Timothy G. Gregoire

The ROS planning system: Evolution, basic concepts, and research needed

Abstract This paper describes the evolution of the concept of the Recreation Opportunity Spectrum (ROS)—a largely resource‐based approach to providing recreational diversity. It explains the needs of the USDA Forest Service and USDI Bureau of Land Management for a recreation resource planning system and relates those needs to the development of the ROS system to guide recreation planning of large areas. The basic concepts and tenets of the ROS system are explained and needed research is outlined.

Parametric modelling of growth curve data: An overview

In the past two decades a parametric multivariate regression modelling approach for analyzing growth curve data has achieved prominence. The approach, which has several advantages over classical analysis-of-variance and general multivariate approaches, consists of postulating, fitting, evaluating, and comparing parametric models for the datas mean structure and covariance structure. This article provides an overview of the approach, using unified terminology and notation. Well-established models and some developed more recently are described, with emphasis given to those models that allow for nonstationarity and for measurement times that differ across subjects and are unequally spaced. Graphical diagnostics that can assist with model postulation and evaluation are discussed, as are more formal methods for fitting and comparing models. Three examples serve to illustrate the methodology and to reveal the relative strengths and weaknesses of the various parametric models.

Model-based inference for biomass estimation in a LiDAR sample survey in Hedmark County, Norway

In forest inventories, regression models are often applied to predict quantities such as biomass at the level of sampling units. In this paper, we propose a model-based inference framework for combining sampling and model errors in the variance estimation. It was applied to airborne laser (LiDAR) data sets from Hedmark County, Norway, where the model error proportion of the total variance was found to be large for both scanning (airborne laser scanning) and profiling LiDAR when biomass was estimated. With profiling LiDAR, the model error variance component for the entire county was as large as 71% whereas for airborne laser scanning, it was 43% of the total variance. Partly, this reflects the better accuracy of the pixel-based regression models estimated from scanner data as compared with the models estimated from profiler data. The framework proposed in our study can be applied in all types of sample surveys where model-based predictions are made at the level of individual sampling units. Especially, it should be useful in cases where model-assisted inference cannot be applied due to the lack of a probability sample from the target population or due to problems of correctly matching observations of auxiliary and target variables.

sampling methods to estimate foliage and other characteristics of individual trees

The total foliar area or mass of a tree is difficult to measure, as is its bark or cambial area, and various other components of aboveground biomass. A variety of sampling methods is proposed and estimators of these characteristics are presented. Based on probability precepts, all estimators are unbiased. An unbiased estimator of variance for each estimator also is presented. The basis in probability rather than a fitted regression equation provides some important safeguards, and is a useful alternative when fitted re- gression functions are unavailable for a particular species and physiographic condition.

Model-assisted estimation of biomass in a LiDAR sample survey in Hedmark County, NorwayThis article is one of a selection of papers from Extending Forest Inventory and Monitoring over Space and Time.

Inasmuch as LiDAR is becoming an increasingly prominent tool for forest inventory, it is timely to develop a framework to understand the statistical properties of LiDAR-based estimates. A model-ass...

Separating the ground and airborne laser sampling phases to estimate tropical forest basal area, volume, and biomass

Airborne laser profiling data were used to estimate the basal area, volume, and biomass of primary tropical forests. A procedure was developed and tested to divorce the laser and ground data collection efforts using three distinct data sets acquired in and over the tropical forests of Costa Rica. Fixed-area ground plot data were used to simulate the height characteristics of the tropical forest canopy and to simulate laser measurements of that canopy. On two of the three study sites, the airborne laser estimates of basal area, volume, and biomass grossly misrepresented ground estimates of same. On the third study site, where the widest ground plots were utilized, airborne and ground estimates agreed within 24%. Basal area, volume, and biomass prediction inaccuracies in the first two study areas were tied directly to disagreements between simulated laser estimates and the corresponding airborne measurements of average canopy height, height variability, and canopy density. A number of sampling issues were investigated; the following results were noted in the analyses of the three study areas. 1) Of the four ground segment lengths considered (25 m, 50 m, 75 m, and 100 m), the 25 m segment length introduced a level of variability which may severely degrade prediction accuracy in these Costa Rican primary tropical forests. This effect was more pronounced as plot width decreased. A minimum segment length was on the order of 50 m. 2) The decision to transform or not to transform the dependent variable (e.g., biomass) was by far the most important factor of those considered in this experiment. The natural log transformation of the dependent variable increased prediction error, and error increased dramatically at the shorter segment lengths. The most accurate models were multiple linear models with forced zero intercept and an untransformed dependent variable. 3) General linear models were developed to predict basal area, volume, and biomass using airborne laser height measurements. Useful laser measurements include average canopy height, all pulses (ha), average canopy height, canopy hits (hc) and the coefficients of variation of these terms (ca and cc). Coefficients of determination range from 0.4 to 0.6. Based on this research, airborne laser and ground sampling procedures are proposed for use for reconnaissance level surveys of inaccessible forested regions.

Habitat characterizations underestimate the role of edaphic factors controlling the distribution of Entandrophragma

Numerous theories have been developed and tested to explain the high botanical diversity in tropical forests, ranging from nonequilibrium theories emphasizing the importance of chance to equilibrium theories depicting highly specialized species occupying narrow ecological niches. Niche-based theories have most often evaluated species adaptation to different light environments, but some studies have evaluated the importance of edaphic attributes in controlling species distributions. We evaluated the role of edaphic factors in controlling the distribution of African mahogany in the genus Entandrophragma on a 100-ha plot in the Dzanga-Sangha Dense Forest Reserve, Central African Republic. This study went beyond simple characterization of edaphic conditions in topographic or other classes to test for specific associations with chemical and physical soil parameters known to be important to plant growth. Trees ≥30 cm dbh of the four species of Entandrophragma evaluated were nonrandomly distributed in the forest. Torus translation tests indicated that none of the species exhibited any topographic preferences. However, three of the four species had significant associations with at least two soil chemical attributes. Randomization tests evaluating links between soil chemical and physical properties and topographic position underscored the complexity of the relationship and suggest that inferring edaphic attributes from broadly and simply defined habitat classes may significantly underestimate the importance of soil heterogeneity in contributing to species coexistence.

Estimating Quebec provincial forest resources using ICESat/GLAS

Ground plots, airborne profiling and space lidar (light detection and ranging) measurements of canopy height and crown closure, space radar topographic data, a Landsat cover type map, and a vegetation zone map were used in a model-assisted, two-phase sampling design to estimate the aboveground biomass and carbon resources of Quebec. It was determined that a simple random sampling estimator, with covariance terms added, could be used to quantify the variabil- ity of regional Geoscience Laser Altimeter System (GLAS) biomass estimates where interorbit distances are, on average, ‡15 km apart. Prediction error increased standard errors, on average, 24.4%, 4.6%, and 2.8% at the cover type, vegetation zone, and provincial levels, respectively. Inclusion of the covariance term in the calculation of grouped cover type variances increased the vegetation zone standard errors up to 3.7 times and the provincial standard errors 15.6 times. In the southern commercial forests of Quebec, GLAS underestimated ground-based biomass values by 7.3% (stratified lin- ear model) and 10.2% (nonstratified linear model). Quebec forests support 2.57 ± 0.33 gigatonnes of carbon (nonstratified linear model). Approximately 25% of that carbon was found to be located in two southern vegetation zones (northern hard- wood and mixedwood), another 25% in two northern vegetation zones (taiga and treed tundra), and the remaining 50% in the boreal zone.

A non-linear mixed-effects model to predict cumulative bole volume of standing trees

For purposes of forest inventory and eventual management of the forest resource, it is essential to be able to predict the cumulative bole volume to any stipulated point on the standing tree bole, while requiring measurements of tree size that can be made easily, quickly and accurately. Equations for this purpose are typically non-linear and are fitted to data garnered from a sample of felled trees. Because the cumulative bole volume of each tree is measured to numerous upper-bole locations, correlations between measurements within a tree are likely. A mixed-effects model is fitted to account for this within-subject (tree) correlation structure, while also portraying the sigmoidal shape of the cumulative bole volume profile.

Use of models in large-area forest surveys: comparing model-assisted, model-based and hybrid estimation

This paper focuses on the use of models for increasing the precision of estimators in large-area forest surveys. It is motivated by the increasing availability of remotely sensed data, which facilitates the development of models predicting the variables of interest in forest surveys. We present, review and compare three different estimation frameworks where models play a core role: model-assisted, model-based, and hybrid estimation. The first two are well known, whereas the third has only recently been introduced in forest surveys. Hybrid inference mixes design-based and model-based inference, since it relies on a probability sample of auxiliary data and a model predicting the target variable from the auxiliary data..We review studies on large-area forest surveys based on model-assisted, model-based, and hybrid estimation, and discuss advantages and disadvantages of the approaches. We conclude that no general recommendations can be made about whether model-assisted, model-based, or hybrid estimation should be preferred. The choice depends on the objective of the survey and the possibilities to acquire appropriate field and remotely sensed data. We also conclude that modelling approaches can only be successfully applied for estimating target variables such as growing stock volume or biomass, which are adequately related to commonly available remotely sensed data, and thus purely field based surveys remain important for several important forest parameters.