Effects of collector types in sampling of atmospheric depositional fluxes

Effects of collector types in sampling of atmospheric depositional fluxes

Journal of Environmental Radioactivity 100 (2009) 198–202 Contents lists available at ScienceDirect Journal of Environmental Radioactivity journal h...

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Journal of Environmental Radioactivity 100 (2009) 198–202

Contents lists available at ScienceDirect

Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad

Effects of collector types in sampling of atmospheric depositional fluxes ˜ as*, M.C. Ferna´ndez, S. Can ˜ ete, J.J. Pe´rez Barea, M. Pe´rez C. Duen ´ laga, Campus de Teatinos, 29071 Ma ´ laga, Spain Department of Applied Physics I, Faculty of Sciences, University of Ma

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 July 2008 Received in revised form 11 November 2008 Accepted 24 November 2008 Available online 19 December 2008

The bulk gross alpha, gross beta and 7Be depositional fluxes were measured in Ma´laga (36.7 N, 4.5 W), a coastal Mediterranean station in the south of Spain for one whole year. In order to quantify the local variation of deposition rates, we have analysed the monthly results from two deposition collectors: a ‘‘pot ‘‘collector with a continuous water-covered surface and a ‘‘funnel’’ collector. In general, the alpha and beta depositional fluxes from the funnel collector were approximately two times lower than the pot collector. Whereas for the cosmogenic 7Be, the depositional flux of 7Be from funnel collector was also approximately two times lower than the pot collector. A good correlation of the depositional flux of 7Be has been obtained from both collectors. Ó 2008 Elsevier Ltd. All rights reserved.

Keywords: Depositional flux Be-7 Pot collector Funnel collector

1. Introduction The deposition of radionuclides on the ground represents an important factor in environmental radioactivity monitoring and an important input parameter in radioecological models (Balkanski et al., 1993; Koch et al., 1996). It is well known that the main part of radioactivity deposition of natural as well as artificial radionuclides from the global nuclear weapons fallout takes place through wet precipitation and dry depositions. Precipitation scavenging is the removal of particulate matter and gases from the atmosphere through various types of precipitation. The process involves the incorporation of the radioactivity into the rain water and the subsequent deposition of the material onto the surface of the Earth. The deposition rates which determine the residence time of the material in the atmosphere can affect the downwind surface and airborne concentration patterns. The removal of radioactive particles and gases from the atmosphere by precipitation scavenging depends on complicated microphysical and microchemical processes which are conditional functions both within and outside the natural cloud-bearing layers. Berylium-7 (half-life 53.29 days) is one of the radionuclides produced by spallation reactions of cosmic rays with light atmospheric nuclei, such as carbon, nitrogen and oxygen. Approximately 70% of 7Be is produced in the stratosphere, with the remaining 30% produced in the troposphere. Most of the 7Be that is produced in

* Corresponding author. Tel.: þ34 952131926; fax: þ34 952132382. ˜ as). E-mail address: [email protected] (C. Duen 0265-931X/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvrad.2008.11.014

the stratosphere does not reach the troposphere except during spring when the seasonal thinning of the tropopause takes place at midlatitudes, resulting in air exchange between the stratosphere and the troposphere. 7Be rapidly associates with submicron-sized aerosol particles. Gravitational settling and precipitation processes largely accomplish transfer to the surface of the earth. 7Be has become recognized as a potentially powerful tool when studying the description of environmental processes such as precipitation, wash-out (precipitation scavenging), atmospheric particle deposition and deposition patterns of airborne contaminants (Papastefanou and Ioannidou, 1991). There is not too much literature on the effect of collector types on the depositional fluxes (Rosner and Winkler, 2001; McNeary and Baskaran, 2003). The aim of this study was twofold (1) to study the influence of the collector surfaces (covered with water or not) and (2) to study the influence of the collector type. This was done by analysing the monthly deposition rates from two deposition collectors, which were located on the SCAI campus of Ma´laga University from February 2005 to January 2006.The aim was to quantify differences in ‘‘funnel’’ and ‘‘pot’’ sampling under the specific conditions of our site. 2. Material and methods The sampling site is one of the environmental radioactivity monitoring network stations operated by the Spanish Nuclear Security Council (CSN), under a cooperative agreement with the University of Ma´laga through the Environmental Radioactivity Research Group. The sampling site is situated 10 m above the ground, on the flat roof of the SCAI building, University of Malaga, Fig. 1.The site where the measurements were carried out is in the north-west of the city (4 280 800 W; 36 430 4000 N), 5 km away from the coastline. The mean of yearly precipitation is

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transported to a Marinelli geometry container. The Marinelli containers were counted using an intrinsic germanium coaxial detector as previously described ˜ as et al., 2002). Samples were counted for 25–48 h to achieve a higher (Duen precision. After exposure, the large particles were removed from the pot collector by filtration on a Micropore paper filter of 45 mm cellulose nitrate membrane. Stable and radioactive Be were concentrated by coprecipitation with Fe hydroxides similarly to the method described by Thompson and Turekian (1976). Briefly, 0.55 mg of FeCl3 was added per litre of sample, which had a pH < 1. After one day of equilibration, Fe (OH)3 was precipitated by adding NH4OH. This precipitate was removed by centrifugation and filtered through a Whatman 42 filter paper (Caillet et al., 2001). The filter was measured in the mentioned intrinsic germanium coaxial detector. The filter was later dissolved by heating in aqua regia. A 5 ml aliquot of the sample was taken for the atomic adsorption spectrometry to determine the chemical yield of Be. The chemical yield varied between 70% and 90%.

3. Results and discussion 3.1. Comparison of two ‘‘pot’’ collectors

550 L m2 .The samples were collected monthly using two collector types. One was a slightly tilted stainless steel tray 1 m2 in area denominated ’’funnel’’ collector and polyethylene vessels of 50 or 25 L capacity for rainwater sample reservoirs. The other collector consisted of a polyethylene cylindrical jar with a surface area of 0.091 m2 denominated ‘‘pot’’ collector. Papaefthymiou et al., 2005 used a pot collector of 0.083 m2. In order to assure efficient collection of the dry fallout and to avoid the removal by wind, the bottom of the ‘‘pot’’ collector was also kept covered with acidulated distilled water continuously. Distilled water was added during dry period. Both collectors were always exposed to the atmosphere, thus the sum of dry and wet fallout (equal to bulk deposition) was collected. At the end of the each month, the funnel collector was rinsed with acidulated water until a sample volume of at least 6.8 L was achieved. Afterwards the liquid samples were acidified with hydrochloric acid to a pH lower than 1. The surface was also cleaned with distilled water to avoid contamination between each collection period. Regarding the pot collector, three litres of 1 M HCl were poured into the pot prior to each deployment in order to prevent adsorption of radionuclides on the pot wall. Stable Be was also added as a tracer for checking the overall recovery. Immediately after collection, the pot was cleaned with repeated rinses of 1 M HCl to remove adsorbed isotopes from the pot. The rinses were combined with the rainwater sample. To determine the monthly gross beta activity in the liquid samples an appropriate volume of the original sample (300 ml) was evaporated to dryness. The residue was transferred quantitatively to a pre-weighted ribbed stainless steel planchet (5 cm of diameter) and dried. The analytical procedure used to determine the gross alpha activity level was that of coprecipitation of a volume of 0.5 L of sample water. This method consists of the selective precipitation of radium isotopes followed by a coprecipitation of the actinoids (Sua´rez et al., 2000). Once they were precipitated, they were separated by filtration. The samples were kept in a desiccator for 5 days after sample preparation and were then counted in order to ensure the complete decay of 222Rn daughter. The gross alpha activity was measured by a solid ZnS (Ag) scintillation counter. The gross beta activity was measured with a gas flow proportional counter of the low-background multiple detector type with four sample detectors (CANBERRA HT-1000). All the calculations have been carried out using the appropriate density thickness corrections for efficiencies to convert the alpha and beta measurements to specific activities with estimates of error at 1,96s. Since the levels of radioactivity found in environmental samples are low, long counting times, of approximately 1000 min per sample were necessary. Detailed description of the analytical procedure calibration process has been given ˜ as et al., 1999). (Duen The gross alpha and the gross beta activities were calculated from: A ¼

CF RVT

where C is the number of counts, T is the counting time, F the background in T, V is the sampling water volume (L) and R is the efficiency. The uncertainties of results were calculated from: 1:96 RV

3ðAÞh

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C F þ T2 T2

All the results were recalculated to deposition data per area. For this purpose, the determined values of the measured results were divided by the open area of the collector. To determine the monthly depositional flux of 7Be from the funnel collector, a volume of 6 L was evaporated at 80  C down to approximately 1 L and then

3.2. Results of the ‘‘pot’’ collector The results from the monthly measurements of gross alpha deposition on the ground, using the pot collector during the 1-year sampling period from February 2005 to January 2006, are presented in Table 1. The large particles were removed by filtration on a paper filter (Whatman 42). The residue on the filter (filtered) was counted to determine the gross alpha. Table 1 shows five columns: month of sampling, rainfall, filtered alpha flux, coprecipitate alpha flux and gross alpha flux (The percentages are given in brackets). From Table 1 an average percentage of fluxes can be calculated for filtered and co-precipitated samples. Concerning alpha fluxes,

Depositional flux (Bq m-2 month-1)

Fig. 1. Sampling station and collectors.

Firstly, we report the results of the bulk depositional fluxes for gross alpha and gross beta, on a monthly basis, for three months, from two pot collectors which were both the same size, had the same capacity and were made of the same material. The only difference was that one of them contained acidified distilled water with a pH lower than 1 and the other contained only distilled water. The obtained results are shown in Figs. 2 and 3. These results clearly show that an acidified ‘‘pot’’ is more effective for trapping radioisotopes than an unacidified ‘‘pot’’. The alpha flux is greater in acidified water than in unacidified water. The same occurs with the beta flux. Both results are in agreement if respective uncertainties are well considered. The three months studied (December 2005, January and February 2006) present different amounts of precipitation. Approximately 50 L m2 were collected at different times throughout the month of December. About 80 L m2 were collected in the last week of February and 56 L m2 were collected in the first week of March.

6

alpha acidified alpha unacidified

5 4 3 2 1 0 December,2004

February,2005

March,2005

Months Fig. 2. Gross alpha depositional flux in acidified and unacidified pot.

˜as et al. / Journal of Environmental Radioactivity 100 (2009) 198–202 C. Duen

200

Table 2 Alpha and beta fluxes of the pot collector.

Depositional flux (Bq m-2 month-1)

25 beta acidified beta unacidified

Month

Rainfall (mm)

Gross alpha flux (Bq m2 month1)

Gross beta flux (Bq m2 month1)

pH

February 2005 March 2005 April 2005 May 2005 June 2005 July 2005 August 2005 September 2005 October 2005 November 2005 December 2005 January 2006

84.0 67.2 8.9 0.8 0.1 0.1 0.5 0.8 23.0 45.0 5.0 90.0

2.00  0.30 4.34  0.40 1.41  0.25 2.53  0.30 2.14  0.30 1.50  0.24 1.97  0.40 1.16  0.23 2.15  0.30 2.40  0.30 2.27  0.30 4.72  0.70

13.7  1.6 17.8  1.7 11.2  2.5 37.4  1.7 12.6  2.1 22.2  5.0 9.2  4.0 2.9  0.9 16.3  5.0 11.7  2.4 2.7  0.8 13.9  8.0

<1 <1 <1 1 <1 <1 <1 <1 <1 <1 <1 <1

20

15

10

5

0 December,2004

February,2005

March,2005

Months Fig. 3. Gross beta depositional flux in acidified and unacidified pots.

the average percentage was 27.7% for filtered samples and, consequently, 72.3% for co-precipitated samples. The depositional gross alpha flux oscillated from 1.16 to 4.72 Bq m2 month1 with an average value, 2.38 Bq m2 month1. The results from the monthly measurements of gross beta flux and gross alpha flux on the ground, for the pot collector during the 1-year sampling period are presented in Table 2, as well as precipitation of every month and water pH. Beta flux has ranged from 2.7 to 37.4 Bq m2 month1 with an average value of 14.3 Bq m2 month1. The beta flux in the month of May presents a high value. In this month two remarkable facts happened, the amount of precipitation was low, and, in addition, the water that was added to the pot to maintain the suitable level was acidified, resulting in the pH final being very low. In that month, high temperatures of air in relation to the average of other years were registered and we added 13.4 L distilled and acidulated water to maintain the water level because the evaporation was very high.

maintenance only requires washing at the end of each month. Comparing both collectors, the funnel collector is easy to manage. In the following section it can be demonstrated that flux values obtained in the pot collector were significantly greater than those of the funnel collector. Table 3 shows the results of the gross alpha fluxes, obtained by the funnel collector. In this table, filtered fraction, co-precipitated fraction and gross flux are considered. As shown in Table 3, the average percentage of alpha flux in the filtered was 39.6% and the average percentage of alpha flux of coprecipitated was 60.4%. Fluxes of filtered had higher values than in the pot collector strengthening their importance in the calculation of the gross alpha flux. The gross alpha flux ranged from 0.53 to 1.80 Bq m2 month1 with an average value of 1.03 Bq m2 month1. Data corresponding to alpha and beta fluxes in the whole the samples obtained by the funnel collector are listed in Table 4. Precipitation and pH are also shown in this table. The gross beta flux corresponding to the whole samples ranged from 2.28 to 13.61 Bq m2 month1, and an average, 6.97 Bq m2 month1 was calculated from these data. Both collectors showed an abnormally high value in gross beta flux in the month of May.

3.3. Results of ‘‘funnel’’ collector

3.4. Comparison of the results obtained with the ‘‘pot’’ and ‘‘funnel’’ collectors

The funnel collector was located a few metres away from the pot collector. This collector did not contain water. The fact that the surface of the ‘‘funnel’’ collector was ten times greater than the one of the pot collector, implies that their results have an uncertainty quite smaller than those of the pot type. The handling was simpler with this collector than with the pot collector, since its

The comparison will show the advantages and disadvantages of using the pot or funnel collector, in an intuitive way. Fig. 4 presents the gross alpha fluxes during the period of measurements for both collectors. All the values of the gross alpha fluxes corresponding to the pot collector are higher than those obtained by the funnel collector. A similar behaviour is observed for

Table 1 Gross alpha flux of the pot collector.

Table 3 Gross alpha flux of the funnel collector.

Month

Rainfall (mm)

Alpha flux (Bq m2 month1) filtered (%)

Alpha flux (Bq m2 month1) coprecipitate (%)

Gross alpha flux (Bq m2 month1)

Month

Rainfall (mm)

Alpha flux (Bq m2 month1) filtered

Alpha flux (Bq m2 month1) coprecipitate

Gross alpha flux (Bq m2 month1)

February 2005 March 2005 April 2005 May 2005 June 2005 July 2005 August 2005 September2005 October2005 November2005 December2005 January 2006

84.0 67.2 8.9 0.8 0.1 0.1 0.5 0.8 23.0 45.0 5.0 90.0

0.16  0.09 (8%) 0.65  0.13 (15%) 0.62  0.12 (44%) 0.61  0.12 (24%) 0.70  0.12 (33%) 0.63  0.12 (42%) 0.63  0.15 (32%) 0.38  0.09 (33%) 0.22  0.08 (10%) 0.93  0.15 (39%) 0.77  0.11 (34%) 0.84  0.22 (18%)

1.84  0.25 (92%) 3.69  0.30 (85%) 0.79  0.14 (56%) 1.92  0.21 (76%) 1.44  0.19 (67%) 0.87  0.12 (58%) 1.34  0.24 (68%) 0.78  0.14 (67%) 1.93  0.21 (90%) 1.47  0.19 (61%) 1.50  0.15 (66%) 3.88  0.50 (78%)

2.00  0.40 4.34  0.40 1.41  0.25 2.53  0.30 2.14  0.30 1.50  0.24 1.97  0.40 1.16  0.23 2.15  0.30 2.40  0.30 2.27  0.25 4.72  0.70

February 2005 March 2005 April 2005 May 2005 June 2005 July 2005 August 2005 September 2005 October 2005 November 2005 December 2005 January 2006

84.0 67.2 8.9 0.8 0.1 0.1 0.5 0.8 23.0 45.0 5.0 90.0

0.10  0.08 (10%) 0.60  0.08 (53%) 0.38  0.05 (43%) 0.58  0.05 (47%) 0.68  0.07 (52%) 0.29  0.03 (55%) 0.43  0.04 (56%) 0.26  0.04 (25%) 0.40  0.10 (46%) 0.66  0.11 (47%) 0.11  0.02 (18%) 0.44  0.14 (24%)

0.91  0.19 (90%) 0.53  0.08 (47%) 0.50  0.06 (57%) 0.66  0.06 (53%) 0.63  0.06 (48%) 0.24  0.02 (45%) 0.34  0.03 (44%) 0.60  0.06 (75%) 0.47  0.12 (54%) 0.75  0.13 (53%) 0.49  0.04 (82%) 1.36  0.24 (76%)

1.01  0.30 1.13  0.16 0.88  0.11 1.24  0.11 1.31  0.13 0.53  0.05 0.77  0.07 0.86  0.10 0.87  0.22 1.41  0.24 0.60  0.06 1.80  0.40

˜as et al. / Journal of Environmental Radioactivity 100 (2009) 198–202 C. Duen Table 4 Alpha and beta fluxes of the funnel collector.

201

Gross alpha flux (Bq m2 month1)

Gross beta flux (Bq m2 month1)

pH

February 2005 March 2005 April 2005 May 2005 June 2005 July 2005 August 2005 September 2005 October 2005 November 2005 December 2005 January 2006

84.0 67.2 8.9 0.8 0.1 0.1 0.5 0.8 23.0 45.0 5.0 90.0

1.01  0.30 1.13  0.16 0.88  0.11 1.24  0.11 1.31  0.13 0.53  0.05 0.77  0.07 0.86  0.10 0.87  0.22 1.41  0.24 0.60  0.06 1.80  0.40

6.13  1.60 2.28  0.60 8.57  0.70 13.61  0.50 9.40  0.40 7.46  1.20 7.63  0.50 2.64  0.30 7.82  0.60 10.67  1.04 2.69  0.70 4.71  2.40

<1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1

Pot

35 30 25 20 15 10 5 0

ov e D mb ec e em r Ja ber n Fe uar br y ua r M y ar ch Ap ril M ay Ju ne Ju A ly Se ug pt ust em O ber c N tob ov e em r D ec be em r Ja ber nu ar y

Rainfall (mm)

Funnel

40

N

Month

Depositional beta flux (Bq m-2 month-1)

45

Fig. 5. Total beta fluxes for both collectors.

results obtained by both collectors. Thus, simultaneous increases and decreases can be observed. There is a statistically significant difference between the standard deviation of the two collector fluxes at the 95.0% confidence level (F ¼ 8.954, P ¼ 0.00105). The higher values were observed in December 2004, March 2005 and January 2006 in samples collected by the pot collector. In summer months distilled acidulated water was used to compensate evaporation in order to maintain a constant water level in the pot collector. The linear correlation coefficient between the alpha fluxes of both collectors is 0.68 with a 95% confidence level. Fig. 5 shows the gross beta flux for the pot and funnel collector. All the beta flux values from the pot collector were higher than those from the funnel collector. May had the highest value. There is a statistically significant difference between the standard deviation of the two collector fluxes at the 95% confidence level (F ¼ 6.962, P ¼ 0.00323). The increases and decreases were not similar when comparing beta fluxes for the pot and funnel collector. The determination of the beta flux was subject to more fluctuations and uncertainties than the determination of the alpha flux. If the acidity of the water is increased, a very thick residue in the planchet is produced. The pH of the water contained in the pot collector was always lower than the pH of the water contained in the funnel collector. The linear correlation coefficient between the beta fluxes of both collectors was r ¼ 0.63 with a 95% confidence level. 3.5. Depositional flux of 7Be Once optimized the deposition of the radioactivity in the rainwater we tried to improve the deposition flux of 7Be. In the pot

water, where we have already shown that more radioactivity was captured, we used a radiochemical process to determine the activity of 7Be in the rainwater. During the nine months, from May 2005 to January 2006 we determined the concentration of 7Be in the water of both collectors. Fig. 6 contains the results of 7Be flux for both collectors and monthly precipitation. In Fig. 6 it can be observed that the values of 7Be flux in the pot collector are higher than those in the funnel collector. There is a statistically significant difference between the standard deviation of the two collector fluxes (excluding the data of January) at the 95.0% confidence level (F ¼ 7.159, P ¼ 0.0187). The flux values evaluated in the pot collector ranged from 21.7 to 441.7 Bq m2 month1 with an average value of 112.78 Bq m2 month1and those of the funnel collector varied between 4.3 and 228 with an average value of 52.06 Bq m2 month1. There is a strong parallelism considering the amount of precipitation in the behaviour of the fluxes from both collectors. The linear correlation coefficient between the 7 Be flux in the pot collector and the amount of monthly rain was 0.9 with a confidence level of 99% and for the flux of 7Be in the funnel collector, 0.93 with a confidence level of 99%, Fig. 7. The amount of precipitation seems to be a factor in controlling the magnitude of the depositional fluxes, playing an important role in the removal of this radionuclide from the troposphere. A linear relationship between the amount of precipitation and 7Be depositional flux has been observed in the literature (Olsen et al., 1985; Dibb, 1989; Todd et al., 1989; ˜ as et al., 2002; Schuler et al., 1991; Baskaran et al., 1993; Duen McNeary and Baskaran, 2003). The pot collector is more appropriate in the capture of radioisotopes but its maintenance is laborious in a warm climate like Ma´laga since the maintenance of the initial amount of water needs

Fig. 4. Total alpha fluxes for both collectors.

70

80

10

0

0 ar

r be

nu Ja

em

be em

ec D

ov

O

ct N

Se

pt em

gu Au

y

20

50 r

30

100

ob er

40

150

be r

50

200

st

60

250

ly

300

Ju

N ov e D mb ec e em r Ja ber n Fe uar br y ua ry M ar ch Ap ril M ay Ju ne Ju A ly Se ugu pt st em O ber c N tob ov er e D mb ec e em r Ja ber nu ar y

0

Beryllium in the collector type funnel

ne

1

350

Ju

2

90

400

ay

3

100 Precipitations Beryllium in the collector type pot

450

M

4

500

Flux (Bq m-2 month-1)

Funnel Pot

5

Fig. 6. Depositional flux of 7Be for both collectors and precipitation.

Precipitation (mm)

Depositional Alpha Flux (Bq m-2 month-1)

6

˜as et al. / Journal of Environmental Radioactivity 100 (2009) 198–202 C. Duen

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approximately two times lower than the pot collector whereas for the cosmogenic 7Be, the depositional flux of 7Be from the funnel collector are approximately also two times lower than the pot collector. A good correlation is obtained between the depositional fluxes of 7Be from both collectors. Although the numerical values found in this work are operationally defined, like many other depositional results, they may indicate to other workers, in similar circumstances, the possible consequences of the choice of the collector type. In our opinion, no attention has been given to this point in the literature.

Depositional flux (Bq m-2 month-1)

500 Be-7 in pot collector Be-7 in funnel collector

450 400

y = 3,9002x + 41,155 R2 = 0,8142

350 300 250 200 150 y = 2,0726x + 13,989 R2 = 0,8693

100

References

50 0 0

20

40

60

80

100

Rainfall (mm) Fig. 7. Correlation between depositional flux of 7Be and rainfall.

to be continuously watched because of evaporation and distilled water needs to be added very frequently. In addition, to determinate the activity of 7Be in the water from the pot collector, it is precise to carry out the radiochemical process described in Section 2. The determination of 7Be in the water from the funnel collector is less laborious but it is less optimal for the collection of radioisotopes. Taking into account these considerations, we have found a correlation between the depositional flux of 7Be in the pot and the funnel, which would allow us to gather the rainwater in the funnel collector and by means of this correlation find the depositional flux of 7Be in the pot collector. The following equation found has been:

Be; pot ¼ 14:7789 þ 1:8828 Be; funnel

ðr ¼ 0:97; p < 0:01Þ

There is a very good correlation because the correlation coefficient is very high with a 99% confidence level. 4. Conclusion Time series of the monthly depositional fluxes of gross alpha, gross beta and 7Be were recorded in two types of collectors (pot and funnel) in Ma´laga for one year. For three months the surfaces of two pot collectors were kept identical by covering them continuously with water, one acidified and another unacidified, thus allowing a comparison of the acidity effect. The results show that the depositional fluxes are very sensitive to acidity. On average, the alpha and beta depositional fluxes from the funnel collector are

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