A Spatiotemporal Ensemble Model to Predict Gross Beta Particulate Radioactivity Across the Contiguous United States

Abstract

Particulate radioactivity, a characteristic of particulate matter, is primarily determined by the abundance of radionuclides that are bound to airborne particulates. Exposure to high levels of particulate radioactivity has been associated with negative health outcomes. However, there are currently no spatially and temporally resolved particulate radioactivity data for exposure assessment purposes. We estimated the monthly distributions of gross beta particulate radioactivity across the contiguous United States from 2001 to 2017 with a spatial resolution of 32 km, via a multi-stage ensemble-based model. Particulate radioactivity was measured at 129 RadNet monitors across the contiguous U.S. In stage one, we built 264 base learning models using six methods, then selected nine base models that provide different predictions. In stage two, we used a non-negative geographically and temporally weighted regression method to aggregate the selected base learner predictions based on their local performance. The results of block cross-validation analysis suggested that the non-negative geographically and temporally weighted regression ensemble learning model outperformed all base learning model with the smallest rooted mean square error (0.094 mBq/m³). Our model provided an accurate estimation of particulate radioactivity, thus can be used in future health studies.

Graphical Abstract

Introduction

Particulate radioactivity (PR) is a radiometric characteristic of airborne particulate matter. The radioactivity level is primarily determined by the concentration of radionuclides within or bound to the surface of particulate matter.¹ In the absence of anthropogenic sources, the major source of these particulate-bound radionuclides is radon-222 (referred to as radon), due to the relative abundance of its parent elements in the earth’s crust, its presence in the atmosphere after exhalation from soil and its relatively short half-life.² Although radon is a gas, its immediate progeny are radioactive solid which can quickly attach to nearby airborne particulates. Radon progeny contribute most of the particulate-sourced beta radiation and alpha radiation, respectively.³ As a result, the spatiotemporal distribution of PR is strongly influenced by the atmospheric concentration of radon. PR levels are also impacted by the concentration of airborne particulates, which scavenges short-lived radon progeny from the atmosphere.^4,5

While human skin is able to block most external exposure to low-level radiation,⁶ particulate-bound radionuclides can be inhaled and continue to emit radiation after deposition on the bronchial epithelium.^7,8 This radiation exposure can cause double-chain DNA breaks and leads to cell death.⁶ Recent studies have found associations between PR exposure and several negative health outcomes including elevated blood pressures,⁹ an increased concentration of inflammatory biomarkers,¹⁰ a decline in renal function,¹¹ and a lower hemoglobin concentration.¹²

Current studies of PR-associated health effects primarily use monitor-base observations from Radiation Network (RadNet) to assess participants’ exposure, due to a lack of spatially resolved PR predictions. This network is composed of over 200 fixed and mobile environmental radiation monitors operated by the U.S Environmental Protection Agency (Supplementary Figure S1). At each site, total suspended particles (TSP) are collected using a high-volume sampler with a 4-inch diameter polyester fiber filter.¹³ These filters are collected approximately semiweekly and sent to the National Analytical Radiation Environmental Laboratory for measurement of gross beta activity. Existing health studies estimate PR exposure using the PR levels observed by the nearest RadNet monitor. However, this method does not account for the spatial gradients of PR and therefore likely introduces both random and non-random exposure misclassification. Specifically, RadNet monitors are usually located in urban centers for better population coverage. The error in exposure estimation may be greater for non-urban participants living farther away from the RadNet monitor. In addition, rural areas have less coverage by RadNet monitors, which limits the generalizability of the associations reported by current population-based studies. A spatially resolved model of PR could address these two limitations.

In this study, we built a model to predict monthly PR concentrations across the contiguous U.S. Our paper is organized as follows. In the Methods and Materials section, we first describe our data sources and then our two-stage ensemble learning method in which the predictions of nine base learning model are aggregated by a spatiotemporal ensemble method. In the Results section, we primarily present the outperformance of our ensemble model against each base learning model and a traditional ensemble model. In the Discussion section, we first specify the presumptive mechanisms of our findings, then the strengths and limitations of our methods, and finally the potential implications of this study.

Methods and Materials

Particulate Radioactivity Observations

RadNet is a national monitoring network for environmental radiation in the air, precipitation, and drinking water under both routine and emergency conditions.¹⁴ We obtained gross beta PR (referred to as PR-β) measurements from 129 monitors with at least one year of continuous air monitoring during the study period of 2001–2017 (Figure 1). At each site, total suspended particles are collected using a high-volume sampler with a 4-inch diameter polyester fiber filter. Samplers are operated continuously over a period of three or four days, after which the filter is sent to the National Analytical Radiation Environmental Laboratory for measurement of PR-β.¹³

Figure 1.

The locations of 129 RadNet monitors included in the study.

The contiguous U.S was subdivided into nine climatically consistent subregions by National Climatic Data Center

Predictors of Particulate Radioactivity

We compiled a database of covariates that characterize the processes governing PR levels in the atmosphere (Supplementary Table S1). These processes include: the natural generation and emission of radon; the anthropogenic emission of radon and its parent elements; the spatial distribution of other beta-emitting radionuclides; and the transport of radon and particulate matter in the atmosphere. Besides accounting for these processes, we also computed covariates to characterize spatiotemporal trends in PR-β.

Radon is formed by the radioactive decay of radium-226, which is a decay product of uranium-238. After formation, radon gas emanates from soil grains, travels through soil layer, and is exhaled into the atmosphere. Therefore, we included the ground surface concentration of uranium-238 in our model, as well as other covariates that could influence the flux of radon into atmosphere. These factors include: (1) snow depth, and accumulated precipitation, which depress exhalation; (2) barometric pressure which is negatively related to radon exhalation,¹⁵ (3) soil temperature, which impact radon concentration in soil gas via a temperature-sensitive gaseous/aqueous partitioning process;¹⁶ (4) soil moisture content, which can slow down the subterranean flow of soil gas, thus impacts the emanation rate of radon;¹⁷ and (6) other temporally invariant soil parameters, including available water capacity, percent of organic matter, saturated hydraulic conductivity, vertical permeability, bulk density, field capacity, porosity, erodibility, depth and the percent of soil components of different granularity (gravel, sand and clay).

Anthropogenic activities may release radionuclides, including the parent elements of radon and radon itself, into nearby environments. Sources considered in our study include (1) uranium facilities, due to the potential for leakage during manufacturing, storage and disposal; (2) coal power plants, which have high levels of uranium-238 in the fly ash;¹⁸ and (3) oil and natural gas development activities due to their potential impacts on local particulate radioactivity.¹⁹ . As a proxy variable for each of these activities, we counted the number of active sources within each category located within a 20k radius.

β-emitting radionuclides other than radon progeny also contribute to the gross PR-β. We collected predictors representing these sources, including: (1) ground surface concentration of potassium-40, a β-emitter that may because airborne via suspension; (2) proximity to nuclear power plants, a potential source of anthropogenic β-emitting radionuclides;²⁰ (3) the monthly sunspot number, which we used to represent the generation of cosmogenic radionuclides in the upper atmosphere;²¹ (4) location elevation, which also influences the concentration of cosmogenic radionuclides; and (5) latitude, which represents the pattern of vertical atmospheric movement that transports cosmogenic radionuclides toward the ground.²²

The atmospheric transport of radon and particulate matter determines PR-β levels. Related factors incorporated in our model include: (1) the monthly concentration of particulate matter with aerodynamic diameter smaller than 2.5 μm (PM_2.5), which we estimated as the monthly average of PM_2.5 concentrations from the nearest 10 PM_2.5 monitors (“spatially-lagged PM2.5”), due to its scavenging effects on short-lived radon progeny;⁵ (2) relative humidity, as water vapor can also scavenge radon progeny;⁵ (3) the height of planetary boundary layer and wind velocity, which influence the concentration of PM_2.5 and radon in the atmosphere; (4) the straight-line distance to the closest coastline as a proxy for the frequency of sea breezes; and (5) air mass sources, as the PR-β concentrations in oceanic air masses are orders of magnitude lower than those of continental air masses.²³ We estimated the air mass source by modelling the backward air mass trajectory over the past three days using Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT),²⁴ and then calculated the percent of time this trajectory spent over the continent (100% indicates a completely continental air mass; 0% indicates a completely oceanic air mass).

Predictors related to the temporal trend of PR-β include: (1) the number of months after the Fukushima accident (March 2011) as a proxy for post-accident long-term temporal trends; (2) calendar year as a proxy for long-term trends, and (3) month of year as a proxy for seasonal variations in PR-β.

Monthly PR-β Prediction

We used a two-stage method to predict the PR-β levels across the contiguous U.S on a monthly basis. The flowchart of our model is shown in Figure 2. Flowchart of the two-stage particulate radioactivity prediction model.Both stages are described below in detail.

Figure 2.

Flowchart of the two-stage particulate radioactivity prediction model.

Processing PR-β Measurements and Predictors

We calculated monitor-wise monthly PR-β concentrations as the average of all PR-β measurements that started or ended in the month. For a PR-β predictor with multiple measurements in a month, we calculated the monthly averages in the same way. We enlarged feature space by adding transformed PR-β predictors, which were generated by: centering and rescaling predictors, log-transforming predictors, exponentiating predictors, and transforming predictors via Box-Cox method. Recursively feature elimination method was subsequently used to remove redundant features, which improve the learning efficiency of the follow-up base model training.

Base Statistical Learning Methods

Stage one was composed of 274 base models, which were trained with six statistical learning methods: random forest (RF),²⁵ neural network (NN),²⁶ generalized linear model via penalized maximum likelihood (GLM),²⁷ gradient boosting machine (GBM),²⁸ generalized additive model by likelihood based boosting (GAM)²⁹, and K nearest neighbors (KNN).³⁰ We pre-defined multiple combinations of hyper-parameters for each type of learning method, thus trained multiple models with the same algorithms. For instance, we created 96 combinations of hyper-parameters for random forest method, which includes the number of trees (2 levels), maximum tree depth (4 levels), minimum node size (2 levels), the proportion of predictors for training (3 levels), and the method to determine the best splitting point (2 levels). Supplementary Table S2 summarized all combinations of hyperparameters, which were used to create different base learning models. Each base model was trained with a 10-fold cross validation method, which is repeated three times. We selected the first five learning methods because they have been used in previous literatures to model the spatiotemporal distribution of other airborne pollutants, and have well-developed software available for their implementation.^31–36 The KNN method was selected to model the spatiotemporal trend of PR-β at different scales.

Base Model Selection

Out of 274 base models in stage one, we selected a subset that have distinct PR-β predictions. The selection was achieved via a process illustrated in Supplementary Figure S2. Specifically, we first arranged all base models by their prediction accuracies from high to low. The base model with the best performance was selected. Then we iteratively went through each remaining base model following the gradient of prediction accuracy and determined whether to select it or not. Every single decision is based on the similarity between the candidate model and the already-selected models, which is calculated as the maximum of Pearson correlation(s) between the base model’s predictions and the predictors of already-selected models. A base model is selected if the maximum correlation is below 0.9. This selection process ensured that each selected base model had good predictive accuracy, meanwhile strengthened our ensemble learning by selecting base models with different predicted PR-β concentrations.

Ensemble Learning Method

In stage two, we aggregated the predictions made by selected base models using a non-negative geographically and temporally weighted regression (NN-GTWR) method, which is a hybrid of non-negative least square regression (NNL) and geographically and temporally weighted regression (GTWR). GTWR is a local linear regression model for spatiotemporally non-stationary processes that have heterogeneous association between the independent and dependent variables over space and time.^37,38 NN-GTWR modifies GTWR by restricting the coefficients of base models to greater than or equal to zero. This is achieved by replacing the ordinary least square estimator in GTWR with a non-negative least square estimator.³⁹ The restriction guarantees that the contribution of a base model is non-negative, even when base predictions of the model are negatively correlated with the observations by accident. Our NN-GWTR model can be written as follows:

$$\begin{gathered} {\widehat{y}}_i=c_{0,i}+\mathbf{\sum }_{k=1,2\cdots n}{c}_{k,i}\cdot {\widehat{z}}_{k,i}+{\text{ε}}_i \\ {\widehat{z}}_{k,i}=f_k{}^{\left({\mathit{X}}_i\right)} \\ {c}_{k,i}\in [0,1) \end{gathered}$$ Eq 1

where ${\widehat{y}}_i$ is the ensembled PR-β prediction for i-th unmonitored point; ${\widehat{Z}}_{k,i}$ is the base PR-β prediction using the k-th base model which is represented as a function (f_k) of covariates $X_i;c_{0,i},c_{1,i},\cdots ,c_{n,i}$ are the local intercept and coefficients for predictions of each base model; and ε_i is the error term. n is the number of selected base models out of stage one.

The NN-GTWR method allows the coefficient of the base models to vary across space and time. Specifically, the NN-GTWR model fits an independent NNL model for each grid cell in the region to estimate local coefficients as follows:

$$\begin{gathered} \left(c_{0,i},c_{1,i},\cdots ,c_{n,i}\right)=argmin\left[\mathbf{\sum }_{j=1,2\cdots n}{w}_j{\left(y_j-c_{0,i}-\mathbf{\sum }_{k=1,2\cdots n}{c}_{k,i}\cdot {\widehat{z}}_{k,j}\right)}^2\right] \\ {c}_{k,i}\in [0,1) \end{gathered}$$ Eq 2

where y_j is the PR-β concentration of the j-th out of n (also called adaptive bandwidth) nearest monitor-based observations neighboring the unmonitored location; ${\widehat{Z}}_{k,j}$ is the holdout prediction from the k-th base model for y_j; and c_k,i is the local coefficient for k-th base model. Due to the presence of spatiotemporal autocorrelation, we created a weight vector composed of n elements in which w_j is used to represent the relative importance of each neighboring observation in fitting the local model. Each element of the weight vector can be computed as:

$$\begin{gathered} w_j(i,j;b)=\frac{1}{(\sqrt{2\pi }b)}{e}^{-\frac{1}{2}{\left(\frac{dist(i,j)}{b}\right)}^2} \\ dist{(i,j)}^2={\lambda }^2\cdot \left[{\left(u_i-u_j\right)}^2+{\left(v_i-v_j\right)}^2\right]+{(1-\lambda )}^2\cdot \left[{\left(t_i-t_j\right)}^2\right]+ \\ 2\lambda \cdot (1-\lambda )\cdot \sqrt{{\left(u_i-u_j\right)}^2+{\left(v_i-v_j\right)}^2}\cdot \left(t_i-t_j\right) \\ \lambda \in (0,1) \end{gathered}$$ Eq 3

where b is the bandwidth constant of the Gaussian kernel function, which is adaptively computed as the median distance between the unmonitored location and the n nearest monitor-based observations in Eq 2; and dist(i,j) is a weighted sum of the two-dimensional Euclidean distance and temporal distance (unit: month), which represents the total distance between the i-th unmonitored grid and j-th neighboring monitor-based observation; The relative importance of the distance in space vs. time is governed by the constant λ, which ranges from 0 to 1. The performance of the model relies on two parameters: n (controls b indirectly) and λ.

Performance Evaluation

We conducted blocked spatial cross-validation (CV) analysis to evaluate the performance of our ensemble learning model. Due to the structure of repeated measurements, the data splitting process for CV was conducted based on monitor, instead of on individual measurements. The dataset was repeatedly split into a primary training dataset (pooled measurements of 81% monitors), a secondary training dataset (pooled measurements of 9% monitors), and a test dataset (pooled measurements of 10% monitors) without overlapping. The primary training dataset was used to fit base models in stage one. The secondary training dataset was used to select base models and to find the optimal combination of two parameters in Eq 3. We relied on the selected base models as well as the parameters to predict the PR-β levels for test dataset, then compared the predictions with observations. We calculated CV correlation (R²) and Rooted mean square error (RMSE) to evaluate the prediction performance of the ensemble model. We also normalized the RMSE by the average PR-β level of each monitor to account for between-monitor heterogeneity.

Monthly PR-β Prediction

Our monthly predictions were output onto a 66×121 Lambert conformal conic grid borrowed from North American Regional Reanalysis dataset with a resolution of approximately 32km.⁴⁰ We obtained the non-transformed and transformed PR-β predictors for each grid cell by month. PR-β predictors with a finer spatiotemporal resolution were averaged to the output resolution. The base models for final ensemble model were determined by the likelihood of being selected according to the secondary training set in CV analysis. We set ensemble-related parameters (n and λ) by using a grid-based searching method, which find the combination of parameters for the best prediction performance in secondary training sets (Supplementary Table S3). Base predictions for un-monitored grids were made by the selected base models, which relied on the collocated predictors. We then ensemble these base predictions with our NN-GTWR method and estimate monthly PR-β level for each grid.

We used the preprocessing, feature selection and statistical learning methods supported in the “caret” package (version 6.0–86)⁴¹ in R (version 3.6.1)⁴² to fit the base learning models. Our NN-GTWR implementation was modified from the package “GWmodel” (version 2.1–4).⁴³ All analyses were conducted on the Cannon cluster, which is supported by the Research Computing Group at Harvard University, Faculty of Arts and Sciences.

Results

A summary of PR-β levels and some important model predictors during the study period are included in Table 1. The average PR-β level during our study period was 0.36 mBq/m³, with a nearly normal distribution. We also grouped the RadNet monitors by the climate regions defined by National Centers for Environmental Information⁴⁴ to calculate region specific seasonally-averaged PR-β observations (Table S4). Regions with high average PR-β observations include the Central, Southern and Southwestern regions, while the region with low PR-β was the Northwestern states. We observed similar seasonal patterns across regions, where the highest average PR-β levels happened in the winter and the lowest levels occurred in the spring. Most climate regions had similar long-term trends, where PR-β levels declined over the second half of the study period. At the end of study period, every climate region except for the West region had a lower PR-β level than the initial concentrations in 2001. (Supplementary Table S5).

Table 1.

Summary table of particle radioactivity (PR) and the selected predictors in our model.

Variable Type	Variable	Unit	Mean ±SD	R2*
PR Observation	Particle Radioactivity	mBq/m3	0.36 ±0.14
Radon Generation	Uranium-238 Concentration	ppm	1.82 ±0.55	0.28
Radon Exhalation	Soil bulk density	Kg/m3	1.44 ±0.08	0.17
Radon Exhalation	Snow depth	m	0.01 ±0.03	0.14
Radon Exhalation	Surface erodibility	unitless	0.30 ±0.07	0.11
Radon Exhalation	Accumulated precipitation	Kg/m2	1.20 ±1.55	−0.14
Radon Exhalation	Gravimetric soil moisture	Kg/m2	518.44 ±141.00	−0.14
Radon Exhalation	Soil temperature	K	286.81 ±9.89	−0.15
Radon Exhalation	Soil porosity	%	45.74 ±3.06	−0.17
Radon Exhalation	Saturated hydraulic conductivity	cm/s	16.97 ±13.76	−0.21
Anthropogenic Sources	Proximity to uranium facilities	Num	52.66 ±243.14	0.11
Anthropogenic Sources	Proximity to coal power plants	Num	0.25 ±0.52	0.05
Anthropogenic Sources	Proximity to UOGD wells	Num	4.27 ±41.79	0.02
Other Radionuclides	Proximity to nuclear power plants	Num	0.01 ±0.11	0.05
Other Radionuclides	Potassium-40 Concentration	ppm	1.03 ±0.45	0.18
Other Radionuclides	Elevation	m	283.85 ±406.00	0.18
Other Radionuclides	Number of sunspots	Num	61.08 ±43.96	0.05
PR transport	Fine particulate matter	ug/m3	9.87 ±3.57	0.41
PR transport	Backward Trajectory over land	%	0.79 ±0.24	0.36
PR transport	Distance to nearest coastline	km	463.80 ±444.89	0.28
PR transport	Relative Humidity	%	68.79 ±15.95	−0.11
PR transport	Wind velocity	m/s	3.05 ±0.63	−0.16
Trend	Months after Fukushima accident	Num	23.13 ±27.25	−0.17

^*R² is the spearman correlation between PR-β without adjusting for other predictors. All predictors listed in the table are significantly correlated with gross-beta particulate radioactivity.

We calculated simple Spearman’s correlations between PR-β levels and key predictors (Table 1). PR-β levels were significantly correlated with the spatially lagged PM_2.5 concentration and the proportion of time each air mass backward trajectory spent over the continent. All generation- and emission-related predictors were significantly positively correlated with PR-β levels. PR-β level was negatively correlated with exhalation-related factors including accumulated precipitation, soil temperature, soil moisture, porosity and hydraulic conductivity. These negative correlations likely suggest the hindering effects of moisture content of soil on the emanation of radon from soil to atmosphere. We also observed a counterintuitive positive correlation between PR-β and snow depth. However, this correlation could be explained by the predominance of continental air mass with higher PR-β in the winter.²²

Our NN-GTWR-based ensemble learning model outperformed all 9 selected base learning models in CV correlation (R²= 0.56) and RMSE (0.094 mBq/m³), as shown in Table 2 . Out of the 9 selected base learning models, stochastic gradient boosting model (number of tree = 200, interaction depth =25, minimum node size =5 and shrinkage = 0.05) had the highest CV R² (0.51). Meanwhile, the NN-GTWR-based ensemble model also outperformed the GLM-based ensemble model concerning both CV R² and CV RMSE (Table 2).

Table 2.

Prediction performance of ensemble learning models and base learning models

Model	CV R2	CV RMSE*
Ensemble Model (NN-GTWR)	0.56	0.094
Gradient Boosting Machine (#90)	0.50	0.100
Random Forest (#103)	0.49	0.102
Random Forest (#14)	0.45	0.105
Gradient Boosting Machine (#25)	0.45	0.108
Neural Network (#22)	0.43	0.108
Generalized Linear Model (#2)	0.44	0.106
KNN (#10)	0.42	0.113
KNN(#3)	0.42	0.116
Gradient Boosting Machine (#26）	0.40	0.124
Global Ensemble Model (Linear Regression)	0.54	0.096

^*The unit of RMSE is identical to original measurement (mBq/m³)

Regional heterogeneity in the prediction accuracy was observed across climate regions. Figure 3 shows both non-normalized and normalized monitor specific RMSEs, which are then grouped by climate zones. Southwestern region has the highest non-normalized RMSE, meaning a relatively lower prediction accuracy. All other climate zones meanwhile have similar average RMSEs. The normalized RMSE is the highest in northwestern region, probably because of the relatively low regional PR level. Bakersfield, CA has the highest monitor specific non-normalized RMSE while Harrisburg, PA has the highest normalized RMSE.

Figure 3.

Dispersion of monitor-specific rooted mean square errors and normalized rooted mean square errors.

We used the NN-GTWR-based ensemble model to predict monthly PR-β levels across the contiguous U.S. Monthly predictions of three representative years (2004, 2010, and 2016) were aggregated by season to show long-term trend of PR-β levels in different region and season (Figure 4). We observed a long-term declining trend in annual PR-β levels across study region. However, the decreasing trend is not temporally monotonous in every climate zone. In southwestern, central, and north west central regions, the predicted PR-β levels bounced remarkably before decreasing again after around 2013, as shown in Supplementary Figure S3, Geographically, inland areas consistently have higher PR-β levels than coastal regions. Spring and summer have lower PR-β levels than those of autumn and winter. The seasonal variation of PR-β in inland areas is greater than that in coastal areas. As shown in Supplementary Figure S4, we observed the long-term declining trend in all four seasons, but the temporary increasement at the beginning of the second half of study period is more pronounced in autumn and winter.

Figure 4.

The annual and seasonal average predicted particle radioactivity levels in 2004, 2010 and 2016 (Winter: December-February; Spring: March-May; Summer: June-August; Fall: September-November).

We calculated the relative importance of predictors in each base learning model except for the KNN methods (Supplementary Table S6), and then summed the model specific ranks of predictors as a proxy to the relative importance of the predictor in the ensemble model. The relative importance of PR predictors varied by model. Overall, the most important predictors were spatially lagged PM_2.5 concentration, the source of air mass, distance to the nearest coastline and the evaporation rate. Then hyper parameter tuning results for each base model and ensemble model are presented in Supplementary Table S2 and Table S3, respectively.

Discussion and Conclusion

In this study, we developed a two-stage prediction model to estimate monthly particulate radioactivity concentrations across the contiguous U.S from 2001 to 2017. We selected a set of predictors characterizing the movement of radon and its progeny in the atmosphere. Instead of relying on a single statistical learning method, we employed the NN-GTWR method to aggregate predictions made by nine distinct base learning models. This NN-GTWR-based learning method outperformed all base learning models as well as a GLM-based ensemble model.

We found a long-term declining trend in PR-β levels in most of the study region (Figure 4). This is likely due to the decrease in PM_2.5 concentrations over the past decade.⁴⁵ Another contributing factor may be the reductions in anthropogenic emissions of radon parent elements and progeny from sources like coal power plants and uranium mines. In addition, climate change has increased sea surface temperature, which intensifies the horizontal atmospheric movement from ocean to land.⁴⁶ The elevated PR-β concentration in the West climate region can be explained by the increased frequency of droughts and wildfires in the region.⁴⁷ Further research is needed to fully understand the driving factors of PR-β trends, including studies of the concentrations of specific radionuclides.

We also noted seasonal pattern in PR-β levels that were relatively consistent across the study region (, Table S4). This is partially due to the seasonal patterns in air mass movement. For example, the contiguous U.S has prevailing northern winds in the winter (continental air mass, high PR-β) and prevailing southern winds in the summer (oceanic air mass, low PR-β).²² In addition, seasonal trends in PR-β may also be explained by the annual cycle of soil moisture and temperature, which impact the emanation rate of radon. The difference between spring and autumn in PR-β levels in northern states may also be partially due to increased moisture content in soil after ice melting in the spring.

Ensemble-based statistical learning methods have been applied successfully in predicting the spatiotemporal distribution of air contaminants other than PR.^48–50 However, most previously applied ensemble-based methods were global models, meaning the relative contribution of each base learning method is constant over space and time.^51–53 The NN-GTWR method used in this study allowed the relative contribution of each base learner to vary locally according to its predicting performance in nearby monitors. Results from our study illustrated the effectiveness of this approach, with the NN-GTWR outperforming all base learning methods as well as a GLM-based ensemble method. This model can be applied to other situations, especially when modeling contaminants over a large and diverse study area.

Our NN-GTWR model restricted the coefficient of each base learner to non-negative values. This is achieved by replacing the ordinary least square regression used in traditional GTWR with a bounded least square regression. Although this replacement risks missing the statistically optimal model, we argued that the predictions of a base learner should be omitted (rather than applied negatively) when the predictions are negatively related to the observations. One limitation of NN-GTWR is the lack of uncertainty estimates for the predictions, because the non-negative coefficient estimation algorithm is a convex optimization problem that cannot be solved analytically.

The relative importance of PR predictors are different among the 9 selected base models (Supplementary Table S6). This illustrated how the selected base learning models characterize the complex associations between PR-β and the predicting factors in different ways. For example, the selected neural network model attached more weight to temporally invariant ground surface U-238 concentration. In contrast, the selected generalized linear model relied more heavily on meteorological factors (Supplementary Table S6). By aggregating the predictions from these different base models, we were able to leverage the strengths of each model and limit the impact of their weaknesses.

Alpha radiation is more harmful than beta radiation for its higher linear transfer energy, thus higher likelihood to cause double strand DNA breaks, cell cycle arrest and micronuclei formation, leading ultimately to cell death.⁶ Particle-bound alpha-emitting radionuclides, such as Polonium-210, in theory contribute most of the biological effects or PR. But gross alpha radiation is not routinely measured by RadNet. We predicted the distribution of PR-β because gross alpha and gross beta radiation are theoretically closely correlated.² A recent study carried out in Boston, MA found that the correlation between the gross alpha activity and gross beta activity bound to PM_2.5 was as high as 0.76.⁵⁴

Our study predicted monthly PR-β level for a nationwide grid system with a medium spatial resolution (approximately 32 km × 32 km). We did not predict at a higher spatial resolution primarily due to the intensive computation power required for backward air mass trajectory estimation. However, the model could be applied at a finer spatial resolution for specific subregions, which would require less computing resource. A further limitation causing the medium spatial resolution is the fact that the exact location of each RadNet monitor is not public, for security reasons, so we used the geometric center of its host city as an approximation. A medium resolution partially accounts for this spatial uncertainty.

In this study, we developed a two-stage ensemble model to predict PR-β levels. To our knowledge, this is the first spatiotemporally resolved prediction of PR across contiguous U.S. According to the spatial CV analysis, our model could predict PR levels in locations without historical measurements with good accuracy. The results of this model can be applied on retrospective population-based studies to investigate the health effects of PR.

• Exposure to elevated particulate radioactivity was linked to negative health outcomes

• We developed a model to predict particulate radioactivity across the contiguous U.S.

• A new ensemble learning method was developed to achieve better prediction performance

• Our predictions can be used to investigate the health effects of particulate matter

Data availability

All data sources are summarized in Supplementary Information Table. S1. The final research data will be stored in a public respiratory upon publication.