Site Index Equations Research Articles

Dynamic Site Index Equation for Thinned Stands of Even-Aged Natural Longleaf Pine

Abstract A dynamic site equation derived using the generalized algebraic difference approach was developed for thinned stands of natural longleaf pine (Pinus palustris Mill.) in the East Gulf region of the United States using 40 years of measurements on 285 permanent plots. The base model predicts height growth of trees once they reach 4.5 ft and was fit using a varying parameter for each tree and global parameters that are constant for all 3,267 trees. Parameters were estimated in one step using the dummy variable approach and a first-order autoregressive error term to account for serial correlation. The final base-age invariant equation allows the user to specify the number of years required for trees to reach 4.5 ft in height.

Base–age Invariant Polymorphic Height Growth and Site Index Equations for Peatland Black Spruce Stands

Abstract The goal of this study was to develop base–age invariant polymorphic height growth and site index equations for peatland black spruce (Picea mariana [Mill.]; BSP) stands situated within the western portion of the Northern Clay section of the Canadian Boreal Forest region. Procedurally, equation parameters were estimated via ordinary least squares analysis using 291 mean dominant height − mean stand age (Hd − As) data pairs derived from 42 permanent sample plots (PSPs). The predictive ability of the resultant height growth equation was evaluated by examining mean absolute and relative errors and associated 95% prediction intervals over 5-, 15-, 25-, 35-, and 45-year projection periods. Furthermore, using an independent data set consisting of 129 Hd − As data pairs derived from 24 PSP, the new height growth equation was compared with two preexisting equations. Overall, the results indicated that the predictions derived from the new equation were unbiased irrespective of error type or projection period length and that the new equation exhibited greater predictive accuracy and was more consistent with expected dominant height development patterns than the preexisting equations. Consequently, the new equations are recommended for use when describing height growth patterns or quantifying site quality within peatland black spruce stands.

Ontario's forest growth and yield modelling program: Advances resulting from the Forestry Research Partnership

The province of Ontario holds approximately 70.2 million hectares of forests: about 17% of Canada’s and 2% of the world’s forests. Approximately 21 million hectares are managed as commercial forests, with an annual harvest in the early part of the decade approaching 200 000 ha. Yield tables developed by Walter Plonski in the 1950s provide the basis for most wood supply calculations and growth projections in Ontario. However, due to changes in legislation, policy, and the planning process, they no longer fully meet the needs of resource managers. Furthermore, Plonski`s tables are not appropriate for the range of silvicultural options now practised in Ontario. In October 1999, the Canadian Ecology Centre- Forestry Research Partnership (CEC-FRP) was formed and initiated a series of projects that collectively aimed at characterizing, quantifying and ultimately increasing the economically available wood supply. Comprehensive, defensible, and reliable forecasts of forest growth and yield were identified as key knowledge gaps. The CEC-FRP, with support from the broader science community and forest industry, initiated several new research activities to address these needs, the results of which are outlined briefly in this paper. We describe new stand level models (e.g., benchmark yield curves, FVS Ontario, stand density management diagrams) that were developed using data collected from permanent sample plots and permanent growth plots established and remeasured during the past 5 decades. Similarly, we discuss new height–diameter equations developed for 8 major commercial tree species that specifically account for stand density. As well, we introduce a CEC-FRP-supported project aimed at developing new taper equations for plantation grown jack pine and black spruce trees established at varying densities. Furthermore, we provide an overview of various projects undertaken to explore measures of site productivity. Available growth intercept and site index equations are being evaluated and new equations are being developed for major commercial tree species as needed. We illustrate how these efforts are advancing Ontario’s growth and yield program and supporting the CEC-FRP in achieving its objective of increasing the supply of fibre by 10% in 10 years while maintaining forest sustainability. Key words: permanent sample plots (PSPs), permanent growth plots (PGPs), normal yield tables, sustainable forest management, NEBIE plot network, forest inventory, Forest Vegetation Simulator

입지환경인자를 바탕으로 한 편백의 지위지수 추정에 관한 연구

This study was conducted to develop the effects of site environmental factors on estimation of site index function for Chamaecyparis obtusa Endlicher stands. We derived nonlinear growth equation and the draw site index curves by applying this estimated equation. This study with Chapman-Richards function showed significant P-value which was less then 0.0001 and <TEX>$R^2$</TEX> value 0.5947. This study was conducted to develop the feasible site index equation of Chamaecyparis obtusa Endlicher. For the table, the data of 82 sample areas that were thought to be without errors among the data of Chamaecyparis obtusa Endlicher sample area located on the value-oriented forest location chart were used and estimated. After analyzing the quantification method I based on 13 environmental factors to develop the score table for the site-index estimation of Chamaecyparis obtusa Endlicher, <TEX>$R^2$</TEX> value of the model was 0.7555. It has been analyzed that the scope value of Soil moisture in horizon A was 7.5045, that of total soil depth was 6.3896, that of topography was 5.3471, that of slope was 4.7000 and that of aspect was 3.2038. After analyzing the partial correlation to examine the factors that affected most the site-index of Chamaecyparis obtusa Endlicher, it has been noted that the partial correlation of climatic zone was 0.4987, which was highest, and it was followed by Soil moisture in horizon A (0.4592), slope (0.4537), topography (0.3299) and total soil depth (0.1035). As a result of conducting the significance test for partial correlation, it has been found that topography, climatic zone, parent rock, slope, altitude, aspect, Soil moisture in horizon A, soil hardness in horizon A and total soil depth were recognized significant with 1% of significance level and sedimentary type and soil texture in horizon A were recognized significant with 5% of significance level.

Classifying Oriental Beech (Fagus orientalis Lipsky.) Forest Sites Using Direct, Indirect and Remote Sensing Methods: A Case Study from Turkey.

Determining the productivity of forest sites through various classification techniques is important for making appropriate forest management decisions. Forest sites were classified using direct and indirect (site index) and remote sensing (Landsat 7 ETM and Quickbird satellite image) methods. In the direct method, forest site classifications were assigned according to edafic (soil properties), climate (precipitation and temperature) and topographic (altitude, slope, aspect and landform) factors. Five different forest site classes (dry, moderate fresh, fresh, moist and highly moist) were determined. In the indirect method, the guiding curve was used to generate anamorphic site index (SI) equations resulting in three classes; good (SI=I-II), medium (SI=III) and poor (SI=IV-V). Forest sites were also determined with a remote sensing method (RSM) using supervised classification of Landsat 7 ETM and Quickbird satellite images with a 0.67 kappa statistic value and 73.3% accuracy assessments; 0.88 kappa statistic value and 90.7% accuracy assessments, respectively. Forest sites polygon themes obtained from the three methods were overlaid and areas in the same classes were computed with Geographic Information Systems (GIS). The results indicated that direct and SI methods were consistent as a 3% dry site (19.0 ha) was exactly determined by both the direct and SI methods as a site class IV. Comparison of SI and RMS methods indicated a small difference as the area was highly homogeneous and unmanaged. While 15.4 ha area (open and degraded areas) was not determined by SI but RSM. A 19.0 ha (100%) poor site was determined by the SI method, 14.9 ha (78%) poor site was in Landsat 7 ETM satellite image and 17.4 ha (92%) poor site in Quickbird satellite image. The relationship between direct and SI methods were statistically analyzed using chi-square test. The test indicated a statistically significant relationships between forest sites determined by direct method and Quicbird satellite image (χ² = 36.794; df = 16; p = 0.002), but no significant relationships with Landsat 7 ETM satellite image (χ² = 22.291; df = 16; p = 0.134). Moderate association was found between SI method and direct method (χ² = 16.724; df = 8; p = 0.033).

Site Index Equation for Smallholder Plantations of Gmelina arborea in Leyte Province, the Philippines

The equation SiteIndex = Height × Log(IndexYear+0.5)/Log(Age+0.5) is suggested as a robust way to classify site index of small private Gmelina arborea plantations in Leyte province in the Philippines. Estimates of site index from this equation correlate well with other indicators of site productivity, including the observed mean annual volume increment and soil depth. An alternative equation based on slope and soil depth offers an indication of potential site productivity on unforested sites where no crop trees are present.

기후대별 입지환경 인자에 의한 소나무류의 지위지수 추정식 및 적지 구명

본 연구는 산림입지 자료를 이용하여 주요 소나무 수종의 기후대별 산림생산력을 추정하기 위해 수행하였다. 이를 위해 강원지방소나무, 중부지방소나무, 그리고 해송의 3개 소나무 수종을 대상으로 입지환경인자에 의한 기후대별 지위지수 추정식을 만들고, 적지 판정 기준에 따라 수종별 적지면적을 산출하였다. 기후대는 수종분포에 따라 온대북부, 온대중부, 온대남부, 그리고 난대의 4개 지역으로 구분하였다. 이를 위해 전국의 산림입지 자료를 기후대별 수종별로 분류한 후, 지위지수 추정식 산출에 필요한 추정자료와 통계 검증에 필요한 검증자료로 분류하였다. 산림입지 자료에 포함된 임령 및 수고에 근거하여 기준 임령을 30년으로 하는 기후대별 수종별 지위지수를 추정하였다. 이를 통해 입지환경 인자에 의한 기준임령 30년에서의 기후대별 수종별 지위지수 추정식을 도출하였으며, 검증자료를 사용하여 통계적 검증을 실시한 후 검증 결과에 따라 최종 기후대별 수종별 지위지수 추정식을 산출하였다. 본 연구에서 산출된 기후대별 소나무 수종의 지위지수 추정식은 <TEX>$4{\sim}8$</TEX>개의 입지환경 인자에 의해 산림생산력을 비교적 잘 추정하는 것으로 판명되었다. 이와 같은 방법으로 도출된 지위지수 추정식을 산림입지 자료에 적용하여 기후대별 수종별 산림생산력을 추정하고, 이에 근거하여 적지를 판정한 후 적지 면적을 산출하였다. 수종별 적지 면적은 강원지방소나무는 온대북부와 온대중부에서 약 24만ha로 추정되었으며, 중부지방소나무는 전체 기후대에 걸쳐 약 49만ha가 적지인 것으로 분석되었다. 온대북부를 제외한 지역에 분포하고 있는 해송의 경우에도 전체 산림면적의 약 4%인 23만ha가 적지인 것으로 판명되었다. This study was conducted to develop site index equations for some pine species by climatic zones based on the relationships between site index and environmental factors. The selected pine species were Pinus densiflora Sieb. et. Zucc., Pinus densiflora for, erecta, and Pinus thunbergii. A total of 28 environmental factors were obtained from a digital forest site map. The influence of 28 environmental factors on site index was evaluated by multiple regression analysis. Four to eight environmental factors were selected in the final site index equation for pine species by climatic zones. The site index equations developed in this study was then verified by three evaluation statistics such as model's estimation bias, model's precision and mean square error type of measure. We concluded that the site index equations for the pine species by climatic Bones were capable of estimating forest site productivity. Based on these site index equations, the amount of productive areas for the species by climatic zones was estimated by applying the GIS technique to digital forest maps.

Classification and mapping forest sites using geographic information system (GIS): a case study in Artvin Province

The productivity of forest sites has been indirectly determined with solo wood production objective in forest management. Forest site productivity should, however, be determined directly in order to implement ecosystem based multipurpose forest management philosophy. This article tackles the problem in distinguishing and mapping forest sites using both direct method and indirect method in Genya Mountain located in central of Artvin State Forest Enterprise. About 112 sample plots were designed and distributed over the area. In each sample plot, soil samples were collected and the classical timber inventory measurements were taken. According to direct method, Soil Moisture Regime (SMR) method is preferred due to a water deficiency in the study area. Water holding capacity was used as an essential criterion for the classification of the forest site. Forest site classifications were assigned regarding the physiographic factors such as landform, aspect, and slope. Five different forest sites classes; dry, moderate fresh, fresh, humid and hygric were determined. According to direct method, the guiding curve was used to generate anamorphic site index (SI) equations and three site index classes; good (SI=I-II), medium (SI=III) and low (SI=IV-V) were determined. Some important differences between the methods were realized. The forest sites determined with site index estimation method indicate that site index I and II is 505.99 ha, III 1095.79 ha and IV and V 992.95 ha, whereas forest sites determined with direct method related to dry site of 937.58 ha, moderate fresh site of 931.90 ha, fresh site of 1,797.71 ha, humid site of 80.48 ha and hygric site of 356.55 ha. The forest site maps of both methods were created using GIS functions. The forest sites of open and degraded areas should be determined according to direct method.

A provisional growth model with a size–density relationship for a plantation of Paraserianthes falcataria derived from measurements taken over 2 years in Pare, Indonesia

A growth model for a plantation of Paraserianthes falcataria was provisionally derived from measurements of 32 permanent plots taken over a period of 2 years in Pare, Indonesia. This model first predicts height growth with the polymorphic site index equation. Then density-related growth and mortality, that is, diameter and stand density, are calculated to satisfy the mathematical relationship for the reciprocal and self-thinning equations, both of which were based on the maximum size–density line with the slope of –1.759 identified in this study. Cumulative predictions on diameter and stand density, starting with each of three age classes, 3, 4, and 5 years after planting, and continuing for the next 2 years, agreed well with the observations of age-class mean. An exception was for stands that were 7 years old, which were marginal, but closest to the rotation age of 8 years. Contrasting height/diameter relationships among the three age classes were described reasonably well with this model, and the predicted basal growth area was found to agree fairly well with observations. These results suggest that the growth model presented here has good potential for applying size–density control for plantations of P. falcataria. However, measurements for an additional few years might be necessary to derive a model that will more accurately predict diameter size at the rotation age.

Site-Index Curves and Growth Intercepts for Young White Spruce Plantations in North Central Ontario

Abstract Site-index (heightߝgrowth) curves, site-index prediction equations, and growth intercepts were developed from internode measurements and stem-analysis data using dominant trees in 69 plots located in white spruce plantations aged 19 to 32 years total age. Site-index curves were based on breast-height (1.3 m) age because our analyses show that height growth below breast height is slow and erratic and is poorly related to site index (dominant height at 15 years breast-height age). The most precise model for computing heightߝgrowth curves was a Newnham constrained polymorphic expression (Newnham, R.M. 1988. A modification of the Ek-Payandeh nonlinear regression model for site-index curves. Can. J. For. Res. 18:115ߝ120) of the Ek nonlinear regression model (Ek, A.R. 1971. A formula for white spruce site-index curves. University of Wisconsin For. Res. Note 161. 2 p). Comparisons showed that site-index curves in North Central Ontario were comparable to site-index curves for white spruce plantations in southeastern Ontario. The first three to five internodes above 2.0 m gave the most precise estimates of site index based on growth intercepts. North. J. Appl. For. 23(4):257–263.

Growth model for predicting stand development of Acacia mangium in South Sumatra, Indonesia, using the reciprocal equation of size–density effect

A growth model consisting of a polymorphic site index equation, a reciprocal equation for the diameter–density effect, and a self-thinning equation was presented to predict the course of stand development of Acacia mangium. This model firstly predicts height growth with the polymorphic site index equation, and then density-related growth and mortality, that is, diameter and stand density, are calculated to satisfy the mathematical relationship for the reciprocal and self-thinning equations. The latter equation relates the rate of reduction in stand density to the diameter increment derived from a fitted trend of the distance from the maximum size–density line. The cumulative predictions, starting with stands 3 years after planting and continuing until they were 9 years old, agreed well with observations of group-age means of measurements calculated for the three levels of initial density. Contrasting height diameter relationships among the three levels of initial density were described reasonably well with this model, and the predicted basal area growth was found to agree well with observations. This indicated a good potential for its use in yield prediction. Simulations for stand growth under different spacing and thinning options were demonstrated in a stand density control diagram, which suggested a reasonable flexibility for practical application.

Construction of site index equations for even aged stands of Tectona grandis (teak) from permanent plot data in India

A quantitative measure of the timber production potential of a given site may be provided by site index equations, which predict site index at a reference age from height and age information of a forest stand. Data from permanent sample plots laid down in even aged stands of Tectona grandis in six states of India were used to develop site index equations. Eleven growth functions were estimated from height–age data using the guide curve method and difference equation method with anamorphic and polymorphic formulations. The applied methods and estimated functions were compared with respect to residual variation, i.e., root mean square error (RMSE) from original data. The difference equation method gave lower RMSE than the guide curve method. A special solution of the difference equation derived from one of the growth functions, where a hyperbolic relationship between site index and a parameter was assumed, gave the best fit to the data. Site index curves with dominant heights in the 11–28 m range at a reference age of 25 years are presented.

Three methods for avoiding the impacts of incompatible site index and height prediction models demonstrated on jack pine curves for Ontario

Fixed base-age site indices are commonly used as a covariate in height prediction models, whereby separate site index prediction equations are used with measured age and height to predict the site index when it is unknown. In such systems, a bias may result in the height prediction if the site index equation is incompatible with the height equation. We demonstrated such bias using as an example recently published models for jack pine in northern Ontario with incompatible site index and height equations. Then we offered solutions that reduce the bias in height predictions assuming that the primary objective was to predict height. First, we re-estimated the site index equation parameters using both the site index and height equations as a common prediction system and holding the published height equation parameters constant while minimizing errors in height predictions. This substantially reduced the incompatibility between the site index and the height equations. Second, we demonstrated the use of two dynamic equations as alternatives to the fixed base-age equations. Even using an irrelevant dynamic equation for another species substantially reduced the bias in short-term jack pine height projections. However, the dynamic equation fit to the jack pine height model was the most effective in reducing the bias for height projections relative to all other considered solutions and produced the least biased, most parsimonious, and most flexible solution. Key words: incompatible site index and height equations, fixed base age equations, dynamic equations

A Site Dependent Simultaneous Growth Projection Model for Pinus kesiya Plantations in Zambia and Zimbabwe

Abstract The aim of this study was to create a stand level yield model for Pinus kesiya (Royle × Gordon) plantations in Zambia and Zimbabwe based on the simultaneous projection model approach. The purpose was to prepare prediction models for the measurable and allometrically related stand variables which characterize the development of planted P. kesiya stands. The modeled stand characteristics are assessable in the inventories of forest plantations and are frequently employed in traditional stand yield tables and modern growth simulators. Special attention was paid to the selection of flexible nonlinear model forms that are simple and stable. Two model forms were developed: (1) a polymorphic and base age invariant site index equation, used as a growth projection model for stand dominant height, and (2) a stand volume prediction model based on Honer's single tree volume model. The projection form of the site index equation was obtained using the algebraic difference approach to solve analytically the rate parameter of the autocatalytic growth model. The simultaneous growth projection model included a model for basal area median diameter. The basal area median diameter was also used as a predictor of stand basal area. This improved the accuracy of stand basal area predictions. A model for the basal area median diameter also makes it possible to apply theoretical diameter distributions for the prediction of future stand stages. FOR. SCI. 48(3):518–529.

Deriving Site Index Equation and Curves for Plantation Forest

Deriving Site Index Equation and Curves for Plantation Forest

Three methods of deriving advanced dynamic site equations demonstrated on inland Douglas-fir site curves

With two examples of five-parameter, fixed-base-age site index and height growth equations, I demonstrate three methods for deriving dynamic equations that are base-age invariant and use only three parameters. These are initial condition difference equations that compute appropriate heights at all base ages and provide compatible height and site index values from one common equation. Despite having fewer parameters, they can model a broader selection of curves than the original equations. The new equations are applicable for all situations in which the original equations could be applied. Methods demonstrated in this paper can enhance the development of all recursive and otherwise implicitly defined equations used for modeling of height, diameter, basal area, volume, number of trees per hectare, and investment yields.

Development of a well-behaved site-index equation: jack pine in north-central Ontario: comment

Development of a well-behaved site-index equation: jack pine in north-central Ontario: comment

Site index equation for Cupressus lusitanica stands in Munessa forest, Ethiopia

The timber production potential of a given site (site quality) is measured by site index, dominant height of the stand at an index age. Stem analysis data from Cupressus lusitanica stands in Munessa Shashemene Forest, Ethiopia, were used to compute site index equations. The proportional curve method was adopted to construct an average guide curve. Four linear and two widely used non-linear equations were fitted to adjusted mean dominant height–age data. The Schumacher equation was chosen as giving the best fit. Site index curves are reproduced, giving dominant heights in the 12–27 m range at a reference of 15 years.

Development of a well-behaved site-index equation: jack pine in north-central Ontario: comment

Development of a well-behaved site-index equation: jack pine in north-central Ontario: comment

Relating Site Index to Ecological Factors in Black Spruce Stands: Tests of Hypotheses

Abstract Modeling dominant height through site index, defined as dominant height at some fixed tree age, requires two equations. The site index must be estimated as the average height of dominant trees at base age, and dominant height must be modeled as a function of age and site index, each model having its own error term. This raises a problem when squared errors are minimized to estimate parameters of interest: the estimates are biased and inconsistent because the error terms are correlated with the explanatory variables. Two additional problems are the autocorrelation among error terms and variance heterogeneity within trees. The generalized method of moments (GMM), which simultaneously takes these problems into account, offers a tool to estimate parameters of the site index and dominant height equations consistently and without bias. Allowing parameters of the height growth model to depend on explanatory variables representing ecological region and drainage class provides useful insight into growth patterns, and improves prediction based on these models. A simulation study confirms that the GMM combined with prewhitening of the time series for each tree produces useful estimates of the parameters and valid statistical tests of hypotheses about their value. For. Sci. 45(4):484-491.