Submicron Particles and Micrometeorology in Highly Densified Urban Environments: Heavy-Tailed Probability Study

Abstract

Submicron particles (SPs), with diameters less than 1.0 μm, are a serious health risk, and urban meteorology variables (MVs), impacted by human activity, can support their sustainability. This study, in a city immersed in a basin geomorphology, is carried out during the summer period of high temperatures and variable relative humidity. An area of high urban density was selected, with the presence of high-rise buildings, urban canyons that favor heat islands, low forestation, intense vehicular traffic, and extreme conditions for MVs. Hourly measurements, in the form of time series, record the number of SPs (for diameters of 0.3, 0.5, and 1.0 μm) along with MVs (temperature (T), relative humidity (RH), and wind speed magnitude (WS)). The objective is to verify whether MVs (RH, T) promote the sustainability of SPs. For this purpose, Spearman’s analysis and a heavy-tailed probability function were used. The central tendency probability, a Gaussian distribution, was discarded since its probability does not discriminate extreme events. Spearman’s analysis yielded significant p-values and correlations between PM₁₀, PM_5.0, PM_2.5, and SPs. However, this was not the case between MVs and SPs. By applying a heavy-tailed probability analysis to extreme events, the results show that MVs such as T and RH act in ways that can favor the accumulation and persistence of SP concentrations. This tendency could have been exacerbated during the measurement period by heat waves and a geographical environment under the influence of a prolonged drought resulting from climate change and global warming.

1. Introduction

Fine particulate matter (PM_2.5 or smaller) is an air pollutant composed of solid and liquid particles with diameters of 2.5 μm or less. It is considered highly hazardous to human health. Particles smaller than 2.5 µm can penetrate deep into the bronchial region and may reach the pulmonary alveoli, where they tend to accumulate over time due to the near impossibility of their removal by physiological mechanisms. This condition, in the long term, leads to serious health effects in exposed individuals, such as the worsening of asthma, increased incidence of cancer and cardiovascular diseases, and overall rises in both mortality and morbidity.

In 2021, a study [1] concluded that particles emitted by gases responsible for planetary warming are linked to 20% of global premature deaths. What chemical elements make up fine particulate matter? Regarding its composition, the primary constituents of fine particulate matter include chemical substances such as sulfate, nitrate, ammonium, hydrogen ion, particle-bound water, elemental carbon, a wide variety of organic compounds, and elements from the Earth’s crust [2,3]. Within this wide range should be included heavy metals (such as nickel, copper, mercury, and lead), volatile organic compounds (VOCs) (which include benzene and other compounds) and ultrafine particles < PM₁, which are the most dangerous and harmful to health. Sources of particulate matter include construction activities, unpaved roads, agricultural burning, chimneys, wildfires, tobacco smoke, cooking, wood burning, candles, and incense.

To get an idea of the dimensions of the particulate matter that can be studied, let us consider that within 10 µm is a pollen particle and particulate matter, within 50 µm is the limit of vision and the tip of a pin, while the thickness of a hair is on the order of 100 µm; around 1 µm are bacteria, above 2.5 µm and less than the upper limit of 10 µm is coarse particulate matter, below 2.5 µm is fine particulate matter, in the middle are red blood cells, and close to the upper limit are cells; in dimensions smaller than 1.0 µm we find viruses of 0.1 µm, submicron particles (SPs), also called ultrafine particulate material, which can reach 0.01 µm (molecular dimensions).

Relative humidity can influence the concentration of fine particulate matter (PM_2.5 or smaller). First, it is important to note that particulate matter (PM) is a mixture of solid and liquid particles suspended in the air. PM_2.5 refers to particles with diameters smaller than 2.5 μm. Relative humidity measures the amount of water vapor present in the air compared to the maximum amount the air can hold at a given temperature. The concentration of PM_2.5 tends to increase with relative humidity [4,5,6], which has significant health implications. PM can be inhaled and cause serious health issues. Particles smaller than 10 μm in diameter can reach deep into the lungs, and some may even enter the bloodstream. Prolonged exposure to PM_2.5 has been associated with cardiopulmonary effects and increased mortality from lung cancer [7,8].

Micrometeorology, Global Warming, and Relative Humidity

Micrometeorology is a branch of meteorology that focuses on observations and processes occurring at small spatial and temporal scales [9]: approximately within 1 km and over periods of one hour or less. These processes are confined to the lower portion of the planetary boundary layer, known as the atmospheric boundary layer (ABL) [10]. Its physical principles are related to the exchange of energy, mass, and gases between the atmosphere and the surface layer, including water bodies, soil, and vegetation. The Earth’s surface greatly influences the atmosphere, particularly the air properties within the ABL. Here, surface friction and the thermal effects of surface heating and cooling generate significant flows that transport momentum, heat, moisture, and material [11].

The study of temperature and wind (turbulence), influenced by external factors such as buildings [12], vegetation, population, and terrain, is highly relevant. Observational data demonstrates the development, intensification, and expansion of the urban heat island (UHI) phenomenon. This effect is attributed to the disruption of heat exchange between the ground and the atmosphere due to changes in surface characteristics. It is estimated that nearly half of the observed changes in relative humidity may be attributed to reduced evapotranspiration resulting from the replacement of vegetation with concrete and asphalt [13,14,15].

Can atmospheric warming—which enhances climate change and increases the atmosphere’s capacity to retain water—promote the persistence of fine particulate matter?

Variables such as urban canyons, urban densification, high-rise construction, the use of high-albedo building materials, the intensive use of fossil fuels due to rising vehicle numbers, the inaccessibility of electromobility for much of the population, the expansion of cities into agricultural lands, the encasement and channeling of natural watercourses, the gradual loss of arboreal vegetation, and the continuous emission of pollutants into the atmosphere, all contribute to a cumulative polluting thermal flux into the atmosphere. This, in turn, enhances its capacity to retain moisture, which may support the sustainability and persistence of fine particulate matter.

Relative humidity (RH or Φ) is the ratio of the partial pressure of water vapor (p_H2O) in the mixture to the equilibrium vapor pressure of water (p*_H2O) at a given temperature [15]. The correspondence between the pressures on a flat surface of pure water at a given temperature is written as follows:

$$\mathrm{RH} = \mathsf{\Phi } = {\mathrm{p}}_{{\mathrm{H}}_2\mathrm{O}}/{\mathrm{p}}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}(~\mathrm{a}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{o} \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l} \mathrm{g}\mathrm{a}\mathrm{s} \mathrm{l}\mathrm{a}\mathrm{w}~{\left({\displaystyle \frac{{\mathrm{n}}_{\mathrm{v}}}{{\mathrm{n}}_{\mathrm{v}\mathrm{p}}}}\right)}_{⌊\mathrm{T}}),$$

(1)

RH is usually expressed as a percentage; a higher percentage means that the air–water mixture is more humid. At 100% relative humidity, the air is saturated, cannot hold more vapor, and as noted, is at its dew point. The polluting system can cause a decrease in relative humidity, contributing to aridity in a basin geomorphology [16]. But due to conservation of mass, water vapor cannot disappear, the atmosphere retains more water, and its release becomes less predictable. The hydration of geographies and fragments of atmospheric layers become chaotic and unpredictable, and its irregular and overflowing emergence can generate high-risk events [16].

During the periods of 2010/2013, 2017/2020 and 2019/2022, urban meteorology (temperature (T), relative humidity (RH) and wind speed magnitude (WS)) and pollutant measurements (PM₁₀, PM_2.5 and CO) were carried out in the form of time series in six communes (spread over an area of 650 km²) in the city of Santiago de Chile (located in a basin geomorphology). Each time series consisted of 28,463 hourly punctual data, giving a total of 3,074,004 data points. The study of these measurements uses the assumptions that the urban meteorology system and the pollutant system are sensitive to initial conditions, have irreversible behaviors, are persistent (the past influences the future), and that pollution induces disorder in the atmosphere, making it unpredictable and highly complex, especially at the boundary layer level. Chaos theory is a mathematical formalism that meets these requirements [17]. A previous step before declaring a time series chaotic is that its chaotic parameters are in the appropriate ranges: maximum Lyapunov exponent (λ > 0), correlation dimension (D_C < 5), maximum Kolmogorov entropy (S_K > 0), Hurst exponent H must be in the range 0.5 < H < 1.0, and Lempel–Ziv complexity (LZ > 0). All series (108) analyzed with a software for time series of chaotic properties [17,18] satisfied the ranges (flowchart diagram, Appendix A). The representative entropies of urban meteorology and pollutants for each commune generate two entropic surfaces (one associated with urban meteorology (S_MV(x,y,z)) and the other associated with pollutants (S_P(x,y,z))). These surfaces or layers are interactive and highly dynamic when comparing the three periods [15,19,20]. The parameter C_K, is defined as follows:

$${{\mathrm{C}(\mathrm{x},\mathrm{y},\mathrm{z})}_{\mathrm{K},\mathrm{C}\mathrm{O}\mathrm{M}\mathrm{M}\mathrm{U}\mathrm{N}\mathrm{E}}={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{S}}_{\mathrm{K},\mathrm{M}\mathrm{V}}}{\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}}}_{\mathrm{C}\mathrm{O}\mathrm{M}\mathrm{M}\mathrm{U}\mathrm{N}\mathrm{E}},$$

(2)

The studies carried out reveal that the value of the parameter depends on the geomorphology: basin (C_K < 1), mountain, and coast (C_K > 1).

The entropic forces, defined as follows:

$$\overrightarrow{\mathrm{F}}=\mathrm{T}\ast \nabla {\mathrm{S}(\mathrm{x},\mathrm{y},\mathrm{z})}_{\mathrm{K}},$$

(3)

arise naturally from this formulation. And the way they manifest is linked to each geomorphology. In the case of a geographic basin, the entropic forces associated with pollutants are dominant and are an agent of atmospheric disorder. They promote anomalous subdiffusion, establishing a regime of extreme events suitable for description by heavy-tail probabilities.

But do these considerations extend to SPs? Spearman’s analysis of the measured data says yes, at least with respect to coarse particulate matter in relation to sub-micron particles. However, it is ambiguous and poorly defined regarding the effect of urban meteorology on sub-micron particles. The heavy-tailed probability calculation using the measured data shows results that are consistent with the observations. (These considerations are discussed later in Section 3.3, Section 3.4 and Section 3.5)

The conformation of entropic surfaces [19,20], as a quotient of entropies between those of urban meteorology and those of pollutants, generates entropic forces in a basin geomorphology that contribute [19,20] to further increase high summer temperatures, which favors the retention of water by the atmosphere, affecting relative humidity, and promoting the sustainability of SPs in the boundary layer close to the ground. During the mornings, it is common to observe an increase in the concentration of SPs.

It is of interest in this study to verify this hypothesis by implementing the presented procedure. The emergence of extreme urban weather patterns favors the increase in diseases in the population, which is well documented [21,22,23,24]. In addition, a combination of other factors influences the sustainability of SPs:

Night-time temperature inversion: On clear nights, the ground surface cools, and the coldest layer of air remains near the surface. This produces a “layer” that traps polluted air, including SPs and fine particulate matter, close to the ground;

Increased vehicular activity: In the mornings, vehicular traffic increases significantly, especially during rush hour;

Emissions from industries, power plants, and factories, which operate during peak traffic hours.

2. Materials and Methods

2.1. Area of Study

The measurements were taken in the city of Santiago, Chile, which is located in a geomorphological basin. The building where the instruments were installed is 12 m high and is located at Almirante Latorre Street, 423, in the heart of the city, Figure 1. This is a highly dense urban area, with a large number of high-rise concrete buildings, urban canyons, narrow streets, low ventilation levels, heavy traffic, etc.

2.2. Measuring Instruments

Measurements of particle count, particle size, temperature, and humidity were conducted using the PCE-PCO 2 sensor and Weather station and data display touch screen., as described in Appendix B.

2.3. Theoretical Framework

If the temperature of the saturated air increases, because of the thermal transfer of the same pollutants, its capacity to contain water vapor will increase and the relative humidity will decrease. From a dynamic perspective, if the entropic forces due to pollutants are greater than those of urban meteorology and RH in particular, they can favor an increase in environmental dryness. The forces of an entropic nature (2) originated by the entropy surface, S (x, y, z), are shown in Figure 2 [25,26,27,28]:

The pressure is p = F/A, so it is then possible to write using (3), following the notation of (1), and we obtain the following expression:

$$\mathrm{R}\mathrm{H}={\displaystyle \frac{{\mathrm{p}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{P}}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}}}={\displaystyle \frac{{\left(\frac{\mathrm{F}}{\mathrm{A}}\right)}_{{\mathrm{H}}_2\mathrm{O}}}{{\left(\frac{\mathrm{F}}{\mathrm{A}}\right)}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}}}={\displaystyle \frac{\left|{\nabla \mathrm{S}}_{{\mathrm{H}}_2\mathrm{O}}\right|}{\left|{\left(\nabla \mathrm{S}\right)}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}\right|}},$$

(4)

an expression that creates a relationship between relative humidity and the gradient of the entropic surface. If the process occurs in a spherical volume, with the operator ∇ only having radial dependence (r), we obtain the following:

$$\mathrm{R}\mathrm{H}={\displaystyle \frac{{\mathrm{p}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{P}}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}}}={\displaystyle \frac{{\left(\frac{\mathrm{F}}{\mathrm{A}}\right)}_{{\mathrm{H}}_2\mathrm{O}}}{{\left(\frac{\mathrm{F}}{\mathrm{A}}\right)}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}}}={\displaystyle \frac{\left|\frac{\partial {\mathrm{S}}_{{\mathrm{H}}_2\mathrm{O}}}{\partial \mathrm{r}}\right|}{\left|{\left(\frac{\partial \mathrm{S}}{\partial \mathrm{r}}\right)}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}\right|}}~{\displaystyle \frac{∆{\mathrm{S}}_{{\mathrm{H}}_2\mathrm{O}}}{{\left(∆\mathrm{S}\right)}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}}}~{\displaystyle \frac{\frac{∆{\mathrm{S}}_{{\mathrm{H}}_2\mathrm{O}}}{∆\mathrm{t}}}{\frac{{\left(∆\mathrm{S}\right)}_{{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}}{∆\mathrm{t}}}}~{\displaystyle \frac{{\mathrm{S}}_{\mathrm{K},{\mathrm{H}}_2\mathrm{O}}}{{\left(\mathrm{S}\right)}_{\mathrm{K},{\mathrm{H}}_2\mathrm{O}}^{\mathrm{*}}}},$$

(5)

which indicates for RH a dependence, considering the assumptions indicated, on the Kolmogorov-type entropies [19,29,30,31,32].

As a note, if we perform the calculation, we obtain the following:

$$\nabla {\displaystyle \frac{{\mathrm{S}}_{\mathrm{K},\mathrm{R}\mathrm{H}}}{{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}}={\displaystyle \frac{{\mathrm{S}}_{\mathrm{K},\mathrm{P}}\nabla {\mathrm{S}}_{\mathrm{K},\mathrm{R}\mathrm{H}}-{\mathrm{S}}_{\mathrm{K},\mathrm{R}\mathrm{H}}\nabla {\mathrm{S}}_{\mathrm{K},\mathrm{P}}}{{{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}^2}}={\displaystyle \frac{\overline{\mathrm{T}}\nabla {\mathrm{S}}_{\mathrm{K},\mathrm{R}\mathrm{H}}-\frac{{\mathrm{S}}_{\mathrm{K},\mathrm{R}\mathrm{H}}}{{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}\overline{\mathrm{T}}\nabla {\mathrm{S}}_{\mathrm{K},\mathrm{P}}}{\overline{\mathrm{T}}{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}}={\displaystyle \frac{{\overrightarrow{\mathrm{F}}}_{\mathrm{R}\mathrm{H}}-\frac{{\mathrm{S}}_{\mathrm{K},\mathrm{R}\mathrm{H}}}{{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}{\overrightarrow{\mathrm{F}}}_{\mathrm{P}}}{\overline{\mathrm{T}}{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}},$$

(6)

and

$$\overline{\mathrm{T}}>0,{\mathrm{S}}_{\mathrm{K},\mathrm{P}}>0\to \overrightarrow{∆}={\overrightarrow{\mathrm{F}}}_{\mathrm{R}\mathrm{H}}-{\displaystyle \frac{{\mathrm{S}}_{\mathrm{K},\mathrm{R}\mathrm{H}}}{{\mathrm{S}}_{\mathrm{K},\mathrm{P}}}}{\overrightarrow{\mathrm{F}}}_{\mathrm{P}}=\left\{\begin{array}{c}<\overrightarrow{0},{\overrightarrow{\mathrm{F}}}_{\mathrm{P}} \mathrm{is} \mathrm{greater}\\ =\overrightarrow{0},\mathrm{not} \mathrm{observed}\\ >\overrightarrow{0},{\overrightarrow{\mathrm{F}}}_{\mathrm{R}\mathrm{H}} \mathrm{is} \mathrm{greater} \end{array}\right.,$$

(7)

where ${\overrightarrow{\mathrm{F}}}_{\mathrm{R}\mathrm{H}}$ is the entropic force associated with relative humidity, and ${\overrightarrow{\mathrm{F}}}_{\mathrm{P}}$ is the entropic force associated with pollutants.

When the contaminant system increasingly invades the boundary layer of the atmosphere with sufficient energy to affect it, the atmospheric air is more likely to expand, and there is more space to contain water vapor [16]. This phenomenon is not static in time, it is extremely dynamic; the entropic layers are very variable and very rough. The entropic force is very variable. This increases the low predictability of the events. What formula $\overrightarrow{∆}$ states is that an entropic force of urban meteorology is related to the entropic force of pollutants (and vice versa) and to C_K [16,19]. Equilibrium has been lost and the systems which have entered irreversible processes are complex, connected and chaotic. Equation (5) is a very crude approximation of the current processes in the atmosphere. But it is possible to show from the entropy ratio the turbulence and disorder of the interactive systems.

If we analyze two systems (one polluting (P) and the other urban meteorology variables (MVs)) that evolve interactively and irreversibly, we have:

$${\mathrm{d}\mathrm{S}}_{\mathrm{P}}={\left(\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P}}+{\sum }_{\mathrm{i}=1}^{\mathrm{M}}{\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{P}},$$

(8)

$\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P}}$ represents the entropy production by pollutants, and the sum refers to the N heat sources from which the system receives or transfers heat at the temperature of the ith source (${\mathrm{T}}_{\mathrm{F}\mathrm{T}\mathrm{i}}$). A similar expression applies to meteorological variables:

$${\mathrm{d}\mathrm{S}}_{\mathrm{M}\mathrm{V}} = {\left(\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P}}+{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{M}\mathrm{V}},$$

(9)

Applying the quotient ${\displaystyle \frac{{\mathrm{d}\mathrm{S}}_{\mathrm{M}\mathrm{V}}}{{\mathrm{d}\mathrm{S}}_{\mathrm{P}}}}$ and considering that ${\mathrm{C}}_{\mathrm{K}}$ < 1 in a basin geomorphology [18]:

$${\displaystyle \frac{{\mathrm{d}\mathrm{S}}_{\mathrm{M}\mathrm{V}}}{{\mathrm{d}\mathrm{S}}_{\mathrm{P}}}}={\displaystyle \frac{\frac{{\mathrm{d}\mathrm{S}}_{\mathrm{M}\mathrm{V}}}{\mathrm{d}\mathrm{t}}}{\frac{{\mathrm{d}\mathrm{S}}_{\mathrm{P}}}{\mathrm{d}\mathrm{t}}}}={\mathrm{C}}_{\mathrm{K}}={\displaystyle \frac{{\left(\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P}}+{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}\right)}_{\mathrm{M}\mathrm{V}}}{{\left(\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P}}+{\sum }_{\mathrm{i}=1}^{\mathrm{M}}\frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}\right)}_{\mathrm{P}}}}<1,$$

(10)

we get

$${\left(\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P}}+{\sum }_{\mathrm{i}=1}^{\mathrm{M}}{\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{M}\mathrm{V}}<{\left(\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P}}+{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{P}},$$

(11)

If we assume N = M sources generating entropy

$${\sum }_{\mathrm{i}=1}^{\mathrm{N}}\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{M}\mathrm{V},\mathrm{i}}+{\left({\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{M}\mathrm{V}}<{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{P},\mathrm{i}}+{\left({\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{P}},$$

(12)

$$\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{M}\mathrm{V},\mathrm{i}}+{\left({\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{M}\mathrm{V}}<\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{P},\mathrm{i}}+{\left({\displaystyle \frac{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}{{\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}}\right)}_{\mathrm{P}},$$

(13)

ordering terms

$$\left({\displaystyle \frac{\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{M}\mathrm{V},\mathrm{i}}-\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{P},\mathrm{i}}}{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{P}}}}+{\displaystyle \frac{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{M}\mathrm{V}}}{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{P}}{\left({\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}\right)}_{\mathrm{M}\mathrm{V}}}}\right){\left({\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}\right)}_{\mathrm{P}}<1,$$

(14)

making the change $\delta \sigma =\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{M}\mathrm{V},\mathrm{i}}-\mathsf{\delta }{\mathsf{\sigma }}_{\mathrm{P},\mathrm{P},\mathrm{i}}$

$${\displaystyle \frac{\left(\frac{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{M}\mathrm{V}}}{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{P}}}\right){\left({\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}\right)}_{\mathrm{P}}}{1-\left(\frac{\delta \sigma }{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{P}}}\right){\left({\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}\right)}_{\mathrm{P}}}}<{\left({\mathrm{T}}_{\mathrm{T}.\mathrm{S},\mathrm{i}}\right)}_{\mathrm{M}\mathrm{V}},$$

(15)

as a particular case it can be assumed that

$${\displaystyle \frac{\delta \sigma }{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{P}}}}\ll 1\to \left({\displaystyle \frac{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{M}\mathrm{V}}}{{{\mathsf{\delta }\mathrm{Q}}_{\mathrm{T}\mathrm{S},\mathrm{i}}}_{\mathrm{P}}}}\right){\left({\mathrm{T}}_{\mathrm{T}\mathrm{S},\mathrm{i}}\right)}_{\mathrm{P}}<{\left({\mathrm{T}}_{\mathrm{T}.\mathrm{S},\mathrm{i}}\right)}_{\mathrm{M}\mathrm{V}},$$

(16)

In the condition of basin geomorphology (C_K < 1), the pollutants emitted by the i-th source contribute to increasing the temperature of the environment, where the temperature is measured of the i-th source that makes up the urban meteorology.

The approach to the dynamics of SPs will be carried out through comparative studies with the Kolmogorov entropy calculated for urban meteorology and pollutants in a defined period, and application of the Spearman probability and the heavy-tailed probability to the measurements, briefly describing these techniques in the results.

3. Results

3.1. Submicron Particles (SP) and Urban Meteorological Measurements

Figures are presented showing the measurements of SPs and urban micrometeorology carried out on 13, 14, 20, and 21 March 2025, in the vicinity of the exterior and interior faces of a 12 m-high building, located in a highly densified urban environment with tall buildings. Figure 3 and Figure 4 represent the measurements on the exterior face of the building, while Figure 5 and Figure 6 present the measurements on the interior face, both measurements were taken on 13 March 2025 (morning (10:52/12:52), noon (13:50/15:51), and afternoon (16:28/18:31)). The remaining figures, corresponding to other measurement days, are included in Appendix A.

A heatwave [32,33,34,35], as shown in

Table 1. (a) Measurements of urban meteorology in the proximity of exterior face of 12 m tall building; and (b) meteorological measurements in the vicinity of the interior face of a 12 m high building (average = av).

(a) OUTSIDE						(b) INSIDE
(STATION 3)	March					(STATION 1)	March
Hours	Days	Tav (°C)	RHav (%)	Tmax (°C)	RHmax	Hours	Days	Tav (°C)	RHav (%)	Tmax (°C)	RHmax
10:52/12:52	13	33.136	30.239	39.8	41.2	11:16/13:14	13	23.849	40.511	27.3	46.7
13:50/15:51	13	29.854	34.877	30.6	40.6	13:37/15:36	13	32.762	29.704	39.8	35.8
16:28/18:31	13	27.823	35.277	29.1	37.3	16:29/18:27	13	31.759	28.592	36.2	32.5
	av	30.27	33.46				av	29.46	32.94
10:27/12:28	14	24.288	51.569	31.8	70.7	11:02/13:01	14	19.815	60.404	22.8	69.8
13:21/15:22	14	23.612	51.626	24.4	53.5	13:26/15:10	14	26.545	44.144	36.2	53.8
16:30/18:28	14	23.335	52.964	24	56.2	16:35/18:34	14	28.824	40.332	33.5	49.8
	av	23.75	52.05				av	25.06	48.29
11:05/13:04	20	31.71	36.775	37.4	51.8	11:31/13:31	20	23.915	49.708	26.5	55.1
13:33/15:31	20	25.917	47.14	26.9	51.2	14:01/16:00	20	32.963	34.579	42.1	50
16:49/18:47	20	25.565	45.593	26.3	48.4	16:59/18:57	20	30.32	35.525	34.3	41.8
	av	27.73	43.17				av	29.07	39.94
11:00/12:58	21	34.064	32.446	43.2	53.4	11:26/13:24	21	25.283	44.349	28.5	51.8
13:36/15:34	21	28.182	39.399	29.1	46.9	14:12/16:10	21	37.218	26.515	44.6	41.7
16:43/18:42	21	27.838	38.884	28.7	41.9	16:53/18:51	21	33.01	29.784	39.3	35.9
	av	30.03	36.91				av	31.84	33.55

and

Table 2. Progressive increase in temperatures across six different locations from the period 2010–2013 to 2017–2020, and their decline during 2019–2022 due to the reduction in human activity caused by the coronavirus pandemic.

Height (msln)	2010/2013	2017/2020	2019/2022
784 (EML)	15.40	16.12	16.10
709 (EMM)	15.86	16.85	14.70
520 (EMN)	15.34	16.17	16.05
469 (EM0)	16.77	16.80	15.31
698 (EMS)	14.69	15.53	15.42
485 (EMV)	15.77	16.85	15.50

below, can manifest itself in a small, highly densified residential area with the presence of urban canyons and over exceptionally short time spans—such as 300 min or less. This brings forth a little-analyzed aspect: the temporal scale at which the phenomenon can occur, favored by a complex urban environment with virtually no tree vegetation. The above, along with the magnitude of the temperature increase during certain hours of the case under study—generally exceeding 10 °C relative to the average value—gives the heatwave event a singular and localized character. The results of urban meteorological data for temperature and relative humidity, measured over four randomly spaced days within a total of nine days during the summer season in basin-type geomorphology are presented in Table 1 and Table 2. The data were collected near the exterior and interior faces—at 9 m above ground level—of an old concrete building with plaster-covered masonry walls and a height of 12 m. In the case of the interior face, the phenomenon is associated with a weakening of RH.

Figure 7 shows, comparatively, the differences in temperature and relative humidity (average) for the exterior and interior areas:

3.2. Historical and Periodic Temperature Measurements

On the other hand, Table 2 shows the variation in average temperature for the periods 2010/2013, 2017/2020, and 2019/2022. These average values were measured at different altitudes due to the natural roughness of the city’s basin-like geomorphology. The most interesting case is the 2019/2022 period, due to the temperature decrease, which disrupts the upward trend observed during the 2010/2013 and 2017/2019 periods. This change is attributed to the drastic reduction in activities in Santiago de Chile caused by the Coronavirus pandemic.

Figure 8 shows the distribution of temperatures: increasing in the pre-pandemic period, followed by stabilization and a slight decrease during the pandemic.

3.3. The Kolmogorov Entropies of Pollutants and Urban Meteorology During the 2019/2022 Period Influence the Entire Basin of Geomorphology

The evolution of the entropy ratio during the periods 2010/2013, 2017/2019, and 2019/2022 [19,20] allows for visualization of the degradation of urban meteorology. Figure 9 shows the municipalities with the highest and lowest resulting entropic flows due to urban meteorology (temperature, relative humidity, wind speed magnitude).

Figure 10 presents the sum of the partial entropies, by municipality, due to the pollutants considered in this study (PM₁₀, PM_2.5, CO) for the 2019/2022 period.

Equation (2) represents the result of the interaction between urban meteorological entropies and pollutant entropies, shown in Figure 11.

3.4. Spearman Correlation

The reason for presenting the previous three figures is to explore a possible link between submicron particles (SPs) and coarse particulate matter. The SP measurements conducted for this study are extremely localized and cover a short summer period (days of a month). For this investigation, the Spearman correlation [36]—also known as Spearman’s rho—will be applied. It is a statistical measure that assesses the strength and direction of the monotonic association between two variables, a relationship that does not need to be linear. These coefficients can be positive, negative, or zero, indicating a positive, negative, or no relationship, respectively.

Unlike Pearson’s correlation [37], which measures the linear relationship between two variables, Spearman’s correlation can detect monotonic relationships (where variables change in the same direction, though not necessarily at the same rate). This analysis allows us to determine whether particulate matter of 2.5 µm and 10 µm has a monotonic association with SPs of 0.3 µm, 0.5 µm, and 1.0 µm. If such a relationship exists, many properties attributed to coarse particulate matter could be extended to SPs: entropy calculation, entropic layers, entropic force, influence of meteorology on SP concentration, etc.

The dataset corresponds to measurements taken on both the exterior and interior faces of the building where the measurement equipment was installed. The results, according to the Spearman analysis [38], are presented in

Table 3. (a) Contains the Spearman analysis for the exterior face of the building, the resulting values are summed in absolute value; (b) shows the Spearman correlation, p-value, summary of summed values in absolute value; (c) contains the Spearman analysis for the exterior face of the building, the resulting values are summed without absolute value; and (d) shows the Spearman correlation, p-value, summary of summed values without absolute value.

(a) + (b)		B 0.3 (µm)	B 0.5 (µm)		B 1 (µm)		B 10 (µm)		B 2.5 (µm)		B 5 (µm)		B RH (%)		B T(°C)		B WS (ms−1)
	B 0.3 (µm)			0.97		0.95		0.75		0.93		0.77		0.32		0.43		0.36
p-value			0.000		0.000		0.000		0.000		0.000		0.035		0.141		0.234
	B 0.5 (µm)					0.95		0.76		0.93		0.78		0.31		0.41		0.38
p-value					0.000		0.000		0.000		0.000		0.010		0.062		0.076
	B 1 (µm)							0.77		0.94		0.78		0.29		0.40		0.39
p-value							0.000		0.000		0.000		0.005		0.030		0.025
	B 10 (µm)									0.81		0.80		0.18		0.29		0.24
p-value									0.000		0.000		0.119		0.107		0.226
	B 2.5 (µm)											0.81		0.24		0.35		0.36
p-value											0.000		0.004		0.029		0.017
	B 5 (µm)													0.24		0.34		0.19
p-value													0.225		0.160		0.014
	B RH (%)															0.87		0.27
p-value															0.000		0.036
	B T (°C)																	0.22
p-value																	0.023
	WS (ms−1)
p-value
(c) + (d)		B 0.3 (µm)	B 0.5 (µm)		B 1 (µm)		B 10 (µm)		B 2.5 (µm)		B 5 (µm)		B RH (%)		B T(°C)		B WS (ms−1)
	B 0.3 (µm)			0.97		0.95		0.75		0.93		0.77		−0.08		0.21		−0.35
p-value			0.000		0.000		0.000		0.000		0.000		0.035		0.141		0.234
	B 0.5 (µm)					0.95		0.76		0.93		0.78		−0.10		0.22		−0.35
p-value					0.000		0.000		0.000		0.000		0.010		0.062		0.076
	B 1 (µm)							0.77		0.94		0.78		−0.09		0.22		−0.34
p-value							0.000		0.000		0.000		0.005		0.030		0.025
	B 10 (µm)									0.81		0.80		0.05		0.10		−0.16
p-value									0.000		0.000		0.119		0.107		0.226
	B 2.5 (µm)											0.81		−0.11		0.25		−0.31
p-value											0.000		0.004		0.029		0.017
	B 5 (µm)													0.11		0.02		−0.12
p-value													0.225		0.160		0.014
	B RH (%)															−0.87		0.16
p-value															0.000		0.036
	B T (°C)																	−0.11
p-value																	0.023
	WS (ms−1)
p-value

and

Table 4. (a) Contains the Spearman analysis for the interior face of the building, the resulting values are summed in absolute value; (b) shows the Spearman Correlation, p-value, summary of summed values in absolute value; (c) contains the Spearman analysis for the interior face of the building, the resulting values are summed without absolute value; and (d) shows the Spearman correlation, p-value, summary of summed values without absolute value.

(a) + (b)		B 0.3 (µm)	B 0.5 (µm)		B 1 (µm)		B 10 (µm)		B 2.5 (µm)		B 5 (µm)		B RH (%)		B T(°C)		B WS (ms−1)
	B 0.3 (µm)			0.95		0.94		0.86		0.90		0.71		0.72		0.68		0.33
p-value			0.000		0.000		0.000		0.000		0.000		0.000		0.000		0.005
	B 0.5 (µm)					0.96		0.89		0.94		0.74		0.68		0.65		0.37
p-value					0.000		0.000		0.000		0.000		0.000		0.000		0.001
	B 1 (µm)							0.87		0.94		0.74		0.67		0.63		0.38
p-value							0.000		0.000		0.000		0.000		0.000		0.001
	B 10 (µm)									0.91		0.73		0.62		0.59		0.32
p-value									0.000		0.000		0.000		0.000		0.104
	B 2.5 (µm)											0.77		0.59		0.55		0.37
p-value											0.000		0.000		0.000		0.004
	B 5 (µm)													0.59		0.57		0.17
p-value													0.000		0.000		0.142
	B RH (%)															0.99		0.27
p-value															0.000		0.000
	B T (°C)																	0.24
p-value																	0.000
	WS (ms−1)
p-value
(c) + (d)		B 0.3 (µm)	B 0.5 (µm)		B 1 (µm)		B 10 (µm)		B 2.5 (µm)		B 5 (µm)		B RH (%)		B T(°C)		B WS (ms−1)
	B 0.3 (µm)			0.95		0.94		0.86		0.90		0.71		0.72		−0.68		−0.25
p-value			0.000		0.000		0.000		0.000		0.000		0.000		0.000		0.005
	B 0.5 (µm)					0.96		0.89		0.94		0.74		0.68		−0.65		−0.28
p-value					0.000		0.000		0.000		0.000		0.000		0.000		0.001
	B 1 (µm)							0.87		0.94		0.74		0.67		−0.63		−0.26
p-value							0.000		0.000		0.000		0.000		0.000		0.001
	B 10 (µm)									0.91		0.73		0.62		−0.59		−0.30
p-value									0.000		0.000		0.000		0.000		0.104
	B 2.5 (µm)											0.77		0.59		−0.55		0.26
p-value											0.000		0.000		0.000		0.004
	B 5 (µm)													−0.59		−0.57		−0.10
p-value													0.000		0.000		0.142
	B RH (%)															−0.99		−0.27
p-value															0.000		0.000
	B T (°C)																	−0.24
p-value																	0.000
	WS (ms−1)
p-value

.

B.0.3, B.0.5, B.1, B.10, B.2.5, B.5, indicates that the relationship is calculated, in pairs, between (B) two variables, according to rows and columns, one of the variables being the diameters of the particulate material (0.3 µm, 0.5 µm, 1.0 µm, 10 µm, 2.5 µm). In the same way, B.R.H, B.T, B.WS: B indicates that the relationship is sought, in pairs, between (B) two variables, one of them being relative humidity (R.H), another is temperature (T), and another is the magnitude of the wind speed (WS), respectively. In addition, the Spearman’s rho value indicates the following: 0.00–0.19, very low correlation; 0.20–0.39, low correlation; 0.40–0.59, moderate correlation; 0.60–0.79, good correlation; and 0.80–1.00, very good correlation. They indicate the ranges of relationship between two systems of variables.

The Tables show a strong correspondence between the SPs and coarse types of particulate matter. It demonstrates that when the level of 2.5 µm particulate matter increases, the level of 0.3 µm particulate matter also rises. This is also confirmed with respect to the 0.5 µm and 1.0 µm data, which, although measured, are not the subject of analysis in this study.

The Spearman method applied to the database of this research (which considers particulate matter of 0.3 µm, 0.5 µm, 1.0 µm, 2.5 µm, 5 µm, and 10 µm, along with meteorological variables) shows low correspondence with urban meteorology (temperature (T), relative humidity (RH), and wind speed magnitude (WS)), which contradicts other studies [39,40,41,42,43] and numerous observations. The authors highlight the high correlation between temperature and relative humidity, confirming the results of a study carried out using entropy [16].

To seek an alternative solution, and considering that the measurement locality experienced a climatology of extremes [44,45] as shown in Table 1(a,b) (with days where temperature exceeded 40 °C), ratios were constructed based on the data measured in this study between SPs and urban meteorological variables temperature and relative humidity. Does the probability calculation of these ratios harmonize with the observations?

3.5. Heavy-Tailed Distribution

The SP data of 0.3 µm were normalized, for each measurement period, by the maximum value of that period, using the expression X = number of particles/maximum value of the measurement period. Relative humidity was normalized similarly, with y = relative humidity data/100, and temperature with z = temperature data/maximum temperature value of the period.

Finally, a dimensionless time series was constructed using the ratios X/y and X/z. The heavy-tail probability density of these quantities was then calculated using the Fréchet equation [45,46,47]:

$$f(x)=\alpha x^{-1-\alpha }{e}^{-x^{-\alpha }}, \mathrm{with} \alpha >0$$

(17)

This was carried out under the hypothesis of SP pollution occurring in an environment characterized by extreme conditions, such as overstressed urban micrometeorology due to heat islands, high human density, tall buildings, low presence of tree vegetation, extensive use of concrete, urban canyons, parallelepiped-type building geometry, narrow wind corridors, etc. The resulting probability distributions are shown in Figure 12, Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17.

Morning:

For the exterior face measurement period from 11:00 to 12:58, the average number of 0.3 µm particles is 64,707, the average relative humidity is 32.5%, and the average temperature is 34.01 °C. For the interior face measurement period (inner courtyard) from 11:26 to 13:24, the average number of 0.3 µm particles is 66,307, the average relative humidity is 44.4%, and the average temperature is 25.3 °C. The heavy-tail probability for extreme events was calculated separately for each period.

The elevated relative humidity observed in case (b) favors the atmospheric persistence of 0.3 µm SPs. This is supported by Figure 13, which indicates that the higher temperature in case (a) contributes to a reduction in the concentration of 0.3 µm particles.

Noon:

For the exterior face measurement period from 13:36 to 15:34, the average number of 0.3 µm particles is 62,237, the average relative humidity is 40.0%, and the average temperature is 28.2 °C.

For the interior face measurement period from 14:12 to 16:10, the average number of 0.3 µm particles is 50,793, the average relative humidity is 26.5%, and the average temperature is 37.2 °C.

The heavy-tail probability for extreme events was calculated separately for each period:

In this time interval, as shown in the figures below, the record of 0.3 µm SPs and the relative humidity on the exterior (Figure 14a) indicate a higher probability of persistence of SPs, which is the opposite for the interior face of the building (Figure 14b). This is further confirmed by Figure 15a, which shows that the amount of SPs has a higher probability of persistence for the same range of the ratio X/z.

Afternoon:

For the measurement period on the exterior side from 16:43 to 18:42, the average value of the number of 0.3 µm particles is 24,135, the average relative humidity is 39.0%, and the average temperature is 27.8 °C.

For the measurement period on the interior side from 16:53 to 18:51, the average number of 0.3 µm particles is 22,670, the average relative humidity is 29.8%, and the average temperature is 33.0 °C.

The heavy-tailed probability for extreme events is calculated for each period, as shown in Figure 16.

In the evening hours, as indicated by the previous figures, the record of SPs of 0.3 µm and the relative humidity on the exterior side (Figure 16a) show a higher probability of SP sustainability, whereas the opposite occurs on the interior side of the building (Figure 16b). This is corroborated by Figure 17a, which shows that the number of SPs has a higher probability of sustainability within lower temperature ranges. Figure 17b indicates that very low temperature ranges, when combined with low relative humidity, lead to a decrease in the probability of SP sustainability.

The application of heavy-tail probability techniques to extreme events suggests that urban meteorological conditions provide a sustaining framework for SPs. The observed upward trend in SP concentration, coupled with the persistence afforded by urban micrometeorology, indicates a shift toward extreme environmental conditions. This evolution presents significant challenges for mitigation, as the scale and complexity of required control measures could have far-reaching impacts across human activities.

4. Discussion

In Chile, the current primary standard for respirable particulate matter PM₁₀ is Supreme Decree No. 12/2022 [48] of the Ministry of the Environment, which, as stated, refers to coarse particulate matter (greater than 2.5 µm). The WHO (World Health Organization) does not have a specific definition for submicron particles, but the scientific community generally defines them within a restricted range from 0.01 to 1 µm. These particles are significant because their small size allows them to penetrate deep into the respiratory system, and they can be long-range transported in the atmosphere. There are no WHO regulations as rigorous as those for PM_2.5 and PM₁₀ for SPs, despite the growing number of studies warning of the greater risk that this range represents to human health.

An average human respiratory cycle includes inhalation (air entering the lungs) and exhalation (air leaving the lungs). Under normal conditions (low activity), the duration of one respiratory cycle is 4 s (s), consisting of approximately 1.5 s for inhalation and 2.5 s for exhalation.

Considering the measurements on the exterior face of the studied building, on 13 March 2025, during the hours 10:52 to 12:52 (100 min of measurements), and focusing on the morning period—when the highest average number of 0.3 µm SPs was observed—we have: 100 min = 6000 s, which corresponds to 1500 full inhalation-exhalation cycles. This implies 2250 s of inhalation, equivalent to 37.5 min.

Today, what reaches the lungs can be directly related to what a sensor measures, specifically in the context of pulmonary function testing and respiratory monitoring. Sensors can detect various parameters related to inhaled and exhaled air, as well as the state of the lung tissue itself, and these measurements can be used to assess lung health [49,50,51].

If the average number of 0.3 µm particles per minute is 57,357.27 particles/min, then, an approximate accumulated average of 2,150,898 particles would be inhaled over the 37.5 min—an enormous number of particles, whose size makes exhalation nearly impossible. The total accumulated count of particles, in very approximate form and under very favorable conditions, over the 100 min period is 5,735,727 particles, with a maximum of 75,852 and a minimum of 31,363.

During the measurement process, the instrument’s alarm was triggered several times, signaling that the particle count exceeded the normative threshold (Appendix C, Figure A14).

This investigation, despite covering a relatively short period, confirms the magnitude of SP presence in areas of high urban density with poor ventilation, and its high persistence in the morning hours. If we assume that the induced processes are of an irreversible and extreme nature, the heavy-tail probability model [45] provides plausible confirmation.

If we accept the strong Spearman correlation between coarse particulate matter and SPs, it becomes possible to extend properties of coarse particulate matter [19,20]—such as entropy, entropic forces, entropic surfaces, strong entropic interaction between particulate matter and urban meteorology, and geomorphology-dependent anomalous diffusion—to SPs as well.

It is worth highlighting that coarse particulate matter exhibits anomalous sub diffusion behavior with α < 1 [20] in basins, implying its settling and persistence in the geographic basin. The health effects of fine particulate matter on the population have been the subject of numerous studies [52,53,54,55,56]. It is necessary to carry out extended and intensive studies on the range of dimensions that involve SPs [57,58,59,60].

Considering that the area selected for these measurements is located within a geomorphological basin, and that the specific measurement site lies in the central part of the basin—characterized by high-rise buildings, urban planning that promotes poor ventilation, low tree cover, narrow and deep urban canyons, narrow streets, high population density, heavy vehicular flow, and intensive use of high-albedo concrete in construction, along with commercial spaces acting as attractors of human presence and interaction, which becomes even more complex under pandemic conditions, it is highly likely that many diseases may be exacerbated in such an artificial environment that favors the persistence of fine particulate matter and SPs, as suggested by the measurements carried out.

This research focused on short-term measurements, given the numerous studies demonstrating the serious consequences of environments with high concentrations of fine particles, now including SPs, on human health. This demonstrates that a combination of urban density, relative humidity, and temperature helps maintain, for a short period, the number of fine particulate matter and SPs at ground level (a level where 100% of the population travels, and, moreover, during a very dry summer period, optimal for facilitating measurements). Studies conducted during other seasonal periods, especially autumn and winter, may demonstrate mitigation of the health effects for the population, but would confirm the risks predicted by the summer records.

5. Conclusions

The analysis of the data obtained from the measurements confirms a very high presence of fine particulate matter during the summer period. The number of SPs is significantly higher in the morning hours. The representations in the figures of the variation in the number of SPs throughout the morning, midday, and afternoon indicate that relative humidity plays a key role during the morning, either increasing or maintaining the number of SPs, particularly the 0.3 µm particles. These results confirm the objectives set out in this study.

In summary, the following can be stated:

• The behavior of SPs around 0.3 µm supports the hypothesis of an extreme condition environment, as its predictability aligns with a heavy-tail probability distribution.
• Urban micrometeorology (at heights below 20 m), characterized by relative humidity and temperature, when exposed to strong thermal stress (urban heat islands, heat waves, and urban canyons), enhances the relevance of the heavy-tail probability model, which reflects the persistence of SPs and fine particulate matter.
• The upper floors of tall buildings (such as those located 12 m above ground level) are not immune to the effects of concentration and persistence of SPs and fine particulate matter.
• There are periods of the day (morning, midday, late afternoon–evening) during which the behavior of particulate matter shows similar heavy-tail probabilities across measurement intervals—regardless of whether the location is inside or outside a building. In this study, the morning period exhibited such behavior.
• The behavioral model described, based on data collected during the summer period, was consistent across all measurements taken over a span of four weeks.
• The behavior and properties of coarse particulate matter can, as a first approximation, be extended to fine particulate matter.
• A highly densified urban environment significantly favors the presence (in both number and concentration) of SPs and fine particulate matter, substantially increasing the probability of severe health impacts on the population.