A8.1 Determination of Activity Concentration, A_i

The determination of annual average radionuclide activity concentrations at the various sites was complicated by the following factors:

not all the radionuclide activity concentrations were measured;

of those that were measured, not all were measured at all sampling sites;

fewer radionuclides were measured in the first phase of the study than in the second phase; and

some new sampling sites were added and some removed during the course of the study.

Details of the sampling data set are given in Table A8.1. The methods of dealing with the complications mentioned above are described in sections A8.1.1 to A8.1.3 below.

Table A8.1 Details of individual radionuclide measurements

1: measured only in phase 1

2: measured only in phase 2

1+2: measured in phases 1 and 2

Shaded areas indicate months during which measurements were made.

Complications also arose from the analysis techniques:

some radiochemical analyses involving very low activities gave negative values due to the statistical nature of the measurement technique; these negative values were included in the calculation of the annual mean values, but any annual mean values less than zero were set to zero.

some IPC-MS analyses involving very low activities gave values below the detection limit; these were set to half the detection limit.

A8.1.1 Estimating the activities of radionuclides not measured at some sites

The following radionuclides:

227Ac, ²³¹Pa, ²¹⁰Pb, ²¹⁰Po, ²²⁸Ra and ²³⁰Th

were not measured at some sampling sites (see Table A8.1). It was found that, at the sites where these radionuclides were measured, the activity values were all very low and varied in a random fashion. The activity of each radionuclide at the sites where measurements were not made was therefore taken to be the mean value for that radionuclide calculated from all the samples at all other sites. The additional doses at the sites where these radionuclides were not measured, resulting from the use of these global mean values, are shown in Table A8.2. The doses are so small that even very large errors will be inconsequential.

Table A8.2 Dose contributions resulting from the use of global mean activity values

A8.1.2 Estimating the activities of radionuclides never measured

The following radionuclides:

228Ac, ²¹⁰Bi, ²¹²Bi, ²¹⁴Bi, ²¹¹Pb, ²¹⁴Pb, ²²⁸Th, ²³¹Th, and ²³⁴Th

having very low dose conversion factors, were never measured. The activity concentration of these radionuclides was simply taken to be equal to the mean activity of all measured radionuclides over all sites (0.00672 Bq/l ). On the basis of this assumption, the never-measured radionuclides contributed only 0.0005 mSv/a to the dose associated with each sampling site. This was deemed to be sufficiently small a contribution that no further sophistication was justified. For example, even if the activity concentration were to be underestimated by a factor of 3, the dose would be underestimated by only 0.001 mSv/a, a trivial amount.

In practice, the interquartile range (± 0.019 Bq/l ) of the mean values of all the measured radionuclides would be a fair first-order estimate of the range of uncertainty of the activity of the never-measured radionuclides. Thus, the uncertainty in the dose contributed by the never-measured radionuclides is 0.0028 mSv/a.

A8.1.3 Extrapolations for radionuclides not measured in phase 1

The following radionuclides:

227Ac, ²³¹Pa, ²¹⁰Pb, ²²⁸Ra, ²²⁷Th, ²³⁰Th and ²³⁴U

The following procedure was used:

1. To decrease the noise influence of values near the detection limit, all values at or below the detection limit or within one standard deviation of 0, were discarded.

2. Those Phase I variables with relatively few values remaining were discarded.

It was also found that some of the stations, for example Station1, had exceedingly high (two orders of magnitude) values of certain variables, for example aluminum. Unfortunately, some stations, including Station 1, were dropped from sampling in the second half of the year. Thus including aluminum in the regression variables would result in extrapolating to aluminum values 100 times higher than were calibrated and tested on.

To ensure that this problem did not occur in other variables, the chosen predictors were inspected to ensure that the calibrating stations covered the full range for the variables.

Stations 10 and 2 had exceptionally high values of phosphate and calcium respectively. Phosphate at Station 10 was 5.7 standard deviations above the mean of the other stations. Calcium at Station 2 was 3 standard deviations above the mean of the other stations. Thus Ca and PO4-P were also excluded from the set of possible predictors.

Those variables left were:

Cl, EC, F, gross alpha, gross beta, K, Mg, Na, NH4-N, NO3+NO2-N, pH, Ra-223, Ra-226, Si, SO4, Sr-diss, TAL as CaCO3, TDS, U-235,

U-238.

3. All subsets shorter than 5 of these variables were tested.

4. For each Phase II variable and for each subset of Phase I variables the data was extracted.

5. If there were too few samples to get a good test of the significance of the fit, that subset was rejected.

6. The samples were divided into a calibration set and a test set.

7. The Phase II variable was fitted to the subset of the Phase I variables using the calibration set.

8. The goodness of fit parameter was calculated, using the regression calculated in the previous step, on the both the calibration and the test data sets. The worst value was reported and used in the next step.

9. The subset with the best-reported goodness of fit was selected.

The goodness of fit parameter was the sum of the squared residuals divided by the number of degrees of freedom, divided by the standard deviation of the variable being fitted i.e. Fitting a subset of length 0, would simply be the mean value of the variable being fitted. The goodness of fit parameter would then simply be 1.

Thus the goodness of fit tells you how much sharper (if < 1) your prediction is than simply taking the mean value as your predictor. It is never worth selecting a subset for which the goodness of fit parameter, is greater than or equal to 1.

It was possible, for only two of the Phase II nuclides (Th-227 and U-234), to find a subset of Phase I nuclides which improved our predictive ability. The per station doses are presented in Table 8.3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 8.3 The per station doses.

A8.1.4 The Uranium - Dose relationship

Plotting U-238 concentration against yearly dose and performing a least squares linear fit gives us the following relationship...