Interaction matrices as a first step toward a general model of radionuclide cycling: Application to the 137 Cs behavior in a grassland ecosystem

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1 DOI: /JRNC Journal of Radioanalytical and Nuclear Chemistry, Vol. 268, No.3 (2006) Interaction matrices as a first step toward a general model of radionuclide cycling: Application to the 137 Cs behavior in a grassland ecosystem H. R. Velasco, 1 J. J. Ayub, 1 M. Belli, 2 U. Sansone 3 * 1 GEA Instituto de Matemática Aplicada San Luis (IMASL), Universidad Nacional de San Luis, Consejo Nacional de Investigaciones Científicas y Técnicas, Ej. de los Andes 950, D5700HHW San Luis, Argentina 2 Agenzia per la Protezione dell Ambiente e per i Servizi Tecnici (APAT), Servizio di Metrologia Ambientale, Via di Castel Romano, 100, I Roma, Italy 3 International Atomic Energy Agency (IAEA), Agency s Laboratories Seibersdorf, A-1400 Vienna, Austria (Received November 21, 2005) Interaction matrices, an expert semi quantitative method to identify multiple interactions among biotic and abiotic components of the ecosystem can be considered as a useful tool to develop conceptual models of the behavior of radionuclides in the environment. This systematic approach facilitates a comprehensible identification of the pathways of the main radionuclides and permits classification of the role of different ecosystem components in terms of cause-effect relationships. The method was applied to study the radiocesium migration in grassland ecosystem affected by the Chernobyl 137 Cs deposition. Interaction matrices have been simultaneously utilized to explore the dynamic changes on the radiocesium migration pathways and to compare the consequences of the various radiation exposure paths to living organisms. Introduction The mobility of the radionuclide in grassland ecosystem involves a number of complex mechanisms, and the transfer of radionuclides through the environmental compartments implies multiple interactions among the biotic and abiotic components of the ecosystem. To the identification of these interactions it is necessary to develop predictive models describing the radionuclide fluxes from the environment to the man. The interaction matrix (IM) is an expert semiquantitative method to identify the main components of the ecosystem and to assess the interactions among them. This methodology has been extensively applied in the past. HUDSON 5 in 1992, has used IM for systematic studies of processes in rock engineering systems. Later, the method was applied to identify the main pathways for dose assessment in a radioactive waste disposal 10 and to develop conceptual models of radionuclide migration and accumulation in forest ecosystems. 1,3,6 Over the last 15 years the Italian Environmental Protection Agency (APAT) has promoted and conducted radioecological research in grassland environments located in the Friuli Venezia Giulia Region (northeastern part of Italy). Following the Chernobyl accident, this region was subjected to heavier rainfall than other Italian regions and received the highest radioactive deposition. The radionuclide activity concentration values were particularly high on the mountain areas and then decreased towards the coast. 2,13 Scientists from different countries actively participated in these studies, and the knowledge on radionuclide behavior in semi-natural ecosystem has been improved significantly, especially for boreal forests and middle European meadow systems which have been extensively investigated. Data sets have been obtained which describe the distribution and the cycling of radionuclides (especially 137 Cs and 90 Sr) within these systems. 9,11,13 The experience achieved in the frame of these activities offered the opportunity to develop a dynamic conceptual model for 137 Cs migration and radiation exposure based on interaction matrices. The methodology of the interaction matrices allowed identifying the main radiation exposure of 137 Cs pathways on living organisms in a grassland ecosystem and their modification by radionuclide deposition. External radiation exposure was considered as attributable to radionuclides in the air or deposited on the ground. Internal exposure was considered as caused by inhalation of air radionuclides or through food and water ingestion. Experimental Interaction matrix and pathway analysis The IM methodology is essentially based on the description of the different processes taking place in a system using an n n matrix (IM). The ecosystem components (n in total) are the elements of the diagonal of the matrix (IM ij, with i = j), while the off-diagonal elements IM ij (i j) represent the interaction between them. A detailed description of this method can be found in Reference 1. Briefly, an element with j>i denotes how the diagonal element IM ii influences the element IM jj, while an off-diagonal element with j<i denotes how the diagonal element IM jj influences the element IM ii. * u.sansone@iaea.org /USD Akadémiai Kiadó, Budapest 2006 Akadémiai Kiadó, Budapest Springer, Dordrecht

2 The matrix should be read clockwise. The resolution of the matrix is n (degree of complexity or simplicity of the system description by the conceptual model) and the n(n 1) gives the number of possible interaction terms. After the identification of the diagonal elements and the binary interactions, it is possible to code the matrix by ranking the interactions in order of importance. Seven environmental components are considered: Atmosphere, Grass, Upper, Medium and Deep soil, Animals and Man (Fig. 1). Three layers in the soil compartment are taken into account. The atmospheric deposition mainly affects the upper soil layer (Soil (U), 0 to 2 cm deep) and the activity concentration in this layer is of relevance to the evaluation of the radiocesium contribution to the external radiation exposure. Medium soil (Soil (M), 2 to 10 cm deep) plays an important role in the soil to plant transfer process and in both external and internal radiation exposure to living organisms. Soil layers deeper than 10 cm (deep soil, Soil (D)) are less affected by 137 Cs activity concentration because radiocesium is mainly fixed in the superficial soil layers. 13 The main processes involved in flux and exposure pathways among the seven environmental components are shown in Fig. 1. On the basis of the IM methodology proposed by AVILA and MOBERG, 1 in the frame of the APAT radioecological research in grassland environments, the main principal ecosystem components (IM diagonal terms) and the interaction terms (IM off diagonal terms) were defined. The expert semi-quantitative method was used to rank the interactions between the different components taking into account the time dependence of the considered environmental processes. This method proposes five interaction categories ranging from zero to four. The numbers: 0, 1, 2, 3 and 4 represent respectively no, weak, medium, strong and critical interactions. To characterize the dynamic modifications in the radionuclide circulation process, four consecutive time periods were proposed. The initial period, represented by t 0, indicates the annual period beginning with the radionuclide release to the environment; t 1 and t 2 represent the first and second annual periods following t 0, respectively, while t 3 indicates the situation of the ecosystem 3 years after the deposition. The developed analysis proposes specific interaction codes, for each interaction, at each time period. When each interaction is codified, IM becomes the Code Matrix (CD). The number in each position, CD ij (i j), represents the category assigned to the interaction between i and j. Exploring CD, it is possible to identify the principal flux pathways in the system. These migration (or exposure) pathways can be seen as multiple interactions in the system, which are represented by combinations of binary interactions in the interaction matrix. 1 In order to compare the strength of pathways that involve different numbers of binary interactions, the following normalized ranks were introduced: 1 Normalized rank (nr) = (ΣBinary interaction rank)/ /(ΣNumber of interaction) (1) Fig. 1. Interaction matrix with 7 diagonal elements describing 137 Cs migration and exposure pathways in a grassland ecosystem 504

3 Cause-effect relationships In cause-effect analysis, the sum of a row in the code matrix explains how the considered environmental component influences all the other components. This sum is defined as the cause (C) associated with this component. Likewise, the sum of a column of the code matrix represents the effect (E) that the rest of the components have on the component whose column was selected. In this way, each component of the system can be represented as a point in a two-dimensional space (C, E). This planar representation permits to distinguish the mode of interaction of each component with the rest of the components of the system. For example, the degree of interaction of a particular component with the others is measured by the distance of the representative point from the origin along the 45 diagonal. The points situated on the left side of the diagonal represent components (subordinated), which influence the system less than the system influences them. The dominant components of the ecosystem have representation in the (C, E) space as points situated on the right side of the diagonal. The cause-effect coordinates of each component change with time after 137 Cs deposition. These changes can be represented, for each component, as trajectories in the (C, E) space. These imprints graphically represent variations in the degree of dominance or subordinance of the different components. The interaction matrices method was used in the past to evaluate radiation exposure pathways. 10 In the present study the methodology has been also applied to describe and to compare different exposure pathway due to 137 Cs on living organism in grassland ecosystem. The principal fluxes through the components of the ecosystem affecting the exposure were considered and their dependence with time discussed. For exposure pathways, a cause-effect analysis was also carried out. Results and discussion Figure 2 shows the coded matrix. The selected environmental components for the grassland ecosystem conform the diagonal elements. For each selected time period, the numbers in each off-diagonal position represent the assumed codes for the related binary interaction. We have considered that immediately after radionuclide release to the atmosphere, the deposition is the most significant process. Other processes gain significance with times. For example, the movements of radionuclides through soil layers determines the transfer towards grass growing. Also the 137 Cs activity concentration of plants controls the activity flux to animals and humans. Initially the grass components are contaminated externally and only at successive phases the activity levels are controlled by the root uptake in grass tissues. For time periods, Table 1 shows the most important 137 Cs flux pathways and the corresponding normalized rank. For the initial time period, 137 Cs deposition is the dominant process. At this time, dry and wet deposition and interception are the main processes involved in 137 Cs cycling in the grassland and they have a critical influence to the future fluxes. Pathways that take into account these processes present high normalized rank (n r = 3.5). Other transfer processes, which involve resuspension, soil vertical migration and transfer into the food chain have a normalized rank of 3. For the following period, t 1, the principal circulation ways include upper and medium soil layers, grass, animals and human components. The movements of radionuclides through the superficial soil layers and the transfer to grass and into the food chain are ranked 2.5 to 2. For the period t 2, the principal pathways are the radionuclide migration into soil layers (upper, medium and deep soils) and the transfer to animals via grass. The deep soil compartment does not take part in the uptake by the root but it plays an important role in the radionuclide balance of the soil. This is in agreement with the grass morphology as the roots of grass are in the top few centimeters of the soil and the uptake takes place only in the superficial layers. 14 Finally, for the period t 3, the pathways does not change considerably in relation to the previous time period, however, normalized ranks are, comparatively, smaller. Figure 3 shows the cause-effect relationships for the migration pathways. The coordinates for each component in the (C, E) space are obtained from the sum of the respective row and column of the code matrix. The results of these sums are shown in the joined row and column of the code matrix (Fig. 2). These coordinates change with time, the movement of each point conforming the trajectories for every component in this space. The position of the points in this graph indicates how the components interact with the other components of the system. The degree of interaction could be assessed considering the sum of the coordinates in the (C+E) space, i.e., the distance of a component from the origin along the 45 diagonal. The atmosphere showed the most important change in the cause-effect relationship. At the initial stage this component is the principal cause of the contamination of the other components of the ecosystem. But, in the final stage, there is no atmospheric contribution to the 137 Cs flux. Initially the grass and upper soil components showed, high causeeffect relationship. Both components are in an elevated interaction with the other components. For successive times, the representative point of the grass in the (C, E) plane moves towards the left side of the diagonal (subordinate components), while the upper soil point 505

4 moves to the right side of the diagonal (dominant components). Initially the medium and deep soil components showed, at low cause-effect relationship. Later on both components tend to affect the other components more because these soil layers are important contributors to the activity circulation in the ecosystem. Initially, animals and humans are strongly affected by the other components. In successive times this influence decreases markedly. Exposure pathways The interaction processes considered in the analysis of exposure pathways (Fig. 1) have been coded (Fig. 4) following the same procedure. The codes were selected taking into account multiple studies of the external and internal exposure due to the 137 Cs content of air, soil, water and foodstuffs. 4,7,8,13 Figure 5 shows the contributions to the exposure expressed in terms of the individual codes associated to each contribution. In the first time period, external exposure due to the direct contact with contaminated air and from radionuclides deposited on superficial soil represents the bigger contribution to the dose of living organisms. The internal exposure to man, via food chains or inhalation, are smaller. However, they may constitute an important contribution in successive times. Resident radionuclides in the superficial soil layers constitute the main contribution to dose in the period of t 2 due to external and internal exposure via the ingestion of contaminated vegetables. For successive times, radiocesium remains practically fixed to the soil components, consequently, the principal contribution to the exposure of living organisms are the radionuclides situated in the superficial soil layers. In Fig. 6 the various components of the ecosystem and they respective trajectories for the analysis of exposure pathways are presented in the (C, E) space. Living organisms are situated on the left zone of the diagonal (subordinate components), with the exception of grass at final time. The atmosphere at the time of deposition and the upper and medium soil layers are the main dominant components in successive time periods. The temporal trajectories of these components are situated on the right zone of the diagonal in the (C, E) space. Fig. 2. Coded matrix for 137 Cs migration pathways in a grassland ecosystem 506

5 Table 1. Normalized ranks of the principal 137 Cs migration pathways for each selected time period Pathway Normalized rank t = t 0 Atmosphere grass soil (U) 3.5 Atmosphere soil (U) grass 3.5 Atmosphere grass animal 3.5 Atmosphere soil (U) soil (M) 3.0 Atmosphere soil (U) atmosphere 3.0 Atmosphere grass animal human 3.0 t = t 1 Soil (U) grass animal 2.5 Soil (U) soil (M) grass 2.5 Soil (U) soil (M) grass animal 2.3 Soil (U) soil (M) grass animal human 2.0 t = t 2 Soil (U) soil (M) grass animal 2.3 Soil (U) soil (M) soil (D) 2.0 Soil (U) grass animal 2.0 Soil (M) grass animal 2.0 t = t 3 Soil (M) grass soil (U) 1.5 Soil (U) grass animal 1.5 Soil (U) soil (M) soil (D) 1.0 Fig. 3. Temporal changes in cause-effect relationships for 137 Cs migration pathways in a grassland ecosystem 507

6 Fig. 4. Coded matrix for 137 Cs exposure pathways in a grassland ecosystem Fig. 5. Temporal variation of the accumulated code for exposure pathways in a grassland ecosystem 508

7 Fig. 6. Temporal changes in cause-effect relationships for 137 Cs exposure pathways in a grassland ecosystem Conclusions The procedure of the interaction matrices represents a useful tool for systematic ecological studies. It can be used as a first step towards a general model of radionuclide cycling. In the present study, the method has been applied to describe the migration of 137 Cs in a grassland ecosystem. The most dominant pathways for the 137 Cs flux through the components of ecosystem have been qualitatively identified for succesive time periods after the deposition of 137 Cs from Chernobyl. The IM method permits the identification of the most relevant processes to be taken into account for their significance at each time interval. The relevance of each interaction among the different ecosystem components and the temporal variation must be considered when remediation strategies are proposed. The exposure pathways are described by interaction matrices. The importance of each possible way of radiation exposure to living organism, after the atmospheric deposition of 137 Cs, has been identified and ordered in terms of relevance, for different time intervals. Cause-effect analysis was carried out for both migration and exposure pathways. The position of each component in the (C, E) space makes possible a graphical representation of the role of each component of the ecosystem. The representative points and their imprints on this virtual space permit us to differentiate, at any time, the mode of interaction of each components and the degree of dominance or subordinance. The interaction matrices inherently includes the element of subjectivity. Involving several experts from different disciplines in the identification and coding of interaction matrices constitutes a necessary condition to increase the objectivity of the method. References 1. R. AVILA, L. MOBERG, J. Environ. Radioact., 45 (1999) M. BELLI, U. SANSONE, S. MENEGON, Sci. Total Environ., 157 (1994) BIOMOVS II, Development of a Reference Biosphere Methodology for Radioactive Waste Disposal, Technical Report No. 6, Swedish Radiation Protection Institute, S. CHEN, Heath Phys., 60 (1991) J. A. HUDSON, Rock Engineering System Theory and Practice, Ellis Horwood, Chichester, U.K. (1992). 6. IAEA, Modeling the Migration and Accumulation of Radionuclides in Forest Ecosystems, IAEA-BIOMASS-1, Waste Safety Section, IAEA, Vienna, Austria, D. KOCHER, A. SJOREEN, Health Phys., 48 (1985) A. RANTAVAARA, Human exposure to radiation via ingestion of food and water, in: Radioecology, Lectures in Environmental Radioactivity, World Scientific Publishing, 1996, p SEMINAT, Long-term Dynamics of Radionuclides in Semi- Natural Environments: Derivation of Parameters and Modeling. European Commission, Research Contract No. F14-CT , Final Report, M. BELLI (Ed.), APAT, Italy, G. M. SMITH, B. M. WATKINS, R. H. LITTLE, H. M. JONES, A. M. MORTIMER, Biosphere Modeling and Dose Assessment for Yuca Mountain, Electrical Power Research Institute, EPRI TR , Palo Alto CA, J. P. TOSO, R. H. VELASCO, J. Environ. Radioact., 53 (2001) H. VELASCO, E. CARREÑO, M. RODRÍGUEZ, M. BELLI, U. SANSONE, J. Environ. Radioact., 73 (2004) R. H. VELASCO, J. P. TOSO, M. BELLI, U. SANSONE, J. Environ. Radioact., 3 (1997) Y. G. ZHU, E. SMOLDERS, J. Exp. Botany, 51 (2000)