作物水分生產(chǎn)函數(shù)研究進(jìn)展*

李中愷, 劉 鵠, 趙文智

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作物水分生產(chǎn)函數(shù)研究進(jìn)展*

李中愷1,2, 劉 鵠1**, 趙文智1

(1. 中國(guó)科學(xué)院西北生態(tài)環(huán)境資源研究院/中國(guó)生態(tài)系統(tǒng)研究網(wǎng)絡(luò)臨澤內(nèi)陸河流域研究站/中國(guó)科學(xué)院內(nèi)陸河流域生態(tài)水文重點(diǎn)實(shí)驗(yàn)室 蘭州 730000; 2. 中國(guó)科學(xué)院大學(xué)資源與環(huán)境學(xué)院 北京 100049)

作物水分生產(chǎn)函數(shù)(crop water production functions, CWPF)一般指作物產(chǎn)量(crop yield,)與蒸散發(fā)(evapotranspiration, ET)之間的函數(shù)關(guān)系, 是作物模型中聯(lián)系水分和生產(chǎn)力的關(guān)鍵。本文系統(tǒng)地梳理了近半個(gè)世紀(jì)以來(lái)CWPF的相關(guān)研究, 發(fā)現(xiàn)CWPF受多種因素影響, 不同地區(qū)獲得的田間試驗(yàn)結(jié)果往往差異較大; 常用的CWPF模型多是基于統(tǒng)計(jì)信息, 缺少堅(jiān)實(shí)的物理基礎(chǔ)和可靠的理論支撐, 在跨地區(qū)、跨物種應(yīng)用時(shí)存在一定缺點(diǎn)。同時(shí)基于碳同化過(guò)程的機(jī)制模型和更為復(fù)雜的作物模型也因?yàn)閰?shù)過(guò)多而不易在實(shí)際中應(yīng)用。在以往研究的基礎(chǔ)上, 從公開(kāi)發(fā)表的41篇文獻(xiàn)中篩選出592組田間試驗(yàn)數(shù)據(jù), 發(fā)現(xiàn)小麥產(chǎn)量與ET基本呈線性關(guān)系, 但數(shù)據(jù)分布相對(duì)離散, 而玉米、棉花、水稻因數(shù)據(jù)量較少其產(chǎn)量與ET關(guān)系不明顯。利用生長(zhǎng)季降水量和累計(jì)蒸發(fā)皿蒸發(fā)數(shù)據(jù)對(duì)不同地區(qū)獲得的小麥水分生產(chǎn)函數(shù)進(jìn)行了修正, 發(fā)現(xiàn)改進(jìn)后的小麥水分生產(chǎn)函數(shù)表現(xiàn)出較好的跨地區(qū)應(yīng)用潛力(2從0.36提高到0.75), 并提出了進(jìn)一步的CWPF修正思路。指出通過(guò)改進(jìn)函數(shù)關(guān)系雖然能提高統(tǒng)計(jì)模型的可移植性, 但發(fā)展機(jī)制模型仍是未來(lái)CWPF研究的根本出路。

水分生產(chǎn)函數(shù); 作物蒸散發(fā); 作物產(chǎn)量; 薈萃分析; 模型修正

作物水分生產(chǎn)函數(shù)(crop water production functions, CWPF)指作物產(chǎn)量(crop yield,)與耗水量之間的函數(shù)關(guān)系[1], 是作物模型中聯(lián)系生產(chǎn)力(crop productivity)與水分因子的關(guān)鍵和紐帶[2]。CWPF中產(chǎn)量一般指單位面積耕地所收獲的有經(jīng)濟(jì)價(jià)值的主要產(chǎn)品總量, 如谷類、豆類作物的子實(shí), 棉花(L.)的籽棉、皮棉等[3]; 而水分因子則可以是灌溉量(irrigation,)、土壤水分儲(chǔ)量(soil water storage,)、蒸騰量(transpiration,)以及蒸散發(fā)量(evapotranspiration, ET)等。受深層滲漏和土壤水分再分配過(guò)程影響, 灌溉量和土壤水分儲(chǔ)量變化并不能精確地反映作物耗水情況, 在某些地區(qū)甚至與真實(shí)作物耗水量相差巨大[4], 因此常用ET做CWPF的水分變量。

在全球人口增長(zhǎng)、水資源和糧食安全面臨挑戰(zhàn)的背景下, 如何用更少的水生產(chǎn)更多的糧食, 成為人類面臨的重大問(wèn)題[5-6]。CWPF是制定農(nóng)業(yè)節(jié)水灌溉策略、分析灌水效益的重要依據(jù), 基于CWPF的灌溉策略可在保證作物產(chǎn)量的前提下避免資源浪費(fèi)[7], 有效提高農(nóng)業(yè)水利用效率(/ET)[8], 如Chemin等[9]與Bastiaanssen[10]利用遙感影像反演的蒸散發(fā)數(shù)據(jù)分析當(dāng)?shù)毓喔刃始白魑锼置{迫情況以制定最優(yōu)灌溉制度; Tasumi等[11]通過(guò)量化蒸散量來(lái)分析種植時(shí)間對(duì)不同作物產(chǎn)量和生長(zhǎng)狀態(tài)的影響等。因此, CWPF一直是農(nóng)業(yè)生產(chǎn)與水資源管理領(lǐng)域的研究熱點(diǎn)[12]。

國(guó)外關(guān)于CWPF的研究可追溯到20世紀(jì)50年代Allison等[13]針對(duì)水稻(L.)開(kāi)展的工作。De Wit[14]從理論上討論了蒸騰過(guò)程與產(chǎn)量的關(guān)系, 之后出現(xiàn)了大量針對(duì)不同作物、不同栽培方式、不同灌溉模式等的田間耗水試驗(yàn)。這些試驗(yàn)以小麥(L.)、玉米(L.)為主, 也涉及水稻、棉花、西紅柿(Mill.)、馬鈴薯(L.)、洋蔥(L.)、甜菜(L.)、胡椒(L.)、苜蓿(L.)、高粱(L.)等其他作物。由于CWPF受到多種因素的影響, 不同地區(qū)的試驗(yàn)結(jié)果往往差異很大, 因此這些研究結(jié)果很難移植到其他地區(qū)。文獻(xiàn)中關(guān)于CWPF的模型大致有3類: 1)基于氣孔擴(kuò)散理論的機(jī)制模型, 2)基于田間試驗(yàn)數(shù)據(jù)的統(tǒng)計(jì)模型, 3)以前兩類模型為基礎(chǔ)發(fā)展起來(lái)的作物模型。3類模型都有其不可避免的缺點(diǎn), 機(jī)制模型或更為復(fù)雜的作物模型由于參數(shù)較多, 不便于實(shí)際應(yīng)用, 而基于觀測(cè)數(shù)據(jù)的統(tǒng)計(jì)模型又很難跨地區(qū)移植。

國(guó)內(nèi)對(duì)CWPF的研究始于20世紀(jì)80年代[15], 先后在不同地區(qū), 針對(duì)不同作物開(kāi)展了大量專項(xiàng)試驗(yàn), 并在經(jīng)典模型的解釋、算法的改進(jìn)、參數(shù)的時(shí)空變化規(guī)律、不同模型在同一地區(qū)的適用性比較等方面取得了大量進(jìn)展[16-19], 這些工作提高了對(duì)作物產(chǎn)量與水分消耗關(guān)系的認(rèn)識(shí), 并為局地產(chǎn)量預(yù)測(cè)與灌溉系統(tǒng)優(yōu)化設(shè)計(jì)起了指導(dǎo)作用[15]。盡管國(guó)內(nèi)外均對(duì)CWPF進(jìn)行了大量研究, 但從現(xiàn)有文獻(xiàn)來(lái)看, 目前仍缺乏簡(jiǎn)單可靠、有堅(jiān)實(shí)物理基礎(chǔ)、可方便移植到不同地區(qū)的CWPF模型。本文從理論研究、數(shù)學(xué)模型和田間試驗(yàn)3個(gè)方面系統(tǒng)闡述了CWPF研究進(jìn)展, 并通過(guò)對(duì)CWPF田間試驗(yàn)數(shù)據(jù)進(jìn)行挖掘和梳理, 在已有的CWPF模型基礎(chǔ)上, 提出基于蒸發(fā)皿蒸發(fā)(evaporation,)和降雨量的CWPF修正方案。

1 作物水分生產(chǎn)函數(shù)理論研究

1.1 理論基礎(chǔ)

作物水分生產(chǎn)函數(shù)(CWPF)本質(zhì)上反映了作物通過(guò)耗水生產(chǎn)干物質(zhì)的能力[1]。作物根系從土壤吸收的水分絕大部分(99%)以葉面蒸騰(transpiration,)的形式消耗[20]。氣孔是葉面蒸騰的主要途徑: 作物生長(zhǎng)過(guò)程中, 葉片打開(kāi)氣孔進(jìn)行CO2同化, 水分也隨之從氣孔擴(kuò)散到大氣。因此, 作物產(chǎn)量的形成基本以蒸騰為代價(jià)[21](圖1)。當(dāng)作物受到水分脅迫時(shí), 氣孔逐漸關(guān)閉, 蒸騰速率與光合速率同時(shí)下降[22], 可見(jiàn)氣孔行為是控制作物生產(chǎn)及水分消耗的核心機(jī)制[21]。同一物種在同一地區(qū)、相同生長(zhǎng)階段的蒸騰效率(TE, 生物量積累與蒸騰量比率[23])從細(xì)胞、葉面到冠層尺度上基本不變[24], 而生物量與產(chǎn)量之間又存在一定的相關(guān)性, 因此田塊水平上蒸騰與產(chǎn)量()之間也存在較為穩(wěn)定的函數(shù)關(guān)系[25](=×TE×HI, 其中HI為收獲指數(shù))?？紤]到土壤蒸發(fā)與作物蒸騰往往同步發(fā)生, 很難利用觀測(cè)手段將其單獨(dú)量化, 因此蒸散發(fā)是反映作物產(chǎn)量與水分關(guān)系的最佳變量[26], 而CWPF通常也被簡(jiǎn)化為作物產(chǎn)量與蒸散發(fā)(ET)關(guān)系(圖1)。

圖1 作物水分生產(chǎn)函數(shù)(CWPF)發(fā)生機(jī)制示意圖

表示蒸騰占蒸散發(fā)的比例, TE與HI分別為蒸騰效率及收獲指數(shù)。indicates the ratio of transpiration to evapotranspiration, TE and HI are transpiration efficiency and harvest index, respectively.

1.2 影響因素

不同地區(qū)田間試驗(yàn)得到的CWPF往往差異較大。以棉花和西紅柿為例, Grimes等[27]、Howell等[28]發(fā)現(xiàn)棉絨產(chǎn)量與蒸散發(fā)之間為二次函數(shù)(quadratic)關(guān)系, 而Hunsaker等[29]在試驗(yàn)中得出棉絨產(chǎn)量與蒸散發(fā)為線性關(guān)系; Zheng等[30]、Ku??u等[31]發(fā)現(xiàn)西紅柿產(chǎn)量與生長(zhǎng)季蒸散發(fā)數(shù)據(jù)可用線性關(guān)系擬合, 而Patanè等[32-33]發(fā)現(xiàn)西紅柿產(chǎn)量與蒸散發(fā)數(shù)據(jù)用二次函數(shù)關(guān)系擬合更優(yōu)。從田間試驗(yàn)得到的大量資料表明, CWPF易受作物種類、氣候、灌溉模式、土壤類型、耕作方式(農(nóng)藝)、施肥管理、遺傳特性及地下水位等多種因素的影響[34-41], 同時(shí)坡度、耕作層深度甚至灌溉水水質(zhì)也會(huì)間接影響CWPF[42-44],其函數(shù)關(guān)系可概括為:

=(ET,,,,,,) (1)

式中:表示氣候條件(climate),表示灌溉水平(irrigation),表示作物品種(variety),表示施肥情況(fertilization),表示土壤類型(soil),代表其他輕微影響CWPF的因子。此外, 作物的自適應(yīng)特性可以抵消小部分環(huán)境變量對(duì)CWPF的影響, 如輕微干旱脅迫能促進(jìn)作物根系生長(zhǎng), 緩解干旱導(dǎo)致的水分虧缺影響[45]。

在眾多影響因素中, 灌溉和施肥等屬于人為可調(diào)控因素, 而氣候條件與土壤類型屬于不可控因素。對(duì)于可控因素, 通過(guò)合理的農(nóng)業(yè)管理措施可以將其控制在理想狀態(tài), 從而使其對(duì)CWPF的影響降到最低, 如可以用同一地區(qū)的最大產(chǎn)量和相應(yīng)的蒸散發(fā)反映一個(gè)地區(qū)的生產(chǎn)力水平[46]。對(duì)于不可控因素, 則需要更多的地區(qū)性經(jīng)驗(yàn)來(lái)獲得當(dāng)?shù)谻WPF, 這造成了很多不便, 因此地區(qū)可移植性一直是CWPF研究的重點(diǎn)內(nèi)容[47]。

2 作物水分生產(chǎn)函數(shù)模型研究進(jìn)展

2.1 基于田間試驗(yàn)(資料)的統(tǒng)計(jì)模型

此類模型多為經(jīng)驗(yàn)或半經(jīng)驗(yàn)?zāi)Ｐ? 通過(guò)對(duì)試驗(yàn)數(shù)據(jù)的回歸分析得到, 描述作物最終產(chǎn)量和生長(zhǎng)季蒸散發(fā)之間的統(tǒng)計(jì)關(guān)系。根據(jù)生長(zhǎng)階段的劃分與否, 可分為全生育期模型和生長(zhǎng)階段模型, 前者可分為線性與非線性模型, 后者可分為連加與連乘模型(表1)。

2.1.1 全生育期線性模型

全生育期CWPF線性模型的數(shù)學(xué)式可表達(dá)為:=+×ET(為參數(shù))。在一定條件下, 多數(shù)作物的產(chǎn)量與其生長(zhǎng)季蒸散發(fā)都可用線性函數(shù)表示。Stewart等[48]對(duì)上式進(jìn)行了改進(jìn), 提出了經(jīng)典統(tǒng)計(jì)模型Stewart S-1模型

Rajput等[52]認(rèn)為土壤和氣候條件是造成Stewart S-1模型在不同地區(qū)產(chǎn)生偏差的主要原因, 并給出了Stewart S-1模型的y表達(dá):

式中:s為平均飽和水汽壓;a為平均實(shí)際水汽壓;s為作物生育期(d);27為最高氣溫低于27 ℃的天數(shù); CS為作物根區(qū)黏土百分比(代表土壤的持水能力)。

此外還有一些經(jīng)典全生育期線性模型直接用作物蒸騰()而非蒸散發(fā)(ET)做自變量, 如Ngigi[53]、Hanks[54], 而De Wit[14]使用水面蒸發(fā)0代替最大蒸騰m來(lái)對(duì)產(chǎn)量進(jìn)行擬合(見(jiàn)表1)。

2.1.2 全生育期非線性模型

式中:a為作物的實(shí)際產(chǎn)量,為經(jīng)驗(yàn)系數(shù)。Liu等[56]也提出了類似的模型(表1)。此外, Vico等[58]提出了一個(gè)新模型來(lái)擬合玉米、小麥產(chǎn)量與蒸散發(fā)之間的非線性關(guān)系:

2.1.3 生長(zhǎng)階段連加模型

作物產(chǎn)量不僅取決于全生育期總的水分供給(生長(zhǎng)季蒸散發(fā)), 也取決于供水量在各生長(zhǎng)階段的分配[49]?？到B忠等[59]研究發(fā)現(xiàn), 相比水分虧缺量, 水分虧缺出現(xiàn)時(shí)間對(duì)作物產(chǎn)量影響更大。生長(zhǎng)階段模型以作物各生育階段的相對(duì)蒸散發(fā)為自變量, 體現(xiàn)了作物各生育階段水分虧缺與作物產(chǎn)量之間的關(guān)系, 根據(jù)模型的數(shù)學(xué)表達(dá)形式又可分為連加模型和連乘模型兩類。連加模型假定作物不同生長(zhǎng)階段ET虧缺對(duì)產(chǎn)量的影響可以相加。

生長(zhǎng)階段連加模型以Stewart S-2模型[48](公式7)和Blank模型(公式8)[59]為代表:

式中:K與A是經(jīng)驗(yàn)系數(shù), 反映不同生長(zhǎng)階段()作物對(duì)水分虧缺的敏感程度, 表達(dá)不同生長(zhǎng)階段缺水對(duì)作物最終產(chǎn)量的影響程度。常用的生長(zhǎng)階段連加模型還有Singh[59]、Howell[60]、Rao-1[50]以及Rajput[52]等(表1), 此外也有連加模型將ET用·的形式表達(dá), 如Paredes模型[61]:

式中:v、f、m分別表示作物營(yíng)養(yǎng)生長(zhǎng)期、開(kāi)花期、成熟期蒸騰量, d表示水分虧缺程度(deficit),c表示最大作物蒸騰量。

2.1.4 生長(zhǎng)階段連乘模型

生長(zhǎng)階段連乘模型用各生長(zhǎng)階段相對(duì)蒸散發(fā)的積表達(dá)不同生長(zhǎng)階段水分狀況對(duì)產(chǎn)量形成過(guò)程的影響。在眾多連乘模型中, Jensen[62](公式10)與康紹忠等[59](公式11)最具代表性, 我國(guó)應(yīng)用也較為廣泛:

式中:λ與δ為不同生長(zhǎng)階段()作物水分脅迫敏感指數(shù)(moisture sensitivity index)。常用的生長(zhǎng)階段連乘模型還有Rao2、Hanks-1等(表1), De Jager[63]在前人的基礎(chǔ)上, 結(jié)合連加與連乘模型, 提出了一個(gè)日尺度的CWPF模型:

式中:c為作物實(shí)際產(chǎn)量,mc為最大潛在產(chǎn)量,yc,g為作物c在生長(zhǎng)階段的響應(yīng)因子, ETac,g為作物c在生長(zhǎng)階段的日實(shí)際蒸散發(fā), ETmc,g為作物c在生長(zhǎng)階段的日最大蒸散發(fā)。

2.2 基于氣孔擴(kuò)散理論的機(jī)制模型

氣孔是作物與大氣之間進(jìn)行水分和CO2交換的共同通道, 植物通過(guò)調(diào)節(jié)氣孔的開(kāi)度控制水分耗散和碳同化過(guò)程, 因此蒸騰作用與光合過(guò)程同步發(fā)生。通過(guò)基于葉面尺度氣孔擴(kuò)散理論的碳水關(guān)系模型(如Jarvis[21]、Farquhar[64]、Leuning[65]等)可方便地建立起生物量與蒸騰過(guò)程之間的關(guān)系, 然后利用凈輻射在冠層潛熱和感熱之間的分配關(guān)系, 以及產(chǎn)量與生物量之間的經(jīng)驗(yàn)關(guān)系(如收獲指數(shù)HI), 再通過(guò)升尺度方法并利用SPAC理論耦合土壤水分動(dòng)態(tài), 就能間接實(shí)現(xiàn)CWPF的推算, 多數(shù)已有的SPAC模型(如Daly[66]、Jensen[67]、Tuzet[68]等)都基本能滿足這樣的需要。

Feddes[38]在研究農(nóng)田水分運(yùn)動(dòng)及作物產(chǎn)量的模擬中, 分析了作物干物質(zhì)形成過(guò)程的特點(diǎn), 提出干物質(zhì)日形成率的計(jì)算式:

2.3 基于統(tǒng)計(jì)或機(jī)制模型的復(fù)雜作物模型

2.3.1 基于CWPF統(tǒng)計(jì)模型的作物模型

在上述統(tǒng)計(jì)模型的基礎(chǔ)上, 發(fā)展出了一些更為復(fù)雜、涉及參數(shù)更多的作物模型, 如SIMDualKc作物模型就是先使用雙作物系數(shù)法分別計(jì)算蒸騰和蒸發(fā), 再使用Stewart統(tǒng)計(jì)模型[48](S-1和S-2)預(yù)測(cè)作物產(chǎn)量[69]; 著名的FAO的作物模型AquaCorp[70]也是在Doorenbos統(tǒng)計(jì)模型[51]的基礎(chǔ)上加入了水生產(chǎn)力參數(shù)(WP)和收獲指數(shù)(HI)來(lái)估算作物產(chǎn)量:

=WP×(15)

=×HI (16)

式中:為生物量,為實(shí)際作物蒸騰,為作物最終產(chǎn)量。這些模型在已有CWPF統(tǒng)計(jì)模型的基礎(chǔ)上加入了水分平衡和作物生長(zhǎng)模塊, 應(yīng)用較為廣泛。但也有存在相應(yīng)的缺點(diǎn), 如參數(shù)過(guò)多(AquaCorp模型需33個(gè)參數(shù)), 沒(méi)有考慮養(yǎng)分條件的限制等。

2.3.2 基于CWPF機(jī)制模型的作物模型

另外一些常見(jiàn)的作物模型則基于CWPF機(jī)制模型來(lái)計(jì)算產(chǎn)量: RS-P-YEC模型(Remote-Sensing– Photosynthesis–Yield Estimation for Crops)[71]通過(guò)葉片瞬時(shí)光合作用的積分得到葉片日總碳同化量, 根據(jù)葉片受光條件獲取冠層尺度的碳同化量, 減去作物自養(yǎng)呼吸后得到作物凈初級(jí)生產(chǎn)力(NPP), 再將NPP與HI相乘得到作物產(chǎn)量, 在此基礎(chǔ)上使用衛(wèi)星反演模塊計(jì)算的蒸散發(fā)數(shù)據(jù)就可以方便地獲得CWPF; SUCROS模型(Simple and Universal Crop Growth Simulator)則利用冠層同化速率、蒸騰作用、呼吸作用及干物質(zhì)分配系數(shù)計(jì)算產(chǎn)量, 得到潛在蒸散與潛在產(chǎn)量的關(guān)系, 然后通過(guò)Penman公式和葉面積指數(shù)(LAI)計(jì)算潛在蒸發(fā)蒸騰進(jìn)而獲得作物潛在產(chǎn)量[72]; WOFOST模型(WOrld FOod STudies)[73]在SUROS模型[72]基礎(chǔ)上, 考慮了氣孔導(dǎo)度(stomatal conductance)與蒸騰及光合速率之間的線性關(guān)系, 使用實(shí)際蒸騰速率計(jì)算碳同化速率, 獲得水分限制條件下的實(shí)際CWPF。

表1 典型CWPF統(tǒng)計(jì)模型(1958—2014年)

2.4 CWPF模型優(yōu)劣分析

統(tǒng)計(jì)模型建立在大量田間試驗(yàn)資料基礎(chǔ)上, 其中線性模型適用于水分脅迫環(huán)境, 而非線性模型適用于充分灌溉環(huán)境[59]。連加模型反映了水分脅迫在不同生長(zhǎng)階段對(duì)作物生長(zhǎng)的影響, 但無(wú)法反映某階段受旱對(duì)整個(gè)生育期的影響; 連乘模型在一定程度上克服了上述不足, 因而更適合在干旱半干旱地區(qū)使用。上述統(tǒng)計(jì)模型雖然在形式上存在差異, 但其基本原理都是將田間試驗(yàn)數(shù)據(jù)進(jìn)行標(biāo)準(zhǔn)化、弱化離散程度, 進(jìn)而擬合出理想的產(chǎn)量-蒸散發(fā)量(耗水量)關(guān)系(CWPF)。其優(yōu)點(diǎn)是計(jì)算簡(jiǎn)單, 所需數(shù)據(jù)類型少, 在同一地區(qū)能夠較為準(zhǔn)確地反映作物產(chǎn)量對(duì)水分因子的響應(yīng)特征[47]。但存在一定的地域限制, 通常不能進(jìn)行跨地區(qū)、跨物種推廣。機(jī)制模型從作物水分生理角度出發(fā)模擬作物生長(zhǎng)過(guò)程(包括同化、吸收及蒸騰過(guò)程), 根據(jù)作物生長(zhǎng)情況逐時(shí)段模擬和預(yù)測(cè)干物質(zhì)積累, 進(jìn)而預(yù)測(cè)作物產(chǎn)量的形成。與統(tǒng)計(jì)模型相比, 機(jī)制模型的地區(qū)可移植性更好。作物模型綜合考慮了各種因素對(duì)作物產(chǎn)量的影響, 適用于不同地區(qū)、時(shí)間和品種。機(jī)制模型與作物模型可在不同地域不同氣候條件下較為成功地體現(xiàn)產(chǎn)量-蒸散發(fā)關(guān)系(CWPF), 但又往往需要?dú)庀?、土壤、作物及水文等多種類型的參數(shù), 部分參數(shù)又很難通過(guò)觀測(cè)獲得, 模型計(jì)算過(guò)程相對(duì)復(fù)雜, 導(dǎo)致應(yīng)用門(mén)檻較高。為了建立一種簡(jiǎn)單可靠, 但又有一定物理基礎(chǔ)、可跨地區(qū)、跨物種應(yīng)用的CWPF模型, 本文選擇應(yīng)用更為廣泛、結(jié)構(gòu)相對(duì)簡(jiǎn)單的統(tǒng)計(jì)模型進(jìn)行修正, 從影響CWPF的主要因素入手, 嘗試克服統(tǒng)計(jì)模型無(wú)法跨地區(qū)應(yīng)用的缺點(diǎn)。

表2 產(chǎn)量-蒸散發(fā)(Y-ET)數(shù)據(jù)集薈萃分析源文獻(xiàn)(1979—2013年)

3 作物水分生產(chǎn)函數(shù)模型修正

3.1 數(shù)據(jù)提取

從近50年來(lái)公開(kāi)發(fā)表的國(guó)際期刊(SCI)中提取了小麥、玉米、棉花、水稻4種作物的CWPF田間試驗(yàn)數(shù)據(jù)(均為論文原始數(shù)據(jù)), 在剔除溫棚試驗(yàn)、產(chǎn)量與蒸散發(fā)量不在同一地點(diǎn)測(cè)量等數(shù)據(jù)后, 從41篇文獻(xiàn)中(表2)篩選出592組-ET有效數(shù)據(jù), 以及試驗(yàn)地點(diǎn)經(jīng)緯度、海拔、作物品種、降雨量、灌溉量、耕作方式(包括施肥設(shè)計(jì))等基本數(shù)據(jù), 另外盡可能收集了蒸發(fā)皿蒸發(fā)、土壤類型、灌溉方式、地下水水位等重要信息, 在此基礎(chǔ)上建立了產(chǎn)量-蒸散發(fā)田間試驗(yàn)數(shù)據(jù)集, 并通過(guò)薈萃分析對(duì)CWPF進(jìn)行了修正。數(shù)據(jù)集中蒸散發(fā)量一般采用水平衡公式、Penman-Monteith公式、稱重式蒸滲儀、雙作物系數(shù)法等計(jì)算, 產(chǎn)量則主要使用烘干法測(cè)量(表2)。

3.2 數(shù)據(jù)分析

小麥ET數(shù)據(jù)總體上基本呈線性關(guān)系(2=0.34), 其產(chǎn)量隨蒸散發(fā)增加而增加, 但數(shù)據(jù)分布相對(duì)離散(圖2); 玉米ET數(shù)據(jù)盡管在單個(gè)試驗(yàn)中基本呈線性, 但整體上趨勢(shì)不明顯, 且數(shù)據(jù)分布更加離散(圖2); 因數(shù)據(jù)量的限制, 棉花皮棉產(chǎn)量(lint yield)、籽棉產(chǎn)量(seed yield)及水稻產(chǎn)量與蒸散發(fā)關(guān)系并不明顯(圖2)。將小麥和玉米的ET數(shù)據(jù)通過(guò)Stewart S-1模型[48]做標(biāo)準(zhǔn)化處理之后發(fā)現(xiàn)只有小麥總體線性關(guān)系明顯(2=0.42), 玉米線性關(guān)系較差(r=0.19), 但這種方法處理后數(shù)據(jù)離散(圖3), 可見(jiàn)傳統(tǒng)CWPF統(tǒng)計(jì)模型存在明顯的地區(qū)局限性。

圖2 小麥、玉米、棉花、水稻的產(chǎn)量-蒸散發(fā)(Y-ET)關(guān)系(CWPF)數(shù)據(jù)集

圖3 小麥、玉米產(chǎn)量-蒸散發(fā)(Y-ET)關(guān)系(CWPF)標(biāo)準(zhǔn)化(Stewart S-1模型)

“1產(chǎn)量最高產(chǎn)量”與“1蒸散發(fā)最大蒸散發(fā)”代表各試驗(yàn)的相對(duì)減產(chǎn)與相對(duì)蒸散發(fā)虧缺。1-maxand 1-ETETmaxrepresent relative yield reduction and relative evapotranspiration deficit of each experiment, in whichandmaxare yield and max yield, ET and ETmaxare evapotranspiration and max evapotranspiration.

3.3 CWPF統(tǒng)計(jì)模型修正

盡管以Stewart為代表的統(tǒng)計(jì)模型在單個(gè)試驗(yàn)中表現(xiàn)良好, 但其很難將不同地區(qū)不同年份的-ET數(shù)據(jù)標(biāo)準(zhǔn)化為理想的線性或拋物線關(guān)系。氣候因子如環(huán)境溫度(emp)、輻照度()、降水(rec)和空氣水汽壓差(VPD)通過(guò)影響氣孔導(dǎo)度控制植物水分狀態(tài)[116], 進(jìn)而影響蒸騰過(guò)程和光合作用[117], 因此氣候差異是限制CWPF統(tǒng)計(jì)模型跨地區(qū)使用的主要障礙[14,51-52]。考慮到環(huán)境溫度、輻照度、降水量對(duì)CWPF的影響可以通過(guò)干旱指數(shù)體現(xiàn)[如標(biāo)準(zhǔn)化降水指數(shù)(SPI)[118]、標(biāo)準(zhǔn)化降水蒸散發(fā)指數(shù)(SPEI)[119]、SPEI-Pe指數(shù)等[120]]; 空氣水汽壓差對(duì)CWPF的影響又可以用經(jīng)驗(yàn)系數(shù)來(lái)修正[121-122]。本文采用了生長(zhǎng)季降水量(rec)與蒸發(fā)皿蒸發(fā)(Pan)的比(rec/Pan)來(lái)反映當(dāng)?shù)氐母珊党潭?蒸發(fā)皿蒸發(fā)包含了水汽壓差的信息), 然后將作物實(shí)際蒸散發(fā)乘以當(dāng)?shù)亍案珊迪禂?shù)”, 得到修正后的CWPF[即(ET′rec/Pan)與的關(guān)系], 并對(duì)其進(jìn)行了檢驗(yàn)。受數(shù)據(jù)集的限制(41篇文獻(xiàn)中只有7篇小麥參考文獻(xiàn)包含當(dāng)年生長(zhǎng)季降雨與蒸發(fā)皿蒸發(fā)數(shù)據(jù)), 本文只針對(duì)小麥水分生產(chǎn)函數(shù)進(jìn)行了修正和檢驗(yàn), 發(fā)現(xiàn)通過(guò)rec/Pan對(duì)小麥水分生產(chǎn)函數(shù)進(jìn)行修正后, (ET′rec/Pan)與相關(guān)性很高(2=0.75), 其中異常值的出現(xiàn)是因?yàn)闃O端干旱事件延遲了當(dāng)年生長(zhǎng)季開(kāi)始時(shí)間[80](圖4)。

圖4 小麥水分生產(chǎn)函數(shù)的修正效果[a. 產(chǎn)量與蒸散發(fā)的關(guān)系(r2=0.36); b: 產(chǎn)量與降水量(Prec)和蒸發(fā)皿蒸發(fā)(EPan)修正的蒸散發(fā)(ET′Prec/EPan)的關(guān)系(r2=0.75)]

下方圖例依次為國(guó)家: 海拔-小麥播種季-土壤類型-灌溉方式-地下水位-氣候及文獻(xiàn)。The legends are shown in the order of “country: elevation-wheat planting season-soil type-irrigation method-groundwater table-climate-journal article”.

3.4 結(jié)果與討論

盡管各試驗(yàn)地點(diǎn)在氣候狀況、經(jīng)緯度、海拔、播種季節(jié)、土壤類型、灌溉方式以及地下水位等條件上差異巨大, 但通過(guò)當(dāng)?shù)亟涤炅?rec)和蒸發(fā)皿蒸發(fā)(Pan)修正后, ET′rec/Pan與線性關(guān)系明顯(圖4), 表明rec/Pan可以將上述條件差異大部分消除。實(shí)際上, ET′rec/Pan=rec′(/Pan+/Pan), 采用蒸發(fā)皿蒸發(fā)(Pan)來(lái)修正CWPF, 相當(dāng)于用(蒸騰)/Pan標(biāo)準(zhǔn)化-關(guān)系(TE)的同時(shí)用/Pan弱化了(蒸發(fā))的差異, 從而使得-ET關(guān)系(CWPF)得到了顯著改善。對(duì)而言, 由于水汽壓差是影響蒸發(fā)皿蒸發(fā)的直接因素, 所以使用Pan對(duì)進(jìn)行校正(/Pan)在一定程度上和Tanner等[24]使用季節(jié)平均蒸汽壓對(duì)蒸騰效率(TE)進(jìn)行矯正效果類似, 矯正后的-關(guān)系相對(duì)穩(wěn)定。對(duì)而言, 由于蒸發(fā)皿蒸發(fā)可以綜合反映區(qū)域潛在蒸發(fā)水平, 因此用/Pan相當(dāng)于弱化了不同地區(qū)的差異對(duì)CWPF的影響; 而乘以rec相當(dāng)于弱化了土壤差異造成的水分差異(生長(zhǎng)季降雨量在一定程度上對(duì)土壤水分進(jìn)行了有效補(bǔ)充, 故降水量與產(chǎn)量呈正比)。因此, 用降雨量(rec)和蒸發(fā)皿蒸發(fā)(Pan)修正后的CWPF線性相關(guān)性強(qiáng)烈。

此外, 我們發(fā)現(xiàn)盡管這7個(gè)田間試驗(yàn)有不同水平的氮肥、磷肥使用量, 但用干旱系數(shù)修正后CWPF依然表現(xiàn)良好。實(shí)際上, 施肥對(duì)CWPF的影響往往和土壤水分含量密切相關(guān), 肥料只有溶于土壤水溶液中才能被作物根系吸收利用。在水分受限環(huán)境下, 施肥對(duì)產(chǎn)量影響有限, 而在水分供給充分時(shí), 施肥雖然會(huì)增加產(chǎn)量, 但同時(shí)也會(huì)增加蒸散發(fā)[34]。Ertek[123]在研究西紅柿CWPF時(shí), 發(fā)現(xiàn)施肥、產(chǎn)量以及蒸散發(fā)之間可以互相用線性關(guān)系表達(dá)。

在此認(rèn)識(shí)的基礎(chǔ)上我們提出了修正后的CWPF統(tǒng)計(jì)模型:

式中:指作物產(chǎn)量;為斜率, 不同作物對(duì)應(yīng)不同值;rec和Pan分別為生長(zhǎng)季降雨量和生長(zhǎng)季累計(jì)蒸發(fā)皿蒸發(fā); ET為作物生長(zhǎng)季蒸散發(fā);為截距;為隨機(jī)誤差。和施肥情況、CO2濃度、個(gè)體基因等密切相關(guān), 難以量化。理想狀況下, 在產(chǎn)量達(dá)到最大值之前我們認(rèn)為它和ET′rec/Pan之間是線性關(guān)系, 之后隨著養(yǎng)分的流失和水澇的發(fā)生產(chǎn)量開(kāi)始快速下降, 最終呈現(xiàn)出拋物線關(guān)系。該方法可以獲得同一物種不同地區(qū)不同氣候不同耕作方式之間相對(duì)可靠的CWPF, 有望改善傳統(tǒng)統(tǒng)計(jì)模型無(wú)法跨地區(qū)推廣的問(wèn)題。

4 結(jié)論與展望

CWPF受氣候、土壤類型、施肥水平和灌溉模式等因素影響, 不同地區(qū)田間試驗(yàn)結(jié)果差異顯著; 基于田間試驗(yàn)的CWPF統(tǒng)計(jì)模型適用范圍有限, 基于碳同化過(guò)程的機(jī)制模型和更為復(fù)雜的作物模型也因?yàn)閰?shù)過(guò)多而不易在實(shí)際中應(yīng)用。本文使用Pan和rec對(duì)CWPF進(jìn)行了修正, 修正后的CWPF在跨地區(qū)應(yīng)用時(shí)表現(xiàn)良好, 但仍有需改進(jìn)的空間。整體上看, 缺少嚴(yán)格的物理機(jī)制仍然限制了統(tǒng)計(jì)模型的應(yīng)用空間, 因此機(jī)制模型仍然是未來(lái)CWPF模型的根本出路。就本文中修正獲得的CWPF而言, 進(jìn)一步的工作還應(yīng)考慮: 1)加強(qiáng)對(duì)修正結(jié)果的理論解釋; 2)由于數(shù)據(jù)集的限制本文只針對(duì)小麥水分生產(chǎn)函數(shù)進(jìn)行了修正, 該方案對(duì)其他作物的適用性有待檢驗(yàn); 3)由于數(shù)據(jù)的限制, 對(duì)CWPF的修正沒(méi)有分生長(zhǎng)階段處理, 借鑒Jensen[62]的思路可能會(huì)進(jìn)一步提高CWPF修正模型的跨地區(qū)應(yīng)用潛力。

總體來(lái)看, CWPF的研究涉及農(nóng)學(xué)、土壤學(xué)、植物學(xué)、水文學(xué)、氣候?qū)W等多門(mén)學(xué)科, 盡管目前已有大量的基礎(chǔ)性研究工作, 但仍沒(méi)有統(tǒng)一的衡量標(biāo)準(zhǔn)來(lái)準(zhǔn)確量化各個(gè)影響因素對(duì)CWPF的影響程度以及不同影響因素之間的相互復(fù)雜作用, 使用當(dāng)?shù)刈畲螽a(chǎn)量與對(duì)應(yīng)的蒸散發(fā)固然可以反映一個(gè)地區(qū)的生產(chǎn)力水平以及不同地區(qū)地理空間差異, 但是無(wú)法做到從機(jī)理層面解釋環(huán)境因子對(duì)CWPF的影響。隨著越來(lái)越多的試驗(yàn)開(kāi)展與數(shù)據(jù)積累, 建立一個(gè)CWPF全球試驗(yàn)數(shù)據(jù)庫(kù)成為可能, 在此基礎(chǔ)上進(jìn)行數(shù)據(jù)挖掘, 繪制CWPF地理分布圖, 對(duì)各影響因素進(jìn)行定量研究, 從而從機(jī)理層面有所突破, 是CWPF未來(lái)研究的重要方向。

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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)

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 () 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 (2= 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 (2increased from 0.36 to 0.75), when seasonal precipitation (rec) and accumulated pan evaporation (Pan) were incorporated. Our results showed that the functional relationship betweenand ET×rec/Panwas more universal, compared with that betweenand 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.

Crop water production function; Crop evapotranspiration; Crop yield; Meta-analysis; Model modification

, E-mail: lhayz@lzb.ac.cn

Apr. 11, 2018;

Jun. 20, 2018

S5-3

A

1671-3990(2018)12-1781-14

10.13930/j.cnki.cjea.180369

* 國(guó)家自然科學(xué)基金項(xiàng)目(91425302)資助

劉鵠, 主要研究方向?yàn)樯鷳B(tài)水文模型。E-mail: lhayz@lzb.ac.cn

李中愷, 主要研究方向?yàn)楦珊祬^(qū)生態(tài)水文。E-mail: lizhongkai16@mails.ucas.ac.cn

2018-04-11

2018-06-20

* This study was supported by the National Natural Science Foundation of China (91425302).

李中愷, 劉鵠, 趙文智. 作物水分生產(chǎn)函數(shù)研究進(jìn)展[J]. 中國(guó)生態(tài)農(nóng)業(yè)學(xué)報(bào), 2018, 26(12): 1781-1794

LI Z K, LIU H, ZHAO W Z. Revisiting crop water production functions in terms of cross-regional applications[J]. Chinese Journal of Eco-Agriculture, 2018, 26(12): 1781-1794