# Statistical Investigation of Climate Change Effects on the Utilization of the Sediment Heat Energy

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- (1)
- Is there a correlation between different months vs. the distance from shore in sediment temperature? At what distance is the maximum sediment heat energy production possible?
- (2)
- Can climate change be advantageous for using sediment heat energy?
- (3)
- What are the benefits for using sediment heat energy if weather temperatures become warmer in summer and winter?

## 2. Materials and Methods

#### 2.1. Data Collection Sites, Method, Descriptions and Validations

#### 2.2. General Statistical Analysis Method

- (1)
- Decide specific points of interest;
- (2)
- Formulate several hypotheses;
- (3)
- Design and choose the necessary data and parameters for analyses;
- (4)
- Collect dummy data to form approximate values based on what was expected to be obtained—some of our original data were used as dummy data during this analysis;
- (5)
- Select appropriate tests;
- (6)
- Carry out the test(s) using the dummy data;
- (7)
- If there are problems, go back to step 3 (or 2); otherwise, proceed to use real data;
- (8)
- Carry out the test(s) using the real data and report the findings and/or return to step 2.

## 3. Results

#### 3.1. Summary of Statistics

#### 3.2. Dependency Analysis

_{0}: the population correlation is zero (i.e., there is no linear relationship). The alternative hypothesis is H

_{1}: the population correlation is not zero. If the correlation result is not statistically significant it means the null hypothesis (H

_{0}) is accepted and the alternative hypothesis (H

_{1}) is rejected. If it is statistically significant, then the alternative hypothesis is accepted and the null hypothesis is rejected. Pearson’s correlation is an appropriate analysis for this kind of non-ranked data, but to use Spearman’s rank correlation, the data must be ranked beforehand.

#### 3.3. ARIMA Modeling Forecast

#### 3.4. Validations by Factor Analysis

#### 3.4.1. Validations by Factor Analysis for City of Vaasa at Suvilahti, Ketunkatu Site Data

#### 3.4.2. Validations by Factor Analysis for the Suvilahti, Liito-Oravankatu Site Data

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ARIMA | Autoregression Integrated Moving Average |

DTS | Distributed Temperature Sensing |

FMI | Finnish Meteorological Institute |

ELY-keskus | Center for Economic Development, Transport, and the Environment |

IPCC | Intergovernmental Panel on Climate Change |

Pt100s | The most common Platinum resistance thermometer |

SAS | Statistical Analysis Software (Enterprise Guide 7.1) |

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**Figure 1.**Suvilahti low-energy network sharing heating and cooling for 42 houses (Vaasan Ekolämpö Oy).

**Figure 4.**Summary of statistical data for sediment temperature in degrees Celsius (°C), summarized for whole depths: mean, standard deviation, and median at Suvilahti, Ketunkatu, in the city of Vaasa.

**Figure 5.**Plot showing Pearson’s correlations between August 2013 temperature and distance at Suvilahti, in the city of Vaasa. Ketunkatu (above) and Liito-oravankatu (below). The meaning of p-value = 14E−43 = 14 × 10

^{−43}(below).

**Figure 6.**Plot showing Pearson’s correlations between September 2013 temperature and distance at Suvilahti, in the city of Vaasa. Ketunkatu (above) and Liito-oravankatu (below). The meaning of p-value = 304E−8 = 304 × 10

^{−8}(above). The meaning of p-value = 17E−31 = 17 × 10

^{−31}(below).

**Figure 7.**Plot showing Pearson’s correlation between October 2013 temperature and distance at Suvilahti in the city of Vaasa. Ketunkatu (above) and Liito-oravankatu (below). The meaning of p-value = 674E−8 = 674 × 10

^{−8}(

**above**). The meaning of p-value = 6E−119 = 6 × 10

^{−119}(

**below**).

**Figure 8.**Plot showing Pearson’s correlation between November 2013 temperature and distances at Suvilahti in the city of Vaasa. Ketunkatu (above) and Liito-oravankatu (below). The meaning of p-value = 12E−60 = 12 × 10

^{−60}(

**above**). The meaning of p-value = 1E−116 = 1 × 10

^{−116}(

**below**).

**Figure 9.**Plot showing Pearson’s correlation between December 2013 temperature and distance at the city of Vaasa, Suvilahti. Ketunkatu (above) and Liito-oravankatu (below). The meaning of p-value = 17E−71 = 17 × 10

^{−71}(

**above**). The meaning of p-value = 1E−155 = 1 × 10

^{−155}(

**below**).

**Figure 10.**Scatter plot matrix showing the months of the year in 2013 vs. distance for both sites at Suvilahti in the city of Vaasa. Ketunkatu (

**left**) and Liito-oravankatu (

**right**).

**Figure 11.**ARIMA analysis for the air temperature forecast over time from the Vaasa airport weather station. In the figure -200 = minus 200. (

**a**) shows temperature forecast from 2041 to 2043. (

**b**) shows forecast in air temperature from 2022 to 2044.

**Figure 12.**ARIMA analysis for the snow-depth forecast over time from the Vaasa airport weather station. In the figure − 500 or −1000 = minus 500 or minus 1000. (

**a**) shows forecast in snow depth since 2033 up to 2035. (

**b**) shows forecast in snow depth from 2022 to 2036.

**Figure 13.**ARIMA analysis for the water temperature forecast over time at a different location than the sediment energy location (Eteläinen Kaupunkiselkä 1) near the city of Vaasa. In the figure – 200 = minus 200. (

**a**) shows forecast in water temperature 2041 up to 2043. (

**b**) shows forecast in water temperature from 2022 to 2044.

**Figure 14.**Scree plot (

**a**) Eigenvalue vs. factors and (

**b**) proportion vs. factors: four factors are retained by the PROPORTION criterion.

**Figure 15.**Six score plots built for four factor combinations at the Ketunkatu site. (

**a**) Factor 2 vs. Factor 1. (

**b**) Factor 3 vs. Factor 1. (

**c**) Factor 3 vs. Factor 2. (

**d**) Factor 4 vs. Factor 1. (

**e**) Factor 4 vs. Factor 2. (

**f**) Factor 4 vs. Factor 3.

**Figure 16.**Scree plots (

**a**) Eigenvalue vs. factors and (

**b**) proportion vs. factor: five factors are retained by the PROPORTION criterion.

**Figure 17.**Four score plots built for five factor combinations at the Liito-oravankatu site. (

**a**) Factor 2 vs. Factor 1. (

**b**) Factor 3 vs. Factor 1. (

**c**) Factor 3 vs. Factor 2. (

**d**) Factor 4 vs. Factor 1.

**Figure 18.**Six score plots built for five factor combinations at the Liito-oravankatu site. (

**a**) Factor 4 vs. Factor 2. (

**b**) Factor 4 vs. Factor 3. (

**c**) Factor 5 vs. Factor 1. (

**d**) Factor 5 vs. Factor 2. (

**e**) Factor 5 vs. Factor 3. (

**f**) Factor 5 vs. Factor 4.4. Discussion.

**Table 1.**Pearson’s correlations analysis between different months and increment of depth/distance at Suvilahti, Ketunkatu in the city of Vaasa. The first row shows Pearson’s correlation results, the second row shows statistical significance, and the third row shows the number of samples in each analysis.

Pearson’s Correlation for Month Temperature vs. Distance | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Distance | Distance | Distance | Distance | Distance | Distance | Distance | |||||||

distance | 1 | 14 January | 0.83502 | 14 July | −0.23757 | 15 January | 0.83798 | 15 July | −0.36584 | 16 January | 0.78473 | 16 July | −0.40112 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | ||||||||

297 | 297 | 297 | 297 | 297 | 297 | 297 | |||||||

13 August | −0.06398 | 14 February | 0.85858 | 14 August | −0.4735 | 15 February | 0.84782 | 15 August | −0.45013 | 16 February | 0.82599 | August | −0.36077 |

0.2717 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | |||||||

297 | 297 | 297 | 297 | 297 | 297 | 297 | |||||||

13 September | −0.26751 | 14 March | 0.88269 | 14 September | −0.33784 | 15 March | 0.861 | 15 September | −0.3517 | 16 March | 0.85545 | 3 October 2016 | −0.06442 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | 0.2684 | |||||||

296 | 297 | 297 | 297 | 297 | 297 | 297 | |||||||

13 October | 0.2583 | 14 April | 0.88997 | 14 October | 0.07311 | 14 April | 0.92268 | 15 October | 0.23263 | 16 April | 0.78695 | 26 October 2016 | 0.56589 |

<0.0001 | <0.0001 | 0.209 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | |||||||

296 | 297 | 297 | 297 | 297 | 214 | 297 | |||||||

13 November | 0.77142 | 13 May | 0.36606 | 14 November | 0.67664 | 15 May | 0.60669 | November 15 | 0.66131 | 16 May | 0.58907 | 16 November | 0.78826 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | |||||||

296 | 297 | 297 | 297 | 297 | 297 | 297 | |||||||

13 December | 0.81126 | 14 June | −0.21912 | 14 December | 0.79345 | 15 June | −0.06697 | 15 December | 0.78921 | 16 June | −0.18148 | December 2016 (10 January 2017) | 0.83927 |

<0.0001 | 0.0001 | <0.0001 | 0.2499 | <0.0001 | 0.0017 | <0.0001 | |||||||

296 | 297 | 297 | 297 | 297 | 297 | 297 | |||||||

28 September 2018 | 0.35938 | ||||||||||||

<0.0001 | |||||||||||||

297 |

**Table 2.**Pearson’s correlations analysis between different months of years and increment of depth/distance at Suvilahti, Liito-oravankatu, in the city of Vaasa. The first row shows Pearson’s correlation results, the second row shows statistical significance, and the third row shows the number of samples in each analysis.

Pearson’s Correlation for Month Temperature vs. Distance | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Distance | Distance | Distance | Distance | Distance | Distance | Distance | |||||

distance | 1 | 14 January | 0.83861 | 14 July | 0.66525 | 15 January | 0.94156 | 15 July | −0.61598 | 16 June | 0.62211 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | |||||||

297 | 297 | 297 | 297 | 297 | 297 | ||||||

13 August | −0.68564 | 14 February | 0.91661 | 14 August | −0.91378 | 15 February | 0.95283 | 15 August | −0.38679 | 16 July | −0.88149 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | ||||||

297 | 297 | 297 | 297 | 297 | 297 | ||||||

13 September | 0.60053 | 14 March | 0.9571 | 14 September | 0.56162 | 15 March | 0.94234 | 15 September | 0.70828 | 16 August | 0.66973 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | ||||||

297 | 297 | 297 | 297 | 297 | 297 | ||||||

13 October | 0.9159 | 14 April | 0.93862 | 14 October | 0.92784 | 15 April | 0.96703 | 15 October | 0.93696 | 3 October 2016 | 0.9117 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | ||||||

297 | 297 | 297 | 297 | 297 | 297 | ||||||

13 November | 0.91276 | 14 May | 0.78181 | 14 November | 0.95282 | 15 May | 0.87094 | 15 November | 0.95067 | 26 October 2016 | 0.94707 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | ||||||

297 | 297 | 297 | 297 | 297 | 297 | ||||||

13 December | 0.95347 | 14 June | −0.67468 | 14 December | 0.96502 | 15 June | 0.80705 | 15 December | 0.96568 | 16 November | 0.95512 |

<0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | ||||||

297 | 297 | 297 | 297 | 297 | 297 | ||||||

December 2016 (10 January 2017) | 0.96501 | ||||||||||

<0.0001 | |||||||||||

297 | |||||||||||

28 September 2018 | 0.89186 | ||||||||||

<0.0001 | |||||||||||

297 |

Input Data Type | Raw Data | ||
---|---|---|---|

Number of Records Read | 298 | ||

Number of Records Used | 213 | ||

N for Significance Tests | 213 | ||

Variance Explained by Each Factor | |||

Factor 1 | Factor 2 | Factor 3 | Factor 4 |

27.479995 | 11.382338 | 2.188676 | 0.227792 |

Input Data Type | Raw Data | |||
---|---|---|---|---|

Number of Records Read | 298 | |||

Number of Records Used | 297 | |||

N for Significance Tests | 297 | |||

Variance Explained by Each Factor | ||||

Factor 1 | Factor 2 | Factor 3 | Factor 4 | Factor 5 |

20.390920 | 5.198181 | 3.196084 | 1.759724 | 0.773356 |

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## Share and Cite

**MDPI and ACS Style**

Girgibo, N.; Mäkiranta, A.; Lü, X.; Hiltunen, E.
Statistical Investigation of Climate Change Effects on the Utilization of the Sediment Heat Energy. *Energies* **2022**, *15*, 435.
https://doi.org/10.3390/en15020435

**AMA Style**

Girgibo N, Mäkiranta A, Lü X, Hiltunen E.
Statistical Investigation of Climate Change Effects on the Utilization of the Sediment Heat Energy. *Energies*. 2022; 15(2):435.
https://doi.org/10.3390/en15020435

**Chicago/Turabian Style**

Girgibo, Nebiyu, Anne Mäkiranta, Xiaoshu Lü, and Erkki Hiltunen.
2022. "Statistical Investigation of Climate Change Effects on the Utilization of the Sediment Heat Energy" *Energies* 15, no. 2: 435.
https://doi.org/10.3390/en15020435