The company has been focused in the area of carbon sinks and sequestration of carbon via forestry. A system has been developed which provides a framework for such tracing and for trading of the offset provided by forestry carbon sinks. Work since inception has focused largely on developing the commercial framework, supplier support, and relationships to make such a system commercially viable.
Back in 2000 we completed our prototype carbon pool. This involved the application of standpak (the precursor to the 300 index) and cchange to approximately 1000ha of pinus radiata located in the upper South Island of New Zealand.
The Proto Carbon Pool
This document attempts to present information, techniques and a process for the collection of field data in planted NZ forests – specifically radiata – in order that a computer based, modeling prediction can be made of the amount of stored carbon within a forest stand.
In order to apply the correct field techniques, the author believes it is necessary for the field worker to have at least a limited understanding of the whole process and so this document begins by discussing some of the concepts and background work that precedes the field work.
Many of the techniques and methods used to assess various parameters in forests are truly well tried and tested. Hence, only cursory coverage is given to established practices. What this document does attempt to do is to bring together a number of diverse concepts which are not normally wellunderstood by one single operator – for instance, planning and the following practicality of locating and measuring a tree in a forest, together with the complex statistical data analysis that occurs to the data back in the office and the subsequent modeling. A broad understanding of each step should help an individual involved at just a single (or several) stages to better understand and thus to be better placed to provide quality input and feedback, as well as feeling a sense of “ownership” and pride in being part of a developing process.
Steps 1 to 20 within the document highlight necessary considerations and actions to be undertaken from initial planning through to final presentation of the data.
The latter parts of this document provide less information than the author considers necessary. This is in part because the author has been less involved at the modeling end of the process and also because, this is a more specialised area, requiring specific tools (proprietary CChange model) and skills.
The author was responsible for the conception of the ProtoCarbon Pool (PCP) project and together with the Aucklandbased Environmental Intermediaries and Trading Group Limited has driven the project through to the present day. The PCP work is not yet complete –either in the field or in reporting. The author earnestly hopes that the considerable work which has already gone into the PCP is not wasted and that the initiatives can be further developed and extended.
The author has undertaken all of the field work and data processing, excepting the specific carbon modeling undertaken by Forest Research, and presentation of the results.
However, much of both the theory and practical methods presented in this document originated from lengthy discussions and the notinconsiderable help willingly proffered by Piers Maclaren, formerly of Forest Research. His book “How much wood has you woodlot got?” (FR Bulletin No. 217) is an invaluable manual to anyone involved in estimating the volume of planted trees. The author wishes to acknowledge Pier’s help with a big “thankyou”.
Background
1) What do we want to achieve?
Why are we measuring?
Selection of suitable stands.
It is appropriate to consider “what we want to achieve” from the collection and analysis of field data and to use this understanding to determine our progress and whether we are meeting both targets (defined and objective) and expectations (more subjective).
A good understanding of what we want, combined with feedback and practical “real” experience “on the ground”, will influence – and perhaps modify – methodologies,
Primary objective: The ProtoCarbon Pool set out to trial and test some of the theory, techniques and practicalities (including cost analysis) of:
 Measuring a sample of trees in an appropriate plantation.
 Analysing and modelling the collected data to determine the present stored carbon within the plantation and predict the levels of stored carbon at future times (producing a carbon profile for the plantation).
 Collating a number of carbon profiles to produce a carbon pool.
Some of the initial criteria / parameters for the PCP were:
 Data from approx. 1,000 ha. of “Kyotocompliant” radiata plantation forests, collected over 8 or more stands and with some geographical spread around NZ.
 Stands to exhibit some (normally encountered) diversity (from each other) – for instance, different terrain types, undergrowth, stocking (both high and low), age, etc.
 Trees to be aged from a minimum of 3 years (any less, too small for meaningful measurements) up to 9 years (any older, then outside Kyoto 1990 timeframe).
 Stands able to be clearly located on a map – preferably with the owner providing a detailed map with NZ Map Grid coordinates for boundaries and significant features and some aerial photographs and details of forest area..
 Forest owners willing for their stands to be involved in “research” type work. Stands to have an accurate history of forest management from planting (especially year of establishment) through to present day, including silviculture.
A secondary objective of the PCP was to demonstrate “action” (vs. words) in the field of carbon sequestration by forests and to involve (and educate) a number of “willing” landowners interested in forest sequestration (who may in the future be the forest owners at the forefront of trading forest stored carbon).
To ensure a positive contribution to these objectives, each trial location for inclusion in the PCP needs to be carefully assessed to ensure that it meets most, if not all, of the above criteria with the end result being the production of a carbon profile that can be “added” to the PCP.
Furthermore, since the PCP has limited funding, each stand “offered” by forest owners for measurement and potential inclusion, has been carefully considered, balancing cost of data collection against quality of data likely to be collected. Some “offers” of stands for inclusion have been politely declined.
Initially, it was envisaged that sampling within a stand would be continued until PLEs of less than 15% were achieved (see later for brief explanation of PLE). Whilst this is “practical” for stocking and height, basal area can require many more plots to bring the PLE down to even 20%. (Note that to date, most stands have not achieved a basal area PLE of 15%). Selection criteria would need to be more rigorous – especially in terms of within stand variability – to achieve PLEs of less than 15% or many more plots (= more data and more cost) would need to be collected.
Step 1 – Understand why data is being collected.
Step 2 – Careful selection of forest stand for field work.
2) Sampling – some basic theory.
This document will only give some very basic theory on “sampling”, hopefully enough to enable the reader to understand “why” certain techniques are used for the PCP.
Why sample?
In a large woodlot, it is not usually necessary to measure every tree. Data collection is expensive, and the goal of a skilful inventory expert should be to obtain an estimate that is sufficiently precise for the intended purpose, at minimum cost. Undoubtedly, a more precise result could be achieved by increasing the sampling intensity, even to the point where every tree is assessed, but it is not normally costeffective to do so.
Even a full enumeration (ie assessment of every tree) is not necessarily totally accurate, because there is inevitably some measurement error. There is a danger that this can be overlooked. Whereas, if a number of samples are taken, they provide an indication of the variability due to measurement error as well as the natural variability within the stand. Both factors are included when confidence limits are calculated for the population mean.
Random vs systematic plot layout.
In any sampling exercise, it is imperative to avoid human bias, where bias is the average or systematic difference between an estimate and its true value. A biased estimate is one that consistently tends to either over or underpredict the true value.
If, for example, a stand was sampled with plots established at, say, 50 metres intervals “twenty metres in from the road” (perhaps to simplify access for fieldworkers), the following problems could result:
 No edge trees would be included in the survey. Trees at the very edges of stands tend to be larger in diameter, shorter, with larger branches, and greater sweep.
 The silvicultural contractors involved in thinning and pruning may have performed satisfactorily within easy view of the road, but unsatisfactorily further back.
 The road may have been formed along a ridge or a valley floor. A line of plots parallel to the road could follow the toeslope or else the steeper part of the sidling. This may not be typical of the whole stand.
The traditional way to sample an area is to lay out plots randomly. One way of doing this is to impose a grid over the map of the stand, and to select coordinates based on numbers obtained from a randomnumber table. Mark these locations on the map. Use a combination of geometry in the office, and compass navigation in the field, to reach the exact locations.
Whatever the method of determining the plot locations, it is important that they be done in the office. A “random” choice of locations determined out in the field will probably not be random at all—subconsciously, the fieldworker will choose a site where the trees are growing unusually well, or where the understorey vegetation is sparse, or where there are no edge trees, etc.
However, random sampling is not without difficulties:
 It is possible for most of the plots to end up in one corner of the stand and for other areas to remain unsampled.
 It is timeconsuming to calculate the distances and compass bearings required to reach every plot. This is particularly the case if there are dozens of plots in a stand.
 Having marked the plots on a map, there is often no simple route that will incorporate all plots without zigzagging and backtracking. This is not costefficient on walking time. If understorey scrub is thick, fieldworkers will not be grateful for any extra “bushbashing” for the sake of statistical purity!
In many circumstances, systematic sampling will be acceptable by superimposing a grid pattern on the map, and selecting plots at the grid junctions in such a way that the correct number of plots are used. If this is done, great care should be taken to ensure that edge trees are not over or under represented.
The advantage of this method is that it is easier to calculate the geometry, walking time is reduced, and all parts of the stand are assessed. Objections are often raised to systematic sampling on the basis that it could be biased. Plots at regular intervals may, for example, coincide with gullies that also occur at regular intervals, but more subtle patterns may exist in the landscape which are not so easily detectable.
Bias attributed to systematic sampling is unlikely to occur in practice. Few landscapes have any features that occur on such a regular basis that it would affect the results.
Plot mixtures.
In an inventory where several types of information are required (for example, height, diameter and stocking), it is sometimes possible to combine them in the same plot. For example, a circular plot can be established where all trees are measured for diameter, a few trees near the centre are measured for height, and the tally of the trees within the circle provides stocking.
When calculating the necessary number of plots, sufficient precision may be obtained for some parameters (eg height and stocking) with only a few plots, but others (eg basal area) require more plots to attain a satisfactory PLE. Additional plots can be incorporated specifically for the parameters with the greatest variability. In the case of basal area, the preferred type of additional plots may be unbounded, consisting of “basal area sweeps” using a prism. The best inventory procedure may then be a mixture of different plot types.
The PCP employs systematic sampling techniques. (Nevertheless, using random techniques to determine the startpoints and orientation of the grid where possible and which gridpoints constitute a plot of a certain type).
The variability of a stand will determine the number of plots that need to be established. A uniform stand will need far less plots than a highly variable stand (even within a single age class, trees can vary greatly due to aspect, soil, planting, etc.).
Experience with the PCP has indicated that between 15 to 30 plots per 100 hectares will be necessary to achieve PLEs approaching (or better than) 15% (see later for more explanation).
Step 3 – Check that sampling technique to be used is appropriate.
3) Navigation.
Area of stand / forest.
Knowing where you are and where you want to get to.
Once the location of sample plots have been determined “in the office”, it is necessary to locate these “in the field”. This very statement should cause pause for reflection  as to whether nicely spaced, regular plots shown on a flat piece of paper (map) can be physically reached and at what cost (both in terms of dollars and the field workers physical wellbeing!)?
It can sometimes be obvious that some plots are going to need an inordinate effort (and expense) to be included in a sampling exercise and it may be prudent  especially after reconsidering “what are we trying to achieve” and the degree of accuracy needed  to “map out” certain areas from consideration and inclusion in the calculations. These mapped out areas will not contribute any carbon to the total stand carbon calculated towards the end of the process. This technique is open to some fair criticism but does balance practical issues against cost (see also the consideration of area of stand later in this section).
Traditional techniques for locating plots on the ground have involved the use of a combination of geometry, compass navigation and distance measurement – for instance with a hipchain. In open, flat terrain, with good, known reference points to work from, this technique has undoubtedly been used with satisfaction and a fair degree of accuracy.
However, once rough terrain and thick undergrowth are encountered the above method has severe limitations, not least in the time needed to travel between plots whilst trying to stay on a steady compass course over terrain with a varying degree of slope (field workers must constantly adjust distance covered over sloping land to give true horizontal distance as appears on a map) and also trying to avoid the inevitable obstruction, such as a cliff.
The recent improvement of Global Positioning Systems (GPS) has revolutionised finding a specific location, at an (universally recognised) exact set of reference coordinates, which can then be simply stored and retrieved indefinitely and the location revisited with a high degree of accuracy.
In the author’s experience, a small hand held GPS unit (eg from Etrex) will nowadays routinely provide an accuracy of around +/ 7 metres (normally varying between 5 to 12 metres) – in effect a “circle” within which the point is located (which, for instance, enables an operator to clearly identify one telephone post from another). Due to satellite configurations, this sometimes deteriorates to around 35 metres. For maximal operation, GPS needs a clear view of a large part of the sky and does have difficulty operating through a forest canopy. However, hard and fast rules on when a GPS unit will provide a valid and accurate reading are difficult to determine.
The author has found that GPS has provided acceptable accuracy on all occasions to date. This has included operating in radiata forests up to 7 years old.
GPS also provides an extremely useful interface through to a mobile, laptop computer system. NZ Topographical Maps are now available on a series of CDs to cover all of New Zealand. GPS interfacing software (eg. Fugawi) allows the uploading and downloading of multiple waypoints (locations identified by specific coordinates, either on the ground or on a map). Routes and tracks can be shown on an electronic map.
After establishing the desired “sampling intensity” for a stand, a suitably scaled grid can be overlaid on the relevant electronic Topographical Map and a series of waypoints established for each plot. These waypoints are then uploaded into the GPS unit. (Note that the above process can be completed manually and waypoints entered directly into the GPS unit [but more laborious and time consuming]).
Efficient operation of the GPS unit in the field requires a fair degree of competence and familiarity with the unit but the author believes that this can be learned in half a day and familiarity developed over a couple of days. A hardcopy printout in the form of a suitably scaled map of the designated plots is a useful addition to the electronic listing held within the GPS. The printout aids “bestroute” identification and overall orientation on the ground. Waypoint information can be stored electronically and printed on demand for paperbased distribution.
In the field, it is possible to select a waypoint and request “Go to” information from the GPS unit – this is provided in the form of a distance and bearing to the waypoint from the present position. A competent operator will be able to begin in the general direction of the waypoint and use the GPS unit to navigate, like a compass. Alternatively, a small handheld compass can be used for direction.
Notification is given to the operator as they approach the waypoint. Ideally, a totally stable and accurate navigation system would give one single, unique position (i.e. zero metres to proceed)  however, as the operator comes within the “circle” of accuracy of the GPS location, the location appears to “move around”. At this point, it would be possible to bias the exact location within the circle of accuracy. In order to negate this subjectivity, the author has utilised a technique whereby an attempt is made to get as close to the location as possible. A mark is made on the ground and the operator then moves 10 metres (or more) in a predetermined (and constant) direction – this needs to be completed accurately, and the final position is then marked by a peg put in the ground. Note that this means that the relevant coordinates for the position are displaced 10 metres from the real position – in order to remove this error, it is most sensible to enter each waypoint as being offset say 10 metres to the north of the desired plot location and then to locate the waypoint and move 10 metres south.
The author is of the opinion that it is the objectivity of locating a plot that is important and not the precise correct location on the ground of the plot shown on the map i.e. to reiterate, to remove the subjectivity of the field worker selecting easier / better / more attractive plot centres. As long as the field worker does not deliberately or inadvertently add bias or systematic error to the location process, then locating a plot to within, perhaps, as much as 50 metres of the exact location may be acceptable. GPS certainly provides this accuracy. (Note that this opinion is open to debate and may not withstand detailed scrutiny and audit. However, for the PCP, the author considers the method acceptable).
What area of trees are we measuring?
Area is a difficult and often costly measurement to obtain. There are a number of ways in which area can be determined with varying degrees of accuracy and a number of “good arguments” as to exactly what should be measured. Specialist assistance is often required to determine area (e.g. photogrammetrists using a stereoplotter to produce maps and measure areas from aerial photographs or surveyors using expensive and time consuming groundbased equipment). However, area is a key measurement to obtain for the stand since utilising only a sampling technique (rather than measuring every tree!) means that to obtain relevant information about a complete stand requires calculating pertinent results, for instance on a per hectare basis, and “scaling up” to provide for the whole stand.
The PCP utilises per hectare results for a stand obtained from modeling using Cchange to provide an overall Cprofile for the total stand. To date, this area of the process has been rather crude and unsatisfactory. The all important calculation is the Net Stocked Area (NSA) being the area actually occupied by trees – it excludes features such as streams, roads, landings, and large canopy gaps. Unfortunately, NSA is further complicated by whether the boundaries of the woodlot are defined by tree stems, the average distance between trees, or the extent of their foliage or dripline. By convention canopy gaps of 0.1 hectare are excluded from calculations of NSA.
A number of scenarios will illustrate the difficulties encountered and problems posed.
a) For a wellstocked stand, it may be possible to determine area within the legal boundary from original survey data (a new owner may have had the property surveyed prior to purchase and planting). This then presupposes that the owner has planted to the legal boundaries (note that fences often used as physical boundaries are not the actual legal boundaries).
b) A good set of aerial photographs may allow the accurate calculation of area – however, there will most likely be some subjective decisions to be made as to whether a “hole” viewed on an aerial is to be counted in or out – and photograph resolution and age of the trees will play a key role here. This method actually calculates the area of trees – as opposed to above which calculates area of ground – but again presupposes that the planted area ties in with the boundaries (if an owner has planted over the boundary, he does not own the trees being considered!). A professional aerial photographic agency may be able to provide an area estimate within 3%.
c) A poorly stocked stand or agroforestry type situation (large row spacing) may not lend itself to the above. The question then needs to be posed – is it necessary and relevant to remove gaps that occur within the stand before sampling and measurement takes place? If it is, then a welldefined criteria needs to be established to be able to mapout these gaps and samples from the overlying grid are then not counted (or visited).
Note that errors are proportionally larger in small blocks. It is (proportionally) more difficult and more expensive to obtain the area of a small block than a large one.
What is important is that the method of determining area is decided before measurement begins. It is not acceptable to locate a plot within a stand and then, because it is poorly stocked (or not stocked at all), not include the measurement (or lack of measurements). Also it is necessary to note that few owners have an accurate measurement of the area of their stand/s (and it is often overcalculated!).
In theory, good random sampling carried out at a sufficient density would be able to accommodate holes in a stand. However, few measurements or none at all, lead to a huge variation in the data collected and thus a distortion of the results – see data analysis later. For instance, as an extreme example, if holes are not mappedout, a stand with mature trees will return actual field measurement ranging from trees with large height and diameter down to (supposedly) trees with no height and diameter!! This is clearly contrary to what is trying to be achieved (and will give some large statistical errors when producing the summary statistics –see later).
GPS can provide a useful first calculation of area, although the process can be time consuming. The boundary of a stand can be walked and waypoints noted at each significant change in boundary direction. These points can then be downloaded to the relevant NZ Topographical Map on a mobile computer and an automatic calculation of the area within the boundary as defined by the linked waypoints is calculated. By a similar method, it is possible to identify holes (perhaps from an aerial or local knowledge) in a stand before sampling and map these areas out of a final calculation.
The whole question of area calculation and perhaps, more specifically, what is relevant to carbon pooling needs a lot more thought ( and experience).
Step 4 – Adopt a suitable, practical navigation system.
Step 5 – Obtain as much relevant, uptodate information as possible on the stand and good maps.
Step 5 – Identify the boundary of the stand and any gaps beforehand if possible.
Step 6 – Overlay a stand map with a suitable sampling grid and determine plot locations. Upload or input into GPS or data sheets.
Step 7 – Make a first calculation of stand area from available information.
4) What do we want to measure?
As discussed above, identifying exactly what we want to achieve will determine what we measure.
Forest Research provided expert advice as to the parameters necessary for input to their present carbon modeling programmes (Cchange which is a bolt on extension to STANDPAK). The pertinent statistics for each stand were determined as being:
 Stocking – stems per hectare.
 Height – Predominant Mean Height.
 Basal Area (BA).
Measurement error and confidence limits.
It is necessary to introduce and try to understand some very simplified mathematical statistics. The author is not well versed in statistics  this section is written to try to give the barest understanding so that field workers can provide sufficient, correct data back to the office for analysis.
PLE – Probably Limit of Error – refers to the confidence limits expressed as a percentage of the estimated mean. Thus, a PLE of 10% at the 95% probability level implies that the true mean is likely to lie within 10% of the estimated mean 95 times out of 100. For example, if the average stocking in sample plots for a stand is 1,000 stems/ha, and the PLE is 15%, the true stocking for the stand will lie between 850 and 1,150 stems/ha; there is only one chance in 20 of it being outside this range. Individual plots, however, may vary widely: PLE does not tell you how much variability there is in a stand. (The way to do this is to use the standard deviation).
The PCP was originally conceived based on a rather arbitrary target PLE figure of 15% for any measured parameter. (Quite simply, there was little practical data tohand which could indicate how achievable any target was going to be, and so part of the objective of the PCP became an exercise to determine what levels of PLE could be achieved in practice). The initial PCP work has shown that it is relatively easy to achieve PLEs of less than 15% for both stocking and height but much more difficult to obtain a PLE of even 20% for basal area. Many more measurements need to be undertaken to achieve the latter, even within a fairly uniform stand.
Plots – shape, size.
Sample measurements are taken within plots. To date the PCP has utilised temporary bounded plots, installed to sample actual performance – these have not been permanently marked (although they should be able to be fairly accurately relocated with GPS). A bounded plot is a geometric shape where the boundaries can be defined on the ground.
The PCP utilises circular plots where the plot is laid out by fixing the plot centre and an appropriate radius, adjusted for slope.
Note that unbounded plots to provide additional information for basal area can and should be utilised where possible. The trees for measurement need to be easily sighted – ideally, pruned stems where the undergrowth does not prevent clear siting of each tress from a static location.
If there are too many trees within a plot, there is a risk of incorrect measurement. A plot with a small number of trees is more likely to be counted correctly; all trees will be easily visible and the plot perimeter will be obvious; smaller plots are easier and quicker to install and measure. However, if the number of trees is too small, there will be considerable variation between plots, even in a relatively homogeneous stand – this will mean that a larger number of plots will have to be measured to get the same precision.
In short, optimum plot size will depend mainly on variability of the stand with respect to the parameter being measured and the cost of establishing plots relative to measuring them. As a rough rule of thumb, 15 to 20 trees are suitable for a bounded plot.
So, in practice, it is helpful to have some prior knowledge of what stocking is likely to be encountered within a stand – as is very often the case for a young stand with good survival.
As an example, if a stocking of 1,000 stems per hectare is expected, and we wish to measure an average of 15 trees per plot; then by simple calculation (15/1,000) = 0.15. A hectare is 10,000 m^{2}; 0.15 of a hectare is 150 m^{2}. From (Area = p.radius^{2}), the radius for a circular plot is 6.91 metres. Simplifying this, a seven metre plot radius will give slightly greater than 15 trees per plot on average.
Step 8 – Try to determine the expected stand stocking (prior to any field measurements).
Step 9 – Determine plot shape (circular) and plot radius to give an average tree count of between 15 to 20 trees per plot.
If the plot is on a slope, then the plot radius needs to be adjusted (area is expressed in horizontal terms not as it actually occurs on the hillside). For the radius of a circular plot, use the following formula:
where R is the radius in metres, A is the plot area in square metres, p is 3.14, and S is the slope angle.
The following table gives some appropriate values for adjusting plot radius:
Slope (degrees) 
Plot radius (m) 
10 
7.05 
15 
7.12 
20 
7.22 
25 
7.35 
30 
7.52 
35 
7.73 
40 
8.00 
Slope is measured in the field with a clinometer.
To date, the PCP work has been in stands where the prior “bestestimate” of stocking has been around 1,000 sph and so, has been conducted with a constant seven metre radius plot, adjusted for slope where appropriate.
Plots – how many?
A basic rule is that stands that vary greatly (e.g. in tree height, DBH, etc.) will require more plots. Also, a smaller stand will require relatively more plots than a larger stand.
It is possible to calculate the number of plots required, provided you know:
 The level of precision (error) required for parameters being assessed.
 The inherent variability of the parameter you are sampling.
We can set the level of precision – say PLE 15%, as noted above – but the variability is unknown until we take some measurements. Even then, it may be that field data and analysis fails to provide the target level of precision. So in practice, the following often occurs:
 First visit to a stand to carry out a pilot survey to determine the stand variability.
 Second visit to conduct the main survey based on the calculated number of plots required.
 Third visit to add extra plots to increase the level of precision to acceptable levels in the event that the number of plots was wrongly calculated.
Three visits is time consuming and costly.
The PCP has condensed the above three steps into two (and sometimes one). Sufficient plots are measured in the first visit to provide the bulk of the data necessary. This has proven to be around 15 to 30 plots per 100 hectares – often determined in practice by how many plots can be completed within a single working day (15 to 30 depending on access, terrain, undergrowth, etc.).
Thus, an overlay grid is scaled (changed in dimensions) to provide approximately this number of plots per 100 hectares – Step 6, as noted above.
The (day’s) collected data is then analysed to determine the PLE for each of the three parameters being determined ie. stocking, height and basal area. This calculation is fully explained under the next section – Summary Statistics.
If the calculated results show that the PLEs are not providing sufficient precision, then to maintain objectivity, the sampling technique – establishing plot locations back in the office  has to be repeated with a completely new set of plot locations generated and these new plots then need to be systematically visited (for instance, the following day). The analysed results may have indicated that only another 10 plots are needed to bring the PLEs within acceptable levels. In order to install just another 10 plots per 100 hectares, it is necessary to generate a new grid to a satisfactory scale giving a systematic spread over the stand.
Stocking.
Stocking – the number of stems per hectare  is assessed by counting the number of trees within each predetermined area (plot), adjusted for slope and then converting this information to an amount per hectare.
Stems per hectare = (N x 10,000/ A)
Where N = tree count per plot; A = area of plot in square metres.
There is some room for debate on stocking. The author has found little information on exactly which stems to count in a plot – for instance, if a stand is 7 years old (and trees are around 10 metres), and a plot contains a tree that has only grown 2 metres, should it be counted? The author has standardised by counting every tree that was planted – often identified by regular spacing – which occurs (i.e. has survived) within a plot.
Tree Height.
For the PCP, it is necessary to have some measure of height that applies to a stand rather than to individual trees. Forest Research advised that the height parameter with most relevance to the PCP is Predominant Mean Height (PMH), which is the average height in metres of the tallest trees in each onehundredth hectare (0.01 ha.) of a plot. Usually at least six trees are measured within each plot to obtain PMH
However, following FR advice, for the PCP, in practice, this has meant that only the tallest single tree within 5.6 metres (adjusted for slope) of each plot centre has been measured and recorded. (The author understands that this advice was given because tree height is neither greatly variable nor of greatest importance to the Cchange modeling. A more rigorous PCP may demand a better assessment of tree height).
Once the tallest tree within a plot has been identified (and it may be necessary to measure two or more if there is some doubt), tree height is measured either directly with a series of height measuring poles or indirectly by establishing a datum point on a tree and employing the use of a tape measure and a hypsometer. Both techniques are well understood and widely used within the forest industry.
Basal Area
BA is defined as the crosssectional area (square metres per hectare, including bark) of stumps in a stand if they were cut at exactly breast height.
Two methods can be used to determine BA.
 By computation from DBH measurements from each plot.
 Directly with the use of unbounded plots and an anglegauge.
DBH (Diameter at breast height) is the diameter of a tree at breast height above ground level on the uphill side of the tree, standardised at 1.4 metres.
DBH is measured most simply with a diameter tape by recording all the stem diameters within each plot.
Again, DBH measurement is widely employed in the forest industry. However, it is necessary to note that to ensure accuracy, care must be taken to measure at 1.4 metres (on the uphill side), at right angles to the stem and to ensure that the tape is neither twisted, sagging or passing around other extraneous vegetation.
To date, the author has only used the measurement of DBH to determine BA. However, the use of an angle gauge and unbounded plots can greatly increase the speed of data collection in suitable stands, where the full stem of each tree being measured can be easily viewed (for instance, in stands pruned to at least two metres, where the undergrowth is thin). This technique requires some practice and skill to ensure accurate results.
Experience has shown that in order to achieve a predetermined PLE, say 15%, BA requires far more sample plots to be established than for stocking or height. Unbounded angle gauge plots – at predetermined locations, accurately located by GPS or otherwise  can be interspersed between circular bounded plots during a stand assessment. This method needs to be developed.
Recording data.
All data needs to be accurately recorded in the field and carefully guarded against loss or damage. A simple recording sheet for each plot showing location, plot identifier, some notes, total tree count, height and DBH should be employed in the field, preferably on waterproof paper.
5) Data handling.
Summary statistics.
The collected data needs to be entered into a spreadsheet and analysed to achieve two aims:
 To check whether enough data has been collected in the field to achieve the desired accuracy i.e predetermined PLEs for each parameter.
 To present the data and summary statistics for input to Forest Research (or other) modeling programmes.
Microsoft Excel is a suitable computerbased spreadsheet for the recording and analysis of data. Sample data from a spreadsheet is included below.
For each plot, the actual field measurements of DBH are listed in Column 1 (in centimetres but this could be millimetres) and the area of the section of the tree stem at breast height, as calculated from DBH is shown in Column 2 [ Area of each stem = p.(((D/100)/2)^{2}]
Column 1 (D) Column 2
Plot (by Way Point #) 
216 

207 







9.0 
0.0064 
8.1 
0.0052 

9.4 
0.0069 
11.3 
0.0100 

9.6 
0.0072 
14.5 
0.0165 

8.5 
0.0057 
5.8 
0.0026 

6.8 
0.0036 
7.4 
0.0043 

7.9 
0.0049 
13.7 
0.0147 

8.2 
0.0053 
8.8 
0.0061 

8.1 
0.0052 
10.7 
0.0090 

11.0 
0.0095 
13.5 
0.0143 

6.4 
0.0032 
9.6 
0.0072 

5.2 
0.0021 
13.4 
0.0141 



14.0 
0.0154 
Some summary figures are then recorded (calculated) as shown below.
Vital Statistics: 







Plot 
216 

207 
Basal area of each plot (a) 
0.0600 

0.1195 
Basal area in sq. metres per hectare (BA) 
3.90 

7.76 
Height (of tallest tree in each plot) (PMH) 
6.2 

6.0 




Number of trees in plot (N) 
11 

12 
Stocking per hectare (S) 
715 

780 




Number of sample plots (b) 
29 


Radius of sample plot (metres) (r) 
7.00 


Where:
(a)  “Basal area” of each plot – this really should not use the term basal area – since this applies to per hectare – but here means the sum of the area of each tree stem at breast height within the plot.
(BA)  Basal area in sq. metres per hectare – this is true basal area, as calculated from scaling up the size of the sample plot. [ BA = a.((10,000/(p.r^{2}))]
(PMH) – recorded directly in the field for each plot.
(N) – the stem count within each plot in the field
(S) – the calculated stocking from N above.
(b) – the total number of plots within the stand.
(r) – the radius (predetermined and constant for each stand) of each sample plot.
Using the figures presented in this table above, it is possible to generate some summary statistics from Excel, for each parameter ie. stocking, height, and basal area – the latter as shown below:
Summary Statistics: 



Basal Area 



Mean (M) 
6.84260034 
Standard Error (SE) 
0.611319744 
Median 
7.053852041 
Mode 
#N/A 
Standard Deviation 
3.348336135 
Sample Variance (v) 
11.21135487 
Kurtosis 
0.870093155 
Skewness 
0.084101895 
Range 
12.44173469 
Minimum 
0.895408163 
Maximum 
13.33714286 
Sum 
205.2780102 
Count 
30 
Confidence Level(95.0%) 
1.250289943 
A competent statistician would easily comprehend this Excel output. What is important for a field worker is to be able to calculate the PLE as determined from all the data presently to hand and then to decide whether the PLE is acceptable or whether more field data needs to be collected and analysed.
For basal area, from above:








Basal Area 






Pilot no. of samples (b) 



29 


Student 't' (t) 



2.048 


Desired PLE (c) 



15 









Required no. of plots (d) 



45 









Error limits +/ (f) 



1.251983 


PLE present (PLE) 



18.3 









Students "t" for 29 samples (ie. 291 = 28) is 2.048 


Where:
(t)  Student ‘t’ is a figure obtained from a standard set of statistical tables.
(c) – Desired PLE is the predetermined precision level for the chosen parameter.
(d) – Required number of plots that need to recorded within the stand to give sufficient data to reduce the PLE from the present calculated level (PLE) down to the desired level (c). This is calculated from the following:
(d) = (100^{2}.t^{2}.v)/ (c)^{2}.M^{2 } and v and M are obtained from the summary statistics above.
(f)  Error limits – calculated as [student ‘t’ x SE] where SE is standard error from the summary statistics generated by Excel above.
PLE – is the probable limit of error for the chosen confidence limits (normally 95%) as calculated from the data already collected from the stand [PLE = ((f/M) x 100), where M is obtained from the summary statistics from Excel.
If the presently calculated PLE is greater than the desired PLE, then the required number of plots will be greater than the number of plots already undertaken and it will be necessary to revisit the stand to obtain more data. This data is, in turn, input into the above records and calculations until the desired PLE is reached.
The required output from the field work for each stand is the all important listing of:
 Stocking for each plot with PLE.
 Height for each plot with PLE.
 Basal area calculated from each plot with PLE.
These figures are then passed for input into a suitable computerbased model, such as Cchange, for the generation of present volumes of timber and carbon and future growth predictions and future carbon levels.
In the Field.
Step 10 – Go into the field!
After having understood some of the basic principles in the Background section of this document, and putting theory into practice in determining the location of sample plots, the size (and shape) of plots, it is now time to proceed into the “real world” – the growing forest – with all its inherent problems of access, terrain, undergrowth, weather, etc.
In the field means out and about, on the ground on a day to day basis as opposed to being in the office either in initial preparation or postsampling. In the field includes ‘onthefly’ analysis of data (but normally done in a sheltered, warm environment, in the evening perhaps) to determine whether sufficient plots have been completed within a stand to give the desired PLEs.
However, it cannot be over emphasised that adequate and clear preparation before entering the forest will greatly assist the field worker in both time and effort. Furthermore, workers must be familiar with the use of their tools – a navigation system, clinometers, hypsometers, height poles, tape measures, etc.
6) Establishing plots – sampling in practice.
A field worker will have made a number of important decisions before reaching the forest. One of these will be an idealised route to follow in order that all sample plots are visited. A startpoint will have been identified and the route may utilise topographical features, roads, rivers, and a knowledge of the undergrowth, etc.. Whilst it is not necessary to stick rigidly to a route, care should be taken to ensure that plots are not missed, which might enforce a long detour later in the day.
The author has experience using the GPS system discussed above and has found this to be a truly excellent (perhaps even revolutionary) tool. But note, that GPS can sometimes misbehave for no apparent reason and it uses a lot of batteries. Take plenty of spare batteries. Of course, it is also possible – prudent – to carry a backup navigation system, certainly in terms of a hand compass and perhaps a hipchain (using the latter though may require a lot of detailed map work – angles, slopes and distances – to be undertaken in the field if this preparation has not already been done).
Step 11 – Locate the plot.
Once a plot is located – by GPS and then moving (say) 10 metres to the south – a metal peg is placed in the ground. This peg has a Ushaped bend at the top and a sturdy rope, already marked out in metres and tenths of a metre is placed over the end of the peg. A reading of the average slope through the plot is taken looking both uphill and downhill and an adjustment to plot radius is noted. The rope is then stretched out to each tree within the immediate vicinity to determine which trees are in and out. Edge tees can be marked with paint of simply have a branch broken and bent down.
To date the author has had no assistance in collecting field data. The identification of trees in dense undergrowth, where the rope becomes tangled and has to be threaded through gaps between trees and bushes, is difficult and would be considerably faster with a second person.
Step 12 – Peg the plot centre.
Step 13 – Mark out the plot boundary trees.
No permanent marker needs to be left at the plot, although trees could be marked if a postsampling checking (auditing) system was envisaged. Using GPS, the plot should be able to be relocated to within 10 metres at least.
7) Measuring in the field
This is the businessend of the whole process.
At each plot it is necessary to record:
 Total number of trees within the plot.
 Height of the tallest tree within 5.6 metres of the plot centre (slope adjusted).
 DBH of each tree within the plot.
These points have been covered in the Background. Actual measuring using basic equipment does not require much skill – it does however, require a systematic, rigorous discipline.
Step 14 – Measure DBH of each tree – record.
Step 15 – Identify the tallest tree and measure height  record.
Step 16 – Sum the number of trees recorded for DBH to record total trees within the plot record.
Practical advice regarding the taking of measurements would include:
 A helper to write down measurements would speed the process somewhat – but of course, this has to be balanced against cost of a second person.
 Work around the plot in a systematic way – so that trees are not missed.
 Be thorough and precise – it is likely that a lot of effort has been put into reaching a plot – it is worthwhile collecting good quality data  but not for this reason only; the output (results) from any investigation are only as good as the input raw data. Give everyone involved the right start by collecting good accurate figures and developing a rigorous process. Every field worker will quickly develop a “name for themselves” in terms of the way in which they approach and carry out a job.
 Check that all data has been faithfully recorded and stored away safely.
 On departing the plot, check that all equipment has been stowed away for future use – it is often a long way back!
8) Data recording, entry and analysis.
Much of this has been noted in various sections above.
If a laptop computer is available – and this is essential for in the field analysis to determine whether sufficient plots have been completed – then data can be transposed from the field recording sheets to Excel. Make a copy of data to a backup medium as soon as possible.
Step 17 – Input data into Excel.
Once data is available within Excel, summary statistics can be produced and a calculation of the PLE for each of stocking, height and basal area completed. If PLEs are not acceptable, then a further computation will show how many more plots need to be undertaken.
Step 18 – Analyse data and produce summary statistics.
Note, that it is often apparent early on in the field whether a stand is exhibiting much variation and thus whether there is going to be a need to take a large number of plots. When entering data into a spreadsheet, the operator needs to carefully watch for transposing figures and other errors and this vigilance combined with a “gutfeeling” from working in the field should always be used as a sanity check on the output summary statistics and the number of plots required. Large deviations in figures from those normally encountered in other stands (i.e. experience) should alert the operator.
9) Further plots and analysis
Much of this has been noted in various sections above.
If data analysis reveals that further plots are required, then these need to be undertaken and the extra data themselves included in a second (or third) analysis.
Step 19 – Establish further plots if necessary and analyse data.
10) Stand Area.
As discussed in the Background above, stand area is an important parameter for the calculation of carbon stocks for the PCP and needs to be determined by some method.
If area is unknown or uncertain, field workers may try to determine stand area using a variety of techniques in the field. The author has used GPS to walk the boundary of a stand and by plotting this data on a computerbased NZ Topographical Map it is simple to calculate the area within the walked boundary. The same technique can be used for calculating the area of any holes mapped in the field.
Step 20 – Determine stand area.
In the Office.
Subsequent to all the field work, there is much further work that needs to be undertaken in the office. The first stage is to produce a carbon profile (Cprofile) for each stand and the second stage is to add each stand Cprofile to the PCP.
To date, the author has been intimately involved with the field data acquisition and analysis. From here the data has been passed across – in the form of an electronic Excel file – to Piers Maclaren at Forest Research.
Maclaren has processed and modeled the data to produce a (paperbased) summary output for each stand which is then returned to the author. Following this, the output is retyped into Excel and presented in graphical format.
11) Data manipulation and modeling.
To date, this has been undertaken by Forest Research. The data is manipulated into a useable format for inputing into what is understood by the author to be basically STANDPAK. This computer modeling programme produces an output data series predicting tree growth over time, up to the mature forest state, accounting for various environmental parameters and forest management (silviculture) regimes.
CChange – proprietary to Forest Research and not available for licensed usage outside FR at present – takes the output from STANDPAK and produces a time series of tonnes carbon per hectare for various parts of the stand e.g. the crown, stem, root, floor and a total stand carbon.
12) Results – presentation.
The output of Cchange can be presented in graphical form from within Excel using a basic graphing package.
In simplest form, the combined crown and stem carbon expressed in tonnes per hectare against stand age (years) can be presented and since this is derived from measurements taken systematically over the whole stand, this could be viewed as being representative – typical – of any hectare of the stand.
In order to depict the stand as a whole, it is necessary to scale up the per hectare tonnes of carbon by the stand area. As noted above, area is difficult to determine and needs much further work to refine and define a useable, reproduceable technique. However, if area is known, then a stand Cprofile can be developed – again, plotting combined crown and stem carbon expressed in tonnes over the whole stand against stand age (years).
Beyond this, there needs to be discussion and agreement between the parties involved in the PCP  with knowledge and reference to what is happening both within applicable scientific circles and the world stage regarding Kyoto, etc. – to decide exactly what and how results need to be presented for the PCP.
The following are just some points that need addressing.
For an individual stand:
 Do we present only total crown and stem carbon?
 Do we present some alternative to the above, for instance, including soil carbon?
 Do we present only the lower of the two limits defined by the PLEs for each parameter? Do we analyse the data taking these PLEs into account during the initial data analysis or do we calculate the Cprofile and then only present the lower amount as determined by the greatest PLE? For instance, if the PLE for basal area was 15%, is it valid to take 85% (100 – 15%) of the carbon profile for portrayal in graphical form? (Remember that a PLE gives both upper and lower error limits and the Cprofile may equally be above the mean as below the mean). Is there any justification to this method – do we understand what we are doing with PLEs?
 What method is used to account for harvesting? This is a “hot topic”. Forestry Research have steadfastly defended the “longterm average” carbon content of a stand i.e. assuming immediate replanting after harvesting, averaging the carbon over a number of rotations. This is roughly equivalent to 50% of the total stand carbon. There are many ‘traps for young players’ here.
 The point immediately above assumes replanting after harvesting. Yet no work has been done on the Cprofile that would result on land undergoing repeated planting, management and harvesting. This is important.
13) Protocarbon pool.
The ProtoCarbon Pool is an amalgamation of individual Cprofiles from distinctly separate (and unique) stands. It attempts to sum individual stand results across one entity – so, for instance, if each Cprofile depicts total crown and stem carbon, then the PCP could sum crown and stem carbon across all the stands included in the PCP. Similarly, if only the average carbon density is being depicted, it would sum this parameter across all the individual stands. Thus the PCP suffers from the same problems as any individual stand.
Again, this area needs a lot of thought.
 What do we want to show?
 What is verifiable and auditable i.e. what will hold up under careful scrutiny?
 What will be acceptable to the international community?
 What will “fit” into an international trading system?
It also needs the input of many others from outside of the present scope of the PCP. For instance, Forest Research must surely become more involved – since they own (and develop) the best Cmodels in NZ and the whole process needs to be more considerate of statistical methodology (ie. are we using figures and statistics in a correct and meaningful way?).