Richards函数拟合多形地位指数曲线模型的研究

本文以Richards函数为基本模型,讨论了不相交多形地位指数曲线的拟合。解决了标准年龄时树高与指数值不一致的问题;给出了根据树高和年龄求指数的实用迭代公式;探讨了标准年龄不同,指数曲线形状是否会变化的问题;最后讨论了本文所用的杉木多形地位指数曲线模型的一些特性。     

Richards函数拟合多形地位指数曲线模型的研究

<正> 当样本资料收集后,要建立一个好的地位指数曲线模型,关键在于选择好数学模型和拟合方法。就建立树高生长过程一类反映生物生长规律的模型而言,一个好的数学模型,不仅要求对样本资料应具有灵活的切合性能,最小的拟合残差和尽可能少的参数,而且其参数应具有生物学意义,从这些基本要求出发,对Richards函数在建立多形地位指数曲线模型中的应用进行了研究,并根据改进后的8参数Richards函数,分别建立了杉木、马尾松多形     

木麻黄工业原料林多形地位指数模型的研究

以木麻黄工业原料林为研究对象,采用Richards非线性生长方程,通过参数置换法,建立了木麻黄多形地位指数模型。结果表明:(1) Richards方程的拟合精度较高,经检验,该模型优势高的理论值和实际值差异不显著,适应性较好,能对木麻黄的优势高生长进行正确预估;(2)研究地区木麻黄工业原料林的基准年龄可确定为3 a;(3)对多形地位指数模型的拐点进行分析,表明该模型能够客观地反映不同立地优势高的生长规律;(4)为推进国内木麻黄数表、模型的研究与应用提供了参考,为木麻黄林分立地质量评价,经营管理提供科技支撑。     

臭松天然次生林地位指数模型研究

以吉林省汪清林业局臭松天然次生林为研究对象,利用172块小班调查数据、178块复位样地数据及96株解析木数据,根据臭松优势木树高生长现状,分别拟合得到最优导向曲线和多形地位指数模型。分别采用标准差法、指数级差法及落点检验法对2种地位指数模型进行精度检验,结果如下:标准差法显示两种地位指数模型精度都较高;指数级差法表明单形模型跳级的情况都高于多形,无跳级次数低于多形;落点检验法发现单形地位指数曲线簇中,散点溢出曲线簇范围的散点占总散点数的10.7%,而多形地位指数曲线簇中,散点溢出曲线簇范围的散点占总数的2.7%。因而,立地类型多形地位指数模型更适宜于编制吉林汪青臭松天然次生林地位指数表。     

湿地松多形与单形地位指数曲线模型的对比研究

选用吉安地区湿地松栽培区10个县(市)的385株具有代表性的平均优势木.以理查德(Richards)函数为基本模型.采用标准差法、变动系数法、相对树高法、比例法,差分方程法和多形曲线等展开成地位指数曲线。通过拟合精度检验.结果表明:由于不同地位指数优势木树高的生长过程曲线簇存在着多形特性.多形模型的预估精度明显高于单形模型。因此.以建立多形模型为宜。     

湿地松多形地位指数曲线模型的研究

根据大量具有代表性的湿地松平均优势木资料，讨论了湿地松地位指数曲线的标准年龄。选用改进了的８参数Ｃｈａｐｍａｎ－Ｒｉｃｈａｒｄｓ函数，用Ｍａｒｑｕａｒｄｔ迭代方法，建立了以地位指数和年龄为解释变量的湿地松多形不相交地位指数曲线模型，由模型直接求出各指数的指数曲线。     

杉木人工林多形地位指数曲线模型的研究

本文根据大量有代表性的杉木人工林单株优势木，选用改进的８参数Ｃｈａｐｍａｎ－Ｒｉｃｈａｒｄｓ函数，用Ｍａｒｑｕａｄｔ迭代法，建立了以地位指数和年龄为解释变量的杉木人工林多形不相交地位指数曲线模型，由模型直接求出各指数级的指数曲线。     

用人工神经网络构建多形地位指数模型

以马尾松人工林132株优势木树干解析数据为训练样本,用145块标准地优势木平均高数据为检验样本,把林分年龄和地位指数或优势木平均高作为输入变量,将优势木平均高或地位指数作为输出变量,通过构建人工神经网络逆模型的途径,分别建立了多形地位指数曲线式和计算式模型。结果表明,多形地位指数曲线式的总体拟合精度为99.64％,总体预测精度达96％以上,比传统技术构建的多形地位指数模型能较真实地模拟各地位级的多形曲线;多形地位指数计算式的总体拟合精度为98.81％,用于计算地位指数,省去用迭代法计算地位指数的工作量。基于BP神经网络模型多形地位指数模型,对马尾松人工林地位指数测定提供指导作用,可为森林立地质量评价提供理论依据。     

福建省阔叶树多形地位(级)指数曲线模型研究

以福建省范围内收集到的1 907套阔叶树样木为建模数据,选择Korf生长方程,应用改进单纯形法,构建阔叶树多形地位(级)指数曲线模型。研究表明:所建立的阔叶树人工林、天然林多形地位(级)指数曲线模型误差较小、精度较高,可在林业生产活动中推广应用。     

马尾松人工林多形地位指数曲线模型的建模方法

利用马尾松人工林优势木树干解析材料,选择合适的生长方程构建了能把地位指数写成年龄和优势高显式表达式的多形地位指数曲线模型,并用遗传算法对其参数作优化求解.误差分析表明：所建立的多形地位指数曲线模型误差小,精度高,便于推广应用.     

Development of site index curves for Pinus kesiya in the Philippines

This study was conducted to develop a height–age growth model and site index curves for site quality evaluation of old secondary-growth stands of Pinus kesiya in the northern Philippines. The Chapman-Richards growth function was used in the guide curve method to generate anamorphic site index curves for this species. In order to evaluate the developed model, coefficient of determination (R ² ), root mean square error (RMSE), bias (ē), absolute mean difference (AMD) and mean percent bias (MPB) were used as statistical criteria. The Chapman-Richards model explained about 96.84% of the total variation of the dominant height. The value of ē was ?0.004 m, AMD was 2.566 m, MPB was 3.88% and RMSE was 3.331. The site index curves developed as a result of this study are significant for forest managers in predicting the growth patterns and classification of site productivities for Pinus kesiya stands.     

Mixed-effects modeling for tree height prediction models of Oriental beech in the Hyrcanian forests

Height–diameter relationships are essential elements of forest assessment and modeling efforts.In this work,two linear and eighteen nonlinear height–diameter equations were evaluated to find a local model for Oriental beech(Fagus orientalis Lipsky) in the Hyrcanian Forest in Iran.The predictive performance of these models was first assessed by different evaluation criteria: adjusted R~2(R~2_(adj)),root mean square error(RMSE),relative RMSE(%RMSE),bias,and relative bias(%bias) criteria.The best model was selected for use as the base mixed-effects model.Random parameters for test plots were estimated with different tree selection options.Results show that the Chapman–Richards model had better predictive ability in terms of adj R~2(0.81),RMSE(3.7 m),%RMSE(12.9),bias(0.8),%Bias(2.79) than the other models.Furthermore,the calibration response,based on a selection of four trees from the sample plots,resulted in a reduction percentage for bias and RMSE of about 1.6–2.7%.Our results indicate that the calibrated model produced the most accurate results.     

Modelling dominant height growth in plantations of Pseudotsuga menziesii (Mirb.) Franco in Spain

A model for predicting dominant height growth and site index of Pseudotsuga menziesii (Mirb.) Franco in Spain was constructed. Data from stem analysis of 117 site trees were used. Four dynamic equations using the algebraic difference approach (ADA) and its generalisation (GADA), which have provided good results in previous studies, were evaluated. The model parameters were estimated with the base?age?invariant method of dummy variables, which considers both global (common to all sites) and local parameters (specific to each site). A GADA equation based on the Bertalanffy–Richards base model yielded the best results. The model provides polymorphic curves with multiple asymptotes. A base age of 20 years is proposed to reference site index.     

Modeling top height growth of red alder plantations

Height growth equations for dominant trees are needed for growth and yield projections, to determine appropriate silvicultural regimes, and to estimate site index. Red alder [Alnus rubra Bong.] is a fast-growing hardwood species that is widely planted in the Pacific Northwest, USA. However, red alder dominant height growth equations used currently have been determined using stem analysis trees from natural stands rather than repeated measurements of stand-level top height from plantations, which may cause them to be biased. A regional dataset of red alder plantations was complied and used to construct a dynamic base-age invariant top height growth equation. Ten anamorphic and polymorphic Generalized Algebraic Difference Approach (GADA) forms were fit using the forward difference approach. The Chapman–Richards anamorphic and Schumacher anamorphic model forms were the only ones with statistically significant parameters that yielded biologically reasonable predictions across a full range of the available data. The Schumacher model form performed better on three independent datasets and, therefore, was selected as the final model. The resulting top height growth equations differed appreciably from tree-level dominant height growth equations developed using data from natural stands, particularly at the younger ages and on lower site indices. Both the rate and shape parameters of the Schumacher function were not influenced by initial planting density. However, this analysis indicates that the asymptote, which is related to site index, may be reduced for plantations with initial planting density below 500 trees ha⁻¹. The final equation can be used for predictions of top height (and thus) site index for red alder plantations across a range of different growing conditions.     

Application of theoretical growth functions for Mongolian oak (Qurcus mongolica)

Four alternative functions are used for fitting tree height and diameter growth models for mongolian oak. (Quercus mongolica Fisch. et Turcz.). The data set includes 1250 random trees and 755 dominant trees coming from 510 temporary plots. The resultsshow that the Richards function is the best model for predicting height. diameter at breast height (DBH) and dominant height from age. The average growth curve of dominant height is used as a guide curve for the construction of a site index table which is partially validated using an independent data set. The Mitscherlich function is the best model for estimating height and dominant height from DBH. (Responsible Editor: Chai Ruihai)     

基准年龄立地质量评价的影响分析

Taking Chinese fir as researched object and Richards function as basic model,the models of single site index and polymorphic site index were established to analyze the affect of stand standard age on the result of site quality evaluation with the ways of ANOVA, multicompare,curve tourning point and change of dominant tree height between site classes. The result showed that with the site class getting higher,curve tourning point volue getting lower,it was impossible to define the standard age before stand growth reached steady. If stand standard age is too small, it would lead to a higher site calss in polymorphic site index evaluation; The difference was notable among stand dominant height from difference standard age,if standard age is too small, it would lead to a lower site class in single site index evalution. Taking the age steady-grown stand as standard age would not make notable affect on the result of site quality evaluation.     

Litterfall in relation to stand parameters and climatic factors in Pinus brutia forests in Turkey

With this study we investigated the effective factors on annual amount of total litterfall and needle litterfall in Pinus brutia forests and estimated them with a regression model based on certain stand parameters. We studied 27 permanent plots representing different stand structure and environmental conditions in South-Western Turkey. Litterfall was collected in three month intervals corresponding to each of four seasons for a three-year period. We found a significant relationship between litterfall and stand properties such as crown closure (%), basal area (m²?ha^?1), stand stem volume (m³?ha^?1), above-ground biomass (t?ha^?1), mean annual volume increment (m³?ha^?1?yr^?1) and site index (T?=?75). Similar relationships also hold true between litterfall and each of such climatic factors as seasonal mean temperature (°C), relative humidity (%) and temperature/precipitation ratio (dimensionless). The mean annual litterfall considerably varied depending on stand characteristics and certain environmental factors. Both needle litterfall and total litterfall may be predicted for long term by regression models using certain stand parameters. Models developed for litterfall of P. brutia forests in this study may be used for national C inventory in Turkey.     

Construction of site index equations for Pinus sylvestris L. using permanent plot data in Sweden

Three general methods for construction of site index equations (the guide curve method, the parameter prediction method and the difference equation method) and 13 growth functions were tested on data from permanent plots in 156 Scots pine (Pinus sylvestris) stands. Most stands were of cultivated origin with known year of establishment. Data consisted of measured top height and total age at the start and at the end of observation periods of different lengths. Functions and construction methods were compared with respect to residual variation (root mean square error (RMSE), meter) from original data. The guide curve method gave RMSE ∼ 0.56 while the difference equation method with the anamorphic formulation gave RMSE ∼ 0.46, with appropriate functions. The difference equation method gave a higher RMSE with polymorphic than with anamorphic formulation. The special formulation of the Hossfeld function for the difference equation method proposed by Cieszewski and Bella [Cieszewski, C.J., Bella, I.E., 1989. Polymorphic height and site index curves for lodgepole pine in Alberta. Can. J. Res. 19, 1151–1160] gave a simple and straigtforward, polymorphic solution with RMSE = 0.40. The parameter prediction method, in combination with the deviation method proposed by Tveite [Tveite, B., 1969. A method for construction of site-index curves. Meddelelser fra Det Norske skogforsoksvesen 27, 134–159] and a four-parameter growth model, gave the lowest RMSE, but this solution had patterns of overfitting. Parameter prediction with the Mitscherlich function gave an equation with almost the same accuracy as the polymorphic difference equation with the Hossfeld function. These functions deviate much at higher ages, but too few observations in old stands in primary data prevented their separation. Published data from yield plots in old, natural stands supported the Hossfeld function. But, indications of a changed growth pattern in later decades still leave open the question of height growth pattern in old pine stands of cultivated origin. The presented Hossfeld equation can only be recommended for use in 10–80-year-old pine stands of cultivated origin.