# Analysis of the Air Quality of the Basque Autonomous Community Using Spatial Interpolation

^{1}

^{2}

^{3}

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^{5}

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^{†}

## Abstract

**:**

## 1. Introduction

#### Normative

## 2. Methodology

#### 2.1. Analyzed Area

#### 2.2. Data

#### 2.3. Analysis

## 3. Theoretical Framework

## 4. Statistical Analysis

## 5. Semivariogram Analysis

## 6. Estimations

#### 6.1. Estimation of Pollutant PM${}_{10}$

^{3}). The parameters of the process and the results are presented in Table 7. The map generated by simple kriging can be seen in Figure 16.

_{10}were generated from 43 measurements. A reduction of the standard deviation of this pollutant is observed, which is a feature of the estimation method as it tends to smooth the data. Given the great extension of the Basque Country and considering the number of observations of the variable under study, the estimated value is equal to or very close to the global mean in all sectors without monitoring stations. The total mean value of the estimate is equal to the statistical mean of the 43 observations, and the change in shape of the histogram is consequence of the over-influence of this position statistic that simple kriging incorporates, Figure 17. The statistics obtained after applying simple kriging can be seen in Table 8.

#### 6.2. Estimation of Pollutant NO${}_{x}$

## 7. Model Validation

## 8. Conclusions

^{a}Diaz de Haro, one of the busiest points in the community. The PM${}_{10}$ high values of Gipuzkoa correspond to the stations of Easo and Ategorrieta (stations in the center of Donostia), and Beasain, a smaller municipality but with an important industrial network, located on the axis of the A-1 motorway, which is a road with heavy traffic. Therefore, anomalous values may be due to traffic, one of the anthropogenic sources that generates the majority of PM${}_{10}$ and NO${}_{x}$ emissions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PM | Particulate Matter |

SK | Simple Kriging |

RBF | Radial Basis Functions |

MLR | Multiple Linear Regression |

SD | Standard Deviation |

ETRS89 | European Terrestrial Reference System 1989 |

RMSE | Root Mean Square Error |

RRMSE | Relative Root Mean Square Error |

## References

- Torres Silva, H. Magnetite as environmental pollution and its incidence on smartphones. DYNA
**2018**, 93, 136. [Google Scholar] [CrossRef] - Urrutia, K.; Stendorf, S.; Molina, P.; Flores, I. Smart zero carbon city: Key factors towards smart urban decarbonization. DYNA
**2019**, 94, 676–683. [Google Scholar] [CrossRef][Green Version] - Valle, L.; Grima, C.; Rodríguez, R.; Llopis, C. Experimental device to evaluate mineral trapping in sandstones as a means of supercritical CO2 (scCO2) storage. DYNA
**2019**, 94, 614–619. [Google Scholar] [CrossRef] - European Environmental Agency. Air Quality in Europe: 2018 Report; Publications Office of the European Union: Luxembourg, 2018. [Google Scholar]
- Gibb, A.G.F.; Pavitt, T.C.; McKay, L.J. Designing for health and safety in cladding installation—Implications from pre-assembly. In Proceedings of the International Conference on Building Envelope Systems and Technologies (ICBEST 2004), Sydney, Australia, 30 March–2 April 2004; pp. 1–7. [Google Scholar]
- DIRECTIVA 2008/50/CE del Parlamento Europeo y del Consejo, de 21 de Mayo de 2008, Relativa a la Calidad del Aire Ambiente y a una Atmósfera Más Limpia en Europa. Available online: https://eur-lex.europa.eu/legal-content/ES/TXT/?uri=CELEX%3A32008L0050 (accessed on 6 April 2020).
- Eustat. Municipal Population Statistics (01/01//2019). Available online: www.eustat.eus (accessed on 6 April 2020).
- Open Data website of the Basque Government. Available online: https://opendata.euskadi.eus/inicio/ (accessed on 6 April 2020).
- Diggle, P.J.; Ribeiro, P.J. Model-Based Geostatistics; Springer Series in Statistics; Springer: New York, NY, USA, 2007. [Google Scholar]
- Matheron, G. Principles of geostatistics. Econ. Geol.
**1963**, 58, 1246–1266. [Google Scholar] [CrossRef] - Matheron, G. The theory of regionalized variables and its applications. In Les Cahiers du Centre de Morphologie Mathematique de Fontainebleu; École Nationale Supérieure des Mines de Paris: Paris, France, 1971. [Google Scholar]
- Zhou, F.; Huai-Cheng, G.; Yun-Shan, H.; Chao-Zhong, W. Scientometric analysis of geostatistics using multivariate methods. Scientometrics
**2007**, 73, 265–279. [Google Scholar] [CrossRef] - Sinclair, A.J.; Blackwell, G.H. Applied Mineral Inventory Estimation; Cambridge University Press: Cambridge, UK, 2002. [Google Scholar]
- Hohn, M.E. Geostatistics and Petroleum Geology; Springer: Boston, MA, USA, 1988. [Google Scholar]
- Hardy, L.R. Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res.
**1971**, 76, 1905–1915. [Google Scholar] [CrossRef] - Buhmann, M.D. Radial basis function. Acta Numer.
**2000**, 9, 1–38. [Google Scholar] [CrossRef][Green Version] - Elsayed, K.; Lacor, C. Robust parameter design optimization using Kriging, RBF and RBFNN with gradient-based and evolutionary optimization techniques. Appl. Math. Comput.
**2014**, 236, 325–344. [Google Scholar] [CrossRef] - Buhmann, M.D. Radial Basis Functions—Theory and Implementations; Cambridge University Press: Cambridge, UK, 2003. [Google Scholar]
- Guttman, H.M. A radial basis function method for global optimization. J. Glob. Optim.
**2001**, 19, 201–227. [Google Scholar] [CrossRef] - Watson, G.S. Smoothing and interpolation by kriging and with splines. J. Int. Assoc. Math. Geol.
**1984**, 16, 601–615. [Google Scholar] [CrossRef] - Myers, D.E. Interpolation with positive definite functions. Sci. Terre
**1988**, 28, 252–265. [Google Scholar] - Cressie, N. Geostatistics. Am. Stat.
**1989**, 43, 197–202. [Google Scholar] - Simón: Si Tenemos una Alta Inmunidad, Perfecto, Pero la Probabilidad de que la Tengamos es Baja. 2020. Available online: https://www.abc.es/sociedad/abci-simon-si-tenemos-alta-inmunidad-perfecto-pero-probabilidad-tengamos-baja-202005031221_noticia.html (accessed on 11 May 2020).

**Figure 10.**Experimental semivariogram of PM${}_{10}$ in the Basque Country (in 10,000 m the horizontal axis).

**Figure 11.**Fit nested structural model of PM${}_{10}$ in each province (in 10,000 m the horizontal axis).

**Figure 12.**Fit nested structural model of PM${}_{10}$ in the Basque Country (in 10,000 m the horizontal axis).

**Figure 14.**Experimental semivariogram of NO${}_{x}$ in each province (in 10,000 m the horizontal axis).

**Figure 15.**Experimental semivariogram and pure nugget effect model of NO${}_{x}$ in the Basque Country (in 10,000 m the horizontal axis).

**Figure 16.**PM${}_{10}$ map in the Basque Country generated by simple kriging (in 10,000 m both axes).

**Figure 18.**Map of the PM${}_{10}$ variance (${\sigma}^{2}$(PM${}_{10}$)) in the Basque Country generated by simple kriging (in 10,000 m both axes).

**Figure 19.**PM${}_{10}$ map in the Basque Country generated by linear-type RBF (in 10,000 m both axes).

**Figure 21.**NO${}_{x}$ map in the Basque Country generated by linear-type RBF (in 10,000 m in both axes).

**Figure 25.**NO map in the Basque Country generated by using the simple linear regression model from NO${}_{x}$ (in 10,000 m in both axes).

**Figure 26.**NO${}_{2}$ map in the Basque Country generated by using the simple linear regression model from NO${}_{x}$ (in 10,000 m in both axes).

Pollutant | Average | Limit Value | Alarm Threshold | Compliance Date |
---|---|---|---|---|

NO${}_{2}$ | Hourly | 200 $\mathsf{\mu}$g/m${}^{3}$ | 400 μg/m^{3} (during 3 h) | 1 January 2010 |

(18 greater values maximum per year) | ||||

Annual | 40 μg/m^{3} | 1 January 2010 | ||

PM${}_{10}$ | Daily | 50 $\mathsf{\mu}$g/m${}^{3}$ | 400 μg/m^{3} (during 3 h) | 1 January 2005 |

(35 greater values maximum per year) | ||||

Annual | 40 $\mathsf{\mu}$g/m${}^{3}$ | 1 January 2005 |

Pollutant | Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. |
---|---|---|---|---|---|---|---|---|

NO (μg/m^{3}) | 20 | 6.73 | 4.30 | 0.75 | 3.32 | 6.77 | 8.42 | 20.25 |

NO${}_{2}$ (μg/m^{3}) | 20 | 17.71 | 7.66 | 4.04 | 11.17 | 17.72 | 23.00 | 35.59 |

NO${}_{x}$ (μg/m^{3}) | 20 | 27.90 | 13.87 | 5.42 | 15.28 | 28.19 | 34.66 | 66.40 |

PM_{10} (μg/m^{3}) | 20 | 15.85 | 3.60 | 10.51 | 12.65 | 15.75 | 18.26 | 22.01 |

Pollutant | Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. |
---|---|---|---|---|---|---|---|---|

NO (μg/m^{3}) | 16 | 7.74 | 4.76 | 1.11 | 3.44 | 8.20 | 9.32 | 19.20 |

NO${}_{2}$ (μg/m^{3}) | 16 | 17.47 | 6.80 | 3.24 | 12.11 | 18.10 | 22.39 | 28.61 |

NO${}_{x}$ (μg/m^{3}) | 16 | 29.21 | 13.73 | 5.09 | 17.51 | 30.17 | 37.02 | 57.88 |

PM${}_{10}$ (μg/m^{3}) | 16 | 15.68 | 3.70 | 11.41 | 13.29 | 15.08 | 16.38 | 23.05 |

Pollutant | Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. |
---|---|---|---|---|---|---|---|---|

NO (μg/m^{3}) | 7 | 4.96 | 3.44 | 0.77 | 2.28 | 4.48 | 8.05 | 8.78 |

NO${}_{2}$ (μg/m^{3}) | 7 | 13.29 | 7.77 | 2.36 | 7.77 | 13.28 | 20.32 | 21.25 |

NO${}_{x}$ (μg/m^{3}) | 7 | 20.95 | 12.79 | 4.03 | 11.93 | 19.05 | 32.62 | 34.49 |

PM${}_{10}$ (μg/m^{3}) | 7 | 12.93 | 2.33 | 8.80 | 12.08 | 13.52 | 14.06 | 15.94 |

Pollutant | Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. |
---|---|---|---|---|---|---|---|---|

NO (μg/m^{3}) | 43 | 6.82 | 4.36 | 0.75 | 3.34 | 7.35 | 8.75 | 20.25 |

NO${}_{2}$ (μg/m^{3}) | 43 | 16.90 | 7.37 | 2.36 | 11.16 | 17.40 | 21.69 | 35.59 |

NO${}_{x}$ (μg/m^{3}) | 43 | 27.26 | 13.64 | 4.03 | 16.25 | 29.10 | 34.48 | 66.40 |

PM${}_{10}$ (μg/m^{3}) | 43 | 15.31 | 3.56 | 8.80 | 12.63 | 14.58 | 16.79 | 23.05 |

Parameter | Value | Unit of Measurement |
---|---|---|

X coordinate in the origin | 459,500 | meters (m) |

Y coordinate in the origin | 4,697,700 | meters (m) |

Cell width in X | 1000 | meters (m) |

Cell width in Y | 1000 | meters (m) |

Number of cells in X | 145 | unities |

Number of cells in Y | 125 | unities |

Total number of cells | 18,125 | unities |

Parameter | Value |
---|---|

Influence ratio | 6 |

Minimmum number of samples | 1 |

Maximum number of samples | 21 |

Semivariogram fitting model | $\gamma \left(h\right)=4.4+9\left(\right)open="("\; close=")">1-exp(-h)$ |

Global mean | 15.31 |

**Table 8.**Descriptive statistics of PM${}_{10}$ in the Basque Country after simple kriging application.

Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. | |
---|---|---|---|---|---|---|---|---|

${Z}^{*}$(PM${}_{10}$) | 7228 | 15.31 | 0.27 | 13.49 | 15.26 | 15.31 | 15.34 | 17.70 |

${\sigma}^{2}$(PM${}_{10}$) | 7228 | 13.30 | 0.25 | 11.38 | 13.33 | 13.39 | 13.40 | 13.40 |

**Table 9.**Descriptive statistics of PM${}_{10}$ in the Basque Country after linear-type RBF application.

Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. | |
---|---|---|---|---|---|---|---|---|

${Z}^{*}$(PM${}_{10}$) | 7228 | 14.85 | 2.81 | 8.86 | 12.93 | 14.38 | 16.23 | 26.75 |

**Table 10.**Form relative statistics of PM${}_{10}$ in the Basque Country after linear-type RBF application.

Sampled Values | Values Estimated by RBF | Difference | |
---|---|---|---|

Bias factor | 0.64 | 1.05 | 0.41 |

Kurtosis | −0.32 | 1.62 | 1.94 |

**Table 11.**Descriptive statistics of NO${}_{x}$ in the Basque Country after linear-type RBF application.

Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. | |
---|---|---|---|---|---|---|---|---|

${Z}^{*}$(NO${}_{x}$) | 7228 | 23.85 | 10.35 | 3.86 | 15.62 | 23.29 | 31.72 | 63.12 |

**Table 12.**Form relative statistics of NO${}_{x}$ in the Basque Country after linear-type RBF application.

Sampled Values | Values Estimated by RBF | Difference | |
---|---|---|---|

Bias factor | 0.49 | 0.42 | 0.20 |

Kurtosis | 0.55 | −0.36 | 0.19 |

**Table 13.**Cross-validation subjected statistics of PM${}_{10}$ and NO${}_{x}$, linear-type RBF model.

Pollutant | Count | Mean | SD | Min. | Q1 | Q2 | Q3 | Max. |
---|---|---|---|---|---|---|---|---|

PM${}_{10}$ | 43 | 15.31 | 3.56 | 8.80 | 12.63 | 14.58 | 16.79 | 23.05 |

PM${}_{10}$ RBF | 43 | 15.72 | 2.57 | 10.79 | 13.85 | 15.48 | 17.36 | 22.02 |

NO${}_{x}$ | 43 | 27.26 | 13.64 | 4.03 | 16.25 | 29.10 | 34.48 | 66.40 |

NO${}_{x}$ RBF | 43 | 28.66 | 9.56 | 12.33 | 22.05 | 29.08 | 32.69 | 56.23 |

Pollutant | RRMSE (%) |
---|---|

PM${}_{10}$ | 30.60 |

NO${}_{x}$ | 19.99 |

Station | Province | East X | North Y | PM_{10} | PM_{10} | Abs. err. | NO${}_{\mathit{x}}$ | NO${}_{\mathit{x}}$ | Abs. err. |
---|---|---|---|---|---|---|---|---|---|

(in
10^{4} m) | (in 10^{4} m) | RBF | PM${}_{10}$ | RBF | NO${}_{\mathit{x}}$ | ||||

1 | Álava | 52.71 | 474.49 | 13.52 | 14.79 | 1.27 | 34.47 | 28.55 | 5.92 |

2 | Biscay | 49.40 | 479.64 | 12.49 | 13.44 | 0.95 | 24.20 | 23.89 | 0.31 |

3 | Álava | 54.95 | 474.42 | 13.54 | 15.81 | 2.27 | 17.71 | 25.40 | 7.69 |

4 | Biscay | 49.82 | 480.10 | 20.90 | 16.62 | 4.28 | 24.12 | 32.40 | 8.28 |

5 | Biscay | 50.10 | 478.83 | 12.46 | 11.70 | 0.76 | 15.31 | 14.32 | 0.99 |

6 | Gipuzkoa | 57.93 | 478.59 | 15.86 | 14.43 | 1.43 | 39.25 | 30.94 | 8.31 |

7 | Gipuzkoa | 58.15 | 479.36 | 11.67 | 13.43 | 1.76 | 20.29 | 22.24 | 1.95 |

8 | Biscay | 50.32 | 478.81 | 12.35 | 15.48 | 3.13 | 13.82 | 38.56 | 24.74 |

9 | Gipuzkoa | 58.43 | 479.71 | 23.05 | 22.00 | 1.05 | 45.90 | 56.23 | 10.33 |

10 | Álava | 52.61 | 474.47 | 15.94 | 13.33 | 2.61 | 34.49 | 31.37 | 3.12 |

11 | Gipuzkoa | 58.02 | 479.57 | 17.34 | 15.54 | 1.8 | 31.24 | 29.08 | 2.16 |

12 | Gipuzkoa | 55.95 | 478.11 | 13.63 | 13.09 | 0.54 | 27.91 | 15.34 | 12.57 |

13 | Biscay | 50.10 | 479.40 | 15.06 | 15.56 | 0.5 | 32.98 | 37.90 | 4.92 |

14 | Biscay | 50.94 | 478.76 | 21.91 | 13.56 | 8.35 | 36.91 | 33.60 | 3.31 |

15 | Gipuzkoa | 56.59 | 476.65 | 21.75 | 14.70 | 7.05 | 34.09 | 29.30 | 4.79 |

16 | Biscay | 50.22 | 478.95 | 12.70 | 14.25 | 1.55 | 21.04 | 28.35 | 7.31 |

17 | Biscay | 52.94 | 477.96 | 16.83 | 16.11 | 0.72 | 34.01 | 30.07 | 3.94 |

18 | Gipuzkoa | 58.26 | 479.60 | 22.06 | 16.46 | 5.6 | 57.88 | 28.16 | 29.72 |

19 | Álava | 53.13 | 470.74 | 11.22 | 18.41 | 7.19 | 6.16 | 21.20 | 15.04 |

20 | Biscay | 50.18 | 479.44 | 16.45 | 16.22 | 0.23 | 40.68 | 33.07 | 7.61 |

21 | Biscay | 50.79 | 478.91 | 13.01 | 20.09 | 7.08 | 35.75 | 40.24 | 4.49 |

22 | Gipuzkoa | 58.30 | 479.10 | 15.89 | 13.78 | 2.11 | 36.27 | 29.72 | 6.55 |

23 | Gipuzkoa | 57.96 | 479.11 | 13.63 | 14.30 | 0.67 | 29.10 | 19.99 | 9.11 |

24 | Álava | 50.30 | 477.68 | 14.58 | 14.84 | 0.26 | 30.77 | 20.13 | 10.64 |

25 | Álava | 52.77 | 474.35 | 12.93 | 13.93 | 1 | 19.05 | 32.99 | 13.94 |

26 | Biscay | 50.44 | 478.96 | 19.38 | 14.60 | 4.78 | 66.40 | 31.67 | 34.73 |

27 | Biscay | 50.53 | 479.05 | 16.59 | 18.20 | 1.61 | 43.23 | 54.94 | 11.71 |

28 | Gipuzkoa | 54.15 | 476.81 | 15.64 | 14.35 | 1.29 | 32.05 | 25.85 | 6.2 |

29 | Biscay | 52.40 | 480.59 | 10.51 | 22.02 | 11.51 | 5.42 | 29.16 | 23.74 |

30 | Biscay | 49.09 | 479.64 | 10.87 | 19.47 | 8.6 | 12.52 | 16.01 | 3.49 |

31 | Gipuzkoa | 56.86 | 478.90 | 11.41 | 13.65 | 2.24 | 5.09 | 24.45 | 19.36 |

32 | Gipuzkoa | 58.24 | 479.49 | 12.23 | 18.20 | 5.97 | 17.18 | 43.24 | 26.06 |

33 | Biscay | 49.08 | 479.78 | 22.01 | 12.43 | 9.58 | 14.88 | 15.64 | 0.76 |

34 | Biscay | 50.56 | 479.40 | 19.94 | 16.56 | 3.38 | 30.76 | 39.99 | 9.23 |

35 | Biscay | 49.65 | 479.78 | 14.59 | 15.82 | 1.23 | 34.30 | 26.88 | 7.42 |

36 | Gipuzkoa | 57.50 | 477.58 | 16.06 | 17.94 | 1.88 | 43.31 | 34.53 | 8.78 |

37 | Gipuzkoa | 57.71 | 479.14 | 12.56 | 14.42 | 1.86 | 15.14 | 15.64 | 0.5 |

38 | Álava | 48.11 | 474.70 | 8.80 | 17.71 | 8.91 | 4.03 | 21.78 | 17.75 |

39 | Biscay | 48.91 | 478.45 | 14.37 | 10.79 | 3.58 | 15.18 | 12.33 | 2.85 |

40 | Biscay | 52.16 | 478.52 | 17.89 | 17.74 | 0.15 | 30.75 | 31.41 | 0.66 |

41 | Biscay | 49.34 | 480.00 | 16.75 | 20.05 | 3.3 | 25.64 | 21.86 | 3.78 |

42 | Gipuzkoa | 57.86 | 479.15 | 14.51 | 13.16 | 1.35 | 15.05 | 23.07 | 8.02 |

43 | Gipuzkoa | 55.57 | 477.05 | 13.53 | 17.00 | 3.47 | 17.61 | 30.91 | 13.3 |

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**MDPI and ACS Style**

Alberdi, E.; Alvarez, I.; Hernández, H.; Oyarbide-Zubillaga, A.; Goti, A.
Analysis of the Air Quality of the Basque Autonomous Community Using Spatial Interpolation. *Sustainability* **2020**, *12*, 4164.
https://doi.org/10.3390/su12104164

**AMA Style**

Alberdi E, Alvarez I, Hernández H, Oyarbide-Zubillaga A, Goti A.
Analysis of the Air Quality of the Basque Autonomous Community Using Spatial Interpolation. *Sustainability*. 2020; 12(10):4164.
https://doi.org/10.3390/su12104164

**Chicago/Turabian Style**

Alberdi, Elisabete, Irantzu Alvarez, Heber Hernández, Aitor Oyarbide-Zubillaga, and Aitor Goti.
2020. "Analysis of the Air Quality of the Basque Autonomous Community Using Spatial Interpolation" *Sustainability* 12, no. 10: 4164.
https://doi.org/10.3390/su12104164