AN EXM!INATION OF THE ACCURACY OF THE DATA COLLECTED FROM THE YIELD RESEARCH
PLOTS OF THE FOREST RESEARCH INSTITUTE
A thesis
submitted in fulfilment
of the requirements for the Degree of
Doctor of Philosophy in Forestry
in the
University of Canterbury
by A.D. McEwen
CHAPTER
I
I I
III
IV
ABSTRACT INTRODUCT
LITERATURE REVIEW
PAGE
1
3
9
1. Development of yield tables and functions 10 2. The collection of growth data1.5
3.
The measurement of tree growth 20( 1) Height growth 23
(2) Diameter growth 2.5
4.
Implications for·this studyF .R.I. YIELD RESEARCH PLOTS
29
31
1. Location and establishment of experiments 32 2. Plot measurements and calculations
33 .
(1) Diameters and tree classification (2) Volumes
(3) Predominant mean height
(4) Crown height
(5) Special measurements
3.
Thinning treatments4.
Data listings and summary sheets5.
CostsCOMPUTER PROGRAM FOR STEM ANALYSIS
33
33 40 40
42
43
45
46
48
1. Requirements
48
2. Features of the program
49
3.
Preparation and checking of the basic data 51 (1) Measurement of ring widths 51 (2) Data checking4. ·
Processing(1) Average diameters (2) Volumes
5.
Program testing52
55
CHAPTER PAGE
v
DATA COLLECTION 571. Plot selection 57
2. Stand history 58
3• Plot history . 58
4. Data collected 59
5. Field measurement 63
( 1) General 63
(2) Surround tree measuremen~s 64 (3) Measurements of plot trees 65 6. Laboratory measurement and basic processing 70 (1) Preliminary investigations 70
(2) Sample points 78
(3) Basic processing 79
VI THE ACCURACY OF THE DATA FROM EXPERIMENT R67 81
1. General plot details 82
2. Diameter measurement 83
3.
Height measurement 88(1) lndividual trees 89
'
(2) Stand height 89
4. Total volume 106
( 1) Individual trees 107
(2) Plot volumes 114
5.
Volume distribution 122(1) Individual trees 122
(2) Plot volume distribution 123 VII DISCUSSION OF THE RESULTS FROM THE F.R.I •. PLOTS 130
1. Tree classification 130
2. Basic measurements 131
3· Stand height 133
4. Volume calculation 135
VIII
X
XI
6.
Measurement and computational errors7.
Temporary sample plot methods SAMPLING PATTERNS FOR INDIVIDUAL TREES139
1~
1~
1. Sampling patterns below breast height ·
142
2. Samplirtg patterns for the whole tree 156
PLOT SAMPLING 169
1~ Preliminary analysis 171
2. Selection of further independent variables
184
3.
Selection of sample trees195
4.
Simulated sampling to compare the use ofdifferent selection methods and different
199
independent variables
5.
Application of the results211
TEST OF METHODS FOR PLOT SAMPLING SUMMARY OF CONCLUSIONS
1. Main conclusions
'
2. Secondary recommendations
3.
Final conclusion213 223
~3
225 228 ACKNOWLmPGEMENTS ' / ; { ' - , - ,
REFERENCES APPENDICES
1
2
3
4
5
6
PROGRAM/STEMANALYSIS A computer program for detailed stem analysis
Conversion factors
Radiata pine permanent sample plots Tree classification
Regional· tree volume formulae
Examples of output from the sample plot computer programs
231
237
366
370
378
APPENDICES
7
8
9
Basic data for 1972 Accuracy tests
Prediction interval tests, individual tree sampling
PAGE
38.5 387
DIAGRAH PAGE
1. Sequences of radial growth 27
2. Nethods of tree classification
34
3.
Plastic bag for increment core storage68
4.
Selection of radii71
5.
Height-diameter regressions93
6.
Volume-line regressions115
7.
Graph of height on diameter, plot 2,1973
134
B.
Basic sampling patterns for the volume149
below breast height
~· Example of the points selected by the 159
different sampling methods
10. Percentage of combinations within a specified 182 percentage of standard plqt volume for greater
than or equal to a given number of years (preliminary analysis)
11. Plot regressions for different independent
190
variables
12. Percentage of combinations within a specified 203 percentage of standard volume for greater than
LIST OF TABLES
TABLE PAGE
1. MethoBs used for volume calculation 41 2. Summary of permanent sample plot data for
60
· experiment R67
3. Results from preliminary investigations 75
·. 4.. Accuracy of diameter data 84
5• · Accuracy of individual tree. height data 90.
6. Height-diameter regressions 95
7. Accuracy
of
mean height data 978. Accuracy of mean top height data 100 9. Accuracy of predominant mean height data 103 10, Accuracy of individual tree volume data 108
(two-dimensional equation)
11. Errors in tree volume resulting from height 110 and diameter errors (two-dimensional volume
equation)
12. Accuracy of individual tree volume data 112 {form-class)
13. Volume-line regressions 117
14. Accuracy of plot volume data 118
15. Accuracy of volume distribution data for 124 individual trees
16. Volume distribution regressions 126
17. Accuracy of plot volume distribution 127 18, Analysis of variance, volumes below breast 146
height
19, Ranking of the mean volumes, sampling below 148 breast height
20. Means for methods 1, 2, and 3, sampling below 150 breast height
21. Summary of prediction interval tests (volumes 153 below breast height)
23. Ranking of the mean volumes, sampling for 162 total volume
24. Sununary of prediction interval tests (sampling 164 above breast height)
25. Sununary of prediction interval tests, total 167 volume, ten-year periods
26. . Results of preliminary analysis for each year 174 27. Number of combinations satisfying the tests 178
for greater than or equal to the stated number of years (preliminary analysis)
28, Number of years for which a given percentage· of 183 combinations gave volumes within specified
limits of the standard volumes (preliminary analysis)
29. Plot regressions 188
.30.
Order of tree size for· each year 19631. Groups of trees· used for simulated sampling 200 32. Average percentage of combinations per year 202
giving a volume within specified limits of the standard volume ··
33. NUmber of years for which a given percentage 208 of samples gave volumes within specified
limits of the standard volumes (main analysis)
34.
Percentage of samples giving volumes within 209 specified liutits for ten or more years35. Accuracy of test sample 215
36. Order of tree size for each year (plot
4)
21637.
Groups of t':'ees for sampling (plot4)
218 38. Average percentage of combinations within 219specified limits (plot
4)
39. No. of years vii thin specified limits (plot 4) 220
lt(), Percentage of samples within specified 222
1 ABSTRACT
~e work described in this thesis arose from a concern that the data being obtained from the yield research plots maintained by the Forest Research Institute of the New Zealand Forest Service were inadequate for present day yield research. This was partly because some of the data were considered to be inaccurate and partly because of deficiencies in the types of data being collected. It was thought that one solution to the problem would be to give each plot a detailed final measurement to obtain additional data to supplement those collecteft during the life of the plot.
The first section of the thesis describes the methods of data collection and processing used for the plots, and includes a detailed comparison between data available in the plot records and data obtained from a detailed stem analysis of each of the trees in two of the plots. It is shown that there are errors in both the basic and the
computed data, the errors being such that the data are
considered unsuitable for detailed research into methods of constructing growth models, particularly those models
based on the growth of individual trees.
should be selected and that sample points should be located near the base of every second annual shoot in each tree. Not only would such a procedure provide accurate data on the growth of individual trees, but it would enable a reduction to be made in the amount of measurement necessary during the life of a plot,
CHAPTER I
3
INTRODUCTION
One of the basic requirements for plannjd forest_manage-ment is the ability to predict the yield of a given stand, or group of stands, at some point in the future. So long as the rate of removal of produce from a forest is well below
.
the rate of growth, neither the rate _of growth itself, nor the accuracy of its measurement and prediction is of great importance. When the rate of removal approaches the rate of growth,however, not only does it become desirable to increase the yield, but it is important that the predictions of growth and removal are accurate .• Increasing competition for land between forest and agricultut'al interests also· meads that accurate production forecasts (for both forests and farms) must be available if land use decisions are to be
soundly based. For this purpose, estimates must be made of the production capability of the land in question,- either by an evaluation of site factors or indices of site factors
(climate, soil, and existing vegetation) or by an examination of the production of existing forest stands (or other crops) on similar sites.
In New Zealand, one of the main sources of data for predictions of the growth and yield of even-aged plantations of exotic conifers, has been the permanent sample plots main-tained and measured by the mensuration section of the Forest Research Institute of the New Zealand Forest Service (the F.R.I. yield research plots). Whyte (1970), has suggested
detailed study of growth and that some of the data may not be accurate .. This study originated from these suggestions. The first objective has been to examine critically the ways in which the plots are, and have been measured, to t.est data from two of the plots to see if, in fact, there is a lack of accuracy and, if there is, how serious a probiem it is and what steps can be taken to reduce it.
The second part of the study arises from the suggestion by some of the F.R.I. staff that, as many of the plots are now reaching maturity and are being felled, an attempt should be made to carry out a final ·measurement to obtain data which could supplement those collected throughout the life of the plot. It was felt that some form of temporary plot measure-ment involving stem analysis could be carried out on trees in the plots, to obtain detailed data on the growth of
individual trees. Therefore, the second objective has been to investigate the application of temporary sample plot
methods to the F. R.I. plots to see how sample trees should be selected from the plots and how sample points should be
located on each sample tree ..
To assess the adequacy of the data from the yield research plots, i t is desirable to consider some aspects of the prediction of growth, before looking at the data required for such predictions. In the discussion, growth may be
5
in time (Spurr, 1952). Thus the yield of a forest is the sum of the growth of utilisable wood up to the time of removal.
One way to increase the yield from a given area of land is to increase the rate of growth of the forest on that land • . Such an increase may be possible, either by applying different
management regimes (e.g. different initial spacings, different thinning treatments, or the use of fertiliser.s), or by
planting a different species or a faster growing race of the same species. The second way in which yield can be increased is to improve the standard of utilisation so that less wood is left behind. Complete tree harvesting in which whole trees, including branches, stumps, and roots are removed and
processed is the highest standard of utilisation which can be achieved.
To provide flexible predictions which are both reliable and useful under different and changing management and
utilisation systems, it is necessary to be able to predict the total yield and also to be able to divide the total into various size, product, and quality classes. Therefore, the measurement of existing stands for yield prediction purposes must include the size, shape, .and quality of the trees in the
stand. The measurements must also be sufficiently accurate to detect the differences, if any, in these three items
between stands which have been treated under different manage-ment regimes, or which are growing on different sites.
of the fundamental growth processes operating on and in trees and stands. This understanding can only come from the combined efforts of scientists working in a wide range of fields including tree physiology, silviculture, wood quality, and utilisation. The role of forest mensuration in· such yield research is to provide efficient and accurate methods and instruments for the quantitative·assessment of
all aspects of forest growth• The resultant data, together with financial considerations, can then be used to plan and regulate the yield from a forest.
The work is presented in two stages. In the first part (Chapters II to VII), the ERI.-yield research plots are examined in some detail. Chapter II reviews various aspects of yield research in order to provide a basis for assessing whether the data collected in the F.R.I. plots are suitable for
present day yield research investigations. How suitable the data are will depend not only on their accuracy but also on what are actually collected. The review, therefore, covers some of the history of yield table and yield function
determined. Chapter III describes the methods of measure-ment and computation which have been, and are currently being used for the F.R.I. plots. To test the accuracy of the data from the plots, one experiment, R67, located in a 30 year old stand of Pinus radiata D. Don (radiata pine) was selected for a detailed examination. Each tree in two of the plots
(representing two thinning treatments) was subjected to a detailed stem analysis to obtain data which could be used as a standard against which the data in the plot records could be tested. Chapter IV describes various features of the computer program (PROGRAM/STEMANALYSIS) which was developed to process the stem analysis measurements. A manual of instructions for using this program (which is suitable for a wide range of stem analysi~ projects) and for the measurement of wood samples {discs or cores) on ADDO tree ring measuring equipment, is attached as Appendix I. The procedures used for the collection of the data from the two plots are outlined in Chapter V and detailed tests are made of the accuracy of these data in Chapter VI. A discussion of the results of the investigations is presented in Chapter VII.
The second part of the study is aimed at developing
reliable sampling procedures for collecting accurate data from trees and plots when temporary sample plot (i.e. stem analysis) techniques are being used. The data from experiment
R67
are also used for this purpose. In Chapter VIII, samplingpatterns for individual trees are examined, to see if a simple method can be developed for obtaining accurate volumes of
tree. Chapter IX looks at ways in which sample trees for. stem analysis can be selected from a plot. The conclusions from this examination, which was conducted on only one of the plots from experiment R67, are tested in Chapter X, using the data from the other plot.
Chapter XI summarises the findings of the thesis and shows how the main conclusions are related to each other. Recommendations are made on ways of improving specific aspects of the organisation of the sample plot system, and the chapter concludes with an assessment of the overall importance of the study.
CHAPTER II LITERATURE REVIEW
In the abstract of a review of the construction of yield tables for managed stands, Curtis (1972) states that "the objective of yield studies is prediction of stand development as a function of time, site, and cultural treatment. 11 The results of the studies are usually expressed as one or more tables or mathematical functions which can be used to predict the growth of stands similar to those from which the tables or functions were derived. The first section of this review looks at the historical development of yield tables and functions, with the
emphasis on the types of data which have been used for their construction. Thi.s is followed by a discussion of different methods which have been used for collecting growth data, taking into account the errors and diffi-culties that can arise with each. Because stand develop-ment is the result of the growth and interactions of the individual trees in the stand, any method of data
collection will involve the measurement of individual
9
tree variables. Consequently, several different approaches to tree measurement are outlined. Particular emphasis is given to the measurement of growth by stem analysis,
1. DEVELOPMENT OF YIELD TABLES AND FUNCTIONS
Assmann
(1970)
credits the German, Paulsen, with thepreparation o~ the first yield tables in
1795.
Spurr(1952) ·
traces the development of yield tables, starting with "normal" yield tables de signed to represent the growth of so-called "fully-stocked" or "normal" stands. Such tables were generally derived by first assigning site classes to the various stands for which data were available, and then plotting stand volume (often obtained by first measuring the diameters of all the trees within a. sample plot, and the heights of a sample of trees, and then using an appropriate volume table) against age f~r each site class • . Entries for the table were obtained from smoothed curves drawn through the points. Difficulties in applying the tables to
partially stocked stands, led to the introduction of
"empirical" yield tables, constructed to represent the growth of the average stand in a particular area. Basic data were often obtained from inventories of the stands for which the tables were required.
Vuokila
(1965)
defines three main types of yield11
plots to be established, and new ta.bles to be prepared, when each new treatment regime is proposed. To help overcome this situation, the concept of "variable density" yield tables Was introduced. Although such tables can b~ prepared for any given set of circumstances, the approach is based on the preparation of mathematical functions to express the interactions between different treatments and stand conditions. This procedure has been strengthened by the use of advanced statistical techniques and, more recently, the availability of computers, which permit manipulation of greater quantities of data to test a wider range of possible solutions than was previously feasible. However, Curtis (1972) warns (p.32) that "Along with this has sometimes gone an uncritical use of purely empirical regression models and the hope that the computer can somehow extract meaning from inadequate measurements and poorly distributed data."
Many of the yield functions have been developed (e.g. Vuokila, 1965; Fries, 1964; Bennett, 1970) by using
least-squares regression analysis to determine which of several linear models provides the best fit for a given set of basic data. Other workers (e.g. Hari, 1969; Moser and Hall, 1969) have started with a hypothetical biological growth model expressed in a mathematical form and have tested its applicability to actual data. If the model proves satisfactory, it can then be used to inter-polate growth for a given set of circumstances. Hari
pre~ious methods as it is not necessary to assume that the effect of each growth variable is of a particular form
2
(e.g. ex or cy , where c is a constant and
x
and y are some measures of growth). Pienaar and Turnbull(1973)
also emphasise that extrapolation outside the range of the basic data should be safer with the hypothet.ical model than withthose methods where a function is calculated to fit a set of available data. In the latter case the data may, for example, indicate a linear relationship, but if additional data were collected over a wider range, a curvilinear relationship could become apparent.
increment, after thinning, of individual trees of Betula verrucosa (Ehrh):
breast height diameter under bark age at breast height
annual diameter increment in the five year period prior to thinning
13
basal area inside bark before and after thinning for the whole sample plot and for a small circular plot with a radius of 5 m, centred on the tree for which increment was being determined
site index
dominant height of the stand length of the prediction period plot altitude.
Work on total biomass production (e.g. Madgwick, 1970), while not directly involved with the prediction of the yield of utilisable forest products, is part of a wider concept of yield research which is concerned with the detailed measure-ment of all aspects of tree growth. Such research involves measurements (including volumes and weights) of all the
vegetation in a stand, including roots, stems, branches, and foliage. The results from such studies may well be used for future predictions of the yield of utilisable wood from a forest.
affected by stand treatment (Busch, Miller, and Beers, 1963, p353). In New Zealand, for example, the site index of a radiata pine stand is defined as the mean top height of the stand at age 20 (Lewis, ·1954). Therefore, if height is to be used to derive an expression of site for use as a variable in growth predictions, it is important that accu~
rate data should be available on height growth and its relationship to stand age. One disadvantage of height growth, particularly in the early years of the life of a stand, is that it can be influenced by the method by which the stand was established, and the way in which the stand was tended during the years before the trees overcame the influence of competing vegetation. Other ways of expressing site are to use a combination of soil and climatic character-istics (Jackson, 1965). An example of a yield investigation from which soil and climate data will be available, is that being carried out in British Columbia (British Columbia Forest Service, 1972).
Thus, it would appear that for future yield research, all aspects of tree and stand growth should be measured. This is rarely feasible. However, it is desirable that sufficient information should be collected to enable the different approaches to yield prediction (e.g. individual trees or whole stands) to be evaluated. An integrated and intensively planned approach to yield research, involving scientists from several fields (such as the study in British Columbia mentionedabove) may prove
15
To balance the greater number of variables being measured on each tree or in each plot, the total number of plots maintained by an organisation could well be reduced, resulting in an overall reduction in field work. In addition, cooperation between research establishments may help to overcome the lack of conformity between measure-ment systems, which Evert (1971), Braathe (1957), and
others have found when trying to correlate the results from several experiments.
2. THE COLLECTION OF GROWTH DATA
One of the main requirements of any method for collect-ing growth data, is that the data are accurate, and that all aspects of the procedures for collection are well documented. The sources of error which can occur are (Cunia,
1965):
(i) instrument errors (ii) operator errors (iii) sampling errors
(iv) errors in the construction and application of volume tables or functions.
A satisfactory method for collecting growth data will be one ·which minimises the errors, at an acceptable cost, bearing
studies usually takes a considerable time, the planning for data collection must consider the types of predictions which may be required when the data become available, not
just those predictions which are wanted at the beginning of the project.
According to Moser and Hall
(1969),
the ideal data for growth functions, are complete chronological records for stands from establishment to harvest. They define such records as a "real growth series". In general,yield predictions and research into prediction methods are based on, or tested against, data from either permanent sample plots (an "approximated real growth series") or temporary sample plots (an "abstract growth series"). The original form of temporary plots involved the location and measurement of plots in stands of different ages, and which had received different treatments. Data from plots on similar sites could then be combined and graphical methods used to determine the average development of the stands.
In
1846,
Heyer in Germany, proposed the use of permanentby the development of equipment for the semi-automated measurement of the widths of annual rings (Eklund,
1971)
and the use of computers to process the data.
Vuokila
(1965)
discusses the following points in a comparison between permanent sample plots and the new approach to temporary plots:(i) whereas permanent plots are susceptible to climatic and biological damage, temporary plots can be located in unaffected stands;
17
(ii) although the treatment applied to permanent plots may not always be consi~tent, it is known in detail. With temporary plots, past treatment must be deduced from stump examinations and forest records;
(iii) measurement and calculation procedures are often changed during the life of a permanent plot. When a temporary plot is being measured, the most efficient techniques available can be used for collecting all the data required from that plot, without the danger of a lack of consistency between the results for different years;
(iv) because all measurement~ in a temporary plot are made at the same time, using the same instruments, techniques, and operators, the calculation of growth is likely to be more accurate. Small errors or inconsistenc-ies at ant single measurement in a permanent plot can lead to large errors in growth (even negative growth), particu-larly with slow growing species;
of any silvicultural schedule which has been applied to an existing stand or stands. Many existing permanent plots are treated according to schedules which have become outdated during the life of the plot and there is often little
interest in the final result;
(vi) the use of temporary plots redu~e~ the often considerable time and money that is involved when permanent plots have to be repeatedly measured and maintained;
(vii) replication of plots for statistical analysis is possible with the temporary plot method by measuring more plots in different stands. With permanent plot~ it is. often difficult to obtain uniform areas on which sufficient plots can be laid out for the replication of all treatments.
In addition, developments in experimental design mean that the designs used when a plot is established may not be the most efficient available at the time when the results are to be analysed;
(viii) representative sample trees cannot be felled for detailed measurement in a permanent plot without affecting th• future of the plot.
There are a number of warnings in the literature regarding the accuracy of permanent sample plot data. ,. Curtis (1967), when using data for Douglas fir in North America, states (p.8) that "The permanent plot data
19
contained numerous inconsistencies in measurement standards and methods of data summarization ••• Errors in tarif
number stemming from errors in height measurement were undoubtedly major sources of error in subsequent
compu ta tiona".
Assmann (1970), recognises that errors may often be p~es~nt in data from permanent plots and that errors in increment, over short periods, can· be considerable. He concludes (p.227) "Only after a searching review and care-ful correction can the results hitherto obtained from thinning experiments be used for comparisons of growth performance. The reason for this is that incremental differences tend to be small on account of the relatively slight differences in treatment, the tre.atment itself being subject to change and only in exceptional instances seen to have been carried out uniformly and consistently."
While it is clear that the temporary plot method has a qertain overall advantage relative to permanent plots, the differences are perhaps less marked when short rotation tree crops are being considered. Even with long rotations, Naslund {1971) still recommends the use of permanent plots for lon~ term checking of the results from temporary plots and for testing particular treatments {including the use of
3.
THE MEASUREHENT OF TREE GROWTHIt has been shown that the collection of data for research on the prediction of yield must be con6e~ned with the measurement of the growth of individual trees and, in particular, the growth of utilisable wood in the main stem. The growth will need to be in terms of volume, and must be estimated, since measurement by water displacement is not possible if the trees are to continue growing. Similarly, growth in the ~leigh t of individual trees cannot be measured directly. As has already been indicated, the growth can be measured either by using permanent plots in which growth in a given period of time is the difference between the
volumes estimated at the beginning and the ~nd of the period, or by stem analysis techniques where the volume at different years is obtained by an analysis of the annual rings.
Suggested methods for the sectional measurement of conifers generally fall into those in which the sampling pattern deliberately avoids nodal and other swellings and those in which it does not. Lawrence (1960); argues for the latter approach when he states that (p.110)" ••• local swellings may extend over only a foot or two of stem length, and yet, when measurement points fall on them, they are allowed to increase the volume for
5
ft either side of them. (If it is undesirable to 'sell the bumps', how much more so :i.s it to sell air?)".21
formula to diameters measured at points clear of nodal swellings. The measurement points were at ground level and at approximately 0.7, 1.4, and 2 m above ground and thereafter at intervals of 1.4 to 1.7 m. No significant difference was found between the calculated volumes and
vo~umes obtained by water displacement. How~ver, tests
on lengths approximately 1.7 m long, taken from the butt, middle, and top of trees, showed that the sectional
measurements significantly overestimated the volume of the butt section. IJ:Ihis is probably because the base of the tree approximates a neiloid whereas Smalian's formula is correct only for a paraboloid. Although not stated, the volume of the remainder of the tree above the butt log was presumably underestimated although this must have been spread throughout the tree so that the differences in the middle and top logs were not significant.
Gleason (1972) compared diameters measured at a fixed height with diameters measured at the middle of the
internode in which the fixed height sample point fell. He concluded (p.26) "••• that the internodal approach to taking diameters is more precise than the fixed-height method", and also noted that there was less variation between operators with the internodal method.
sample points can be located so that the drop in diameter between each pair of adjacent sample points is approximately the same. Lawrence (1960) advocates sample points at
approximately 10 ft
(3
m) inte~vals with much smaller intervals in the butt swell region. Whyte (1971),following up work by Grosenbaugh (1966), advocates regular drops in diameter above breast height (1.4 m) so that the sample points are closest together where the shape of the tree is changing most rapidly. He measures only ope point below breast height, at 0.7 m above ground level. The "taper step" method, as Whyte's is known in New Zealand, was derived on mathematical grounds for tuations where it may be desirable to interpolate diameters at points other than those chosen as sample points. It should, therefore, be a preferable method in yield studies where it is necessary
to p~edict the volumes of different size classes. In th.e
·same article, Whyte cone ludes that when the volume of a section of a tree is to be calculated, the formula used should be that for the frustum of a cone. His conclusion is based on the fact that the volume of a conic frustum is intermediate between the volumes of neiloidal and para-boloidal frusta which have the same end diameters. There-fore, the error is likely to be minimised for trees which are made up of a mixture of paraboloidal, neiloidal, and conoidal sections.
23
an added advantage in that the annual ring pattern on tree cross sections and on increment cores will not be distorted by knots. However, the "taper step" method for defining the distances between points may not be applicable since the shape of the tree in earlier years may not have been the same as it is when the sampling is carried out. A review of the patterns of height and diameter growth in a tree stem may prove useful as a basis for selecting sample points for stem analysis. These patterns have been studied in coniferous trees by several workers.
(1) Height Growth
Doak (1935, p.10) considers the stem of a pine tree to be made up of stem units, each composed of "an internode together with the node and nodal appendages at its distal extremity." The nodal appendages are branches and cones. An annual shoot is a portion of the stem in which all the stem units present were initiated in a single growing season. Such a shoot may consist of one (uninodal) or more (multi-nodal) stem units. Bannister (1962) uses Doak's terminology to discuss the pattern of height growth for radiata pine in New Zealand.
summer, the spiral pattern is steep, but as height growth slows down the spirals become compressed and the scars may become so crowded together that they form a shallow band. This band is normally formed once a year, thus marking the · boundary between two annual shoots. Generally the band is
adjacent to the last branch cluster of the annual shoot but it may extend some distance beyond the cluster. To
·simplify his studies, Bannister used the last brp.nch cluster of an annual shoot to mark the division between that shoot and the next.
The number of stem units in any one annual ~hoot can vary between·zero and six. There is considerable variation between trees on any one site and also some variation with
age within individual trees. The penultimate cluster for any one year (in annual shoots with two or more stem units) is generally produced after
80
to95%
of the annualextension has occurred. Therefore, when an annual shoot is composed of only two stem units, the first is much
ionger than the second. When there are three or more stem units the relative·lengths are more even. Stem cones are rarely prese~t in the last one or two clusters formed in any one year but they can occur in all other clusters in the annual shoot.
The results of Bannister's study provide a basis for the recognition end hence measurement of the annual height growth of radiata pine. However, the pattern can be
25
because extension growth of a young tree does not appear to be as closely related to the seasons as i t is in later years. Also, no cones are produced by young trees. Therefore, if height growth is to be determined for the whole of the life of the tree, the lower parts of the stem will have to be sectioned and the annual rings examined.
Some apparent anomalies are caused by height and diameter growth occurring during winter months (N,Z.F.S., 1966 ' p. 24). Other problems are caused by terminal die-back, loss of terminal buds, or the loss of apical
dominance. Such accidents may make i t appear that no annual shoot was produced for one or more years, or that a shoot was shorter than expected when compared with those
formed in earlier and later years.
(2) Diameter Growth
Annual diameter growth can be studied from measurements of the width of annual rings. For many species, including radiata pine, the wood produced by the vascular cambium in the spring is composed of large thin-walled cells. Wood produced later in the growing season is composed of flattened, thicker-walled cells. While the transition from early wood to late wood during the year may be gradual, there is
usually a sharp boundary marking the change from one
favourable growth conditions in the autumn can lead to the apparent formation of two rings in one growing season.
The same effect can be produced when defoiiation by insects fs followed by the growth of new foliage in the same season~ Conversely, particularly with suppressed trees on poor
~ites, there may be no diameter growth on som~ or all of the stem during a growing season. Lack of growth can also be the result of damage by fire, lightning, or sil vi cultural. operations. Many of the anomalies can be resolved for
individual trees by studying both the annual shoots and the annual rings.
To study the pattern of ring width (and hence diameter) growth within a tree, it is convenient to use the three
sequences of radial growth de scribed by Duff and Nolan ( 1953).
The sequences are:
(i) oblique the sequence of radial growth in any one year (i.e. AA' in diagram 1)
( ii) horizon tal -the sequence from pith to bark at any one height (BB')
(iii) vertical - the sequence of ring widths which are in the same po tion relative -to the pith (CC 1) .
Whyte (1974) states that for radiata pine, within any one oblique sequence (i.e. within any one annual ring), as the ring is followed downwards, the width increases to a maximum at a point which is generally a little above the height of the baGe of the green crown that existed when the ring was formed. From the maximum, the width
27
A
B
pith
C'
A'
\
any one mul tinodal annual sh.oot, there is little or no difference in the width of a given annual ring (which is at least the third ring out from the pith) at successive
internodes. Most of the taper within an annual shoot is th~ result of taper in the pith and the annual ring
closest to the pith.
Since under stand conditions, there is generally an increase. with time in the height of the green crown, the height of the point of maximum width of successive annual rings w.ill also increase. Therefore, the same pattern of increasing and then decreasing ring widths is found in a horizontal sequence. However, as the horizontal sequence
is composed of rings laid down in different growing seasons, the pattern in this sequence can be confused by changes in environmental conditions from year to year.
The pattern of ring widths in a vertical sequence also tends to show a maximum. Shea and Armson (1972) have
demonstrated that in the case of jack pine (Pinus banksiana Lamb.) the changes in ring width are closely related to changes in the rate of annual height growth.
29
stands caused a reduction in taper (i.e. an iacrease in diameter growth at
5
m) although there was no effect on the length of the crown. Despite the evidence on the changes in form which can be caused by treatment, Evert (1971, p30) notes that there have been few studies which have assessed the effect of initial spacing on stem form, and that form factor is usually obtained from standard volume tables which only require measurements of the diameter at breast height and of total height.Whyte (1970 and 1974) used the information on growth patterns to propose a suitable sampling design for detailed stem analysis. He suggested that ring measurements should be made at sample points situated at the middle of the
internode of the lowest stem section of each annual shoot. This will provide good estimates of the volume and volume increment for each year for each annual shoot (and hence for the tree) in uninodal trees, and nearly as good
estimates for multinodal trees, particularly when successive annual shoots have the same number of stem sections.· The greatest errors are likely to occur when volumes and volume increments are being estimated for. the inside rings of an annual shoot. Errors can also occur in the volumes of young trees (including the volumes for the first few years of
trees which are now mature).
4,
IMPLICATIONS FOR THIS STUDYfactors which must be taken into account when looking at the accuracy and adequacy of the F.R.I. yield research plots. To be adequate for the requirements of forestry in New Zealand, sufficient data should be collected for the calculation of the production of total and utilisable volume, for a rang~ of different treatment regimes and utilisation requirements. At the same time, the way in which the data have been collected must be flexible enough for different approaches to the prediction of yield to be compared. If the objective of yield studies suggested by Curtis is to be met~ the data from the plots must contain enough information for reliable and quantitative expressions to be· formulated for both site and treatment.
The review of the patterns of growth has shown that different cultural treatments will affect the shapes of trees in different ways. The methods of measurement will have to assess these shapes, not only so that the predicted total volumes can be divided into different size and quality classes, but so that tree (and hence plot) volumes can be calculated accurately.
CHAPTER III
F,R,l. YIELD RESEARCH PLOTS
The only official manual of instructions issued for the permanent sample plots maintained for yield research by the mensuration section of the Forest Research Institute, is the "Manual of Standing Instructions. Provisional Section 213. Permanent Sample Plots", dated March
1949.
In the years following the introduction of the manual, several amend-ments were issued before i t eventually fell into disuse. This chapter gives details of the procedures which have been used for the measurement of the plots and shows the changes in methods which have occurred over the years. A list of the permanent plots established in stands of radiata pine is given in Appendix3.
31
The definition of a permanent sample plot given in the manual of instructions is "• •• any small area which, having been demarcated on the ground, surveyed and recorded on a map, is maintained for periodic remeasurement for a number of years, in general exceeding ten. As used in these instructions the term 'Permanent Sample Plot' implies a series of sub-plots each with its own surround. These instructions are limited to the use of such plots for the study of tree crop response to various grades of thinning and for the compilation of normal yield tables."
rather than normal yield tables. Therefore, the last sentence in the definition would be more correct if i t was amended to read " ••• for the study of tree crop response to various manage-ment regimes and for the collection of data for the preparation of yield functions".
The term experiment has now replaced the word pJ.ot for a trial laid down at one location and the major divisions of an experiment are called plots instead of sub-plots.
terminology will be used throughout this thesis.
1. LOCATION AND ESTABLISHMENT OF EXPERIMENTS
The latter
When an experiment was to be established, the site chosen was required to be fully stocked with crop density and growth
characteri~tics, soil tyoe, asnect, ground vegetation, and
slone as uniform as possible over the whole area to be occupied
33
All trees in each plot were to be numbered and marked with a paint band
4.5
ft(1.37
m) above ground level on the uphill side of the tree (breast height band). Scale diagrams were to be prepared showing individual tree locations and the positions of permanent photo points. A detailed survey of the location of the experiment was also requir~d.2. PLOT MEASUREMENTS AND CALCULATIONS
Initially each plot was to be measured at three-yearly intervals but since 1960 all radiata pine plots have been measured at intervals of two years.
(1) Diameters and Tree Classification
When a plot was established, and at each remeasurement, the diameter at the breast height band of each tree was measured with a diameter tape. Each tree was classified according to its position in the canopy and its crown and stem
form. Initially tree classification was carried out at each remeasurement but more recently it has only been done at "full measurements", which occur when plots are thinned, or at every fourth measurement if no thinning has been required. The method of classification has changed several times since the instructions were first issued. Diagram 2 summarises the various methods. Full details are ven in Appendix
4.
(2) Vol~
1947-55
1 967-68
1969-1 DOIGNANT I b
I
I : - ·l
L
I
I
1 b c
~·q:;
r--·-··-a
c
I
d1 DONTIL\NT
b c
D
DOliTI~AHT
2 a b c
ltP
1 DONDU\.NT
1 DOIUNANT
I
b2 C0-DOf!III'J11..NT a
I
b 1 cJ
d a
t j m
3
1a b c a b
rtlm
ltfm
d a
I
c a3
S1.i13-DONINANT
d a
I
b2 CO-DOIHNANT
b c
c
CO-DONINANT
2
3
c
~""b
c a b~m
~
2 CO-DONINANT
2 CO-DOI-1INANT
l
bI
d
c
c
4 5
SUPPRESSED · DEAD OR DYING
a
t
j
m1 a b
~
a
a
3
INTEID'IEDIATE
b c
I
INTEill,lEDIATE 2
c a b c a
tf
tfrr
3
INTEID'IEDIATE
3
TI'JTEID1EDIATE
I
bI
d a
t j m
3 1
b c a b
I
t!m
d a
c a
c
6 DISEASED a
I
4 SUPPRESSED
. b c
s
SUPPRESSED 2
a b c a
tfm
ftfm
4 SUPPRESSED
4 SUPPRESSED
I
b II
1\
-~
d
'
I
J3
!
b
cl
I
d
l
I3~
trees and the methods for the calculation of plot volumes have undergone several changes since the manual of instructions was issued. The instructions assumed that there would be very little or no difference in form between the different plots when an experiment was first established, and at the first remeasuremen t. Therefore, on these two occasions the sample trees were selected to represent the whole experiment.
Selection and measurement was by one of the following three methods:
(i) a systematic sample of twelve trees was selected from all the normal (i.e. single-leadered) trees in the two rows of trees outside, hut adjacent to the surround boundaries of all plots. An additional sample of three trees in the "upper
diameter group" was selected at random around and near the centre plot. The sample trees were felled and sectioned at the mid-points of a five foot butt log (i.e. at 2.5 ft) and subsequent ten foot logs (i.e. at 10ft, 20ft, etc.), at the mid-points of the residual logs (less than 10 ft long) ending at the points where the diameter inside bark was six inches and four inches, and at "form point" (half way between breast height and the top of the tree). Diameters over- and under-bark and of the heartwood were measured at each point where the tree was sectioned. Heights were measured from ground level to the top of the tree, to the first cluster in which all branches were live, to the first green branch, and to the
selected from trees thinned from the plots, the measurements being supplemented where necessary with data obtained by climbing main crop trees. Each malformed tree was measured in the same way as a normal tree, except that the butt portion and each leader were treated separately. The volume of each
sample tree was obtained by adding the sectional volumes, which were calculated using Huber's formula. The sample tree
volumes were plotted against their basal areas and a straight line was fitted to the points. The volume for each diameter class present in the plot was read from the graph and multi-plied by the number of trees in the class. Plot volume was the sum of the volumes for each diameter class;
(ii) instead 'of felling sample trees, the sam-ple could be selected within the plots and measurements obtained by climbing the trees. Apart from this, the measurements made and the subsequent calculationc were essentially the same as when sample trees were felled;
(iii) when volume tables were available for the forest or region in which the experiment was located, no sectional measurements were made for normal trees. Instead, thirty trees per -plot were selected to cover the range of diameters present and the total height of each one was measured. The heights were graphed against diameter and a smooth curve drawn through the points. The height corresponding to each diameter class was read from the graph and the volume per tree for each class was obtained from the tahles. (The tables were two-dimensional ones constructed by graphical methods requiring only breast height diameter and total
'
37
in each diameter class.
At the first remeasurement of a plot, selection and measurement of sample trees and calculation of plot volumes were done by either method (ii) (climbed sample trees) or method (iii) (volume tables). The manual aid not ~pecify the procedure to be adopted for subsequent remeasurements.
Beekhuis (pars. comm.) states that separate volume lines were constructed for each plot, each one based on eight to ten sample trees. If a thinning was being carried out, half the sample trees were selected from the thinnings and half from the main crop. If sufficient normal trees were not available
within a particular ~lot, additional sample trees were sometimes taken (and still are) from the surround to make up the required number. Such trees were not permanently identified, although they could be used as sample trees on more than one occasion.
From about
1955,
instead of measuring a separate sample of forked trees, the total volume of each such tree was calculated as though i t had no forks. A percentage correction, which depended on mean stand height and was obtained from tables produced by Duff(1956),
was apulied to the volume.In
1955,
following the publication of a form-class volumetable (Lewis,
1955),
sectional measurement of sample trees was discontinued. Instead, eight to ten sample trees were selected from each plot, and on each one measurements were made of total height, diameter at breast height over and under bark, anddiameter over bark at half the total height. Volumes for the sample trees were calculated using the form-class tables. Plot volumes were obtained using a graphical volume line as before.
'
volume line from measurement to measurement were inconsistent. About this time suppressed trees were excluded from selection as sample trees.
Work towards new form-class volume tables in 1960 led to the measurement of diameters (overbark) at 5%, 10%, 25%, and 50% of total tree height. Bark thicknesses were also measured at these points from 1961 onwards. The number of sample treeP selected waR still 16 per plot but from 1962, although the
heights of all 16 trees were measured, upper diameters were only measured on ten trees. No new form-class tables were Produced and the old ones continued in use until the processing of sample plot data was transferred to a computer, beginning in 1962.
It is claimed (Beekhuis, 1966, p5) that computer processing would not allow the form-class tables to be used, so they were
replaced by regional two-dimensional volume equations. The
equation used is the Schumacher solution (Spurr, 1952) but with a modified height term:
h
ln v
=
a ln d + b ln (h-4.5)-
cwhere v is total tree volume under bark (ft3 ) d is diameter at breast height overbark (in) h is total tree heir;h t (ft)
39
v
=
v, d as before b0, b
1 are the regression constant and coefficient.
The original computer program, which ran on an IBM 650 computer, has been modified to run on an Elliott 503 and is currently being redesigned for an ICL 19048. No effort appears to have been made to reintroduce the form-class volume tables or any other method of volume calculation which would cater for differences in tree form due to different treatments.
In 1972 work on form-class tables was revived by J.C. Ellis. As a result of his work the measurement of sample trees was
changed again. Only one upper diameter measurement is now
made, at the fixecl height of 6m above ground, on ten 0f the 16 trees whose total hei.P'hts are measured. Bark thicknesses at the
breast height band and at
6
m are also measured on the ten trees.Since nrocesFing hv computer was introduced, the results from all the earlier measurements of the plots have been recomputed using the two-dimensional volume equati0n for the region in which the experiment is located.
A least square8 regression:
=
Schmidt (1967) as Petterson's curve. As a result of a program change during preparation of the programs for the ICL computer, some plot summaries produced in 1974 used the tree of mean diameter to obtain mean height, but the program has since been changed back to use the tree of mean basal area.
A summary of the various methods used for the calculation of volumes is shown in Table 1.
(3) Predominant Mean Height
Since 1951-1 the heights of 8 trees per plot have been
measured for the calculation of predomin~nt mean height. This measure of stand height is defined (Beekhuis, 1966) as the
average heip:ht of thP tallest LJO stemF per acre (100 stems/ha), selected at the rate of one tree in each 0.025 acre (0.01 ha). Each plot is divided into quadrats of 0.025 ac (0.5 ch (10m) x 0 •. 5 ch) and the heir;ht of the talleBt tree in each of eight of the quadrats is measured. The average height of the eight trees provides an estimate of predominant mean height. Some of the trees selected may also have been sample trees for the calculation of volumes.
(4) Crown Height
41
TABLE 1 METHODS USED FOR VOLtmlli CALCULATION
PERIOD NO. OF METHOD OF CALCULATING THE COMJ.IENTS S.Mfi>LE TREES VOLUMES OF S.Mfi>LE TREES
191±7-54 15/trial Sectional measurement by At establishment and felling or climbing; Huber's first remeasurement formula
OR
30/plot Measurement of total height
.
"
and dbh; two-dimensional volume table
8-10/plot Sectional measurement or 2nd and subsequent volume tables as above remeasurements
1955-57 8-10/plot Heasurement of total height, dbh(ob), dbh(ib), d(ob) at half height. Form-class volume tables
1958-61 16/plot Form-class volume table as above
1962- 16/plot Measurement of total height All earlier volumes and dbh ( o b) • Two dimensional recomputed on this
[image:49.595.67.558.62.483.2]green whorl. Where the crown is lopsided, an estimate is made of the average base of fu:l crown. Generally only a single
measurement (from the ground) is made, but on sample trees which have been climbed to obtain measurements of upper
diamf':ters; crown height is often the result of direct measure-ments of the height from ground level to the first green branch and the first green whorl.
(5) Special Measurements
The manual of instructions required several types of special measurements to be made.
(a) Analysis of Annual Height Growth. On all felled sample trees the height from ground level to the terminal bud, and to each branch cluster which could be distinguished as marking the end of a years height growth, was to be recorded.
(b) Stem Analysis. When an experiment was established,
f0ur of the felled sample trees were chosen to represent average dominants (in ter~s of form and height). On each of these trees the number of annual rings present at each point where diameters had been measured, was to be counted and recorded.
(c) Wood Density. To obtain data on the effect of thinning treatment on wood density, samples were to be collected at the second and subsequent thinnings (provided that the trees were at least twenty years old). Three trees were to be chosen in each plot to represent the largest,
surrounding stand if i t had not been thinned. From each tree a sample disc, two to three inches thick was to be taken from an internode where the number of annual rings was five fewer than the age of the tree. A bolt 14 inches long for strength tests was also to be cut at the same sampling position, from the tree representing the average diameter class, in the medium grade of thinning.
(d) Soil Descriptions. In each plot a soil pit was to be dug and the different layers in the profile described. The description was to include the thickness of each layer and its colour, texture, structure, consistency, cohesion, porosity, and the presence of tree roots and soil fauna. The general moisture conditions and drainage were to be noted, together with the weather conditions prior to measurement.
(e) Vegetation. Each layer of vegetation (mosses, herbs,
shrubs, small trees, dominant canopy) was to be described separately.
Although the plot records do contain some of these data, the special measurements are no longer made and for many of the plots, they may never have been made.
3.
THINNING TREATMENTSfactor which determined how many of the optional trees were
removed. Prescribed thinning grades (not necessarily all
present in any one trial)were:
A. low thinning, in which suppressed and sub-dominant trees were removed. There were three grades:
Grade I - light thinning in which suppressed, diseased, and damaged trees, defective sub-dominants, and whips were removed;
Grade II - moderately heavy thinning, aimed at leaving a well distributed crop of good dominants. Therefore, all diseased, damaged, and suppressed trees, and whips were removed
immediately. All sub-dominants, the majority of co-dominants
and some of the worst formed dominants were removed as soon as possible, provided that no gaps were created in the canopy; Grade III - heavy thinning, aimed at leaving a crop of the best dominants only. The same as grade II with the additional removal as soon as possible of all co-dominants, defective dominants, and some of the well developed dominants;
B. crown thinning, designed to remove competition amongst the dominant trees:
Grade I - light thinning to leave a well distributed crop of dominants of good form and the best co-dominants. The
suppressed trees were left if necessary to prevent opening up large canopy gaps;
Grade II - heavy thinning aimed at giving the best treatment to those dominant trees which were expected to form the final crop.
were classified using relative spacing (Hart, 1928, cited in Beekhuis, 1966):
s
=
100 X S/Hr
where
s
is relative spacing (%) rs
is triangular spacingH is predominant mean height.
At any given height, the greater the stocking, the lower is the relative spacing. If the stocking remains constant while the height increases, relative spacing decreases. Using this index, lightly thinned plots (grade 1) were kept at a mean relative spacing of 18% or less, medium thinned plots (grade 2) were maintained at 19 to 22% and heavily thinned plots
(grade 3) at 23% and over. No distinction was made between low thinning and crown thinning.
were expressed in the form:
Thinning prescriptions
thinning grade/number of thinnings/predicted predominant mean height at the end of the rotation.
