火山碎屑空降沉积的二维数值模拟

2D-NUMERICAL SIMULATION OF DISPERSION OF TEPHRA FALLOUT

从大气中火山灰扩散的二维微分方程出发 ,采用Suzuki(1983)对火山空降碎屑灾害数值模拟的数学模型 ,研制出用于单个火山一次性喷发事件的碎屑物空降沉积分布的实用程序。介绍了编程的基本思想 ,讨论了编程过程中所遇到的实际问题 ,同时结合长白山火山物理研究工作给出的长白山火山动力学参数 ,对长白山火山喷发空降碎屑厚度分布进行了具体模拟应用 ,针对实际模拟结果对程序提出了改进意见 。

Tephra falls is one of the most serious volcanic hazards. The purpose of the quantitative simulation of this complex dynamic process is to build up a model for real time prediction of this hazard of volcanic eruption. Tephra falls are controlled by many factors, so that it is difficult to build up a quantitative model, and possible only to build up a semiquantitative model. Another purpose of the simulation is to get quantitative information of eruption source based on the survey of tephra fallout. The results can also be applied to the assessment of volcanic hazards. The dispersion of tephra is a function of many factors: total mass, median diameter and standard deviation of material erupted, height of the eruption column, wind velocity, and the nature of particle diffusion from the eruption column. The relationship between these factors and the dispersion of tephra can be described by using a model of two dimensional diffusion in atmosphere. We adopt here the mathematic model for dispersion of tephra proposed by Suzuki (1983). Basing on Suzuki's formula, we compile a practical program for simulating the dispersion of tephra fallout from a single volcano at one event of eruption. Combined with the dynamic parameters of the eruption of Tianchi volcano obtained from physical volcanologic research, this program is applied to simulating the dispersion of tephra from Tianchi volcano. One outstanding characteristics of volcanic tephra dispersion is that the size and thickness of particles demonstrate an exponential attenuation with increasing distance from the source area. This relationship had been used as a base for calculating the total mass of tephra fallout. Unfortunately, no overall theory at present can be used to predict this kind of behavior. The following opinions are proposed for improving the mathematical model: (1) The physical units used in the empirical formulation are not uniform: some are in m/kg·s -1 , and some are in cm/g·s -1 . This may cause a deviation of several orders of magnitude from the real result. A coordination of the units has been made in this paper. (2) The integrations of particle size and the height are not an independent but a coupling process, so that the double integration of particle size and height can not be separated as the time of two single integrations. (3) No boundary condition is assumed in this model, so we need not to limit the model for hazard assessment of iso mass distribution larger than 1g/cm 2, but to use also the model for iso mass distribution of less than 1g/cm 2 for the purpose of environmental protection. The practice has demonstrated that the tephra of smaller size is more dangerous to the engine of airplane and may cause breathing difficulties for humans. Therefore, the iso mass distribution contours should be divided into two types: one for the purpose of hazard assessment and the other for environmental protection.