Inventory Practice for Managed Forests

C.J. Goulding M.E. Lawrence

FRI BULLETIN NO . 171

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INVENTORY PRACTICE FOR MANAGED FORESTS

by C.J. Goulding M.E. Lawrence

1992 Published by the Forest Research Institute Private Bag 3020 Rotorua New Zealand

Telephone (07) 347-5899 Facsimile (07) 347-9380

ISSN 0111-8129 ODC 524.6

2 TABLE OF CONTENTS

CHAPTER 1- INTRODUCTION ...... 5 1.1 Preamble ...... 5 1.2 Management inventory ...... 6 1.3 Preharvest inventory ...... 6

CHAPTER 2- BASIC STATISTICS ...... 8 2.1 Sa1npling ...... 8 2.2 So1ne tenninology ...... 8 2.3 Variance, standard error, and covariance ...... 9 2.4 Confidence lin1its ...... 14 2.5 Variances of products and sums ...... 15 2.6 Sampling methods ...... 18

CHAPTER 3- PLANNING AN ASSESSMENT ...... 20 3.1 Definition of the inventory ...... 20 3.2 Calculating the size of the sample ...... 20 3.3 Locating and demarcating plots ...... 25 3.4 Size and shape of bounded plots ...... 27 3.5 Angle gauge or point sampling ...... 29 3.6 Horizontal line sampling ...... 30

CHAPTER 4- FIELD PROCEDURE ...... 32 4.1 Transects I grid lines ...... 32 4.2 Bounded plots ...... 32 4.3 Angle gauge points ...... 34 4.4 Horizontal line plots ...... 37 4.5 Field equipment ...... 38 4.6 Sampling for total height ...... 39

3 REFERENCES ...... 41

APPENDICES ...... 42 Table 1-Random numbers ...... 42 Table 2- Student's "t" values for probability of 95% ...... 43 Table 3- Conversion of true distance to slope distance ...... 44 Table 4- Half diagonal length for diamond-shaped plots ...... 45 Table 5- Radii of circular plots ...... 46 Table 6- Horizontal marginal distances for BAFs ...... 47 Table 7- Height formulae ...... 48 Table 8- Height tables- method 1 (degrees) ...... 49 Table 9- Height tables- method 2 (percent) ...... 50

FIGURES Figure 1-Example of a map used for inventory planning ...... 28 Figure 2- Use of a prism ...... 35 Figure 3- Use of a relaskop ...... 35 Figure 4- Prism placed on a Suunto ...... 36

4 CHAPTER 1 INTRODUCTION

1.1 Preamble This is a manual on the elementary and practical aspects of planning and conducting inventories in forests managed primarily for timber production. A managed forest for the purposes of this manual is one in which stands of trees may be established either by planting or natural regeneration and one or more silvicultural operations take place in addition to felling. It is assumed that forest maps exist and stocked areas are known reasonably accurately. Most of the experience used in compiling this manual has been obtained in fast-grown, intensively-managed coniferous forests comprising stands which contain one or at most three species. The special problems of multi-species, tropical hardwood, or extensive unmanaged boreal forests are not described. National forest inventory is a subject on its own, and is also not covered. The manual should be useful to operational staff who are called upon to provide stand information for management planning and control, for marketing and sale purposes, and for the assessment of merchantable volume. The chapter on basic statistics is limited to those practical aspects of sampling likely to be of day-to-day use to inventory personnel. No theory is given, but formulae are, even though nowadays staff may have access to computer programs which will perform the necessary calculations. A more thorough description of elementary forest sampling is given by Freese (1962), of forest inventory by Loestch and Hailer (1973), and of forest mensuration by Husch et al. (1982) or Philip (1983). The other chapters and appendices are designed to assist inventory staff firstly in planning and defining their procedures, and secondly in compiling their own detailed manual, specific to their needs. For managed forests, inventory can be divided into two basic types: 1. Management inventory, which estimates the basic stand parameters used to control silvicultural operations, to provide stand records and as input for growth models. 2. Preharvest inventory, which provides marketing and logging personnel with information on the likely product volume yield shortly before harvesting.

5 1.2 Management inventory Inventories associated with silvicultural operations such as pruning and thinning are classified as management inventories. Rate-setting inventories are used to collect information about the stand in order to formulate a prescription for a forest operation and to set a work target or contract rate for the job. Quality control inventories ensure that the work is performed in an acceptable manner, and the information on the residual stand may also be stored in stand records to be used for projecting the stand's subsequent growth and yield. When a stand is untended or the information stored in the records about the stand is regarded as suspect, an inventory may be carried out to update the records and provide the data needed by the growth prediction system. The parameters assessed are usually confined to numbers of stems per hectare, basal area per hectare, total height, and possibly some indication of future merchantability. Management inventory procedures can provide broad-based estimates of standing volume and are adequate where there is little differential in the value of products. They are inadequate where merchantable reduction factors cannot be obtained from past experience or where it is required to differentiate between the merchantability of individual stands destined for diverse markets.

1.3 Preharvest inventory Preharvest inventory methods provide information for the planning and administration of harvest operations and for forest valuation. They assist in marketing and logging planning by estimating the crop yield by different log types and by defining the quantity and location of high value products such as peeler logs. As an aid in allocating logging equipment and setting bonus targets, they provide information on total recoverable volume, on average merchantable sizes for hauls, and on numbers and sizes of individual logs. They can also be used to provide merchantability factors as a control for long­ term yield forecasting. The MARVL inventory procedure typifies such a system. MARVL stands for Method of Assessment of the Recoverable Volume by Log-types, and is implemented on IBM compatible personal computers as MicroMARVL (Deadman 1990). MARVL recognises the potential of stands to yield different products when subjected to different stem cross-cutting ("bucking") patterns. The approach used is to observe and record stem quality and size on a sample of standing trees and then to predict the results of cross-cutting these trees under the influence of a variety of log specifications and requirements, as

6 specified by the inventory officer. No merchantability factors are required. However, because of the cruising involved, the field crew must be competent in measuring or estimating by eye upper diameters and heights, and more importantly, in recognising the changes in stem quality that determine log grade.

7 CHAPTER 2 BASIC STATISTICS

2.1 Sampling When every tree in a stand is measured it is said that a 100% sample has been carried out. For small areas with irregular boundaries where the estimate of area is likely to be inaccurate, 100% measurement or counting may be the most appropriate method of inventory. However, because it may be impossible, impractical, or too costly to measure every tree in larger areas, only a proportion of the trees are measured, that is, sampled. Often this proportion may be very low, less than 1 or 2%, but if the sampling design is correct, the information obtained will be every b:i1: as useful and satisfactory for management as if every tree had been measured. This is because it is often not necessary to know the information with 100% accuracy, without any error, in order to make correct management decisions. Sampling also provides an opportunity to obtain both more accurate information by concentrating the measurement effort on fewer trees and more timely information by reducing the quantity of measurement.

2.2 Some terminology A population is the entity on which an inventory is carried out. It is an aggregate of units where each unit could be measured for some information. For example, the unit could be 0.1 ha plots which are to be measured for volume per hectare. The definition of the units must be clearly expressed so that it is known whether a given unit belongs to the population or not. The population could be a small stand of trees forming a logging setting within a compartment, a whole compartment, several compartments composed of similar stands, or the whole forest. The objectives of the inventory will be defined in terms of the population. A parameter is a constant which characterises the population, for example, the total volume of a stand or the mean height of trees within a stand. The inventory will estimate the value of one or more of the population's parameters. This estimated value is known as the sample estimate. A characteristic which varies from individual to individual is known as a variable, for example, tree height, tree diameter at breast height (dbh), or plot volume per hectare. Accuracy refers to the closeness of the sample estimate to the true value of the population. A sample estimate may be inaccurate because of bias or lack of precision, or both.

8 Bias is a systematic error which may be due to poor sampling or to poor measurement techniques. Examples are the consistent failure to include edge trees in the sample because plots are always located away from the stand boundary, the measurement of dbh too low on a tree, or a faulty hypsometer. No matter how many sampling units are measured, any bias present will persist. It can be reduced by careful training and checking of techniques. If the amount of bias is known, or can be estimated, then a correction can be made to the sample estimate. Precision is the degree of clustering of the values of the sample units around their mean. If the spread or range of the values of a sample is wide, the sample is said to be imprecise. Errors in estimating a population parameter due to lack of precision can be reduced by increasing the number of units sampled. The precision of an estimate is an expression of the variability that would occur if a large number of similar inventories were carried out on the same population, and it measures the spread of these estimates about the true mean. Normally only one inventory is carried out on a population at any one time and the precision is expressed as confidence limits about the estimated mean. These define a range of values which are likely to contain the true mean, with a given probability. The probable limits of error or PLE, a term peculiar to New Zealand forestry, refers to the confidence limits expressed as a percentage of the estimated mean. For example, a PLE of 10% at the 95% probability level implies that the true mean was likely to lie within 10% of the estimated mean 95 times out of 100.

2.3 Variance, standard error, and covariance The variance of individual sample units in a population is a measure of the variability of the unit values about the mean value. Usually it is unknown and is estimated from the sample by first calculating the sums of squares (S.S.) of deviations from the mean:

2 (Lx)2 s.s. Ix - '---"­ ' n

Then the sample variance is: s.s. n- 1

X. the value of the ith observation where I n the number of sample units.

9 The term n-1 denotes the number of degrees of freedom (d.f.) of the sample. An estimate of the standard deviation of the population (s) is calculated from the square root of the variance

s = JS2

The standard error (s,) of the sample is the shortened name for the standard error of the estimate of the mean of the samples. If several inventories were carried out on the same population, each with the same number of sample units, then there would be several estimates of the mean valueofthe population. It is possible to calculate the standard deviation of these estimates of the mean to indicate the variability in the estimates. The term standard error is simply the standard deviation of these means. When simple random sampling without replacement has been carried out, the standard error (s,) can be estimated directly from the variance of the sample units:

S- x where variance of the sample units number of sample units number of units in the entire population.

The term n/N is known as the sampling fraction. Where this is small, less than 5%, it can be ignored and set to zero in the above formula. This is often the case even with small stand-based inventories. It is equal to zero for angle gauge sampling (see Section 3.5). The standard error then becomes:

S- x where variance of the sample units number of sample units.

The coefficient of variation (C) is a measure of the variability of the population expressed as a percentage of the mean: s c X 100% X

10 where s standard deviation of the sample x sample mean. The larger this value, the more variable is the parameter being measured. Note that it is dimensionless, that is, it remains the same value regardless of whether it is measured in mm, cm, or m. When two variables are measured on each sample unit, it is possible to calculate the covariance between them to measure how much the two vary in relation to one another. Where no relationship exists between them the variables are said to be independent and their covariance will be equal to zero. In this case, knowing the value of one variable provides no information as to the value of the other. Where larger values of one variable imply larger values of the other, the covariance will be positive; where larger values of one imply smaller values of the other, the covariance is negative. If the relationship between the two variables is linear in some form, then the variables are said to be linearly correlated and the family of regression estimators can be used to improve the estimate of the mean of one, given the other. For simple random samples, the estimated covariance is:

(Lx)(Ly) n 11 - 1

where values of ith observation of variables x and y respectively n number of sample units

All the above statistics can be readily calculated for any inventory. For example, five 0.1 ha bounded plots were randomly located in a 4 ha stand to estimate the average stocking. The estimates from the five plots were 400,270,230,470, and 460 stems/ha respectively.

The mean stocking =-=--=--+'-=2 '-7O::..._c_+-"2=-=3--=0_+c.-=4-'-7-=-0-'+----=-~ stems Jha 5 1830 stems/ha 5 366 stems/ha

11 Estimates of the variability can be obtained by first calculating the sums of squares

1830 2 = (400 2 + 2702 + .. .) 5 1830 2 718 300 5 48 520 followed by the variance

48 520 4 12 130 then the standard deviation of the population

110.1 stems/ha

The standard error of the mean stocking estimates can be derived from the variance. If the sampling fraction (proportion of the stand measured) is less than 5% (0.05) it can be ignored, otherwise

The sampling fraction

5 (the number of 0.1 ha samples in a 4 ha stand) (4/0.1) 0.125

The standard error of the mean

130 = X (1 - 0.125)) 5

46.07

12 Ignoring the sampling fraction, or if sampling had been done using angle gauges, the standard error of the mean

12 130 5 49.25

Finally, the variability of the stocking estimates can be expressed as a percentage of the mean by calculating:

The coefficient of variation

110.1 X 100% 366

30.1%

At the time the plots we reassessed for stocking, the individual trees were also measured for dbh, and the average diameter of each of the five plots was calculated as 20.2, 24.1, 25.2, 16.3, and 17.1 cm respectively. Any linear relationship between the two plot variables stocking and diameter, can be established by calculating the covariance:

The covariance

1830 X 102.9 35 910 - 5 4

437.9

The large negative value implies that as the stocking incrcases in the plot, the average diameter decreases (not unexpectedly!). A positic.>e ualue would imply that both variables incrcase or decrease together.

13 2.4 Confidence limits The confidence limits of a sample indicate the range of values within which the true mean of the population is likely to be found. They are normally expressed as the estimated mean plus or minus some interval, so that: True mean = estimated mean ± t x 5x where Student's t, with n- 1 degrees of freedom

S-x the standard error of the mean estimated from the sample n number of sample units.

For this formula to be correct, the distribution of estimates of the mean must be normal (i.e., follow a bell-shaped frequency distribution). This may not be true if the number of sample units, n, is small and the distribution of the sample units themselves differs markedly from the normal distribution. In this case, the number of sample units should be increased, i.e., n should be larger, in order for the formulae to be applied. For forest management purposes, it has become customary to adopt the 95% probability levelfor sampling. This implies thatthere is a 5% or a 1 in 20 chance of the true mean lying outside of these limits, and if enough inventories are carried out one of them is likely to have a true value outside what is expected. The values oft can be found in most statistical text books. It is necessary to find the column corresponding to the required probability level, and the value will be on the row with the correct degrees of freedom. (Table 2 of the Appendix gives the values oft at the 95% probability level.)

In the previous example, the mean stocking based on the five plots was 366 stems/ ha, with a standard error of 46.07. The value oft for (5-1) = 4 degrees of freedom at the 0.05 (95%) probability level is 2.776. The true mean should therefore lie between the estimated mean of 366 stems/ha ± the 95% confidence interval, i.e.:

X S- X ± t x 366 ± 2.776 x 46.07 stems/ha 366 ± 128 stems/ha

The probable limits of error (PLE)

128 X 100% 366

35%

14 The estimate of stocking based on the five plots is, therefore, 366 ± 128 stems/ha, or, 366 stems/ha ± 35%. The true mean should therefore be found between 238 and 494 stems/ha, unless a one in twenty chance has occurred.

2.5 Variances of products and sums The total volume of a stand or forest can be calculated from inventory estimates of volume per hectare by multiplying the mean volume per hectare by the total area. When the variance and standard error of the mean volume per hectare are calculated from the sample, it is also possible to calculate the variance and standard error of the total volume.

If T kxx where T is a total k is a constant (e.g., area) x is a variable having a variance of 5x 2 and standard error s, then the variance of T

X S- and the standard error of T k x

Suppose, for example, the mean volume from an inventory of 46 ha was estimated as 3 3 3 350 m /ha, with confidence limits of± 35 m and a standard error of 17.1m •

The total volume 46 X 350m3 16 100m3 The confidence interval of the total volume ±46 x 35m3 ± 1610 m3 and the standard error of the total volume 46 x 17.1m3 786.6 m3

Note: the PLE of the total volume remains unchanged from that of the mean volume/ha.

15 Sometimes it is necessary to calculate a value by multiplying two variables whose means have been estimated, for example, the number of stems per hectare and mean individual tree basal area, to give basal area per hectare. Alternatively, the calculation may be the sum of two estimated variables: the volume of sawlogs and the volume of pulpwood to derive total yield per hectare. In both cases, if the variables had been sampled and measured independently, as would be the case in separate surveys, the covariance between the two would be zero. However, if the two variables had been measured as a pair in the same plot, even if by different methods, it is quite likely that there will be some correlation between the two and their covariance needs to be estimated and included in the calculation as follows:

If T=xxy Variance (xy)

If T=x+y

2 2 Variance (x+y) s x + s y + 2s xy where x and y are variables having variances of s}, s/, and covariance s,v respectively. · ·

Supposing top height (H) and basal area per hectare (B) were measured for each plot in an inventory, and the volume per hectare (V) can be calculated such that:

V = 0.3 X H X B

If the mean of the top heights is 22.6 m with a variance of2.225,and similarly, the mean of the basal area estimates is 34.0 with a variance of7.387 and the covariance is 3.927, then the volume

= 0.3 x 22.6 x 34.0 m3 jha

= 230.5 m3 jha

16 the variance of the volume

7.387 2 X 3.927, ~ + 34.02 + 34.0 X 22.6 ) ./ = 1114.0 and the standard deviation

= 33.4 m3/ha

If a separate inventory had been conducted in another area or forest, it would be possible to combine the two results and obtain an estimate of the resulting standard error and confidence interval. So long as the inventories were independent, the covariance between the two estimates would be zero. If the first inventory covered 46 ha with an 3 3 estimated total volume of 350m /ha and a standard error of 17.1 m , and if the second inventory covered 120 ha with an estimated total volume of 455m3/ha and a standard 3 error of 21.6 m :

The total combined volume

46 X 350 +120 X 455

70 700 711 3

The combined variance

= 7 337 204

The combined standard error 337 204 2 709m3

17 2.6 Sampling methods In forest inventory, the procedures adopted for choosing samples are based on the principles of random sampling. However, because random sampling is sometimes difficult to manage, some form of systematic approach is more commonly used. Simple random sampling or unrestricted random sampling occurs when individual units are selected at random from the entire population and measured to obtain estimates of population mean values directly. The selection of any sample unit should be completely independent of the selection of every other unit, that is, once a sample unit is selected it in no way influences whether another possible sample unit is also selected. Every possible combination of n units should have an equal chance of being selected. Sampling without replacement implies that a particular sample unit is selected only once. This is usually the case with bounded plots. Sampling with replacement occurs when each unit is allowed to be part of the sample as often as it is selected. For example, angle gauge sampling is sampling with replacement because an individual tree can be measured in two plots if the plots are close enough together and the tree diameters are large enough. In systematic sampling, the individual units are selected on a systematic and predictable basis. However, if the distribution of the units in a population is random, then a sampling scheme which selects samples at regular intervals can be thought of as random sampling. For example, if the volumes on all possible bounded plots in a stand are random with respect to the location of the plot, then selecting plots by using a grid is effectively random sampling. A population can be subdivided into strata so that differences within each stratum are less than the differences among the strata. Stratified random sampling involves partitioning the population into strata and sampling at random within each stratum. The strata must be identifiable on the ground and on maps, and the area of each must be known. Plots are analysed separately within each stratum to obtain per hectare values for each stratum. These are combined using the areas of the strata to obtain an average value for the whole population. To obtain any benefits from stratification, it is important that strata are created from "natural" divisions as opposed to "administrative" ones. Not only must the areas be well-defined and measurable, but the differences should be fairly obvious- pruned versus unpruned stands, high stockings versus low stockings. Provided the variability among strata is high relative to the variability within a stratum, the PLE of the

18 population estimates should be considerably improved relative to simple random sampling. Often insufficient information is available prior to the inventory to enable stratification. A population can be subdivided into strata after the inventory (post-stratification), but only on the basis of differences in supplementary observations, not on the differences in the measurements used to estimate the means of the parameters of interest. Several populations can be combined by redefining them as strata to obtain an estimate of a larger population with narrow confidence limits. However, if the inventory has been well planned it is unlikely that a single stratum can be redefined as a population and the estimate of the mean still meet the original desired confidence limits. Dividing a population into strata is purely a statistical technique to improve the precision of the estimated mean value of the population. Double sampling can be used when there is a good relationship between a variable that can be measured quickly and easily, and the variable of interest, which might be more expensive to measure. A larger sample of the quickly measured variable is taken to obtain a precise estimate of its mean, and a subsample of the units is also measured for the variable of real interest. An example is where a proportion of the plots is measured quickly and easily for basal area only and the remainder cruised for recoverable volume. The relationship between the recoverable volumes and basal area must be good, however, because this is derived from the intensively measured plots and used to convert all the estimates of basal area to recoverable volumes. In a similar fashion, heights are often obtained by double sampling. Only a few of the trees measured for diameter are also measured for height and a height/ diameter regression curve is calculated from them and applied to all the trees. Two stage sampling occurs where the selection of the sample units occurs in two stages (multi-stage sampling involves more than two stages). In the first stage a primary sample is made, then within each of the selected sample units of the primary sample, a second sample of units to be measured is made. In a large inventory where access to stands is difficult or expensive, the first stage may involve the random selection of compartments to be visited within one or more forests. Then the second stage could be the random selection of plot locations within the selected compartments.

19 CHAPTER 3 PLANNING AN ASSESSMENT

3.1 Definition of the inventory Forest inventories may be carried out at any staged uring the life of a stand. The person responsible for an inventory should always provide a formal, written definition of each inventory. This may be a simple form filled out for an assessment that is carried out frequently and routinely, or it may be a detailed document written specifically for an important inventory to be carried out only once. It should be filed for future reference along with the data collected during the inventory. Frequently all or part of the data will be re-analysed some time subsequent to that inventory, and almost certainly someone will query some detail of the operation. It must include: • a definition of the objectives of the inventory, including which parameters are to be estimated, along with their desired confidence levels or PLE percentage; • a statement of the area and the boundaries of the population, and the areas and boundaries of any strata; • maps for each compartment in the population, with reference to the relevant aerial photography, if available; • the shape, size, and number of plots to be sampled, including details on the maps of how plots are to be numbered and located on the ground, and how they are to be distributed between any strata; • the field procedure and equipment required; • a definition of any log grades or stem qualities to be recognised in the field; • the procedures for checking measurements.

3.2 Calculating the size of the sample Before any inventory is carried out, the objectives of the inventory, the populations, the desired confidence limits or probable limits of error (PLE), and the way in which the results will be used must be specified. This last item can be used to decide the desirable maximum size of the PLE. Where the value or volume is very high and the information from the assessment critical, a PLE of 2% to 5% may be required, this being easily translated into an equivalent dollar value. Where the results will be translated into a statement such as, "The area to be logged should take the contractor at least 8 months, but no longer

20 than 10 months", a required PLE can be determined, here 11% (± 1 month about the mean of 9). Many preharvest inventories are planned to obtain a standard 10% PLE for total recoverable volume. This limit should be seen as the minimum acceptable level given the large differences in product values and the much wider confidence limits on the estimates of individual log types. Sufficient plots must be measured to obtain the necessary PLE. In variable stands this may be a large number (anywhere from 25 to 60). It is recommended that no fewer than 10 plots be used. The number of plots required to obtain a desired PLE% can be calculated using an estimate of the variance among plots obtained from a previous inventory if the number of plots and PLE% achieved are known. It is sound practice to plan for extra plots because a few are invariably lost to unmapped roads, gaps, and over-eager logging crews. The variance between plots can be estimated from a previous inventory as follows:

111

where p is the PLE % of the previous inventory X is the mean value of the previous inventory is the appropriate value oft (see Appendix, Table 2) m is the number of plots of the previous inventory.

If there are no previous results on which to base the calculations, a pilot survey should be carried out to obtain an estimate of the variability in the stand. This can bedoneverysimply for volume-based inventories by obtaining several estimates of basal area from random samples, basal area being a good surrogate for volume.

2 The variance between the plots (s ) can be calculated from the following equation (see page 9):

Ix' - I

Ill -1 where m the number of plots in the pilot survey X. I= 1,2 .... m are the values on each plot. I

21 The following formulae assume that the sampling fraction, the proportion of the stand actually measured, is low. The number of plots required, n, is calculated iteratively. As a first approximation,

n X 1002

where d is the desired PLE % t isanappropriatevalueoft,say about2.1 at95% probability X is an estimate of the mean value.

Given the first approximation to the value of n, a more appropriate value of t is found from tables, and the calculation repeated. Two iterations are usually sufficient, as the estimates are likely to be approximate only. The number of plots is always obtained by rounding up the value of n.

For example, a pilot survey of 80 ha of radiata pine was carried out to enable 2 planning of a preharvest inventory. Using a prism (angle gauge) with a BAF of 5m / ha, eight estimates of the basal area per hectare were obtained.

Plot Count Basal area (m 2/ha)

1 8 40 2 7 35 3 10 50 4 4 20 5 9 45 6 8 40 7 6 30 8 9 45

The mean basal area per hectare is 38.12 m2jha.

22 The variance between the eight plots can be calculated as follows:

93 025 12 275 8

7 92.41

The target PLE for the inventory is 10%. Using a value oft= 2.1, and substituting in the equation given for n, the number of plots required can be calculated:

2 2.1 X 92.41 ) 11 1002 ( 102 X 38.12 2

n 28

The value oft for 28 plots,27 degrees of freedom, is 2.052. Because the value oft is only marginally less than 2.1, a second iteration only reduces the number of plots required to 27.

These formulae are directly applicable to simple random sampling. They could also be used for stratified random sampling if nothing is known about the variances of the individual strata. For this the total number of plots required is calculated from an estimate of the variance of the whole population, and then partitioned over the strata in proportion to stratum areas. Care must be taken to ensure that each stratum has at least two plots. The confidence limits actually obtained from an assessment made after doing this should be better than anticipated and presumably the benefits of stratification will be felt when using the results, rather than in any savings of field work. In practice, it is often a good idea to adopt this approach to ensure that the confidence limits are lower than stated in the inventory objectives. However, if it is desired to calculate the number of plots required for a given PLE and to optimally allocate these amongst the strata to minimise the number of plots required, the calculations are more complex. It is necessary to have an estimate of the variance among plots for each stratum and to know the area of each stratum. Once again, this information could come from either a previous inventory or a pilot survey incorporating all the strata.

23 Total number (n) of plots required is:

11

Number of plots in the ith stratum (n) is:

11. I where A the area of the ith stratum I A the total area of the population d the desired PLE% X an estimate of the mean value of the population an appropriate value oft (e.g., 2.1 at 95% probability) s2 an estimate of the variance among plots of the ith stratum I s. an estimate of the standard deviation of the ith stratum I = [5( 2: sum from i = 1 to the number of strata.

With double sampling, there is no simple way of accurately estimating the number of samples required for a given PLE. As the objective of using double sampling is to reduce the confidence limits of the estimate, an upper limit to the number of intensively measured plots required can be calculated using the formulae above for either unstratified or stratified sampling respectively, and these can be supplemented with tally plots. Experience with point sampling has shown that equal numbers of tally to measured plots will reduce the PLE by approximately 30% over measured plots alone. However, increasing the proportion past 50% however appears to show diminishing returns.

24 3.3 Locating and demarcating plots It will always prove worthwhile to visit as many of the stands as possible prior to the inventory to verify stand records upon which any stratification may be based and to locate on the ground any roads, tracks, and other access points which can greatly facilitate the field work. Once the number of plots has been determined, their locations must be established on maps that will be taken out into the field. It is important that this be done in the office prior to the field work itself. As much preplanning as possible of the routes to be taken should be done in the office, and bearings and distances should be marked on the map to reduce the possibility of errors, and to allow check measurements at a later date (see Figure 1). Experience has shown that relying on the field crew to establish plot locations on the map out in the field increases the likelihood of map scales and distances being misread, and a bewildered field party may find itself in a thorn-infested gully, or discover that their plot centre falls in the middle of a main road, or even that they measure the wrong compartment. It is generally recommended that a systematic sampling scheme be employed. Transects (grid lines) should be regularly spaced to cover the population and plots should be located along them at regular intervals. The transects must run across any contours, whether the contours are in elevation (i.e., transects should run up and downhill) or changes in stand characteristics. The distance between transects and between plot centres should be about equal, i.e., a square grid pattern. Recent aerial photographs should be used to check stand conditions, and in particular to check that the regular pattern of the plots does not coincide with any pattern in the stand, for example ridge tops. Where the parameter to be measured clearly has a trend from one side of the population to the other, for example, volume per hectare may decrease as exposure increases up the hill, then spacing of the transects and plot centres must reflect the proportion of land likely to contain trees with any given value of the parameter. Less frequently both transects and plots, or plots only, are located randomly. A grid is placed on the map and plot centres are located on some of the grid intersections chosen at random. Table 1 in the Appendix provides random numbers for selection of grid intersections. It is important that the entire population is covered when locating plots, and "inconvenient bits" are not neglected. Similarly, trees on or close to the boundary of a stand must be sampled as quality may be different and log size larger than in the stand interior. Plots should not be located in marked gaps or on internal roads because these areas will not have been included in the stocked area. They can, however, be located alongside these areas and be treated in the same way as

25 a plot by the stand edge. When the plots have been located on the map, bearings and distances from a permanent, identifiable point on the ground to the transects and plots should be marked on the map. There is much debate as to whether using a fixed grid pattern allows the calculation of confidence limits, which assumes random location of plots. If the placement of the grid on the map is essentially random, and care is taken that the obvious problems of using fixed regular intervals as mentioned above are avoided, then in practice the formulae applicable to random sampling give a fair indication of the confidence limits. Experience has shown that the systematic location of plots on a grid is easier to administer and more efficient for field work than a pure random sample. A grid pattern should ensure that all parts of the population are covered by the inventory, and operations and management personnel do not receive unpleasant surprises about parts of stands that have not been measured. There is no substitute for walking throughout the entire stand. To determine the grid size to be used, firstly obtain the area of the population to be inventoried. The grid size in metres, g, assuming a square grid, with plot centres spaced as far apart on the transect as the transects are apart, is then calculated from:

g 100 Jii~ where A is the area in hectares n is the number of plots required.

The grid size is rounded down to a convenient whole number, usually a multiple of 10 metres. Where the stand of trees has highly irregular boundaries or has many gaps that have been mapped out, then a smaller grid size will be necessary as many of the grid intersections will fall outside of the population. It will always be better to measure more plots than indicated in the formula above, rather than fewer, as the estimate of n is just that, an estimate.lt will also be significantly more expensive and inconvenient to add extra plots afterwards if the confidence limits prove to be wider than expected. Grids can be drawn up by hand on graph paper or sometimes obtained from the local draughting office. A good alternative is to obtain a large sheet of transparent graph paper which can be placed over the stand map. This enables an almost infinite range of grid sizes to be evaluated, and it can be re-used any number of times.

26 Finally, the grid size and its orientation (magnetic) must be noted on the maps to be used. The true grid bearing can be converted to a magnetic compass bearing by subtracting the magnetic declination from the true bearing. This difference (approximately 20° in New Zealand) varies from region to region and changes over time.ltcan be calculated from the information in the margin of the appropriate Map Series map for the locality upon which the forest maps are based (Figure 1).

3.4 Size and shape of bounded plots The plot size is chosen so that on average about 15 to 40 trees are contained in a plot. The most common size is 0.05 ha, but it can range from a minimum of 0.02 ha up to 0.2 ha. On slopes, plot size must be adjusted to obtain the equivalent horizontal area. Because of the assumptions inherent in sampling, it is important that the same plot type and size (or BAF) is used throughout a stratum. It is permissable, however, to vary the type or size between strata. Strip (transect) plots are advantageous in rough conditions, with poor access and high variability, and where the number of trees in a stand are sparse. They are usually 100 m long with 2.0 m or 2.5 m on either side of the transect. Length is corrected for slope. Strip plots should sample across trends in the stand, for example, at right angles to any elevation contours or systematic changes in stocking. They can provide a good indication of conditions throughout the stand, especially where changes occur in a striated manner. However, they must not be laid out to run parallel with tree rows. With high stockings there can be problems with many trees on the plot boundary, and per hectare values can be seriously in error. Variability between plots is usually higher than, or as high as, similar-sized circular or diamond-shaped plots. A well-motivated crew can cruise strip plots faster than circular or square plots because the access time to plots and the plot demarcation times are substantially reduced. A three-person crew is considered optimal, though four are sometimes used. Circular or diamond-shaped plots are more suited to higher density stands, especially younger ones where rows may be very evident. Diamond-shaped plots are in fact square, but oriented so that one of their diagonals is parallel, or nearly so, to the transect or row of trees. Where conditions are reasonably uniform (i.e., the variability among trees is as important as the variability among patches of stand) a given precision will be obtained with fewer plots if circular or diamond-shaped plots are used in preference to strip plots. However, where the stand is patchy or striated it may be more difficult to obtain a representative sample of the stand. Where access is difficult or plots

27 FIGURE 1-Example of a map used for inventory planning KAINGAROA S.F.1 1 : 10 000

Bearings : 70°/160°/250°/340° magnetic This area very rough Plots : 150m x 150m grid M -full measurement 1309 T -tally only

6314 000 mN

N CfJ 1271

z E 0 0 0 (0 (') CO C\J

1275 Starting at skid A, Team A measure plots 15, 11, 10 and 9 Team B plots 16, 21, 18, 19 and 17

Starting at skid B, Team A measure plots 7, 6, 5 and 20 Team B plots 8, 3, 2 and 4 STAND PPA NSA 01 64.0 64.0 Plots 1 and plots 14, 13 and 12 to be picked up from the road scattered randomly, much unproductive time will occur in access to the plots and travel between trees. This is especially so if vehicle travel is involved between plots. A two-person crew is adequate, though three are often used.

3.5 Angle gauge or point sampling Angle gauge sampling, also known as point sampling, prism cruising, or variable-plot sampling, has gained wide acceptance in many parts of the world. Thorough descriptions are given by Husch et al. (1982), and Dilworth and Bell (1968). The advantages over bounded plot methods include a potentially substantial saving of field time without loss of accuracy, and improved sampling because larger trees are more likely to be measured than smaller ones. Angle gauge sampling is therefore recommended as being more efficient for measuring basal area, volume, or value.lt is particularly suited to double-sampling schemes because measurements of trees are required only for the subsample points; at all remaining points only a count of the trees selected is needed, and this can be performed very quickly. However, where the prime aim of the inventory is to determine the number of stems per hectare, bounded plots will prove more efficient. In bounded plots a tree is determined as "in" depending on its position relative to the plot boundary, whereas in point sampling a tree is determined as "in" depending on both its breast height basal area (or its dbh) and its distance from the plot centre. Once trees have been selected, measurements on individual trees are identical. Under point sampling a tree is selected if the angle its dbh subtends at the plot centre exceeds a given critical value. The angle is measured by an angle gauge, preferably an optical wedge prism or a wide band Spiegel Relaskop. Each tree selected represents a fixed contribution to the plot estimate of basal area per hectare; the magnitude of this contribution is called the Basal Area Factor (BAF), and is dependent on the critical angle used. Prisms and the Spiegel Relaskop are calibrated in terms of BAF. For example, with a BAF of 10, each tree selected "in" contributes 10m2 /ha, so that a count of six trees "in" implies that the estimate of basal area is 60m2 /ha at that point. It is important to realise that the estimate at each sampling point is on a per hectare basis, even though the field procedure does not involve laying out a fixed area of a plot. Prisms can be obtained which have been ground to specific BAFs, and it is recommended that a range of prisms with BAFs of 1, 2, 3, 5, 7, and 10m2 /ha be made available when conducting plantation inventories. The wide band Spiegel Relaskop has BAFs of 1, 4, 9, 16, 25 ... plus intermediate values (see

29 Section 4.3). Factors of 2, 3, or 5 are likely to be more suitable for management inventories, whereas factors of 5, 7, or 10 are often used for preharvest inventory. A simple angle gauge can be constructed from a straight stick with a sight made from a piece of wood or metal of known width attached at right angles to the stick. A less accurate instrument can consist simply of one's thumb held vertically while extending the arm. The BAF m2 /ha of such devices is calculated (approximately, but sufficiently accurately in practice) as follows:

(sow 'v BAF '\ d) where w is the width of the sight (cm) d is distance from the eye to the sight (cm). For example, to construct an angle gauge with a BAF of 5 m2 /ha, use a sight 3 cm wide attached to a stick 67.1 cm long. It is recommended that a BAFbe chosen so that, on average, six to eight trees will be selected per point, e.g., with an expected basal area of 45m2 /ha, select a BAF of seven to use for the assessment. If the field conditions are such that there is poor visibility and much undergrowth, it is desirable to keep the number of trees selected per point low, and increase the number of plots. In clear conditions the reverse can apply. With a lower BAF more trees will be sampled at a given point, and borderline trees will be further away from the plot centre, involving more work in checking. If this is borne in mind when planning the assessment, conditions of dense undergrowth should not prevent point sampling from being used. In untended crops where there is persistent heavy branching at breast height, there may be considerable difficulty in seeing the actual stem because of the accumulation of needles and litter in the branch angles, and the speed of stem counts may be reduced. The distance to each tree must be compensated for slope, and in broken or hilly country the Spiegel Relaskop is very useful as this compensation is performed automatically. The use of either a prism or the Spiegel Relaskop requires a certain degree of skill and practice before the results can be obtained quickly and accurately. A crew of two people is usually sufficient.

3.6 Horizontal line sampling Horizontal line sampling is an application of the same angle count technique used in point sampling. The method is a "cross" between a strip plot and a

30 point sample; a line is measured on the ground and trees are counted "in" relative to the line using an angle gauge. Horizontal line sampling provides an estimate of mean diameter, as opposed to a direct estimate of basal area from point samples and stocking from bounded plots. Because the line is generally shorter (typically 20 m) than that employed in strip plots, there are fewer borderline trees (and hence less room for error), and plot establishment should be faster. However, as in point sampling, the lower the BAF the greater the number of trees sampled at a given point. This will increase both the number of borderline trees (to check) and the chances of undergrowth obscuring the target. Care should be taken to ensure the lines do not coincide with tree rows or other natural trends in the stands.

31 CHAPTER 4 FIELD PROCEDURE

4.1 Transects/ grid lines The start of each transect should be clearly marked with paint so that it can be located again if necessary. It is critical that the field crew are positive they are starting the transect from the correct location. Failure to do so can lead to plots being established in the wrong stratum, stand, or compartment. Any problems can usually be avoided if the areas have been checked on the ground in the early stages of planning. The correct bearing is always established using a compass and all distances should be measured, not paced. (Warning: metal framed spectacles may cause the compass to deviate from the correct bearing.) A correction for slope over 1oo is made by taking a reading of the average slope along the line of the transect for every 50 m length (less if the slope changes considerably over a shorter distance) and increasing the transect length by the appropriate amount (see Table 3 in the Appendix).

4.2 Bounded plots Bounded plots may be either strip (sometimes called "transects"), circular, or diamond-shaped. They should not be relocated in the field because of ground vegetation or tree stocking; if by chance a plot lands wholly or partially in a gap it is a valid sample and can only be discarded if the gap is large enough to be identified on maps or photos and its area deducted from the area of the stand. Strip plots are located along the length of the transect and corrected for slope. They are quick and easy to establish, particularly in heavy undergrowth, but have large numbers of trees on the plot boundary which can give rise to sampling errors. Strip plots are frequently 100 m long and either 4 or 5 m in width. It is important that the tape forming the centre line of the plot is stretched straight and doesn't meander through the scrub, or the plot area may be reduced. Plot width is established conveniently by using a light pole held horizontally. A borderline tree is "in" the plot if the centre of the stem at breast height is less than half the plot width from the tape. All trees within the plot should be marked and preferably numbered using paint. A gap of a least 10 m is left between strip plots on the transect. If a three­ man field crew is being used, it is possible for one member to continue along the transect measuring heights, while the second measures diameters and pruned heights (if required) and the third walks parallel to but a short distance

32 from the transect, to observe stem features at right angles to the transect while recording. Heights can often be measured along the transect (either direction) with the tape used for the plot centre doubling to measure the distance to the height tree. At the far side of the stand, the last part of a transect may be too short for a full plot. The crew should return on the adjacent transect completing the plot by commencing measurement at the same side of the stand. Circular plots are often used because they are simple to establish and avoid the problems associated with too many borderline trees. Once the plot centre has been located on the transect, its area must be corrected for slope by measuring the steepest slope and the slope 180° opposite, then averaging them ignoring the plus and minus signs. For example, if the steepest uphill slope from the centre was +22° and the slope opposite was -8°, the average slope is (22+8) /2 = 15°. The plot radius is then corrected for slope by reference to the appropriate table (Table 5 in the Appendix). If the plot area on the t1atis 0.05 ha 2 (500m ), the radius for a plot on a 15° slope would increase from 12.62 m to 12.84 m. For slopes less than 1oo corrections can be a voided by holding theta pe horizontal between the plot centre and each tree. Borderline trees are in the plot if the centre of the stem at breast height is in the plot. All trees should be marked with paint and numbered. When the plot is complete a check should be made to ensure that all the trees have been numbered and assessed as prescribed. Diamond or square plots are another form of bounded plot, although they are more commonly used for permanent plots. (Note: diamond plots are simply square plots rotated at an angle to the tree rows). To establish a diamond plot, locate the plot centre and measure the uphill and downhill angles along the line of maximum slope. The mean of these two angles is the slope of the plot. Determine the half diagonal length from Table 4 in the Appendix. Run out the tape on one diagonal along the line of maximum slope, or parallel to the tree planting lines, with half the diagonal length on either side of the plot centre. The other diagonal is oriented at right angles to the first. Note that each half diagonal is of equal length. The plot is then formed by the area enclosed by the four corners. Once again, borderline trees are "in" the plot if the centre of the stem at breast height is in the plot. All plot trees should be marked with paint and preferably numbered prior to measurement. When the plot is complete a check should be made to ensure that all plot trees have been assessed and numbered as prescribed. When double sampling is being used, a proportion of the plots will be "tally­ plots". Trees in a bounded tally plot are measured for dbh only. No heights are taken, nor are the trees cruised for quality and defect. Tally plots can be

33 measured very quickly to provide an estimate of basal area and number of trees per hectare.

4.3 Angle gauge points Trees are selected as "in" using either a prism, an angle gauge, or the Spiegel Relaskop, turning through a full 360°, except in the case of edge plots (see below). They are numbered using paint. Viewed through the prism, the image of the tree stem at breast height is deflected when compared to the direct line of sight. If the displacement is greater than the diameter of the tree it is "out", ifless it is "in", and if the same it is borderline (Figure 2). The prism itself must be held over the plot centre and the observer must circle around the prism. When the Spiegel Relaskop is used with the wide scale, the basal area factor BAF (m2 /ha) is obtained by squaring the number of relaskop units (whole 2 bands counted from right to left). Thus two units represent a factor of 4m / ha, 3 units 9 m 2 /ha, etc. Intermediate BAFs can be obtained by including the quarter units, e.g. 2% units represent 5.0625 m 2 /ha, 2% units represent 7.5625 m 2 /ha. When viewed at breast height a tree is "in" if it appears wider than the number of bands in use for the required BAF (Figure 3). With an angle gauge, the tree is "in" if the dbh appears to be wider than the width of the sight held at the distance of the stick away from the eye. For both an angle gauge and the Spiegel Relaskop, the observer's eye must be kept over the plot centre point. It is necessary to correct for slope for each tree individually with the prism but not with the relaskop which does this automatically. The correction with a prism is made by rotating the prism around the line of sight by an angle equal to the angle of the slope to the tree. This can be done by placing the prism on a Suunto hypsometer and tilting the Suunto until the required angle is read off on the side, having first determined the slope to the tree (Figure 4). With borderline trees, the horizontal distance to the tree centre from the plot centre should be obtained and the dbh measured. Each BAF has a given plot radius factor which, when multiplied by the dbh of the tree, gives the plot radius for that tree. If this individual-tree plot radius is greater than the horizontal distance to the centre of the tree at breast height, the tree is "in" the plot. For example, with a BAFof5m2 /ha theplotradiusfactoris0.22356,hence a tree of 40 cm dbh has an individual plot radius of 40 x 0.2236 = 8.94 m; if the tree is less than this distance from the centre it is "in" the plot. This distance is also known as the horizontal marginal distance.

34 FIGURE 2- Use of a prism to determine whether a tree is "in" a plot

Stem

p=---:- L lu c1/ j I ~~ I~· .P, .~1 ~ \ }11:.1 .~ ' ~· I. U ~ l ' ~. tll ~ ,'11 ' I~ L\ : ,I ~·~ ','1

~r'<1j J,,. ,,~ J l \1! ( "out" "in" "borderline"

----~------

3- Use of a Wide-band Spiegel Relaskop to determine whether a tree is"in" a plot of 9m2/ha (three units or three band widths)

Stem Stem

I I I) ~I I I

whole units quarter units

I! out"

35 FIGURE 4- Prism placed on a Suunto hypsometer and rotated to compensate for a slope of 20°

Table 6 in the Appendix contains marginal distances for individual trees of given diameters for a range of common BAFs. For BAFs other than those given in Table 6, a simple table can be constructed with a spreadsheet by multiplying the plot radius factor, PRF, by a range of diameters where:

1 PRF 2)BAF

Stand edge trees must be included in the sample. The edge of a stand must be sampled differently when there is a considerable portion of the stand along

36 the boundaries, as occurs in small irregularly shaped areas. The edge zone is defined as that area which contains trees that could be included in point samples located beyond the edge of the stand. If a sample point falls into this zone, a half-sweep of 180° is made towards the stand from a line parallel to the boundary. The BAF for that plot is recorded after multiplying it by 2. If the sample point falls in a corner of the stand, then a one-quarter sweep of 90° is made towards the stand, this time multiplying the BAF by 4. This method is only approximate, but should suffice for most operational conditions. When double sampling is being used, a proportion of the plots will be "tally­ plots", that is, no further work is done following the layout of the plot other than recording the "tally", or number of trees counted in the plot, on the tally plot form. In the other plots, as in all plots when double sampling is not being used, each tree is numbered, measured, and assessed for quality in exactly the same way as with bounded plots. The selection of trees may be speeded up if it is remembered that where the dbh of a tree is obscured by ground vegetation, if the tree is "in" when viewed further up the stem, it will certainly be "in" when viewed at breast height. Similarly, on sloping ground, if a tree is "in" when viewed by a prism without rotating the prism, it will be "in" when slope is accounted for. In both instances it will not be necessary to strictly measure the slope to the tree. Conversely, where a tree appears to be nearly "out", the marginal distance should be determined using a tape. Note that moving the plot centre even a short distance may give quite a different count of trees. Similarly, any one estimate of basal area from a single point is quite imprecise and an accurate estimate for the stand will be obtained only from a sufficient number of samples.

4.4 Horizontal line plots Horizontal line plots are located along the length of the transect and corrected for slope. They are about 20 m in length but have no width because trees are selected as "in" with an angle gauge, a prism, or the Spiegel Relaskop, using the same practices as with angle gauge plots (Section 4.3). It is important that the tape forming the centre line of the plot is straight and doesn't meander through the bush or the plot area will be reduced. The prism itself must be held over the plot line and the observer must move along it selecting trees on either side. Moving the prism even a short distance from the centre line may give quite a different count of trees. When the Spiegel Relaskop is used with the wide scale, the BAF (m2 /ha) is obtained by squaring the number of relaskop units (whole bands counted from right to left). For both an angle gauge and the

37 Spiegel Relaskop, the observer's eye must be kept over the centre line. At both ends of the plot a compass bearing should be taken at right angles to the line to ensure that trees beyond the end of the line are not included. It is necessary to correct for slope for each tree individually with the prism but not with the relaskop which does this automatically. With borderline trees, the horizontal distance to the tree from the plot centre line should be obtained and the dbh measured. Table 6 in the Appendix gives the marginal distances for individual trees of given dbhs for a range of common BAFs. Alternatively the plot radius factor, PRF, can be calculated from the equation given in Section 4.3.

4.5 Field equipment The following equipment is needed for forest inventory. Some items are mandatory regardless of plot type while others are optional or required only for certain plot types: 1 compass (preferably with a good "siting" mechanismforfollowing transects) 1 50 m tape (measuring transects and tree heights) 1 hip chain (ideal for transects because it enables plots to be re-visited easily) 1 dbh tape 1 Suunto Hypsometer with 15 m and 20 m direct scales and angles in degrees or percent spray paint clipboard, pens, and pencils plot location maps field forms or electronic data recorder tables for: - slope corrections for transect distances - height methods - marginal distances (point or horizontal line sampling)

The following equipment is optional and dependent on plot type: 1 light pole 2.5 m long, marked at 1.0 m, breast height (1.4 m), and 2.0 m (strip plots)

38 1 dbh callipers (measuring "out-of-round" in butt logs) 1 height pole (6 m, telescopic) marked at 0.1 m intervals (for measuring pruned height) prisms of appropriate BAF, rhost commonly 3m2 /ha, 5m2 /ha, and 7m2 I ha (point sampling) 1 Spiegel Relaskop- metric wide band (point sampling and/ or measuring upper stem diameters) 1 programmable calculator (if not using an electronic data recorder, with formula to check height measurements)

Warning: The Suunto compass is specific to latitude, that is, a Suunto compass calibrated by the factory for the Northern Hemisphere is not suitable for the Southern Hemisphere, and vice-versa.

4.6 Sampling for total height Sufficient trees must be measured for total height to establish a reliable height/ diameter curve either for each stratum or for the whole population, as defined in the inventory definition. Because heights vary considerably for a given diameter, it is recommended that 30 or more heights be measured per curve. Trees should be selected across the diameter range with emphasis on the larger trees as these tend to be more variable in height and more valuable. All trees except those with dead or broken tops are eligible as height trees. This includes both normal and malformed trees, which must be included to ensure that the height/ diameter curve is truly representative. The usual sampling procedure is to select the first 10 or so height trees at random and then to select specific trees to fill in the diameter range. Every plot, or alternatively every second or third plot, should have at least one height tree, thus spreading the height sample across the area. There are five methods of height measurement which can be used (see Appendix 7 for a diagram and the correct formulae). In all of them the Suunto hypsometer is the preferred instrument for measuring angles. Measurements are recorded on the appropriate forms, but the immediate calculation of tree height (in the field) is highly recommended so that errors can be found more readily. Method: 1- Distance measured by tape, angles recorded in degrees.

39 2- Distance measured by tape, angles recorded in percentages. 3- Direct method (including the 45° method). 4- Distance measured by rangefinder, angles recorded in degrees. 5- Distance measured by rangefinder, angles recorded in percentages. The Suunto hypsometer can be used to obtain a direct (Method 3) reading of height by standing 15 m or 20 m away from the tree on the horizontal and reading the heights off the appropriate scale, sighting to the top and to the datum points of the tree. The alternative direct method is the 45° method. A position on the ground is found where the top of the tree can be seen at exactly 45° and a horizontal line from the observer to the tree intersects the stem at a point which can be measured from the ground. The height from the ground to the horizontal on the stem is measured and added to the horizontal distance to give the total height of the tree. Direct measurement using the Suunto fixed distance scales is suited to flat land (slopes less than 10°), good conditions where the top and base datum points of the trees can be easily seen, and where trees are between 7 m and 25 m tall. Trees less than 7 m tall can be measured using a height pole. All the other methods involve measuring upper and lower angles, either in degrees or percentages. Where there is good visibility, a rangefinder with a vertically (beware of butts well or lean, especially on slopes) hung target can be used for distance measurement; otherwise a tape must be used. A point is found at a distance from the tree about equal to the tree height and at right angles to the direction of any lean, where both the top of the tree and the base datum point can be seen clearly. Usually the only way to ascertain the direction of lean is to walk completely around the tree. Distance is measured to the base datum point on the tree from the eye of the observer who should stand a whole number of metres away to simplify height calculation from tables. Tree heights should be calculated soon after measurement using either tables or electronic calculators and the formulae given in Table 7 of the Appendix. Suggested restrictions to minimise possible measurement errors are:

Upper angle +30° to +50° (+58% to +119%) Lower angle + 1 oo to - 30° (+17% to- 58%)

Angles should be measured to the nearest 0.5°, heights and distances to the nearest 0.1 m.

40 REFERENCES

DEADMAN, M.W. 1990: MicroMARVL user guide. FRI Software Series No. 7. DILWORTH, J.R.; BELL, J.F. 1968: Variable plot cruising. O.S.U. Bookstores, Corvallis, Oregon. FREESE, F. 1962: Elementary forest sampling. USDA Forest Service, Agriculture Handbook 232. HUSCH, B.; MILLER, C.I.; BEERS, T.W. 1982: Forest mensuration. 3rd ed. Wiley, New York. LOETSCH, F.; HALLER, K.E. 1973: Forest inventory. 2nd ed. BLV Verlagsgesellschaft, Munich. PHILIP, M. 1983: Measuring trees and forests. University of DarEs Salaam.

41 TABLE 1- Random numbers

08426 98002 59232 70610 08620 12166 93825 56086 25073 63163 68819 09311 41322 98337 52747 18553 46022 80373 46709 49122 86081 13558 84836 71450 81664 03197 91144 46761 71351 92842 97613 76996 72784 19066 37330 93466 27669 46839 47533 50454 51432 08229 00468 24407 82075 83125

60026 70202 2829<1 61927 38680 71563 80817 95473 67419 64643 96291 63250 56406 28220 02432 58918 53192 62896 99929 96592 29188 66533 93756 13538 92610 73175 23131 61881 29967 19405 97270 07596 90673 05529 19770 02244 37821 23239 60203 05097 34425 58268 07196 23214 82866 38306 09529 97596 74750 23201

47722 99016 05017 03846 14577 31237 75806 34213 30000 69403 20830 92661 97734 35878 02944 04170 78158 26477 97194 66168 14453 25307 67321 29496 81'256 86044 56144 08737 29737 65544 47823 35102 34952 60440 38245 10604 84068 49980 34536 24029 15224 89219 70092 57219 75533 05119 98093 82132 15096 93651

76317 97092 73130 40328 99703 65013 12354 03686 81437 23697 58918 30747 87191 46515 89362 94891 14938 20951 84406 13347 91055 59800 12626 53546 32309 15306 87251 32323 73380 57378 64633 05466 69398 33699 23493 17485 10645 52361 28028 99846 33177 68476 21043 31961 27524 03744 11241 08139 95719 90780

10063 70253 67058 23301 67577 36127 54668 13456 84189 23641 69852 29424 30483 92888 14065 74817 35602 64596 15547 54933 18315 09969 36254 18995 61263 58828 17136 55251 61952 76435 21741 52395 67974 58994 39246 15152 48419 94074 14950 09801 62061 94332 88996 49330 30194 45364 69449 19889 99301 59085

17725 59554 96694 17794 95432 25542 80324 77244 40377 33643 07054 45814 50521 19471 50726 52929 26646 04304 04919 76482 62096 40211 58298 51841 05763 76894 84671 85399 86175 37630 96162 89441 50217 19596 89060 54586 90098 91781 48896 11788 94975 80665 24037 67828 72514 95907 60013 37834 13324 42883

52612 6338 59635 05940 06731 34440 04773 36916 82589 40944 14370 53435 96926 79547 22949 74871 61016 16897 79632 99514 19595 87297 63894 04271 81686 06540 36899 92050 43882 60285 20708 22191 71489 68612 73636 15814 02019 56022 37507 86798 15323 42972 74058 30295 24763 83683 67904 26716 03478 97930

54206 20467 64035 70477 87516 14746 07586 33424 52510 22858 30451 36108 20328 39665 38079 99795 51478 78534 93204 25920 34743 06175 87571 24103 31013 79424 19308 38722 22644 43731 91102 20946 71506 74377 26783 28054 55031 46887 91130 47303 95310 92603 73755 94141 63709 66456 40194 44008 47278 97754

17913 68086 67841 24841 01679 98835 67152 61937 82985 63014 36266 22345 52332 37184 22924 33131 99704 17332 18243 54585 92243 82215 94357 40442 59601 69403 61481 93832 37566 90018 30941 96172 98661 51026 12685 38617 66477 77688 96456 61152 57216 47632 22781 58272 63767 93569 27129 72563

96128 06524 64833 30451 83268 10614 34396 96383 24988 74583 42601 30170 46766 68930 16225 67675 31970 67306 06466 29686 73478 08705 34556 67987 98918 20732 42630 09937 73017 89077 25383 86820 82572

42 -~-~~~~~~-.. ·-- TABLE 2- Student's "t" values for probability of 95%

~··-·-~---

Degrees of freedom Value of

4 2.776 34 2.033 5 2.571 35 2.031 6 2.447 36 2.029 7 2.365 37 2.027 8 2.306 38 2.025 9 2.262 39 2.023 10 2.228 40 2.021 11 2.201 41 2.019 12 2.179 42 2.018 13 2.160 43 2.017 14 2.145 44 2.016 15 2.131 45 2.015 16 2.120 46 2.014 17 2.110 47 2.013 18 2.101 48 2.012 19 2.093 49 2.011 20 2.086 50 2.010 21 2.080 51 2.009 22 2.074 52 2.008 23 2.069 53 2.007 24 2.064 54 2.006 25 2.060 55 2.005 26 2.056 56 2.004 27 2.052 57 2.003 28 2.048 58 2.002 29 2.045 59 2.001 30 2.042 60 2.000 31 2.039 70 1.994 32 2.037 80 1.989 33 2.035 90 1.986

43 TABLE 3- Conversion of true distance to slope

Slope" Horizontal 100 200 300 400 500 600 700 800

100.0 200.0 300.0 400.1 500.1 600.1 700.1 800.1 100.1 200.1 300.2 400.2 500.3 600.4 700.4 800.5 3 100.1 200.3 300.4 400.5 500.7 600.8 701.0 801.1 4 100.2 200.5 300.7 401.0 501.2 601.5 701.7 802.0 5 100.4 200.8 301.1 401.5 501.9 602.3 702.7 803.1 6 100.6 201.1 301.7 402.2 502.8 603.3 703.9 804.4 7 100.8 201.5 302.3 403.0 503.8 604.5 705.3 806.0 8 101.0 202.0 302.9 403.9 504.9 605.9 706.9 807.9 9 101.2 202.5 303.7 405.0 506.2 607.5 708.7 810.0 10 101.5 203.1 304.6 406.2 507.7 609.3 710.8 812.3 913.9

11 101.9 203.7 305.6 407.5 509.4 611.2 713.1 815.0 916.8 12 102.2 204.5 306.7 408.9 511.2 613.4 715.6 817.9 920.1 13 102.6 205.3 307.9 410.5 513.2 615.8 718.4 821.0 923.7 14 103.1 206.1 309.2 412.2 515.3 618.4 721.4 824.5 927.6 15 103.5 207.1 310.6 414.1 517.6 621.2 724.7 828.2 931.7 16 104.0 208.1 312.1 416.1 520.1 624.2 728.2 832.2 936.3 17 104.6 209.1 313.7 418.3 522.8 627.4 732.0 836.6 941.1 18 105.1 210.3 315.4 420.6 525.7 630.9 736.0 841.2 946.3 19 105.8 211.5 317.3 423.0 528.8 634.6 740.3 846.1 951.9 20 106.4 212.8 319.3 425.7 532.1 638.5 744.9 851.3 957.8

21 107.1 214.2 321.3 428.5 535.6 642.7 749.8 856.9 964.0 22 107.9 215.7 323.6 431.4 539.3 647.1 755.0 862.8 970.7 23 108.6 217.3 325.9 434.5 543.2 651.8 760.5 869.1 977.7 24 109.5 218.9 328.4 437.9 547.3 656.8 766.2 875.7 985.2 25 110.3 220.7 331.0 441.4 551.7 662.0 772.4 882.7 993.0 26 111.3 222.5 333.8 445.0 556.3 667.6 778.8 890.1 1001.3 27 112.2 224.5 336.7 448.9 561.2 673.4 785.6 897.9 1010.1 28 113.3 226.5 339.8 453.0 566.3 679.5 792.8 906.1 1019.3 29 114.3 228.7 343.0 457.3 571.7 686.0 800.3 914.7 1029.0 30 115.5 230.9 346.4 461.9 577.4 692.8 808.3 923.8 1039.2

31 116.7 233.3 350.0 466.7 583.3 700.0 816.6 933.3 1050.0 32 117.9 235.8 353.8 471.7 589.6 707.5 825.4 943.3 1061.3 33 119.2 238.5 357.7 476.9 596.2 715.4 834.7 953.9 1073.1 34 120.6 241.2 361.9 482.5 603.1 723.7 844.4 965.0 1085.6 35 122.1 244.2 366.2 488.3 610.4 732.5 854.5 976.6 1098.7 36 123.6 247.2 370.8 494.4 618.0 741.6 865.2 988.9 1112.5 37 125.2 250.4 375.6 500.9 626.1 751.3 876.5 1001.7 1126.9 38 126.9 253.8 380.7 507.6 634.5 761.4 888.3 1015.2 1142.1 39 128.7 257.4 386.0 514.7 643.4 772.1 900.7 1029.4 1158.1 40 130.5 261.1 391.6 522.2 652.7 783.2 913.8 1044.3 1174.9

41 132.5 265.0 397.5 530.0 662.5 795.0 927.5 1060.0 1192.5 42 134.6 269.1 403.7 538.3 672.8 807.4 941.9 1076.5 1211.1 43 136.7 273.5 410.2 546.9 683.7 820.4 957.1 1093.9 1230.6 44 139.0 278.0 417.0 556.1 695.1 834.1 973.1 1112.1 1251.1 45 141.4 282.8 424.3 565.7 707.1 848.5 989.9 1131.4

horizontal distance Slope distance= Cos (slope)

44 TABLE 4- Half diagonal length for diamond-shaped plots

Slope' Half dif!gonallengths (m) for plot sizes (ha)

0.01 0.02 0.04 0.06 0.08 0.10

0 7.07 10.00 14.14 17.32 20.00 22.36 1 7.07 10.00 14.14 17.32 20.00 22.36 2 7.07 10.00 14.15 17.33 20.01 22.37 3 7.08 10.01 14.15 17.33 20.01 22.38 4 7.08 10.01 14.16 17.34 20.02 22.39 5 7.08 10.02 14.17 17.35 20.04 22.40 6 7.09 10.03 14.18 17.37 20.06 22.42 7 7.10 10.04 14.20 17.39 20.07 22.44 8 7.11 10.05 14.21 17.41 20.10 22.47 9 7.12 10.06 14.23 17.43 20.12 22.50 10 7.13 10.08 14.25 17.45 20.15 22.53

11 7.14 10.09 14.27 17.48 20.19 22.57 12 7.15 10.11 14.30 17.51 20.22 22.61 13 7.16 10.13 14.33 17.55 20.26 22.65 14 7.18 10.15 14.36 17.58 20.30 22.70 15 7.19 10.17 14.39 17.62 20.35 22.75 16 7.21 10.20 14.42 17.67 20.40 22.81 17 7.23 10.23 14.46 17.71 20.45 22.87 18 7.25 10.25 14.50 17.76 20.51 22.93 19 7.27 10.28 14.54 17.81 20.57 23.00 20 7.29 10.32 14.59 17.87 20.63 23.07

21 7.32 10.35 14.64 17.93 20.70 23.14 22 7.34 10.39 14.69 17.99 20.77 23.22 23 7.37 10.42 14.74 18.05 20.85 23.31 24 7.40 10.46 14.80 18.12 20.92 23.39 25 7.43 10.50 14.86 18.19 21.01 23.49 26 7.46 10.55 14.92 18.27 21.10 23.59 27 7.49 10.59 14.98 18.35 21.19 23.69 28 7.53 10.64 15.05 18.43 21.28 23.80 29 7.56 10.69 15.12 18.52 21.39 23.91 30 7.60 10.75 15.20 18.61 21.49 24.03

31 7.64 10.80 15.28 18.71 21.60 24.15 32 7.68 10.86 15.36 18.81 21.72 24.28 33 7.72 10.92 15.44 18.91 21.84 24.42 34 7.77 10.98 15.53 19.02 21.97 24.56 35 7.81 11.05 15.63 19.14 22.10 24.71 36 7.86 11.12 15.72 19.26 22.24 24.86 37 7.91 11.19 15.82 19.38 22.38 25.02 38 7.97 11.27 15.93 19.51 22.53 25.19 39 8.02 11.34 16.04 19.65 22.69 25.36 40 8.08 11.43 16.16 19.79 22.85 25.55

41 8.14 11.51 16.28 19.94 23.02 25.74 42 8.20 11.60 16.41 20.09 23.20 25.94 43 8.27 11.69 16.54 20.25 23.39 26.15 44 8.34 11.79 16.67 20.42 23.58 26.36 45 8.41 11.89 16.82 20.60 23.78 26.59

1/2 diagollallcngfll =

45 TABLE 5- Radii of circular plots

0 5.64 7.98 11.28 12.62 13.82 15.96 1 5.64 7.98 11.28 12.62 13.82 15.96 2 5.64 7.98 11.29 12.62 13.82 15.96 3 5.65 7.98 11.29 12.62 13.83 15.97 4 5.65 7.99 11.30 12.63 13.84 15.98 5 5.65 7.99 11.31 12.64 13.85 15.99 6 5.66 8.00 11.31 12.65 13.86 16.00 7 5.66 8.01 11.33 12.66 13.87 16.02 8 5.67 8.02 11.34 12.68 13.89 16.04 17.93 9 5.68 8.03 11.35 12.69 13.91 16.06 17.95 10 5.69 8.04 11.37 12.71 13.93 16.08 17.98

11 5.69 8.05 11.39 12.73 13.95 16.11 18.01 12 5.70 8.07 11.41 12.76 13.97 16.13 18.04 13 5.72 8.08 11.43 12.78 14.00 16.17 18.07 14 5.73 8.10 11.46 12.81 14.03 16.20 18.11 15 5.74 8.12 11.48 12.84 14.06 16.24 18.15 16 5.75 8.14 11.51 12.87 14.10 16.28 18.20 17 5.77 8.16 11.54 12.90 14.13 16.32 18.24 18 5.79 8.18 11.57 12.94 14.17 16.36 18.29 19 5.80 8.21 11.60 12.97 14.21 16.41 18.35 20 5.82 8.23 11.64 13.01 14.26 16.46 18.40

21 5.84 8.26 11.68 13.06 14.30 16.52 18.46 22 5.86 8.29 11.72 13.10 14.35 16.57 18.53 23 5.88 8.32 11.76 13.15 14.40 16.63 18.60 24 5.90 8.35 11.81 13.20 14.46 16.70 18.67 25 5.93 8.38 11.85 13.25 14.52 16.76 18.74 26 5.95 8.42 11.90 13.31 14.58 16.83 18.82 27 5.98 8.45 11.95 13.37 14.64 16.91 18.90 28 6.00 8.49 12.01 13.43 14.71 16.98 18.99 29 6.03 8.53 12.07 13.49 14.78 17.06 19.08 30 6.06 8.57 12.13 13.56 14.85 17.15 19.17

31 6.09 8.62 12.19 13.63 14.93 17.24 19.27 32 6.13 8.66 12.25 13.70 15.01 17.33 19.37 33 6.16 8.71 12.32 13.78 15.09 17.43 19.48 34 6.20 8.76 12.39 13.86 15.18 17.53 19.59 35 6.23 8.82 12.47 13.94 15.27 17.63 19.71 36 6.27 8.87 12.55 14.03 15.36 17.74 19.84 37 6.31 8.93 12.63 14.12 15.46 17.86 19.96 38 6.36 8.99 12.71 14.21 15.57 17.98 20.10 39 6.40 9.05 12.80 14.31 15.68 18.10 20.24 40 6.45 9.12 12.89 14.41 15.79 18.23 20.38

41 6.49 9.18 12.99 14.52 15.91 18.37 20.54 42 6.54 9.26 13.09 14.63 16.03 18.51 20.70 43 6.60 9.33 13.19 14.75 16.16 18.66 20.86 9.41 13.30 14.87 16.29 18.81 21.04 9.49 13.42 15.00 16.43 18.98 21.22

10 000 x plotsize radius= n x Cos (slope)

46 TABLE6- Horizontal marginal distances (m) for BAFs

DBH BAF DBH BAF 1 2 3 5 7 10 1 2 3 5 7 10

Plot radius factors Plot radius factors 0.5000 0.3536 0.2887 0.2236 0.1890 0.1581 0.5000 0.3536 0.2887 0.2236 0.1890 0.1581

1 0.50 0.35 0.29 0.22 0.19 0.16 51 25.50 18.03 14.72 11.40 9.64 8.06 2 1.00 0.71 0.58 0.45 0.38 0.32 52 26.00 18.38 15.01 11.63 9.83 8.22 3 1.50 1.06 0.87 0.67 0.57 0.47 53 26.50 18.74 15.30 11.85 10.02 8.38 4 2.00 1.41 1.15 0.89 0.76 0.63 54 27.00 19.09 15.59 12.07 10.21 8.54 5 2.50 1.77 1.44 1.12 0.94 0.79 55 27.50 19.45 15.88 12.30 10.39 8.70

6 3.00 2.12 1.73 1.34 1.13 0.95 56 28.00 19.80 16.17 12.52 10.58 8.85 7 3.50 2.47 2.02 1.57 1.32 1.11 57 28.50 20.15 16.45 12.75 10.77 9.01 8 4.00 2.83 2.31 1.79 1.51 1.26 58 29.00 20.51 16.74 12.97 10.96 9.17 9 4.50 3.18 2.60 2.01 1.70 1.42 59 29.50 20.86 17.03 13.19 11.15 9.33 10 5.00 3.54 2.89 2.24 1.89 1.58 60 30.00 21.21 17.32 13.42 11.34 9.49

11 5.50 3.89 3.18 2.46 2.08 1.74 61 30.50 21.57 17.61 13.64 11.53 9.64 12 6.00 4.24 3.46 2.68 2.27 1.90 62 31.00 21.92 17.90 13.86 11.72 9.80 13 6.50 4.60 3.75 2.91 2.46 2.06 63 31.50 22.27 18.19 14.09 11.91 9.96 14 7.00 4.95 4.04 3.13 2.65 2.21 64 32.00 22.63 18.48 14.31 12.09 10.12 15 7.50 5.30 4.33 3.35 2.83 2.37 65 32.50 22.98 18.76 14.53 12.28 10.28

16 8.00 5.66 4.62 3.58 3.02 2.53 66 33.00 23.33 19.05 14.76 12.47 10.44 17 8.50 6.01 4.91 3.80 3.21 2.69 67 33.50 23.69 19.34 14.98 12.66 10.59 18 9.00 6.36 5.20 4.02 3.40 2.85 68 34.00 24.04 19.63 15.21 12.85 10.75 19 9.50 6.72 5.48 4.25 3.59 3.00 69 34.50 24.40 19.92 15.43 13.04 10.91 20 10.00 7.07 5.77 4.47 3.78 3.16 70 35.00 24.75 20.21 15.65 13.23 11.07

21 10.50 7.42 6.06 4.70 3.97 3.32 71 35.50 25.10 20.50 15.88 13.42 11.23 22 11.00 7.78 6.35 4.92 4.16 3.48 72 36.00 25.46 20.78 16.10 13.61 11.38 23 11.50 8.13 6.64 5.14 4.35 3.64 73 36.50 25.81 21.07 16.32 13.80 11.54 24 12.00 8.49 6.93 5.37 4.54 3.79 74 37.00 26.16 21.36 16.55 13.98 11.70 25 12.50 8.84 7.22 5.59 4.72 3.95 75 37.50 26.52 21.65 16.77 14.17 11.86

26 13.00 9.19 7.51 5.81 4.91 4.11 76 38.00 26.87 21.94 16.99 14.36 12.02 27 13.50 9.55 7.79 6.04 5.10 4.27 77 38.50 27.22 22.23 17.22 14.55 12.17 28 14.00 9.90 8.08 6.26 5.29 4.43 78 39.00 27.58 22.52 17.44 14.74 12.33 29 14.50 10.25 8.37 6.48 5.48 4.59 79 39.50 27.93 22.81 17.66 14.93 12.49 30 15.00 10.61 8.66 6.71 5.67 4.74 80 40.00 28.28 23.09 17.89 15.12 12.65

31 15.50 10.96 8.95 6.93 5.86 4.90 81 40.50 28.64 23.38 18.11 15.31 12.81 32 16.00 11.31 9.24 7.16 6.05 5.06 82 41.00 28.99 23.67 18.34 15.50 12.97 33 16.50 11.67 9.53 7.38 6.24 5.22 83 41.50 29.34 23.96 18.56 15.69 13.12 34 17.00 12.02 9.81 7.60 6.43 5.38 84 42.00 29.70 24.25 18.78 15.87 13.28 35 17.50 12.37 10.10 7.83 6.61 5.53 85 42.50 30.05 24.54 19.01 16.06 13.44

36 18.00 12.73 10.39 8.05 6.80 5.69 86 43.00 30.41 24.83 19.23 16.25 13.60 37 18.50 13.08 10.68 8.27 6.99 5.85 87 43.50 30.76 25.11 19.45 16.44 13.76 38 19.00 13.44 10.97 8.50 7.18 6.01 88 44.00 31.11 25.40 19.68 16.63 13.91 39 19.50 13.79 11.26 8.72 7.37 6.17 89 44.50 31.47 25.69 19.90 16.82 14.07 40 20.00 14.14 11.55 8.94 7.56 6.32 90 45.00 31.82 25.98 20.12 17.01 14.23

41 20.50 14.50 11.84 9.17 7.75 6.48 91 45.50 32.17 26.27 20.35 17.20 14.39 42 21.00 14.85 12.12 9.39 7.94 6.64 92 46.00 32.53 26.56 20.57 17.39 14.55 43 21.50 15.20 12.41 9.62 8.13 6.80 93 46.50 32.88 26.85 20.80 17.58 14.70 44 22.00 15.56 12.70 9.84 8.32 6.96 94 47.00 33.23 27.14 21.02 17.76 14.86 45 22.50 15.91 12.99 10.06 8.50 7.12 95 47.50 33.59 27.42 21.24 17.95 15.02

46 23.00 16.26 13.28 10.29 8.69 7.27 96 48.00 33.94 27.71 21.47 18.14 15.18 47 23.50 16.62 13.57 10.51 8.88 7.43 97 48.50 34.29 28.00 21.69 18.33 15.34 48 24.00 16.97 13.86 10.73 9.07 7.59 49.00 34.65 28.29 21.91 18.52 15.50 49 24.50 17.32 14.15 10.96 9.26 7.75 49.50 35.00 28.58 22.14 18.71 15.65 50 25.00 17.68 14.43 11.18 9.45 7.91 50.00 35.36 28.87 22.36 18.90 15.81

DBH Hori:ollfalmargillal di::;tn11ct' = 2 x[ifAf

47 TABLE 7- Height formulae

Method 1. H = d Cos B (Tan A- Tan B) + c

Method 2. H = d (P- Q) 1J10000 + 0 2 + c Method 4. H = d Cos2B (Tan A- Tan B) (1 + 0.03 Tan B) + c

Method 5. H = d (P- 0) (100 + 0.03 Q) I (10000 + 0 2) + c where Upper angle A degrees or P percent Lower angle B degrees or Q percent Slope distance d metres Datum height c metres Tree height H metres

48 TABLE 8- Height tables: method 1 (degrees) Height in metres for 1 m tape distance with upper and lower angles in degrees

1--~~,----~--~----~~~------~~~~------Upper angle

Lower a~e ~ ~ n ~ ~ ~ % ~ ~ ~ W ~ ~ ~ M ~ % ~ ~ fi ~

-30 LOO L02 L04 L06 L08 L11 L13 L15 L18 L20 L23 L25 L28 L31 L34 L37 L40 1.43 L46 1.50 L53 -29 0-99 L01 L03 LOS L07 LlO 1.12 1.14 1.17 L19 L22 L25 L27 L30 L33 L36 L39 L42 L46 L49 L53 -28 0.98 LOO L02 L04 L07 L09 L11 L13 1.16 L18 L21 L24 L26 L29 L32 L35 L38 1.42 L45 1.49 L52 -27 0.97 0.99 L01 L03 L05 1.08 LJO L13 1.15 1.18 L20 L23 L26 L28 L31 1.34 L38 1.41 1.44 1.48 1.52 -26 0.96 0.98 1.00 L02 L04 1.07 L09 L12 1.14 L17 L19 1.22 1.25 L28 L31 1.34 1.37 1.40 1.44 L47 1.51

-25 0.95 0.97 0.99 1.01 L03 L06 L08 L11 L13 L16 L18 L21 1.24 L27 L30 1.33 1.36 1.39 1.43 1.47 1.50 -24 0.93 0.96 0.98 1.00 1.02 LOS 1.07 LlO L12 1.15 L17 L20 L23 L26 1.29 L32 1.35 1.39 1.42 L46 1.50 -23 0.92 0.94 0.97 0.99 L01 1.04 L06 L08 1.11 L14 1.16 1.19 1.22 1.25 L28 L31 1.34 1.38 L41 L45 L49 -22 0.91 0.93 0.95 0.98 LOO L02 L05 L07 1.10 L13 L15 L18 L21 L24 L27 1.30 1.33 1.37 L40 L44 1.48 -21 0.90 0.92 0.94 0.96 0.99 L01 L04 L06 L09 1.11 L14 1.17 1.20 L23 1.26 L29 1.33 1.36 1.40 L43 L47

-20 0.88 0.91 0.93 0.95 0.98 1.00 1.02 1.05 1.08 1.10 1.13 L16 1.19 1.22 L25 L28 1.32 1.35 1.39 1.42 L46 -19 0.87 0.89 0.92 0.94 0.9 0.99 L01 L04 L06 L09 1.12 LJS L18 L21 L24 1.27 1.30 1.34 1.38 L41 L45 -18 0.86 0.88 0.90 0.93 0.95 0.97 LOO 1.03 1.05 1.08 L11 1.14 L17 L20 1.23 1.26 L29 1.33 1.37 1.40 L44 -17 0.84 0.87 0.89 0.91 0.94 0.96 0.99 1.01 1.04 1.07 L09 L12 L15 1.18 1.22 1.25 1.28 1.32 1.35 L39 L43 -16 0.83 0.85 0.88 0.90 0.92 0.95 0.97 LOO 1.03 LOS 1.08 1.11 L14 1.17 1.20 1.24 1.27 1.31 L34 1.38 1.42

-15 0.82 0.84 0.86 0.89 0.91 0.94 0.96 0.99 1.01 L04 1.07 LJO L13 L16 1.19 1.22 1.26 L29 1.33 1.37 1.41 -14 0.80 0.82 0.85 0.87 0.90 0.92 0.95 0.97 1.00 1.03 1.06 1.09 L12 1.15 1.18 1.21 L25 L28 1.32 L36 1.40 -13 0.79 0.81 0.83 0.86 0.88 0.91 0.93 0.96 0.99 1.01 1.04 L07 LlO 1.13 L17 1.20 1.23 1.27 1.31 1.35 L39 -12 0.77 0.80 0.82 0.84 0.87 0.89 0.92 0.94 0.97 1.00 L03 1.06 1.09 L12 L15 1.19 1.22 1.26 1.29 1.33 1.37 -11 0.76 0.78 0.80 0.83 0.85 0.88 0.90 0.93 0.96 0.99 L01 L04 1.07 1.11 L14 L17 L21 L24 1.28 L32 L36

-10 0.74 0.77 0.79 0.81 0.84 0.86 0.89 0.92 0.94 0.97 LOO 1.03 L06 1.09 L12 1.16 L19 L23 L27 1.31 1.35 -9 0.73 0.75 0.77 0.80 0.82 0.85 0.87 0.90 0.93 0.96 0.99 1.02 1.05 1.08 L11 L14 L18 1.22 L25 1.29 1.33 -8 0.71 0.73 0.76 0.78 0.81 0.83 0.86 0.89 0.91 0.94 0.97 LOO 1.03 1.06 LlO L13 L16 1.20 1.24 1.28 L32 -7 0.69 0.72 0.74 0.77 0.79 0.82 0.84 0.87 0.90 0.93 0.95 0.98 1.02 1.05 1.08 1.11 L15 LJ9 1.22 1.26 L30 -6 0.68 0.70 0.73 0.75 0.78 0.80 0.83 0.85 0.88 0.91 0.94 0.97 LOO L03 1.06 LJO L13 LJ7 L21 1.25 1.29

-5 0.66 0.69 0.71 0.73 0.76 0.78 0.81 0.84 0.87 0.89 0.92 0.95 0.98 L02 L05 LOS L12 1.16 L19 1.23 L27 -4 0.65 0.67 0.69 0.72 0.74 0.77 0.79 0.82 0.85 0.88 0.91 0.94 0.97 1.00 1.03 1.07 LJO L14 1.18 L22 L26 -3 0.63 0.65 0.68 0.70 0.73 0.75 0.78 0.80 0.83 0.86 0.89 0.92 0.95 0.98 1.02 1.05 1.09 L12 L16 L20 L24 -2 0.61 0.64 0.66 0.68 0.71 0.73 0.76 0.79 0.82 0.84 0.87 0.90 0.93 0.97 LOO 1.03 L07 1.11 1.14 L18 1.23 -1 0.59 0.62 0.64 0.67 0.69 0.72 0.74 0.77 0.80 0.83 0.86 0.89 0.92 0.95 0.98 1.02 1.05 1.09 L13 L17 1.21

0 0.58 0.60 0.62 0.65 0.67 0.70 0.73 0.75 0.78 0.81 0.84 0.87 0.90 0.93 0.97 LOO 1.04 L07 1.11 L15 1.19

1 0.56 0.58 0.61 0.63 0.66 0.68 0.71 0.74 0.76 0.79 0.82 0.85 0.88 0.91 0.95 0.98 L02 L05 L09 L13 1.17 2 0.54 0.57 0.59 0.61 0.64 0.66 0.69 0.72 0.75 0.77 0.80 0.83 0_86 0.90 0.93 0.96 1.00 1.04 1.08 1.11 1.16 3 0.52 0.55 0.57 0.60 0.62 0.65 0.67 0.70 0.73 0.76 0.79 0.82 0.85 0.88 0.91 0.95 0.98 1.02 1.06 1.10 1.14 4 0.51 0.53 0.55 0.58 0.60 0.63 0.66 0.68 0.71 0.74 0.77 0.80 0.83 0.86 0.89 0.93 0.96 1.00 1.04 1.08 1.12 5 0.49 0.51 0.54 0.56 0.58 0.61 0.64 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.87 0.91 0.94 0.98 1.02 1.06 1.10

6 0.47 0.49 0.52 0.54 0.57 0.59 0.62 0.64 0.67 0.70 0.73 0.76 0.79 0.82 0.86 0.89 0.93 0.96 1.00 1.04 1.08 7 0.45 0.47 0.50 0.52 0.55 0.57 0.60 0.63 0.65 0.68 0.71 0.74 0.77 0.80 0.84 0.87 0.91 0.94 0.98 1.02 1.06 8 0.43 0.46 0.48 0.50 0.53 0.55 0.58 0.61 0.63 0.66 0.69 0.72 0.75 0.78 0.82 0.85 0.89 0.92 0.96 1.00 1.04 9 0.41 0.44 0.46 0.48 0.51 0.54 0.56 0.59 0.62 0.64 0.67 0.70 0.73 0.76 0.80 0.83 0.87 0.90 0.94 0.98 1.02 10 0.39 0.42 0.44 0.47 0.49 0.52 0.54 0.57 0.60 0.62 0.65 0.68 0.71 0.74 0.78 0.81 0.85 0.88 0.92 0.96 1.00

--~-~~~-~~------~~~----~~~-----~~--~~~--~~~---~~------NOTE: Multiply tape distance by table value and add datum to obtain total tree height.

49 TABLE 9- Height tables: method 2 (percent) in metres for 1 m tape distance with upper and lower percent

Upper angle

46 50 54 58 62 66 70 74 78 82 86 90 94 98 102 106 110 114 118

-58 0.90 0.93 0.97 1.00 1.04 1.07 1.11 i.14 1.18 1.21 1.25 1.28 1.31 1.35 1.38 1.42 1.45 1.49 -56 0.89 0.92 0.96 0.99 1.03 1.06 1.10 1.13 1.17 1.20 1.24 1.27 1.31 1.34 1.38 1.41 1.45 1.48 1.52 -54 0.88 0.92 0.95 0.99 1.02 1.06 1.09 1.13 1.16 1.20 1.23 1.27 1.30 1.34 1.37 1.41 1.44 1.48 1.51 -52 0.87 0.90 0.94 0.98 1.01 1.05 1.08 1.12 1.15 1.19 1.22 1.26 1.30 1.33 1.37 1.40 1.44 1.47 1.51

-50 0.86 0.89 0.93 0.97 1.00 1.04 1.07 1.11 1.14 1.18 1.22 1.25 1.29 1.32 1.36 1.40 1.43 1.47 1.50 -48 0.85 0.88 0.92 0.96 0.99 1.03 1.06 1.10 1.14 1.17 1.21 1.24 1.28 1.32 1.35 1.39 1.42 1.46 1.50 -46 0.84 0.87 0.91 0.94 0.98 1.02 1.05 ,1.09 1.13 1.16 1.20 1.24 1.27 1.31 1.34 1.38 1.42 1.45 1.49 -44 0.82 0.86 0.90 0.93 0.97 1.01 1.04 1.08 1.12 1.15 1.19 1.23 1.26 1.30 1.34 1.37 1.41 1.45 1.48 -42 0.81 0.85 0.89 0.92 0.96 1.00 1.03 1.07 1.11 1.14 1.18 1.22 1.25 1.29 1.33 1.36 1.40 1.44 1.48

-40 0.80 0.84 0.87 0.91 0.95 0.98 1.02 1.06 1.10 1.13 1.17 1.21 1.24 1.28 1.32 1.36 1.39 1.43 1.47 -38 0.79 0.82 0.86 0.90 0.93 0.97 1.01 1.05 1.08 1.12 1.16 1.20 1.23 1.27 1.31 1.35 1.38 1.42 1.46 -36 0.77 0.81 0.85 0.88 0.92 0.96 1.00 1.03 1.07 1.11 1.15 1.19 1.22 1.26 1.30 1.34 1.37 1.41 1.45 -34 0.76 0.80 0.83 0.87 0.91 0.95 0.98 1.02 1.06 1.10 1.14 1.17 1.21 1.25 1.29 1.33 1.36 1.40 1.44 -32 0.74 0.78 0.82 0.86 0.90 0.93 0.97 1.01 1.05 1.09 1.12 1.16 1.20 1.24 1.28 1.31 1.35 1.39 1.43

-30 0.73 0.77 0.80 0.84 0.88 0.92 0.96 1.00 1.03 1.07 1.11 1.15 1.19 1.23 1.26 1.30 1.34 1.38 1.42 -28 0.71 0.75 0.79 0.83 0.87 0.91 0.9 0.98 1.02 1.06 1.10 1.14 1.17 1.21 1.25 1.29 1.33 1.37 1.41 -26 0.70 0.74 0.77 0.81 0.85 0.89 0.93 0.97 1.01 1.05 1.08 1.12 1.16 1.20 1.24 1.28 1.32 1.35 1.39 -24 0.68 0.72 0.76 0.80 0.84 0.88 0.91 0.95 0.99 1.03 1.07 1.11 1.15 1.19 1.23 1.26 1.30 1.34 1.38 -22 0.66 0.70 0.74 0.78 0.82 0.86 0.90 0.94 0.98 1.02 1.05 1.09 1.13 1.17 1.21 1.25 1.29 1.33 1.37

-20 0.65 0.69 0.73 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20 1.24 1.27 1.31 1.35 -18 0.63 0.67 0.71 0.75 0.79 0.83 0.87 0.91 0.94 0.98 1.02 1.06 1.10 1.14 1.18 1.22 1.26 1.30 1.34 -16 0.61 0.65 0.69 0.73 0.77 0.81 0.85 0.89 0.93 0.97 1.01 1.05 1.09 1.13 1.17 1.20 1.24 1.28 1.32 -14 0.59 0.63 0.67 0.71 0.75 0.79 0.83 0.87 0.91 0.95 0.99 1.03 1.07 1.11 1.15 L19 1.23 1.27 1.31 -12 0.58 0.62 0.66 0.70 0.73 0.77 0.81 0.85 0.89 0.93 0.97 1.01 1.05 1.09 1.13 1.17 1.21 1.25 1.29

-10 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.03 1.07 1.11 1.15 1.19 1.23 1.27 -8 0.54 0.58 0.62 0.66 0.70 0.74 0.78 0.82 0.86 0.90 0.94 0.98 1.02 1.06 1.10 1.14 1.18 1.22 1.26 -6 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20 1.24 -4 0.50 0.54 0.58 0.62 0.66 0.70 0.74 0.78 0.82 0.86 0.90 0.94 0.98 1.02 1.06 1.10 1.14 1.18 1.22 -2 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20

0.46 0.50 0.54 0.58 0.62 0.66 0.70 0.74 0.78 0.82 0.86 0.90 0.94 0.98 1.02 1.06 1.10 1.14 1.18

0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 0.42 0.46 0.50 0.54 0.58 0.62 0.66 0.70 0.74 0.78 0.82 0.86 0.90 0.94 0.98 1.02 1.06 1.10 1.14 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 0.38 0.42 0.46 0.50 0.54 0.58 0.62 0.66 0.70 0.74 0.78 0.82 0.86 0.90 0.94 0.98 1.02 1.06 1.10 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.03 1.07

0.34 0.38 0.42 0.46 0.50 0.54 0.58 0.62 0.66 0.70 0.73 0.77 0.81 0.85 0.89 0.93 0.97 1.01 1.05 0.32 0.36 0.40 0.44 0.48 0.51 0.55 0.59 0.63 0.67 0.71 0.75 0.79 0.83 0.87 0.91 0.95 0.99 1.03 0.30 0.34 0.38 0.41 0.45 0.49 0.53 0.57 0.61 0.65 0.69 0.73 0.77 0.81 0.85 0.89 0.93 0.97 1.01 0.28 0.31 0.35 0.39 0.43 0.47 0.51 0.55 0.59 0.63 0.67 0.71 0.75 0.79 0.83 0.87 0.91 0.94 0.98

NOTE: Multiply tape distance by table value and add datum height to obtain total tree height.

50 NOTES

51 NOTES

52