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Assimilation of Observations with Crop Growth Model Based on the Constrained Analysis of Parameters
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摘要: 同化观测数据可为作物生长模型的区域应用提供支持。该文定义了观测数据对模型参数的约束性，研究发现华北夏玉米观测数据对WOFOST模型的可约束参数主要包括初始总干物重、不同发育阶段的比叶面积、初始最大CO2同化速率、叶片衰老系数、初始土壤有效水、最大根深日增量以及初始根深的初始土壤水分含量等。建立了基于参数约束性分析的观测数据与作物生长模型同化方法和流程, 利用优化算法进行作物生长模型所有参数和变量初值的敏感性分析，遴选出各状态变量的敏感参数；根据拟合度与优化结果之间关系进行敏感参数的约束性分析，获得不同变量的可约束参数；组合优化可约束参数得到各参数最优值，由此实现了观测数据与作物生长模型的同化。约束性体现了观测数据对模型参数或变量初值的控制能力，可约束参数作为待优化参数使数据模型同化获得了最优结果。Abstract: Data assimilation may support regional applications of crop growth model, in which the selection of parameters and initial value of variables need lots of optimizing. Constraint reflects the controllability of observations on model parameters or variable initial value. Optimization of constrained parameters will most likely reach optimal results in data assimilation. An assimilation method of observations and crop growth model is established based on constrained analysis of model parameters. Sensitive parameters and initial value of the state variables in crop growth models are first selected using sensitivity analysis based on optimization algorithms. Constrained parameters of different variables are then obtained through constrained analysis, which is defined according to the relation of goodness of fit (QT) and optimization results of parameters. The optimal value of each parameter is got by means of combinatorial optimization of constrained parameters at last. Based on the constrained analysis, observations of summer maize leaf area index (LAI) in North China can constrain initial total crop dry weight (TDWI), initial specific leaf area (SLA1), initial maximum leaf CO2 assimilation rate (Amax1) and life span of leaves growing at 35 Celsius (SPAN) in WOFOST under optimal soil water condition. Dry weight of living storage organs (WSO) with the same results as the LAI is achieved. Total above ground production (TAGP) still include specific leaf area between jointing stage and tasseling stage (SLA2). Constrained parameters of LAI under water stress level include not only TDWI, SLA1, Amax1, and SPAN, but also initial amount of available water in total root zone (WAV), maximum daily increase in rooting depth (RRI), and maximum initial and soil moisture content of the initial root depth (SMLIM). Parameters constrained by LAI, WSO, TAGP and soil moisture content (SM) are not exactly the same with each other. The values of crop and soil parameters and initial conditions in WOFOST are obtained using observations over North China in 2009. Simulation shows that WOFOST can reflect the process of summer maize development, growth, and yield formation. The assimilation approaches are the foundation for application of crop growth model at regional scale.
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Key words:
- constrained analysis;
- assimilation;
- crop growth model;
- observations
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图 1 基于参数约束性分析的观测数据与作物生长模型同化方法
Fig. 1 Assimilation method of observations with Crop Growth Model based on the analysis of constrained character
图 2 潜在生产水平下WOFOST模型同化LAI时QT随参数取值变化 (2009年CK处理)
Fig. 2 The changes of QT values with parameter values in assimilating LAI to WOFOST under potential production level (CK treatment in 2009)
表 1 WOFOST模型的主要参数
Table 1 Main parameters in WOFOST
参数 定义 单位 TDWI 初始地上部总干物重 kg·hm-2 SLA 比叶面积 hm2·kg-1 SPAN 叶片衰老系数 d EFF 单叶光能利用率 kg·hm-2·h-1·J-1·m2·s Amax 叶片最大CO2同化速率 kg·hm-2·h-1 RML 叶片相对维持呼吸速率 kgCH2O·kg-1·d-1 RMO 贮存器官相对维持呼吸速率 kgCH2O·kg-1·d-1 RMS 茎相对维持呼吸速率 kgCH2O·kg-1·d-1 RDRS 茎相对死亡速率 kg·kg-1·d-1 CFET 蒸散速率订正系数 RDI 初始根深 cm RRI 根深最大日增量 cm·d-1 WAV 初始土壤有效水 cm SMLIM 初始根深的初始水分含量 cm3·cm-3 
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表 2 以LAI和TAGP为同化数据时WOFOST模型的模拟误差 (2009年)
Table 2 Errors of WOFOST while LAI and TAGP as assimilation data in 2009
同化数据 参变量 统计量 生产水平 潜在 水分胁迫 LAI Amax1 绝对误差/(kg·hm-2·kg-1) 3 2.5 相对误差/% 6 5 SPAN 绝对误差/d 0.1 0.08 相对误差/% 0.2 0 SLA1 绝对误差/(hm2·kg-1) 0.0001 0 相对误差/% 3 0 WSO 绝对误差/(kg·hm-2) 76 96 相对误差/% 0.9 1 TAGP 绝对误差/(kg·hm-2) 179 271 相对误差/% 1 2 TAGP TDWI 绝对误差/(kg·hm-2) 2 1.1 相对误差/% 4 2 SLA2 绝对误差/(hm2·kg-1) 0.0001 0 相对误差/% 6 0 SPAN 绝对误差/d 4 4 相对误差/% 8 8 WSO 绝对误差/(kg·hm-2) 70 62 相对误差/% 0.9 1 TAGP 绝对误差/(kg·hm-2) 96 100 相对误差/% 0.6 1
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表 3 WOFOST模型敏感参数的拟合度QT
Table 3 QT of sensitivity parameters in WOFOST
参数 潜在生产水平 (2009年CK处理) 水分胁迫生产水平 (2009年K2处理) LAI WSO/(kg·hm-2) TAGP/(kg·hm-2) LAI WSO/(kg·hm-2) TAGP/(kg·hm-2) SM/% TDWI 0.35 1295.89 1142.58 0.31 1542.93 251.96 4.05 SLA1 0.37 1291.53 980.39 0.29 305.24 269.21 3.89 Amax1 0.37 1293.18 1029.72 0.29 808.56 439.72 4.26 EFF2 0.41 1075.47 0.34 1088.23 1437.47 SLA2 0.47 805.91 909.88 0.31 1568.69 1597.23 3.91 Amax2 0.66 1265.34 1008.89 0.34 1009.37 1088.11 4.65 EFF1 0.96 1075.38 0.79 1426.45 2340.61 SPAN 1.00 1278.54 980.71 0.64 532.05 1130.70 4.67 RMO 1019.33 910.88 1476.14 Amax4 1043.29 929.49 1413.26 2690.93 Amax3 1216.73 1336.32 2646.97 SLA3 1271.46 1056.22 1704.76 2856.13 4.67 Amax5 1117.89 972.11 RDRS3 1205.73 RML 1208.80 960.28 RRI 0.25 322.81 268.69 4.43 WAV 0.29 305.41 245.65 4.68 SMLIM 0.31 313.93 249.74 4.32 RDI 0.32 1732.18 4.58 CFET2 0.90 1288.60 4.38 CFET1 0.56 1474.08 2236.67 4.58
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表 4 水分胁迫生产水平下不同观测数据在WOFOST模型中的可约束参数 (2009年K2处理)
Table 4 Constrained parameters of different observations in WOFOST under water stress production level (K2 treatment in 2009)
状态变量 可约束参数 LAI WAV, Amax1, SLA1, RRI, SMLIM, TDWI, SPAN WSO WAV, SLA1, SMLIM, SLA2, SPAN, RRI TAGP WAV, SLA1, RRI, SMLIM, TDWI SM WAV, RRI, SMLIM, TDWI, SPAN
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表 5 WOFOST模型同化观测数据后可约束参数的最优值 (2009年)
Table 5 Optimal values of constrained parameters while assimilation of observations with WOFOST in 2009
项目 潜在生产水平 (CK处理) 水分胁迫生产水平 (K2处理) LAI WSO TAGP LAI WSO SM 可约束参数 TDWI/(kg·hm-2) SLA1/(hm2·kg-1) SPAN/d SLA2/(hm2·kg-1) AMAX1/(kg·hm-2·h-1) RRI/(cm·d-1) SMLIM/(cm3·cm-3) SLA2/(hm2·kg-1) WAV/cm 参数优化值 22.41 0.0028 49.81 0.0015 74.82 0.74 0.24 0.0011 23.07
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