# Slope Micrometeorological Analysis and Prediction Based on an ARIMA Model and Data-Fitting System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure of SMMPS

#### 2.1. Slope Micrometeorological Monitoring Module

^{2}.

#### 2.2. Cloud Platform Server

#### 2.2.1. Micrometeorological Analysis System

#### 2.2.2. ARIMA Prediction System

^{2}and typhoons with a wind speed greater than 8 m/s at the slope.

## 3. Experimental Verification

#### 3.1. Project Summary

#### 3.2. System Layout

#### 3.3. Micrometeorological Monitoring Data

#### 3.4. Micrometeorological and Atmospheric Data Fitting

^{2}) was above 0.95, and the air temperature data was above 85%. Therefore, the first-order Fourier was used for fitting; that is, n = 1. The circular frequency ω of the micrometeorological temperature series was about 0.0003868, and the circular frequency ω of the atmospheric temperature data series was about 0.01823, and the goodness of fit R

^{2}was better.

#### 3.5. Prediction Based on ARIMA Time Series

## 4. Discussion

#### 4.1. Meteorological Data Analysis and Siscussion

#### 4.2. Error Analysis of Micrometeorological Fitting System

#### 4.3. Error Analysis of ARIMA Prediction System

## 5. Conclusions

- (1)
- In the early stage, the SMMPS can log into the cloud platform server through the remote computer client to obtain data that had been automatically monitored and uploaded by sensors, which do not need to read the data on site, thereby reducing labor costs.
- (2)
- There was a strong correlation between slope micrometeorological and atmospheric data, but the fluctuation of some slope micrometeorological factors were much lower than those of the atmospheric data due to various environmental factors.
- (3)
- The meteorological fitting system of the SMMPS can establish the relationship between atmospheric meteorological and slope micrometeorological data, so that the slope does not need long-term sensor monitoring. The system can effectively reduce the labor and instrument costs of long-term sensor monitoring, and only need CMDSC data to be input to get the relevant slope micrometeorological data.
- (4)
- The ARIMA prediction module of the SMMPS can accurately predict future slope meteorological data. It can effectively protect the slope from the advent of harsh conditions, such as high temperature and low temperatures, which result in further slope instability or even damage, causing engineering construction delay.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Slope micrometeorological ARIMA model flow chart and judgment formula. Where the lag k refers to the correlation between the observed data with an interval of k time periods. $logL\left(\widehat{\theta}\right)$ is the likelihood function; K is the total number of model parameters; N is the number of observations; $\widehat{{y}_{i}}$ is the model’s predicted value; ${y}_{i}$ is the actual value. The established regression model was evaluated according to the mean absolute error (MAE), mean squared error (MSE) and root mean square error (RMSE).

**Figure 3.**The sensor node in the experimental setup consists of multiple sensors, fixed brackets, wireless communication system and solar energy supply system. The facility is located at Hangzhou Meteorological Station 58,457 (30°14′ N, 120°10′ E). (

**a**) Slope micrometeorological environment monitoring system instrument and local schematic diagram. (

**b**) Slope micrometeorological environment monitoring point layout.

**Figure 4.**The slope was monitored for one year with meteorological data that could not be found in the Hangzhou station atmospheric data. Each image represents a single meteorological unit of monitoring data. From top to bottom are the relative soil moisture, dew point temperature and solar radiation intensity.

**Figure 5.**Atmospheric data from the Hangzhou station were collected for one year and the image was contrasted with the slope micrometeorological data. Each image represents a single meteorological unit of monitoring data. From top to bottom are relative atmospheric humidity, mean atmospheric temperature, instantaneous wind speed, and cumulative rainfall.

**Figure 6.**The data-fitting system of cloud platform server is used to fit the slope micrometeorological temperature monitoring data and atmospheric temperature data, in which the blue curve represents the Fourier function fitting curve, and the black represents each data point. (

**a**) Fitting curve and fitting deviation of slope micrometeorological temperature monitoring data; (

**b**) Fitting curve and fitting deviation of atmospheric temperature monitoring data.

**Figure 7.**The specific process and a series of tests of establishing ARIMA time series monitoring temperature model include ACF, PACF, AIC, BIC and QQ-plot test images.

**Figure 8.**A time-series prediction model for slope air temperature monitoring based on ARIMA model, in which (

**a**) training set data simulation and prediction using machine learning (

**b**) comparison images of actual predicted values and monitored values.

**Table 1.**First-order Fourier function records fitting parameters of micrometeorological slope temperature data and atmospheric temperature data.

First-Order Fourier Fitting Parameters | a | b | c | 𝜔 (Calculate) | ${\mathit{T}}_{\mathit{m}}$ | $\Delta {\mathit{T}}_{\mathit{R}}$ | $\mathit{\phi}$ |
---|---|---|---|---|---|---|---|

Micrometeorological slope temperature data | 24.27 (24.23, 24.32) | 9.165 (9.134, 9.196) | −1.224 (−1.348, −1.1) | 0.000359 | 24.27 | 9.246 | $-$82.39 |

Atmospheric temperature data | 17.93 (17.42, 18.44) | 10.26 (9.712, 10.81) | 1.487 (−0.0174, 0.0190) | 0.01823 | 17.93 | 10.367 | 81.75 |

**Table 2.**Fourier function is used to fit the fitting error between micrometeorological slope temperature data and atmospheric temperature data.

First Order Fourier Fitting Error | SSE | R-Square | RMSE | $\mathit{\omega}\left(\mathbf{Actual}\right)$ |
---|---|---|---|---|

Micrometeorological slope data | 3.297e+04 | 0.9549 | 1.423 | 0.0003868 |

Air data | 3150 | 0.8681 | 2.946 | 0.01823 |

**Table 3.**ARIMA time series model is used to compare the prediction of slope micrometeorological monitoring temperature.

Frequency of Slope Temperature Monitoring | Actual Temperature Monitoring Value (°C) | ARIMA Temperature Prediction Value (°C) | 95% Confidence Interval Maximum Predicted Value (°C) | 95% Confidence Interval Minimum Predicted Value (°C) |
---|---|---|---|---|

15,030 | 32.4 | 32.46 | 32.29 | 32.64 |

15,031 | 32.4 | 32.42 | 32.16 | 32.69 |

15,032 | 32.3 | 32.37 | 32.03 | 32.73 |

15,033 | 32.3 | 32.33 | 31.90 | 32.76 |

15,034 | 32.2 | 32.28 | 31.78 | 32.80 |

…… | …… | …… | …… | …… |

15,052 | 32 | 32.08 | 30.29 | 33.03 |

15,053 | 32.1 | 32.13 | 30.33 | 33.07 |

15,054 | 32.1 | 32.17 | 30.35 | 33.14 |

15,055 | 32.2 | 32.22 | 30.35 | 33.16 |

15,056 | 32.2 | 32.24 | 30.35 | 33.20 |

15,057 | 32.3 | 32.29 | 30.36 | 33.27 |

**Table 4.**ARIMA time series model is used to compare the prediction of slope micrometeorological monitoring temperature.

Slope Micrometeorological to Predict | ARIMA (p,d,q) | MSE | MAE | RMSE | MAPE | D–W |
---|---|---|---|---|---|---|

Prediction of Slope temperature | (7,1,7) | 0.00671 | 0.0611 | 0.082 | 0.00191 | 2.0001 |

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**MDPI and ACS Style**

Liu, D.; Chen, H.; Tang, Y.; Liu, C.; Cao, M.; Gong, C.; Jiang, S.
Slope Micrometeorological Analysis and Prediction Based on an ARIMA Model and Data-Fitting System. *Sensors* **2022**, *22*, 1214.
https://doi.org/10.3390/s22031214

**AMA Style**

Liu D, Chen H, Tang Y, Liu C, Cao M, Gong C, Jiang S.
Slope Micrometeorological Analysis and Prediction Based on an ARIMA Model and Data-Fitting System. *Sensors*. 2022; 22(3):1214.
https://doi.org/10.3390/s22031214

**Chicago/Turabian Style**

Liu, Dunwen, Haofei Chen, Yu Tang, Chao Liu, Min Cao, Chun Gong, and Shulin Jiang.
2022. "Slope Micrometeorological Analysis and Prediction Based on an ARIMA Model and Data-Fitting System" *Sensors* 22, no. 3: 1214.
https://doi.org/10.3390/s22031214