灰色GM(1,1)-小波变换-GARCH组合模型预测松花江流域水质

Forecasting of water quality using grey GM(1,1)-wavelet-GARCH hybrid method in Songhua River Basin

为了研究松花江流域水质变化情况,预测未来水质变化趋势以及对松花江流域水质的保护提供理论依据和决策方案,通过对松花江抚远段2012年前15周的实测溶解氧(dissolved oxygen,DO)、高锰酸盐指数CODMn、氨氮NH3-N数据分析,以灰色GM(1,1)模型、小波分解与重构和广义自回归条件异方差(generalized auto-regressive conditional heteroskedasticity,GARCH)模型为基础,建立了灰色GM(1,1)和灰色GM(1,1)-小波变换-GARCH组合的混合预测模型,并以抚远段实测DO、CODMn、NH3-N数据为实例进行验证,预测结果极显著(P<0.01),预测误差分别为3.39%、8.56%、7.83%,表明该预测模型精度较高,适用于对水质变化的预测研究。最后,利用该模型对松花江抚远、黑河、嘉荫和同江段2013年前8周的4个污染指标进行预测分析,预测结果与实测数据误差较小,基本符合水质未来变化趋势,为相关部门对松花江流域水质预测和保护提供参考。

In order to predict water quality changes in the future, and to provide the theoretical basis and decision-making processes for protecting the ecological environment of water resource and for the sustainable development in Songhua river basin, a reasonable forecasting model needs to be developed to safeguard quality of drinking, irrigation and industrial water uses from Songhua river basin. To determine the changes of current water quality, and offer scientific methods for managing water quality, we proposed a short time series hybrid forecasting method based on wavelet transform, grey model and autoregressive conditional heteroscedasticity（GARCH）. Firstly, the actual measured data ratio has been worked out, and we considered the ratio as the condition to decide whether to use the GM（1,1） as the initial forecast model or not. If the final forecasting has less error than actual measured data and the class of accuracy arrived at 1 level（posterior error ratio≤0.35）,then we took the model as the forecast model. Else, we took the grey-wavelet-GARCH as the final forecast model. Secondly,when using the grey-wavelet-GARCH model, we tried to use DB3 to decompose and reconstruct into approximate series and detailed series, and analyzed the approximate series data and tested its ration in condition of grey model until its ratio met required precision（in this paper, the precision was the class of accuracy arrived at 1 level）. After that, we used GM（1,1） to forecast the approximate series to find out its future values while the detailed series future values were forecasted by GARCH model. The detailed series had a large fluctuation so it was better to use the GARCH model to forecast it. The GARCH model had advantage in time series forecasting with a large fluctuation. Finally, the sum of the approximate and detailed series future values was used as the final forecast values. In this paper, there were three contamination factors as the key factors to study the water quality, and there were CODMn, DO and NH3-N. They were selected according to the edition of GB3838-2002（the Environmental Quality Standard for Surface Water）. the limit of basic project standard. Items that would exceed the Ⅱ class standard limit of the project were used as the limit for the pollution factors. Considering that CODMn, COD and BOD were related to the content of organic matter in water, and from past research we learned that CODMn is the main pollution factor in Songhua river environment. It reflects the level of aerobic content in water. As such,we chose the CODMn as one of the main pollution factors. The total nitrogen, total phosphorus and dissolved oxygen reflect the eutrophication status. At the same time, dissolved oxygen is also one of the important factors for the solubility of heavy metals and for all kinds of life organisms in water, we chose it as one of the main pollution factors. NH3-N is the product of microbial decomposition of nitrogen containing organic matter. We selected it as one of the main pollution factors. The model was tested by actual measured data of DO in Fu-Yuan county from first week to 15 th week in 2012. The prediction by the model had no significant difference with actually measured data（P=0.0010.01, errors 3.39%）, showing high accuracy of the model, and the model was suitable for the prediction of water quality changes. After that, we used this model to predict and analyze the three pollution indicators of four counties in Songhua river basin from first week to eighth week in2013. The forecasting showing that the errors of dissolved oxygen was between 2.96% and 6.11%, CODMn was between1.75% and 5.1%, and NH3-N was between 2.37% and 9.77%. The predicted results had less errors to the measured data, and the forecasting was basically in agreement with measured data. This study can provide a reference for the relevant departments to take the reasonable measures to protect the Songhua river.