九州大学学術情報リポジトリ Kyushu University Institutional Repository

FOREST INVENTORY BY SAMPLING METHODS. 1953

Kinashi, Kenkichi

https://doi.org/10.15017/14955

出版情報：九州大学農学部演習林報告. 23, pp.1-153, 1954-03-30. Research Institution of University , Faculty of Agriculture, Kyushu University バージョン： 権利関係： PART 1. INTRODUCTION

CHAPTER 1. GENERAL DESCRIPTION 1. A motive for studying this subject. is concerned not only with the individual , but also with groups of , such as stands or forests. Especially, in the sciences of manege ment and forest mensuration, this study is needed. Since olden times, many statistical studies for forestry and forest mensuration have been made by many famous people, but these methods have been brought to a deadlock. The sample-plot method as hitherto used has the defect of being inadequate for precision measurement. With the recent development of sampling methods, it has come to be demanded of timber surveyors as of workers in other fields of statistical research that they have a clear conception of sampling errors. In Japan, we have not been able to study the science of modern statistics applied to forestry. There are 3 important reasons for this, I think. The first of them was the imitation of German forestry, the second was that insufficent attention was paid to the importance of forest mensuration and the third was the organization of our state and our educational system of forestry. Many students and graduates from universities majoring in forestry have many unsolved questions about forest mensuration in their fields of research and practice. Moreover, they did not have the methodical foundation of modern statistics. But there were useful works and laborious achivements made in the past, and detailed inventories were made in many countries. In the National Forest Service, complete maps and timber volume lists over the whole subcompartments are prepared. And even in the private forests, there are concise maps and timber volume lists. However, we cannot gauge their pre cision and reliability. This defect is a vital problem. Because the old method. is very expensive and inefficient, it should be discontinued. Then there is the necessity for the reconstruction of forest mensuration in Japan. And it must begin as soon as possible, because it is clear that the practice and science of forestry can not expect further developments without information based upon the recent progressive statistics. 2. The science of modern statistics applied to forestry. There are many problems of statistics involved in practice and scientific reseach. First, forest mensuration is a problem in biological statistics, and it is the foundation of forestry. , and need the technique of sampling methods and experimental designs. And, also the other sciences of forestry are situated in the same relationship. These problems must be solved in accordance with the given cost and the resercher's ability. 3. The objects of this study. There are two main objectives in making this study. The first objective is to apply the practical forestry inventories by sampling methods supported by the Japanese Forest Service. The second objective is the modern statistical reconstruction of forest mensuration in Japan. Japanese forests have many charactristics, i.e. the patch of stand, the steep slope, the artificial , etc. So line-plot methods or strip survey can not be used in Japan. Usually we have used the sample-area method. It is clear that these jugement sample plots are dangerous. Also these jugement plots never supply any information as to the aggregate. Our forest mensura tion was based on the foundation of the jugement sampling method. If ran dom sampling methods are used, our old forest mensuration method should be reconstructed on the foundation of modern statistics. This is the second objective. But it is a very large and difficult problem and is impossible to solve without the cooperation of many research workers.

CHAPTER 2. RECENT DEVELOPMENTS OF SAMPLING SURVEYS IN FORESTRY. 4. Recent developments in sampling surveys in American forestry (16)(17)(20) First it is very useful to learn of the progressive traces of sampling surveys in !American forestry. They are coveniently devided into four stages of age. In each of these stages we can find many informative reports as follows ; (1) The first stage ; By W. G. WRIGHT (1925), R. H. CANDY and W. M. ROBERTSON (1927) the number of plots needed for constant accuracy was calculated by the standard error formula. It is elementary work but it is the primary basic foundation of the recent development of sampling designs. Their methods of caluculation of the number of plots are shown as follows. If the standard deviation is noted by s and the standard error is noted by S ,

We can accept the line-plot method as a more precise and reasonable method than the strip method. The line-plot method is easily applied by a systimatic sampling procedure. This is the foundation of the most recent sampling method in forestry. (2) The second stage ; Since the McSwenyMcNary act was passed, there has been much done in reseach for the area by forest types, timber volumes and growth-rates (1928). SCHUMACHERand BULL (1932) worked out a line-plot survey in the forest of Salix and Populus on the Mississippi delta zone. 10 parallel lines apart 3 miles from each other running across the river from east to west, and 1918 1/4-acre plots spaced 10 chains on the lines are measured over 503,000 acres, with 0.1 per cent of total area. There are many similarities between the plot count method and the line measurement data. But both data are treated by numeri cal formula. The percentages of forest types determined by both methods are almost identical. Units of 1/2 mile are best to estimate the mean. The total volume is calculated by the formula ;

This study is very informative for plotsampling and can be applied to Japanese regions consisting of many patched forests. GOODSPEED'S(1943) im proved line-plot method has the 1/8-acre plots spaced 165 feet from each other on parallel lines 330 feet apart. This method can be worked by one man. The same result was obtained by the strip method with a 33' width. Also in the volume, the difference be tween these two methods is not significant by the F-test. The strip method is more expensive than the plot method. J. F. PRESTON (1934) described how to do the combination between the forest mensuration and the modern statistics in the illustration of the cruising to pulp . His cruising methods cannot be accepted as perfect but in our country even this level of perfection has not been reached yet. MUDGETT and GEVORKIANTZ (1934), in order to verify the precision of estimate, analyzed mathematically their survey data according to the distributions of Bernoullian, Poisson and Lexis Series. And they claimed that the distribution of the forest types were not due to the Bernouelian distribution illustrated by SCHUMACHERand BULL, but due to the Poisson distribution. For surveys made of large areas of forest, if the Poisson condition can be used, there are sufficient budgets for reseach. If the budget is insufficient, the Lexian condition should be used. (3) The third stage ; A. A. HASEL (1938) tried the analysis of variation of the Black mountain forest. This report was very interesting to us, and gave us our motive to start research in the Shiragadake forest. The total area was divided into nine sections each one mile square. A section was divided into four quarters, a quarter into four forties, a forty into four tens, a ten into two fives, and a five into two basic plots. A basic plot is 2.5 acres, that is about 1 ha. The timber volume on the basic plot was distributed normally. SNEDECOR'S F-test was tried on these variance ratios. Then he recognized that these volumes changed heterogeneously from place to place. His F-tests were sig nificantly different in all cases. The narrow shaped plot with the longer side set at right angles to the contour line is more effective. The variance of the mean is given in the fol lowing formula ;

There are many small area stands having irreguler boundaries in Japan, therefore the shape of the blocks will not be constant unless the boundary of the adjoining subcompartrnent is removed. If we work out the large scale inventory without restriction of boundaries, we could use this method. But our inventory system consists of the summation of many subcompartments with detailed lists of individual stands. There are many problems in conec tion with sampling designs. HASEL (1941) studied the variance of the volume of standing timber in the pine region of California. For the purpose of an estimate of variance two plots were taken at random within each block and the following formula applied ;

where s2 is the variance of volume per plot, x1 and x2 are the volumes of the two plots cruised in a block, and n is the number of plots cruised. The size of block is constant, being 20 acres, with dimensions 10 by 20 chains. It is about 8 hectare (200 m x 400 m). Plot length is always taken parallel to the long side of the block, the single plot per block is taken in the center. Plot size varies from 1 by 2 chains in a 1 % cruise to 1 by 20 chains in a 10 % cruise. Sampling error will vary according to the values shown. The degree of vari ance will depend upon the size of the tree and the distribution of stems on the ground. The relationships between variance and mean volume per plot, between variance and the average number of trees is shown as linear on loga rithmic scales respectively. From these facts we found that heavier stands generally require less sampling size than lighter stands for the same degree of accuracy. Moreover, Bert LEXEN (1941) and HASEL (1942) contributed to the , log measurement and the mathematical treatment of strips. (4) The fourth stage WILLIAM W. BARTON and C. B. STOTT (1946) made a guide for cruise by diagram. The reliability of the estimate of volume depends upon the degree to which the following three factors are present : timber tract size, density of stocking in commercial trees, and uniformity of their arrengement on the timber tract. Then using 3 degrees of accuracy, 3 degrees of density and 3 degrees of uniformity there are 27 sheets of diagrams for a forty. J. G. OSBORNE (1942), JOHNSONand MEYER (1949), SCHUMACHERand CHAP MANN (1948), L. S. GROSS (1950), FERGUSON (1951), GROSENBAUGH (1952), JOHNSON and HIXEN (1952), GAISER (1951), JEFFERS (1952), BICKFORD (1952) and many other researchers and writers contributed to the great developments in this field. I have not space or time to write of these great progressive works, and moreover, we should keep in mind the recent application of statis tics to photogrammetry in America. 5. Recent development of sampling surveys in other countries except U.S.A. I have little information concerning the recent developments in other countries except in America. But we know that three countries in North Eu rope, e. i. Sweden, Norway and Finland have made great progress in this field, as well as England and Canada. Even in Germany, modern statistics are rap idly being applied to . Other countries, such as India,* South east Borneo (1949) and Java (1950) have objected to using sampling designs. ILUVESSALO reported the third national surveys in Finland (1951), and in Germany PRODAN'S " Messung der Waldbestande " and ECKERT'S " Unter suchungen uber die Eignung and Anwendung statistischen Methoden als Hilfs mittel forstlicher Inventuren" (1951) we found that german forestry has started this new field. And BITTENLICH's Winkel Method(29) (1948) is a very progres sive method. Finally we must add that the method has spread not only, in this country, but in all the countries of the world according to J. D. B. HARRISON'S " To Planning a National Inventory (1950)" 6. A recent development of sampling cruising study in Japan. Until we were introduced to the development of the forest sampling

* I know that great progressive works have been carried out in India, from the in formation in the India Forest Bulletin No. 146 (Dr. FINNEY; The efficiency of Enumerations; I. Volume Estimation of Standing Timber by Sampling. II. Random and systematic sampling in Timber Suiveysj, published by the Forest Research Institute, Dehra Dun, India. And this book was supplied by Dr. KITAGAWA. method in America°16> (1949) , there had never been a research applied to the sampling method in Japan. We had learned that forest mensuration originated from German forestry, but we did not recognize the value of modern statistics in forestry until after the end of the War. Since then the recent method of mathematical statistics was introduced by Dr. KITAGAWA and Dr. MASUYAMA and other Japanese statisticians for the population census, agricaltural researches, fisheries yield researches, the design of agricaltural experiments and quarity control in industry. The principles and techniques of modern statistics have been applied rapidly in the alone fields in Japan. Early in 1950 we established the first sampling experimental forest at Shiragadakem which stimulated great developments in forestry fields. The Japanese Forestry Service desired to study this and commissioned us (1950) . Recently many people reported their research results and they put the result at least partialy in practice, but in Japan there are many problems in this field. First of all, fundamental study is needed. Second we need reconstruction of forest mensuration on the basis of modern statistics. Third the manner of forest research must be considered. Fourth, the system of management must be changed to be suitable to the sampling work. If the old system is used, it will be very difficult to apply the new method of management. Fifth, we need airplanes and must study aerial photogrammetry. We do not have enough results yet from these studies but we have gained much important information concerning the modern statistical methods for our forests. In Japan there are many researchers in this field, Dr. TERASAKI (Tokyo Forestry Experimental Station), MINE (Tokyo University), KONDO (Utsuno miya University), TAKAHASHI (Mie University), TAKASE (Ehime University), NISIZAwA (Niigata University), KAIBARA (Forest Service), in mainly forestry field, and few mathematical statisticians KITAGAWA (Kyushu University), MASU YAMA (Tokyo University), HAYASHI and MATSUSHITA (Mathematical Institute) and so on.

CHAPTER 3. BIOGRAPHY

7. The classification of literature concerning this study are divided into the following three groups; The literature of Japan The literature of foreign countries The literature of the aerial photogrammetory concerning the sampl ing method. All this literature is not necessarily in our hands. 8. The literature of Japan ; 1. W. TERASAKI : Some aspects of the method of research concerning the management system of natural forests in Manchukuo. 1942. 2. H. NAKAYAMA: The method of the national forest survey in Northern Europe. Jap. Jou. For. 16 (11) . 1934. 3. H. NAKAYAMA: One illustration of forest survey by stripmethod and the method of statistical calculation of the percentage of areas of different timber species. Jap. Jou. For. 19 (9) . 1936. 4. H. NAKAYAMA: One illustration of calculation errors of forest area by strip survey. Jap. Jou. For. 1939. 5. H. KOBATA : Concerning the method of stand volume cruising. Jap. Jou. For. 1941. Dr. TERASAKI first introduced the method of analysis variance applied to natural forest in Manchukuo in Japan. H. NAKAYAMA introduced the national forest survey in Finland. They are the pioneers in the recent method in Japan. Then on the field of plant association the fundamental problems of the statis tical method have been picked up recently.

6. M. NUMATA : The basic problem of community research. (1949). 7. M. NUMATA : Concerning the community and density of individuals. Science. (1948). 8. M. NUMATA : The foundation of the theory of sampling in the plant community statistics. Jap. Jou. Bot. (1949). 9. M. NUMATA ; The problem of sampling error in the plant community statistics. Biology and Medicine. (1949). 10. M. NUMATA ; The coefficient of variation in plant community. 11. I. MOTOMURA; The statistical treaty of community. Jou. Anni. (1932) . 12. M. NUMATA ; The bias of sampling in the statistics of plant com munitiesStudies on the structure of plant communities III. Bot. Mag. 62 (729-730) . 1949. 13. M. NUMATA : The plant community as a stochastic population. Bot. Mag. 63 (741-742) . 1950. 14. M. NUMATA : The homogeneity of plant communitiesstudies on the stracture of plant communities VI. B. M. 63 (747-748). 1950. Laws concerning the sociological structure of " Biological Uni verses." Bul. Chiba. Uni. 1951. 15. M. NUMATA : The investigation of vegitation by means of sampling methodStudies on the structure of plant communities V. Bot. iVlag. 63 (745-746). 1950. In the field of forestry literature applied by the modern statistics is in creasingly found ; 16. K. KINASHI and M. NISHIZAWA : Concerning the forestsurveys by sam pling method in America. Kyushu Jou. (1949) . 17. K. KINASHI and M. NISHIZAWA : The forestsurveys by sampling meth ods. Dantairin. (1949). 18. KINASHI, NISHIZAWA and YOSHIDA; The report of the establishment of sampling experimental forest in Shiragadake. Kyushu Jou. For. and Dantairin. (1950) . 19. K. KINASHI: Study of forestsurveys by sampling methods. 1—Preliminary report (Shiragadake experimental forest). Jou. For. (1950). 2—An analisis of variance of Sugi Stand. Jou. For. Kyushu. (1950) . 3—The most effective plot shape. Jou. For. (1951). 4—The relation between mean volume and variance. Kyushu Jou. For. (1951). 5—Sampling error in stratified stand (Oya National Forest). Jou. For. (1951). 6—The analysis variance of Hinoki stand in Oya. Jou. For. (1951). 7—The most effective plot shape by cost consideration. Kyushu, Jou. For. (1952), 8—The analysis variance of Akamatsu stand (Kirishima National Forest). Kyushu Jou. For. (1952). 9—The analysis variance of natural stand (Takanabe National Forest). Jou. For. (1953). 20. K. KINASHI : Study of timber cruising by sampling methods. I (1951), II (1952). Forest Service. 21. K. KINASHI ; Forest research by sampling methods. Kumamoto Re gional Forestry Bureau. (1952). 22. M. NISHIZAWA: Concerning the forest variation coefficient. (1949). 23. K. KINASHI and M. NISHIZAWA : The measure of cost of plot cruising. Kyushu Jou. For. (1950). 24. K. KINASHI and T. MITSUKUBO: The nursary inventory by sampling methods. Kyushu Jou. For. (1950) . 25. K. KINASHI : Subsampling in Sugi stand. Jou. For. (1951) . 26. K. KINASHI: Double sampling in broadleaved forest. Kyushu Jou. For. (1951) . 27. K. KINASHI : The utility of regression and ratio estimate to sample tree method. Jou. For. (1951) , 28. K. KINASHI: Timber volume estimation by stratified 2 multistage ' sampling in Izumi Working unit . (1), (2). Jou. For. (1952). 29. K. KINASHI: Plotless sampling. (application to slope area). Kyushu Jou. For. (1952) . 30. K. KINASHI: Test case of the forestry sampling inventory for the Matsu stratum of J-LVIII Basic District, in Kagoshima prefecture. (1) . Jou. For. (1953) . Forest Service Reports (1) , (2) . 31. K. KINASHI: Concerning the variance of estimate ratio of sample trees. Kyushu Jou. For. (1952). 32. K. KINASHI : Some calculation examples of serial correlation coeffi cient of stand timbe volumes. Bulletin of Faculty of Agriculture Kyushu University. 13 (1-4). (1951). 33. K. KINASHI: The utilization of regression in sampling of test trees. Bul. Kyushu University. For. 21. (1952). 34. M. KoNDO : On the socalled sample-tree method. Bul. Utsunomiya Univ. 1 (3) . 1952. 35. M. KoNDO : On the efficiency of sample plots of varying shape and size. Bul. Utsunomiya. Univ. 1 (3) . 1952. 36. M. KoNDO: Pre-test for the construction of actual yield table by random sampling. Jou. For. 1952. 37. T. TAKAHASHI : Study on the model of the stand . Jou. For. 1952. 38. M. NISHIZAWA : A few problem concerning on a tree volume table. Bul. Niigata Univ. 3. 1952. 39. G. TAKASE : Studies on cubing formula of cut log. Jou. For . 34 (2). 1952. 40. G. TAKASE : Studies on estimation of volume in timber stand by random sampling. Jou. For. 34 (5). 1952. 41. G. TAKASE : Studies on increase of mean diameter and decrease of stem volume of stand by thinning, especially on applications of these to compilation of yield table. Jou. For. 34 (11). 1952. 42. M. NISHIZAWA : Concerning on the adjustment of an yield table by means of sampling method. Niigata For. (1952). 43. K. TAKATA : Studies on the volume and growth measurements by the sampling methods. Kyushu. Jou. For. (1952) . 44. K. TAKATA : What difference is the d. b. h. by the azimuth ? Kyushu Jou. For. (1952) . 45. K. TAKATA : Study on the method of the measurement of the basal area in the timber trees. Kyushu. Jou. For. (1952) , 46. HAYASHI and MATSUSHITA : Forest inventory-The model case of sam pling survey. (Forest Service) . 1952. These studies and reports make great contributions to Japanese forestry in this field and moreover Dr. MAStJYAMAdid the development of BITTENLICH'S method from circle to oval and Dr. KITAGAWA supplied many statistical meth ods to this field, as WALD'S method, DEMING'S method, incomplete block designs and so on. And Dr. TERASAKI wrote an article in which he treats the modern statistical progress in recent Japanese forestry. (1951 Jou. For.). MINE, assist ant professor of Tokyo University wrote a book of forestmensuration in which sampling works are introduced first in Japan. Hereafter we can expect that this trend will rapidly increase and the meth ods and techniques will reach more perfect forms. 9. The literature of foregin countries. There is so much literature that we can not collect all of it. 47. ILUVESSALO,Y.: The forest resources and the condition of the forests of Finland. (The second National Forest Survey) . Helsinki. 1942. 48. ILUVESSALO,Y.: The first phase of the third national forest survey of Finland. 1951. 49. D. J. FINNEY : Volume estimation of standing timber by sampling. India Forest Bulletin, No. 146. 50. D. J. FINNEY : Random and systematic sampling in timber surveys. India Forest Bulletin, No. 146. 51. W. G. WRIGHT : Variation in stands as a factor in accuracy of estimates. Jou. For. 1925. 52. R. H. CANDY: Accuracy of method in estimating timber. Jou. For. 1927. 53. W. M. ROBERTSON: The line-plot system, its use and application. Jou. For. 1927. 54. SCHUMACHER, F. X. and BULL : Determination of the errors of estimate of a. forest survey, with special reference to the bottom-land hard wood forest region. Jou. Agr. Res. 1932. 55. GOODSPEED,A.: A modified plot method of timber cruising applicable in southern new England. Jou. For. 1934. 56. PRESTON, J. F.: Better cruising methods. Jou. For. 1934. 57. MUDEGETT, B. D. and GEVORKIANTZ,S. R.: Reliability of forest surveys. Jou. Amer. Stat. Asso. 1934. 58. A. A. HASEL : Sampling error in timber surveys. Jou. Agr. Res. 1938. 59. A. A. HASEL : Sampling error of cruises in the California. Jou. For. 1942. 60. Bert LExEN : The application of sampling. Jou. For. 1941. 61. Bert LExEN : Sale of stumpage on the basis of tree measurement. Jou. For. 1942. 62. William W. BARTON and C. B. STOTT : Simplified guide to intensity of cruises. Jou. For. 1946. 63. Floyd A. JOHNSON: Statistical aspects of timbervolume sampling in the pacific Northwest. Jou. For. 1949. 64. James G. OSBORN: On the precision of estimates from systematic ver sus random samples. Science. Vol. 94. 65, James G. OSBORN: Sampling errors of systematic and random surveys of cover-type area. Jou. Amer. Stat. Asso. Vol. 37. 1942. 66. F. A. JOHsoN : A statistical study of sampling methods for tree nur sery inventories. Jou. For. 1934. 67. BRUCE and SCHUMACHER: Forest mensuration. III. 1950. 68. CHAPMAN and MEYER : Forest mensuration. 1951. 69. SCHUMACHERand CHAPMAN Sampling method in forestry. 1948. 70. F. YATES : Sampling methods for censuses and surveys. 1949. 71. SNEDECOR: Statistical method. 1949. 72. R. A. FISHER : Statistical method for research workers. 1951. 73. W. E. DEMING : Statistical adjustment of data. 1948. 74. W. E. DEMING : Some theory of sampling. 1949. 75. W. G. COCHRAN: Sampling survey techniques. (lecture) , 1948. 76. C. H. GOULDEN: Methods of statistical analysis. 1950. 77. M. EZEKIEL : Methods of correlation analysis. 1950. 78. HASEL : Arrangement of cruise plots to permit a valid estimate of sampling error. For. Ran. Ex. St. 1937. 79. HASEL : Estimation of vegitation type areas by linear measure ment. Jou. For. 39. 1937. 80. GIRARD, J. W. and GEVORKIANTZ, S. R.: Timber cruising. U. S. Dept. Agri. Forest Service. Wash. 1939. 81. HASEL : Estimation of volume in timber stand by strip sampling. Ann. Math. Stat. 13. 1942. 82. NEYMAN, J. Lectures and conference on mathematical statistics. 1938. 83. NEYMAN, J.: Contribution to the theory of sampling human popula tion. J. A. S.A. 33. 1938. 84. WOLD, H.: A study in the analysis of stationary time series. 1938. 85. HURWITZ, W. N.: Working plan for annual census of produced in 1943. U.S. Dept. Agri. Forest Service. 1943. 86. BLYTHE, R. H.: The economics of sample size applied to the scaling of saw logs. Biometrica. 1. 1945. 87. THOMPSON, A. P.: A sampling approach to New Zealand timber cruising problems. N. Z. J. F. 5. 1945. 88. FOGH, L. F.: Sampling methods in log scaling. Chron. 19. 1943. 89. Loomis, R. D.: Accuracy timber estimating. For. Chron. 22. 1946. 90. ROBERTSON W. M. and MULLOY G. A.: Sampling plot methods. Domin ion Forest Service. Ottawa. 1946. 91. RICHERSTOFF, A.: One-fifth acre versus one-tenth acre plots in sampl ing for nature stands. Dominion Forest Service, Canada. 1947. 92. RICHERSTOFF, A.: Sampling efficiency of line plot survey on riding moun tain research area. D.F.S.C. Silviculture research note. 84. 1947. 93. SOEST, J. Van ; The main problems in sample plots 2 diameter measure ment. Ned. BoschbTijdschr. 23 (6). 1951. 94. BENASSI, L.: Criteria for the selection of sample trees for volume estimation. Ital. For. Mout. 6 (2) . 1951. 95. TIDEMAN, P.: Outlines of the methods of forest surveys as applied on the Islands outside Java. Tectona. 40 (2). 1950. 96. LVENGREEN, J. A.: Mirror instrument for setting circular sample plots and basal-area enumaration tested by the State Forest Research Branch. Dansk Skovforen. Tidsskr. 35 (10). 1950. 97. BooN, D. A.: The reliability of sample strips in the Ironwood region of southeast Borneo. Tectona. 39 (4) . 1949. 98. RAWAT, A. S.: Sampling techniques for estimating tree growth and volume by selection of sample trees for measurement within in dividual sample plots. India For. 75 (10) . 1949. 99. PATTERSON, A. E. and COLSON,J. H.: The effective compass direction on the measurement of diameter breast high of shortleaf pine. Jou. For. 50 (1) . 1951. 100. FERGUSON, J. H. A.: Optical estimation of stand basal area by Bitten lich's method. Tectone. 41 (1). 1952. 101. GROSENBAUGH,L. R.: Plotless timber estimates-new, fast, easy. Jou. For. 50 (1) . 1952. 102. JOHNSON,F. A. and HIxoN. H. J.: The most efficient size and shape of plot to use for cruising in oldgrowth Douglas-Fir Timber. Jou. For. 50 (1). 1952. 103. GAISER, R. N.: Random sampling within circular plot by means of polar coordinates. Jou. For. 49 (12) . 1951. 104. JEFFERS, J. N. R.: Use of rang of standarddeviation tables. Forestry 25 (1). 1952. 105. BICKFORD, C. A.: The sampling design used in the forest survey of the northeast. Jou. For. 50 (4) . 1952. 106. BELCHER, R. G.: Application of punched card method to pulpwood scaling. Pulp paper mag. Can. 53 (3) . 1952. In these lists a few common statistical books which are contributing to the development of the sampling method in forestry are included. Information is increasing. It seems to be a new trend in forestry. 10. The literature of the aerial photogrammetry concerning the sampling works in forestry. The relation between the sampling works and the aerial photogrammetry is very close. It is clear that the perfect sampling works in forestry cannot be successful without the cooperation of the aerial photogrammetry. Then, for reference purposes, we ought to add some literary sources concerning them. But here they were omitted.

CHAPTER 4. MATHEMATICAL FOUNDATION FOR SAMPLING SURVEYS IN FORESTRY 11. Matematical basis of the sampling method. Concerning the details of the foundations of sampling works, we should depend upon mathematical statistical books. The statistical mathematical foundation should be arranged so as to be easily applied to the forest investi gations. By COCHRAN(75) , sample surveys deal with samples drawn from the pop ulation which contains a finite number N of units. The values of the item that are being measured are denoted by y ,y2 , •• , yN . In general no particular frequency distribution is assumed for these values. In practical applications it is, however frequently taken for granted that the means of samples of size are approximately normally distributed. This assumption implies that the ori ginal values are not far removed from a normal distribution. The population mean :

The population variance :

Simple random sampling is defined as follows : a method of selecting n items out of N so that it gives every one of the NC, groups an equal chance of being chosen. In factorial notation this is expressed as N!/(N—n)! n! ways. Let yn denote the mean of a simple random sample of n size, and consider E(yn) as the average over all the NCn possible samples. Theorem la : Theorem lb :

Theorem 2: Variance of the mean of the mean of a random sample.

(N—n)/N is called a finite population correction term. (f.p.c.). Theorem 3: Estimation of 02 from the sample data.

is an unbiased estimate of 62.

Hence, the estimated standard error of is

If n is reasonably large and n/N is not too large, y,z will be assumed approxi mately normally distributed about y D. Thus, approximate confidence limits may be constructed in the ordinary way by writing

where t(a, n-1) is the value of t corresponding to a significance level a, for (n —1) degree of freedom. The formula (7) and (8) are the most necessary for the forest cruising to attain a desired standard of accuracy. The accuracy required is usually defined by specifying a probability level (e.g., .05), and a margin of error d is allowable in the sample mean. That is,

If this equation holds, the probability that the sample mean lies within a dis tance d of the population mean is (1— a) , and can be made as close to cer tainty as we like by making sufficiently small. If a were to be correct ,

If N is very large, the second term in the denominator can be neglected, In practice, we can not arrive at the value of a. Therefore, a is estimated from previous samplings of a similar population, or simply by intelligent guess work. Since the estimated a is likely to be itself in error, we can not expect more than a rough estimate of n. The sampling methods in forestry use the unbiased estimate of a2 i.e. a2 to obtain the standard error of the mean. The standard error is called the sampling error. In sampling works formula a2 is substituted by unbiased estimate s2, we obtain

Qin2 is called the estimate of variance of the mean of the sample. Let e de note the per cent of the sampling error,

And let C denote the per cent of the standard deviation which is called the coefficient of variation,

from (12) we obtain,

From this equation we obtain the sampling error multiplying by the value of t corresponding to a significance level for some degree of freedom . In general, we can calculate as t = 2, but if n is small, the result of it would not be exact . GEVORKIANTZ and DUERR'S formula is treated as t = 2. And they expressed forest factor by f. 2 C = i/ f , f = (2 C)2 . 12. The sampling methods in forestry. (1) Simple random sampling. (69) For timber cruising, we can consider various elements as ultimate units . A tree or a stand existing on a unit area can be as an ultimate unit or a ran dom sampling unit. In Japanese forests, there are commomly rather small stands and small areas. They are mainly artificial with rela tively small sized trees, whose mean height is less than about 25 meters and the mean d. b. h.. is less than about 40 cm. Usually the number of trees on a unit area is large and the topographical conditions are very un stable. If we consider the unit of the area, the smallest unit is likely to be a 10 m x 10 m square plot. This unit can not devided into smaller cells except in very young plantations and in the nursery bed. Beyond this limit , the construction of the stand will be analyzed according to the individual tree . Even in Japan, a 1 are-plot is too small to measure for timber cruising. Then the random sampling unit is likely to be the combination and conection of four or more 1 areplots. These relationships are illustrated in other chapters. But measuring unit 1 are-plot is very convinient in practice. The strip can be considered as the narrow belt consisting of 1 are-plots. So a random sampling unit consists of these ultimate units. (69) The value of random sampling unit is measured respectively,

The unbiased estimate of the standard deviation of the random sampling unit will be gained from the following formula,

where

Therefore the variance of sample mean ; with finite population correction

The sampling error is obtained from the standard error which is the square root of the variance of mean. Should the chance of error be fixed at 5 out of 100, then the value of t corresponding to this probability based on (n —1) degree of freedom is multiplied. Obtainable true value is expressed as follows ;

where standard error

(2) The systematic sampling. Usually we must cruise irregular areas in Japanese stands. In these cases, the total area is divided into many continuous strips involving the numbers of ultimate units. This stratified random sampling by strip is better than random sampling from total area or systematic sampling, but it is very ex haustive and difficult in practice. The systematic sampling is easier and comparatively precise. These problem should be treated in later chapters. (3) The stratified sampling. (69) This method is more important for large areas than for small areas. Usually we do not make special forest surveys. The land surveys are carried on separetly from timber cruising. Detail mappings are usually prepared . Then, if we want to stratify, we can do so. When the sampling works cover the whole subcompartments, we can consider them as one kind of stratified sampl ing. In this case, there are two kinds of sampling, and the other one is proportional. The case of disproportional sampling ; estimate of population total:

estimate of total variance :

The case of proportional sampling ; estimate of population total:

estimate of total variance :

The number of strata or subcompertments

It is desired that the area of the subcompartment is a . comparatively large with homogeneous stand, such as the artificial plantation, and the size of sub compartment (stratum) is as small as possible. (4) The weighted sample and the estimate of its variance. If we must treat the patched forest area consisting of small irregular subcom partments, it is frequently convenient to do every tree measuring in the chosen subcompartment. Other cases are one of the strips with different length. In such cases we shall use the weighted mean. If y is the sum of the ob servations on the w ultimate units of a random sampling unit, the observed value on the ultimate unit basis is

If the sample consists of n random sampling units of variable weight w, the weighted sample mean is. In a working unit consisting of many comparatively small areas of subcom partments, some numbers of them are randomly drawn from the total area, and then the drawn subcompartments are cruised. Each drawn subcompart ment area is aj in hectar and yi in cubic meter respectively. where i is 1, 2, • • • , n. (Fig. 1) .

Area Volume Volume per ha

Weighted mean

Variance of weighted mean

In spite of every tree measurement, if the strip method is convinient, the length of strip would be used as the weight. (Fig. 2) .

drawn subcompartment drawn strip in a subcompartment

Fig. ] Fig. 2

(5) Simultanious sampling : (69) There are 3 groups, such as the mixed forest with the following species ; Sugi, Hinoki and Broadleaved-tree. Group ; x S(x) ,Group ; z S(z) , Group ; y S(y) ,Total ; x + y + z S(x + y + z) , Each group variances are the following respectively, For total:

expanding,

Covariance terms are usually calculated as follows ;

At last, multipied by the finite correction factor.

(6) Subsampling method : We have the formula of the subsampling method in forestry from ScHu MACHER and CHAPMANN, as the following : (69)

where B, the number of blocks, Q, major divisions (continuous strips), q, drawn strips, P, minor divisions (subdivisions), p, drawn subdivisions, C and D are obtained from the following analysis of variance : This system of sampling cannot be carried out in Japan except in special research of plantations or nursery inventories. In stead we must use the method of the 2 or 3 multistage stratified sampling method given by HvxwITz and illustrated by DEMING or COCHRAN. If we can use the sampling method with the probability proportionate to size, we will be able the following formula : (74) , (75)

where Xifk••.observation value of subsampling unit .711.1.•-mean value of unit and subsampling unit in a unit respectively X.•-estimate total No—number of subunit in a unit Ni• ••number of subunit in a stratum Mi •• number of unit in a stratum xi f, xi• •• population value of Xu , Xi respectively nif•••drawn subunit number (ni) R---number of strata ci;2•-variance within unit

(7) Double sampling method ; (69) Double sampling method method is widly used in timber cruising and re search of timber increment. Usually we take the following formula ;

V(Y)••-variance of Y sy x2 • •estimate of the variance of that part of the individual ob servations, y, which is independent of x. xL -large sample mean x,s • •small sample mean V(b)••-variance of regression coefficient sz2 •• •variance of large sample mean

CHAPTER 5. THE SCOPE OF THIS STUDY 13. The outline of field work. We began with a study of fundamental statistics and a collection of liter ature about sampling works in forestry which covered the year 1949.06) (17) In the eary spring we established an experimental forest in Shiragadake with the object of studing sampling. It took about 3 months and this field work was very laboriously completed with Nishizawa. (1950)(19) (18)(20) Based on this research we tried many analyses and had much information regarding the Sugi plantation in Japan, and in December of 1950, we tried a 2nd research of Shiragadake with the object of measuring individual trees. In the winter of 1951,(20)(25) we tried surveys for the natural mixed forest of Kirishima National Forest and also gained a chance to use the subsampling method for the Sugi plantation in Japan, which has been supplied by ScHu MACHER and CHAPMAN. In the spring of this year the research of the natural broadleaved forest in Takano National Forest(26)c20 was done with the object of testing double sampling. In the summer we tried survey for a relatively large area in Oya National Forest.(19) (20) The Hinoki plantation was also analized. In autumn we tried a survey for the Izumi National Forest using the method of stratified 2 multistage sampling(24) with the cooporation of the Kumamoto regional forest research crews. In the summer of 1952(19) we analized Matsu plantation in the Kirishima National Forest and in autumn we took the data concerning the measuring errors of tree height and breast high diameter in the Nanatsuishi National Forest. In December we again tried the analysis of natural broadleaved forest mixed with conifers in Ishi kawachi National Forest."19j Moreover we tried to study the method of re search in a private forest in Koyama district of Kagoshima prefecture in the winter of 1953.(3°) Nursery inventory and plantation inventory were tried in 1950(24) and in 1952 respectively, to test sampling methods.

14. The scope of this study. In this study we tested the sampling methods applied to timber volume inventories. Therefore, the study concerning the growth of the stand is not included in this report, which is a very important problem in forestry. The growth problem is so great and difficult that we desire much more research and study. Problems which were considered are shown as follows :

The analysis of variance of Sugi artificial plantation (19) The analysis of variance of Hinoki artificial plantation."9) The analysis of variance of Matsu artificial plantation.(19) The analysis of variance of natural broadleaved with conifers forest (19) The study of sampling unit.09) The forest variation coefficient (19)(20)(21) Sampling error and measuring error. Sampling methods applied to small areas and large areas .(19)(28'09) These basic data are restricted within Kyushu, but Sugi, Hinoki, Matsu artificial plantation and natural conifer are considerably similar conditions through the whole of Japan, except Hokkaido where these species do not exist. And they are representative in all points. Their located points are shown as following map. (Fig. 3).

Fig. 3. Kyushu Island

Nanatsuishi National Forest. Oya National Forest. Izumi Working Unit. Ishikawachi National Forest. Kirishima National Forest. Shiragadake Experimental Forest. Koyama Private Forest District. Takano National Forest.

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