Investigating the Effects of k and Area Size on Variance Estimation of Multiple Pixel Areas Using a k-NN Technique for Forest Parameters

Combining auxiliary variables and field inventory data of forest parameters using the model-based approach is frequently used to produce synthetic estimates for small areas. These small areas arise when it may not be financially feasible to take ground measurements or when such areas are inaccessible. Until recently, these estimates have been calculated without providing a measure of the variance when aggregating multiple pixel areas. This paper uses a Random Forest algorithm to produce estimates of quadratic mean diameter at breast height (QMDBH) (cm), basal area (m2 ha−1), stem density (n/ha−1), and volume (m3 ha−1), and subsequently estimates the variance of multiple pixel areas using a k-NN technique. The area of interest (AOI) is the state owned commercial forests in the Slieve Bloom mountains in the Republic of Ireland, where the main species are Sitka spruce (Picea sitchensis (Bong.) Carr.) and Lodgepole pine (Pinus contorta Dougl.). Field plots were measured in summer 2018 during which a lidar campaign was flown and Sentinel 2 satellite imagery captured, both of which were used as auxiliary variables. Root mean squared error (RMSE%) and R2 values for the modelled estimates of QMDBH, basal area, stem density, and volume were 19% (0.70), 22% (0.67), 28% (0.62), and 26% (0.77), respectively. An independent dataset of pre-harvest forest stands was used to validate the modelled estimates. A comparison of measured values versus modelled estimates was carried out for a range of area sizes with results showing that estimated values in areas less than 10–15 ha in size exhibit greater uncertainty. However, as the size of the area increased, the estimated values became increasingly analogous to the measured values for all parameters. The results of the variance estimation highlighted: (i) a greater value of k was needed for small areas compared to larger areas in order to obtain a similar relative standard deviation (RSD) and (ii) as the area increased in size, the RSD decreased, albeit not indefinitely. These results will allow forest managers to better understand how aspects of this variance estimation technique affect the accuracy of the uncertainty associated with parameter estimates. Utilising this information can provide forest managers with inventories of greater accuracy, therefore ensuring a more informed management decision. These results also add further weight to the applicability of the k-NN variance estimation technique in a range of forests landscapes.

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Systematic Sampling for Estimating Harvest-Induced Changes of a Forest Stand

Science and Humanities Journal ◽

10.47773/shj.1998.091.4 ◽

2009 ◽

Vol 9 (1) ◽

pp. 39-55

Author(s):

Dennis Peque ◽

Keyword(s):

Sample Size ◽

Standard Error ◽

Basal Area ◽

Systematic Sampling ◽

Relative Standard Error ◽

Stem Density ◽

Relative Standard ◽

The Individual ◽

Induced Changes ◽

Forest District

This study was conducted in Compartment 2012a in Bosinghausen Forest District in Germany covering an area of 5 hectared. Twenty two sampling plots were laid out in the field following systematic sampling design. Results showed that all estimates for all variables (e.g. tree heights, DBH, stem density, basal area and volume) under trees that were marked for cutting have higher relative standard error. This was due to higher dispersion of individual estimates in each plot. On the other hand, the simulation study shows that sampling efficiency can be acheived by increasing the sample size. When more samples are included, the relative standard error becomes low. From this study, it can be concluded that the variability of the estimates were affected by sample size and the variability of individual units in the population or the individual esitmates (in this case, estimates in each plot).

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An approximate point-based alternative for the estimation of variance under big BAF sampling

Forest Ecosystems ◽

10.1186/s40663-021-00304-0 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Thomas B. Lynch ◽

Jeffrey H. Gove ◽

Timothy G. Gregoire ◽

Mark J. Ducey

Keyword(s):

Forest Inventory ◽

Variance Estimation ◽

Basal Area ◽

Volume Estimation ◽

Delta Method ◽

Sampling Point ◽

Variance Estimator ◽

Computer Simulation Studies ◽

New Formula ◽

Estimation Of Variance

Abstract Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of $\frac {1}{n}$ 1 n where n is the number of sample points.

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Exploring the Recruitment Dynamics of Sugar Maple and Yellow Birch Saplings into Merchantable Stems Following Harvesting in the Acadian Forest Region of New Brunswick, Canada

Canadian Journal of Forest Research ◽

10.1139/cjfr-2021-0226 ◽

2021 ◽

Author(s):

Alex Noel ◽

Jules Comeau ◽

Salah-Eddine El Adlouni ◽

Gaetan Pelletier ◽

Marie-Andrée Giroux

Keyword(s):

New Brunswick ◽

Sugar Maple ◽

Basal Area ◽

Stem Density ◽

Yellow Birch ◽

Probability Of Occurrence ◽

Silvicultural Treatment ◽

Forest Region ◽

Wide Range ◽

Acadian Forest

The recruitment of saplings in forest stands into merchantable stems is a very complex process, thus making it challenging to understand and predict. The recruitment dynamics in the Acadian Forest Region of New Brunswick are not well known or documented. Our objective was to draw an inference from existing large scale routine forest inventories as to the different dynamics behind the recruitment from the sapling layer into the commercial tree size layer in terms of density and occurrence of sugar maple (Acer saccharum Marsh.) and yellow birch (Betula alleghaniensis Britt.) following harvesting, by looking at many factors on a wide range of spatial and temporal scales using models. Results suggest that the variation in density and probability of occurrence is best explained by the intensity of silvicultural treatment, by the merchantable stem density in each plot, and by the proportion of merchantable basal area of each group of species. The number of recruits of sugar maple and yellow birch stems tend be higher when time since last treatment increases, when mid to low levels of silvicultural treatment intensity were implemented, and within plots having intermediate levels of merchantable stem density. Lastly, our modeling efforts suggest that the probability of occurrence and density of recruitment of both species tend to increase while its share of merchantable basal area increases.

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Tree density, basal area and species diversity in a disturbed dry tropical forest of northern India: implications for conservation

Environmental Conservation ◽

10.1017/s0376892906003237 ◽

2006 ◽

Vol 33 (3) ◽

pp. 256-262 ◽

Cited By ~ 42

Author(s):

R. SAGAR ◽

J.S. SINGH

Keyword(s):

Species Diversity ◽

Tropical Forest ◽

Basal Area ◽

Tree Density ◽

Dry Forest ◽

Conservation Strategies ◽

Stem Density ◽

Dry Tropical Forest ◽

Number Of Species ◽

Northern India

Dry tropical forest communities are among the world's most threatened systems and urgent measures are required to protect and restore them in degraded landscapes. For planning conservation strategies, there is a need to determine the few essential measurable properties, such as number of species and basal area, that best describe the dry forest vegetation and its environment, and to document quantitative relationships among them. This paper examines the relationships between forest basal area and diversity components (number of species and evenness) for a disturbed dry tropical forest of northern India. Data were collected from five sites located in the Vindhyan dry tropical forest of India, selected on the basis of satellite images and field observations to represent the entire range of conditions in terms of canopy cover and disturbance regimes. These sites represented different communities in terms of species composition. The forest was poorer in species richness, and lower in stem density and basal area than wet forests of the tropics. Across sites (communities), the diversity components and tree density were positively related with total tree basal area. Considering basal area as a surrogate of biomass and net production, diversity is found to be positively associated with productivity. A positive relationship between basal area, tree density and species diversity may be an important characteristic of the dry forest, where recurring disturbance does not permit concentration of biomass or stems in only a few strong competitors. However, the relationships of basal area with density, alpha diversity and evenness remain statistically significant only when data from all sites, including the extremely disturbed one, are used in the analysis. In some sites there was a greater coefficient of variation (CV) of basal area than in others, attributed to patchy distribution of stems and resultant blanks. Therefore, to enhance the tree diversity of these forests, the variability in tree basal area must be reduced by regulating local disturbances. Conservation activities, particularly fuelwood plantations near human settlements, deferred grazing and canopy enrichment through multi-species plantations of nursery-raised or wild-collected seedlings of desirable species within the forest patches of low basal area, will be needed to attain restoration goals, but reforestation programmes will have to be made attractive to the forest-dwelling communities.

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

10.21203/rs.3.rs-698917/v1 ◽

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.

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Tree Mortality Following Mixed-Severity Prescribed Fire Dramatically Alters the Structure of a Developing Pinus taeda Forest on the Mid-Atlantic Coastal Plain

Fire ◽

10.3390/fire2020025 ◽

2019 ◽

Vol 2 (2) ◽

pp. 25 ◽

Cited By ~ 1

Author(s):

David G. Ray ◽

Deborah Landau

Keyword(s):

Loblolly Pine ◽

Prescribed Fire ◽

Tree Mortality ◽

Basal Area ◽

Growing Season ◽

Pine Forest ◽

Atlantic Coastal Plain ◽

Relative Reduction ◽

Stem Density ◽

Horizontal Structure

This case study documents the aftermath of a mixed-severity prescribed fire conducted during the growing season in a young loblolly pine forest. The specific management objective involved killing a substantial proportion of the overstory trees and creating an open-canopy habitat. The burn generated canopy openings across 26% of the 25-ha burn block, substantially altering the horizontal structure. Mortality of pines was high and stems throughout the size distribution were impacted; stem density was reduced by 60% and basal area and aboveground biomass (AGB) by ~30% at the end of the first growing season. A nonlinear regression model fit to plot data portrays a positive relationship between high stocking (i.e., relative density > 0.60) and postburn mortality. Survival of individual trees was reliably modeled with logistic regression, including variables describing the relative reduction in the size of tree crowns following the burn. Total AGB recovered rapidly, on average exceeding levels at the time of the burn by 23% after six growing seasons. Intentional mixed-severity burning effectively created persistent canopy openings in a young fire-tolerant precommercial-sized pine forest, meeting our objectives of structural alteration for habitat restoration.

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What influences the long-term development of mixtures in British forests?

Forestry An International Journal of Forest Research ◽

10.1093/forestry/cpaa003 ◽

2020 ◽

Vol 93 (4) ◽

pp. 545-556 ◽

Cited By ~ 1

Author(s):

W L Mason ◽

T Connolly

Keyword(s):

Functional Traits ◽

Scots Pine ◽

Shade Tolerance ◽

Basal Area ◽

Sitka Spruce ◽

Picea Sitchensis ◽

Silver Birch ◽

Western Hemlock ◽

Larix Kaempferi ◽

Pure Stand

Abstract Six experiments were established between 1955 and 1962 in different parts of northern and western Britain which used replicated randomized block designs to compare the performance of two species 50:50 mixtures with pure stands of the component species. The species involved were variously lodgepole pine (Pinus contorta Dougl.), Japanese larch (Larix kaempferi Lamb. Carr.), Scots pine (Pinus sylvestris L.), silver birch (Betula pendula Roth.), Sitka spruce (Picea sitchensis Bong. Carr.) and western hemlock (Tsuga heterophylla Raf. Sarg.). The first four species are light demanding, while Sitka spruce is of intermediate shade tolerance and western hemlock is very shade tolerant: only Scots pine and silver birch are native to Great Britain. In three experiments (Bickley, Ceannacroc, Hambleton), the mixtures were of two light-demanding species, while at the other three sites, the mixture tested contained species of different shade tolerance. The experiments were followed for around 50 years, similar to a full rotation of even-aged conifer stands in Britain. Five experiments showed a tendency for one species to dominate in mixture, possibly reflecting differences in the shade tolerance or other functional traits of the component species. In the three experiments, the basal area of the mixtures at the last assessment was significantly higher than predicted based on the performance of the pure stands (i.e. the mixture ‘overyielded’). In two of these cases, the mixture had had a higher basal area than found in the more productive pure stand indicating ‘transgressive overyielding’. Significant basal area differences were generally more evident at the later assessment date. The exception was in a Scots pine: western hemlock mixture where greater overyielding at the earlier date indicated a nursing (‘facilitation’) effect. In the remaining experiments, the performance of the mixture conformed to predictions from the growth of the component species in pure stands. Taken overall, the results suggest that functional traits can be used to interpret the performance of mixtures but prediction of the outcome will require better understanding of the interplay between species and site characteristics plus the influence of silvicultural interventions.

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Stand growth responses after fertilization for thinned lodgepole pine, Douglas-fir, and spruce in forests of interior British Columbia, Canada

Canadian Journal of Forest Research ◽

10.1139/cjfr-2019-0188 ◽

2019 ◽

Vol 49 (11) ◽

pp. 1471-1482

Author(s):

Woongsoon Jang ◽

Bianca N.I. Eskelson ◽

Louise de Montigny ◽

Catherine A. Bealle Statland ◽

Derek F. Sattler ◽

...

Keyword(s):

British Columbia ◽

Picea Glauca ◽

Lodgepole Pine ◽

Basal Area ◽

Stand Density ◽

Site Index ◽

Douglas Fir ◽

Picea Sitchensis ◽

Growth And Yield ◽

Growth Responses

This study was conducted to quantify growth responses of three major commercial conifer species (lodgepole pine (Pinus contorta Douglas ex Loudon var. latifolia Engelm. ex S. Watson), interior Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca (Beissn.) Franco), and spruce (white spruce (Picea glauca (Moench) Voss) and hybrid spruce (Picea engelmannii Parry ex. Engelm. × Picea glauca (Moench) Voss × Picea sitchensis (Bong.) Carrière))) to various fertilizer blends in interior British Columbia, Canada. Over 25 years, growth-response data were repeatedly collected across 46 installations. The fertilizer blends were classified into three groups: nitrogen only; nitrogen and sulfur combined; and nitrogen, sulfur, and boron combined. The growth responses for stand volume, basal area, and top height were calculated through absolute and relative growth rate ratios relative to a controlled group. Fertilizer blend, inverse years since fertilization, site index, stand density at fertilization, and their interactions with the fertilizer blend were used as explanatory variables. The magnitude and significance of volume and basal area growth responses to fertilization differed by species, fertilizer-blend groups, and stand-condition variables (i.e., site index and stand density). In contrast, the response in top height growth did not differ among fertilization blends, with the exception of the nitrogen and sulfur fertilizer subgroup for lodgepole pine. The models developed in this study will be incorporated into the current growth and yield fertilization module (i.e., Table Interpolation Program for Stand Yields (TIPSY)), thereby supporting guidance of fertilization applications in interior forests in British Columbia.

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LiDAR and Weibull modeling of diameter and basal area

The Forestry Chronicle ◽

10.5558/tfc84866-6 ◽

2008 ◽

Vol 84 (6) ◽

pp. 866-875 ◽

Cited By ~ 30

Author(s):

V. Thomas ◽

R D Oliver ◽

K. Lim ◽

M. Woods

Keyword(s):

Finite Mixture Models ◽

Basal Area ◽

Weibull Model ◽

Mixture Modeling ◽

Finite Mixture ◽

Stem Density ◽

Promising Technique ◽

Diameter Class ◽

Modelling Approach ◽

Diameter Distributions

This study investigates the ability to predict forest diameter distributions from light detection and ranging (LiDAR) data using Weibull modelling for forest stands in central Ontario. Results suggest that the unimodal 2-parameter Weibull model is a promising technique for the prediction of diameter class distributions, with strong relationships evident for several subgroups (at 95% confidence, r2adj=0.83, 0.78, 0.88, 0.80, 0.83, and 0.65, with validation RMSE of 4.09 m2/ha, 0.61 stems/ha, 6.05, 0.64, 4.73, and 0.09 for basal area, stem density, and the Weibull a and b parameters for basal area and stem density, respectively). The unimodal models were found to be least effective for the irregularly shaped diameter distributions, particularly for low-density coniferous plots that have undergone shelterwood treatment. A significant improvement in results for these irregular plots was found with a finite mixture modelling approach, suggesting that finite mixture models may extend our ability to predict diameter distributions over large portions of the landscape. Key words: LiDAR, Weibull, finite mixture modeling, diameter class distributions, multiple linear regression

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Using survival analysis to predict the harvesting of forest stands in Quebec, Canada

Canadian Journal of Forest Research ◽

10.1139/cjfr-2016-0498 ◽

2017 ◽

Vol 47 (8) ◽

pp. 1066-1074 ◽

Cited By ~ 4

Author(s):

L.C. Melo ◽

R. Schneider ◽

R. Manso ◽

J.-P. Saucier ◽

M. Fortin

Keyword(s):

Survival Analysis ◽

Random Effect ◽

Basal Area ◽

Permanent Plots ◽

Stem Density ◽

Time Varying ◽

Spatial Correlations ◽

Explanatory Variables ◽

Interval Censored ◽

Level Model

Survival analysis methods make better use of temporal information, accommodate multiple levels of explanatory variables, and are meant to deal with interval-censored data. In a context of harvest modeling, this approach could improve some known limitations. In this study, we used data from a network of permanent plots in the province of Quebec, Canada, as a real-world case study. We tested the potential of survival analysis to predict plot-level harvest probabilities from plot- and regional-level variables. The approach also included random effects to account for spatial correlations. The results showed the potential of survival analysis to provide annual predictions of harvest occurrence. Both regional and time-varying variables, as well as spatial patterns, had important effects on the probability of a plot to be harvested. Respectively, reductions in the annual allowable cut volumes led to a decrease in the harvest probabilities. Greater harvest probabilities were associated with the broadleaved dynamics class and higher values of basal area. In contrast, they were decreased by stem density and slope classes. The spatial random effect resulted in an improvement of the model fit. Our plot-level model improved some limitations reported in previous studies by taking the effect of a time-varying regional variable into account.

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