human population are involved in various activities such as; leisure, occupation and others. At each location, shore sediment samples were taken from an approximate 7 to 10 meters away from high tide at a depth of 20 centimetres by using hand scooper. After each sample was cleared of debris it was allowed to dry at a temperature of 110˚ for 24 hours. Prior to gamma analysis, the samples were then left to stand for thirty (30) days for secular equilibrium to be reached between long-lived parent radionuclide and their short-lived daughter radionuclides in the ^{238}U and ^{232}Th decay series. On the attainment of secular equilibrium, the samples were then counted for 8 hours on a gamma spectroscopy system with HPGe Detector housed in the International Centre for Environmental and Nuclear Sciences, University of the West Indices Mona Campus, Kingston, Jamaica with 70% efficiency and a resolution of 1.8 keV at the 1.3 MeV Cobalt line. The detector was calibrated with respect to energy and efficiency before measurements. Standards of known concentrations of radionuclides were used. Background measurement which is the natural occurring radioactivity were taken and appropriately subtracted from the measured gamma ray spectrum of each samples in order to obtain net counts for the samples. The spectrum obtained from the standards was then employed to carryout energy and efficiency calibrations which were used in the determination of the activity concentration of the radioactive nuclides in Bq∙kg^{−1}.

2.3. Experimental Data Collection

A total of 800 closed ended questionnaires were administered to participants along the coastline in the beaches of Swakopmund, Walvis Bay and Henties Bay. The exposure-related activities of the studied population included leisure and work/occupation i.e. fishing, diving, walking, picnic at the shore, horse riding, sun bathing, relaxation at beach house, vendor, shop retailer, sanitation work and others.

Data from the questionnaires were used to calculate the outdoor and indoor occupancy factor. A model relating time budget for the various activities such as leisure, occupational and others that involves indoor and outdoor parameters has been developed.

2.4. Modelling the Data

The following assumptions were considered in the development of this model:

1) Absorption rate of NORMs is directly proportional to the amount of time spent in exposure.

2) Each population group was assumed to have a time fraction of leisure, occupation and other activities.

3) Each activity was assumed to have a time fraction of indoor and outdoor function.

4) The total time spent indoor and outdoor in a day is 24 hours for each population group.

5) Each activity was regarded as an independent time variable.

6) Indoor and outdoor time spent is linearly dependent on the activities.

If we consider “I” to represent the time spent indoor and “O” for the time spent outdoor for any given activity, and considering assumptions four (4) above. We have that;

(1)

The indoor time component was modelled as;

(2)

where = indoor fractional time parameter for k^{th} activity.

= observed total time spent for k^{th} activity.

The outdoor time component was modelled as;

(3)

where = outdoor fractional time parameter for k^{th} activity.

Adding Equations (2) and (3), leads to

(4)

From Equations (1) and (4), we obtain

(5)

Substituting Equation (2) into Equation (5), yields

It follows that

(6)

Similarly, substituting Equation (3) into Equation (5)

(7)

Adding Equation (2) and Equation (6)

(8)

Similarly, adding Equation (3) and Equation (7), we obtain

(9)

Let, where T_{k} represents the total fractional time parameter for k^{th} activity. Therefore;

(10)

(11)

Therefore the sum of (10) and (11) equals (1).

The model (Equations (10) and (11)) were used in MATLAB to determine the fractional time parameter estimates for indoor and outdoor occupancy.

3. Results and Discussion

3.1. Occupancy Factor

Table 1 presents the mean time allocated for each activity. Table 2 is the value of the estimated indoor and outdoor fractional time parameter for each activity while Table 3 and Table 4 represent the values of the total fraction of time parameters for each group and the computed time spent indoor and outdoor. Using the factor model above, the computed time spent outdoor in the coastline of the Erongo region (Table 4) was obtained in the range from 18.59 to 8.40 h for leisure activities and 13.14 to 8.26 h for occupational related activities. The value for indoor activity was calculated to range from 15.60 to 5.41 h for leisure and 15.74 to 10.86 h for occupational related activities. The average time spent for outdoor activity by an average visitor to the coastline has been evaluated to be 11.46 h. This accounted for 48% of the total time per day for which an individual maybe exposed to radioactive elements along the coastline. Similarly, the average time spent for indoor activities has been calculated to be 12.54 h. This implies that on an average, visitors to the coastline spent 52% of their total time per day in indoor related activities. The outdoor occupancy factor of 0.48 for this present study is 2.4 times the UNSCEAR value of 0.2% or 20% which is significant. The data shows that the indoor factor of 0.52 for an average person who visit the coastline is 35% below the world average factor of 0.8 [19] .

Table 1. The mean time allocated for each activity.

Table 2. Values of estimated indoor (λ) and outdoor (σ) fractional time parameter.

^{*}Not applicable.

Table 3. Values of the total fractional time parameters.

^{*}Not applicable.

Table 4. Computed time spent outdoor and indoor.

3.2. Activity Concentration

The mean specific activity concentrations obtained for shore sediment samples collected along the coastline of Erongo region are presented in Table 5 and a comparison of the absorbed dose and annual effective dose rate from the study areas with world average value (UNSCEAR) are shown in Table 6 and Figure 2 respectively. The activity concentrations of^{238}U, ^{232}Th and ^{40}K in the sediment samples ranged from142.79 to 199.76 Bq∙kg^{−1} with a mean of 173.00 ± 8.8 Bq∙g^{−1}, 29.69 to 42.47 Bq∙kg^{−1} with a mean of 37.77 ± 2.7 Bq∙kg^{−1} and 354.38 to 611.19 Bq∙kg^{−1} with a mean of 441.78 ± 2.5 Bq∙kg^{−1}, respectively.

3.2.1. Absorbed Dose Rate (ADR)

The absorbed dose rate calculation was based on the mean activity concentrations of ^{238}U, ^{232}Th and ^{40}K con- verted into dose rate on the bases of the UNSCEAR conversion factor [1] .

(12)

where D is the absorbed dose rate

The average absorbed dose rate for all the sampled locations are above the world average value (51 nGy.h^{−1}) [1] .

3.2.2. Annual Effective Dose Rate (AEDR)

The annual effective dose received by visitors to the coastline was calculated from the absorbed dose rate by applying dose conversion factor of 0.7 Sv/Gy and the occupancy factor for outdoor and indoor. According to UNSCEAR [1] , the outdoor and indoor factors are 0.2 (5/24) and 0.8 (19/24) respectively. The annual effective dose (outdoor) was determined using the following equations

(13)

(14)

Figure 2. Comparison of effective dose rate of UNSCEAR and present factors with world average values.

Table 5. Mean activity concentrations from beaches along the coastline.

Table 6. Absorbed dose rate, annual effective dose rate using the UNSCEAR and present factor and the world average value.

WAV world average value (UNSCEAR).

The AEDR (Outdoor) using the UNSCEAR factor ranges from 121.01 to 176.61 mSv×y^{−}^{1} with an average value of 142.52 mSv×y^{−}^{1}. The AEDR for the present factor was calculated to range from 292.60 to 413.63 mSv×y^{−}^{1} with an average value of 339.36. Although, this study showed that the AEDR using the UNSCEAR factor and the present factor have values higher than the world average value of 70 mSv×y^{−}^{1}, the present factor have however showed that the estimated outdoor effective dose to the population who visit the coastline for different activities would be underestimated by ~24% if the UNSCEAR factor is employed. The increase in this present factor can be attributed to the arid weather condition of the country and the serenity the coastline provides to its visitor. The values obtained for AEDR in this study agree with values found by other studies which give credence to our methodology and objective of study. The current study did not evaluate the indoor effective dose because the essential data on the average concentration of radon build-up in indoor atmosphere along the coastline were not available.

4. Conclusion

This study has attempted to model a mathematical representation of time spent for outdoor and indoor activities for the coastline of the Erongo region of Namibia. The result obtained has been used to evaluate the occupancy factor for outdoor/indoor activities by the population involved in leisure, occupational or other activities. The average time spent for outdoor activities is given by 11.46 h and indoor with a value of 12.54 h. This value has been shown to be significantly higher than the world value by 2.4 times (outdoor) and below the world value by 35% indoor. The factors suggest that the effective dose to population along the coastline would be underestimated by 24% for outdoor if the world average value by UNSCEAR is used. Equally, the mean values obtained for AEDR are found to be higher than the world average values (70 µSv∙y^{−1}) [1] . This finding is in agreement with previous studies [20] [21] where an increase outdoor factor over UNSCEAR value is attributed to differences in lifestyle and occupational activities.

Acknowledgements

Thanks are due to the International Centre for Environmental and Nuclear Sciences, University of the West Indices Mona Campus, Kingston, Jamaica for helping with gamma spectrometric analysis. We gratefully acknowledge Mr. Lawrence Olotu for his assistance in fieldwork.

NOTES

^{*}Corresponding author.

Cite this paper

Onjefu, S. , Kgabi, N. , Taole, S. , Mtambo, O. , Grant, C. and Antoine, J. (2016) Occupancy Factor Model for Exposure to Natural Radionuclides along the Coastline of Erongo Region, Namibia.*Journal of Geoscience and Environment Protection*, **4**, 117-126. doi: 10.4236/gep.2016.45012.

Onjefu, S. , Kgabi, N. , Taole, S. , Mtambo, O. , Grant, C. and Antoine, J. (2016) Occupancy Factor Model for Exposure to Natural Radionuclides along the Coastline of Erongo Region, Namibia.

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