1.What is the difference between Accuracy and precision?

.Precision: the closeness of the measurement to the true value

.Accuracy: the degree of agreement in a series of measurements

2.Measures of central tendency:

. The Arithmetic mean:

. Mode:

3. Measures of variability:

. The standard deviation: is a measure of the spread of scores within a set of data (La desviación estándar es una medida de la extensión de las puntuaciones dentro de un conjunto de datos).

-Population standard deviation: our population contains all the values we are interested in.

-Sample standard deviation: if all you have is a sample, but you wish to make a statement about the population standard deviation from which the sample is drawn.

. How to determine the basal area (BA) of trees: : Basal area is the common term used to describe the average amount of an area occupied by tree stems (Área basal es el término común utilizado para describir la cantidad promedio de un área ocupada por tallos de árboles).

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-The cross-sectional cut of a tree in DBH 1.3 m above the ground

. Quadratic mean diameter (QMD): It is a central tendency which is considered more appropriate than arithmetic mean for characterizing the group of trees that have been measured.

In indigenous forests uneven aged.

It is the square root of the arithmetic mean of squared values.

4. Direct & Indirect ways of measurement:

. Volume: direct; xylometre. Indirect; approximation, using mathematical procedures.

. Diameter: direct; traditional approaches i.e., (tape). Indirect; remote sensing techniques.

. Height: direct; vertical measuring pole, tape through climbing (medición vertical pértiga y

cinta a través de la escalada). Indirect: using trigonometric techniques, using geometrical techniques.

5. Determination of tree age.

The age of a tree is defined as the period of time which elapsed (transcurrido) since germination and in some cases, especially in commercial forestry, since the time of planting.

On trees with recognizable annual layers of wood, age can be determined either by felling the tree, counting the number of annual rings at stump height and adding the estimated period of time the tree requires to reach stump height. (En árboles con capas anuales de madera reconocibles, la edad se puede determinar ya sea derribando el árbol, contando el número de anillos anuales a la altura del tocón y agregando el período estimado de tiempo que el árbol requiere para alcanzar la altura del tocón.)

Using increment borer to extract the radial core of the tree stem. (Usando barrenador incremental para extraer el núcleo radial del tallo del árbol).

False rings: False ring formation, a common source of error in tree ring research, is triggered by drought during the growing season (Fritts, 1976)

Missing rings:  because of the effect of environmental pollution or pathogens stresses.

6. Bark thickness.

Bark thickness is measured because tree volume is calculated under bark while diameter is measured over bark.

Bark thickness is expressed in millimeters and it is measured with a bark gauge, which is bored into the tree stem, and cause a negligible damage to the stem.

(El grosor de la corteza se mide porque el volumen del árbol se calcula bajo la corteza, mientras que el diámetro se mide sobre la corteza.)

El grosor de la corteza se expresa en milímetros y se mide con un medidor de corteza, que se perfora en el tallo del árbol y causa un daño insignificante en el tallo.)

7. Tree diameter

Tree diameter is measured at 1.3 m above the ground level (reference height for diameter measurements of standing trees, DBH).

Often correlates closely with other things, which are more difficult to measure, like the wood volume in the stem of a tree or the weight (or biomass, as it is called) of the tree.

May reflect the monetary worth (valor) of the tree. May reflect the competitive position of a tree in a stand.

-Rules: Measurements should be carried out horizontal to the tree stem. Trees forking above 1.3 m are measured as one tree, while (Los árboles que se bifurcan por encima de 1,3 m se miden como un árbol, mientras que) trees which are forking below 1.3 m they are measured as two separate trees. On slopes the measurement is always taken from the upper side of the stem. (En pendientes, la medición siempre se toma desde la parte superior del tallo.)


It measures the tree diameter. The fixed arm is placed along one side of the tree at 1.3 m above the ground. The moveable arm is then placed flush against the other side of the tree and the diameter is read directly from the scale of the calliper. The callipers must be located perpendicular to the stem axis. (El brazo fijo se coloca a lo largo de un lado del árbol a 1.3 m sobre el suelo. El brazo móvil se coloca a ras contra el otro lado del árbol y el diámetro se lee directamente de la escala del calibrador. Las pinzas deben estar ubicadas perpendicularmente al eje del vástago.)

Important is to always get two measurements perpendicularly and use the average (promedio) value (especially in case of deformed stem forms).

9. Measuring tapes:

When using the measuring tape we are actually measuring  the tree circumference, however the diameter tape has graduations that are based on the relationship between the diameter and the circumference (C) of a circle. Relation between diameter and radius:

d = 2r, r = d/2, 

C = 2πr, D = c/π

The last relationship is therefore (por lo tanto) providing direct readings of diameter from the diameter tape.

The accuracy of the tape must be checked regularly and the tape must be cleaned after use. Also stems that are not circular (elliptical stems) usually contain errors.

10.Biltmore stick:

Estimation of tree diameter at DBH – usually in inches

Stand away from the tree (Párese lejos del árbol) ~ 25 inch or 63.5 cm

Do not forget in case where the tree that we are measuring is not symmetric, two measurements is a must.

11. Estimation of tree height:

-Total height of a tree is defined as the linear distance from the ground level to the (highest point) of the tree.

Tree height is required to determine: the site class or site index of a stand  to estimate the volume of standing trees.

-Merchantable tree height refers to the usable portion of the tree stem (usually when the tree start branching) i.e., the part for which the tree volume is computed from (Avery and Burkhart, 1983). Used mainly in broadleaves because is difficult to evaluate the total height on the contrary in coniferous tree species we can easily evaluate the total height.

12. Indirect measurements for height evaluation using hypsometers/altimeters

Taller standing trees are usually measured indirectly using hypsometers. Hypsometer is a collective name given to all instruments that are used to measure tree height. Hypsometers are used to measure angles and distances to points on the tree, from which height is derived.

Geometric (similar triangles) or trigonometric principles are embodied in the use of hypsometers.

The biltmore stick can be used to measure the merchantable height.


The relascope and relascope measurement was invented and introduced by Austrian forest scientist Walter Bitterlich (Bitterlich 1947, 1948). The method is widely used because it is simple, handy and quick. (El método es ampliamente utilizado porque es simple, práctico y rápido.)

It is primarily used to measure the height of a tree, the basal area of a tree and the diameter of a tree anywhere along the bole.(en cualquier lugar a lo largo del tronco).

14. Azimuth:

Angle that is measured from the North in favor of the hands of the clock. Measuring tape and compass are used in classic approaches. In modern approaches are used Example of GNSS Receiver by Trimble company, total stations.

15. Basic tree attributes:

Age, Diameter, Basal area, Height, Volume, Bark thickness, Growth, Tree crown

16.Basal area:

This volumetric description is a ratio of the tree’s cross-sectional area at DBH to the total area and called basal area or BA. (Esta descripción volumétrica es una relación del área de la sección transversal del árbol en el DBH al área total y se llama área basal)

Indicator of growing stock.

Relascope is one way how we can estimate the basal area (BA) of a tree.

17. Tree volume calculation methods

Water displacement, Geometry of solid shape approximating tree stem shape, Cut stem into several sections, then measure and sum (logs), measurement can be done on either cut or uncut stems, Tree volume estimation using volume tables.( Desplazamiento de agua, Geometría de forma sólida aproximada a forma de tallo de árbol. Cortar el tallo en varias secciones, luego medir y sumar (troncos).La medición se puede hacer en tallos cortados o sin cortar. Estimación del volumen del árbol usando tablas de volumen.

. A very simple model consists out of assuming the trunk is cylindrical

 (well doesn’t seem it is the case in reality).

. In case of conical shape stem the total stem volume will be:

.  Taper functions are used to predict upper-stem diameters as a function of DBH and height, but give no information about age-related changes, since the effect of site and stand density on DBH and height is ignored.

. Based on cut sections:  Measure each section separately using the

 below formulas. Summarize all sections to derive the tree total volume.

18. Growth:

Growth can be defined as the enlargement of large of live system by assimilation activity. It depends on the age and the environment.

19. Concept of tree crown development:

Tree crown is strongly related to the tree growth. Bare in mind that crown ratio decreases with age (Ten en cuenta que la proporción de la corona disminuye con la edad.)

How to measure it?: Between 4 – 8 radii per tree (stand)

First we need to find the longest radii (longest branch), after that we need to record the orientation of this branch with the help of a compass (sometimes by naked eye)

Then we need  to follow the same principle for every 90 deg. – N,E,S,W, depending on the total number of trees inside the forest stand.

20. What is the meaning of a diameter distribution?

A diameter distribution, either for a whole stand or for a sample of trees, may be specified by listing the diameter measurements, a tree list. If instead of repeating values we assign to each unique measurement value the number of 12 times it appears in the list, we have the equivalent of a discrete frequency function. Bare in mind that the frequencies may be given as absolute numbers, as numbers per hectare, or as proportions.

Stand tables or diameter distributions have always played an important role in forestry.

(Se puede especificar una distribución de diámetros, ya sea para un rodal completo o para una muestra de árboles, enumerando las medidas de diámetro, una lista de árboles. Si en lugar de repetir los valores asignamos a cada valor de medición único el número de 12 veces que aparece en la lista, tenemos el equivalente de una función de frecuencia discreta. Tenga en cuenta que las frecuencias se pueden dar como números absolutos, como números por hectárea o como proporciones.

Las tablas de rodal o las distribuciones de diámetros siempre han jugado un papel importante en la silvicultura.)

21. Expressions of mean height in a stand:

Several stand height methodologies select only the biggest trees to avoid (para evitar) the effects of thinning and tree mortality on stand height estimates. Here are the methods that have been used to obtain the average height of a stand:

Measure and average (promediar) the heights of all trees, or a sample of trees regardless (independientemente) of their size. This corresponds to an unweighted mean stand height (una altura rodal media no ponderada)

Measure and average the heights of dominant trees or of dominant and co-dominant trees (also called dominant and co-dominant height.

Measure and average heights of a fixed number of   largest trees (usually largest based on their diameter of trees) per unit area (i.e. 100 tallest trees per hectare). This is also called top height. In European literature, top height is the average height of the 100 largest diameter trees per hectare in the stand.

Determine the average height weighted (ponderada) by basal area, so called Lorey`s mean height.

22. Site index curves

The site index of a stand is a mensurational statistic which is used as an easily accessible variable expressing the combined effect of those edaphic and climatic characteristics which have an impact on growth and yield of a given tree species

In the USA and many other countries the site index of a stand is defined as the mean height of the dominants and co-dominants.

In general, given the: stand height, age.

23.Sampling methods:

Sampling method is a statistical approach and it is the process of selecting a representative group from the population under study.

Quantitative information is primarily obtained by: ground surveys (encuestas de tierra), aerial photographs, and satellite imagery.

24.Plot shapes:

Circular (It tends to produce less borderline trees, the plot boundaries can be conveniently       located [Los límites de la parcela se pueden ubicar convenientemente.]), Rectangular (In plantation forests, it is convenient to establish rectangular plots, with the

longest side coinciding with the direction of the planting rows [hileras]), square, transect.

25. Types of sampling:

Random sampling (Stratified, Multiphase sampling, Multi-stage sampling) and systematic sampling.

26. Difference between Growth and Yield

Yield is the total available amount for harvest at given time, while yield can be regarded (considerado) as the summation of the annual increments.

Growth shows elongation and thickening (engrosamiento) of roots, stems and branches.

27. MAI and PAI

MAI: (Mean Annual Increment); growth during the whole growth period (life) from age 0 to age t (present age).

PAI: Periodic annual increment is the change in the size of a tree between the beginning and ending of a growth period, divided by the number of years that was designated as the growing period.

28. Volumen Tables

Heinrich Cotta (German silviculturist) suggested the idea of a volume table.

A volume table of a particular species is defined as a table showing the average volume of trees or logs for one or more given characteristics such as DBH alone or DBH and height or DBH, height and form or taper. The main objective of volume tables is to facilitate estimating the average volume of standing trees for which the diameter and height are known.