基于双参数和Morlet多时间尺度特性的冬小麦单产估测

为进一步研究冬小麦在不同时间尺度下长势及产量变化情况，以陕西省关中平原为研究区域，选择与作物长势密切相关的条件植被温度指数（VTCI）和叶面积指数（LAI）作为研究指数，Morlet小波作为函数，利用小波变换和交叉小波变换分别分析不同时间尺度下冬小麦各生育时期VTCI和LAI与单产时间序列间的主振荡周期和共振周期。通过计算小波互相关度，确定各生育时期VTCI和LAI的权重，从而分别构建基于加权VTCI、加权LAI的单参数和双参数估产模型。结果表明，不同生育时期VTCI和LAI与单产间存在不同的主振荡周期和共振周期；通过小波变换构建的基于加权VTCI、加权LAI单产估测模型的归一化均方根误差（NRMSE）分别为16.88%、13.58%，决定系数（R2）分别为0.259、0.520，基于双参数的估产模型NRMSE为13.52%， R2为0.531，表明基于双参数估产模型精度更高。通过交叉小波变换构建的基于加权VTCI、加权LAI单产估测模型的NRMSE分别为16.83%、13.56%，R2分别为0.263、0.522，基于双参数的估产模型NRMSE为13.40%，R2为0.533，表明基于交叉小波构建的估产模型比基于小波变换的估产模型精度均有所提高。利用共振周期构建的双参数估产模型对关中平原2011—2018年冬小麦的单产进行估测，结果显示，产量分布呈现西部高东部低的空间分布特征。

Yield Estimation of Winter Wheat Based on Two Parameters and Morlet Multi-scale Characteristics

In order to further study growth trend and yield changes of winter wheat at different time scales, remotely sensed vegetation temperature condition index (VTCI) and leaf area index (LAI) which are closely related to crop water stress and crop growth were selected as two key variables for indicating crop growth condition and estimating crop yields in the Guanzhong Plain, China. Taking Morlet wavelet as a function, wavelet transform and cross wavelet transform were used to analyze the main oscillation period and resonance cycle between VTCI, LAI and time series yield at different time scales. The weights of VTCI and LAI at each growth stage were determined by calculating the wavelet cross-correlation degree, which were used to construct the single-parameter and double-parameter yield estimation models, respectively. The results showed that VTCI, LAI and yield had different main oscillation periods and resonance cycles. The normalized root mean square errors (NRMSE) of the weighted VTCI and weighted LAI yield estimation models constructed by the wavelet transform were 16.88% and 13.58%, respectively, the values of the coefficient of determination (R2) were 0.259 and 0.520, respectively, and the NRMSE and R2 of the double-parameter estimation model were 13.52% and 0.531, respectively. These results indicated that the yield estimation model based on double-parameters had higher accuracy. For the cross wavelet transform, NRMSEs based on weighted VTCI and weighted LAI yield estimation model were 16.83% and 13.56%, R2 were 0.263 and 0.522, respectively. NRMSE based on double-parameter estimation model was 13.40% and R2 was 0.533. Therefore, it can be concluded that the estimation models based on the cross wavelet transform had higher accuracy than those based on the wavelet transform. The double-parameter yield estimation model constructed by resonance cycles was used to estimate the yields in the Guanzhong Plain from 2011 to 2018, and the results showed that the yield was high in the west and low in the east.