Modelling the bimodal distribution of indoor gamma-ray dose-rates in Great Britain

Gamma radiation from naturally occurring sources (including directly ionizing cosmic-rays) is a major component of background radiation. An understanding of the magnitude and variation of doses from these sources is important, and the ability to predict them is required for epidemiological studies. In the present paper, indoor measurements of naturally occurring gamma-rays at representative locations in Great Britain are summarized. It is shown that, although the individual measurement data appear unimodal, the distribution of gamma-ray dose-rates when averaged over relatively small areas, which probably better represents the underlying distribution with inter-house variation reduced, appears bimodal. The dose-rate distributions predicted by three empirical and geostatistical models are also bimodal and compatible with the distributions of the areally averaged dose-rates. The distribution of indoor gamma-ray dose-rates in the UK is compared with those in other countries, which also tend to appear bimodal (or possibly multimodal). The variation of indoor gamma-ray dose-rates with geology, socio-economic status of the area, building type, and period of construction are explored. The factors affecting indoor dose-rates from background gamma radiation are complex and frequently intertwined, but geology, period of construction, and socio-economic status are influential; the first is potentially most influential, perhaps, because it can be used as a general proxy for local building materials. Various statistical models are tested for predicting indoor gamma-ray dose-rates at unmeasured locations. Significant improvements over previous modelling are reported. The dose-rate estimates generated by these models reflect the imputed underlying distribution of dose-rates and provide acceptable predictions at geographical locations without measurements

A ‘Baby GDA’: Norwich’s Airspace during the Second World War

Throughout the Second World War, the Luftwaffe attacked Norwich on various occasions. The impact this had on the city was recorded visually on the ‘Norwich Bomb Map’. This cartographic depiction, however, only records a single ‘horizontal’ component of the aerial ‘battlescape’. In reality, the aerial battlefield comprised a combination of Norwich’s air defences and the flightpaths of the Luftwaffe bombers, which existed in three-dimensional space. As other scholars have developed methodologies for reconstructing anti-aircraft ‘fire domes’, this article will combine these concepts with a new approach that reconstructs historic flightpaths to give a three-dimensional overview of Norwich’s ‘Gun Defended Area’. By examining all components of Norwich’s airspace, this article will demonstrate the importance of considering the vertical component of a battlescape

Levels of naturally occurring gamma radiation measured in British homes and their prediction in particular residences

Gamma radiation from natural sources (including directly ionising cosmic-rays) is an important component of background radiation. In the present paper indoor measurements of naturally occurring gamma-rays that were undertaken as part of the UK Childhood Cancer Study are summarised, and it is shown that these are broadly compatible with an earlier UK National Survey. The distribution of indoor gamma-ray dose-rates in Great Britain is approximately normal with mean 96 nGy/h and standard deviation 23 nGy/h. Directly ionising cosmic-rays contribute about one-third of the total. The expanded dataset allows a more detailed description than previously of indoor gamma-ray exposures and in particular their geographical variation. Various strategies for predicting indoor natural background gamma-ray dose-rates were explored. In the first of these a geostatistical model was fitted, which assumes an underlying geologically-determined spatial variation, superimposed on which is a Gaussian stochastic process with Matérn correlation structure that models the observed tendency of dose-rates in neighbouring houses to correlate. In the second approach a number of dose-rate interpolation measures were first derived, based on averages over geologically- or administratively-defined areas, or distance-weighted averages of measurements at nearest-neighbour points. Linear regression was then used to derive an optimal linear combination of these interpolation measures. The predictive performances of the two models were compared via cross-validation, using a randomly selected 70% of the data to fit the models, and the remaining 30% to test them. The mean square error (MSE) of the linear-regression model was lower than that of the Gaussian-Matérn model (MSE 378 and 411, respectively). The predictive performance of the two candidate models was also evaluated via simulation; the OLS model performs significantly better than the Gaussian-Matérn model

Levels of naturally occurring gamma radiation measured in British homes and their prediction in particular residences

Gamma radiation from natural sources (including directly ionising cosmic rays) is an important component of background radiation. In the present paper, indoor measurements of naturally occurring gamma rays that were undertaken as part of the UK Childhood Cancer Study are summarised, and it is shown that these are broadly compatible with an earlier UK National Survey. The distribution of indoor gamma-ray dose rates in Great Britain is approximately normal with mean 96 nGy/h and standard deviation 23 nGy/h. Directly ionising cosmic rays contribute about one-third of the total. The expanded dataset allows a more detailed description than previously of indoor gamma-ray exposures and in particular their geographical variation. Various strategies for predicting indoor natural background gamma-ray dose rates were explored. In the first of these, a geostatistical model was fitted, which assumes an underlying geologically determined spatial variation, superimposed on which is a Gaussian stochastic process with Matérn correlation structure that models the observed tendency of dose rates in neighbouring houses to correlate. In the second approach, a number of dose-rate interpolation measures were first derived, based on averages over geologically or administratively defined areas or using distance-weighted averages of measurements at nearest-neighbour points. Linear regression was then used to derive an optimal linear combination of these interpolation measures. The predictive performances of the two models were compared via cross-validation, using a randomly selected 70 % of the data to fit the models and the remaining 30 % to test them. The mean square error (MSE) of the linear-regression model was lower than that of the Gaussian–Matérn model (MSE 378 and 411, respectively). The predictive performance of the two candidate models was also evaluated via simulation; the OLS model performs significantly better than the Gaussian–Matérn model

Levels of naturally occurring gamma radiation measured in British homes and their prediction in particular residences

Gamma radiation from natural sources (including directly ionising cosmic rays) is an important component of background radiation. In the present paper, indoor measurements of naturally occurring gamma rays that were undertaken as part of the UK Childhood Cancer Study are summarised, and it is shown that these are broadly compatible with an earlier UK National Survey. The distribution of indoor gamma-ray dose rates in Great Britain is approximately normal with mean 96 nGy/h and standard deviation 23 nGy/h. Directly ionising cosmic rays contribute about one-third of the total. The expanded dataset allows a more detailed description than previously of indoor gamma-ray exposures and in particular their geographical variation. Various strategies for predicting indoor natural background gamma-ray dose rates were explored. In the first of these, a geostatistical model was fitted, which assumes an underlying geologically determined spatial variation, superimposed on which is a Gaussian stochastic process with Matérn correlation structure that models the observed tendency of dose rates in neighbouring houses to correlate. In the second approach, a number of dose-rate interpolation measures were first derived, based on averages over geologically or administratively defined areas or using distance-weighted averages of measurements at nearest-neighbour points. Linear regression was then used to derive an optimal linear combination of these interpolation measures. The predictive performances of the two models were compared via cross-validation, using a randomly selected 70 % of the data to fit the models and the remaining 30 % to test them. The mean square error (MSE) of the linear-regression model was lower than that of the Gaussian–Matérn model (MSE 378 and 411, respectively). The predictive performance of the two candidate models was also evaluated via simulation; the OLS model performs significantly better than the Gaussian–Matérn model