灰色季节性指数自记忆模型及其在海河区降水模拟与预测中的应用

准确的降水模拟与预测，对防汛、抗旱及区域水资源管理有着重要的指导作用。由于降水序列波动较大，传统的灰色模型所得到的降水模拟值和预测值往往趋于平均值，论文从输入数据和模型结构改进两个方面对传统的灰色模型进行改进——采用季节性指数法对降水数据进行平滑处理，引入自记忆函数，构建灰色季节性指数自记忆模型（SS-GM），并将其应用于海河区降水过程的模拟和预测。结果表明：①该模型较传统灰色模型而言，模拟效果有很大程度的提高，能够准确模拟年和月尺度的降水过程，各水资源二级区的月尺度Nash-Sutcliffe 系数（NSE）和决定系数（R²）均达到了0.60 以上，大部分区域年降水模拟的NSE和R²均在0.70 以上，且在较大的时空尺度上，模拟效果更佳；②模型具有一定的月降水量的预测能力，在1~2 月预见期内，各分区降水预测值NSE达到0.50 以上，大部分地区NSE值超过0.60；③模型结构简单、计算方便，能很好地反映降水数据序列的变化趋势，且具有较高的模拟及预测精度。

Application of Seasonal Index Self-memory Grey Model in Simulation and Prediction of Precipitation in Haihe River Basin

The accurate simulation and prediction of precipitation is beneficial to risk control of drought and flood and management of water resources. Time series analysis method is playing an important role in hydrologic regular analysis and hydrologic simulation as well as hydrologic forecasting and so on. Compared with the distributed hydrological model, the uncertainty methods such as Grey Theory have less parameter to be calibrated and requirements of data are less strict. However, the precipitation simulated and predicted by traditional grey model tends to be the average when the time series fluctuates drastically and the results are usually not acceptable. The study improved the grey model in input and structure with the smooth processing and self- memory theory and built the Seasonal Index Self- memory Grey Model (SS-GM). Based on the GM(1,1) which was used as the core of dynamic and the equation of self-memory, the parameters of the SS-GM were calculated by the method of least squares. The model was applied to the simulation and prediction of precipitation in Haihe River Basin, the results showed that: 1) compared with the traditional grey model, the model performed much better with both the Nash-Sutcliffe efficiency (NSE) and determination coefficient (R²) more than 0.6 in the sub-basins and ones were more than 0.7 in most parts of the basin in simulation of annual precipitation. The model was suited for the simulation at large spatial and temporal scales as the NSE and R² were more than 0.75 in the whole Haihe River Basin in simulation of annual precipitation. 2) The model was applicable to predicting the precipitation during the future one or two months as NSE was above 0.5 (the NSE in most parts was more than 0.6), but the model performed badly when it was used to predict the precipitation during the future three or four months. 3) The SS-GM was simple and easy to be calculated. The result predicted by the model can reflect the characteristics of precipitation and prediction can be more accurate by the rotational correction with the update precipitation.