In this article we will discuss about:- 1. Definition of Timber Inventory 2. Purpose of Timber Inventory 3. Objectives 4. Sampling Design 5. Stand Measurements 6. Volume Equations.

**Definition of Timber Inventory:**

Timber inventory is defined as the procedure for obtaining information on the quantity and quality of timber resources available in an area on which the trees are growing. The timber inventory is an extensive survey of the timber resources on a particular forest area. Timber inventory is an accounting of timber and their related characteristics of interest over a well-defined land area. It is the enumeration of trees in a particular area for assessing the timber availability.

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It may be compared to census methods of human population. Similarly timber inventories seek to enumerate the population of trees within a forest and ascertain other information, such as – species composition, timber volume, value and growth. Complete enumeration is carried out only in exceptional cases where very high value timber species are present in smallest tracts of land. Complete enumeration of individual trees is usually infeasible and survey sampling techniques are required. A timber cruise is a sample measurement of a stand used to estimate the amount of standing timber that the forest contains.

**Purpose of Timber Inventory: **

The prevailing reason for conducting a timber inventory is to make informed decisions about forest management. The primary need has been the quantification of volumetric product yield and structural composition of the forest. The volume of the timber resource is typically categorized by species, product and size. In addition, quantities like the number of trees and basal area per unit area are often desired.

While collection of data on other components of ecosystem is increasing, the timber resource still remains the main focus for most timber inventories. Both spatial and temporal scales are normally addressed in the planning of an inventory. The most obvious dichotomy is in time- a timber inventory may be initiated for an assessment of current conditions (growing stock), or it may be repeated at future periods in time, yielding estimates of change in volume or basal area and possibly other components of growth, mortality and removals (due to harvest). Spatially, the size of the area in question may range from a small woodlot or individual stand to a national inventory. Different methods are required for differing spatial scales.

**Objectives of Timber Inventory:**

**The objectives for conducting a timber inventory include: **

i. To examine stands that focus specifically on making stand-level decisions over a short planning horizon with regard to the prescription of silvicultural treatments e.g., thinning.

ii. To prepare short term operational plans for harvesting.

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iii. To estimate the volume and value of an area and to determine the total availability of timber for sale prior to a commercial harvest.

iv. To assess the damage on residual trees through postharvest inventories.

v. To assess the adequacy of regeneration stocking following a regeneration treatment and such efforts may be repeated to estimate survival rates.

vi. To develop long term strategic plan through large-scale inventories for determining allowable harvest rates or optimal harvest scheduling plans.

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vii. To determine the value of the forest for accounting purposes.

viii. To conduct survey for the valuation of land and timber to be purchased, sold or exchanged.

ix. To conduct countrywide surveys often mandated by law for making high-level policy decisions and broad-scale resource monitoring.

**Estimating the Area and Mapping the Site: **

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The starting point for forest measurement involves developing a good map of the area that shows the type of the forest, age (if planted) and past management. If tree management, performance, provenance, age, soil types or environment are quite clearly different and have effected the growth in parts of forest, these should be treated as separate areas and marked on the map.

A common method of measuring the area of a stand is to use a large-scale aerial photograph (1:10,000) and calculate the area using a dot grid or planimeter. Topographic maps may be suitable where a person can clearly delineate the boundaries of different forest areas (e.g., 1:25,000 map). Many computer programmes can determine areas of irregularly shaped polygons drawn over scanned photographs or maps, thereby providing an easy estimate of ground areas.

**Sampling Design of Timber Inventory: **

Timber inventory field work is extremely costly and so it is generally well worth the effort to spend time ensuring that the design of the inventory is as efficient as possible and so gain maximum accuracy at minimal cost. Sample points should be located on a map and the same map is used in the field to locate the sampling points. It is desirable to ensure that the samples cover the complete area of interest.

Sampling is a process in which inventory is carried out only in a representative portion of the whole. For example, a forest may be of 1,000 ha out of which only 100 ha has been selected for inventory and estimate of the whole population of 1,000 ha is made, it is called sampling. Sample is defined as a part of population consisting of one or more sampling units, selected and examined as a representative of the whole.

The advantages of sampling over total inventory are reduced cost and saving of time, relative accuracy, knowledge of error and greater scope.

**The important sampling designs used in timber inventory are: **

1. Simple random sampling.

2. Stratified random sampling.

3. Systematic sampling.

4. Multi-phase and Multistage sampling.

**1. Simple Random Sampling:**

It is a selection process in which every possible combination of sample units has an equal and independent chance of being selected. Sampling units are chosen completely at random. Samples are either chosen with replacement or without replacement, the latter means that once a sampling unit is chosen it may not be chosen again.

**2. Stratified Random Design: **

The most commonly used sampling design is the stratified random design where plots or points are located at random within strata. The stratification into approximately homogenous strata reduces the number of samples that are required to meet an overall precision target for sampling precision.

A population is divided into sub- population of known size and a simple random sample of at least two units is selected in each subpopulation. In forests, stratification can be done on the basis of stand type, stand age, site quality, climate region or ecosystem.

In principle, variable probability is more efficient as the strata with higher timber yields can be sampled at greater intensity and this will improve the overall precision of the inventory. It is efficient both statistically and economically. If the forest is very heterogeneous, then it is possible to use variable probability sampling and to concentrate the samples in the strata with greatest volume or basal area.

This approach may also assist future practical management of the forest as it may be sensible to treat each stratum, or perhaps a group of strata, separately, in order to best meet harvesting or other silvicultural objectives. If strata differ widely in terms of a variable of interest (basal area or volume) then it is possible to adjust the sampling level accordingly and so reduce the number of samples required to achieve a desired precision. Some inventory specialist prefer to use equal probability sampling between strata even though it is more expensive as it makes computation easier and it is easier to explain what is happening to managers.

**3. Systematic Sampling: **

The initial sample unit (i.e., first plot) is randomly selected. All other units (plots) are spaced at uniform intervals throughout the forest. Sampling units are easy to locate and appear to be representative. Generally acceptable estimates for the population mean are obtained. Systematic sampling is generally satisfactory for estimating means in typical forest conditions.

When an objective numerical statement of precision need not be appended to inventory estimates, systematic sampling may provide more information for the time expended than simple random sampling. In cases in which estimates of variance are important or little is known about the basic characteristics of the population being sampled, it is good to use simple random sampling than systematic sampling. If adequate care is taken not to introduce a systematic bias then systematic sampling may be quite appropriate in some inventories.

**4. Multi-Phase and Multi-Stage Sampling: **

The differentiation between multi-phase and multi-stage sampling is often clouded. These sampling procedures occur more generally in large national timber inventories than in timber inventories generally used for valuing smaller forests. The idea is to start from a complete area and to stratify that, selecting sample areas, such as forest reserves, watersheds, or bio-geographic regions.

This provides the first stage samples and a number of these are selected, but not all. Then for each first stage sample the area is stratified in more detail and second stage samples are selected from this level. This procedure can be repeated to any depth. This is the multi part of the names.

The separation into multi-phase or multi-stage is generally based on the methods of stratification. If the stratification of each level is basically the same, only increasing in depth, then it is called multi-stage sampling. If the stratification is based on quite different bases, for example the first stage being administrative regions, the second remote sensing imagery and the third on aerial photography or more intensive, then the procedure is generally called multi-phase. For most forest valuation work, it is often considered more appropriate to ensure that all first stage and generally all second stage strata are sampled. In this case, the sampling is just stratified random sampling.

**Point Sampling: **

Point sampling or angle count sampling use angle gauges such as Spiegel relaskop or the simple optical wedge prism. Point samples have some definite advantages in that they give a higher priority to the larger trees which are generally the more important, and there are generally less of them in the forest.

On the other hand, it is more difficult to address problems near the boundary of the forest or the stratum and quite sophisticated procedures have been developed to account for this. If point samples are used to determine growth then there is generally an increase in sampling error as trees that were considered “out” during the first measurement may now be considered “in”. A commonly adopted rule of thumb is to use point samples if re-measurement is not expected.

**Optical Prisms (Wedge Prisms): **

The optical properties of wedge shaped prisms are particularly suited to angle count sampling, and since the early 1960s, the optical wedge or wedge prism has been used extensively as an angle gauge for basal area estimates. A wedge prism can be used to estimate quickly the Basal Area per hectare and one costs only 2 per cent the price of a Spiegel relascope. It is a simple wedge-shaped prism of glass or see- through plastic, typically 5×2 cm. It distorts the light and shifts the position of a tree stem when looked at through the prism. Different factors of prism relascopes are available, with common Basal Area Factors being 5, 8, or 10.

The technique with the wedge prism is to stand at one point among the trees and to complete a 360 degree sweep around, counting all the trees that are ‘IN’. Those that are ‘borderline’ should be counted every other time considering it as “Half In”, and those that are ‘Out’ are not counted.

To estimate the basal area simply multiply the number of counted trees by the basal area factor (e.g., 5, 8 or 10). One should conduct as many sweeps around the stand of trees, as this will provide a more accurate estimate when averaged over the stand. Thus, the wedge prism is sometimes claimed to be faster and more accurate than the Spiegel relaskop.

**Basal Area Measurement with Spiegel Relaskop: **

The relaskop can generate nine Basal Area Factors (BAFs) using bands 1, 2 and combinations of the quarter bands. Choose the appropriate BAF and combination of bands. Then, standing over the sample point, hold the brake button down and make a sweep of 360 degrees while comparing the tree diameters at breast height with the selected bands. Count the number of trees whose diameter at breast height appears greater (wider) than the selected bands (IN trees).

Ensure trees are not hidden behind closer trees by stepping to one side and checking before returning to the sample point. Where trees appear to be the same width as the selected Relaskop bands, it refers to the borderline calculations and considered as “Half In”. Once the sweep has been completed, multiply the count of IN trees by the appropriate BAF to get stand basal area (m^{2 }per ha).

**Plot Sampling: **

Because measuring trees can be a time consuming and costly operation, most foresters only measure a sample of trees as an estimate to the growth of different parts or blocks of the forests. An absolute minimum of 3 plots should be established in any uniform section, unless one or two plots cover most of the site, in which case all trees should be measured.

For very large uniform forests, the total area of all the plots should be an absolute minimum of 2 per cent of the total forest area. For example, in a forest of 10 hectares, a total area of 0.2 hectares should be measured. If the plots are to be 0.04 hectares in size then at least 5 plots would be required for a sufficient sample.

Plots can be kept within the stratum or forest boundary more easily and do provide a consistent area base for determining growth. However because they sample a fixed area, they may not provide as good an estimate for the largest tree diameter classes and commonly over sample the smaller diameter classes. A commonly adopted rule of thumb is to use plot sampling if re-measurement is expected.

**Circular or Rectangular Plots: **

Plots are generally circular or rectangular. Rectangular plots are useful and preferred in stands where planting rows are well defined, as in young stands or in heavily stocked forests. Circular plots, on the other hand, are easier to lay out in mature or irregularly spaced stands with low stocking rates or where the rows are poorly defined or not present, such as in native forests.

**Plot Size: **

In order to obtain a representative sample, between 15 and 30 trees per plot is required (12 being the absolute minimum). Plot size will therefore depend on the stocking rate. The more sparse the trees, the larger the plot will need to be to include sufficient trees. Tree stocking can be quickly estimated from the average spacing or, alternatively the size of the plot can be gradually increased until it includes sufficient trees.

**Plot area for each shape is calculated as follows: **

Rectangular Plots: Plot Area (Ha) = Length (m) x Width (m)/10000

Circular Plots: Plot Area (Ha) = [Radius (m)]^{2} x 3.142/10000

**Highly Irregular Forests: **

Where the forest is very irregular, rather than establishing fixed area plots, it may be preferable to identify a number of individual “plot trees” scattered through the forest that are measured individually.

**Farm Forestry Trees: **

In farm forestry, trees are planted in small blocks, belts or strips with many, perhaps most, of the trees growing on the edge. In this case, it is better to measure the trees in a length of belt to assess yield per 100 meters of belt (rather than yield per ha).

**Stand Measurements of Timber Inventory: **

**Stocking Rate: **

The tree density or stocking rate of a forest is described as the number of trees per hectare

Stocking Rate (stems/ha) = Trees in Plot/ Plot area (ha)

**Stand Diameter: **

While measuring diameter, the form of the tree must be inspected and form factor should be recorded.

**Stand Height: **

Measuring the heights of trees can be difficult and time consuming. The heights of the tallest trees in a plantation or native forest are usually quite uniform and therefore, rather than measure the height of all trees in the sample plot, it is common to select a sub-sample. In most cases, a number of the fattest trees (largest DBH) of good form are measured for height and this is called the “Mean Dominant Height” (MDH).

Mean Top Height (MTH) is most commonly used in some countries. It is the height predicted by reading from a height – diameter curve (commonly the Pettersen Curve) for a DBHOB corresponding to the mean top dbh (MTDBH). Mean top dbh (MTDBH) is defined as the quadratic mean of the largest 100 trees (by diameter or dbhob) per hectare. If the stocking is less than 100 trees per ha then the mean is across all the trees.

**Empirical Height Equations: **

Because tree height measurement is costly, it is common to measure all trees for diameter but to measure only a sample of trees for height and then to use a model based on these data to predict tree height for all trees. Tree height is necessary as tree volume (V) is commonly derived from a function of diameter (DBH) or (D) and tree height (H), i.e. (V = f [D, H]). Tree height generally increases as tree diameter increases with the rate of increase decreasing with increasing diameter. Tree height often approaches an asymptote.

**A wide range of height equations are used to estimate the height of trees using diameter values: **

H = b_{0} + b_{1}D (Linear)

H = 1.3 + b_{1}D_{ }+ b_{2}D^{2} (Quadratic)_{ }

H = b_{0} + b_{1}1n(D) (Log linear)

H = b_{0} + b_{1}/D^{b2} (Inverse linear)

H = b_{0}D^{b1 }(Power)

H = b_{0} exp (b_{1}/D) (Exponential)

In (H) = b_{0} + b_{1}1n(D) (Log – log)

In (H) = b_{0} + b_{1}/D (Log inverse linear)

1/ {(H -1.3)^{0.4}} = b_{0} + b_{1}/D (Pettersen curve)

D/ {(H -1.3)^{0.4}} = b_{0} + b_{1}D (Alternative Pettersen Curve)

It can be argued that it is important to see which function best suits a particular species and region and that the best curve may also change during the life of a plantation. Of the models presented, four latter models will produce biased predictors as the model is fitted to a transformed dependent variable and so when the predictor is transformed back to predict height a small bias is introduced. This is generally ignored as it is small relative to the errors in the basic measurements.

**Stand Basal Area: **

Stand Basal Area (SBA) is simply the cross sectional area of all the trees at breast height per hectare of forest or plantation (m^{2}/ha). Stand basal area can be used to estimate stand volume and is a useful measure of the degree of competition in the stand. SBA is often quoted when planning thinning prescriptions. The basal area of stand or plot can be measured in two ways: sum of individual tree basal areas and optical method using Spiegel relaskop or wedge prism.

**Sum of Individual Tree Basal Areas: **

The most accurate method of assessing the basal area of a stand of trees is to measure all tree diameters at breast height in a plot, calculate individual tree basal areas and add these up. A quicker method is also available to calculate the stand basal area using the average tree diameter.

Tree Basal Area (m^{2}) = (DBH/200)^{2} x 3.142

Stand Basal Area (M^{2}/ha) x [Sum of the basal area of each tree in plot/Area of the plot (ha)]

Stand Basal Area (m^{2}/ha) = [(Basal area of the average tree diameter) x Stocking (trees/ha)]

**Stand Volume/ Forest Volume: **

**Total forest volume or stand volume can be calculated from the plot measurements: **

Standing Forest Volume (m /ha) = Plot Volume (m^{3}) / Plot Area (ha)

Forest basal area measurements can be used to calculate tree and butt log volumes in the same way that tree volumes are calculated. In plantations where we might assume all the trees are quite uniform, a quick estimate of total volume can be made from the Stand Basal Area and Dominant Tree Height using form factor.

Standing Forest Volume (m^{3}/ha) = SBA x MDH x Form Factor

Where, SBA = Stand Basal Area, MDH = Mean Dominant Height

**Mean Annual Increment (MAI) and Current Annual Increment (CAI): **

Mean annual increment is simply the average volume production per year for a forest of known age.

Mean Annual Increment (m^{3}/ha/yr) = [Stand Volume (m^{3}/ha) / Age of Stand (yrs)]

Current Annual Increment (CAI) is the increase in volume at a particular age and is determined by annual measurements of standing volume. It is simply defined as the volume increment of a stand in a single year.

CAI (m^{3}/ha/yr) = Stand Volume at current year – Stand Volume of previous or last year

**Volume Equations used in Timber Inventory: **

There is need to predict tree volume or stand volume and one way is to develop tree volume equations that just require tree diameter and either tree height or upper stand height.

**The most commonly used model form is: **

Y = b_{0} +b_{1}D^{2}H

Where,

Y is the tree volume

D is tree DBHOB (diameter at breast height over bark)

H is the tree height

It is often the case that the residuals suggest a σ proportional to the independent variable D2H. Better estimates for the parameters b_{0} and b_{1} are therefore obtained by fitting the equation.

**Commonly used typical local volume equation forms (based on DBH): **

Y = b_{0} + b_{1}D^{2}

Y = b_{0}D^{b}‘

Y = b_{0}D + b_{1}D^{2}

In (Y) = ln (b_{0}) + b_{1} ln (D)

Y/D = b_{0 }+b_{1}D

The parameters b_{0} and b_{1} may be estimated by simple linear regression.

**Commonly used general volume equation (based on DBH and height): **

Y = b_{0} + b_{1}D^{2}H + b_{2}D^{2} + b_{3}H

Y = b_{0} + b_{1}D^{2} + b_{2}H + b_{3}D^{2}H

Y = b_{0 }+ b_{1} (D – b_{2})^{2 }(H – b_{3})

Y = b_{0} + b_{1} (D^{2 }– b_{2}) (H – b_{3})

And even

Y = b_{1} D^{b2}H^{b3}

which can be transformed by taking logarithms into an intrinsically linear model form

ln (Y) = b_{1} +b_{2} ln(D) + b_{3}ln(H)

Using the concept of dimensional analysis the sum (b_{2} + b_{3}) in the last equation should equal 3.0 with (b_{2} = 2.0, b_{3} = 1.0). However as trees are not cylinders but can generally be approximated by a neiloid or second degree paraboloid and then the parameter values generally fall in the ranges (b_{2} = 2.2 – 2.5, b_{3} = 0.5 – 0.8) with the (b_{2} + b_{3 }= 3).

Choice of model may depend on modeling objective, data used in the estimation of coefficients and error structure. These basic equations implicitly assume a single-stemmed form and may require modification or replacement for species with a more complex form.

In addition, when equations are used to estimate the logarithm of a variable, a negative bias is introduced when the predicted logarithm is converted back to arithmetic units. This bias is approximately the order of magnitude of one-half of the residual variance of the equation.

**Volume Table: **

Volume table is defined as a table showing for a given species the average contents of trees, logs or sawn timber for one or more given dimensions. The main objective of the volume table is to estimate the volume of average standing trees of known dimensions.

**The given dimensions may be: **

i. dbh alone

ii. dbh and height

iii. dbh, height and some measure of form or taper

**On the basis of application, volume tables are classified as follows: **

**1. General Volume Table (GVT): **

These tables are usually based on two variables named diameter at breast height (dbh) and total tree height. These are based on the average volume of trees growing over a large geographical area. These are used to derive local volume table and to estimate the volume of trees in the form of standard timber.

**2. Local Volume Table (LVT): **

These tables are generally based on one independent variable i.e., dbh. These tables are derived only from restricted locality (local area). These are used to estimate the volume of growing stand and to make confidential volume of coupe or compartment.