Sampling strategy and stratification

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Sampling strategy and stratification

Nicolas Picard, Laurent Saint-André, Matieu Henry

To cite this version:

Nicolas Picard, Laurent Saint-André, Matieu Henry. Sampling strategy and stratification. Training Material Sampling Strategy, UN-Reducing Emissions from Deforestation and forest Degradation (UN-REDD). Genève, CHE.; Food and Agriculture Organization (FAO). ITA., Jun 2012, Hanoi, Vietnam. 22 p. �hal-02804111�

Sampling Strategy and

Stratification

Pham Cuong, Inoguchi Akiko

Hanoi, June 18 - 22

₂₀₁₂

Authors : N. Picard (CIRAD), L. Saint-André

(CIRAD - INRA), and M. Henry (FAO)

Context

Forests are basically heterogonous, in tree size, tree species,

ecological growth conditions etc…

So which sampling strategy

should we adopt ?

Turn heterogeneity into

Homogeneity

Global rules: stratify the variability ! (to get homogeneous entities on

which measurements will be done)

For example, at the scale of a country

With the objective of quantifying C stocks,

Then the stratification should be made according to :

-ecological regions,

-site index within each region, -age within each site index class,

-and stand density within each age class…..

For example, at the scale of an eddy-correlation site

With the objective of comparing NEP estimates (from the flux tower and from

destructive measurements)

Then the stratification should be done according to :

-the age of the stand,

-the season within each studied year, -the foot print of the flux tower….

Turn heterogeneity into

Homogeneity

Global rules : Drawing of the sampling chain highlighting the objectives of

the study

For example:

Country Ecological _situations Stands Measured _Trees Allometric_Equation

Volume/Biomass of a single tree

Volume/Biomass of the average tree Volume/Biomass of the selected stand

Volume/Biomass of an other stand ?

Prediction



_{This step is then objective-dependent}

and the availability of time, staff and money (!)

Practically, it is the result of two constraints:



the wanted accuracy



Turn heterogeneity into

Homogeneity

More specifically, the optimum sampling design can not be reached

for volume and biomass equations …. The choice for the appropriate

equation is generally done “a posteriori”

Sampling strategy

Some theoretical considerations, case study relating tree volume to D

_H

This model makes the hypothesis that the

relationship between tree volume and D

_{H is}

linear and that the error distribution

ε

follows a

normal law of mean 0 and variance

_σ

It can be fitted using n trees on which volume and D

_{H were measured –}

This sample also gives

The volume prediction for one single tree (knowing D* and H*) is then given by :

the average of D

H on the sample

Estimated volume

Sampling strategy

Some theoretical considerations, case study relating tree volume to D

_H

If now, we want to assess how many trees (n) we should sample to have a

precision of E on this tree (D* and H* are known)

Making the choice of sampling randomly the trees into the stand, then

With

µ

=

and

τ

the standard deviation of D2H on the sample

Sampling strategy

Some theoretical considerations, case study relating tree volume to D

_H

Taking E=5%, a tree volume of 2m

,

µ

=5m

and

τ

=1m

……

n=98 trees

Is there a way to lower this number of trees, ie, to optimize the sampling ?

Minimize this value (but

difficult to do in practice

on the field

Maximize this value =

sampling the

extreme trees….

Sampling strategy

Some theoretical considerations, case study relating tree volume to D

_H

BUT, strong drawbacks if……

Sampling strategy

Practical applications: biomass equations for an eucalyptus clone in

Congo

Reference: Laclau 1996



30 sampled trees

Models fitted with 6, 12, 18, 24 trees equally spread out in all classes of tree basal area, 20 repetitions for each fitting

R2 and biomass estimates variations decrease with the number of sampled trees. 12 to 18 trees is a good

compromise between time consuming and the wanted accuracy.

Sampling strategy

Practical applications: generic biomass equations for eucalyptus in

Congo

Stand selection :

afforestation Savannah

0 11 19 25 years

High Forest C1 Coppice C1 High Forest C2

Plantations Plantations

Cycle N°1 Cycle N°2

G1 G2 G3A G3B G3C G3D _{Time from savannah}

afforestation Savannah

0 11 19 25 years

High Forest C1 Coppice C1 High Forest C2

Plantations Plantations

Cycle N°1 Cycle N°2

G1 G2 G3A G3B G3C G3D

Tree selection : 4 to 12 trees per stand according to their basal area

Reference: Saint-André et al. 2005



Field Constraint

Sampling strategy

Practical applications : volume tables for the main species in France

Reference: Vallet et al, 2006



Eawy

Camp Cusson Côte aux Hêtraux

Camp Souverain Camp Cusson 2 Camp Cusson 1 1929 1934 1949 Retz

Forêt Peuplement Placette Eclaircie

… …

… …

…

Forêt de provenance des échantillons Forêt Nonbre de Peuplement Nombre de Jeux Bellême 3 12 Blois 4 10 Champenoux 2 7 Haye 1 1 Tronçais 5 12 C h ê n e TOTAL 15 42 Barres 2 2 St Just d'Avray 1 5 D o u g la s TOTAL 3 7 Clusaz 1 2 Doubs 1 1 Noirmont 1 2 Risol 1 2 Sixt 1 1 E p ic éa TOTAL 5 8

Sampling strategy

Some Indications (Pardé et Bouchon, 1988):

Mono-specific and even-aged stands : 30 trees



A 15ha group of stand : 100 trees



Forest of 1000ha : 400 trees



region scale : 800 trees



Ecological range of a given species : 2000 to 3000 trees



Chave et al. 2004:

One tropical rain forest in Panama: 300 trees



Sampling strategy

Selecting trees on the field

Tree selection after a first inventory



It is recommended to use the tree-basal-area bar charts (equal width of basal area classes) because

the largest trees contribute more to the total stand volume than the smallest ones (if volumes are normally distributed)

and because the variance of volume, biomass or nutrient content increase with the tree size

It is then better to sample the largest trees to catch this variability

Note: for multiple-stem trees, use the sum of stem basal area to get the average diameter of the

trees; in some particular cases (ex: dry zones) it is better to use the base of the trunk than the breast height 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100

% of trees (ranked by tree size)

% o f to ta l st an d v o lu m e The 20% largest trees provide 50% total stand volume

Sampling strategy

Selecting trees on the field

Same number of trees by basal area classes ? Or proportionality to the number of trees within each class ?



 _{This is the usual case when the objective is to get a robust model}

(ex: one equation for several ages):

Extreme trees have to be sampled to act upon the building and the fitting of the model

Same number of trees

 _{This is the usual case when the objective is to get an equation}

devoted to one particular purpose (ex: tree volume at age 7years)

Proportionality to the number of trees within each class

Practically, we often use a mixture of these two options



Sampling strategy

Selecting trees on the field

Case of non-homogeneous stands



Here again, the sampling to be applied is a function of the wanted accuracy and the available means

Frequency (% of trees)

Classes of basal area

Specie 1

Specie 2

-add a new level of stratification ?

-how many trees to be felled for each specie ?

If so

Equal ?

Proportional ?

if no

Sampling strategy

Selecting trees on the field

Case of non-homogeneous stands



Example: coppices of Quercus Ilex in Morocco

One stand, 20 trees to be felled

14% of multiple-stem trees

86% of single-stem trees

17 trees

3 trees

Histograms of tree basal areas

0 0.05 0.1 0.15 0.2 0.25 0.3 0 100 200 300 400 500 600 700

Tree basal area (cm2)

F re q u e n cy ( % o f tr ee s) Multiple-stem Single-stem

Sampling strategy

Selecting trees on the field

It is also preferable to avoid particular trees (top broken, sinuous shapes, etc…)

EXCEPT if these trees represent a big proportion of the stand, or if the objective is to quantify these defects

Lastly it is necessary to avoid trees located near the roads or near the forest limits

Sometimes, field constraints change drastically the

sampling designed on the computer

It is preferable to select trees within plot that satisfy two main criteria: no high rates of mortality to ensure an homogeneous and representative tree growth

Sampling strategy

Estimation of the overall stand volume or biomass

Once the biomass equation is built, the question of the sampling strategy for forest inventory remains

with and N the total number of trees measured in the plot It can be shown that the previous equation can be rewritten as follows

with e denoting the values calculated on the sample used to calibrate the equation

And the confidence interval of total volume is given by

Sampling strategy

Estimation of the overall stand volume or biomass

Without stratification, the variance of total volume is given by

With stratification, the variance of total volume is given by

Where h denotes the strata, N_h the total number of trees measured in the strata, n_h the number of trees felled in the strata for building the allometric equation

Sampling strategy

Estimation of the overall stand volume or biomass

Size of the plot to be inventoried ? Smaller is the plot= smaller is the representativity in natural forests 0 2 4 6 8 10 12 14 16 18 20 225 325 425 525 625 0 10 20 30 40 50 60 50 ₂₅0 ₄₅0 ₆₅0 ₈₅0 1250 0 100 200 300 400 500 600 125 375 750 ₁₂50 ₁₇50 ₂₂50 ₂₇50 ₄₇50 AGB (Mg ha-1₎ Plot size = 20 x 20 m

Plot size = 10 x 10m _{Plot size = 100 x 100m}

Chave, J., R. Condit, et al. (2003). "Spatial and temporal variation of biomass in a tropical forest: results from a large census plot in Panama." Journal of Ecology 91: 240–252.

Henry, M., S. Adu-Bredu, et al. (submitted). "Structure and functioning of rain forests ecosystems in Ghana " International Journal of forestry Research.

Sampling strategy

Estimation of the overall stand volume or biomass

Size of the plot to be inventoried ?

In general, for a given sampling effort :

Number of plots

Plot area

Zone area

If the stand is heterogeneous, it is better to install numerous small plots; while in homogeneous stands, it is better to install few large plots