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Additive crown width models comprising nonlinear simultaneous equations for Prince Rupprecht larch (Larix principis-rupprechtii) in northern China

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Crown width models developed using nonlinear simultaneous equations with a two-step procedure provided the best performance and are recommended to predict the crown components and crown width of Prince Rupprecht larch.

Abstract

Crown width (CW) is defined as an average of two crown diameters at two cardinal directions: east–west and south–north, obtained from measurements of four crown radii (crown components) at four directions: east, west, south, and north. CW is one of the important tree variables in forest growth and yield modeling, and forest management. Reliable estimates of CW are central elements of forest management. However, the additivity of CW and crown components and their inherent correlations have not been addressed in existing CW models. In this study, two alternative procedures for nonlinear simultaneous equations (NSE) were used to develop CW models. The procedures included a disaggregation model structure with one- and two-step, proportional weighting systems, and two commonly used additivity methods, adjustment in proportion (AP) and ordinary least squares with separating regression (OLSSR). These methods were compared using data from a total of 3369 Prince Rupprecht larch (Larix principis-rupprechtii Mayr.) trees in 116 permanent sample plots in northern China. It was found that these methods effectively ensured that the sum of the crown components was equal to twice the total CW. The NSE accounted for the inherent correlations among the crown components and CW. The CW models developed using the NSE with the two-step procedure provided the best performance, followed by the models developed with AP and OLSSR. This methodology can be adapted to develop a system of CW models for other tree species.

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Acknowledgements

We thank the Fundamental Research Funds for the Central Non-profit Research Institution of CAF (Grant No. CAFYBB2016SZ003), the Forestry Public Welfare Scientific Research Project of China (Grant No. 201404417) and the Chinese National Natural Science Foundations (Grant Nos. 31470641, 31300534, and 31570628) for financial support. We also appreciate the valuable comments and the constructive suggestions from two anonymous referees and the Associate Editor.

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Authors and Affiliations

  1. Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing, 100091, People’s Republic of China

    Liyong Fu & Shouzheng Tang

  2. Center for Statistical Genetics, Pennsylvania State University, Loc T3436, Mailcode CH69, 500 University Drive, Hershey, PA, 17033, USA

    Liyong Fu

  3. Key Laboratory for Silviculture and Conservation of Ministry of Education, School of Forestry, Beijing Forestry University, Beijing, 100083, People’s Republic of China

    Wei Xiang

  4. Department of Geography and Environmental Resources, Southern Illinois University at Carbondale, Carbondale, IL, 62901, USA

    Guangxing Wang

  5. Shanxi Academy of Forestry Sciences, Taiyuan, 030012, Shanxi, People’s Republic of China

    Kaijie Hao

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  1. Liyong Fu
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  2. Wei Xiang
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  3. Guangxing Wang
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  4. Kaijie Hao
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  5. Shouzheng Tang
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Correspondence to Liyong Fu.

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Communicated by E. Priesack.

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Fu, L., Xiang, W., Wang, G. et al. Additive crown width models comprising nonlinear simultaneous equations for Prince Rupprecht larch (Larix principis-rupprechtii) in northern China. Trees 31, 1959–1971 (2017). https://doi.org/10.1007/s00468-017-1600-0

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