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

^{1}

^{2}

^{3}

^{*}

## 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) |

## References

- Hiltunen, E.; Martinkauppi, J.B.; Mäkiranta, A.; Rinta-Luoma, J.; Syrjälä, T. Seasonal temperature variation in heat collection liquid used in renewable, carbon-free heat production from urban and rural water areas. Agron. Res.
**2015**, 13, 485–493. [Google Scholar] - Likens, G.E.; Johnson, N.M. Measurement and analysis of the annual heat budget for the sediment in two Wisconsin lakes. Limnol. Oceanogr.
**1969**, 14, 115–135. [Google Scholar] [CrossRef] - Oceanography 101 (Miracosta). (15 February 2021). Available online: https://geo.libretexts.org/@go/page/9666 (accessed on 18 July 2021).
- Savola, A. Fluid Flow Modeling Inside Heat Collection Pipes with Finite Element Method. Master’s thesis, University of Vaasa, Vaasa, Finland, 2012. [Google Scholar]
- Mäkiranta, A. Distributed Temperature Sensing Method–Usability in Asphalt and Sediment Heat Measurement. Master’s thesis, University of Vaasa, Vaasa, Finland, 2013. [Google Scholar]
- Ukil, A.; Braendle, H.; Krippner, P. Distributed temperature sensing: Review of technology and applications. IEEE Sens. J.
**2012**, 12, 885–892. [Google Scholar] [CrossRef] [Green Version] - Wilcock, W.S.D.; Kauffman, P.C. Development of a seawater battery for deep-water applications. J. Power Sources
**1997**, 66, 71–75. [Google Scholar] [CrossRef] - Wang, Y.; Liu, D.; Richard, P.; Li, X. A geochemical record of environmental changes in sediments from Sishili Bay, northern Yellow Sea, China: Anthropogenic influence on organic matter sources and composition over the last 100 years. Mar. Pollut. Bull.
**2013**, 77, 227–236. [Google Scholar] [CrossRef] - Reimers, C.R.; Tender, L.M.; Fertig, S.; Wang, W. Harvesting energy from the marine sediment-water interface. Environ. Sci. Technol.
**2001**, 35, 192–195. [Google Scholar] [CrossRef] [PubMed] - Hiltunen, E.; Martinkauppi, J.B.; Zhu, L.; Mäkiranta, A.; Lieskoski, M.; Rinta-Luoma, J. Renewable, carbon-free heat production from urban and rural water areas. J. Clean. Prod.
**2015**, 153, 379–404. [Google Scholar] [CrossRef] - Mäkiranta, A.; Martinkauppi, J.B.; Hiltunen, E. Seabed sediment—A natural seasonal heat storage feasibility study. Agron. Res.
**2017**, 15 (Suppl. S1), 1101–1106. [Google Scholar] - Mäkiranta, A.; Martinkauppi, J.B.; Hiltunen, E. Correlation between temperature of air, heat carrier liquid and seabed sediment in renewable low energy network. Agron. Res.
**2016**, 14 (Suppl. S1), 1191–1199. [Google Scholar] - Mäkiranta, A.; Martinkauppi, B.; Hiltunen, E.; Lieskoski, M. Seabed sediment as an annually renewable heat source. Appl. Sci.
**2018**, 8, 290. [Google Scholar] [CrossRef] [Green Version] - Sebok, E.; Müller, S. The effect of sediment thermal conductivity on vertical groundwater flux estimates. Hydrol. Earth Syst. Sci.
**2019**, 23, 3305–3317. [Google Scholar] [CrossRef] [Green Version] - Goto, S.; Yamano, M.; Morita, S.; Kanamatsu, T.; Hachikubo, A.; Kataoka, S.; Tanahashi, M.; Matsumoto, R. Physical and thermal properties of mud-dominant sediment from the Joetsu Basin in the eastern margin of the Japan Sea. Mar. Geophys. Res.
**2017**, 38, 393–407. [Google Scholar] [CrossRef] [Green Version] - Guo, Y.; Ma, J. Temperature Rise of Seawater Simulation under the Influence of Sediment-Water Heat Exchange. Water
**2018**, 10, 656. [Google Scholar] [CrossRef] [Green Version] - Golosov, S.; Kirillin, G. A parameterized model of heat storage by lake sediments. In Environmental Modeling and Software; Elsevier: Amsterdam, The Netherlands, 2010; Volume 25, pp. 793–801. [Google Scholar] [CrossRef]
- Pivato, M.; Carniello, L.; Gardner, J.; Silvestri, S.; Marani, M. Water and sediment temperature dynamics in shallow tidal environments: The role of the heat flux at the sediment-water interface. Adv. Water Resour.
**2018**, 113, 126–140. [Google Scholar] [CrossRef] - Hamilton, D.P.; Magee, M.R.; Wu, C.H.; Kratz, T.K. Ice cover and thermal regime in a dimictic seepage lake under climate change. Inland Waters
**2018**, 8, 381–398. [Google Scholar] [CrossRef] - Ellis, C.R.; Stefan, H.G.; Gu, R. Water temperature dynamics and heat transfer beneath the ice cover of a lake. Limnol. Oceanogr.
**1991**, 36, 324–335. [Google Scholar] [CrossRef] - Smith, P.N. Observations and simulations of water-sediment heat exchange in a shallow coastal lagoon. Estuaries
**2002**, 25, 483–487. [Google Scholar] [CrossRef] - Tsay, T.-K.; Ruggaber, G.J.; Effler, S.W.; Driscoll, C.T. Thermal Stratification modeling of lakes with sediment heat flux. J. Hydraul. Eng.
**1992**, 118, 407–419. [Google Scholar] [CrossRef] - Meyers, L.S.; Gamst, G.; Guarino, A.J. Data Analysis Using SAS Enterprise Guide; Cambridge University Press: Cambridge, UK, 2009; ISBN -13. [Google Scholar]
- Dytham, C. Choosing and Using Statistics—A Biologist’s Guide, 3rd ed.; John Wiley & Sons: Hoboken, NJ, USA, 2011; ISBN 978-1-4443-2843-1. [Google Scholar]
- IPCC. Climate Change 2021: The Physical Science Basis. In Proceedings of the Contribution of Working Group— I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR6 WGI), 2021. Available online: https://www.ipcc (accessed on 31 July 2021).
- Drucker-Godard, C.; Ehlinger, S.; Grenier, C. Validity and Reliability. In Doing Management Research; SAGE Publication Ltd.: London, UK, 2011; pp. 196–220. [Google Scholar] [CrossRef]
- Kim, T.W.; Cho, Y.K. Calculation of heat flux in a macrotidal flat using FVCOM. J. Geophys. Res. Ocean.
**2011**, 116, 869–881. [Google Scholar] [CrossRef] [Green Version] - Rinehimer, J.P.; Thomson, J.T. Observations and modeling of heat fluxes on tidal flats. J. Geophys. Res. Ocean.
**2014**, 119, 133–146. [Google Scholar] [CrossRef] - Guarini, J.M.; Blanchard, G.F.; Gros, P.; Harrison, S.J. Modelling the mud surface temperature on intertidal flats to investigate the spatio-temporal dynamics of the benthic microalgal photosynthetic capacity. Mar. Ecol. Prog. Ser.
**1997**, 153, 25–36. [Google Scholar] [CrossRef] - Fang, X.; Stefan, H.G. Temperature variability in lake sediments. Water Resour. Res.
**1997**, 34, 717–729. [Google Scholar] [CrossRef]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## 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