J. For. Sci., 2007, 53(7):320-333 | DOI: 10.17221/2078-JFS

Improving RBS estimates - effects of the auxiliary variable, stratification of the crown, and deletion of segments on the precision of estimates

J. Cancino1, J. Saborowski2
1 Facultad de Ciencias Forestales, Universidad de Concepción, Concepción, Chile
2 Fakultät für Forstwissenschaften und Waldökologie, Georg-August-Universität Göttingen, Göttingen, Germany

Randomized Branch Sampling (RBS) is a multistage sampling procedure using natural branching in order to select samples for the estimation of tree characteristics. The existing variants of the RBS method use unequal selection probabilities based on an appropriate auxiliary variable, and selection with or without replacement. In the present study, the effects of the choice of the auxiliary variable, of the deletion of segments, and of the stratification of the tree crown on the sampling error were analyzed. In the analysis, trees of three species with complete crown data were used: Norway spruce (Picea abies [L.] Karst.), European mountain ash (Sorbus aucuparia L.) and Monterey pine (Pinus radiata D. Don). The results clearly indicate that the choice of the auxiliary variable affects both the precision of the estimate and the distribution of the samples within the crown. The smallest variances were achieved with the diameter of the segments to the power of 2.0 (Norway spruce) up to 2.55 (European mountain ash) as an auxiliary variable. Deletion of great sized segments yielded higher precision in almost all cases. Stratification of the crown was not generally successful in terms of a reduction of sampling errors. Only in combination with deletion of stem segments, a clear improvement in the precision of the estimate could be observed, depending on species, tree, target variable, and definition and number of strata on the tree. For the trees divided into two strata, the decrease in the coefficient of variation of the estimate lies between 10% (European mountain ash) and 80% (old pine) compared with that for unstratified trees. For three strata, the decrease varied between 50% (European mountain ash) and 85% (old pine).

Keywords: randomized branch sampling; multistage sampling; unequal selection probabilities; auxiliary variables; pps-sampling

Published: July 31, 2007  Show citation

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Cancino J, Saborowski J. Improving RBS estimates - effects of the auxiliary variable, stratification of the crown, and deletion of segments on the precision of estimates. J. For. Sci. 2007;53(7):320-333. doi: 10.17221/2078-JFS.
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    References

    1. Cancino J., 2003. Analyse und praktische Umsetzung unterschiedlicher Methoden des Randomized Branch Sampling. [Dissertation.] Fakultät für Forstwissenschaften und Waldökologie der Georg-August-Universität Göttingen: 191. http://webdoc.sub.gwdg.de/diss/2003/cancino/index.html
    2. Cancino J., Gockel S., Saborowski J., 2002. Randomized Branch Sampling - Varianten, Programm Branch und erste Analysen. Deutscher Verband Forstlicher Forschungsanstalten, Sektion Forstliche Biometrie und Informatik, 14. Tagung, Tharandt, 3.-5. April 2002: 76-87.
    3. Cancino J., Saborowski J., 2005. Comparison of randomized branch sampling with and without replacement at the first stage. Silva Fennica, 39: 201-216. 1 http://webdoc.sub.gwdg.de/diss/2003/cancino/index.html Go to original source...
    4. Cochran W.G., 1977. Sampling Techniques. New York, Wiley: 428.
    5. Gaffrey D., Saborowski J., 1999. RBS, ein mehrstufiges Inventurverfahren zur Schätzung von Baummerkmalen. I. Schätzung von Nadel- und Asttrockenmassen bei 66-jährigen Douglasien. Allgemeine Forst- und Jagdzeitung, 170: 177-183.
    6. Good M., Paterson M., Brack C., Mengersen K., 2001. Estimating tree component biomass using variable probability sampling methods. Journal of Agricultural, Biological and Environmental Statistics, 6: 258-267. Go to original source...
    7. Gregoire T.G., Valentine H.T., Furnival G.M., 1995. Sampling methods to estimate foliage and other characteristics of individual trees. Ecology, 76: 1181-1194. Go to original source...
    8. Hartley H.O., Rao J.N.K., 1962. Sampling with unequal probabilities and without replacement. Annals of Mathematical Statistics, 33: 350-374. Go to original source...
    9. Horvitz D.G., Thompson D.J., 1952. A generalisation of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47: 663-685. Go to original source...
    10. Jessen R.J., 1955. Determining the fruit count on a tree by randomized branch sampling. Biometrics, 11: 99-109. Go to original source...
    11. Mundson A., Smith K., Horvath R., Ruel J.C., Ung C.H., Bernier P., 1999. Does harvesting (CPRS) mimic fire? Verifying for black spruce forests in central Québec. Project Report 11: 16.
    12. Parresol B.R., 1999. Assessing tree and stand biomass. A review with examples and critical comparisons. Forest Science, 45: 573-593. Go to original source...
    13. Raulier F., Bernier P., Ung C.H., 1999. Canopy photosynthesis of sugar maple (Acer saccharum). Comparing big-leaf and multilayer extrapolations of leaf-level measurements. Tree Physiology, 19: 407-420. Go to original source... Go to PubMed...
    14. Saborowski J., Gaffrey D., 1999. RBS, ein mehrstufiges Inventurverfahren zur Schätzung von Baummerkmalen. II. Modifizierte RBS-Verfahren. Allgemeine Forst- und Jagdzeitung, 170: 223-227.
    15. Sampford M.R., 1967. On sampling without replacement with unequal probabilities of selection. Biometrika, 54: 499-513. Go to original source... Go to PubMed...
    16. Shinozaki K.K., Yoda K., Hozumi K., Kira T., 1964a. A quantitative analysis of plant form - the pipe model theory. I. Basic analyses. Japanese Journal of Ecology, 14: 97-105.
    17. Shinozaki K.K., Yoda K., Hozumi K., Kira T., 1964b. A quantitative analysis of plant form - the pipe model theory. II. Further evidence of the theory and its application in forest ecology. Japanese Journal of Ecology, 14: 133-139.
    18. Snowdon P., Raison J., Keith H., Montagu K., Bi H., Ritson P., Grierson P., Adams M., Burrows W., Eamus D., 2001. Protocol for sampling tree and stand biomass. National Carbon Accounting System Technical Report No. 31. Draft-March 2001. Australian Greenhouse Office: 114.
    19. Valentine H.T., Hilton S.J., 1977. Sampling oak foliage by the randomized-branch method. Canadian Journal of Forest Research, 7: 295-298. Go to original source...
    20. Valentine H.T., Tritton L.M., Furnival G.M., 1984. Subsampling trees for biomass, volume, or mineral content. Forest Science, 30: 673-681.
    21. Valentine H.T., Baldwin Jr. V.C., Gregoire T.G., Burkhart H.E., 1994. Surrogates for foliar dry matter in loblolly pine. Forest Science, 40: 576-585. Go to original source...
    22. Williams R.A., 1989. Use of randomized branch and importance sampling to estimate loblolly pine biomass. Southern Journal of Applied Forestry, 13: 181-184. Go to original source...
    23. Xiao Q., McPherson G., Ustin S., Grismer M., Simpson J., 2000. Winter rainfall interception by two mature open-grown trees in Davis, California. Hydrological Processes, 14: 763-784. Go to original source...

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