Nonlinear Feature of the Abrupt Transitions between Multiple Equilibria States of an Ecosystem Model

Based on a five-variable theoretical ecosystem model, the stability of equilibrium state and the nonlinear feature of the transition between a grassland state and a desert state are investigated. The approach of the conditional nonlinear optimal perturbations （CNOPs）, which are the nonlinear generalization of the linear singular vectors （LSVs）, is adopted. The numerical results indicate that the linearly stable grassland and desert states are nonlinearly unstable to large enough initial perturbations on the condition that the moisture index # satisfies 0.3126 〈 μ 〈 0.3504. The perturbations represent some kind of anthropogenic influence and natural factors. The results obtained by CNOPs, LSVs and Lyapunov vectors （LVs） are compared to analyze the nonlinear feature of the transition between the grassland state and the desert state. Besides this, it is shown that the five-variable model is superior to the three-variable model in providing more visible signals when the transitions occur.

Intermediately Complex Models for the Hydrological Interactions in the Atmosphere-Vegetation-Soil System

This paper investigates the hydrological interactions in the atmosphere-evegetation-soil system by using the bucket model and several new simplified intermediately complex models. The results of mathematical analysis and numerical simulations show that these models, despite their simplicity, can very clearly reveal the essential features of the rather complex hydrological system of atmosphere-ecosystem-soil. For given atmospheric variables, these models clearly demonstrate multiple timescales, the ＂red shift＂ of response spectra, multi-equilibria and limit cycles, bifurcation, abrupt change, self-organization, recovery, ＂desertification＂, and chaos. Most of these agree with observations. Especially, the weakening of ＂shading effect＂ of living canopy and the wilted biomass might be a major mechanism leading to the desertification in a relatively short period due to overgrazing, and the desertification in a relatively long period or in climate of change might be due to both Charney＇s mechanism and the shading effect. These ideas could be validated with further numerical simulations. In the paper, some methods for improving the estimation of timescales in the soil water evolution responding to the forcing are also proposed.

Optimization and analysis of winglet configuration for solar aircraft

Installing winglets can notably improve the aerodynamic performance of solar aircraft.This paper proposes a multi-constraints optimization method of winglets for solar aircraft,aiming to enhance the corresponding uninterrupted cruising capability.An optimization objective function is formed and is separately studied in aerodynamic and structural terms.Qualitative analysis shows that the winglet design parameters are restricted by four special constraints(geometry,aerodynamics,energy and stability)of solar aircraft.The optimization process is constructed on the basis of a multi-island genetic algorithm,and carried out for a 15 m wingspan solar aircraft.Although the designed winglet is not as good as the traditional winglet in terms of drag and structural weight,the designed winglet provides a better 24 h cruising capability.The sensitivity between the objective function and the design parameters is investigated,and the winglet effects vary with respect to the wing aspect ratio(AR=10,15,19.6).The effect of the constraints is analysed quantitatively,and some basic laws are obtained.Moreover,the feasible design region and the possible optimal design parameters of winglets for different wing configurations are explored.The calculation results show that when the aspect ratio exceeds a certain value,the winglets will not benefit the aircraft.

Ecological dynamic model of grassland and its practical verification

Based on the physico-biophysical considerations, mathematical analysis and some approximate formulations generally adopted in meteorology and ecology, an ecological dynamic model of grassland is developed. The model consists of three interactive variables, I.e. The biomass of living grass, the biomass of wilted grass, and the soil wetness. The major biophysical processes are represented in parameterization formulas, and the model parameters can be determined inversely by using the observational climatological and ecological data. Some major parameters are adjusted by this method to fit the data (although incomplete) in the Inner Mongolia grassland, and other secondary parameters are estimated through sensitivity studies. The model results are well agreed with reality, e.g., (I) the maintenance of grassland requires a minimum amount of annual precipitation (approximately 300 mm); (ii) there is a significant relationship between the annual precipitation and the biomass of living grass; and (iii) the overgrazing will eventually result in desertification. A specific emphasis is put on the shading effect of the wilted grass accumulated on the soil surface. It effectively reduces the soil surface temperature and the evaporation, hence benefits the maintenance of grassland and the reduction of water loss in the soil.