Operational adjustment to site index study (OASIS) Results from the Bulkley TSA pilot study. Report prepared by A.F. Linnell Nemec for BC Ministry of Forests, March 1998.

Adjustment of site index is a relatively easy way of updating or improving estimates of future timber supplies. Two general methods of adjustment have been developed: the paired-plot method, which was developed for the Old Growth Site Index (OGSI) Project, and incorporation of empirical (SIBEC) relationships between site index and site series, which is the method used in the Operational Adjustment to Site Index Study (OASIS). Central to the OASIS approach is estimation of the proportional areas of the site series that make up a timber supply area (TSA). Simple random sampling has been suggested for this purpose. To test the adequacy of the proposed design, a pilot survey of the Bulkley TSA was conducted in the fall of 1997. Specific objectives of the pilot study were: (i) to develop and test field procedures for future OASIS surveys, (ii) to obtain improved variance estimates for calculating sample sizes, (iii) to determine the frequency of occurrence of inaccessible plots, and (iv) to test the application of the OASIS methodology in a timber supply analysis.

This report describes the pilot survey and its results. Section 2 outlines the survey design and the type of data that were collected. Methods of analysis are described in Section 3 and the results are presented in Section 4. Testing of the pilot survey results in a timber supply analysis is currently underway. The outcome of that analysis will be reported later.

The OASIS sampling design for estimating site-series areas is described in Nemec (1997). To test the effectiveness of the design, and associated field methods, a pilot survey of the Bulkley TSA was carried out in the fall of 1997. The Bulkley TSA is located in the vicinity of Smithers, B.C., in the southwest part of the Prince Rupert Forest Region. It encompasses 11 subzones and covers a total of 758,432 hectares. All types of land, including operable and inoperable land, parks, private land, and urban areas were included in the survey.

Five hundred survey points were randomly selected from those ~758,432 points on the 100m ´ 100m provincial grid that lie within the boundaries of the Bulkley TSA (this grid is the sampling frame for the Vegetation Resources Inventory). Ecological data were collected at each sample point by one of three possible methods: (1) photo-interpretation, (2) field measurement, or (3) air call. Photo-interpretation was reserved for points that were inaccessible from both ground and air (e.g., remote locations, locations with no road access and no suitable landing area for a helicopter), as well as points requiring no further investigation (e.g., points in large bodies of water or urban areas). If a sample point could be reached from the ground then a 400m² (11.28m radius) circular plot was centered on the point and the required data were gathered in the field. Air calls were used to obtain data from all remaining points, which were accessible by helicopter but inaccessible on the ground (e.g., private land to which access was denied).

Table 1 lists the sample measurements. Areas of the dominant site series, and areas of up to four minor site series, were recorded as a percentage of the total area of the ground plots. Only one site series (100% area) was recorded when the assessment was based on photo-interpretation or an air call. All sample points were located on or near the target points. Actual positions were (where possible) confirmed with a Geographic Positioning System (GPS) device and recorded for future reference.

                    Table 1. Sample measurements for Bulkley TSA pilot survey.

                      Sample identification number (1-500)

                      Mapsheet identification number

                      Ownership

                      Biogeoclimatic zone, subzone, and variant (transitional subzone)

                      Dominant site series (soil moisture, SMR, and nutrient regimes, SNR)

                      Area of plot (%) occupied by dominant site series (SMR, SNR)

                      Minor site series (SMR, SNR)

                      Area of plot (%) occupied by minor site series (SMR, SNR)

Estimates of the proportional areas of site series (soil moisture and nutrient regimes) were obtained by averaging the relevant areas for the n = 500 sample points, that is,

      [1]

where is the estimated area (% of total area of Bulkley TSA) occupied by Site Series j in Subzone/Variant i and y_ijk is its measured area for the k-th sample point. The sample values y_ijk are 0 or 100% for air calls and photo-interpreted points. If a site series was absent from a plot then y_ijk is 0 and the numerator of Equation 1 is equivalent to summing over those plots in which the site series occurred (i.e., plots with with y_ijk > 0).

The estimated standard error (s.e.) of was calculated by substituting the measured values y_ijk into the usual formula for random sampling:

      [2]

where is the sample variance:

.       [3]

The finite population correction is omitted from Equations 2 and 3 because the sampling fraction ( 500 / 758,432 ) is less than 0.001.

To investigate the effect of reducing the sample size, the preceding calculations were repeated for samples comprising the first n = 100, 200, 300, and 400 plots. The resulting reduction in precision was assessed by plotting versus s.e.() for each sample size. In addition, the empirical standard errors were compared with the corresponding estimates for binomial sampling:

      [4]

which corresponds to the special case where sample areas (y_ijk ) are 0 or 100% for all n points.

The feasibility of stratifying the sample locations by leading species, site class, and age was assessed by determining the distribution of points among the proposed strata - species: balsam, hemlock, lodgepole pine, spruce, deciduous trees, or "not applicable"; site index: SI £ 10 or SI > 10; and age: age £ 140 or age > 140 years. Preliminary results (based on information for only 206 of the 500 sample locations) suggested that the sample size (500 points) was too small to support post-stratification by all three variables (Table 2). Stratification by age class or site class (but not both) is possible (i.e., expected sample sizes are in the range 200 - 300 points per stratum). However, further analysis of the stratified data was not pursued because site index and age were unavailable for over half the samples.

Table 2. Distribution of sample points among strata. Percentages are based on information for 206 of the 500 samples and are not necessarily representative of the full sample.

Percentage of sample points

             £ 140 years                    > 140 years                          Total

Field plots were established at 379 of the 500 sample points; 71 points were assessed by air call; and 50 points were evaluated by photo-interpretation (Figure 1). The sample data (500 plots) are in Appendix 1. Data codes, including codes for several new site series (e.g., CA, CF), are given in Appendix 2.

Figure 1. Distribution of sample types in Bulkely TSA pilot survey.

Estimated proportional areas of the site series that make up the Bulkley TSA, and the corresponding proportional areas of soil moisture (SMR) and nutrient (SNR) regimes, are given in Appendices 3 and 4. Subzone/variants are listed on the left side of each page and the site-series (SMR/SNR) areas (expressed as a percentage of the total area of the Bulkley TSA) are listed on right, together with their estimated standard errors (s.e.). Sub-totals for subzone/variants (i.e., sums over site series or SMR/SNR) are underlined. Each pair of columns corresponds to different sample size (n = 100 - 500 plots). To obtain approximate error margins (95% confidence intervals), the standard errors should be multiplied by 1.96. For instance, the estimated proportional area of the AT zone is 9.80 ± 1.96 ´ 1.33 = 9.80% ± 2.61% at the 95% level of confidence (see Appendix 3, n = 500 plots).

Table 3 gives the estimated breakdown of the Bulkley TSA by subzone/variant. Two sets of estimates of the proportional areas are given. The first set was generated by the provincial Geographic Information System (GIS) and the second set of estimates was derived from the OASIS survey (Appendix 3, n = 500 plots). Total areas (in hectares) are from the GIS. Comparison of the GIS and OASIS estimates (Fig. 2) shows that the two sets of estimates are consistent (i.e., within the associated error margins).

Table 3. Estimated areas of subzone/variants in Bulkely TSA.

                                     Subzone/            Area            GIS           OASIS

                                     Variant                (ha)             (%)              (%)

The number of site series that were sampled by the first n points and the estimated average area of those site series are given in Table 1. As expected (see Fig. 4 in Nemec 1997), the number of sampled site series increases (Fig. 2) while the average area decreases with increasing sample size.

Table 4. Number of sampled site series and corresponding average areas.

Figure 2. Comparison of GIS and OASIS (n = 500 plots) estimates of subzone/variant areas in Bulkley TSA (see Table 3).

Figure 3. Number of site series in sample (n = 100 - 500 plots).

Figure 4 illustrates the relationship between standard error and sample size. The upper panel shows the estimated standard error plotted against the estimated proportional area of site series identified in the first 100, 200, 300, 400, and 500 plots (Appendix 3). Standard errors based on the binomial formula (Eqn. 4) are also shown for comparison. The lower panel is a enlargement of the upper panel for those site series with areas £ 1% of the total area of the Bulkley TSA. In general, the binomial formula provides a good approximation for site series constituting 1%-16% of the total area. However, the binomial formula tends to over-estimate the standard error for site series occupying £ 1% of the area. This effect arises only when measured areas include values other than 0% and 100% of the plot area (i.e., when ground samples are used).

Random sampling is a simple means of estimating the proportional areas of site series in a TSA or other large geographic area. Required sample sizes n can be calculated from the binomial formula:

where p is the proportional area of the site series, e is the maximum acceptable error margin for a (1- a ) ´ 100% confidence interval, and za _/2 is the corresponding critical value for the normal distribution (e.g., za _/2 = 1.96 for a 95% confidence interval). For instance, to estimate the proportional area of a site series that accounts for approximately p = 15% of the total area, with an error no greater than ± 3% (95% confidence limit), the required sample size is 545. The preceding formula is based on the binomial expression for the standard error (Eqn. 4), which is conservative (i.e., tends to over-estimate the standard error and required sample size) for site series that occupy relatively small areas (£ 1% of total area). If estimates of site-series areas are required for individual strata (based on post-stratification of the sample) then sample sizes must be increased to ensure that the expected sample size is sufficiently large for each stratum. Therefore, depending on the number of strata, post-stratification may increase considerably the sample-size requirement.

Figure 4. Estimated standard errors of proportional areas of site series: 100 plots (solid triangles), 200 plots (open squares), 300 plots (solid squares), 400 plots (open circles), 500 plots (solid circles), and binomial formula (Eqn. 4, solid curve). The lower panel is an enlargement of the upper panel for site series with estimated areas £ 1% of total area of Bulkley TSA.

B.C. Ministry of Forests. 1997. Average site index for select tree species and ecosystems in British Columbia: SIBEC Guidebook, B.C. Min. For., Victoria, B.C.

Nemec, A.F.L. 1997. Operational Adjustment to Site Index Study (OASIS): Sampling design for estimating proportional areas of site series. Report prepared for Resources Inventory Branch, B.C. Min. For., Victoria, B.C.

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