ESTIMATING DIAMETER AND HEIGHT DISTRIBUTIONS FROM AIRBORNE LIDAR VIA COPULAS

Συγγραφείς

  • Ting-Ru Yang Faculty of Forestry and Environmental Management University of New Brunswick
  • John A. Kershaw, Jr. Faculty of Forestry, University of New Brunswick

Λέξεις-κλειδιά:

stand structure, height-diameter relationships, bivariate distributions, copulas, moment-based parameter recovery

Περίληψη

Estimates of quantitative variables in forest stands often are required. Light Detection and Ranging (LiDAR) can create three-dimensional point clouds of forest structures and ground surface
elevation maps. These features are useful for quantifying forest stand parameters such as volume and canopy height at broad scales. This study explores the potential of applying copulas and LiDAR metrics to obtain diameter and height estimates. Predicted values were compared with field measurements. Diameter and height distributions were obtained using moment–based parameter recovery and prediction of moments using nonlinear least squares from LiDAR attributes. We then used copula methods to link the diameter and height distributions. Using the diameter and height distributions, other attributes such as volume or carbon content can be estimated and summed to obtain area-based estimates.

Βιογραφικό Συγγραφέα

  • John A. Kershaw, Jr., Faculty of Forestry, University of New Brunswick

    Professor of Forest Biometrics

    Faculty of Forestry and Envir. Mgmt

Αναφορές

Arias-Rodil, M., Diéguez-Aranda, U., Álvarez-González, J.G., Pérez-Cruzado, C., Castedo-Dorado, F., and González-Ferreiro, E. 2018. Modeling diameter distributions in radiata pine plantations in Spain with existing countrywide LiDAR data. Ann. For. Sci. 75: 36. doi: https://doi.org/10.1007/s13595-018-0712-z

Asner, G.P., Hughes, R.F., Mascaro, J., Uowolo, A.L., Knapp, D.E., Jacobson, J., Kennedy-Bowdoin, T., and Clark, J.K. 2011. High-resolution carbon mapping on the million-hectare Island of Hawaii. Front. Ecol. Environ. (e-View): 28. doi: https://doi.org/10.1890/100179

Ayrey, E., Fraver, S., Kershaw, J.A., Jr., Kenefic, L.S., Hayes, Weiskittel, A.R., and Roth. 2017. Layer stacking: A novel algorithm for individual forest tree segmentation from LiDAR point clouds. Can. J. Remote Sens. 43(1): 16–27. doi: https://doi.org/10.1080/07038992.2017.1252907

Ayrey, E., Hayes, D.J., Fraver, S., Kershaw, J.A., Jr., and Weiskittel, A.R. 2019. Ecologically-Based Metrics for Assessing Structure in Developing Area-Based, Enhanced Forest Inventories from LiDAR. Can. J. Remote Sens. 45(1): 88–112. doi: https://doi.org/10.1080/07038992.2019.1612738

Bailey, R.L., and Dell, T.R. 1973. Quantifying diameter distributions with the Weibull function. For. Sci. 19(2): 97–104. doi: https://doi.org/10.1080/07038992.2019.1612738

Borders, B.E., and Patterson, W.D. 1990. Projecting stand tables: A comparison of the Weibull diameter distribution method, a percentile-based projection method, and a basal area growth projection method. For. Sci. 36(2): 413–424. doi: https://doi.org/10.1093/forestscience/36.2.413

Brandtberg, T., Warner, T.A., Landenberger, R.E., and McGraw, J.B. 2003. Detection and analysis of individual leaf-off tree crowns in small footprint, high sampling density lidar data from the eastern deciduous forest in North America. Remote Sens. Environ. 85: 290–303. doi: https://doi.org/10.1016/S0034-4257(03)00008-7

Breiman, L. 2001. Random forests. Mach. Learn. 45(1): 5–32.

Burk, T.E., and Newberry, J.D. 1984. A simple algorithm for moment-based recovery of Weibull distribution parameters. For. Sci. 30(2): 329–332. doi: https://doi.org/10.1093/forestscience/30.2.329

Bury, K.V. 1975. Statistical Models in Applied Science. Robert E. Krieger Publishing Company, INC., Malabar, Florida.

Cleveland, W.S. 1979. Robust Locally Weighted Regression and Smoothing Scatterplots. J. Am. Stat. Assoc. 74(368): 829–836.

Clutter, J.L., Fortson, J.C., Pienaar, L.V., Brister, G.H., and Bailey, R.L. 1983. Timber management: A quantitative approach. First. John Wiley & Sons, New York.

Culvenor, D.S. 2002. TIDA: an algorithm for the delineation of tree crowns in high spatial resolution remotely sensed imagery. Comput. Geosci. 28(1): 33–44. doi: https://doi.org/10.1016/S0098-3004(00)00110-2

de Conto, T., Olofsson, K., Görgens, E.B., Rodriguez, L.C.E., Almeida, G. 2017. Performance of stem denoising and stem modelling algorithms on single tree point clouds from terrestrial laser scanning. Comput. Electron. Agric., 143:165-176. doi: https://doi.org/10.1016/S0098-3004(00)00110-2

Frees, E.W., and Valdez, E. 1998. Understanding relationships using copulas. North Am. Actuar. J. 2(1): 1–25. doi: https://doi.org/10.1080/10920277.1998.10595667

Gaveau, D.L.A., and Hill, R.A. 2003. Quantifying canopy height underestimation by laser pulse penetration in small-footprint airborne laser scanning data. Can. J. Remote Sens. 29(5): 650–657. doi: https://doi.org/10.5589/m03-023

Genest, C., and MacKay, J. 1986. The Joy of Copulas: Bivariate distributions with uniform marginals. Am. Stat. 40: 280–283. doi: https://doi.org/10.1080/00031305.1986.10475414

Gobakken, T., and Næsset, E. 2004. Estimation of diameter and basal area distributions in coniferous forest by means of airborne laser scanner data. Scand. J. For. Res. 19(6): 529–542. doi: https://doi.org/10.1080/02827580410019454

Gove, J.H. 2003. Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling. Environmental Ecol. Stat. 10(4): 455–467. doi: https://doi.org/10.1023/A:1026000505636

Hafley, W.L., and Schreuder, H.T. 1977. Statistical distributions for fitting diameter and height data in even-aged stands. Can. J. For. Res. 7(3): 481–487. doi: https://doi.org/10.1139/x77-062

Hayashi, R., Kershaw, J.A., Jr., and Weiskittel, A.R. 2015. Evaluation of alternative methods for using LiDAR to predict aboveground biomass in mixed species and structurally complex forests in northeastern North America. Math. Comput. For. Nat. Resour. Sci. 7(2): 49–65. available from: https://mcfns.net/index.php/Journal/article/view/MCFNS7.2_2 [accessed Nov. 23, 2021]

Hayashi, R., Weiskittel, A.R., and Kershaw, J.A., Jr. 2016. Influence of prediction cell size on LiDAR-derived area-based estimates of total volume in mixed-species and multicohort forests in northeastern North America. Can. J. Remote Sens. 42(5): 473–488. doi: https://doi.org/10.1080/07038992.2016.1229597

Henning, J.G. and Radtke, P.J. 2006. Detailed stem measurements of standing trees from ground-based scanning lidar. For. Sci., 52(1):67-80. doi: https://doi.org/10.1093/forestscience/52.1.67

Hsu, Y.-H., Yang, T.-R., Chen, Y., and Kershaw, J.A., Jr. 2020. Sample strategies for bias correction of regional LiDAR-assisted forest inventory estimates on small woodlots. Ann. For. Sci. 77:75, 12p. doi: https://doi.org/10.1007/s13595-020-00976-8

Hummel, S., Hudak, A.T., Uebler, E.H., Falkowski, M.J., and Megown, K.A. 2011. A comparison of accuracy and cost of LiDAR versus stand exam data for landscape management on the Malheur National Forest. J. For. 109(5): 267–273. doi: https://doi.org/10.1093/jof/109.5.267

Kaartinen, H., Hyyppä, J., Yu, X., Vastaranta, M., Hyyppä, H., Kukko, A., Holopainen, M., Heipke, C., Hirschmugl, M., Morsdorf, F., Næsset, E., Pitkänen, J., Popescu, S., Solberg, S., Wolf, B.M., and Wu, J.-C. 2012. An International Comparison of Individual Tree Detection and Extraction Using Airborne Laser Scanning. Remote Sens. 4(4): 950–974. doi: https://doi.org/10.3390/rs4040950

Kershaw, J.A., Jr., and Maguire, D.A. 1996. Crown structure in western hemlock, Douglas-fir, and grand fir in western Washington: horizontal distribution of foliage within branches. Can. J. For. Res. 26(1): 128–142. doi: https://doi.org/10.1139/x26-014

Kershaw, J.A., Jr., Richards, E.W., McCarter, J.B., and Oborn, S. 2010. Spatially correlated forest stand structures: A simulation approach using copulas. Comput. Electron. Agric. 74(1): 120–128. doi: https://doi.org/10.1016/j.compag.2010.07.005

Kershaw, J.A., Jr., Weiskittel, A.R., Lavigne, M.B., and McGarrigle, E. 2017. An imputation/copula-based stochastic individual tree growth model for mixed species Acadian forests: a case study using the Nova Scotia permanent sample plot network. For. Ecosyst. 4: 15. doi: https://doi.org/10.1186/s40663-017-0102-2

Kutner, M., Nachtsheim, C., and Neter, J. 2004. Applied linear regression models. Fourth Ed. McGraw-Hill, New York.

Li, W., Guo, Q., Jakubowski, M., and Kelly, M. 2012. A new method for segmenting individual trees from the lidar point cloud. Photogramm. Eng. Remote Sens. 78(1): 75–84. doi: https://doi.org/10.14358/PERS.78.1.75

Liang, X., Kankare, V., Yu, X., Hyyppä, Y., and Holopainen, M. 2014. Automated Stem Curve Measurement Using Terrestrial Laser Scanning. IEEE Trans. Geosci. Remote Sens., 52(3):1739-1748. doi: https://doi.org/10.1109/TGRS.2013.2253783

Little, S.N. 1983. Weibull diameter distributions for mixed stands of western conifers. Can. J. For. Res. 13(1): 85–88. doi: https://doi.org/10.1139/x83-012

Liu, C., Zhang, L., Davis, C.J., Solomon, D.S., and Gove, J.H. 2002. A finite mixture model for characterizing the diameter distributions of mixed-species forest stands. For. Sci. 48(4): 653–661. doi: https://doi.org/10.1093/forestscience/48.4.653

Loo, J., and Ives, N. 2003. The Acadian Forest: Historical condition and human impacts. For. Chron. 79(3): 462–474. doi: https://doi.org/10.5558/tfc79462-3

Maas, H., Bienert, A., Scheller, S., and Keane, E. 2008. Automatic forest inventory parameter determination from terrestrial laser scanner data. Int. J. Remote Sens., 29(5):1579-1593. doi: https://doi.org/10.1080/01431160701736406

MacPhee, C., Kershaw, J.A., Jr., Weiskittel, A.R., Golding, J., and Lavigne, M.B. 2018. Comparison of approaches for estimating individual tree height–diameter relationships in the Acadian forest region. Forestry 92: 132–146. doi: https://doi.org/10.1093/forestry/cpx039

Maltamo, M., Mustonen, K., Hyyppä, J., Pitkänen, J., and Yu, X. 2004. The accuracy of estimating individual tree variables with airborne laser scanning in a boreal nature reserve. Can. J. For. Res. 34: 1791–1801. doi: https://doi.org/10.1139/x04-055

Maltamo, M., Peuhkurinen, J., Malinen, J., Vauhkonen, J., Packalén, P., and Tokola, T. 2009. Predicting tree attributes and quality characteristics of Scots pine using airborne laser scanning data. Silva Fenn. 43(3). doi: https://doi.org/10.14214/sf.203

McGarrigle, E., Kershaw, J.A., Jr., Ducey, M.J., and Lavigne, M.B. 2013. A new approach to modeling stand-level dynamics based on informed random walks: Influence of bandwidth and sample size. Forestry 86(3): 377–389. doi: https://doi.org/10.1093/forestry/cpt008

Mehtätalo, L., Maltamo, M., and Packalén, P. 2007. Recovering plot-specific diameter distribution and height-diameter curve using als based stand characteristics. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. XXXVI: 288–293.

Næsset, E., and Økland, T. 2002. Estimating tree height and tree crown properties using airborne scanning laser in a boreal nature reserve. Remote Sens. Environ. 79: 105–115. doi: https://doi.org/10.1016/S0034-4257(01)00243-7

Narsky, I. 2003a. Goodness of fit: What do we really want to know? In Proceedings. Physics Statistics 2003. pp. 70–74. available from: http://www.slac.stanford.edu/econf/C030908/papers/MOCT004.pdf [accessed Nov. 23, 2021]

Narsky, I. 2003b. Estimation of goodness-of-fit in multidimensional analysis using distance to nearest neighbor. High Energy Physics, California Technical University. available from: https://arxiv.org/pdf/physics/0306171 [accessed Nov. 23, 2021]

Nelsen, R.B. 2006. An Introduction to Copulas. 2nd Ed. Springer, New York.

Olofsson, K. and Holmgren, J. 2016. Single tree stem profile detection using terrestrial laser scanner data, flatness saliency features and curvature properties. Forests, 7(9): 207. doi: https://doi.org/10.3390/f7090207

Palahí, M., Pukkala, T., Blasco, E., and Trasobares, A. 2007. Comparison of beta, Johnson's SB, Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (northeast of Spain). Eur. J. For. Res. 126(4): 563–571. doi: https://doi.org/10.1007/s10342-007-0177-3

Pitkänen, T.P., Raumonen, P. and Kangas, A. 2019. Measuring stem diameters with TLS in boreal forests by complementary fitting procedure. ISPRS Journal of Photogrammetry and Remote Sensing. 147:294-306. doi: https://doi.org/10.1016/j.isprsjprs.2018.11.027

Plotnick, R.E., Gardner, R.H., and O'Neill, R.V. 1993. Lacunarity indices as measures of landscape texture. Landsc. Ecol. 8(3):201–211. doi: https://doi.org/10.1007/BF00125351

Pueschel, P., Newnham, G., Rock, G., Udelhoven, T., Werner, W., and Hill, J. 2013. The influence of scan mode and circle fitting on tree stem detection, stem diameter and volume extraction from terrestrial laser scans. ISPRS J. Photogramm. Remote Sens., 77:44-56. doi: https://doi.org/10.1016/j.isprsjprs.2012.12.001

R Development Core Team. 2021. R: A Language and Environment for Statistical Computing. Available from http://www.R-project.org [accessed Nov. 23, 2021]

Reutebuch, S.E., Andersen, H.-E., and McGaughey, R.J. 2005. Light Detection and Ranging (LIDAR): An Emerging Tool for Multiple Resource Inventory. J. For. 103: 286–292.

Ripley, B.D. 2004. Spatial statistics. Wiley, Hoboken, NJ.

Roussel, J.-R., Auty, D., Boissieu, F.D., Meador, A.S., and Jean-François, B. 2020. Airborne LiDAR Data Manipulation and Visualization for Forestry Applications. available from: https://github.com/Jean-Romain/lidR [accessed Nov. 23, 2021]

Schilling, M.F. 1986. Multivariate two-sample tests based on nearest neighbors. J. Am. Stat. Assoc. 81(395): 799–806. doi: https://doi.org/10.1080/01621459.1986.10478337

Schreuder, H.T., and Hafley, W.L. 1977. A useful bivariate distribution for describing stand structure of tree heights and diameters. Biometrics 33(3): 471–478. doi: https://doi.org/10.2307/2529361

Srinivasan, S., Popescu, C.S., Eriksson, M., Sheridan, D.R., and Ku, N. 2015. Terrestrial laser scanning as an effective tool to retrieve tree level height, crown width, and stem diameter. Remote Sens., 7(2):1877-1896. doi: https://doi.org/10.3390/rs70201877

Temesgen, H., and Ver Hoef, J.M. 2015. Evaluation of the spatial linear model, random forest and gradient nearest-neighbour methods for imputing potential productivity and biomass of the Pacific Northwest forests. Forestry 88(1): 131–142. doi: https://doi.org/10.1093/forestry/cpu036

Thomas, V., Oliver, R.D., and Woods, M. 2008. LiDAR and Weibull modeling of diameter and basal area. For. Chron. 84(6): 866–875. doi: https://doi.org/10.5558/tfc84866-6

Treitz, P.; Lim, K.; Woods, M.; Pitt, D.; Nesbitt, D.; Etheridge, D. 2012. LiDAR sampling density for forest resource inventories in Ontario, Canada. Remote Sensing 4:830–848. doi: https://doi.org/10.3390/rs4040830

Ver Planck, N.R., Finley, A.O., Kershaw, J.A., Jr., Weiskittel, A.R., and Kress, M.C. 2018. Hierarchical Bayesian models for small area estimation of forest variables using LiDAR. Remote Sens. Environ. 264: 287–295. doi: http://dx.doi.org/10.1016/j.rse.2017.10.024

Wang, M., Rennolls, K., and Tang, S. 2008. Bivariate distribution modeling of tree diameters and heights: Dependency modeling using copulas. For. Sci. 54(3): 284–293. doi: https://doi.org/10.1093/forestscience/54.3.284

Wang, M., Upadhyay, A., and Zhang, L. 2010. Trivariate distribution modeling of tree diameter, height, and volume. For. Sci. 56(3): 290–300. doi: https://doi.org/10.1093/forestscience/56.3.290

Wang, S.S. 1998. Aggregation of correlated risk portfolios: Models & algorithms. Proc. Casualty Actuar. Soc. 85(163): 848–937. available from: https://www.casact.org/sites/default/files/database/proceed_proceed98_1998.pdf [accessed Nov. 23, 2021]

White, J.C., Wulder, M.A., and Varhola, A. 2013. A best practices guide for generating forest inventory attributes from airborne laser scanning data using an area-based approach. Natural Resources Canada, Canadian Forest Service, Canadian Wood Fibre Centre, Victoria, BC, Canada. available from: https://cfs.nrcan.gc.ca/publications/download-pdf/34887 [accessed Nov. 23, 2021]

Wulder, M.A., Bater, C.W., Coops, N.C., Hilker, T., and White, J.C. 2008. The role of LiDAR in sustainable forest management. For. Chron. 84(6): 807–826. doi: https://doi.org/10.5558/tfc84807-6

Xu, Q., Hou, Z., Maltamo, M., and Tokola, T. 2014. Retrieving suppressed trees from model-based height distribution by combining high and low density airborne laser scanning data. Can. J. Remote Sens. 40(3): 233–242. doi: http://dx.doi.org/10.1080/07038992.2014.935933

Xu, Q., Li, B., Maltamo, M., Tokola, T., and Hou, Z. 2019. Predicting tree diameter using allometry described by non-parametric locally-estimated copulas from tree dimensions derived from airborne laser scanning. For. Ecol. Manag. 434: 205–212. doi: https://doi.org/10.1016/j.foreco.2018.12.020

Yan, J. 2007. Enjoy the joy of copulas: With a package copula. J. Stat. Softw. 21(4): 1–21. doi: https://doi.org/10.18637/jss.v021.i04

Yang, T.-R., Kershaw, J.A., Weiskittel, A.R., Lam, T.Y., and McGarrigle, E. 2019. Influence of sample selection method and estimation technique on sample size requirements for wall-to-wall estimation of volume using airborne LiDAR. Forestry 92(3): 311–323. doi: https://doi.org/10.1093/forestry/cpz014

Yang, T.-R., Kershaw, J.A., Jr., and Ducey, M.J. 2021. Development of allometric systems of Equations for Compatible Area-Based LiDAR-Assisted Estimation. Forestry 94(1):36-53. doi: https://doi.org/10.1093/forestry/cpaa019

Zutter, B.R., Oderwald, R.G., Farrar, R.M., Jr., and Murphy, P.A. 1982. WEIBUL: A program to estimate parameters of forms of the Weibull distribution using complete, censored, and truncated data. Publication, Virginia Polytechnic Institute and State University, Blacksburg, VA, School of Forestry and Wildlife Resources. available from: https://vtechworks.lib.vt.edu/bitstream/handle/10919/93556/FWS-3-82.pdf [accessed Nov. 23, 2021]

Zutter, B.R., Oderwald, R.G., Murphy, P.A., and Farrar, R.M. 1986. Characterizing diameter distributions with modified data types and forms of the Weibull distribution. For. Sci. 32(1): 37–48. doi: https://doi.org/10.1093/forestscience/32.1.37

Δημοσιευμένα

2022-04-30

Τεύχος

Ενότητα

GIS and Remote Sensing

Πώς να δημιουργήσετε Αναφορές

ESTIMATING DIAMETER AND HEIGHT DISTRIBUTIONS FROM AIRBORNE LIDAR VIA COPULAS. (2022). Mathematical and Computational Forestry & Natural-Resource Sciences (MCFNS), 14(1), 1-14(14). https://tmp.mcfns.com/index.php/Journal/article/view/14.1

##plugins.generic.recommendBySimilarity.heading##

1-10 των 38

##plugins.generic.recommendBySimilarity.advancedSearchIntro##

##plugins.generic.recommendByAuthor.heading##