# Embedded Temporal Convolutional Networks for Essential Climate Variables Forecasting

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## Abstract

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## 1. Introduction

- We propose a novel deep learning architecture for forecasting future values which gracefully handles the high-dimensionality of observations.
- We introduce novel datasets of satellite derived geophysical parameters, namely land surface temperature and surface soil moisture, obtained on monthly periodicity over 17.5 years.
- We performed a detailed analysis of both state-of-the-art and proposed deep learning models for the problem of climate variables prediction.

## 2. Related Work

## 3. Materials and Methods

#### 3.1. The E-TCN Framework

#### 3.2. Analysis Ready Dataset

- A set of $28\times 28$ pixel images with per pixel resolution equal to 5 km. These images were acquired from the region in Idaho shown in Figure 2.
- A set of $28\times 28$ pixel images with per pixel resolution equal to 5 km. These images were acquired from the region in Sweden shown in Figure 3.
- A set of $60\times 60$ pixel images with per pixel resolution equal to 1 km. These images were acquired from the region in Sweden shown in Figure 4.
- A set of $140\times 140$ pixel images with per pixel resolution equal to 1 km. These images were acquired from the region in USA shown in Figure 5.

## 4. Results

#### 4.1. Performance Evaluation Metrics

#### 4.2. Ablation Study

#### 4.3. Prediction of Land Surface Temperature at Various Resolutions

#### 4.4. Dependence on the Number of Training Examples

#### 4.5. Impact of Region Size

#### 4.6. Evaluation on Different Time Instances

#### 4.7. Prediction of Soil Moisture

## 5. Discussion

- Higher spatial resolution makes the problem more challenging.
- Prediction of large areas leads to better prediction accuracy.

- E-TCN achieved higher overall performance for both soil moisture and surface temperature.
- E-TCN achieved better performance in term of prediction quality with respect to training set size.
- E-TCN are characterized by a smaller number of parameters, and thus less prone to overfitting.
- E-TCN is a more compact network (in term of network parameters), making it more appealing for real-time/large-scale applications.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The proposed Embedded Temporal Convolutional Network. The square block at the left shows the inner structure of the used residual block.

**Figure 2.**The square shows the area in Sweden from which we obtained land surface temperature in images of $28\times 28$ pixels, with a resolution (per pixel) of 1 km.

**Figure 3.**The square shows the area in Sweden from which we land surface temperature in images of $28\times 28$ pixels, with a resolution (per pixel) of 5 km.

**Figure 4.**The square shows the area in Sweden from which we obtained land surface temperature in images of $60\times 60$ pixels, with resolution (per pixel) of 1 km.

**Figure 5.**The square shows the area in USA from which we obtained our images of $140\times 140$ pixels, with resolution (per pixel) of 1 km.

**Figure 6.**The squares shows the area in Idaho (

**top**) and Arkansas (

**bottom**) from which we obtained soil moisture values, with resolution of 5 km per pixel.

**Figure 7.**PCC as a function of the receptive field (

**top left**), the number of filters in each of the 2D convolutional layers at the encoder part (

**top right**), and the hyperparameter timesteps (

**bottom**).

**Figure 8.**The true values of the daytime land surface temperature in June 2020 as a function of the predicted values when the dataset consisted of 210 images of $28\times 28$ obtained from a region in Sweden with resolution (per pixel) (

**a**) 1 km, (

**b**) 5 km. (

**a**) LST prediction for 1 km spatial resolution. (

**b**) LST prediction for 5 km spatial resolution.

**Figure 12.**PCC for different the timesteps predicted images and the timesteps true images as a function of the last month of the timesteps predicted images.

**Figure 13.**Pearson correlation coefficient between proposed and the state-of-the-art method for LST prediction over different months of 2020.

**Figure 14.**Mean absolute error between proposed and the state-of-the-art method for LST prediction over different months of 2020.

**Figure 16.**The true values of the soil moisture in June 2020 as a function of the predicted values when the dataset consisted of images of $28\times 28$ at 1 km per pixel resolution, obtained from a region in (

**a**) Idaho and (

**b**) Oklahoma. (

**a**) Predictions scatter plot for a region in Ihado. (

**b**) Predictions scatter plot for a region in Oklahoma.

**Table 1.**Table to show the hyperparameters that were chosen for the E-TCN for each of the experiments. W represents the hyperparameter timesteps and Drop., the dropout rate. The third column shows the number of filters at the three 2D convolutional layers in the encoder network.

Case | W | Encoder’s Filters | 2D Conv Kernel | 1D Conv Kernel | TCN | Drop |
---|---|---|---|---|---|---|

1 | 12 | 32, 64 & 64 | (4, 4) | 3 | 3 residual blocks of 64, 49 & 49 filters | 0.3 |

2 | 8 | 48, 48 & 96 | (4, 4) | 2 | 3 residual blocks of 96, 49 & 49 filters | 0.3 |

3 | 12 | 8, 16 & 16 | (6, 6) | 2 | 3 residual blocks of 225, 225 & 225 filters | 0.3 |

4 | 10 | 32, 64 & 64 | (4, 4) | 4 | 3 residual blocks of 64, 49 & 49 filters | 0.3 |

5 | 18 | 32, 64 & 64 | (4, 4) | 4 | 3 residual blocks of 64, 64 & 49 filters | 0.4 |

**Table 2.**Error metrics for the predicted

**land surface temperature**values, number of trainable parameters and training time (in msec per step), when the dataset consisted of images of $28\times 28$ pixels obtained from a region in Sweden. The second column shows the spatial resolution (S.R.) of the dataset.

Model | S.R. | PCC | MSE | ubRMSE | Parameters | Training Time |
---|---|---|---|---|---|---|

E-TCN | 1 km | 0.95 | 0.00091 | 0.0053 | 258,659 | 50–70 |

ConvLSTM | 1 km | 0.90 | 0.00052 | 0.0072 | 446,913 | 430–450 |

E-TCN | 5 km | 0.89 | 0.00038 | 0.0053 | 291,136 | 40–60 |

ConvLSTM | 5 km | 0.82 | 0.00120 | 0.0077 | 366,701 | 340–360 |

**Table 3.**PCC for different number of training images as resulted by using the E-TCN and the ConvLSTM model.

Number of Training Images | PCC (E-TCN) | PCC (ConvLSTM Model) |
---|---|---|

89 | 0.94 | 0.85 |

149 | 0.93 | 0.87 |

209 | 0.95 | 0.90 |

**Table 4.**Error metrics, number of trainable parameters and training time (msec per step) for the dataset consisted of images of $60\times 60$ pixels with 1 km per pixel obtained from a region in Sweden.

Model | PCC | MSE | ubRMSE | Parameters | Training Time |
---|---|---|---|---|---|

E-TCN | 0.85 | 0.000092 | 0.0078 | 926,920 | 100–130 |

ConvLSTM | 0.83 | 0.0032 | 0.012 | 1,087,101 | 2000 |

**Table 5.**The average PCC, MSE and ubRMSE between the predicted values and the ground truth over the 25 predicted images. This table also illustrates the number of trainable parameters and the training time in msec per step both for the E-TCN and the ConvLSTM mode when the dataset consisted of images of $140\times 140$ pixels.

Model | PCC | MSE | unRMSE | Parameters | Training Time |
---|---|---|---|---|---|

E-TCN | 0.78 | 0.0018 | 0.028 | 277,190 | 50–60 |

ConvLSTM | 0.59 | 0.0026 | 0.039 | 446,913 | 350–390 |

Model | PCC | MSE | ubRMSE | Parameters |
---|---|---|---|---|

E-TCN (Idaho) | 0.74 | 0.0062 | 0.0828 | 343,814 |

ConvLSTM (Idaho) | 0.71 | 0.0076 | 0.0669 | 446,913 |

E-TCN (Arkansas) | 0.97 | 0.0431 | 0.0030 | 343,814 |

ConvLSTM (Arkansas) | 0.95 | 0.0738 | 0.0078 | 446,913 |

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## Share and Cite

**MDPI and ACS Style**

Villia, M.M.; Tsagkatakis, G.; Moghaddam, M.; Tsakalides, P. Embedded Temporal Convolutional Networks for Essential Climate Variables Forecasting. *Sensors* **2022**, *22*, 1851.
https://doi.org/10.3390/s22051851

**AMA Style**

Villia MM, Tsagkatakis G, Moghaddam M, Tsakalides P. Embedded Temporal Convolutional Networks for Essential Climate Variables Forecasting. *Sensors*. 2022; 22(5):1851.
https://doi.org/10.3390/s22051851

**Chicago/Turabian Style**

Villia, Maria Myrto, Grigorios Tsagkatakis, Mahta Moghaddam, and Panagiotis Tsakalides. 2022. "Embedded Temporal Convolutional Networks for Essential Climate Variables Forecasting" *Sensors* 22, no. 5: 1851.
https://doi.org/10.3390/s22051851