Improved allometric equations for tree aboveground biomass estimation in tropical dipterocarp forests of Kalimantan,Indonesia

Background： Currently, the common and feasible way to estimate the most accurate forest biomass requires ground measurements and allometric models.Previous studies have been conducted on allometric equations development for estimating tree aboveground biomass（AGB） of tropical dipterocarp forests（TDFs） in Kalimantan（Indonesian Borneo）.However, before the use of existing equations, a validation for the selection of the best allometric equation is required to assess the model bias and precision.This study aims at evaluating the validity of local and pantropical equations; developing new allometric equations for estimating tree AGB in TDFs of Kalimantan; and validating the new equations using independent datasets.Methods： We used 108 tree samples from destructive sampling to develop the allometric equations, with maximum tree diameter of 175 cm and another 109 samples from previous studies for validating our equations.We performed ordinary least squares linear regression to explore the relationship between the AGB and the predictor variables in the natural logarithmic form.Results： This study found that most of the existing local equations tended to be biased and imprecise, with mean relative error and mean absolute relative error more than 0.1 and 0.3, respectively.We developed new allometric equations for tree AGB estimation in the TDFs of Kalimantan.Through a validation using an independent dataset,we found that our equations were reliable in estimating tree AGB in TDF.The pantropical equation, which includes tree diameter, wood density and total height as predictor variables performed only slightly worse than our new models.Conclusions： Our equations improve the precision and reduce the bias of AGB estimates of TDFs.Local models developed from small samples tend to systematically bias.A validation of existing AGB models is essential before the use of the models.

On the validity of the Boltzmann–BGK model through relaxation evaluation

The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.