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Acta Forestalia Fennica ACTA FORESTALIA FENNICA Voi. 116, 1971 Studies on improvement of the efficiency of systematic sampling in forest inventory Systemaattiseen otantaan perustuvan metsän inventoinnin tehokkuudesta Aarne Nyyssönen, Pentti Roiko-Jokela and Pekka Kilkki SUOMEN METSÄTIETEELLINEN SEURA Suomen Metsätieteellisen Seuran julkaisusarjat ACTA FORESTALIA FENNICA. Sisältää etupäässä Suomen metsätaloutta ja sen perusteita käsitteleviä tieteellisiä tutkimuksia. Ilmestyy epäsään- nöllisin väliajoin niteinä, joista kukin käsittää yhden tutkimuksen. SILVA FENNICA. Sisältää etupäässä Suomen metsätaloutta ja sen perusteita käsitteleviä kirjoitelmia ja lyhyehköjä tutkimuksia. Ilmestyy neljästi vuodessa. Tilaukset ja julkaisuja koskevat tiedustelut osoitetaan Seuran toimis- toon, Unioninkatu 40 B, Helsinki 17. Publications of the Society of Forestry in Finland ACTA FORESTALIA FENNICA. Contains scientific treatises mainly dealing with Finnish forestry and its foundations. The volumes, which appear at irregular intervals, contain one treatise each. SILVA FENNICA. Contains essays and short investigations mainly on Finnish forestry and its foundations. Published four times annually. Orders for back issues of the publications of the Society, subscrip- tions, and exchange inquiries can be addressed to the office: Unio- ninkatu 40 B, Helsinki 17, Finland. STUDIES ON IMPROVEMENT OF THE EFFICIENCY OF SYSTEMATIC SAMPLING IN FOREST INVENTORY SYSTEMAATTISEEN OTANTAAN PERUSTUVAN METSÄN INVENTOINNIN TEHOKKUUDESTA AARNE NYYSSÖNEN, PENTTI ROIKO-JOKELA and PEKKA KILKKI HELSINKI 1971 Suomalaisen Kirjallisuuden Kirjapaino Oy Helsinki 1971 PREFACE The authors of this paper are grateful to attended to the bulk of the computation many persons who have in different ways required, while KILKKI put a great deal of been engaged in this study, which is based effort into regression analysis and efficiency upon rather extensive field and computation calculations. NYYSSÖNEN was in charge of work carried out during the course of a the work in the planning, field work and number of years. The National Research analysis stages, and wrote the manuscript. Council for Agriculture and Forestry provided Discussion between the authors was an essen- financial support for the work in the years tial factor in giving form to this paper. 1966—1968. Helsinki, January 1971. In regard to the authors, ROIKO-JOKELA CONTENTS Page 1. Introduction 4 2. Sample size calculations 4 21. Test materials 4 22. Simulation of systematic sampling 5 23. Comparison between some forms of systematic and random sampling 6 24. Regression equations for standard error in systematic sampling 8 241. Plot sampling 8 242. Strip sampling 10 25. Sample size in plot sampling 13 3. Time studies 14 31. Factors affecting total costs 14 32. Tree tally 14 321. Measurements made 14 322. Discussion of the results 15 33. Additional factors of total time 17 4. Efficiency comparisons 18 41. Uniform plot sampling 19 42. Non-uniform plot sampling 21 43. Strips and variable plots as opposed to circular plots 22 5. Summary and conclusions 23 References 24 Seloste 25 1. INTRODUCTION This paper represents a continuation of an be measured to permit of the estimation of earlier study made in the Department of sample sizes in a way which would be more Forest Mensuration and Management, Uni- generally applicable. Simultaneously, it seem- versity of Helsinki (NYYSSÖNEN, KILKKI and ed helpful to embark upon a more detailed MIKKOLA 1967). That study gave growing study of, for instance, those combinations of stock variation data based upon four test fixed-area plots in which large trees are tallied areas in Finland, and one in Mexico, along upon a larger area than are small ones. with comparisons drawn between different However, the main reason for continued stu- sampling methods. Further, the problem of dies was the aim of evaluating the relative estimation of the precision in systematic efficiency of different alternatives. Conse- sampling was discussed, and in conclusion quently, attention had to be paid to inventory regression equations were presented for the costs arrived at by the analysis of time stu- determination of sample size. dies; earlier, publication has been limited to Since the main results of the above study some preliminary results in respect of effi- were based on one test area only, it was ciency (cf. NYYSSÖNEN 1966). considered necessary that additional material 2. SAMPLE SIZE CALCULATIONS 21. Test materials characteristics classified, and the average size of stands, were the same as in Evo. The principal test area, Evo (Area 1), In the following set-up, figures are indi- described in the paper by NYYSSÖNEN, KILKKI cated in respect of the volume of the growing and MIKKOLA (1967), and comprising 100 hec- stock and number of stems: tares of land, is also one of the two areas Evo Toivala analyzed in the present study. Another area Volume, cu.m./ha. incl. bark of the same size is Toivala, which in part total 151 131 overlaps Area 2 of the earlier paper, and D.B.H. more than 20 cm. 120 95 has similar general features. Stem number/ha total 686 1141 Measurements were made in Toivala very D.B.H. between 2 and much on the same lines as in Evo earlier. » 10 cm 295 674 It is essential that information on the grow- » between 10 and ing stock can be computed by squares of 20 cm 204 289 » more than 20 cm. 187 178 100 square metres, 10 000 in total. For this purpose, the D.B.H. of all trees of not less Since the volume percentages of the trees than 10 cm. was measured, and that of smaller of a D.B.H. exceeding 20 cm., are 80 and trees on 20 or 25 sq.m. in each square. 73, respectively, and in the eastern half of Variable plots, with the application of BAF Southern Finland commonly 55 to 60 (KUU- 4 for sq.m./ha. (equals 17.424 for sq.f./acre), SELA and SALOVAARA 1968, p. 48), the trees and in general 30 m. apart, were measured, on test areas are relatively large in size. 1 092 in total. The number of sample trees Moreover, the growing stock volumes are for volume calculations was 2 914. The stand rather high in these areas. No. 1 No. 3 No. 2 Fig. 1. Mosaic maps of the growing stock volumes in Evo. Nos. 1 to 3 explained on p. 6. Higher volumes are indicated by darker dots; black ones refer to the 100 sq.m. plots with a volume more than 300 cu.m./ha. (The deviation from the square is due to the form of printer output.) No. 1 No. 3 Fig. 2. Maps of the growing stock volumes in Toi- vala. Cf. Fig. 1. Table 1. Area percentages, mean volumes and exceeding 2 cm. were assumed to have been standard deviations of different size plots, by treat- calipered on the whole plot. (As mentioned ment classes and in total in Toivala. previously, trees with a D.B.H. less than Plots size in 100 sq.m. 10 cm. were tallied on the 1/4 or 1/5 of the Treat- Area Mean area; however, the inherent error is very ment per- volume 1 2 4 9 small.) The plot sizes were as follows: class centage Standard deviation cu .m./ha No. 1. 10 x 10 m. = 100 sq.m. No. 2. 10 X 20 m. = 200 sq.m. The mean results of 0 7.4 0 0 0 0 0 the rectangles of 1 7.5 60.4 54.9 50.6 48.0 42.2 that size in both iy 11.7 86.7 77.6 59.8 53.2 45.8 directions were 2 7.5 155.5 91.0 74.6 60.7 52.8 applied 3 42.2 169.1 87.0 69.5 56.5 48.5 No. 3. 20 x 20 m. = 400 sq.m. 4 17.0 177.7 86.4 65.6 52.0 43.5 No. 4. 30 X 30 m. = 900 sq.m. 5 2.3 87.6 63.8 57.9 39.2 31.9 6 4.4 56.6 53.8 46.5 46.8 40.5 B. Combination plots. Trees with a D.B.H. Total 100 131.2 97.4 83.6 75.6 69.1 between 2 and 10 cm. are calipered on the area of 25 sq.m., those between 10 and 20 cm. on 100 sq.m., and those exceeding 20 cm. Figs. 1 and 2 provide a general impression on the whole plot. All the plot sizes men- of the distribution of growing stock volumes tioned above were used, viz. in both areas. Furthermore, the Toivala data, No. 5. 10 x 20 m. = 200 sq.m. like the Evo data, are available on punched No. 6. 20 x 20 m. = 400 sq.m. cards at the Department of Forest Mensura- No. 7. 30 x 30 m. = 900 sq.m. tion and Management of the University of Helsinki. In the efficiency comparisons to be made Table 1 includes further information from later, it will be assumed that the various size Toivala; corresponding figures from Evo were trees are tallied from concentric circles, al- given in the earlier paper by NYYSSÖNEN, though sample size data are not exact for KILKKI and MIKKOLA (1967). The treatment such plots; they are based upon square or classes were also explained there (p. 6). rectangle plots, and information in respect of Coefficients of variation on the total area, trees of less than 20 cm. comes from 100 sq.m. calculable from Table 1, are very similar to at one end of 200 sq.m. plots, and one corner those in Evo (p. 19). In the results of single of 400 sq.m. plots. In 900 sq.m. plots, the treatment classes, some effect of the small small trees have been tallied around the plot size and irregular shape of stands is dis- centre.
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