Modeling height–diameter relationship for Populus euphratica in Shoosh riparian forests, Khoozestan province

Document Type : Complete scientific research article

Authors

1 3Assistant professor, Range and Watershed Management Department., Faculty of Natural Sciences, Behbahan Khatam Alanbia University of technology, I.R. of Iran.

2 Associate professor, Department of Forestry, Faculty of Natural Resources and the Environment, Behbahan Khatam Al-Anbia University of Technology, Iran.

Abstract

Background and objectives: Accurate in situ measurement of DBH is easy and cost-effective but, height measurement is labor-intensive, time-consuming and expensive. Understanding its height–diameter relationship is essential for developing growth, biomass production and carbon storage prediction models to be applied in the current forest management projects. The existence of a strong relationship between the diameter and the height of trees is considered as a useful index in forest management and it can be described with mathematical models. Considering that non-linear models are flexible, interpretable and strong, therefore some of the most important models were used in this study.
Materials and methods: In this research, 21 widely used candidate nonlinear and one simple linear models were fitted to tree height and diameter at breast height (DBH) data for Populus euphratica Oliv. within a 100 square meter plots at Shoosh area of Khuzestan province. Data from 1163 trees were used and split randomly into two sets: 80 % of the data were used to estimate model parameters (model fitting), and the remaining data (20 %) were reserved for model validation. All model performances were evaluated and compared by means of model performance criteria such as t-statistics of model parameters, root mean square error percentage (RMSE%), mean absolute error percentage (MAE%), mean bias error percentage (ME%), Akaike’s information criterion (AIC) and Bayesian information criterion (BIC).
Results: The parameters of 8 models were not significant at a level of 5%. RMSE, MAE, Bias, AIC and BIC values for M12 model were obtained: 8.98%, 6.78%, -0.0010%, 1451.82 and 1469.73, respectively. The same values were obtained for M21 model: 9.15%, 6.94%, 0.0005%, 1476.95 and 1494.86 respectively. The predicted and actual height values in these two models were not significantly different at a level of 5%. The results of the paired sample t test showed that the nonlinear models M21 and M12 have predicted the height of Populus euophratica trees with appropriate accuracy. Two models (Prodan1 with the name of M12) and (Prodan2 with the name of M21) were selected as the best models based on the ranking of all model performance evaluation criteria in fit and validity data.
Conclusion: The majority of two-parameter models and some three-parameter models showed a significant fit with the data. However, in terms of all performance evaluation criteria, two three-parameter models were chosen as the best models. According to the results of this study and the wide range of non-linear two and three parameter models, mixed models that include one or two covariates in the modeling in addition to the main variables, more research is needed in larger geographical areas, wider sites and stands with different structures are done.

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 1.Eusemann, P., Petzold, A., Thevs, N., and Schnittler, M. 2013. Growth patterns and genetic structure of Populus euphratica Oliv. (Salicaceae) forests in NW China: implications for conservation and management. Forest Ecology and Management. 297: 27-36.
2.Basiri, R., Moradi, M., Kiani, B., and Maasumi Babaarabi, M. 2018. Evaluation of distance methods for estimating population density in Populus euphratica Olivier natural stands (case study: Maroon riparian forests, Iran). J. of forest science. 64: 5. 230-244.
3.Kuba, M., Aishan, T., Cyffka, B., and Halik, U. 2013. Analysis of connections between soil moisture, groundwater level, and vegetation vitality along two transects at the lower reaches of the Tarim River, Northwest China. Geo-Oko. 34: 103-128.
4.Molto, Q., He´rault, B., Boreux, J.J., Daullet, M., Rousteau, A., and Rossi, V. 2014. Predicting tree heights for biomass estimates in tropical forests: a test from French Guyana. Biogeosciences. 11: 3121-3130.
5.Wang, Y.F., Yue, T.X., Du, Z.P., and Zhao, M.W. 2015. Improving the accuracy of the height–diameter equation using the classified factors method. Environmental Earth Sciences. 74: 8. 6471-6480.
6.Schmidt, M., Kiviste, A., and Gadow, V.K. 2011. A spatially explicit height–diameter model for Scots pine in Estonia. European J. of Forestry Research. 130: 2. 303-315.
7.Nascimento, R.G.M., Vanclay, J.K., Figueiredo Filho., A., Machado, S.DO A., Ruschel, A.R., Hiramatsu, N.A., and Freitas, L.J.M.de. 2020. The tree height estimated by non-power models on volumetric models provides reliable predictions of wood volume: the Amazon species height modeling issue. Trees, Forests, and People. 2: art.100028, DOI: https://doi.org/10.1016/j.tfp.2020.100028.
8.Bolat, F., Urker, O., and Günlü, A. 2022. Nonlinear height-diameter models for Hungarian oak (Quercus frainetto Ten.) in Dumanlı Forest Planning Unit, Anakkale/Turkey. Austrian J. of forest science. 139: 199-220.
9.Vargas-Larreta, B., Dorado, F.C. Lvarez Gonzalez, G.J. Barrio-Anta, M., and Cruz Cobos, F. 2009. A generalized height-diameter model with random coefficients for uneven-aged stands in El Salto, Durango (Mexico). Forestry. 82: 445-462.
10.Aishan, T., Halik, U., Betz, F., Gartner, P., and Cyffka, B. 2016. Modeling height–diameter relationship for Populus euphratica in the Tarim riparian forest ecosystem, Northwest China. J. of forestry research. 27: 4. 889-900.
11.Hassanzad Navroodi, I., Alavi, S.J., Ahmadi, M.K., and Radkarimi, M. 2016. Comparison of different non-linear models for prediction of the relationship between diameter and height of velvet maple trees in natural forests (Case study: Asalem Forests, Iran). J. of Forest Science. 62: 2. 65-71.
12.Mohammadi, J., and Shataee, Sh. 2017. Study of different height-diameter models for hornbeam (Carpinus
betulus
L.) in uneven-aged stands of Shastkalateh forest of Gorgan. Iranian J. of Forest and Poplar Research. 24: 4. 700-712. (In Persian)
13.Wang, T.Y., and Lam, T.Y. 2021. Modeling the height-diameter relationship of fifteen tree species planted on reclaimed agricultural lands with random species effects. Tropical Forestry. 1053: 1-5 doi:10.1088/1755-1315/1053/1/012013.
14.Hamidi, S.K., Fallah, A., Bayat, M., and Hosseini Yekani, S.A. 2021. Investigating the diameter and height models of beech trees in uneven age forest of northern Iran (Case study: Forest Farim). Ecology of Iranian Forests. 9: 17. 30-40.
15.Imani, F., Moradi, M., and Basiri, R. 2018. Biological diversity of vegetation in the dunes after two decades of consolidation activities and afforestation (Case study: Region Magran Susa). J. of plant research (Iranian J. of Biology). 31: 1. 12-23.
16.Zobeiri, M. 2019. Forest inventory measurement of trees and forest. Tehran Univ. Press, 424p. (In Persian)
17.Clarkson, B.R., Sorrell, B.K., Reeves, P.N., Champion, P.D., Partridge, T.R., and Clarkson, B.D. 2004. Handbook for monitoring wetland condition coordinated monitoring of New Zealand wetlands. A Ministry for the Environment Sustainable Management Fund Project (5105). 73p.
18.Han, L., Wang, H., Zhou, Z., and Li, Z. 2008. Spatial distribution pattern and dynamics of the primary population in a natural Populus euphratica forest in Tarim Basin, Xinjiang, china. Frontiers of Forestry in China. 3: 4.  456-461.
19.Subedi, M.R., Oli, B.N., Shrestha, S., and Chhin, S. 2018. Height-diameter modeling of Cinnamomum tamala grown in natural forest in mid-hill of Nepal. International J. of Forestry Research. https://doi.org/10.1155/ 2018/ 6583948.
20.Alijani, V., Namiranian, M., Feghhi, J., Bozorg-Haddad, O., and Etemad, V. 2020. Investigation of height-diameter models in different development stages of unmanaged Beech forest (Case study: educational and research forest of Kheirud). J. Environmental Science Technology, 21: 12. 125-134.
21.Naslund, M. 1937. Skogsf¨orsoksanstaltens gallringsf¨ors¨ok i tallskog (Forest research intitute’s thinning experiments in Scots pine forests). Meddelanden frstatens skogsf¨ors¨oksanstalt. 29: 1-169.
22.Peschel, W. 1938. Mathematical methods for growth studies of trees and forest stands and the results of their application. Tharandter Forstliches Jahrbuch. 89: 169-247.
23.Loetsch, F., Haller, K.E., and Zöhrer, F. 1973. Forest Inventory. BLV Verlagsgesellschaft, Munich, 905p.
24.Curtis, R.O. 1967. Height-diameter-age equations for second-growth Douglas-fir. Forest Science. 13: 365-375.
25.Schumacher, F.X. 1939. A new growth curve and its application to timber yield studies. J. of Forestry. 37: 819-820.
26.Schreuder, H.T., Hafley, W.L., and Bannett, F.A. 1979. Yield prediction for unthinned natural slash pine stands. Forest Science. 25: 25-30.
27.Huang, S., Titus, S.J., and Wiens, D.P. 1992. Comparison of nonlinear height-diameter functions for major Alberta tree species. Canadian J. of Forest Research. 22: 9. 1297-1304. https://doi.org/10.1139/x92-172.
28.Mehtatalo, L. 2005. Height-diameter models for Scots pine and birch in Finland. Silva Fennica. 39: 1. 55-66.
29.Wykoff, W.R., Crookston, N.L., and Stage A.R. 1982. User’s guide to the stand prognosis model. General technical report INT-133. Ogden, Intermountain Forest, and Range Experiment Station. USDA Forest Service. 112p.
30.Sharma, R.P. 2011. Allometric models for total-tree and componenttree biomass of Alnus nepalensis D. Don in Nepal. Indian Forester. 137: 1386-1390.
31.Watts, S.B. 1983. Forestry handbook for British Columbia. 4th Ed. Vancouver, University of British Columbia: 773p.
32.Huang, S., Price, D., and Titus, S.J. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management. 129: 1-3. 125-141.
33.Strand, L. 1959. The accuracy of some methods for estimating volume and increment on sample plots.Medd. norske Skogfors. 15: 4. 284-392. In Norwegian with English summary.
34.Sibbesen, E. 1981. Some new equations to describe phosphate sorption by soils. European J. of Soil Science, 32: 67-74.
35.Ratkowsky, D.A. 1990. Handbook of nonlinear regression models, M. Dekker, New York, 241p.
36.Flewelling, J.W., and De Jong, R. 1994. Considerations in simultaneous curve fitting for repeated height-diameter measurements. Canadian J. of Forest Research. 24: 1408-1414.
37.Weibull, W. 1951. A statistical distribution function of wide applicability. J. of Applied Mechanics. 18: 3. 293-297.
38.Ratkowsky, D.A., and Reedy, T.J. 1986. Choosing near-linear parameters in the four-parameter logistic model for radio ligand and related assays. Biometrics. 42: 575-582.
39.Richards, F.J. 1959. A flexible growth function for empirical use. J. of Experimental Botany. 10: 29. 290-300.
40.Prodan, M. 1968. Forest biometrics. Oxford, Pergamon Press: 447p.
41.Burnham, K.P., and Anderson, D.R. 2002. Model selection and multimodel inference: A practical information-theoretic approach, Springer, New York, NY, USA, 2nd edition. 488p.
42.Saud, P., Lynch, T., and Guldin, J. 2016. Using quadratic mean diameter and relative spacing index to enhance height–diameter, and crown ratio models fitted to longitudinal data. Forestry International J. of Forest Research. 89: 215-229.
43.Aertsen, W., Kint, V., Orshoven, J.V., Ozkan, K., and Muys, B. 2010. Comparison and ranking of different modeling techniques for prediction of site index in Mediterranean mountain forests. Ecological modeling. 221: 8. 1119-1130.
44.Vanclay, J.K., and Skovsgaard, J.P. 1997. Evaluating forest growth models. Ecological Modelling. 98: 1. 1-12.
45.Grothendieck, G. 2022. nls2: Non- linear regression with brute force. (Version 0.3-3) https://github.com/ ggrothendieck/nls2.
46.R Development Core Team. 2013. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. ISBN 3-900051-07-0, URL http://www.R-project.org.
47.Alemi, A., Oladi, J., Fallah, A., and Maghsoudi, Y. 2018. Evaluating of height-diameter nonlinear models for Alnus specie in Hyrcanes forest (Case study: Golestan Rezaeian forest). J. of Natural Ecosistems of Iran. 9: 2. 1-12. (In Persian)
48.Meng, S.X., Huang, S., Lieffers, V.J., Nunifu, T., and Yang, Y. 2008. Wind speed and crown class influence the height-diameter relationship of lodgepole pine: Nonlinear mixed effects modeling. Forest Ecology and Management. 256: 4. 570-577.
49.Mehtatalo, L., de-Miguel, S., and Gregoire, T. 2015. Modeling height-diameter curves for Prediction. Canadian J. of Forest Research. 45: 7. 826-837.
50.Ahmadi, K., Alavi, S.J., and Aertsen, W. 2014. Comparison of non-linear height and diameter functions for oriental beech (Fagus orientalis Lipsky.) in a mixed and uneven-aged Caspian forest (Case study: Tarbiat Modares University forest research station). Iranian J. of Forest. 6: 1. 11-22.
51.Temesgen, H., LeMay, V., and Mitchell, S.J. 2005. Tree crown ratio models for multi-species and multi-layered stands of southeastern British Columbia. The Forestry Chronicle. 81: 1. 133-141.
52.Esteban, G.G., Ulises, D.A., Fernando, C.D., and Felipe, C.C. 2014. A comparison of model forms for the development of height–diameter relationships in even-aged stands. J. of forestry research. 60: 3. 560-568.