尹鑫衛(wèi), 李曉玲, 王 琦, 張永梅

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壟溝集雨系統(tǒng)Laio土壤水分動(dòng)態(tài)隨機(jī)模型參數(shù)敏感性分析及優(yōu)化*

尹鑫衛(wèi)1,2, 李曉玲3, 王 琦4**, 張永梅1,2

(1. 中國(guó)科學(xué)院新疆生態(tài)與地理研究所/阜康荒漠生態(tài)國(guó)家野外科學(xué)觀測(cè)研究站 烏魯木齊 830011; 2. 中國(guó)科學(xué)院大學(xué) 北京 100049; 3. 甘肅農(nóng)業(yè)大學(xué)水利水電工程學(xué)院 蘭州 730070; 4. 甘肅農(nóng)業(yè)大學(xué)草業(yè)學(xué)院 蘭州 730070)

水文模型參數(shù)的敏感性分析、優(yōu)化和驗(yàn)證對(duì)提高模型計(jì)算精度和效率具有重要意義。為探討Laio土壤水分動(dòng)態(tài)隨機(jī)模型(Laio模型)各參數(shù)在壟溝集雨系統(tǒng)的敏感性, 同時(shí), 確定參數(shù)優(yōu)化和模型驗(yàn)證的最佳方案, 本文結(jié)合多因素敏感性分析法以及改進(jìn)單純形法(ISM)、粒子群優(yōu)化算法(PSO)和混合粒子群優(yōu)化算法(HPSO), 利用中國(guó)氣象局定西干旱氣象與生態(tài)環(huán)境試驗(yàn)基地2012—2013年壟溝集雨燕麥生長(zhǎng)季降雨、徑流和土壤水分等實(shí)測(cè)數(shù)據(jù), 對(duì)壟溝集雨系統(tǒng)Laio模型的13個(gè)參數(shù)進(jìn)行敏感性分析、優(yōu)化和驗(yàn)證。結(jié)果表明, 平均降水量和凋萎系數(shù)w對(duì)土壤水分概率密度函數(shù)(s)最敏感,(s)對(duì)參數(shù)的敏感性在低土壤含水率下更明顯, 對(duì)參數(shù)w的敏感性在高土壤含水率下更明顯; 3種算法(ISM、PSO和HPSO)的優(yōu)化參數(shù)值均能對(duì)壟溝集雨系統(tǒng)土壤水分概率密度函數(shù)進(jìn)行較好模擬, 峰值(CPV)、峰值位置(PP)和95%置信區(qū)間(CI95%)實(shí)測(cè)值與模擬值的相對(duì)誤差均小于10%, CM指數(shù)均大于0.5; 同時(shí), HPSO算法優(yōu)化參數(shù)的模擬效果和收斂速度均顯著優(yōu)于PSO算法和ISM算法, 能較顯著克服ISM算法和PSO算法存在的缺陷。HPSO算法可作為壟溝集雨系統(tǒng)土壤水分動(dòng)態(tài)隨機(jī)模型參數(shù)優(yōu)化的待選方案。

壟溝集雨系統(tǒng); 土壤水分動(dòng)態(tài); Laio土壤水分動(dòng)態(tài)隨機(jī)模型; 敏感性分析; 模型參數(shù)優(yōu)化

水資源短缺是全球旱地農(nóng)業(yè)面臨的共同難題。如何充分利用天然降雨資源、確保糧食生產(chǎn)安全和維持農(nóng)田生態(tài)系統(tǒng)穩(wěn)定是實(shí)現(xiàn)旱農(nóng)區(qū)“農(nóng)業(yè)-生態(tài)-經(jīng)濟(jì)”耦合系統(tǒng)協(xié)調(diào)、持續(xù)發(fā)展的關(guān)鍵[1]。同時(shí), 研發(fā)和推廣高效、低廉、環(huán)保的旱作栽培技術(shù)對(duì)提高旱農(nóng)區(qū)作物產(chǎn)量及水分利用效率具有重要的意義[2]。壟溝集雨系統(tǒng)利用田間起壟、溝壟相間、壟面產(chǎn)流、溝內(nèi)高效集雨, 并依靠增溫、抑蒸、保土等生理生態(tài)效應(yīng), 已成為水分缺乏的半干旱區(qū)農(nóng)田生態(tài)系統(tǒng)一項(xiàng)重要的集水節(jié)灌措施[3-4]。其在緩解旱農(nóng)區(qū)人口急劇增長(zhǎng)、糧食日益緊缺與農(nóng)業(yè)生態(tài)惡化的矛盾中發(fā)揮著至關(guān)重要的作用。

土壤水分是半干旱農(nóng)田生態(tài)系統(tǒng)植物水分的主要來(lái)源, 是養(yǎng)分循環(huán)和流動(dòng)的載體, 在土壤-植被-大氣系統(tǒng)物質(zhì)和能量轉(zhuǎn)化中起著核心和紐帶的重要作用[5]。認(rèn)識(shí)半干旱農(nóng)田生態(tài)系統(tǒng)與土壤水分關(guān)系和相互作用機(jī)理, 對(duì)揭示農(nóng)田生態(tài)系統(tǒng)穩(wěn)定性及其水土關(guān)鍵要素的變化過(guò)程具有重要意義[6]。由于影響土壤水分動(dòng)態(tài)的各因素(降水、蒸散發(fā)、土壤異質(zhì)性、地形等)具有隨機(jī)性, 特別是降雨事件發(fā)生及降雨量分布的隨機(jī)性, 決定了土壤水分動(dòng)態(tài)模型只有以概率形式描述才更具有實(shí)際意義[7]。自Eagleson等[8]首次將隨機(jī)理念納入土壤水量平衡方程, Milly[9]、Rodriguez-Iturbe等[10]、Laio等[11]、Porporato等[12]、Pan等[13]先后對(duì)不同時(shí)空尺度的土壤水分動(dòng)態(tài)建立了隨機(jī)數(shù)學(xué)模型, 并得到廣泛應(yīng)用。Laio土壤水分動(dòng)態(tài)隨機(jī)模型(Laio模型)在蒸散發(fā)項(xiàng)上引進(jìn)了2個(gè)土壤水分臨界值(凋萎系數(shù)和吸濕系數(shù)), 能對(duì)干旱半干旱區(qū)農(nóng)田生態(tài)系統(tǒng)土壤水分動(dòng)態(tài)進(jìn)行更真實(shí)地描述, 可為旱農(nóng)區(qū)土壤水分的有效利用與管理提供理論指導(dǎo)。

由于半干旱區(qū)壟溝集雨系統(tǒng)土壤水分與多種物理、化學(xué)和生物過(guò)程以及降雨、徑流、蒸散發(fā)、土壤特性、微地形及覆蓋材料等密切相關(guān), 長(zhǎng)期處于動(dòng)態(tài)變化狀態(tài), 且變化過(guò)程比較復(fù)雜[14-16], 所以利用Laio模型對(duì)該系統(tǒng)土壤水分動(dòng)態(tài)進(jìn)行模擬和研究是很有必要的。Laio模型共涉及土壤、植被和氣候等13個(gè)參數(shù), 部分參數(shù)很難通過(guò)觀測(cè)直接獲取, 且參數(shù)值存在極大不確定性[17-18]。故在模型應(yīng)用前需考慮模型“本地化”和“區(qū)域化”問(wèn)題, 即需對(duì)模型參數(shù)進(jìn)行敏感性分析和優(yōu)化。目前針對(duì)Laio模型參數(shù)敏感性及獲取方法已有相關(guān)研究, 如姚淑霞等[7]在科爾沁沙地對(duì)Laio模型參數(shù)敏感性進(jìn)行了分析, 并將參數(shù)按敏感性強(qiáng)弱分為了3類; Milly等[9]對(duì)Laio模型參數(shù)的獲取及敏感性分析發(fā)現(xiàn), 最大蒸散量(max)和水分脅迫點(diǎn)(*)最難獲取, 且敏感性也最強(qiáng); 任慶福[17]利用PSO算法對(duì)太行山山前平原典型井灌農(nóng)區(qū)Laio模型參數(shù)進(jìn)行了優(yōu)化, 發(fā)現(xiàn)經(jīng)率定的參數(shù)能更好地模擬作物生長(zhǎng)期土壤水分的隨機(jī)變化特征。然而, 對(duì)不同含水率條件下壟溝集雨系統(tǒng)Laio模型參數(shù)的敏感性, 以及各種優(yōu)化算法對(duì)模型參數(shù)優(yōu)化的適應(yīng)度和有效性尚缺乏系統(tǒng)研究。鑒此, 建立方便可行的壟溝集雨系統(tǒng)Laio模型參數(shù)優(yōu)化、敏感性分析和有效性驗(yàn)證的方法體系對(duì)提高參數(shù)率定效率, 控制模型計(jì)算誤差和拓寬模型應(yīng)用領(lǐng)域具有極其重要的意義。

本文利用中國(guó)氣象局定西干旱氣象與生態(tài)環(huán)境試驗(yàn)基地2012—2013年壟溝集雨燕麥()生長(zhǎng)季降雨、徑流和土壤水分等實(shí)測(cè)數(shù)據(jù)資料, 采用多因素敏感性分析法, 對(duì)半干旱區(qū)壟溝集雨系統(tǒng)Laio土壤水分動(dòng)態(tài)隨機(jī)模型參數(shù)敏感性進(jìn)行分析和分類。同時(shí), 基于ISM、PSO和HPSO算法, 對(duì)壟溝集雨系統(tǒng)Laio模型的13個(gè)參數(shù)進(jìn)行優(yōu)化和優(yōu)選, 并利用實(shí)測(cè)數(shù)據(jù)資料對(duì)3種算法優(yōu)化參數(shù)的有效性進(jìn)行驗(yàn)證和評(píng)價(jià), 以期建立壟溝集雨系統(tǒng)Laio模型參數(shù)敏感性分析、優(yōu)化和驗(yàn)證的有效方法體系, 為L(zhǎng)aio模型參數(shù)校正和區(qū)域應(yīng)用提供科學(xué)理論依據(jù)。

1 材料與方法

1.1 田間試驗(yàn)和數(shù)據(jù)測(cè)定

試驗(yàn)于2012—2013年在中國(guó)氣象局蘭州干旱氣象研究所定西干旱氣象與生態(tài)環(huán)境試驗(yàn)基地(35°33′N, 104°35′E, 海拔1 896.7 m)進(jìn)行, 該基地屬黃土高原西部丘陵區(qū)和半干旱地區(qū), 具有典型的溫帶大陸性季風(fēng)氣候[16]。1971—2014年平均降雨量388 mm, 冬季和夏季月平均降雨量分別為20~80 mm和150~270 mm。降雨在年內(nèi)分布極不均勻, 7—10月降雨量占年降雨量的86.9%, 蒸發(fā)強(qiáng)烈, 年均潛在蒸發(fā)量達(dá)1 500 mm。試驗(yàn)地地勢(shì)平坦, 土壤為重壤土, 0~100 cm土壤平均容重為1.38 g·cm-3, 田間持水量為25.60%, 飽和含水量為43.87%, 永久凋萎系數(shù)為6.70%, 地下水埋深10.4 m, 土壤水與地下水的水力聯(lián)系微弱。當(dāng)?shù)馗髦贫葹橐荒?熟, 主要種植作物有春小麥()、燕麥和馬鈴薯()等, 主要種植牧草有紫花苜蓿()和紅豆草()等。

試驗(yàn)采用田間壟溝集雨覆蓋種植技術(shù), 以燕麥為指示作物, 壟覆蓋作為集雨區(qū), 溝無(wú)覆蓋作為種植區(qū), 小區(qū)隨機(jī)排列, 共設(shè)9個(gè)處理(3種溝壟比×3種覆蓋材料), 重復(fù)3次。3種覆蓋材料分別為生物可降解膜、普通塑料膜和土壤結(jié)皮, 3種溝壟比分別為60 cm︰30 cm、60 cm︰45 cm和60 cm︰60 cm(溝寬︰壟寬)。生物可降解地膜和普通塑料膜厚度均為0.08 mm; 土壟為人工原土夯實(shí), 經(jīng)風(fēng)吹雨打形成自然土壤結(jié)皮。土壟、生物可降解地膜壟和普通地膜壟的代表符號(hào)分別為SR、BMR和CMR。根據(jù)當(dāng)?shù)胤N植經(jīng)驗(yàn), 集雨壟的坡度為40°, 高為25 cm, 長(zhǎng)為10 m, 每1小區(qū)有4條壟和3條溝。試驗(yàn)設(shè)計(jì)見表1，種植示意圖見圖1。相關(guān)種植管理方法按前期研究者[19]所述進(jìn)行。由于本試驗(yàn)3種溝壟比對(duì)該系統(tǒng)土壤水分時(shí)空動(dòng)態(tài)影響不顯著[16-19], 故本文土壤含水量均為同一覆蓋材料下, 3種試驗(yàn)溝壟比之均值。

表1 壟溝集雨種植燕麥試驗(yàn)設(shè)計(jì)

圖1 壟溝集雨種植燕麥?zhǔn)疽鈭D

試驗(yàn)期降雨量數(shù)據(jù)由試驗(yàn)基地自記雨量計(jì)測(cè)定。土壤含水量采用烘干法(105 ℃, 10 h)于燕麥播種前(4月10日左右)、收獲后(8月20日左右)和降雨后(降雨量>5 mm)測(cè)定, 測(cè)定深度140 cm, 分層深度為20 cm, 共記錄7個(gè)土層的土壤含水量, 每1小區(qū)隨機(jī)在溝內(nèi)選取3個(gè)樣點(diǎn), 同一層次土壤含水量取3個(gè)樣點(diǎn)平均值。集雨壟徑流量由降雨量數(shù)據(jù)基于美國(guó)水土保持局研制的SCS-CN模型反推確定[20]。土壤容重采用環(huán)刀法測(cè)定, 測(cè)定深度140 cm, 分層深度為20 cm, 每層3個(gè)重復(fù), 取均值。根系層深度通過(guò)實(shí)地調(diào)查燕麥根系生物量分布范圍測(cè)定[7]。同期氣象數(shù)據(jù)由鄰近的試驗(yàn)基地氣象觀測(cè)站獲得。

1.2 Laio土壤水分動(dòng)態(tài)隨機(jī)模型

土壤水分隨機(jī)模型的理論基礎(chǔ)是物質(zhì)平衡原理: 單位時(shí)間內(nèi)土壤含水量的變化等于土壤水分輸入項(xiàng)和水分損失項(xiàng)的差。基于前期研究者[21]對(duì)土壤水分隨機(jī)模型的研究, Laio等[11]通過(guò)引進(jìn)兩個(gè)臨界土壤含水量(土壤吸濕系數(shù)和土壤凋萎系數(shù)), 在空間一點(diǎn)上建立了時(shí)間尺度為1 d的土壤水分平衡方程, 具體模型(Laio模型)可表述為:

將降雨隨機(jī)過(guò)程同土壤水分損失項(xiàng)(土壤水蒸散發(fā)與深層滲漏之和)相結(jié)合是土壤水分隨機(jī)模型建立的基礎(chǔ)[21-22]。由于降雨是隨機(jī)過(guò)程, 故需建立土壤水分概率密度函數(shù)求解土壤水平衡過(guò)程(公式1)。通過(guò)將Laio模型的各土壤水分損失過(guò)程轉(zhuǎn)化為查普曼-柯爾莫哥洛夫前進(jìn)方程(Chapman- Kolmogorov Forward Function)可分析求解導(dǎo)出土壤水分概率密度函數(shù), 其具體表達(dá)式[7,11,21-22]為:

表2 壟溝集雨系統(tǒng)Laio模型參數(shù)取值范圍及其不同覆蓋處理的初始值

表中模型參數(shù)取值范圍由相關(guān)實(shí)測(cè)數(shù)據(jù)和文獻(xiàn)資料[11,16]獲得。UBV: 參數(shù)取值下限; LBV: 參數(shù)取值上限。Values ranges of model parameters in the table were obtained from the relevant measured data and literatures[11,16]. UBV: upper bound value of model parameter; LBV: lower bound value of model parameter.

1.3 模型參數(shù)敏感性分析原理

模型參數(shù)的敏感性分析是研究參數(shù)變化所引起的模型響應(yīng), 是模型參數(shù)不確定分析的重要內(nèi)容之一, 也是研發(fā)和評(píng)價(jià)模型不可缺少的重要環(huán)節(jié)[23]。同時(shí), 參數(shù)敏感性分析有助于深入理解模型的特性并改進(jìn)模型結(jié)構(gòu)的穩(wěn)定性[24]。為不失一般性, 可將土壤水分概率密度函數(shù)表示為:

1.4 模型參數(shù)優(yōu)化算法原理

1.4.1 改進(jìn)單純形法尋優(yōu)原理

1.4.2 粒子群優(yōu)化算法尋優(yōu)原理

1.4.3 混合粒子群優(yōu)算法尋優(yōu)原理

為提高優(yōu)化算法在全局和局部意義下的搜索能力和收斂效率, 以粒子群優(yōu)算法流程為基礎(chǔ), 引入改進(jìn)單純形搜索方法構(gòu)成混合粒子群優(yōu)算法(Hybrid Particle Swarm Optimization, HPSO)[29], 即在每1次迭代中先用PSO算法對(duì)群體進(jìn)行全局尋優(yōu), 然后通過(guò)ISM算法對(duì)粒子群中部分精英粒子在其較優(yōu)解領(lǐng)域內(nèi)進(jìn)行局部搜索, 尋找更優(yōu)解。

1.5 Laio模型轉(zhuǎn)換與參數(shù)優(yōu)化

1.6 模型的驗(yàn)證與評(píng)價(jià)方法

通過(guò)比較研究區(qū)不同處理實(shí)測(cè)土壤水分概率密度函數(shù)曲線與ISM、PSO和HPSO算法優(yōu)化參數(shù)值模擬曲線的特征, 評(píng)價(jià)以上3種算法對(duì)Laio模型參數(shù)優(yōu)化的有效性。驗(yàn)證評(píng)價(jià)指標(biāo)選擇CM(Consistency Measure)指數(shù)[32], 其表示兩目標(biāo)曲線的一致性程度, 計(jì)算方法如下:

式中: 表示目標(biāo)曲線1下方的面積, 表示目標(biāo)曲線2下方的面積, 表示目標(biāo)曲線1和目標(biāo)曲線2下方的公共面積(圖2a, b, c)。顯然, 目標(biāo)曲線1與目標(biāo)曲線2一致性越好, 越大, CM指數(shù)越大; 反之, 一致性越差, 越小, CM指數(shù)越小。CM指數(shù)的變化范圍為[0, 1], 當(dāng)CM=1時(shí), 表明目標(biāo)曲線1和目標(biāo)曲線2一致性最佳; 當(dāng)CM=0時(shí), 表明目標(biāo)曲線1和目標(biāo)曲線2之間不存在一致性(見圖2d, e)。

2 結(jié)果與分析

2.1 Laio模型參數(shù)敏感性分析

圖3 不同土壤含水率下不同覆蓋處理的壟溝集雨系統(tǒng)Laio模型各參數(shù)敏感性分析

模型參數(shù)的意義見表2。Meanings of parameters are shown in the table 2.

圖4 基于SOM神經(jīng)網(wǎng)絡(luò)聚類法的壟溝集雨系統(tǒng)Laio模型參數(shù)敏感性分類

模型參數(shù)的意義見表2。Meanings of parameters are shown in the table 2.

圖5 參數(shù)α(生長(zhǎng)季平均降水量)和sw(凋萎系數(shù))對(duì)壟溝集雨系統(tǒng)土壤水分概率密度函數(shù)[p(s)]的影響

2.2 基于ISM、PSO和HPSO算法的模型參數(shù)優(yōu)化

為確保算法的優(yōu)化精度和有效性, 當(dāng)算法運(yùn)行過(guò)程中符合下列3個(gè)終止準(zhǔn)則之一時(shí)停止計(jì)算[35]。準(zhǔn)則1: 兩次迭代的最優(yōu)目標(biāo)函數(shù)值對(duì)應(yīng)的參數(shù)距離小于給定精度1≤10-5; 準(zhǔn)則2: 兩次迭代的目標(biāo)函數(shù)值之差小于給定精度2≤10-5; 準(zhǔn)則3: 循環(huán)的最大次數(shù)已達(dá)到。同時(shí), 為盡可能消除算法隨機(jī)性對(duì)各算法比較的影響, 每個(gè)優(yōu)化算法均隨機(jī)獨(dú)立運(yùn)行10次后取各參數(shù)平均最優(yōu)解和計(jì)算效率。算法運(yùn)行結(jié)果和優(yōu)化參數(shù)驗(yàn)證見表3及圖6所示。

從3種優(yōu)化算法(ISM、PSO和HPSO)對(duì)Laio模型參數(shù)優(yōu)化結(jié)果(表3)和優(yōu)化效率(圖6)可看出, ISM算法優(yōu)化參數(shù)的有效性明顯低于另外兩種算法, 其對(duì)模型參數(shù)初始值依賴性較強(qiáng), 如果不事先用具有較強(qiáng)全局尋優(yōu)能力的算法獲取一組較優(yōu)初始值, 其優(yōu)化結(jié)果將易陷入局部最優(yōu)。PSO算法具有較強(qiáng)的全局尋優(yōu)能力, 優(yōu)化參數(shù)的有效性較強(qiáng), 但其在算法迭代后期收斂速度相對(duì)較慢, 存在有早熟、局部收斂等缺陷。HPSO算法優(yōu)化參數(shù)的有效性明顯優(yōu)于ISM算法和PSO算法的優(yōu)化解, 其不但具有較強(qiáng)的全局搜索能力, 而且具有較快的收斂速度, 能較顯著地克服ISM算法和PSO算法相互存在的缺陷。這與陳俊風(fēng)等[29]對(duì)HPSO算法的仿真實(shí)驗(yàn)結(jié)論相一致, 說(shuō)明其有利于增強(qiáng)全局和局部意義下優(yōu)化結(jié)果的可靠性和算法的優(yōu)化性能, 是求解優(yōu)化問(wèn)題的一種有效的算法。

表3 基于ISM、PSO和HPSO算法的壟溝集雨系統(tǒng)Laio模型參數(shù)優(yōu)化結(jié)果

模型參數(shù)的意義見表2。Meanings of parameters are shown in the table 2.

圖6 基于ISM、PSO和HPSO算法的壟溝集雨系統(tǒng)Laio模型參數(shù)優(yōu)化效率和有效性驗(yàn)證

SMC: 土壤含水量; NCF: 正態(tài)曲線擬合; SPSO: PSO優(yōu)化參數(shù)模擬曲線; SISM: ISM優(yōu)化參數(shù)模擬曲線; SHPSO: HPSO優(yōu)化參數(shù)模擬曲線。SMC: soil moisture content; NCF: normal curve fitting; SPSO: simulating curves with PSO-optimized parameters; SISM: simulating curves with ISM-optimized; SHPSO: simulating curves with HPSO-optimized parameters.

2.3 模型參數(shù)有效性驗(yàn)證與評(píng)價(jià)

采用試驗(yàn)區(qū)2012—2013年田間壟溝集雨系統(tǒng)各處理(SR、CMR和BMR)降雨、徑流、土壤含水率等實(shí)測(cè)數(shù)據(jù)資料, 基于3種算法(ISM、PSO和HPSO)對(duì)Laio模型參數(shù)優(yōu)化值, 比較模型模擬與實(shí)測(cè)的土壤水分概率密度函數(shù)在曲線形狀[峰值、峰值出現(xiàn)的位置, 95%置信區(qū)間(CI95%)]和CM指數(shù)之間的匹配程度, 評(píng)價(jià)3種算法對(duì)Laio模型參數(shù)優(yōu)化的有效性, 選擇較優(yōu)模型參數(shù)優(yōu)化值及參數(shù)優(yōu)選算法類型。圖6和表4為3種算法的壟溝集雨系統(tǒng)Laio模型優(yōu)化參數(shù)有效性驗(yàn)證與評(píng)價(jià)結(jié)果。

表4 基于ISM、PSO和HPSO算法的壟溝集雨系統(tǒng)Laio模型參數(shù)優(yōu)化性能比較

CPV: 峰值; PP: 峰值位置; CI95%: 95%置信區(qū)間; CM: 一致性指數(shù)。CPV: the curve peak value; PP: the position of the peak; CI95%: the confidence interval of 95%; CM: the consistency measure.

從圖6和表4可看出, 3種算法優(yōu)化模型參數(shù)值均能比較準(zhǔn)確地描繪出曲線的形狀, 捕捉到峰值的位置, 描述出土壤水分概率密度函數(shù)的主要特征, 且CPV、PP和CI95%實(shí)測(cè)值與模擬值相對(duì)誤差均小于10%, CM指數(shù)均大于0.5, 說(shuō)明3種算法優(yōu)化參數(shù)值對(duì)壟溝集雨系統(tǒng)土壤水分概率密度函數(shù)模擬效果較好。同時(shí), HPSO算法優(yōu)化參數(shù)的模擬效果(CM指數(shù)均值為0.901)優(yōu)于PSO算法(CM指數(shù)均值為0.848), PSO算法優(yōu)于ISM算法(CM指數(shù)均值為0.678), 且HPSO算法優(yōu)化參數(shù)的收斂速度(進(jìn)化代數(shù)均值為285)均快于PSO算法(進(jìn)化代數(shù)均值為503), 說(shuō)明HPSO算法優(yōu)化模型參數(shù)值可較顯著提高壟溝集雨系統(tǒng)土壤水分概率密度模擬精度和效率,故HPSO算法可作為該系統(tǒng)土壤水分動(dòng)態(tài)隨機(jī)模型參數(shù)優(yōu)選的較優(yōu)待選方案。但是, 相關(guān)研究表明[36], 全局算法與局部算法相混合得到的混合優(yōu)化算法,盡管可以提高局部收斂速度和性能, 但也加劇了陷入局部極小的可能。因此, 構(gòu)建能顯著提高局部搜索能力, 且能高概率搜索全局最優(yōu)解的混合優(yōu)化算法, 有待進(jìn)一步深入的研究。

3 結(jié)論

本文采用多因素敏感性分析法, 對(duì)半干旱區(qū)壟溝集雨系統(tǒng)Laio土壤水分動(dòng)態(tài)隨機(jī)模型參數(shù)的敏感性進(jìn)行了分析和分類。同時(shí), 基于3種優(yōu)化算法(ISM、PSO和HPSO), 對(duì)壟溝集雨系統(tǒng)Laio模型的13個(gè)參數(shù)進(jìn)行了優(yōu)化和優(yōu)選, 并利用實(shí)測(cè)數(shù)據(jù)資料對(duì)3種算法優(yōu)化參數(shù)的有效性進(jìn)行了驗(yàn)證和評(píng)價(jià)。得到的主要結(jié)論如下:

3)3種算法的優(yōu)化參數(shù)值均能較好地模擬壟溝集雨系統(tǒng)土壤水分概率密度函數(shù), 各處理的CPV、PP和CI95%實(shí)測(cè)值與模擬值相對(duì)誤差均小于10%, CM指數(shù)均大于0.5。

4)HPSO算法優(yōu)化參數(shù)的模擬效果和收斂速度均顯著優(yōu)于PSO算法和ISM算法, 且能較顯著克服ISM算法和PSO算法存在的缺陷, HPSO算法可作為壟溝集雨系統(tǒng)土壤水分動(dòng)態(tài)隨機(jī)模型參數(shù)優(yōu)選的較優(yōu)待選方案。

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Sensitivity analysis and optimization of parameters for Laio soil moisture dynamic stochastic model for ridge-furrow rainwater harvesting system*

YIN Xinwei1,2, LI Xiaoling3, WANG Qi4**, ZHANG Yongmei1,2

(1. Fukang Station for Desert Ecosystem Observation and Experiment / Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China; 2. University of Chinese Academy of Sciences, Beijing 100049, China; 3. College of Water Conservancy and Hydropower Engineering, Gansu Agricultural University, Lanzhou 730070, China; 4. College of Grassland Science, Gansu Agricultural University, Lanzhou 730070, China)

Sensitivity analysis of parameters, calibration and validation of eco-hydrological modelsare essential for model evaluation and application. It is important in model application to accurately estimate the values of model parameters and to further improve model prediction capacity. Based on eco-hydrological process, the Laio soil moisture dynamics stochastic model (Laio model) was used to describe daily water balance in active soil depth of ridge-furrow rainwater harvest system during growing season to analyze the effects of the interactions among plants, soil and environment under different climatic conditions on soil water balance and plant water conditions. The performance of the Laio model varied with climatic zone due to the heterogeneity of climate, vegetation and soil characteristics. In this study, in order to establish an effective system for parameter sensitivity analysis, calibration and validation of the Laio model in a ridge-furrow rainwater harvesting system in a semi-arid area, a field experiment with a randomized complete block design was conducted during the 2012 and 2013 oat growing seasons at Dingxi Arid Meteorology and Ecological Environment Experimental Station. The experiment was designed to investigate the parameter sensitivity and to determine the optimal mode of parameter optimization of the Laio model under various mulching materials (common plastic film, biodegradable film mulch and manually compacted soil) and various ridge-furrow ratios (60 cm∶30 cm, 60 cm∶45 cm and 60 cm∶60 cm). The methods included multi-factor sensitivity analysis, simplex method (ISM), particle swarm optimization algorithm (PSO) and hybrid particle swarm optimization algorithm (HPSO). Also continuously monitored soil moisture, precipitation runoff and daily precipitation data for 2012–2013 were used to run the model. The results indicated that: (1) mean precipitation per rainfall event () and soil saturation degree at wilting point (w) were the most sensitive parameters for probabilistic density function of soil moisture [(s)] in different experimental treatments. While the sensitivity of(s) towas more obvious under low soil moisture content, that towwas more obvious under high soil moisture content. (2) There were good agreements among the results of modelling using optimized parameters of the Laio model for the three optimization algorithms (ISM, PSO and HPSO) and the observation values, which were determined from the(s) curve. This included curve peak value (CPV), curve peak position (PP), 95% confidence interval (CI95%) and consistency measure (CM). All of these indicated that the optimized parameters of the Laio model using the ISM, PSO and HPSO methods correctly estimated(s) of ridge-furrow rainwater harvesting. (3) The HPSO method not only improved global optimization performance, but also quickened convergence and gave robust results with good quality. It was an effective optimization method for the Laio model calibration and validation. The study improved the efficiency of model parameter calibration, upgraded the accuracy of model simulation results and provided guidance for application of the Laio model in ridge-furrow rainwater harvesting research.

Ridge-furrow rainwater harvesting system; Soil moisture dynamic; Laio soil moisture dynamic stochastic model; Sensitivity analysis; Model parameter optimization

, E-mail: wangqigsau@gmail.com

Aug. 14, 2017;

Nov. 28, 2017

10.13930/j.cnki.cjea.170737

S152.7

A

1671-3990(2018)05-0746-13

王琦, 主要從事牧草、草坪及作物節(jié)水灌溉方面研究。E-mail: wangqigsau@gmail.com 尹鑫衛(wèi), 主要研究方向?yàn)楦珊祬^(qū)水文生態(tài)學(xué)。E-mail: xinweiyin@foxmail.com

2017-08-14

2017-11-28

* This study was supported by the National Natural Science Foundation of China (41461062, 41661059).

* 國(guó)家自然科學(xué)基金項(xiàng)目(41461062, 41661059)資助

尹鑫衛(wèi), 李曉玲, 王琦, 張永梅. 壟溝集雨系統(tǒng)Laio土壤水分動(dòng)態(tài)隨機(jī)模型參數(shù)敏感性分析及優(yōu)化[J]. 中國(guó)生態(tài)農(nóng)業(yè)學(xué)報(bào), 2018, 26(5): 746-758

YIN X W, LI X L, WANG Q, ZHANG Y M. Sensitivity analysis and optimization of parameters for Laio soil moisture dynamic stochastic model for ridge-furrow rainwater harvesting system[J]. Chinese Journal of Eco-Agriculture, 2018, 26(5): 746-758