J Radioanal Nucl Chem DOI 10.1007/s10967-014-3622-z
Statistical validation of the model of diffusion-convection (MDC) of 137Cs for the assessment of recent sedimentation rates in coastal systems Paulo Alves de Lima Ferreira • Eduardo Siegle • Carlos Augusto Franc¸a Schettini • Michel Michaelovitch de Mahiques Rubens Cesar Lopes Figueira
•
Received: 21 July 2014 Ó Akade´miai Kiado´, Budapest, Hungary 2014
Abstract This study aimed the validation of the model of diffusion-convection (MDC) of 137Cs for the calculation of recent sedimentation rates in 13 sedimentary cores of two Brazilian coastal systems, the Cananeia-Iguape and SantosSa˜o Vicente estuarine systems. The MDC covers key factors responsible for 137Cs vertical migration in sediments: its diffusion to the interstitial water and the vertical convection of this water through the sediments. This study successfully validated the MDC use to determine sedimentation rates, which was statistically validated not only with 210Pbxs (unsupported 210Pb) models, widely used in oceanographic studies, but also by literature values for those regions. Keywords Diffusion Santos-Sa˜o Vicente
210
Pb Cananeia-Iguape
Introduction Radionuclides are elements that, for having energetic instabilities in their atomic structure, emit various kinds of
P. A. de Lima Ferreira (&) E. Siegle M. M. de Mahiques R. C. L. Figueira Instituto Oceanogra´fico, Universidade de Sa˜o Paulo (IO-USP), Pc¸a. do Oceanogra´fico, 191, Butanta˜, Sa˜o Paulo, SP 05508 120, Brazil e-mail:
[email protected] C. A. F. Schettini Centro de Tecnologia e Geocieˆncias, Universidade Federal de Pernambuco (CTG-UFPE), Av. Prof. Moraes Rego, 1235, Cidade Universita´ria, Recife, PE 50670 901, Brazil
particles in order to become more stable. The discovery of radioactivity and the possibility of measuring the levels of radionuclides in a mixture of isotopes opened a new range of possibilities for the study of Earth sciences, since these radionuclides can act as tracers for various oceanographic processes, whether they be of chemical, physical, biological or geological nature [1, 2]. The development of analytical techniques aimed at the determination of radionuclides in environmental matrices such as water, soil and sediment, thrived mainly due to all the scientific advances of the second half of the 20th century, spurred by the World War II and the Cold War and its advances regarding the construction of nuclear bombs [3]. Among the different processes in which radionuclides can function as environmental tracers, most scientific works that use radionuclides are studies regarding sedimentation and sediment transport, as changes in sediment inputs can be identified and interpreted through radiometric levels in cores [1, 4]. The patterns of sediment dynamics are governed by a myriad of processes with natural and man-induced variations. Anthropogenic disruptions in the environment alter the sediment budget in a given region by modifying naturally occurring processes with, for instance, rectification of drainage channels and construction of dams and breakwaters [5]. This interference of man in nature can be evaluated through the study of the record of those interventions present in the sediments. The use of radionuclides in Oceanography is concentrated in the assessment of sedimentation rates and age modeling. The evaluation of sedimentation rates has been a tool of great relevance in studies that intend to establish rates of geological and geomorphological processes and ages of samples such as sediments and rocks. Several papers focused on the development of methodologies and
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mathematical models [6–8] and application of radioanalytical techniques [8–10]. They are widely used for assessing recent sedimentation rates [11–13] and age modeling [14, 15] in lakes, estuaries, and other coastal systems. 137 Cs, one of several isotopes of Cs, is one of the two main artificial radionuclides (together with 90Sr) produced by the fission of 235U. This nuclide is characterized by a high fission yield, half-life of 30.17 year and decay to 137 Ba by emitting b and c radiations [16]. Considering that 137 Cs has a strong affinity with the suspended matter, this element has a tendency to have the sediments as final sink [17]. Its study is important because it is a harmful contaminant [18] and the possibility of functioning as a tracer of sedimentary processes [19]. Many studies made use of 137Cs along with other radiometric models of sedimentation (e.g. unsupported 210 Pb) to evaluate recent sedimentation rates in lacustrine, coastal and marine ecosystems worldwide [2, 20–24]. However, 137Cs behavior in sediments is complex due to numerous factors such as its vertical diffusion through sediment pore water and the percolation of deposited particles in the sedimentary column [25, 26]. Thus, this radionuclide can only be used to accurately evaluate sedimentation rates through the use of a mathematical model that considers the main causes of the temporal variations in its vertical distribution, such as the model of diffusionconvection (MDC) [27]. This study aimed at establishing a validation for the model of diffusion-convection of 137Cs for the assessment of recent (secular time scale) sedimentation rates through the statistical comparison of its results with those from unsupported 210Pb modeling, which is widely used by the world scientific community for the purpose of calculating sediment rates [1, 11, 20, 21, 28]. For this study, two Brazilian coastal systems were chosen: Cananeia-Iguape and Santos-Sa˜o Vicente estuarine systems (Fig. 1). Both systems have many similarities, they are recent coastal systems formed during the Quaternary [29] with geomorphologies conditioned by tidal currents [30, 31], multiple system mouths, pristine areas (Cardoso Island and Bertioga Channel) and deep anthropic modifications in their environments due to the creation of the artificial channel of Valo Grande (in the Cananeia-Iguape system) [14, 32] and the activities of Santos Port and industrial zone of Cubata˜o (in the Santos-Sa˜o Vicente system) [20]. These characteristics result in the deposition of finegrained sediments, proper for the accumulation of radionuclides, and complex sedimentary budgets, highlighting the relevance of sedimentation studies in these areas. Therefore, the selected systems are suitable for this proposed study with radionuclides.
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Experimental Sampling Thirteen vertical sediment cores were collected (Fig. 1, Table 1) in the study areas with a vibracorer (Rossfelder, model VT-1) between 2008 and 2011. These cores were sliced into subsamples containing 2 cm layers, frozen, lyophilized, macerated in a porcelain mortar to homogenize grain size distribution, weighted and transferred to cylindrical polyethylene containers proper for gamma spectrometry analysis. Gamma spectrometry analysis For the radionuclides measurements, approximately 20 g of sediment were transferred into air-sealed cylindrical polyethylene containers (base circular area of 21.7 cm2, height of 1.1 cm and volume of 23.9 cm3) for gamma counting in an EG&G ORTECÒ low-background gamma spectrometer (hyperpure Ge, model GMX50P). This equipment is characterized by a mean resolution of 2.01 keV for the 1332.35 keV 60Co photopeak, and is coupled with an EG&G ORTECÒ buffer type system (SPECTRUM MASTER, model 919). The analysis of the gamma spectra was made in an EG&G ORTECÒ software (MAESTRO, version 6). The method, previously described by [2], [3] and [21], consists of daily detector calibration with calibrated sources of 60Co and 137Cs, background radiation detection, detector counting efficiency assessment with the counting of certified reference materials (IAEA-326, IAEA-327 and IAEA385) and sample counting for 50,000 s. The photopeaks used in this analysis were 46.52 keV for 210 Pb, 609.31 keV for 226Ra and 661.67 keV for 137Cs. The 609.31 photopeak corresponds to gamma-ray emissions of a 226Ra daughter (214Bi). If secular equilibrium in the radioactive decay series of 238U is considered, which is achieved after 1 month of sampling sealing, this peak corresponds to 226Ra activity. The self-absorption correction of the samples was done for gamma lines of energy inferior to 100 keV (e.g. 46.52 keV photopeak of 210Pb). It was made by comparison of the areas of the 59.54 keV peak of 241Am of the background container coupled with a 241Am (59.54 keV) source, and the sample coupled with a 241Am source, according to [2] and [3]. The determination of the minimum detectable activities (MDA) of the elements of interest (the lowest activity that can be determined with 95 % of certainty) was performed according to [2], resulting in MDAs of 1.47 Bq kg-1 for 210 Pb, 1.66 Bq kg-1 for 226Ra and 0.28 Bq kg-1 for 137Cs.
J Radioanal Nucl Chem Fig. 1 Cananeia-Iguape (a) and Santos-Sa˜o Vicente (b) systems, SE Brazil. Location of core sampling points
Moreover, the precision and accuracy of the methodology were evaluated through the determination of the radionuclides of interest (210Pb, 226Ra and 137Cs) in three certified reference materials: IAEA-326 (soil), IAEA-327 (soil) and IAEA-385 (marine sediment). The precision was checked using relative standard deviation (RSD), and the accuracy was assessed using the relative error (RE) of the data generated from these measurements. Table 2 shows
that the activity concentrations obtained for the certified radionuclide were close to the reported values with mean deviations and errors not exceeding 6 % [33]. Model of diffusion-convection of
137
Cs
The mathematical-chemical model of diffusion-convection (MDC) of 137Cs [26, 27] states that the temporal evolution
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J Radioanal Nucl Chem Table 1 Description of the core profiles and their sampling sites at Cananeia-Iguape and Santos-Sa˜o Vicente estuarine systems (SE Brazil) Core profile
Study area
Latitude
C2
Cananeia-Iguape estuarine system
24°42.480 S
C4
Longitude
0
47°32.790 W 0
Length (cm) 78
24°43.42 S
47°33.86 W
75
C5
24°45.240 S
47°37.370 W
138
C7
24°48.900 S
47°41.610 W
88
24°43.13 S
47°33.700 W
100
23°52.430 S
46°9.720 W
100
0
C15 B1 B2
Santos-Sa˜o Vicente estuarine system
0
0
23°54.08 S
46°11.66 W
120
B3
23°55.130 S
46°16.230 W
140
B4
23°55.550 S
46°14.580 W
60
B5
23°54.540 S
46°12.920 W
90
S1
23°55.150 S
46°18.660 W
56
0
0
S2
23°54.86 S
46°19.87 W
120
S8
23°53.18’S
46°22.220 W
52
(from q = 0 corresponding to 1963 to q = years of sample deposition since 1963, in year); D = vertical diffusion coefficient of 137Cs in the sediment (in cm2 year-1); m = local sedimentation rate (in cm year-1). As the use of Euler method requires an initial value for the differential equation, the following boundary conditions must be considered: (i) all 137Cs that has entered the location is due to the global fallout of past nuclear tests, which reached a maximum level around 1963, a consistent statement for sediments from the Southern Hemisphere [15] (ii) there tends to be no 137Cs in sediments with higher depth values (z ? ?), also a suitable affirmation since this nuclide has a natural decay that will eventually lead to its disappearance, and (iii) the temporal characteristic of 137Cs decay in sediments, i.e. its half-life, must take into account 137 Cs residence time in the system (rocks, soils, water column) before final deposition in the sediments according to Eq. (3), as this time intervals is non-negligible [27].
AðtÞ ¼ A0 e
ln2 T t T1=2
ð3Þ 137
of 137Cs activity in a sedimentary column (qA/qt) results from its vertical convective flux [-m(qA/qz)], vertical diffusive flux [D(q2A/qz2)] and natural decay (-kA), according to Eq. (1). oA oA o2 A ¼ m þ D 2 kA ot oz oz
ð1Þ
In which: A = activity per unit of volume (in mBq cm-3); t = time (in year); m = mean sedimentation rate (in cm year-1); z = depth (in cm); D = vertical diffusion coefficient of 137Cs in the sediment (in cm2 year-1); k = 137Cs decay constant (=2.30910-2 year-1). The model considers activity per unit of volume (A) instead of the most commonly used activity per unit of mass (a). To transform activity per unit of mass to activity per unit of volume it is used the relation A = qa, in which q is the air-dry bulk density of the sediment, determined according to [34]. Equation (1) is a second-order ordinary differential equation without general or particular solution [35]. Given the time dependence of the solution, an explicit method is proper for its resolution [36] and, therefore, Euler method [37] was used to solve Eq. (1), resulting in Eq. (2). Aqþ1 ¼ Aqp ðkdtÞ þ D p Aqp1 Þ
d2 t q dt ðA 2Aqp þ Aqp1 Þ v ðAqp dZ 2 pþ1 dZ ð2Þ
In which: A = activity per unit of volume (in mBq cm-3); p = step value for depth (from p = 0 to p = core length, in cm); q = step value for deposition year
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In which: A(t) = time-variable Cs activity for z = 0 (in mBq cm-3); A0 = initial 137Cs activity inputted due to T the 1963 global fallout (in mBq cm-3); T1=2 = 137Cs global half-life (considers 137Cs half-life and its residence time in the surrounding environment before its final destination in the sediments) (in year). As the MDC equation has no direct analytical solution, an approximated solution was derived from the finite difference method [Eq. (2)] with the assistance of the statistical package Solver for Microsoft ExcelÒ 2013 (from Microsoft). The package Solver allows, from the inclusion of data of the experimental profiles of 137Cs, the determination of theoretical profiles predicted by the MDC by minimizing the v2 (Chi square) value between them, thus T calculating the model key variables (m, D, T1=2 and A0). Unsupported 210
210
Pb models
Pb is a natural radioactive isotope of Pb, characterized by its half-life of 22.3 year, short-lived if compared with other natural radionuclides, such as 40K, and 235U. It is one of the isotopes of 238U decay series, a byproduct of 226Ra branch decay. 226Ra decays to 222Rn, a gas that partially escapes from the sediment to the atmosphere and returns to the soils/water/sediments as it decays to 210Pb. Therefore, 210Pb in sediments can be separated in two parts according to its origin: one that is atmospheric-originated, or unsupported, and one that is produced inside the sedimentary matrix without the escape of 222Rn, or supported. 210Pbxs (unsupported 210Pb) can be measured by the difference between the total 210Pb in the sample (210Pbt)
J Radioanal Nucl Chem Table 2 Analysis of 210Pb, 226 Ra and 137Cs activities (in Bq kg-1) in standard reference materials. Quality control of the methodology
Nuclide 210
Pb
226
Ra
a
Corrected due to nuclides decay (based in their half-life)
b
Activity values represented in the form mean ± determination error c
137
Cs
Reference material
Mean correcteda certified activity (Bq kg-1) 38.40
39.79 ± 1.22
3.07
3.62
42.36
43.14 ± 1.33
3.08
1.84
IAEA-385
25.07
25.16 ± 1.23
4.89
0.36
Mean values
3.68
1.94
IAEA-326
32.45
30.55 ± 1.50
4.91
5.86
IAEA-327
33.95
32.92 ± 1.54
4.68
3.03
IAEA-385
22.59
20.96 ± 1.52
7.25
7.22
Mean values
5.61
5.37
IAEA-326
c
c
c
c
IAEA-327
19.56
19.34 ± 1.11
5.74
1.12
IAEA-385
26.09
26.66 ± 1.03 Mean values
3.86 4.80
2.18 1.65
Pbt ðzÞ ¼ 210 Pbxs ðzÞ þ 210 Pbs ¼ 210 Pb0 eCz þ 226 Ra
ð4Þ
In which the decay of 210Pbxs [210Pbxs(z)] is represented as an exponential curve with a depth decay coefficient (C). From this principle, several models were developed in order to enable sedimentation assessment and age modeling in coastal systems. For the purpose of validating MDC to determine sedimentation rates, CIC, CFCS and ADE models of 210Pbxs were chosen, as those models were made predicting a mean sedimentation rates for a given time period in sediment cores, an assumption they share with MDC. In terms of sedimentary budget, both CIC (constant initial concentration) [8] and CFCS (constant flux and constant sedimentation) [6] models assume that there is a continuous sediment input to the system and, therefore, a time-integrated sedimentation rate. Equations (5) and (6) represent the calculus of the sedimentation rate with 210 Pbxs with CIC and CFCS, respectively.
m¼
k b
Accuracy (RE) (%)
IAEA-326
and the supported 210Pb (210Pbs), evaluated with a gammaemitting 210Pb parent nuclide, such as 226Ra (used in this study), represented in Eq. (4).
m¼
Precision (RSD) (%)
IAEA-327
It is not a reference material for 137Cs
210
Measured activity (Bq kg-1)b
ð5Þ
depth (z) as in CIC model. The mass-depth [Eq. (7)] is a parameterization done in order to normalize the effects of sediment porosity and core compaction [7, 38]. f ¼ zqs ð1 UÞ
ð7Þ
In which: f = mass-depth (in g cm-2); qs = mean bulk density of sediments (assumed to be 2.45 g cm-3 [38] ). Finally, the ADE (advection–diffusion equation) [Eq. (8)] model [39, 40] uses mathematics to parameterize the phenomena of advection and diffusion of solutes (in this case, 210Pb) through porous means (in this case, sediments). With an analytical equating proposed by [40], ADE model determines mean sedimentation rates modeling 210 Pb behavior in the presence of diffusion, similarly to how MDC models 137Cs behavior. rffiffiffi 210 210 a m ln Pbxs z ¼ ln Pbxs 0 z ð8Þ d 2d In which: (210Pbxs)z = ln 210Pbxs for sample from depth z (in Bq kg-1); (210Pbxs)0 = ln 210Pbxs for core top sample (z = 0) (in Bq kg-1); a = 210Pb advection coefficient (in year-1); d = 210Pb diffusion coefficient (in cm2 year-1). Statistical validation of the MDC
1 k U b
ð6Þ
In which: k = 210Pb decay constant (=3.12910-2 year-1); U = mean porosity (measured according to [38] based in the samples water content); b = slope of the linear regression between ln 210Pbxs and z (in cm-1); b = slope of the linear regression between ln 210Pbxs and f (in cm2 g-1). For the use of CFCS model, the decay of 210Pbxs is measured in relation to mass-depth parameter (f) instead of
In this study, the values of sedimentation rates generated vary and depend on the selected core and on the applied model. Therefore, two-way ANOVA (analysis of variance) was the test chosen to validate the sedimentation rates provided by the application of the MDC through the statistical comparison of the results between MDC and all 210 Pbxs models used. In order to perform this analysis, two factors (or ways) were defined (core and model) to divide the sedimentation rates values, and the analysis of interaction between the
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J Radioanal Nucl Chem
results of the MDC and the 210Pbxs models (CIC, CFCS and ADE) among the cores was the focus of this statistical assay, as it represents the attempt at the validation for the use of the MDC to calculate sedimentation rates.
210
Pb = exponential decay behavior, 226Ra = vertically linear behavior, 137Cs = curve with a single peak. For the purpose of the determination of unsupported 210Pb, the value used as supported 210Pb used was the mean value of 226 Ra in the core, as supported 210Pb tends to be vertically constant.
Results and discussion In all cores, no sample presented 137Cs, 210Pb and 226Ra activity values below the MDA. The self-absorption factors for the determination of 210Pb varied between 100 and 125 %. The determination errors of the activities ranged between 6 and 9 % for 137Cs, between 3 and 10 % for 210 Pb and between 3 and 8 % for 226Ra for the analyzed sample set, statistically acceptable values for this analysis [33]. v2 test was applied to remove activity values that imply in significant deviations from the expected behavior of the radionuclide in the core, according to the method proposed in [2]. The expected vertical behaviors of the nuclides are:
Fig. 2 137Cs vertical profiles (in mBq cm-3), v2 test and Pearson linear correlation (a = 0.05) for the CananeiaIguape system (SE Brazil). Points correspond to experimental profiles (spectrometric analysis) and curves to theoretical ones (MDC). a C2, b C4, c C5, d C7, e C15
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Model of diffusion-convection of
137
Cs
The model of diffusion-convection (MDC) of 137Cs was solved based on the mathematical formulation previously presented and with the aid of the Solver package coupled with the v2 method to calculate the model parameters, among which is the sedimentation rate. Figures 2 and 3 represent the experimental (from the gamma spectrometry analysis) and theoretical (modeled by the MDC) vertical profiles (calculated by MMV) of 137Cs for the cores from Cananeia-Iguape and Santos-Sa˜o Vicente systems, respectively.
J Radioanal Nucl Chem Fig. 3 137Cs vertical profiles (in mBq cm-3), v2 test and Pearson linear correlation (a = 0.05) for the CananeiaIguape system (SE Brazil). Points correspond to experimental profiles (spectrometric analysis) and curves to theoretical ones (MDC). a B1, b B2, c B3, d B4, e B5, f S1, g S2, h S8
All 137Cs vertical profiles represented its expected behavior, which is a curve with a maximum point, attributed to the 1963 maximum of global fallout from past nuclear tests. It can also be seen in Figs. 2 and 3 that the adjusted curves proposed by the MDC are quite close to the
experimental values, determined by spectrometric technique. These theoretical curves are not only visually similar to the experimental ones, but all also showed statistically significant correlation with them (a = 0.05) (p values
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J Radioanal Nucl Chem Table 3 MDC coefficients for the studied cores
a
Value ± determination error
Core
MDC coefficientsa m (cm year-1)
D (cm2 year-1)
A0 (mBq cm-3)
T T1=2 (year)
C2
0.84 ± 0.04
0.77 ± 0.03
33.27 ± 1.44
10.40 ± 0.45
C4 C5
1.11 ± 0.02 0.91 ± 0.05
0.02 ± 0.00 0.44 ± 0.02
62.07 ± 1.94 16.99 ± 0.85
13.01 ± 0.22 16.99 ± 0.85
C7
1.00 ± 0.03
1.35 ± 0.04
20.73 ± 0.36
6.14 ± 0.19
C15
1.28 ± 0.03
0.00 ± 0.00
68.55 ± 1.44
4.37 ± 0.09
B1
0.80 ± 0.07
0.29 ± 0.02
13.73 ± 1.16
11.06 ± 0.93
B2
0.81 ± 0.03
0.00 ± 0.00
20.40 ± 0.82
15.82 ± 0.64
B3
1.02 ± 0.06
0.24 ± 0.01
11.42 ± 0.68
18.94 ± 1.13
B4
1.73 ± 0.09
0.39 ± 0.02
22.03 ± 1.20
11.55 ± 0.63
B5
0.89 ± 0.06
0.75 ± 0.05
20.99 ± 1.32
9.41 ± 0.59
S1
1.01 ± 0.10
0.75 ± 0.07
12.77 ± 1.28
15.23 ± 1.53
S2
0.90 ± 0.09
0.23 ± 0.02
8.87 ± 0.92
24.41 ± 2.52
S8
0.82 ± 0.06
0.85 ± 0.13
14.97 ± 2.23
14.05 ± 2.09
inferior to a imply statistically significant correlation). At first instance, these observations demonstrate that the MDC can successfully reproduce 137Cs vertical profile. Thus, based on this similarity, it can be stated that this model summarizes the main phenomena responsible for the chemical behavior of this nuclide in the sedimentary column: interstitial diffusion and vertical convection through sediment pore water. Table 3 presents the coefficients of the MDC calculated with the Solver package from Eqs. (2) and (3). The diffusion coefficient (D) varied much between the cores in the study areas, expected as 137Cs diffusion depends on many environmental factors (local hydrodynamics and site geomorphology, bioturbation, sediment porosity, grain size distribution, eH, molecular sorption/desorption mechanisms, etc.) that locally suffer variations influencing this phenomenon [27, 41, 42]. Also, it must be mentioned that Cs, as an alkali metal, presents geochemistry similar to K [42], and, therefore, high reactivity with water. The range of values found for D are within those from the literature (0.04–0.42 cm2 year-1 [27], 0.06–0.64 cm2 year-1 [26]). The coefficient A0 represents 137Cs initial concentration in the sediments if assumed that all 137Cs entered the system in 1963, which is a practical approach as this is the year of maximum global fallout. The values are quite similar between the cores and the study areas, with the exception of C4 (62.07 mBq cm-3) and C15 (68.55 mBq cm-3), which showed higher values than the average of the other three cores in Cananeia-Iguape (23.66 mBq cm-3). And these are precisely the closest cores to the mouth of the Valo Grande channel, which is a known source of fine sediments to this coastal system [14]. Fine sediments generally have higher metal contents than
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coarse sediments, and this could be a cause for the higher levels of 137Cs observed in this area of the estuarine system factor. T Regarding the global half-life coefficient (T1=2 ), that 137 quantifies the difference in half-life of Cs (of about 30 year) caused by its residence time in the surrounding environment (water column, for instance) before its deposition. When it is lower than T1/2, it shows that the nuclide remained a non negligible time in the water column [27], which is the expected for this nuclide, which tends to remain in solution due to its chemical behavior as an alkali metal. Finally, the sedimentation rate (m) presented values in the same scale of magnitude of other Brazilian coastal systems, such as Guajara´ Bay (N Brazil) (0.53–1.02 cm year-1) [2] and Guaratuba Bay (S Brazil) (0.52–0.61 cm year-1) [43]. The outcome of the comparison of these values with the sedimentation rates provided by 210Pbxs models will result in the MDC validation or not for determining sedimentation rates.
Unsupported
210
Pb models
The principle for all 210Pbxs models is the same, which is the exponential vertical decay of this nuclide content with a known time factor (the half-life of 210Pb). This principle enables the determination of sedimentation rates in coastal systems, as discussed previously. Figures 4 and 5 present total 210Pb content in the sampled cores and the approximations of its decay according to Eq. (4). The curves calculated with Eq. (4) are the basis for the calculation of sedimentation rates for all the used models. Through the observation of vertical profiles of 210Pb, it can
J Radioanal Nucl Chem Fig. 4 Total 210Pb vertical profiles (in Bq kg-1), v2 test and Pearson linear correlation (a = 0.05) for the CananeiaIguape system (SE Brazil). Points correspond to experimental profiles (spectrometric analysis) and curves to theoretical ones. a C2, b C4, c C5, d C7, e C15
be seen that all presented a strong tendency of vertical decay with depth and all exponential fits for this correlation between 210Pb and depth are statistically significant at a confidence level of 95 %. This behavior is common in coastal systems and shows that, for the studied situations, the sedimentation rates suffered little variation for the analyzed time scale (which is a range of 10 T1/2 for 210Pb, or about 220 years). This is a very relevant point as it implies that the chosen systems for the validation of MDC are suitable for such, since this model calculates mean sedimentation rates, i.e. without evaluating temporal variations of this variable. Based on the adjustments applied in total 210Pb vertical profiles (Figs. 4 and 5), the CIC, CFCS and ADE models {Eqs. (5) (6) and (8), respectively] were applied for the calculation of sedimentation rates (Table 4). The models had similar results, since all of them are based on the 210 Pbxs temporal exponential decay. Moreover, the derived values are similar to those reported for the region of Cananeia-Iguape system (0.89 ± 0.17 cm year-1, CIC model) [14, 32] and for
Bertioga Channel (1.02 ± 0.12 cm year-1, CIC model) [20]. Both CIC and CFCS models consider the vertical behavior of 210Pbxs not accounting for variations in 210Pb input for the studied areas, thereby resulting in mean results comparable to those provided by MDC. It was also found that the results of ADE model tend to be smaller than the others, perhaps by its mathematical nature, as it considers the vertical diffusion of 210Pb in sediments. In general, its vertical diffusion is not accounted for in the calculation of sedimentation for coastal systems because the scale of magnitude for its diffusive processes (10-5 cm2 year-1) [40] is negligible compared to the scale of sedimentation in these systems (1 cm2 year-1). Accordingly, its response tends to differ from the other models as it has different assumptions and theoretical basis, as described above. From the values of sedimentation rate calculated by these models, methods widely used in studies of coastal sedimentation quantification, it can be performed a comparison with the values determined by the MDC and base the validation of this model.
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J Radioanal Nucl Chem Fig. 5 Total 210Pb vertical profiles (in Bq kg-1), v2 test and Pearson linear correlation (a = 0.05) for the CananeiaIguape system (SE Brazil). Points correspond to experimental profiles (spectrometric analysis) and curves to theoretical ones. a B1, b B2, c B3, d B4, e B5, f S1, g S2, h S8
Statistical validation of the MDC To perform the validation of the MDC, two-way analysis of variance (ANOVA) was used to statistically compare the values obtained by this model with those from the models of 210Pbxs. Table 5 presents the ANOVA results, including the assessment of the assumptions of data normality and
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homoscedasticity with Anderson–Darling and Levene tests, respectively, prerequisites for the application of ANOVA. The tests chosen are robust for checking these assumptions when the sample size is low and there is the possibility of violation of assumptions, as is the case of this work [44]. The results presented in Table 5 confirmed that no statistically significant difference (a = 0.05) between the
J Radioanal Nucl Chem Table 4 Sedimentation rates (m) (in cm year-1) from CIC, CFCS and ADE models of 210Pbxs for the studied cores (SE Brazil) Core
Sedimentation rate (m) (cm year-1)a CIC
CFCS
ADE
C2
0.58 ± 0.07
0.88 ± 0.11
0.76 ± 0.11
C4
1.08 ± 0.11
1.17 ± 0.12
1.00 ± 0.11
C5 C7
0.98 ± 0.15 0.49 ± 0.09
1.10 ± 0.16 1.06 ± 0.19
0.88 ± 0.13 0.88 ± 0.16
C15
1.10 ± 0.21
1.10 ± 0.21
1.18 ± 0.23
B1
0.84 ± 0.15
1.08 ± 0.19
0.94 ± 0.16
B2
0.92 ± 0.17
1.18 ± 0.22
0.71 ± 0.13
B3
0.80 ± 0.04
0.98 ± 0.05
0.75 ± 0.04
B4
1.24 ± 0.19
1.25 ± 0.20
1.72 ± 0.27
B5
0.80 ± 0.04
0.51 ± 0.03
0.71 ± 0.04
S1
1.30 ± 0.05
1.37 ± 0.06
1.12 ± 0.05
S2
1.11 ± 0.05
1.05 ± 0.04
1.02 ± 0.04
S8
0.83 ± 0.03
0.93 ± 0.04
0.94 ± 0.04
a
Value ± determination error
Table 5 Statistics and p-values of Anderson–Darling test, Levene test and two-way ANOVA (a = 0.05) for the sedimentation rates from MDC of 137Cs and 210Pbxs models for the studied cores (SE Brazil) Test
Compared models (test samples)
Test statistic
p value
Anderson-Darlinga
All models
0.63
0.10
Leveneb
MDC x CIC
0.17
0.69
MDC x CFCS
0.12
0.74
MDC x ADE
0.03
0.85
MDC x CIC
1.41
0.26
MDC x CFCS
0.33
0.58
MDC x ADE
1.20
0.29
ANOVAc
a
p value greater than a accepts the null hypothesis of approximately normal distribution of samples
anthropogenic radionuclide, its existence in environmental matrices is limited to its release by human activities. In the case of this nuclide, sedimentation rates determined based on its geochemistry is valid only since the late 40’s, the beginning of 137Cs liberation in the world through warheads testing and nuclear plant accidents, such as Chernobyl and Fukushima disasters.
Conclusions This work has achieved the statistical validation of the model of diffusion-convection (MDC) of 137Cs for the calculation of sedimentation rates in coastal systems. Thirteen sedimentary cores, sampled in SE Brazilian coastal systems, were used, and the obtained values were not only compared with those derived from models of unsupported 210Pb, widely used in oceanographic and sedimentation studies, but also by literature values for these areas. The model proved proper for such, with assumptions and mathematical development that cover the major phenomena responsible for 137Cs vertical migration in sediments: its diffusion to the interstitial water and the vertical convection of this water in sediments. This nuclide is more commonly used only as an auxiliary parameter for unsupported 210Pb modeling. Now, with this model, it passes to a major analytical level, enabling quantitative 137Cs-based assessments of coastal sedimentation. Finally, a point that should be highlighted is the temporal limitation of the MDC, which is valid for sedimentation rates only since the late 40’s, starting point for this radionuclide presence in the world environment. Acknowledgments The authors acknowledge the Fundac¸a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo (FAPESP no 2012/086346, 2011/50581-4 and 2009/01211-0) that financed this work.
b p value greater than a accepts the null hypothesis of homogeneity of variance between the samples c p value greater than a accepts the null hypothesis that there is no difference between the samples
results of sedimentation rate from the MDC of 137Cs and from models CIC, CFCS and ADE of 210Pbxs between the samples cores, as they all present similar assumptions for determining this variable. These statistical analyses validate the result of the mathematical principles for the proposed calculus with MDC. Thus, it can be said with certainty that the model of diffusion-convection of 137Cs is suitable for the determination of recent sedimentation rates in coastal systems. A point to be noted is the temporal limitation of the sedimentation rates provided by the MDC. As 137Cs is an
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