Modeling diameter distributions in radiata pine plantations in Spain with existing countrywide LiDAR data

  • Manuel Arias-Rodil
  • Ulises Diéguez-Aranda
  • Juan Gabriel Álvarez-González
  • César Pérez-Cruzado
  • Fernando Castedo-Dorado
  • Eduardo González-Ferreiro
Original Paper
Part of the following topical collections:
  1. SilviLaser


Key message

We evaluated the use of low-density airborne laser scanning data to estimate diameter distributions in radiata pine plantations. The moment-based parameter recovery method was used to estimate the diameter distributions, considering LiDAR metrics as explanatory variables. The fitted models explained more than 77% of the observed variability. This approach can be replicated every 6 years (temporal cover planned for countrywide LiDAR flights in Spain).


The estimation of stand diameter distribution is informative for forest managers in terms of stand structure, forest growth model inputs, and economic timber value. In this sense, airborne LiDAR may represent an adequate source of information.


The objective was to evaluate the use of low-density Spanish countrywide LiDAR data for estimating diameter distributions in Pinus radiata D. Don stands in NW Spain.


The empirical distributions were obtained from 25 sample plots. We applied the moment-based parameter recovery method in combination with the Weibull function to estimate the diameter distributions, considering LiDAR metrics as explanatory variables. We evaluated the results by using the Kolmogorov–Smirnov (KS) test and a classification tree and random forest (RF) to relate the KS test result for each plot to stand-level variables.


The models used to estimate average (dm) and quadratic (dg) mean diameters from LiDAR metrics, required for recovery of the Weibull parameters, explained a high percentage of the observed variance (77 and 80%, respectively), with RMSE values of 3.626 and 3.422 cm for the same variables. However, the proportion of plots accepted by the KS was low. This poor performance may be due to the strictness of the KS test and/or by the characteristics of the LiDAR flight.


The results justify the assessment of this approach over different species and forest types in regional or countrywide surveys.


PNOA (Plan Nacional de Ortofotografía Aérea de España) project Airborne laser scanning (ALS) Remote sensing Weibull Distribution function Moment-based parameter recovery method 


Funding information

Spanish Ministry of Science and Innovation (AGL2008-02259/FOR); Eduardo González-Ferreiro was financially supported by the Plan galego de investigación, innovación e crecemento 2011-2015 (Plan I2C) (Official Journal of Galicia - DOG nº 52, 17/03/2014 p. 11343, exp: POS-A/2013/049) - Galician Government (Dirección Xeral de Ordenación e Calidade do Sistema Universitario de Galicia - Consellería de Educación e Ordenación Universitaria) and European Social Fund. Manuel Arias-Rodil was financially supported by an FPU grant (AP2012-05337) from the Spanish Ministry of Education.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

13595_2018_712_MOESM1_ESM.doc (3.5 mb)
ESM 1 (DOC 3622 kb)


  1. Ahokas E, Yu X, Oksanen J, Hyyppä J, Kaartinen H, Hyyppä H (2005) Optimization of the scanning angle for countrywide laser scanning. In: Vosselman G, Brenner C, Hyyppä J (eds) Laser scanning 2005. International Society for Photogrammetry and Remote Sensing (ISPRS), Enschede, pp 115–119Google Scholar
  2. Bailey RL, Dell TR (1973) Quantifying diameter distributions with the Weibull function. For Sci 19:97–104Google Scholar
  3. Belsley DA (1991) Conditioning diagnostics: collinearity and weak data in regression. John Wiley & Sons Inc, New York 396 ppGoogle Scholar
  4. Bollandsås OM, Næsset E (2007) Estimating percentile-based diameter distributions in uneven-sized Norway spruce stands using airborne laser scanner data. Scand J Forest Res 22:33–47CrossRefGoogle Scholar
  5. Borders BE (1989) Systems of equations in forest stand modeling. For Sci 35:548–556Google Scholar
  6. Borders BE, Bailey RL (1986) A compatible system of growth and yield equations for slash pine fitted with restricted three-stage least squares. For Sci 32:185–201Google Scholar
  7. Breidenbach J, Gläser C, Schmidt M (2008) Estimation of diameter distributions by means of airborne laser scanner data. Can J For Res 38:1611–1620CrossRefGoogle Scholar
  8. Burk TE, Newberry JD (1984) Notes: a simple algorithm for moment-based recovery of Weibull distribution parameters. For Sci 30:329–332Google Scholar
  9. Burkhart H, Tomé M (2012) Modeling forest trees and stands. Springer Science & Business Media, Berlin 458 ppCrossRefGoogle Scholar
  10. Castedo Dorado F, Diéguez-Aranda U, Barrio Anta M, Sánchez Rodríguez M, von Gadow K (2006) A generalized height–diameter model including random components for radiata pine plantations in northwestern Spain. For Ecol Manag 229:202–213CrossRefGoogle Scholar
  11. Castedo-Dorado F, Diéguez-Aranda U, Álvarez-González JG (2007) A growth model for Pinus radiata D. Don stands in north-western Spain. Ann For Sci 64:453–465CrossRefGoogle Scholar
  12. Castedo-Dorado F, Gómez-Vázquez I, Fernandes PM, Crecente-Campo F (2012) Shrub fuel characteristics estimated from overstory variables in NW Spain pine stands. For Ecol Manag 275:130–141CrossRefGoogle Scholar
  13. Diéguez-Aranda U, Burkhart HE, Rodríguez-Soalleiro R (2005) Modelling dominant height of radiata pine (Pinus radiata D. Don) plantations in north-western Spain. For Ecol Manag 215:271–284CrossRefGoogle Scholar
  14. Diéguez-Aranda U, Rojo Alboreca A, Castedo-Dorado F, Álvarez González JG, Barrio-Anta M, Crecente-Campo F, González-González JM, Pérez-Cruzado C, Rodríguez Soalleiro R, López-Sánchez CA, Balboa-Murias MA, Gorgoso Varela JJ, Sánchez Rodríguez F (2009). Herramientas selvícolas para la gestión forestal sostenible en Galicia. Xunta de Galicia.Google Scholar
  15. Frazier JR (1981) Compatible whole-stand and diameter distribution models for loblolly pine plantations. Dissertation, Virginia Polytechnic Institute and State University. 125 ppGoogle Scholar
  16. Gobakken T, Næsset E (2004) Estimation of diameter and basal area distributions in coniferous forest by means of airborne laser scanner data. Scand J Forest Res 19:529–542CrossRefGoogle Scholar
  17. Gobakken T, Næsset E (2005) Weibull and percentile models for lidar-based estimation of basal area distribution. Scand J Forest Res 20:490–502CrossRefGoogle Scholar
  18. Gómez-Vázquez I, Crecente-Campo F, Diéguez-Aranda U, Castedo-Dorado F (2013) Modelling canopy fuel variables in Pinus pinaster Ait. and Pinus radiata D. Don stands in northwestern Spain. Ann For Sci 70:161–172CrossRefGoogle Scholar
  19. González-Ferreiro E, Diéguez-Aranda U, Crecente-Campo F, Barreiro-Fernández L, Miranda D, Castedo-Dorado F (2014) Modelling canopy fuel variables for Pinus radiata D. Don in NW Spain with low-density LiDAR data. Int J Wildland Fire 23:350–362CrossRefGoogle Scholar
  20. González-Ferreiro E, Arellano-Pérez S, Castedo-Dorado F, Hevia A, Vega JA, Vega-Nieva D, Álvarez-González JG, Ruiz-González AD (2017) Modelling the vertical distribution of canopy fuel load using national forest inventory and low-density airbone laser scanning data. PLoS One 12:e0176114CrossRefPubMedPubMedCentralGoogle Scholar
  21. Gorgoso JJ, González JÁ, Rojo A, Grandas-Arias JA (2007) Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. For Syst 16:113–123Google Scholar
  22. Guerra-Hernández J, Bastos-Görgens E, García-Gutiérrez J, Estraviz-Rodriguez LC, Tomé M, González-Ferreiro E (2016a) Comparison of ALS based models for estimating aboveground biomass in three types of Mediterranean forest. Eur J Remote Sens 49:185–204CrossRefGoogle Scholar
  23. Guerra-Hernández J, Tomé M, González-Ferreiro E (2016b) Using low density LiDAR data to map Mediterranean forest characteristics by means of an area-based approach and height threshold analysis. Spanish J Remote Sens 46:103–117Google Scholar
  24. Hawkins DM (2004) The problem of overfitting. J Chem Inf Comput Sci 44:1–12CrossRefPubMedGoogle Scholar
  25. Henningsen A, Hamann JD (2007) Systemfit: a package for estimating systems of simultaneous equations in R. J Stat Softw 23:1–40CrossRefGoogle Scholar
  26. Holopainen M, Vastaranta M, Rasinmäki J, Kalliovirta J, Mäkinen A, Haapanen R, Melkas T, Yu X, Hyyppä J (2010) Uncertainty in timber assortment estimates predicted from forest inventory data. Eur J For Res 129:1131–1142CrossRefGoogle Scholar
  27. Hyink DM, Moser JW (1983) A generalized framework for projecting forest yield and stand structure using diameter distributions. For Sci 29:85–95Google Scholar
  28. Hyyppä J, Inkinen M (1999) Detecting and estimating attributes for single trees using laser scanner. Photogramm J Finland 16:27–42Google Scholar
  29. Kalliovirta J, Laasasenaho J, Kangas A (2005) Evaluation of the laser-relascope. For Ecol Manag 204:181–194CrossRefGoogle Scholar
  30. Kangas A, Mehtatalo L, Maltamo M (2007) Modelling percentile based basal area weighted diameter distribution. Silva Fenn 41:425–440CrossRefGoogle Scholar
  31. Liaw A, Wiener M (2002) Classification and regression by randomForest. R News 2:18–22Google Scholar
  32. Lilliefors HW (1967) On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc 62:399–402CrossRefGoogle Scholar
  33. Liu C, Zhang SY, Lei Y, Newton PF, Zhang L (2004) Evaluation of three methods for predicting diameter distributions of black spruce (Picea mariana) plantations in central Canada. Can J For Res 34:2424–2432CrossRefGoogle Scholar
  34. Lumley T, based on Fortran code by Miller A (2017). Leaps: regression subset selection. R package version 3.0Google Scholar
  35. Magnussen S, Renaud JP (2016) Multidimensional scaling of first-return airborne laser echoes for prediction and model-assisted estimation of a distribution of tree stem diameters. Ann For Sci 73:1089–1098CrossRefGoogle Scholar
  36. Maltamo M, Gobakken T (2014) Predicting tree diameter distributions. In: Maltamo M, Næsset E, Vauhkonen J (eds) Forestry applications of airborne laser scanning: concepts and cases studies. Springer, Dordrecht – Heidelberg – New York – London, pp 269–292CrossRefGoogle Scholar
  37. Maltamo M, Puumalainen J, Päivinen R (1995) Comparison of beta and Weibull functions for modelling basal area diameter distribution in stands of Pinus sylvestris and Picea abies. Scand J Forest Res 10:284–295CrossRefGoogle Scholar
  38. Maltamo M, Eerikäinen K, Packalén P, Hyyppä J (2006) Estimation of stem volume using laser scanning-based canopy height metrics. Forestry 79:217–229CrossRefGoogle Scholar
  39. Maltamo M, Suvanto A, Packalén P (2007) Comparison of basal area and stem frequency diameter distribution modelling using airborne laser scanner data and calibration estimation. For Ecol Manag 247:26–34CrossRefGoogle Scholar
  40. Maltamo M, Næsset E, Bollandsås OM, Gobakken T, Packalén P (2009) Non-parametric prediction of diameter distributions using airborne laser scanner data. Scand J Forest Res 24:541–553CrossRefGoogle Scholar
  41. McGaughey RJ (2015) FUSION/LDV: software for LIDAR data analysis and visualization. Version 3.50. USDA Forest Service – Pacific Northwest Research Station. Accessed 31 Jan 2016
  42. Montealegre AL, Lamelas MT, Tanase MA, de la Riva J (2014) Forest fire severity assessment using ALS data in a Mediterranean environment. Remote Sens 6:4240–4265CrossRefGoogle Scholar
  43. Næsset E, Gobakken T, Holmgren J, Hyyppä H, Hyyppä J, Maltamo M, Nilsson M, Olsson H, Persson Å, Söderman U (2004) Laser scanning of forest resources: the Nordic experience. Scand J Forest Res 19:482–499CrossRefGoogle Scholar
  44. Newby MJ (1980) The properties of moment estimators for the Weibull distribution based on the sample coefficient of variation. Technometrics 22:187–194Google Scholar
  45. Packalén P, Maltamo M (2008) Estimation of species-specific diameter distributions using airborne laser scanning and aerial photographs. Can J For Res 38:1750–1760CrossRefGoogle Scholar
  46. Parent S, Messier C (1995) Effets d’un gradient de lumière sur la croissance en hauteur et la morphologie de la cime du sapin baumier régénéré naturellement. Can J For Res 25:878–885CrossRefGoogle Scholar
  47. Parker RC, Matney TG (1999) Comparison of optical dendrometers for prediction of standing tree volume. For Sci 23:100–107Google Scholar
  48. Pascual C, Mauro F, Hernando A, Martín-Fernández S (2013) Inventory techniques in participatory forest management. In: Martínez-Falero E, Martín-Fernández S, García-Abril A (eds) Quantitative techniques in participatory forest management. CRC Press (Taylor & Francis Group), Boca Ratón, pp 53–134CrossRefGoogle Scholar
  49. Persson A, Holmgren J, Söderman U (2002) Detecting and measuring individual trees using an airborne laser scanner. Photogramm Eng Remote Sens 68:925–932Google Scholar
  50. Peuhkurinen J, Mehtätalo L, Maltamo M (2011) Comparing individual tree detection and the area-based statistical approach for the retrieval of forest stand characteristics using airborne laser scanning in Scots pine stands. Can J For Res 41:583–598CrossRefGoogle Scholar
  51. Poudel KP, Cao QV (2013) Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. For Sci 59:243–252Google Scholar
  52. R Core Team (2016) R: a language and environment for statistical computing. The Comprehensive R Archive Network (CRAN) http://wwwR-projectorg/ 01 Dec 2016
  53. Reif DM, Motsinger AA, McKinney BA, Crowe JE, Moore JH (2006) Feature selection using a random forests classifier for the integrated analysis of multiple data types. In: 2006 I.E. Symposium on Computational Intelligence and Bioinformatics and Computational Biology, Toronto, pp 1–8Google Scholar
  54. Reitberger J, Krzystek P, Stilla U (2008) Analysis of full waveform LIDAR data for the classification of deciduous and coniferous trees. Int J Remote Sens 29:1407–1431CrossRefGoogle Scholar
  55. Rodríguez R, Sánchez F, Gorgoso J, Castedo F, López C, Gadow KV (2002) Evaluating standard treatment options for Pinus radiata plantations in Galicia (north-western Spain). Forestry 75:273–284CrossRefGoogle Scholar
  56. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  57. Shang C, Treitz P, Caspersen J, Jones T (2017) Estimating stem diameter distributions in a management context for a tolerant hardwood forest using ALS height and intensity data. Can J Remote Sens 43:79–94CrossRefGoogle Scholar
  58. Siipilehto J, Mehtätalo L (2013) Parameter recovery vs. parameter prediction for the Weibull distribution validated for Scots pine stands in Finland. Silva Fenn 47:1–22CrossRefGoogle Scholar
  59. Therneau T, Atkinson B, Ripley B (2017). rpart: recursive partitioning and regression trees. R package version 4.1–11. Accessed 24 May 2017
  60. Thomas V, Oliver RD, Lim K, Woods M (2008) LiDAR and Weibull modeling of diameter and basal area. For Chron 84:866–875CrossRefGoogle Scholar
  61. Treitz P, Lim K, Woods M, Pitt D, Nesbitt D, Etheridge D (2012) LiDAR sampling density for forest resource inventories in Ontario, Canada. Remote Sens 4:830–848CrossRefGoogle Scholar
  62. Valbuena R, Maltamo M, Packalen P (2016) Classification of multi-layered forest development classes from low-density national airborne lidar datasets. Forestry 89:392–401CrossRefGoogle Scholar
  63. Vihervaara P, Mononen L, Auvinen AP, Virkkala R, Lu Y, Pippuri I, Packalen P, Valbuena R, Valkama J (2015) How to integrate remotely sensed data and biodiversity for ecosystem assessments at landscape scale. Landsc Ecol 30:501–516CrossRefGoogle Scholar
  64. Villikka M, Maltamo M, Packalén P, Vehmas M, Hyyppä J (2007) Alternatives for predicting tree-level stem volume of Norway spruce using airborne laser scanner data. Photogramm J Finland 20:33–42Google Scholar
  65. Villikka M, Packalen P, Maltamo M (2012) The suitability of leaf-off airborne laser scanning data in an area-based forest inventory of coniferous and deciduous trees. Silva Fenn 46:99–110CrossRefGoogle Scholar
  66. Wagner W, Hollaus M, Briese C, Ducic V (2008) 3D vegetation mapping using small-footprint full-waveform airborne laser scanners. Int J Remote Sens 29:1433–1452CrossRefGoogle Scholar
  67. White JC, Wulder MA, Varhola A, Vastaranta M, Coops NC, Cook BD, Pitt D, Woods M (2013) A best practices guide for generating forest inventory attributes from airbone laser scanning data using an area based approach (version 2.0). Information report Canadian Wood Fibre Center FI-X-010 2013Google Scholar
  68. Yu X, Hyyppä J, Vastaranta M, Holopainen M, Viitala R (2011) Predicting individual tree attributes from airborne laser point clouds based on the random forests technique. ISPRS-J Photogramm Remote Sens 66:28–37CrossRefGoogle Scholar
  69. Zaffalon M (2005) Credible classification for environmental problems. Environ Model Softw 20:1003–1012CrossRefGoogle Scholar
  70. Zellner A, Theil H (1962) Three-stage least squares: simultaneous estimation of simultaneous equations. Econometrica 30:54–78CrossRefGoogle Scholar

Copyright information

© INRA and Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  • Manuel Arias-Rodil
    • 1
    • 2
  • Ulises Diéguez-Aranda
    • 1
  • Juan Gabriel Álvarez-González
    • 1
  • César Pérez-Cruzado
    • 1
  • Fernando Castedo-Dorado
    • 3
  • Eduardo González-Ferreiro
    • 1
    • 4
    • 5
  1. 1.Unidade de Xestión Forestal Sostible (UXFS) – Departamento de Enxeñería Agroforestal, Escola Politécnica SuperiorUniversidade de Santiago de CompostelaLugoSpain
  2. 2.Centro de Estudos Florestais, Instituto Superior de AgronomiaUniversidade de LisboaLisbonPortugal
  3. 3.Departamento de Ingeniería y Ciencias Agrarias, Escuela Superior y Técnica de Ingeniería AgrariaUniversidad de LeónPonferradaSpain
  4. 4.Department of Forest Engineering, Resources and Management (FERM)Oregon State UniversityCorvallisUSA
  5. 5.Laboratory of Applications of Remote Sensing in Ecology (LARSE)US Forest Service - Pacific Northwest Research StationCorvallisUSA

Personalised recommendations