Development of a High-Resolution Indoor Radon Map Using a New Machine Learning-Based Probabilistic Model and German Radon Survey Data.

BACKGROUND: Radon is a carcinogenic, radioactive gas that can accumulate indoors and is undetected by human senses. Therefore, accurate knowledge of indoor radon concentration is crucial for assessing radon-related health effects or identifying radon-prone areas. OBJECTIVES: Indoor radon concentration at the national scale is usually estimated on the basis of extensive measurement campaigns. However, characteristics of the sampled households often differ from the characteristics of the target population owing 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. METHODS: A multistage modeling approach was used by applying a quantile regression forest that uses environmental and building data as predictors to estimate the probability distribution function of indoor radon for each floor level of each residential building in Germany. Based on the estimated probability distribution function, a probabilistic Monte Carlo sampling technique was applied, enabling 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. RESULTS: The results show an approximate lognormal distribution of indoor radon in dwellings in Germany with an arithmetic mean of 63 Bq/m3, a geometric mean of 41 Bq/m3, and a 95th percentile of 180 Bq/m3. The exceedance probabilities for 100 and 300 Bq/m3 are 12.5% (10.5 million people affected) and 2.2% (1.9 million people affected), respectively. In large cities, individual indoor radon concentration is generally estimated to be lower than in rural areas, which is due to the different distribution of the population on floor levels. DISCUSSION: The advantages of our approach are that is yields a) an accurate estimation of indoor radon concentration even if the survey is not fully representative with respect to floor level and radon concentration in soil, and b) an estimate of the indoor radon distribution with a much higher spatial resolution than basic descriptive statistics. https://doi.org/10.1289/EHP14171.

Strategy and Metrological Support for Indoor Radon Measurements Using Popular Low-Cost Active Monitors with High and Low Sensitivity.

Traditionally, for indoor radon testing, predominantly passive measurements have been used, typically applying the solid-state alpha track-etch method for long-term and the charcoal method for short-term measurements. However, increasingly, affordable consumer-grade active monitors have become available in the last few years, which can generate a concentration time series of an almost arbitrary duration. Firstly, we argue that consumer-grade monitors can well be used for quality-assured indoor radon assessment and consequent reliable decisions. Secondly, we discuss the requirements of quality assurance, which actually allow for reliable decision-making. In particular, as part of a rational strategy, we discuss how to interpret measurement results from low-cost active monitors with high and low sensitivity with respect to deciding on conformity with reference levels that are the annual average concentration of indoor radon. Rigorous analysis shows that temporal variations in radon are a major component of the uncertainty in decision-making, the reliability of which is practically independent of monitor sensitivity. Manufacturers of low-cost radon monitors already provide sufficient reliability and quality of calibration for their devices, which can be used by both professional inspectors and the general public. Therefore, within the suggested measurement strategy and metrologically assured criteria, we only propose to clarify the set and values of the key metrological characteristics of radon monitors as well as to upgrade user-friendly online tools. By implementing clear metrological requirements as well as the rational measurement strategy for the reliable conformity assessment of a room (building) with radon safety requirements, we anticipate significant reductions in testing costs, increased accessibility, and enhanced quality assurance and control (QA/QC) in indoor radon measurements.

A new perspective in radon risk assessment: Mapping the geological hazard as a first step to define the collective radon risk exposure.

Radon is a radioactive gas and a major source of ionizing radiation exposure for humans. Consequently, it can pose serious health threats when it accumulates in confined environments. In Europe, recent legislation has been adopted to address radon exposure in dwellings; this law establishes national reference levels and guidelines for defining Radon Priority Areas (RPAs). This study focuses on mapping the Geogenic Radon Potential (GRP) as a foundation for identifying RPAs and, consequently, assessing radon risk in indoor environments. Here, GRP is proposed as a hazard indicator, indicating the potential for radon to enter buildings from geological sources. Various approaches, including multivariate geospatial analysis and the application of artificial intelligence algorithms, have been utilised to generate continuous spatial maps of GRP based on point measurements. In this study, we employed a robust multivariate machine learning algorithm (Random Forest) to create the GRP map of the central sector of the Pusteria Valley, incorporating other variables from census tracts such as land use as a vulnerability factor, and population as an exposure factor to create the risk map. The Pusteria Valley in northern Italy was chosen as the pilot site due to its well-known geological, structural, and geochemical features. The results indicate that high Rn risk areas are associated with high GRP values, as well as residential areas and high population density. Starting with the GRP map (e.g., Rn hazard), a new geological-based definition of the RPAs is proposed as fundamental tool for mapping Collective Radon Risk Areas in line with the main objective of European regulations, which is to differentiate them from Individual Risk Areas.

True and spurious anomalies in ambient dose rate monitoring.

Ambient dose rate surveys reveal zones of an elevated dose rate. As the observation results from two physical processes-the 'true' process in nature that one wants to assess and the observation process that consists of measuring under certain conditions-an observed anomaly can have its cause in either process. Anomalous effects rooted in the observation process are called spurious. Distinction between true and spurious anomalies may not be straightforward in many cases. As an example, dose rate surveying using a specific instrument is discussed, whose analysis shows the presence of both types of anomalies. Examples of both types are shown. The physical cause of a true anomaly can often be identified by inspecting the environment or by more sophisticated investigation, e.g. by gamma spectrometry. Identification of spurious anomalies is more difficult and requires investigation of count time series.

Geological control of terrestrial background radiation in Garhwal Himalaya, India.

Activity concentrations of 226Ra, 232Th, and 40K were measured in soil samples from several areas of Garhwal Himalaya, Northern India, by gamma-ray spectrometry. In this region, which extends around the Himalayan Main Central Thrust, a tectonic line that separates several geological provinces, background levels of natural terrestrial radiation were assessed. The maximum levels of radium, 285 Bq/kg and 136 Bq/kg, respectively, were found in the Budhakedar and Uttarkashi regions, exceeding the world average value of 35 Bq/kg. The mean radiation levels were found to be different between the areas, which reflects the geological diversity in the region. The overall absorbed dose rate owing to radionuclide presence in the Uttarkashi area ranged from 79 to 188 nGyh-1, with an average of 118 nGyh-1. That is more than UNSCEAR's world-populated weighted average value of 59 nGyh-1. The present investigation indicated that the absorbed dose rates are greater in Uttarkashi and Budhakedar than in other places. The multiple comparison analysis between geology and absorbed dose rate shows that the geology of Uttarkashi and Budhakedar are statistically similar. According to several hazard indices, terrestrial background radiation is not of radiological concern in the investigated region.

Characteristics of 222Rn and 220Rn equilibrium factors in the indoor environments.

Humans receive a significant portion (˃50%) of the total dose attributed to all the natural radiation sources from indoor radon (222Rn), thoron (220Rn), and their progeny. While progeny contributes an overwhelming part to the dose, in most surveys, only radon gas is measured because of the simplicity of measurement. Progeny concentration is usually estimated by multiplying gas concentration with an assumed factor, called the equilibrium factor, and taken from literature. Recently, results of the measurements of equilibrium factors for 222Rn and 220Rn were reported from various parts of the globe. In India, many such studies have been conducted in the current decade. The studies show a wide variation of equilibrium factors which suggests that they depend on environmental factors and measurement conditions. Therefore, they should be determined site specifically if accurate site-specific dose estimation is targeted. This paper summarizes concepts, definitions, and methods to determine equilibrium factors and reviews literature about reported equilibrium factors worldwide, focusing on data reported from India.

Citizen monitoring of ambient dose rate: the SAFECAST project.

Citizen Science (CS) is research performed by citizens who are not professional scientists in general. SAFECAST was founded in Japan after the Fukushima accident 2011, motivated by distrust in the perceived biassed information by authorities about radiation situation. Measurements of ambient dose rate (ADR) performed by citizens were intended to verify and complement official data using bGeigieNano designed for purpose, recording ADR, GPS coordinates and date/time allowing projection on digital maps. The project expanded internationally, by mid-2022 containing ⁓180 million measurements. CS generates large amount of data as valuable source for science; it has educational value and serves communication between citizens and professionals. Problems consist in quality assurance (QA): citizens who are no trained metrologists are usually little familiar with notions of representativeness, measurement protocols and uncertainty that are the central QA topics. We discuss variability of response of instruments of the same kind under same ambient conditions and isotropy of response under field conditions.

Machine learning in environmental radon science.

Temporal dynamic as well as spatial variability of environmental radon are controlled by factors such as meteorology, lithology, soil properties, hydrogeology, tectonics, and seismicity. In addition, indoor radon concentration is subject to anthropogenic factors, such as physical characteristics of a building and usage pattern. New tools for spatial and time series analysis and prediction belong to what is commonly called machine learning (ML). The ML algorithms presented here build models based on sample and predictor data to extract information and to make predictions. We give a short overview on ML methods and discuss their respective merits, their application, and ways of validating results. We show examples of 1) geogenic radon mapping in Germany involving a number of predictors, and of 2) time series analysis of a long-term experiment being carried out in Chiba, Japan, involving indoor radon concentrations and meteorological predictors. Finally, we identified the main weakness of the techniques, and we suggest actions to overcome their limitations.

Evaluation of tectonically enhanced radon in fault zones by quantification of the radon activity index.

This work highlights the importance of the Geogenic Radon Potential (GRP) component originated by degassing processes in fault zones. This Tectonically Enhanced Radon (TER) can increase radon concentration in soil gas and the inflow of radon in the buildings (Indoor Radon Concentrations, IRC). Although tectonically related radon enhancement is known in areas characterised by active faults, few studies have investigated radon migration processes in non-active fault zones. The Pusteria Valley (Bolzano, north-eastern Italy) represents an ideal geological setting to study the role of a non-seismic fault system in enhancing the geogenic radon. Here, most of the municipalities are characterised by high IRC. We performed soil gas surveys in three of these municipalities located along a wide section of the non-seismic Pusteria fault system characterised by a dense network of faults and fractures. Results highlight the presence of high Rn concentrations (up to 800 kBq·m-3) with anisotropic spatial patterns oriented along the main strike of the fault system. We calculated a Radon Activity Index (RAI) along north-south profiles across the Pusteria fault system and found that TER is linked to high fault geochemical activities. This evidence confirms that TER constitutes a significant component of GRP also along non-seismic faults.

Radon hazard vs. radon risk - On the effectiveness of radon priority areas.

The detrimental health effects of radon have been acknowledged by national and international legislation such as the European Union Basic Safety Standards (EURATOM-BSS Article 103/3) which requires member states to delineate radon priority areas. These radon priority areas are conventionally based on the concept of hazard by using indoor radon concentration or geogenic radon potential for its delineation. While this approach is efficient for finding many affected buildings with limited resources and, hence, reducing the individual risk, it is probably inefficient for reducing the collective risk if hazard and risk areas differ. In this study we map collective radon risk for Germany by linking information of geogenic radon hazard with exposure (residential building stock). The resulting map of affected residential buildings reveals distinct spatial contrasts compared to the hazard-based map. Further, an analysis based on hypothetical hazard zones elucidates that in Germany the vast majority of affected buildings (i.e., above threshold concentration) are located outside of areas of high and very high hazard. Consequently, in Germany, a radon policy focusing on areas of very high hazard only and within these areas on high concentration buildings only would presumably have no significant effect on the reduction of the total number of radon attributable lung cancer fatalities, i.e. less than 1% of annual radon attributable lung cancer fatalities. We conclude that for reducing the collective risk significantly, also complementary measures are of particular relevance.

Effects of Storage Time and Pre-Etching Treatment of CR-39 Detectors on Their Response to Alpha Radiation Exposure.

Radon passive monitors based on solid state nuclear track detectors (SSNTD), especially CR-39, are widely used in radon and thoron studies. They may be subjected to the influence of external factors, like changing of temperature, humidity, and pressure, both before and during the measurement. Evaluation of the exposed detectors involves chemical processing, whose conditions also influence the measurement results. The aim of this study was to check several factors, as to whether they may modify the response of CR-39 detector: concerning the phase before evaluation, storage time, and temperature during storage; and concerning the evaluation procedure, etching time, and pre-etching treatment using hot water and carbon dioxide atmosphere. Two experiments were conducted by irradiation of CR-39 detectors using alpha particles emitted from a mono-energetic 241Am source and exposed in radon atmosphere. Track density dependence of the age of production was found to be statistically not significant. On the other hand, pre-etching treatment using hot water and carbon dioxide with different etching times showed statistically significant effects on track area, track sensitivity, and roundness. It was concluded that there are simple methods to increase performance of nuclear track detectors, and that storage time is not a factor of concern.

Mapping indoor radon hazard in Germany: The geogenic component.

Indoor radon is considered as an indoor air pollutant due to its carcinogenic effect. Since the main source of indoor radon is the ground beneath the house, we utilize the geogenic radon potential (GRP) and a geogenic radon hazard index (GRHI) for predicting the geogenic component of the indoor Rn hazard in Germany. For this purpose, we link indoor radon data (n = 44,629) to maps of GRP and GRHI and fit logistic regression models to calculate the probabilities that indoor Rn exceeds thresholds of 100 Bq/m3 and 300 Bq/m3. The estimated probability was averaged for every municipality by considering only the estimates within the built-up area. Finally, the mean exceedance probability per municipality was coupled with the respective residential building stock for estimating the number of buildings with indoor Rn above 100 Bq/m3 and 300 Bq/m3 for each municipality. We found that (1) GRHI is a better predictor than GRP for indoor radon hazard in Germany, (2) the estimated number of buildings above 100 Bq/m3 and 300 Bq/m3 in Germany is ~2 million (11.6% of all residential buildings) and ~ 350,000 (1.9%), respectively, (3) areas where 300 Bq/m3 exceedance is greater than 10% comprise only 0.8% of the German building stock but 6.3% of buildings with indoor Rn exceeding 300 Bq/m3, and (4) most urban areas and, hence, most buildings (77%) are located in low hazard regions. The implications for Rn protection are twofold: (1) the Rn priority area concept is cost-efficient in a sense that it allows to find the most buildings that exceed a threshold concentration with a given amount of resources, and (2) for an optimal reduction of lung cancer risk areas outside of Rn priority areas must be addressed since most hazardous indoor Rn concentrations occur in low to medium hazard areas.

Mapping the geogenic radon potential for Germany by machine learning.

The radioactive gas radon (Rn) is considered as an indoor air pollutant due to its detrimental effects on human health. In fact, exposure to Rn belongs to the most important causes for lung cancer after tobacco smoking. The dominant source of indoor Rn is the ground beneath the house. The geogenic Rn potential (GRP) - a function of soil gas Rn concentration and soil gas permeability - quantifies what "earth delivers in terms of Rn" and represents a hazard indicator for elevated indoor Rn concentration. In this study, we aim at developing an improved spatial continuous GRP map based on 4448 field measurements of GRP distributed across Germany. We fitted three different machine learning algorithms, multivariate adaptive regression splines, random forest and support vector machines utilizing 36 candidate predictors. Predictor selection, hyperparameter tuning and performance assessment were conducted using a spatial cross-validation where the data was iteratively left out by spatial blocks of 40 km*40 km. This procedure counteracts the effect of spatial auto-correlation in predictor and response data and minimizes dependence of training and test data. The spatial cross-validated performance statistics revealed that random forest provided the most accurate predictions. The predictors selected as informative reflect geology, climate (temperature, precipitation and soil moisture), soil hydraulic, soil physical (field capacity, coarse fraction) and soil chemical properties (potassium and nitrogen concentration). Model interpretation techniques such as predictor importance as well as partial and spatial dependence plots confirmed the hypothesized dominant effect of geology on GRP, but also revealed significant contributions of the other predictors. Partial and spatial dependence plots gave further valuable insight into the quantitative predictor-response relationship and its spatial distribution. A comparison with a previous version of the German GRP map using 1359 independent test data indicates a significantly better performance of the random forest based map.

Mean ambient dose rate in various cities, inferred from Safecast data.

Safecast is a citizen science project, aimed to environmental monitoring. Its main activity is measuring ambient dose rate all over the world. The freely accessible data, currently (January 2020) more than 120 million observations, were used to calculate mean values of dose equivalent rate in various cities where sufficient data is available. The results mainly reflect dose rate from terrestrial radiation, whose variability is controlled by the one of geochemistry, namely the concentrations of uranium, thorium and potassium. Further influence comes from cosmic radiation and in a few cases, from anthropogenic radiation caused by nuclear fallout. Mean dose rate has been calculated for 330 cities and towns worldwide. Results are shown in tables, graphs and as maps.

Validation of a database of mean uranium, thorium and potassium concentrations in rock samples of Portuguese geological units, generated of literature data.

The European Atlas of Natural Radiation, recently published, contains a collection of maps of Europe showing the levels of natural sources of radiation. Among the lacunae of the Atlas are maps of U, Th and K concentrations in rocks due to lack of European-wide geochemical surveys of bedrock units. The objective of this paper is to investigate the usability of scattered geochemical data of rock samples for large-scale mapping of U, Th and K concentrations in geological units. For this purpose, geochemical data were compiled from literature sources to produce a geochemical database (LIT database) that includes 2817 entries of U, Th and K concentrations measured in rock samples of geological units outcropping in Portugal. Given the methodical heterogeneity within LIT database, the influence of the geochemical analysis techniques was assessed through a three-way analysis of variance (ANOVA) using geological units, geochemical analysis techniques and loss on ignition (LOI) as categorical variables. The percentage of variation explained by geological factors was large (>35%), while the percentage of variation explained by the geochemical analysis techniques and LOI was generally lower than 5%. The geological factors were the main source of variability in the data, followed by the error component which can be assumed to represent the true spatial variability of geochemical concentrations. The pairwise comparison of the least square (LS) means computed through the ANOVA for each geochemical analysis technique indicates that LIT database can be considered consistent within itself, thus, reliable. In order to validate the usability of literature data the terrestrial gamma dose rate (TGDR) calculated from LIT database (TGDRcalc) was compared to the TGDR displayed in the Radiometric Map of Portugal (TGDRobs). The correlation between TGDRcalc and TGDRobs was highly significant (p < 0.001) and the results of a paired sample t-test and Wilcoxon median tests indicate that the differences between the arithmetic means of TGDRcalc and TGDRobs were not statistically significant (p = 0.126 and p = 0.14, respectively). Distributions of TGDRcalc and TGDRobs were seemingly equal according to the Kolmogorov-Smirnov and Anderson-Darling tests. Although, systematic discrepancies between TGDRcalc and TGDRobs were observed for sedimentary rocks, the compatibility of the RMP and LIT databases can be considered acceptable, which implies that the estimation of the contents of terrestrial radionuclides using literature data for large-scale mapping of U, Th and K contents in geological units is reasonable.

Development of a Geogenic Radon Hazard Index-Concept, History, Experiences.

Exposure to indoor radon at home and in workplaces constitutes a serious public health risk and is the second most prevalent cause of lung cancer after tobacco smoking. Indoor radon concentration is to a large extent controlled by so-called geogenic radon, which is radon generated in the ground. While indoor radon has been mapped in many parts of Europe, this is not the case for its geogenic control, which has been surveyed exhaustively in only a few countries or regions. Since geogenic radon is an important predictor of indoor radon, knowing the local potential of geogenic radon can assist radon mitigation policy in allocating resources and tuning regulations to focus on where it needs to be prioritized. The contribution of geogenic to indoor radon can be quantified in different ways: the geogenic radon potential (GRP) and the geogenic radon hazard index (GRHI). Both are constructed from geogenic quantities, with their differences tending to be, but not always, their type of geographical support and optimality as indoor radon predictors. An important feature of the GRHI is consistency across borders between regions with different data availability and Rn survey policies, which has so far impeded the creation of a European map of geogenic radon. The GRHI can be understood as a generalization or extension of the GRP. In this paper, the concepts of GRP and GRHI are discussed and a review of previous GRHI approaches is presented, including methods of GRHI estimation and some preliminary results. A methodology to create GRHI maps that cover most of Europe appears at hand and appropriate; however, further fine tuning and validation remains on the agenda.

Digital version of the European Atlas of natural radiation.

The European Atlas of Natural Radiation is a collection of maps displaying the levels of natural radioactivity caused by different sources. It has been developed and is being maintained by the Joint Research Centre (JRC) of the European Commission, in line with its mission, based on the Euratom Treaty: to collect, validate and report information on radioactivity levels in the environment of the EU Member States. This work describes the first version of the European Atlas of Natural Radiation, available in digital format through a web portal, as well as the methodology and results for the maps already developed. So far the digital Atlas contains: an annual cosmic-ray dose map; a map of indoor radon concentration; maps of uranium, thorium and potassium concentration in soil and in bedrock; a terrestrial gamma dose rate map; and a map of soil permeability. Through these maps, the public will be able to: familiarize itself with natural environmental radioactivity; be informed about the levels of natural radioactivity caused by different sources; have a more balanced view of the annual dose received by the European population, to which natural radioactivity is the largest contributor; and make direct comparisons between doses from natural sources of ionizing radiation and those from man-made (artificial) ones, hence, to better assess the latter. Work will continue on the European Geogenic Radon Map and on estimating the annual dose that the public may receive from natural radioactivity, by combining all the information from the different maps. More maps could be added to the Atlas, such us radon in outdoor air and in water and concentration of radionuclides in water, even if these sources usually contribute less to the total exposure.

Mapping uranium concentration in soil: Belgian experience towards a European map.

A map of uranium concentration in soil has been planned for the European Atlas of Natural Radiation. This Atlas is being developed by the Radioactivity Environmental Monitoring (REM) group of the Joint Research Centre (JRC) of the European Commission. The great interest in uranium compared to other terrestrial radionuclides stems from the fact that radon (222Rn) is in the decay chain of uranium (238U) and that public exposure to natural ionizing radiation is largely due to indoor radon. With several different databases available, including data (albeit not calibrated) from an airborne survey, Belgium is a favourable case for exploring the methodology of uranium mapping. A harmonized database of uranium in soil was built by merging radiological (not airborne) and geochemical data. Using this harmonized database it was possible to calibrate the data from the airborne survey. Several methods were used to perform spatial interpolation and to smooth the data: moving average without constraint, by soil class and by geological unit. When using the harmonized database, it is first necessary to evaluate the uranium concentration in areas without data or with an insufficient number of data points. Overall, there is a reasonable agreement between the maps on a 1 km × 1 km grid obtained with the two datasets (airborne U and harmonized soil U) with all the methods. The agreement is better when the maps are reduced to a 10 km × 10 km grid; the latter could be used for the European map of uranium concentration in soil.

Dose estimation derived from the exposure to radon, thoron and their progeny in the indoor environment.

The annual exposure to indoor radon, thoron and their progeny imparts a major contribution to inhalation doses received by the public. In this study, we report results of time integrated passive measurements of indoor radon, thoron and their progeny concentrations that were carried out in Garhwal Himalaya with the aim of investigating significant health risk to the dwellers in the region. The measurements were performed using recently developed LR-115 detector based techniques. The experimentally determined values of radon, thoron and their progeny concentrations were used to estimate total annual inhalation dose and annual effective doses. The equilibrium factors for radon and thoron were also determined from the observed data. The estimated value of total annual inhalation dose was found to be 1.8 ± 0.7 mSv/y. The estimated values of the annual effective dose were found to be 1.2 ± 0.5 mSv/y and 0.5 ± 0.3 mSv/y, respectively. The estimated values of radiation doses suggest no important health risk due to exposure of radon, thoron and progeny in the study area. The contribution of indoor thoron and its progeny to total inhalation dose ranges between 13-52% with mean value of 30%. Thus thoron cannot be neglected when assessing radiation doses.

Variation of indoor radon concentration and ambient dose equivalent rate in different outdoor and indoor environments.

Subject of this study is an investigation of the variations of indoor radon concentration and ambient dose equivalent rate in outdoor and indoor environments of 40 dwellings, 31 elementary schools and five kindergartens. The buildings are located in three municipalities of two, geologically different, areas of the Republic of Macedonia. Indoor radon concentrations were measured by nuclear track detectors, deployed in the most occupied room of the building, between June 2013 and May 2014. During the deploying campaign, indoor and outdoor ambient dose equivalent rates were measured simultaneously at the same location. It appeared that the measured values varied from 22 to 990 Bq/m(3) for indoor radon concentrations, from 50 to 195 nSv/h for outdoor ambient dose equivalent rates, and from 38 to 184 nSv/h for indoor ambient dose equivalent rates. The geometric mean value of indoor to outdoor ambient dose equivalent rates was found to be 0.88, i.e. the outdoor ambient dose equivalent rates were on average higher than the indoor ambient dose equivalent rates. All measured can reasonably well be described by log-normal distributions. A detailed statistical analysis of factors which influence the measured quantities is reported.