鄭 策，高萬(wàn)德，陳云飛，盧玉東，劉秀花

季節(jié)性凍土區(qū)包氣帶水汽熱耦合運(yùn)移研究進(jìn)展

鄭 策，高萬(wàn)德，陳云飛，盧玉東，劉秀花※

（1. 長(zhǎng)安大學(xué)水利與環(huán)境學(xué)院，西安 710064；2. 長(zhǎng)安大學(xué)旱區(qū)地下水文與生態(tài)效應(yīng)教育部重點(diǎn)實(shí)驗(yàn)室，西安 710064）

季節(jié)性凍土區(qū)占據(jù)中國(guó)超過(guò)一半的國(guó)土面積，凍融作用會(huì)顯著改變土壤性質(zhì)與包氣帶水、熱傳輸過(guò)程，并且由于溫度與氣態(tài)水對(duì)土壤水分運(yùn)移影響顯著，開(kāi)展水汽熱耦合研究對(duì)于探究季節(jié)性凍土區(qū)土壤水循環(huán)過(guò)程十分關(guān)鍵。該研究綜述了包氣帶水汽熱耦合運(yùn)移理論的提出與發(fā)展歷程，闡明了季節(jié)性凍融作用對(duì)水汽熱耦合運(yùn)移研究中水力參數(shù)及水分相態(tài)轉(zhuǎn)化過(guò)程的影響，探討了水汽熱耦合模型適用性，總結(jié)了溫度梯度驅(qū)動(dòng)下氣態(tài)水運(yùn)移規(guī)律及其重要性，并對(duì)該領(lǐng)域尚需加強(qiáng)研究的方向提出建議：1）聚焦“土壤-植被-大氣”系統(tǒng)水循環(huán)過(guò)程，構(gòu)建適用于季節(jié)性凍土區(qū)的包氣帶水汽熱-植被耦合模型，探究土壤水資源生態(tài)效應(yīng)，為植被恢復(fù)與生態(tài)系統(tǒng)穩(wěn)定提供理論指導(dǎo)；2）在寒旱區(qū)工程建設(shè)中考慮氣態(tài)水的影響，明確覆蓋層下水汽運(yùn)移機(jī)理，對(duì)建設(shè)過(guò)程中由水汽運(yùn)移引起的工程病害提出具體防治措施。通過(guò)本研究梳理歸納以期為深化包氣帶水汽熱耦合運(yùn)移理論以及解決季節(jié)性凍土區(qū)相關(guān)實(shí)際問(wèn)題提供科學(xué)依據(jù)與參考。

水；熱；數(shù)值分析；包氣帶；水汽運(yùn)移；水文循環(huán)；季節(jié)性凍土區(qū)

0 引 言

包氣帶作為地球關(guān)鍵帶的重要組成部分，不僅是大氣圈、水圈、巖石圈等相互作用的聯(lián)系紐帶，也為土-氣界面間質(zhì)能交換、土壤水熱傳輸以及植物根系吸水等水分與能量交換活動(dòng)提供了場(chǎng)所[1]。土壤和水是包氣帶中的核心要素，其中水是進(jìn)行質(zhì)、能交換的主要驅(qū)動(dòng)力，土壤水分變化反映了蒸發(fā)、入滲、徑流、截留、滲漏等多界面的水文過(guò)程及土壤水文性質(zhì)[2-4]。傳統(tǒng)的包氣帶水分運(yùn)移研究主要圍繞液態(tài)水展開(kāi)，而忽略了氣態(tài)水的影響。近年來(lái)隨著研究深入，包氣帶氣態(tài)水運(yùn)移及水-汽相變過(guò)程對(duì)于土壤水、熱傳輸過(guò)程的影響逐漸被證實(shí)[5-6]。尤其是對(duì)于干旱半干旱地區(qū)，氣態(tài)水可為生態(tài)脆弱區(qū)植被生長(zhǎng)及生態(tài)系統(tǒng)穩(wěn)定提供重要水分來(lái)源，其作用不可被忽略[7-8]。

中國(guó)是世界上凍土分布面積第三大國(guó)，其中季節(jié)性凍土區(qū)占據(jù)超過(guò)一半的國(guó)土面積，且多數(shù)季節(jié)性凍土廣泛分布于干旱半干旱地區(qū)[9]。在這些地區(qū)，降雨稀少且蒸發(fā)強(qiáng)烈，土壤干燥缺水，土地荒漠化突出，冬季土壤年凍結(jié)時(shí)間長(zhǎng)達(dá)4～6個(gè)月。季節(jié)性凍融作用不僅會(huì)引起諸如土壤結(jié)構(gòu)、容重等物理性質(zhì)發(fā)生變化，同時(shí)會(huì)顯著改變包氣帶水、熱特性及其傳輸過(guò)程，進(jìn)而影響到區(qū)內(nèi)農(nóng)業(yè)生產(chǎn)及諸多工程建設(shè)活動(dòng)[10-12]。相比于非凍結(jié)時(shí)期，凍結(jié)期內(nèi)由于土壤孔隙中冰的存在會(huì)阻礙液態(tài)水運(yùn)移，氣態(tài)水在土壤水分運(yùn)移中的影響會(huì)更加明顯，開(kāi)展包氣帶水汽熱耦合研究對(duì)于厘清季節(jié)性凍土區(qū)土壤水循環(huán)過(guò)程尤為關(guān)鍵[13]。然而，關(guān)于季節(jié)性凍土區(qū)包氣帶水汽熱耦合運(yùn)移的研究現(xiàn)狀及應(yīng)加強(qiáng)研究的重點(diǎn)領(lǐng)域鮮有報(bào)道。

鑒于此，本文綜述包氣帶水汽熱耦合運(yùn)移理論的提出與發(fā)展過(guò)程，闡述季節(jié)性凍融作用對(duì)水汽熱耦合運(yùn)移研究的具體影響，探討數(shù)值模擬技術(shù)在包氣帶水汽熱耦合運(yùn)移研究中的應(yīng)用，總結(jié)溫度梯度驅(qū)動(dòng)下氣態(tài)水運(yùn)移規(guī)律及其影響，并從季節(jié)性凍土區(qū)研究實(shí)際需求的視角提出了未來(lái)亟待加強(qiáng)研究的重點(diǎn)方向，以期為深化包氣帶水汽熱耦合運(yùn)移理論以及解決季節(jié)性凍土區(qū)相關(guān)實(shí)際問(wèn)題提供科學(xué)依據(jù)。

1 包氣帶水汽熱耦合運(yùn)移理論

1.1 理論提出與發(fā)展

基于Richards方程，包氣帶水分運(yùn)移研究開(kāi)始由靜態(tài)、定性描述為主向動(dòng)態(tài)、定量分析的方向發(fā)展。而隨著水汽運(yùn)移概念的提出，Philip等[14]首次將非等溫條件下水汽運(yùn)移過(guò)程引入包氣帶水分運(yùn)移研究中，提出了包氣帶水汽熱耦合運(yùn)移理論，即最初的PDV理論。PDV理論認(rèn)為當(dāng)土壤顆粒間存在溫度差時(shí)土壤水分會(huì)在較熱一端蒸發(fā)、較冷一端凝結(jié)，總體蒸發(fā)與凝結(jié)速率相等，即為水汽運(yùn)移速率，包氣帶總水分通量可被看作是由溫度梯度與含水量梯度分別驅(qū)動(dòng)下的水、汽通量組成。以PDV理論為基礎(chǔ)，眾多學(xué)者圍繞水汽熱耦合運(yùn)移過(guò)程展開(kāi)研究并不斷完善相關(guān)理論。例如，Hanks等[15]提出若忽略溫度影響，計(jì)算蒸發(fā)量時(shí)會(huì)產(chǎn)生約10%的誤差，且這一比例在干旱條件下會(huì)增大；Milly[16]提出水分運(yùn)移的驅(qū)動(dòng)力之一應(yīng)為基質(zhì)勢(shì)而不是PDV模型中的含水量，由此模型可被用于非均質(zhì)土壤中的研究；Cass[17]提出了水汽通量的增強(qiáng)因子計(jì)算方式；Cahill等[18]通過(guò)野外試驗(yàn)證明淺層土壤中水汽通量不僅占據(jù)總水分通量的25%，同時(shí)也導(dǎo)致了超過(guò)50%的熱通量。

當(dāng)冬季土壤凍結(jié)后，包氣帶孔隙中水、汽、冰三相共存（圖1）。隨溫度降低/升高，包氣帶中未凍水含量減小/增大，冰-水相變過(guò)程對(duì)于包氣帶水、熱運(yùn)移過(guò)程影響顯著?；诙嗫捉橘|(zhì)水分運(yùn)移和熱平衡理論，Harlan[19]首次提出了適用于非飽和凍土研究的水熱耦合模型，并利用有限差分法求解模型。隨后，Cary等[20-22]逐步完善了Harlan模型，如建立了液態(tài)水與溫度之間的聯(lián)系等。然而由于水-汽-冰-熱耦合復(fù)雜性，在早期非飽和凍土水分運(yùn)移研究中并未考慮氣態(tài)水的影響。逐漸地，Nakano等[23-25]研究結(jié)果均指出深層氣態(tài)水不斷向凍結(jié)鋒處運(yùn)移會(huì)促進(jìn)冰的形成，并且會(huì)主導(dǎo)凍層內(nèi)水分運(yùn)移過(guò)程，氣態(tài)水對(duì)凍結(jié)情況下土壤水、熱傳輸過(guò)程的重要性逐漸被認(rèn)可。

1.2 數(shù)學(xué)方程

對(duì)于一維垂向包氣帶水分運(yùn)移過(guò)程，當(dāng)考慮氣態(tài)水、冰以及溫度共同影響時(shí)，土壤水、熱傳輸控制方程可分別表示為如下形式[26]：

式中θ、θ和θ分別為土壤液態(tài)水含水量、氣態(tài)水含水量與含冰量，cm3/cm3；ρ、ρ和ρ分別為液態(tài)水、氣態(tài)水與冰密度，g/cm3；為時(shí)間，d；為垂向坐標(biāo)軸（向上為正），cm；為基質(zhì)勢(shì)，cm；為溫度，K；K和K分別為等溫液態(tài)水與氣態(tài)水水力傳導(dǎo)度，cm/d；K和K分別為非等溫液態(tài)水與氣態(tài)水水力傳導(dǎo)度，cm2/(K·d)；w和L分別為蒸發(fā)潛熱與凍結(jié)潛熱，J/kg；為土壤熱導(dǎo)率，W/(m·K)；q和q分別為土壤液態(tài)水和氣態(tài)水通量，cm/d；C為土壤的體積熱容量，J/(m3·K)；C和C分別表示土壤中液態(tài)水及氣態(tài)水的體積熱容量，J/(m3·K)。

圖1 非飽和凍土中水-汽-冰-熱耦合示意圖

在水分運(yùn)移方程中，方程左端包含了液態(tài)水、氣態(tài)水及含冰量的變化，右端則分別為基質(zhì)勢(shì)梯度、重力勢(shì)梯度及溫度梯度驅(qū)動(dòng)的液態(tài)水運(yùn)移，以及基質(zhì)勢(shì)梯度與溫度梯度驅(qū)動(dòng)的氣態(tài)水運(yùn)移。選取van Genuchten-Mualem公式作為非飽和液態(tài)水水力傳導(dǎo)度計(jì)算公式，式（1）中涉及的傳導(dǎo)度及相關(guān)參數(shù)計(jì)算方式如表1所示[26]。在熱傳導(dǎo)方程中，方程左端包含了土壤熱容量、冰-水相變潛熱及水-汽相變潛熱變化，右端分別為熱傳導(dǎo)、液態(tài)水流動(dòng)引起的熱擴(kuò)散、氣態(tài)水流動(dòng)引起的熱擴(kuò)散及氣態(tài)水相變潛熱。

表1 水力傳導(dǎo)度及相應(yīng)參數(shù)計(jì)算[26]

2 凍融作用對(duì)包氣帶水汽熱耦合運(yùn)移的影響

2.1 水力參數(shù)

由表1可知，包氣帶水汽熱耦合運(yùn)移過(guò)程涉及參數(shù)較多。與未凍結(jié)時(shí)期不同，凍結(jié)后由于冰的存在以及冰-水相變過(guò)程影響，土壤水、熱性質(zhì)發(fā)生改變，探究?jī)鋈谧饔糜绊懴碌陌鼩鈳麩狁詈线\(yùn)移過(guò)程時(shí)需重點(diǎn)關(guān)注以下參數(shù)：

1）土壤凍結(jié)曲線

在土壤凍結(jié)后，包氣帶中未凍水含量變化受土壤溫度（負(fù)溫）影響，兩者之間關(guān)系密切。土壤凍結(jié)曲線不僅可以刻畫土壤水、熱之間聯(lián)系，同時(shí)也是求解水熱傳輸方程中不可或缺的重要參數(shù)，通常情況下可通過(guò)經(jīng)驗(yàn)公式法與土水特征曲線法求取土壤凍結(jié)曲線。

在傳統(tǒng)研究中，學(xué)者們提出了不同形式經(jīng)驗(yàn)公式（冪函數(shù)[27]、線性[28]、指數(shù)函數(shù)[29]等）來(lái)描述土壤凍結(jié)曲線。雖然這些經(jīng)驗(yàn)公式形式簡(jiǎn)單，但由于不同質(zhì)地土壤性質(zhì)變化差異較大，且通過(guò)試驗(yàn)方式獲取適宜的經(jīng)驗(yàn)參數(shù)較為困難，總體上該方法在當(dāng)前研究中應(yīng)用面臨一定困難[30-31]。

另一方面，由于土壤凍結(jié)過(guò)程與土壤逐漸排水干燥過(guò)程相似，在凍結(jié)過(guò)程中水分不斷向凍結(jié)鋒處運(yùn)移，因而可以根據(jù)土水特征曲線的概念得到土壤凍結(jié)曲線[32]。利用Claperon方程建立負(fù)溫與基質(zhì)勢(shì)之間關(guān)系，隨后將其代入Brooks and Corey方程[33]、Garder方程[34]、van Genuchten方程[35]等土水特征曲線中，即可建立負(fù)溫與未凍水含量之間關(guān)系，如下所示（以VG方程為例）[36]：

式中T為液態(tài)水凍結(jié)溫度（可由基質(zhì)勢(shì)計(jì)算得到），K；、、為經(jīng)驗(yàn)參數(shù)。相比于傳統(tǒng)的經(jīng)驗(yàn)公式計(jì)算法，通過(guò)土水特征曲線法求解結(jié)果更加精確且合理，因而被廣泛應(yīng)用[37-38]。

2）非飽和水力傳導(dǎo)度

隨著溫度降低土壤孔隙逐漸被冰占據(jù)，土壤水分在凍土中運(yùn)移過(guò)程受到影響，非飽和水力傳導(dǎo)度顯著減小。通常情況下，土壤凍結(jié)時(shí)非飽和水力傳導(dǎo)度與含冰量密切相關(guān)，其計(jì)算方法主要有3種，分別為半理論方法、經(jīng)驗(yàn)公式法以及基于未凍結(jié)時(shí)期水力傳導(dǎo)度的計(jì)算方法。

第一種方法主要基于毛細(xì)管理論及吸附理論，假設(shè)冰的形成發(fā)生在毛細(xì)管中央，該方法結(jié)果與實(shí)測(cè)值擬合較好，但由于計(jì)算過(guò)程較為復(fù)雜，不易應(yīng)用于數(shù)值模型中[39]。相比較而言，第二種方法計(jì)算過(guò)程簡(jiǎn)單，但與經(jīng)驗(yàn)公式法獲取土壤凍結(jié)曲線類似，該方法中涉及的參數(shù)經(jīng)驗(yàn)值隨土壤性質(zhì)變化較大且不易獲取，因此在相關(guān)研究中同樣較少使用[40]。

由于在前兩種方法存在明顯的局限性，因此在當(dāng)前研究中計(jì)算非飽和凍土中水力傳導(dǎo)度時(shí)通常會(huì)采用第三種方法[41]。該方法認(rèn)為土壤凍結(jié)后非飽和水力傳導(dǎo)度減小的程度與相同基質(zhì)吸力情況下土壤未凍結(jié)時(shí)的水力傳導(dǎo)度數(shù)值有關(guān)，即可以通過(guò)土壤未凍結(jié)時(shí)土水特征曲線與飽和水力傳導(dǎo)度計(jì)算得到。為了體現(xiàn)冰的出現(xiàn)對(duì)水力傳導(dǎo)度降低的影響，Taylor等[42-43]提出了不同形式阻抗因子的概念，由于該方法考慮了凍融過(guò)程實(shí)際影響，其參數(shù)具有一定的物理含義，并且使用較為便利，因而被廣泛應(yīng)用。盡管如此，該方法同樣存在不足之處，如凍結(jié)（或融化）過(guò)程中基質(zhì)勢(shì)不斷變化而阻抗因子為定值、不同未凍水含量情況下阻抗因子的確定等問(wèn)題，亟待進(jìn)一步研究[41,44]。

2.2 水分相態(tài)轉(zhuǎn)化

季節(jié)性凍融作用引發(fā)冰-水相變過(guò)程，對(duì)于土壤水分時(shí)空分布以及水分運(yùn)移過(guò)程影響明顯。根據(jù)質(zhì)量守恒定律，非飽和凍土中總含水量由固、液、氣三相組成，如式（4）所示。

式中為土壤總含水量，cm3/cm3。當(dāng)土壤溫度低于凍結(jié)點(diǎn)（由于土壤處于非飽和狀態(tài)，凍結(jié)點(diǎn)會(huì)略低于0 ℃），土壤孔隙中的液態(tài)水開(kāi)始轉(zhuǎn)化為冰，并隨著溫度逐漸降低含冰量持續(xù)增大且未凍水含量顯著減小，最終在溫度足夠低時(shí)液態(tài)水只剩下土壤顆粒附近的吸附水和薄膜水[45-47]。需要注意的是，不論溫度多低，這部分水總是以液態(tài)形式存在。長(zhǎng)期以來(lái)，明確土壤水分的相態(tài)轉(zhuǎn)化過(guò)程及各組分體積分?jǐn)?shù)是探究季節(jié)性凍土區(qū)水分運(yùn)移過(guò)程的關(guān)鍵，其中氣態(tài)水含量可通過(guò)監(jiān)測(cè)水汽壓、水汽密度等參數(shù)并利用經(jīng)驗(yàn)公式計(jì)算獲取，而液態(tài)水含量則可直接通過(guò)布設(shè)傳感器來(lái)實(shí)時(shí)監(jiān)測(cè)。如基于頻域分解法原理的傳感器，其工作原理是通過(guò)分解土壤中介電常數(shù)的實(shí)部與虛部來(lái)確定土壤體積含水量，由于土壤中各組分介電常數(shù)值相差較大，其中液態(tài)水介電常數(shù)值約為78，遠(yuǎn)超過(guò)土壤基質(zhì)、冰、空氣等其他組分，因而被證實(shí)適用于凍土中液態(tài)水含水量監(jiān)測(cè)[48-49]。根據(jù)式（4）及相應(yīng)的液態(tài)水與氣態(tài)水?dāng)?shù)據(jù)，并通過(guò)烘干法測(cè)定土壤總含水量，可最終確定凍土層內(nèi)土壤含冰量數(shù)值。由于在水勢(shì)梯度與溫度梯度作用下，土壤深部液態(tài)水與氣態(tài)水不斷向凍結(jié)鋒處運(yùn)移，因此相比于凍結(jié)之前，季節(jié)性凍土層內(nèi)總含水量在融化后往往呈現(xiàn)出增大的趨勢(shì)。

3 數(shù)值模擬技術(shù)在水汽熱耦合運(yùn)移研究中的應(yīng)用

由于季節(jié)性凍土區(qū)野外工作的不確定性，完全依賴野外試驗(yàn)很難揭示復(fù)雜的包氣帶水汽熱耦合運(yùn)移過(guò)程背后機(jī)理，尤其是在當(dāng)前研究中針對(duì)氣態(tài)水的監(jiān)測(cè)仍難以實(shí)現(xiàn)，因而數(shù)值模擬方法逐漸成為了相關(guān)研究的主要工具。

3.1 耦合模型構(gòu)建與適用性分析

基于土壤水分運(yùn)移及熱傳導(dǎo)基本理論，構(gòu)建適宜的耦合模型是探究包氣帶水汽熱耦合運(yùn)移過(guò)程的基礎(chǔ)。在不考慮凍融過(guò)程影響時(shí)，許多簡(jiǎn)單的模型被用于研究包氣帶水汽熱耦合運(yùn)移過(guò)程。隨著計(jì)算機(jī)技術(shù)的發(fā)展，逐漸出現(xiàn)了功能較為完整且操作便利的數(shù)值模擬軟件，圍繞特定時(shí)刻包氣帶水、汽、熱通量分布以及特定深度包氣帶水、汽、熱通量變化規(guī)律展開(kāi)研究，取得較多成果，相關(guān)模型也都被證實(shí)適用于野外實(shí)際研究中。

當(dāng)考慮凍融過(guò)程后，受冰-水相變過(guò)程影響，耦合數(shù)值模型的構(gòu)建面臨較大挑戰(zhàn)。合理的簡(jiǎn)化在確保模型精度的前提下有助下模型構(gòu)建，在研究中應(yīng)用較多，然而過(guò)度簡(jiǎn)化則對(duì)模型結(jié)果有較大影響。例如，采用固定凍結(jié)溫度方法計(jì)算含冰量時(shí)，當(dāng)計(jì)算出的土壤溫度低于凍結(jié)點(diǎn)時(shí)，土壤中液態(tài)水全部轉(zhuǎn)化為冰。由土壤凍結(jié)曲線可知，不論土壤溫度多低，孔隙中總有液態(tài)水存在，含水量值與溫度有關(guān)。因此這種過(guò)度簡(jiǎn)化的方法不僅會(huì)給計(jì)算結(jié)果帶來(lái)較大誤差，同時(shí)也并不符合實(shí)際情況[36]。此外，當(dāng)考慮凍融作用后，模型計(jì)算時(shí)會(huì)出現(xiàn)數(shù)值程序不穩(wěn)定的現(xiàn)象。例如，在冰-水相變過(guò)程中，由于相變潛熱變化導(dǎo)致熱容量突變會(huì)造成土壤溫度計(jì)算不收斂[50]。諸如此類現(xiàn)象的存在，使得有必要優(yōu)化程序計(jì)算過(guò)程以確保耦合模型運(yùn)行穩(wěn)定性。當(dāng)數(shù)值程序穩(wěn)定運(yùn)行后，模型計(jì)算精度與耗時(shí)平衡問(wèn)題同樣值得注意。如何在確保獲取較為精確結(jié)果的前提下，通過(guò)設(shè)置合理的時(shí)間與空間步長(zhǎng)以控制模型運(yùn)行時(shí)長(zhǎng)有重要意義[51]。

諸如SHAW、CoupModel、Hydrus-1D、STEMMUS、COMSOL等功能強(qiáng)大的數(shù)值軟件出現(xiàn)，為研究?jī)鋈谧饔糜绊懴掳鼩鈳疅醾鬏斶^(guò)程提供了便利[52]。由于起初研究目的不同，不同軟件建模時(shí)采用的控制方程與物理機(jī)制存在差異。例如在傳統(tǒng)水汽熱耦合運(yùn)移理論中，假定土壤中空氣壓強(qiáng)與大氣壓強(qiáng)保持平衡，因而忽略了空氣流動(dòng)影響，只考慮了水汽擴(kuò)散過(guò)程，導(dǎo)致了部分水汽通量計(jì)算誤差。為了消除這一誤差，STEMMUS中將空氣壓強(qiáng)作為狀態(tài)變量，引入了空氣流動(dòng)方程，考慮了水汽對(duì)流、彌散過(guò)程影響[13]。相比較而言，Hydrus-1D軟件在包氣帶水、汽、熱運(yùn)移研究中應(yīng)用最為廣泛[53-55]。以該軟件為例，具體介紹此類軟件在水汽熱耦合運(yùn)移研究中的應(yīng)用?；赟aito等[56]的研究成果，水汽熱耦合模塊被嵌入了標(biāo)準(zhǔn)版的Hydrus-1D 4.0版本中，并由此被廣泛應(yīng)用于土壤未凍結(jié)條件下農(nóng)業(yè)灌溉、水資源合理利用等方面的研究中。以該模塊為基礎(chǔ)，結(jié)合Hansson等[26]提出的Hydrus-1D凍融模塊，Zheng等[57]開(kāi)發(fā)了適用于凍融過(guò)程的包氣帶水汽熱耦合運(yùn)移程序，并利用榆林、錫林郭勒、瑪曲等不同凍土區(qū)實(shí)測(cè)數(shù)據(jù)驗(yàn)證模型精度，證實(shí)所建立的模型適用性。在修改后的程序中，基于有效能量方法修改了相變過(guò)程中由于表觀熱容增大引發(fā)的數(shù)值計(jì)算問(wèn)題，并優(yōu)化了含冰量計(jì)算程序，相比于Hansson版本，模型運(yùn)行穩(wěn)定性顯著提高，且并未遇見(jiàn)數(shù)值計(jì)算問(wèn)題。

3.2 氣態(tài)水運(yùn)移規(guī)律及其重要性

利用上述模型，學(xué)者們圍繞包氣帶水汽熱耦合運(yùn)移過(guò)程展開(kāi)大量研究，其中關(guān)于液態(tài)水運(yùn)移機(jī)制及其影響研究取得較多成果，在此不過(guò)多介紹，重點(diǎn)探討氣態(tài)水運(yùn)移規(guī)律。通常在季節(jié)性凍土區(qū)，4—10月以及11月—次年3月間土壤分別處于未凍結(jié)與凍結(jié)狀態(tài)。如圖2所示，受包氣帶溫度季節(jié)性變化影響，水汽運(yùn)移呈現(xiàn)顯著的季節(jié)性變化規(guī)律。在未凍結(jié)時(shí)期，表層土壤溫度較高，溫度梯度方向向下，驅(qū)動(dòng)氣態(tài)水向土壤內(nèi)部運(yùn)移。土壤內(nèi)部存在有聚集型零通量面，隨著土壤溫度不斷升高，其位置也不斷向下移動(dòng)。通常在夏季7月、8月時(shí)溫度梯度最大，此時(shí)向下的水汽通量值最大。而從9月開(kāi)始，隨著氣溫下降，土壤溫度降低，包氣帶向外放熱，淺層開(kāi)始出現(xiàn)發(fā)散型零溫度梯度面并不斷向土壤內(nèi)部移動(dòng)，驅(qū)動(dòng)深層氣態(tài)水不斷向表層運(yùn)移。整體來(lái)看，在非凍結(jié)期內(nèi)氣態(tài)水主要向包氣帶內(nèi)部運(yùn)移，而在土壤凍結(jié)后則主要向地表處運(yùn)移。此外，氣態(tài)水同樣存在顯著的日變化規(guī)律，主要表現(xiàn)為白天淺層土壤溫度較高時(shí)向深部運(yùn)移，而在夜間主要由深部向地表處運(yùn)移。

注：箭頭表示包氣帶內(nèi)不同時(shí)期氣態(tài)水運(yùn)移方向。

相比于液態(tài)水通量，在包氣帶絕大多數(shù)層位中氣態(tài)水通量數(shù)值相對(duì)較小，尤其是在40 cm以下范圍內(nèi)，氣態(tài)水通量普遍小1～2個(gè)數(shù)量級(jí)。但在淺層土壤中，氣態(tài)水對(duì)水分運(yùn)移的影響是不可被忽略的，造成這種現(xiàn)象一方面是由于淺層土壤含水量較低，土壤通氣孔隙較多，導(dǎo)致水力傳導(dǎo)度較大；另一方面，淺層土壤溫度受氣溫變化影響明顯，溫度梯度較大，即水汽運(yùn)移驅(qū)動(dòng)力較大。對(duì)于水資源較為短缺的干旱半干旱地區(qū)，土壤含水量較低、液態(tài)水通量小，淺層土壤中水汽通量在總水分通量中占比往往在10%～30%之間，并且水-汽相變過(guò)程對(duì)于熱通量變化同樣影響顯著[58-61]。而對(duì)于降雨極為稀少的干旱地區(qū)，Du等[62]研究表明淺層氣態(tài)水通量在總水分通量占據(jù)主導(dǎo)地位。雖然在深層土壤中水汽通量數(shù)值較小，但氣態(tài)水卻在始終不間斷運(yùn)移，累積的水分對(duì)于干旱的包氣帶而言同樣至關(guān)重要[63]。由于干旱半干旱地區(qū)降雨主要集中在夏季，在其他時(shí)期降雨較少，包氣帶含水量偏低，而土壤孔隙中相對(duì)濕度總是處于近飽和狀態(tài)，只要溫度變化就會(huì)引發(fā)水汽凝結(jié)現(xiàn)象，在溫度梯度作用下水汽源源不斷從包氣帶內(nèi)部向淺層遷移并凝結(jié)，可以補(bǔ)充淺層土壤中由于蒸發(fā)作用所消耗的水分。此外，在冬季土壤凍結(jié)后，冰的出現(xiàn)會(huì)阻礙液態(tài)水運(yùn)移，造成液態(tài)水通量數(shù)值減小1～5個(gè)數(shù)量級(jí)，此時(shí)氣態(tài)水將會(huì)主導(dǎo)凍層內(nèi)水分運(yùn)移。并且在溫度梯度驅(qū)動(dòng)下，深層土壤中氣態(tài)水源源不斷向凍結(jié)鋒處運(yùn)移，引起凍層內(nèi)總含水量增大[64]?？梢钥闯?，不論是在非凍結(jié)期還是凍結(jié)期，溫度梯度驅(qū)動(dòng)下的氣態(tài)水通量均為總水分通量的重要組成部分，其對(duì)季節(jié)性凍土區(qū)包氣帶水分與能量平衡影響不可被忽略。

4 現(xiàn)有研究不足及進(jìn)一步研究建議

盡管相關(guān)研究已經(jīng)取得了一定的成果，為深化包氣帶水循環(huán)理論提供了重要參考，但是在現(xiàn)有研究中仍存在一定局限性。受季節(jié)性凍土區(qū)野外試驗(yàn)與監(jiān)測(cè)條件限制，部分研究現(xiàn)象以及耦合模型建立是基于室內(nèi)試驗(yàn)數(shù)據(jù)開(kāi)展。相較于復(fù)雜的野外實(shí)際情況，如土-氣界面復(fù)雜性、土壤非均質(zhì)性等，室內(nèi)試驗(yàn)存在一定局限性，并不能很好反映野外實(shí)際情況。并且由于耦合模型建立過(guò)程中涉及參數(shù)較多，參數(shù)精度對(duì)于模型驗(yàn)證及模擬結(jié)果可靠性影響較大，對(duì)于諸如水汽增強(qiáng)因子與冰的阻抗因子等參數(shù)而言，其數(shù)值隨土壤質(zhì)地等條件改變而明顯變化，因而應(yīng)盡可能通過(guò)采用試驗(yàn)手段而非經(jīng)驗(yàn)公式來(lái)獲取此類參數(shù)，并結(jié)合反算等方法進(jìn)一步優(yōu)化參數(shù)，以獲取更為精確且可靠的研究結(jié)果[65]。同時(shí)，現(xiàn)有的研究大多偏重于理論探索，在實(shí)際應(yīng)用層面取得的成果較少?；诂F(xiàn)有包氣帶水汽熱耦合運(yùn)移研究理論成果，結(jié)合季節(jié)性凍土區(qū)實(shí)際情況，應(yīng)圍繞生態(tài)水文、水災(zāi)害等實(shí)際問(wèn)題展開(kāi)進(jìn)一步研究：

1）由于季節(jié)性凍土區(qū)多屬于干旱半干旱區(qū)域，區(qū)內(nèi)降雨稀少，植被較為稀疏、生長(zhǎng)緩慢，土地荒漠化突出，這些地區(qū)因此成為生態(tài)建設(shè)的重點(diǎn)區(qū)和“硬骨頭”。雖然實(shí)施了一系列生態(tài)保護(hù)措施，沙地植被發(fā)生明顯變化，但由于部分地區(qū)種植密度過(guò)大，植物耗水過(guò)多，不僅導(dǎo)致了地下水位下降，并且由于沙地土壤水分被大量消耗，引發(fā)了人工造林植被的衰退和死亡現(xiàn)象[66-67]。受降水較少及部分地區(qū)地下水位較深影響，土壤水資源成為諸如沙柳、樟子松等固沙造林植被生長(zhǎng)的重要支撐，生態(tài)效應(yīng)顯著，而其中氣態(tài)水通量的影響不可忽視，水汽凝結(jié)與聚集有助于植被克服土壤干旱脅迫，對(duì)于維系荒漠植被生態(tài)系統(tǒng)有重要意義[54,68-69]。然而在現(xiàn)有研究中，關(guān)于氣態(tài)水對(duì)植被根系吸水的影響尚未形成統(tǒng)一的認(rèn)識(shí)。更重要的是，受凍融期根系吸水影響因素復(fù)雜及其與土壤水、汽運(yùn)移之間的互饋?zhàn)饔貌幻鞯戎萍s，對(duì)于季節(jié)性凍土區(qū)土壤水資源生態(tài)效應(yīng)研究仍處于探索階段。通過(guò)建立合理的植被根系生長(zhǎng)與吸水模型，將其耦合進(jìn)包氣帶水汽熱傳輸方程中，聚焦“土壤-植被-大氣”系統(tǒng)水循環(huán)過(guò)程，最終建立適用于季節(jié)性凍土區(qū)、可獲得穩(wěn)定及精確數(shù)值解的包氣帶水-汽-冰-熱-植被耦合模型，闡明包氣帶水汽熱-根系吸水耦合動(dòng)力學(xué)機(jī)制，可為生態(tài)系統(tǒng)脆弱區(qū)的植被恢復(fù)與生態(tài)系統(tǒng)穩(wěn)定提供科學(xué)依據(jù)。

2）在溫度梯度驅(qū)動(dòng)下，凍融期內(nèi)氣態(tài)水向土壤表層聚集、遷移的過(guò)程，對(duì)于許多工程建設(shè)活動(dòng)影響較為明顯。如李強(qiáng)等[70]發(fā)現(xiàn)在西北干旱半干旱地區(qū)，高速公路與鐵路路基存在有大范圍凍脹以及稀泥狀土現(xiàn)象，這主要是受不透氣覆蓋層影響。在覆蓋層下氣態(tài)水運(yùn)移受阻，以冰的形式儲(chǔ)存于表層土體，并且由于凍層內(nèi)水汽密度減小也加劇了深層水汽向上遷移過(guò)程。傳統(tǒng)研究主要側(cè)重于凍脹過(guò)程中液態(tài)水遷移，在工程建設(shè)中也會(huì)考慮防水作用，但卻很少考慮氣態(tài)水遷移影響，進(jìn)而容易引起工程病害[71]。針對(duì)該問(wèn)題，賀佐躍等[72]通過(guò)室內(nèi)試驗(yàn)發(fā)現(xiàn)當(dāng)考慮氣態(tài)水遷移成冰作用時(shí)，產(chǎn)生的凍脹量與實(shí)測(cè)值擬合較好，較好地解釋了凍脹現(xiàn)象發(fā)生的原因。通過(guò)進(jìn)一步開(kāi)展現(xiàn)場(chǎng)監(jiān)測(cè)與相關(guān)室內(nèi)試驗(yàn)，結(jié)合數(shù)值模擬等手段明確不同覆蓋層下水汽運(yùn)移機(jī)理，為此類問(wèn)題提出具體防治措施，對(duì)于寒旱區(qū)工程建設(shè)而言十分必要。

5 結(jié) 論

綜合分析國(guó)內(nèi)外研究，本文回顧了包氣帶水汽熱耦合運(yùn)移理論的發(fā)展歷程與研究現(xiàn)狀。對(duì)于季節(jié)性凍土區(qū)，土壤凍結(jié)后孔隙中水、汽、冰三相共存，凍融作用不僅會(huì)引起土壤水、熱性質(zhì)發(fā)生改變，而且對(duì)于土壤水分相態(tài)轉(zhuǎn)化與剖面土壤水分分布影響明顯。由于季節(jié)性凍土區(qū)野外工作復(fù)雜性，數(shù)值模擬技術(shù)逐漸成為研究水汽熱耦合運(yùn)移過(guò)程的主要手段。通過(guò)構(gòu)建適宜的耦合模型模擬分析，液態(tài)水與氣態(tài)水運(yùn)移模式及其驅(qū)動(dòng)力機(jī)制逐漸被揭示，并通過(guò)定量描述闡明了氣態(tài)水對(duì)于包氣帶水分運(yùn)移過(guò)程的影響。研究結(jié)果表明開(kāi)展包氣帶水汽熱耦合運(yùn)移研究不僅符合季節(jié)性凍土區(qū)實(shí)際情況，而且有助于探究土壤水循環(huán)過(guò)程背后機(jī)理。

然而，現(xiàn)有研究大多偏重于理論探索，在實(shí)際應(yīng)用層面取得的成果較少。結(jié)合季節(jié)性凍土區(qū)情況，應(yīng)圍繞生態(tài)水文、水災(zāi)害等實(shí)際問(wèn)題展開(kāi)進(jìn)一步研究：1）聚焦“土壤-植被-大氣”系統(tǒng)水循環(huán)過(guò)程，建立適用于季節(jié)性凍土區(qū)的包氣帶水汽熱-植被耦合模型，探究土壤水資源生態(tài)效應(yīng)，為植被恢復(fù)與生態(tài)系統(tǒng)穩(wěn)定提供科學(xué)依據(jù)；2）在寒旱區(qū)工程建設(shè)中考慮氣態(tài)水的影響，明確覆蓋層下水汽運(yùn)移機(jī)理，對(duì)建設(shè)過(guò)程中由水汽運(yùn)移引起的工程病害提出具體防治措施。

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Review of coupled water, vapor, and heat transport of the vadose zone in the seasonal frozen soil region

Zheng Ce, Gao Wande, Chen Yunfei, Lu Yudong, Liu Xiuhua※

(1.,,710064,; 2.,,710064,)

Seasonally frozen soil regions refer to those areas where soil is frozen for 15 days or more per year. More than half of land surface is occupied with the seasonal snow cover in China. The freeze-thaw process can significantly change the soil properties, as well as the water and heat transferring in the vadose zone. Among them, temperature and water vapor have posed a significant impact on the soil moisture, due to the soil subjected to the dry condition in most of the seasonally frozen regions (belonging to the arid and semi-arid areas). It is gradually recognized as the significant effect of vapor flow on the soil water movement for both freezing and non-freezing periods over the past several decades. It is a high demand to couple the water, vapor, and heat transport suitable for the actual conditions of seasonally frozen soil regions, in order to reveal the influencing mechanism of soil hydrological cycle. The coupled theory of water, vapor, and heat transport was firstly proposed by Philip and de Vries. The total soil water flux was then divided into four components, including the liquid water flux and water vapor flux driven by water potential and temperature gradients, respectively. Since then, extensive researches were also carried out to continuously improve on the coupled transport. Once the soil was frozen, the liquid water, vapor, and ice were coexisted in the unsaturated zone. Two aspects were also observed in the influence of phase changes between liquid water and ice on the coupled water, vapor, and heat transport. Several hydraulic parameters were calculated to determine the hydrological cycle, such as the soil freezing curve, and hydraulic conductivity for the liquid water. The spatial and temporal distributions of soil moisture in the vadose zone were dominated by the seasonally freeze-thaw process as well. The contents of unfrozen water and ice also changed significantly with the variations of soil temperature. Numerical simulation was gradually utilized in this research field with the ever-increasing computational capacity and simulation accuracy. Great challenges were still remained on the coupled numerical model, due to the influence from the ice-water phase change. An appropriate coupling model was crucial to the numerical simulation via the reasonable simplification. The underlying mechanism of coupled water and vapor flow was gradually revealed from the simulation using different models. Specifically, the vapor flux was one of the most important components in the soil water movement, usually accounting for 10%-30% of the total water flux. Furthermore, the vapor flux was depended mainly on the relatively low soil moisture and large temperature gradient in the shallow layer. The vapor flow was much more significant during the freezing period, due mainly to the impeded flow of liquid water in the presence of ice. Consequently, some research directions that needed to be strengthened in this field were proposed to deepen the theoretical fundamentals and the practical tasks in the seasonal frozen soil areas. Firstly, the condensation and accumulation of water vapor can greatly contribute to the vegetation under soil drought and freezing stress. It is of great significance to maintain the desert vegetation ecosystem, where the soil water is critical to the vegetation growth in the fragile ecological areas. The vegetation module can be combined with the coupled model water, vapor, and heat transferring. Further studies can be implemented to explore the specific impact of liquid water and vapor on the surface vegetation in seasonal frozen region. Secondly, the coupled transport of liquid water and vapor can also impact many engineering construction activities as well, such as the frost heave in the railway embankments that caused by the continuous liquid water and vapor transport from the deep soil layer. Finally, in-situ monitoring and simulation can be strengthened to reveal the detailed process of liquid and vapor transport below the surface impermeable layer. The finding can also provide the scientific basis for the disaster prevention and control during freeze-thaw process.

water; heat; numerical analysis; vadose zone; vapor transport; hydrological cycle; seasonal frozen soil region

10.11975/j.issn.1002-6819.2022.24.012

S152.7

A

1002-6819(2022)-24-0110-08

鄭策，高萬(wàn)德，陳云飛，等. 季節(jié)性凍土區(qū)包氣帶水汽熱耦合運(yùn)移研究進(jìn)展[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2022，38(24)：110-117.doi：10.11975/j.issn.1002-6819.2022.24.012 http://www.tcsae.org

Zheng Ce, Gao Wande, Chen Yunfei, et al. Review of coupled water, vapor, and heat transport of the vadose zone in the seasonal frozen soil region[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2022, 38(24): 110-117. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2022.24.012 http://www.tcsae.org

2022-08-21

2022-10-10

國(guó)家自然科學(xué)基金資助項(xiàng)目(42202279，41877179)；中國(guó)博士后科學(xué)基金(2022M720536)

鄭策，博士，講師，研究方向?yàn)楹祬^(qū)土壤水文與生態(tài)水文。Email：zhengce@chd.edu.cn

劉秀花，博士，教授，研究方向?yàn)楹祬^(qū)水生態(tài)與水安全。Email：Liuxh68@chd.edu.cn