A new model for predicting the total tree height for stems cut-to-length by harvesters in Pinus radiata plantations

Abstract

A new model for predicting the total tree height for harvested stems from cut-to-length (CTL) harvester data was constructed for Pinus radiata (D.Don) following a conceptual analysis of relative stem profiles, comparisons of candidate models forms and extensive selections of predictor variables. Stem profiles of more than 3000 trees in a taper data set were each processed 6 times through simulated log cutting to generate the data required for this purpose. The CTL simulations not only mimicked but also covered the full range of cutting patterns of nearly 0.45 × 10⁶ stems harvested during both thinning and harvesting operations. The single-equation model was estimated through the multiple-equation generalized method of moments estimator to obtain efficient and consistent parameter estimates in the presence of error correlation and heteroscedasticity that were inherent to the systematic structure of the data. The predictive performances of our new model in its linear and nonlinear form were evaluated through a leave-one-tree-out cross validation process and compared against that of the only such existing model. The evaluations and comparisons were made through benchmarking statistics both globally over the entire data space and locally within specific subdivisions of the data space. These statistics indicated that the nonlinear form of our model was the best and its linear form ranked second. The prediction accuracy of our nonlinear model improved when the total log length represented more than 20% of the total tree height. The poorer performance of the existing model was partly attributed to the high degree of multicollinearity among its predictor variables, which led to highly variable and unstable parameter estimates. Our new model will facilitate and widen the utilization of harvester data far beyond the current limited use for monitoring and reporting log productions in P. radiata plantations. It will also facilitate the estimation of bark thickness and help make harvester data a potential source of taper data to reduce the intensity and cost of the conventional destructive taper sampling in the field. Although developed for P. radiata, the mathematical form of our new model will be applicable to other tree species for which CTL harvester data are routinely captured during thinning and harvesting operations.

Keywords

Stem profiles / Cut-to-length simulations / Harvester data / Model construction / Nonlinear multiple-equation GMM estimation / Benchmarking prediction accuracy

References

[1] Alin A. Multicollinearity. Wiley Interdiscip Rev Comput Stat, 2010, 2(3): 370-374.

[2] Allen DM. The relationship between variable selection and data agumentation and a method for prediction. Technometrics, 1974, 16(1): 125-127.

[3] Barth A, Holmgren J. Stem taper estimates based on airborne laser scanning and cut-to-length harvester measurements for preharvest planning. Int J For Eng, 2013, 24(3): 161-169.

[4] Barth A, Möller JJ, Wilhelmsson L, Arlinger J, Hedberg R, Söderman U. A Swedish case study on the prediction of detailed product recovery from individual stem profiles based on airborne laser scanning. Ann Sci, 2015, 72(1): 47-56.

[5] Belsley DA. Collinearity and forecasting. J Forecast, 1984, 3(2): 183-196.

[6] Belsley DA. Conditioning diagnostics: collinearity and weak data in regression, 1991, New York: Wiley Series in Probability 396

[7] Bi H. Trigonometric variable-form taper equation for Australian eucalypts. For Sci, 2000, 46(3): 397-409.

[8] Bi H, Long Y. Flexible taper equation for site-specific management of Pinus radiata in New South Wales, Australia. For Ecol Manag, 2001, 148(1): 79-91.

[9] Bi H, Jurskis V, O’Gara J. Improving height prediction of regrowth eucalypts by incorporating the mean size of site trees in a modified Chapman–Richards equation. Aust For, 2000, 63(4): 257-266.

[10] Bi H, Fox JC, Li Y, Lei Y, Pang Y. Evaluation of nonlinear equations for predicting diameter from tree height. Can J For Res, 2012, 42(4): 789-806.

[11] Caccamo G, Iqbal IA, Osborn J, Bi H, Arkley K, Melville G, Aurik D, Stone C. Comparing yield estimates derived from LiDAR and aerial photogrammetric point-cloud data with cut-to-length harvester data in a Pinus radiata plantation in Tasmania. Aust For, 2018, 81(3): 131-141.

[12] Cook D, Swayne DF, Buja A. Interactive and dynamic graphics for data analysis: with R and GGobi, 2007, New York: Springer 188

[13] Erkoç A, Tez M, Akay KU (2010) On multicollinearity in nonlinear regression models. Selçuk J Appl Math, Special Issue: 65–72

[14] Friendly M, Kwan E. Where’s Waldo? Visualizing collinearity diagnostics. Am Stat, 2009, 63(1): 56-65.

[15] Galmacci G. Collinearity detection in linear regression models. Comput Econ, 1996, 9(3): 215-227.

[16] Geisser S. The predictive sample reuse method with applications. J Am Stat Assoc, 1975, 70(350): 320-328.

[17] Gerasimov Y, Seliverstov A, Syunev V. Industrial round-wood damage and operational efficiency losses associated with the maintenance of a single-grip harvester head model: a case study in Russia. Forests, 2012, 3(4): 864-880.

[18] Gerasimov Y, Sokolov A, Syunev V. Development trends and future prospects of cut-to-length machinery. Adv Mater Res, 2013, 705: 468-473.

[19] Greene WH. Econometric analysis, 2012 7 Boston: Prentice Hall 1232

[20] Gujarati DN, Porter DC. Essentials of econometrics, 2010 4 Boston: Irwin/McGraw-Hill 554

[21] Hauglin M, Hansen E, Sørngård E, Næsset E, Gobakken T. Utilizing accurately positioned harvester data: modelling forest volume with airborne laser scanning. Can J For Res, 2018, 48(999): 1-10.

[22] Hayashi F. Econometrics, 2000, Princeton NJ: Princeton University Press 712

[23] Heinimann HR. Forest operations engineering and management—the ways behind and ahead of a scientific discipline. Croat J For Eng, 2007, 28(1): 107-121.

[24] Holmgren J, Barth A, Larsson H, Olsson H. Prediction of stem attributes by combining airborne laser scanning and measurements from harvesters. Silva Fenn, 2012, 46(2): 227-239.

[25] Holopainen M, Vastaranta M, Rasinmäki J, Kalliovirta J, Mäkinen A, Haapanen R, Melkas T, Yu X, Hyyppä J. Uncertainty in timber assortment estimates predicted from forest inventory data. Eur J For Res, 2010, 129(6): 1131-1142.

[26] Horne R, Robinson GL. Development of basal area thinning prescriptions and predictive yield models for Pinus Radiata plantations in New South Wales, 1962–1988, 1988, Sydney: Forestry Commission of New South Wales 37

[27] Huang SM. Ecoregion-based individual tree height-diameter models for lodgepole pine in Alberta. West J Appl For, 1999, 14(4): 186-193.

[28] Huang SM, Titus SJ, Wiens DP. Comparison of non-linear height-diameter functions for major Alberta tree species. Can J For Res, 1992, 22(9): 1297-1304.

[29] Huang SM, Yang Y, Wang Y. Amaro A, Reed D, Soares P. A critical look at procedures for validating growth and yield models. Modelling forest systems, 2003, Oxford: CABI Publishing 271 293

[30] Huyler NK, LeDoux CB (1999) Performance of a cut-to-length harvester in a single-tree and group selection cut. USDA Forestry Service, Northeastern Research Station, Research Paper NE-711, p 6

[31] Kiljunen N. Estimating dry mass of logging residues from final cuttings using a harvester data management system. Int J For Eng, 2002, 13(1): 17-25.

[32] Koenker R. Quantile regression: 40 years on. Annu Rev Econ, 2017, 9(1): 155-176.

[33] Koenker R (2018) quantreg: quantile regression. R package version 5.38. https://cran.r-project.org/package=quantreg. Accessed 15 Nov 2018

[34] Lang AH, Baker SA, Greene WD, Murphy GE. Individual stem value recovery of modified and conventional tree-length systems in the southeastern United States. Int J For Eng, 2010, 21(1): 7-11.

[35] Lu K, Bi H, Watt D, Strandgard M, Li Y. Reconstructing the size of individual trees using log data from cut-to-length harvesters in Pinus radiata plantations: a case study in NSW, Australia. J For Res, 2018, 29(1): 13-33.

[36] Malinen J, Laitila J, Väätäinen K, Viitamäki K. Variation in age, annual usage and resale price of cut-to-length machinery in different regions of Europe. Int J For Eng, 2016, 27(2): 95-102.

[37] Maltamo M, Bollandsås OM, Vauhkonen J, Breidenbach J, Gobakken T, Næsset E. Comparing different methods for prediction of mean crown height in Norway spruce stands using airborne laser scanner data. Forestry, 2010, 83(3): 257-268.

[38] Möller JJ, Arlinger J, Hannrup B, Larsson W, Barth A (2011) Harvester data as a base for management of forest operations and feedback to forest owners. In: Ackerman P, Ham H and Gleasure E (eds) Proceedings of 4th forest engineering conference: innovation in forest engineering—adapting to structural change. Stellenbosch University, White River, South Africa, 5–7 April 2011, pp 31–35

[39] Müller F, Jaeger D, Hanewinkel M. Digitization in wood supply—a review on howIndustry 4.0 will change the forest value chain. Comput Electron Agric, 2019, 162: 206-218.

[40] Murphy G. Procedures for scanning radiata pine stem dimensions and quality on mechanised processors. Int J For Eng, 2003, 14(2): 11-21.

[41] Murphy G, Wilson I, Barr B. Developing methods for pre-harvest inventories which use a harvester as the sampling tool. Aust For, 2006, 69(1): 9-15.

[42] Nash JE, Sutcliffe JV. River flow forecasting through conceptual models part I—A discussion of principles. J Hydrol, 1970, 10(3): 282-290.

[43] Nordfjell T, Björheden R, Thor M, Wästerlund I. Changes in technical performance, mechanical availability and prices of machines used in forest operations in Sweden from 1985 to 2010. Scand J For Res, 2010, 25(4): 382-389.

[44] Olivera A, Visser R. Development of forest-yield maps generated from Global Navigation Satellite System (GNSS)-enabled harvester StanForD files: preliminary concepts. N Z J For Sci, 2016 46 1 3

[45] Olivera A, Visser R, Acuna M, Morgenroth J. Automatic GNSS-enabled harvester data collection as a tool to evaluate factors affecting harvester productivity in a Eucalyptus spp. harvesting operation in Uruguay. Int J For Eng, 2016, 27(1): 15-28.

[46] Palander T, Vesa L, Tokola T, Pihlaja P, Ovaskainen H. Modelling the stump biomass of stands for energy production using a harvester data management system. Biosyst Eng, 2009, 102(1): 69-74.

[47] Peuhkurinen J, Maltamo M, Malinen J. Estimating species-specific diameter distributions and saw log recoveries of boreal forests from airborne laser scanning data and aerial photographs: a distribution-based approach. Silva Fenn, 2008, 42(4): 625-641.

[48] Rasinmäki J, Melkas T. A method for estimating tree composition and volume using harvester data. Scand J For Res, 2005, 20(1): 85-95.

[49] Roberts DR, Bahn V, Ciuti S, Boyce MS, Elith J, Guillera-Arroita G, Hauenstein S, Lahoz-Monfort JJ, Schröder B, Thuiller W, Warton DI. Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography, 2017, 40(8): 913-929.

[50] Rossit DA, Olivera A, Céspedes VV, Broz D. A Big Data approach to forestry harvesting productivity. Comput Electron Agric, 2019, 161: 29-52.

[51] Roth G (2016) StanForD as a data source for forest management: a forest stand reconciliation implementation case study. M.Sc. thesis, University of Canterbury, New Zealand, p 55

[52] Saukkola A, Melkas T, Riekki K, Sirparanta S, Peuhkurinen J, Holopainen M, Hyyppä J, Vastaranta M. Predicting forest inventory attributes using airborne laser scanning, aerial imagery, and harvester data. Remote Sens, 2019 11 7 797

[53] Sellén D (2016) Big Data analytics for the forest industry: a proof-of-concept built on cloud technologies. M.Sc. thesis, Mid Sweden University, Ostersund, Sweden, p 80

[54] Siipilehto J, Lindeman H, Vastaranta M, Yu X, Uusitalo J. Reliability of the predicted stand structure for clear-cut stands using optional methods: airborne laser scanning-based methods, smartphone-based forest inventory application Trestima and pre-harvest measurement tool EMO. Silva Fenn, 2016 50 3

[55] Söderberg J (2015) A method for using harvester data in airborne laser prediction of forest variables in mature coniferous stands. M.Sc. thesis, Swedish University of Agricultural Science, Uppsala, Sweden, p 31

[56] Stendahl J, Dahlin B. Possibilities for harvester-based forest inventory in thinnings. Scand J For Res, 2002, 17(6): 548-555.

[57] Stone M. Cross-validatory choice and assessment of statistical predictions. J R Stat Soc B, 1974, 36(2): 111-133.

[58] Strandgard M, Walsh D, Acuna M. Estimating harvester productivity in Pinus radiata plantations using StanForD stem files. Scand J For Res, 2013, 28(1): 73-80.

[59] Swayne D, Cook D, Buja A, Lang D, Wickham H, Lawrence M (2006) GGobi Manual. http://www.ggobi.org/docs/manual.pdf. Accessed 5 Jan 2018

[60] Uusitalo J. Introduction to forest operations and technology, 2010, Hämeenlinna: JVP Forest Systems Oy 287

[61] Uusitalo J (2017) Big data is transforming forestry. www.luke.fi/en/big-data-transforming-forestry. Accessed 1 Mar 2018

[62] Varjo J (1995) Latvan hukkaosan pituusmallit männylle, kuuselle ja koivulle metsurimittausta varten. In: Verkasalo E (ed) Puutavaran mittauksen kehittämistutkimuksia 1989–93, Finnish Forest Research Institute, Research Papers 558, pp 21–23 (in Finnish). https://jukuri.luke.fi/handle/10024/521187

[63] Vesa L, Palander T. Modeling stump biomass of stands using harvester measurements for adaptive energy wood procurement systems. Energy, 2010, 35(9): 3717-3721.

[64] Vonesh EF. Generalized linear and nonlinear models for correlated data: theory and applications using SAS, 2012, Cary: SAS Institute.

[65] Wackerly DD, Mendenhall W, Scheaffer RL. Mathematical statistics with applications, 1996, Belmont: Duxbury Press 798

[66] Williams C, Ackerman P. Cost-productivity analysis of South African pine sawtimber mechanised cut-to-length harvesting. South For J For Sci, 2016, 78(4): 267-274.

[67] Zhang L, Bi H, Cheng P, Davie CJ. Modelling spatial variations in tree diameter—height relationships. For Ecol Manag, 2003, 189: 317-329.

[68] Zhang YH, Li Y, Bi H. Converting diameter measurements of Pinus radiata taken at different breast heights. Aust For, 2015, 78(1): 1-5.