# Forest Inventory Glossary

 Content: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

## A

Areal sampling frame
The sampling frame or continuum (area) from which dimensionless samples points are selected based on a statistical sampling design.
Accuracy
The accuracy of an estimate is the degree of closeness of the estimated mean of a variable to the actual (true) value of the population. A measure of accuracy is the bias.
Allometric models
predict the value of a variable of an object from values of other variables of the same object; a common example is allometric biomass models that predict biomass of an individual tree from “other metrics” (that is the meaning of the term “allometric”) such as diameter at breast height (dbh) and tree height.
Attribute
The terms “attribute” and “variable” are used interchangeably.
Autocorrelation
While “correlation” describes the statistical relationship between two variables, autocorrelation describes the statistical relationship between to observations of the same variable. In forest monitoring, it is mainly spatial autocorrelation that is relevant.

## B

Basal area
Sum of the cross sectional areas (in 1.3 meter height) of all trees per hectare (in m2/ha).
Bias
A systematic error that prevents an accurate estimate of the true value of a variable of interest. A bias can be introduced by a biased selection of population units (selection bias), by biased estimators (estimator bias) or systematic errors in measurements (observer bias). A systematic error cannot be compensated by increasing sample size.
Bitterlich sampling
Or: "Angle count sampling", "relascope sampling", "point sampling". An unequal probability sampling approach (or plot design). Trees are included in a sample, if they appear bigger that a defined opening angle. Basal area can be estimated by counting all included trees and multiply this number with a counting factor that is depended on the defined opening angle.

## C

Cluster plot
Sample plot that is composed of unconnected sub plots. As the subplots are not selected independently, a cluster gives only one observation.
Concentric circular sample plots
See: Nested plots.
Confidence interval
For statistical estimations, the confidence interval defines an upper and lower limit within which the true (population) value is expected to come to lie with a defined probability.
Cost efficiency
Also related to statistical efficiency. The Relation between invested resources and resulting quality of information (e.g. precision of estimates).

## D

DBH
Diameter at breast height (1.3 meter above ground).
Design based sampling
A sampling design where unbiasedness is entirely based on the randomized selection of the samples; that is: unbiasedness is guaranteed regardless of the structure of the population sampled.
Development models (Growth models)
predict the value of a variable over time. Typical examples include growth models.

## E

Expansion factor
Reciprocal of the inclusion probability. The factor with which observations have to be multiplied to derive an estimate of the total for the area of interest (or per hectare).
Error
In the forest monitoring context, the term error is used in different meanings: in statistical estimation, the error describes the variability of estimates, usually quantified in terms of root mean square error or error variance or standard error. It describes inherent residual variability and can be used to construct a confidence interval.
Estimation
The process of approximation of a true parametric value by means of sampling.
Estimator
The algorithm (formula) used to calculate estimations. An estimator needs to fit to the sampling design and plot design employed in order to produce unbiased estimates.

## F

Field protocol
Defines in detail which measurements should be taken in which way. As the field protocol also defines which elements are to be included at each sampling location, it is a synonym for the stipulated plot design.
Fixed area sample plots
sample plots with defined area size.
Forest area
Area that fulfills all components of a certain forest definition (typically including minimum crown cover, minimum area, minimum width and tree height).
Forest Assessment
See “Forest Monitoring”
Forest Inventory
See “Forest Monitoring”
Forest Monitoring
The terms “Forest monitoring”, “Forest inventory”, "Forest Assessment” and “Forest Survey” are sometimes used interchangeably, although linguistically they focus on different points: “Forest inventory” focuses on the generation of data on the forests with an emphasis on statistical approaches; “Forest monitoring” has a focus on changes in the forests where such information may come from repeated forest inventories; “Forest assessment” has a focus on the interpretation and evaluation of inventory and monitoring results; and “Forest survey” has a surveying connotation but is frequently used in the same meaning like “Forest inventory” focusing on sampling (survey sampling).
Forest Survey
See “Forest Monitoring”

## H

Independent selection
Observations are independently selected if for each observation a new (=independent) randomization was done (the selection of one sample does not affect the selection of another sample).
Independent variables
Two variables are independent if their joint probability can be directly calculated from the marginal probabilities. However, “dependent variables” must not be confused with “correlated variables”; which is a different concept.
Indicator
A variable with a particular explanatory meaning for a complex variable.

## I

Inclusion probability
Probability that a single population unit is included in a sample based on the actual plot design.
Inventory design
See: sampling design

## K

k-tree sampling
Or: "Distance sampling", "Plotless sampling": A plot design that includes a fixed number of k (nearest) population units at each sampling location (contrary to include all units on fixed area plots). Most known in forestry is the so called 6-tree sample.

## L

Line intersect sampling
A sampling design in which lines serve as observation units. Total length of linear features is estimated based on the number of intersections with sample lines.
Line intercept sampling
A sampling design with lines as observation units. Relative proportions of land use classes are estimated based on the length of sample lines (proportion) that comes to lie in a target area class.

## M

Measurement
A measurement is the process of generating a datum which is characterized by just one error source, the measurement error.
Model
A model produces a value of a target variable from a set of values of input variables. In forest monitoring it is mainly two types of models that are used: “allometric models” and “development models”.
Model error
Predictions from models carry a residual variability, the model error.
Model based sampling
A sampling framework where unbiasedness relies on a model of the population. The model is usually population-specific.

## N

Nested plots
Nested sub-plots of different size at one sampling location for the separate assessment of e.g. different diameter classes.
Neyman (optimal) allocation
An allocation scheme to distribute total sample size to different strata in stratified sampling under consideration of the estimated variance of the target variable in different strata.

## O

Observation
An observation is the process that produces one datum. It could be based on a measurement, a model prediction or an expert guess.
Observation design
See plot design.

## P

Parameter
In sampling statistics, the term “parameter” is reserved for the true population value of a variable. The parameters of a population remain unknown (unless a full census is done) and are approximated by estimates from sampling studies.
Plot
A plot is the basic observation unit in forest sampling = observational unit. The population is imagined to consist of a certain number of plots. A plot is selected according to the defined sampling design, usually by means of a sample point that defined the location of the plot. The “plot design” defines how the objects (e.g. trees) are being selected from that sample point and which measurements are taken. One plot produces one observation for a particular variable.
Plot design
Or: "Observation design", "Response design": Defines which elements are to be included at each sampling location and how measurements are taken. It is the "field protocol" that is implemented at each sample point. Typical examples are fixed area plots or Bitterlich sampling.
Population
The domain of interest of a sampling study. The population in the sense of sampling is the set of all “elements” for which estimates shall be produced. In forest monitoring, the population is usually defined in terms of area (see sampling frame). In national forest monitoring the population is defined either as the country´s forest area (if the monitoring refers only to forest land) .
Precision
Or: "reproducibility", "repeatability": The precision is the degree to which repeated estimates under unchanged conditions show the same results. A measure of precision of estimates is the standard error.The terms “precision” and “accuracy” are sometimes used interchangeably to characterize the reliability of results from empirical studies; as such they are both used as measures of “uncertainty” and play an important role in reporting results.
Prediction
The process of approximation of an unknown value by means of modeling. Some authors use the term “prediction” and “estimation” interchangeably.
Proportional allocation
An allocation scheme to distribute total sample size to different strata in stratified sampling under consideration of stratum size (area).
The protocol is the detailed and step-by-step description of any empirical study, including national forest monitoring. Also referred to as “Field manual” or “Field protocol” when referring to field inventories or “classification guide” or “interpretation guide” when referring to image analysis. A field protocol describes in detail sampling design, plot design, all variables including definitions, classifications, measurement devices, measurement procedures.
Robust
The term “robust” is sometimes used as an acclaim for a methodology that can favorably be applied in many situations. A clear definition is not available.

## R

Random selection
A random selection of e.g. sampling locations ensures that each population unit has a positive probability to be included in a sample (or be selected as sample). See also: Simple random sampling.

## S

Sampling
The process of selecting a subset of population elements with the goal to produce estimates for target parameters of the population. A sampling study is technically defined by its sampling design, plot design (see also: “plot”) and estimation design (see also “estimator”).
Sample plot
A certain area or "decision rule", defining which population units are to be included at each sampling location.
Sampling design
The statistical framework or design that describes how sampling locations are selected (e.g. simple random sampling or systematic sampling).
Sampling frame
The part of the total population (e.g. area of interest) that has a probability (>0) to be selected as sample (observed).
Sampling intensity
Proportion of the population that is been sampled. In forest inventories the area proportion that was observed in the sampling study (e.g. 3% of the total area). Contrary to sample size, sampling intensity does not have an immediate relationship to precision of estimation.
Sample size
The number of independently selected observations. In forest monitoring the number of sample plots. Sample size is one important determinant of precision of estimation.
a sample selection that does possibly lead to the preferred selection of population elements with particular characteristics (e.g. because of missing randomization and/or subjective selection).
Selection probability
Probability that a unique set of k population units is selected as sample based on the actual plot design (the probability for the respective observation). In case of distance sampling with k=1 similar to the inclusion probability.
Simple random sampling (SRS)
A sampling design that is based on a random selection of samples. SRS is basis for all statistical estimators.
Spatial autocorrelation
Or: "Self-correlation" describes the relationship between two observations of the same variable, taken at two different objects or times. Spatial autocorrelation refers to the correlation between observations made on plots in different distances.
Species richness
An indicator for biodiversity. Total number of (e.g. tree-) species in an area of interest. Species richness is a nominal variable that can be estimated by sampling.
Standard Error
Standard deviation of all possible sample outcomes. The standard error is estimated based on the sample at hand and is an estimate of precision.
Stratified sampling
A sampling technique based on the partitioning of the total population (or area) in more homogeneous sub-populations (strata) that can improve precision. Sometimes, and confusingly for samplers, the term “stratification” is also used in the meaning of classification, which does also refers to a subdivision of the population, but without any sampling connotation.
Systematic sampling
A sampling design that is based on a systematic selection of samples.
Sub-plot
If one plot is sub-divided into two or more sub-units, these are referred to as sub-plots. The entire plot, consisting of spatially disjunct sub-plots is also called cluster-plot (=cluster of sub-plots). The observations on one sub-plot alone do not constitute an independent observation for the sample; rather, one independent observation comes from the set of all sub-plots of one plot. See also Cluster_sampling.

## T

Total
Aggregate value of the quantitative characteristic of interest in the entire population (e.g. total volume in the area of interest).
Tree height
Perpendicular distance between the ground level and the level of the top of a tree in meter.

## U

Uncertainty
See accuracy and precision. A general term to describe the level of variability of a result. In national forest monitoring, the term “uncertainty” is predominantly used in the policy context; it requires a clear definition in terms of precision and accuracy to be operational.
Uniform allocation
An allocation scheme to distribute total sample size to different strata in stratified sampling.

## V

Variable
A characteristic of the objects of interest that can take on different values and follows a distribution. In statistics also: “random variable”. Examples of variables in forest monitoring are dbh, height, species, development class, forest type, slope,... Variables are either directly measured (example: slope) or observed (such as tree species) or calculated from a set of measured variables.

## W

Wedge prism
A measurement device that is used to make an angle count sample.