湖泊富营养化趋势的灰色马尔柯夫预测

Gray Markov forecast of lake eutrophication

根据水质时间序列具有趋势性和波动性的特点,将灰色马尔柯夫模型应用于太湖、滇池、巢湖三大湖泊水质富营养化趋势预测,其预测值可看成趋势项和随机波动项之和.预测过程如下:①用t检验准则判断并剔除序列中的异常数据,保证GM(1,1)模型精度;②建立GM(1,1)模型,对时序数据进行拟合,找出其变化趋势并建立趋势项;③根据最大残差划分状态空间,进行马尔柯夫预测,找出波动性规律并建立随机波动项.预测结果显示:太湖、滇池、巢湖预测结果的相对误差分别为3.59%、1.73%、2.20%,平均相对误差为2.50%,比单纯的灰色GM(1,1)模型降低了0.32%.

Because water quality time series have characteristic trends and fluctuations, the Gray Markov Model was used to forecast the eutrophication trend for three lakes： Tai Lake, Dian Lake and Chao Lake. The forecast value can be seen as the sum of the trend and fluctuation components. The main procedures of this approach include： （1） abnormal data are identified and removed using t-test criteria; （2） the GM（ 1,1 ） model is built and trend items established through finding the various trends ; （3） state space is divided according to the maximum error and fluctuation items are established using the Markov forecast. The forecast results show ： the relative errors of the three lakes are 3.59% , 1.73% and 2.20%. The average relative error is 2.50% , which is 0.32% lower than the pure GM（ 1,1 ） model.