Kernel regression based mapping of indoor radon concentrations in Switzerland
Abstract for the workshop on the geological aspects of radon risk mapping“, Prague,2012.
G. Kropat, F. Bochud, M. Palacios (Gruson), C. Murith, J.-P. Laedermann, S. Baechler
Introduction
In Switzerland, the Federal Office of Public Health (FOPH) carried out about 229,000 radon concentration measurements in the last 30 years in dwellings. Indoor radon concentrations are known to be subject to a variety of influencing variables of both categorical and continuous types. In addition, many of those variables do not have a physical interpretation, e.g. house type, year of construction, room type, etc. Hence the determination of a physically meaningful parametric model is difficult. Alternatively, powerful data-driven machine learning algorithms, such as kernel regression algorithms, prove to be able to make good predictions in cases where the estimation of a parametric model does not yield satisfying results (Foresti, Tuia et al. 2011). The aim of this project is to use kernel regression algorithms to obtain a better estimate of indoor radon concentrations at locations where no measurements are available.
Data and methods
Indoor radon concentrations were mainly measured by means of passive alpha track and electret detectors over a time period of about 3 months. Each indoor radon measurement included a filled questionnaire containing information about house and measurement characteristics. House characteristics are type of house, type of foundation, geographical coordinates, altitude, year of construction and address. Measurement characteristics included period of measurements, habitation conditions (inhabited or non inhabited rooms), room type, room level and dosimeter type. Additional information about the lithology corresponding to the house was integrated in the model by sampling from the lithological map of Switzerland (1:500,000) and the European Soil Database at a resolution of (1:1,000,000).
The development of a physical model is not straightforward since the processes determining the indoor radon concentrations are too complex. Hence we applied non-parametric kernel methods to estimate the joint probability distribution of the radon dataset and used this joint probability distribution to carry out indoor radon predictions with the known house and measurement proper variables. We used the R package “np” (Li and Racine 2003) to implement the non-parametric kernel regression. This package can deal with mixed continuous and discrete variables. It is also implemented for parallel computation. We carried out the bandwidth selections on a 32 core Dell Poweredge R910 compute cluster. We performed the predictions by stratification of certain variables (e.g. house foundation, habitation characteristics). The predictions were validated by dividing the dataset into a training and a test set. The training set contained 80% and the test set 20% of the instances of the whole dataset.
Results & Discussion
Stratification by foundation and habitation characteristics yield an R2=31% for measurements in the ground floor of houses with earth foundation. Radon concentrations in the ground floor of houses with concrete foundation can be predicted with an R2=23%. The predictions of measurements carried out in the ground floor of farms with earth foundation show an R2=36%. Subsequent feature elimination shows that the lithology and soil data does not improve the performance of the model. This is due to correlations of those variables with longitude, latitude and altitude. Another reason may be the low spatial resolution of the lithological and soil data. Also the coarse scale leads to misclassifications near the borders of geological units. Finally, since most of the area of the Alps is not populated, the mapping of indoor radon concentrations in the mountains is not reliable.
Conclusion
Kernel regression methods appear to be a promising tool to map indoor radon concentrations since they take into account categorical as well as continuous variables in an efficient way. Their robustness makes them particularly useful since indoor radon concentrations are subject to a high frequency of spatial outliers. In addition they do not need a priori knowledge on the complex physical processes determining indoor radon concentrations.
Reference List:
- Foresti, L., D. Tuia, et al. (2011). "Learning wind fields with multiple kernels." Stochastic Environmental Research and Risk Assessment 25(1): 51-66.
- Li, Q. and J. Racine (2003). "Nonparametric estimation of distributions with categorical and continuous data." Journal of Multivariate Analysis 86(2): 266-292.
