# Correlation Methodologies between Land Use and Greenhouse Gas emissions: The Case of Pavia Province (Italy)

^{*}

## Abstract

**:**

## 1. Introduction

#### Study Area: Pavia Province

## 2. Materials and Methods

^{®}software, ver. 10.8.2, to calculate Moran’s autocorrelation index and the kernel density. The authors utilize INEMAR CO

_{2}eq. emissions data as the fundamental experimental data, exploring new methods for calculating emissions through four techniques (Spearman, Pearson, Moran, and Kernel). The research aims to simplify the interpretation of spatial data compared to INEMAR algorithms, identifying the relative determinants and correlations between them and emissions.

#### 2.1. Environmental Indicator

_{2}eq. (carbon dioxide equivalent) emissions as an environmental quantitative indicator due to their comparatively lower level of uncertainty when compared with concentrations. In this study, we consider the CO

_{2}equivalent as “CO

_{2}eq.” emissions represent total greenhouse gas emissions, weighted based on their contribution to the greenhouse gas effect. The estimated aggregate GHG emissions are based on Formula (1) [22]:

- CO
_{2}eq.: CO_{2}equivalent emissions in kt/year; - GWPi: “Global Warming Potential”, coefficient IPCC 2014 equal to 1, 0.025, and 0.298, respectively, for CO
_{2}, CH_{4}, and N_{2}O. INEMAR considers a GWP100 (100 years); - Ei: CO
_{2}emissions (in kt/year), CH_{4}, and N_{2}O etc.

#### 2.2. Socio-Demographic Indicators

- Population: Population growth can significantly impact land use. Increasing population can drive up demand for housing, infrastructure, and industrial and commercial areas, leading to urbanization and land consumption.
- Population density: A dense population can exert pressure on agriculture and natural resources, prompting changes in land use such as converting agricultural land into residential or industrial areas.
- GDP (Gross Domestic Product): The GDP of a region can indicate the level of economic and industrial development, thereby affecting land use. For instance, a high GDP may correlate with increased urbanization, infrastructure expansion, and industrialization, resulting in changes like loss of natural habitats or conversion of rural areas into industrial or urban zones.

#### 2.3. Geographic and Territorial Indicators

- Territorial area (sqm);
- Residential area (sqm): including residential buildings and appliances;
- Gross floor area (sqm);
- Settlements area (sqm): industrial, commercial, and craft settlements, farmhouses, quarries, landfills, cemeteries, campsites, technological system, hospital settlements, degraded or obliterated areas and amusement parks;
- Road lines (m): including road networks;
- Arable land (sqm): including rice fields and agriculture;
- Vegetated land (sqm): including woods, meadows, grasslands, and groves.

_{2}emissions, the 5 most emissive municipalities, and the 5 least emissive municipalities of the province of Pavia with relative socio-demographic and geographical data. The data of all municipalities are in Supplementary Materials.

#### 2.4. Analytic Correlation Analysis Output

- Nonparametric/rank: Spearman’s rank correlation coefficient;
- Parametric/linear correlation: Pearson’s correlation coefficient.

#### 2.4.1. Spearman’s Rank Correlation Coefficient

- ${\rho}_{s}$: Spearman’s coefficient;
- di: rank differences;
- n: number of data.

#### 2.4.2. Pearson’ s Correlation Coefficient

- $r$: Pearson’s coefficient;
- $n$: number of data;
- $x$: first variable;
- $\overline{x}:$ mean of the first variable;
- $y$: second variable;
- $\overline{y}:$ mean of the second variable.

- r = 1 is total positive correlation;
- r = −1 is total negative correlation;
- 0.5 < r < 1 means that the two values are completely or perfectly positively correlated, that is, one variable’s value increases as the other variable’s value increases;
- −1 < r < −0.5 means that the two values are perfectly negatively correlated, that is, one variable’s value decreases as the other variable’s value increases;
- r = 0 means that there is no relationship between two variables and indicates that the two variables are not linearly correlated.

#### 2.5. Spatial Correlation Analysis Output

_{2}eq. environmental indicator and a socio-demographic or territorial indicator [35,36].

#### 2.5.1. Moran’s Spatial Autocorrelation Index

- $n$ is the number of spatial units (in our case, municipalities);
- ${x}_{i}$ and ${x}_{j}$ are the values of the variables of interest (e.g., the number of inhabitants or CO
_{2}emissions) for spatial units i and j; - $\overline{x}$ is the mean of the values of the variables across all spatial units;
- ${w}_{ij}$ is the weight associated with the pair of spatial units i and j. These weights represent the spatial connection between the units and can be defined based on geographical proximity.

#### 2.5.2. Kernel Density

- ${\lambda}_{\left(L\right)}$: The intensity of the point distribution, measured at point L;
- ${L}_{\left(i\right)}$: i-th event;
- $k()$: kernel function;
- $\tau $: bandwidth defined as the radius of the circle generated by the intersection of the surface within which the density of the point will be evaluated, with the plane containing the study region R.

## 3. Results

#### 3.1. Analytic Correlation

#### 3.1.1. Spearman Rank Correlation Coefficient

_{2}equivalent and the other indicators obtained the results in Table 2.

_{2}equivalent and the following indicators: population, GDP, territorial area, residential area, GFA (gross floor area), settlements area, road lines, and arable land.

_{2}equivalent to these indicators.

#### 3.1.2. Pearson Correlation Coefficient and Bivariate Map

_{2}equivalent and the other indicators. The data were normalized using various functions, including natural logarithm, square root, reciprocal, inverse of the logarithm, Box–Cox transformation, and Johnson transformation.

_{2}equivalent and the other variables will be exponential, and the equations that link the variables follow Formula (7):

- y: dependent variable;
- x: independent variable;
- ${\beta}_{0}$: the coefficient representing the intercept or the amplitude;
- ${\beta}_{1}$: exponent determining the rate of growth or decay;
- e: the base of the natural logarithm.

_{2}eq. and the socio-demographic and territorial indicators following Formula (7).

_{2}eq. emissions are similar to each other, exhibiting a distinct pattern across the northern and southern parts of the province. In the northern part, where there is an average high value of population density and GDP, there is also a medium–high value of CO

_{2}eq. emissions. Conversely, in the southern part, characterized by an average low value of population density and GDP, there is a medium–low value of CO

_{2}eq. emissions. Generally, areas with a higher population tend to have higher emissions, whereas the distribution of population density appears more random, with a correlation index of 0.38. A cold spot (low density and low emissions) is observed in the south of the province. The municipalities of Pavia, Vigevano, and Voghera, which are more populous, denser, and have higher GDP, are highlighted in red.

_{2}eq., but in the south and east of the province, many municipalities (purple) exhibit a large territorial extension with low CO

_{2}emissions. Regarding residential area, although there is a positive correlation, many municipalities (yellow) show a high rate of emissions compared to residential area. For GFA, the map is more evenly distributed.

#### 3.1.3. Multiple Regression Analysis

- ${\beta}_{0}:$ intercept;
- ${\beta}_{1}:\text{}$inclination of y with respect to variable ${x}_{1}$ holding constant variables ${x}_{2}$,… ${x}_{\mathrm{n}}$;
- ${\beta}_{2}$: inclination of y with respect to variable ${x}_{2}$ holding constant variables ${x}_{1}$, … ${x}_{\mathrm{n}}$.

_{2}eq. present within the province of Pavia without referring to INEMAR algorithms. To verify the effectiveness of this formula, CO

_{2}eq. was calculated based on the indicator values, and the average of the obtained values is equal to the average of the CO

_{2}eq. values provided by INEMAR.

#### 3.2. Spatial Autocorrelation

#### 3.2.1. Moran’s I and Cluster Map

_{2}eq. ratio with each socio-demographic and territorial indicator, at each feature location, is clustered [51] as shown in Table 5. This result is validated by observing the p-values and z-scores. The p-value obtained is less than 0.05 (p < 0.05), rejecting the null hypothesis of randomness and independence in the data values. The z-score obtained is greater than 2.58 (z-score > 2.58) for all three years, indicating less than a 1% probability that the observed model is the result of a stochastic process.

^{®}.

_{2}equivalent values compared to other demographic and territorial indicators, illustrating how these values are grouped or distributed within the province.

- Not Significant: There is no statistical evidence of significant spatial clustering in the data. In other words, there are no obvious spatial patterns that emerge from the analysis.
- High–High Cluster: A cluster of areas with a high CO
_{2}equivalent value and high values of other demographic or territorial indicators. This means that the areas in this cluster have relatively high values for both variables. - High–Low Outliers: Areas with high CO
_{2}equivalent values but low values of other demographic or territorial indicators. - Low–High Outliers: Areas with low CO
_{2}equivalent values but high values of other demographic or territorial indicators. - Low–Low Cluster: A cluster of areas with low CO
_{2}equivalent values and low values of other demographic or territorial indicators. This means that the areas in this cluster have relatively low values for both variables.

_{2}eq./ population mainly highlights two clusters: one LL in the area around the municipality of Pavia and one H-H to the west of the province, with blue municipalities indicating a low level of emissions compared to the population. In the map CO

_{2}eq./ density, two main clusters are evident: one LL to the east and one H-H to the west of the province, with red municipalities indicating a high CO

_{2}value compared to the population density. In the map CO

_{2}eq./ GDP, mainly two clusters are highlighted: one LL to the east and one H-H to the west of the province. The map CO

_{2}eq./ territorial area shows an L-L cluster south of the province where the municipalities have fewer emissions than the territorial area, possibly due to the large presence of vegetation and the low presence of industrial settlements. In the maps CO

_{2}eq./ residential area and CO

_{2}eq./ GFA, two types of clusters are primarily identified: the cluster containing the municipalities LL and HL to the south of the province and the cluster containing the municipalities H-H and L-H to the west. In Figure 3b, the map CO

_{2}eq. highlights the relevant cluster to the west containing the municipalities H-H due to the large presence of industrial settlements in the area. In the map CO

_{2}eq./ road, the low level of roads in the southern part of the province is evident.

#### 3.2.2. Kernel Density

^{®}, as shown in Figure 4a,b, provides a visual representation of the spatial distribution of point data, allowing for the identification and analysis of clusters or areas of high density of certain phenomena [40] within the province of Pavia. From the images, it can be noted that higher values are concentrated in the northeast area of the province, while lower values are in the south.

## 4. Discussion

_{2}equivalent, and the key socio-demographic and territorial indicators in the province of Pavia. It recognizes the critical importance of understanding these dynamics for effective environmental and spatial management strategies. The complex interaction between emissions and changes in land use is crucial for mitigating their impacts on ecosystems and ensuring the long-term sustainability of human societies. The methods of analytic correlation and spatial autocorrelation highlight the positive correlation between GHG emissions (in terms of CO

_{2}equivalent) and land use (in terms of socio-demographic and geographic and territorial indicators). Linear correlation is based on a direct linear relationship, while spatial correlation focuses on the spatial distribution of the data. The Spearman rank correlation coefficient reveals a significant non-linear correlation between CO

_{2}equivalent emissions and several indicators, underscoring the diverse nature of the relationship. Moreover, the subsequent normalization of the data and recalculated Pearson correlation coefficients confirm the presence of exponential relationships, emphasizing the need for a nuanced understanding and modeling of these interactions. Spatial autocorrelation analysis using Moran’s index highlights a positive autocorrelation/clustering of high emissions areas, spatial heterogeneity, and localized hotspots of emissive areas. Figure 5 shows analogies and differences between the methods used in the paper.

## 5. Conclusions

- To forecast emissions based on planning choices, which may concern the distribution of different urban functions within a municipality or the entire province under study.
- To identify areas that require further investigation, especially those elements that represent uniqueness and particular elements (L-L and H-H). This helps to highlight elements of punctual criticality that necessitate further examination.
- With these simplified formulas, it is possible to upscale to the whole national/regional territory. This allows for a first verification to validate the predicted results using the formulas in Table 4 on page 9 and to see if the study can be generalized to other territories outside the Italian context and then to other contexts around the world.
- The simplification of some algorithms that are otherwise very complex and require years of work is important for understanding the order of magnitude of the phenomena observed, particularly the emissions of greenhouse gases. These emissions are important worldwide mainly for macro values and not so much in specific detail, which is measured very precisely by INEMAR, which is the scientific data.

## Supplementary Materials

_{2}eq., population, population density, GDP, territorial area residential area, GFA, settlements area, 3 road lines, arable land, vegetated land data of municipalities in Pavia Province.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Bivariate map CO

_{2}eq. and population–population density–GDP–territorial area–residential area–GFA. (

**b**) Bivariate map CO

_{2}eq. and settlements area–road lines–arable land–vegetated land.

**Figure 3.**(

**a**) Clustered map ratio between CO

_{2}eq. and population–population density–GDP–territorial area. (

**b**) Clustered map ratio between CO

_{2}eq. and residential area–GFA–settlements area–road lines–arable land–vegetated land.

**Figure 4.**(

**a**) Kernel density map ratio between CO

_{2}eq. and population–population density–GDP–territorial area–residential area–GFA. (

**b**) Kernell density map ratio between CO

_{2}eq. and settlements area–road lines–arable land–vegetated land.

**Figure 5.**Analogies and differences between Pearson’s correlation, Spearman’s rank correlation, Moran’s spatial autocorrelation, and Kernel density.

Municipality | CO_{2}eq. [kt/year] | Population [inhab.] | Population Density [inhab./sqkm] | GDP [EUR] | Territorial Area [sqkm] | Residential Area [sqm] | GFA [mq] | Settlements Area [sqm] | Road Lines [m] | Arable Land [sqm] | Vegetated Area [sqm] |
---|---|---|---|---|---|---|---|---|---|---|---|

Ferrera Erbognone | 2870 | 1171 | 59.9 | 15,442,841.00 | 19.17 | 517,337 | 667,532 | 2,438,116 | 43,778 | 14,728,155 | 1,295,014 |

Sannazzaro de’ Burgondi | 2245 | 5533 | 237.3 | 77,957,469.00 | 23.33 | 1,385,716 | 1,429,065 | 2,120,149 | 78,233 | 16,561,204 | 1,886,223 |

Voghera | 886 | 39,356 | 621.9 | 637,341,042.00 | 63.44 | 7,261,991 | 6,785,758 | 3,556,511 | 274,498 | 48,037,718 | 2,467,872 |

Pavia | 351 | 71,297 | 1134.2 | 1,502,659,302.00 | 63.25 | 8,983,402 | 10,776,269 | 4,734,546 | 346,757 | 38,550,845 | 7,294,540 |

Vigevano | 287 | 63,268 | 768 | 970,129,252.00 | 81.36 | 10,876,712 | 8,962,370 | 4,413,324 | 434,552 | 43,620,466 | 18,250,505 |

Verretto | 2 | 402 | 147.3 | 4,957,052.00 | 2.71 | 194,653 | 96,498 | 128,278 | 11,439 | 2,031,408 | 327,641 |

Golferenzo | 2 | 196 | 45.1 | 2,804,711.00 | 4.42 | 224,208 | 91,058 | 20,452 | 27,638 | 2,992,303 | 1,118,606 |

Rea | 1.5 | 431 | 145.6 | 5,745,015.00 | 2.16 | 202,116 | 163,207 | 83,606 | 12,558 | 1,313,383 | 234,622 |

Lirio | 1.56 | 130 | 75.1 | 1,324,318.00 | 1.75 | 130,811 | 59,931 | 22,973 | 11,928 | 1,347,821 | 193,722 |

Calvignano | 1 | 127 | 18.4 | 1,206,421.00 | 6.98 | 209,447 | 667,532 | 17,173 | 27,830 | 4,600,624 | 1,962,481 |

**Table 2.**Spearman rank correlation coefficient between environmental, socio-demographic, and territorial indicators in the province of Pavia.

Correlation | Population [inhab.] | Population Density [inhab/sqkm] | GDP [EUR] | Territorial Area [sqkm] | Residential Area [sqkm] | GFA [sqm] | Settlements Area [sqm] | Road Lines [m] | Arable Land [sqm] | Vegetated Land [sqm] |
---|---|---|---|---|---|---|---|---|---|---|

CO_{2}eq. | 0.750 | 0.383 | 0.727 | 0.631 | 0.713 | 0.779 | 0.790 | 0.488 | 0.760 | 0.241 |

**Table 3.**Pearson correlation coefficient between environmental, socio-demographic, and territorial indicators in the province of Pavia.

Correlation | Population [inhabitants] | Population Density [inhab/skmq] | GDP [EUR] | Territorial Area [kmq] | Residential Area [mq] | GFA [mq] | Settlements Area [mq] | Road Lines [m] | Arable Land [mq] | Vegetated Land [mq] |
---|---|---|---|---|---|---|---|---|---|---|

CO_{2}eq. | 0.726 | 0.396 | 0.704 | 0.614 | 0.634 | 0.773 | 0.782 | 0.504 | 0.707 | 0.194 |

Dependent Variable y | Independent Variable x | Equation |
---|---|---|

CO_{2}eq. | Population | ${CO}_{2}eq.={e}^{-2.45}\times Pop{lation}^{0.73}$ |

GDP | ${CO}_{2}eq.={e}^{-8.08}{\times GDP}^{0.65}$ | |

Territorial Area | ${CO}_{2}eq.={e}^{-0.26}{\times TerritorialArea}^{0.99}$ | |

Residential Area | ${CO}_{2}eq.={e}^{-8.56}{\times ResidentialArea}^{0.85}$ | |

GFA | ${CO}_{2}eq.={e}^{-9.36}{\times GFA}^{0.95}$ | |

Settlements Area | ${CO}_{2}eq.={e}^{-6.01}{\times SettlementsArea}^{0.72}$ | |

Road Lines | ${CO}_{2}eq.={e}^{-4.86}{\times RoadLines}^{0.72}$ | |

Arable Land | ${CO}_{2}eq.={e}^{-16.12}{\times Arableland}^{1.18}$ | |

Vegetated land | ${CO}_{2}eq.={e}^{0.44}{\times Vegetatedland}^{0.17}$ |

**Table 5.**Moran’s Index between ratio between CO

_{2}eq. and socio-demographic and territorial indicators in the province of Pavia.

Correlation | CO_{2}eq./Population | CO_{2}eq./Population Density | CO_{2}eq./GDP | CO_{2}eq./Territorial Area | CO_{2}eq./Residential Area | CO_{2}eq./GFA | CO_{2}eq./Settlement Area | CO_{2}eq./Road Lines | CO_{2}eq./Arable Land | Co_{2}eq./Vegetated Land |
---|---|---|---|---|---|---|---|---|---|---|

Moran I | 0.726 | 0.396 | 0.704 | 0.614 | 0.634 | 0.773 | 0.782 | 0.504 | 0.707 | 0.194 |

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**MDPI and ACS Style**

De Lotto, R.; Bellati, R.; Moretti, M.
Correlation Methodologies between Land Use and Greenhouse Gas emissions: The Case of Pavia Province (Italy). *Air* **2024**, *2*, 86-108.
https://doi.org/10.3390/air2020006

**AMA Style**

De Lotto R, Bellati R, Moretti M.
Correlation Methodologies between Land Use and Greenhouse Gas emissions: The Case of Pavia Province (Italy). *Air*. 2024; 2(2):86-108.
https://doi.org/10.3390/air2020006

**Chicago/Turabian Style**

De Lotto, Roberto, Riccardo Bellati, and Marilisa Moretti.
2024. "Correlation Methodologies between Land Use and Greenhouse Gas emissions: The Case of Pavia Province (Italy)" *Air* 2, no. 2: 86-108.
https://doi.org/10.3390/air2020006