Methodological Comparisons of Absorptive and Transport Fine Root Production, Mortality and Decomposition in A Loblolly Pine Plantation Forest

Background and aims Fine roots can be functionally classified into an absorptive fine root pool (AFR) and a transport fine root pool (TFR) and their production, mortality and decomposition play a critical role in forest soil carbon (C) cycling. Different methods give significant estimates. However, how methodological difference affects AFT and TFR production, mortality, and decomposition estimates remains unclear, impeding us to accurately construct soil C budgets. Methods We used dynamic-flow model, a model combining measurements of litterbags and soil cores, and balanced-hybrid model, a model combining measurements of minirhizotrons and soil cores, to quantify these fine root estimates in a managed loblolly pine forest. Results Temporal changes in production, mortality or decomposition estimates using both models were not different for both AFRs and TFRs. Annual production, mortality, and decomposition were comparable between AFRs and TFRs when measured using the dynamic-flow model but significantly higher for AFRs than for TFRs when measured using the balanced-hybrid model. Annual production, mortality and decomposition estimates using the balanced-hybrid model were 75%, 71% and 69% higher than those using the dynamic-flow model (P < 0.05 for all), respectively, for AFRs, but 12%, 6% and 5% higher than those using the dynamic-flow model (P > 0.05 for all), respectively, for TFRs. Model test showed that the balanced-hybrid model had greater estimation accuracy than the dynamic-flow model. Lower AFR estimates using the dynamic-flow model appeared to result from the underestimated AFR mass loss rate induced by the litterbag method. Conclusions Methodological difference had a more significant impact on AFR estimates than on TFR estimates. These results have important implications for better quantifying the most dynamic fraction of fine root system and understanding soil C cycling.

An Extended Model for Disaster Relief Operations Used on the Hagibis Typhoon Case in Japan

This paper presents a generalization of a previously defined lexicographical dynamic flow model based on multi-objective optimization for solving the multi-commodity aid distribution problem in the aftermath of a catastrophe. The model considers distribution of the two major commodities of food and medicine, and seven different objectives, and the model can easily be changed to include more commodities in addition to other and different priorities between the objectives. The first level in the model is to maximize the amount of aid distributed under the given constraints. Keeping the optimal result from the first level, the second level can be solved considering objectives such as the cost of the operation, the time of the operation, the equity of distribution for each type of humanitarian aid, the priority of the designated nodes, the minimum arc reliability, and the global reliability of the route. The model is tested on a recent case study based on the Hagibis typhoon disaster in Japan in 2019. The paper presents a solution for the distribution problem and provides a driving schedule for vehicles for delivering the commodities from depots to the regional centers in need for humanitarian aid.

Probabilistic constrained optimization on flow networks

Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the probability for random boundary data to be feasible, discussing their advantages and disadvantages. In this context, feasible means, that the flow corresponding to the random boundary data meets some box constraints at the network junctions. The first method is the spheric radial decomposition and the second method is a kernel density estimation. In both settings, we consider certain optimization problems and we compute derivatives of the probabilistic constraint using the kernel density estimator. Moreover, we derive necessary optimality conditions for an approximated problem for the stationary and the dynamic case. Throughout the paper, we use numerical examples to illustrate our results by comparing them with a classical Monte Carlo approach to compute the desired probability.