Please wait a minute...
Journal of Integrative Agriculture  2017, Vol. 16 Issue (04): 858-866    DOI: 10.1016/S2095-3119(16)61493-4
Physiology·Biochemistry·Cultivation·Tillage Advanced Online Publication | Current Issue | Archive | Adv Search |
Simple nonlinear model for the relationship between maize yield and cumulative water amount
LIU Cheng1, 2, SUN Bao-cheng2, TANG Huai-jun2, WANG Tian-yu3, LI Yu3, ZHANG Deng-feng3, XIE Xiao-qing2, SHI Yun-su3, SONG Yan-chun3, YANG Xiao-hong1, LI Jian-sheng1

1 Maize Research Center, China Agricultural University, Beijing 100193, P.R.China

2 Institute of Grain Crops, Xinjiang Academy of Agricultural Sciences, Urumqi 830091, P.R.China

3 Institute of Crop Sciences, Chinese Academy of Agricultural Sciences, Beijing 100081, P.R.China

 

 

 

 

 

 

Download:  PDF in ScienceDirect  
Export:  BibTeX | EndNote (RIS)      
Abstract  Both the additive and multiplicative models of crop yield and water supply are polynomial equations, and the number of parameters increases linearly when the growing period is specified.  However, interactions among multiple parameters occasionally lead to unreasonable estimations of certain parameters, which were water sensitivity coefficients but with negative value.  Additionally, evapotranspiration must be measured as a model input.  To facilitate the application of these models and overcome the aforementioned shortcomings, a simple model with only three parameters was derived in this paper based on certain general quantitative relations of crop yield (Y) and water supply (W).  The new model, Y/YmWk/(Wk+whk), fits an S or a saturated curve of crop yield with the cumulative amount of water.  Three parameters are related to biological factors: the yield potential (Ym), the water requirement to achieve half of the yield potential (half-yield water requirement, wh), and the water sensitivity coefficient (k).  The model was validated with data from 24 maize lines obtained in the present study and 17 maize hybrids published by other authors.  The results showed that the model was well fit to the data, and the normal root of the mean square error (NRMSE) values were 2.8 to 17.8% (average 7.2%) for the 24 maize lines and 2.7 to 12.7% (average 7.4%) for the 17 maize varieties.  According to the present model, the maize water-sensitive stages in descending order were pollen shedding and silking, tasselling, jointing, initial grain ?lling, germination, middle grain ?lling, late grain ?lling, and end of grain ?lling.  This sequence was consistent with actual observations in the maize field.  The present model may be easily used to analyse the water use efficiency and drought tolerance of maize at specific stages.
Keywords:  yield      water,      model      maize      water sensitivity      drought tolerance  
Received: 03 June 2016   Accepted:
Fund: 

This work was supported by grants provided by the National Sci-Tech Key Program of Development of Transgenic Animals and Plants, Ministry of Science and Technology, China (2014ZX08003-004).

Corresponding Authors:  LI Jian-sheng, Tel: +86-10-62732422, E-mail: lijiansheng@cau.edu.cn; WANG Tian-yu, Tel: +86-10-62186632, E-mail: wangtianyu@caas.cn; LI Yu, Tel: +86-10-62186632, E-mail: liyu03@caas.cn   
About author:  LIU Cheng, Tel: +86-991-4507086, E-mail: liuchengxj@126.com

Cite this article: 

LIU Cheng SUN Bao-cheng, TANG Huai-jun, WANG Tian-yu LI Yu, ZHANG Deng-feng, XIE Xiao-qing, SHI Yun-su, SONG Yan-chun, YANG Xiao-hong, LI Jian-sheng . 2017. Simple nonlinear model for the relationship between maize yield and cumulative water amount. Journal of Integrative Agriculture, 16(04): 858-866.

Barrett J W. 1980. Crop production functions and the allocation and use of irrigation water. Agricultural Water Management, 3, 53–66.
Blank H. 1975. Optimal irrigation decisions with limited water. Ph D thesis. Colorado State University, Collins, CO.
Briggs L J. 1914. Relative water requirements of plants. Journal of Agricultural Research, 3, 1–63.
Chen Y. 1998. Study on crop water model considering the hysteresis effect of water shortage. Journal of Hydraulic Engineering, 4, 70–74. (in Chinese)
Claassen M M, Shaw R H. 1970. Water deficit effects on corn. I. Grain components. Agronomy Journal, 62, 652–655.
Cong Z, Zhou Z W, Lei Z D. 2002. New definition and solution of water sensitivity index of Jensen model. Advances in Water Science, 13, 730–735. (in Chinese)
Fan X W. 2011. Study on drought resistance and harvest index of different maize genotypes under different water gradient. Modern Agricultural Science and Technology, 21, 57–58.
Guo Z L. 1994. Optimization model of nonlinear water saving and high yield. Advance in Water Science, 5, 58–63. (in Chinese)
Hanks R J. 1975. Model for predicting plant yield as influenced by water use. Agronomy Journal, 66, 660–655.
Jamieson P D, Porter J R, Wilson D R. 1991. A test of the computer simulation model ARC-WHEAT1 on wheat crops grown in New Zealand. Field Crops Research, 27, 337–350.
Jensen M E. 1973. Consumptive Use of Water and Irrigation Water Requirements. American Society of Civil Engineers, New York.
Jiao X Y, Lei Z D, Peng S Z. 2005. Robust regression method for the establishment of crop water production function. In: Proceedings of the 2005 Annual Conference of the Chinese Academy of Agricultural Engineering. China. pp. 97–100. (in Chinese)
Jiao X Y, Lei Z D, Yang S X. 2002. Development of water science using BP neural network to describe crop water model. Journal of Hebei Engineering and Technical College, 1, 2–5. (in Chinese)
Jiao X Y, Peng S Z. 2004. The reason and solution of negative value of sensitivity index of Jensen model. Journal of Shenyang Agricultural University, 35, 439–442. (in Chinese)
Li H C, Shen R K. 1997. A preliminary study on the Feddes model of crop water dynamic yield model. Irrigation and Drainage, 16, 1–5. (in Chinese)
Li J. 1997. Advances in the development and application of crop growth simulation models. Journal of Northwest Agricultural University, 25, 102–107. (in Chinese)
Li Y H. 1999. Theory and Technology of Water Saving Irrigation. Wuhan Water Conservancy and Electric Power University Press, China. pp. 84–851. (in Chinese)
Liu T M, Xie G S. 2010. Agricultural System Analysis and Simulation. Science Press, China. (in Chinese)
Mehdi M, Sepaskhah A R, Zand-Parsa S. 2014. Estimation of yield and dry matter of winter wheat using logistic model under different irrigation water regimes and nitrogen application rates. Archives of Agronomy and Soil Science, 60, 1661–1676.
Minhas B S, Parikh K S, Srinivasan T N. 1974. Towards the structure of a production function for wheat yields with dated in puts of irrigation water. Water Resources Research, 10, 383–393.
Morgan T H, Biere A W, Kanemasu E T. 1980. A dynamic model of corn yield response to water. Water Resources Research, 16, 59–64.
Paredes J P, de Melo-Abreu J P, Alves I, Pereira L S. 2014. Assessing the performance of the FAO AquaCrop model to estimate maize yields and water use under full and deficit irrigation with focus on model parameterization. Agricultural Water Management, 44, 81–97.
Peng S Z, Bian L M, Zhu C L. 2000. Research and development of crop water production function. Development of Water Conservancy and Hydropower Science and Technology, 20, 17–20. (in Chinese)
Rajput G S, Singh J. 1986. Water production functions for wheat under different environmental conditions. Agricultural Water Management, 11, 319–332.
Rao N H, Sarma P B S, Chander S. 1988. A simple dated production function for use in irrigated agriculture. Agricultural Water Management, 13, 25–32.
Robins J S, Domingo C E. 1953. Some effect of severe soil moisture deficits at specific growth stages in corn. Agronomy Journal, 45, 618–621.
Shabani A, Sepaskhah A R, Kamgar-Haghighi A A. 2015. A model to predict the dry matter and yield of rapeseed under salinity and deficit irrigation. Archives of Agronomy and Soil Science, 61, 525–542.
Shang S H, Mao X M, Lei Z D. 2009. Dynamic Simulation Model of Soil Moisture and Its Application. Science Press, China. (in Chinese)
Shen X Z, Cui Y L, Shen H Z. 2001a. Neural network method for crop water shortage sensitivity analysis. China Rural Water Conservancy and Hydropower, 5, 12–15. (in Chinese)
Shen X Z, Zhu L Z, Cui Y L, Shen H Z. 2001b. Modified Morgan model for dynamic production functions of crop water and fertilizer. Irrigation and Drainage, 20, 17–20. (in Chinese)
Singh P N, Joshi B P, Singh G. 1987. Water use and yield response of wheat to irrigation and nitrogen on an alluvial soil in North India. Agricultural Water Management, 12, 323–329.
Stewart J I, Hagan R M. 1969. Functions to predict effects of crop, water deficits. Journal of Irrigation and Drainage Division, 95, 91–104.
Stewart J I, Hagan R M, Pruitt W O. 1976. Production Functions and Predicted Irrigation Programmers for Principal Crops as Required for Water Resources Planning and Increased Water Use Efficiency. Final Report U.S. Department of Interior, Washington, D.C. p. 80.
Taylor H M, Jordan W R, Sinclair T R. 1983. Limitations to Efficient Water Use in Crop Production. American Society of Agronomy, Crop Science Society of America, Soil Science Society of America, Madison, Wl. pp. 393–411.
Wang H Z, Zhang L, Dawes W R, Liu C. 2001. Improving water use efficiency of irrigated crops in the North China Plain — measurements and modeling. Agricultural Water Management, 48, 151–167. (in Chinese)
Wang Z. 1988. Irrigation and Drainage Engineering. China Agriculture Press, China. pp. 41–43. (in Chinese)
Wei Y L. 2004. Modeling of water production functions of winter wheat. MSc thesis, Tsinghua University, China. (in Chinese)
Wei Z M, Chen Y X, Shi H B. 2002. Preliminary study on crop water model of spring wheat with BP neural network. Irrigation and Drainage, 21, 12–16. (in Chinese)
Westgate M E. 1994. Seed formation in maize during drought. In: Boote K J, ed., Physiology and Determination of Crop Yield. American Society of Agronomy, Crop Science Society of America, Soil Science Society of America, Madison, WI. pp. 361–364.
Willmott C J, Rowe C M, MIntz Y. 1985. Climatology of terrestrial seasonal water cycle. International Journal of Climatology, 5, 589–606.
de Wit C T. 1958. Transpiration and Crop Yields. Institute of Biological and Chemical Researchon on Field Crops and Herbage, Wageningen, The Netherlands. p. 64.
Xia H, Yang L H. 2003, Research progress on crop water production function. Journal of Hebei Engineering and Technical College, 2, 5–8. (in Chinese)
Zhang H J. 2009. Water yield model and its application in several field crops. Chinese Journal of Ecological Agriculture, 17, 997–1001. (in Chinese)
[1] Lichao Zhai, Shijia Song, Lihua Zhang, Jinan Huang, Lihua Lv, Zhiqiang Dong, Yongzeng Cui, Mengjing Zheng, Wanbin Hou, Jingting Zhang, Yanrong Yao, Yanhong Cui, Xiuling Jia. Subsoiling before winter wheat alleviates the kernel position effect of densely grown summer maize by delaying post-silking root–shoot senescence[J]. >Journal of Integrative Agriculture, 2025, 24(9): 3384-3402.
[2] Ling Ai, Ju Qiu, Jiuguang Wang, Mengya Qian, Tingting Liu, Wan Cao, Fangyu Xing, Hameed Gul, Yingyi Zhang, Xiangling Gong, Jing Li, Hong Duan, Qianlin Xiao, Zhizhai Liu. A naturally occurring 31 bp deletion in TEOSINTE BRANCHED1 causes branched ears in maize[J]. >Journal of Integrative Agriculture, 2025, 24(9): 3322-3333.
[3] Dili Lai, Md. Nurul Huda, Yawen Xiao, Tanzim Jahan, Wei Li, Yuqi He, Kaixuan Zhang, Jianping Cheng, Jingjun Ruan, Meiliang Zhou. Evolutionary and expression analysis of sugar transporters from Tartary buckwheat revealed the potential function of FtERD23 in drought stress[J]. >Journal of Integrative Agriculture, 2025, 24(9): 3334-3350.
[4] Yuheng Wang, Furong Kang, Bo Yu, Quan Long, Huaye Xiong, Jiawei Xie, Dong Li, Xiaojun Shi, Prakash Lakshmanan, Yueqiang Zhang, Fusuo Zhang. Magnesium supply is vital for improving fruit yield, fruit quality and magnesium balance in citrus orchards with increasingly acidic soil[J]. >Journal of Integrative Agriculture, 2025, 24(9): 3641-3655.
[5] Zhongru Ye, Yongjian Liu, Fuyu Ye, Hang Li, Ju Luo, Jianyang Guo, Zelin Feng, Chen Hong, Lingyi Li, Shuhua Liu, Baojun Yang, Wanxue Liu, Qing Yao. Automatic diagnosis of agromyzid leafminer damage levels using leaf images captured by AR glasses[J]. >Journal of Integrative Agriculture, 2025, 24(9): 3559-3573.
[6] Jinpeng Li, Siqi Wang, Zhongwei Li, Kaiyi Xing, Xuefeng Tao, Zhimin Wang, Yinghua Zhang, Chunsheng Yao, Jincai Li. Effects of micro-sprinkler irrigation and topsoil compaction on winter wheat grain yield and water use efficiency in the Huaibei Plain, China[J]. >Journal of Integrative Agriculture, 2025, 24(8): 2974-2988.
[7] Baohua Liu, Ganqiong Li, Yongen Zhang, Ling Zhang, Dianjun Lu, Peng Yan, Shanchao Yue, Gerrit Hoogenboom, Qingfeng Meng, Xinping Chen. Optimizing management strategies to enhance wheat productivity in the North China Plain under climate change[J]. >Journal of Integrative Agriculture, 2025, 24(8): 2989-3003.
[8] Ziqiang Che, Shuting Bie, Rongrong Wang, Yilin Ma, Yaoyuan Zhang, Fangfang He, Guiying Jiang. Mild deficit irrigation delays flag leaf senescence and increases yield in drip-irrigated spring wheat by regulating endogenous hormones[J]. >Journal of Integrative Agriculture, 2025, 24(8): 2954-2973.
[9] Qing Li, Zhuangzhuang Sun, Zihan Jing, Xiao Wang, Chuan Zhong, Wenliang Wan, Maguje Masa Malko, Linfeng Xu, Zhaofeng Li, Qin Zhou, Jian Cai, Yingxin Zhong, Mei Huang, Dong Jiang. Time-course transcriptomic information reveals the mechanisms of improved drought tolerance by drought priming in wheat[J]. >Journal of Integrative Agriculture, 2025, 24(8): 2902-2919.
[10] Xue Wang, Hefeng Chen, Xianfeng Zhang, Zhengshuang Wu, Shuai Zhang, Lei Shuai, Lulu Wang, Weijie Li, Jinliang Wang, Wenxing Liu, Xijun Wang, Zhiyuan Wen, Jinying Ge, Yuntao Guan, Xijun He, Weiye Chen, Zhigao Bu. Establishment of goat infection model of the peste des petits ruminants virus isolated in China for vaccine efficacy evaluation[J]. >Journal of Integrative Agriculture, 2025, 24(8): 3199-3211.
[11] Xuehao Zhang, Qiuling Zheng, Yongjiang Hao, Yingying Zhang, Weijie Gu, Zhihao Deng, Penghui Zhou, Yulin Fang, Keqin Chen, Kekun Zhang. Physiology and transcriptome profiling reveal the drought tolerance of five grape varieties under high temperatures[J]. >Journal of Integrative Agriculture, 2025, 24(8): 3055-3072.
[12] Dan Lü, Jianxin Li, Xuehai Zhang, Ran Zheng, Aoni Zhang, Jingyun Luo, Bo Tong, Hongbing Luo, Jianbing Yan, Min Deng. Genetic analysis of maize crude fat content by multi-locus genome-wide association study[J]. >Journal of Integrative Agriculture, 2025, 24(7): 2475-2491.
[13] Zhongwei Tian, Yanyu Yin, Bowen Li, Kaitai Zhong, Xiaoxue Liu, Dong Jiang, Weixing Cao, Tingbo Dai. Optimizing planting density and nitrogen application to mitigate yield loss and improve grain quality of late-sown wheat under rice–wheat rotation[J]. >Journal of Integrative Agriculture, 2025, 24(7): 2558-2574.
[14] Chunxiang Li, Yongfeng Song, Yong Zhu, Mengna Cao, Xiao Han, Jinsheng Fan, Zhichao Lü, Yan Xu, Yu Zhou, Xing Zeng, Lin Zhang, Ling Dong, Dequan Sun, Zhenhua Wang, Hong Di. GWAS analysis reveals candidate genes associated with density tolerance (ear leaf structure) in maize (Zea mays L.)[J]. >Journal of Integrative Agriculture, 2025, 24(6): 2046-2062.
[15] Martín Flores-Saavedra, Pietro Gramazio, Santiago Vilanova, Diana M. Mircea, Mario X. Ruiz-González, Óscar Vicente, Jaime Prohens, Mariola Plazas. Introgressed eggplant lines with the wild Solanum incanum evaluated under drought stress conditions[J]. >Journal of Integrative Agriculture, 2025, 24(6): 2203-2216.
No Suggested Reading articles found!