# Modeling Hourly Soil Temperature Using Deep BiLSTM Neural Network

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}), respectively. Moreover, the method adopted in this study displays a stronger ST prediction ability than the traditional methods under all climate types involved in the experiment, the hourly ST produced by it can be used as a driving parameter for high-resolution biogeochemical models, land surface models and hydrological models and can provide ideas for an analysis of other time series data.

## 1. Introduction

_{2}O, CO, N

_{2}, and CH

_{4}in soil [22,23,24], simulating soil respiration by land surface models [25], and quantifying hydrological and biological processes in hydrological models [26,27]. However, most of the current studies have focused on daily or monthly ST predictions, and hourly ST predictions remain scarce. Third, as a branch of machine learning, deep learning technology performs well in nonlinear data processing, and therefore, has achieved success in predicting the solar radiation [28,29,30], wind speed [31,32,33], and soil moisture [34], whereas studies on ST prediction are relatively few in number.

## 2. Data

## 3. Methodology

#### 3.1. BiLSTM Networks

#### 3.2. Integrated BiLSTM Model

#### 3.3. Benchmark Models

## 4. Results

#### 4.1. Model Comparisons

^{2}generated by every model at each observation, and as the figure indicates, the integrated BiLSTM was the best model with the highest R

^{2}value at each observation station. According to statistics, based on the R

^{2}index, the integrated BiLSTM is 1.3–4.8%, 2.4–8.0%, 5.1–8.3%, 3.2–9.3%, 4.4–45.0%, and 23–57.4% more accurate than LSTM, BiLSTM, DNN, RF, SVR, and LR, respectively. The performance of the LSTM model is slightly better than that of the BiLSTM, and the performance of the LR model is still not ideal. We also noted that the R

^{2}value of the LR is less than zero at the two sites labeled 2218 and 2147, which indicates that LR model is unsuitable for processing data with a nonlinear correlation.

^{2}, it can be clearly seen from Figure 6, Figure 7 and Figure 8 that favorable agreements exist between the results of the RF model and these three deep learning models, and the prediction results at multiple sites are better than DNN, which confirms the potential of using the RF model for an estimation of the hourly ST.

^{2}) are used as the evaluation criteria. From Table 3 and Table 4, we can clearly see that the performance of the integrated BiLSTM model developed in this study showed the best results. For the 30 observation stations involved in the experiment, the RMSE, MAE, and R

^{2}values obtained for the integrated BiLSTM are within the range of 0.95–2.53 °C, 0.76–1.99 °C, and 0.823–0.976, respectively.

^{2}obtained by DNN is 0.613, while the worst R

^{2}of RF is 0.656.

^{2}, and the minimum RMSE and MAE (the best results), with values of 0.923, 1.53 °C, and 1.22 °C, respectively, were obtained using the integrated BiLSTM. By contrast, the minimum R

^{2}, and the maximum RMSE and MAE values, were found to be 0.518, 3.43 °C, and 2.76 °C when using the LR. The integrated BiLSTM, BiLSTM, and LSTM perform better than the DNN, RF, SVR, and LR. DNN is inferior to LSTM-based method in processing time series data. Among the deep learning methods, the integrated BiLSTM method achieves the best prediction results for the hourly ST, whereas within the range of traditional machine learning, the random forest model achieves the best performance.

#### 4.2. Model Performance at Different Depths

^{2}, the integrated BiLSTM models generally show the best performance at all soil depths, and the LSTM model is the second-best prediction algorithm.

^{2}, the accuracy of the integrated BiLSTM model increases from 5 to 20 cm, and decreases from 50 to 100 cm, whereas the R

^{2}values of the other models decrease with an increase in depth. This result differs from the conclusions in [21] and [53], the experimental results of which show that the accuracy of the machine learning algorithm will gradually decrease at a soil depth of 10 to 100 cm. This may be related to the different models used and the different climatic conditions.

#### 4.3. Model Performance at Different Climates

^{2}, respectively. The LR was the worst model, producing the minimum R

^{2}, and the maximum RMSE and MAE, under all climate types involved in the experiment. With respect to the RMSE, the BiLSTM performed slightly better than the integrated BiLSTM under the BWh climate.

^{2}of these five models is the lowest under the Dfa climate type.

#### 4.4. Compared with the Other Literatures

## 5. Conclusions

^{2}, respectively. We compared the prediction results of each algorithm for the ST at different depths, and demonstrated that the integrated BiLSTM developed in this study is better than the benchmark algorithm in terms of ST prediction at the five soil depths involved in the experiment, and has greater potential than the benchmark algorithm in terms of a deeper ST prediction. By comparing the prediction results according to the climate type, it was found that the algorithm proposed in this study performs better than the benchmark algorithm under all climate types involved in the experiment, especially in warm or dry areas.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Correlation coefficients of (x) daily weather parameters and (y) soil temperature (ST) amplitude for different depths.

**Figure 3.**Correlation coefficients of daily average (x) weather parameters and (y) ST for different depths.

**Figure 6.**Performance comparison of forecasting models for 30 sites in terms of root mean squared error (RMSE).

**Figure 7.**Performance comparison of forecasting models for 30 sites in terms of mean absolute error (MAE).

Climate Type | Site id | Elevation (m) | Period | Site id | Elevation (m) | Period |
---|---|---|---|---|---|---|

BSk | 2107 | 1221 | 2011~2019 | 2152 | 1322 | 2010~2019 |

2131 | 1251 | 2011~2019 | 2160 | 1779 | 2010~2019 | |

2132 | 1718 | 2011~2019 | 2169 | 1477 | 2009~2019 | |

2133 | 1558 | 2013~2019 | 2171 | 1595 | 2010~2019 | |

2139 | 2131 | 2011~2019 | ||||

BWh | 2129 | 1526 | 2010~2019 | 2183 | 169 | 2012~2019 |

2140 | 1620 | 2011~2019 | 2185 | 806 | 2012~2019 | |

2158 | 1628 | 2010~2019 | 2186 | 1110 | 2012~2019 | |

Cfa | 2013 | 235 | 2013~2019 | 2083 | 71 | 2011~2019 |

2037 | 37 | 2011~2019 | 2174 | 49 | 2010~2018 | |

2070 | 50 | 2011~2017 | 2177 | 82 | 2015~2017 | |

2076 | 215 | 2011~2019 | ||||

Csa | 2189 | 822 | 2012~2019 | 2218 | 1129 | 2015~2019 |

2215 | 2385 | 2015~2019 | ||||

Dfa | 2014 | 323 | 2010~2019 | 2147 | 336 | 2010~2015 |

2031 | 327 | 2010~2019 | 2196 | 328 | 2013~2019 | |

2042 | 742 | 2010~2014 |

ST Amplitude Forecast Task | Daily Average ST Forecast Task |
---|---|

Hour of the day | Month |

Air Temperature Maximum | Day of the month |

Air Temperature Minimum | Air Temperature Observed |

Wind Speed Average | Air Temperature Maxium |

Solar Radiation Average | Air Temperature Minimum |

Relative Humidity Minimum | Wind Speed Average |

Relative Humidity Maximum | Solar Radiation Average |

Vapor Pressure | Dew Point Temperature |

Relative Humidity Minimum | |

Relative Humidity Maximum | |

Vapor Pressure |

Method | RMSE | MAE | R^{2} | |||
---|---|---|---|---|---|---|

Best | Site id | Best | Site id | Best | Site id | |

Integrated BiLSTM | 0.95 °C | 2042 | 0.76 °C | 2042 | 0.976 | 2171 |

LSTM | 1.22 °C | 2042 | 0.93 °C | 2042 | 0.964 | 2171 |

BiLSTM | 1.29 °C | 2083 | 0.95 °C | 2083 | 0.965 | 2171 |

DNN | 1.22 °C | 2042 | 0.97 °C | 2042 | 0.961 | 2171 |

RF | 1.42 °C | 2042 | 1.07 °C | 2083 | 0.954 | 2171 |

SVR | 1.56 °C | 2013 | 1.24 °C | 2013 | 0.953 | 2183 |

LR | 2.33 °C | 2083 | 1.86 °C | 2083 | 0.906 | 2183 |

Method | RMSE | MAE | R^{2} | |||
---|---|---|---|---|---|---|

Worst | Site id | Worst | Site id | Worst | Site id | |

Integrated BiLSTM | 2.53 °C | 2183 | 1.99 °C | 2183 | 0.823 | 2014 |

LSTM | 3.03 °C | 2183 | 2.44 °C | 2183 | 0.701 | 2014 |

BiLSTM | 3.22 °C | 2183 | 2.55 °C | 2183 | 0.658 | 2218 |

DNN | 3.21 °C | 2028 | 2.80 °C | 2028 | 0.613 | 2014 |

RF | 2.90 °C | 2218 | 2.26 °C | 2218 | 0.656 | 2014 |

SVR | 3.33 °C | 2218 | 2.66 °C | 2218 | 0.388 | 2218 |

LR | 4.87 °C | 2186 | 4.03 °C | 2186 | −0.311 | 2218 |

Method | RMSE(°C) | MAE(°C) | R^{2} |
---|---|---|---|

Integrated BiLSTM | 1.53 | 1.22 | 0.923 |

LSTM | 1.76 | 1.39 | 0.896 |

BiLSTM | 1.85 | 1.44 | 0.882 |

DNN | 1.99 | 1.58 | 0.865 |

RF | 1.92 | 1.49 | 0.874 |

SVR | 2.18 | 1.75 | 0.808 |

LR | 3.43 | 2.76 | 0.518 |

Method | BSk | BWh | Cfa | Csa | Dfa |
---|---|---|---|---|---|

Integrated BiLSTM | 1.56 | 1.82 | 1.34 | 1.63 | 1.25 |

LSTM | 1.86 | 2.09 | 1.51 | 1.92 | 1.44 |

BiLSTM | 1.92 | 1.75 | 1.57 | 2.07 | 1.54 |

DNN | 2.13 | 2.16 | 1.60 | 2.35 | 1.56 |

RF | 2.03 | 2.17 | 1.67 | 2.08 | 1.64 |

SVR | 2.25 | 2.46 | 1.82 | 2.64 | 1.90 |

LR | 3.56 | 3.81 | 2.88 | 4.16 | 3.04 |

Method | BSk | BWh | Cfa | Csa | Dfa |
---|---|---|---|---|---|

integrated BiLSTM | 1.27 | 1.44 | 1.07 | 1.30 | 1.00 |

LSTM | 1.47 | 1.67 | 1.20 | 1.50 | 1.11 |

BiLSTM | 1.50 | 1.74 | 1.22 | 1.57 | 1.19 |

DNN | 1.68 | 1.72 | 1.26 | 1.84 | 1.22 |

RF | 1.58 | 1.69 | 1.30 | 1.61 | 1.26 |

SVR | 1.82 | 2.02 | 1.44 | 2.11 | 1.51 |

LR | 2.86 | 3.09 | 2.29 | 3.30 | 2.48 |

Method | BSk | BWh | Cfa | Csa | Dfa |

Integrated BiLSTM | 0.94 | 0.94 | 0.94 | 0.89 | 0.87 |

LSTM | 0.91 | 0.92 | 0.92 | 0.83 | 0.83 |

BiLSTM | 0.91 | 0.91 | 0.91 | 0.81 | 0.80 |

DNN | 0.89 | 0.92 | 0.90 | 0.78 | 0.77 |

RF | 0.89 | 0.92 | 0.89 | 0.80 | 0.78 |

SVR | 0.86 | 0.88 | 0.87 | 0.56 | 0.67 |

LR | 0.65 | 0.69 | 0.67 | −0.02 | 0.15 |

Soil Depth | Feng’s Research | Our’ Research | ||
---|---|---|---|---|

RMSE | MAE | RMSE | MAE | |

5 cm | 1.85 | 1.44 | 2.04 | 1.63 |

10 cm | 2.05 | 1.6 | 1.69 | 1.34 |

20 cm | 2.47 | 1.91 | 1.55 | 1.44 |

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**MDPI and ACS Style**

Li, C.; Zhang, Y.; Ren, X.
Modeling Hourly Soil Temperature Using Deep BiLSTM Neural Network. *Algorithms* **2020**, *13*, 173.
https://doi.org/10.3390/a13070173

**AMA Style**

Li C, Zhang Y, Ren X.
Modeling Hourly Soil Temperature Using Deep BiLSTM Neural Network. *Algorithms*. 2020; 13(7):173.
https://doi.org/10.3390/a13070173

**Chicago/Turabian Style**

Li, Cong, Yaonan Zhang, and Xupeng Ren.
2020. "Modeling Hourly Soil Temperature Using Deep BiLSTM Neural Network" *Algorithms* 13, no. 7: 173.
https://doi.org/10.3390/a13070173