Forestry & Forest Sciences · Mensuration, Inventory & Geospatial Analysis · also Forest Inventory, Timber Cruising, Forest Resource Assessment
Planning and running forest inventories: kinds of enumeration, sampling designs and plot types, sample size, estimation and error, from a timber cruise to a national forest inventory.
In the exams: ICAR AICE-JRF 59 Unit 4 (forest inventory, kinds of enumeration, sampling methods, sample plots); ICAR AIEEA-PG Group 09 (forest inventory); IFoS Forestry Paper II Section A; SAF Certified Forester; Indonesia timber-cruiser certification
A forest inventory is the organised collection of information about a forest: how much land it covers, what trees and other resources it contains, how much they are worth, and how they are changing. Inventories range from a timber cruise of a single coupe before sale, through the stock maps and enumeration of a working plan, to national forest inventories that report a country's growing stock, carbon and biodiversity to its government and to international bodies. In every case the forester must decide what to measure, where, how often and how precisely, and then turn field measurements into estimates with a stated error.
Almost no inventory measures every tree. Instead a sample of plots, points or strips is measured, and statistics are used to estimate totals for the whole forest and the uncertainty of those totals. This subject is therefore applied sampling theory: simple random, systematic, stratified, cluster, multistage and multiphase designs; fixed-area and variable-radius plots; the calculation of sample size and sampling error; and the practical procedures of cruising, permanent plots and data processing. It builds on forest mensuration, which supplies the tree- and stand-level measurements, and feeds forest management, which uses the estimates to regulate yield.
Inventory is examined in two ways. Indian entrance and fellowship papers (ICAR AICE-JRF subject 59 Unit 4 and AIEEA-PG Group 09) and the UPSC Indian Forest Service Forestry optional ask about kinds of enumeration, sampling methods and sample plots, often with short calculations. Professional examinations, such as the Society of American Foresters' Certified Forester examination and timber-cruiser certification in Indonesia and elsewhere, ask the forester to design a cruise, compute a mean, standard error, confidence interval and sample size, and interpret the result. This manual gives the formulas in words with worked numbers, and states where conventions differ between countries.
Every inventory begins with its objectives, because they decide everything else. A timber sale needs the volume and value of merchantable trees by species and grade in one coupe, with an error small enough for buyer and seller to agree a price. A working plan needs the area of each forest type and age class, the growing stock and its increment, and the condition of regeneration, compartment by compartment. A national inventory needs unbiased estimates of forest area, growing stock, growth, removals, carbon and biodiversity indicators for the whole country and its regions, repeated over time. A carbon project needs biomass and its change with a precision set by a carbon standard. A wildlife or non-timber inventory needs the abundance of particular species.
The objectives fix the population to be sampled, the variables to measure, the units of reporting, the precision required (often stated as an allowable error in per cent at a given probability), the time and money available, and how often the inventory will be repeated. A well-written inventory plan states all of these before any fieldwork begins, together with the sampling design, plot type, measurement rules, quality control and data processing.
The information sources available also shape the design. Maps, earlier inventories, aerial photographs and satellite images can be used to stratify the forest, to place plots and to combine with field data in multiphase designs, often reducing the field work needed for a given precision.
Enumeration means counting and measuring trees. In complete enumeration, also called total enumeration or a 100 per cent inventory, every tree above a set minimum size in the area is measured. It is used for small, valuable areas: a coupe of high-value timber marked for sale, a seed stand, an urban park, a research plot, or a compartment where trees must be marked individually anyway. Complete enumeration has no sampling error, but it still has measurement and recording errors, and it is slow and expensive, so its results are not necessarily more accurate than those of a good sample.
In partial enumeration, or sampling, only a portion of the area is measured and the results are expanded to the whole. Sampling is cheaper and faster, and because a smaller crew can work more carefully, measurement errors are often lower. Its estimates carry a sampling error, which can be calculated from the data if the sample was chosen by a proper probability design. Sampling is the normal method for all large areas.
Sampling designs fall into two broad families. In probability sampling every unit has a known, non-zero chance of selection, so that unbiased estimates and their errors can be calculated. Simple random, systematic, stratified, cluster and multistage designs are probability designs. In non-probability sampling, such as choosing typical or accessible plots by judgement, no valid error can be computed and bias is likely; it has a place in reconnaissance and in choosing sites for research, not in estimating totals.
Inventory estimates are subject to four kinds of error. Sampling error arises because only part of the population is measured; it decreases as the sample grows and can be quantified. Measurement error arises from instruments and observers, such as a diameter tape not wrapped at right angles or heights misread. Prediction or model error arises when tree volume, biomass or height is predicted from an equation rather than measured. Bias, or systematic error, arises from poor design or procedure: plots placed subjectively, edge trees always counted in, an instrument out of calibration, or a volume equation applied outside the range of data used to build it.
Precision describes how closely repeated estimates would agree with each other, and is measured by the standard error. Accuracy describes how close the estimate is to the true value, and depends on both precision and bias. A large sample can give a very precise but badly biased result. Good inventory practice therefore controls bias through design and field procedure, and reports sampling error honestly.
In simple random sampling every possible sample of n units from a population of N units has the same chance of selection. In a forest the population is usually the set of all possible plots of a given size, and plot centres are chosen with random coordinates. The sample mean is the sum of the plot values divided by n. The sample variance is the sum of squared deviations from the mean divided by n − 1, and the standard deviation is its square root. The coefficient of variation (CV) is the standard deviation as a percentage of the mean.
The standard error of the mean is the standard deviation divided by the square root of n. When the sample is a sizeable fraction of a finite population, this is multiplied by the finite population correction, the square root of (1 − n/N); the correction is usually ignored when the sampling fraction is below about 5 per cent, and for area sampling the population of possible plots is effectively infinite.
Worked example. Ten plots in a stand give volumes of 210, 180, 250, 190, 230, 200, 170, 240, 220 and 210 cubic metres per hectare. The mean is 2,100 ÷ 10 = 210 m³/ha. The squared deviations sum to 6,000, so the variance is 6,000 ÷ 9 = 666.7 and the standard deviation is 25.8 m³/ha. The CV is 25.8 ÷ 210 = 12.3 per cent. The standard error is 25.8 ÷ √10 = 8.16 m³/ha, or 3.9 per cent of the mean.
A confidence interval gives a range likely to contain the true mean. It is the mean plus or minus t times the standard error, where t is taken from Student's t distribution for n − 1 degrees of freedom and the chosen probability. For 95 per cent confidence, t is 2.262 with 9 degrees of freedom, 2.093 with 19, 2.045 with 29 and approaches 1.96 for large samples; many field manuals round it to 2. In the example above the 95 per cent confidence interval is 210 ± 2.262 × 8.16 = 210 ± 18.5 m³/ha, that is, from about 191.5 to 228.5 m³/ha.
To estimate the total for the forest, the mean per hectare is multiplied by the area, and so are the standard error and the confidence limits. If the stand covers 50 hectares, the estimated total volume is 210 × 50 = 10,500 m³, with a standard error of 8.16 × 50 = 408 m³.
The sampling error is often reported in per cent: t times the standard error divided by the mean, times 100. Here it is 18.5 ÷ 210 = 8.8 per cent at 95 per cent probability. Contracts and working plans frequently specify an allowable sampling error, such as 10 per cent at 95 per cent probability for a sale cruise; the exact requirement varies by agency.
In systematic sampling the units are spread at regular intervals, usually on a square or rectangular grid with a random starting point. Most forest inventories, from cruises to national inventories, use systematic grids because they are easy to lay out and follow on the ground, they spread the sample evenly over the forest so that every part is represented, and they also produce a map of the forest's variation. A line-plot cruise, with plots at fixed intervals along parallel lines, is a systematic design.
The weakness of systematic sampling is statistical. Because the units are not independent random draws, there is no unbiased formula for its sampling error from a single systematic sample. In practice the simple random sampling formulas are applied. When the forest varies gradually or in patches, this usually overestimates the error, so the result is conservative. The exception is a periodic pattern in the forest, such as plantation rows, ridges and valleys, or old extraction lines, that coincides with the grid spacing; then the sample can be badly biased. Grids should therefore be oriented and spaced so that they do not align with such patterns, for example by running lines across the contours or at an angle to plantation rows.
The sampling intensity, or cruise intensity, is the proportion of the area actually measured. If plots of 0.05 hectare are placed on a 100 m by 50 m grid, each plot represents 0.5 hectare, so the intensity is 0.05 ÷ 0.5 = 10 per cent.
In stratified sampling the population is divided into non-overlapping subpopulations, called strata, and a separate sample is taken in each. Strata are chosen so that units within a stratum are as alike as possible and strata differ from one another: forest types, age classes, density classes, site classes, or zones mapped from aerial photographs or satellite images. Because the variation within strata is smaller than the variation of the whole forest, stratified sampling usually gives a more precise estimate for the same number of plots. It also gives separate estimates for each stratum, which managers often need, and allows different plot sizes or intensities in different strata.
Stratification is useful only if the strata really differ in the variable of interest. Stratifying by a feature unrelated to volume adds work without improving precision. Strata must be mapped and their areas known, because the estimate weights each stratum by its share of the total area.
The stratified mean is the weighted average of the stratum means, each weighted by the stratum's proportion of the total area, Wh = Ah ÷ A. Its variance, ignoring the finite population correction, is the sum over strata of Wh squared times the stratum variance divided by the number of plots in that stratum. The standard error is the square root of this sum.
Worked example. A forest of 1,000 hectares has two strata: dense forest of 600 hectares with mean 250 m³/ha and standard deviation 50 m³/ha, and open forest of 400 hectares with mean 150 m³/ha and standard deviation 40 m³/ha. Twelve plots were measured in the dense stratum and eight in the open stratum. The weights are 0.6 and 0.4. The stratified mean is 0.6 × 250 + 0.4 × 150 = 210 m³/ha. The variance of the mean is 0.36 × 2,500 ÷ 12 + 0.16 × 1,600 ÷ 8 = 75 + 32 = 107, so the standard error is √107 = 10.3 m³/ha. The total volume is 210 × 1,000 = 210,000 m³.
A common mistake is to average the plot values without weighting, which gives the right answer only if plots were allocated in exact proportion to area. Another is to add the stratum standard errors directly rather than combining the weighted variances.
Once the total number of plots is fixed, it must be divided among the strata. In proportional allocation each stratum receives plots in proportion to its area: in the example, 20 plots would be split 12 and 8 for strata of 600 and 400 hectares. In optimum or Neyman allocation each stratum receives plots in proportion to its area multiplied by its standard deviation, so that more variable strata receive more plots. In the example, the products are 600 × 50 = 30,000 and 400 × 40 = 16,000, so of 20 plots the dense stratum receives 20 × 30,000 ÷ 46,000 = 13.0 and the open stratum 7.0. When the cost of a plot differs between strata, the allocation is further adjusted, giving fewer plots where plots are expensive.
Neyman allocation needs advance estimates of the stratum standard deviations, which come from earlier inventories or a pilot survey. If these estimates are poor, the gain over proportional allocation is small. Every stratum should receive at least two plots so that its variance can be calculated.
Post-stratification is the grouping of plots into strata after they have been measured, using maps prepared later. It gives most of the benefit of stratification when the stratum areas are known accurately, and is widely used in national inventories that classify plots by remote sensing.
In cluster sampling the sampling unit is a group of smaller plots, the cluster, located close together, and all plots in a selected cluster are measured. Clusters reduce travel time, which is often the largest cost in large or remote forests: a crew that has walked for hours to reach a location measures several subplots rather than one. National inventories commonly use clusters of four or more subplots arranged in a fixed pattern, such as a square or triangle, or a cross-shaped tract.
The price of clusters is statistical. Plots close together tend to be similar, so a cluster of four subplots contains less information than four independent plots. For estimation the cluster, not the subplot, is the unit: the cluster mean or total is computed first, and the standard error is calculated from the variation among clusters. Treating subplots as independent understates the error. The best cluster design balances travel cost against the loss of information from correlation within clusters.
In multistage sampling the population is divided into large primary units, a sample of these is selected, and then smaller secondary units are sampled within each selected primary unit, and so on. For example, a state's forests might be divided into compartments (first stage); a random set of compartments is chosen; within each chosen compartment a set of plots is measured (second stage); and within each plot a sample of trees is measured for height (third stage). The method concentrates field work in the selected primary units and needs maps or lists only for the primary units at the start and for the selected primary units later.
The variance of a two-stage estimate has two components: variation among primary units and variation among secondary units within primary units. When primary units differ greatly, precision is improved by sampling more primary units and fewer secondary units in each; when they are similar, more secondary units per primary unit can be measured cheaply. Primary units of unequal size are often selected with probability proportional to their size.
In multiphase or double sampling, a large first-phase sample measures a cheap auxiliary variable, and a smaller second-phase sample, chosen within the first, measures both the auxiliary variable and the expensive variable of interest. The relationship between them, estimated from the second phase, is used to adjust the estimate of the variable of interest using the large first-phase sample.
In double sampling for regression or ratio, the auxiliary variable might be volume estimated from aerial photographs or from LiDAR canopy height at many points, and the variable of interest ground-measured volume at a subset of those points. With the ratio estimator, the ratio of ground mean to auxiliary mean on the second-phase plots is multiplied by the auxiliary mean from the large first phase. If ground plots average 180 m³/ha where the photo estimate on the same plots averages 150 m³/ha, and the photo estimate over the full first-phase sample averages 160 m³/ha, the ratio estimate is 180 ÷ 150 × 160 = 192 m³/ha. Ratio estimation works best when the relationship passes close to the origin; regression estimation handles a relationship with an intercept.
In double sampling for stratification, a large sample of photo points is classified into strata, which estimates the stratum proportions; a subsample of these points is visited on the ground to estimate stratum means. This is the classic design of many twentieth-century national inventories and of the first phase of the US Forest Inventory and Analysis programme. Double sampling pays when the auxiliary variable is cheap and strongly correlated with the variable of interest.
A fixed-area plot has a set area, and every tree above the minimum size whose centre lies within the boundary is measured. Plots may be circular, square or rectangular. Circular plots are the most common in sample inventories because a single radius defines them, they have the smallest perimeter for a given area (so fewer borderline trees), and they are quick to establish with a tape or rangefinder. A 0.04-hectare circular plot (400 m²) has a radius of 11.28 m, a 0.05-hectare plot 12.62 m and a 0.1-hectare plot 17.84 m. Square and rectangular plots are easier to lay out in dense or plantation forest and are preferred for permanent research plots and for some biodiversity work.
The plot expansion factor converts plot counts to per-hectare values; it is one hectare divided by the plot area. On a 0.05-hectare plot the factor is 20, so 18 trees counted represent 360 trees per hectare. Volumes and basal areas are expanded the same way.
Plot size is a compromise. Small plots are quick to measure but more variable, and more of their trees are borderline; large plots are less variable but take longer, and fewer can be measured. In practice plot size is chosen to contain a reasonable number of trees, often around 10 to 20 measured trees, but the right size depends on stand density and cost. Nested plots use concentric circles of different radii: small trees are measured only in the inner circle and large trees in the outer one, which saves time while still sampling the rare large trees adequately.
In variable-radius sampling, also called point sampling, angle-count sampling or Bitterlich sampling after its Austrian inventor, the observer stands at a sample point and counts every tree whose diameter at breast height appears larger than a fixed angle projected by an instrument such as an angle gauge, prism or relascope. Each counted tree represents the same basal area per hectare, the basal area factor (BAF). Basal area per hectare is simply the count times the BAF: a count of 12 trees with a BAF of 2 m²/ha gives 24 m²/ha.
Each tree has its own limiting distance, within which it is counted; in metric units this distance in metres equals the diameter in centimetres times 0.5 divided by the square root of the BAF. A 40-cm tree with a BAF of 4 is counted out to 40 × 0.5 ÷ 2 = 10 m. Large trees are therefore sampled from farther away, so trees are selected with probability proportional to their basal area, which is efficient for estimating basal area and volume. Each counted tree represents BAF divided by its own basal area trees per hectare; the 40-cm tree above represents 4 ÷ 0.1257 = 31.8 trees per hectare. Borderline trees must be checked by measuring distance and diameter. The details of instruments are covered in forest mensuration.
Permanent sample plots are established to be remeasured at intervals, giving direct estimates of growth, mortality, ingrowth and removals. Their centres and boundaries are marked with buried or durable markers and recorded by GPS and by bearings and distances to witness trees; individual trees are numbered and their diameter measurement points painted, so that the same trees are measured the same way each time. Permanent plots must be treated exactly like the surrounding forest; if they are favoured, avoided or obviously marked, they cease to represent it. Temporary plots, measured once, are cheaper and suit one-off estimates of current stock.
Plots that fall across the forest boundary or across a stand boundary create edge effects. Simply moving such plots inward biases the estimate, because the edge zone is under-sampled. Correct methods include the mirage method, in which the part of the plot outside the boundary is reflected back inside and trees in the reflected zone are counted twice, and the walkthrough method used in point sampling. Slope correction is also needed: plot radii are defined as horizontal distances, so measuring along a slope without correction gives plots that are too small.
The number of plots needed depends on the variability of the forest, the precision required and the confidence level. For simple random sampling from a large population, the sample size is t squared times the CV squared divided by the allowable error squared, with the CV and the allowable error both in per cent. If the CV of plot volume is 40 per cent, the allowable error is 10 per cent at 95 per cent probability and t is taken as 2, then n = 2² × 40² ÷ 10² = 4 × 1,600 ÷ 100 = 64 plots. The same formula can be written with the standard deviation and an allowable error in absolute units.
Because t depends on n, an exact calculation iterates: start with t = 2, compute n, look up t for n − 1 degrees of freedom, and recompute until n stops changing. For large samples the change is small. When the population is finite and the sample a noticeable part of it, the infinite-population result n0 is corrected: n = n0 ÷ (1 + n0 ÷ N). With n0 = 64 and N = 400 possible plots, n = 64 ÷ 1.16 = 55.2, rounded up to 56.
The formula shows three rules worth remembering. Sample size rises with the square of the CV, so a forest twice as variable needs four times as many plots. Halving the allowable error quadruples the number of plots. Raising the confidence level from 95 to 99 per cent raises t from about 2 to about 2.6 and the sample size by about two-thirds.
Sample size calculations need an advance estimate of the CV. It can come from a previous inventory of the same or similar forest, from published values for the forest type and plot size, or from a small pilot survey. CVs of plot volume commonly range from around 20 per cent in uniform plantations to well over 100 per cent in heterogeneous natural forest with small plots, so borrowed values must match the plot size and forest. Larger plots usually have lower CVs, but each takes longer to measure, so the most efficient plot size is the one that gives the required precision at the lowest total cost, including travel.
The standard error of a mean expresses the sampling error alone; it says nothing about bias or measurement error. The standard error in per cent equals the CV divided by the square root of n: with a CV of 30 per cent and 36 plots it is 30 ÷ 6 = 5 per cent. A confidence interval stated as 95 per cent means that if the inventory were repeated many times with new random samples, about 95 per cent of the intervals would contain the true mean.
Errors combine in predictable ways. The error of a total is the area times the error of the mean if the area is known exactly; if the area is itself estimated, its error must be combined. When independent estimates are added, their variances add. When an estimate is the product of two independent estimates, such as area times volume per hectare, the squared percentage errors approximately add. A national total built from many strata may have a small percentage error even though each district's estimate is imprecise, which is why national inventories report reliable national figures but warn against over-interpreting small areas.
Planners sometimes ask for more precision than the decision needs. The value of an inventory lies in the decision it supports; precision should be set by the cost of making a wrong decision, not by habit.
Cruising is the field estimation of timber volume and value in a defined area, usually before sale or harvest. A cruise must be planned for the stand, the products and the required precision; the crew is given a map, a compass bearing and spacing for the lines, the plot type and size, measurement rules and data sheets or field computers. Quality is controlled by check cruising, in which a sample of plots is remeasured independently and compared.
The traditional cruising methods differ in the shape of the sampling unit. In a strip cruise the unit is a long strip of fixed width; in a line-plot cruise it is a series of plots spaced along lines; in a point cruise it is a series of sample points at which an angle gauge is used. All three are usually laid out systematically.
In a strip cruise the crew walks parallel lines across the forest, and every tree within a fixed distance on either side of the centre line is tallied. The strip width and the distance between strip centre lines fix the cruise intensity: strips 20 m wide with centre lines 200 m apart sample 20 ÷ 200 = 10 per cent of the area. Strips are usually run across the contours and across drainage, so that each strip samples the full range of conditions from ridge to valley.
Strip cruising was the standard method in many tropical and South Asian forests and is still used for enumeration in working plans and for pre-harvest inventory in tropical logging concessions, where 100 per cent enumeration of commercial trees above a minimum diameter is often required in the block to be cut. Its advantages are simplicity and continuous coverage along the lines. Its drawbacks are the difficulty of keeping the strip width accurate in dense undergrowth, the large number of borderline trees along the long edges, and the fact that only the strip, not the strip's individual trees, can be treated as a sampling unit for error calculation.
In a line-plot cruise, fixed-area plots, usually circular, are measured at regular intervals along parallel cruise lines. With plots of 0.1 hectare spaced 100 m apart on lines 100 m apart, each plot represents 1 hectare and the intensity is 10 per cent. Line-plot cruising has fewer borderline trees than strip cruising, gives a clear set of sample units for statistics, and is easier to check, so it has largely replaced strip cruising in North America and in many inventory manuals.
In a point cruise, angle-count sampling is done at points along the lines. Because each point is quick to measure, many points can be sampled for the same cost, and because large, valuable trees are sampled with higher probability, point cruising is efficient for volume and value in stands of mixed sizes. It is widely used in North American timber cruising. Its drawbacks are the need to check borderline trees carefully, sensitivity to hidden trees in dense stands, and the risk of large errors if the instrument or BAF is misused. A large BAF counts fewer trees per point; a common rule of thumb is to choose a BAF that gives a moderate count at most points.
Sample-tree methods are often added to any of these designs: all trees on the plot are tallied by species and diameter, but heights and grades are measured only on a subsample, and the relationship between height and diameter is used to estimate the rest.
A national forest inventory (NFI) is a statistically designed, repeated survey of a country's forests. Its products include forest area by type and ownership, growing stock, increment, removals and mortality, carbon stocks and changes, forest health and biodiversity indicators. These figures support national policy, the forest and land-use parts of greenhouse gas inventories reported under the UN Framework Convention on Climate Change, and country reports to FAO's Global Forest Resources Assessment, which FAO compiles at intervals of about five years.
The Nordic countries were the first to run national inventories, beginning in the 1920s in Finland and Sweden with systematic line surveys across the whole country. Most NFIs today use a systematic grid of permanent field clusters or plots, combined with remote sensing for stratification, area estimation and mapping. The United States Forest Inventory and Analysis programme uses a national hexagonal grid with one field plot per roughly 2,400 hectares (6,000 acres), each made up of four subplots, with a share of plots measured each year so that the whole set is remeasured over a cycle of years. In India, the Forest Survey of India, set up in 1981 as the successor of the Pre-Investment Survey of Forest Resources, assesses forest cover by satellite imagery and growing stock by field inventory on a grid, and publishes the biennial India State of Forest Report. Many tropical countries have established NFIs with FAO support, often designed to meet the reporting needs of REDD+.
NFI design balances national precision, regional detail, cost and continuity. Changing plot design or definitions breaks the time series, so changes are made carefully and with overlap periods.
Continuous forest inventory (CFI) is a system of permanent plots remeasured at regular intervals, so that growth and change are measured directly on the same trees. It was developed in North America in the mid-twentieth century and adopted by many large forest owners and public agencies. Each remeasurement gives the current stock and the components of change since the last measurement.
The components of change follow standard definitions, from Beers and others. Survivor growth is the growth of trees alive at both measurements. Ingrowth is the volume of trees that grew past the minimum measurable size during the period. Mortality is the volume of trees that died, and cut is the volume harvested. If V1 and V2 are the volumes at the two measurements, M mortality, C cut and I ingrowth, then gross growth including ingrowth equals V2 + M + C − V1, and net growth including ingrowth equals V2 + C − V1. For example, if V1 = 180, V2 = 200, M = 8 and C = 15 m³/ha, gross growth including ingrowth is 200 + 8 + 15 − 180 = 43 m³/ha and net growth including ingrowth is 200 + 15 − 180 = 35 m³/ha over the period. Divided by the number of years, these give periodic annual increment.
Remeasuring the same plots gives precise estimates of change, because the positive correlation between successive measurements cancels much of the variation. But permanent plots can become unrepresentative over time if they are treated differently, and they give less information about current conditions in parts of the forest that have changed. Sampling with partial replacement (SPR) addresses this by remeasuring only part of the permanent plots at each occasion and replacing the rest with new plots, then combining both in the estimate. Panel or rotating designs, in which a fixed fraction of plots is measured each year, spread the work evenly and give annual estimates. The choice depends on whether the main aim is estimating current stock or estimating change.
Non-timber forest products (NTFPs), such as bamboo, rattan, medicinal plants, resins, fruits, nuts, tendu and other leaves, mushrooms and honey, are inventoried to set sustainable harvest levels, to support community management and to value the forest. Their inventory faces particular problems. Many NTFP species are clumped, rare or seasonal; their useful parts, such as fruits or bark, vary from year to year; and the people who know where they grow are often local collectors rather than inventory crews.
Designs are adapted accordingly. Bamboo is inventoried by counting clumps and culms by age class on plots, because culm age determines harvestability. Rattan and climbers are counted by stem length classes along strips. For rare and clustered species, adaptive cluster sampling adds neighbouring plots whenever a plot contains the species, which improves efficiency for patchy populations. Yield studies on marked individuals measure how much product a plant gives and how harvesting affects its survival and regrowth. Participatory resource assessment involves collectors in mapping, plot measurement and monitoring, which improves both local knowledge and the acceptance of harvest limits. Results are combined with market and use surveys to judge sustainability.
Biodiversity inventory records species composition and structure. Trees are usually recorded on the same plots as the timber inventory, with smaller nested quadrats for saplings, shrubs and herbs, because smaller organisms are more numerous. The number of quadrats needed to capture most of the species in a community is judged from a species-area or species-accumulation curve, which levels off as additional quadrats add few new species.
Standard summaries include species richness, the number of species; the Shannon index, minus the sum over species of each species' proportion times the natural logarithm of that proportion, which rises with both richness and evenness; and the Simpson index, the sum of squared proportions, which measures dominance (its complement or reciprocal is used as a diversity measure). In Indian and other tropical phytosociological studies the importance value index (IVI) of each species is the sum of its relative density, relative frequency and relative dominance (basal area), each in per cent, so the IVI of all species together sums to 300.
Structural indicators that matter for biodiversity, such as large old trees, standing dead trees, deadwood volume, canopy layers and regeneration, are now measured in many NFIs. Deadwood lying on the ground is often sampled by line-intersect sampling: the diameters of pieces crossed by a transect are recorded, and the volume per hectare is π squared times the sum of squared diameters divided by eight times the transect length. With diameters in centimetres and transect length in metres, this gives cubic metres per hectare directly; a 100-m transect crossing pieces of 10, 20 and 30 cm gives 9.87 × 1,400 ÷ 800 = 17.3 m³/ha.
Carbon inventory estimates the carbon stored in forest pools: above-ground biomass, below-ground biomass, deadwood, litter and soil organic carbon, as defined in IPCC guidance. Above-ground biomass is estimated from tree measurements using allometric equations or by converting volume with wood density and biomass expansion factors; below-ground biomass with root-to-shoot ratios; and carbon from biomass with a carbon fraction (IPCC's default for wood is 0.47, but species values differ). Soil carbon needs separate sampling by depth with bulk density. The choice of equations and factors is often the largest source of error, so inventories should state them and, where possible, use local equations.
Other resources inventoried with forests include grazing capacity, wildlife (by transects, camera traps, track counts and pellet counts, covered in wildlife subjects), water and recreation use. The general principles remain the same: a clear objective, a probability design, standard measurement rules and an honest statement of error.
Data processing begins with checking. Field records are screened for missing values, impossible values (a diameter of 500 cm, a height of 3 m for a 60-cm tree), wrong species codes and duplicated plots, and suspicious records are checked against field notes or remeasured. Electronic field recorders reduce transcription errors and can apply checks at the time of entry.
Next, missing tree variables are filled in by models. Heights not measured on every tree are predicted from local height-diameter equations fitted to the sample trees. Tree volume is computed from volume equations or tables, chosen for the species and region and applied only within the range of sizes on which they were built. Biomass and carbon are computed from allometric equations or conversion factors. Each tree is then multiplied by its expansion factor, the number of trees per hectare it represents: the plot expansion factor for fixed-area plots, or BAF divided by tree basal area for point sampling.
Expanded tree values are summarised in standard tables. A stand table gives the number of trees per hectare by species and diameter class. A stock table gives the basal area or volume per hectare by species and diameter class, often split by product or grade. These tables are computed for each plot and then averaged using the design's estimators, for example weighted by stratum area for a stratified design or computed per cluster for a cluster design, so that each figure carries a standard error.
Totals for the forest are the per-hectare estimates multiplied by the area of each stratum or the whole forest. Area itself comes from maps, GIS or remote sensing, and its error should be stated where it is estimated rather than known. Growth, mortality and removals come from remeasured permanent plots. Many inventories also produce maps, by combining plot data with satellite images or LiDAR through modelling, which give estimates for small areas but carry model error that must be assessed separately.
An inventory report states the objectives, the area and population covered, the definitions used (minimum tree size, merchantable limits, forest definition), the sampling design and plot type, the number of plots measured, the volume and biomass equations used, the estimates with their standard errors or confidence intervals and the probability level, and the known limitations. A table of results without errors and methods cannot be judged or compared.
Quality assurance covers the whole chain: training and certification of crews, written field manuals, a share of plots remeasured blind by an independent check crew, calibration of instruments, documented data processing, and archiving of raw data so that results can be recalculated when better equations become available. Tolerances for check-crew differences in diameter, height and tree count are set in each programme's manual.
Two errors in reporting are common. One is presenting precise-looking figures, such as volume to the nearest cubic metre for a whole district, when the sampling error is several per cent. The other is comparing two inventories that used different definitions, plot designs or volume equations and treating the difference as real change. Change should be estimated from remeasured plots or from inventories that are designed to be comparable.
A student should be able to compute a mean, standard deviation, coefficient of variation, standard error and confidence interval from a set of plot values by hand, calculate sample size for a stated allowable error, find plot radius and expansion factor for any plot size, and work out cruise intensity for strips, line plots and grids. Field practice should include laying out circular plots with slope correction, running a compass line, tallying trees on a line-plot cruise and using an angle gauge. Learn to explain why systematic sampling is used despite its statistical weakness and why stratification improves precision.
A forester five years into practice plans and supervises inventories: writing cruise specifications for a sale, choosing plot type and size, setting the number of plots for the allowable error in the contract, training crews and running check cruises. In public service the forester conducts enumeration for working plans, maintains permanent plots, and prepares stand and stock tables. The forester must judge whether results are good enough for the decision at hand and explain the uncertainty to buyers, managers and community committees.
A senior forester with twenty-five years' experience designs inventory systems for a large owner, a state or a nation: deciding the grid, plot design, remeasurement cycle and use of remote sensing; balancing national precision with district detail and cost; maintaining continuity of definitions over decades; and ensuring that inventory results meet the reporting needs of working plans, certification, greenhouse gas inventories and FAO's global assessment. The senior forester also commissions audits of inventory quality and defends results when they are challenged.
A researcher with long inventory experience develops and tests designs and estimators: model-assisted and model-based estimation combining field plots with LiDAR and satellite data, small-area estimation for districts and compartments, sampling for rare species and deadwood, estimation of change and its uncertainty, and the propagation of model error from volume and biomass equations into national totals. Such work shapes national inventory designs and the methods accepted for carbon reporting.
This manual gives the standard design-based estimators in words with worked examples; it does not derive them or give the full variance formulas for two-stage, multiphase and sampling-with-partial-replacement designs, which are in the sampling texts listed. Model-based and model-assisted estimation with LiDAR and satellite data is introduced only briefly; it belongs with remote-sensing-forestry and forest-gis-lidar. Tree measurement, volume equations and angle-count instruments are covered in forest-mensuration. National details (plot designs, grid densities, remeasurement cycles, minimum diameters, check-crew tolerances and allowable errors in contracts) are given only where they are well established and otherwise left to each programme's current field manual, because they change. Wildlife census methods are left to the wildlife subjects.
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions.
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