Combining 3D digitizing data and architectural modelling to simulate shoot growth and geometry in apple.

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Copyright

Combining 3D digitizing data and architectural

modelling to simulate shoot growth and geometry in

apple.

Benoit Pallas, Jérome Ngao, M. Saudreau, Evelyne Costes

To cite this version:

Benoit Pallas, Jérome Ngao, M. Saudreau, Evelyne Costes. Combining 3D digitizing data and ar-chitectural modelling to simulate shoot growth and geometry in apple.. X International Symposium on Modelling in Fruit Research and Orchard Management, Jun 2015, Montpellier, France. Acta Horticulturae, 1160, pp.28, 2015, �10.17660/ActaHortic.2017.1160.5�. �hal-01269059�

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Combining 3D digitizing data and

architectural modelling to simulate shoot

growth and geometry in apple.

ISHS Symposium, June 2015

B. Pallas

1

_{, J. Ngao}

2

_{, M. Saudreau}

2

_{, E. Costes}

1

_{INRA, UMR AGAP, Montpellier, France}

(3)

Objectives and context

Digitizing is precise but time consuming:

• Few trees measured

• But digitizing can be performed on trees in agronomic conditions

• Can be used as reference for model validation

Objectives.

• Use digitized trees at cycle n as input data and built tree at cycle n+x using statistical Markov models for terminal and axillary bud fates and apple tree geometrical characteristics

• Build a flexible tool for 3D reconstruction and evaluation of light interception of trees at any stage

Costes et al., 2008

Simulations of tree development (MappleT) form 1yo to x-y-old

based on Markov models for GU successions and branching

• Computational time can be long for running several consecutive years

• Do not integrate the agronomic conditions (especially pruning) • Difficulty to compare the random trees generated with real trees.

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Modelling description – digitizing data as input files

(xini,yini,zini)

(xend,yend,zend)

x y z Vegetative shoot Bourse shoot 2

• Simplified digitizing methodology.

(e.g. Massonet et al. 2008)

- Spatial coordinates of beginning and end of 1 year old

shoot.

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L LF M MF S SF D 0.23 0.26 0.62 0.26 0.51 0.15

Medium shoot Floral

Medium

Modelling description – simulation of growing unit succession

(xini,yini,zini)

(xend,yend,zend)

x

y

z

Vegetative shoot Bourse shoot

• Discretization of GU types

based on length

(short,

medium, long).

• First order

transition

probabilities after vegetative

growth units.

• Second order

transition

probabilities after reproductive

growth units. (fruit number is then computed using a

fruit set parameter)

Representation of the transition probability matrix (from Costes and Guédon, 2012).

L : long M : medium S: short F : floral D: dead

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F

Modelling description – simulation of branching pattern

M D D D S S S S D D, D D D S S S S S, D D D D S S S S D, D D F F F F, D D D D F F F F, D D D D F F F F, D D D S D S S D S S, D D D Generation of a collection of random sequences Observation distribution Occupation distribution Transition frequencies

(xini,yini,zini)

(xend,yend,zend)

x

y

z

• Hidden semi Markov chain formalisms

(from Guédon et al., 2001;

Costes and Guédon, 2002; Costes et al. 2008)

•

Random choice of a sequence corresponding to the length of the GU

• GU internode number computed from allometric relationships.

D D S S D F F D S D

P

robab

ility

Latent Short Floral Latent Short Floral Latent Short Floral

State 0 State 1 State 2

0 2 4 6 8 10 12 14 0.00 0.05 0.10 0.15 0.20 0.25 Phytomer number 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 P robab ility 0.0 0.2 0.4 0.6 0.8 1.0

P

robab

ility

0 0.62 1 2 0.26 0.37 3 1 1 SEMI-MARKOV CHAIN 4

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(xini,yini,zini)

(xend,yend,zend)

x

y

z

Modelling description – geometrical features

α + ε α + ε α + ε β + ε β + ε

•

Shoot length distribution to

determine shoot length according to shoot type.

•

Shoot geometry :

- Branching angle for branches and after an inflorescence (mean value and standard deviation)

- no shoot bending

•

Internode profile to locate all the branches along the 1 year old branch 50-85 0 10 20 30 0.0 0.1 0.2 0.3 0.4 _Small Medium Long P robab ility GU length (cm) Phytomer rank 0 5 10 15 20 Int er no de l en gt h (c m ) 0 2 4 6 8 1/2 1 exp( ( ) / ) MaxIn In rank In sIn    

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(xini,yini,zini)

(xend,yend,zend)

x

y

z

Modelling description – simulation of leaf distribution along shoots

7

•

Allometric relationships at shoot scale based on shoot length L (short, medium, long) and type, and at leaf scale

(Sonohat et al., 2006).

• At shoot scale: total leaf surface area (TSA), number of leaves (LN), internode length (IN) distribution and leaf area distribution along shoot.

• At leaf scale: length, width, surface area and distributions of leaf rolling angle and leaf inclination angle.

 Single leaf surface area (LS)

LS = TSA / LN

 Single Leaf length (LL) and width (LW)

LL = f(LS) LS = f(LL)

 Leaf angles: Measurements of distributions of leaf rolling angle and leaf inclination angle by shoot type

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Model calibration

•

Model calibrated

on the ‘Jubilé ‘cultivar (9 trees),

data collected from 2007 until 2013.

•

Growth units succesion matrix

estimated on sequences recorded on second and third order

branches. (140 shoots)

•Geometrical features

(branching angles, allometric relationships, length distribution) were

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Type 1 (51.8%) : B B B B S B S S S Type 2 (30.9%) : B B B B F B F F F Type 3 (17.4%) : S B S S S

Model calibration

9

•

Calibration of the hidden semi Markov model.

• Performed on around 100 branching sequences

collected in 2013 .

• Model estimation with openalea plateform. • A unique model for each growth unit was used.

• Simple patterns were observed.

Observation distribution Occupation distribution Transition frequencies P robab ility

P

robab

ility

SEMI-MARKOV CHAIN 0 0.62 1 2 0.17 0.37 3 1 1 0.83

• Branching pattern only adapted for « small size GU » (old tree).

Zone 1 Zone 1 Zone 2 Zone 2 Zone 3 B : latent bud S: short F: floral

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Model simulation and validation

Input tree

Simulation of tree growth « Rebuild tree model »

Tree 3D visualization « Vegestar » Simulated trees

Year N

Year N+1

• 2 trees digitized in 2013 and 2014 (8 year-old).

• 2013 data were used as input files and simulations(15 random trees) were compared to 2014 data.

• A modeling framework coupling the ‘simulation’ model, a 3D visualization software and a light interception model (RATP, Sinoquet et al. 2001) was built.

• Validations were performed on shoot demography, leaf area distribution and light interception.

• Except for the probability of flowering occurrence (ON, OFF trees), all the parameters were identical for the two trees.

Simulation of light interception

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Model validation, shoot demography and leaf area (tree 1)

Leaf area (m²) GU number Observed 3.39 439 Simulated (n = 15) 3.17 +/- 0.28 371 +/- 21.3 Axis length (cm) 0 5 10 15 20 25 Fr eq uenc ies 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Obseved values Simulated values Small shoots Medium shoots Large shoots

Long Medium Small Inflo. Fruits

Types C ounts 0 50 100 150 200 250 Simulated values Observed values

• Observed tree

• Simulated trees

Random seed 602

Random seed 601

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Model validation, light interception inside the canopy (tree 1)

• Observed tree

STAR at the tree scale Observed 0.350 Simulated n = 15 0.349 +/- 0.011 Random seed 602 Random seed 601

• Simulated trees

0 0.05 0.1 0.15 0.2 0.25 0.3 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 F re q u e n c y Simulated trees (15) Obsevred tree

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Model validation, shoot demography and leaf area (tree 2)

• Observed tree

• Simulated trees

Leaf area (m²) GU number Observed 4.42 451 Simulated (n = 15) 4.60 +/- 0.18 492.1 +/- 26.2 Random seed 600 Random seed 605 Axis length (cm) 0 5 10 15 20 25 Fr eq uencies 0.0 0.1 0.2 0.3 0.4 0.5 Obseved values Simulated values Small shoots Medium shoots Large shoots

Long Medium Small Inflo. Fruits Types C ount s 0 50 100 150 200 Simulated values Observed values 11

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Model validation, light interception inside the canopy (tree 1)

• Observed tree

• Simulated trees

STAR at the tree scale Observed 0.386 Simulated n = 15 0.332 +/- 0.008 Random seed 600 Random seed 605 0 0.05 0.1 0.15 0.2 0.25 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 F re q u e n c y Simulated trees (15) Obsevred tree

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End 2013 (observed tree) 2014 (simulated tree) 2015 (simulated tree) 2016 (simulated tree) 15

Multi-years simulations

•

The model is able to simulate tree growth over years.

• 2015 digitizing data are needed to validate the model on a 2 years time step • The tree response to pruning should be integrated.

• A branch bending submodel (Costes et al. 2008) should be integrated to simulate branch geometry over years

Combining 3D digitizing data and architectural modelling to simulate shoot growth and geometry in apple.

Combining 3D digitizing data and architectural

modelling to simulate shoot growth and geometry in

apple.

Combining 3D digitizing data and

architectural modelling to simulate shoot

growth and geometry in apple.

B. Pallas

, J. Ngao

, M. Saudreau

, E. Costes

INRA, UMR AGAP, Montpellier, France

Objectives and context

Digitizing is precise but time consuming:

Objectives.

Simulations of tree development (MappleT) form 1yo to x-y-old

Modelling description – digitizing data as input files

• Simplified digitizing methodology.

- Spatial coordinates of beginning and end of 1 year old

shoot.

Modelling description – simulation of growing unit succession

• Discretization of GU types

based on length

(short,

medium, long).

• First order

transition

probabilities after vegetative

growth units.

• Second order

transition

probabilities after reproductive

growth units. (fruit number is then computed using a

fruit set parameter)

Modelling description – simulation of branching pattern

• Hidden semi Markov chain formalisms

•

Modelling description – geometrical features

•

•

•

Modelling description – simulation of leaf distribution along shoots

•

Model calibration

Model calibrated

on the ‘Jubilé ‘cultivar (9 trees),

data collected from 2007 until 2013.

Growth units succesion matrix

estimated on sequences recorded on second and third order

branches. (140 shoots)

•Geometrical features

(branching angles, allometric relationships, length distribution) were

Model calibration

Calibration of the hidden semi Markov model.

Model simulation and validation

Year N

Year N+1

Model validation, shoot demography and leaf area (tree 1)

• Observed tree

• Simulated trees

Model validation, light interception inside the canopy (tree 1)

• Observed tree

• Simulated trees

Model validation, shoot demography and leaf area (tree 2)

• Observed tree

• Simulated trees

Model validation, light interception inside the canopy (tree 1)

• Observed tree

• Simulated trees

Multi-years simulations

The model is able to simulate tree growth over years.

Conclusions and perspectives

Development of a new modelling approach

• Including and adapting already used statiscal models

• Linked with a light interception model

Allowing the valorisation of time consuming digitizing data.

First calibration of the model

• On Jubilé cultivar (old tree).

• At different scales (whole tree, voxels)

Limits and forthcoming works.

_{, J. Ngao}

_{, M. Saudreau}

_{, E. Costes}

_{INRA, UMR AGAP, Montpellier, France}