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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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slide1

Hierarchical treatment of multi-scale processes in tree and stand modelsIntroduction and welcome

Annikki Mäkelä

University of Helsinki

madame programme
MaDaMe Programme
  • The Academy of Finland
  • 2000-2003
  • Mathematics, Data, Methods
  • Purpose: application of mathematical and numerical methods to sciences
this project background
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
partners
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/

slide5

This presentation

Research problem: scales of structure and function

Hierarchical systems

Available models

Work in progress

Expectations of this meeting

slide7

Months

m2

Seconds

cm2

Years

ha

slide8

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
slide10

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

slide11

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

slide12

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”
slide13

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

slide15

LIGNUM

Photo-

synthesis

ACROBAS

FEF

Shading

tree and stand growth
Tree and stand growth

LIGNUM

aCrobas

FEF

photosynthesis
Photosynthesis

Shoot photosynthesis

Stomatal conductance

Function of driving variables

(Hari et al.)

Biochemistry and leaf fine structure

Principles and mechanisms

(Hari and Juurola)

shading
Shading

Shoot-shoot interactions, tree-tree interactions

Poisson canopy

Oker-Blom et al. 1989

Shading by each shoot

LIGNUM

Shading by voxels

LIGNUM

slide20

Individual model development & mathematical methods

    • (demos of LIGNUM and aCrobas, Harri Hakula’s presentation)
  • Aggregation, two-way linkages between models
    • structure
    • functioning
slide21

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

case studies on scaling
(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)

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

Welcome to all!