Developing a new model for predicting the diameter distribution of oak forests using an artificial neural network

Authors

  • Shisheng Long Central South University of Forestry and Technology
  • Siqi Zeng Faculty of Forestry, Central South University of Forestry and Technology, Changsha, Hunan
  • Guangxing Wang Southern Illinois University, Carbondale

DOI:

https://doi.org/10.15287/afr.2020.2060

Keywords:

diameter distribution, Artificial neural network, Oak secondary forest, model

Abstract

The parameters of the probability density function (PDF) may be estimated using the parameter prediction method (PPM) and the parameter recovery method (PRM). However, these methods can suffer from accuracy issues. We developed and evaluated the prediction accuracy of two PPMs (stepwise regression model and dummy variable model) and an artificial neural network (ANN) to predict diameter distribution using data collected from 188 oak forest plots. The results demonstrated that the Weibull distribution performed well in fitting the diameter distribution. Compared with the stepwise regression model, the PPM model with stand type as a dummy variable reduced the predictional errors in estimating the parameters b and c of the Weibull distribution, but the prediction accuracy of the diameter distribution showed no significant improvement. Compared with the two PPM models, the ANN model with diameter class (C), average diameter (D) and stand type (T) as input variables decreased the RRMSE by 2.9% and 4.33% in estimating diameter distribution, respectively. The satisfactory prediction accuracy and simple model structure indicated that an ANN worked well for the prediction of the diameter distribution with few requirements and high practicality.

References

Abbasi B., Rabelo L., Hosseinkouchack M., 2008. Estimating parameters of the three-parameter Weibull distribution using a neural network. European Journal of Industrial Engineering 2(4): 428-445. https://doi.org/10.1504/ejie.2008.018438Álvarez-González J.G., Schröder J., Rodrı́guez Soalleiro R., Ruı́z González A.D., 2002. Modelling the effect of thinnings on the diameter distribution of even-aged Maritime pine stands. Forest Ecology and Management 165(1-3): 57-65. https://doi.org/10.1016/S0378-1127(01)00650-8Ashraf M.I., Zhao Z.Y., Bourque C.P.A., MacLean D.A., Meng F.R., 2013. Integrating biophysical controls in forest growth and yield predictions with artificial intelligence technology. Canadian Journal of Forest Research 43(12):1162-1171. https://doi.org/10.1139/cjfr-2013-0090Bailey R.L., Dell T.R., 1973. Quantifying diameter distributions with the Weibull function. Forest Science 19(2): 97-104. https://doi.org/10.1093/forestscience/19.2.97Binoti D.H.B., Leite H.G., Nogueira G.S., Silva M.L.M., Garcia S.L.R., Cruz J.P., 2010. Three-parameter Weibull distribution in a diametric distribution model for thinning Eucaliptus stands. Revista Árvore 34(1):147-156. https://doi.org/10.1590/S0100-67622010000100016Borders B.E., 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. Forest Science 36(2): 413-424. https://doi.org/10.1093/forestscience/36.2.413Bowling E.H., Burkhart H.E., Burk T.E., Beck D.E., 1989. A stand-level multispecies growth model for Appalachian hardwoods. Canadian Journal of Forest Research 19(4): 405-412. https://doi.org/10.1139/x89-064Brooks J.R., Borders B.E., Bailey R.L., 1992. Predicting diameter distributions for site-prepared loblolly and slash pine plantations. Southern Journal of Applied Forestry 16(3):130-133. https://doi.org/10.1093/sjaf/16.3.130Cai S., Kang X., Zhang L.X., Gong Z., Qin L., Chen P., 2010. A model for tree diameter distribution in stands based on artificial neural network. International symposium on intelligence processing and trusted computing (IPCT). IEEE Computer Society 332e336. https://doi.org/10.1109/iptc.2010.44Cao Q.V., 2004. Predicting parameters of a Weibull function for modeling diameter distribution. Forest Science 50(5): 682-685. https://doi.org/10.1093/forestscience/50.5.682Carretero A.C., Torres Alvarez E., 2013. Modelling diameter distributions of Quercus suber L. stands in "Los Alcornocales" Natural Park (Cadiz-Malaga, Spain) by using the two parameter Weibull functions. Forest Systems 22(1): 15-24. https://doi.org/10.5424/fs/2013221-02142Chen D.S., Huang X.Z., Zhang S.G., Sun X.M., 2017. Biomass modeling of Larch (Larix spp.) Plantations in China based on the mixed model, dummy variable model, and bayesian hierarchical model. Forests 8(8): 268. https://doi.org/10.3390/f8080268Clutter J.L., Bennett F.A., 1965. Diameter distributions in old-field slash pine plantations (Report 13). Macon: Report of Georgia Forest Research Council.Clutter J.L., Harms W.R., Brister G.H., et al., 1984. Stand structure and yields of site-prepared loblolly pine plantations in the lower coastal plain of the Carolinas, Georgia, and north Florida. USDA Forest Service, Southeastern Forest Experiment Station, Asheville, General Technical Report SE-27.Coomes D A., Allen R.B., 2007. Mortality and tree-size distributions in natural mixed-age forests. Journal of Ecology 95(1): 27-40. https://doi.org/10.1111/j.1365-2745.2006.01179.xCorne S.A., Carver S.J., Kunin W.E., Lennon J.J., Van Hees W.W.S., 2004. Predicting forest attributes in southeast Alaska using artificial neural networks. Forest Science 50(2): 259-276. https://doi.org/10.1093/forestscience/50.2.259Dande P., Samant P., 2018. Acquaintance to artificial neural networks and use of artificial intelligence as a diagnostic tool for tuberculosis: a review. Tuberculosis 108: 1-9. https://doi.org/10.1016/j.tube.2017.09.006Diamantopoulou M.J., 2005. Artificial neural networks as an alternative tool in pine bark volume estimation. Computers and Electronics in Agriculture 48(3): 235-244. https://doi.org/10.1016/j.compag.2005.04.002Dorsett D., Webster J.T., 1983. Guidelines for variable selection problems when dummy variables are used. The American Statistician 37(4a): 337-339. https://doi.org/10.1080/00031305.1983.10483138García O., 1981. Simplified method of moments estimation for the Weibull distribution. New Zealand Journal of Forestry Science 11(3): 304-306.Goelz J.C.G., Leduc D.J., 2002. A model describing growth and development of longleaf pine plantations: consequences of observed stand structures of structure of the model. Gen. Tech. Rep. SRS–48. Asheville, NC: US Department of Agriculture, Forest Service, Southern Research Station. pp. 438-442.Gurney K., 1997. An introduction to neural networks. London: UCL Press. 234 p.Hafley W.L., Schreuder H.T., 1977. Statistical distributions for fitting diameter and height data in even-aged stands. Canadian Journal of Forest Research 7(3): 481-487. https://doi.org/10.1139/x77-062Hou Y.S., Chen X.L., Sun G.J., 2017. Oaks management. China Forestry Press: Beijing, China. 9 pHuang J.R., 2000. Studies on the suitability of Weibull distribution in Masson pine plantations. Guizhou Forestry Science and Technology 1: 7-13.Hyink D.M., Moser J.W., 1983. A generalized framework for projecting forest yield and stand structure using diameter distributions. Forest Science 29: 85-95. https://doi.org/10.1093/forestscience/29.1.85Jiang L.C., Brooks J.R., 2009. Predicting diameter distributions for young longleaf pine plantations in Southwest Georgia. Southern Journal of Applied Forestry 33(1): 25-28. https://doi.org/10.1093/sjaf/33.1.25Johnson N.L., 1949. Systems of frequency curves generated by methods of translation. Biometrica 36(1-2): 149-176. https://doi.org/10.2307/2332539Johnston M.H., Williamson T.B., Munson A.D., Ogden A.E., Moroni M.T., Parsons R, Price D.T., Stadt J.T., 2010. Climate change and forest management in Canada: impacts, adaptive capacity and adaptation options. A State of Knowledge report. Sustainable Forest Management Network, Edmonton. 54 p.Kayes I, Deb J.C., Comeau P., Das S., 2012. Comparing normal, lognormal and Weibull distributions for fitting diameter data from Akashmoni plantations in the north-eastern region of Bangladesh. Southern Forests 74(3): 175-181. https://doi.org/10.2989/20702620.2012.717409Kilkki P., Maltamo M., Mykkanen R., et al., 1989. Use of the Weibull function in estimating the basal area DBH-distribution. Silva Fennica 23(4): 311-318. https://doi.org/10.14214/sf.a15550Leak W.B., 1964. An expression of diameter distribution for unbalanced, uneven-aged stands and forests. Forest Science 10(1): 39-50. https://doi.org/10.1093/forestscience/10.1.39Lee F.Y., 1974. On the dummy variable technique and covariance analysis in testing equality among sets of coefficients in linear regressions: An expository note. The Journal of Financial and Quantitative Analysis 9(3): 491-495. https://doi.org/10.2307/2329876Lee Y.J., Coble D.W., 2006. A new diameter distribution model for unmanaged loblolly pine plantations in East Texas. Southern Journal of Applied Forestry 30(1): 13-20. https://doi.org/10.1007/s10035-008-0092-4Li W.Y., Wang B., Li G.C., 2001. Ecological benefits and economic values of Oaks species and countermeasures for their resource protection. For. Sci. Techol 8: 13-15. https://doi.org/10.13456/j.cnki.lykt.2001.08.004Lima R.A.F. de, Batista J.L.F., Prado P.I., 2015. Modeling Tree Diameter Distributions in Natural Forests: An Evaluation of 10 Statistical Models. Forest Science 61(2): 320-327. https://doi.org/10.5849/forsci.14-070Lima R.B. de, Bufalino L., Alves F.T., da Silva J.A.A., Ferreira R.L.C., 2017. Diameter distribution in a Brazilian tropical dry forest domain: predictions for the stand and species. Anais Da Academai Brasileira De Ciencias 89(2): 1189-1203.Lindsay S.R., Wood G.R., Woollons R.C., 1996. Stand table modeling through the Weibull distribution and usage of skewness information. For. Ecol. Manage 81: 19-23. https://doi.org/10.1016/0378-1127(95)03669-5Little S.N., 1983. Weibull diameter distributions for mixed stands of western conifers. Canadian Journal of Forest Research 13 (1): 85-88. https://doi.org/10.1139/x83-012McCrohan K.F., Harvey J.W., 1989. A comparison of dummy variable versus traditional multiple discriminant function analysis. Health Marketing Quarterly 6(4): 147-157. https://doi.org/10.1300/J026v06n04_11Meyer H.A., 1952. Structure, growth, and drain in balanced uneven-aged forests. Journal of Forestry 50(2): 85-92. https://doi.org/10.1093/jof/50.2.85Miranda R., Fiorentin L., Péllico Netto S., Juvanhol R., Corte A.D., 2018. Prediction system for diameter distribution and wood production of Eucalyptus. Floresta e Ambiente 25(3): e20160548. https://doi.org/10.1590/2179-8087.054816Mønness E.N., 1982. Diameter distributions and height curves in even-aged stands of Pinus sylvestris L. Reports of the Norwegian Forest Research Institute 36(15): 43 p.Nelson T.C., 1964. Diameter distribution and growth of loblolly pine. Forest Science 10(1): 105-114. https://doi.org/10.1093/forestscience/10.1.105Nixon K.C., 1993. Infrageneric classification of Quercus (Fagaceae) and typification of sectional names. Annals of Forest Science 36: 25-34. https://doi.org/10.1051/forest:19930701Oettel J., Lapin K., Kindermann G., Steiner H., Schweinzer K.M., Frank G., Essl F., 2020. Patterns and drivers of deadwood volume and composition in different forest types of the Austrian natural forest reserves. Forest Ecology and Management 463: 118016. https://doi.org/10.1016/j.foreco.2020.118016Özçelik R., Diamantopoulou M.J., Crecente-Campo F., Eler U., 2013. Estimating Crimean juniper tree height using nonlinear regression and artificial neural network models. Forest Ecology and Management 306: 52-60. https://doi.org/10.1016/j.foreco.2013.06.009Perea R., López-Sánchez A., Dirzo R., 2017. Differential tree recruitment in California oak savannas: Are evergreen oaks replacing deciduous oaks? Forest Ecology and Management 399: 1-8. https://doi.org/10.1016/j.foreco.2017.05.018Pérez-López E., Santiago-García W., Quiñonez-Barraza G., Rodríguez-Ortiz G., Santiago-García E., Ruiz-Aquino F. 2019. Estimation of diameter distributions for Pinus patula with the Weibull function. Madera y Bosques 25(3): e2531626. http://doi.org/10.21829/myb.2019.2531626Podlaski R., Zasada M., 2008. Comparison of selected statistical distributions for modelling the diameter distributions in near-natural Abies-Fagus forests in the Świętokrzyski National Park (Poland). European Journal of Forest Research 127(6): 455-463. https://doi.org/10.1007/s10342-008-0229-3Pogoda P., Ochał W., Orzeł S., 2019. Modeling diameter distribution of black alder (Alnus glutinosa (L.) Gaertn.) stands in Poland. Forests 10(5): 412. https://doi.org/10.3390/f10050412Quiñonez-Barraza G., De los Santos Posadas H.M., Cruz-Cobos F., Martinez A.V., Perez G.Á., Valverde G.R., 2015. Dynamic modeling for diameter distribution on Pinus mixed stands in Durango, Mexico. Madera y Bosques 21(2): 59-71.Souza Retslaff F.A. de, Figueiredo Filho A., Dias A.N., Bernett L.G., Figura M.A., 2012. Growth and yield prognosis in diameter classes for thinning Eucalyptus grandis stands in Brazil south. Revista Árvore 36(4): 719-732. https://doi.org/10.1590/S0100-67622012000400013Samarasinghe S., 2006. Neural networks for applied sciences and engineering. Florida, USA: Taylor and Francis Inc. 608 p.Schreuder H.T., Swank W.T., 1974. Coniferous stands characterized by the Weibull distribution. Canadian Journal of Forest Research 4: 518-523. https://doi.org/10.1139/x74-075Schütz J.P., Rosset C., 2020. Performances of different methods of estimating the diameter distribution based on simple stand structure variables in monospecific regular temperate European forests. Annals of Forest Science 77(47): 1-11. https://doi.org/10.1007/s13595-020-00951-3Scrinzi G., Marzullo L., Galvagni D., 2007. Development of a neural network model to update forest distribution data for managed alpine stands. Ecological Modelling 206(3-4): 331-346. https://doi.org/10.1016/j.ecolmodel.2007.04.001Siipilehto J., 1999. Improving the accuracy of predicted basal-area diameter distribution in advanced stands by determining stem number. Silva Fennica 33(2): 281-301. https://doi.org/10.14214/sf.650Smalley G.W., Bailey R.L., 1974. Yield tables and stand structure for loblolly pine plantations in Tennessee, Alabama, and Georgia highlands. USDA For. Serv. Res: Paper SO-96. 81 p.Sun S.C., Cao Q.V., Cao T.J., 2019. Characterizing diameter distributions for uneven-aged pine-oak mixed forests in the Qinling mountains of China. Forests 10(7):596. https://doi.org/10.3390/f10070596Wang M., Borders B.E., Zhao D., 2008. An empirical comparison of two subject-specific approaches to dominant heights modeling-the dummy variable method and the mixed model method. Forest Ecology and Management 255(7): 2659-2669. https://doi.org/10.1016/j.foreco.2008.01.030Wang W.W., Chen X.Y., Zeng W.S., Wang J.J., Meng J.H., 2019. Development of a mixed-effects individual-tree basal area increment model for Oaks (Quercus spp.) considering forest structural diversity. Forests 10(6): 474. https://doi.org/10.3390/f10060474Weibull W., 1951. A statistical distribution function of wide applicability. J. Appl. Mech 18: 293-297. https://doi.org/10.1093/qjmam/6.4.453Wekesa J.S., Luan Y, Chen M, Meng J., 2019. A hybrid prediction method for plant lncRNA-protein interaction. Cells 8(6): 521. https://doi.org/10.3390/cells8060521Zankis S.H., 1979. A simulation study of some simple estimations for the 3-parameter Weibull distribution. Journal of Statistical Computation and Simulation 9: 101-116. https://doi.org/10.1080/00949657908810302Zhang L., Ye Y., Zeng W., Chiaradia A., 2019. A systematic measurement of street quality through multi-sourced urban data: a human-oriented analysis. Int J Environ Res Public Health 16(10): 1782. https://doi.org/10.3390/ijerph16101782

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2021-12-25

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