# MODIS-Based Estimation of Terrestrial Latent Heat Flux over North America Using Three Machine Learning Algorithms

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## Abstract

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## 1. Introduction

^{2}of 0.717 and a root mean square error of 1.11 mm. Compared with multiple linear regression and the Priestley-Taylor method, the ANN method estimated the most accurate LE with all of the available variables. El-Shafie et al. [24] used ANN models for prediction evapotranspiration in Iran. The results demonstrated that an ANN model predicted daily E with a significant level of accuracy using only the maximum and minimum temperatures successfully. Shrestha and Shukla [25] used SVM for predicting generic crop coefficient (Kc) and crop evapotranspiration (ETc), using a uniquely large dataset from lysimeters for multiple crop-season combinations under plastic mulch conditions. The results showed that the SVM model was superior to the Artificial Neural Network and Relevance Vector Machine models, two data-driven models used in hydrology. Deo et al. [26] used three machine learning algorithms, including Relevance Vector Machine (RVM), Extreme Learning Machine (ELM), and MARS for the prediction of monthly evaporative loss using limited meteorological data from the Amberley weather station in Australia. All three machine learning models performed well, with RVM proving to be the best. They also found that incident solar radiation and air temperatures are the two most influential factors in determining the performance of machine learning algorithms.

^{2}of 0.75. When compared to neural network and multiple regressions, SVM performed better. Adnan et al. [28] developed a model to estimate evapotranspiration with meteorological parameters (temperature, relative humidity, wind speed, and precipitation) using different machine learning techniques. They found that ANN performed better than LLSVM, MARS, and M5Tree models and gave the nearest values as compared with the actual value. Therefore, substantial differences still exist in simulating LE for different machine learning algorithms. Moreover, there is a lack of validating and evaluating different machine learning algorithms for LE estimation at different PFTs over North America.

## 2. Materials and Methods

#### 2.1. Machine Learning Algorithms

#### 2.1.1. Artificial Neural Network

#### 2.1.2. Support Vector Machine

_{n}), and n is the total number of data sets.

#### 2.1.3. Multivariate Adaptive Regression Spline

#### 2.2. Experimental and Simulated Data

#### 2.2.1. Eddy Covariance Observations

_{n}), ground heat flux (G), and LE. We acquired daily data from aggregated half-hourly or hourly data without using additional quality control [38,39,40] and removed the zero values. For the unclosed energy problem, we used the following method that was developed by Twine et al. [41] to correct the LE for all flux towers:

#### 2.2.2. MODIS and MERRA Data

_{n}, RH, Ta, and Ws products with a spatial resolution of 1/2° × 2/3° from MERRA data provided by National Aeronautics and Space Administration (NASA) to evaluate the performance of all the LE algorithms for all the flux tower sites in this study. To match MODIS pixels, we used the method proposed by Zhao et al. [43] which is a spatial interpolation method using a cosine function to interpolate coarse-resolution MERRA data to 1 km

^{2}pixels. Theoretically, this method uses the four MERRA cells surrounding a given pixel to remove sharp changes from one side of a MERRA boundary to the other to improve the accuracy of MERRA data for each 1 km pixel.

#### 2.2.3. Criteria of Evaluation

^{2}); the average deviation of ground-measured LE value and estimated LE value (Bias); and, root mean square error (RMSE) [45,46].

^{2}can be defined as the square of correlation coefficient R. The difference between it and the correlation coefficient is to remove |R| = 0 and 1, as it can prevent an exaggerated interpretation of the correlation coefficient. The closer that R

^{2}is to 1, the more relevant the observations and estimates. The following equation was used to calculated coefficient of determination:

#### 2.2.4. Experimental Setup

_{n}as output variables, and built the ANN/SVM/MARS model. Then, we put the input variables of testing data to the model and got the predicted LE/R

_{n}. To get the predicted LE, we multiplied the results by the R

_{n}of the testing data. Finally, we evaluated the predicted LE with the ground-measured LE of the testing data. Meteorology data including Ta, RH, Ws, and R

_{n}were acquired from EC flux tower sites and MERRA data, respectively.

## 3. Results

#### 3.1. Algorithms Evaluation Based on Specific Site Data

^{2}was very close among the three algorithms, the highest R

^{2}of ANN was 0.81, while the lowest R

^{2}was 0.03 lower than that and each of the three algorithms had a large RMSE greater than 20 W/m

^{2}. Meanwhile, ANN had a lower bias than SVM and MARS. ANN for DBF had the best performance with the highest R

^{2}(0.89/0.88) (p < 0.01) and lower RMSE (14.48/17.17 W/m

^{2}) in comparison to other PFTs for training and validation, respectively. This may be caused by the characteristic of the DBF. Although the R

^{2}of SHR was the lowest among the five PFTs for validation results, the bias and the RMSE of SHR were lower than any other PFTs, with the lowest bias and RMSE reaches of −0.17 and 13.35 W/m

^{2}. For ENF and GRA sites, the lowest RMSE of the estimated LE versus ground observations was approximately 17.74 and 16.14 W/m

^{2}, respectively, and the R

^{2}was approximately less than 0.8. Especially, for GRA sites, the ANN algorithm that was driven by tower-specific meteorological variables and satellite-based NDVI had an absolutely higher R

^{2}and a lower bias and RMSE than the other machine learning algorithms tested.

#### 3.2. Algorithms Evaluation Based on MERRA Data

^{2}, bias, and RMSE of the three algorithms that are driven by MERRA meteorology for five PFTs. The value of R

^{2}was lower and RMSE was higher when compared to the results that are driven by tower-specific meteorology. With similar results being shown in Figure 5, the ANN demonstrated the best performance among the three machine learning algorithms at both the training and validation stages. The biggest difference, however, was that the ANN performed absolutely higher R

^{2}than any of the other algorithms in Figure 7, while the R

^{2}is very close among the three algorithms in Figure 5 for CRO and DBF. Since the only difference in input was meteorology data, the most likely reason that the ANN performed better than than SVM and MARS when using inaccurate input variables (besides MERRA meteorology data being more inaccurate than the tower-specific meteorology data) has to do with the ANN’s own characteristics. As for bias, ANN performed much better than the others, while SVM showed the poorest performance for most PFTs. As for RMSE, results of SVM may be a little better than results of MARS for some PFTs, but on the whole, their performances were similar.

#### 3.3. Mapping of Terrestrial LE Using Three Machine Learning Algorithms

^{2}, appearing on the area with latitudes lower than 20°N. The biggest difference between the three algorithms was the ANN estimated higher LE values on the east coast of the United States and lower LE values in areas of the western United States when compared to the SVM and the MARS, which returned similar results.

## 4. Discussion

#### 4.1. Performance of the Machine Learning Algorithms

^{2}(0.81 and 0.70) (p < 0.01) and lowest RMSE (17.33 and 20.22 W/m

^{2}) in comparison to the SVM and MARS algorithms for tower-specific and MERRA meteorological data, respectively (Figure 9 and Figure 10). The results were consistent with the findings of Lu and Zhuang, 2010, which used remote sensing data from the MODIS, meteorological and eddy flux data, and an ANN technique to develop a daily product for the period of 2004–2005 for the conterminous U.S. [49]. They found that the ANN predicted daily LE well (R

^{2}= 0.52–0.86).

_{n}at high values when compared with ground measurements [49,58]. Recent studies have also revealed errors in MODIS NDVI when compared with ground measurements [49,57].

#### 4.2. Comparison between Different LE Products

^{2}(Figure 11c). The relevant differences between the flux estimations at the Mexican highlands, which are surrounded by Sierra Madre, may be mostly caused by the land surface heterogeneity and the different plant functional types. The PFT of the highlands is mainly grassland, while coastal and southeastern parts are covered with rainforest. The spatial differences among three machine learning algorithms may be mostly caused by different PFTs. The ANN showed higher LE for ENF and DBF, which are mostly located at the coasts of North America. In the center and west of the study area, due to the relatively high elevation and its own geographic and geomorphic conditions, the PFTs mostly contain SHR or GRA, so the ANN yielded lower LE than SVM and MARS. However, the results that are presented by SVM and MARS show no obvious difference for different PFTs.

^{2}in most areas. Given the accuracy of MERRA meteorology data and the MODIS LE product, we can conclude that machine learning algorithms are applicable for terrestrial LE mapping and the inversion results have a relatively small gap when compared to the MODIS LE product.

#### 4.3. Limitations and Recommendations for Future Research

## 5. Conclusions

_{n}as output data to build training models. All three machine learning algorithms proved to be reliable and robust for major land cover types in North America but the ANN algorithm performed better than the SVM and MARS algorithms based on specific site and MERRA data.

^{2}and a lower RMSE than SVM, for other sites, SVM perform a little better than MARS.

^{2}in most areas, and machine learning algorithms performing better at the area where MODIS LE product overestimated LE.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**One-dimensional linear regression with $\epsilon $-insensitive band for the support vector machine (SVM) algorithm.

**Figure 3.**The hinge functions and knot location in the multivariate adaptive regression spline (MARS) model.

**Figure 4.**Location of the 85 eddy covariance flux towers used in this study. INV means the data of this site were used to inverse, TRA means that the data of this site were used for training.

**Figure 5.**Bar graphs of the training and validation statistics (R

^{2}, Bias and root mean square error (RMSE)) of three algorithms driven by tower-specific meteorology for five PFTs at the 85 flux tower site. All R

^{2}values are significant with a 99% confidence.

**Figure 6.**Examples of the eight-day terrestrial latent heat flux (LE) average as measured and estimated using different machine learning algorithms for the different PFTs.

**Figure 7.**Bar graphs of the training and validation statistics (R

^{2}, Bias and RMSE) of three algorithms driven by MERRA meteorology for five PFTs at the 85 flux tower sites. All of the R

^{2}values are significant with a 99% confidence.

**Figure 8.**The map of mean annual terrestrial LE from 2002 to 2004 at a spatial resolution of 0.05° using three machine learning algorithms driven by MERRA meteorology over North America.

**Figure 9.**Comparison of daily LE observations for all 85 flux tower sites and LE estimates using different machine learning algorithms driven by tower-specific meteorology.

**Figure 10.**Comparison of daily LE observations for all 85 flux tower sites and LE estimates using different machine learning algorithms driven by MERRA meteorology.

**Figure 11.**Spatial differences in the average annual terrestrial LE (2002–2004) between three machine learning algorithms. .

**Figure 12.**Spatial differences in the average annual terrestrial LE (2002–2004) between MODIS LE product and LE product using three machine learning algorithms.

**Table 1.**Training and validation statistics for the different algorithms based on specific site. All of the coefficient of determination (R

^{2}) values are significant with a 99% confidence.

R^{2} | Bias (W/m^{2}) | RMSE (W/m^{2}) | |||||
---|---|---|---|---|---|---|---|

PFT | Algorithms | Train | Test | Train | Test | Train | Test |

CRO | ANN | 0.83 | 0.81 | 0.4 | 0.6 | 16.47 | 21.86 |

SVM | 0.83 | 0.8 | −0.54 | 1.1 | 17.92 | 24.37 | |

MARS | 0.81 | 0.78 | 1.15 | 2.7 | 19.23 | 25.38 | |

DBF | ANN | 0.89 | 0.88 | −0.08 | 0.7 | 14.48 | 17.17 |

SVM | 0.89 | 0.84 | 1.19 | 1.6 | 17.25 | 17.91 | |

MARS | 0.88 | 0.85 | −0.8 | −1.6 | 17.15 | 18.19 | |

ENF | ANN | 0.82 | 0.77 | 0.55 | 1.05 | 12.15 | 17.74 |

SVM | 0.83 | 0.72 | −1.35 | −3.47 | 13.69 | 20.02 | |

MARS | 0.81 | 0.72 | −1.88 | −2.36 | 14.63 | 20.05 | |

GRA | ANN | 0.83 | 0.8 | 1.1 | 3.55 | 15.05 | 16.14 |

SVM | 0.84 | 0.62 | 5.3 | 8.37 | 15.81 | 24.76 | |

MARS | 0.83 | 0.6 | 4.12 | 6.35 | 16.45 | 25.39 | |

SHR | ANN | 0.72 | 0.7 | 0.13 | 0.25 | 13.05 | 13.35 |

SVM | 0.7 | 0.64 | −0.08 | −0.17 | 14.24 | 15.22 | |

MARS | 0.67 | 0.6 | 0.2 | −0.71 | 14.78 | 15.95 |

**Table 2.**Training and validation statistics for the different algorithms based on MERRA data. All R

^{2}values are significant with a 99% confidence.

R^{2} | Bias (W/m^{2}) | RMSE (W/m^{2}) | |||||
---|---|---|---|---|---|---|---|

PFT | Algorithms | Train | Test | Train | Test | Train | Test |

CRO | ANN | 0.81 | 0.77 | −0.6 | 1.4 | 23.2 | 25.9 |

SVM | 0.63 | 0.57 | −1.8 | 2.1 | 20.83 | 29.22 | |

MARS | 0.58 | 0.53 | 0.9 | 1.7 | 25.35 | 30.33 | |

DBF | ANN | 0.88 | 0.85 | 1.3 | 2.1 | 13.25 | 17.45 |

SVM | 0.75 | 0.72 | 2.82 | 3.06 | 22.42 | 28.39 | |

MARS | 0.79 | 0.76 | −1.03 | −1.19 | 19.92 | 23.44 | |

ENF | ANN | 0.78 | 0.75 | 1.06 | 2.05 | 13.34 | 16.18 |

SVM | 0.77 | 0.74 | −2.81 | −3.95 | 16.13 | 17.31 | |

MARS | 0.76 | 0.72 | −1.9 | −2.65 | 14.12 | 18 | |

GRA | ANN | 0.73 | 0.67 | −0.35 | 3.75 | 20.85 | 23.3 |

SVM | 0.72 | 0.66 | 5.27 | 6.37 | 21.01 | 23.68 | |

MARS | 0.66 | 0.63 | 4.8 | 5.35 | 21.68 | 24.43 | |

SHR | ANN | 0.69 | 0.65 | 0.22 | 0.61 | 12.08 | 14.85 |

SVM | 0.68 | 0.63 | −1.81 | −1.04 | 11.22 | 15.63 | |

MARS | 0.69 | 0.62 | −0.31 | −1.5 | 16.21 | 17.1 |

© 2017 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**

Wang, X.; Yao, Y.; Zhao, S.; Jia, K.; Zhang, X.; Zhang, Y.; Zhang, L.; Xu, J.; Chen, X. MODIS-Based Estimation of Terrestrial Latent Heat Flux over North America Using Three Machine Learning Algorithms. *Remote Sens.* **2017**, *9*, 1326.
https://doi.org/10.3390/rs9121326

**AMA Style**

Wang X, Yao Y, Zhao S, Jia K, Zhang X, Zhang Y, Zhang L, Xu J, Chen X. MODIS-Based Estimation of Terrestrial Latent Heat Flux over North America Using Three Machine Learning Algorithms. *Remote Sensing*. 2017; 9(12):1326.
https://doi.org/10.3390/rs9121326

**Chicago/Turabian Style**

Wang, Xuanyu, Yunjun Yao, Shaohua Zhao, Kun Jia, Xiaotong Zhang, Yuhu Zhang, Lilin Zhang, Jia Xu, and Xiaowei Chen. 2017. "MODIS-Based Estimation of Terrestrial Latent Heat Flux over North America Using Three Machine Learning Algorithms" *Remote Sensing* 9, no. 12: 1326.
https://doi.org/10.3390/rs9121326