黄花植株三维动态生长及产量模拟模型

doi:10.12133/j.smartag.SA202310011

Smart Agriculture ›› 2024, Vol. 6 ›› Issue (2): 140-153.doi: 10.12133/j.smartag.SA202310011

• 专刊--农业信息感知与模型 • 上一篇

黄花植株三维动态生长及产量模拟模型

张悦¹, 李伟佳², 韩志平¹, 张琨¹, 刘佳雯¹, HENKE Michael³()

^1. 山西大同大学农学与生命科学学院/设施农业技术研发中心，山西大同 037005，中国
^2. 山西大同大学煤基生态碳汇技术教育部工程研究中心，山西大同 037005，中国
^3. 湖南农业大学农学院，湖南长沙 410128，中国

收稿日期:2023-10-12 出版日期:2024-03-30
基金项目:
山西省高等学校科技创新计划(2021L398); 山西省科技厅应用基础研究计划(202203021222295); 大同市科技计划项目(2023063); 山西大同大学校级科学研究项目(2020CXZ8); 山西大同大学博士科研启动项目(2022-B-03); 山西大同大学大学生创新创业项目(XDC2022176)
作者简介:
张悦，研究方向为植物功能-结构-环境互作的系统仿真与数字孪生。E-mail：zhangyue@sxdtdx.edu.cn
通信作者:
HENKE Michael，博士，教授，研究方向为植物（三维）表型研究与应用研发。E-mail：mhenke@hunau.edu.cn

Three-Dimensional Dynamic Growth and Yield Simulation Model of Daylily Plants

ZHANG Yue¹, LI Weijia², HAN Zhiping¹, ZHANG Kun¹, LIU Jiawen¹, HENKE Michael³()

^1. College of Agronomy and Life Sciences/Facility of Agriculture Technology Research and Development Center, Shanxi Datong University, Datong 037005, China
^2. Engineering Research Center of Coal-based Ecological Carbon Sequestration Technology of the Ministry of Education, Shanxi Datong University, Datong 037005, China
^3. College of Agronomy, Hunan Agricultural University, Changsha 410128, China

Received:2023-10-12 Online:2024-03-30
Foundation items:Science and Technology Innovation Project of Higher Education Institutions in Shanxi Province(2021L398); Applied Basic Research Programs of Shanxi Province(202203021222295); Applied Basic Research Programs of Datong City(2023063); Basic Research Programs of Shanxi Datong University(2020CXZ8); Doctoral Research Project of Shanxi Datong University(2022-B-03); Shanxi Datong University Students Innovation and Entrepreneurship Project(XDC2022176)
About author:
ZHANG Yue, E-mail: zhangyue@sxdtdx.edu.cn
Corresponding author:
HENKE Michael, E-mail: mhenke@hunau.edu.cn

摘要/Abstract

摘要：

[目的/意义] 为探究并表达环境因素对黄花各器官生长发育、形态结构和产量的影响，提出一种基于源库关系的黄花植株三维动态生长及产量模拟模型。 [方法] 以大同地区黄花主要栽培种植品种大同黄花为研究材料，采集黄花叶片、花葶、花蕾等形态数据和叶片光合生理参数，利用功能-结构植物模型（Functional-Structural Plant Model，FSPM）平台的三维建模技术，建立基于云量的室外地表太阳辐射模型及适配黄花的光合作用模型，同时基于黄花源库关系建立黄花光合产物碳分配模型，利用β生长函数构建黄花各器官生长模拟模型，计算黄花生长期内逐日形态数据，最终实现黄花植株三维动态生长及产量模拟。 [结果和讨论] 采用实测数据对模型进行检验。结果显示，室外地表太阳辐射实测值和模拟值R²为0.87；剩余标准差（Root Mean Squared Error，RMSE）为28.52 W/m²，黄花各器官模拟模型实测值和预测值R²为0.896~0.984，RMSE为1.4~17.7 cm；平均花蕾产量模拟R²为0.880，RMSE为0.5 g；整体F值为82.244~1 168.533，Sig.值均小于显著水平0.05，表明上述模型拟合度和显著性较好。 [结论] 模型能够准确地表现黄花植株在3个主要生长时期的生长规律和形态特征，模拟结果与实际情况相符合，表现出较高的可信度。因此，本模型具有理想的模拟效果，足以满足精细农业领域的研究需求。

关键词: 黄花, 源库关系, 光合作用模型, 形态模型, 三维动态生长模拟, 产量模拟

Abstract:

[Objective] The daylily, a perennial herb in the lily family, boasts a rich nutritional profile. Given its economic importance, enhancing its yield is a crucial objective. However, current research on daylily cultivation is limited, especially regarding three-dimensional dynamic growth simulation of daylily plants. In order to establish a technological foundation for improved cultivation management, growth dynamics prediction, and the development of plant variety types in daylily crops, this study introduces an innovative three-dimensional dynamic growth and yield simulation model for daylily plants. [Methods] The open-source GroIMP software platform was used to simulate and visualize three-dimensional scenes. With Datong daylily, the primary cultivated variety of daylily in the Datong area, as the research subject, a field experiment was conducted from March to September 2022, which covered the growth season of daylily. Through actual cultivation experiment measurements, morphological data and leaf photosynthetic physiological parameters of daylily leaves, flower stems, flower buds, and other organs were collected. The functional-structural plant model (FSPM) platform's three-dimensional modeling technology was employed to establish the Cloud Cover-based solar radiation models (CSRMs) and the Farquhar, von Camerer, and Berry model (FvCB model) suitable for daylily. Moreover, based on the source-sink relationship of daylily, the carbon allocation model of daylily photosynthetic products was developed. By using the β growth function, the growth simulation model of daylily organs was constructed, and the daily morphological data of daylily during the growth period were calculated, achieving the three-dimensional dynamic growth and yield simulation of daylily plants. Finally, the model was validated with measured data. [Results and Discussions] The coefficient of determination (R²) between the measured and simulated outdoor surface solar radiation was 0.87, accompanied by a Root Mean Squared Error (RMSE) of 28.52 W/m². For the simulated model of each organ of the daylily plant, the R² of the measured against the predicted values ranged from 0.896 to 0.984, with an RMSE varying between 1.4 and 17.7 cm. The R² of the average flower bud yield simulation was 0.880, accompanied by an RMSE of 0.5 g. The overall F-value spanned from 82.244 to 1 168.533, while the Sig. value was consistently below the 0.05 significance level, suggesting a robust fit and statistical significance for the aforementioned models. Subsequently, a thorough examination of the light interaction, temperature influences, and photosynthetic attributes of daylily leaves throughout their growth cycle was carried out. The findings revealed that leaf nutrition growth played a pivotal role in the early phase of daylily's growth, followed by the contribution of leaf and flower stem nutrition in the middle stage, and finally the growth of daylily flower buds, which is the crucial period for yield formation, in the later stages. Analyzing the photosynthetic traits of daylily leaves comprehensively, it was observed that the photosynthetic rate was relatively low in the early spring as the new leaves were initially emerging and reached a plateau during the summer. Considering real-world climate conditions, the actual net photosynthetic rate was marginally lower than the rate verified under optimal conditions, with the simulated net assimilation rate typically ranging from 2 to 4 μmol CO₂/(m²·s). [Conclusions] The three-dimensional dynamic growth model of daylily plants proposed in this study can faithfully articulate the growth laws and morphological traits of daylily plants across the three primary growth stages. This model not only illustrates the three-dimensional dynamic growth of daylily plants but also effectively mimics the yield data of daylily flower buds. The simulation outcomes concur with actual conditions, demonstrating a high level of reliability.

Key words: Daylily citrina Baroni, source-sink relationship, photosynthesis model, morphological model, three-dimensional dynamic growth simulation, yield simulation

张悦, 李伟佳, 韩志平, 张琨, 刘佳雯, HENKE Michael. 黄花植株三维动态生长及产量模拟模型[J]. 智慧农业(中英文), 2024, 6(2): 140-153.

ZHANG Yue, LI Weijia, HAN Zhiping, ZHANG Kun, LIU Jiawen, HENKE Michael. Three-Dimensional Dynamic Growth and Yield Simulation Model of Daylily Plants[J]. Smart Agriculture, 2024, 6(2): 140-153.

图/表 14

图1

表1

图2

表2

黄花植物功能-结构模型中的能量平衡方程、光合作用模型（FvCB模型［31］）、气孔导度（BWB模型［32］）

模型类型	公式	描述
叶片能量平衡模型	$T L = T a + R a b s - ε σ T a 4 - λ g v D / P a c p g h + g r + λ [d e s (T a) / d T P a] g v$ （6）	叶片温度 $T L$ 的能量平衡方程
	$g r = 4 ε σ T L 3 C p$ （7）	叶片辐射电导
	$g h = g b × 0.135 / 0.147$ （8）	用于叶片传热计算的叶边界层电导
	$g v = 0.5 × g s g b g s + g b$ （9）	叶片边界层电导
	$e s T = 0.611 e x p (17.502 T 240.97 + T)$ （10）	在T ℃下的叶饱和蒸气压
	$e = 2 g V e s (T L) - e a P a$ （11）	叶片蒸腾速率
光合作用模型（FvCB模型）	$A = V c - 0.5 V 0 - R d = m i n A c, A j, A p - R d$ （12）	净光合速率
	$A c = V c m a x C c - Γ * C c + K c (1 + O / K o)$ （13）	Rubisco限制条件下光合速率
	$A j = J (C i - Γ ) 4 (C i + 2 Γ )$ （14）	RuBP再生限制条件下光合速率
	$θ J 2 - I 2 + J m a x J + I 2 J m a x = 0$ （15）	电子传输速率的光依赖性
	$I 2 = I (1 - f) (1 - δ) / 2$ （16）	光系统II对PAR的吸收
	$A p = 3 P u$ （17）	TPU限制条件下光合速率
	$K T = k 25 e x p E a (T L - 25) 298 R T L + 273$ （18）	Arrhenius函数； $K c, K o, R d, V c m a x$ 的温度依赖性
	$J m a x =$ $J m 25 e x p T p - 25 E a R T p + 273 298 1 + e x p S 298 - H R 298 1 + e x p S T p + 273 - H R (T p + 273)$ （19）	$J m a x$ 的温度依赖性
	$Γ * = 36.9 + 1.88 T p - 25 + 0.036 (T p - 25) 2$ （20）	$Γ *$ 的温度依赖性
	$f ξ = d 0 1 - e x p - d 1 ξ e x p (- d 2 ξ)$ （21）	$J m a x, V c m a x$ 和 $P u$ 的叶龄依赖性
	$C i = C a - A (1 g b + 1 g s) P a$ （22）	胞间CO₂浓度
	$C c = C i - A g m P a$ （23）	叶绿体内CO₂浓度
	$g m = e x p (c - ∆ H a R T k) 1 + e x p (∆ S × T k - ∆ H d R T)$ （24）	叶肉细胞对于CO₂的电导
气孔导度模型（BWB模型）	$g s = b + m A h s (C s / P a)$ （25）	气孔导度
	$Γ = R d K c (1 + O / K o) + V c m a x Γ * V c m a x - R d$ （26）	CO₂补偿点，考虑呼吸作用（R_d ）
	$C s = C a - A g b P a$ （27）	叶片表面CO₂分压
	$g b = 0.147 u / d$ （Gr/Re² >1）（28） $g b = 0.055 ∙ (T p - T a d) 14$ （Gr/Re² <1）（29） $d = 0.72 w$ （30）	水蒸气的边界层电导
	$a h h s 2 + b h h s + c h = 0$ 其中 $a h = (g 1 A) / C s b h = g 0 + g b - (g 1 A / C s) c h = - R H g b - g 0$ （31）	$将 h s 和 g s$ 与扩散方程相结合得到的二次方程

表2

表3

黄花植物功能-结构模型中的能量平衡方程、光合作用模型和气孔导度符号说明

符号类型	符号	含义及单位
光合作用	$Γ$	存在R_d 时的CO₂补偿点［μbar］
	$Γ *$	无R_d 时的CO₂补偿点［μbar］
	$ξ$	以展开后的天数计算的叶龄［day］
	$θ$	电子传递对PAR的响应曲率［0.7，-］
	$δ$	叶反射率加上透射率［0.15，-］
	$A$	叶片净光合速率［μmol/（m²·s）］
	$A c$	Rubisco限制的CO₂同化率［μmol/（m²·s）］
	$A j$	电子传输限制的CO₂同化率［μmol/（m²·s）］
	$A m a x$	环境条件下光饱和CO₂同化速率［CO₂］［μmol/（m²·s）］
	$A p$	磷酸丙糖再利用受限的CO₂同化率［μmol/（m²·s）］
	$C a$	空气CO₂分压
	$C i$	细胞间CO₂分压［μbar］
	$d 0$	叶龄效应的比例因子［1.296，-］
	$d 1$	叶龄效应生长的经验系数［0.146 8，-］
	$d 2$	叶龄效应下降斜率的经验系数［0.010 3，-］
	$E a$	活化能［kJ/mol］
	$f$	光谱校正因子［0.15，-］
	$H$	$J m a x$ 温度依赖性的曲率参数［219.4 kJ/mol］
	$I$	入射PAR ［μmol photons/（m²·s）］
	$J$	光合电子传递速率［μmol electrons/（m²·s）］
	$J m 25$	25 °C 时电子传输的潜在速率［36.8 μmol/（m²·s）］
	$K c 25$	CO₂的Rubisco-Michaelis-Menten常数［267 μbar］
	$K o 25$	25 °C时O₂的Rubisco-Michaelis-Menten常数［164 mbar］
	O	氧分压［205 mbar ］
	$P u 25$	25 °C时磷酸丙糖利用率［10.35 μmol/（m²·s）］
	R	通用气体常数［8.314 J/（mol·K）^［31］］
	$R d 25$	25 °C时光照条件下的线粒体呼吸作用［0.0089V_cmax25 ］
	S	电子传输温度响应参数［704.2 J/（mol·K）］
	$V c$	羧化率［μmol/（m²·s）］
	$V c m 25$	25 °C时的光合Rubisco潜力［92.07 μmol/（m²·s）］
	$V o$	氧合率［μmol/（m²·s）］
温度相关的变量	E	每个过程的活化能
	$J m a x$	最大电子传输速率［μmol/（m²·s）］
	$K c$	CO₂的Rubisco-Michaelis-Menten常数［μmol/（m²·s）］ E_Kc 80 990
	$K o$	O₂的Rubisco-Michaelis-Menten常数［μmol/（m²·s）］ E_Ko 36 000
	$P u$	磷酸丙糖利用率［μmol/（m²·s）］ E_Pu 47 140.1
	$R d$	光下的线粒体呼吸速率［μmol/（m²·s）］ E_Rd 46 390
	$V c m a x$	Rubisco羧化的最大速率［μmol/（m²·s）］ E_Vcmax 65 330
气孔导度模型	b	光补偿点时BWB模型对水汽的最小气孔导度［0.096 0 mol/（m²·s）］
	$C a$	环境CO₂分压［μbar］
	$C s$	叶面CO₂分压［μbar］
	$g b$	边界层对水蒸气的电导［mol/（m²·s）］
	$g s$	气孔对水蒸气的导度［mol/（m²·s）］
	$g h$	用于传热的叶片边界层传导率［mol/（m²·s）］
	$g v$	叶边界层电导［］
	$h s$	叶面相对湿度［］
	m	BWB模型中g_s 对A、C_s 和h_s 敏感度的经验系数［10.055，-］
能量平衡方程	$ε$	叶片热发射率［0.97］
	$σ$	斯特藩-玻尔兹曼常数［ $5.67 × 10 - 8 W / (m 2 · K 4)$ ］
	$λ$	25 ℃时的潜热［44.0 kJ/mol］
	$c p$	空气的比热容［29.3 J/（mol·℃）］
	D	环境空气的水蒸气压差［kPa］
	$D s$	叶片表面的水蒸气压差［kPa］
	E	单位叶面积的蒸腾速率［mol/（m²·s）］
	$e a$	单位投影叶面积的蒸腾速率［kPa］
	$e s$	叶片表面的水蒸气压力［kPa］
	$g h$	边界层单位表面叶面积的热传导率［mol/（m²·s）］
	$g r$	单位表面叶面积的辐射传导率［mol/（m²·s）］
	$g v$	单位表面叶面积的总水蒸气传导率［mol/（m²·s）］
	$P a$	大气压力［kPa］
	$R a b s$	单位表面叶面积吸收的长波和短波辐射能量［W/m²］
	$T a$	周围空气温度［℃］

表3

图3

图4

图5

图6

图7

图8

表3

图9

图10

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形态指标（生长最终值）	最大值	最小值	极差	平均值	标准差
叶片长度（1~13叶位）/cm	70.30、84.10、98.20、102.40、109.80、112.70、120.80、122.20、124.10、130.90、132.30、134.20、136.40	45.80、54.20、66.30、71.70、77.90、80.20、81.80、88.00、92.20、94.50、99.30、101.40、102.90	24.50、29.90、31.90、30.70、31.90、32.50、39.00、34.20、31.90、36.40、33.00、32.80、33.50	55.35、64.45、76.85、82.25、90.25、94.63、98.20、104.83、106.28、115.43、120.20、126.38、127.66	8.90、11.53、12.46、10.26、11.90、10.84、14.01、10.20、10.52、12.20、9.83、10.38
叶片宽度/mm	29.44	16.32	13.12	24.61	2.19
花蕾长度/mm	153	91	62	127	1.27
花蕾直径/mm	13.07	8.11	4.96	10.42	1.08
花蕾鲜重/g	6.17	1.92	4.25	3.79	0.84
薹蕾数/（蕾/薹）	59.00	18.00	41.00	40.10	11.48
花葶高度/cm	133.90	86.50	47.40	118.57	16.12
花葶鲜重/g	45.47	25.02	20.45	38.48	7.14

类别	R ²	RMSE	F	Sig.
叶位1	0.984	0.028	304.046	1.14×10^-5
叶位2	0.943	0.064	82.244	2.73×10^-4
叶位3	0.980	0.057	344.191	3.28×10^-7
叶位4	0.938	0.083	106.812	1.72×10^-5
叶位5	0.916	0.142	109.306	1.06×10^-6
叶位6	0.938	0.111	166.137	5.56×10^-8
叶位7	0.919	0.177	158.659	5.01×10^-9
叶位8	0.896	0.144	138.523	2.72×10^-9
叶位9	0.934	0.111	270.099	1.09×10^-12
叶位10	0.920	0.123	230.845	1.9×10^-12
叶位11	0.951	0.123	508.713	1.35×10^-18
叶位12	0.909	0.147	278.480	4.41×10^-16
叶位13	0.926	0.129	426.891	7.99×10^-21
花葶长	0.972	0.088	1 168.533	6.49×10^-28
平均花蕾长	0.914	0.014	211.946	9.72×10^-12
平均花蕾鲜重	0.880	0.511	146.685	1.15×10^-10

黄花植株三维动态生长及产量模拟模型

Three-Dimensional Dynamic Growth and Yield Simulation Model of Daylily Plants

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