朱中華,韓 拓,柳金權(quán),朱高峰

(1.甘肅省水利水電學(xué)校 蘭州 730021;2.蘭州大學(xué)資源環(huán)境學(xué)院/西部環(huán)境教育部重點(diǎn)實(shí)驗(yàn)室 蘭州 730000; 3.華亭縣水務(wù)局 華亭 744100)

基于貝葉斯方法的光合作用生化模型參數(shù)估計(jì)及其在干旱區(qū)葡萄上的應(yīng)用*

朱中華1,韓 拓2**,柳金權(quán)3,朱高峰2

(1.甘肅省水利水電學(xué)校 蘭州 730021;2.蘭州大學(xué)資源環(huán)境學(xué)院/西部環(huán)境教育部重點(diǎn)實(shí)驗(yàn)室 蘭州 730000; 3.華亭縣水務(wù)局 華亭 744100)

以無(wú)核白葡萄為試材,測(cè)定了其在不同季節(jié)(6—9月)、不同胞間CO2濃度下的凈光合速率,根據(jù)貝葉斯方法,結(jié)合蒙特卡羅馬爾科夫鏈算法對(duì)光合生化模型參數(shù)進(jìn)行估算,以期獲得不同季節(jié)的模型參數(shù)值,并與最小二乘法所得結(jié)果對(duì)比,探討貝葉斯方法在解決高維度復(fù)雜模型參數(shù)估計(jì)問(wèn)題中的可行性和葡萄光合作用關(guān)鍵參數(shù)季節(jié)變化規(guī)律。結(jié)果表明,最大羧化速率(Vcmax)、最大電子傳遞速率(Jmax)、磷酸丙糖利用速率(TPU)均有明顯的季節(jié)變化特性,出現(xiàn)先增后減的趨勢(shì),8月達(dá)最高,分別為54.30μmol?m-2?s-1、88.45μmol?m-2?s-1和6.56μmol?m-2?s-1;9月最小,分別為34.66μmol?m-2?s-1、58.86μmol?m-2?s-1和4.38μmol?m-2?s-1。葉肉導(dǎo)度(gm)在各個(gè)月份波動(dòng)不大,6—9月分別為5.16μmol?m-2?s-1?Pa-1、5.29μmol?m-2?s-1?Pa-1、5.39μmol?m-2?s-1?Pa-1和5.41 μmol?m-2?s-1?Pa-1。與傳統(tǒng)的最小二乘法相比,貝葉斯方法估算的Vcmax值偏小,Jmax、TPU和gm無(wú)明顯差異。同時(shí)貝葉斯方法估計(jì)出的模型參數(shù)是在考慮參數(shù)先驗(yàn)信息的基礎(chǔ)上獲得的,生化意義更加顯著。試驗(yàn)表明,光合作用生化模型(FvCB模型)在應(yīng)用于光合作用模擬時(shí),應(yīng)充分考慮其參數(shù)的季節(jié)變化性;結(jié)合蒙特卡羅馬爾科夫鏈算法的貝葉斯參數(shù)估計(jì)能更有效解決FvCB模型中參數(shù)估計(jì)問(wèn)題。

干旱區(qū);葡萄;貝葉斯參數(shù)估計(jì);光合作用生化模型;光合作用參數(shù);季節(jié)變化

近年來(lái),光合作用的模型研究得到人們?nèi)找骊P(guān)注[1-2]。其中,von Caemmerer等[3-6]的光合作用機(jī)理模型(以下簡(jiǎn)稱(chēng)FvCB模型)因具有明確生物學(xué)意義而被廣泛應(yīng)用于光合作用研究中,并被多數(shù)碳循環(huán)模型(如SiB、CLM等)所采用。在該模型中,最大羧化速率(Vcmax)、最大電子傳遞速率(Jmax)、磷酸丙糖利用速率(TPU)是表征植物光合能力的關(guān)鍵參數(shù)。如何利用實(shí)測(cè)凈光合速率/胞間CO2濃度變化曲線(A/Ci曲線)估計(jì)這些參數(shù)不僅是植物生態(tài)學(xué)研究的熱點(diǎn),也是提高陸地碳循環(huán)模擬精度的關(guān)鍵[7]。

前人以不同植物為研究對(duì)象對(duì)模型參數(shù)估計(jì)做了較多研究。Harley[8]等和Wullschleger[9]用分段估計(jì)法對(duì)棉花(Gossypiumspp.)和 109種 C3植物的Vcmax,、暗呼吸速率Rd和葉肉導(dǎo)度gm進(jìn)行了估計(jì),但此類(lèi)方法以胞間CO2濃度分壓等于20 Pa為節(jié)點(diǎn)進(jìn)行數(shù)據(jù)的經(jīng)驗(yàn)性分割,不但受人為因素?cái)_動(dòng)較大,而且當(dāng)數(shù)據(jù)集較小時(shí)收斂較為困難;Dubois等[10]和Miao等[11]結(jié)合格點(diǎn)搜索利用非線性最小二乘法同時(shí)估計(jì)出Vcmax、Jmax、TPU和Rd,但該方法是以求誤差的最小值來(lái)逼近參數(shù)真值,較適用于連續(xù)性函數(shù)的參數(shù)估計(jì),而對(duì)于分段不連續(xù)且高維的FvCB模型難以獲得全局最優(yōu)結(jié)果;Su等[12]將遺傳算法應(yīng)用到FvCB模型主要參數(shù)的估計(jì)當(dāng)中,克服了傳統(tǒng)迭代方法容易陷入局部最優(yōu)解的缺陷,但該算法后期適應(yīng)度容易趨向一致,使優(yōu)秀的個(gè)體在產(chǎn)生后代時(shí)優(yōu)勢(shì)不明顯,導(dǎo)致算法進(jìn)化后期搜索效率較低;近年來(lái),Zhu等[13]和Feng等[14]先后將貝葉斯方法應(yīng)用到光合作用模型參數(shù)估計(jì)當(dāng)中,較其他方法有明顯的優(yōu)勢(shì)。與其他參數(shù)估計(jì)方法相比,貝葉斯方法在充分考慮觀測(cè)誤差和模型結(jié)構(gòu)誤差的基礎(chǔ)上,獲得參數(shù)的分布范圍,大大提高了擬合精度。然而將該方法應(yīng)用于光合作用生化模型參數(shù)估計(jì),獲取適用于我國(guó)西北干旱區(qū)葡萄的模型參數(shù)的研究尚鮮見(jiàn)報(bào)道。

本文以我國(guó)西北干旱綠洲典型農(nóng)田生態(tài)系統(tǒng)經(jīng)濟(jì)作物葡萄(Vitis vinifera)為研究對(duì)象,利用便攜式光合作用-熒光測(cè)量系統(tǒng)獲取不同季節(jié)葡萄凈光合速率隨胞間CO2濃度變化的數(shù)據(jù)。在此基礎(chǔ)上,應(yīng)用貝葉斯方法對(duì)FvCB模型參數(shù)進(jìn)行估計(jì),并分析其與葉片特性的關(guān)系,以驗(yàn)證貝葉斯方法在解決高維度復(fù)雜模型參數(shù)估計(jì)問(wèn)題的可行性,并估計(jì)出模型參數(shù)和具有的生化意義,揭示葡萄光合作用關(guān)鍵參數(shù)季節(jié)變化規(guī)律及其與葉片特性的關(guān)系,增進(jìn)對(duì)干旱綠洲典型經(jīng)濟(jì)作物葡萄光合特征的認(rèn)識(shí),為提高農(nóng)田生態(tài)系統(tǒng)的產(chǎn)量提供科學(xué)指導(dǎo),推動(dòng)貝葉斯方法在植被光合作用模型參數(shù)估計(jì)研究上的應(yīng)用。

1 研究區(qū)概況

試驗(yàn)地位于甘肅省敦煌市陽(yáng)關(guān)鎮(zhèn)南湖綠洲西南部,距市區(qū)約70 km,東、南、北三面環(huán)山(三危山、祁連山、北塞山),西接塔克拉瑪干沙漠,觀測(cè)點(diǎn)地理坐標(biāo)為39°53′N(xiāo),94°07′E,海拔1 100～1 297 m;深居內(nèi)陸,屬暖溫帶干旱性氣候,日照時(shí)間長(zhǎng),晝夜溫差大,降水稀少,蒸發(fā)量大,年均降水量36.9 mm,年均潛在蒸發(fā)量達(dá) 2 486 mm[15]。年日照時(shí)數(shù)為3 115～3 247 h,年均氣溫9.3℃;土壤主要為隱域性土壤,包括沼澤土、草甸土和鹽漬土等。觀測(cè)點(diǎn)位于南湖綠洲西南部,屬農(nóng)田生態(tài)系統(tǒng),土壤類(lèi)型為綠洲灌耕土,葡萄園每月下旬進(jìn)行一次人工大水漫灌,確保植物在充分供水條件下生長(zhǎng)。

2 材料與方法

2.1 試驗(yàn)材料

試驗(yàn)材料為‘無(wú)核白葡萄’(Thompson Seedless),平均冠層高度1.84 m,平均胸徑3.2 cm,樹(shù)齡13 a。隨機(jī)選取4棵植株,利用便攜式光合作用-熒光測(cè)量系統(tǒng)(GFS-3000)進(jìn)行CO2響應(yīng)曲線(A/Ci)測(cè)定。觀測(cè)日期分別為2014年的6月、7月、8月、9月,涵蓋了葡萄的開(kāi)花期、坐果期、漿果生長(zhǎng)期、漿果成熟期4個(gè)典型生長(zhǎng)期。觀測(cè)時(shí)間處于每月中下旬某一晴天的10:00—16:00。觀測(cè)葉片則選取位于冠層中上部的成熟陽(yáng)生葉片,用于不同季節(jié)自然條件下的活體測(cè)定,每株選3片葉子進(jìn)行重復(fù)試驗(yàn)。

測(cè)量前,使葉片處在飽和光照條件下(PARtop=1 200 mol?m-2?s-1)適應(yīng)30 min,此時(shí)酶活性被完全激活。6、7、8、9月葉室溫度(Tcuv)分別設(shè)置為25℃、30℃、30℃和20℃,保證了與當(dāng)月自然環(huán)境溫度的一致性。環(huán)境大氣壓強(qiáng)(Pamb)為86 kPa,葉片溫度(Tleaf)設(shè)定范圍為24～34℃,樣品室相對(duì)濕度(RH)控制在40%～65%,均處在當(dāng)月光合作用的最佳范圍內(nèi),氣流速率為750μmol?s-1,保證了CO2的充分吸收。在以上設(shè)置不變的情況下,調(diào)整CO2絕對(duì)濃度(CO2abs)來(lái)完成不同植株、不同葉片在不同季節(jié)的A/Ci曲線測(cè)定。CO2abs最初設(shè)為120 kPa,而后為100 kPa、80 kPa、60 kPa、50 kPa、40 kPa、30 kPa、20 kPa、10 kPa和5 kPa共10個(gè)水平,在每個(gè)CO2濃度下適應(yīng)2～3 min后開(kāi)始測(cè)定,且每個(gè)梯度記錄3次,求均值。

2.2 模型簡(jiǎn)介

FvCB模型將整個(gè)光合作用過(guò)程劃分為3個(gè)限制階段:二磷酸核酮糖羧化酶限制階段(Rubisco限制)、二磷酸核酮糖再生限制階段(RuBP限制)和磷酸丙糖利用限制階段(TPU限制),其表達(dá)式為[3-5]:

式中:An為凈光合速率(μmol?m-2?s-1),Ac、Aj和Ap分別為Rubisco限制、RuBP限制和TPU限制階段的凈CO2同化速率(μmol?m-2?s-1),Vcmax為最大羧化速率(μmol?m-2?s-1),J為電子傳遞速率(μmol?m-2?s-1), TPU為磷酸丙糖利用速率(μmol?m-2?s-1),Rd為暗呼吸速率(μmol?m-2?s-1),f*為CO2補(bǔ)償點(diǎn)(Pa),A為光合速率(μmol?m-2?s-1),Kc和Ko分別為羧化作用和加氧作用的米氏常數(shù)(kPa和Pa),Cc和o分別為Rubisco中CO2分壓(Pa)和O2分壓(21 kPa)[16],Jmax為最大電子傳遞速率 (μmol?m-2?s-1),gm為葉肉導(dǎo)度(μmol?m-2?s-1?Pa-1),Ci為胞間CO2濃度(Pa),θ為光響應(yīng)曲線斜率(0.90),a為電子轉(zhuǎn)移的量子產(chǎn)率(0.30),Q為光合作用量子通量密度(0.093μmol?m-2?s-1)[7]。

2.3 參數(shù)估計(jì)方法

貝葉斯定理認(rèn)為,參數(shù)的后驗(yàn)分布與先驗(yàn)分布和概率密度函數(shù)的乘積成正比[17],其表達(dá)式為:

式中:b為由待估參數(shù)構(gòu)成的參數(shù)向量(包括Vcmax、Jmax、TPU和gm),D為觀測(cè)數(shù)據(jù),p(b|D)為后驗(yàn)分布,p(D|b)為抽樣分布的概率密度函數(shù),p(b)為待估參數(shù)b的先驗(yàn)概率分布,p(D)為隨機(jī)變量的邊緣分布。樣本抽取采用Markov Chain Monte Carlo MCMC)方法[18-20]。

最小二乘法在FvCB模型參數(shù)估計(jì)中應(yīng)用較早,其基本思想是通過(guò)最小化誤差的平方和尋找數(shù)據(jù)的最佳函數(shù)匹配[10]。假設(shè)有一組數(shù)據(jù)xi,yi,i=1,2,…,N,且已知該組數(shù)據(jù)滿足a為待定參數(shù)向量,則最小二乘法的目標(biāo)是求出一組待定參數(shù)值,可以定義出最優(yōu)化問(wèn)題,如下:

3 結(jié)果與分析

3.1 光合作用參數(shù)估計(jì)結(jié)果

以無(wú)核白葡萄為研究對(duì)象,同時(shí)選用最小二乘法和貝葉斯方法對(duì)FvCB模型運(yùn)用同一套觀測(cè)數(shù)據(jù)集進(jìn)行參數(shù)估計(jì)(圖1)。從圖中可以看出:無(wú)論是貝葉斯方法還是最小二乘法,參數(shù)季節(jié)變化顯著。對(duì)于參數(shù)Vcmax、Jmax和TPU,其值呈先增大后減小的趨勢(shì),8月達(dá)到最大,9月最小;而gm則是6月和9月略大于7月和8月,且兩種參數(shù)估計(jì)結(jié)果的季節(jié)變化規(guī)律一致。值得注意的是,傳統(tǒng)的最小二乘法獲得的參數(shù)估計(jì)結(jié)果是一個(gè)定值,而基于貝葉斯方法的估計(jì)結(jié)果不但可以獲得參數(shù)估計(jì)結(jié)果的中值,還可以獲得參數(shù)的分布范圍。此外,從表1可以看出,最小二乘法估計(jì)出的參數(shù)Vcmax在4個(gè)月中均大于貝葉斯方法估計(jì)結(jié)果,最大差別可達(dá)15.51mmol?m-2?s-1(9月),而參數(shù)Jmax、TPU和gm無(wú)此現(xiàn)象。

圖1 不同月份基于貝葉斯后驗(yàn)分布及最小二乘法的葡萄光合參數(shù)估計(jì)結(jié)果(I代表貝葉斯后驗(yàn)分布范圍)Fig.1 Posterior mean estimates results given by the Bayesian method and the least square method estimation results of grape photosynthetic parameters in different months(I represents posterior distribution ranges based the Bayesian method)

表1 不同月份基于最小二乘法參數(shù)估計(jì)結(jié)果和基于貝葉斯方法的參數(shù)先驗(yàn)信息與估計(jì)結(jié)果Table 1 Parameters estimation results based on the least square method and the prior information and estimation results based on the Bayesian method in different months for grape photosynthesis

與最小二乘法不同,貝葉斯方法是一種參數(shù)區(qū)間估計(jì)方法,其目標(biāo)不是在參數(shù)可行區(qū)間內(nèi)找到一個(gè)使模型模擬效果最好的最優(yōu)參數(shù)組合,而是在充分考慮先驗(yàn)信息誤差的前提下在一定的置信水平上估計(jì)模型參數(shù)的分布區(qū)間。從不同月份參數(shù)的先驗(yàn)信息及后驗(yàn)分布結(jié)果可以看出(表1):基于先驗(yàn)信息的貝葉斯參數(shù)估計(jì)方法可以有效地縮小給定的參數(shù)先驗(yàn)分布范圍。定義UR(uncertainty reductions)為參數(shù)不確定性相對(duì)減小量(UR=1-CIposterior/CIprior,其中CIposterior和CIprior分別為后驗(yàn)分布和先驗(yàn)分布的95%置信區(qū)間)[21],則對(duì)參數(shù)Vcmax、Jmax和TPU,在不同月份其不確定性相對(duì)減小量近50%,最高達(dá)72%;而對(duì)于gm,UR值相對(duì)較小,僅略大于10%(表2)。由此可見(jiàn),參數(shù)Vcmax、Jmax和TPU收斂效果很好,在貝葉斯方法下可被很好地估計(jì)。

表2 95%置信區(qū)間下葡萄光合參數(shù)不同月份后驗(yàn)分布相較于先驗(yàn)分布的不確定性相對(duì)減小量Table 2 Relative uncertainty reductions in the length of 95% credible interval form prior to posterior distribution of grape photosynthesis in different months %

3.2 基于觀測(cè)值和模擬值的模型評(píng)價(jià)

在不同胞間CO2濃度下,基于貝葉斯方法的凈光合速率估計(jì)值(Ansim)和凈光合速率觀測(cè)值(Anobs)的線性回歸如圖2所示,可以看出:4個(gè)月的相關(guān)系數(shù)均較高,R2均在0.90以上;同時(shí),各月觀測(cè)/擬合趨勢(shì)線趨近于1∶1直線,且在8月和9月更為顯著(表3)。此外,與最小二乘法相比,貝葉斯方法所得觀測(cè)/擬合數(shù)據(jù)點(diǎn)整體分布在更加靠近1∶1直線的區(qū)域,充分表明貝葉斯方法具有更強(qiáng)的收斂性,獲得了更高精度的參數(shù)估計(jì)結(jié)果。

圖2 不同月份葡萄凈光合速率觀測(cè)值和貝葉斯方法及最小二乘法擬合的線性回歸Fig.2 Regressions of grape net photosynthesis rate between measured value(Anobs)and modeled value(Ansim)by the Bayesian method and the least square method in different months

光合作用對(duì)胞間CO2濃度的響應(yīng)曲線(A/Ci曲線)是分析光合作用機(jī)理的重要指標(biāo)。將不同方法的參數(shù)估計(jì)結(jié)果應(yīng)用于FvCB模型,A/Ci曲線擬合結(jié)果如圖3所示。從圖中可以看出:對(duì)于貝葉斯方法的擬合結(jié)果,凈光合速率(An)隨胞間CO2濃度(Ci)的升高呈現(xiàn)出明顯的3個(gè)階段,與FvCB模型結(jié)構(gòu)相吻合,即:當(dāng)Ci相對(duì)較低時(shí),An隨Ci的升高呈直線快速上升,此時(shí)處于光合作用第1階段——Rubisco限制階段;隨著Ci的變大,An隨Ci升高的增速逐漸變小,此時(shí)處于第2階段——RuBP限制階段;當(dāng)Ci繼續(xù)增大到一定數(shù)值時(shí),An不再隨Ci的升高而變大,而是趨于穩(wěn)定,此時(shí)處于第3階段——TPU限制階段。且4個(gè)月第1階段和第2階段轉(zhuǎn)折點(diǎn)對(duì)應(yīng)的Ci分別為31.68 Pa、48.19 Pa、50.82 Pa和35.67 Pa,出現(xiàn)了明顯的季節(jié)差異性。此外,不同月份最大凈光合速率分別為:13.49mmol?m-2?s-1、15.32mmol?m-2?s-1、18.49mmol?m-2?s-1、12.28mmol?m-2?s-1,與參數(shù)估計(jì)結(jié)果有相同的季節(jié)變化規(guī)律。而對(duì)于最小二乘法的擬合結(jié)果,盡管確保了均方根誤差保持在較小的范圍,由于估計(jì)時(shí)參數(shù)之間的相互作用,只擬合出了二磷酸核酮糖再生限制階段(RuBP限制)和磷酸丙糖利用限制階段(TPU限制),導(dǎo)致了生理生態(tài)學(xué)意義不夠明顯?？梢?jiàn),相較于最小二乘法,貝葉斯方法可以估計(jì)出具有生化意義的模型參數(shù),參數(shù)優(yōu)化后的FvCB模型可用于模擬我國(guó)西北干旱綠洲作物的光合速率。

表3 基于貝葉斯方法的葡萄不同月份凈光合速率觀測(cè)值(Anobs)和擬合值(Ansim)的統(tǒng)計(jì)信息Table 3 Statistical information of measured(Anobs)and estimated(Ansim)values of net photosynthesis rate of grape based on the Bayesian method in different months

圖3 不同月份葡萄凈光合速率隨細(xì)胞間二氧化碳濃度(Ci)變化趨勢(shì)圖Fig.3 Prediction of net photosynthesis rate(An)of grape as a function of intercellular carbon dioxide concentration(Ci)in different months

4 討論

無(wú)核白葡萄為多年生木本,參數(shù)Vcmax、Jmax和 TPU 的估計(jì)范圍與 Wullschleger[9]結(jié)果相似, Wullschleger選取了109種C3植物,基于A/Ci曲線的非線性回歸技術(shù)估計(jì)了不同植被類(lèi)型的參數(shù)值,給出參數(shù)變化范圍:Vcmax為6～94mmol?m-2?s-1,Jmax為17～372mmol?m-2?s-1,TPU為4.9～20.1mmol?m-2?s-1,其中一年生草本植物參數(shù)值大于多年生木本植物。本文利用貝葉斯方法精準(zhǔn)地估計(jì)了模型參數(shù),且結(jié)果在前人所給結(jié)果范圍內(nèi)。同時(shí),傳統(tǒng)參數(shù)估計(jì)方法:如Harley等[8]利用分段方法估計(jì)出了Vcmax、Rd和gm,但該方法將A/Ci曲線中Rubisico限制階段和RuBP限制階段的轉(zhuǎn)折點(diǎn)設(shè)為定值,而本文貝葉斯擬合結(jié)果顯示出轉(zhuǎn)折點(diǎn)明顯的季節(jié)差異性,反映出分段估計(jì)法受人為分割的擾動(dòng)會(huì)產(chǎn)生較大誤差; Sharkey等[7]用微軟電子表格同時(shí)估計(jì)出Vcmax、Jmax、TPU、Rd和gm;Dubois等[10]和Miao等[11]結(jié)合了格點(diǎn)搜索和非線性最小二乘法估計(jì)出Vcmax、Jmax、TPU和Rd,這些方法都是派生的最優(yōu)化方法,不但計(jì)算量較大、對(duì)初始值的設(shè)定十分敏感,而且適用于連續(xù)函數(shù)的參數(shù)估計(jì),而對(duì)于分段不連續(xù)的FvCB模型難以得出全局最優(yōu)結(jié)果。相反,貝葉斯方法不需要通過(guò)求導(dǎo)函數(shù)實(shí)現(xiàn)目標(biāo)函數(shù)的最小化,同時(shí)又結(jié)合了先驗(yàn)信息,所以該方法在解決高維復(fù)雜不連續(xù)函數(shù)的參數(shù)估計(jì)問(wèn)題上有很大優(yōu)越性。本文首次將該方法應(yīng)用在我國(guó)西部極端干旱的敦煌綠洲,準(zhǔn)確估計(jì)了當(dāng)?shù)刂饕?jīng)濟(jì)作物葡萄在典型生長(zhǎng)季(6月、7月、8月和9月)內(nèi)不同階段(開(kāi)花期、坐果期、漿果生長(zhǎng)期、漿果成熟期)的模型參數(shù),對(duì)提高農(nóng)田生態(tài)系統(tǒng)的產(chǎn)量有一定指導(dǎo),為陸地生態(tài)系統(tǒng)碳循環(huán)模型研究提供一定的借鑒。

不同月份參數(shù)估計(jì)結(jié)果表現(xiàn)出明顯的季節(jié)差異,與葡萄在不同季節(jié)氮分配策略相關(guān)。無(wú)核白葡萄為C3植物,約60%～80%的葉片氮以核酸和酶的形式存在于葉片中[22-23]。前人研究表明,葉片含氮量與光合作用能力存在正相關(guān)關(guān)系[24-25]。在光合能力較強(qiáng)的月份,所需氮素多,酶活性強(qiáng);反之,光合能力較弱的月份,氮素消耗較少,酶活性較弱[26-27]。Vcmax是Rubisco限制階段的最重要參數(shù),此時(shí)CO2的固定受Rubisco活性的制約,所以在8月,參數(shù)Vcmax也處于最大值;而在以9月份為代表的漿果成熟期,葉片趨于衰老,酶活性較弱,在無(wú)大量氮素消耗時(shí),葉片氮向木質(zhì)部轉(zhuǎn)移貯存,參數(shù)Vcmax也出現(xiàn)較低值。同理,分別作用于RuBP限制階段和TPU限制階段的參數(shù)Jmax和TPU也表現(xiàn)出相同的季節(jié)變化特性。而參數(shù)gm則受溫度和太陽(yáng)輻射影響較大,7月和8月相較于6月和9月具有較高的溫度和較強(qiáng)的太陽(yáng)輻射,此時(shí)葉片為防止大量蒸發(fā)失水,會(huì)出現(xiàn)氣孔關(guān)閉情況,從而導(dǎo)致較小的氣孔導(dǎo)度。

5 結(jié)論

1)基于貝葉斯方法估計(jì)出FvCB模型中4個(gè)主要參數(shù)范圍:最大羧化速率(Vcmax)為23.76～90.69mmol?m-2?s-1,最大電子傳遞速率(Jmax)為47.26～123.98mmol?m-2?s-1,磷酸丙糖利用速率(TPU)為3.14～8.61mmol?m-2?s-1,葉肉導(dǎo)度(gm)為1.42～9.40mmol?m-2?s-1?Pa-1。

2)參數(shù)大小存在明顯的季節(jié)變化規(guī)律,最大羧化速率(Vcmax)、最大電子傳遞速率(Jmax)和磷酸丙糖利用速率(TPU)參數(shù)大小出現(xiàn)先增后減的趨勢(shì),8月最大9月最小,氣孔導(dǎo)度(gm)則6月和9月略大于7月和8月。

3)與傳統(tǒng)的最小二乘法相比,貝葉斯參數(shù)估計(jì)能夠有效解決高維度復(fù)雜不連續(xù)模型的參數(shù)估計(jì)問(wèn)題,可以基于觀測(cè)數(shù)據(jù)有效估計(jì)出具有生化意義的合理參數(shù)值。

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Biochemically-based model for photosynthetic parameter estimation using Bayesian method and its application in grapes in arid region*

ZHU Zhonghua1,HAN Tuo2**,LIU Jinquan3,ZHU Gaofeng2
(1.Gansu Provincial Water Conservancy and Hydropower School,Lanzhou 730021,China;2.College of Earth and Environmental Sciences,Lanzhou University/Key Laboratory of Environmental Systems of Western China of Ministry of Education,Lanzhou 730000,China;3.Huating County Water Authority,Huating 744100,China)

The response of photosynthesis to CO2concentration can provide a number of important parameters related to environmental factors.Using white seedless grape as the tested material in this study,net photosynthetic rates of leaves were measured for different intercellular CO2concentrations during two typical growing seasons from June to September in 2014and 2015.A widely used biochemical model(FvCB model)in the simulation of CO2and H2O gas exchange at the leaf scale was parameterized using data obtained from situ leaf-scale observations.In order to obtain the photosynthetic parameters values,to explore seasonal variations in the photosynthetic parameters in different seasons and to discuss the feasibility and advantage of the Bayesian method in solving high dimensional and complex model parameters estimation,the Bayesian approach was used to estimate the parameters of the FvCB model.In order to generate the Bayesian posterior probability distribution,a version of the Markov Chain Monte Carlo(MCMC)technique was used.In contrast,the least square procedure was used in the application of the same set of observational data.The results showed that maximum ribulose 1.5-bisphosphate carboxylase/oxygenase(Rubisco)carboxylation rate(Vcmax),potential light-saturated electron transport rate(Jmax)and the rate of use of triose-phosphates utilization(TPU)had evident seasonal variations which increased from June to August,and then decreased in September.The maximum values were observed in August(54.30μmol?m-2?s-1,88.45μmol?m-2?s-1and 6.56μmol?m-2?s-1, respectively)and minimum values in September(34.66μmol?m-2?s-1,58.86μmol?m-2?s-1and 4.38μmol?m-2?s-1,respectively).The trend in mesophyll conductance(gm)was relatively stable in different months,with respective values of 5.16μmol?m-2?s-1?Pa-1,5.29 μmol?m-2?s-1?Pa-1,5.39μmol?m-2?s-1?Pa-1,5.41μmol?m-2?s-1?Pa-1from June to September.In comparison with traditional least square method,the values ofVcmaxestimated by the Bayesian method were relatively small and those ofJmax,TPU andgmhad no obvious difference.Also because the estimated parameters by the Bayesian method were obtained after adequate consideration of prior information,each parameter was in biological sense obviously more meaning.As a consequence,it indicated that the Bayesian approach combined with Markov Chains and Monte Carlo(MCMC)sampling algorithm was an effective way of estimation of the parameters in the FvCB model.As the parameters in the FvCB model were different in different seasons,it was necessary to consider these variations in using the parameters in the FvCB model.

Arid region;Grape;Bayesian parameter estimation;Biochemical photosynthesis model;Photosynthetic parameter; Seasonal variation

Oct.29,2016;accepted Mar.1,2017

Q945.79

A

1671-3990(2017)06-0876-08

10.13930/j.cnki.cjea.160967

朱中華,韓拓,柳金權(quán),朱高峰.基于貝葉斯方法的光合作用生化模型參數(shù)估計(jì)及其在干旱區(qū)葡萄上的應(yīng)用[J].中國(guó)生態(tài)農(nóng)業(yè)學(xué)報(bào),2017,25(6):876-883

Zhu Z H,Han T,Liu J Q,Zhu G F.Biochemically-based model for photosynthetic parameter estimation using Bayesian method and its application in grapes in arid region[J].Chinese Journal of Eco-Agriculture,2017,25(6):876-883

* 國(guó)家自然科學(xué)基金(41571016)和中央高校基本科研業(yè)務(wù)費(fèi)(861944)資助

**通訊作者:韓拓,主要從事生態(tài)水文方面的研究。E-mail:hant14@lzu.edu.cn

朱中華,主要研究方向?yàn)樗姾蜕鷳B(tài)水文。E-mail:hant16@lzu.edu.cn

2016-10-29 接受日期:2017-03-01

* This study was supported by the National Natural Science Foundation of China(41571016)and the National Higher-education Institution General Research and Development Project of China(861944).

**Corresponding author,E-mail:hant14@lzu.edu.cn