GM(1,1)分解模型与ARIMA模型在岩溶地下水模拟中的对比研究——以柳林泉流量模拟为例

李华敏; 吴敬; 赵娇娟; 郝永红; 王亚捷; 曹碧波

doi:10.3969/j.issn.1001-4810.2011.03.004

GM(1,1)分解模型与ARIMA模型在岩溶地下水模拟中的对比研究——以柳林泉流量模拟为例

doi: 10.3969/j.issn.1001-4810.2011.03.004

1.
天津师范大学城市与环境科学学院
2.
天津财经大学理工学院统计系
3.
天津师范大学天津市水环境与水资源重点实验室

基金项目: 国家自然科学基金(40972165,40572150)、天津市科技发展战略研究计划项目09JCYBJC27500、天津市水资源与水环境重点实验室开放基金52XS1015

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出版历程
- 收稿日期: 2011-03-07
- 发布日期: 2011-09-25

Comparative study on karst ground water simulation between GM(1, 1)decomposition model and ARIMA model: A case study on discharge simulation of the Liulin Spring

1.
College of Urban and Environmental Sciences, Tianjin Normal University
2.
Department of Statistics, Tianjin University of Finance and Economics
3.
Tianjin Key Lab of Water Environment and Water Resources, Tianjin Normal University

摘要

摘要: 本文运用GM(1,1)分解模型和ARIMA模型分别模拟柳林泉流量。根据影响特征将泉水流量变化分为两个时段研究:1957—1973年泉水流量处于自然状态;1974—2009年泉水流量受气候变化和人类活动双重影响。运用第1时段的数据建模获得自然状态下泉水流量的模型,将模型外推,获得第2阶段自然状态下泉水流量,然后根据水量平衡原理,减去同期实测流量,获得人类活动对泉水流量衰减的贡献。GM(1,1)分解模型的结果显示,从20世纪70年代到21世纪初柳林泉衰减量为2.26m3/s;ARIMA模型的结果为2.32m3/s;与同期实际衰减量2.27m3/s比,相对误差分别为0.44%和2.20%,表明两种模型都适用于泉水流量的模拟。对比人类活动和气候变化对柳林泉流量衰减的贡献,两个模型得到同样结果,即人类活动的贡献是气候变化的8～9倍。实证研究显示,GM(1,1)模型适用于指数序列的模拟,对具有周期波动的泉水流量,可通过周期修正提高精度;而ARIMA模型能够较好地反映泉水流量相对于降水量的时间滞后效应,能比较准确地模拟泉水流量与降水量的量化关系。
- GM(1,1)分解模型 /
- ARIMA模型 /
- 分时段分析 /
- 岩溶泉流量
Abstract: The discharge of the Liulin spring is simulated with GM(1,1) decomposition model and ARIMA model respectively. According to the hydrological characteristics, the Liulin spring flow series could be divided into two periods. First, from 1957 to 1973 the spring flow was under natural state; second, from 1974 to 2009 the spring flow was impacted by both climate change and human activities. Using the data of first period, the spring flow under the natural state is fitted with GM(1,1) decomposition model and ARIMA model, and then the models are extrapolated to obtain the second periods’spring flow under the natural state. According the water balance principle, the spring flow decrement contributed by human activities is acquired by subtracting the observed discharge from simulated spring flow of the second period under the natural state. Thus, it is differentiated the effects of human activities from climate change. The simulated Liulin Springs’attenuation from 1970s to early 21st century is 2.26 m3/s by GM(1,1)decomposition model and 2.36 m3/s by ARIMA model with the relative error being 0.44% and 2.20% respectively, showing both GM(1, 1)decomposition mode land ARIMA model are suitable for spring flow simulation. Comparing the effects of human activities and climate change to the depletion of the Liulin Spring’s discharge, the authors find that the contribution of human activities is 8 to 9 times higher than that of the climate change. The empirical studies have shown that the GM (1,1) model is of high precision in simulating the exponential series. It can also improve accuracy by periodic amendment, when simulate the spring flow with periodic fluctuations. ARIMA model could reflect time-lag between precipitation and spring discharge and accurately simulate their quantitative relation.
- GM(1,1)decomposition model /
- ARIMA model /
- piecewise analysis /
- karst spring discharge

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