基于数理统计方法的降水量预测模型建立及应用

降水量是一个随机事件,但在一个相当长的时间段内又有一定的规律性。由于降水过程存在高度随机性和不确定性,很难用物理成因等方法来确定某一时段确切的降水量值。在国内具有代表性的权马尔科夫链预测降水量方法的基础上,结合数理统计的知识,提出了一种改进的预测降水量思路,即对原始降水量序列进行3 a滑动平均,并考虑序列间的相关程度,以减弱原始序列的随机因素,用新序列进行降水量预测的方法,并对北京、延安等5个站点的降水量序列进行了应用检验。检验结果表明,除了在极端年份(如岢岚站点2006年,偏关站点2006、2009年均为枯水年)时预测有较大误差外,其余年份的预测结果比较令人满意,总体上合格率达到80%。由于权马尔科夫链模型建立时在统计学基础上利用了降水量序列的均值和均方差,预测值是在一定概率条件下趋向于某一状态,而极端条件发生的概率较小,因此在预测极端条件时会出现较大误差。

Establishment and Application of Precipitation Prediction Model Based on Mathematical Statistics Methods

Precipitation is a random event, but it has certain regularity during a long time period. As the high randomness and uncertain of the precipitation process, it is difficult to use physical genesis method to determine the exact values of a certain period precipitation. Based on domestic representative weighted Markov chain forecast precipitation method, combined with the knowledge of mathematical statistics, an improved precipitation prediction method is proposed. Precipitation prediction can using a new sequence of original precipitation series 3 years moving average, which weakening the random factors of original sequence by considering the correlation between sequences. And precipitation series of 5 stations including Beijing and Yan＇ an etc. are selected to test. The results show that the station forecast results are rather satisfactory besides in extreme years （ such as dry years of Kelan station in 2006, Pianguan station in 2006 and 2009） , the prediction of pass rate reaches to 80%. Because of the weighted Markov chain model found by using the mean and mean square error of precipitation sequence based on the statistics, the predicted value is a particular state trend under certain probabilistic condition, and the probability is small for occurring in extreme conditions, so there will be a large error when predicting in extreme conditions.