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Annikki Mäkelä University of Helsinki

Hierarchical treatment of multi-scale processes in tree and stand models Introduction and welcome Annikki Mäkelä University of Helsinki MaDaMe Programme The Academy of Finland 2000-2003 Ma thematics, Da ta, Me thods Purpose: application of mathematical and numerical methods to sciences

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Annikki Mäkelä University of Helsinki

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  1. Hierarchical treatment of multi-scale processes in tree and stand modelsIntroduction and welcome Annikki Mäkelä University of Helsinki

  2. MaDaMe Programme • The Academy of Finland • 2000-2003 • Mathematics, Data, Methods • Purpose: application of mathematical and numerical methods to sciences

  3. This project: Background • Models of tree growth and physiology at different scales since late 70s • Empirical work, data, mathematical methods, computing • MaDaMe: an opportunity to bring the work together, consider the theoretical basis of scaling, aggregation, and hierachies

  4. Partners University of Helsinki, Dept. Forest Ecology (Annikki Mäkelä, Eero Nikinmaa, Pertti Hari, Tero Kokkila, Janne Karimäki, Sakari Ilomäki) Helsinki Univ. of Technology, Dept. Mathematics (Olavi Nevanlinna, Harri Hakula, Lasse Palovaara) Metla, Vantaa Research Centre (Risto Sievänen, Jari Perttunen, Mika Lehtonen) http://www.metla.fi/hanke/3282/madame/

  5. This presentation Research problem: scales of structure and function Hierarchical systems Available models Work in progress Expectations of this meeting

  6. Scales of structure and function

  7. Months m2 Seconds cm2 Years ha

  8. Rationale • Forest ecosystem: a hierarchical entity • Multitude of temporal and spatial scales • Moving from one scale to another needed • No generally accepted method has emerged: • semi-empirical components for long-term averages • mixed-scale approach • hierarchy theory, modular systems • Allen and Starr 1982, O’Neill et al. 1986 • Reynolds et al. 1993, Robinson and Ek 2001

  9. Modelling hierarchical systems

  10. Definitions • An organization whose components are arranged in levels from a top level down to a bottom level. (Arbib) top intermediate bottom holons levels More: http://www.science.mcmaster.ca/Biology/faculty/Kolasa/Biology/faculty/Kolasa/images/levels.jpg

  11. Properties • Process rates define levels and holons frequent infrequent slow constant intermediate dynamic fast effective mean More: http://www.science.mcmaster.ca/Biology/faculty/Kolasa/Biology/faculty/Kolasa/images/levels.jpg

  12. Implications Loose vertical coupling relative isolation of objects Loose horizontal coupling • “The old imagery of the natural world having everything connected with everything else is shortsighted. It is the relative disconnection that constitutes the organisation of the system”

  13. Conclusion: Model Structure Structural constraints Environmental constraints L+1 Not top-down! Not bottom-up! Stand growth Outputs L Inputs L-1 Structure and metabolism

  14. Available models

  15. LIGNUM Photo- synthesis ACROBAS FEF Shading

  16. Tree and stand growth LIGNUM aCrobas FEF

  17. Photosynthesis Shoot photosynthesis Stomatal conductance Function of driving variables (Hari et al.) Biochemistry and leaf fine structure Principles and mechanisms (Hari and Juurola)

  18. Shading Shoot-shoot interactions, tree-tree interactions Poisson canopy Oker-Blom et al. 1989 Shading by each shoot LIGNUM Shading by voxels LIGNUM

  19. Work in progress

  20. Individual model development & mathematical methods • (demos of LIGNUM and aCrobas, Harri Hakula’s presentation) • Aggregation, two-way linkages between models • structure • functioning

  21. Aggregation based on hierarchy theory • Including finer scale phenomena = introducing variation in constant parameters due to driving variables and state variables • Modular systems • Summary models Root activity: Nissinen and Hari 1998 Stem structure: Mäkelä et al. 1997 Photosynthesis: Mäkelä 1990

  22. (1) Linking LIGNUM and CROBAS through structural parameters (Risto Sievänen) Case studies on scaling (2) From biochemistry to shoot photosynthesis (Pepe Hari) (3) Estimation of annual productivity parameters using finer scale models (Janne Karimäki)

  23. Expectations

  24. Expectations • Exchange of ideas • Criticisms • Future collaboration • Stimulating discussions Welcome to all!

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