Results and Discussion Bias of Estimates

The basal area estimates produced by 1000 simulations for all sampling methods were averaged and compared to the true basal area per acre for these stands. The averaged point and plot sampling estimates were within one percent of the true value in the northern hardwood and lowland softwood stands and within 2.6 percent of the true value in the red pine and upland softwood stands. In the red pine plantation, all the averaged plot and point basal area estimates underestimated the true value, while in the upland softwood stand the estimates were higher than the true basal area per acre (Table 1).

Table 1. Percent differences of the average sample mean from the true mean basal area per acre in four mapped stands in northern Ontario. Percent differences are calculated as the (averaged 1000 mean estimates of basal area per acre for a single sampling method - true mean) divided by the true mean basal area per acre for the stand. Positive percentages indicate overestimates of averaged means of a sampling method, while negative percentages indicate underestimates. Asterisks (*) denote sampling method estimates following a normal distribution, according to the Shapiro-Wilks test for normality.

Sampling Number of Northern hardwood Plantation red pine Lowland softwood Upland softwood method plots

mean of ratio of mean of ratio mean of ratio of mean of ratio of ratios means ratios ofmeans ratios means ratios means

3-tree 1 4 1 1 .2 -8.1 -3.0 4.4 13.3 -13.7 4.3 -5.9

2 8 1 2.4 - 10.2 -4.0 2.8 1 3 . 2 -15.4 4.0 -8.5

5-tree 1 4 6 . 1 -7.0 -2.7 4.2* 10.3 -8. 1 4.9 -3.9*

28 5 . 6 -7.6 -3.6* 2.3* 8.5 - 1 1 .2 3 . 5 -6. 1

7-tree 1 4 4.8 -4.3 -3.3 1.5* 6.9 -6.5 3 . 5 -3.1

28 4.4 -5.1 -3.2* 1.4* 6.5 -7.8 3 . 7 -3.9

1/5 ac plot 4 -0.3* -2.5 -0.6 1 . 1

1 4 - 1 .0• -2.3* -0.6* o.5*

1/10 ac plot 4 -0.3 -1 . 1 0.8 2 . 6

1 4 0.6* -1 .5 • -0.3 * 1.9*

BAF lO 4 -0.6* - 1 . 2 -0.9 o.5*

1 4 -0.1• -1 . 2· 0.4* 0.9*

BAF 20 4 -0.1 -1 .5 0.1 • 1 .5

1 4 o.o• - 1 .2 -0.5 0 . 8

Table 2 . Coefficients o f variation calculated as the square root o f the empirical variance over the average basal area estimate.

Sampling Number of Northern hardwood Plantation red pine Lowland softwood Upland softwood

method plots

mean of ratio of mean of ratio of mean of ratio of mean of ratio of

ratios means ratios means ratios means ratios means

3-tree 1 4 53.3 25 . 8 30.9 1 6.5 53.8 32.5 38.9 26.7

28 5 1 .3 1 7.5 1 8.5 1 1 .5 40.7 22.0 33.9 1 7.9

5-tree 1 4 27.9 1 9.5 1 2.9 1 2.0 32. 1 25. 2 24.7 19.9

28 19.7 14.2 8 . 8 9.0 2 1 .4 1 7.7 1 8.4 14.0

7-tree 1 4 20.4 17.6 9 . 7 10.2 23.4 2 1 . 0 2 1 . 0 17.0

2 8 1 4 . 2 1 1 . 8 6 . 9 7 . 2 1 6.2 15.0 15.4 1 2.4

1/5 ac plot 4 1 6.3 5 . 1 1 2. 7 1 4 . 1

1 4 8 . 9 2.6 6 . 8 7.8

1/10 ac plot 4 23 . 1 5 . 9 1 7 .4 19.2

1 4 1 1 . 6 3 . 5 8 . 9 1 0 . 1

BAF 10 4 _{18. 1} 9.9 22.8 22.6

14 1 1 . 8 5 . 1 1 1 . 9 1 1 .6

BAF 20 4 1 8.0 1 3 .6 29.7 28.4

14 9.9 6.9 1 6 . 3 1 5 . 7

For the n-tree distance methods, the bias decreased as either the number of trees included in a sample or sampling locations increased, but was most sensitive to increased numbers of trees. The averaged estimates produced by the mean of ratio estimators overestimated by between 3.5% and 13.3% in the hardwood and two softwood stands, while those of the ratio of means underestimated by 3.1 % to 15.4% . The results of these averaged estimates were opposite in the red pine plantation. The mean of ratio estimates underestimated the true basal area per acre by averages between 2.7% and 4.0% , in contrast to the overestimates of 1.4% to 4.4% for the ratio of means estimates (Table 1). These results are probably due to the spatial patterns of the trees within these stands. The red pine stand was more regular than random. The spatial patterns within the northern hardwood stand and the upland softwood stands were nearly random, while the lowland softwood stand was more clustered than random. The distance to the nth tree is dependent on the spatial pattern of the trees. A field study by ^LESSARD et.al. (1994) compared n-tree distance sampling with point and plot sampling in three forest types (northern hardwood, plantation red pine, and clustered hardwoods) in northern Michigan. That study produced a similar pattern of over- and underestimation of basal area per acre for n-tree sampling as was produced in this study. In the field study, estimates were calculated as the mean of ratios and averages of estimates produced by the traditional point and plot estimates were used for comparison since the true basal area per acre was not known. Similar results of over- and underestimation of density and volume estimates, due to various spatial patterned forests, were found in the simulation study by ^{J ONSSON} et al. (1992).

Variance of Estimates

The coefficients of variation (CV) were calculated for each of the sampling methods as in equation (7). Within stands, plot and point sampling methods produced lower CVs than any of the n-tree distance methods. As expected, the CVs generally decrease with increasing plot sizes for plot sampling, increasing numbers of trees for n-tree methods, and decreasing basal area factor for point sampling. Coefficients of variation produced by ratio of means estimates for n-tree sampling were lower than those produced by the mean of ratios estimates, especially in the case of 3-tree sampling where CVs from mean of ratios estimates were nearly twice those of the ratio of means estimates (Table 2).

LESSARD et al. (1994) compared n-tree distance sampling with point and plot sampling in three stand types (northern hardwood, plantation red pine, and clustered hardwood) and found CVs for estimates of basal area consistent with these trends, but the magnitude of the CVs were smaller in the field study. The field study served as one sampling result, whereas the simulations produced one thousand actualizations. Mean square error followed the same general trends as the coefficients of variation. The percent difference of the average sample variation from the empirical variation for all sampling techniques were within 13.3% and there was no obvious pattern, either in magnitude or in over- or underestimation, due to forest types, number of samples, or sampling procedure.

Confidence Intervals of Estimates

The percentage of times, out of one thousand repetitions of each sample simulation, that the 95% confidence intervals {Cl) captured the true basal area per acre were generally between 80-95%. In general these percentages within stands increased with increased numbers of sample locations. Percentages for all point and plot sampling methods were similar for all stands. Point and plot methods generally had slightly higher percentage rates than n-tree methods for equal numbers of locations. The skewness of the distributions of

most of the n-tree estimates may be a contributing factor (Table 1). For the n-tree sampling methods, the percentages increased with increased numbers of trees included at a sample location. In the northern hardwoods and the two softwood stands, the mean of ratios confidence intervals (generally 88-93% ) captured the true basal area per acre more often than the ratio of means (generally 82-87% ). The ratio of means estimates were especially low, between 71-81% , for 3- and 5-tree sampling in the lowland softwood. In contrast, the ratio of means confidence intervals (90-93% ) had a higher capture rate of the true basal area per acre in the red pine plantation than did those of the mean of ratio estimates (80-88% ).

Cost Effectiveness

Although the sample variance produced by n-tree sampling methods is greater than that of the plot and point sampling, if one considers the cost (measured in time) of sampling, the 3-tree method does produce competitive results. In the field study by LESSARD et al.

(1994), the number of locations needed to produce a maximum allowable error of 20% was calculated assuming an infinite population. The average time needed to sample a location was determined for each sampling technique within a forest type. The field study showed that in the northern hardwood stand, 3-tree, ^1/10 acre plot, and BAF 10 point sampling techniques required the least amount of time to sample in order to produce a 20%

allowable error. In the red pine plantation 7-tree sampling required the least time, followed by 3-tree and BAF ¹⁰ point sampling techniques. The time comparison only considers the time spent measuring at the locations and not the travel time among them.

However, if the sample locations are placed along transects, the travel times among locations may be equivalent if the area covered is the same. Using adjusted times from the field study for cost comparison purposes in the simulation study, it was found that BAF 20, 3-tree ratio of means, and BAF 10 point sampling required the least amount of sampling time in the northern hardwood stands to achieve an error less than 20% . In the red pine plantation, the time requirements for all sampling methods were very close (Table 3).

Again, the differences in variation between this simulation study and the field study account for the differences in the cost comparisons.

Table 3. Time in hours needed to sample in order to produce an allowable error that is 20% of the mean basal area per acre. Time estimates are based on the average time needed to sample at a location from a field study carried out in similar forest types (LESSARD et.al. 1994). Relative adjustments of those times were made for the plot and point sampling methods to account for the extra trees to be sampled in the mapped stands, having higher density and basal area per acre than the field study stands. No time adjustment was made for the n-tree sampling, since that is based on a fixed number of trees per sampling location. Travel time between sample locations is not included in these estimates. N-tree results are for the ratio of means estimates.

Sampling method Northern hardwood Plantation red pine

3-tree 1 . 7 0.6

5-tree 3 . 8 0.6

7-tree 6.7 0.8

1/5 ac plot 2.4 0.5

1/10 ac plot 2 . 1 0 . 4

BAF IO ^{1 . 8 0.6}

BAF 20 1 .5 0.5

2.5.4 Conclusions

In general, estimates of basal area per acre produced by the traditional plot and point sampling techniques were less biased than those of either the n-tree ratio of means or mean of ratios sampling methods. The magnitudes of percent bias of the n-tree ratio of means and mean of ratio techniques were nearly the same within stands when the numbers of trees and plots were equal, however the mean of ratios over-estimated the true basal area per acre in the northern hardwood and two softwood stands, while the ratio of means under-estimated the true value. A reverse trend was found for the red pine plantation. The reason for this difference very likely lies in the spatial patterns of these stands. The trees within the red pine plantation were more regularly spaced. Both the northern hardwood and upland softwood stands had random spatial patterns, while the lowland softwood stand was more clustered.

The coefficients of variation (CV) were lowest for all sampling techniques within the red pine plantation and highest within the lowland softwoods. The CVs within both the northern hardwood and upland softwood stands were very similar for the same sampling techniques. The CVs of the n-tree methods were always higher than those of the point and plot methods. Within the n-tree methods, the mean of ratios coefficients of variation were generally higher than those of the ratio of means, and this was more pronounced in the 3-tree methods. As expected, CVs generally decreased as numbers of plots increased.

Although, the values were not the same, the CVs in the simulated study followed the same patterns as those of the field study by LESSARD et al. (1994), comparing n-tree sampling with point and plot sampling.

The BAF 20, 3-tree, and BAF 10 sampling methods required the least amount of time needed to sample on order to produce a 20% error in the northern hardwood stand, while in the red pine plantation, the times were very close for all methods.

2.5.5 Summary

In summary, variations of n-tree sampling, especially 3-tree sampling, are more biased and more variable than traditional point and plot forest inventory methods in all stand types examined. N-tree methods are fast, however, which allows them to be cost-competitive with traditional inventory methods. There is little justification for changing to n-tree methods as preferred forest inventory methods for estimating basal area per acre. N-tree methods are cost-competitive with traditional methods in estimating basal area or density, but have the added advantage of being capable of providing estimates of spatial pattern parameters, due to distance measures which are an integral part of n-tree sampling, but not always recorded for plot and point techniques, which may be of interest in ecological sampling ( PIELOU 1977).

2.5.6 Acknowledgements

The authors wish to express our gratefulness to Dr. Alan R. Ek, University of Minnesota, St. Paul, Minnesota, for kindly providing the data for the northern hardwood, red pine plantation, and the lowland softwood stern maps and to Dr. Bijan Payandeh, Forestry Canada, Great Lakes Forestry Center, Saulte Ste. Marie, Ontario, for generously sharing the data for the upland softwood stem map mentioned above.

This study was supported by United States Mcintire-Stennis Act funds.

2.5. 7 References

COCHRAN, W.G ., 1977: Sampling Techniques, 3rd edition. New York, John Wiley & Sons. 428 pp.

EBERHARDT, L.L., 1969: Some developments in 'distance sampling'. Biometrics, vol. 23: 207-216.

EK, A.R., 1969: Stem map data for three forest stands in northern Ontario. Canadian Forestry Service, Department of Fisheries and Forestry, Information Report 0-X-113, 23 pp.

JONSSON , B.; H OLM, S.; KALLUR, H. , 1992: A forest inventory method based on density-adapted circular plot size. Scand. j. for. res., vol. 7: 405-421 .

LESSARD, V.; REED, D.D.; MONKEVICH, N., 1994: Comparing n-tree distance sampling with point and plot sampling in northern Michigan forest types. Northern Journal of Applied Forestry, vol.

11, 1: 12-16.

ODERWALD , R.G., 1981: Comparison of point and plot sampling basal area estimators. For. sci., vol. 27, 1: 42-48.

PAYANDEH, B. , 1974: Spatial pattern of trees in the major forest types of northern Ontario. Can. j.

for. res., vol. 4: 8-14.

PA YANDEH, B.; EK , A.R ., 1986: Distance methods and density estimators. Can. j. for. res., vol. 16:

918-924.

PIELOU, E.C., 1977 : Mathematical Ecology. New York, John Wiley & Sons. 385 pp.

THOMPSON, H.R., 1956: Distribution of distance to nth neighbor in a population of randomly distributed individuals. Ecology, vol. 37, 2: 391-394.

2.6 Provincial Forest Inventory in British Columbia. What's next

? Sam Otukol, Ulf Soderberg

Summary

The Province of British Columbia, Canada, is planning a multi-resource vegetation inventory. The objectives of the new inventory are to provide a foundation for estimating broad summary statistics at the provincial level and to provide a framework for management planning, long-term change detection, and monitoring. Two, competing sampling designs have been proposed, i.e., 1) grid-based sampling, and 2) sampling from a sorted polygon list.

The grid-based sampling would consist of two components. The first component would be the establishment of a systematic grid system over the province. Ground measurements would be obtained from a cluster of plots at each grid point. The second component would be management-unit based, and it would involve photo classification of the vegetation cover types, attribute estimation, and supplementary ground sampling. Maps would be produced at the management unit level.

The sampling from a polygon list would be management unit based, and would have two phases. The first phase would be the photo classification, polygon delineation, and attribute estimation. The formed polygons, representing different vegetation cover types, would then be compiled into a list which would be sorted. Sample polygons would then be selected from the list, and visited on the ground. Ratios of ground estimated attributes to the photo estimated attributes would be used to adjust the photo attributes for the polygons which are not visited on the ground.

The grid approach seems to have several advantages over sampling from a polygon list, but depending on what objective is considered to be most important, the method selected can change.

Keywords: multi-resource inventory, systematic grid, sorted list

2.6.1 Introduction

Forest inventory in British Columbia on the provincial level has a fairly recent history.

The first complete provincial inventory was carried out in 1951-1957 (MALCOLM 1957).

The objective was to estimate average volumes for strata. Strata were defined as groups of related forest types (summary types) by age, height and stocking class. The second and so far the last complete inventory was done in 1961-1977 with the objective to estimate total volume for aggregate forest types in each management unit (Public Sustained Yield Unit).

The target population (mature timber) was divided into strata which consisted of 42 inventory type groups, nine age classes, eight height classes and four site classes. This results in more than 1 2 000 strata for which a minimum of ten samples were required for each. Over all 50,000 samples were collected. About 77% of the current inventory information originates from these data (THROWER 1992).

The aim of the inventory was to use stratified random sampling. This could not be achieved due to logistic, budgetary and administrative difficulties. These difficulties have also reduced the ambition of other inventory efforts performed so far. The random sampling was abandoned for a subjective selection of strata of older age classes and of

strata with the largest areas. The magnitude of the bias introduced by the subjectively located plots is not known and also makes the calculated sampling errors and other statistics of uncertain value.

After the last provincial inventory the inventory efforts were directed towards getting more stand specific estimates of volume and other attributes. This required changes in classification, sampling, data bases, compilation including methods of estimating volumes for individual stands. Another major change in the period from 1978 to present time was the conversion of the inventory data base to continuous variables instead of the formerly used class-based descriptions. During this period the amount of ground sampling has been limited. An approach with multi-phase stratified sampling using 70 mm low level photography and ground samples was tried, but later abandoned due to logistic problems.

Most activities have concentrated on a history update program for major depletions from harvesting, fire, insects and a re-inventory program for reclassification.

A number of deficiencies of the inventory has been revealed during the last years and demands for additional information that so far has not been collected (considered) are requested from several users of the inventory and from the general public. It is realized that future inventories must not only consider present and future utilization of timber, but also the need for more information about many other components of the forest. As in most countries information about ecological and environmental characteristics of the land base are needed. Different solutions are used, incorporation and enlargement of existing forest inventories (SODERBERG 1993) or establishment of totally new inventories ^(SCOTT et al.

1993).

Between 1988 and 1991, there was a major initiative to establish the status of the current inventory ^(SPANDLI 1994). The British Columbia Forest Resource Commission (FRC) was asked to examine the state of the province's land base and to recommend improvements to the way it is managed (FRC 1991). Among other things, the FRC recommended the formation of a Resource Inventory Committee (RIC). The RIC, through the Terrestrial Ecosystem Task Force (TETF) is responsible for the new inventory initiative. The primary objective of the new vegetation inventory is to develop a multi­

resource inventory to include disciplines such as range, ecology, wildlife, soil, timber, recreation, etc. The other objectives include:

1) To provide a foundation for estimating broad summary statistics at the provincial and

Im Dokument Köhl, M., Bachmann, P., Brassel, P., & Preto, G. (Eds.). (1995). The Monte Verità Conference on Forest Survey Designs. "Simplicity versus Efficiency" and Assessment of Non-Timber Resources. Swiss Federal Institute for Forest, Snow and Landscape Research (Seite 85-92)