Flicker Noise in Vertical Fluxes of Particle-Associated Contaminants

Environmental Chemistry Department, CID, CSIC, Jordi Girona 18-26, E-08034 Barcelona, Catalunya, Spain, and IAEA Marine Environment Laboratory, P.O. ...
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Research Communications Flicker Noise in Vertical Fluxes of Particle-Associated Contaminants in the Marine Environment

to a state that is independent of the initial conditions, i.e., the state is an attractor of the system dynamics. The attractor is a critical state in the sense that the system is susceptible to small changes or noise that produce fluctuations (avalanches) of all sizes, even though it cannot be too sensitive or it would not have evolved to such a critical state. A detailed discussion of the SOC and nonlinear dynamic systems can be found elsewhere (10-15).

JORDI DACHS,† J O S E P M . B A Y O N A , * ,† A N D SCOTT W. FOWLER‡

Experimental Methods

Environmental Chemistry Department, CID, CSIC, Jordi Girona 18-26, E-08034 Barcelona, Catalunya, Spain, and IAEA Marine Environment Laboratory, P.O. Box 800, MC-98012 Monaco

Introduction Sediment trap experiments in the marine environment carried out over the last two decades have shown that the vertical fluxes of persistent organic contaminants (e.g., PAHs, PCBs, and DDTs) are mainly governed by biogenic (1-4), physical, and geochemical processes (5, 6). Nevertheless, mechanisms that drive vertical particle transport in the sea are complex, interactive, and far from understood (1-7). A great variety of transport processes in nature show the occurrence of “flicker” or 1/f noise (8). In this paper, vertical particle fluxes from the western Mediterranean were analyzed, and 1/f noise was found for compounds associated with biogenic particles. The 1/f noise is identified whenever the Fourier spectra of a time series fits to a power law with a slope nearly -1 or when the log-log plot of probability (P) (or fractional occurrence that a variable, e.g., PAH fluxes, has a certain intensity) versus the magnitude or flux intensity (F) is a straight line:

P ≈ cF-d;

d>0

log P ≈ -d log F + log c

(1)

where c and d are the parameters obtained by least-squares regression, and d is near unity. Very recently, similar methodology has been applied to temporal changes of epidemics in isolated populations (9). It has been suggested that self-organized criticality (SOC) is the common underlying mechanism behind 1/f noise (10). In this paper, we attempt to show that not only a vertical transport of biogenic matter (i.e., fecal pellets, organic carbon) but also of some priority organic contaminants would behave like a spatially extended dynamic system, viz., one showing self-organized criticality behavior with both temporal and spatial degrees of freedom (11, 12). Self-organized means that the marine environment evolves * Corresponding author telephone: +34-3-4006100; fax: 34-32045904; e-mail address: [email protected]. † Environmental Chemistry Department. ‡ IAEA Marine Environment Laboratory.

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Data Origin. In order to assess the occurrence of SOC behavior in the vertical transport of particles in the marine environment, four data sets of particle fluxes from different locations of the western Mediterranean Sea have been considered (Figure 1): (i) open Alboran Sea (FebruaryMay 1992), (ii) coastal waters offshore Monaco (June 1978August 1990), (iii) Gulf of Lions (September-October 1983, July 1985-April 1986), and (iv) offshore Corsica (April 1986November 1987). A detailed discussion of procedures used for particle sampling and the analysis of PAHs, organic carbon, and other parameters can be found elsewhere (2, 6, 16-19). Data Analyses. The log-log plots have been computed for each of the following vertical fluxes: organic carbon, mass, aluminum (Al), fecal pellets, PCBs, DDTs, and total PAHs. Total PAHs were the sum of fossil fuel (i.e., methyland dimethylphenanthrenes, methyl- and dimethyldibenzothiophenes, chrysene) and pyrolytic (i.e., fluoranthene, benzofluoranthenes, benzo[a]pyrene, benzo[e]pyrene, and perylene) PAHs. PCB data were computed as Clophen A40 equivalents, and DDTs were the sum of 4,4′-DDE and 4,4′DDT. The rank or difference between the maximum and minimum of the different variables was determined for each set of samples. The rank was then divided into intervals, from 5 to 7. The number of samples that have values between the limits of each interval were counted, and the probability or fractional occurrence that the selected variable has a certain value in each interval was obtained. Then the log of probability (P) of each interval was plotted versus the log of the corresponding vertical flux (F). Fourier spectra for the set of samples from Monaco were computed without either previously filtering or smoothing data. When a gap in a time series was present, it was interpolated by cubic splines. The Fourier transform was not computed for the other data sets due to sparseness of long time series. The most widely accepted definition of chaos is the sensitivity to small initial conditions, which is measured by the Lyapunov exponent (h) (15). This exponent gives the average exponential rate of divergence of the infinitesimal nearby initial conditions. In order to identify dependence on initial conditions, only the sign of the highest exponent is relevant. The magnitude of the exponents is related to the rate at which the system processes, creates, or destroys information, thus the units of Lyapunov exponents are given as “bits orbit-1”. In this work, we will focus on the sign of the exponent.

S0013-936X(96)00120-4 CCC: $12.00

 1996 American Chemical Society

FIGURE 1. Map showing the location where the sediment traps were deployed: (A) open Alboran sea (16), (B) coastal waters offshore Monaco (6), (C) Gulf of Lions (17), and (D) offshore Corsica (19). References where data was retrieved are indicated.

Lyapunov exponents can be computed from an experimental time series using the methodology described by Wolf et al. (20) in which the phase space is reconstructed from the experimental time series and then the exponential divergence of nearby points in the phase space is computed. Lyapunov exponents for total PAHs and organic carbon fluxes in Monaco coastal water were computed, taking into account different values of parameters in the reconstruction of the phase space (lag time, etc.), and an average value of the exponent was obtained. The Lyapunov exponents for the other data sets were not computed due to the sparseness of available data from those field experiments of shorter duration.

Results and Discussion Computed Fourier spectra of organic carbon and PAH time series fluxes in Monaco coastal waters (Figure 2) show a power law distribution P(f) ≈ f-β with β values of 1.2 ( 0.1 and 1.42 ( 0.16 for organic carbon and PAHs, respectively. Although the Fourier spectrum is quite noisy, the power law trend is statistically significant with a confidence level higher than 99%. Power laws can be the consequence of different mechanistic and random processes, i.e., in randomlike processes a power law is obtained, but in case of a random walk the exponent β is 2, which is much higher than the values found in our data sets. In case of white or uncorrelated noise, the value of the exponent is 0. Thus processes showing 1/f noise are midway between white noise and a random walk (21). There are some physical processes in the marine environment that follow a power law in their Fourier spectrum, e.g., the spectrum of energy of surface gravity and internal waves follows power laws with exponents 4 and 2, respectively (22). Although physical processes may have an important role in explaining some trends, they are not able to produce flicker noise. In addition, it has been demonstrated experimentally that competing plankton species produce important fluctuations of their biomass without changes in the physical conditions in their environment (23). However, the exponents of 1/f noise (β) reported range from 0.7 to 2 (8, 12), thus particle and contaminant data computed in our study clearly show flicker, or 1/f noise, since β values fall within this range, which is attributable to some kind of self-organization process in a critical state. Values of exponents of Fourier spectra obtained for the set of Monaco data are confirmed by the log P - log F plots

FIGURE 2. Fourier spectra of (A) organic carbon and (B) PAH fluxes from Monaco coastal waters (station B in Figure 1).

(see eq 1). Concurrently, data from the four locations in the western Mediterranean (Figure 1) were also computed. Resultant power law exponents, confidence levels, and regression coefficients obtained by least squares regression are shown in Figure 3, and the corresponding log P - log F plots are presented in Figure 4. Fluxes of total PAHs in the Alboran Sea do not fit well to a power law (power law exponent d ) 0.94 ( 0.39, with a confidence level (CL) of 90.1%, r2 ) 65.5%, Figure 3). Nevertheless, because the fate of PAHs in the marine environment is associated with their source (16), we have subdivided the PAH fluxes into two categories, fossil fuel and pyrolytic derived. While fossil fuel PAHs fit quite well to a power function (d ) 0.93 ( 0.12, CL ) 99.5%, r2 ) 95.1%; Figure 3), the least-squares fit for pyrolytic PAHs is not as good (d ) 0.96 ( 0.35, CL ) 88.8%; r2 ) 78.8%, Figure 3). Indeed, for the set of samples from the Alboran Sea, it has been reported (16) that the fossil fuel PAH fluxes are correlated with fluxes of both organic carbon and zooplankton fecal pellets, whereas pyrolytic PAHs are more closely related to the total mass flux. These observations are in good agreement with the derived power law relationship for organic carbon and fecal pellet fluxes (Figure 3, d ) 1.17 ( 0.17; CL ) 97.5; r2) 92.5% and d ) 1.09 ( 0.18; CL ) 99.1%; r2 ) 95%, respectively). Conversely, total particulate fluxes do not follow a power function (Figure 3, d ) 1.36 ( 0.6; CL ) 82.7%; r2 ) 68.3%), reflecting the contrasting behavior between the biogenic and nonbiogenic fluxes. Other studies have suggested that the fate of hydrophobic contaminants like PCBs and PAHs in the marine environment is controlled by biological processes that play an

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FIGURE 3. Regression results of the log P - log F plots defined in eq 1 for the different fluxes (i.e., fecal pellets, organic carbon, PCBs, DDTs, etc.): (A) slope of the log P - log F plots (d), (B) confidence level (CL), and (C) regression coefficients (r2) from the least squares regression of eq 1.

important role in the biogeochemical cycles of these contaminants (1-4, 16-19, 24). Taking into account those observations and the results obtained from the present assessment, we propose that the downward fluxes of organic carbon, fecal pellets, and fossil fuel PAH exhibit the signature of a SOC due to the relationship between these variables and the population dynamics of microbiota such as phytoand zooplankton. Computer simulations have demonstrated that population dynamics and species coexistence may show self-organizing spatial dynamics with a critical attractor (11). Furthermore, it has been suggested from experimental data that plankton biomass could have a fractal structure (25, 26) with a chaotic attractor, which may explain the temporal variability of phytoplanktonic populations (27). SOC is the more feasible mechanism, which explains how fractal structures develop. Theoretical biologists have proposed that coexisting species could drive the ecosystem to the “edge of chaos” (28-30) in large-scale evolution, a transition point running from order to chaos. However, that kind of approach leads to SOC behavior in the transition zone, and it has been suggested that complex systems may self-organize in a critical state. Although further data are needed in order to confirm if marine

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FIGURE 4. Log P - log F plots defined in eq 1 of (A) organic carbon fluxes from Monaco coastal waters, (B) fossil fuel PAH fluxes from the open Alboran Sea, and (C) PCB fluxes from the Gulf of Lions.

planktonic biomass follows a system with SOC, it is reasonable that the vertical biogenic and associated contaminant fluxes described above show 1/f noise as a consequence of critical phenomena in plankton populations producing the particles. On the other hand, since pyrolytic PAHs are strongly associated with atmospheric deposition of soot particles, they are therefore less influenced by biological processes. Accordingly, the least-square regression of the power functions is not statistically significant for all sets of data computed. The 1/f behavior for the vertical flux data from offshore Monaco is similar to that found for particle fluxes in the Alboran Sea. In the former case, however, both fossil fuel and pyrolytic PAHs exhibited flicker noise. This different spatial behavior in the pyrolytic PAHs could be accounted for by the fact that particle flux only displays the fingerprinting of SOC in the coastal areas where runoff inputs

predominate over the atmospheric deposition prevailing in the open sea (31). It is also noteworthy that the distribution of organochlorine compounds (i.e., PCBs and DDTs) follows a power law for both Alboran Sea and Gulf of Lions samples (Figure 3). The mechanism producing this behavior could be similar to that discussed above for fossil fuel PAHs. Indeed, it has been established that hydrophobic organochlorine compounds are strongly associated with fecal pellets and the organic carbon content of sinking particles (1, 16). Since Al is associated with aluminosilicate materials in atmospheric particles, the corresponding particulate Al fluxes through NW Mediterranean waters have also been considered. Measurement of Al fluxes in sinking particulate material has been proposed to trace the fate of atmospheric particles in the marine environment (18). The log-log plot of Al data fits quite well with a confidence level of 99.3% (d ) 1.44 ( 0.17; r2 ) 93.3% in Figure 3), a finding that may be attributable to the primary influence of fecal pellets in the vertical transport of Al (18). From the results shown in Figure 3, it is apparent than the vertical fluxes of the compounds associated with biogenic particles in the open Alboran Sea exhibit 1/f noise since their exponents, d, are closer to unity (0.93-1.17) whereas those from the NW Mediterranean are generally higher (1.28-1.57). Deep-water upwelling in the Alboran Sea allows the transport of nutrients to surfacial waters (32), leading to a higher primary productivity with less nutrient limitations as is found in the open NW Mediterranean. Recently, SOC has been proposed for highly productive terrestrial ecosystems (33), and such a hydrographic situation in the Alboran Sea could facilitate the system to be driven near the critical state. Although it is not possible to confirm these results by using only the log P - log F plots of temporal series data, we might assume they are valid from ancillary data of spatial series. Indeed, it has been observed that the spatial distribution of plankton biomass follows power laws with exponents approximately 1.67 (25), a pattern that would be expected in the case of SOC. Nevertheless, it is not possible to extrapolate those results to sedimenting biogenic particles, and in any event the role of time and space are analogous in net particle production and carbon export to the deep sea. A self-organized system near the critical state may display a chaotic behavior, where chaos can be characterized by Lyapunov exponents (h). The highest h value defines the average exponential rate of divergence of the nearby initial conditions (15). Therefore, the highest Lyapunov exponent of the temporal variability of PAH and organic carbon fluxes from the Monaco station (Figure 2) were found to be 0.14 ( 0.077 and 0.12 ( 0.034, respectively. Despite the limitation of available data, the h values are positive, and in the case of the PAH data a zero value cannot be rejected within a confidence level of 95%. These small but positive values of the highest Lyapunov exponents demonstrate a slightly chaotic behavior and are very near the expected dynamics of critical systems in which the Lyapunov exponent is zero, since critical systems are located at an intermediate point between order and chaos. These observations support our previous conclusion about SOC of vertical organic contaminant fluxes in the marine environment.

The spatiotemporal SOC in the downward fluxes of PAHs and PCBs may indicate that the mechanism controlling the fate of contaminants in marine waters is complex and appears to be closely linked to trophic processes. In this kind of behavior, most of the vertical fluxes (avalanches) fall inside a quite small range of values, and higher values are reached with a probability that follows a power law. In spite of avalanches, the system will sink toward the critical state. For marine transport processes in which SOC may be present, care must be taken in making generalizations from small data sets since, in the case that a large avalanche occurs during sampling, results can be significantly overestimated. For instance, if the vertical fluxes are controlled by a SOC mechanism, the forecasting capabilities are limited since strong and short pulses of contaminant fluxes (avalanches) are feasible, which indeed can be highly enriched in hydrophobic organic contaminants. Obviously, the ecotoxicological implications are enormous because benthic communities can be exposed to high pollution episodes whenever an avalanche is produced. In summary, the SOC of certain biogenically associated organic contaminants in the marine environment has been proposed, and the influence of some environmental factors such as their different association to biogenic particles and different ecosystem behavior has been studied. Further research is needed in order to fully understand the specific mechanisms that control particle fluxes through the water column. The confirmation that the flicker noise observed in sediment trap data is due to SOC could be achieved by obtaining ancillary spatial flux data and by applying realistic computer simulations, in which a specific model could be postulated and tested.

Acknowledgments J.D. is recipient of a predoctoral fellowship from the CSIC. Financial support was obtained from the Spanish National Plan for Research (AMB93-0693) and from the EU Marine Science and Technology Program as part of the EROS 2000 Project (EV4V0111F). The IAEA Marine Environmental Laboratory operates under a bipartite agreement between the International Atomic Energy Agency and the Government of the Principality of Monaco.

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Received for review February 9, 1996. Revised manuscript received July 23, 1996. Accepted August 1, 1996. ES9601200