Tools for planning large-scale measurement surveys for the assessment of indoor environmental pollutants: the case of radon

Sample size

One of the first steps in planning a national, regional or large-area radon measurement survey is to calculate how many homes will need to be measured within the administrative districts. A simple way to define the total number of dwellings to be measured in the survey is to use an algorithm based on population^[23] or based on number of dwellings $$ N_{M}^{dw} $$ in municipalities provided by the National Institute of Statistics. For each municipality $$ M $$, the sample size $$ K_{M}^{dw} $$ of dwellings to be measured can be calculated with the algorithm:

The parameter $$ p $$ depends on the survey resources, and is chosen according to the maximum total number of indoor radon measurements that can be made in the survey. The parameter $$ m $$ is set as the minimum sample size to ensure that the parameter error estimated from radon concentrations is less than a certain value. In SD-based surveys it may be preferable to consider only dwellings on the ground floors so, using the number $$ N_M^{d w}\left(f_0\right) $$ of dwellings on the ground floors, the sample $$ K_M^{d w}\left(f_0\right) $$ of dwellings on the ground floors to be measured is given by:

When the number $$ N_M^{d w}\left(f_0\right) $$ in municipalities is not provided by the National Institute of Statistics, it can be estimated in a municipality $$ M $$ from data on the number of residential buildings by number of above-ground storeys ($$ a g s $$). Buildings with $$ a g s= $$ 1 have only ground floor $$ f_0 $$, buildings with $$ a g s=2 $$ have ground floor $$ f_0 $$ and first floor $$ f_1 $$, and so on. The total number of ground floors of buildings, $$ N_M^{f_0} $$, in municipality $$ M $$ corresponds to the number of buildings, because all buildings have the ground floor. The total number of $$ i $$-th floor in the municipality $$ M $$, is given by:

where $$ i $$=0, 1, … $$ Z $$-1 is the floor level in the building.

The total number $$ N_M^f $$ of floors in buildings in municipality $$ M $$ is given by:

The fraction of ground floor $$ \%_M^{f_0} $$ in municipality $$ M $$ is given by:

Assuming that dwellings are evenly distributed on the floors of buildings, the total number $$ N_M^{d w}\left(f_0\right) $$ of dwellings on the ground floor in municipality $$ M $$ is given by:

In the case of Italy, where the population of about 60 million is distributed in about 8, 000 municipalities, the data show that 43% of the dwellings are on the ground floor and that in the most populated cities the $$ \%_M^{f_0} $$ is lower because the buildings are taller on average. Municipalities with populations above 300, 000 have $$ \%_M^{f_0}<40\% $$, while municipalities with populations below 300, 000 can reach $$ \%_M^{f_0}\sim 100\% $$ [Figure 1].

Figure 1. Fraction of ground floors in the municipalities as a function of the population.

Given $$ N_M^{d w}\left(f_0\right) $$, it is possible to use expression (2) to calculate $$ K_M^{d w}\left(f_0\right) $$.

Choosing $$ p=0.4 $$ and $$ m=10 $$, and considering all $$ N_{IT}^{d w} $$ dwellings in Italy, Equation (1) allows us to calculate the nationwide sample of dwellings, which would equal 173, 253 dwellings. Considering only ground-floor dwellings, Equation (2) and Equation (3) allow estimating the total sample of dwellings to be measured nationwide, $$ K_{IT}^{d w}\left(f_0\right) $$, equal to 128, 432. To decrease the cost of the survey by giving up part of the information, lower values of the p and $$ m $$ parameters can be chosen Table 1.

Samplig plan tool

The Sampling Plans Tool (SPT) is a computer tool that supports the planning of house sampling when designing an indoor radon measurement survey. Having defined the type of sampling, which depends on the objectives of the survey, the tool identifies the number of dwellings to be measured within each 1 km grid square based on the population, considering the average number of occupants per dwelling in municipality $$ M $$ provided by the National Institute of Statistics. The spatial distribution of the sample of dwellings is then represented on a map. The JRC GEOSTAT, a regular grid map of 1 km × 1 km grid squares, developed by European Commission Joint Research Centre with the collaboration of Eurostat, reporting the number of residents for the year 2018 for Europe, was used for the population data^[24].

Intersecting the $$ 1 \mathrm{\; km} $$ grid squares $$ S_i $$ with the polygons of the municipalities we obtain fractions $$ F_{ij} $$ of the grid squares:

where $$ A\left(S_i\right) $$ is the area of the grid square $$ S_i $$; and $$ N_i $$ is the number of $$ F_{ij} $$ that form $$ S_i $$.

Each $$ F_{ij} $$ has:

$$ A\left(F_{ij}\right) $$, area in sqkm of the fraction $$ F_{ij} $$;

$$ Pop\left(F_{ij}\right)=Pop\left(S_i\right) / A\left(F_{ij}\right) / 1000000 $$, population within the $$ F_{ij} $$ proportional to its area $$ A\left(F_{ij}\right) $$.

If $$ S_i $$ is entirely within a municipality, then:

$$ A\left(S_i\right)=A\left(F_{i i}\right) \text {, for } j=i. $$

When the $$ S_i $$ intersects the municipal boundary, one of the $$ F_{ij} $$ will be larger than the others, so suppose that: $$ A\left(F_{i k}\right)=\operatorname{Max}\left[A\left(F_{ij}\right)\right] \text {, when } j=k \text {. } $$

The SPT selects the $$ F_{ij} $$ in which dwellings are to be sampled ($$ sampling =1 $$) in the following way:

this allows for the exclusion of smaller $$ F_{ij} $$ that fall outside municipal boundaries;

this makes it possible to exclude $$ F_{ij} $$ with a small number of inhabitants. In this application, the threshold $$ Pop_{\min }=20 $$ was chosen to exclude $$ F_{ij} $$ with less than 20 inhabitants.

Sample of dwellings from a spatial distribution of the population-based survey

When the objective of the measurement survey is to know the spatial distribution of indoor radon levels, a sample of ground-floor dwellings uniformly distributed over the area of interest can be selected. First the SPT sorts the $$ F_{ij} $$ by increasing municipality code and then by decreasing $$ Pop(F_{ij}) $$ in order to identify the $$ F_{ij} $$ where the dwellings to be measured are to be sampled, according to Equation (4), Equation (5) and Equation (6). In each municipality $$ M $$ we have a number $$ K_{M}^{d w}\left(f_0\right) $$ of ground-floor dwellings to be sampled and a number $$ N_{M, ij} $$ of $$ F_{ij} $$ in which $$ K_{M, ij}^{d w}\left(f_0\right) $$ dwellings are to be sampled.

In each municipality M we have [Table 2]:

$$ K_M^{d w}\left(f_0\right) $$, number of dwellings on the ground floor to be sampled, given by (2); $$ N_{M, ij} $$, number of $$ F_{ij} $$ in which $$ K_M^{d w}\left(f_0\right) $$ dwellings are to be sampled, identified according to Equation (4), Equation (5) and Equation (6); $$ K_{M, ij}^{d w}\left(f_0\right) $$, number of ground-floor dwellings to be sampled attributed to each $$ F_{ij} $$, such that:

The resulting number of ground-floor dwellings $$ K_{M, ij}^{d w}\left(f_0\right) $$ to be selected in the $$ F_{ij} $$ is calculated by the SPT and varies as a function of $$ K_M^{d w}\left(f_0\right) $$ and $$ N_{M, ij} $$ of municipality $$ M $$ [Table 2].

The SPT provides the spatial distribution map of the sample $$ K_{M, ij}^{d w}\left(f_0\right) $$ indicating the number of ground-floor dwellings to be measured for each $$ 1 \mathrm{\; km} $$ grid square [Figure 2A]. The resulting sampling plan includes radon measurements at ground floors in both major population centers and less densely populated areas, resulting in more accurate information on the spatial distribution of radon levels.

Figure 2. (A) Detail of sampling plans of an SD-based survey and (B) a PD-based survey obtained by SPT considering ground-floor dwellings and parameters p = 0.4, $$ m=10, Pop_{min}=20 $$. PD: Population density; SD: spatial distibution; SPT: Sampling Plan Tool.

Sample of dwellings from a population density-based survey

When the objective of the radon measurement survey is to assess population exposure, the sample must be representative of the population, so it is necessary to select a sample of dwellings in all floors of buildings proportional to the population.

In this case, the SPT sorts the $$ F_{ij} $$ by increasing municipality code and then by decreasing $$ Pop\left(F_{ij}\right) $$ in order to identify the $$ F_{ij} $$ in which the $$ K_{M, ij}^{d w} $$ dwellings to be measured are to be sampled. In each $$ F_{ij} $$ the fraction of $$ Pop\left(F_{ij}\right) $$ of the total population of the municipality $$ Pop(M) $$ is calculated:

Then the number $$ K_{M, ij}^{d w} $$ of dwellings to be sampled in $$ F_{ij} $$ is given by:

The SPT provides the spatial distribution map of the sample $$ K_{M, ij}^{d w} $$ indicating the number of dwellings to be measured per 1 km grid square. This sampling plan includes radon measurements in dwellings in major population centers, resulting in more representative information of the population; however, less populated areas are not well represented. Expression (7) can also be applied by considering only ground-floor dwellings $$ K_M^{d w}\left(f_0\right) $$ in order to obtain a sample proportional to the population but referring to ground floors [Figure 2B]. This salmple, while not representative of population exposure, will better represent the major population centers and could be used for the identification of areas with high radon levels.

An additional parameter $$ h $$ can be included in Equation (7) to obtain a sample of $$ K_{M, ij}^{d w} $$ dwellings that retains more information in the most densely populated centers but extended to more $$ F_{ij} $$ to characterize smaller population centers as well: $$ K_{M, ij}^{d w}=K_M^{d w} \cdot \%\left[Pop\left(F_{ij}\right)\right] / h $$, with $$ h=1 $$ the sample is proportional to the population as in (7).

The procedure allows obtaining national sampling plans based on the survey objectives and defined criteria [Figure 3]. The sampling plan obtained for the SD-based survey [Figure 3A] reaches a larger portion of the country, with about 24, 000 $$ S_i $$ 1 km grid squares more [Table 3] than the sampling plan of the PD-based survey [Figure 3B], because in the former case the dwellings selected for indoor radon measurement are more spatially distributed, while in the latter case they are concentrated in the major population centers. This can be appreciated from the larger dark areas that result in the map of the national sampling plan of the SD-based survey compared to the map of the PD-based survey [Figure 3].

Figure 3. National sampling plan maps of dwellings in Italy for (A) SD-based survey and (B) PD-based survey obtained from SPT considering ground floor dwellings and parameters p = 0.4, $$ m=10, Pop_{min}=20 $$. PD: population density; SD: spatial distibution; SPT: sampling Plan Tool.

Sample recruitment

The sampling plan indicates the number of dwellings to be measured in each 1 km grid square calculated with the criteria and parameters established according to the objectives of the survey [Figure 2]. After that, the dwellings must be physically identified in order to ask the owners or occupants to join the survey, i.e., to obtain the opportunity to install radon detectors to carry out the indoor radon concentration measurement. If in a grid square the SPT has indicated 3 dwellings to be measured [Figure 4], it is preferable to triple the number of dwellings to be selected in the grid square to account for refusals by homeowners or occupants to participate in the survey.

Figure 4. Grid square (1 sqkm) in which SPT indicates a sample of 3 dwellings to be selected for making indoor radon measurement. The background map shows building polygons and addresses. From the attribute tables of the open-source vector data, residential buildings can be distinguished. SPT: Sampling Plan Tool.

To locate a $$ K_{M, ij}^{dw} $$ number of dwellings to be measured in an $$ F_{ij} $$, a number $$ K_{M, ij}^{dw} $$ of dwelling addresses must be selected in the $$ F_{ij} $$. To obtain a random location of dwellings in the $$ F_{ij} $$, one must generate random values of coordinate pairs that have values internal to the $$ F_{ij} $$ and obtain the addresses of those locations (or the nearest addresses within the grid square) from a geocoding system.

These addresses can be searched in registry office lists and will correspond to as many names of residents. People can be contacted by telephone, by retrieving the phone from telephone utility databases, or by letter to be delivered by the municipal government or a central institution that is organizing the survey, or even door-to-door, in order to obtain consent to participate in the indoor radon measurement survey.

Passive radon detectors used in extended measurement surveys are small and lightweight, so they can be mailed to survey participants, or they can be delivered door-to-door to selected homes and installed by operational teams. In most municipalities, which are small in size, radon detectors can be delivered to homes by municipal government contact persons.

In this way, the sample of homes where indoor radon measurements are to be made has been selected from an exhaustive set of addresses within each sampling unit^[25].

National strategy for the identification of radon areas

A national radon protection strategy is a programme of actions that must include indoor radon measurement surveys, radon risk information campaigns for the population and workers, financial support for radon measurements and remedial actions, and much more. National authorities have to take decisions because implementing these actions is very complex and costly. High radon levels can be found anywhere in the country but, for mainly geological reasons, there are areas where buildings with high radon levels are much more likely to be found. The radon action programme may be implemented preferentially in these areas, and in buildings that are heavily occupied^[10].

The European regulation requires Member States to identify areas where the annual average radon concentration in a significant number of buildings is expected to exceed the relevant national RL (art.103)^[11].

Since both the radon concentration and the population vary spatially, there will be areas in which both variables take on high values. These areas, which are likely to be small compared to the entire country, contain a large fraction of the total risk. By carrying out radon measurement surveys in these areas it will be much more likely to identify buildings that exceed the RL than outside, obtaining a great advantage in terms of cost effectiveness. National authorities should carry out national radon measurement surveys in order to identify radon areas in a relevant way, because this means optimising available resources. The SPT can support this task by enabling the planning of household sampling according to the set objectives, providing the tools to control the survey by helping to reduce possible sources of bias and providing the expected results in a form suitable for regulators.

By substituting $$ K_M^{d w}\left(f_0\right) $$ in expression (7), we consider only ground floor housing to be conservative. The resulting sampling plan outlines a national PD-based survey representative of the ground floor housing stock in each municipality $$ M $$ [Figure 3B]. Using the data measured in the PD-based survey, it will be possible to estimate the parameters of the log-normal distribution of radon concentrations and calculate the fraction of the distribution that exceeds the RL^[26], corresponding to the fraction of ground floor dwellings that exceed the RL, $$ \%_M^{dw>RL}\left(f_0\right) $$.

Without a proper sampling plan, if the sample of dwellings to be measured were based on scattered measurement surveys or derived from citizens' requests stimulated by information campaigns, we would have no guarantee that the $$ \%_M^{dw>RL}\left(f_0\right) $$ estimated for the municipality is correct. An overestimation would lead us to invest resources where it is not justified, an underestimation to neglect the problem by shifting resources to other areas. To avoid these biases, we would need such a large number of measures (sample size) to be able to represent the real situation of the municipality in each case.

In municipality $$ M $$, the number of dwellings on ground floors where the radon concentration is above the RL is given by:

Where $$ N_M^{dw}\left(f_0\right) $$ is the total number of ground floor dwellings in municipality $$ M $$, estimated using Equation (3).

By defining the value of $$ N_M^{dw>RL}\left(f_0\right) $$ that is considered significant, it is possible to decide whether municipality $$ M $$ is identified as a radon area in accordance with European regulations^[11]. Identified radon areas can be provided to the EU Member state regulators in the form of a list of administrative districts, such as municipalities^[27]. It would be more useful to identify radon areas with 1 km grid squares but regulators often prefer to use administrative areas, such as municipalities, because they are more directly related to the responsibilities and decisions of the competent authorities. In these areas, remedial actions to reduce the radon concentration of buildings above the RL will allow to reduce the exposure of residents by prioritizing situations above the RL (EC 2013^[11]), and to reduce average concentrations of radon in dwellings (IAEA 2015^[19]). Achieving the same result by acting outside the areas would require much greater effort.

Radon areas must be used to prioritize the most important situations, without neglecting the rest. To act on the remaining part of the risk in the country, which is located outside the areas, it is necessary to implement a national radon strategy that impacts exposure in the long term, introducing appropriate practices in the construction of new buildings and regulations on building materials, identifying the typologies of workplaces, work activities and buildings with public access that have greater risk, training health and safety professionals and establishing synergies with national strategies against tobacco smoking and those for energy efficiency in buildings. Continuing radon surveys is equally important and the radon areas can be updated over time by incorporating additional municipalities.

Detection of RL exceedances within radon areas

The large-scale survey made it possible to identify radon areas by taking a few annual average radon concentration measurements in selected dwellings in each municipality. Now it is necessary to carry out dense measurement surveys with many measurements in a few selected municipalities (radon areas).

A comprehensive radon measurement survey within the radon areas will identify many RL exceedances, but not all buildings in these municipalities exceed the RL, and measuring all dwellings would be too expensive. Information indicating where RL exceedances are most likely to be found is needed in order to make the ratio of detected exceedances to radon measurements made efficient.

Previously made indoor radon measurements for the identification of radon areas already provide some indications to guide the dense survey but further information is needed.

Since the main source of indoor radon concentration is soil, many authors have focused on investigating geological factors. European regulators have taken these aspects into account in the Council Directive (Annex XVIII)^[11]. The strategy for conducting surveys to measure indoor radon concentration could be supplemented with additional parameters, such as soil and rock types, permeability and radium-226 content of rock or soil. By overlaying appropriate digital geological maps^{[28, 29]}, each $$ F_{ij} $$ can include a set of parameters that allow its geogenic radon weight to be calculated. Each $$ F_{ij} $$ would be characterized by its area $$ A(F_{ij}) $$, population $$ Pop(F_{ij}) $$, and geogenic weight $$ W(F_{ij}) $$. The new $$ W(F_{ij}) $$ parameter gives sampling priority in areas with higher geogenic potential. The SPT can sort the $$ F_{ij} $$ by increasing municipality code and then by decreasing $$ W(F_{ij}) $$ and decreasing $$ Pop(F_{ij}) $$, resulting in a SD-based survey sampling plan spatially targeted to the inhabited areas with higher geogenic potential. Similar to the exclusion threshold $$ Pop_{min} $$ used for population, a threshold $$ W_{min} $$ can be introduced in order to exclude $$ F_{ij} $$ with lower geogenic weights. The resulting sampling plan would include radon measurements in ground-floor dwellings in the most densely populated areas selected from those with the highest radon geogenic potential, resulting in the opportunity to identify more dwellings exceeding the reference level.

Since European legislation imposes compulsory radon measurements in workplaces on ground floors and basements within radon areas (art.54)^[11], national authorities can also use these measures to improve the orientation of the dense survey.

Acknowledgments

The National Inspectorate for nuclear safety and radiation protection (ISIN) took over responsibility for nuclear safety and radiation protection from 1 January 2019. The research, carried out without specific funding, is a research initiative of the author and does not commit ISIN as the technical regulatory authority for nuclear safety and radiation protection.

Authors' contributions

The author contributed solely to the article.

Availability of data and materials

The JRC-GEOSTAT 2018 gridded population estimates are available from the Eurostat, GISCO webpage: https://ec.europa.eu/eurostat/web/gisco/geodata/reference-data/population-distribution-demography/geostat.

Financial support and sponsorship

None.

Conflicts of interest

All authors declared that there are no conflicts of interest.

Ethical approval and consent to participate

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Copyright

© The Author(s) 2024.