Properties of the quadratic mean diameter in balanced diameter distributions

1985 ◽  
Vol 15 (2) ◽  
pp. 474-476
Author(s):  
Donald J. Weatherhead ◽  
Roger C. Chapman ◽  
John H. Bassman
Keyword(s):  
Stand Structure ◽  
Basal Area ◽  
Tree Size ◽  
Diameter Distribution ◽  
Quadratic Mean ◽  
Growing Stock ◽  
Mean Diameter ◽  
Quadratic Mean Diameter ◽  
Stand Basal Area ◽  
Diameter Distributions

Balanced diameter distributions are widely used to describe stand structure goals for residual growing stock in uneven-aged forests. The quadratic mean diameter is frequently used as a descriptor of a balanced diameter distribution. In this paper the quadratic mean diameter is shown to be independent of stand basal area for balanced diameter distributions with a common class width, maximum and minimum diameters, and de Liocourt's q ratio. Additionally it is shown that the quadratic mean diameter is relatively insensitive to changes in maximum tree size and q ratios for q ratios 1.5 and larger.

Eastern cottonwood clonal mixing study: predicted diameter distributions

1994 ◽  
Vol 24 (2) ◽  
pp. 405-414 ◽  
Author(s):  
Steven A. Knowe ◽  
G. Sam Foster ◽  
Randall J. Rousseau ◽  
Warren L. Nance
Keyword(s):  
Weibull Distribution ◽  
Basal Area ◽  
Diameter Distribution ◽  
Minimum Diameter ◽  
Quadratic Mean ◽  
Parameter Recovery ◽  
Eastern Cottonwood ◽  
Mean Diameter ◽  
Quadratic Mean Diameter ◽  
Diameter Distributions

A parameter recovery procedure for the Weibull distribution function was modified to incorporate monocultures and mixtures of eastern cottonwood (Populusdeltoides Bartr.) clones planted in Mississippi and Kentucky. Components of the system included functions to predict stand-level basal area and four percentiles (0th, 25th, 50th, and 95th) of the cumulative diameter distribution. Basal area was predicted as a function of surviving number of trees, dominant height, age, planting location, and the proportion of each clone planted. Clonal proportions, which accounted for 3.6% of the variation in observed basal area, were more important than differences in planting locations, which accounted for 3.0% of the variation. Interactions between clones in mixtures were not significant (p = 0.5676), but some cases of both over- and under-compensation appeared to be developing. Percentiles of the cumulative diameter distribution were predicted as functions of quadratic mean diameter, and therefore included indirect effects of both genetic and planting site differences. Only the minimum diameter (D0) was directly affected by proportions of clones planted. Most of the monocultures and mixtures of clones had smaller minimum diameters than expected for a given value of quadratic mean diameter. The predicted quadratic mean diameter and percentiles were used to recover parameters of the Weibull distribution such that the predicted diameter distribution has the same quadratic mean diameter as obtained from the stand basal area model. The predicted distributions indicated that a common stand-level model was not sufficient for accounting for variations in diameter distributions of eastern cottonwood clones. As a result of the differences in diameter distributions, monocultures and mixtures of the Texas clones appeared to have less volume and greater stand variance than the Mississippi clones.

scholarly journals Modeling Dynamics of Structural Components of Forest Stands Based on Trivariate Stochastic Differential Equation

Forests ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 506 ◽  
Author(s):  
Petras Rupšys
Keyword(s):  
Differential Equation ◽  
Basal Area ◽  
Growth And Yield ◽  
Mixed Effect ◽  
Stand Volume ◽  
Quadratic Mean ◽  
Stand Growth ◽  
Mean Diameter ◽  
Quadratic Mean Diameter ◽  
Stand Basal Area

Research Highlights: Today’s approaches to modeling of forest stands are in most cases based on that the regression models and they are constructed as static sub-models describing individual stands variables. The disadvantages of this method; it is laborious because too many different equations need to be assessed and empirical choices of candidate equations make the results subjective; it does not relate to the stand variables dynamics against the age dimension (time); and does not consider the underlying covariance structure driving changes in the stand variables. In this study, the dynamical model defined by a fixed-and mixed effect parameters trivariate stochastic differential equation (SDE) is introduced and described how such a model can be used to model quadratic mean diameter, mean height, number of trees per hectare, self-thinning line, stand basal area, stand volume per hectare and much more. Background and Objectives: New developed marginal and conditional trivariate probability density functions, combining information generated from an age-dependent variance-covariance matrix of quadratic mean diameter, mean height and number of trees per hectare, improve stand growth prediction, and forecast (in forecast the future is completely unavailable and must only be estimated from historical patterns) accuracies. Materials and Methods: Fixed-and mixed effect parameters SDE models were harmonized to predict and forecast the dynamics of quadratic mean diameter, mean height, number of trees per hectare, basal area, stand volume per hectare, and their current and mean increments. The results and experience from applying the SDE concepts and techniques in an extensive whole stand growth and yield analysis are described using a Scots pine (Pinus sylvestris L.) experimental dataset in Lithuania. Results: The mixed effects scenario SDE model showed high accuracy, the percentage root mean square error values for quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare predictions (forecasts) were 3.37% (10.44%), 1.82% (2.07%), 1.76% (2.93%), 6.65% (10.41%) and 6.50% (8.93%), respectively. In the same way, the quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare prediction (forecast) relationships had high values of the coefficient of determination, R2, 0.998 (0.987), 0.997 (0.992), 0.997 (0.988), 0.968 (0.984) and 0.966 (0.980), respectively. Conclusions: The approach presented in this paper can be used for developing a new generation stand growth and yield models.

scholarly journals Thinning Response and Potential Basal Area in a Mixed Sub-humid Low-elevation Oak-Hornbeam Forest

2021 ◽  
Author(s):  
Mathias Neumann ◽  
Hubert Hasenauer
Keyword(s):  
Stand Structure ◽  
Basal Area ◽  
Climatic Conditions ◽  
Diameter Distribution ◽  
Stem Density ◽  
Growing Stock ◽  
A Site ◽  
Water Nutrients ◽  
Related Mortality

Abstract Competition for resources (light, water, nutrients, etc.) limits the size and abundance of alive trees a site can support. This carrying capacity determines the potential carbon sequestration in alive trees as well as the maximum growing stock. Lower stocking through thinning can change growth and mortality. We were interested in the relations between stand structure, increment and mortality using a long-unmanaged oak-hornbeam forest near Vienna, Austria, as case study. We expected lower increment for heavy thinned compared to unmanaged stands. We tested the thinning response using three permanent growth plots, whereas two were thinned (50% and 70% basal area removed) and one remained unmanaged. We calculated stand structure (basal area, stem density, diameter distribution) and increment and mortality of single trees. The heavy thinned stand had over ten years similar increment as the moderate thinned and unthinned stands. Basal area of the unthinned stand remained constant and stem density decreased due to competition-related mortality. The studied oak-hornbeam stands responded well even to late and heavy thinning suggesting a broad “plateau” of stocking and increment for these forest types. Lower stem density for thinned stands lead to much larger tree increment of single trees, compared to the unthinned reference. The findings of this study need verification for other soil and climatic conditions.

A Stocking Guide for Southern Bottomland Hardwoods

1995 ◽  
Vol 19 (3) ◽  
pp. 103-104 ◽  
Author(s):  
J. C. G. Goelz
Keyword(s):  
Basal Area ◽  
Bottomland Hardwoods ◽  
Quadratic Mean ◽  
Mean Diameter ◽  
Quadratic Mean Diameter

Abstract A stocking guide was developed from the data of Putnam, et al. (1960). The form of the stocking guide follows Gingrich (1967), although the “B”-line is based on the suggested residual stocking of Putnam, et al. (1960) rather than on minimum full stocking. This stocking guide is similar to the stocking guide for central upland hardwoods constructed by Gingrich, except that 100% stocking is 5-7 ft2² of basal area lower for the southern bottomland guide, across a range of quadratic mean diameter. South. J. Appl. For. 19(3):103-104.

Compatible basal-area growth and yield model for thinned and unthinned stands

1983 ◽  
Vol 13 (4) ◽  
pp. 563-571 ◽  
Author(s):  
Robert L. Bailey ◽  
Kenneth D. Ware
Keyword(s):  
Loblolly Pine ◽  
Basal Area ◽  
Growth And Yield ◽  
Yield Model ◽  
Projection Model ◽  
Quadratic Mean ◽  
Basal Area Growth ◽  
Area Growth ◽  
Mean Diameter ◽  
Quadratic Mean Diameter

A measure of kind and level of thinning is developed and its relationship to other stand attributes such as number of trees, basal area, and volume removed in thinning is quantified. This measure or thinning index is based on the ratio of the quadratic mean diameter of thinned trees to the quadratic mean diameter of all trees before thinning. The thinning index is then logically incorporated into a thinning multiplier from which is derived a compatible basal-area growth projection model to generalize the previous concepts for thinning effects in systems for predicting growth and yield. Empirical tests with data from thinned and unthinned natural stands of loblolly pine, from thinned and unthinned slash pine plantations, and from thinned western larch stands show the model to provide estimates with improved properties. Hence, the thinning index and the thinning multiplier are also proposed for other situations involving effects of thinning.

Partial Calibration of "ONTWIGS": A Forest Growth and Yield Projection System Adapted for Ontario

1994 ◽  
Vol 11 (2) ◽  
pp. 41-46 ◽  
Author(s):  
Bijan Payandeh ◽  
Pia Papadopol
Keyword(s):  
Basal Area ◽  
Forest Growth ◽  
Data Sets ◽  
Prediction Errors ◽  
Northern Ontario ◽  
Quadratic Mean ◽  
Tree Survival ◽  
Mean Diameter ◽  
Quadratic Mean Diameter ◽  
Stand Attributes

Abstract "ONTWIGS" (an adaptation of "LSTWIGS" for Ontario), was partially calibrated for permanent plots data sets from northern Ontario. Stand attributes used for calibration were quadratic mean diameter, number of trees, and basal area/ha. Simple local calibration was accomplished by adjusting tree survival and potential diameter growth coefficients so as to reduce the prediction errors to within 10% of the actual values over a 5-yr period. This resulted in prediction errors ranging from -9.9 to 6.9%, but with an overall average of only: -1.4, 1.0, and 0.2% for the spruce fir data; from -8.5 to 2.8%, but with an overall average of only -0.7, 0.5, and 0.4% for a black spruce drainage and fertilization experiment; and from -6.6 to 9.8%, but with an overall average of only -1.7, 0.0, and -1.8% for an unthinned red pine plantation for number of trees/ha, quadratic mean diameter, and basal area/ha, respectively. Results indicate that "ONTWIGS" may be locally calibrated through simple procedures to increase its prediction accuracy to ±5% of the observed stand attributes, averaging less than 3% for the major timber species in northern Ontario and for short to medium projection periods. However, the uncalibrated model should be used with caution for short terms, only and where no other projection tools are available. More extensive calibrations of "ONTWIGS" on larger and more representative data sets are currently underway. North. J. Appl. For. 11(2):41-46.

scholarly journals Development of Water Tupelo Coppice Stands on the Mobile-Tensaw River Delta for Five Years After Precommercial Thinning and Cleaning

2001 ◽  
Vol 25 (4) ◽  
pp. 165-172 ◽  
Author(s):  
J.C.G. Goelz ◽  
J.S. Meadows ◽  
T.C. Fristoe
Keyword(s):  
Basal Area ◽  
Individual Tree ◽  
Quadratic Mean ◽  
Precommercial Thinning ◽  
Mean Diameter ◽  
Water Tupelo ◽  
Rotation Age ◽  
Large Water ◽  
Quadratic Mean Diameter ◽  
The Individual

Abstract Three 4-yr-old stands (or locations) were selected for treatment. Treatment consisted of two components: (1) thinning water tupelo (Nyssa aquatica L.) stump sprouts and (2) cutting all stems of Carolina ash (Fraxinus caroliniana Mill.) and black willow (Salix nigra Marsh.) (cleaning). Contrary to results in other areas, survival of water tupelo coppice was very high and was not affected by the treatments. Cleaning had little or no positive effect on the individual tree or stand-level variables we measured. Thinning sprout clumps significantly increased diameter growth of water tupelo; the effect of thinning was considerably larger for one location. Stand basal area growth was decreased by thinning sprout clumps. However, quadratic mean diameter was increased by thinning, particularly at one location. Although thinning decreased basal area 5 yr after treatment, the increase in quadratic mean diameter was sufficient for there to be no significant effect of thinning on total volume 5 yr after treatment. Because of this, and in anticipation of imminent natural thinning of the unthinned plots, we suspect that the thinned plots will eventually have significantly greater standing volume than the unthinned plots, at least for the location where density of large sprouts was initially the highest. Rotation age will be decreased for that stand because stems will achieve merchantable size sooner. Thus we consider precommercial thinning of sprout clumps to be a potentially effective practice in stands with a high density of large water tupelo sprouts. South. J. Appl. For. 25(4):165–172.

Calibrating predicted diameter distribution with additional information in growth and yield predictions

2003 ◽  
Vol 33 (3) ◽  
pp. 430-434 ◽  
Author(s):  
Annika Kangas ◽  
Matti Maltamo
Keyword(s):  
Growth Models ◽  
Basal Area ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Individual Tree ◽  
Forest Management Planning ◽  
Growing Stock ◽  
Additional Information ◽  
Tree Models ◽  
Diameter Distributions

Diameter distribution of the growing stock is essential in many forest management planning problems. The diameter distribution is the basis for predicting, for example, timber assortments of a stand. Usually the predicted diameter distribution is scaled so that the stem number (or basal area) corresponds to the measured value (or predicted future value), but it may be difficult to obtain a distribution that gives correct estimates for all known variables. Diameter distributions that are compatible with all available information can be obtained using an approach adopted from sampling theory, the calibration estimation. In calibration estimation, the original predicted frequencies are modified so that they respect a set of constraints, the calibration equations. In this paper, an example of utilizing diameter distributions in growth and yield predictions is presented. The example is based on individual tree growth models of Scots pine (Pinus sylvestris L.). Calibration estimation was utilized in predicting the diameter distribution at the beginning of the simulation period. Then, trees were picked from the distribution and their development was predicted with individual tree models. In predicting the current stand characteristics, calibrated diameter distributions proved to be efficient. However, in predicting future yields, calibration estimation did not significantly improve the accuracy of the results.

Incorporating the effects of interspecific competition and vegetation management treatments in diameter distribution models for Douglas-fir saplings

1992 ◽  
Vol 22 (9) ◽  
pp. 1255-1262 ◽  
Author(s):  
Steven A. Knowe ◽  
Timothy B. Harrington ◽  
Robert G. Shula
Keyword(s):  
Interspecific Competition ◽  
Douglas Fir ◽  
Diameter Distribution ◽  
Cumulative Probability ◽  
Quadratic Mean ◽  
Vegetation Control ◽  
Mean Diameter ◽  
Coast Ranges ◽  
Siskiyou Mountains ◽  
Quadratic Mean Diameter

A parameter recovery procedure for the Weibull distribution function, based on diameter percentiles, was modified to incorporate the effects of interfering vegetation in young Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco var. menziesii) plantations. The applicability of the system was tested by using data from sites in the Coast Ranges of Oregon and Washington and in the Siskiyou Mountains of southwestern Oregon. Four percentiles (0, 25th, 50th, 95th) of the cumulative probability distribution were predicted as functions of quadratic mean diameter and age. In the Siskiyou study, cover and total vegetation control affected quadratic mean diameter and all four percentiles; intensity of the vegetation treatments affected the 0 and 25th percentiles, and the interaction between intensity and timing of treatment affected quadratic mean diameter. In the Coast Ranges study, only quadratic mean diameter was affected by cover of woody vegetation, while quadratic mean diameter and the 25th percentile were significantly affected by total vegetation control. The predicted distributions showed decreasing variance with increasing cover, particularly in the Siskiyou Mountains. In the Coast Ranges study, the coefficient of variation increased with increasing cover, indicating that the variance of stem diameters was affected by average size. On xeric sites in the Siskiyou Mountains, high diameter variability in plots with total vegetation control suggests that interspecific competition may inhibit the expression of microsite variation.

scholarly journals Relating Forest Attributes with Area- and Tree-Based Light Detection and Ranging Metrics for Western Oregon

2010 ◽  
Vol 25 (3) ◽  
pp. 105-111 ◽  
Author(s):  
Michael E. Goerndt ◽  
Vincente J. Monleon ◽  
Hailemariam Temesgen
Keyword(s):  
Basal Area ◽  
Light Detection And Ranging ◽  
Stem Volume ◽  
Height Distribution ◽  
Light Detection ◽  
Quadratic Mean ◽  
Crown Width ◽  
Mean Diameter ◽  
Forest Attributes ◽  
Quadratic Mean Diameter

Abstract Three sets of linear models were developed to predict several forest attributes, using stand-level and single-tree remote sensing (STRS) light detection and ranging (LiDAR) metrics as predictor variables. The first used only area-level metrics (ALM) associated with first-return height distribution, percentage of cover, and canopy transparency. The second alternative included metrics of first-return LiDAR intensity. The third alternative used area-level variables derived from STRS LiDAR metrics. The ALM model for Lorey's height did not change with inclusion of intensity and yielded the best results in terms of both model fit (adjusted R2 = 0.93) and cross-validated relative root mean squared error (RRMSE = 8.1%). The ALM model for density (stems per hectare) had the poorest precision initially (RRMSE = 39.3%), but it improved dramatically (RRMSE = 27.2%) when intensity metrics were included. The resulting RRMSE values of the ALM models excluding intensity for basal area, quadratic mean diameter, cubic stem volume, and average crown width were 20.7, 19.9, 30.7, and 17.1%, respectively. The STRS model for Lorey's height showed a 3% improvement in RRMSE over the ALM models. The STRS basal area and density models significantly underperformed compared with the ALM models, with RRMSE values of 31.6 and 47.2%, respectively. The performance of STRS models for crown width, volume, and quadratic mean diameter was comparable to that of the ALM models.

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