Data processing

Statistical data processing

The statistical data processing is performed in two basic steps. The first step is the evaluation of the results from aerial photo classification. This provides the information on areas of the particular land-use classes. The second step is the statistical assessment of the information collected by field inventory. It is directly linked to the first step as it uses the assessed areas of the four main land-use classes for extrapolation of data from the field survey. The aim of second phase is to provide detailed information about state of the four major land-use classes, namely Agroforestry, Open forest, Forest and Shrubland.

The statistical methods used in the Field-Map Inventory Analyst (FMIA) are standard approaches used for the stratified sampling design as listed, e.g., in Thomson (1992).

The statistical variables estimated by FMIA are population total (for example, the total stand volume of a certain forested area) and sample mean (for example, mean stand volume per hectare). The confidence limit for α = 0.1 for each statistical variable is estimated as well.

The estimates of statistical inventory always include the assessed sampling errors in a form of confidence intervals.

Statistics overview

The section below defines the basic statistical variables used for the statistical evaluation using the Field-Map Inventory Analyst (FMIA) application. The list of statistics and example application is summarized in Table 1.

Estimating the population total

Suppose within stratum h any specified design is used to select the sample sh of nh units, and suppose that one has an estimator with respect to that design. Let denote the variance of , and suppose that one has an unbiased estimator of that variance.

Then an unbiased estimator of the overall population total is obtained by adding together the stratum estimators:

The variance of the stratified estimator, because of the independence of the selections in different strata, is the sum of the individual stratum variances:

An unbiased estimator of that variance is the sum of individual stratum estimators:

If the sample is selected by a simple random sampling procedure without replacements in each stratum, then

is an unbiased estimator of t h, where

is the sample mean for stratum h.

An unbiased estimator for the population total t is

having variance

where

is the finite population variance from stratum h.

An unbiased estimator of the variance of is

where

is the sample variance from stratum h.

Estimating the population mean

Since , the stratified estimator for m is

Assuming that the selection in different strata have been made independently, the variance of the estimator is

with unbiased estimator of variance

With stratified random sampling, an unbiased estimator of the population mean m is the stratified sample mean:

Its variance is

An unbiased estimator of this variance is

Confidence intervals

When all the stratum sample sizes are sufficiently large, an approximate 100(1-a)% confidence interval for the population total is provided by

where t is the upper a/2 point of the normal distribution. For the mean, the confidence interval is

Usually, the normal approximation may be used if all the sample sizes are at least 30. With small sample sizes, the t-distribution with and approximate degrees of freedom may be used. The Satterthwaite (1946) approximation for the degrees of freedom d to be used is

where

Considering variable weights

Let us consider the variable xi weighted by value wi (i = 1,…,n). In equations for moments of y we should multiply any terms as yi or by wi and replace n by . Consequently we receive the following set of equations:

where D(.) is the operator of variance.

Weights are standardized before their further application such a way as W=N, i.e., each wi is replaced by wi×N/W.

Table 1 : A list of equations in the Field-Map Inventory Analyst applied for statistical calculations for individual sample plots and for the whole dataset.

Variable	Calculation for plot	Plot weight	Calculation for the set of plots	Example
Total				Total volume for inventory plots;Total volume for the whole territory under study with the representative net of inventory plots
Average sum				Mean volume (mean volume per plot; divided by plot area it gives mean volume per hectare)
Mean of means				Concentration of carbon in the wood, mean wood density etc.
Mean of weighted means				Mean tree defoliation(weighted by tree volume)
Normalized mean of sums				Volume per hectare by species(tree volume of individual species is related to the representative area of this species);The plot weight can be, e.g., the sum of tree individual areas;
Normalized mean of weighted means				Mean defoliation by species;The plot weight can be, e.g., the sum of tree individual areas;This approach points out the different share of given species within a plot; in contrast with mean of weighted means the weights of different plots are not the same;

where the symbols are defined as follows:

xi	– the value of the variable under study for i-th entity (e.g., tree) within the plot j
vi	– the weight of i-th entity within the plot j
m	– the number of entities within the plot j
Xj	– the sum of the variable under study for plot j
	– the mean value of the variable under study for plot j
	– the mean value of the variable under study per unit v for plot j
wj	– the weight of the j-th plot from the set of inventory plots
Y	– the total of the variable under study for the whole dataset of plots
Ytot	– the total of the variable under study for the whole territory of interest
	– the mean value of the variable under study for the dataset of plots
	– the mean value of the variable under study for the dataset of plots per hectare
n	– the total number of inventory plots in the dataset
s	– the area of inventory plot in hectares
S	– the area of the total territory of interest in hectares

Pre-processing

To enter statistical data processing as above, the information collected in the field must be adequately prepared. This phase is called pre-processing.

Data pre-processing starts with the calculation of secondary variables (e.g., modeling of missing tree heights, calculating of stem volume, aboveground biomass, carbon content etc.), classification of continuous variables into user-defined classes (e.g., stump base diameter into diameter classes) and re-classification of discrete values into more coarse classes (e.g., species into species groups). All these steps are facilitated by the specific functions of the Field-Map Inventory Analyst (FMIA) software.

Calculation of secondary variables

Secondary variables are tree parameters, which could not be measured directly in the field. They are derived from basic dendrometric parameters as breast height diameter, height, horizontal crown projection etc. using models. Based on tree growth form, NFI Cape Verde uses one of two different approaches for calculating secondary variables. The type of tree growth form is distinguished as follows:

1. Tree-like growing species … species predominantly growing with one main well-defined stem.
2. Shrub-like growing species … species predominantly growing with multi bifurcated stem.

Table 2: Re-classification of species into Tree type groups

Modeling of missing tree heights

NFI Cape Verde includes height measurement for all qualified trees. In exceptional cases of missing tree height, (about 0.5 % of the qualified trees) , the corresponding tree height is estimated using either DBH-Height relation (tree-like growing species) or Horizontal crown projection-Height relation (shrub-like growing trees).

Volume estimation for tree-like growing species

Stem volumes for tree-like growing species was estimated on the basis of stem profile models developed specifically within the NFI Cape Verde project. Non-destructive stem profile measurement was carried out for four main tree-like growing species (i.e., Cupressus sp., Eucalyptus sp., Grevillea sp. and Pinus sp.). Thereafter, Field-Map Stem Analyst was used to parametrize a global stem model. The global stem model was used to estimate the total stem volume over bark (base to tip) and merchantable volume over bark (base to 5 cm of diameter) for remaining tree-like growing tree species.

Biomass estimation for tree-like growing species

Total aboveground biomass for tree-like growing species was estimated using biomass conversion and expansion factors, (BCEF, IPCC 2006).

BCEFs are selected based on total merchantable growing stock per hectare.

Growing stock volume and tree species (conifers):

• below 20 m3/ha, BCEF = 5 (6)
• between 20 to 40 m3/ha, BCEF = 1.9 (1.2)
• between 41 to 100 m3/ha, BCEF = 0.8 (0.6)
• above 100 m3/ha, BCEF = 0.66 (0.55)

The specific single tree BEFC factors were derived using smoothed exponential function.

Table 3: Parameters of exponential models for estimating total aboveground biomass for tree-like growing species

MGS … merchantable growing stock [m3/ha]

Biomass estimation for shrub-like growing species

Total aboveground biomass for shrub-like growing species was estimated using biomass models developed specifically within the NFI Cape Verde project. The study on biomass models used destructive sampling of Prosopis juliflora that was carried out on three islands, namely Santo Antao, Santiago and Maio. The parameterized models for total aboveground biomass and for fine aboveground biomass fraction (diameter < 5 cm) are listed in Table 3 and Table 4, respectively. The selection of a suitable biomass model depends on input variables available for particular tree.

Virtual DBH was calculated as follows:

Gi … basal area of stem with DBH>5 cm [cm2]

GStems25 … average basal area of stems with DBH between 2-5 cm [cm2]

NStems25 … stem number with DBH between 2-5 cm [pcs]

Table 4: Biomass models for estimating total dry-weight aboveground biomass for shrub-like growing species

EDBHt … virtual DBH [cm]

Ht … tree height [m]

SNt … stem number with D>5 cm [pcs]

CWt … horizontal crown projection [m2]

Table 5: Biomass models for estimating dry-weight fine fraction biomass for shrub-like growing species

EDBHt … virtual DBH [cm]

Ht … tree height [m]

SNt … Stem number with D>5 cm [pcs]

Merchantable dry-weight biomass was calculated by subtracting fine fraction biomass from total aboveground biomass.

For other species than Prosopis juliflora the calculated biomass was adjusted using species-specific density factor.

Volume estimation for shrub-like growing species

Stem volume and merchantable volume of shrub-like growing trees were calculated by dividing total aboveground biomass/merchantable biomass by density factor.

Carbon stock estimation

Carbon stock in aboveground biomass was estimated based on the assumption of 50% carbon content in dry-weight biomass (IPCC 2003).

Classification of continuous variables

Selected continuous variables collected in the field are used as classifiers for some statistical estimation and tabular outputs. Prior that it is necessary to classify those variables into defined classes (e.g., stump diameter into diameter classes).

The statistical data processing utilizes the following classifications:

1. Stump diameter classes: start from base diameter of 10 cm with an equal step of 4 cm.
2. Endemic plant count classes: number of endemic plants registered in inventory plot is classified into four classes (i.e., 0, 1-2, 3-4, 5 and more endemic plants).

Re-classification of discrete variables

Species composition (e.g., area by species) is the only statistical task that uses as a classifier the species recorded in the field. Other statistical tasks use species groups or classification into broadleaves/conifers as classifier.

The re-classification scheme for the species groups and broadleaved/conifers is shown in Table 6.

Table 6: Re-classification of species into species groups and broadleaved/conifers groups

Formulation of statistical processing tasks

Individual statistical processing tasks were defined with a view to hierarchic ranking of the individual assessed items. The initial group comprises the tasks related to area. These tasks link the data of interpreted aerial photos with the ground survey data. Data on areas are tied up with the concrete tasks according to thematic topics. These include tasks linked to volume, biomass or carbon estimation followed by tasks describing extent of different tree damage and task linked to stumps or site characteristics. Since there were less data collected in the initial phase of the inventory (i.e., Santiago Island), not all statistical tasks could be evaluated for all islands. The list of statistical tasks is shown in Table 7.

Table 7: List of statistical tasks by islands