-E LST input (the first column), as compared with the current ESI (the second column), and the weekly US Drought Monitor (USDM) drought map (the third column).

Site No. | Site Location | Lat (N)/Lon(W) | Surface Type * |
---|---|---|---|

1 | Bondville, IL | 40.05/88.37 | Crop Land |

2 | Fort Peck, MT | 48.31/105.10 | Close Shrubland |

3 | Goodwin Creek, MS | 34.25/89.87 | Deciduous Forest |

4 | Table Mountain, CO | 40.13/105.24 | Crop Land |

5 | Sioux Falls, SD | 43.73/96.62 | Grass Land |

6 | Pennsylvania State University, PA | 40.72/77.93 | Mixed Forest |

**Table 2.**LST derived from AMSR-E Ascending data with the single-channel algorithm in relative to MODIS LST in daytime.

Seasons | Correlation Coefficient | MAE (K) | RMS (K) | Sample Number |
---|---|---|---|---|

Spring | 0.89 | 4.73 | 5.99 | 215,184 |

Summer | 0.70 | 4.56 | 6.44 | 348,823 |

Fall | 0.67 | 4.45 | 6.54 | 341,448 |

Winter | 0.83 | 4.22 | 5.42 | 168,043 |

**Table 3.**LST derived from AMSR-E Descending data with the single-channel algorithm in relative to MODIS LST in nighttime.

Seasons | Correlation Coefficient | MAE (K) | RMS (K) | Sample Number |
---|---|---|---|---|

Spring | 0.82 | 5.03 | 6.28 | 139,793 |

Summer | 0.75 | 3.56 | 5.34 | 255,269 |

Fall | 0.61 | 3.89 | 5.23 | 253,139 |

Winter | 0.74 | 4.51 | 6.01 | 105,963 |

**Table 4.**LST derived from the AMSR-E ascending data with the four-channel algorithm. [20] vs. MODIS LST product.

Seasons | Correlation Coefficient | MAE (K) | RMS (K) | Sample Number |
---|---|---|---|---|

Spring | 0.90 | 3.21 | 4.12 | 215,184 |

Summer | 0.88 | 3.35 | 4.32 | 348,823 |

Fall | 0.90 | 2.89 | 3.87 | 341,448 |

Winter | 0.93 | 2.43 | 3.02 | 168,043 |

**Table 5.**LST derived from the AMSR-E descending data with the four-channel algorithm [36] vs. MODIS LST product.

Seasons | Correlation Coefficient | MAE (K) | RMS Error (K) | Sample Number |
---|---|---|---|---|

Spring | 0.89 | 2.21 | 3.27 | 139,793 |

Summer | 0.92 | 2.03 | 2.40 | 255,269 |

Fall | 0.93 | 1.85 | 2.34 | 253,139 |

Winter | 0.87 | 2.43 | 3.27 | 105,963 |

**Table 6.**LST derived from the AMSR-E ascending data with the proposed new five-channel algorithm, compared with the MODIS LST product during daytime.

Seasons | Methods | Correlation Coefficient | MAE (K) | RMS (K) | Sample Number |
---|---|---|---|---|---|

Spring | L | 0.92 | 2.95 | 3.95 | 215,184 |

RT | 0.99 | 0.16 | 0.83 | ||

Summer | L | 0.90 | 3.32 | 4.38 | 348,823 |

RT | 0.99 | 0.70 | 0.84 | ||

Fall | L | 0.91 | 2.92 | 3.98 | 341,448 |

RT | 0.99 | 0.70 | 0.78 | ||

Winter | L | 0.95 | 2.25 | 2.99 | 168,043 |

RT | 0.99 | 0.63 | 0.46 |

**Table 7.**LST derived from the AMSR-E descending data with the proposed new five-channel algorithm, as compared with the MODIS LST product during nighttime.

Seasons | Methods | Correlation Coefficient | MAE (K) | RMS (K) | Sample Number |
---|---|---|---|---|---|

Spring | L | 0.89 | 2.25 | 3.02 | 139,793 |

RT | 0.99 | 0.33 | 0.43 | ||

Summer | L | 0.91 | 1.88 | 2.55 | 255,269 |

RT | 0.99 | 0.41 | 0.52 | ||

Fall | L | 0.94 | 1.83 | 2.44 | 253,139 |

RT | 0.99 | 0.46 | 0.57 | ||

Winter | L | 0.88 | 2.52 | 3.35 | 105,963 |

RT | 0.99 | 0.39 | 0.64 |

**Table 8.**LST derived from the AMSR-2 Ascending data with five-channel algorithm, as compared with the GOES LST at 1.5 h before noon.

Seasons | Methods | Correlation Coefficient | Mean Absolute Error (K) | Root Mean Squared Error (K) | Total Number of Instances |
---|---|---|---|---|---|

Spring | L | 0.93 | 2.96 | 3.83 | 382,965 |

RT | 0.985 | 1.18 | 1.64 | ||

Summer | L | 0.91 | 3.22 | 4.14 | 757,026 |

RT | 0.981 | 1.21 | 1.70 | ||

Fall | L | 0.92 | 2.88 | 3.70 | 897,344 |

RT | 0.990 | 1.048 | 1.44 | ||

Winter | L | 0.92 | 2.54 | 3.29 | 203,571 |

RT | 0.990 | 0.912 | 1.27 |

**Table 9.**LST derived from the AMSR-2 descending data with five-channel algorithm, as compared with the GOES LST at 1.5 h after sunrise.

Seasons | Methods | Correlation Coefficient | Mean Absolute Error (K) | Root Mean Squared Error (K) | Total Number of Instances |
---|---|---|---|---|---|

Spring | L | 0.84 | 2.63 | 3.38 | 159,725 |

RT | 0.982 | 0.881 | 1.25 | ||

Summer | L | 0.84 | 2.33 | 3.07 | 550,810 |

RT | 0.977 | 0.815 | 1.17 | ||

Fall | L | 0.87 | 2.18 | 2.87 | 613,528 |

RT | 0.986 | 0.841 | 1.16 | ||

Winter | L | 0.82 | 2.83 | 3.86 | 195,493 |

RT | 0.982 | 0.902 | 1.29 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sun, D.; Li, Y.; Zhan, X.; Houser, P.; Yang, C.; Chiu, L.; Yang, R. Land Surface Temperature Derivation under All Sky Conditions through Integrating AMSR-E/AMSR-2 and MODIS/GOES Observations. *Remote Sens.* **2019**, *11*, 1704.
https://doi.org/10.3390/rs11141704

**AMA Style**

Sun D, Li Y, Zhan X, Houser P, Yang C, Chiu L, Yang R. Land Surface Temperature Derivation under All Sky Conditions through Integrating AMSR-E/AMSR-2 and MODIS/GOES Observations. *Remote Sensing*. 2019; 11(14):1704.
https://doi.org/10.3390/rs11141704

**Chicago/Turabian Style**

Sun, Donglian, Yu Li, Xiwu Zhan, Paul Houser, Chaowei Yang, Long Chiu, and Ruixin Yang. 2019. "Land Surface Temperature Derivation under All Sky Conditions through Integrating AMSR-E/AMSR-2 and MODIS/GOES Observations" *Remote Sensing* 11, no. 14: 1704.
https://doi.org/10.3390/rs11141704