Guidelines for constructing allometric models for the prediction of woody biomass: How many individuals to harvest?

Abstract

Abstract. The recent development of biomass markets and carbon trading has led to increasing interest in obtaining accurate estimates of woody biomass production. Aboveground woody biomass (B) is often estimated indirectly using allometric models, where representative individuals are harvested and weighed, and regression analyses used to generalise the relationship between individual mass and more readily measured non-destructive attributes such as plant height and stem diameter (D). To satisfy regulatory requirements and/or to provide market confidence, allometric models must be based on sufficient data to ensure predictions are accurate, whilst at the same time being practically and financially achievable.Using computer resampling experiments and allometric models of the form B ¼ aD b the trade-off between increasing the sample size of individuals to construct an allometric model and the accuracy of the resulting biomass predictions was assessed. A range of algorithms for selecting individuals across the stem diameter size-class range were also explored. The results showed marked variability across allometric models in the required number of individuals to satisfy a given level of precision. A range of 17-95 individuals were required to achieve biomass predictions with a standard deviation within 5% of the mean for the best performing stem diameter selection algorithm, while 25-166 individuals were required for the poorest. This variability arises from (a) inherent uncertainty in the relationship between diameter and biomass across allometric models, and (b) differences between the diameter size-class distribution of individuals used to construct a model, and the diameter size-class distribution of the population to which the model is applied. Allometric models are a key component of quantifying land-based sequestration activities, but despite their importance little attention has been given to ensuring the methods used in their development will yield sufficiently accurate biomass predictions. The results from this study address this gap and will be of use in guiding the development of new allometric models; in assessing the suitability of existing allometric models; and in facilitating the estimation of uncertainty in biomass predictions.

Carbon in Mature Native Forests in Australia: The Role of Direct Weighing in the Derivation of Allometric Equations

“…The number of trees considered in each equation varied considerably, from as few as five trees [26] to over 100 trees [22,23]. Roxburgh et al [53] suggested that for allometric equations constructed using an adequate size-class distribution of DBH in the population, a minimum sample size of 55 trees for generic Eucalypt species was required. However, this was based on typically younger trees with a smaller DBH range than found in more mature forests-it is expected that the minimum sample size for mature native forest trees to be higher, as they are less uniform and more likely to be impacted by decay.…”

Above-ground woody biomass allocation and within tree carbon and nutrient distribution of wild cherry (Prunus avium L.) – a case study

“…Where appropriate, normality was tested with a Shapiro-Wilk test. It is common practice to use allometric biomass equations as a cost effective and efficient method of relating an easily measurable parameter to that of a less obtainable dependent factor such as dry tree weight, or total bark weight (Parresol 1999;Zianis et al 2005;Picard et al 2012;Morhart et al 2013;Roxburgh et al 2015;Cifuentes Jara et al 2015). The biomass models used within this study follow the form given in Eq.…”

“…This is common practice within biomass estimation procedures to allow for full statistical scrutiny of the data (Sprugel 1983). The log transformation of data on both x and y axis renders a linear relationship thus denoting the correct fitment of an allometric power model (Picard et al 2012;Morhart et al 2013) and also corrects data for heteroscedasticity (Zeng and Tang 2011;Roxburgh et al 2015), which is typical for biomass data (Parrasol 1999). The R package: systemfit was used for the regression analysis (Henningsen and Hamann 2007) seemingly unrelated regression (SUR) analysis was applied to ensure the additivity of the calculated biomass equations (Parresol 1999(Parresol , 2001).…”

“…The site layout was planted in a randomised block ) growing seasons, the total number of sampled trees (n = 39) is in the range of that suggested by Roxburgh et al (2015). Since the trees were felled during the period of winter dormancy, biomass refers to leafless above ground biomass.…”

Above- and belowground tree biomass models for three mangrove species in Tanzania: a nonlinear mixed effects modelling approach

“…Results and conclusions based on regression analysis are only reliable if these assumptions are met (Ritz and Streibig 2008;Zuur et al 2009). For biological data, however, such assumptions may be difficult to meet.…”