SOURCE-DEPENDENT PROBABILITY DENSITIES EXPLAINING FREQUENCY DISTRIBUTIONS OF AMBIENT DOSE RATE IN THE NETHERLANDS

Several sources and processes contribute to the natural radiation background level, causing significant fluctuations in time. Quantified knowledge on the probability of these variations is desirable for many reasons, e.g. to discriminate between natural and human-induced factors or to support the management of nuclear emergency networks. Frequency distributions of ambient dosc rate, as observed by the Dutch National Radioactivity Monitoring Network over the period 1990-1994, have been explained through the joint contribution of five time-varying sources, including counting statistics. Normalised probability density functions (with a normal shape for noise. terrestrial and cosrnogenic radiation, and an exponential shape for airborne and deposited radioactivity from radon progeny) add up to one joint probability density function, which agrees with long-term data distributions over four orders of magnitude. This comparison yields parameter values describing the probable impact of rainout and washout of radon progeny and the typical fluctuation band of terrestrial radiation as observed in the Netherlands.


INTRODUCTION
A research programme aimed at obtaining quantified descriptions of the processes responsible for variations in natural radioactivity and radiation levels in the etherlands is currently in operation at the RIYM(I). The experimental data necessary for this study -which are supposed to have adequate resolution in space and time -are obtained from the Dutch National Radioactivity Monitoring network (NRM)m A major part of this programme involves the assessment of ambient dose rates. In a recent paper, an analysis on time-series yielded quantified information on the various processes and sources contributing to the natural background in the Dutch outdoor environment':". It was shown that most of the observed temporal variations could be explained by variations in airborne concentrations of 222Rn progeny, precipitation and air pressure, and simplified expressions were presented to estimate the natural background within a small uncertainty range. Other parameters, such as the radon soi I profi le and the cosmogenic source strength, were found to be less influential. These findings were adequate to provide a dynamic compensation method for natural background radiation; however, they do not provide all the information needed to estimate the range and distribution of ambient dose rate data likely to be observed over a long period of time. Knowledge of this kind not only classifies the impact of various sources and processes on variations in outdoor radiation levels, but is also desired, for instance, to establish sensitive warning levels in automated emergency networks"·2).
To compensate for this lack of information, the element of probability is taken into account. This paper will propose simple probability density functions for the various sources contributing to the ambient dose rate in the Netherlands so as to predict the likelihood of dose rate contributions over a long period of time, e.g. one year. These source-specific probability densities are merged into one joint probability density function, which is compared to annual frequency distributions of dose rate, as recorded by the NRM (see Figure I). This approach is believed to make sense; firstly, because location dependent annual average values of ambient dose rate remain very stable over the years(lA), and secondly, because frequency distributions obtained from various locations and years (see Figure 2) show a remarkable similarity in shape. More than 20 annual data histograms were analysed, yielding distribution functions and parameter values and describing the influence of each relevant natural source on the range of ambient dose rate data in the Netherlands.

INSTRUMENTATION
Radiological data are obtained from the NRM. Measurements of external irradiation levels (at 58 locations) and airborne radioactivity (at 14 locations) are recorded every 10 rnin and stored in a relational database. NRM locations are identified by their names, followed by three digits in brackets, like 'Wijnandsrade (133)'. Technical specifications of the network, including location numbers and positions, and the performance it shows as an emergency network, are found elsewhere!". RM recordings were shown to meet the requirements of examining small variations in natural background radiation levels as they occur in the Netherlandsv'<:'"; technical information presented here is therefore restricted to the essentials. For the monitoring of external irradiation levels the NRM is equipped with proportional counters (Bitt Technology Inc.' RS02 tube with an accessory RM IOE readout unit'?'). Recordings are converted to the dosimetric quantity ambient dose-equivalent rate at 10 mm depth, H*( I0)(7) which is further abbreviated to (ambient) dose rate. The NRM dose rate meters hold some systematic errors (for instance, they overestimate the cosmogenic dose rate), but these errors are correctable and do not affect the dynamic response of the equipment':". The reproducibility and mutual interchangeability of the applied radiation counters were shown to be very satisfactory; the accuracy of the data is, apart from counting statistics, estimated at 1% (1ucel) for typical background levels'J''". The counter tubes are mounted I m above the roof top of the NRM measuring cabins, about 3.5 m above ground level. Although most NRM locations are found in rural areas, recordings of ambient dose rate are influenced by the presence of pavements or small structures in the vicinity of the measuring sites(4.8) Recordings of airborne radioactivity are conducted using a moving-tape air sampler (FAG Kugelfischer Georg Schafer KGaA FRG, type: FHT 59S(9»), It was shown"? that recordings of natural gross (X activity concentrations in air can be converted to the actual equilibrium-equivalent decay product concentration of 222Rn, EEDC('O) The total uncertainty (1u cel ) in the determination of the EEDC is estimated at 12%, Any contribution of 220Rn progeny to the initial recordings can be neglected for various reasons, one of them being the air sampling height of almost 5 m':". Meteorological data are supplied by the Royal Netherlands Meteorological Institute (KNMI),

METHOD
Consider an arbitrary normalised probability density function, U('Y), expressing the probability that a certain source or process yields a contribution to the ambient dose rate, 'Y, between 'Yand 'Y+ dv. Next, consider two such probability density functions, U('Y) and V('Y), describing the probable contributions of two (uncorrelated) sources, The function W('Y), representing the 'probable sum' of these independent sources, is calculated as follows: If U('Y) and V('Y) are both normal distributions, W('Y) is also normally shaped, having a mean value f.L "'" 'Yw = 'Yu+ 'Yv and a standard deviation U "'" U w (u~+ U~)II2, We will apply this result to the dose rate contributions from cosmogenic and terrestrial radiation, which we assume to be normally distributed, The influence of counting statistics on recorded data can also be described by a normal distribution; in this approach, we treat 'counting statistics' as the third 'normally distributed (virtual) radiation source', The contributions from these three 'sources' are thus easily combined, However, dose rates due to airborne and deposited v-emitters Hence, the probability density function of the cosmic ray contribution conforms to the air pressure distribution. Longrange air pressure data are available, showing fairly normal shaped distributions.
The long-term average value for the Netherlands is 10 I 5 hPa but annual average values vary between 1012 and 1018 hPa (12) The stan-dard deviation of an annual distribution, up' is typically 10 hPa. The cosmogenic probability density function, C()I), can thus be approximated by a normal distribution with shape parameters fL == "tc and c == Ue. At standard air pressure (1013 hPa), the average cosmogenic contribution to the ambient dose rate is estimated at 40 nSv.h-'(4.11) The standard deviation is calculated as the product of C, and up' yielding Ue = 1.20 rtSv.h", with an estimated uncertainty of 0.10 nSv.h-'.

Terrestrial radiation
Gamma radiation from primordial radionuclides in soil (and building materials) forms the second most significant contribution to the ambient dose rate. This contribution is strongly location-dependent due to different soil types. Some of the most important radionuclides in this context are short-lived decay products of a radon isotope (e.g. 1I4Bi, 214Pb and 208TI). One may therefore expect the terrestrial component to show fluctuations in time as a result of temporal variations in the radon soil profile(4.8.13.14). However, from the analysis of timeseries these variations seem fairly low in the Netherlands':':"; In this approach, the terrestrial probability density function (including possible effects of the built-up environment) is represented by a normal distribution, with a location-dependent mean value, )IT, in the range of 15-75 nSv.h-' and a presumably small standard deviation, UT, yet to be determined. ." "Y -.I' "". ,," "" ""

Counting statistics
Radiation data are generally affected by counting statistics. Nuclear decay obeys Poisson statistics and the associated short-term temporal variations in radiation data are, in general, normally distributed around the average value, with a relative standard deviation equal to n-1I2 , n being the (average) number of counts received in one sampling period. For this to be true demands the registration of photon counts to be uncorrelated. In our case, this assumption seems valid due to the very small geometric detection efficiency of the counter tube and the applied sampling time of 10 min, which is short when compared to the half-lives of the short-lived 'Yemitting radionuclides of the 220Rn and 222Rn decay chains. Counting statistics can thus be regarded as a 'virtual' radiation source with a normal probability density function, N('Y), with shaping parameters f.l. == 'YN= 0 and U == UN = 'Yavgn-l12 = 'Y!~Ñ~"2 The parameter No stands for the average number of counts registered per unit dose rate per sampling period. For the equipment used, No was found to be 29 counts per nSv.h-' per 10 min!".
Based on the above, the probability density function S('Y) describing the joint contribution from counting statistics, cosmogenic and terrestrial radiation to the ambient dose rate is thus represented by a normal distribution, where the mean 'Ys= 'Ye+ 'YTand the standard deviation Us = (u~+ u~.+ U~)"2 Two of the five parameters, i.e. 'YT and UT, are free and yet have to be determined from measured frequency distributions.

Airborne radioactivity
The contribution of airborne radioactivity to the ambient dose rate is dominated by 'Yradiation from two short-lived 222Rn decay products, 214Bi and 214Pb; it is assumed to be linearly proportional to the concentration of the equilibrium equivalent decay product concentration of 222Rn in air, EEDC. The EEDC values are independently measured from the ambient dose rate by the FAG FHT59S monitors of the NRM(2.51, and the probability function of this source can thus be deduced from the measured frequency distribution of EEDC recordings. Figure 3 shows the 1990 EEDC frequency distribution for Bilthoven (627), which may be considered representative for the situation in the Netherlands. This distribution is normalised and converted to the ambient dose rate by applying a conversion coefficient, C EEDe , equal to 0.5 nSv.h-'.Bq-'.m3(,.3.4) Similarly shaped distributions were found at other NRM sites(4.'5) Apart from a discrepancy near zero, which is not very relevant because the influence of this part of the EEDC data on the dose rate is insignificant, the shape of such a distribution is fairly well described by a normalised 'one parameter' function, A('Y): The mean value of this probability density function, 'YA, is calculated as: 10-1 -- Ambient doserate(nSV.h-1) The median of this distribution, "Ymed;an' follows from: Lned"'" q e-q,{ d"y = 0.50 Values for q can thus be estimated from the annual mean or median values of airborne radioactivity concentrations, for instance, as reported in regular RM data reports' [16][17][18][19] The q values obtained for Bilthoven (627) Similar results obtained for other RM locations show a typical discrepancy of 10% between q values computed from either mean or median EEDC values, indicating that the proposed probability density function is just an approximation.
Based on all the RM locations (14) and years (6) where EEDC data have been collected so far, the shaping parameter q is found to vary between 0.6 and 2.5 h.nSv-1 in the etherlands (location being the most sensitive parameter), with a typical value of 1.2 h.nxv ".

Wet deposition
The highest temporal increase of ambient dose rate in the etherlands caused by natural processes comes from rainfall due to the washout of short-lived decay products of 222Rn. Dose rate elevations related to rainfall can be computed, using an actual time-series of precipitation rate and EEDC as input':':". Although this equation is easy to use in explaining or predicting elevated dose rate in a given situation, it is too complex to render the 'long-term' probability distribution of elevated dose rate due to rainfall. Instead, the expression for the probability density function for deposition, 0("1) presented here is deri ved semi-experimentally.
A probability density function for deposition fairly similar to the one presented in Equation 2 was derived from analysing high dose rate tails observed in actual frequency distributions with, however, one modification. In the case of airborne radioactivity, the same parameter, q, was used both to determine the slope of the distribution and to normalise the probability density function to I. In the case of wet deposition, a different (4) normalisation factor has to be used to match the observed data with the suggested probability density.
The reason for this is obvious: most of the ti me the ambient dose rate is not affected by rainfall at all as it rai ns as much as 7% of the year in the Netherlands (12) Moreover, deposited daughters of 222Rn contribute to the ambient dose rate for just a few hours after the rain has stopped. When considering wet periods only, probable dose rate elevations can be characterised by a distribution similar to Equation 2. During the rest of the time the contribution from wet deposition is virtually zero. The following normalised probability density function, 0("1), is therefore suggested: 0("1) = r -p 0("1) + p e-ry for ("I 2: 0) r and 0("1) = 0 for ("I < 0) The delta function introduced in this equation ensures proper normalisation to unity. As will be shown later on, the normal isation and slope parameters p and r can be determined from the high tail of the experimentally observed frequency distribution.

FREQUENCY DISTRIBUTIONS OF AMBIENT DOSE RATE
year and statistical scattering becomes important. To examine the goodness of fit for those parts of the distribution X~values, defined as(22': Twenty-five annual frequency distributions, obtained from RM sites located in the middle. the north-east. the south-east, the south-west and the western part of the Netherlands were analysed over the period 1990-1994. On four occasions dose rate distributions were strongly disturbed due to frequent malfunction of equipment or human interference and had to be excluded from the test!".

Location-dependent
annual average values of air pressure':"! and EEDC"6 '9, were applied to calculate the input parameters -Ye and q. The parameter <:re was calculated, assuming a fixed air pressure standard deviation, <:rp, equal to 10 hPa. The standard deviation due to counting noise, <:rN, was calculated using a fixed value for the parameter No of 29 counts per nSv.h-' per 10 rnin counting interval. The parameters p and r were fitted from the high tail of the data distribution, while the parameters 'Y-r and <:rT were adjusted to match the joint probability density function with the top and the lower half of the histogram.
Calculated and measured values extend over a range of four orders of magnitude. Two quantities were used to adjust the free parameters and to evaluate the goodness of fit. Around the top of the distribution some 10 2 -10' data are recorded per interval per year, showing good statistics. In this region the relati ve di fference between the joint probability density function and the normalised histogram was evaluated. Away from the top, especially at the high tail of the distribution, just a few (say < 100) recordings are expected per interval per   Figure 4(b). The small mismatch observed at the top (histogram data are shifted slightly to the left), originating from assuming a normal air pressure distribution, is also noticed in other results. In fact, the air pressure distribution is often slightly asymmetric, with a shorter wing in the high and a longer wing in the low air pressure region. In Figure 4(a), we see a reverse profile in the experimental data due to the negative correlation between cosmogenic dose rate and air pressure. This feature also explains the fairly high  Best estimates for the parameters expressing the influence of rainfall, i.e. p and r, show considerable variations (see Figure 5), both in location and time. Variations between years reflect the variable character of weather conditions, while spatial variations are merely due to differences in local ground surface characteristics. These influence the ambient dose rate following a given deposition of radionuclides. Mean and median values found for p are 0.015 and 0.016 h.rtSv ", respectively; for r these values were found to be 0.18 and 0.19 h.rrSv'", respectively. Typical values, as indicated in Figure 5, were taken in between. The quotient of the latter, i.e. P,ypr~y'p, equals 8.4 X 10-2 Ambient dose rate is thus on the average influenced by rainfall for approximately 8.5% of the time. Being slightly higher than the average period of rainfall in the Netherlands, which is 7% in the long term'!", this value agrees with the expected value. The annual ambient dose due to the washout and rainout of 222Rn progeny, computed from the typical parameter values for p and r, equals 4 f.1Sv.a-'. Taking a precipitation rate of 800 mrn.a ", as normally observed in the Netherlands"?', the time-integrated ambient dose following one unit of precipitation is, on average, 5 nSv.mm-'. This value compares to the 4.1 nSv.mm-' derived from the analysis of individual rain showers at Bilthoven (627)<3.4). Rainfall may occasionally lead to highly elevated recordings of ambient dose rate, but the total impact from this source is very small; it contributes less than I% to the total timeintegrated ambient dose. This contribution is even less than the average annual contribution of airborne radioactivity to the ambient dose, which is, with q being typically 1.2 h.nSv-', of the order of 7 u.Sv.a ".
The other parameter of interest, UT' expressing the temporal variation in the terrestrial dose rate contribution, ranges from virtually zero to I nSv.h-'. Some of the higher values, however, are probably overestimated due to factors like changes in the built-up surroundings and replacement of equipment not accounted for in the present description. On the other hand, NRM equipment underestimates the terrestrial dose rate by some 10%(4) The mean and median values derived from this test, with 0.67 and 0.75 nSv.h-' close to each other, are therefore considered representative. Temporal variations in terrestrial radiation are thus, in general, confined to a range of ±2 nSv.h-' in the Netherlands. A similar result was found from the analysis of monthly averaged data for the 14 principal NRM locations over the period 1990-1994(3.4) In Table I, typical values to describe the influences of various sources on the ambient dose (rate) in the etherlands are summarised. Some of the figures in this table, such as the typical value for 'YT,were taken from related studies not evaluated in this paper.

DISCUSSION AND CONCLUSIONS
Frequency distributions of ambient dose rate data, as observed by the Dutch National Radioactivity Monitoring Network, were shown to be well described by considering only five (virtual) sources and processes using simple expressions for the likelihood of their occurrence. Over one million data pairs, obtained from various locations and years, were used in this analysis, of The measured frequency distribution is broadened due to counting statistics; for the NRM set-up the corresponding standard deviation is typically 1.6 nSv.h-' for a 10 min sampling time. These three sources add up to a normal distribution with a location-dependent mean value in the range 50-120 nSv.h-' and a standard deviation of typically 2.1 nSv.h-'.
On average, airborne and deposited short-lived decay products of 222Rn have a low impact on the natural background radiation (i.e. si % each) but their contributions can occasionally lead to significant dose rate elevations.
In both cases the likelihood of their dose rate contribution is expressed by an exponential function, stating that the probability of a certain contribution decreases exponentially with increasing dose rate. In the case of washout of 222Rn progeny, this exponential probability was found to be present for approximately 8.5% of the year. In the remaining period the contribution from this source is zero. In our approach it is assumed that sources and processes under consideration are not correlated. In fact, some correlation does exist, for instance, between air pressure and EEDC, and air pressure and precipitation; however, these correlations were found to be rather This study yields quantified knowledge on the probability of temporal variations in ambient dose rate due to natural causes, which can serve in the management of nuclear emergency networks.
The ranges and likelihood of dose rate variations presented here can be used to establish proper warning levels, where it is important to find a precise balance between sensitive detection of radiological accidents and occasional false alarms caused by fluctuations of natural background levels' 1.2). This kind of information can also facilitate the validation of data and the control of equipment, thus supporting the quality assurance of the network.