刘鹄1,,,
赵文智1
1.中国科学院西北生态环境资源研究院/中国生态系统研究网络临泽内陆河流域研究站/中国科学院内陆河流域生态水文重点实验室 兰州 730000
2.中国科学院大学资源与环境学院 北京 100049
基金项目: 国家自然科学基金项目91425302
详细信息
作者简介:李中恺, 主要研究方向为干旱区生态水文。E-mail:lizhongkai16@mails.ucas.ac.cn
通讯作者:刘鹄, 主要研究方向为生态水文模型。E-mail:lhayz@lzb.ac.cn
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出版历程
收稿日期:2018-04-11
录用日期:2018-06-20
刊出日期:2018-12-01
Revisiting crop water production functions in terms of cross-regional applications
LI Zhongkai1, 2,,LIU Hu1,,,
ZHAO Wenzhi1
1. Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences/Linze Inland River Basin Research Station, Chinese Ecosystem Research Network/Key Laboratory of Ecohydrology of Inland River Basin, Chinese Academy of Sciences, Lanzhou 730000, China
2. College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100049, China
Funds: the National Natural Science Foundation of China91425302
More Information
Corresponding author:LIU Hu, E-mail: lhayz@lzb.ac.cn
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摘要
摘要:作物水分生产函数（crop water production functions，CWPF）一般指作物产量（crop yield，Y）与蒸散发（evapotranspiration，ET）之间的函数关系，是作物模型中联系水分和生产力的关键。本文系统地梳理了近半个世纪以来CWPF的相关研究，发现CWPF受多种因素影响，不同地区获得的田间试验结果往往差异较大；常用的CWPF模型多是基于统计信息，缺少坚实的物理基础和可靠的理论支撑，在跨地区、跨物种应用时存在一定缺点。同时基于碳同化过程的机制模型和更为复杂的作物模型也因为参数过多而不易在实际中应用。在以往研究的基础上，从公开发表的41篇文献中筛选出592组田间试验数据，发现小麦产量与ET基本呈线性关系，但数据分布相对离散，而玉米、棉花、水稻因数据量较少其产量与ET关系不明显。利用生长季降水量和累计蒸发皿蒸发数据对不同地区获得的小麦水分生产函数进行了修正，发现改进后的小麦水分生产函数表现出较好的跨地区应用潜力（r2从0.36提高到0.75），并提出了进一步的CWPF修正思路。指出通过改进函数关系虽然能提高统计模型的可移植性，但发展机制模型仍是未来CWPF研究的根本出路。
关键词:水分生产函数/
作物蒸散发/
作物产量/
荟萃分析/
模型修正
Abstract:As populations grow and demand for food increases in the world with limited water supply, the production of more food with less water becomes a significant global challenge facing us in the decades to come. Crop water production function (CWPF), i.e., the functional relationship between crop yield (Y) and evapotranspiration (ET), is the link between water use and crop productivity in crop models. However, most of studies on CWPF have been based on local observations and therefore results derived have not been accurate and not applicable to other regions. Most recent advances in CWPF researches were reviewed in this work, including related theories, models and field experiments. It showed that CWPF was affected by many factors, including climatic conditions, irrigation strategies, soil types, nutrient levels, crop species and even crop cultivars. However few theories had so far provided a comprehensive framework connecting these factors to CWPF. Because of the lack of solid physical foundation and reliable theoretical support, observation-based models were limited in providing beyond local prediction for a given type of crop. Also the mechanistic models and more complex crop models that were largely based on carbon assimilation processes were difficult to apply in practice because of far too many parameters. Through summary analysis of published work, a total of 592 sets of field data were screened from 41 literatures. We found that although the data distribution was relatively sparse, linear correlations (r2=0.34) existed between yield and evapotranspiration for wheat. However, similar correlations were not detected for corn, cotton and rice, probably due to the small amount of available experimental data. Using meta-analysis, a new method of modification of CWPF was proposed and tested in order to improve the performance of CWPF for cross-regional applications. It was found that the statistical method used was good to get better and more stable CWPF for given species across different cultivation environments (r2 increased from 0.36 to 0.75), when seasonal precipitation (Prec) and accumulated pan evaporation (EPan) were incorporated. Our results showed that the functional relationship between Y and ET×Prec/EPan was more universal, compared with that between Y and ET in cross-regional application. Although more reliable and even flexible CWPF models were derived by the inclusion of other calculation algorithms in this framework, we argued that mechanistic models were needed in future extrapolations of measured relationships beyond simply assuming that they were statistically significant. Future work needed to focus on:1) strengthening theoretical interpretations of the revised results; 2) testing the potentials for modification to accommodate other crops; 3) considering the growth stages in CWPF to improve its potential for cross-regional applications.
Key words:Crop water production function/
Crop evapotranspiration/
Crop yield/
Meta-analysis/
Model modification
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图1作物水分生产函数(CWPF)发生机制示意图
β表示蒸腾占蒸散发的比例, TE与HI分别为蒸腾效率及收获指数。β indicates the ratio of transpiration to evapotranspiration, TE and HI are transpiration efficiency and harvest index, respectively.
Figure1.Schematic diagram of the crop water production function (CWPF)
下载: 全尺寸图片幻灯片
图2小麦、玉米、棉花、水稻的产量-蒸散发(Y-ET)关系(CWPF)数据集
Figure2.Date sets of yield (Y) and evapotranspiration (ET) relationship (CWPF) of wheat, maize, cotton and rice
下载: 全尺寸图片幻灯片
图3小麦、玉米产量-蒸散发(Y-ET)关系(CWPF)标准化(Stewart S-1模型)
“1-产量/最高产量”与“1-蒸散发/最大蒸散发”代表各试验的相对减产与相对蒸散发亏缺。1-Y/Ymax and 1-ET/ETmax represent relative yield reduction and relative evapotranspiration deficit of each experiment, in which Y and Ymax are yield and max yield, ET and ETmax are evapotranspiration and max evapotranspiration.
Figure3.Normalization of yield-evapotranspiration (Y-ET) relationships (CWPF) for wheat and maize (Stewart's model S-1)
下载: 全尺寸图片幻灯片
图4小麦水分生产函数的修正效果[a.产量与蒸散发的关系(r2=0.36); b:产量与降水量(Prec)和蒸发皿蒸发(EPan)修正的蒸散发(ET×Prec/EPan)的关系(r2=0.75)]
下方图例依次为国家:海拔-小麦播种季-土壤类型-灌溉方式-地下水位-气候及文献。The legends are shown in the order of “country: elevation-wheat planting season-soil type-irrigation method-groundwater table-climate-journal article”.
Figure4.Relationships between yield and evapotranspiration (ET) of wheat [a: relationship between yield and ET; b: relationship between yield and precipitation (Prec) and pan evaporation (EPan)-modified ET (ET×Prec/EPan)]
下载: 全尺寸图片幻灯片表1典型CWPF统计模型(1958—2014年)
Table1.Typical statistical models of CWPF (1958-2014)
| 模型分类 Model classification | 表达式 Function | 作者(年份) Author (year) |
| 全生育期线性模型 Line models for whole growing period | $\left( {1 - \frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}}} \right) = {K_{\text{y}}}\left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)$ | Stewart et al.[48] (1977) (S-1) |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}};\;\;\frac{Y}{{{Y_{\text{m}}}}} = \frac{T}{{{T_{\text{m}}}}}$ | Hanks[54] (1974) (H-1) | |
| $\left( {\frac{{{Y_{\text{m}}} - {Y_{\text{a}}}}}{{{Y_{\text{m}}}}}} \right) = {K_{\text{y}}}\left( {\frac{{{\text{E}}{{\text{T}}_{\text{p}}} - {\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{p}}}}}} \right)$ | Doorenbos et al.[51] (1980) | |
| $Y = {\text{m}}\frac{T}{{{E_0}}}$ | De Wit[14] (1958) | |
| $\left( {1 - \frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}}} \right) = {K_{\text{y}}}\left( {1 - \frac{{{T_{\text{a}}}}}{{{T_{\text{m}}}}}} \right)$ | Ngigi et al.[53] (2006) | |
| 全生育期非线性模型 Non-line models for whole growing period | ${Y_{\text{a}}} = {\text{a}} + {\text{b}}\left[ {1 - {{\left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)}^2}} \right]$ | Hiler et al.[57] (1971) |
| $Y = {Y_{{\rm{max}}}}\frac{{{\rm{ET}}_{{\rm{seas}}}^{\rm{a}}}}{{{\rm{ET}}_{{\rm{seas}}, 50\% }^{\rm{a}} + {\rm{ET}}_{{\rm{seas}}}^{\rm{a}}}} $ | Vico et al.[58] (2011) | |
| $1 - \frac{Y}{{{Y_{\text{m}}}}} = \frac{{ - {c_2}{\text{ET}}_{\text{m}}^2}}{{{Y_{\text{m}}}}}{\left( {1 - \frac{{{\text{ET}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)^2}$ | Liu et al.[56] (2002) | |
| 生长阶段连加模型 Addition models for growth stages | $1 - \frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = \mathop \sum \limits_{i = 1}^n {K_{{\text{y}}i}}{\left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)_i}$ | Stewart et al.[48] (1977) (S-2) |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = \mathop \sum \limits_{i = 1}^n {A_i}{\left( {\frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)_i}$ | Kang et al.[59] (1996) | |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = \mathop \sum \limits_{i = 1}^n {B_i}\left[ {1 - {{\left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{{\text{m}}i}}}}} \right)}^2}} \right]$ | Kang et al.[59] (1996) | |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = {a_0} + \mathop \sum \limits_{i = 1}^n {b_i}\left[ {1 - \left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)_i^2} \right]$ | Rajput et al.[52] (1986) | |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = 1 - \frac{A}{{{Y_{\text{m}}}}}\mathop \sum \limits_{i = 1}^n {b_i}\left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)_i^2$ | Howell et al.[60] (1975) | |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = 1 - \mathop \sum \limits_{i = 1}^n {K_i}{\left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)_i}$ | Rao et al.[50] (1988) (R-1) | |
| ${Y_{\text{a}}} = {Y_{\text{m}}} - \frac{{{Y_{\text{m}}}({\beta _{\text{v}}}{T_{{\text{d}}, {\text{v}}}} + {\beta _{\text{f}}}{T_{{\text{d}}, {\text{f}}}} + {\beta _{\text{m}}}{T_{{\text{d}}, {\text{m}}}})}}{{{T_{\text{c}}}}}$ | Paredes et al.[61] (2014) | |
| 生长阶段连乘模型 Multiplication models for growth stages | $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = \mathop \prod \limits_{i = 1}^n {\left( {\frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)_i}^{\lambda i}$ | Jensen [62] (1968) |
| $\frac{Y}{{{Y_{\text{m}}}}} = \mathop \prod \limits_{k = 1}^n \left( {\frac{{{T_{\text{a}}}}}{{{T_{\text{m}}}}}} \right)_k^{{b_k}}$ | Hanks et al.[54] (1974) (H-2) | |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = \mathop \prod \limits_{i = 1}^n {\left[ {1 - \left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)_i^2} \right]^{\delta i}}$ | Kang et al.[59] (1996) | |
| $\frac{{{Y_{\text{a}}}}}{{{Y_{\text{m}}}}} = \mathop \prod \limits_{i = 1}^n \left[ {1 - {K_i}{{\left( {1 - \frac{{{\text{E}}{{\text{T}}_{\text{a}}}}}{{{\text{E}}{{\text{T}}_{\text{m}}}}}} \right)}_i}} \right]$ | Rao et al.[50] (1988) (R-2) | |
| ${Y_{\text{c}}} = {\text{y}}{{\text{m}}_{\text{c}}}\prod\nolimits_{g = 1}^4 {\left\{ {1 - {\text{k}}{{\text{y}}_{{\text{c}}, g}}\left[ {1 - \left( {\frac{{\mathop \sum \nolimits_g {\text{ET}}{{\text{a}}_{{\text{c}}, g}}}}{{\mathop \sum \nolimits_g {\text{ET}}{{\text{m}}_{{\text{c}}, g}}}}} \right)} \right]} \right\}} $ | De Jager [63] (1994) |
下载: 导出CSV表2产量-蒸散发(Y-ET)数据集荟萃分析源文献(1979—2013年)
Table2.Literatures of yield-evapotranspiration (Y-ET) data set for meta-analysis (1979-2013)
| 国别 Country | 地点 Location | 年份 Year | 数据源文献 Reference of date |
| 小麦Wheat (Triticum aestivum L.) | |||
| 美国USA | Yellow Jacket | 1993—1994 | [74] |
| 印度India | Memari | 1989—1991 | [76] |
| 阿根廷Argentina | Parana | 1998—1999 | [78] |
| 摩洛哥Morocco | Meknes | 1993—1995 | [80] |
| 中国China | Dingxi | 1997 | [82] |
| 中国China | Xifeng | 1988—1991 | [77] |
| 印度India | Pantnagar | 1983—1985 | [85] |
| 叙利亚Syria | Tel Hadya | 1992—1996 | [87] |
| 印度India | Karnal | 1986—1988 | [89] |
| 澳大利亚Australia | Merredin | 1987 | [91] |
| 中国China | Gaochen etc. | 1982—1985 | [93] |
| 中国China | Quzhou | 1988—1989 | [95] |
| 澳大利亚Australia | Tasmania | 1982—2011 | [96] |
| 罗马尼亚Romania | Fundulea | 2008—2009 | [94] |
| 中国China | Luancheng | 2006—2009 | [99] |
| 中国China | Changwu | 2006—2007 | [101] |
| 中国China | Changwu | 2005—2008 | [102] |
| 中国China | Changwu | 2010—2011 | [103] |
| 中国China | Shiwang | 2007—2013 | [104] |
| 印度India | Hol Pune | 2004—2006 | [105] |
| 中国China | Luancheng etc. | 2006—2009 | [106] |
| 中国China | Changwu | 1995—1998 | [41] |
| 棉花Cotton (Gossypium hirsutum L.) | |||
| 美国USA | California | 1981—1983 | [28] |
| 美国USA | Maricopa | 1993—1994 | [108] |
| 澳大利亚Australia | NewSouthWales | 1996—1999 | [110] |
| 土耳其Turkey | Sanl?urfa | 1999 | [112] |
| 叙利亚Syria | Damascus | 2007—2008 | [114] |
| 玉米Maize (Zea mays L.) | |||
| 中国China | Xiaobakou | 1997—1998 | [75] |
| 中国China | Xifeng | 1998—1991 | [77] |
| 印度India | Pantnagar | 1993—1995 | [79] |
| 土耳其Turkey | Harran Plain | 1998—1999 | [81] |
| 美国USA | Coastal Plain | 1993 | [83] |
| 美国USA | Dakota | 1989—1991 | [84] |
| 美国USA | Texas | 1994—1995 | [86] |
| 美国USA | Texas | 1992 | [88] |
| 土耳其Turkey | Sanl?urfa | 2000 | [90] |
| 中国China | Changwu | 2010—2011 | [92] |
| 罗马尼亚Romania | Fundulea | 2008—2009 | [94] |
| 中国China | Changwu | 1987 | [56] |
| 肯尼亚Kenya | Kampi | 2007—2010 | [97] |
| 美国USA | Nebraska | 2005—2006 | [98] |
| 美国USA | Nebraska | 2005—2006 | [100] |
| 水稻Rice (Oryza sativa L.) | |||
| 澳大利亚Australia | Echuca | 1997—1998 | [107] |
| 印度India | Pantnagar | 1983—1984 | [109] |
| 美国USA | BelleGlade | 1979—1980 | [111] |
| 印度India | Luhdiana | 1996—1997 | [113] |
| 中国China | Zhejiang | 2004 | [115] |
下载: 导出CSV参考文献
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