Annikki Mkel

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

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MaDaMe Programme

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

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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

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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/

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This presentation

• Research problem scales of structure and
  function
• Hierarchical systems
• Available models
• Work in progress
• Expectations of this meeting

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Scales of structure and function
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Months m2
Seconds cm2
Years ha
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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, ONeill et al.
1986 Reynolds et al. 1993, Robinson and Ek 2001
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Modelling hierarchical systems
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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/facul
ty/Kolasa/Biology/faculty/Kolasa/images/levels.jpg
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Properties
Process rates define levels and holons
frequent
infrequent
slow
constant
intermediate
dynamic
fast
effective mean
More http//www.science.mcmaster.ca/Biology/facul
ty/Kolasa/Biology/faculty/Kolasa/images/levels.jpg
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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

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Conclusion Model Structure


Environmental constraints
Structural constraints
L1
Not top-down!
Not bottom-up!
Stand growth
Outputs
L
Inputs
L-1
Structure and metabolism
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Available models
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LIGNUM
Photo- synthesis
ACROBAS
Shading
FEF
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Tree and stand growth
LIGNUM
aCrobas
FEF
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Photosynthesis
Shoot photosynthesis Stomatal conductance Function
of driving variables (Hari et al.)
Biochemistry and leaf fine structure Principles
and mechanisms (Hari and Juurola)
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Shading
Shoot-shoot interactions, tree-tree interactions
Poisson canopy Oker-Blom et al. 1989
Shading by each shoot LIGNUM
Shading by voxels LIGNUM
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Work in progress
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• Individual model development mathematical
  methods
• (demos of LIGNUM and aCrobas, Harri Hakulas
  presentation)

• Aggregation, two-way linkages between models
• structure
• functioning

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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
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Case studies on scaling

• (1) Linking LIGNUM and CROBAS through structural
  parameters (Risto Sievänen)

(2) From biochemistry to shoot photosynthesis
(Pepe Hari)
(3) Estimation of annual productivity parameters
using finer scale models (Janne Karimäki)
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Expectations
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Expectations

• Exchange of ideas
• Criticisms
• Future collaboration
• Stimulating discussions

Welcome to all!