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WOFOST Model Parameter Calibration Based on Agro-climatic Division of Winter Wheat
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摘要: 以1981—2010年河南省113个气象观测站影响冬小麦生长及产量形成的主要气象因素为区划指标，利用K均值聚类算法，将河南省划分为5个农业气候生态区。根据2013—2017年地面农业气象观测数据，利用Sobol全局敏感性分析方法，各分区选择总敏感指数大于0.01的作物参数，得到9种敏感参数。以产量与叶面积指数为代价函数，采用差分进化马尔科夫链蒙特卡洛方法对敏感参数进行分区标定，并使用2018—2019年观测数据进行验证。结果表明：分区进行参数标定时，叶面积指数动态模拟精度和产量模拟精度均显著优于使用默认参数或整个研究区使用同一套优化参数时的精度，其中，使用分区调参后验平均值模拟关键生育期叶面积指数的总均方根误差为0.655，其模拟产量的均方根误差为672.016 kg·hm-2。该方法将农业气候学知识与差分进化马尔科夫链蒙特卡洛优化算法相结合，通过合理、高效地分区域标定作物模型参数，可为作物模型区域应用和模型参数调整优化提供科学依据。Abstract: Crop model parameter calibration is an important work of extending point-scale crop model to regional application.Using K-means method with the main meteorological factors affecting the growth and yield formation of winter wheat obtained from 113 meteorological stations from 1981 to 2010 as zoning indicators, Henan Province is divided into five different agro-climatic ecological zones and the cumulative temperature parameters are calculated for each zone. Based on the observations during 2013-2017, nine sensitive parameters are obtained by using Sobol global sensitivity analysis method to analyze and select crop parameters with total sensitivity index greater than 0.01. The sensitive parameters selected from different agro-climatic ecological zones of different winter wheat varieties are highly consistent. A cost function is constructed with yield and leaf area index(LAI), and each partition is calibrated for sensitive parameters using Differential Evolution Markov Chain method. The results show that the simulated leaf area index in the different agro-climatic ecological zones are in good agreement with the observed values, the root mean square error (RMSE) using the posterior mean value of regional parameters adjustment to simulate the LAI of key growth periods is 0.655, which is obviously higher than that of using default parameters or using the same set of optimized parameters in the whole study area. Results show that the WOFOST model based on agro-climatic division can accurately simulate the growth process of crops. In terms of yield estimation accuracy, the yield simulation accuracy of regional parameter adjustment is also significantly improved. The best accuracy of simulated yield is achieved by using the posterior mean of regional parameters and RMSE is 672.016 kg·hm-2, 70.55% reduction than the yield simulation error when using the default parameters, or 48.75% reduction than the yield simulation error when the same set of optimized parameters (posterior mean) are used for the entire area. The method takes advantage of the knowledge of agro-climatology with the scientific and efficient Differential Evolution Markov Chain optimization algorithm to provide a scientific and theoretical basis for the application of crop models and optimization of regional model parameters through rational and efficient zonal calibration of the study area.
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图 2 5个农业气候生态区参数的总敏感性指数
Fig. 2 Total sensitivity index of parameters in five agro-climatic ecological zones
图 3 2019年产量与叶面积指数验证结果
Fig. 3 Verification results of yield and leaf area index in 2019
表 1 不同区域冬小麦积温(单位：℃·d)
Table 1 Accumulated temperature parameters of winter wheat in different zones(unit:℃·d)
生育阶段 Ⅰ区 Ⅱ区 Ⅲ区 Ⅳ区 Ⅴ区 播种至出苗 1170 1180 1100 1150 1250 出苗至开花 600 620 610 600 610 开花至成熟 110 120 120 130 120 
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表 2 待分析参数及其围绕默认值的变化比例
Table 2 The proportion of changes of parameters to be analyzed around the default value
参数 定义 最小比例 最大比例 AM00 发育期为0时CO2最大同化速率 0.7 1.5 AM10 发育期为1时CO2最大同化速率 0.7 1.5 AM13 发育期为1.3时CO2最大同化速率 0.7 1.5 AM20 发育期为2时CO2最大同化速率 0.7 1.5 SL00 发育期为0时比叶面积 0.7 1.5 SL05 发育期为0.5时比叶面积 0.7 1.5 SL20 发育期为2时比叶面积 0.7 1.5 FL 总物质分配到叶片的比例 0.5 2.0 FO 总物质分配到储存器官的比例 0.8 1.2 FR 总物质分配到根的比例 0.5 2.0 SP 35℃时叶片的生命周期 0.7 1.5 TB 出苗最低温度 0.5 1.5 TD 初始总干物质重量 0.9 1.3 TE 出苗最高有效温度 0.9 1.3 TM00 日平均温度为0℃时CO2最大同化速率减小因子 0.7 1.5 TM10 日平均温度为10℃时CO2最大同化速率减小因子 0.7 1.3 TM15 日平均温度为15℃时CO2最大同化速率减小因子 0.7 1.5 TM25 日平均温度为25℃时CO2最大同化速率减小因子 0.7 1.5 TM35 日平均温度为35℃时CO2最大同化速率减小因子 0.7 1.5 RD 根的相对死亡速率 0.9 1.0 RG 叶面积指数最大日增量 0.9 1.3
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表 3 参数标定所用建模数据和验证数据
Table 3 Modeling data and verification data used for parameter calibration
研究区 优化数据 验证数据 年份 站点 年份 站点 Ⅰ区 2013 林州 2014 汤阴 2015 安阳 2018—2019 汤阴 2016 濮阳 2017 范县 Ⅱ区 2013 郑州 2014 商丘 2015 伊川 2018—2019 郑州 2016 济源 2017 郑州 Ⅲ区 2013 许昌 2014 许昌 2015 黄泛区 2018—2019 黄泛区 2016 驻马店 2017 南阳 Ⅳ区 2013 信阳 2014 正阳 2015 新野 2018—2019 潢川 2016 潢川 2017 固始 Ⅴ区 2013 卢氏 2014 三门峡 2015 三门峡 2018—2019 卢氏 2016 卢氏 2017 卢氏
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表 4 河南省Ⅰ区敏感参数的后验分布
Table 4 The posteriori distribution of sensitive parameters in Zone Ⅰ of Henan Province
参数 平均值 中值 最大似然值 均方根误差 95%置信区间 AM00 1.369 1.414 1.470 0.00396 [1.361, 1.377] AM10 1.351 1.374 1.426 0.00301 [1.345, 1.357] AM13 0.729 0.722 0.704 0.00070 [0.728, 0.731] SL00 1.443 1.455 1.500 0.00130 [1.440, 1.445] SL05 0.774 0.770 0.707 0.00127 [0.771, 0.776] FL 1.904 1.932 1.994 0.00220 [1.900, 1.909] FO 0.857 0.856 0.860 0.00023 [0.856, 0.857] FR 1.423 1.429 1.487 0.00131 [1.421, 1.426] SP 0.831 0.829 0.826 0.00026 [0.831, 0.832]
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表 5 河南省Ⅱ区敏感参数的后验分布
Table 5 The posteriori distribution of sensitive parameters in Zone Ⅱ of Henan Province
参数 平均值 中值 最大似然值 均方根误差 95%置信区间 AM00 0.761 0.750 0.704 0.00176 [0.757, 0.764] AM10 1.397 1.410 1.412 0.00274 [1.392, 1.403] AM13 0.793 0.785 0.760 0.00235 [0.788, 0.798] SL00 1.350 1.361 1.458 0.00385 [1.342, 1.357] SL05 0.772 0.759 0.737 0.00195 [0.768, 0.775] FL 1.823 1.848 1.973 0.00496 [1.813, 1.833] FO 0.921 0.920 0.901 0.00055 [0.919, 0.922] FR 0.946 0.964 1.112 0.00573 [0.934, 0.957] SP 0.822 0.824 0.824 0.00034 [0.822, 0.823]
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表 6 河南省Ⅲ区敏感参数的后验分布
Table 6 The posteriori distribution of sensitive parameters in Zone Ⅲ of Henan Province
参数 平均值 中值 最大似然值 均方根误差 95%置信区间 AM00 0.715 0.711 0.702 0.00040 [0.714, 0.716] AM10 0.891 0.872 0.869 0.00319 [0.885, 0.897] AM13 0.738 0.730 0.700 0.00089 [0.737, 0.740] SL00 1.352 1.376 1.498 0.00296 [1.346, 1.358] SL05 1.082 1.067 1.144 0.00383 [1.075, 1.090] FL 1.326 1.334 1.215 0.00426 [1.317, 1.334] FO 0.809 0.807 0.802 0.00023 [0.809, 0.810] FR 0.790 0.787 0.794 0.00397 [0.782, 0.798] SP 0.932 0.938 0.940 0.00042 [0.932, 0.933]
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表 7 河南省Ⅳ区敏感参数的后验分布
Table 7 The posteriori distribution of sensitive parameters in Zone Ⅳ of Henan Province
参数 平均值 中值 最大似然值 均方根误差 95%置信区间 AM00 1.446 1.460 1.496 0.00094 [1.444, 1.447] AM10 1.118 1.127 0.744 0.00472 [1.109, 1.128] AM13 1.418 1.441 1.497 0.00151 [1.415, 1.421] SL00 1.174 1.188 0.918 0.00304 [1.168, 1.180] SL05 0.799 0.777 0.711 0.00164 [0.796, 0.802] FL 1.090 1.076 1.297 0.00250 [1.085, 1.095] FO 1.033 1.021 1.124 0.00076 [1.031, 1.034] FR 0.625 0.595 0.602 0.00198 [0.621, 0.629] SP 0.834 0.829 0.828 0.00027 [0.833, 0.834]
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表 8 河南省Ⅴ区敏感参数的后验分布
Table 8 The posteriori distribution of sensitive parameters in Zone Ⅴ of Henan Province
参数 平均值 中值 最大似然值 均方根误差 95%置信区间 AM00 1.082 1.070 1.333 0.00562 [1.071, 1.093] AM10 0.732 0.724 0.705 0.00068 [0.730, 0.732] AM13 0.728 0.721 0.708 0.00057 [0.727, 0.729] SL00 1.481 1.484 1.492 0.00036 [1.480, 1.481] SL05 0.718 0.715 0.708 0.00026 [0.717, 0.718] FL 1.880 1.885 1.792 0.00203 [1.876, 1.884] FO 0.937 0.935 0.915 0.00046 [0.936, 0.938] FR 0.532 0.527 0.502 0.00059 [0.531, 0.533] SP 0.738 0.741 0.748 0.00030 [0.738, 0.739]
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表 9 河南省同一套敏感参数的后验分布
Table 9 The posteriori distribution of sensitive parameters for the whole Henan Province
参数 平均值 中值 最大似然值 均方根误差 95%置信区间 AM00 0.758 0.747 0.756 0.00170 [0.755, 0.761] AM10 0.724 0.717 0.709 0.00072 [0.722, 0.725] AM13 0.714 0.711 0.702 0.00044 [0.714, 0.715] SL00 1.483 1.485 1.499 0.00048 [1.482, 1.484] SL05 0.712 0.709 0.701 0.00032 [0.711, 0.712] FL 1.855 1.853 1.856 0.00178 [1.851, 1.858] FO 0.901 0.899 0.892 0.00046 [0.900, 0.902] FR 0.553 0.544 0.538 0.00149 [0.550, 0.556] SP 0.896 0.896 0.906 0.00015 [0.895, 0.896]
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