分形入渗下非饱和-饱和系统中水流的时空变化  

The temporospatial variations of water flow in an unsaturated-saturated system under infiltrations of fractional Gaussian noise and fractional Brownian motion

作　　者：杨晨[1,2] 张幼宽[2] 梁修雨[2] 

机构地区：[1]南京大学地球科学与工程学院,南京210023 [2]南京大学水科学研究中心,南京210093

出　　处：《南京大学学报（自然科学版）》2015年第6期1279-1290,共12页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(41272260;41330314;41302180);江苏省自然科学基金(SBK201341336)

摘　　要：通过分析非饱和-饱和系统(USS)中压力水头的时空变化,定量刻画了USS对水流波动的阻尼作用及地表入渗的时间尺度性指数(β)对该作用的影响.结果显示,USS对其中的水流具有阻尼/滤波作用,过滤掉水流的短期波动,使其波动减弱、短期相关性增强;阻尼作用随深度增加逐渐减弱,可能与土壤含水率有关;阻尼作用随入渗序列β值的增大而减弱;分数高斯噪声入渗引起的水头波动起初为非平稳波动最终为平稳波动,β越大,非平稳阶段越长;分数布朗运动入渗引起的水头波动为非平稳波动,β越大,非平稳性越强;入渗的时间分形性是引起地下水位分形波动的重要因素.The damping effect of an unsaturated-saturated system （USS）on the fluctuations of water flow and the effect of the scaling exponent of infiltration （β）on the damping effect were investigated.The moment equations of the pressure head （ψ）were solved numerically to obtain the variance ofψat 7 observation points.Power spectrum ofψ（Sψψ）were estimated by directly solving the equations of the unsaturated-saturated system.Results show that USS filters out the short-term fluctuations ofψ,so the fluctuations ofψare weakened and the short-term correlation increases.The damping effect decreases with depth and should be soil moisture dependent.The damping effect decreases with the increase of the value ofβ.The fluctuations ofψare first non-stationary and finally stationary under the infiltration of fractional Gaussian noise and the larger the value ofβ,the longer the non-stationary period.The fluctuations ofψare non-stationary all the time under the infiltration of fractional Brownian motion and the larger the value ofβ,the stronger the non-stationarity.The temporal scaling is an important factor inducing the scaling ofnbsp;temporal fluctuations of groundwater levels.

关 键 词：阻尼作用 非饱和饱和系统 时间尺度性 分形 分数高斯噪声 分数布朗运动 

分 类 号：P641[天文地球—地质矿产勘探]