基于冠层时序植被指数的冬小麦单产预测

doi:10.3864/j.issn.0578-1752.2020.18.005

中国农业科学 ›› 2020, Vol. 53 ›› Issue (18): 3679-3692.doi: 10.3864/j.issn.0578-1752.2020.18.005

• 耕作栽培·生理生化·农业信息技术 • 上一篇下一篇

基于冠层时序植被指数的冬小麦单产预测

项方林(),李鑫格,马吉锋,刘小军,田永超,朱艳,曹卫星,曹强()

南京农业大学/国家信息农业工程技术中心/农业农村部农作物系统分析与决策重点实验室/智慧农业教育部工程研究中心/江苏省信息农业重点实验室,南京 210095

收稿日期:2019-12-09 接受日期:2020-03-12 出版日期:2020-09-16 发布日期:2020-09-25
通讯作者: 曹强
作者简介:项方林,E-mail： 2017101003@njau.edu.cn。
基金资助:
国家重点研发计划(2016YFD0300608);国家自然科学基金青年科学基金(31601222);中央高校基本科研业务费专项资金项目(KJQN201725);江苏现代农业产业技术体系建设专项资金(JATS[2019]433);江苏现代农业产业技术体系建设专项资金(JATS[2019]141)

Using Canopy Time-Series Vegetation Index to Predict Yield of Winter Wheat

XIANG FangLin(),LI XinGe,MA JiFeng,LIU XiaoJun,TIAN YongChao,ZHU Yan,CAO WeiXing,CAO Qiang()

Nanjing Agricultural University/National Engineering and Technology Center for Information Agriculture/Key Laboratory for Crop System Analysis and Decision Making, Ministry of Agriculture and Rural Affairs/Engineering and Research Center for Smart Agriculture, Ministry of Education/Jiangsu Key Laboratory for Information Agriculture, Nanjing 210095

Received:2019-12-09 Accepted:2020-03-12 Online:2020-09-16 Published:2020-09-25
Contact: Qiang CAO

摘要/Abstract

摘要：

【目的】研究冬小麦冠层时序植被指数的动态变化规律并基于其构建单产预测模型,为田间实时、准确获取作物单产信息提供有效的技术手段。【方法】本研究于2017—2019年在江苏省兴化市万亩粮食产业园开展不同品种及氮肥水平的田间小区试验,利用主动传感器RapidSCAN CS-45获取冠层归一化红边植被指数（normalized difference red edge,NDRE）和归一化植被指数（normalized difference vegetation index,NDVI）,基于双Logistic函数拟合时序植被指数并提取曲线特征参数,进而分析各特征参数与单产的相关关系,并以独立试验数据对单产预测模型进行验证。【结果】NDRE在孕穗期和抽穗期与单产关系最好,R²达到0.84以上;通过多元逐步线性回归法发现,利用2个或多个时期NDRE预测单产的效果较单生育时期有所提高,且第一和第二被选择的时期分别为拔节期和孕穗期。基于全生育时期相对NDRE（relative NDRE,RNDRE）和相对NDVI（relative NDVI,RNDVI）构建时序曲线,并利用曲线特征参数建立单产预测模型,其中RNDRE和RNDVI的最大值、累积值及增长速率与单产关系较好。利用独立试验数据对上述单产预测模型进行检验,结果表明基于RNDRE时序曲线最大值和累积值所构建的单产模型验证效果较好,R²大于0.80,相对均方根误差和相对误差均小于10%,其验证效果优于单时期或多时期基于NDRE的预测模型,且优于基于NDVI构建的单产模型。【结论】基于冠层时序植被指数提取的特征参数RNDRE最大值和累积RNDRE具有良好估测单产的潜力,研究结果为田间进行实时、准确预测冬小麦单产提供了技术支持。

关键词: 冬小麦, 冠层传感器, 时序植被指数, 单产, 预测模型

Abstract:

【Objective】The research elaborated the dynamic change trend of canopy time series vegetation index in winter wheat. The yield prediction model was constructed based on time series vegetation index in wheat, which provided effective technical support for obtaining crop yield information timely and accurately. 【Method】 From 2017 to 2019, the field experiments involving different nitrogen (N) rates and varieties were conducted in Ten Thousand Acres Grain Industrial Park located in Xinghua, Jiangsu province. The normalized difference red edge (NDRE) and normalized difference vegetation index (NDVI) were obtained from the active canopy sensor RapidSCAN CS-45. The curve of time-series vegetation index was fitted based on the double logistic function, and the characteristic parameters of curve were extracted. The correlation between each characteristic parameters and yield were analyzed. The yield estimation models were verified with independent test data. 【Result】 The results of the study indicated that the relationship between NDRE and yield was performed well at booting and heading stage, and R² of them was 0.86 and 0.85, respectively. The results of multiple stepwise linear regression showed that the yield prediction models could be improved using NDRE of two or more growth stages, compared with using single growth stage information. The first and second selected periods were jointing and booting stage, respectively. Based on the relative NDRE (RNDRE) and relative NDVI (RNDVI) of the whole growth period, the time-series curve was constructed and the yield prediction models were developed using the characteristic parameters of the curve. The maximum value, accumulative value and growth rate of RNDRE and RNDVI time series curve had a good relationship with the yield. The yield prediction models based on the maximum and accumulative values of RNDRE performed satisfactorily with validation using independent data, the R² was greater than 0.80, and the relative root mean square error and relative error were less than 10%. The validation effect was better than NDRE-based prediction model with the single-period or multi-period, which was better than NDVI-based yield predicted model. 【Conclusion】 The maximum and the accumulative RNDRE extracted from the canopy time series vegetation index had a good potential to estimate the yield, which provided technical support for real-time and accurate yield prediction in the field.

Key words: winter wheat, canopy sensor, time series vegetation index, yield, prediction model

项方林,李鑫格,马吉锋,刘小军,田永超,朱艳,曹卫星,曹强. 基于冠层时序植被指数的冬小麦单产预测[J]. 中国农业科学, 2020, 53(18): 3679-3692.

XIANG FangLin,LI XinGe,MA JiFeng,LIU XiaoJun,TIAN YongChao,ZHU Yan,CAO WeiXing,CAO Qiang. Using Canopy Time-Series Vegetation Index to Predict Yield of Winter Wheat[J]. Scientia Agricultura Sinica, 2020, 53(18): 3679-3692.

0
/ / 推荐

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: https://www.chinaagrisci.com/CN/10.3864/j.issn.0578-1752.2020.18.005

https://www.chinaagrisci.com/CN/Y2020/V53/I18/3679

图/表 12

图1

表1

表2

图2

图3

图4

表3

表4

表5

表6

表7

图5

参考文献 42

[1]	谭昌伟, 杜颖, 童璐, 周健, 罗明, 颜伟伟, 陈菲. 基于开花期卫星遥感数据的大田小麦估产方法比较. 中国农业科学, 2017,50(16):3101-3109. doi: 10.3864/j.issn.0578-1752.2017.16.005
	TAN C W, DU Y, TONG L, ZHOU J, LUO M, YAN W W, CHEN F. Comparison of the methods for predicting wheat yield based on satellite remote sensing data at anthesis. Scientia Agricultura Sinica, 2017,50(16):3101-3109. (in Chinese) doi: 10.3864/j.issn.0578-1752.2017.16.005
[2]	侯学会, 牛铮, 高帅, 黄妮. 基于SPOT-VGT NDVI时间序列的农牧交错带植被物候监测. 农业工程学报, 2013,29(1):142-150.
	HOU X H, NIU Z, GAO S, HUANG N. Monitoring vegetation phenology in farming-pastoral zone using SPOT-VGT NDVI data. Transactions of the Chinese Society of Agricultural Engineering, 2013,29(1):142-150. (in Chinese)
[3]	冯美臣, 杨武德, 张东彦, 曹亮亮, 王慧芳, 王芊. 基于TM和MODIS数据的水旱地冬小麦面积提取和长势监测. 农业工程学报, 2009,25(3):103-109.
	FENG M C, YANG W D, ZHANG D Y, CAO L L, WANG H F, WANG Q. Monitoring planting area and growth situation of irrigation-land and dry-land winter wheat based on TM and MODIS data. Transactions of the Chinese Society of Agricultural Engineering, 2009,25(3):103-109. (in Chinese)
[4]	任建强, 陈仲新, 周清波, 刘佳, 唐华俊. MODIS植被指数的美国玉米单产遥感估测. 遥感学报, 2015,19(4):568-577.
	REN J Q, CHEN Z X, ZHOU Q B, LIU J, TANG H J. MODIS vegetation index data used for estimating corn yield in USA. Journal of Remote Sensing, 2015,19(4):568-577. (in Chinese)
[5]	苏腾飞, 刘全明, 苏秀川. 基于多种植被指数时间序列与机器学习的作物遥感分类研究. 江苏农业科学, 2017,45(16):219-224.
	SU T F, LIU Q M, SU X C. Remote sensing classification of crops based on time series of multiple vegetation indices and machine learning. Jiangsu Agricultural Sciences, 2017,45(16):219-224. (in Chinese)
[6]	WARDLOW B D, EGBERT S L, KASTENS J H. Analysis of time-series MODIS 250 m vegetation index data for crop classification in the U.S. central great plains. Remote Sensing of Environment, 2007,108(3):290-310.
[7]	ZHENG H B, CHENG T, YAO X, DENG X Q, TIAN Y C, CAO W X, ZHU Y. Detection of rice phenology through time series analysis of ground-based spectral index data. Field Crops Research, 2016,198:131-139.
[8]	PAN Y Z, LI L, ZHANG J S, LIANG S L, ZHU X F, SULLA-MENASHE D. Winter wheat area estimation from MODIS-EVI time series data using the crop proportion phenology index. Remote Sensing of Environment, 2012,119:232-242. doi: 10.1016/j.rse.2011.10.011
[9]	陈鹏飞, 杨飞, 杜佳. 基于环境减灾卫星时序归一化植被指数的冬小麦单产估测. 农业工程学报, 2013,29(11):124-131.
	CHEN P F, YANG F, DU J. Yield forecasting for winter wheat using time series NDVI from HJ satellite. Transactions of the Chinese Society of Agricultural Engineering, 2013,29(11):124-131. (in Chinese)
[10]	ANTHONY N R, ANATOLY G, YI P, ELIZABETH W S, BRYAN L, TIMOTHY A. Continuous monitoring of crop reflectance, vegetation fraction, and identification of developmental stages using a four band radiometer. Agronomy Journal, 2013,105(6):1769. doi: 10.2134/agronj2013.0242
[11]	LIU X J, FERGUSON R, ZHENG H B, CAO Q, TIAN Y C, CAO W X, ZHU Y. Using an active-optical sensor to develop an optimal NDVI dynamic model for high-yield rice production (Yangtze, China). Sensors, 2017,17(4):672.
[12]	MAGNEY T S, EITEL J U H, HUGGINS D R, VIERLING L A. Proximal NDVI derived phenology improves in-season predictions of wheat quantity and quality. Agricultural and Forest Meteorology, 2016,217:46-60. doi: 10.1016/j.agrformet.2015.11.009
[13]	SHAVER T M, KHOSLA R, WESTFALL D G. Evaluation of two ground-based active crop canopy sensors in maize: growth stage, row spacing, and sensor movement speed. Soil Science Society of America Journal, 2010,74(6):2101-2108.
[14]	TANAKA S, KAWAMURA K, MAKI M, MURAMOTO Y, YOSHIDA K, AKIYAMA T. Spectral Index for quantifying leaf area index of winter wheat by field hyperspectral measurements: A case study in Gifu prefecture, central Japan. Remote Sensing, 2015,7(5):5329-5346.
[15]	THOMPSON L J, FERGUSON R B, KITCHEN N, FRAZEN D W, MAMO M, YANG H, SCHEPERS J S. Model and sensor-based recommendation approaches for in-season nitrogen management in corn. Agronomy Journal, 2015,107(6):2020-2030.
[16]	王仁红, 宋晓宇, 李振海, 杨贵军, 郭文善, 谭昌伟, 陈立平. 基于高光谱的冬小麦氮素营养指数估测. 农业工程学报, 2014,30(19):191-198.
	WANG R H, SONG X Y, LI Z H, YANG G J, GUO W S, TAN C W, CHEN L P. Estimation of winter wheat nitrogen nutrition index using hyperspectral remote sensing. Transactions of the Chinese Society of Agricultural Engineering, 2014,30(19):191-198. (in Chinese)
[17]	ZHOU X, ZHENG H B, XU X Q, HE J Y, GE X K, YAO X, CHENG T, ZHU Y, CAO W X, TIAN Y C. Predicting grain yield in rice using multi-temporal vegetation indices from UAV-based multispectral and digital imagery. ISPRS Journal of Photogrammetry and Remote Sensing, 2017,130:246-255.
[18]	LU J J, MIAO Y X, SHI W, LI J X, YUAN F. Evaluating different approaches to non-destructive nitrogen status diagnosis of rice using portable RapidSCAN active canopy sensor. Scientific Reports, 2017,7(1):14073. doi: 10.1038/s41598-017-14597-1 pmid: 29074943
[19]	LI S Y, DING X Z, KUANG Q L, ATA-UI-KARIM S T, CHENG T, LIU X J, TIAN Y C, ZHU Y, CAO W X, CAO Q. Potential of UAV-based active sensing for monitoring rice leaf nitrogen status. Frontiers in Plant Science, 2018,9:1834. doi: 10.3389/fpls.2018.01834 pmid: 30619407
[20]	BONFIL D J. Wheat phenomics in the field by RapidScan NDVI vs. NDRE. Israel Journal of Plant Sciences, 2016,64:41-45.
[21]	RUSSELLE M P, WILHELM W W, OLSON R A, POWER J F. Growth analysis based on degree days. Crop Science, 1984,24:28-32. doi: 10.2135/cropsci1984.0011183X002400010007x
[22]	FRANCH B, VERMOTE E F, BECKER-RESHEF I, CLAVERIE M, HUANG J, ZHANG J, JUSTICE C, SOBRINO J A. Improving the timeliness of winter wheat production forecast in the United States of America, Ukraine and China using MODIS data and NCAR growing degree day information. Remote Sensing of Environment, 2015,161:131-148. doi: 10.1016/j.rse.2015.02.014
[23]	MCMASTER G S, SMIKA D E. Estimation and evaluation of winter wheat phenology in the central great plains. Agricultural and Forest Meteorology, 1988,43(1):1-18.
[24]	WANG X X, WANG Q J, FAN J, SU L J, SHEN X L. Logistic model analysis of winter wheat growth on China's loess plateau. Canadian Journal of Plant Science, 2014,94(8):1471-1479. doi: 10.4141/CJPS2013-293
[25]	FISCHER A. A model for the seasonal variations of vegetation indices in coarse resolution data and its inversion to extract crop parameters. Remote Sensing of Environment, 1994,48(2):220-230. doi: 10.1016/0034-4257(94)90143-0
[26]	SHMUELI G. To explain or to predict? Statistical Science, 2010,25(3):289-310. doi: 10.1214/10-STS330
[27]	AKAIKE H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1974,19(6):716-723.
[28]	BOZDOGAN H. Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions. Psychometrika, 1987,52(3):345-370.
[29]	MKHABELA M S, BULLOCK P, RAJ S, WANG S, YANG Y. Crop yield forecasting on the Canadian prairies using MODIS NDVI data. Agricultural and Forest Meteorology, 2011,151(3):385-393. doi: 10.1016/j.agrformet.2010.11.012
[30]	王长耀, 林文鹏. 基于MODIS EVI的冬小麦单产遥感预测研究. 农业工程学报, 2005,21(10):90-94.
	WANG C Y, LIN W P. Winter wheat yield estimation based on MODIS EVI. Transactions of the Chinese Society of Agricultural Engineering, 2005,21(10):90-94. (in Chinese)
[31]	HASSAN M A, YANG M J, RASHEED A, YANG G J, REYNOLDS M, XIA X C, XIAO Y G, HE Z H. A rapid monitoring of NDVI across the wheat growth cycle for grain yield prediction using a multi-spectral UAV platform. Plant Science, 2019,282:95-103. doi: 10.1016/j.plantsci.2018.10.022 pmid: 31003615
[32]	KANKE Y TUBAÑA B, DALEN M, HARRELL D. Evaluation of red and red-edge reflectance-based vegetation indices for rice biomass and grain yield prediction models in paddy fields. Precision Agriculture, 2016,17(5):507-530.
[33]	DEMPEWOLF J, ADUSEI B, BECKER R I, HANSEN M, POTAPOV P, KHAN A, BARKER B. Wheat yield forecasting for Punjab province from vegetation index time series and historic crop statistics. Remote Sensing, 2014,6:9653-9675. doi: 10.3390/rs6109653
[34]	MENG L H, ZHANG X L, LIU H J, GUO D, YAN Y, QIN L L, PAN Y. Estimation of cotton yield using the reconstructed time-series vegetation index of Landsat Data. Canadian Journal of Remote Sensing, 2017,43(3):244-255. doi: 10.1080/07038992.2017.1317206
[35]	ZHANG K, GE X K, SHEN P C, LI W Y, LIU X J, CAO Q, ZHU Y, CAO W X, TIAN Y C. Predicting rice grain yield based on dynamic changes in vegetation indexes during early to mid-growth stages. Remote Sensing, 2019,11(4):387.
[36]	WARDLOW B D, EGBERT S L. Large-area crop mapping using time-series MODIS 250 m NDVI data: An assessment for the U.S. central great plains. Remote Sensing of Environment, 2008,112(3):1096-1116. doi: 10.1016/j.rse.2007.07.019
[37]	CHU L, LIU Q S, HUANG C, LIU G H. Monitoring of winter wheat distribution and phenological phases based on MODIS time-series: A case study in the Yellow River Delta, China. Journal of Integrative Agriculture, 2016,15(10):2403-2416. doi: 10.1016/S2095-3119(15)61319-3
[38]	JOHNSON D M. An assessment of pre- and within-season remotely sensed variables for forecasting corn and soybean yields in the United States. Remote Sensing of Environment, 2014,141:116-128. doi: 10.1016/j.rse.2013.10.027
[39]	HUANG J X, TIAN L Y, LIANG S L, MA H Y, BECKER-RESHEF I, HUANG Y B, SU W, ZHANG X D, ZHU D H, WU W B. Improving winter wheat yield estimation by assimilation of the leaf area index from Landsat TM and MODIS data into the WOFOST model. Agricultural and Forest Meteorology, 2015,204:106-121. doi: 10.1016/j.agrformet.2015.02.001
[40]	MA H Y, HUANG J X, ZHU D H, LIU J M, SU W, ZHANG C, FAN J L. Estimating regional winter wheat yield by assimilation of time series of HJ-1 CCD NDVI into WOFOST-ACRM model with Ensemble Kalman filter. Mathematical and Computer Modelling, 2013,58(3/4):759-770. doi: 10.1016/j.mcm.2012.12.028
[41]	TAO J B, WU W B, ZHOU Y, WANG Y, JIANG Y. Mapping winter wheat using phenological feature of peak before winter on the north China plain based on time-series MODIS data. Journal of Integrative Agriculture, 2017,16(2):348-359. doi: 10.1016/S2095-3119(15)61304-1
[42]	DUVEILLER G, LOPEZ-LOZANO R, CESCATTI A. Exploiting the multi-angularity of the MODIS temporal signal to identify spatially homogeneous vegetation cover: A demonstration for agricultural monitoring applications. Remote Sensing of Environment, 2015,166:61-77. doi: 10.1016/j.rse.2015.06.001

植被指数 Vegetation index	品种 Variety	样本 Sample	拔节期 Jointing stage	孕穗期 Booting stage	抽穗期 Heading stage	开花期 Flowering stage	灌浆期 Filling stage
NDRE	镇麦12 Zhenmai 12	30	0.66	0.89	0.88	0.86	0.89
	扬麦23 Yangmai 23	30	0.46	0.83	0.82	0.75	0.84
	宁麦13 Ningmai 13	30	0.72	0.92	0.92	0.91	0.91
	所有品种 All	90	0.60	0.86	0.85	0.81	0.81
NDVI	镇麦12 Zhenmai 12	30	0.62	0.79	0.81	0.84	0.83
	扬麦23 Yangmai 23	30	0.54	0.79	0.75	0.77	0.75
	宁麦13 Ningmai 13	30	0.81	0.86	0.81	0.84	0.85
	所有品种 All	90	0.63	0.79	0.77	0.80	0.76

植被指数 Vegetation index	回归方程 Regression equation	决定系数 R²	相对均方根误差 RRMSE (%)	相对误差 RE (%)	赤池信息准则 AIC
NDRE	y= -2.16x₁+16.83x₂+9.15x₃-4.40x₄-2.35x₅-0.75	0.86	8.98	9.82	-97.95
	y= -2.85x₁+17.69x₂+5.67x₃-3.23x₅-0.90	0.86	8.99	9.84	-99.74
	y= -2.54x₁+21.94x₂-2.14x₅-0.81	0.86	9.02	9.82	-101.37
	y= -2.53x₁+19.90x₂-0.75	0.86	9.02	9.84	-103.01
NDVI	y=0.14x₁+11.23x₂-13.22x₃+23.12x₄-3.57x₅-8.31	0.81	10.41	11.70	-71.45
	y=11.25x₂-13.36x₃+23.27x₄-3.38x₅-8.36	0.81	10.40	11.76	-73.44
	y=12.21x₂-14.79x₃+19.45x₄-7.45	0.81	10.43	11.62	-74.96

植被指数 Vegetation index	氮处理 N treatment	曲线参数 Parameters of curves						决定系数 R²	均方根误差 RMSE
植被指数 Vegetation index	氮处理 N treatment	A₁	A₂	a	b	c	d	决定系数 R²	均方根误差 RMSE
RNDRE	N0	0.655	0.506	7.10	0.21	11.84	0.84	0.78	0.066
	N1	0.876	0.714	8.97	0.27	14.25	0.85	0.91	0.063
	N2	0.969	0.791	11.42	0.28	15.04	0.88	0.96	0.047
	N3	0.988	0.786	12.74	0.28	15.51	0.90	0.97	0.043
	N4	0.995	0.788	12.70	0.28	15.10	0.90	0.97	0.043
RNDVI	N0	0.837	0.668	5.85	0.18	14.29	0.86	0.79	0.082
	N1	0.956	0.785	8.80	0.23	15.70	0.88	0.91	0.062
	N2	0.987	0.776	11.59	0.23	16.60	0.92	0.94	0.053
	N3	0.997	0.760	12.29	0.24	16.22	0.93	0.96	0.044
	N4	0.996	0.754	12.46	0.24	15.84	0.93	0.95	0.045

氮处理 N treatment	RNDRE				RNDVI
氮处理 N treatment	最大值 Maximum	累积值 Accumulative value	增长速率 Increase rate	下降速率 Decrease rate	最大值 Maximum	累积值 Accumulative value	增长速率 Increase rate	下降速率 Decrease rate
N0	0.582	0.349	0.721	1.187	0.750	0.456	0.772	1.693
N1	0.809	0.464	1.245	1.841	0.911	0.558	1.186	2.091
N2	0.931	0.550	1.598	2.037	0.968	0.623	1.396	2.039
N3	0.963	0.580	1.731	2.028	0.981	0.637	1.452	1.983
N4	0.968	0.583	1.737	2.018	0.980	0.639	1.488	1.885

植被指数 Vegetation index	特征参数 Characteristic parameter	单产预测模型 Yield prediction model	R²	RRMSE (%)	RE (%)	AIC
RNDRE	最大值 Maximum	y = 8.72x - 1.37	0.80	10.2	12.9	62.29
	累积值 Accumulative value	y = 14.39x - 1.22	0.82	9.9	12.9	60.41
	增长速率 Increase rate	y = 3.32x + 1.38	0.82	9.9	12.8	60.35
	下降速率 Decrease rate	y = 3.73x - 0.75	0.73	12.0	14.3	71.98
RNDVI	最大值 Maximum	y = 14.24x - 7.03	0.77	11.0	13.4	66.48
	累积值 Accumulative value	y = 18.24x - 4.58	0.80	10.2	12.9	62.18
	增长速率 Increase rate	y = 4.82x - 0.02	0.81	10.2	12.8	61.84
	下降速率 Decrease rate	y = 5.04x - 3.72	0.22	20.3	25.6	103.41

基于冠层时序植被指数的冬小麦单产预测

Using Canopy Time-Series Vegetation Index to Predict Yield of Winter Wheat

RichHTML

PDF

赞

可视化

摘要/Abstract

引用本文

使用本文

图/表 12

参考文献 42

相关文章 15

Metrics

本文评价

推荐阅读 0

植被指数 Vegetation index	模型 Model	单产预测模型 Yield prediction model	R²	RRMSE (%)	RE (%)
RNDRE	单生育时期线性回归单产模型 Yield model based on linear regression in single growth stage	拔节期 Jointing y=12.47x+1.67	0.59	24.3	23.5
		孕穗期 Booting y =17.34x-0.65	0.79	18.7	18.2
		抽穗期 Heading y =17.46x-0.73	0.77	17.4	16.6
		开花期 Flowering y =17.97x-0.87	0.79	17.7	16.7
		灌浆期 Filling y =17.46x+0.13	0.71	15.5	14.4
	多元逐步线性回归模型 Yield model based on stepwise multiple linear regression	y= -2.16x₁+16.83x₂+9.15x₃-4.40x₄-2.35x₅-0.75	0.81	17.6	17.3
		y= -2.85x₁+17.69x₂+5.67x₃-3.23x₅-0.90	0.80	17.8	17.6
		y= -2.54x₁+21.94x₂-2.14x₅-0.81	0.78	18.3	18.2
		y= -2.53x₁+19.90x₂-0.75	0.79	17.7	17.4
RNDVI	单生育时期线性回归单产模型 Yield model based on linear regression in single growth stage	拔节期 Jointing y = 8.8027x - 0.4221	0.56	14.2	17.2
		孕穗期 Booting y = 11.822x - 3.4517	0.73	13.6	14.4
		抽穗期 Heading y = 12.877x - 4.3125	0.68	16.1	17.4
		开花期 Flowering y = 17.707x - 8.1348	0.73	17.5	19.5
		灌浆期 Filling y = 13.383x - 3.9326	0.75	16.4	15.3
	多元逐步线性回归模型 Yield model based on stepwise multiple linear regression	y=0.14x1+11.23x2-13.22x3+23.12x4-3.57x5-8.31	0.69	16.6	19.6
		y=11.25x2-13.36x3+23.27x4-3.38x5-8.36	0.69	16.7	19.7
		y=12.21x2-14.79x3+19.45x4-7.45	0.68	16.3	18.2

特征参数 Characteristic parameter	RNDRE			RNDVI
特征参数 Characteristic parameter	R²	RRMSE (%)	RE (%)	R²	RRMSE (%)	RE (%)
最大值 Maximum	0.81	8.0	8.4	0.65	12.1	15.1
累积值 Accumulative value	0.80	9.6	9.9	0.72	16.9	15.9
增长速率 Increase rate	0.36	19.8	20.8	0.01	78.1	90.8
下降速率 Decrease rate	0.44	24.3	23.7	0.07	46.0	44.8

[1]	徐久凯, 袁亮, 温延臣, 张水勤, 李燕婷, 李海燕, 赵秉强. 畜禽有机肥氮在冬小麦季对化肥氮的相对替代当量[J]. 中国农业科学, 2023, 56(2): 300-313.
[2]	王洋洋,刘万代,贺利,任德超,段剑钊,胡新,郭天财,王永华,冯伟. 基于多元统计分析的小麦低温冻害评价及水分效应差异研究[J]. 中国农业科学, 2022, 55(7): 1301-1318.
[3]	伊英杰,韩坤,赵斌,刘国利,林佃旭,陈国强,任昊,张吉旺,任佰朝,刘鹏. 长期不同施肥措施冬小麦-夏玉米轮作体系周年氨挥发损失的差异[J]. 中国农业科学, 2022, 55(23): 4600-4613.
[4]	相玉婷, 王晓龙, 胡新中, 任长忠, 郭来春, 李璐. 燕麦品种间脂肪酶活性差异及低脂肪酶优质品种的预测[J]. 中国农业科学, 2022, 55(21): 4104-4117.
[5]	苏媛媛,张德权,古明辉,张春娟,李少博,郑晓春,陈丽. 不同来源ATP表征冷鲜羊肉新鲜度[J]. 中国农业科学, 2022, 55(19): 3841-3853.
[6]	刘丰,蒋佳丽,周琴,蔡剑,王笑,黄梅,仲迎鑫,戴廷波,曹卫星,姜东. 美国软麦籽粒品质变化趋势及对我国弱筋小麦标准达标度分析[J]. 中国农业科学, 2022, 55(19): 3723-3737.
[7]	韩守威,司纪升,余维宝,孔令安,张宾,王法宏,张海林,赵鑫,李华伟,孟鈺. 山东省冬小麦产量差与氮肥利用效率差形成机理解析[J]. 中国农业科学, 2022, 55(16): 3110-3122.
[8]	孟雨,温鹏飞,丁志强,田文仲,张学品,贺利,段剑钊,刘万代,冯伟. 基于热红外图像的小麦品种抗旱性鉴定与评价[J]. 中国农业科学, 2022, 55(13): 2538-2551.
[9]	高志源,许吉利,刘硕,田汇,王朝辉. 大田群体冬小麦氮收获指数变异特征研究[J]. 中国农业科学, 2021, 54(3): 583-595.
[10]	毛安然,赵护兵,杨慧敏,王涛,陈秀文,梁文娟. 不同覆盖时期和覆盖方式对旱地冬小麦经济和环境效应的影响[J]. 中国农业科学, 2021, 54(3): 608-618.
[11]	向晓玲,陈松鹤,杨洪坤,杨永恒,樊高琼. 秸秆覆盖与施磷对丘陵旱地小麦产量和磷素吸收利用效应的影响[J]. 中国农业科学, 2021, 54(24): 5194-5205.
[12]	高兴祥,张悦丽,安传信,李美,李健,房锋,张双应. 山东省冬小麦田杂草群落调查及其变化原因分析[J]. 中国农业科学, 2021, 54(24): 5230-5239.
[13]	宗毓铮,张函青,李萍,张东升,林文,薛建福,高志强,郝兴宇. 大气CO₂与温度升高对北方冬小麦旗叶光合特性、碳氮代谢及产量的影响[J]. 中国农业科学, 2021, 54(23): 4984-4995.
[14]	王金凤,王壮壮,谷丰序,牟海萌,王宇,段剑钊,冯伟,王永华,郭天财. 氮密调控对两个冬小麦品种碳氮代谢及产量的影响[J]. 中国农业科学, 2021, 54(19): 4070-4083.
[15]	陶晡, 齐永志, 屈赟, 曹志艳, 赵绪生, 甄文超. 基于增强回归树的海河平原小麦赤霉病预测模型构建与验证[J]. 中国农业科学, 2021, 54(18): 3860-3870.