ABSTRACT
Forest carbon stocks and sinks (CSSs) have been widely estimated using climate classification tables and linear regression (LR) models with common independent variables (IVs) such as the average diameter at breast height (DBH) of stems and root shoot ratio. However, this approach is relatively ineffective when the explanatory power of IVs is lower than that of unobservable variables. Various environmental and anthropogenic factors affect target variables that cause the correlation between them to be chaotic. Here, we designed a knife set (KS) approach combining LR models and the wandering through random forests (WTF) algorithm and applied it in a specific case of Phyllostachys edulis (Carrière) J. Houz. (P. edulis) forests, which have an irregular relationship between their belowground carbon (BGC) stocks and average DBH. We then validated the KS approach performed by cluster computing to estimate the aboveground carbon (AGC) and BGC stocks and the total net primary production (TNPP). The estimated CSSs were compared to the benchmark of the methodology that applied Tier 1 in the Intergovernmental Panel on Climate Change (IPCC) Guidelines for National Greenhouse Gas Inventories via 10-fold cross validation, and the KS approach significantly increased precision and accuracy of estimations. Our approach provides general insights to accurately estimate forest CSSs relying on evidence-based field data, even if some target variables are divergent in specific forest types. We also pointed out the reason why current fancy models containing machine learning (ML) or deep learning algorithms are not effective in predicting the target variables of certain chaotic systems is perhaps that the total explanatory power of observable variables is less than that of the total unobservable variables. Quantifying unobservable variables into observable variables is a linchpin of future works related to chaotic system estimation.
Subject(s)
Carbon Sequestration , Carbon , Climate ChangeABSTRACT
When we collect the growth curves of many individuals, orderly variation in the curves is often observed rather than a completely random mixture of various curves. Small individuals may exhibit similar growth curves, but the curves differ from those of large individuals, whereby the curves gradually vary from small to large individuals. It has been recognized that after standardization with the asymptotes, if all the growth curves are the same (anamorphic growth curve set), the growth curve sets can be estimated using nonchronological data; otherwise, that is, if the growth curves are not identical after standardization with the asymptotes (polymorphic growth curve set), this estimation is not feasible. However, because a given set of growth curves determines the variation in the observed data, it may be possible to estimate polymorphic growth curve sets using nonchronological data.In this study, we developed an estimation method by deriving the likelihood function for polymorphic growth curve sets. The method involves simple maximum likelihood estimation. The weighted nonlinear regression and least-squares method after the log-transform of the anamorphic growth curve sets were included as special cases.The growth curve sets of the height of cypress (Chamaecyparis obtusa) and larch (Larix kaempferi) trees were estimated. With the model selection process using the AIC and likelihood ratio test, the growth curve set for cypress was found to be polymorphic, whereas that for larch was found to be anamorphic. Improved fitting using the polymorphic model for cypress is due to resolving underdispersion (less dispersion in real data than model prediction).The likelihood function for model estimation depends not only on the distribution type of asymptotes, but the definition of the growth curve set as well. Consideration of these factors may be necessary, even if environmental explanatory variables and random effects are introduced.
