基于主成分分析和Copula函数的干旱影响评估研究

Drought Impact Assessment Based on Principal Component Analysis and Copula Function

摘要:

干旱是关中平原主要的农业灾害之一，准确地评估干旱的影响，对抗旱减灾及作物稳产具有重要意义。基于关中平原2008—2013年冬小麦主要生育期旬尺度的条件植被温度指数（VTCI）干旱监测结果，将Copula函数用于评估冬小麦主要生育时期干旱对其产量的影响。针对多元变量导致Copula函数参数求解困难的问题，采用主成分分析法(PCA)提取主要生育时期的VTCI的主成分因子，形成新的相互独立的指标，进而结合Copula函数建立PCA-Copula法，确定关中平原主要生育时期的综合VTCI，并构建其与冬小麦单产间的线性回归模型，评估干旱对产量的影响。结果表明，应用PCA-Copula法得到的综合VTCI与单产间的相关性达到极显著水平(P<0.001)，所建回归模型的拟合度与熵值法的结果相比有所提高，决定系数由039提高到049，且对应模型的估测单产与实测单产间的均方根误差较熵值法的结果降低了30.2kg/hm2，平均相对误差降低了0.66%，表明PCA-Copula法能较好地应用于评估冬小麦主要生育时期干旱对其产量的影响。

Abstract:

Drought is one of the most important agricultural disasters in the Guanzhong Plain, China. Assessing the influence of the droughts in the plain accurately can provide reference for drought mitigation and maintaining stable crop yields. Based on remotely sensed vegetation temperature condition index (VTCI) which was calculated at tenday intervals for monitoring droughts in the years of 2008—2013 in the plain, the Copula function method was used to assess the effect of drought at the main growth stages of winter wheat on the yields. The mutually independent principal factors were extracted from the VTCIs at the main growth stages of winter wheat by using principal component analysis (PCA), overcoming difficulty of parameter estimation for multivariate Copula, and then incorporated into the Copula function to establish a PCA-Copula method. The comprehensive values of VTCIs at the main growth stages were determined by the PCA-Copula method, and then linear regression model between the comprehensive VTCIs and wheat yields was established to assess the effect of drought on the yields. The results showed that the linear correlation coefficient between the wheat yields and comprehensive VTCIs was at the extremely significant level (P<0.001). Compared with the linear regression model based on the entropy value method, the determination coefficient of the model with the PCA-Copula method reached 0.49 from 0.39, which indicated that the fitting degree of the model was improved, and the root mean square error and average relative error between the estimated and measured yields reduced by 30.2kg/hm2 and 0.66%, respectively. These results indicated that the PCA-Copula method was a better approach for accessing the impact of droughts at the main growth stages of winter wheat on the yield.