预测陕西关中地区需水量的改进GM(1,1)模型

Modified GM(1,1) model for predicting the water resource demand in the Guanzhong Region, Shaanxi Province, China

需水量评价与预测是水资源规划与管理一项重要的研究内容。本文采用定额法计算需水量。通过对陕西关中地区需水量要素组成的分析,认为需水量要素属平稳时间序列,且一阶累加生成数据系列满足指数规律,符合灰色预测条件。为了提高GM(1,1)模型的精度,采用一种改变背景值的新方法,即:中心逼近方法。通过精度检验,中心逼近式GM(1,1)模型平均误差百分比、误差平方和分别比传统的GM(1,1)模型提高了0.147和1.579。用中心逼近式GM(1,1)模型预测需水量各要素近期和中长期值,经检验,其中非农业人口、农业人口、耕地面积、工业总产值预测模型满足一级模型,等级为良好。牲畜头数预测模型为不合格模型,分析其原因,主要是因为时间序列数据不完全符合指数规律。通过定额法计算,预计75%保证率时2005年和2010年关中地区工农业需水量分别占总需水量的92.21%和89.75%,生活需水量分别占7%和9.04%。

Assessment and prediction of water resources demand are the important issues in water resources planning and management. In this paper, the quota method is used to calculate water resources demand. After analyzing the components of water resources demand in the Guanzhong region, Shaanxi Province, it is considered that the different components of water resources demand in the Guanzhong region belong to the stable time series, and the time series produced from the first-order data accumulation accord with the exponential laws and the Grey prediction conditions for Grey model. In order to improve the Grey model precision, a new method of changing the background data, i.e., a center approach GM （ 1,1 ） model, is presented for analyzing the parameters of water resources demand. By precision test, the average error percentage and the error quadratic sum of the center approach GM （ 1,1 ） model are 18.6% and 0.807 respectively, whereas the average error percentage and error quadratic sum of the conventional GM （ 1,1 ） model are 33.3% and 2.386 respectively. Therefore, the precision of the center approach GM （1,1） model is higher than that of the conventional GM （1,1） model. The center approach GM （ 1,1 ） model was applied to predict the short-term and long-term water resources demands in the Guanzhong region, and the results can satisfy the precision test. The prediction models can satisfy the first-level model in predicting the non-agriculture population, agriculture population, farmland area and total industrial output value, and precision assessment grade is good. The prediction model of animal-breeding quantity is not eligible because the time series data.do not fit to the exponential laws. The results show that the proportions of agricultural and industrial water resources demands in the Guanzhong region occupy 92.21% and 89.75% of the total water resources demand in 2005 and 2010 respectively, and those of life water resources demand occupy 7.00% and 9.04% in 2005 and 2010 respectively. In order to improve the utilization rate and the economic efficiency, the agricultural and industrial water resources demands should be reduced by implementing some water-saving measures.