Allometry – Carbon allocation and partitioning

(1)

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Allometry – Carbon allocation and partitioning

Laurent Saint-André, Yann Nouvellon, Nicolas Picard

To cite this version:

Laurent Saint-André, Yann Nouvellon, Nicolas Picard. Allometry – Carbon allocation and partition-ing. General overview - Allometry, Sep 2013, pp.44 slides. �hal-02804089�

(2)

Allometry – Carbon allocation

and partitioning

(3)

INTRODUCTION

GPP = Gross Primary Production Photosynthesis Reco = Ecosystem Respiration Respiration

Net Ecosystem Exchange (carbon uptake or Release) : NEE = GPP – Reco

NPP = GPP – Ra =

∆biomass+L

= Net primary production

AR= (root turnover and exudates)

L= Litterfall

BC = L+AR-Rh - Drainage = Soil Carbon Balance Rh = Litter decomposition Rs = Soil Respiration _AutotrophicRa = Respiration

Carbon POOLS

and fluxes in

forest ecosystems

ABOVEGROU ND Biomass BELOWGROUND Biomass SOIL ORGANIC CARBON LITTER and DEADWOOD Biomass

(4)

Carbon Sequestration in Forest

Ecosystems ?

tC /ha Years High Sequestration Low sequestration Regeneration Or plantation

Carbon stocked in the forest

Trees (above- and below-ground) / Litter / Soil And its corollary, the permanent stock in a given forest

Time

tC/ha

Increase of the surface occupied by the forests

Stocks (biomass, litter, soil) 230 tC/ha for boreal forests, 270 tC/ha for temperate forests et 290 tC/ha for tropical forests

1

high variation between sites and the partitioning soil/biomass

(43%/57% in average) varies with the latitude

(5)

Main Factors influencing Carbon Budgets in Forest

Ecosystems

Carbon Budget in Forest

Ecosystems

Genetic

(species efficiency)

Sylviculture

(Thinning, rotation length, soil preparation, Slash management, fertilization) Climate

Long term changes (CO2, temperature, rainfall)

Short term events (drought periods, storms) Soil fertility

Notion of VARIABILITY,

SENSIBILITY, and

VULNERABILITY

(6)

Methods for assessing carbon pools at stand

scale

Picard N., Saint-André L., Henry M. 2012. Manuel de construction d’équations allométriques pour l’estimation du volume et la biomasse des arbres: de la mesure de terrain à la prédiction.

Organisation des Nations Unies pour l’alimentation et ’agriculture, et Centre de Coopération Internationale en Recherche Agronomique pour le Développement, Rome, Montpellier, 222 pp. ©2012, CIRAD et FAO

Available in French, English and Spanish

http://www.fao.org/forestry/fma/80797/en/

A 7 steps

methodology, including

field protocols

(7)

Methods for assessing carbon pools at stand

scale

_Destructive

Semi Destructive

(on felled trees)

Semi Destructive

(on standing trees)

(8)

Methods for assessing carbon pools at stand

scale

Measurement

of the branches

Laboratory

analysis

(9)

Methods for assessing carbon fluxes at

stand scale

_{Capture of}

atmospheric CO2 (GPP) Ecosystem Respiration (Re)

NEP (Net Ecosystem Production) = ΣΝΕΕ

Re is obtained from night measurements of NEE (no photosynthetic activity). This respiration includes different

components (trees, litter decomposition..)

GPP is obtained from NEP and Re NEP = GPP– Re

(10)

GPP

ANPP_feuillage ANPP_bois Resp_feuillage Rfoliage Resp_troncs+ Branches (Rwood) BNPP + exsudation Resp_racines

TBCA

Methods for assessing carbon allocation at

stand scale

Total above-ground C allocation

Total below-ground C allocation

Soil respiration Litter-fall

Wood respiration

Changes in C stocks in soil, forest floor,

roots

Growth measurements

Measurement of leaf fall and changes in leaf biomass Measurement of leaf respiration

t

C

L

F

TBCA

L s R RM a s

∆

+

∆

+

∆

+

∆

+

−

=

foliage foliage wood wood

R

ANPP

R

ANPP

TACA

=

+

TACA

TBCA

GPP

=

+

(11)

Allometry, some theoritical and

biological aspects

(12)

Broad definition : within a given population, there is a statistical relationship between

the size of an organism and the size of any part of it (Gould, 1966)

H

D

CD

For example: between height and diameter; diameter and crown size; biomass and diameter; etc..

û

_{Can be used to predict some}

difficult-to-measure tree characteristics from easily

collected data.

Volume prediction

_Ä

Volume tables Biomass prediction

_Ä

Biomass equations Nutrient content prediction

_Ä

Nutrient content equations

(13)

What is Allometry ?

More restrictive definition : proportionality between the relative increments of

two metrics measured on an organism (Huxley, 1924)

û

relative increment in Biomass relative increment in Diameter Allometric coefficient

Which gives by integration And by extension

Where a gives the proportionality between the relative increments, b gives the proportionality between biomass and diameter (given a) and c is the biomass of the tree when D=0 (if D was measured at a height different from zero)

a

D

b

c

(14)

What is Allometry ?

The literature on biomass equations dangles between two opposites sides:

A- The group of West, Brown and Enquist have been developing an appealing theory of biological allometry relying on the fractal properties of branching networks, referred as allometric biomass partitioning theory (APT) by McCarthy and Enquist (2007)

s1 accounting for the constraint of biomechanical stability

s2 accounting for the minimization of hydrodynamic resistance through

the vascular network. Two main parameters:

From West et al. 1997:

When taking s1=1 to fit the hypothesis of volume filling and uniform biomechanical constraints, the tree mass is predicted to

be related to the tree diameter raised to a power a=8/3≈2.67

But rather stands for an average tree model to explore biomass variations among plant size orders than being predictive for single species

(15)

What is Allometry ?

The literature on biomass equations dangles between two opposites sides:

B- The very large group of purely statistical equations, with little regard to the understanding of the biological processes involved. Such models are only reliable within their domain of validity

Often calibrated on small number of trees, covering a little part of tree size variations for a given species

Equations of various forms

Catalogues and databases start to be available for all continents (ex: Zianis for Europe; Navar for south America; Henry for Africa)

(16)

What is Allometry ?

A good candidate set of volume or biomass equations should be simultaneously:

(i)

consistent:

standardized biomass partition and additivity of tree compartments

,

(ii)

generic:

common form of the models whatever the tree species or the forest structure.

Meaningful parameters (ie related to the biology)

.

(iii)

robust:

system operating correctly across a wide range of operational conditions with a

low sensitivity to the sampling design and the working hypotheses

(iv)

accurate.

Building appropriate volume and biomass equations are then still challenging

scientifically:

(17)

Biological concepts

Genetic

Climate

conditions

Soil fertility

Management

Tree growth encompasses primary growth (height) and secondary growth

(cambium activity) : a highly complex process

(18)

Biological concepts

Tree and stand growth: case of even-aged and monospecific forests

-Wood production

(volume) of a given tree species at a given stand mean (or top) height should be identical for all site classes.

- Soil fertility (site index) determines the time need to attain this height and volume.

-

A- Stand production

-

Eichhorn’s rule

-

Assmann’s yield

level theory

-There are some range of variations of wood production at a given top height (variations related to the stockability issue)

-

Langsaeter

Hypothesis

-Losses in productivity if the standing stock is too low

(19)

Biological concepts

Tree and stand growth: case of even-aged and monospecific forests

-

B- Tree production

function of the overall stand production (see previously) which gives the potential

moderated by two reducers

-an Index of Stand density (global pressure on the tree)

(stand density in itself (Sd), stand basal area (G), hart-becking, spacing factor based on tree growth without competition, Reinecke density index (Rdi) and stand density Index (Sdi) based on the self-thinning law, etc…)

- an Index of Social status of the tree (between tree competition)

(20)

Biological concepts

Tree and stand growth: case of even-aged and monospecific forests

-

C- Biomass partitioning in the tree

-

Ring area increases linearly from the

top of the tree to the crown basis and

remains constant below the crown

-

Pressler’s law

Ring area (cm2) D is ta nc e f ro m th e t op o f t he tr e e ( m ) Ring width(cm)

-

From the pith to the bark and along

the tree bole. A three dimension map !

-

Wood density variations

Trunk shape tends to become

more cylindrical with time. E.urophylla*pellita de 19 ans

0,30 0,40 0,50 0,60 0,70 0,80 0,90 -200 -100 0 100 200 in fr a d e n si té ( g /c m 3) A B C

(21)

Biological concepts

From biology to allometric equations

D2H = surrogate of tree volume (=treeVol * formFactor)

and biomass = volume * wood density

D2H is therefore well correlated to the tree biomass and nutrient content

Biom = b(D2H)*

c

+a

This parameter encompasses the form factor and the wood density;

it gives the proportionality between the cumulative values of biomass and volume

This parameter gives the tree

biomass just before it reaches 1m30 height

This parameter gives the proportionality between biomass increments and volume increments

and nutrient content = biomass * nutrient concentration

(22)

Conceptual

model

Stem wood d²h (m3/tree) B io m as s (k g /t re e)

Crown (leaves or branches)

Age d²h (m3/tree) B io m as s (k g /t re e) Age Ontogenic effect

Social status effect

a )

b )

From Saint-Andre et al. (2005) MacCarthy and Enquist 2007, and Genet et al. 2011, we drew the following patterns:

1- both internal (changes in wood properties with ontogeny APT ) and external factors (e.g., growing conditions, social status of the tree OPT) are of importance concerning tree biomass relationship – The main consist in identifying the proportion between APT and OPT

2- The observed pattern may vary strongly from one species to another, but our hypothesis is that species of similar traits (e.g., crown

architecture, wood structure) would exhibit similar to identical biomass models

(23)

A generic equation between species ?

(24)

Biomass proportion

0% 20% 40% 60% 80% 100% Unfertilized Fertilized A b o v e g ro u n d b io m a s s p a rt iti o n in g Branch Stem bark Stem wood 40% 50% 60% 70% 80% 90% 100% 13 30 50 81 Age (years) A b o v e g ro u n d b io m as s p a rt iti o n in g Leaves Branch Stem 0% 20% 40% 60% 80% 100% 3 12 29 81 145 Age (years) T o ta l b io m a ss p ar ti ti o n in g Aboveground Belowground (1) (3) (2)

Belowground about 20% of total Biomass As and when the tree grows, branch and leaf proportions are decreasing while the stem wood proportion increases

Fertilization has a significant effect on the proportions (less branches and more stem wood)

Ex Beech in France

(25)

Biomass proportion

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 15 25 35 55 Proportion de biomasse

Tronc Bois Tronc Ecorce Branches 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 10 20 30 50 80 90 110 130 + Proportion de biomasse

Age du peuplement (ans)

Tronc Bois Tronc Ecorce Br 0-4 Br 4-7 Br>7

Similarities between species (stem wood proportion increases from young to mature stands)

Dissimilarities between species (stem bark proportion decreases for Beech, is almost constant for Oak tress and increases for Douglas fir)

The proportion of medium size branches (4-7) decreases with stand age for oak trees while it remains constant for the beech

Beech

Chêne

(26)

Test of the conceptual

model

Stem total 0 50 100 150 200 250 300 0 50 100 150 200 Age (years) β (a d im ) Leaves 0 10 20 30 40 0 50 100 150 200 Age (years) β (a d im ) Branches 0 50 100 150 200 0 50 100 150 200 Age (years) β (a d im )

Stem total (ρ = β / form)

0 100 200 300 400 500 600 700 0 50 100 150 200 Age (years) ρ ' ( a d im )

Stem total (β' = β x form)

0 0.5 1 1.5 0 0.5 1 1.5 Age (years) β ' ( a d im ) b measured b estimated Measurements Model a b c d

Bingo !

The slope of the relationship between tree biomass and d2h does follow an exponential decrease for crown

compartments and an increase for stem wood

(27)

Test of the conceptual

model

Not only eucalyptus and fagus

have the same pattern, they do

also follow the same line !

(especially for stem wood and

branches)

Branch 0 0.5 1 1.5 2 2.5 3 -1 0 1 2 3 log(Age) (years) lo g (β ) (a d im ) Bole 0 0.5 1 1.5 2 2.5 3 -1 -0.5 0 0.5 1 1.5 2 2.5 log(Age) (years) lo g (β ) (a d im ) Foliage -0.5 0 0.5 1 1.5 2 2.5 -1 0 1 2 3 log(Age) (years) lo g (β ) (a d im ) Foliage -0.5 0 0.5 1 1.5 2 2.5 -1 -0.5 0 0.5 1 1.5 2 2.5 lo g (β ) (a d im

) European beech - France

Eucalyptus - Congo Eucalyptus - Brasil Eucalyptus - Brasil Eucalyptus - Brasil

(28)

Test of the conceptual

model

Genet et al. 2011

Biological explanation for these patterns ?

b' = f(age) 0 100 200 300 400 500 600 700 0 50 100 150 200 Age (years) b ' ( ad im ) b measured b estimated b = f(age) 0 50 100 150 200 250 300 350 0 50 100 150 200 Age (years) b ( ad im )

**b = Form (= Volume / d²h) * b’**

STEM WOOD

Av: 554 kg/m3  b’=wood density

Residual variability = growth conditions

b variations in the young stages = mostly changes in stem form (moving from conical to cylindrical shape)

b variations in the old stages = mostly changes in wood density (slight increase)

(29)

Test of the conceptual

model

Genet et al. 2011

CROWN COMPARTEMENTS

1- Decrease with growth height of the leaf to sapwood area ratio (Al/As) on most of coniferous and broadleaves species, in order to minimize size related

constraints of the whole plant hydraulic conductance (McDowell et al. 2002).

2- sapwood area increments remain lower than diameter increments (Gebauer et al. 2008). 3- xylem vulnerability to embolisation increases with age

(30)

Test of the conceptual

model

Genet et al. 2011 Total aboveground and stem wood models are reliable

the rest of the models are biased when transposed to fertilized or mixed stands but the magnitude of the bias is low (les than 9%)

except for the bark (genetic effect ?) or the branches in the mixed stand (effect of the mixture ?)

Belgium France

Mixed Control Fertilized Fertized Alocrisol Calcisol Rendisol Rendosol Total

Compartiment Critère n=12 n=34 n=46 n=30 n=8 n=8 n=8 n=8 n=32 Biais 4% -1% 2% 3% 7% 4% 9% 14% 8% MEF 0.990 0.991 0.992 0.989 0.979 0.988 0.876 0.875 0.955 Biais 3% 8% 9% 5% 9% 6% 5% 12% 8% MEF 0.980 0.931 0.983 0.986 0.916 0.975 0.957 0.906 0.943 Biais -9% -52% -52% -11% -20% -31% -10% -8% -18% MEF 0.820 0.387 0.380 0.959 0.866 0.762 0.955 0.961 0.856 Biais 25% -8% 3% -4% -1% 8% 19% 27% 11% MEF 0.81 0.895 0.965 0.913 0.91 0.969 0.087 0.668 0.810 Biais - - - -12% - - - - -MEF - - - 0.863 - - - - -Branches Leaves

Data sets used for the model evaluation

Germany France soil sequence

Total aboveground Stem wood

(31)

Test of the conceptual

model

Genet et al. 2011

Can this model reconcile the apparent heterogeneity of published biomass equations ?

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 γ γag e -100 -50 0 50 100 150 200 250 300 350 400 0 100 200 300 400 β β ag e 0 5 10 15 20 25 30 35 40 45 50 0 10 20 30 40 50 β β ag e -100 -50 0 50 100 150 200 250 300 350 400 0 200 400 β existing Beech equations

β = f( a g e ) Série1 Y=X Série7 Stem total Aboveground Stem wood Living branches 0 5 10 15 20 25 30 35 40 45 50 0 β existing Beech 20 40 equations β = f( a g e ) Série1 Y=X Série7 Leaves Stem bark -100 -50 0 50 100 150 200 250 300 350 400 0 200 400 β existing Beech equations

β = f( a g e ) Série1 Y=X Série7 Stem total Aboveground Stem wood Living branches 0 5 10 15 20 25 30 35 40 45 50 0 β existing Beech 20 40 equations β = f( a g e ) Série1 Y=X Série7 Leaves Stem bark

From Zianis et al. (2005) catalogue. 48 references equations. None

succeeded in simulating correctly our european data set

Using stand ages given in each paper and our model, we can estimate the parameter b which can be confronted to the

published one

In most of the cases we were able to retrieve the published parameter, meaning that the main factor of “heterogenity” in the published biomass equations was stand age

(32)

Test of the conceptual

model

Work is ongoing on different tree species

Stem

Branches

Species

α

β

γ

Poplar

NS

Cte by Clone

Cte 1

Decrease Age

Douglas

NS

Croissant Age

Cte 1

Decrease Age

Cte

Increase Age

Beech

NS

Increase Age

Cte 1

Decrease Age

Oak

NS

Cte

Cte 1

Decrease Age

Maritime Pine

Data

Eucalyptus

Cte

Cte1

Cte

But some unexpected patterns occured for some species (Oak, Douglas)

for stem wood and stem bark…. (new conceptual model has been

(33)

Model in use to study the ecosystem

functioning

(34)

Stand growth with confidence

intervals

From the tree to the stand, Monte-Carlo

simulations

û

Model for mean

Model for variance

Y = f(input data, parameters, error term)

β, γ : estimated by the fitting procedure. We got their mean and their asymptotic standard deviation. They are correlated (within a given compartment and between compartments)

Diameter (d) and height (h). Both contained errors. We assumed that

σ=0.3 cm for diameter

σ=3% of height if less than 15 m

σ=1 m if above 15 m _{Saint-André et al. 2010}

Eucalyptus, Congo

)

,

(

)

,

(

X

f

Y

=

β

+

ε

γ

h

d

age

e

age

₅ 2 4 3 2 1

(

β

)

β

µ

=

+

−

+

−

(

2

)

γ2

)

γ

ε

=

N(0,

1

d

h

(35)

Stand growth with confidence

intervals

Biomasse aerienne 10 15 20 25 30 35 01/10/2000 09/01/2001 19/04/2001 28/07/2001 05/11/2001 13/02/2002 24/05/2002 01/09/2002 Date B io m as se ( t/ h a)

Y = a + b.X

+

Ν( 0 ,σ)

Only the error term varies

Saint-André et al. 2010

Eucalyptus, Congo

(36)

Stand growth with confidence

intervals

Y = a + b.X

+

Ν( 0 ,σ)

Error term & parameters of the mean vary

Ν( α

,σα)

Ν( β ,σβ)

Eucalyptus, Congo

(37)

Stand growth with confidence

intervals

Y = a + b.X

+

Ν( 0 ,σ)

Ν( α

,σα)

Ν( β ,σβ)

Error term, parameters of the mean, and input data vary

Ν( α

,σα)

Ν( β ,σβ)

Ν(

X

,σ

x

)

Eucalyptus, Congo

(38)

Stand growth with confidence

intervals

For most compartments, errors were small with regard to standing biomass (below 10%)

Total 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 Age (months) B io m a s s ( t/ h a ) Biomass Interval of confidence G3A G3B G3C G3D G2 G1

At 100 months :

Total biomass = 128 ± 1.9 t/ha

Above-Ground = 104 ± 1.8 t/ha

Below-ground = 24 ± 1 t/ha

Eucalyptus, Congo

(39)

Stand growth with confidence

intervals

Except for the dead branches biomass (worst model)

At 100 months :

Dead B = 1.9 ± 0.3 t/ha

Dead Branches 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 Age (months) B io m a s s ( t/ h a ) Biomass Interval of confidence G3A G3B G3C G3D G2 G1 Saint-André et al. 2010

Eucalyptus, Congo

(40)

Stand growth with confidence

intervals

Same principles of simulations can be applied also to ratios

(41)

Stand growth with confidence

intervals

Biomass increments

Plot Age (months) Year Start date End date Total biomass increment (t/ha) G3A 9 to 22 2001 23/03/2001 23/03/2002 19.5  1.6 G3A 22 to 34 2002 23/03/2002 02/04/2003 25.6  3.3 G3B 26 to 38 2001 08/01/2001 27/12/2001 12.0  0.9 G3B 38 to 49 2002 27/12/2001 28/11/2002 12.9  1.0 G3C 49 to 61 2001 12/01/2001 11/01/2002 9.6  1.9 G3C 61 to 74 2002 11/01/2002 31/01/2003 _{15.3  2.4} G3D 74 to 86 2001 13/01/2001 11/01/2002 14.7  2.9 G3D 86 to 99 2002 11/01/2002 31/01/2003 10.9  2.8

Standard errors where relatively large (from 7 to 25 % of the biomass increment)

For the eddy-correlation site, ∆biomass2002 = 12.9  1.0 t/ha/year

Eucalyptus,

Congo

(42)

Impact of fertilization

Sicard et al. 2006

Fertilized trees are more efficient, but the pattern differs between the two species Douglas (more wood with the same quantity of leaves in fertilized trees) Norway Spruce (same amount of wood with less leaves in fertilized trees)

+ No effect on the other compartments

0 5 10 15 20 25 30 35 40 45 50 0 20 40 60 80 B io m as s ( k g ) Control Fertilised

Norway Spruce, Leaves

Stem girth at 1m30 (cm) 0 50 100 150 200 250 300 350 400 0 20 40 60 80 100 Control Fertilised

Douglas, Stem Wood

B io m as s ( k g ) Stem girth at 1m30 (cm)

(43)

Impact of fertilization

Same result for eucalyptus in Brazil : fertilized trees are more efficient (same amount of wood produced with less leaves but the effect is significant only for the young stages)

Sicard et al. 2006 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 d2h (m3) B io m a s s e ( k g /a rb re ) Témoins Potassium Sodium 0 5 10 15 20 25 30 35 0 0.1 0.2 0.3 d2h (m 3) B io m a s s e ( k g /a rb re ) Témoins Potassium Sodium