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Introduction to the Development of Models of Radionuclides

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Introduction to the Development of Models of Radionuclides 729 SplSSN614-087-X INTRODUCTION TO THE DEVELOPMENT OF MODÉLS OF RADIONUCLIDES TRANSFER García-Olivares, Antonio CENTRO DE INVESTIGACIONES ENERGÉTICAS, MEDIOAMBIENTALES Y TECNOLÓGICAS MADRID, 1994 CLASIFICACIÓN DOE Y DESCRIPTORES: 540230 540130 RADIONUCLIDE MIGRATION MATHEMATICAL MODELS ECOSYSTENS RADIOECOLOGY RADIATION MOMITORING Toda correspondencia en relación con este trabajo debe dirigirse al Servicio de Información y Documentación, Centro de Investigaciones Energéticas, Medioam- bientales y Tecnológicas, Ciudad Universitaria, 28040-MADRID, ESPAÑA. Las solicitudes de ejemplares deben dirigirse a este mismo Servicio. Los descriptores se han seleccionado del Thesauro del DOE para describir las materias que contiene este informe con vistas a su recuperación. La catalogación se ha hecho utilizando el documento DOE/TIC-4602 (Rev. 1) Descriptive Cataloguing On- Line, y la clasificación de acuerdo con el documento DOE/TIC.4584-R7 Subject Cate- gories and Scope publicados por el Office of Scientific and Technical Information del Departamento de Energía de los Estados Unidos. Se autoriza la reproducción de los resúmenes analíticos que aparecen en esta publicación. Este trabajo se ha recibido para su impresión en Marzo de 1993 Depósito Legal n° M-19026-1993 ISBN 84-7834-202-8 ISSN 614-087-X ÑIPO 238-94-018-1 IMPRIME CIEMAT Preliminary note. This monograph is the resume of two seminars given by the author in the University of Kiev, Jannuary 1990, in the Course: "Systematic Assessment of Dose to Man following Radionuclide Reléase into the Environment", in the frame of the project "International Assessment of Chernobyl's Radiological Consequences", organized by IAEA, CEC, FAO, UNSCEAR and WHO. I thank my collegues David Cancio, Beatriz Robles, Inmaculada Simón and Ana Suañez for their help in the revission of the manuscript as well as in the plotting work. INTRODUCTION TO THE DBVELOPMENT OF MODELS OF RADIONUCLJDES TRANSFER IN THE ENVIRONMENT COMPREHENSIVE INDEX. 1. Introduction. The dispersión of radionuclides in the biosphere and its impact in the human populations. The biosphere as the life ecotope and the biosphere as a self-organizing system. The dose 1 2. The dispersión in a complex inedia. Heterogeneity of phasés and heterogeneity of proceses and dispersive properties 4 3. The physic dispersión in a homogeneous inedia 6 a) Difusión and molecular random walk 7 b) Media's advection vs. contaminant's advection 8 c) Turbulent transport. Correlations and diffusivity. Fractal intermittency 9 3.1 Steady dispersión of a punctual systematic reléase Gaussian dispersión. Channeled dispersión 11 3.2 Dispersión in rivers, lakes and seas 13 4. Dispersión in porous media 17 5. Dispersión in interphases 18 5.1 Resuspension and deposition between atmosphere and soil 19 5.2 Infiltration of radionuclides from soil surfaces...22 5.3 ¥ater-sediment interaction 23 5.4 Estuaries 24 5.5 Runoff and drainage of radionuclides 26 6. Transfer into biologic systems 28 6.1 Crops contamination 28 6.2 Transfer to milk and cattle meat 30 7. Theoretical models and modelization 32 The digital computer and the systemic methodology. 7.1 The construction of a conceptual model in radiological assessment. Subsistems. Dispersión in and between subsistems 34 7.2 The mathematical models.From the conceptual model to the mathematical model 38 7.3 The compartiment models.The reduction of continuous dispersión proceses to dispersión through networks..40 7.4 Construction of the computer model. Calculation and documentation of results 42 Integrator of the set of equations.Iterations. Algorithm. Methods of numerical integration. Computer languages and computer model. 7.5 Resume of the operations to construct a mathematical model 44 8. Parameters obtaining 48 8.1 General considerations 48 8.2 Parameters in equilibrium models and parameters in dynamical models. Types of parameters. Literature reviews and international institutions dealing ¥ith parameters reports 48 9. Models uncertainties. Types of uncertainties. Uncertainties coming from the model structure. Uncertainties in data and parameters and montecarlo techniques. Natural variability. Uncertanties coming from the environmental and cultural evolution 53 10. Long-term problems and probabilistic models 58 10.1 General problem: Evolution of the dispersión scenario. Models of hypothetic scenarios. Models of proceses generating the scenario. Climatic change and biosferic change 58 10.2 Long term evolution and uncertainties 60 Processes that genérate scenarios and long term uncertinties. The macroescale and the microescale in the proceses. Sinergetic approach. Equations for the uncertainty propa- gation: Master, Fokker-Planck and Langevin equations. Long term atractors. Ref erences 6¿ 1. INTRODUCTION. The study of the processes controlling the dispersión of radionuclides and other trace substances through the biosphere derivates its importance from the potential impact that the radionuclides have on the health of the human populations. The intention of the work is to explore the foundations of radioecological modelization with environmental assessment purposes. In particular its relation with the theory of dynamic systems, and the basic hypothesis underlying the modelization practices. Some very theoretical considerations will be followed by some guidelines for the application of the concepts to specific problems of radiological modelization in assessment of consequences. In general the starting point in the radioecological assessment of a biospheric scenario is an área source of radionuclides. These nuclides are flowing into and through the biosphere in a concentration that is a potential risk for human populations. The concept 'biosphere' has been traditionally understood as a synonime of 'place' and 'scenario' vhere the life developes. However this definition in order to be operative for modelizatimi purposes has to be made more precise, therefore ve will consi'Jei the biosphere as a complex assamblage of processes. More specifically they will be: - Material processes - Energetic processes - Informational processes These processes are, we assume, partially self-organized in a stable way (in the temporal scale of interest). This complex set of flows and forces are previous to any radiological scenario of human origin. The description of these flows is relevant to be able to model the dispersive properties of the environment and the actual dispersión of radionuclides in the scenario of interest. This formulation is cióse to the concept of 'biospheric system', a much more dynamic concept where we have not simply an 'ecosphere' or physical médium, but a system of biological processes that interact and co-evolve with its physical médium [Odum 1972] [Margalef 1977] [Lovelock, Margulis and other 1989]. The concept of biospheric system includes so: a) a physical médium, b) a set of processes and flows of energy, materials and information that define the selforganization of 'Life', and (c) the interactions between the living beings and the ecosystems they are dependent. The physical médium is a narrow band included in a layer 10 Km above and below the sea level. It includes matter in different phases: gaseous materials in the atmosphere; liquid materials in oceans,drainage waters in continents, underground waters...; crystalline and amorphous phases in rocks and soils; dissolved and resuspended phases in aquatic solutions , nuclides dissol-'ed j<> rocks, atmospheric aerosols,...; temporary plasma phases in lightnings and fires; and complex combinations of some of the phases above, like in the underground porous media. The life is a set of processes that (meta)stably self-organize in that physical médium. This self-organization implies a partial autonomy of the relations and interactions that defines to the system in relation to the fluctuations of the environment. Finally, the biospheric 'complex' system mantains its partial autonomy by means of a permanent thermodynamic interchange with other (meta)stable systems in its environment. These systems ('litosphere', 'atmosphere', 'hydrosphere', 'criosphere'...) are not separed from the biosphere by clear cut boundaries. The individual living beings are described in modern cybernetics as 'autopoietic systems'. That means that they are systems that produce their own existence generating continuosly their constituent elements and their own organization [Várela & Maturana 1974]. These individuáis are continuously subjected to disorganizing perturbations coming from the environment. The alfa, beta and gamma radiation ('ionizing radiation'), natural or artificial, is one of these sources of potentially disorganizing perturbations. A living being protects itself from the disorganization with a permanent reorganization that includes a routinary reparation of tissues, substitution of cells and cellular repair of damaged parts in the ADN. High levéis of ionizing radiation increases the probability of appearance of genetic damages that may not be repared with enough celerity in order to allow a correct celular replication. The coincidence of several damages like these in the same cell may start a cancerous process. The "dose" of radiation received by a tissue is an important concept in radiological protection. It is defined as the en°'cy intercepted per unit mass of tissue. The concept of dose malees possible to relate the quantity and distribution of the ionizing radiation received by a person with 3 the health risk through functions experimentally stablished. The risk includes mainly the
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