Predicting AspenPatch Growth Subject to Environmental Change

1
Predicting Aspen-Patch Growth Subject to
Environmental Change

• Kathryn E. Lenz
• Mathematics Statistics, U. Minnesota Duluth
• Engineering Mathematics, U. Bristol, 9/04 12/04
• Presented at Forest Research Seminar, 14/9/04
• Research Agency of the Forestry Commission
  Biometrics, Surveys Statistics Division, Alice
  Holt Lodge, Wrecclesham-Farnham

2
Outline

• Aspen FACE Experiment
• ECOPHYS Overview (modeling component of Aspen
  FACE)
• Aspen-Patch Simulation
• Consequences of Competition for Light
• Bud Dynamics, Green-leaf drop, and Branch Death
  Responsive to Light Competition Environmental
  Change
• Conclusions

3
Linking Modeling and Experimentation Aspen FACE

• FACE - Free-air CO2 Enrichment
• Large scale studies to assess the effects of
  greenhouse gasses on the natural environment
• Seven FACE installations in US, 15 worldwide

http//aspenface.mtu.edu
4
Aspen FACE Experiment CONTROL, ?O3, ?CO2 ,
?O3 ?CO2
5
Aspen FACE Experimental Design

• Four treatments, 3 replicates
• 2x CO2
• 2x O3
• 2x CO2 O3
• Control
• Measure the response of trees, soil system,
  insects and disease

6
ECOPHYS Process model for Populus

• Genus Populus
• P. tremuloides Trembling Aspen
• Most widespread and economically important
  species in eastern United States
• P. eugenei (deltoides x nigra) and other hybrid
  poplar clones
• Grown for fiber and energy production
• Populus has a long
• history of physiological
• and ecological research

2 yr old poplar plantation in Minnesota, USA
7
ECOPHYS Tree Simulation

• George Host, Kathryn Lenz, Harlan Stech
• NRRI UMD
• Multi-year growth of poplar and aspen clones
• Predict growth based on physiological factors and
  environment
• Time scales hour, day, year
• Inputs Temp, PPFD, RH, CO2, O3, Latitude,
  Genetics

8
Photosynthate Productivity Drives ECOPHYS Growth

• For each leaf each hour
• Calculate leaf-level sun and shade light
  interception
• Calculate photosynthetic rate variation of the
  Harley model with ozone effects on photosynthetic
  rate
• M. Martin, G. Host, K. Lenz, J. Isebrands,
  2001
• Compute photosynthate produced, accumulate and
  distributed daily.

9
Use and Transport of Photosynthate

• Psyn used for growth and maintenance.
• Leaf, internode, and root photosynthate
  transportation base on radiotracer data and
  source/sink relationships
• Y. Guan MS thesis 2002
• A. Laconite, J. Isebrands, G. Host 2002

10
0

• Intercepted Light
• Neighbors provide significant shade after 3
  yrs.
• Heterogeneous patch on Beowulf cluster, different
  computer processors devoted to different trees in
  patch. Trees communicate canopy architectures
  daily
• -- Harlan Stech,
• Matt Zagrabelny

11
Consequences of Light Competition

• Necessary for predicting long-term patterns of
  growth within a patch of trees.
• Individual tree genetics and environmental
  growth histories.
• These drive complex interactions among
  physiological processes at the leaf and branch
  levels.
• Hypothesis These interacting processes can be
• adequately simulated at hourly, daily, and
  yearly time steps, taken over multiple-years of
  simulated patch-growth.

12
Abundant Psyn ? GrowthInsufficient Psyn ?
Death

• Disruption or interruption of conditions
  necessary for psyn production ? low
  photosynthesis ? low carbon availability ?
  respiration needs unmet ? death
• Why do trees die? Agricultural Extension
  Service, U of Tennessee
• Branches generating insufficient psyn die and
  eventually fall off
• Tree Anatomy Erv Evans, NC State Univ.

13
Bud Dynamics

• Branchs bud-set timing predetermined in its
  bud.
• Each buds size (primordia) is determined by
  its parent leafs and branchs productivity, LPI,
  and genetics.
• Buds where leaves are present at fall senescence.
• If a bud is too small, then it dies.
• Small surviving buds ? short shoots.
• Largest bud(s) ? indeterminate branch(es).
• Intermediate size bud ? determinate branch
  with bud-set date corresponding to parent buds
  size.

14
Green-Leaf Drop

• A leaf drops if it cant meet its maintenance
  (respiration) needs.
• Each day for each leaf, compute weighted daily
  average over current and past 14 days of net psyn
  per unit leaf area
• Beyond a threshold, probability of dropping
  increases as weighted average decreases

15
Leaf Drop Algorithm

• For each leaf
• P(d) (net psyn(d))/LeafArea(d).
• w(t) Aeat, t 0, -1, -2, -14
• e.g. a 0.2, A 0.19
• Pwa(d)
• AP(d) Ae-aP(d-1) Ae-2aP(d-2)
  Ae-14aP(d-14))
• If Pwa(d) t (threshold)
• the leaf will not drop that day.

16
Fading memory weights for a 0.1, 0.2, 0.3
17
Leaf Drop Algorithm continued

• Uniform random ?
• 0 lt ? lt 1
• for variability due to unmodelled dynamics
• Leaf drops if
• Pwa(d) lt t and ? 1eK ,
• where K (Pwa(d) - t)d
• e.g. d 3, t 0.05
• If Pwa(d) lt t,
• probability leaf drops is 1eK.

K vs 1eK
18
Green-wood Branch Death

• Green-wood branch death is based on branch
  productivity.
• A branch withers if it doesnt produce enough
  psyn to maintain its attachment to older wood.
• Each day for each branch compute branchs rolling
  weighted average net psyn over current day and
  past 14 days.
• Probability of branch death increases as
• weighted average psyn decreases below
  threshold

19
Green-Wood Death Algorithm

• P(d) remaining psyn in a given branch after
  all transport, and respiration processes
• w(t) Aeat, where
• A(1e-ae-2a e-14a) 1
• Pwa(d)A(P(d)e-aP(d-1)e-2aP(d-2)
• e-14aP(d-14))
• If Pwa(d) t (threshold), branch will not die
  that day.

20
Green-Wood Death Algorithm - continued

• Uniform random ? such that 0 lt ? lt 1
• for variability due to unmodelled dynamics
• Branch dies if Pwa(d) lt t and ? 1eK
• where K (Pwa(d) - t)d
• e.g. d 5, t 0.03
• If Pwa(d) lt t,
• probability of branch death is 1eK

21
Older Wood Death

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

22
Architectural Influences of Bud Set Parameters, 5
Years of Growth

• Vary only the bud-set parameters t (threshold)
  and d (probability factor).
• Pictures generated by Kyle Roskoski
• t 0, d 0 t 0, d 20
• (turned off) (high probability
  factor)
• t 3, d 1 t 3, d 20
• (high threshold) (both high)

23
? 0, ? 0
? 0, ? 20
? 3, ? 20
? 3, ? 1
24
Predicting Aspen-Patch Growth Subject to
Environmental Change

• Genetics, environmental conditions, carbon
  allocation patterns, phenological processes,
  competition and other factors contribute to
  aspen-patch growth.
• These variables drive complex, multi-year dynamic
  feedbacks and interdependencies among
  phenological and growth processes.
• Simulations such as ECOPHYS can be developed to
  incorporate models of various physiological
  processes and their responses to environmental
  change.
• Simulation models can aid in understanding
  interactions among trees and the environment and
  how these interactions produce aspen-patch growth.

25
Acknowledgements

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