Periodicity in Domestic Radon Time Series

Home , Radon

Periodicity in Domestic Radon Time Series - Evidence for Earth Tides C J Groves-Kirkby1, A R Denman1, R G M Crockett2, P S Phillips3 1Medical Physics Department, Northampton General Hospital, Northampton NN5 1 BD, UK E-Mail: [email protected] 2School of Technology and Design, University College Northampton, St. George's Avenue, Northampton NN2 6JD, U.K. 3SITA Centre, School of Environmental Science, University College Northampton, Northampton NN2 7AL, UK Abstract. Although long-term average radon levels in domestic properties determine the overall lung cancer risk to occupants, for a variety of reasons it is generally preferable to make radon determinations using short-term methods. However, while accurate radon determination is technically possible on a time-scale of hours, typical diurnal radon variation may span one or two orders of magnitude, hindering characterization of long-term concentration from short-term measurement. Averaging over more than one day eliminates diurnal fluctuations, but is susceptible to day-to-day variations, due to factors such as lifestyle, weather patterns etc. To explore the use of short-term exposures as measures of long-term trends, the time-dependence of radon levels in three homes was monitored over periods ranging from three to seven months, using Durridge RAD-7 monitors, providing continuous data sets for radon level at hourly intervals throughout the measurement periods. Two of the sites are situated 2 km apart on similar, but not identical, geology (Northampton Sand) and both possess cellars, providing relatively undisturbed measuring environments. Despite these similarities, radon levels at the two sites differ by an order of magnitude. Regression and cross-correlation of radon levels with environmental parameters showed weak contributions to variability from mean temperature and rainfall. Autocorrelation and Fourier transformation of the radon time-sequences identified a number of characteristically periodic features. Daily, weekly and monthly contributions, some common to more than one property, others location-specific, were identified, with differing strengths reflecting local occupation patterns. Two properties exhibited components having periodicity of 23.9 hours (the luni-solar diurnal period) and 24.0 hours (the solar day), while one gave indication of a 168 hour (one week) cycle. In addition, evidence appeared of periodicity around 661 hours (27 days, 13 hours), the Lunar Month, together with positive correlation with tidal strength, suggesting that 'Earth Tides' contribute to the periodic liberation of radon, possibly via geophysically driven variations in ground-water level.

1. Introduction

Radon is a naturally occurring radioactive noble gas, having variable distribution in the geological environment as a decay product of natural uranium found, in differing degrees, in a wide range of rocks and soils, and in building materials incorporating or manufactured from these. There are three naturally occurring isotopes, 222Rn, a direct product of 226Ra in the 238U decay-series with a half-life of 3.8 days, 220Rn, a decay product of 232Th, with a half-life of 55.6 s, and 219Rn, a decay product of 235U, with a half-life of 3.6 s. Radon has high mobility, enabling it to move out of underlying rocks into caves, mines and the built environment. Of the three isotopes, 222Rn is the most significant, its relatively long half-life enabling it to migrate quite significant distances within the geological environment before decaying. Although radon dissipates rapidly once in outdoor air, it concentrates in the built environment. For UK dwellings, the mean radon level is around 20 Bq·m-3, compared to 4 Bq·m-3 in outside air [1], but levels up to 10,000 Bq·m-3 have been found in domestic housing.

Ionising radiation is well known to have adverse health effects, and inhalation of radon and its progeny 218Po and 214Po adsorbed onto atmospheric particulates is currently believed [2] to provide the majority of dose to the respiratory system. This damages the sensitive inner lining of the lung, increasing the risk of cancer, and it is estimated [2] that the annual mortality from exposure to radon in buildings represents 6 % of all deaths from lung cancer in England. The total annual mortality from this type of cancer is between 30,000 and 35,000, suggesting that between 1,800 and 2,100 deaths annually are caused by exposure to radon and its progeny. There is therefore a significant motivation for the development of reliable techniques for characterising baseline domestic radon levels.

Determination of domestic radon concentration based on short-term measurements is confounded by the presence of numerous periodicities affecting mechanisms driving the liberation of radon gas from the soil. Thus, a measurement extending over a few hours may be influenced by the time of day at

1 which the data is taken. Similarly, a measurement lasting a day or a few days may depend on which days in the week are involved. On the longer time-scale, this problem has been recognized by the application of seasonal correction factors [3] to one-month and three-month measurements. Although techniques exist for accurate determination of radon levels over intervals of the order of hours or less, typical diurnal variation in radon level may be two to three orders of magnitude, militating against reliable short-period characterization of domestic premises. By averaging over periods of more than one day, diurnal fluctuations can be effectively eliminated, providing a more meaningful assessment of true radon concentration, but simultaneously introducing potential confusion from day-to-day variations, due to factors such as lifestyle, weather patterns etc.

Our recent and ongoing studies on domestic radon levels have addressed radon baseline concentration characterization through relatively short exposures [4]. To explore the viability of utilising short-term, e.g. 3-day or 7-day, exposures as measures of long-term trends, the time-dependence of radon levels in three homes was monitored over extended periods. This approach provided continuous data sets for radon level and ambient temperature at hourly intervals. We present here some observations and conclusions arising from analysis of the periodicities occurring in these data sets.

2. Methodology

2.1. Instrumentation

For quasi-continuous time-series monitoring of domestic radon concentrations, two sets of Durridge RAD-7 radon detection equipment 1 were available. The RAD-7 is a portable instrument, operating by electrostatic collection of α-emitters with associated spectral analysis, capable of measuring the ambient radioactivity concentration in a matter of minutes and operating in unattended continuous mode for several weeks. Air from the sampling point is drawn by a pump through a length of flexible tube, passing through a drying column and two filters before entering the 0.7 litre sample cell. The immediate product of any radon decay occurring in the cell is a positively charged 218Po ion, which moves under the influence of the internally applied electric field and is deposited onto the solid-state detector. Subsequent decays produce further α-particles, which have a 50 % probability of entering the detector and which are counted in two main energy channels, Channel A for 218Po and Channel C for the subsequent progeny 214Po. The results, up to 999 in any continuous automatic cycle, are stored as a data table and can be printed as a time-series at the end of each measurement cycle, when the mean radon concentration during the cycle is calculated.

The RAD-7 is calibrated by the manufacturer against a master instrument, which, in turn, is calibrated against a standard maintained by the National Radiological Protection Board (NRPB). The overall calibration accuracy is estimated to be about ±5 %. In most circumstances, the precision of individual RAD-7 measurements of radon concentration is limited by counting statistics. Some examples of normal mode counting precision are given in Table I.

Table I. RAD-7 Normal mode counting errors – counting time = 1 hour

Radon Concentration[Bq·m-3] 20 400 1000 Number of counts (N) 15 300 750 Error: ± 2σ = ±2√N ±52 % ±12 % ±7 %

2.2. Instrumentation Placement

Sets of RAD-7 equipment were initially installed in infrequently-used cellars in two domestic properties, A and B, situated around 2 km apart on similar geology, Northamptonshire Sand, in the town of Northampton, England. Despite these similarities, the two sites exhibit radon levels differing by an order of magnitude or more, reflecting differing values of radon potential [5] at the two sites.

1 Durridge RAD-7 Professional Radon Detector. Durridge Company, 7 Railroad Avenue, Suite D, Bedford, MA 01730, USA.

Following a period of approximately six months when both Property A and Property B were monitored simultaneously, Property B and Property C, also on Northamptonshire Sand but without a cellar, were compared for a further three months. Both sets of equipment were then operated in close proximity in an infrequently-used ground-floor room in Property C for a period of around six weeks, following which they were operated for three months (July – September 2003) in a relatively undisturbed room in Property D, a workplace location known [6] to have relatively high radon levels. The relevant operation dates, measurement periods and locations are summarized in Table II.

Table II. Operating Locations and Schedule for RAD-7 Equipment Sets

Equipment Identifier Property Start Date Finish Date Duration [d] 'a' TS1a B 27th June 2002 19th December 2002 175 B 19th December 2002 9th January 2003 21 TS2a B 9th January 2003 27th March 2003 77 TS3a C 4th April 2003 17th May 2003 43 TS4a D 6th June 2003 10th September 2003 96 'b' TS1b A 27th June 2002 19th December 2002 175 TS2b C 9th January 2003 27th March 2003 77 TS3b C 4th April 2003 17th May 2003 43 TS4b D 6th June 2003 10th September 2003 96

2.3. Calibration and Correlation

Prior to commencement of the measurement schedule, both RAD-7 equipment sets were calibrated by NRPB in accordance with the manufacturers' recommendations. The opportunity to operate both sets of equipment in close proximity permitted assessment of the degree of correlation of the respective outputs, providing confidence in the reported radon concentrations. As indicated in Table II, both sets of equipment were operated simultaneously a few cm apart in a rarely-visited and isolated room, with known high radon level [6], in Property D, where it was operated continuously for three months.

300

250

200

150

100

0 0 50 100 150 200 250 300 Series TS4a

FIG. 1. Time-Correlated response of two RAD-7 equipment sets operated simultaneously in close proximity : Time series TS4a and TS4b

FIG. 1 shows the x-y scatter plot of time-correlated pairs of readings from the series TS4a and TS4b respectively. The outcome of statistical analysis of the two sets of data is summarized in Table III.

Table III. Statistical analysis of RAD-7 comparison experiments

Slope 1.055 Intercept 2.405 Correlation Coefficient 0.904

3. Results and Analysis

3.1. Time Series

FIG. 2 and FIG. 3 show radon concentration time-series TS1a+TS2a and TS1b, monitored at hourly intervals over periods of nine and six months respectively, with superimposed 72-hour moving average plots to demonstrate the nature of the variability.

5000 Radon

4500 72 hour Moving Average

4000

3500

3000

2500

2000

1500

1000

500

0 22-Jun-02 20-Jul-02 17-Aug-02 14-Sep-02 12-Oct-02 9-Nov-02 7-Dec-02 4-Jan-03 1-Feb-03 1-Mar-03 29-Mar-03 Date/Time FIG. 2. Temporal Variation of Radon level: TS1a+TS2a, June 2002 to March 2003 Points: individual hourly interval radon levels. Solid curve: 72-hour moving-average.

500 Radon

450 72 hour Moving Average

400

350

300

250

200

150

100

0 15-Jun-02 13-Jul-02 10-Aug-02 7-Sep-02 5-Oct-02 2-Nov-02 30-Nov-02 28-Dec-02 Date/Time FIG. 3. Temporal Variation of Radon level: TS1b, June 2002 to December 2002 Points: individual hourly interval radon levels. Solid curve: 72-hour moving-average.

Although absolute radon levels differ, due to the differing geological environments of the two properties, the two plots are qualitatively similar, exhibiting periodicity on day and longer time-scales.

3.2. Linear Regression Against Environmental Parameters

Properties A and B are situated approximately equidistantly 2.5 km from Meteorological Office Climatic Station C4364, operated by University College Northampton, from which daily meteorological data for maximum and minimum air temperature, grass temperature, rainfall and mean relative humidity, was available. Multivariate linear regression of radon concentration against these variables provided the numerical coefficients summarized in Table IV. Although the response in TS1a+TS2a appears to be dominated by the influence of meteorological conditions to a relatively greater extent than are the other two series, there is no consistent dependence over all time-series.

Table IV. Multivariate Regression: Series TS1a+TS2a, TS1b and TS2b vs. Meteorological Conditions

Parameter TS1a+TS2a TS1b TS2b Mean over series 1226.392 47.037 35.697 Intercept 1227.74 182.13 41.87

Tmax -0.366 0.575 0.0536

Tmin 34.474 -2.718 0.201

Tgrass -44.197 1.626 -0.764 Rain -2.690 0.747 0.232 Relative Humidity -0.0690 -1.586 -0.0976 R2 0.070 0.117 0.183

3.3. Autocorrelation Analysis

The Auto-Correlation function of a time-dependent series is the average measure of its time-domain properties, being the average product of the signal f(t) and a time-shifted version of itself, and is a function of the imposed time shift , τ. Formally, the Autocorrelation function is defined as:

T0 lim 1 2 r ()τ = f (t) ⋅ f (t +τ ) ⋅ dτ (1) xx T T ∫ 0→∞ −T0 2

1.0 TS1a TS1b TS2a 0.8 TS2b

0.6

0.4

0.2

0.0

-0.2 0 24 48 72 96 120 144 168 Lag [hours] FIG. 4. Autocorrelation plots of four radon time-series derived from three residential properties 3-hour moving-average smoothing – 7-day time-shift

1.0 TS1a TS1b 0.8 TS2a TS2b

0.6

0.4

0.2

0.0

-0.2

-0.4 0 120 240 360 480 600 720 Lag [hours] FIG. 5. Autocorrelation plots of four radon time-series derived from three residential properties 3-hour moving-average smoothing –30-day time-shift

FIG. 4 and FIG. 5 show auto-correlation plots of four radon time-series (three-hour moving average smoothing) derived from the residential properties A, B and C, already considered. In each series, there is strong evidence of short-range 24-hour periodicity; some series also have much clearer, longer-range 24-hour cycles (TS2a has clear, long-range 24-hour cycles; TS1b has only short-range). There is no evidence of 12.4 or 24.8-hour cycles (tidal). There is some slight evidence for longer- period periodicity, details of which remain to be explored further.

3.4. Cross-Correlation Analysis

The Cross-Correlation function of two time-dependent series f1(t) and f2(t) is defined as:

T0 lim 1 2 r ()τ = f (t) ⋅ f (t +τ ) ⋅ dτ (2) xx T T ∫ 1 2 0→∞ −T0 2 where τ is a time-shift imposed on one of the signals. As such, it is essentially a time-averaged measure of shared signal properties, and is consequently very suitable for comparing random signals.

Radon time series were investigated for meteorological influence, with the daily mean radon levels cross-correlated with the daily mean parameters recorded at the Northampton meteorological station. Results from TS1a and TS2a (same location, different epochs) showed a marginal correlation with rainfall with a 14-day lag. TS1b also showed marginal correlation with rainfall, but with a shorter, 10- day, lag, while TS2b shows weak correlation with mean daily temperature with a 6-day lag. Overall, no consistent meteorological influence was identified as giving rise to variability in the data.

3.5. Fourier Analysis

A periodic signal, f(t), with period equal to T can be represented by the Fourier series:

∞ ∞ f (t) = A0 + ∑ An cos(nω1t) + ∑ Bn sin(nω1t) (3) n=1 n=1 where ω1 = 2π /T .

Fourier transformation of the recorded radon concentration time-sequences from the properties with cellars identified a number of characteristic periodic features, with time-scales representative of astronomical rather than geophysical phenomena. Daily, weekly and monthly contributions, some common to both properties, others specific to one or other, were identified, with differing weighting

6 factors reflecting local conditions and activity patterns. Table V and Table VI summarize the results from the two properties, ranked by relative strength of Fourier component and by period, respectively.

Table V. Principal Fourier components from radon time-sequences, ranked by decreasing strength

TS1a TS1b Rank Period [h] Period [d] Strength Period [h] Period [d] Strength 1 24.050 1.002 0.241 516.000 21.500 0.082 2 721.500 30.063 0.190 286.667 11.944 0.069 3 1443.000 60.125 0.188 1720.000 71.667 0.069 4 288.600 12.025 0.173 645.000 26.875 0.053 5 23.917 0.997 0.153 469.091 19.545 0.053 6 541.125 22.547 0.143 24.000 1.000 0.049 7 360.750 15.031 0.130 23.889 0.995 0.047 8 24.597 1.025 0.121 172.000 7.167 0.047 9 149.276 6.220 0.119 271.579 11.316 0.044 10 23.027 0.959 0.117 5160.000 215.000 0.040

Table VI. Principal Fourier components from radon time-sequences, ranked by increasing period

TS1a TS1b Period [h] Period [d] Strength Period [h] Period [d] Strength 23.027 0.959 0.117 23.889 0.995 0.047 23.917 0.997 0.153 24.000 1.000 0.049 24.050 1.002 0.241 172.000 7.167 0.047 24.597 1.025 0.121 271.579 11.316 0.044 149.276 6.220 0.119 286.667 11.944 0.069 288.600 12.025 0.173 469.091 19.545 0.053 360.750 15.031 0.130 516.000 21.500 0.082 541.125 22.547 0.143 645.000 26.875 0.053 721.500 30.063 0.190 1720.000 71.667 0.069 1443.000 60.125 0.188 5160.000 215.000 0.040

4. Discussion

4.1. Lifestyle

UK urban life tends to follow daily and weekly cycles, the latter generally comprising five working days of relatively constant routine, followed by a two-day weekend of differing routine and characterized by greater domestic occupancy. If domestic activity influences radon level variation, evidence of these cycles in the form of 24 hour and 168 hour components would be expected to appear in the long-term record. Although significant periodicity is apparent in the raw and time-averaged time-series data sets, it is difficult to identify regular patterns of behaviour in this format. Under autocorrelation, however, short-range 24-hour periodicity is strongly evident in the records from all sites, with evidence of long-range periodicity apparent in TS1b. Although this supports the supposition that lifestyle factors may influence radon fluctuations, operation of the radon sensing equipment in relatively undisturbed basement/cellar environments might be expected to be relatively immune to perturbation by domestic activity. However, local seismic events external to the home, e.g. vibrations

7 induced by road and rail traffic, have been shown to have short-range influence on domestic radon levels [7], and the 24-hour periodicity identified here is potentially attributable to this cause.

4.2. Meteorology

Climate is a time-dependent phenomenon. In the UK, in addition to the annual seasonal variation, the climate exhibits short-term structure, dominated by easterly-moving weather systems arriving from the Atlantic Ocean and taking four or five days to pass through the region, interspersed with stable periods defined by near-stationery high-pressure systems. Climent et al. [8] described the use of cross- correlation between time-series of radon concentration and meteorological/seismological parameters, with the objective of identifying a causal relationship between environmental variables and radon liberation. They showed that radon concentration correlated inversely with air temperature and soil temperature at 300 mm depth, and directly with humidity, rainfall and wind direction, in each case without time delay. No correlation was evident with temperature at 100 mm depth, with wind speed or with seismic activity within a 100 km range.

The results reported here support these conclusions. One site, represented by TS1a+TS2a, showed a measure of correlation of radon with rainfall, with a 14 day lag not reported in the Japanese work, while one record showed weak correlation with mean daily temperature, again with a lag, this time of 6 days. Examination of the regression parameters presented in Table IV demonstrates little evidence of consistency, leading to the conclusion that meteorological influences, while demonstrably capable of influencing radon levels over extended periods, make a minimal contribution to the short-term variability. Similar conclusions were drawn from a recent extensive radon time-series analysis [9].

4.3. Geophysical and Astrophysical Influences

As shown in Table V, Fourier analysis identified periodicities of the order of 23.9 hours (the luni-solar diurnal period, K1), 24.0 hours (the solar day), and 661.3 hours, the Lunar Month (Mm), suggesting that astronomical influences play a part in controlling radon release from the soil. Attention has recently been drawn [10] to the influence on instantaneous radon levels of 'Earth Tides', deformations of the Earth's crust in response to the orbital motion of the moon around the earth and the earth's axial rotation relative to the sun. These deformations, typically 200-300 mm peak to peak in the UK [11], have been postulated to be responsible for the periodic liberation of radiation, principally via the pumping of ground-water in response to the opposing effects of aquifer compression and crustal displacement [12]. At periods of decreasing dilation (corresponding to the periods of peaks of gravity components during Earth compression), the groundwater rises closer to the surface. As the volume of soil-air is bounded at its lower extent by the groundwater, soil-air and entrained radon are pushed out of the upper soil horizon, escaping freely into the atmosphere or into dwellings.

In addition to Earth Tides, Northampton has been demonstrated to be susceptible to oceanic tidal effects [13], despite being situated as far from the sea (80 – 100 km) as it is possible to get in the UK. Surface loading of the Earth's crust due the weight of the ocean tides causes a time-dependent deformation of the solid Earth, referred to as 'Ocean Tide Loading' [13], having both vertical and horizontal components, the latter typically smaller by a factor of 3 or more. In the UK, the vertical component varies spatially, having a maximum of 120 mm peak to peak (Spring tides) in Cornwall, but less than 10 mm in the vicinity of the Irish Sea and the eastern English Channel [14]. For Northampton, Lat. 52.23º, Long. –0.9º, the maximum vertical component is of the order of 25 mm [15].

Table VII summarizes the principal periodic components of tidal movements, representing the complex interactions between the earth, moon and sun [16]. FIG. 6 shows the cross-correlation of the radon levels in TS1a and TS1b against the tidal strength at Northampton. Both plots show short-range correlation, with characteristic periods of the order of 14 days and 28 days respectively. However, whereas TS1a shows a lag of 6 days, the corresponding figure for TS1b is almost double this, at 11 days.

Table VII. Principal Fourier components of terrestrial and oceanic tides

Definition Symbol Period [hours]

Luni-solar semi-diurnal K2 11.97

Principal solar S2 12.00

Principal lunar M2 12.42

Larger lunar elliptic semi-diurnal N2 12.66

Luni-solar diurnal K1 23.93

Principal solar P1 24.07

Principal lunar diurnal O1 25.82

Larger lunar elliptic diurnal Q1 26.87

Lunar monthly Mm 661.31

0.08 TS1a

0.06 TS1b

0.04

0.02

0.00

-0.02

-0.04

-0.06

-0.08 -30-25-20-15-10-5 0 5 1015202530 Tide/Radon Lag [day] FIG. 6. Correlation between radon time-series TS1a, TS1b, and tidal strength at Northampton

5. Conclusions

Using a variety of mathematical analysis approaches, a set of radon concentration time-series have been analysed to identify a basis for relating short-term measurements of domestic radon concentration to mean annual levels. All of the series investigated exhibited time-variability of sufficient scale to support the conclusion that a three-day exposure is inadequate to characterize the baseline UK domestic radon concentration. Moving-average smoothing, correlation and Fourier transform processing all confirm that, even for exposure periods of fourteen days or longer, there remains variability potentially outside the scope of the Seasonal Correction Factor approach. Attempts to correlate the observed data-sets with concurrent meteorological conditions fail to provide a rigorous causal link, although weak correlations with rainfall and mean daily temperature were identified. Notwithstanding this finding, the accepted longer-term influence of meteorological conditions on radon release demands that any integration period should be statistically longer than the prevailing weather periodicity, which in the UK shows a well-defined tendency towards cycles of the order of four or five days.

The appearance of contributions to the radon variability with periodicity of the order of one lunar month introduces a dimension apparently not considered previously in the analysis of UK radon data, namely the influence of Earth Tides and Ocean Tide Loading on radon release. Potential routes to compensating for this effect include restricting short-term measurements to the epochs of average lunar influence, i.e. at the first and third quarter, and the introduction of a Lunar Correction Factor, reflecting the lunar phase over the measurement period.

6. Acknowledgements

The study reported here forms part of work carried out with financial support from the Department for Environment, Food and Regional Affairs (DEFRA) under Contract EPG 1/4/72.

7. References

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2. Darby, S., Hill, D., Doll, R., Radon: a likely carcinogen at all exposures, Annals of Oncology, 12:1341-1351, (2001).

3. Pinel, J., Fearn, T., Darby, S.C., Miles, J.C.H., Seasonal correction factors for indoor radon measurements in the United Kingdom. Radiat. Prot. Dosim., 58:127-132, (1995).

4. Denman, A.R., Crockett, R.G.M., Groves-Kirkby, C.J., Phillips, P.S., Woolridge, A., Reliability of integrating radon gas measurements in the domestic environment – an intercomparison between 1-week, 1-month and 3-month sampling. in Proceedings of the 11th International Congress of the International Radiation Protection Association, Madrid, 2004.

5. Appleton, J., Ball, T. Geological radon potential mapping. in Geo-Environmental Mapping, edited by P. Bobrowsky, Balkema, Rotterdam (1995).

6. Denman, A.R., Barker, S.P., Parkinson, S., Phillips, P.S., The health benefits and cost effectiveness of the radon mitigation programme in NHS properties in Northamptonshire. J. Rad. Prot., 17:253-259, (1997).

7. Schmid, S., Wiegand, J., Seismic waves in the urban environment triggering radon release from the soil. Il Nuovo Cimento, 22C:475-481, (1999).

8. Climent, H., Tokonami, S., Furukawa, M., Statistical analysis applied to radon and natural events. in Proc. Int.Conference on Radon in the Living Environment, Athens, p.241-254 (1999).

9. Aumento, F., Radon tides on an active volcanic island: Terceira, Azores. Geofisica Internat., 41:499-505, (2002).

10. Barnet, I., Prochazka, J., Skalsky, L., Do the earth tides have an influence on short-term variations in radon concentration. Rad. Prot. Dosim., 69:1-60, (1997).

11. King, M.A., University of Newcastle upon Tyne, personal communication, 2003.

12. Bredehoft, J.D., Response of well-aquifer systems to Earth tides. J. Geophys. Res., 72:3075- 3087, (1967).

13. Baker, T.F., Tidal deformations of the Earth. Science Progress, 69:97-233 (1984).

14. King, M., Clarke, P., Allinson, C., The ups and downs of GPS heighting in Britain – part 1: ocean tide loading. Engineering Surveying Showcase, October 2003.

15. Ocean Tide Loading Provider. Onsala Centre for AstroPhysics and Space Science, Chalmers University, Sweden. http://www.oso.chalmers.se/~loading/index.html.

16. Pugh, D.T, Tides, surges and mean sea-level: a handbook for engineers and scientists. Wiley, Chichester, (1987).