干旱半干旱区灌丛斑块与降水量响应关系的熵模型模拟

Relationship and response of shrub patches to precipitation using the entropy model in arid and semiarid regions of China

灌丛斑块分布格局是灌木在干旱缺水条件下对生存环境的自我调节和适应的具体表现。应用熵理论和Klausmier模型,解释了灌丛斑块水分聚集原理并模拟了不同年降水条件下灌丛斑块的最佳面积比值(即最佳灌丛盖度)。研究结果表明:灌丛斑块生物量与其土壤含水量呈反比例函数关系,当生态系统处于稳定状态时(即熵最大状况下),年降水量与灌丛斑块面积比值符合一定的线性关系。研究采用内蒙古草原地区的野外调查数据,获得模型所需参数,进而模拟了不同年降水量条件下灌丛斑块最佳面积比值,研究结果可为半干旱地区植被保护与恢复提供参考。

In arid and semiarid regions, shrubs are often spatially distributed in patchy patterns, allowing shrubs to self- regulate and adapt to dry conditions. Shrub encroachment （also known as shrub invasion） is a typical pattern of patchy shrub distribution. This phenomenon represents one of the major environmental problems faced by the world＇s grassland ecosystems, and widely occurs in Africa, the USA, Australia, Asia, Europe. Shrub encroachment is exacerbated by overgrazing, prairie fires, climate change, atmospheric carbon dioxide concentrations, and biotic and abiotic environmental factors. Precipitation is considered to be an influential factor of patchy shrub distribution in arid and semiarid regions, which may regulate shrub coverage and the patch size. Theoretically, a steady shrub ecosystem would have a balance between water supply and demand, while certain levels of precipitation should correspond with optimal shrub coverage, i.e., the optimal ratio of shrub patch size to the total area in the steady patchy shrub ecosystem. The maximum entropy production principle （MEP） to living systems may be used to quantitatively explain optimization in the non-equilibrium process, such as the evolution of biological macromolecules and the plant optimization theory at different scales. Shrub patches and interspace may be considered as a water gathering system, in which entropy production is mainly caused by two processes： （ 1 ） soil water mixing in shrub patches and （2） either rainfall or outside runoff. For entropy flow, the main contributing factors are precipitation, evaporation, and transpiration processes in shrub patches. In this study, a modified model for a shrub patch ecosystem was built. It was applied to explain the moisture gathering in shrub patches. The model was based on the entropy change theory and Klausmier moisture gathering model, consisting of a pair of partial differential equations on soil moisture and plar/t biomass in the two-dimension plane. Based on the principle of maximum entropy production （MEP）, the optimal ratio of shrub patches responding to different annual precipitation may be simulated. The simulation results showed a negative correlation between biomass and soil water content, which was verified by field experiments. When the ecosystem was steady （and the MEP principle was satisfied）, the annual precipitation and the optimal ratio of shrub patches had a certain linear relationship. The existing data for Inner Mongolia was used to set up the model parameters, from which the optimal ratio of shrub patches responding to different annual precipitation values varying from 50 mm to 450 mm was simulated. Then the optimal shrub area ratios for practical application were determined in arid and semiarid regions. For example a region with 300 mm precipitation produCed a shrub patch ratio of around 30%. This result provided theoretical support and practical guidance for ecosystem protection and plant recovery in arid and semiarid regions. The simulated values varied considerably, which may be because the effects of surface runoff were simplified to a linear relationship with precipitation in the modified model. Therefore, surface runoff sensitivity to patchy shrub distribution patterns requires further research.