David W. MacFarlane

Incorporating uncertainty into the parameters of a forest process model

Abstract ‘Process-based’ models have been advanced to incorporate current knowledge regarding forest processes explicitly into model structure, yet uncertainty regarding these processes is often omitted from parameter estimation. This problem reflects the fact that parameters have been traditionally viewed as constants. In process models this is often unrealistic, since physiological rates and morphological characteristics, which have known variation, are often parametrized. Reasonable estimates for parameters can, and should be, abstracted from the vast body of forestry literature, and formulated into probability distributions which reflect uncertainty in their potential value. Here probability distributions are estimated for 14 physiological or morphological parameters of Pipestem , a stand-level model of carbon allocation and growth for loblolly pine ( Pinus taeda ), based on an extensive review of published information. Investigation of parameters revealed a wide range of variation in accumulated knowledge regarding their value, and led to the development of generic parameters which may be transferrable to other similar models. Parameter uncertainty also appeared tractable in some cases and might be reduced through reformulation of the model. Some parameters investigated had known co-dependency on model variables or other parameters, and may be better expressed as dependent variables. This study was part of a larger study in which a Bayesian analysis was used to assess the uncertainty in the predictions of a forest growth model.

A Hierarchical Model for Quantifying Forest Variables Over Large Heterogeneous Landscapes With Uncertain Forest Areas

We are interested in predicting one or more continuous forest variables (e.g., biomass, volume, age) at a fine resolution (e.g., pixel level) across a specified domain. Given a definition of forest/nonforest, this prediction is typically a two-step process. The first step predicts which locations are forested. The second step predicts the value of the variable for only those forested locations. Rarely is the forest/nonforest status predicted without error. However, the uncertainty in this prediction is typically not propagated through to the subsequent prediction of the forest variable of interest. Failure to acknowledge this error can result in biased estimates of forest variable totals within a domain. In response to this problem, we offer a modeling framework that will allow propagation of this uncertainty. Here we envision two latent processes generating the data. The first is a continuous spatial process while the second is a binary spatial process. The continuous spatial process controls the spatial association structure of the forest variable of interest, while the binary process indicates presence of a possible nonzero value for the forest variable at a given location. The proposed models are applied to georeferenced National Forest Inventory (NFI) data and spatially coinciding remotely sensed predictor variables. Due to the large number of observed locations in this dataset we seek dimension reduction not just in the likelihood, but also for unobserved stochastic processes. We demonstrate how a low-rank predictive process can be adapted to our setting and reduce the dimensionality of the data and ease the computational burden.

Modeling loblolly pine canopy dynamics for a light capture model

Abstract Advances in forest modeling make it possible to estimate light capture for every tree in a stand, and may allow for improvements in modeling stand dynamics. A major difficulty in using such models is that they rely heavily on parameterization of crown characteristics, which presumably differ from stand to stand. We reformulated crown parameters of the tRAYci light capture model for describing crown shape, relative foliar shell thickness and leaf area density (LAD) into generalized equations, which can be used to describe canopy dynamics in even-aged loblolly pine ( P. taeda L . ) stands. We used parameter equations to model 8 years of change in the canopy of 36, 17-year-old experimental loblolly pine stands, planted under a variety conditions, and estimated annual light capture for every tree over the study period. The results of our analysis suggest that differences in LAD between stands were effectively captured by our parameter estimation methods, but model predictions remained sensitive to parameters describing crown shape and foliar shell thickness. Our results suggest that estimated light capture from tRAYci is somewhat robust to different parameter settings because light capture estimation is strongly influenced by individual tree dimensions, and our methods enhanced this quality. General regression equations were developed for predicting crown characterization parameters from site index, stand age and stand density, but these equations did not fully capture differences in parameter values predicted from stand measurement data. Regression analysis and C p analysis suggest that planting density was a superior predictor variable for characterizing canopy dynamics when compared to current density. Also discussed in this manuscript are general patterns in canopy dynamics with special references to tRAYci model structure and behavior.

Evaluating a non-destructive method for calibrating tree biomass equations derived from tree branching architecture

Key messageFunctional branch analysis (FBA) is a promising non-destructive method that can produce accurate tree biomass equations when applied to trees which exhibit fractal branching architecture.AbstractFunctional branch analysis (FBA) is a promising non-destructive alternative to the standard destructive method of tree biomass equation development. In FBA, a theoretical model of tree branching architecture is calibrated with measurements of tree stems and branches to estimate the coefficients of the biomass equation. In this study, species-specific and mixed-species tree biomass equations were derived from destructive sampling of trees in Western Kenya and compared to tree biomass equations derived non-destructively from FBA. The results indicated that the non-destructive FBA method can produce biomass equations that are similar to, but less accurate than, those derived from standard methods. FBA biomass prediction bias was attributed to the fact that real trees diverged from fractal branching architecture due to highly variable length–diameter relationships of stems and branches and inaccurate scaling relationships for the lengths of tree crowns and trunks assumed under the FBA model.

Modeling larval malaria vector habitat locations using landscape features and cumulative precipitation measures.

BackgroundPredictive models of malaria vector larval habitat locations may provide a basis for understanding the spatial determinants of malaria transmission.MethodsWe used four landscape variables (topographic wetness index [TWI], soil type, land use-land cover, and distance to stream) and accumulated precipitation to model larval habitat locations in a region of western Kenya through two methods: logistic regression and random forest. Additionally, we used two separate data sets to account for variation in habitat locations across space and over time.ResultsLarval habitats were more likely to be present in locations with a lower slope to contributing area ratio (i.e. TWI), closer to streams, with agricultural land use relative to nonagricultural land use, and in friable clay/sandy clay loam soil and firm, silty clay/clay soil relative to friable clay soil. The probability of larval habitat presence increased with increasing accumulated precipitation. The random forest models were more accurate than the logistic regression models, especially when accumulated precipitation was included to account for seasonal differences in precipitation. The most accurate models for the two data sets had area under the curve (AUC) values of 0.864 and 0.871, respectively. TWI, distance to the nearest stream, and precipitation had the greatest mean decrease in Gini impurity criteria in these models.ConclusionsThis study demonstrates the usefulness of random forest models for larval malaria vector habitat modeling. TWI and distance to the nearest stream were the two most important landscape variables in these models. Including accumulated precipitation in our models improved the accuracy of larval habitat location predictions by accounting for seasonal variation in the precipitation. Finally, the sampling strategy employed here for model parameterization could serve as a framework for creating predictive larval habitat models to assist in larval control efforts.

Quantifying tree and forest bark structure with a bark-fissure index

Tree bark provides habitat for many organisms in forest ecosystems, but forest bark structure is typically not considered when important forest structural attributes are discussed. We describe a new metric for quantifying bark structure: a bark-fissure index (BFI). We examined species-specific changes in the frequency and depth of bark fissures caused by both horizontal and vertical splitting of bark layers for trees of different sizes and found that BFI generally scaled exponentially with stem diameter, with distinctively different patterns for 15 different tree species. We found a strong correlation between BFI and tree species preferences of the white-breasted nuthatch, a bark-foraging bird species. We demonstrate how BFI can be scaled up to define forest-scale bark structure using simple stand structural data, such as stand tables. This research contributes a new, objective, and repeatable way of quantifying tree and forest bark structure using simple bark measurements.