重力驱动指流的观测和数学模拟研究综述

李海龙,夏玉强

(1.中国地质大学(武汉)环境学院,湖北 武汉 430074;2.中国地质大学(北京)水资源与环境科学学院,北京 100083;3.美国天普大学土木与环境工程系,费城 19122)

重力驱动指流(gravity-driven fingers),又称优势流,简称指流或指状分支流,是地表水在重力作用下渗入非饱和土壤中时经常发生的一种现象,其特征是渗入土壤中的水流在土壤中形成固定的指状优势通道。Gerke[1]指出“指流包括水流和溶质不经其他土壤部分而沿某些特定通道运移的所有现象”。土壤中指流的存在大大加速了地表水在土壤中的渗流速度,提高了各种养分及污染物在包气带中的运移传输速度,加剧了工农业生产排放的污染物对土壤的污染。因此,指流的研究已成为与农业、林业、生态环境保护等行业密切相关的基础研究课题之一。

1 指流的形成原因

指流的形成原因复杂多样,一种众所周知的简单情形就是多孔介质中孔隙的随机分布导致一些较大的孔隙连在一起而形成“优势通道”。当水流在重力作用下渗入多孔介质时,会倾向于沿着这样的优势通道形成指流。指流研究的复杂性在于其产生原因的多样性[2]。例如,Coppola等[3]在单个土体尺度上,根据指流产生机制的不同划分了4种指流形式:大孔隙(非毛细管孔)流,结构性孔隙流,湿锋面不稳定性引起的指流,以及由土壤湿润度(或斥水性)空间分布的不规则性和时间动态性引起的指流。总体来说,导致指流的因素除土壤孔隙度和渗透性空间分布不均(非均质性)外,还有非饱和土壤中孔隙水分布不均[4]、毛细作用及其滞后效应[5]、土壤质地和根系结构[6-9]、孔隙类型和分布[10-11]、施加于土壤表面的入渗流量[12]、非饱和土壤中的气流以及大气波动效应等。一个简单而基本的例子是,在实验室平板玻璃模型中人工选择的严格均质砂样中同样会产生指流。这种现象在宏观均质的多孔介质中,包括在直径变化范围很小的玻璃珠堆成的人工多孔介质中也会发生[13-14]。Wallach等[15]的最新研究结果表明,由于土壤的斥水性,土壤孔隙含水量的空间分布不一定取决于土壤孔隙和渗透性的非均质性。

2 近10年来指流研究的主要内容

指流研究始于20世纪60年代[16-18]。过去的10多年中,在国际土壤和水文环境领域中涌现了大量关于指流研究的文献[4],表明指流的研究是该领域前沿研究的一个热点。这些研究的内容主要集中在以下几个方面:①综述性文章[1-3,4,10-11,19-36];②确定性理论模型和数值模拟[5,37-53];③室内试验、观测方法改进和机理定性描述[6-7,12,26,41,54-72];④室内试验和机理分析(包括野外采样后进行室内分析)[2,13-15,49,61,73-93];⑤野外现场试验(可能有室内试验)[9,94-106]。

通过对上述研究的分析整理,得出以下主要认识:①由于指流研究的复杂性,其试验研究目前仍以室内分析为主,野外研究较少且其尺度与室内试验差不多。②指流研究所涉及的主要数学工具仍然是以微分方程为主的确定性理论,很少有以随机理论为主要工具来研究指流的文献。一方面,随机理论可以被用来确定数学模型中水文地质参数的时空分布;另一方面,在这种分布被确定后,探讨模型解的性质如它是如何依赖于多孔介质的水文地质参数等,还需要微分方程所表示的确定性理论来完成。

目前国内有关指流的研究主要集中于大孔隙流、试验描述以及指流研究进展的介绍等,对于指流的理论研究偏少,尤其是缺少对指流数学模型的研究。因此,笔者将着重介绍和总结重力驱动指流的精细观测及其数学模拟方面的国际研究进展。

3 重力驱动指流的观测及其数学模拟研究的重要进展

3.1 新的高时空分辨率的观测方法

随着新的试验观测方法如X-射线断层摄影术(X-raytomography,CT)以及光投射法(light transmission method,LTM)的应用[28-29,56-57,62,107],在指流试验中可实现对孔隙水饱和度的高分辨率测定,其时空分辨率分别可达1s和1mm。而Deinert等[41]所采用的中子射线实时摄影法的时空分辨率分别可达30ms和0.5mm。这种硬件观测水平的提高为开展高水平的理论研究提供了可靠、翔实的试验观测数据和以前试验中难以发现的新现象。例如DiCarlo[60]所做的饱和度观测试验表明,孔隙尺度水平上的物理过程控制着水饱和度在指流指尖处的峰值,从而控制了指流的进一步发展。又如 Bayer等[54]用X-射线断层摄影术测得的毛细压力在初始阶段的增高过程与传统描述非饱和带水流的Richards方程所刻画的单相流有着显著的差异。

3.2 有关Richards方程或传统的水-气两相流模型能否完整地刻画和描述指流的争论

Nieber[108]利用带有毛细滞后效应的Richards方程,在多孔介质水饱和度初值为零的情形下模拟了指流的生成和持续过程。他发现,为了能够在数值模拟中得到指流,剖分节点间非饱和水力传导系数的计算不得不采用下游加权格式。之后,Ritsema等[109]、Nguyen等[110-111]以及Nieber等[49]在进行斥水沙质土壤中指流的数值模拟时得到了类似结果,其共同点是都采用了下游加权格式。此外,Ritsema等[109]给出了在斥水沙质土壤中指流形成过程及其复发的野外现场图像,并用水-气两相流数值模型和对液相采用下游加权格式,重现了某种斥水沙质土壤中的指流。但未提及若对水和气都用上游加权格式将会得出什么结果。

Eliassi等[44]考虑了Richards方程是否能够完整地描述非饱和多孔介质中指流的问题,怀疑Richards方程的解是否真的可以产生试验中观测到的水饱和度在指流指尖处的非单调峰值。他们认为,Nieber[108]和Ritsema等[109]所得到的具有水饱和度非单调峰值的“指状”数值解只是一种由于数值解的振荡和过饱和而引起的假象,而数值解的振荡和过饱和是由于下游加权法和网格剖分不够细引起的数值计算误差。若利用上游加权法或者网格剖分足够细,这种人为产生的“指状”数值解就会消失。因此,他们认为 Richards方程或者与之等价的水-气两相流模型,加上由Mualem[112-113]和Van Genuchten[114]给出的关于相对渗透系数和毛细效应滞后现象的基本关系式所构成的数学模型不足以描述指流。

Braddock等[40]对 Eliassi等[44]的工作从数学角度进行了评论。评论指出:①在二维情形,Eliassi等[44]所提出的关于Richards方程解的单调性假设有待进一步验证;②关于时间离散的截断误差引起了数值解的振荡现象;③振荡现象对毛细滞后关系中切换值的选择造成了很大的困难。Eliassi等[46]回应说虽然在二维情形下没有Richards方程解的单调性的理论结果,但是已有的数百篇公开发表的论文所给出的二维情形下的解析和数值解,在均质和初边值条件为常数时都表现出了单调性质。

Deinert等[59]对Eliassi等[44]的工作做了另一番评论。认为Eliassi等[44]对Nieber[108]所做工作的评论有些言过其实。因为Nieber[108]用简单模型所得出的模拟结果和观测资料相符。Nieber[108]所用的下游加权格式,只是在模拟观测得到的指流及其不稳定特征时所选择的一个参数而已,这与 Deinert等[115]利用试验所得到的一种类似于达西形式的表达式所定义的动态毛细压力所描述的不稳定性是一致的。Eliassi等[47]回应Nieber[108]所做的数值模拟是基于下游加权格式的,因此只能说是假的指流。下游加权格式会产生足够大的数值误差,从而导致用数值方法所求解的方程实际上不是Richards方程本身。当网格被适当加密以后,数值误差减小,而数值解所产生的人工指流也随之消失。

试验观测和理论研究表明,在均质非饱和土壤中,连续入渗条件下水饱和度曲线会在入渗前锋处形成一个非单调的突起,这个突起不能用传统的Richards方程来描述[5,60,82]。Nieber等[5]所做的线性稳定性分析表明,传统的Richards方程对无穷小扰动是无条件稳定的,即不会产生指流;而把Richards方程和动态毛细压力结合起来所得到的模型却是有条件稳定的,即有可能产生指流。他们对上述动态毛细压力机制作了回顾并将之扩展到了含水量小于田间持水量的很干的土壤中。

DiCarlo[82]的最新研究进展表明,上述动态毛细压力机制(DiCarlo在文中称之为非平衡毛细压力,其实是一样的)也不能很好地描述指流。在传统的Richards方程基础上,加之以动态毛细压力,虽然能使模型描述指流的情况大有改善,例如可以预测出指流发生的流量范围等,但对指流尖端处水饱和度非单调突起的描述仍差强人意。而且当多孔介质的固体颗粒尺寸和粗糙程度稍有变化时,为了能拟合指流发生的流量范围,就需要对动态毛细压力项做大幅度的调整。这些结果说明,现有的动态毛细压力表达式尚未包含控制指流尖端处水饱和度非单调突起的物理机制[82]。DiCarlo[61]在实验室中观测到了在入渗前锋处形成的毛细压力的非单调突起,且和上述水饱和度曲线的非单调突起类似。

3.3 有关新机制和新效应的模型

Eliassi等[37]研究了试验观测到的水饱和度在指流垂直剖面上呈现的称之为“后推堆积”(hold-backpile-up)的效应,这种效应是以多孔连续介质为基础的Richards方程无法描述的。他们对传统的Richards方程作了若干不同形式的拓展,使之能够描述这种效应。每种拓展都由2项组成:即传统的Darcy-Buckingham通量项和另一对应于“后推堆积”效应的项。但正如他们所总结的那样,这种拓展在更一般意义上的有效性尚存在疑问,且其表达式在整个理论框架中的物理意义无完整的定义,有关参数也没有进行测定。为了全面考察对“后推堆积”的模拟能力,有必要利用控制方程的各种拓展形式进行直接数值模拟试验,以验证其有效性。在孔隙尺度水平试验观测研究的基础上,Glass等[85-86,116]提出了与现有的理论框架完全不同的新机理模型,即“修正的侵入渗透”模型(modifiedinvasion percolation)。这种模型包含了重力、沿相-相界面上的局部界面弯曲、湿润和非湿润流体的同时入侵以及再次入侵等因素对指流的影响,该模型在描述指流中发生的各种现象如水饱和度的非单调性、碎裂、跳动等方面取得了初步进展。Shiozawa等[13]在室内用初始状态是干的粒状多孔介质所作的一维向下限流量入渗试验及其分析表明,从孔隙尺度的角度来看,在入渗水流前锋所在的水气交界处,孔隙含水量和水压是不连续的,因此Darcy定律不能用在这样的水气界面上。DiCarlo等[43]在 Eliassi等[37]所提出的拓展形式的基础上,将传统的Richards方程扩展为带有非单调的毛细压力-饱和度曲线和双曲项(水压关于时间的二阶导数项)的非线性波动方程,并推导出该方程的行波解。该解的水饱和度曲线在入渗前锋处确实有非单调突起。若要保证该解的唯一性,则还需加上1个正则项。

4 研究体会

Ursino等[117]用 Richards方程讨论了潮间带湿地植物根部呼吸的通风状况、蒸腾作用引起的水分运移以及植物生长状态之间的相互关系,其模型忽略了气流。笔者以TOUGH2数值模拟程序为基础,就同一问题用水-气两相流模型所做的工作[118]表明,Richards方程不足以完全描述植物根部呼吸的通风条件。对于同一类型的水力传导系数在10-6～10-5m/s之间的沼泽地土壤,水 气两相流模型所给出的潮间带湿地植物根围空气饱和度总是大于零。而根据Ursino等[117]的计算,Richards方程所给出的根围空气饱和度在海潮周期的某一段时间内为零。这说明包气带中气流对水流的影响非常显著,不能忽略。基于Richards方程的单相流模型由于忽略了气流,不能用来定量地描述潮间带湿地土壤的通风条件。

通过文献搜集和研究整理的结果[119-120]表明,尚无文献在气流对指流影响方面做过专门探讨。尽管如此,笔者认为气流对指流的发生和发展会有重大影响,并相信在指流研究中气流效应不能被忽视,甚至它主导与指流相关的某些现象(如碎裂和跳动)。已有的实验室研究(如Touma等[121])以及野外现场试验(如Dixon等[122])都表明,当水流从土壤表面渗入土壤中时,被水流挤压的空气能显著降低水流的入渗速度。而当气压充分高时,空气会冲破土壤表层孔隙水对其的限制,从土壤表面逸出,从而造成土壤内气压的急剧降低以及增加水流入渗速度[121]。这有可能引起指流的跳动和碎裂。

由于指流研究是一个多学科的问题,其机制的研究离不开定量的数学描述,而机制、试验和定量的数学模型之间是相辅相成、互相验证的关系。一个新的机制,只有经过试验和模型验证之后才能证明它的正确性和适用范围。因此,寻找既具有最少的模型参数,又能刻画水气交界处水流和气流流动的最简单的、具有物理背景意义的数学模型,很可能是解开指流复杂性的关键所在。

5 几个关键的科学问题

综上所述,在指流的研究中,尚存在大量亟待解决的又很有意义的挑战性前沿课题。主要概括为如下几点:①能在更小的时空尺度上刻画指流发生和发展机制的试验观测装置。②能否以传统的多孔介质理论为基础,结合新的动态毛细压力机制,来完整地描述已经观测到的但是现有模型还不能满意地描述的指流尖端处水饱和度和压力的非单调突起。③建立和完善有关新的机制和效应的模型,例如孔隙尺度水平上的微观模型以及上述“后推堆积”效应模型。特别地,如何用数学模型简单而自然地描述在入渗水流前锋的水气界面处的水-气两相流。④新模型的解,包括解的性质分析和数值求解方法。指流的理论模型及数值模拟方面的突破,将打破其对相关学科发展的制约,不仅对土壤物理学和水文地质学的理论基础本身,而且对其他相关学科如应用数学、环境资源、农业和生态学等,都具有重要的推动作用。

[1]GERKE HH.Preferential flow descriptions for structured soils[J].Journal of Plant Nutrition and Soil Science-Zeitschrift Fur Pflanzenernahrung Und Bodenkunde,2006,169(3):382-400.

[2]WANG Zhi,JURY W A,TULI A,et al.Unstable flow during redistribution:controlling factors and practical implications[J].Vadose Zone Journal,2004,3(2):549-559.

[3]COPPOLA A,KUT ÍLEK M,FRIND E O.Transport in preferential flow domains ofthe soilporous system:measurement,interpretation,modelling,and upscaling[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):1-3.

[4]De ROOIJG H.Modeling fingered flow of water in soils owing to wetting front instability:a review[J].Journal of Hydrology,2000,231:277-294.

[5]NIEBER JL,DAUTOV RZ,EGOROV A G,et al.Dynamic capillary pressure mechanism for instability in gravity-driven flows;Review and extension to very dry conditions[J].Transport in PorousMedia,2005,58(1/2):147-172.

[6]陈风琴,石辉.岷江上游三种典型植被下土壤优势流现象的染色法研究[J].生态科学,2006,25(1):69-73.

[7]李怀恩,拦继元,史文娟,等.层状土壤指流实验研究[J].干旱地区农业研究,2007,25(6):111-115.

[8]董宾芳,傅瓦利.土壤优势流的植物根系效应[J].安徽农业科学,2006,34(23):6249-6251;6262.

[9]程竹华,张佳宝,徐绍辉.黄淮海平原三种土壤中优势流现象的试验研究[J].土壤学报,1999,36(2):154-161.

[10]冯杰,郝振纯.水及溶质在有大孔隙的土壤中运移机制研究进展[J].河海大学学报:自然科学版,2002,30(2):63-70.

[11]郝振纯,冯杰.水及溶质在大孔隙土壤中运移的实验研究进展[J].灌溉排水,2002,21(1):67-71.

[12]郭会荣.优先流影响下的入渗补给过程及溶质运移实验与模拟[D].武汉:中国地质大学,2008.

[13]SHIOZAWA S,FUJIMAKI H.Unexpected water content profiles under flux-limited one-dimensional downward infiltration in initially dry granular media[J].Water Resources Research,2004,40(7):W07404.(doi:10.1029/2003WR002197).

[14]ANNAKA T,HANAYAMA S.Dynamic water-entry pressure for initially dry glass beads and sea sand[J].Vadose Zone Journal,2005,4(1):127-133.

[15]WALLACH R,BEN-ARIE O,GRABER E R.Soil water repellency induced by long-term irrigationwith treated sewage effluent[J].Journal of Environmental Quality,2005,34(5):1910-1920.

[16]SAFMAN P G,TAYLOR S G.The penetration of fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid[J].Proc Roy Soc A,1958,245:312-329.

[17]PALMQUIST W N,JOHNSON A I.Vadose zone in layered non layered materials[J].Geol Surv Res,1962,199:142-143.

[18]TABUCHI T.Infiltration and ensuing percolation in columnsof layered glass particles packed in laboratory[J].Trans.Agric.Eng.Soc.Jpn,1961,1:13-19.

[19]刘亚平,陈川.土壤非饱和带中的优先流[J].水科学进展,1996,7(1):85-89.

[20]李贺丽,李怀恩,王智,等.多孔介质中指流的研究综述及展望[J].土壤,2008,40(1):27-33.

[21]DEBANO L F.Water repellency in soils:a historicaloverview[J].Journal of Hydrology,2000,231:4-32.

[22]CLOTHIER B E,GREEN S R,DEURER M.Preferential flow and transport in soil:progress and prognosis[J].European Journal of Soil Science,2008,59(1):2-13.

[23]KÖ HNE J M,KÖ HNE S,SIMUNEK J.A review of model applications for structured soils:a)water flow and tracer transport[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):4-35.

[24]KÖ HNE J M,KÖ HNE S,SIMUNEK J.A review of model applications for structured soils:b)pesticide transport[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):36-60.

[25]程竹华,张佳宝.土壤中优势流现象的研究进展[J].土壤,1998,6:315-319;331.

[26]冯杰,郝振纯,陈启慧.分形理论在土壤大孔隙研究中的应用及其展望[J].土壤,2001,33(3):123-130.

[27]冯杰,郝振纯.土壤大孔隙流研究中分形几何的应用进展[J].水文地质工程地质,2001,28(3):9-13.

[28]冯杰,郝振纯.CT在土壤大孔隙研究中的应用评述[J].灌溉排水,2002,21(3):71-76.

[29]李德成,张桃林,VELDE B.CT分析技术在土壤科学研究中的应用[J].土壤,2002,34(6):328-332.

[30]李伟莉,金昌杰,王安志,等.土壤大孔隙流研究进展[J].应用生态学报,2007,18(4):888-894.

[31]倪余文,区自清.土壤优先水流及污染物优先迁移的研究进展[J].土壤与环境,2000,9(1):60-63.

[32]倪余文,区自清,应佩峰.土壤优先水流及溶质优先迁移的研究[J].应用生态学报,2001,12(1):103-107.

[33]牛健植,余新晓.优先流问题研究及其科学意义[J].中国水土保持科学,2005,3(3):110-116;126.

[34]牛健植,余新晓,张志强.优先流研究现状及发展趋势[J].生态学报,2006,26(1):231-243.

[35]秦耀东,任理,王济.土壤中大孔隙流研究进展与现状[J].水科学进展,2000,11(2):204-207.

[36]徐绍辉,张佳宝.土壤中优势流的几个基本问题研究[J].水文地质工程地质,1999,26(6):27-30;34.

[37]ELIASSI M,GLASS R J.On the porous-continuum modeling of gravity-driven fingers in unsaturated materials:extension of standard theory with a hold-back-pile-up effect[J].Water Resources Research,2002,38(11):1234.(doi:10.1029/2001WR001131).

[38]DiCARLO D A.Quantitative network model predictions of saturation behind infiltration fronts and comparison with experiments[J].Water Resources Research,2006,42(7):W07408.(doi:10.1029/2005WR004750).

[39]BENSON D A.A model of water streaking down a wall[J].Water Resources Research,2001,37(2):427-430.

[40]BRADDOCK R D,NORBURY J.Comment on“On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state”by M.Eliassi and R.J.Glass[J].Water Resources Research,2003,39(9):1249.(doi:10.1029/2002WR001565).

[41]DEINERT M R,PARLANGE J Y,STEENHUIS T,et al.Measurement of fluid contents and wetting front profiles by real-time neutron radiography[J].Journal of Hydrology,2004,290:192-201.

[42]DiCARLO D A,BLUNT M J.Determination of finger shape using the dynamic capillary pressure[J].Water Resources Research,2000,36(9):2781-2785.

[43]DiCARLODA,JUANESR,LAFORCET,etal.Nonmonotonic traveling wave solutions of infiltration into porous media[J].Water Resources Research,2008,44(2):W02406.(doi:10.1029/2007WR005975).

[44]ELIASSI M,GLASS R J.On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state[J].Water Resources Research,2001,37(8):2019-2035.

[45]ELIASSI M,GLASS R J.On the porous continuum-scale modeling of gravity-driven fingers in unsaturated materials:numerical solution of a hypodiffusive governing equation that incorporates a hold-back-pile-up effect[J].Water Resources Research,2003,39(6):1167.(doi:10.1029/2002WR001535).

[46]ELIASSI M,GLASS R J.Reply to comment by R.D.Braddock and J.Norbury on“On thecontinuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equationwith standard monotonic constitutive relations and hysteretic equations of state”[J].Water Resources Research,2003,39(9):1250.(doi:10.1029/2002WR001753).

[47]ELIASSI M,GLASS R J.Reply to comment on“On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state”by Mehdi Eliassi and Robert J.Glass[J].Water Resources Research,2003,39(9):1264.(doi:10.1029/2003WR002053).

[48]MAJDALANI S,ANGULO-JARAMILLO R,Di PIETRO L.Estimating preferential water flow parameters using a binary genetic algorithm inversemethod[J].Environmental Modelling&Software,2008,23(7):950-956.

[49]NIEBER J L,BAUTERS T W J,STEENHUIS T S,et al.Numerical simulation of experimental gravity-driven unstable flow inwater repellent sand[J].Journal ofHydrology,2000,231:295-307.

[50]URSINO N.Linear stability analysis of infiltration,analytical and numerical solution[J].Transport in Porous Media,2000,38(3):261-271.

[51]程金花,张洪江,史玉虎,等.长江三峡库区优先流模型修正及验证[J].山东农业大学学报:自然科学版,2007,38(4):605-609.

[52]任理,秦耀东,王济.非均质饱和土壤盐分优先运移的随机模拟[J].土壤学报,2001,38(1):104-113.

[53]冯杰,张佳宝,郝振纯,等.水及溶质在有大孔隙的土壤中运移的研究(Ⅱ):数值模拟[J].水文地质工程地质,2004,31(4):77-82.

[54]BAYER A,VOGEL H J,ROTH K.Direct measurement of the soil water retention curve using X-ray absorption[J].Hydrology and Earth System Sciences,2004,8(1):2-7.

[55]CRIST J T,MCCARTHY J F,ZEVI Y,et al.Pore-scale visualization ofcolloid transportand retention in partly saturated porous media[J].Vadose Zone Journal,2004,3(2):444-450.

[56]DAR NAULT C J G,DiCARLO D A,BAUTERS T W J,et al.Measurement of fluid contents by light transmission in transient three-phase oil-water-air systems in sand[J].Water Resources Research,2001,37(7):1859-1868.

[57]DAR NAULT C J G,DiCARLO D A,BAUTERS T W J,et al.Visualization and measurement of multiphase flow in porous media using light transmission and synchrotron X-rays[J].Visualization and Imaging in Transport Phenomena,2002,972:103-110.

[58]DAR NAULT C J G,GARNIER P,KIM Y J,et al.Preferential transport of Cryptosporidium parvum oocysts in variablysaturated subsurfaceenvironments[J].Water Environment Research,2003,75(2):113-120.

[59]DEINERT M,PARLANGE J Y,CADY K B,et al.Comment on“On the continuum-scale modeling of gravity-driven fingers in unsaturated porousmedia:The inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state”by Mehdi Eliassi and Robert J.Glass[J].Water Resources Research,2003,39(9):1263.(doi:10.1029/2002WR001785).

[60]DiCARLO D A.Experimental measurements of saturation overshoot on infiltration[J].Water Resources Research,2004,40(4):W04215.(doi:10.1029/2003WR002670).

[61]DiCARLO D A.Capillary pressure overshoot as a function of imbibition flux and initialwater content[J].Water Resources Research,2007,43(8):W08402.(doi:10.1029/2006WR005550).

[62]NIEMET M R,SELKER J S.A new method for quantification of liquid saturation in 2D translucent porous media systems using light transmission[J].Advances in Water Resources,2001,24(6):651-666.

[63]NISSEN H H,MOLDRUP P,KACHANOSKI R G.Time domain reflectometry measurementsof solute transport across a soil layer boundary[J].Soil Science Society of America Journal,2000,64(1):62-74.

[64]COPPOLA A,COMEGNA V,BASILE A,et al.Darcian preferential water flow and solute transport through bimodal porous systems:experiments and modelling[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):74-83.

[65]KUTILEK M,GERMANN P F.Converging hydrostatic and hydromechanic concepts of preferential flow definitions[J].Journal of Contaminant Hydrology,2009,104(1):61-66.

[66]KUT ÍLEK M,JENDELE L,KREJCA M.Comparison of empirical,semi-empirical and physically based models of soil hydraulic functions derived for bi-modal soils[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):84-89.

[67]HINCAPIE I,GER MANN P F.Impactof initial and boundary conditions on preferential flow[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):67-73.

[68]ROSENBOM A E,THERRIEN R,REFSGAARD J C,et al.Numerical analysis of water and solute transport in variablysaturated fractured clayey till[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):137-152.

[69]李德成,VELDE B,DELERUE JF,等.利用土壤切片和数字图像方法研究土壤孔隙的垂直空间变异性[J].土壤与环境,2000,9(2):135-138.

[70]李德成,VELDE B,DELERUE J-F,等.用于研究土壤孔隙三维结构的连续数字图像的制备[J].土壤与环境,2001,10(2):108-110.

[71]李贺丽.指流特性及其影响因素的实验研究[D].西安:西安理工大学,2007.

[72]王焕之.稻田土壤水分优先流的发生、发展与模拟研究[D].杭州:浙江大学,2002.

[73]BAUTERS T W J,DiCARLO D A,STEENHUIS T S,et al.Soil water content dependent wetting front characteristics in sands[J].Journal of Hydrology,2000,231:244-254.

[74]BAUTERS T W J,STEENHUIS T S,DiCARLO D A,et al.Physics of water repellent soils[J].Journal of Hydrology,2000,231:233-243.

[75]CHO H,De ROOIJ G H.Pressure head distribution during unstable flow in relation to the formation and dissipation of fingers[J].Hydrology and Earth System Sciences,2002,6(4):763-771.

[76]CHO H,De ROOIJ G H,INOUE M.The pressure head regime in the induction zone during unstable nonponding infiltration:theoryand experiments[J].Vadose Zone Journal,2005,4(4):908-914.

[77]CULLIGAN PJ,BANNOK,BARRYD A,etal.Preferential flow of a nonaqueous phase liquid in dry sand[J].Journalof Geotechnical and Geoenvironmental Engineering,2002,128(4):327-337.

[78]DAR NAULT C J G,STEENHUIS T S,GARNIER P,et al.Preferential flow and transport of Cryptosporidium parvum oocysts through the vadose zone:Experiments and modeling[J].Vadose Zone Journal,2004,3(2):736-736.

[79]DEKKER L W,RITSEMA C J.Wetting patterns and moisture variability in water repellent Dutch soils[J].Journal of Hydrology,2000,231:148-164.

[80]DEKKER L W,RITSEMA C J,OOSTINDIE K.Extent and significance of water repellency in dunes along the Dutch coast[J].Journal of Hydrology,2000,231:112-125.

[81]De ROOIJ G H,STAGNITTI F.Spatial and temporal distribution of solute leaching in heterogeneous soils:analysis and application to multisampler lysimeter data[J].Journal of Contaminant Hydrology,2002,54(3/4):329-346.

[82]DiCARLO D A.Modeling observed saturation overshoot with continuum additions to standard unsaturated theory[J].Advances in Water Resources,2005,28(10):1021-1027.

[83]DOERR S H,THOMAS A D.The role of soil moisture in controlling water repellency:new evidence from forest soils in Portugal[J].Journal of Hydrology,2000,231:134-147.

[84]GEIGER S L,DURNFORD D S.Infiltration in homogeneous sands and a mechanistic model of unstable flow[J].Soil Science Society of America Journal,2000,64(2):460-469.

[85]GLASS R J,CONRAD S H,YARRINGTON L.Gravitydestabilized nonwetting phase invasion in macroheterogeneous porousmedia:near-pore-scale macro modified invasion percolation simulation of experiments[J].Water Resources Research,2001,37(5):1197-1207.

[86]GLASS R J,YARRINGTON L.Mechanistic modeling of fingering,nonmonotonicity,fragmentation,and pulsation within gravity/buoyant destabilized two-phase/unsaturatedflow[J].Water Resources Research,2003,39(3):1058.(doi:10.1029/2002WR001542).

[87]JARAMILLO D F,DEKKER L W,RITSEMA C J,et al.Occurrence of soilwater repellency in arid and humid climates[J].Journal of Hydrology,2000,231:105-111.

[88]KIM Y J,DARNAULT C J G,BAILEYN O,et al.Equation for describing solute transport in field soils with preferential flow paths[J].Soil Science Society of America Journal,2005,69(2):291-300.

[89]KIM Y J,STEENHUIS T S,NAM K.Movement of heavy metals in soil through preferential flow paths under different rainfall intensities[J].Clean-Soil Air Water,2008,36(12):984-989.

[90]NEKTARIOS P A,PETROVIC A M,STEENHUIS T S.Effect of surfactant on fingered flow in laboratory golf greens[J].Soil Science,2002,167(9):572-579.

[91]NICHOLL M J,GLASS R J.Infiltration into an analog fracture:experimental observations of gravity-driven fingering[J].Vadose Zone Journal,2005,4(4):1123-1151.

[92]WANG Zhi,WU Q J,WU Lao-sheng,et al.Effects of soil water repellency on infiltration rate and flow instability[J].Journal of Hydrology,2000,231:265-276.

[93]WEISBROD N,NIEMET M R,SELKER J S.Imbibition of saline solutions into dry and prewetted porous media[J].Advances in Water Resources,2002,25(7):841-855.

[94]EGUCHI S, HASEGAWA S.Determination and characterization of preferential water flow in unsaturated subsoil of andisol[J].Soil Science Society of America Journal,2008,72(2):320-330.

[95]FRANKLIN D H,WEST L T,RADCLIFFE D E,et al.Characteristics and genesis of preferential flow paths in a piedmont ultisol[J].Soil Science Society of America Journal,2007,71(3):752-758.

[96]HANGEN E,GER KE H H,SCHAAF W,et al.Flow path visualization in a lignitic mine soil using iodine-starch staining[J].Geoderma,2004,120(1/2):121-135.

[97]HEILIG A,STEENHUIS T S,WALTER M T,et al.Funneled flow mechanisms in layered soil:field investigations[J].Journal of Hydrology,2003,279:210-223.

[98]ORR S.Enhanced heap leaching-Part 1:Insights[J].Mining Engineering,2002,54(9):49-56.

[99]KUNG K J S,KLADIVKO E J,GISHT J,et al.Quantifying preferential flow by breakthrough ofsequentially applied tracers:silt loam soil[J].Soil Science Society of America Journal,2000,64(4):1296-1304.

[100]PERSSON M,BERNDTSSON R.Transect scale solute transport measured by time domain reflectometry[J].Nordic Hydrology,2002,33(2/3):145-164.

[101]RITSEMA C J,DEKKER L W.Preferential flow in water repellent sandy soils:principles and modeling implications[J].Journal of Hydrology,2000,231:308-319.

[102]RITSEMA C J,Van DAM J C,DEKKER L W,et al.A new modelling approach to simulate preferential flow and transport in water repellent porous media:model structure and validation[J].Australian Journal of Soil Research,2005,43(3):361-369.

[103]SANDER T,GERKE H H.Preferential flow patterns in paddy fields using a dye tracer[J].Vadose Zone Journal,2007,6(1):105-115.

[104]SANDER T,GERKE H H.Modellingfield-dataof preferential flow in paddy soil induced by earthworm burrows[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):126-136.

[105]FUCHS J W,FOX G A,STOR M D E,et al.Subsurface transport of phosphorus in riparian floodplains:influence of preferential flow paths[J].Journal of Environmental Quality,2009,38(2):473-484.

[106]冯杰,张佳宝,郝振纯,等.水及溶质在有大孔隙土壤中运移的研究(I):田间实验[J].水文地质工程地质,2004,31(3):20-24.

[107]TIDWELL V C,GLASS R J.X-rayand visible-lighttransmission for laboratory measurement of 2-dimensional saturation fields in thin-slab systems[J].Water Resources Research,1994,30(11):2873-2882.

[108]NIEBER J L.Modeling finger development and persistence in initially dry porous media[J].Geoderma,1996,70(2/3/4):207-229.

[109]RITSEMA C J,DEKKER L W,NIEBER J L,et al.Modeling and field evidence of finger formation and finger recurrence in a water repellent sandy soil[J].Water Resources Research,1998,34(4):555-567.

[110]NGUYEN H V,NIEBER J L,ODURO P,et al.Modeling solute transport in a water repellent soil[J].Journal of Hydrology,1999,215:188-201.

[111]NGUYEN H V,NIEBER J L,RITSEMA C J,et al.Modeling gravity driven unstable flow in a water repellent soil[J].Journal of Hydrology,1999,215:202-214.

[112]MUALEM Y.Conceptual model of hysteresis[J].Water Resources Research,1974,10(3):514-520.

[113]MUALEM Y.New modelforpredicting hydraulic conductivityofunsaturated porous-media[J].Water Resources Research,1976,12(3):513-522.

[114]Van GENUCHTEN M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Sci Soc Am J,1980,44(5):892-898.

[115]DEINER T M,PARLANGE J Y,STEENHUIS T S,et al.Real-time measurement of water profiles in a sand using neutron radiography[C]RAMIREZ J A.Hydrology Days 2002:Proceedings of the 22ndAnnual American Geophysical Union Hydrology Days.FortCollins:ColoradoState Univers,2002:56-63.

[116]GLASS R J,YARRINGTON L.Simulation of gravity fingering in porous media using amodified invasion percolation model[J].Geoderma,1996,70(2/3/4):231-252.

[117]URSINO N,SILVESTRI S,MARANI M.Subsurface flow and vegetation patterns in tidal environments[J].Water Resources Research,2004,40(5):W05115.(doi:10.1029/2003WR002702).

[118]LI Hai-long,LI Ling,LOCKINGTON D.Aeration for plant root respiration in a tidal marsh[J].Water Resources Research,2005,41(6):W06023.(doi:10.1029/2004WR003759).

[119]JIAO J J,LI Hai-long.Subsurface airflow induced by natural forcings[J].Advances in Earth Sciences,2004,19(3):413-421.

[120]JIAO J J,LI Hai-long.Breathing of coastal vadose zone induced by sea level fluctuations[J].Geophysics Research Letters,2004,31:L11502.(doi:10.1029/2004GL019572).

[121]TOUMA J,VACHAUD G,PARLANGE J Y.Air andwater flow in a sealed,ponded vertical soil column:experimental and model[J].Soil Science,1984,137:181-187.

[122]DiXON R M,LINDEN D R.Soil air pressure and water infiltration under border irrigation[J].Soil Science Society of America Journal,1972,36:948-953.