基于联系数和马尔可夫链耦合的山东省旱情动态预测评价

为增强区域旱情预测评价模型的合理性、可解释性和预测评价结果的准确性,以山东省1972-2001年旱情历史序列作为评价样本,选取水库蓄水量距平百分率、地下水埋深、土壤含水量和降水量距平百分率4个旱情评价指标,采用基于加速遗传算法的模糊层次分析法确定评价指标权重,通过计算评价样本的指标数联系数、指标值联系数并利用最小相对熵原理得到样本的平均联系数,由属性识别法确定了各年份的旱情等级,建立了基于集对分析五元联系数和马尔可夫链耦合的区域旱情动态预测评价模型(简称CNMC模型),将CNMC模型应用于山东省2000、2001年旱情等级动态预测评价中,判定山东省旱情等级,将该模型确定的旱情等级与属性识别法评价结果进行对比分析。结果表明:采用CNMC模型得到的旱情等级计算值与属性识别法的评价结果一致,可发现CNMC模型中由集对分析法确定的权重值较自相关系数法确定的权重值分布均匀,克服了自相关系数法的计算不稳定性;以联系数分量为基础的属性识别法克服了直接将指标数值与评价标准匹配得到的马尔可夫链状态等级空间的粗糙性;以前5 a各年份的联系数分量为基础,充分利用了1~5步长状态转移概率矩阵,克服了普通马尔可夫链法中仅采用状态转移概率矩阵中某一行信息所带来的局限性。CNMC模型有助于深入刻画和解析预测对象与预测因子之间的复杂关系,以联系数分量为基础,不同步长的马尔可夫链状态转移概率矩阵为驱动所建立的模型能更精准地刻画系统的不确定性趋势且计算简单、操作方便,为区域旱情动态预测评价提供了一种新途径。

Dynamic Prediction and Evaluation of Drought in Shandong Province Based on Connection Number and Markov Chain Coupling

In order to enhance the rationality,releasability and accuracy of the regional drought prediction and evaluation model,taking the drought historical series from 1972 to 2001 in Shandong Province as evaluation samples,four drought evaluation indexes,namely the percentage of reservoir water storage anomaly,the buried depth of groundwater,the soil water content and the percentage of precipitation anomaly are selected,and AGA-FAHP is used to determine the evaluation index weights.By calculating the index number connection number and index value connection number of evaluation samples and using the principle of minimum relative entropy to get the average connection number of samples,the drought grades of each year are determined by attribute recognition method,and a regional drought dynamic prediction and evaluation model based on Connection Number of set pair analysis and Markov Chain coupling(CNMC model)is established,which is applied to the dynamic prediction and evaluation of drought grades in Shandong Province in 2000 and 2001 to determine the drought grade of Shandong Province.Finally,the drought grades determined by this model are compared with the evaluation results of attribute recognition method.The results show that the calculated value of drought grade obtained by CNMC model is consistent with the evaluation result of attribute recognition method,and it can be found that the weight value determined by set pair analysis in CNMC model is more evenly distributed than that determined by autocorrelation coefficient method,which overcomes the computational instability of autocorrelation coefficient method;The attribute recognition method based on connection number component weakens the roughness of Markov chain state grade space obtained by directly matching index value with evaluation standard;Based on the connection number components of each year in the previous five years,the 1~5 step-size state transition probability matrix is fully utilized,which overcomes the limitation of using only one line of information in the state transition probability matrix in the ordinary Markov chain method.CNMC model is helpful to deeply describe and analyze the complex relationship between prediction objects and prediction factors.CNMC model based on connection number component and driven by Markov chain state transition probability matrix with different step sizes can more accurately describe the uncertainty trend of the system,and it is simple to calculate and convenient to operate,which provides a new way for regional drought dynamic prediction and evaluation.