Simulating Aspen Growth Subject to Environmental Change

1
Simulating Aspen Growth Subject to
Environmental Change

• Kathryn E. Lenz
• Mathematics Statistics, Univ. Minnesota Duluth
• Engineering Mathematics, Univ. Bristol, 9/04
  12/04
• Presented at Engineering Mathematics BCANM
  Seminar,
• University of Bristol, 15/10/04

2
Environmental Change Forests

• Tropospheric ?Temp ?CO2 ?O3 Todayfuture
• Boreal forest in Northern US and Canada, mostly
  wild lands
• Aspen major forest tree,
• Aspen come back first after fire or
  blow-down,
• economically important

3
CO2 Heater Fertilizer

• ?CO2 has a greenhouse effect
• Today forests help regulate CO2
• Q Will ?CO2 increase forest growth ?
• Q Will ?Temp stress cause forests to add
• to ?CO2 problem ?

4
?O3 is BAD

• ?O3 widespread toxic to plants,
• aspen especially sensitive
• ?O3 decreases aspen growth changes
• aspen populations
• Q Will ?CO2 fertilization cancel out bad ?O3 ?

5
Free-air CO2 Enrichment FACE

• Large scale studies to assess the effects of
  greenhouse gases on the natural environment
• Currently 7 FACE installations in US, 15
  worldwide

http//aspenface.mtu.edu
6
Aspen FACE Experiment CONTROL, ?O3, ?CO2 ,
?O3 ?CO2
7
Goal Assess ?CO2 and ?O3 induced interactions in
aspen ecosystems
8
ECOPHYSEcological Physiological Simulation

• Test physiological and growth response hypotheses
• H1 ? rate of growth due to ?CO2 diminishes
  with time
• H2 July weather last summer determines ?CO2
  induced growth-rate
• response this summer.
• Predict growth responses to varying environment
• Central growth-process is photosynthesis
• There are not too many leaves in an aspen patch
• 3 lt (total leaf area)/ (land area) lt 4

9
ECOPHYS Tree Patch Simulation

• George Host, NRRI,
• original ECOPHYS, tree physiology forestry
  connections
• Harlan Stech students scientific computation,
  especially shading visualization
• Kathryn students system component modeling,
  cross-discipline interpretation coordination

10
Where our modelling fits in

• Laboratory, green house, open-top chamber, and
  field (Aspen FACE) experiments
• Interpretation/ abstraction/ synthesis
• ECOPHYS tree patch simulation, (large,
  finite-dimensional, nonautonomous, and
  stochastic)
• Interpretation/ abstraction/ synthesis
• More stream-lined mathematical models ?

11
Photosynthate Productivity Drives ECOPHYS Growth

• Inputs hourly PPFD, temp, RH, CO2, O3,
• Initial conditions Latitude, Genetics,
  initial tree
• Hourly leaf-level
• light interception fL(sun direction, canopy,
  PPFD)
• photosynthetic rate fP(fL, temp, RH, CO2,
  O3, leaf age)
• Daily distribute photosynthate to grow
  maintain leaves, branches, trunk, roots, and
  store
• Yearly spring leaf flush, summer growth, bud
  set, fall growth and storage

12
Povray 6 year old tree canopy
13
6 year-old canopy 2 meter spacing
14
50 cm spacing trees not responding to
competition for light
15
Consequences of Light Competition

• First-order consequences green-leaf and branch
  growth death, bud locations sizes, bud-set
  timing
• Necessary for simulating/predicting multi-year
  patterns of growth death within a patch.
• Genetics, environmental growth histories
  ?
• Interactions among leaf branch processes
  ?
• Leaf, branch, bud growth/mortality ?
  tree
• architecture
• Hypothesis Our modelling is sufficient to
  capture essentials of competition within aspen
  patch

16
Interpretation/abstraction of Green-Leaf Drop
Biology

• Mature leaf has plenty of psyn ? maintain self,
  export, reserves
• Just enough psyn ? maintain self
• Psyn reserves lt threshold ? drop off

17
Leaf Drop Algorithm

• For each leaf on each day d,
• P(d) (net psyn(d))/LeafArea(d).
• Choose a, then A so that A(1e-a e-14a) 1
• Pwa(d)A(P(d)e-aP(d-1)e-14aP(d-14))
• Leaf drops if Pwa(d) lt t (threshold) and ?
  1eK
• (random 0 lt ? lt 1), where K (Pwa(d) - t)d
• Probability this leaf drops this day is 1eK

18
Interpretation/abstraction of Green-wood Branch
Death

• Green-wood branch death is based on branch psyn
  productivity.
• A branch withers if it doesnt produce enough
  psyn to maintain its attachment to older wood.

19
Green-Wood Death Algorithm

• For each green branch each day d,
• P(d) net days psyn in the branch after
• transport, growth, maintenance
  processes
• Choose a, then A such that A(1e-a e-19a)
  1
• Pwa(d)A(P(d)e-aP(d-1) e-19aP(d-19))
• Branch dies if Pwa(d)lt t (threshold) and ? 1eK
  
• (random 0 lt ? lt 1), where K (Pwa(d) - t)d
• Probability this branch dies this day is 1eK

20
Older Wood Death

• Older wood dies incrementally as supporting
  leaves and green wood die.
• Finally, a tree dies when all its branches are
  dead.

21
Interpretation/abstraction Bud Dynamics

• branches leaves ? buds ? branches leaves
• Each buds size (primordia) determined by
  parent leafs branchs productivity, genetics
  and location of branch on tree.
• Buds form where leaves are present in the fall.
• Too-small buds ? die
• Small live buds ? short shoots
• Largest buds ? long branches
• Intermediate size buds ? intermediate length
  branches

22
Branchs bud-set timing model

• 1st part Size of bud which issued branch
  determines nominal bud-set date.
• 2nd part Current-season stress causes bud set
  prior to nominal date. Intermediate stage of
  green-branch death algorithm.

23
Architectural Influences of Bud Set Parameters, 5
Years of Growth

• Leave out 1st part of bud set model.
• In 2nd part vary the threshold t and probability
  factor d .
• Pictures generated by Kyle Roskoski
• t , d 0 t 0, d 20
• (turned off) (high probability
  factor)
• t 3, d 1 t 3, d 20
• (high threshold) (threshold,
  high probability)

24
? 0, ? 0
? 0, ? 20
? 3, ? 20
? 3, ? 1
25
Predicting Aspen-Patch Growth

• Genetics, environmental conditions, physiological
  processes (cellular organ-levels), and
  competition for resources contribute to
  aspen-patch growth dynamics.
• Simulations such as ECOPHYS can incorporate
  models of key physiological and growth processes,
  architectural features and responses to
  competition environment.
• Goal help identify understand key interactions
  among trees environment for predicting future
  aspen-patch growth and inform policy makers.

26
Acknowledgements

• Funded by the Northern Global Change Program of
  the USDA Forest Service Northeastern Forest
  Experiment Station and the National Science
  Foundation.