# Advancing of Land Surface Temperature Retrieval Using Extreme Learning Machine and Spatio-Temporal Adaptive Data Fusion Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Extreme Learning Machine (ELM) Algorithm

**Figure 1.**Structure of the single hidden layer feed forward neural network using Extreme Learning Machine (ELM).

- (i)
- Allocate the input weight ${\mathbf{w}}_{i}$ and bias ${b}_{i},i=1,2,\cdots ,\tilde{N}$ arbitrarily.
- (ii)
- Compute the hidden layer output matrix $\mathbf{H}$.
- (iii)
- Use the equation $\mathbf{\beta}={\mathbf{H}}^{-1}\mathbf{T}$ to calculate the output weight matrix $\mathbf{\beta}$.

#### 2.2. Spatio-Temporal Adaptive Data Fusion Algorithm for Temperature Mapping (SADFAT)

_{i}denotes the fraction of each Landsat pixel, (x, y) represents a given location, t is the acquisition date, and k

_{1}, k

_{2}are the coefficients for the relative adjustment for the Landsat and MODIS radiance pixels [42]. Therefore, if there are two pairs of Landsat ETM+ and MODIS image acquired at t

_{1}and t

_{2}, respectively, Equation (2) indicates that the ratio of the radiance change of j

_{th}L pixel to the radiance of corresponding M pixel is constant for a certain L pixel can be quantified as below:

_{j}is denoted as the conversion coefficient for the purpose of consistency, ω reflects the phase shift of a pixel and is related with the thermal characteristics of land cover, and it is a constant if the land surface materials does not change in the period of observation [42]. Thus, if there is a pair of L and M radiance images at t

_{0}and an M radiance image at t

_{p}, the L radiance image at t

_{p}can be predicted by the following equation:

_{i}represents the weight of a neighboring similar pixel, and $N$ is the number of the spectral similar pixel. In this paper, after predicting the radiance image using SADFAT method, enhanced Landsat ETM+ TIR data with both high spatial and temporal resolution would be converted to LST using the generalized single channel method [46]. More details of SADFAT can be referred to Weng et al. [42].

#### 2.3. Implementation of the Proposed Data Fusion Model

_{1}and t

_{2}and one M image at the prediction date t

_{p}.

- (i)
- Two L images were used to search for the spectrally similar pixels using the method described by Gao et al. [34] that define a difference threshold between the central pixel and the neighbouring pixels in a moving window.
- (ii)
- The combined weight and conversion coefficient for each similar pixel were computed. Here, a similar pixel with higher thermal similarity and shorter distance to the central pixel would yield a higher weight and the conversion coefficients were decided by the regression analysis of the similar pixels [35].
- (iii)
- Equation (5) was employed to compute the desired predicted image at t
_{p}. Considering the temporal weights of the two images given by the temporal changes in coarser radiance images, an accurate radiance image can be computed by using the weighted combination of the two predicted radiance images as follows:$$L({x}_{s/2},{y}_{s/2},{t}_{p})={T}_{{t}_{1}}\times {P}_{{t}_{1}}({x}_{s/2},{y}_{s/2},{t}_{p})+{T}_{{t}_{2}}\times {P}_{{t}_{2}}({x}_{s/2},{y}_{s/2},{t}_{p})$$_{1}and t_{2}as the base image, respectively, in which the temporal weight T_{k}can be calculated as:$${T}_{k}=\frac{1/({\displaystyle {\sum}_{i=1}^{s}}{\displaystyle {\sum}_{j=1}^{s}}M({x}_{i},{y}_{j},{t}_{k},B)-{\displaystyle {\sum}_{i=1}^{w}}{\displaystyle {\sum}_{j=1}^{w}}M({x}_{i},{y}_{j},{t}_{p},B))}{{\sum}_{k={t}_{1},{t}_{2}}1/({\displaystyle {\sum}_{i=1}^{s}}{\displaystyle {\sum}_{j=1}^{s}}M({x}_{i},{y}_{i},{t}_{k},B)-{\displaystyle {\sum}_{i=1}^{w}}{\displaystyle {\sum}_{j=1}^{w}}M({x}_{i},{y}_{j},{t}_{p},B))}$$ - (iv)
- Finally, the LST images can be derived using the generalized single channel method.

**Figure 2.**Flowchart of the proposed fusion model for predicting synthetic LST image at 30 m resolution.

## 3. Results

#### 3.1. Study Area

#### 3.2. Experiment Results

**Figure 5.**Thermal spatial sharpening results of testing experiments via ELM algorithm. False colour images of downscaled Landsat ETM+ multispectral data at 60 m (

**upper row**), downscaled TIR images at 120 m (

**middle row**) and sharpened TIR images at 60 m (

**lower row**). The original TIR images at 60 m refer to the middle row in Figure 6. From left to right, they were acquired on 20 October, 7 December and 23 December 2013.

**Figure 6.**Thermal spatial sharpening results of simulated experiments using ELM algorithm. False colour images of observed Landsat ETM+ multispectral data at 30 m (

**upper row**), TIR images at 60 m (

**middle row**) and Enhanced TIR images at 30 m (

**lower row**). From left to right, they were acquired on 20 October, 7 December and 23 December 2013.

Date | 20 October 2013 | 7 December 2013 | 23 December 2013 |
---|---|---|---|

CC | 0.8788 * | 0.8251 * | 0.8017 * |

RMSE | 0.0844 | 0.0891 | 0.0909 |

AD | −9.8940e-06 | −2.1980e-06 | 6.3913e-06 |

AAD | 0.0595 | 0.0620 | 0.0614 |

**significant at 0.001 level (p ＜ 0.001).**

^{*}_{1}and t

_{2}were input into the SADFAT fusion model developed by Weng et al. [42]. Figure 7 and Figure 8 showed the results of predicted images at 60 m and 30 m on 7 December 2013, respectively. For both the testing and simulated experiments, the predicted LST images (Figure 7b and Figure 8b) are visually similar to the original Landsat LST images (Figure 7c and Figure 8c), but they provide higher spatial details in terms of thermal information.

**Figure 7.**SADFAT result in the testing experiment.

**(a)**MODIS LST images resampled from 1 km to 60 m;

**(b)**SADFAT-derived image at 60 m;

**(c)**original Landsat ETM+ LST image at 60 m spatial on 7 December 2013.

**Figure 8.**SADFAT result in simulated experiment.

**(a)**MODIS LST images resampled from 1 km to 30 m;

**(b)**SADFAT-derived image at 30 m;

**(c)**up-scaled Landsat ETM+ LST image at 30 m spatial on 7 December 2013.

**Figure 9.**Scatter plots between the predicted and original LSTs at 60 m of the testing experiment on 7 December 2013. x-axis denotes the original LSTs, and y-axis denotes the prediction LSTs.

Indicator | CC | RMSE | AD | AAD |
---|---|---|---|---|

testing experiment | 0.7554 ^{*} | 1.8242 | 1.6354 | 1.6498 |

**significant at 0.001 level (p < 0.001).**

^{*}## 4. Discussion

## 5. Conclusion

## Acknowledgments

## Author Contributions

## Appendix A. Extreme Learning Machine (ELM) Algorithm

**(x**is N, where ${x}_{i}={\left[{x}_{i1},{x}_{i2},\cdots ,{x}_{in}\right]}^{\text{T}}\in {R}^{n}$ and ${t}_{i}={\left[{t}_{i1},{t}_{i2},\cdots ,{t}_{im}\right]}^{\text{T}}\in {R}^{m}$, the standard SLFNs equipped with $\tilde{N}$ hidden neurons and activation function $g\left(x\right)=\mathrm{sig}\left({w}_{i}\cdot {x}_{i}+{b}_{i}\right)$ can be mathematically expressed as:

_{i}, t_{i})_{th}hidden neuron; ${w}_{i}={\left[{w}_{i1},{w}_{i2},\cdots ,{w}_{in}\right]}^{T}$ denotes the weight vector connecting the i

_{th}hidden neuron and the input neurons; ${\beta}_{i}={\left[{\text{\beta}}_{i1},{\text{\beta}}_{\text{i2}}{\text{,L,\beta}}_{im}\right]}^{\text{T}}$ stands for the weight vector connecting the i

_{th}hidden neuron and the output neurons.

## Appendix B. Spatio-Temporal Adaptive Data Fusion Algorithm for Temperature Mapping (SADFAT)

_{1}and t

_{2}, respectively, the changes of radiance of a M pixel between t

_{1}and t

_{2}can be computed as:

_{i}denotes the fraction of each Landsat pixel, t is the acquisition date, and k

_{1}is the coefficient for the relative adjustment for the Landsat and MODIS radiance pixels. Considering the seasonal change of LST based on ATC, and through the Planck’s law, the radiance change of an L pixel from t

_{1}to t

_{2}can be expressed as:

_{th}L pixel at date t

_{1}and t

_{2}are known, the equation can be formulated as Equation (10):

_{th}L pixel to the radiance of the corresponding M pixel is constant for a certain L pixel, which can be quantified as below:

## Conflicts of Interest

## References

- Kalma, J.D.; McVicar, T.R.; McCabe, M.F. Estimating land surface evaporation: A review of methods using remotely sensed surface temperature data. Surveys Geophys.
**2008**, 29, 421–469. [Google Scholar] [CrossRef] - Cammalleri, C.; Anderson, M.; Ciraolo, G.; D’Urso, G.; Kustas, W.; La Loggia, G.; Minacapilli, M. Applications of a remote sensing-based two-source energy balance algorithm for mapping surface fluxes without in situ air temperature observations. Remote Sens. Environ.
**2012**, 124, 502–515. [Google Scholar] [CrossRef] - Srivastava, P.K.; Han, D.; Ramirez, M.R.; Islam, T. Machine learning techniques for downscaling smos satellite soil moisture using modis land surface temperature for hydrological application. Water Resour. Manag.
**2013**, 27, 3127–3144. [Google Scholar] [CrossRef] - Song, X.; Leng, P.; Li, X.; Li, X.; Ma, J. Retrieval of daily evolution of soil moisture from satellite-derived land surface temperature and net surface shortwave radiation. Int. J. Remote Sens.
**2013**, 34, 3289–3298. [Google Scholar] [CrossRef] - Bateni, S.; Entekhabi, D.; Castelli, F. Mapping evaporation and estimation of surface control of evaporation using remotely sensed land surface temperature from a constellation of satellites. Water Resour. Res.
**2013**, 49, 950–968. [Google Scholar] [CrossRef] - Tang, R.; Li, Z.-L.; Jia, Y.; Li, C.; Chen, K.-S.; Sun, X.; Lou, J. Evaluating one-and two-source energy balance models in estimating surface evapotranspiration from Landsat-derived surface temperature and field measurements. Int. J. Remote Sens.
**2013**, 34, 3299–3313. [Google Scholar] [CrossRef] - Anderson, M.; Kustas, W.; Norman, J.; Hain, C.; Mecikalski, J.; Schultz, L.; González-Dugo, M.; Cammalleri, C.; D’Urso, G.; Pimstein, A. Mapping daily evapotranspiration at field to continental scales using geostationary and polar orbiting satellite imagery. Hydrol. Earth Syst. Sci.
**2011**, 15, 223–239. [Google Scholar] [CrossRef] [Green Version] - Wong, M.S.; Nichol, J.E. Spatial variability of frontal area index and its relationship with urban heat island intensity. Int. J. Remote Sens.
**2013**, 34, 885–896. [Google Scholar] [CrossRef] - Weng, Q.; Fu, P. Modeling annual parameters of clear-sky land surface temperature variations and evaluating the impact of cloud cover using time series of landsat tir data. Remote Sens. Environ.
**2014**, 140, 267–278. [Google Scholar] [CrossRef] - Goward, S.N.; Masek, J.G.; Williams, D.L.; Irons, J.R.; Thompson, R. The landsat 7 mission: Terrestrial research and applications for the 21st century. Remote Sens. Environ.
**2001**, 78, 3–12. [Google Scholar] [CrossRef] - Anderson, M.C.; Allen, R.G.; Morse, A.; Kustas, W.P. Use of landsat thermal imagery in monitoring evapotranspiration and managing water resources. Remote Sens. Environ.
**2012**, 122, 50–65. [Google Scholar] [CrossRef] - Almeida, T.; de Souza Filho, C.; Rossetto, R. Aster and landsat ETM+ images applied to sugarcane yield forecast. Int. J. Remote Sens.
**2006**, 27, 4057–4069. [Google Scholar] [CrossRef] - Sameen, M.I.; Al Kubaisy, M.A. Automatic surface temperature mapping in arcgis using landsat-8 tirs and envi tools, case study: Al Habbaniyah Lake. J. Environ. Earth Sci.
**2014**, 4, 12–17. [Google Scholar] - Li, Y.-Y.; Zhang, H.; Kainz, W. Monitoring patterns of urban heat islands of the fast-growing shanghai metropolis, china: Using time-series of landsat tm/etm+ data. Int. J. Appl. Earth Obs. Geoinf.
**2012**, 19, 127–138. [Google Scholar] [CrossRef] - Masek, J.G.; Collatz, G.J. Estimating forest carbon fluxes in a disturbed southeastern landscape: Integration of remote sensing, forest inventory, and biogeochemical modeling. J. Geophys. Res.
**2006**, 111. [Google Scholar] [CrossRef] - Ju, J.; Roy, D.P. The availability of cloud-free landsat ETM+ data over the conterminous united states and globally. Remote Sens. Environ.
**2008**, 112, 1196–1211. [Google Scholar] [CrossRef] - Leckie, D.G. Advances in remote sensing technologies for forest surveys and management. Can. J. For. Res.
**1990**, 20, 464–483. [Google Scholar] [CrossRef] - Justice, C.O.; Vermote, E.; Townshend, J.R.; Defries, R.; Roy, D.P.; Hall, D.K.; Salomonson, V.V.; Privette, J.L.; Riggs, G.; Strahler, A. The moderate resolution imaging spectroradiometer (modis): Land remote sensing for global change research. IEEE Trans. Geosci. Remote Sens.
**1998**, 36, 1228–1249. [Google Scholar] [CrossRef] - Stathopoulou, M.; Cartalis, C. Downscaling avhrr land surface temperatures for improved surface urban heat island intensity estimation. Remote Sens. Environ.
**2009**, 113, 2592–2605. [Google Scholar] [CrossRef] - Pohl, C.; Van Genderen, J. Review article multisensor image fusion in remote sensing: Concepts, methods and applications. Int. J. Remote Sens.
**1998**, 19, 823–854. [Google Scholar] [CrossRef] - Smith, M.I.; Heather, J.P. A review of image fusion technology in 2005. In Defense and Security, 2005; International Society for Optics and Photonics: Bellingham WA, USA, 2005; pp. 29–45. [Google Scholar]
- Ha, W.; Gowda, P.H.; Howell, T.A. A review of potential image fusion methods for remote sensing-based irrigation management: Part II. Irrig. Sci.
**2013**, 31, 851–869. [Google Scholar] [CrossRef] - González-Audícana, M.; Saleta, J.L.; Catalán, R.G.; García, R. Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition. IEEE Trans. Geosci. Remote Sens.
**2004**, 42, 1291–1299. [Google Scholar] [CrossRef] - Naidu, V.; Raol, J. Pixel-level image fusion using wavelets and principal component analysis. Def. Sci. J.
**2008**, 58, 338–352. [Google Scholar] [CrossRef] - Tu, T.-M.; Huang, P.S.; Hung, C.-L.; Chang, C.-P. A fast intensity-hue-saturation fusion technique with spectral adjustment for ikonos imagery. IEEE Geosci. Remote Sens. Lett.
**2004**, 1, 309–312. [Google Scholar] [CrossRef] - Choi, M. A new intensity-hue-saturation fusion approach to image fusion with a tradeoff parameter. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 1672–1682. [Google Scholar] [CrossRef] - Amolins, K.; Zhang, Y.; Dare, P. Wavelet based image fusion techniques—An introduction, review and comparison. ISPRS J. Photogramm. Remote Sens.
**2007**, 62, 249–263. [Google Scholar] [CrossRef] - Zhang, Y.; Hong, G. An ihs and wavelet integrated approach to improve pan-sharpening visual quality of natural colour ikonos and quickbird images. Inf. Fus.
**2005**, 6, 225–234. [Google Scholar] [CrossRef] - Zhan, W.; Chen, Y.; Zhou, J.; Li, J.; Liu, W. Sharpening thermal imageries: A generalized theoretical framework from an assimilation perspective. IEEE Trans. Geosci. Remote Sens.
**2011**, 49, 773–789. [Google Scholar] [CrossRef] - Rodriguez-Galiano, V.; Pardo-Iguzquiza, E.; Sanchez-Castillo, M.; Chica-Olmo, M.; Chica-Rivas, M. Downscaling Landsat 7 ETM+ thermal imagery using land surface temperature and NDVI images. Int. J. Appl. Earth Obs. Geoinf.
**2012**, 18, 515–527. [Google Scholar] [CrossRef] - Rodriguez-Galiano, V.; Ghimire, B.; Pardo-Igúzquiza, E.; Chica-Olmo, M.; Congalton, R. Incorporating the downscaled landsat tm thermal band in land-cover classification using random forest. Photogramm. Eng. Remote Sens.
**2012**, 78, 129–137. [Google Scholar] [CrossRef] - Hong, S.-H.; Hendrickx, J.M.; Borchers, B. Up-scaling of sebal derived evapotranspiration maps from Landsat (30m) to MODIS (250m) scale. J. Hydrol.
**2009**, 370, 122–138. [Google Scholar] [CrossRef] - Jeganathan, C.; Hamm, N.; Mukherjee, S.; Atkinson, P.M.; Raju, P.; Dadhwal, V. Evaluating a thermal image sharpening model over a mixed agricultural landscape in India. Int. J. Appl. Earth Obs. Geoinf.
**2011**, 13, 178–191. [Google Scholar] [CrossRef] - Gao, F.; Masek, J.; Schwaller, M.; Hall, F. On the blending of the Landsat and MODIS surface reflectance: Predicting daily landsat surface reflectance. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 2207–2218. [Google Scholar] [CrossRef] - Zhu, X.; Chen, J.; Gao, F.; Chen, X.; Masek, J.G. An enhanced spatial and temporal adaptive reflectance fusion model for complex heterogeneous regions. Remote Sens. Environ.
**2010**, 114, 2610–2623. [Google Scholar] [CrossRef] - Hilker, T.; Wulder, M.A.; Coops, N.C.; Seitz, N.; White, J.C.; Gao, F.; Masek, J.G.; Stenhouse, G. Generation of dense time series synthetic landsat data through data blending with MODIS using a spatial and temporal adaptive reflectance fusion model. Remote Sens. Environ.
**2009**, 113, 1988–1999. [Google Scholar] [CrossRef] - Roy, D.P.; Ju, J.; Lewis, P.; Schaaf, C.; Gao, F.; Hansen, M.; Lindquist, E. Multi-temporal modis—Landsat data fusion for relative radiometric normalization, gap filling, and prediction of landsat data. Remote Sens. Environ.
**2008**, 112, 3112–3130. [Google Scholar] [CrossRef] - Zurita-Milla, R.; Clevers, J.G.; Schaepman, M.E. Unmixing-based Landsat TM and MERIS FR data fusion. IEEE Geosci. Remote Sens. Lett.
**2008**, 5, 453–457. [Google Scholar] [CrossRef] - Huang, B.; Song, H. Spatiotemporal reflectance fusion via sparse representation. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3707–3716. [Google Scholar] [CrossRef] - Song, H.; Huang, B. Spatiotemporal satellite image fusion through one-pair image learning. IEEE Trans. Geosci. Remote Sens.
**2013**, 51, 1883–1896. [Google Scholar] [CrossRef] - Huang, B.; Wang, J.; Song, H.; Fu, D.; Wong, K. Generating high spatiotemporal resolution land surface temperature for urban heat island monitoring. IEEE Geosci. Remote Sens. Lett.
**2013**, 10, 1011–1015. [Google Scholar] [CrossRef] - Weng, Q.; Fu, P.; Gao, F. Generating daily land surface temperature at landsat resolution by fusing Landsat and MODIS data. Remote Sens. Environ.
**2014**, 145, 55–67. [Google Scholar] [CrossRef] - Huang, G.-B.; Zhou, H.; Ding, X.; Zhang, R. Extreme learning machine for regression and multiclass classification. IEEE Trans. Syst. Man. Cybern. B Cybern.
**2012**, 42, 513–529. [Google Scholar] [CrossRef] [PubMed] - Yao, W.; Han, M. Fusion of thermal infrared and multispectral remote sensing images via neural network regression. J. Image Gr.
**2010**, 15, 1278–1284. [Google Scholar] - Huang, G.-B.; Zhu, Q.-Y.; Siew, C.-K. Extreme learning machine: A new learning scheme of feedforward neural networks. In Proceedings of the 2004 IEEE International Joint Conference on Neural Networks, Budapest, Hungary, 25–29 July 2004; pp. 985–990.
- Jiménez-Muñoz, J.C.; Sobrino, J.A. A generalized single-channel method for retrieving land surface temperature from remote sensing data. J. Geophys. Res.
**2003**, 108. [Google Scholar] [CrossRef] - Wan, Z.; Zhang, Y.; Zhang, Q.; Li, Z.-L. Quality assessment and validation of the MODIS global land surface temperature. Int. J. Remote Sens.
**2004**, 25, 261–274. [Google Scholar] [CrossRef]

© 2015 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 license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bai, Y.; Wong, M.S.; Shi, W.-Z.; Wu, L.-X.; Qin, K.
Advancing of Land Surface Temperature Retrieval Using Extreme Learning Machine and Spatio-Temporal Adaptive Data Fusion Algorithm. *Remote Sens.* **2015**, *7*, 4424-4441.
https://doi.org/10.3390/rs70404424

**AMA Style**

Bai Y, Wong MS, Shi W-Z, Wu L-X, Qin K.
Advancing of Land Surface Temperature Retrieval Using Extreme Learning Machine and Spatio-Temporal Adaptive Data Fusion Algorithm. *Remote Sensing*. 2015; 7(4):4424-4441.
https://doi.org/10.3390/rs70404424

**Chicago/Turabian Style**

Bai, Yang, Man Sing Wong, Wen-Zhong Shi, Li-Xin Wu, and Kai Qin.
2015. "Advancing of Land Surface Temperature Retrieval Using Extreme Learning Machine and Spatio-Temporal Adaptive Data Fusion Algorithm" *Remote Sensing* 7, no. 4: 4424-4441.
https://doi.org/10.3390/rs70404424