Bogotá is located at the western side of the eastern Andes cordillera at an average altitude of 2640 m a.s.l. (above sea level) (Fig. ). The urban area of Bogotá is divided in 20 localities, 5 of which were included in the present study Fig. ;. Bogotá's temperature ranges between 8 and 19 °C throughout the year, with an annual average value of 13 °C. It has an average precipitation of 80 mm per month throughout the year with a minimum of around 40 mm in January and a maximum of around 120 mm in May . The geology of the Bogotá region is characterized by outcrops from the late Cretaceous to the Quaternary . According to the Geologic Map of Colombia the main lithologies in Bogotá with their respective chronostratigraphic codes are limestones and shales (k1k6-Stm) near the municipality of La Calera, alluvial fans and colluvial deposits (Q-ca) to the east of the city, and clays (Q1-l) in the central area of Bogotá (see Fig. ). Additionally, due to an excessive extraction of water from underlying aquifers, there is strong subsidence in the city, reaching values of 3.5 cm yr-1 . Furthermore, Bogotá's rapid growth in the first half of the 20th century resulted in nearly 35 % of the houses in the city being built over 40 years ago .

Since this study was performed during the COVID-19 pandemic, an online registration form was sent via social media and filled out by 79 owners of residences who wanted to participate. Based on previous studies the selection criteria to determine which dwellings would be sampled were the type of residence (house or apartment), the presence of a basement and the lithology below the dwelling . The influence of these factors on IRC is presented in Table . The selection of houses was also made to ensure that indoor measurements in the five localities surveyed would have a minimum sampling rate of one sample every 15 km2.

Several methods for measuring radon currently exist; however, the most economic and widely used is the alpha-track detectors e.g.,. In this study, Kodak LR-115 alpha-track detectors were placed in the selected houses for a period of 35 d between 20 February and 28 March 2021. The detectors were supplied by the Applied Nuclear Physics and Simulation (FINUAS) laboratory, and the diffusion chambers were assembled as shown in Fig. .

The LR-115 film was placed in the upper part of the diffusion chamber as described by (see Fig. b). The dimensions of the diffusion chamber were selected to ensure that the conversion factor (1.4 tracks cm-2 (kBq m-3 h)-1) used by could be applied. This conversion factor has been used with LR-115 film and validated against active methods seefor details.

The alpha-track detectors were placed at a height of 60–180 cm above the ground; at a minimum distance of 15 cm from the walls; and away from doors, windows and electronic devices to avoid environmental interference that may induce larger measurement errors . Additionally, a thin film of polyethylene was added to the lower part of the chamber to avoid humidity and/or dust. Once installed, residents of the dwellings sent pictures of the sensors on a weekly basis so that any changes in the location and/or conditions of the detector could be recorded.

After the 35 d exposure, the detectors were retrieved and shipped to the FINUAS lab in Tunja, Colombia, where they were analyzed. The analysis consisted of etching the LR-115 film with the process described by . The alpha-track density (ρtr) was then determined by counting the number of etched tracks per square centimeter under the microscope. Afterwards, IRC was calculated using the conversion factor determined by as described in Eq. (). 1IRCBqm3=ρtrt⋅CF⋅1000, where ρtr represents the density of alpha tracks (tracks per square centimeter), t is the time exposed (h) and the conversion factor (CF = (1.4 tracks cm-2 (kBq m-3 h)-1) is the same determined by .

To evaluate the precision of the detectors, duplicate LR-115 film was included in 11 of the diffusion chambers selected randomly and placed in front of the other film inside the diffusion chamber. The relative percent difference (RPD) was calculated as suggested by (see Eq. ). 2RPD=|IRCsample-IRCduplicate|mean(IRC)×100

The predictor variables for fitting the regression model, which include geologic, meteorological and building-specific factors, were acquired from multiple sources. These sources included an online form completed by the participants and six other distinct data sources listed in Table . The spatial distribution of the meteorological and geologic variables can be found in Appendix  in the additional images.

The regression model used three dummy variables which included the house age and two variables related to the lithology. For the variables explaining the lithologies in the area, the reference category was selected to be the lithology characterized by clays (Q1-l). Furthermore, the houses built after 1980 were chosen as the reference category for the house age variable.

Finally, the dataset to which the regression model was applied was retrieved from Bogotá's cadaster dataset. A subset of the dataset was selected while making sure that the residences followed two criteria: (i) buildings with less than three stories (houses) and (ii) buildings where one of the three studied lithologies, analyzed in the statistical analysis, was present. The data of the predictor variables were finally added to each house in this dataset.

The result of the pre-processing resulted in two tabular datasets that from now on will be called the in situ dataset and cadaster dataset for simplicity. In the first one, the data consisted of the in situ measurements and the predictor variables. On the other hand, the second one contains the spatial and predictor information of the houses in the cadaster to which the regression model was applied.

The statistical analysis consisted of (i) fitting a log-linear regression model to the dataset with in situ measurements, (ii) evaluating the performance using cross-validation, (iii) undergoing a process of feature selection, (iv) fitting a final log-linear regression model, (v) estimating the radon concentration using the final model and (vi) visualizing the IRC estimations spatially (Fig. ).

A log-linear multivariate regression model was used to establish the association between one dependent variable (log⁡(IRC)) and five independent variables. The model included geologic, meteorological and construction variables. Similar approaches have been used to estimate IRC in other study areas . The log-linear regression model was fitted with Eq. (). Every independent variable in the log-linear model can be interpreted by finding a percentage change in IRC due to an increase of that independent variable by a unit. This percentage change can be calculated for each variable as described in Eq. (). The statistical analysis was performed using the statsmodels and scikit-learn packages in Python 3.11. 3log⁡(IRC)=β⋅X+ξ, where β represents a vector with coefficients for each independent variable, X is a matrix with the values of the independent variables and ξ is the error. 4Percentagechangei[%]=100⋅eβi-1

The performance of the regression model was assessed using the leave-one-out cross-validation approach. This cross-validation method gives an estimation of the test error that is approximately unbiased . To measure the error of the model, the root mean squared error (RMSE) was used as described in Eq. (). 5RMSE=∑i=1ny^i-yi2n

In addition to the leave-one-out cross-validation, the Python package spacv (https://github.com/SamComber/spacv, last access: 17 April 2024) was used to perform a 15-fold spatial cross-validation to further validate the robustness and generalization capabilities of the regression model's predictions . Spatial cross-validation accounts for potential spatial auto-correlations in the data, providing a more comprehensive assessment of the model's performance across diverse spatial contexts .

Originally, the log-linear model included four more variables that we considered could have an association with high IRC (fault proximity, temperature, urban/rural area and land subsidence). Nevertheless, they were later removed to reduce the chance of overfitting and increase the model performance by focusing on the most informative features. According to their high variance inflation factor, the variables of land subsidence, temperature and urban/rural area introduced multicollinearity problems into the model; therefore they were discarded. Moreover, since fault proximity values in houses of Bogotá are above the 150 m threshold that previous authors have shown to have a significant association with higher IRC in dwellings, this variable was not considered in the present study . Removing these features did not substantially affect the cross-validation estimation of the test error.

The fitting of the final model was finally done with the selected features. The final log-linear regression model followed Eq. () and was trained using the statsmodels and scikit-learn packages in Python 3.11.

The log-linear multivariate regression model fitted with the in situ dataset was used to produce a map of estimated IRC with the cadaster dataset. The IRC estimated for the houses was then aggregated in a grid of cells of 100 m × 100 m. The grid was created and then visualized using the GeoPandas and Plotly packages in Python 3.11.

A dashboard web application that allows for the modeling and spatial visualization of estimated IRC by using in situ measurements was developed. The dashboard layout consists of three main blocks that are shown in Fig. . In the first block, the user is expected to add the two sets of tabular data (previously called the in situ and cadaster dataset). Then, the second block allows the user to explore the in situ data, choose the parameters for the modeling and run the model (left section of block 2 in Fig. ). The visualizations in this block show the distribution of IRC measured with respect to reference levels, a correlation matrix of the predictors in the in situ dataset and the variance inflation factor for the predicted variables (right section of block 2 in Fig. ). Furthermore, the parameters that can be chosen by the user are the type of model to be fitted, features selected to train the model, a high-quality model to get a higher-spatial-resolution result and the projected coordinate reference system in which the cadaster data are projected. Finally, the third block exhibits the results of the model. On the left side the feature importance and the cross-validation scores are presented, and on the right side the spatial distribution modeled is presented in an interactive map.

The dashboard web application was built and deployed using the Dash package in Python 3.11 and the servers of pythonanywhere.com (https://eu.pythonanywhere.com/, last access: 17 April 2024). Furthermore, the dashboard can be accessed at http://ircmodelingdashboard.eu.pythonanywhere.com/ (last access: 17 April 2024).

The study of residential 222Rn in Latin America and the Caribbean (LAC) remains largely unexplored . This was the third study of indoor 222Rn conducted in Colombia and had the second largest number of observations . Both previous studies were conducted in Manizales and presented a mean IRC of 8.5 and 68 Bq m-3 . Our study presents the highest levels found in the country. The higher levels found in Bogotá with respect to Manizales could be explained by a smaller ventilation rate, related with a lower frequency of window and door opening, caused by lower mean temperatures . Additionally, the exclusive measurement in ground floors and basements in our study could also explain the high IRC levels measured . The proximity of these areas to radon sources contributes to the higher accumulation of 222Rn in these spaces .

The mean values reported in the 31 previous studies done in the LAC region ranged between 9 and 358 Bq m-3 (Fig. a). The IRC measured in this study is in the upper range of the reported levels for the LAC region. Until 2020, it was reported that 24 out of the 31 studies had measured IRC in more than 30 residences Fig. b. The geometric mean IRC of the current study exceeds the geometric mean of 58 % of these 24 studies Fig. c. This corroborates the high IRC measured in Bogotá compared to the values reported in the region.

The WHO's recommended level (100 Bq m-3) was exceeded in 57 % of the residences analyzed in this study (Fig. ). Even though the Colombian action level (400 Bq m-3) was exceeded only in one house (Fig. ), there is enough scientific evidence to assert that the exposure to IRC, even below the WHO's recommended level, can affect human health . Therefore, high IRC levels such as the ones found in this study raise concerns about the potential health impacts that 222Rn could be causing in Bogotá's population.

Considering the absence of monitoring programs in the country and that our study had a limited sample set, the modeling dashboard developed in this study was used to create a prediction map of the potential distribution of IRC. This map represents an alternative to assess the magnitude of 222Rn hazard in the city and establish target areas for future studies (Fig. ). The map predicted IRC ranging from 21 to 220 Bq m-3. Moreover, considering the smoothing tendency of the models used and that prediction uncertainty was not accounted for in the statistical analysis, the model suggests that a minimum of 32 % of the 551 570 houses (177 008 residences) could have IRC above the WHO's recommended level Fig. a;. Considering that the mean household density in Bogotá is 2.9 inhabitants per household, a total of 513 323 people could be exposed to IRC above recommended levels. Notably, the average IRC in the localities of Los Mártires, Fontibón, Teusaquillo, Barrios Unidos and Puente Aranda was estimated to be above 100 Bq m-3 (Fig. b). All of these localities are found near downtown Bogotá, which is the oldest area of the city. Even though the map created in our study shows the highest predicted IRC in zones built before 1980, it is necessary to extend the direct measurements to other areas to confirm our predictions.