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 ↑O3Today&future • 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 < (total leaf area)/ (land area) < 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 < 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(1+e-a+ … +e-14a) = 1 • Pwa(d)=A(P(d)+e-aP(d-1)+…+e-14aP(d-14)) • Leaf drops if Pwa(d) < t (threshold) and ξ ≤ 1–eK (random 0 < ξ < 1), where K = (Pwa(d) - t)·d Probability this leaf drops this day is 1–eK

18. Interpretation/abstraction of Green-wood Branch Death • Green-wood branch death is based on branch psyn productivity. • A branch withers if it doesn’t 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 day’s psyn in the branch after transport, growth, & maintenance processes • Choose a, then A such that A(1+e-a+ … +e-19a) = 1 • Pwa(d)=A(P(d)+e-aP(d-1)+ … +e-19aP(d-19)) • Branch dies if Pwa(d)< t (threshold) and ξ ≤ 1–eK (random 0 < ξ < 1), where K = (Pwa(d) - t)·d Probability this branch dies this day is 1–eK

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 bud’s “size” (primordia) determined by parent leaf’s & branch’s 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. Branch’s 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.