Application of Short-Term Measurements to Estimate the Annual Mean Indoor Air Radon-222 Activity Concentration

Abstract

A method was developed to estimate the average annual indoor radon activity concentration from three-week short-term measurements using active radon-222 measuring devices, taking into account the relevant influencing parameters (season, temperature difference, temporal air pressure gradient, etc.) during the short-term measurements. A total of 24 long-term measurements (6 months) and 50 short-term measurements (3 weeks) were carried out in 24 indoor spaces in private houses in four Austrian federal states between October 2022 and July 2023. At the same time as the short-term measurements, ambient parameters (outside and inside temperature, air pressure inside, outside, air humidity inside, outside, wind speed, wind direction, amount of precipitation) were also recorded to investigate their influence on the measured radon-222 activity concentrations. Building and usage data of the indoor spaces examined were also collected. Based on the evaluation of the radon-222 measurements carried out, a first guideline was developed for estimating the annual mean value of the radon-222 activity concentration from short-term measurements lasting around three weeks. The result shows that by applying the developed method, the approximation to the long-term average value can be significantly improved, at least by a factor of 2. This criterion is only valid for the 24 indoor spaces examined in this study. Generalisation requires a test and validation study of the method presented. It is planned to test and validate the developed method in other indoor spaces by means of further measurements and in-depth physical-statistical considerations, and to improve the functional relationships and the approximation to the long-term average value.

1. Introduction

The indoor air radon activity concentration (IRC) is influenced by several factors. These include mainly geological factors, such as the rock subsoil and the soil conditions under the building, the condition of the building (type of foundation, insulation, etc.), the usage behaviour of the residents (ventilation habits, room temperature, etc.), as well as meteorological influences (outside temperature, air pressure, etc.) [1]. Due to the influences mentioned, the IRC is subject to fundamental changes over time [2]. Buildings, therefore, also have diurnal, seasonal, and annual behaviour in relation to the IRC [3]. The main factors influencing the temporal variability of the IRC value in an interior are meteorology and user behaviour.

Several studies indicate that the indoor air radon activity concentration IRC (Bq/m³) is influenced by meteorological parameters [1,4,5]. Miles et al. showed in a study that the IRC in different houses reacts very differently to outside temperature, wind speed, and wind direction [4]. A Swiss study by Rey et al. shows that the outside temperature is the parameter that most strongly affects the IRC, and usually anticorrelates with the IRC. The IRC also depends on the wind, but the influence is based on the intensity and on the direction the wind is arriving, as well as on the construction of the building. The amount of precipitation also influences the height of the IRC. External air pressure and relative humidity do not appear to be major factors influencing the IRC [1].

A number of studies have found that IRC in a variety of countries generally follows seasonal variations. These show that the most common behavioural pattern corresponds to high IRC in winter and low concentrations in the summer months [6,7,8]. One reason for this is the occurrence of the chimney effect in winter due to increased heating behaviour of residents. In summer, on the other hand, high outside temperatures cause the pressure indoors to be greater than outside, thus generally reducing the amount of inert gas that can penetrate. Another reason for a lower IRC in the summer months is the ventilation behaviour of the residents. Due to the higher temperatures in the summer months, residents normally ventilate more frequently, which dilutes the radon with the outside air and consequently lowers the IRC [1].

The level of IRC also depends on the residents’ usage behaviour [9]. A major factor is ventilation behaviour, since intensive ventilation leads to a high rate of air exchange with the outside air and a large proportion of the radon gas can escape into the open air [2,10]. The IRC can return to its initial level just two hours after ventilation [11]. Since people tend to ventilate less at night, there is often an increase in IRC [9]. Not only does the exchange of air with the outside air influence the level and the temporal course of the IRC in the respective rooms, but so does the exchange of air within a building (for example, by opening interior doors) [9].

In addition to ventilation behaviour, IRC also depends on the heating behaviour of the residents [9]. When it is cold outside, turning up the heating creates a large temperature difference between the inside of the house and the outside. The warmer air inside has a lower density than the cold air outside and rises. The resulting drop in pressure causes cold air to flow in from the ground and the surrounding area at the foundation, which can also cause radon gas to enter the house [1,9,12]. Since this phenomenon is often observed with chimneys, it is commonly referred to as the ‘stack effect’ [13].

Due to the seasonal variations in meteorological influences, the assessment of the mean annual IRC legally in Austria requires long-term measurement of the activity concentration over a period of at least six months, with at least half of the measurement time being in the winter season (15 October until 15 April, specified, for example, in Annex 2 of the Austrian Radon Protection Ordinance) [14]. Although a short-term measurement with active measuring instruments is more complex than a long-term measurement with a passive, integrating measuring method (e.g., nuclear track detectors), it may be necessary to determine the radon situation in a building in a shorter period than six months—e.g., within three weeks—to be able to make decisions quickly. In certain cases—e.g., because of possible health risks associated with a greatly increased IRC, for a rapid assessment of the effectiveness of radon remediation on a building or during real estate transactions—a short-term assessment of the annual mean IRC is desirable or necessary. Furthermore, it is desirable, and often necessary, to be able to carry out a short-term measurement as a basis for short-term decisions, regardless of the prevailing season (as opposed to six-month measurements, half in and half out of the winter season).

Within this work, a method was developed to estimate the average annual IRC from three-week short-term measurements using active radon-222 measuring instruments, considering the relevant influencing parameters.

2. Materials and Methods

2.1. Definitions, Quantities and Variables

This is the compilation of the terms and formula symbols used:

• IRC, Bq/m³: radon-222 activity concentration of the indoor air (Indoor Radon Concentration).
• SIRC, Bq/m³: IRC mean value of the short-term measurement (Short-term IRC).
• LIRC, Bq/m³: IRC mean value of the long-term measurement (Long-term IRC).
• EIRC, Bq/m³: IRC annual mean value, estimated from a short-term measurement (Estimated IRC).
• c_Rn, Bq/m³: individual measured value of the Rn-222 activity concentration (e.g., 10 min mean value, 1 h mean value).
• u(x): standard (measurement) uncertainty (extension factor k = 1) of the (measured) value x (in the respective unit).
• u_rel(x): relative standard (measurement) uncertainty (extension factor k = 1) of the measured value x (related to the (measured) value x; optional in %).
• x*: mean value of a series of measured values x over a period (e.g., hourly mean value, three-week mean value, annual mean value).
• sr(x): relative standard deviation of a series of measured values x over a period.
• ρ: Spearman rank correlation coefficient ρ can take values between −1 (perfect anti-correlation) and +1 (perfect correlation).

2.2. Selection of the Sites

To distinguish between temporal changes in IRC and the stochastic noise of the measuring instruments, the selected study households should exhibit a minimum radon potential. For this purpose, an indicative Rn-222 value of 100 Bq/m³ was set at the beginning of this study. In principle, a higher IRC can be expected in radon protection areas, old buildings, and in living spaces in contact with the ground [15]. These criteria were considered when selecting the houses.

Due to the necessary minimum radon potential and the limited number of available measuring devices, 24 private households were ultimately selected for the study. Ten houses are in southern Lower Austria, eight in radon-protected areas in Upper Austria, three in Tyrol, two in the northern part of Lower Austria, and one in Vienna [16] (Figure 1).

The participants in the study were given a questionnaire that, in accordance with an approved template of the Austrian Agency for Health and Food Safety AGES, contains questions on relevant parameters that IRCs can strongly influence. On the one hand, building-specific data such as year of construction, type of foundation, basement, window density, etc., were collected, and on the other hand, the ventilation behaviour in each room was queried. In addition, the participants were advised to maintain their everyday usage behaviour during the measurements.

2.3. Active Radon-222 Measurement Instruments

The study investigated the diurnal and seasonal variations in IRC in the living spaces of a wide range of private households in Austria. This required active radon measuring devices that measure and record the IRC hourly.

Three-week periods for the short-term measurements were chosen because numerous radon measurements had shown that meteorological and other influencing factors (e.g., room use, ventilation) vary sufficiently over this period. This ensures that no constant conditions lead to one-sided results. Furthermore, a measurement period of three weeks is practically acceptable for quick assessment of the radon situation in an interior. Three weeks is long enough to capture typical changes in radon concentration influenced by various factors such as weather conditions, ventilation behaviour, and daily use of the room. At the same time, this period is short enough to be acceptable for most people, providing reliable results without the need to wait for months—as would be the case, for example, when making a house purchase decision, where a quick and informed assessment is important.

The Radiation Protection Laboratory of Vienna, MA 39, an accredited testing, inspection and certification body for active and passive radon measurements according to ISO/IEC 17025, supported the study with an AlphaGuard (DF2000, Bertin Instruments, Frankfurt, Germany, model year 2020), as well as three AlphaE (Bertin Instruments). Seibersdorf Laboratories, Austria, also accredited for passive radon measurements according to ISO/IEC 17025 [15], provided two AlphaGuard (P30, Bertin Instruments, model year 1995).

The instruments mentioned work according to the principle of an ionisation chamber. For the study, the Rn-222 activity concentrations (Bq/m³), as well as their uncertainties, were recorded and stored at the top of every hour. In addition to the IRC, the devices provided values for the room temperature (°C), air pressure (mbar), and relative humidity (%).

The Austrian Federal Office of Metrology and Surveying BEV provided a RadonEye Plus2 (RD200P2, FTLAB, San Jose, California, USA, model year 2019). Within the study an additional RadonEye Plus2 (RD200P2, FTLAB, model year 2022) was applied. These ionisation chamber instruments recorded the radon activity concentration (Bq/m³), the room temperature (°C), and the relative humidity (%).

To ensure the reliability of all measurement results, the applied measuring instruments used were compared with a validly calibrated reliable reference measuring device at different levels of the Rn-222 activity concentration. For this purpose, several comparative measurements were carried out with all of the devices available at the time of the measurements. The measuring instruments were positioned next to each other at the same locations for several hours, and the IRC was recorded hourly. Subsequently, all measured values were evaluated and subjected to a comparative analysis. A correction factor was determined for each device, which describes the deviation of the respective measured values from the results of the calibrated reference device. By applying the correction factors to the values output by the respective measuring instrument, reliable measured values of the Rn-222 activity concentration within the respective uncertainty intervals of the measuring instruments were obtained.

2.4. Passive Radon-222 Measurement Methods

In addition to the short-term variations in the IRC, the long-term mean IRC was also assessed. For this purpose, long-term measurements were carried out with passive track etch detectors. A six-month period for the long-term measurements had been chosen because the six-month measurement period—half in and half out of the heating season—was the legally approved reliable standard in Austria. Since half of the six-month measurement periods fall within the winter heating period and half of the time falls outside of the heating period, the seasonal influences could be kept within an acceptable uncertainty range.

For long-term measurements, we used track etch detectors because we had limited access to radon monitors (only 9 instruments for 24 sites). So, we could use the monitors at several sites on several occasions. The two participating accredited (ISO/IEC 17025 [17]) laboratories, Radiation Protection Laboratory of Vienna, MA 39, and Seibersdorf Laboratories SL, have each provided 49 passive track etch detectors (polyallyl diglycol carbonate PADC, also known as CR-39) for the study. The long-term measurements according to ISO 11665-4 [18] should adhere to the Austrian requirements for an accredited radon measurement (6-month long-term measurement, at least half of the time between 15 October and 15 April [19]). For this reason, the measurements in all participating households were started between mid-December and early January and evaluated at the end of June 2023.

Due to the large number of available detectors, an average of four track etch dosimeters could be placed in the participants’ homes. This made it possible to determine the average IRC in different rooms and on different floors of some houses. To evaluate the quality of the long-term measurements, detectors from both institutes (MA 39 and SL) were placed in some rooms.

2.5. Taking Measurements

As part of the study, at least two short-term measurements were carried out in each household, one during the winter months and one outside the heating season. The main heating period in Austria generally starts in November and ends in March. Therefore, short-term measurements outside the heating period were carried out between the end of March and the end of August (for details, see Figures 3 and 7). For a single short-term measurement, an active measuring device was set up in one of the most frequently used rooms, preferably in living rooms and bedrooms, and connected to the local power supply. After the active measuring device was switched on, it automatically started recording and storing the Rn-222 hourly mean values and the environmental parameters.

The active measuring devices were placed according to reliable practice [20] in a location with the following characteristics:

-

It is not directly next to a window and is not subject to draughts.

-

It is not directly next to a wall (at least 10 cm distance).

-

It is not heated to high temperatures.

-

It is at normal breathing height (1 to 2 m).

-

It is inaccessible to small children and pets.

-

It does not show any condensation.

The location of the measuring device was not changed during the measurement. The individual usage habits of the residents in the rooms were also maintained during the measurements (ventilation and heating habits, room usage times, etc.). In each household, the location of the measuring device was kept the same for all short-term measurements (winter and summer measurements).

2.6. Correlation Analysis of the Results of Short-Term Radon Measurements with Influencing Variables

Based on the results of the physical-statistical evaluation of metrological surveys using Spearman correlation analysis performed with SPSS^® (version 29) mathematical statistical software [21], in combination with physical considerations, influencing parameters were identified, tested in functions, and we finally determined which ones demonstrably significantly influence the IRC. These influencing parameters were determined or obtained in a suitable manner for the estimation of the annual mean value of the IRC during the three-week short-term measurements (data from the measuring stations of the meteorological service GeoSphere Austria Data Hub, online). The values of the influencing parameters had been determined using state-of-the-art technology, either by measurements or by obtaining the data from Geosphere Austria Data Hub at or as close as possible to the measurement locations and evaluated for the period of the short-term radon measurement (mean values, standard deviation and, as far as possible and appropriate, uncertainties).

Correlation analyses were carried out with the approximately 500 hourly mean values of the three-week short-term measurements and the hourly mean values of the influencing quantities.

2.7. Fitting the Short-Term Measurements with the Results of the Long-Term Measurements

In a subsequent step, the most strongly correlated (or anti-correlated) influencing variables were determined, with which the mean values of the 3-week radon short-term measurements could be most significantly approximated to the results of the 6-month long-term measurements. The method used was least squares regression with the mathematics software SigmaPlot^® (version 15) [22].

From the 50 three-week short-term measurements—about 500 hourly mean values c_Rn* over the three-week period for each measurement—of the radon-222 activity concentration in the investigated indoor room, the three-week mean values SIRC of the hourly mean values c_Rn* of the radon activity concentration, the standard measurement uncertainties (k = 1) of the three-week mean value u (SIRC) were determined, considering the uncertainties u(c_Rn*) of the hourly mean values and the relative standard deviation sr(c_Rn*) of the hourly mean values c_Rn* of the radon activity concentration.

In this work, the influences of the building situation (e.g., hillside location, basement) and user behaviour (e.g., ventilation, holidays) were not initially considered. These influences were observed qualitatively in the hourly mean values of the IRC over the course of the day but could not yet be quantified beyond doubt with the help of the three-week mean values. These influencing factors are to be examined in more detail in a subsequent study and taken into account if necessary.

3. Results

3.1. Results of the Rn-222 Measurement Instrument Comparisons

Before starting the radon short-term measurements, a comparison exercise was necessary. We had to measure some sites with different instruments at different times because of limited access to radon monitors (9 instruments for 24 sites). To combine the results of different monitors at one site, we had to consider instrument specific correction factors resulting from the comparison exercise. The results of the necessary comparison of the instruments used carried out at higher Rn-222 activity concentrations are given here as an example of the comparison measurements performed to determine the correction factors of the instruments used at different Rn-222 measuring ranges. A sleeping room in a household in southern Lower Austria was used as the comparison location because the room had higher IRC during the winter measurements. The comparison measurement was carried out between 3 and 10 March 2023. An AlphaGuard DF2000 was used as reference device for the comparative measurement, which had a reliable and precise calibration at the time of the comparison measurement. During the comparative measurement, which lasted 186 h (7.75 days), the reference device recorded an average IRC of about 560 Bq/m³. Figure 2 shows the hourly IRC mean values over time, as recorded by the respective active measuring devices.

Table 1. Instruments comparison: assessed correction factors of the measuring instruments.

Rn-222 Range 330 Bq/m³ to 800 Bq/m³
		AlphaGuard DF2000	AlphaE			AlphaGuard P30		RadonEye
	Instrument i	G2 (Reference)	E1	E2	E4	G3	G4	R1	R2
Number of measurement values	n	187	187	187	187	187	187	187	187
Mean measurement value	cRn (Bq/m3)	561	596	621	583	553	562	685	745
Uncertainty	u(cRn) (Bq/m3)	4	15	16	15	3	3	5	5
Correction factor	Fi		0.94	0.90	0.96	1.01	1.00	0.82	0.75
Uncertainty	u(Fi)		0.03	0.02	0.03	0.01	0.01	0.01	0.01
Relative uncertainty	u(Fi) (%)		2.7	2.6	2.6	0.8	0.8	0.9	0.9

shows that the readings of the AlphaGuard devices, including those of the two older models (P30, model year 1995), were in very good agreement with the readings of the calibrated reference device (Alpha Guard DF2000, model year 2020). The two RadonEye Plus 2 devices always showed higher values than the reference device, but their correction factors could be determined with extremely low uncertainty. The hourly mean values of the AlphaE devices showed strong fluctuations but, on average, over several hours, they showed smaller deviations than the RadonEye Plus 2 devices. As a result, the AlphaE devices had correction factors close to the ideal value 1.00, but with larger uncertainties.

The correction factors F_i, determined at different Rn-222 ranges, were used to correct the Rn-222 activity concentration value given by the measuring device i,

$$c_{Rn}=F_i·m_{Rn}$$

(1)

• F_i: correction factor of measuring instrument i
• c_Rn: real Rn-222 activity concentration value (Bq/m³)
• m_Rn: reading Rn-222 activity concentration value shown by the measuring instrument (Bq/m³)

3.2. Results of the Short-Term and Long-Term Measurements

Between October 2022 and August 2023, short-term measurements were carried out by all study households during the winter months, as well as outside the heating season (summer or spring). Each series of measurements was corrected according to the device-specific correction factor (Equation (1),

Table 2. Results of the short-term (3 week) and long-term (6 month) IRC measurements.

	Short-Term Measurements		Long-Term Measurements
	Winter	Summer or Spring
	SIRC*		LIRC*
Location	Bq/m³
Southern Lower Austria
NOE_01	313 ± 11	244 ± 8 *)	252 ± 9
		166 ± 6 **)
NOE_02	1371 ± 73	916 ± 47 *)	901 ± 21
		212 ± 12 **)
NOE_03	824 ± 28	607 ± 20	570 ± 13
NOE_04	145 ± 5	137 ± 5	122 ± 5
NOE_05	2889 ± 154	2835 ± 150	2419 ± 65
NOE_06	659 ± 22	235 ± 8	374 ± 16
NOE_07	722 ± 24	391 ± 13	434 ± 9
NOE_08	220 ± 12	174 ± 10	168 ± 5
NOE_09	382 ± 13	83 ± 3	201 ± 5
NOE_10	519 ± 28	96 ± 5	418 ± 15
Northern Lower Austria and Vienna
FJM_01	129 ± 7	68 ± 4	99 ± 5
FJM_02	106 ± 6	72 ± 4	110 ± 6
FJM_03	107 ± 6	43 ± 3	82 ± 3
Upper Austria
OOE_01	535 ± 45	580 ± 49	401 ± 8
OOE_02	165 ± 16	179 ± 17	122 ± 3
OOE_03	732 ± 62	516 ± 44	365 ± 8
OOE_04	2371 ± 190	727 ± 60	1597 ± 36
OOE_05	480 ± 16	366 ± 32	405 ± 10
OOE_06	716 ± 61	494 ± 39	451 ± 10
OOE_07	134 ± 13	173 ± 15	125 ± 4
OOE_08	417 ± 37	146 ± 13	151 ± 4
Tyrol
TIR_01	445 ± 15	165 ± 6	211 ± 5
TIR_02	365 ± 12	43 ± 2	209 ± 6
TIR_03	238 ± 8	82 ± 3	174 ± 5

*) measurement in spring. **) measurement in summer.

).

The long-term measurements (track etch detectors) were carried out in the same rooms as the short-term measurements.

In Table 2, the IRC mean values of the two (or three) short-term measurements (3 weeks in winter and summer or spring) SIRC* are compiled together with the results of the respective long-term measurements (6 months, from December 2022 until July 2023) LIRC* in the investigated rooms. The results show that the short-term mean values SIRC* can vary greatly between winter and summer (spring). Accordingly, the IRC mean values of the short-term measurements SIRC* can also deviate greatly from the mean annual IRC of the long-term measurements LIRC*.

3.3. Results of the Correlation Analysis of the Short-Term Measurements

Table 3. Significance of the correlations of c_Rn* (hourly mean values) with influencing ambient condition factors. The bold numbers indicate the high numbers of correlations (anti-correlations).

	Air Pressure Indoor	Temperature Indoor	Relative Air Humidity Indoor	Air Pressure Outdoor	Temperature Outdoor	Relative Air Humidity Outdoor	Precipitation	Wind Speed	Wind Direction	Air Pressure Difference (Indoor − Outdoor)	Temperature Difference (Indoor − Outdoor)
	Number of correlations
with ρ > 0.2	3	7	16	5	3	25	1	2	3	10	23
with ρ > 0.3	3	3	9	4	3	20	1	1	0	4	17
with ρ > 0.5	1	1	5	2	1	5	0	0	0	2	5
	Number of anti-correlations
with ρ < −0.2	7	18	5	10	26	1	2	16	4	6	3
with ρ < −0.3	5	10	3	6	17	1	0	8	1	1	2
with ρ < −0.5	1	0	0	1	7	0	0	2	0	0	1
Total number of measurements	35	50	50	50	50	50	50	50	50	35	50

shows a summary of the Spearman rank correlations of the measured c_Rn hourly mean values with the meteorological parameters, the environmental parameters, and the derived variables. The Spearman rank correlation coefficient ρ can take values between −1 (perfect anti-correlation) and +1 (perfect correlation). The numerical entries correspond to the number of correlations of all 50 short-term measurements.

In the context of short-term indoor radon measurements, which are known to be subject to relatively high uncertainties, we evaluated the statistical significance of the influencing factors as weak (0.2 < ρ ≤ 0.3), medium (0.3 < ρ ≤ 0.5) and significant (0.5 < ρ ≤ 1.0). In Table 3, weak significant correlations are marked in light green, medium significant correlations in green, and strong significant correlations in dark green. Weak significant anticorrelations are marked in light red, medium significant anticorrelations in red and strong significant anticorrelations in dark red. For parameters that showed many (anti-)correlations with the c_Rn, the numerical entries are marked ‘bold’ and ‘larger’. Since the RadonEye measuring devices do not record air pressure, no correlations of the c_Rn with the indoor air pressure could be determined for the 15 RadonEye short-term measurements. Accordingly, it was not possible to determine the correlations with the derived variable ‘pressure difference’. As a result, only 35 instead of 50 short-term measurements were available for these two parameters.

Table 3 shows that there were many correlations between the c_Rn and the parameters ‘relative air humidity indoor’, ‘relative air humidity outdoor’, and the derived variables ‘air pressure difference (indoor–outdoor)’ and ‘temperature difference (indoor–outdoor)’. Observations suggest that the correlations between the IRC and the relative humidity are not causal. Many households ventilate more frequently during the day, which means that the IRC tends to be higher at night. Similarly to the diurnal course of the IRC, the relative humidity increases on cold nights due to the reduced water vapour absorption capacity of the air. In addition, the c_Rn showed many anti-correlations with the parameters ‘temperature indoor’, ‘temperature outdoor’, and ‘wind speed’.

Most significant anti-correlations occurred between c_Rn and outdoor temperature. At least weak anti-correlations with ρ < −0.2 were found in 52%. 17 out of 50 short-term measurements (34%) showed at least a medium anti-correlation with ρ < −0.3. In 7 out of 50 (14%) of all short-term measurements, and strong significant anti-correlations with ρ < −0.5 were even found. In many cases, the significance level of the individual Spearman correlation coefficients found is 0.05, in some cases 0.01.

3.4. Result of the Regression Analysis to Fit the Short-Term Measurements to the Results of the Long-Term Measurements

Based on the results of the physical-statistical evaluation of metrological surveys using Spearman correlation analysis (performed with SPSS software) and on physical considerations, a set of influencing parameters were identified, tested in suitable functions and finally determined that demonstrably significantly influence the IRC. These parameters are to be measured by the measurement instruments directly or obtained in a suitable manner (e.g., including data from the online GeoSphere Austria Data Hub) in the three-week short-term measurement periods.

By applying the regression analysis—fitting short-term measurement data to long-term measurement data, considering the main influencing ambient parameters using the least-square fit method [23] realised by SigmaPlot^® mathematical software—a multiplicative model was established to estimate the annual mean value of the radon-222 activity concentration EIRC from the data (three-week mean values) of a short-term measurement of SIRC,

$$\mathit{EIRC}\mathbf{=}\mathit{SIRC}\mathbf{·}{\displaystyle {\mathbf{\prod }}_{\mathit{i}}}{\mathit{p}}_{\mathit{i}}\mathbf{=}\mathit{SIRC}\mathbf{·}{\mathit{p}}_{\mathbf{TDJ}}\mathbf{·}{\mathit{p}}_{\mathbf{TTX}}\mathbf{·}{\mathit{p}}_{\mathbf{MON}}\mathbf{·}{\mathit{p}}_{\mathbf{FFX}}\mathbf{·}{\mathit{p}}_{\mathbf{VVX}}\mathbf{·}{\mathit{p}}_{\mathbf{TIA}}\mathbf{·}{\mathit{p}}_{\mathbf{sr}}\mathbf{·}{\mathit{p}}_{{\mathbf{PPX}}^{\prime }}\mathbf{·}{\mathit{p}}_{{\mathbf{TIA}}^{\prime }}\mathbf{·}{\mathit{p}}_{\mathbf{sym}}$$

(2)

with functions p_i of the influencing parameters,

p_TDJ = 0.905 − 0.1992 · cos(TDJ)

(3)

TDJ: day of (calendar) year (midway through 3-week measurement period), 1 … 365, considering the seasonal influence—winter/spring/summer/autumn—on the IRC.

p_TTX = 0.875 + 0.0227 · TTX*

(4)

TTX: outdoor temperature, °C, hourly (mean) value (from GeoSphere Austria Data Hub).

p_MON = if (MON > 5 and MON < 9) then 1.589 else 0.959

(5)

MON: number of the month of the (calendar) year (midway through the 3-week measurement period), 1 … 12, considering strong ventilation by users during the ‘hot’ summer months of June to August.

p_FFX = 0.512 + 6.24 · 10 − 3 · FFX*

(6)

FFX: relative humidity of the outside air, %, hourly (mean) value (from GeoSphere Austria Data Hub).

p_VVX = 1.053 − 0.0342 · VVX*

(7)

VVX: wind speed, m/s, hourly (mean) value (from GeoSphere Austria Data Hub).

p_TIA = 0.978 + 1.683 · 10 − 3 · TIA*

(8)

TIA: difference between indoor and outdoor temperature, °C.

p_sr = 1.111 − 0.225 · sr(c_Rn)

(9)

sr: relative standard deviation of the series of measured values (e.g., hourly mean values) of the radon-222 activity concentration c_Rn, considering the variability of the measured radon activity concentration in the 3-week short-term measurement period.

p_PPX′ = 0.881 − 0.339 · PPX′_<0*

(10)

PPX′: change (temporal gradient) of the external air pressure in one hour, mbar/h (determined, e.g., from the hourly (mean) values PPX of the GeoSphere Austria Data Hub (note: sea level correction of the air pressure values may be necessary).

PPX′_<0*: mean value of all PPX′ values < 0, determined in the measurement period, considering the “air pressure radon pump”.

p_TIA′ = 0.674 + 0.405 · TIA′_>0*

(11)

TIA′: change (temporal gradient) of the difference between indoor and outdoor temperature in one hour, °C/h, considering the change in the indoor-outdoor temperature difference.

TIA′_<0*: mean value of all TIA′ values > 0 during the measurement period, °C/h, considering the “temperature radon pump”.

p_sym = 0.962

(12)

Constant factor to adjust the symmetry of all minimum and maximum values of the EIRC/LIRC ratios around the ideal value of 1.00 (EIRC = LIRC).

With Functions (3) to (12), the essential influences found in the work by means of Spearman correlation analysis and from the literature-known radioecological-physical relationships and regression calculations—both on the radon entry into the measured interior and through ventilation (dilution) with outside air—are quantitatively taken into account to determine the EIRC with Formula (2). Since we are combining a set of influencing factors in one product function, indeed the combination of even low and medium influencing factors influences the combined result significantly, even if (other) influencing factors do not have significant effects in individual cases.

Figure 3, Figure 4, Figure 5 and Figure 6 show examples of the functional dependencies found here between the SIRC readings from the short-term measurements and the environmental parameters. It should be noted that these individual functional relationships are exemplary and shown for their EIRC values of 300 Bq/m³. This value was chosen because it is the reference value for indoor radon according to the Austrian Radon Protection Ordinance.

Figure 3 shows the cosine-like dependence of SIRC (Formula (3)) over the course of a calendar year. Radon measurements in the winter season, and measurements in summer, respectively, overestimate and underestimate the annual average IRC. The lower the outside temperature in relation to the (more-or-less remaining constant) indoor temperature, the higher the SIRC in relation to the EIRC (Figure 4). The influence of the variability of the measured c_Rn values, indicated be the standard deviation of the c_Rn values, is shown in Figure 5. The effect of the “air pressure radon pump” is recognisable at Figure 6.

It should be noted that the individual dependencies shown here as examples are eventually incorporated into the product, Formula (2), of the influence functions. Therefore, only the product of the individual influence functions ultimately describes the real influence of all dependencies on the result of EIRC.

3.5. Results of the Uncertainty Analysis

The standard measurement uncertainty u(EIRC) of the EIRC using Formula (2) was estimated according to the state of the art [24]. The measurement uncertainties were calculated by means of the generally used propagation of uncertainties (error propagation). Two of the nine measuring instruments used were calibrated, while the other seven instruments were linked to the calibrations by means of the comparison exercise carried out.

In doing so, the uncertainties of the mean values SIRC of the measured hourly mean values c_RN* have been calculated with the uncertainties of the individual hourly mean values u(c_RN*) in a suitable manner. The standard uncertainties of the individual hourly mean values—mainly caused by the uncertainty of the calibration of the radon measuring instrument used and the counting statistical uncertainty—were outputted in most cases by the radon measuring instruments together with hourly mean values: c_RN* ± u(c_RN*).

The relative uncertainty u_rel($\prod _{\mathit{i}}{\mathit{p}}_{\mathit{i}}$) of the function $\prod _{\mathit{i}}{\mathit{p}}_{\mathit{i}}$ of Formula (2) was estimated by adding a plausible constant (relative) contribution of 3% to the total uncertainty u_rel(EIRC),

u_rel(EIRC) = u_rel(SIRC) + 3%

(13)

Unlike the AlphaGuard and AlphaE devices, the RadonEye Plus 2 measuring instruments do not record the measurement uncertainty u(c_Rn*) of the IRC hourly mean values c_Rn*, which is why these were estimated using Formula (14).

$$u\left(c_{Rn}^{*}\right)=\sqrt{{f_1·c}_{Rn}^{*}}+f_2·c_{Rn}^{*}$$

(14)

with

f₁ = 1·Bq/m³, which factorise the estimated stochastic part of the uncertainty, because the sensitivity of the RadonEye Plus2 instrument is about 30 counts per hour at 37 Bq/m³, this means in 1 h: $u(=\sqrt{counts})=\sqrt{30}\approx \sqrt{37}(=\sqrt{\left\{c_{Rn}^{*}\right\}}$)).

f₂ = 0.05, which factorise the estimated non-stochatic part of the relative uncertainty (mainly the calibration uncertainty).

3.6. Application of the Regression Analysis on the Short-Term Measurments

In Figure 7 and Figure 8, the results of the regression analysis by adjusting the short-term measurement data to the long-term measurement data (least-square-fit) are shown, considering the identified influencing parameters of the 50 short-term and 24 long-term Rn-222 measurements in the 24 investigated rooms in the period from October 2022 to July 2023. In each of the 24 rooms, one long-term measurement and at least one short-term measurement each in the winter and summer seasons were carried out, with two rooms additionally being measured in spring. Figure 3 shows the ratio values over the measurement period; Figure 4 shows the distributions of the ratio values (sorted in ascending order).

Figure 7 shows that the application of the physical-statistical model based on Spearman’s correlation analysis and further physical considerations has significantly improved the estimation of the annual mean value (EIRC) compared to the short-term measurements (SIRC). While the ratios of 32 out of 50 short-term measurements (62%) deviate from the optimal value of 1.0 by more than ±30%, only 10 out of 50 EIRC values (20%) are outside of the ±30% interval.

Figure 8 shows that for the 24 rooms examined, all EIRC/LIRC ratios of the 50 short-term measurements lie within the interval 0.4 to 1.6, while the SIRC/LIRC values lie in the larger interval 0.2 to 2.8. 11 of 24 long-term radon averages LIRC (46%) are greater than 300 Bq/m³ (Figure 4; note: the 24 long-term averages of the 24 investigated rooms are distributed among the 50 short-term averages).

4. Discussion and Conclusions

The present study developed a procedure that allowed the estimation of the annual indoor radon-222 mean value from three-week measurements of the radon-222 activity concentration (hourly mean values) with active radon measuring devices, taking into account defined influencing parameters. The procedure was developed on the basis of measurements in 24 interior spaces in four Austrian federal states. With the developed method, the significant influences on the short-term measurements could be ‘calculated out’ and the deviations of the results of the short-term measurements from the results of the long-term measurement could be significantly reduced.

If a 3-week short-term measurement is used to check whether the annual average value has fallen below an annual mean radon-222 reference value, the EIRC value multiplied by the safety factor 2.5 can be used to determine with sufficient certainty (confidence > 95%) whether the radon-222 annual mean limit value is not exceeded,

$$EIRC·2.5<\text{Rn-222} \mathrm{reference} \mathrm{value}$$

(15)

For example, if the Rn-222 reference value is 300 Bq/m³, then EIRC < 120 Bq/m³ ensures that the reference value is not exceeded with a confidence level of >95%. If the short-term measurement SIRC directly were used for this determination, the safety factor has to be set to 5.0—two times higher than 2.5,

$$SIRC·5.0<\text{Rn-222} \mathrm{reference} \mathrm{value}$$

(16)

This showed that, by applying the short-term radon measurement method developed here, an improvement by a factor of two can be achieved in the approximation of the long-term average. However, these criteria only apply to the interiors examined in this study. A generalisation requires a test and validation study of the introduced method, which a study that has already been started.

When applying the results of the analyses carried out here, it should be noted that the long-term average IRC value determined by measurement (6-month measurement, of which 3 months were in the winter season) of an indoor room also represents only a more or less certain estimate of the ‘hypothetical’ annual IRC mean value.

An alternative practical approach using short-term radon measurements to check the conformity with annual radon reference levels had been introduced by Tsapalov and Kovler [25]. This method considers the influence of all possible factors in a general ‘temporal uncertainty’ in relation to the measurement duration without specifying specific influencing factors as we do.

Based on further measurements and similar physical-statistical analyses, it should be possible to test and improve the generalisation of the method to other indoor spaces and to further develop the functional relationships. To validate and improve the method presented regarding reliable application, similar measurements will be carried out in further indoor spaces (in different regions and different types of buildings) in a continuation of the investigations. Corresponding adjustments will be made in the selection of the influencing parameters and their functional relationships, or existing measurements will be evaluated in this respect.

In this research, indoor rooms with an estimated minimum (annual mean) radon concentration of 100 Bq/m³ were specifically selected. This approach enabled differentiation between temporal changes in IRC and the stochastic noise of the measuring devices. However, future investigations should also include houses with lower radon levels to examine whether the findings can be confirmed under these conditions.

The analyses conducted so far suggest that ventilation behaviour has a significant impact on the measurement results. However, the participants’ statements about whether they ventilate extensively or minimally are strongly influenced by their subjective perception. To better interpret the results, a standardised ventilation protocol could be implemented in future studies.

In further investigations, the influence of wind should be analysed in greater detail, as the previous analysis only determined the correlation between wind speed and IRC, as well as wind direction and IRC, without examining the functional relationships in depth. Regarding the impact of wind speed on IRC, wind direction and the location of the buildings should therefore be taken into account.

Furthermore, additional analyses of the existing measurements are needed to determine whether the observed correlations between IRC and air pressure are due to the stack effect, or if they occurred for other reasons.

In the present study, the three-week mean values of the radon activity concentration and the influencing factors were used to determine the estimated value of the annual mean value of the radon activity concentration. In a follow-up study, which has already been started, the information from the hourly mean values of the radon activity concentration during the short-term measurement period is to be used in relation to the hourly mean values of the influencing factors to estimate the annual mean value of the radon activity concentration. In addition, we plan to use an AI-based neural network method to directly infer the annual mean from the hourly mean values of the radon concentration during the short-term measurement period.