Estimation of Winter Wheat Yield Using Assimilated Bi-variables and PCA-Copula Method
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摘要: 为了进一步提高冬小麦产量估测的精度，基于集合卡尔曼滤波算法和粒子滤波（particle filter, PF）算法，对CERES–Wheat模型模拟的冬小麦主要生育期条件植被温度指数（vegetation temperature condition index，VTCI）、叶面积指数（leaf area index, LAI）和中分辨率成像光谱仪（moderate-resolution imaging spectroradiometer, MODIS）数据反演的VTCI、LAI进行同化，利用主成分分析与Copula函数结合的方法构建单变量和双变量的综合长势监测指标，建立冬小麦单产估测模型，并通过对比分析选择最优模型，对2017—2020年关中平原的冬小麦单产进行估测。结果表明，单点尺度的同化VTCI、同化LAI均能综合反映MODIS观测值和模型模拟值的变化特征，且PF算法具有更好的同化效果；区域尺度下利用PF算法得到的同化VTCI和LAI所构建的双变量估产模型精度最高，与未同化VTCI和LAI构建的估产模型精度相比，研究区各县（区）的冬小麦估测单产与实际单产的均方根误差降低了56.25 kg/hm2，平均相对误差降低了1.51%，表明该模型能有效提高产量估测的精度，应用该模型进行大范围的冬小麦产量估测具有较好的适用性。Abstract:Objectives Accurate, timely and effective monitoring of the growth and yield of winter wheat over a large area can help optimize the wheat planting structure, adjust the regional layout and ensure the country's food security. Therefore, it is very important to further improve the estimation accuracy of winter wheat yield.Methods Vegetation temperature condition index (VTCI) and leaf area index (LAI) at the main growth period of winter wheat, which were simulated by the CERES (crop environment resource synthesis)-Wheat model and retrieved from MODIS (moderate resolution imaging spectroradiometer) data, were assimilated by using ensemble Kalman filtering (EnKF) algorithm and particle filtering (PF) algorithm. In addition, the principal component analysis combined with the Copula function was used to develop univariate (VTCI or LAI) and bi-variate (VTCI and LAI) winter wheat yield estimation models, and the optimal model was selected to estimate winter wheat yields from 2017 to 2020.Results The experimental results show that, at the sampling-sites scale, both VTCI and LAI after assimilated can comprehensively reflect the variation characteristics of MODIS observed and model simulated values, and the application of PF algorithm has a better assimilation effect. At the regional scale, the bivariate yield estimation model developed by using PF algorithm has the highest accuracy. Compared with the accuracy of the models constructed by VTCI and LAI without assimilation, the root mean square error of the optimal assimilation model is reduced by 56.25 kg/hm2, and the average relative error is reduced by 1.51%.Conclusions The above results indicate that the model can effectively improve the accuracy of winter wheat yield estimation and has good applicability for large area yield estimation.
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图 1 研究区位置及地面调查点分布
Figure 1. Location of Study Area and Distribution of Ground Sampling Sites
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图 3 2017年不同样点VTCI的变化趋势
Figure 3. Changing Trend of VTCI at Different Sampling Sites in 2017
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图 4 2017年不同旱作样点观测VTCI、同化VTCI与降水量之间Pearson相关系数的热力图
Figure 4. Heat Map of Pearson Correlation Coefficients Between Observed and Assimilated VTCIs and Rainfall Amounts at Different Rain-fed Sampling Sites in 2017
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图 5 2017年不同样点LAI的变化趋势
Figure 5. Changing Trend of LAI at Different Sampling Sites in 2017
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图 6 估测单产与实际单产的精度评价结果
Figure 6. Accuracy Evaluation Results of Estimated Yield and Actual Yield
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图 7 关中平原2017—2020年冬小麦单产估算结果
Figure 7. Estimates of Winter Wheat Yields in the Guanzhong Plain from 2017 to 2020
表 1 关中平原冬小麦的遗传参数取值
Table 1 Genetic Coefficients of Winter Wheat in the Guanzhong Plain
遗传参数 定义 标定值 P1V/d 春化作用系数 46 P1D/% 光周期系数 68 P5/(℃·d) 灌浆期积温 500 G1/g 开花期单位冠层重量的籽粒数 29 G2/mg 最佳条件下标准籽粒质量 29 G3/g 成熟期非胁迫下单株茎穗标准干质量 2 PHINT/(℃·d) 完成一片叶生长所需积温 90 
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表 2 基于不同同化算法的同化VTCI和LAI精度评价
Table 2 Accuracy Evaluation of Assimilated VTCI and LAI Based on Different Assimilation Algorithms
指标 R2 RMSE EnKF VTCI 0.32 0.16 PF VTCI 0.65 0.12 EnKF LAI 0.45 0.97 m2·m-2 PF LAI 0.72 0.65 m2·m-2
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表 3 VTCI和LAI的主成分贡献率
Table 3 Principal Component Contribution Rates of VTCI and LAI
指标 主成分 贡献率/% 累积贡献率/% VTCI 第一主成分 59.15 59.15 第二主成分 30.05 89.20 EnKF VTCI 第一主成分 59.50 59.50 第二主成分 31.25 90.75 PF VTCI 第一主成分 61.88 61.88 第二主成分 27.68 89.56 LAI 第一主成分 88.50 88.50 第二主成分 9.72 98.22 EnKF LAI 第一主成分 92.26 92.26 第二主成分 5.51 97.77 PF LAI 第一主成分 89.08 89.08 第二主成分 8.05 97.13 VTCI+LAI 第一主成分 51.52 51.52 第二主成分 27.74 79.52 第三主成分 11.65 90.91 EnKF VTCI+LAI 第一主成分 59.43 59.43 第二主成分 19.65 79.07 第三主成分 12.13 91.21 PF VTCI+LAI 第一主成分 62.59 62.59 第二主成分 17.15 80.09 第三主成分 10.98 90.72
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表 4 冬小麦单产估测模型
Table 4 Winter Wheat Yield Estimation Models
指标 回归模型 决定系数 VTCI Y(V) = 1 547.05V + 3 982.71 0.18 LAI Y(L) = 2 219.71L + 3 293.02 0.52 VTCI+LAI Y(G) = 1 937.77G + 3 404.26 0.45 EnKF VTCI Y(VEnKF) = 1 407.92VEnKF + 3 982.71 0.19 EnKF LAI Y(LEnKF) = 2 161.94LEnKF + 3 313.03 0.53 EnKF VTCI+LAI Y(GEnKF) = 2 178.14GEnKF + 3 303.70 0.54 PF VTCI Y(VPF) = 1 462.60VPF + 3 538.15 0.21 PF LAI Y(LPF) = 2 226.60LPF + 3 277.80 0.55 PF VTCI+LAI Y(GPF) = 2 201.01GPF + 3 286.14 0.55 注：Y表示冬小麦估测单产（kg/hm2）；V、VEnKF和VPF分别为综合VTCI、综合VTCI-EnKF和综合VTCI-PF；L、LEnKF和LPF分别为综合LAI、综合LAI-EnKF和综合LAI-PF；G、GEnKF和GPF分别为综合G、综合G-EnKF和综合G-PF
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