A Flexible Height–Diameter Model for Tree Height Imputation on Forest Inventory Sample Plots Using Repeated Measures from the Past

Abstract

Abstract:In this study, height-diameter relations were modeled using two different mixed model types for imputation of missing heights from longitudinal data. Model Type A had a hierarchical structure of sample plot-specific and measurement occasion-specific random effects. In Model Type B, a possible temporal variance was modeled by a sample plot-specific linear time trend. Furthermore, various calibration strategies of random effects were performed on past and current data, and a combination of both. The performance of the mixed models was compared on independent data using bias and root mean square error (RMSE). The results showed that Model Type A achieved the highest precision (lowest RMSE), if sample plot-specific random effects were predicted from old data and measurement occasion-specific ones were predicted from new data. In comparison, however, Model Type B had a higher RMSE, and lower bias. Model performance was almost unaffected from the usage of past or current data for the prediction of random effects. Results revealed that a certain calibration strategy should be simultaneously applied to all random effects from the same hierarchy level. Otherwise, predictions would become imprecise and a serious bias may result. In comparison with traditional uniform height curves, the novel mixed model approach performed slightly better.

Tree profile equations are significantly improved when adding tree age and stocking degree: an example for Larix gmelinii in the Greater Khingan Mountains of Inner Mongolia, northeast China

“…One of the earliest examples of the inclusion of random effects in forestry applications was the generation of height growth curves (Lappi and Bailey 1988). In the same line as our results, NLME models have been successfully applied to the development of taper equations (Özçelik et al 2011), crown width equations (Fu et al 2013;Yang and Huang 2017), biomass equations (Njana et al 2016), tree height and diameter equations (Gollob et al 2018;MacPhee et al 2018;Mehtätalo et al 2015), and top height equations (Sharma and Reid 2018). This suggests that the inclusion of random-effects parameters significantly improves the fit of the corresponding equations by capturing part of the natural variability related to biological processes involved in tree growth.…”

Development of a Tree Growth Difference Equation and Its Application in Forecasting the Biomass Carbon Stocks of Chinese Forests in 2050

“…Many scholars believe that validation is an important part of modeling, because validation precision can show the model's reliability [50]. Aggregating similar species into one species can increase the amount of modeling data and improve the fitting precision, and using the nonlinear function to fit the equation directly can avoid transformation bias [51,52]. Model efficiencies can commonly exceed 0.50 for distance-independent individual-tree diameter growth models fit for related forest types [53].…”

Defining Deforestation Patterns Using Satellite Images from 2000 and 2017: Assessment of Forest Management in Miombo Forests—A Case Study of Huambo Province in Angola

“…We used a versatile nonlinear growth function, the Näslund function [55], to fit the data. This function has frequently been used to model the height-diameter relationship for several tree species because of its flexibility [56][57][58][59]. The Näslund function is:…”

“…Developing precise stand-specific height-diameter models is considered one of the most important tasks in forest planning, inventory design, and monitoring of stand dynamics [56]. Precise height-diameter models developed with subject-specific (e.g., sample plot-specific) variations are included in the model [57,59,66]. The presented sample plot-specific mixed effects height-diameter model can be used for characterization of the vertical stand structures, estimation of volume and biomass, and simulation of stand dynamics for each vegetation zone of the studied forest.…”

“…We chose the best functional form (Näslund function) to adequately describe the variations in the height-diameter relationship of individual trees for each vegetation type (Figure 3). Näslund function is based on the growth theory (faster increase of height in earlier stages and slower increase in the later stages) [56,61,65,73] and is best suited to our data due to its pronounced flexibility for fitting data acquired from multiple tree species [58,59]. By looking at the growth curve patterns, we hoped to discover some similar patterns or principles that govern the growth of the species in the respective vegetation types.…”