Model errors in tree biomass estimates computed with an approximation to a missing covariance matrix
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METHODOLOGY
Model errors in tree biomass estimates computed with an approximation to a missing covariance matrix Steen Magnussen1* and Oswaldo Ismael Carillo Negrete2
Abstract Background: Biomass and carbon estimation has become a priority in national and regional forest inventories. Biomass of individual trees is estimated using biomass equations. A covariance matrix for the parameters in a biomass equation is needed for the computation of an estimate of the model error in a tree level estimate of biomass. Unfortunately, many biomass equations do not provide key statistics for a direct estimation of model errors. This study proposes three new procedures for recovering missing statistics from available estimates of a coefficient of determination and sample size. They are complementary to a recently published study using a computationally intensive Monte Carlo approach. Results: Our recovery approach use survey data from the population targeted for an estimation of tree biomass. Examples from Germany and Mexico illustrate and validate the methods. Applications with biomass estimation and robust recovered fit statistics gave reasonable estimates of model errors in tree level estimates of biomass. Conclusions: It is good practice to provide estimates of uncertainty to any model-dependent estimate of above ground biomass. When a direct approach to estimate uncertainty is impossible due to missing model statistics, the proposed robust procedure is a first step to good practice. Our recommended approach offers protection against inflated estimates of precision. Keywords: Linear regression, Nonlinear regression, Weighted regression, Residual variance, Robust estimation, Parametric bootstrap Background The importance of forest biomass for the global carbon cycle is widely recognized [1–4]. The imperative of maintaining global levels of forest biomass and slowing regional rates of decline [5] has fostered international cooperation, initiatives, and projects to this end [6–8]. A large number of countries have agreed to implement an accounting system for forest carbon and to report on national-level annual gains and losses [9–11]. With few exceptions, the forest carbon accounting system has a national forest inventory at its core, and a suite of models to expand and transform inventory data to *Correspondence: [email protected] 1 Natural Resources Canada, 506 West Burnside Road, Victoria, BC V8Z 1M5, Canada Full list of author information is available at the end of the article
forest carbon [12–14]. Carbon components not fully covered by an inventory are typically estimated from activity data (e.g. harvest, disturbance, and erosion) and models fitted to data from research studies of, for examples: litter-fall; litter-decomposition; fine-root turnover; seed production; and dead and downed-woody debris. An estimate of the uncertainty in a carbon balance has become a routine requirement [15, 16]. When the core inventory data comes from a probability sample, the uncertainty arises from three sources:
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