  Radon is a carcinogenic, radioactive gas that can accumulate indoors.
Therefore, accurate knowledge of indoor radon concentration is crucial for
assessing radon-related health effects or identifying radon-prone areas. Indoor
radon concentration at the national scale is usually estimated on the basis of
extensive measurement campaigns. However, characteristics of the sample often
differ from the characteristics of the population due to the large number of
relevant factors that control the indoor radon concentration such as the
availability of geogenic radon or floor level. Furthermore, the sample size
usually does not allow estimation with high spatial resolution. We propose a
model-based approach that allows a more realistic estimation of indoor radon
distribution with a higher spatial resolution than a purely data-based
approach. A two-stage modelling approach was applied: 1) a quantile regression
forest using environmental and building data as predictors was applied to
estimate the probability distribution function of indoor radon for each floor
level of each residential building in Germany; (2) a probabilistic Monte Carlo
sampling technique enabled the combination and population weighting of
floor-level predictions. In this way, the uncertainty of the individual
predictions is effectively propagated into the estimate of variability at the
aggregated level. The results show an approximate lognormal distribution with
an arithmetic mean of 63 Bq/m3, a geometric mean of 41 Bq/m3 and a 95 %ile of
180 Bq/m3. The exceedance probability for 100 Bq/m3 and 300 Bq/m3 are 12.5 %
(10.5 million people) and 2.2 % (1.9 million people), respectively.
