FUNCTIONAL STRUCTURAL TREE MODELLING relating environment with growth and wood.
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1 FUNCTIONAL STRUCTURAL TREE MODELLING relating environment with growth and wood. Dr. M. Paulina Fernández Depto. of Ecosystems and Environment Faculty of Agronomy and Forest Engineering Pontificia Universidad Católica de Chile September 2015 Oregon State University
2 If we look at the world
3 If we compare Chile with USA 17 o to 56 o latitude south 72 to 73 o longitude west It is 4270 km long, but just 190 km width in average
4 Chilean landscape, forests, production North of Chile: Desert, volcanoes, high andean plateau (altiplano... Over 5000 masl), saltlakes, gold and cupper mines. Some desertic forests
5 Chilean landscape, forests, production North of Chile: Desert, volcanoes, high andean plateau (altiplano... Over 5000 masl), saltlakes, gold and cupper mines. Some desertic forests
6 Chilean landscape, forests, production Central Chile: Agriculture (famous wineyards, fruits and grain production) mountains (ski centers), main cities, sea... Mediterranean forests.
7 Chilean landscape, forests, production Central Chile: Agriculture (famous wineyards, fruits and grain production) mountains (ski centers), main cities, sea... Mediterranean forests.
8 Chilean landscape, forests, production Central Chile: Agriculture (famous wineyards, fruits and grain production) mountains (ski centers), main cities, sea... Mediterranean forests.
9 Chilean landscape, forests, production South of Chile: lakes, decidious forests and evergreen rainforest, vulcanoes, rivers (fishing, hunting), agriculture and forestry production
10 Chilean landscape, forests, production South of Chile: lakes, decidious forests and evergreen rainforest, vulcanoes, rivers (fishing, hunting), agriculture and forestry production
11 Chilean landscape, forests, production South of Chile: lakes, decidious forests and evergreen rainforest, vulcanoes, rivers (fishing, hunting), agriculture and forestry production
12 Chilean landscape, forests, production South of Chile: lakes, decidious forests and evergreen rainforest, vulcanoes, rivers (fishing, hunting), agriculture and forestry production Pinus radiata from California to Chile
13 Chilean landscape, forests, production South of Chile: lakes, decidious forests and evergreen rainforest, vulcanoes, rivers (fishing, hunting), agriculture and forestry production million ha Radiata pine plantations (68% of Chilean plantations)
14 Chilean landscape, forests, production South of Chile: lakes, decidious forests and evergreen rainforest, vulcanoes, rivers (fishing, hunting), agriculture and forestry production Chile is the 9th producer of pulp in the world, the 13th producer of sawn wood, with a fundamental participation of Radiata pine in our economy
15 Chilean landscape, forests, production Patagonia: open landscape, wildlife, decidous and evergreen forests...end of the world
16 Chilean landscape, forests, production Patagonia: open landscape, wildlife, decidous and evergreen forests...end of the world
17 Chilean landscape, forests, production Patagonia: open landscape, wildlife, decidous and evergreen forests...end of the world
18 Comercial distribution of the species Comercial distribution of the species: 33 to 39.5 o lat south Equivalent to a distribution from a bit north of San Diego, California, to a bit north of Ukiah, California
19 Total range of the species Total distribution of the species: 31.6 (Illapel) to 54.8 o lat south in Ushuaia (Argentina) Equivalent to a distribution from Baja California in Mexico to the Gulf of Alaska
20 Functional structural plant modelling of Pinus radiata
21 Radiata pine architecture Morphology of Pinus radiata a b c d e f g h i j Key questions: When to start a new growth unit with a cluster of branches? When to develope reproductive structures How many branches are normally in a cluster? When occurs the phase change of the species
22 Morphology of Pinus radiata
23 Morphology of Pinus radiata
24 Site 1 Los Alamos Site index years old 21.7 m height Site 2 La Granja Site index years old 17.5 m height Morphology of Pinus radiata Nº growth untis per annual shoot Juvenile stage Mature stage Ontogenetical age Nº growth units per annual shoot Growth unit length (cm) Annual shoot length (cm) (a) 89.8 branches 13.5 growth units 7.3 m Length (cm) Nº growth untis per annual shoot Ontogenetical age Juvenile stage Mature stage (b) Nº growth units per annual shoot Growth unit length (cm) Annual shoot length (cm) 89.3 branches 14.8 growth units 8.0 m Length (cm)
25 Phase change and wood density in P. radiata?
26 The model main concept Energy Operative unit Operational Rules (Biosynthesis and development rules) Internal product (Net biomass and local architecture) Supplies (CO 2, O 2 ) Factory Tree in t =i System restrictions (biomass balance, distribution and plant allometry) Growth results files t = t+1 Supplies (Nutrients, Water) Final product Virtual sawing
27 The tree as a system ne am am am ca Vegetative growth unit ne st ca Growth unit with male strobili ne ca co Growth unit with female strobili Growth unit
28 OPERATIONA L RULES OF THE BUD Y Y pr pr Y Y t F Y C : : 5 t4 t+ 1 t+ 1 t +1
29 Y Y Y F ij(2) F ij(2) F ij(2) F F ij(2) ij(2) FF ij(1) F ij(1) ij(1) F ij(1) F ij(1) pr Y F Y : 5 t t+ 1 t+ 1 t+n+1 t t+1 t
30 Model structure and associated research
31 Module of environmental resources 2. MODULE OF ENVIRONMENTAL RESOURCES RADIATION as a driving factor in photosynthesis RADIATION as a driving factor in photosynthesis
32 Module of environmental resources 2. MODULE OF ENVIRONMENTAL RESOURCES RADIATION as a driving factor in photosynthesis ET/ETx 1 TEMPERATURE 0.8 ET/ETx GOOD SITE, SITE INDEX 34 ET/ETx ET/ETx WATER BALANCE expressed as ET/ETmax 0.8 WATER BALANCE Months Months Months REGULAR SITE, SITE INDEX Months expressed as ET/ETmax
33 Module of environmental resources if ET ETx < 0.2 or t max > omega or t min < Good site (red line) Regular site (black line) tmd t fi fi then cron = 0 else cron = 6.75 omega fi 2 tmd t fi omega fi 3 dday 60 t nday t
34 GOOD SITE, SITE INDEX 34, Total accumulation in 14 years = crons REGULAR SITE, SITE INDEX 27, Total accumulation in 14 years = crons RS/GS = 78%
35 Site 1 Los Alamos Site index years old 21.7 m height Site 2 La Granja Site index years old 17.5 m height Morphology of Pinus radiata Nº growth untis per annual shoot Juvenile stage Mature stage Ontogenetical age Nº growth units per annual shoot Growth unit length (cm) Annual shoot length (cm) (a) 89.8 branches 13.5 growth units 7.3 m Length (cm) Nº growth untis per annual shoot Ontogenetical age Juvenile stage Mature stage (b) Nº growth units per annual shoot Growth unit length (cm) Annual shoot length (cm) 89.3 branches 14.8 growth units 8.0 m Length (cm)
36 Model of balance at the subsystem level Note: The internal balance b ij (photosynthesis Respiration) of each level of branches is evaluated. Source and sink subsystems are identified. The corresponding balances at order two branches and at total tree level (bal t ) are calculated. There can be branches that are sink or source.
37 Compensation sub-model: death of branches If bal t < 0 (+) - (-) Deliver reserves to the system Eliminate branches until the balance is restore to zero value (Note: it mimics the death of branches normally at lower parts of the crown) (+) (+) (+) (-) (-) (-) (+) btot= b s b s = (ph ij -r ij ) (-)
38 Sub-model of biomass distribution bal t > 0 New biomass bal t > 0 New biomass New biomass Stem Branches Foliage Roots Stem Branches Foliage Roots pstem pbranch pfol proot The model assumes an allometric relation between LIVING or active main compartments (stem, branches, foliage, roots). If there is a nonequilibrated state, the destination of biomass (1) restore the balance and (2) generates and extra growth. The real allometry should be between respiring, active conducting structures and photosynthetic structures. Stem Branches Foliage Roots
39 Sub-model of structural biomass distribution at internode level balstem = balstemelong + Y t+1 F ij(2) F ij(1) balstemdiam Y t+1 F ij(2) F ij(1) Main questions: How much biomass to deliver to each growth unit so as a whole they form the wood mantle Which is the new conducting area necessary to satisfy transport requirements What is the density of the new wood matter
40 Assumptions: Sub-model of ring width and wood density aflux 1j aw 1j s 1 bf 1 bf 2 Sap flux s 3 (1) (2) s 2 s 4 Aflux = A Aw = ω Bf t t t 1 ω2 t aflux 2j aw2j There is an allometric relation between leaf biomass (water demanding structure) and the cross sectional area that contributes to that biomass (Mäkela, 2002; Fernández 2007) The density of wood is negatively correlated with the conductive property of the cross sectional area (Santiago et al., 2004; Bucci et al. 2004) Comment: the knowledge about hydraulic architecture would improve the model s performance
41 Allometry studies During 12 month foliage expansion, stem elongation, twigs elongation and wood ring formation were followed in a Pinus radiata plantation. Fondecyt project : Functional-structural modeling of wood density ant its variations intra and inter growth rings in Radiata Pine (Pinus radiata D. Don).
42 Ring sampling and analysis Microcores were harvested every 15 days, and later on every 1 month In collaboration with Iván Lillo, Computer Sciences Departament, PUC X-ray MRI
43 Three trees per month were felled, complete packed and transported for biomass measurement and discs sampling. E0 E1 New ring related with E0 Previous rings related with E1
44
45 Some relationships to considere in the model
46 Allometries Growth unit cross section area (cm- 2 ) a Above foliar biomass (g) b
47 Allometries
48 Specific Leaf Area (cm-2 per g) Needles density (g cm-3) Needles age Needles length (cm) Newly formed needles One year old needles
49 Ring width (cm) Differences (estimated real) (cm) EFECT OF USING THE WRONG ALOMETRIC RELATIONSHIP The importance of sampling season Coefficient values (Foliage biomass / cross section ratio) Coefficient values (Foliage biomass / cross section ratio) Real value new ring = 0.59 cm
50 Model testing Basal diameter and height evolution for Los Alamos.
51 Model testing Length of the order 1 growth units for Los Alamos. Growth units length (cm) in Los Alamos (simulation and validation data) Simulation database Validation database Mean Stdev Sample size Frequency Bin More % % 80.00% 60.00% 40.00% 20.00% 0.00% Simulated Lower and upper confident interval (95%) [ ] [ ] % Minimum and maximum [ ] [14 166] Frequency % 80.00% 60.00% 40.00% 20.00% Validation No significant differences between the averages Bin More 0.00%
52 Model testing Basal diameter of order 2 branches for Los Alamos. Basal diameter of branches of order 2 Simulation database Validation database Mean Stdev Frequency % % 80.00% 60.00% 40.00% 20.00% Simulated Sample size % Lower and upper confident interval (95%) [ ] [ ] Minimum and maximum [ ] [0.1 10] The model overestimates the basal diameter of order 2 branches, and consequently the size of knots. Frequency % % 80.00% 60.00% 40.00% 20.00% 0.00% Validation
53 Model testing Growth evolution in 3D (crown architecture). Note: Some 3D images of Pinus radiata generated by the model, and corresponding real structures. Needles are not represented because of computer memory comsumption.
54
55 MODEL TESTING 1800 NHA 400 NHA 13.3 cm 16.5 cm
56 Some final products WOOD PRODUCTS
57
58 Thank you!
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