Introduction

The knowledge about how the globe is suffering from continuous atmospheric degradation is what motivates this study which is focused on air pollution in port-cites. Universally, several summits have been developed for decades to tackle shipping emissions. Since until 31st December 2019, for ships operating outside the ECA,Footnote 1 the limit for sulphides content of ships’ fuel oil was 3.50% m/m (mass by mass); from 1st January 2020 onwards, 0.50% m/m limitation must be applied concerning the IMOFootnote 2 established in the 16th October 2008 committee. This deadline was set in the MARPOL treaty. Mainly, air pollution caused by vessels and aviation are referred to sulphur dioxide (SO2), nitrogen dioxide (NO2) (Rivera et al. 2015) and particle matters (PM) (Chaloulakou et al. 2005; Agrawal et al. 2008; Grivas et al. 2018); thereby, this study is focused on these pollutants. Moored ships are also responsible for smoke in the air in port-cities, basically, due to the powerful engines usage in secondary electricity supply devices (Adamo et al. 2014). Moreover, European Directive 2008/50/EC (EU directive, 2008) establishes several thresholds and an AQIFootnote 3 for every pollutant as mentioned in the study about particular matter with an aerodynamic diameter < 10 µm (PM10) (Vicente et al. 2012).

As stated in (Westmoreland et al. 2007), nitric oxide (NO) together with NO2 is known as NOx and all kind of high-temperature combustions, as vehicles engines, are related to them mainly in urban areas (Chaloulakou et al. 2008). According to (Carslaw et al. 2007), NO2 emissions are more associated with diesel engines. The extent of this research is to assess how is the real air quality scope in a controversial zone to face future predictive studies (Turias et al. 2008; Munoz et al, 2014; González-Enrique et al. 2019a). To tackle researches about air quality, a complex scenario where several pollution sources interact was chosen. The Bay of Algeciras is a strategic point with several oil refineries, steel factories, and other industries. Algeciras port together with Gibraltar airport, which are connected by many roads with plenty of freight transport and constant private traffic, contributes to very complicated air pollution conditions. The second most populated city in the Bay is La Línea with 63,147 inhabitants in 2019. Algeciras is the major town in the Bay with a population of 121,957 inhabitants in 2019. Its port is of real importance not only in Spain but also in the world.

Overwhelming pieces of evidence show that particle pollution in the outdoor air we breathe, those coming from vehicles exhaust pipes (Crabbe et al. 1999; Carslaw et al. 2007; Bozkurt et al. 2018), coal-fired power plants, petroleum refineries and other industrial sources, can cause lung cancer and higher mortality rates in urban areas (Finkelstein et al. 2003). It was observed that several substances, including PM10, reached higher levels in urban sites in the winter season (Bozkurt et al. 2018). Long-term pollution exposure to nitrogen oxides or sulphides can contribute to ailments such as cancer or asthma (Clench-Aas et al. 2000; Finkelstein et al. 2003). It is essential to control immissions since these affect human beings. Air pollutants are spread to different cities close to the emission points by winds (Cheung et al. 2020). Previous studies of SO2 demonstrated that short-term were better than medium-term predictions, and the reverse in the case of PM10 concentrations (Turias et al. 2008). A recent study related to PM pollutants shows that even though when the heavy industries have decreased their manufacturing in the first lockdown period during the SARS-COV-2 (Covid-19) health crisis, severe pollution is not reduced when meteorology is adverse (Wang et al. 2020). Furthermore, it must be considered that if ozone (O3) suffers from ozonolysis in presence of high levels of SO2 and H2O, the potential formation of secondary aerosols depends on relative humidity and meteorological conditions (Diaz-de Mera et al. 2017). Also, secondary aerosols (NO2) are formed in the chemical reaction between the NO and O3 (Westmoreland et al. 2007). Thus, air pollution in urban centres is a complex toxic-components mixture affected with the weather conditions and with a high impact on inhabitants, above all in those with cardiac insufficiency and respiratory distress (Kolehmainen et al. 2001). PM10 pollutant enters the body exclusively through the respiratory system (Vicente et al. 2012). Therefore, it is primordial to identify the temporal evolution of pollutant concentrations in the air in urban regions to ensure the living standard. Immission data were collected from a monitoring network located in this study area by the Environmental Agency of Andalusian Government in the south of Spain. The study region has also a peculiar local meteorological scenario due to the closeness to The Strait of Gibraltar. The study contains descriptive statistical methods and more sophisticated statistical tools, such as p-values in regression analysis, or trend predictions.

Citizens or administrations have the need for reliable information about the possible risks they are exposed. One of the main aims of this study: knowing the most important variables and causes of high levels of pollution and, on the contrary, the variables that foster low levels of pollution. In this work, these challenges are achieved through a data-driven approach. Using historical data, a statistical analysis has been performed including three stages: i) descriptive, ii) predictive, and iii) prescriptive, which will be explained more deeply in the next sections.

The rest of this paper is organized as follows. Section 2 describes the data and the case study. Section 3 introduces the methodology. Section 4 presents and discusses the results, and finally, Sect. 5 establishes the main conclusions.

Materials and Methods

This section introduces a description of the database. A map of the area of study with reference to Spain is shown in Fig. 1(a), and a general location of the Bay of Algeciras is shown in Fig. 1(b). In this figure, the position of Algeciras port can be seen with its massive dimension, a total length of 17,750Footnote 4 m amongst berths and seawalls. The situation of the two main cities of the bay, where this study focuses, Algeciras and La Línea, are located in front of each other as seen in Fig. 1(b). There are two dominant winds in this region, Levante (East) and Poniente (West), which seem to be produced by the situation of the bay in the proximity of the Strait of Gibraltar in connection with the Mediterranean Sea and the Atlantic Ocean. This special location of the bay creates a powerful air stream. Besides, as shown in Fig. 1(b), the pollutants and meteorological stations are spread over the bay.

Fig. 1
figure 1

Area of study with the monitoring stations: a Site location: Bay of Algeciras (South of Spain) and b Location of pollutants and meteorological monitoring stations, b (Scale = 1/100000). The monitoring stations codes are collected in Tables 1 and 2

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Naturally, a higher amount of available resources in data collection, such as sampling points and sensors, will chaise more reliable management of immission measuring. The Andalusian Government maintains its air quality monitoring station system throughout the Bay, where pollutant concentrations and atmospheric parameters were collected from the period of 2010 to 2015 and kindly provided to the University of Cádiz. The Bay of Algeciras counts on sixteen monitoring stations for collecting air pollutants and five meteorological specialized sensors. Three of the weather sensors are located inside a petroleum refinery (CEPSA) at three different heights (Table 1). Table 2 shows every pollutant in the monitoring stations. NO2 pollutant is recorded in fourteen stations, SO2 in sixteen stations, and PM10 in ten stations.

Table 1 Meteorological monitoring stations
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Table 2 Monitoring stations and the pollutants measured. NO2 is recorded in a total of fourteen stations, SO2 in sixteen, and PM10 in ten stations
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The data have been collected hourly during the period of six years, from 2010 to 2015, with an apparent total database of 52,560 hourly data. Besides, twenty-four meteorological variables, described in Table 3, were collected hourly, as well. Following previous works (Turias et al. 2008; Munoz et al, 2014; González-Enrique et al. 2019b, 2019c), a procedure of missing data imputation was developed as a preprocessing step. The meteorological variables analysed are wind speed (WS), wind direction (WD), solar radiation (SR), atmospheric pressure (AP), rainfall (RF), relative humidity (RH), temperature (T) and the pollutants are NO2, SO2 and PM10. These are the main substances expelled by the principal sources of air pollution in this area.

Table 3 Meteorological variables
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After data imputation, this study analyses the concentrations database together with the weather variables. Statistical parameters are obtained in every station to study their correlations and to study trend connections with other stations (descriptive approach). Then multivariate regression models (Romero et al. 2020) have been established for every pollutant in each station to check the relevant features and to dispose of estimation models to chaise a virtual sensor with numerous applications, such as, missing data imputation, a real-time usage in a robust monitoring net or prediction of the air pollution (a predictive approach). Previously, authors have used these methods (Turias et al. 2008; Munoz et al, 2014; Moscoso-López et al. 2019; Ruiz-Aguilar et al. 2021) in different works. Finally, measuring higher values of immission pollutants concentrations, a complete assessment of relative risks was developed to have at our disposal cause-effect knowledge about which are the main hazardous variables to prevent and take decisions (a prescriptive approach).

Descriptive analysis

Correlation

An in-depth statistical assessment was developed to get a general idea of the scope of the pollution in the study area. In Table 4, the mean, median, mode, variance, kurtosis and skewness are collected for every pollutant and study city. On the other hand, a linear correlation analysis was developed. A correlation is a reciprocal relation between two or amongst different variables which are expected to have some kind of connection, even though correlation does not mean relation. For instance, if one of these variables grows, the other is expected to increase or even decrease. Multidimensional correlation results were computed (see Fig. 2a, b and c). Pearson correlation coefficient (r) is shown in Eq. (1) where the numerator corresponds to COV(X,Y), the covariance between every pair of independent variables, and the denominators are, respectively, σx · σy, the typical deviations of them.

$$r = \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {xi - \vec{x}i } \right)\left( {yi - \overline{y}i} \right)}}{{ \sqrt {\mathop \sum \nolimits_{i = 1}^{n} \left( {xi - \overline{x}i } \right)^{2} } \sqrt {\mathop \sum \nolimits_{i = 1}^{n} \left( {yi - \overline{y}i} \right)^{2} } }}$$
(1)
Table 4 Descriptive statistical measurements in Algeciras (1) and La Línea (13) monitoring stations
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Fig. 2
figure 2

Plots of correlation values and mutual information among pollutants monitoring stations and meteorological variables a N02, b SO2, c PM10

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Mutual information

Mutual information (MI) (Shannon, 1948) is based on Shannon’s information theory. MI measures the statistical dependence between two variables, and thus, independency implies a low mutual information between them. Mutual information is a nonnegative measure (Kullback, 1968). MI uses the concept of entropy as a measure of uncertainty, since its maximum is when all values have equal probability of occurrence (Shannon, 1948). The advantage of mutual information is its ability to estimate a general dependence between variables, as opposed to correlation between variables where only linear relationships are considered.

To specify how much common certainty there are in two data samples, MI uses the concept of crossentropy \(H\left( {X,Y} \right)\):

$${\text{MI}}\left( {X,Y} \right) = H\left( X \right) + H\left( Y \right) - H\left( {X,Y} \right)$$
(2)

where \(H\left( X \right)\) is the entropy of \(x\) variables and \(H\left( Y \right)\) is the entropy of the output \(y\) (Cover and Thomas, 1993).

MI can be computed using Eq. 2 through an estimation adaptive partitioning (Darbellay and Vajda, 1999) procedure as authors previously used in González-Enrique et al. (2021). The ITE Toolbox (Szabó, 2014) has been applied in this work for MI calculation.

Trend analysis

In order to study trends between the monitoring stations for each air pollutant, we have used nonparametric trials and non-normality tests such as Wilcoxon rank test, Wilcoxon signed test and Wilcoxon signed-rank test to be compared with T-test (Box et al. 1976). Data are grouped into pairs of observations or monitoring stations, (\(x\) i,\(y\) i), which are aimed at getting to know if every pair is equal or not from a statistic point of view. The assumptions in these models are that if \(y\) i− \(x\) i ≠ 0, samples are independent, and they have a continuous and symmetric distribution concerning the same common median \(\theta\). These tests consist in returning a logical value indicating the test decision within a confidence interval, conventionally, of 95%. The decision will vary according to the kind of test we use. Basically, if the logical value it returns is 1, this indicates a rejection of the null hypothesis, and if the logical value it returns is 0, this indicates a failure to reject the null hypothesis at 5% of the significance level. Wilcoxon rank test is used when two samples have different lengths and they are independent. It tests the null hypothesis that data are samples from continuous distributions with equal medians, against the alternative that they are not. Wilcoxon sign test is the simplest nonparametric test applied in paired samples (Wasserman, L., 2004a). It is usually used to test the median of a population and returns the p-value for a two-sided sign test through a binomial distribution (Wasserman, L., 2004b). Wilcoxon signed-rank test is used instead of a T-test when normality in the sample cannot be proved, besides this test is the nonparametric of the dependent samples T test. A T test is used to compare two groups determining if there is a significant difference between their means, which might be related to certain features. Results of the several tests applied are collected in Table 5.

Table 5 Trend tests for similarity amongst monitoring stations
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Predictive analysis

Linear regression is a linear approach to modelling the relationship between two variables, used as a predictive tool for studying the response of one dependent variable, or response \(Y\), and the covariate variable \(X\), also called feature or predictor (Eq. 3).

$$R\left( x \right) = E\left( {{\raise0.7ex\hbox{$Y$} \!\mathord{\left/ {\vphantom {Y X}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$X$}} = x} \right) = \int {yf\left( {{\raise0.7ex\hbox{$y$} \!\mathord{\left/ {\vphantom {y x}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$x$}}} \right)} dy$$
(3)

Multiple regression is a many-to-one relationship amongst independent variables \(x\) i and the response \(y\). Adding more predictors to the model does not mean a better response, and it may produce overfitting or multicollinearity. The sum of linear parameters and an error gives the multiple regression model (4).

$$yi = \mathop \sum \limits_{i = 1}^{n} (\beta o + \beta i\cdot Xij ) + \varepsilon {\text{i}}$$
(4)

where \(\beta {\text{o}}\) is the intercept, \(\beta i\) are coefficients which show the weight of every independent variable \(Xi\), and Ɛ\({\text{i}}\)Footnote 5 is the error or residual. When this equation is estimated, we get the predicted value of the dependent variable, \(\hat{y}i\), obtaining \(b0, b1, b2,...bi,\) the estimates of \(\beta {\text{o}}\), \(\beta 1\), \(\beta 2\),…,\(\beta {\text{i}}\), respectively.

As it is well known, the coefficient of determination, R2, is preferably closer to one as possible. In addition, the p-value of each variable was calculated in order to discard all of the redundant independent variables whose p-value is ≥ 0.01. Generalization is key in data analysis since it is the ability to get good results with new unseen data. Building a model that fits the data sorely well does not always guarantee that the model is useful. The model should work well not only with the data it has learned from but also with the data that have not been used so far. The procedure to measure generalization is to divide our data into two sets: the training set and the test set. The training set, larger than the test set, contains the data used by the model to learn the parameters, and the test set contains unseen data not used in learning. The test set will be used to know how the model behaves with new data. In this analysis, the period 2010–2014 is used as a training set and the year 2015 is used as the test set. The results have been collected to these “new” data.

Prescriptive analysis

An analysis can be descriptive or predictive when representing an event, or prescriptive when researching a cause-effect occurrence, and this fact can be used in order to have a support decision tool (Schmidt and Kohlmann, 2008). The consequence can be evaluated by the relative risk analysis, which is explained briefly here. There are two methods for measuring the risk: Odd Ratio and Risk Ratio, both dimensionless and accompanied by the confidence interval (CI), which is a measure of the precision of the estimation (Tripepi et al. 2007). Their usage depends on the design of our study.

Odds Ratio (OR) it is used when a retrospective design is applied. This means that the first step is focusing on the consequences and then analysing the causes. The odds are a way of representing probability (Tripepi et al. 2007). OR is also known as “Cases and Controls'' (Ganguly 2006). Basically, odds is the ratio that represents the probability of occurrence of an event by means of the quotient between the happening event probability and the non-happening event probability (Bland and Altman 2000). It indicates how higher is the probability of occurrence of an event towards its non-occurrence (Sumargo 2018). These terms are described below.

$${\text{OR}} = \frac{{{\text{Odds}}1}}{{{\text{Odds}}0}} = \frac{{{\raise0.7ex\hbox{${R_{1} }$} \!\mathord{\left/ {\vphantom {{R_{1} } {\left( {1 - R_{1} } \right)}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\left( {1 - R_{1} } \right)}$}}}}{{{\raise0.7ex\hbox{${R_{0} }$} \!\mathord{\left/ {\vphantom {{R_{0} } {\left( {1 - R_{0} } \right)}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\left( {1 - R_{0} } \right)}$}}}} = \frac{{a_{1} b_{0} }}{{a_{o} b_{1} }}$$
(5)

Risk Ratio (RR) also called relative risk. It is a statistical concept used as a measure of association between dependent and independent variables. It is indicated to prospective studies, beginning in the reviews of the causes and their supervision until examining the consequences. RR is also called “Cohort study'' (Finkelstein et al. 2003; Schechtman 2002). The relative risk can be calculated as the ratio between the two incidence proportions or two incidence rates (Tripepi et al. 2007). It is the quotient between the proportion of cases with risk factor (subindex 1) and the proportion of cases without risk factor (subindex 0).

$${\text{RR}} = \frac{R1}{{R0}} = \frac{{{\raise0.7ex\hbox{${a_{1} }$} \!\mathord{\left/ {\vphantom {{a_{1} } {n_{1} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${n_{1} }$}}}}{{{\raise0.7ex\hbox{${a_{0} }$} \!\mathord{\left/ {\vphantom {{a_{0} } {n_{0} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${n_{0} }$}}}}$$
(6)

The terms are calculated counting and separating the individuals of the sample in cases-no factor, cases-factor, no cases-no factor, and no cases-factor. The total of individuals with no factor is n0 and the total of individuals with factor is n1. The sum of individuals with cases-no factor is a0, the sum of individuals with cases-factor is a1, the sum of individuals with no cases-no factor is b0, and the sum of individuals with no cases-factor is b1. Thus, it is easy to imagine that n0 = a0 + b0 and n1 = a1 + b1.

For instance, the relative risk of a situation is the ratio of risks of the treated group and the control group (Schechtman 2002). Observing Eqs. (5) and (6) is immediate to realise that when OR > 1 or RR > 1, a positive association, the presence of the factor is related to a higher occurrence of the event, and the reverse if the association is negative, OR < 1 or RR < 1 (Finkelstein et al. 2003). Conversely, when OR = 1 or RR = 1, there is no association between the presence of the factor and the event. There are several existing linkages between OR and RR. RR is more perceptive. OR lets us adjust by confounding variables through logistic regression, although it is not applied in this study.

Results and discussion

An overview of the in-depth analysis is shown in this section. Firstly, a descriptive statistical assessment was performed showing the most relevant features. Likewise, a linear correlation analysis was conducted to find out and determine which pairs of variables shared information. Also, a trend analysis was developed in order to establish those stations with similarities. Secondly, a linear multiple regression analysis was performed allowing to determine which variables are the most explanatory for every pollutant and location (with p-value < 0.01), and besides, to be able to establish how much variability can be fully explained with these models. These regression models can serve as virtual sensors because they are capable of inferring a measure (the concentration of a pollutant in a certain location) based on other variables. Therefore, they can be used for the imputation of missing data or as robust control in a monitoring network. Similarly, or with the same objectives, an approximation has been made to calculate which monitoring stations are equivalent to others, in this case using statistical comparison tests on their means.

UNECEFootnote 6 announced that air pollution is now considered to be the world’s largest environmental health threat, accounting for 7 million deaths around the world every year. The main substances affecting health are: nitrogen oxides (NOx), sulphur oxides (SOx), ozone and particulate matter. Both extent and duration of the exposure influence health diseases. This study and its results are interesting in order to give information about air pollution to citizens. Besides, regarding the economic costs of air pollution, WHOFootnote 7 and OECDFootnote 8 estimated in 2015 that the amount of money related to premature deaths and disabilities in Europe reached almost USD 1.6 trillion. Therefore, preventing long exposures could be useful to avoid risk factors for major diseases.

Finally, some results are collected on the statistical risks of interactions of the variables. Thus, we have obtained the most influenced interaction values for pollutants (especially in the case of the highest pollution values or, in contrast, of the lowest).

Descriptive analysis

The statistical terms of mean, median, variance, kurtosis, and skewness are collected in Table 4 for each pollutant recorded in the stations in both cities. Simply looking at this board we can have an idea of their relevance. Generally, the means of pollutant concentrations are very similar in Algeciras (number 1) and La Línea stations (number 13). Roughly, during the study period, it was observed that the highest mean occurs in La Línea for all pollutants except for NO2. All medians are beneath the mean concentrations which indicate that fifty percent of concentration values are upper the median, proof that the database does not follow a normal distribution. This is also appreciated with a positive skewness (> 0) when symmetry tends to values higher than the mean. The sharpest graph is the one with the highest kurtosis coefficient, corresponding to the PM10 in La Línea monitoring station (13).

Correlation

Figure 2 exposes the correlation values for every pair of variables. These plots represent the resulting correlation results, showing in colours closer to yellow the values of highest correlation coefficients tending to one. Coefficients of one, those of bright yellow in the diagonal, correspond to every variable with itself (it is not representative). Hereafter, the most significant correlation values in Algeciras and La Línea stations with the rest monitoring stations and atmospheric variables are exposed here. Speaking in absolute values, the correlations do not exceed r = 0.6781, which correspond to Carteya station correlated with Algeciras station for the PM10 pollutant and, continuedly, also the stations Los Barrios and El Zabal show similar correlation. For this pollutant, similar values of correlations are depicted in La Línea for Los Barrios, Algeciras, and El Zabal stations. Observing weather variables for PM10, wind direction is the highest correlated variable in Algeciras station and wind speed in La Línea. Moreover, regarding weather variables, the highest values of correlation connect wind direction in weather stations W1, W2, and W4 with Algeciras station for NO2. Besides, this pollutant in Algeciras station presents a correlation with Palmones, El Rinconcillo, and Los Barrios stations. On the other hand, La Línea station presents a connection with Campamento, Escuela de Hostelería, and Los Barrios stations for the same pollutant. In the case of La Línea station for the NO2 pollutant, the weather variables more correlated are wind direction in W1, W2 stations, and temperature in W4. Finally, for SO2 wind direction is the weather variable that most correlates both cities and also relative humidity in La Línea station measured in W3. Considering monitoring stations for SO2, Algeciras is correlated with Palmones, Los Cortijillos, and San Roque stations. La Línea is correlated with El Zabal, Puente Mayorga, and Campamento stations, which makes sense due to their proximity.

Mutual information

In order to get knowledge about the nonlinear behaviour amongst the variables, MI has been computed. In this sense, MI provides a different and more general criterion for investigating relationships between variables.

Regarding to the MI results between the studied variables, it is observed that there is not much nonlinear information between the monitoring stations. The maxima were found in the combinations of the meteorological variables W1-T, W2-RF, W3-RF, and W5-AP. This information complements to that calculated with the linear correlation and allows us to assume that these variables could be used in nonlinear regression or prediction models. Nevertheless, most of the shared information is linear rather than nonlinear with the limits of values observed in Fig. 2 (maximum 0.7 approximately). The behaviour is very similar for the three studied pollutants, with higher MI values only in the case of SO2 in the monitoring stations when a combination with the variables W1-T, W2-RF, W3-RF, and W5-AP was tested.

Trend analysis

The tendency is a measurement of variability between two samples regarding to their means. In this section, two samples coming from different stations are measured in order to obtain if they have the same trend or not from a statistical point of view, using, henceforth, hypotheses test for both daily and weekly means. In daily calculation, all database is divided into twenty-four intervals, or hours, and the mean is calculated for every hour (see Fig. 3). In weekly calculation, data are divided into groups of 52 weeks in order to calculate the mean of every interval that is the weekly mean for the total of the six years (see Fig. 4). The figures show daily data that give the hourly mean concentration for every pollutant in Algeciras (EPSA) and La Línea (Fig. 3), and weekly data giving the daily mean concentration (Fig. 4). In these figures, we can see that the highest levels of SO2 and PM10 pollutants mainly affect the city of La Línea, and for the NO2 pollutant, the highest level is obtained in Algeciras. Checking Fig. 3(a), a NO2 concentration level peaks appears at 38.88 µg/m3 which corresponds to the city of Algeciras in contrast to the highest concentration level peak of 31.79 µg/m3 in La Línea. In both cities, the NO2 concentrations grow strikingly at 10 p.m., together with a lower peak at 10 a.m. In Fig. 4(a) is noticed that the highest level of NO2, 43.17 µg/m3, corresponds to Algeciras achieved on Wednesday, and in La Línea the highest level of NO2 is 38.29 µg/m3 obtained on Monday. In the case of SO2, Fig. 3(b) shows in La Línea a steadily rise until the highest value of 13.94 µg/m3 at 12 a.m. and very close, 13.49 µg/m3 at 2 p.m. in Algeciras. Figure 4(b) shows that Wednesday is the day of highest values, very similar both in La Línea (14.39 µg/m3) and Algeciras (14.26 µg/m3). Concerning PM10 pollutant, Fig. 3(c) depicts a steep downward in both cities at 12 p.m. and also the highest mean-hour is 36.04 µg/m3 corresponding to La Línea at 11 p.m. In Algeciras, the value is 33.28 µg/m3 at 10 p.m. Figure 4(c) shows the highest value of 37.41 µg/m3 in La Línea corresponds to Tuesday and in Algeciras 34.27 µg/m3 the Thursday. In general, at Algeciras station exists a major fluctuation for every pollutant, obtaining the lowest values of concentrations. At La Línea station, the values are maintained higher, probably caused by its proximity with industrial environment combined to west winds. On the other hand, after applying several trend-tests for both daily and weekly data to get those stations with similar behaviour, promising trend results were obtained for NO2, SO2 and PM10 in the cities of Algeciras and La Línea (see Table 5). Trend results for similar stations demonstrate that for SO2 pollutant Algeciras station (number 1) is always similar to Los Barrios station and in the case of Wilcoxon rank and Sign tests is also equal to La Línea station (number 13). This argument is used in the rest of tests. Regarding PM10, the situation is strongly different since several stations show similar behaviour with all tests except Wilcoxon sign for weekly data test, which presents none of them.

Fig. 3
figure 3

Average day. Comparison between the hourly mean concentration of pollutants in Algeciras and La Línea during the period 2010–2015: a NO2 b SO2 c PM10

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Fig. 4
figure 4

Average week. Comparison between the hourly mean concentrations of pollutants in Algeciras and La Línea during the period 2010–2015: a NO2 b SO2 c PM10

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Predictive analysis

A Multiple linear regression (MLR) analysis was applied in order to estimate the three different air pollutants as a function of meteorological variables and the rest of monitoring stations. In this work, the estimation of the parameters was done using the data in the period 2010–2014 (training or design set) and the regression results were collected using the year 2015 (as a test set). The best regression model is obtained when highest R2 and lowest MSE. Regression results in Algeciras and La Línea are displayed in Table 6. We observe that in Algeciras station the best regression value is for PM10 and in La Línea for NO2, nevertheless, SO2 presents similar values in both cities. Finally, using the p-value < 0.01 of the regression, the most relevant features can be selected in every model. Their weights or estimates (\(\beta i\)) and the intercept (\(\beta 0\)) of each regression equation are shown in Table 7 along with the most relevant variables for every pollutant and station. Those variables with positive estimates indicate that the dependent variable (i.e. each air pollutant concentration) are positively affected by these variables and reversely with negative sign. For instance, regarding the weather variables, Algeciras station is positively influenced by wind speed in W4 and negatively in W1 for all pollutants. Considering the regression among monitoring stations, Algeciras is more positively affected by Los Barrios for all pollutants and also by Palmones station in the case of SO2. Besides, Algeciras is affected negatively by San Roque for NO2. In the case of La Línea station, the variables that more influence positively are wind speed (in W1 and W4 weather variables) for all pollutants and also wind direction (in W1 for SO2). Regarding monitoring stations, La Línea is positively affected by El Zabal in the case of NO2 and SO2 pollutants and Los Barrios station in the case of PM10.

Table 6 Multiple linear regression values for every pollutant in Algeciras (1) and La Línea (13) monitoring stations
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Table 7 Relevant weather variables and monitoring stations (with regression p-values < 0.01) are shown for each pollutant in monitoring stations of Algeciras (1) and La Línea (13). βi are the estimates, and β0 is the intercept of the regression models
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In contrast, La Línea station is negatively affected by Cortijillos station for the NO2 pollutant. Negatively, the weather station that more leverages La Línea station is W5, wind speed (in the case of NO2 and PM10) and wind direction in the case of SO2. The rest of the values can be depicted in the same way. Tables 1, 2, 3, and Fig. 1 can be checked to locate every station and to observe these interesting relations.

Prescriptive analysis

In this study, the relative risks RR > 1.25 have been considered as long as statistically significant with a p-value < 0.05 in a Chi test. The highest and significant RR values in stations are shown in Table 8. Considering the NO2 pollutant measured in W2, lower degrees (first quartile, Q1) of wind direction (WD) produce the highest relative risk (3.08) of suffering from an elevation of this pollutant above the mean in Algeciras station. Furthermore, we observe that higher degree values of wind direction (third quartile, Q3) in W2 do not present any risk of enduring a rise of NO2 in La Línea station above the mean. In fact, they act as a protection in this station for this pollutant and weather variable and also occur to WD recorded in W1. Focusing on the SO2 pollutant, if the relative humidity (RH) is high, measured in weather station W1 (this means that it is located in fourth quartile, Q4), produces the existence of high relative risk (3.48) to suffer from SO2 rise (having a value greatest that the mean) in Algeciras station as also happens to wind speed measured in W5 station. Nevertheless, higher values of temperature and wind direction (Q4) recorded in W4 station present protection in La Línea station for SO2. In the case of PM10, in Algeciras station higher values (Q4) of wind speed measured in W5 and W4 stations act as a protection of not suffering from an elevation above the mean concentration. However, in La Línea station higher values (Q4) of wind speed, in W4 and W1, do affect the risk increase of undergoing overruns above the mean.

Table 8 Highest relative risks computed between pollutants and meteorological variables. Risk 0 means non-risk (protection), risk 1 means risk
Full size table

Conclusion

An exhaustive statistical analysis in a complex scenario characterized by a real industrial region along with a quite singular meteorological situation was performed in this study. In general terms, in the period analysed it is observed that Algeciras station recorded higher values of NO2 pollutant than La Línea station, however, considering SO2, the values were very similar. In the case of PM10, La Línea station collected the highest values.

Regarding regression models, the hypothesis that winds are important in this area is tested in this study, showing the relevance of correlation and highest regression coefficients for the two wind components (speed and direction) measured in different weather stations amongst other variables. Regression rates go from values of R2 above 0.5346 to the max R2 of 0.8655 that corresponds to NO2 with La Línea station. Moreover, wind speed appears to be the most relevant variable in the majority of cases in both cities. The two wind components trigger an apparent particle movement which leads to an air-cleaning effect in The Bay of Algeciras. However, Algeciras is highly affected by east winds (Levante) and La Línea is more impacted by west winds (Poniente). Generally, considering the monitoring stations, Los Barrios station presents higher affection with Algeciras for all pollutants. In La Línea, El Zabal station seems to be more relevant. Both of them could be used with relevance in a robust virtual sensor of Algeciras and La Línea stations along with wind variables.

Considering relative risk results, Algeciras is affected negatively by lower degrees of wind direction for the NO2 pollutant. For SO2 the variables that affect the most to Algeciras are higher values of relative humidity, which produce a rise of SO2 above the mean. This increase might be in concordance with the research of (Diaz-de Mera, 2017). In addition, higher values of wind speed produces also a relative risk in Algeciras. Nevertheless, in the case of PM10, the highest values of wind speed cause protection leverage in this city, just the reverse than in La Línea station, where higher values of wind direction and higher temperatures act as protection. Admittedly, PM10 pollutant is spread from Algeciras to La Línea through wind speed.

According to trend analysis, NO2 pollutant presents similarities between Algeciras and La Línea stations. In the case of SO2, the similarity is between Algeciras and Los Barrios station and with regard to PM10 it can be measured indistinctly in Algeciras-Los Barrios, El Rinconcillo-La Línea or El Zabal-La Línea stations. These results, in general, are confirmed with the regression models.

According to the OECD, outdoor air pollution could cause 6–9 million premature deaths a year by 2060 and cost 1% of global GDPFootnote 9—around USD 2.6 trillion annually—as a result of sick days, medical bills and other issues.

In accordance with recent estimates by the WHO, exposure to air pollution is thus a more important risk factor for major diseases. New tools such the one presented in this work have proven to be an effective tool in avoiding hazardous situations. Preventing potentially health risk events helps citizens in preventing morbidity and premature mortality, one of the targets under Sustainable Development Goal (objective 3) on good health and promoting wellbeing.

To summarise the above, an air pollution modelling approach based on different perspectives (descriptive, predictive, and prescriptive) was performed on this singular area using different statistical methods. The results obtained can be used as a virtual sensor in the case of sensor failures and also as a support decision tool for institutions and citizens to prevent peak-situations. Furthermore, this proposed approach could be used in different regions or scenarios in future researches.