Using quadratic mean diameter and relative spacing index to enhance height–diameter and crown ratio models fitted to longitudinal data

Abstract

The inclusion of quadratic mean diameter (QMD) and relative spacing index (RSI) substantially improved the predictive capacity of height-diameter at breast height (d.b.h.) and crown ratio models (CR), respectively. Data were obtained from 208 permanent plots established in western Arkansas and eastern Oklahoma during 1985-1987 and remeasured for the sixth time (2012-2014). Existing height-d.b.h. and CR estimation models for naturally occurring shortleaf pine forests (Pinus echinata Mill.) were updated and modified for improved performance. Additionally, eight height-d.b.h. relationship models that use only d.b.h. (fundamental local models) were modified using covariates. The model performance was evaluated using fit statistics [root mean square error (RMSE), Fit index and Akaike information criteria (AIC)]. The results showed that the best model form which was an extended non-linear model with autoregressive first order AR (1) structure and power variance function performed better than extended mixed-effects models and predicted well as an ordinary least squares non-linear model. The autocorrelation within individual trees was larger for the height-d.b.h. relationship than for CR estimation. The addition of QMD to mean dominant height (H D) greatly improved height-d.b.h. relationship with a reduction of 8 per cent in RMSE, compared with the use of basal area per hectare. Similarly, multiplying a fundamental local model by using QMD raised to a parametric power reduced RMSE by 16 per cent, improved Fit index by 12 per cent and decreased the AIC value by 7 per cent. D.b.h., H D and RSI best explained the crown ratio relationship with an improved Fit index by 6.7 per cent compared with alternative non-linear models without RSI. The logistic model for CR also provided prediction accuracy similar to that of a commonly used non-linear model. A non-linear model with an application of remedial measures to enhance adherence to modelling assumptions can provide better parameter estimates than mixedeffects modelling approach.

Evidence of climate effects on the height-diameter relationships of tree species

“…The social status index was calculated as the ratio between the DBH of the target tree and the mean quadratic diameter (MQD) of its plot. The inclusion of plot MQD in HD relationship models was already found to substantially improve their fit (Saud et al 2016). In all the models that included this effect, our results showed that the dominant trees tended to be more tapered than trees with a diameter close to the MQD while dominated trees were more slender, a pattern that is typically observed in even-aged stands (Pretzsch 2009, p. 189).…”

“…The existing literature provides a large array of plot metrics that have been tested in HD relationship models, including stem density, basal area, dominant height, or diameter, arithmetic or quadratic mean diameter, relative spacing indices, and age Garber et al 2009;Crecente Campo et al 2014;Mehtätalo et al 2015;Sharma and Breidenbach 2015;Adamec and Drápela 2016;Saud et al 2016). However, climate variables have been overlooked in most studies.…”

Estimation of Forest Biomass in Beijing (China) Using Multisource Remote Sensing and Forest Inventory Data

“…In addition, we computed the relative RMSE (RMSE%), the bias and the relative bias (bias%). Bias was calculated as the difference between a population mean of the measurements or test results and an accepted reference or true value, R 2 values were used to judge the model, and RMSE, Bias%, RMSE% reflect the precision of the model [45].…”

An Annual basal area growth model with multiplicative climate modifier fitted to longitudinal data for shortleaf pine

“…However, recently Zell (2018) used periodic re-measurement data from experimental forest management trials in Switzerland to study the impact of climate variables on individual tree growth. Saud et al (2016) also used this type of data. Further, most studies have used climate variables as linearly added terms to the argument diameter growth or ABAG models and have shown modest improvement in model prediction.…”

“…Further, most studies have used climate variables as linearly added terms to the argument diameter growth or ABAG models and have shown modest improvement in model prediction. Although Saud et al (2016) fitted ABAG model for shortleaf pine with climate variables (terms linearly added to the argument of a logistic function), investigation of the potential improvement from using climate variables and climate-based ABAG model sensitivity to climate change scenarios was lacking. Moreover, studies investigating the use of climate variables to show potential improvement in a climate-based growth model with re-measurement data to fit ABAG models are lacking as well.…”