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作物水分生产函数研究进展

李中恺 刘鹄 赵文智

李中恺, 刘鹄, 赵文智. 作物水分生产函数研究进展[J]. 中国生态农业学报(中英文), 2018, 26(12): 1781-1794. doi: 10.13930/j.cnki.cjea.180369
引用本文: 李中恺, 刘鹄, 赵文智. 作物水分生产函数研究进展[J]. 中国生态农业学报(中英文), 2018, 26(12): 1781-1794. doi: 10.13930/j.cnki.cjea.180369
LI Zhongkai, LIU Hu, ZHAO Wenzhi. Revisiting crop water production functions in terms of cross-regional applications[J]. Chinese Journal of Eco-Agriculture, 2018, 26(12): 1781-1794. doi: 10.13930/j.cnki.cjea.180369
Citation: LI Zhongkai, LIU Hu, ZHAO Wenzhi. Revisiting crop water production functions in terms of cross-regional applications[J]. Chinese Journal of Eco-Agriculture, 2018, 26(12): 1781-1794. doi: 10.13930/j.cnki.cjea.180369

作物水分生产函数研究进展

doi: 10.13930/j.cnki.cjea.180369
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

  • 中图分类号: S5-3

Revisiting crop water production functions in terms of cross-regional applications

Funds: 

the National Natural Science Foundation of China 91425302

More Information
  • 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。
  • 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.

    Figure  1.  Schematic diagram of the crop water production function (CWPF)

    图  2  小麦、玉米、棉花、水稻的产量-蒸散发(Y-ET)关系(CWPF)数据集

    Figure  2.  Date sets of yield (Y) and evapotranspiration (ET) relationship (CWPF) of wheat, maize, cotton and rice

    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.

    Figure  3.  Normalization of yield-evapotranspiration (Y-ET) relationships (CWPF) for wheat and maize (Stewart's model S-1)

    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”.

    Figure  4.  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)]

    表  1  典型CWPF统计模型(1958—2014年)

    Table  1.   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)

    Table  2.   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 Sanlõurfa 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 Sanlıurfa 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
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