biocro: an r package for crop simulation and...

Background Models Process-based model BioCro Photosynthesis Optimizing Carbon Allocation Methods Results

BioCro: an R package for Crop Simulation andStatistics

Fernando E. Miguez

Department of AgronomyIowa State University

[email protected]

Jul 8, 2010


Outline

1 Background

2 Models

3 Process-based model

4 BioCro

5 Photosynthesis

6 Optimizing Carbon Allocation

7 Methods

8 Results


Education and Research

Education

B.S. Agronomy (University of Buenos Aires, 2001)

M.S. and PhD in Crop Sciences (University of Illinois, 2004,2007)

M.S. Applied Statistics (University of Illinois, 2007)

Post-Doc at the Energy Sciences Institute (University ofIllinois, 2008 – 2009)

Assistant Professor, Department of Agronomy, Iowa StateUniversity

Research

Miscanthus Production and Modeling

Model Development for Biomass Crops


Outline

1 Background

2 Models


4 BioCro

5 Photosynthesis


7 Methods

8 Results


Statistical vs. Process-based models

Statistical modely = f(x; θ) + ε

Process-based model

y =M(X; parm, const)

statistical model is data-driven

M >>> f

parm >>> θ

X >>> x


Outline

1 Background

2 Models


4 BioCro

5 Photosynthesis


7 Methods

8 Results


WIMOVAC

Developed by SteveHumphries and Steve Long(UIUC)

Created mainly 1994-1998

User-friendly

Written in Visual Basic

On-line documentation andbinary (Win XP)

http://www.life.illinois.edu/plantbio/wimovac/model.htm

http://www.life.illinois.edu/plantbio/wimovac/model.htm


Outline

1 Background

2 Models


4 BioCro

5 Photosynthesis


7 Methods

8 Results


BioCro (R package)

Features

Statistics Built-in algorithms for parameter estimation, modeldiagnostics and graphics

Interactive Lets the user modify input and parameters andquickly plot the results

Documentation Built-in documentation

Modular Allows the user to directly test components

Computational Written in C/R

Flexibility Easily coupled with other tools and software

Portability Cross-platform and scalable

Maintenance Currently under active development

Limitations

User-friendliness Not as intuitive as WIMOVAC


Outline

1 Background

2 Models


4 BioCro

5 Photosynthesis


7 Methods

8 Results


Photosynthesis: an important part of crop models

Measured with a Li-COR6400

CO2 uptake

stomatal conductance

intercellular CO2


Typical A/Q curve

Quantum flux

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ptak

e

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Photosynthesis model from Collatz

Input: light, temperature, relative humidity, atm CO2

Output: CO2 uptake, stomatal conductance, intercellar CO2

Parameters: Vmax, alpha, k, theta

350 lines C code in BioCro R package

In R, package BioCro:

> args(c4photo)function (Qp, Tl, RH, vmax = 39, alpha = 0.04,

kparm = 0.7, theta = 0.83,beta = 0.93, Rd = 0.8, Catm = 380,b0 = 0.08, b1 = 3, StomWS = 1,ws = c("gs", "vmax"))

Collatz et al (1992) Coupled Photosynthesis-Stomatal Conductance Model for Leaves of C4 Plants. Aust. J. Plant

Physiol.


Testing the photosynthesis modelMiscanthus x giganteus diurnals

hour

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Optimization

D =M(input, θ)

RSS(θ) =∑

(D′ −D)2

where

D = simulated , D′= observed

Quantum flux

CO

2 up

take

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Optimization in BioCro

Opc4photo function in BioCro

Objective function: RSS(θ)It uses the R built-in function optim internally

mOpc4photo and MCMCc4photo available

> head(aq26, n = 3)A PARi Tleaf RH_S

41 30.1 1958 27.0 0.6042 28.8 1465 26.2 0.6043 26.1 977 25.5 0.59> op6 <- Opc4photo(aq26)...

best lower upperVmax 31.372 30.858 31.886alpha 0.054 0.052 0.056


Outline

1 Background

2 Models


4 BioCro

5 Photosynthesis


7 Methods

8 Results


Estimating Dry Biomass Partitioning Coefficients

Objective Model carbon allocation to plant components

Harvestable Biomass Mostly stems are harvested

Carbon Storage How much carbon is stored belowground

Water and nutrient cycling Dynamics during the season


Stages and Dry Biomass Partition CoefficientsExample for a perennial grass

Stage Thermal Leaf Stem Rhizome RootEmergence 0–562 0.48 0.47 -1e-4 0.05Juvenile 562–1312 0.14 0.64 -8e-5 0.21Induction 1312–2063 0.01 0.53 0.3 0.13Post-induction 2063–2673 0.01 0.53 0.3 0.13Flowering 2673–3211 0.01 0.53 0.3 0.13Post-flowering 3211–4000 0.01 0.53 0.3 0.13


Estimating Dry Biomass Partitioning Coefficients

24 parameters

Linear restrictions

Constrained parameters


Outline

1 Background

2 Models


4 BioCro

5 Photosynthesis


7 Methods

8 Results


Parameter Estimation Methods

DIFF compute the relative difference in biomass increase

UNLOwT unconstrained non-linear optimization withtransformation

CNLO constrained non-linear optimization

SA simulated annealing (stochastic search method)


Method: DIFF

Thermal Time

Dry

Bio

mas

s (M

g/ha

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StemLeafRootRhizomeGrainLAI

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Estimate the coefficients by calculatingthe relative increase in biomass for eachstage

Instantaneous

Note: Fails with missing data

idbp function in BioCro package


Method: UNLOwT

Thermal Time

Dry

Bio

mas

s (M

g/ha

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From the simplex S to <Use the additive logratio transform

θ = alr(z) =(log(

z1zk

), . . . , log(zk−1

zk))

Perform the optimization in theunconstrained space

OpBioGro function which usesoptim


Method: CNLO

Thermal Time

Dry

Bio

mas

s (M

g/ha

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Impose linear constrains onthe parameters

Example x = (x1, x2, x3, x4)x1 + x2 + x3 ≤ 1xi > 0contrOpBioGro functionwhich uses constrOptim


Method: SA

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Dry

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mas

s (M

g/ha

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Generate candidate solutions(θ1,θ2,. . . ,θn)

The candidate vectors (θi) aresubjected to the constraints

Accept solutions that improve theobjective function (RSS) andsome that don’t

Gradual improvement of theobjective function exploring theparameter space to avoid gettingstuck in local optima


Experimental Design

Objective: evaluate the ability of the different methods torecover the “true” coefficients.

Generated simulated data from known (“true”) coefficients

Simulated 6, 8, 10, 15 samples (time points)

Simulated samples with missing data (2,3,4,5)

Run the methods 100 times

Calculated distance from “true” to estimated

Calculated RSS∗T


Outline

1 Background

2 Models


4 BioCro

5 Photosynthesis


7 Methods

8 Results


Results (complete cases)

Distance

Res

idua

l Sum

of S

quar

es

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10

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0.615

UNLOwTCNLOSA

UNLOwT: preciseand accurate

CNLO: veryprecise andaccurate

SA: less preciseand accurate thanCNLO andUNLOwT


Results (missing data)

Distance

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idua

l Sum

of S

quar

es

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15

UNLOwTCNLOSA

UNLOwT: mostlyunstable (badstarting values)

CNLO: preciseand accurate(often unstable)

SA: much morerobust thanUNLOwT andCNLO


Real Life Example

Thermal Time

Dry

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mas

s (M

g/ha

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Miscanthusbiomassmeasurementsin England(missing rootdata)

Used theCNLO method

Questions ?

biocro: an r package for crop simulation and...

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