水分与植物生长交互的建模与仿真研究
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摘要
虚拟植物是指用计算机来模拟在生理过程驱动及环境影响下植物在三维空间中生长发育的状况，在农学、林学、生态学等领域有着广阔的应用前景。虚拟植物与环境交互是虚拟植物研究领域中需要解决的重要技术和研究热点之一；如何用数学语言来描述以及用计算机来模拟植物与环境的交互作用也是虚拟植物研究的一个难点。水分是植物生长过程中不可缺少的环境条件，暂时或永久性的水分胁迫是植物生长发育过程频繁遇到的情况。与其它环境因素相比，水分胁迫会严重限制植物的生长和分布。本文的研究重点是对植物与水分交互进行建模，在计算机上模拟植物在水分胁迫（干旱）条件下的生理、形态反应，并通过3D可视化技术展示。论文主要研究内容和贡献如下：
①构建了一种植株器官与水分交互的生长模型。定义了“水分亏缺度”来描述植物整体的水分状态，包含水分亏缺持续时间、水分亏缺强度以及植物对水分亏缺敏感性三个要素；采用“电路类比水分传输模型”来估计植物单器官的水势，进而描述植物器官局部水分状态；采用“源汇生物量分配模型”建立不同汇与水分亏缺度、器官水势之间的联系，实现植物器官生长与水分的反馈；采用不同水分环境下玉米生长的数据集，验证了所构建模型的正确性和有效性。结果表明该模型能够有效地模拟在水分亏缺环境下玉米各器官的形态变化。
②构建了一种基于根向水性的植物根系吸水模型。采用体素分割根系生长区域，利用三维Richards方程模拟土壤水分布的动态过程以及与根系结构的相互作用；采用空间殖民算法计算根尖感知的向水性方向，综合根尖原生长方向、向重力方向以及向水性方向，合成新的根尖生长方向；对比分析了向水性对根累计吸水量、根长随深度分布的影响。采用L-系统控制和模拟根系的生长发育，模拟根生长与土壤水分的交互，结果表明该方法能有效地展示向水性对于根系结构发展的影响。
③构建了一种整株植物与水分交互的生长模型。针对把植物地上和地下部分分开研究存在的缺陷，提出一种分层水分传输模型，不同层分别用于计算由水蒸腾作用对植物地上器官水势以及地下土壤水分传输的影响。在计算出植物地上器官水势之后，依据基尔霍夫电流定律，计算根系中根段的水流量，从而修改Richards的汇项，模拟蒸腾驱动下根水分吸收以及土壤水分运动；分析了植株不同位置水势随土壤水势变化的特征；模拟了在不同水分亏缺环境下，整个植物整体的生长过程。结果表明该方法能够填补把植物地上和地下部分分开研究存在的缺陷，实现模拟植株整体的目标。
④研发完成了一组支持交互模型的模拟软件。采用面向对象的编程语言Java，基于Eclipse平台，实现了基于虚拟器官的思想，支持植物株体、根系和整株与水分的交互，并借助Java3D图形库对模拟结果进行可视化，借助Matlab对土壤含水量的三维空间和累计吸水量进行可视化。
Virtual plant is a kind of technology which simulates plant growth that iscontrolled by physiological processes and driven by environment in three-dimensionalspace and to show the growth process with visualization technologies based oncomputer. It has potential applications including agriculture, forestry, ecology，remotesensing and other subjects. On the one hand, interaction between environment andvirtual plant is one of the key techniques and also is one of the difficult and hot spots inresearch on virtual plants. On the other hand, although botanists have already studiedthe interaction between plant and environment，it is difficult to describe thoseprocesses through the mathematical model and simulate those processes bycomputer. Water deficit stress known as drought stress is commonly encountered.Permanent or temporary, it limits growth and distribution of natural vegetation andperformance of cultivated plants more than any other environmental factors do. Thegoal of the paper is to model plant and water environ interaction and demonstrate plantphysiological and morphological responses to water deficit stress by3Dvisualization.The main studies and contributions in this dissertation are as followings
①A growth model for interaction between plant organs and water isconstructed.A index called water deficit degree（WDD） is defined to estimate waterstatus of whole plant by including three factor：water deficit intensity，water deficiduration and plant resistance to water deficit.A water transport electrical-circuit analogymodel is used to estimate plant single organ water potential which is defined to describelocal organ water status.The feedback between plant growth and water is achieved bymodeling the organ sink with water potential and WDD using source sink model.Amaize dataset under different water regims is used to validate the proposed model. Theresults show that the model can simulate morphological changes of maize organs underwater deficit well during vegetation growth stage.
②A root system model based on hydrotropism is proposed. Voxel technology isused to subdivide root growth zone.3D Rachirds equation is used to simulate thedynamic process of soil water distribution and interaction between soil water and rootarchitecture.The space colonization algorithm is used to sense direction of hydrotropismand then direction of root growth will be synthetical by hydrotropism, gravitropism and original growth direction. Water uptake and root length fraction alongdeep affected by hydrotropism are analyzed. L-Systems are used to control rootgrowth and development and interaction with soil water. The results show that theproposed method can demonstrate root structure influenced by hydrotropism effectively.
③A growth model for interaction between whole plant and water is constructed.To solve defect for plant aboveground and underground parts separate study, a tieredwater transprot model is proposed to calculate water potential of aboveground organsand effect of belowground soil water transport induced by transpiration. Aftercalculating water potential the aboveground organs, flux of root segment is calculatedaccording to Kirchhoff’s current law and then the sink term of Richards equation will bemodified to simulate root water uptake and soil water transport driven by transpiration.The water potential characteristics of plant different locations are analysed with changesin soil water potential. The growth process of whole plant is simulated in different waterdeficits. The results show that the method can be able to fill the gap betweenaboveground and underground parts study separately, and to achieve the goal tosimulate the plant as a whole under water deficit.
④A set of simulation woftwre to support the interactive model are research anddevelopmentresearch and developmentresearched and developed completely. Base onthe concept ot virtual organ, oriented object program language(JAVA) is used toprogram aboveground, root system and the whole palnt interaction with water inWindows operation system on Eclipse platform. JAVA3D graphics library is used forvisualization of simulation results. Matlab is used for visualization of soil waterdistribution and water uptake.
①构建了一种植株器官与水分交互的生长模型。定义了“水分亏缺度”来描述植物整体的水分状态，包含水分亏缺持续时间、水分亏缺强度以及植物对水分亏缺敏感性三个要素；采用“电路类比水分传输模型”来估计植物单器官的水势，进而描述植物器官局部水分状态；采用“源汇生物量分配模型”建立不同汇与水分亏缺度、器官水势之间的联系，实现植物器官生长与水分的反馈；采用不同水分环境下玉米生长的数据集，验证了所构建模型的正确性和有效性。结果表明该模型能够有效地模拟在水分亏缺环境下玉米各器官的形态变化。
②构建了一种基于根向水性的植物根系吸水模型。采用体素分割根系生长区域，利用三维Richards方程模拟土壤水分布的动态过程以及与根系结构的相互作用；采用空间殖民算法计算根尖感知的向水性方向，综合根尖原生长方向、向重力方向以及向水性方向，合成新的根尖生长方向；对比分析了向水性对根累计吸水量、根长随深度分布的影响。采用L-系统控制和模拟根系的生长发育，模拟根生长与土壤水分的交互，结果表明该方法能有效地展示向水性对于根系结构发展的影响。
③构建了一种整株植物与水分交互的生长模型。针对把植物地上和地下部分分开研究存在的缺陷，提出一种分层水分传输模型，不同层分别用于计算由水蒸腾作用对植物地上器官水势以及地下土壤水分传输的影响。在计算出植物地上器官水势之后，依据基尔霍夫电流定律，计算根系中根段的水流量，从而修改Richards的汇项，模拟蒸腾驱动下根水分吸收以及土壤水分运动；分析了植株不同位置水势随土壤水势变化的特征；模拟了在不同水分亏缺环境下，整个植物整体的生长过程。结果表明该方法能够填补把植物地上和地下部分分开研究存在的缺陷，实现模拟植株整体的目标。
④研发完成了一组支持交互模型的模拟软件。采用面向对象的编程语言Java，基于Eclipse平台，实现了基于虚拟器官的思想，支持植物株体、根系和整株与水分的交互，并借助Java3D图形库对模拟结果进行可视化，借助Matlab对土壤含水量的三维空间和累计吸水量进行可视化。
Virtual plant is a kind of technology which simulates plant growth that iscontrolled by physiological processes and driven by environment in three-dimensionalspace and to show the growth process with visualization technologies based oncomputer. It has potential applications including agriculture, forestry, ecology，remotesensing and other subjects. On the one hand, interaction between environment andvirtual plant is one of the key techniques and also is one of the difficult and hot spots inresearch on virtual plants. On the other hand, although botanists have already studiedthe interaction between plant and environment，it is difficult to describe thoseprocesses through the mathematical model and simulate those processes bycomputer. Water deficit stress known as drought stress is commonly encountered.Permanent or temporary, it limits growth and distribution of natural vegetation andperformance of cultivated plants more than any other environmental factors do. Thegoal of the paper is to model plant and water environ interaction and demonstrate plantphysiological and morphological responses to water deficit stress by3Dvisualization.The main studies and contributions in this dissertation are as followings
①A growth model for interaction between plant organs and water isconstructed.A index called water deficit degree（WDD） is defined to estimate waterstatus of whole plant by including three factor：water deficit intensity，water deficiduration and plant resistance to water deficit.A water transport electrical-circuit analogymodel is used to estimate plant single organ water potential which is defined to describelocal organ water status.The feedback between plant growth and water is achieved bymodeling the organ sink with water potential and WDD using source sink model.Amaize dataset under different water regims is used to validate the proposed model. Theresults show that the model can simulate morphological changes of maize organs underwater deficit well during vegetation growth stage.
②A root system model based on hydrotropism is proposed. Voxel technology isused to subdivide root growth zone.3D Rachirds equation is used to simulate thedynamic process of soil water distribution and interaction between soil water and rootarchitecture.The space colonization algorithm is used to sense direction of hydrotropismand then direction of root growth will be synthetical by hydrotropism, gravitropism and original growth direction. Water uptake and root length fraction alongdeep affected by hydrotropism are analyzed. L-Systems are used to control rootgrowth and development and interaction with soil water. The results show that theproposed method can demonstrate root structure influenced by hydrotropism effectively.
③A growth model for interaction between whole plant and water is constructed.To solve defect for plant aboveground and underground parts separate study, a tieredwater transprot model is proposed to calculate water potential of aboveground organsand effect of belowground soil water transport induced by transpiration. Aftercalculating water potential the aboveground organs, flux of root segment is calculatedaccording to Kirchhoff’s current law and then the sink term of Richards equation will bemodified to simulate root water uptake and soil water transport driven by transpiration.The water potential characteristics of plant different locations are analysed with changesin soil water potential. The growth process of whole plant is simulated in different waterdeficits. The results show that the method can be able to fill the gap betweenaboveground and underground parts study separately, and to achieve the goal tosimulate the plant as a whole under water deficit.
④A set of simulation woftwre to support the interactive model are research anddevelopmentresearch and developmentresearched and developed completely. Base onthe concept ot virtual organ, oriented object program language(JAVA) is used toprogram aboveground, root system and the whole palnt interaction with water inWindows operation system on Eclipse platform. JAVA3D graphics library is used forvisualization of simulation results. Matlab is used for visualization of soil waterdistribution and water uptake.
引文
[1] GUO Y. Plant modeling and its applications to agriculture [M].2nd International Symposiumon Plant Growth Modeling, Simulation, Visualization and Applications. Beijing, PEOPLES RCHINA; Ieee Computer Soc.2006:135-41.
[2] VOS J, EVERS B, BUCK-SORLIN G H, et al. Functional–structural plant modelling: a newversatile tool in crop science [J]. Journal of Experimental Botany2010,61(8):2101-15.
[3]曹宏鑫,石春林,金之庆.植物形态结构模拟与可视化研究进展[J].中国农业科学,2008,41(3):669-77.
[4] HANAN J, PRUSINKIEWICZ P. Foreword: studying plants with functional–structuralmodels [J]. Functional Plant Biology,2008,35:1-3.
[5] SHAO H B, CHU L Y, JALEEL C A, et al. Water-deficit stress-induced anatomical changesin higher plants [J]. Comptes Rendus Biologies,2008,331(3):215-25.
[6]屈洪春.虚拟植物智能生理引擎及关键技术研究[D].重庆;重庆大学,博士学位论文,2009.
[7]刘骥.植物生长模拟与可视化研究[D].重庆;重庆大学,博士学位论文,2009.
[8]曾令秋.虚拟植物器官生长和变形技术研究[D].重庆;重庆大学,博士学位论文,2009.
[9]郭焱,李保国.虚拟植物的研究进展[J].科学通报,2001,46(1):1-4.
[10] MATHIEU A, COURN DE P H, LETORT V, et al. A dynamic model of plant growth withinteractions between development and functional mechanisms to study plant structuralplasticity related to trophic competition [J]. Annals of Botany,2009,103(8):1173-86.
[11] DU N, GUO W, ZHANG X, et al. Morphological and physiological responses of Vitexnegundo L. var. heterophylla (Franch.) Rehd. to drought stress [J]. Acta PhysiologiaePlantarum,2010,32(5):839-48.
[12] F RODRIGUEZ M B, JL GUZMAN. A virtual course on automation of agricultural systems[J]. IntJEngngEd,2006,22(6):1197-210.
[13] WIT C T D. Photosynthesis of leaf canopies [M]. Agricultural Reseach Report. WageningenUniversity.1965.
[14] DUNCAN W G L R S, WILLIAMS W A, HANAU R. A model for simulating photosynthesisin plant communities [J]. Hilgardia1967,38:181-205.
[15]谢云，KINIRYJR.国外作物生长模型发展综述[J].作物学报,2002,28(2):190-5.
[16] BARNSLEY M.F. D S. Iterated function systems and global construction of fractals [J].Proceedings of the Royal Society of London,Series A,Mathematical and Physical Sciences,1985,1817(399):243-75.
[17] MICHAEL F.BARNSLEY J H E, DOUGLAS P.HARDIN. Recurrent iterated functionsystems [J]. Constructive Approximation,1989,5:3-31.
[18] P.PRUSINKIEWICZ M H. Automata language and iterated function systems [M]. FractalModeling in3D Computer Graphics and Imagery. ACM SIGGRAPH.1991:115-43.
[19] P.DE REFFYE C E, J.FRANCON,M.JAEGER,C.PUECH. Plant models faithful to botanicalstructure and development [J]. Computer Graphics,1988,22(4):151-8.
[20] WILLIAM T.REEVES R B. Approximate and probabilistic algorithms for shading andrendering structured particle systems [J]. Computer Graphics,1985,19(3):313-22.
[21] LINDENMAYER. Mathematical models for celluar interaction in development,Part I Part II[J]. Journal of Theoretical Biology,1968,18:280-315.
[22] P.PRUSINKIEWICZ, J.HANNAN. Lindenmayer Systems,fractals,and plants [M]. NewYork:Springer-Verlag.1990:25-30.
[23] P.PRUSINKIEWICZ R K, B.LANE. The L+C plant modelling language [M].Functional-Structural Plant Modelling in Crop Production,J.Vos et al.(eds.),Springer,2007.
[24] HONDA H. Description of the form of trees by the parameters of the tree-like body: effects ofthe branching angle and the branch length on the shape of the tree-like body [J]. Journal ofTheoretical Biology1971,31:331-8.
[25] HACKETT C. A model of the extension and branching of a semihal root of barley, and its usein studying relations between root dimensions. I. The model [J]. Australian Journal of Botany,1972,25:669-79.
[26] FISHER J B. A quantitative analysis of terminalia branch [M]. In: Tomlinson (ed). TropicalTrees as Living Systems. New York: Cambridge University Press,1978.
[27] PERTTUNEN J N E, MARTIN J, LECHOWICZ, SIEV NEN R, MESSIER C. Application ofthe functional-structural tree model Lignum to sugar maple saplings (acer saccharum Mmarsh)growing in forest gaps [J]. Annals of Botany2001,88(3):471-81.
[28] YAN H P K M Z, DE REFFYE P, DINGKUHN M. A dynamic architectural plant modelsimulating resource-dependent growth [J]. Annals of Botany,2004,93:591-602.
[29] GUO Y M Y T, ZHAN Z G, LI B G, DINGKUHN M, LUQUET D, DE REFFYE P.Parameter optimization and field validation of the functional–structural model GREENLABfor maize [J]. Annals of Botany,2006,97:217-30.
[30] KURTH W. Morphological models of plant growth: possibilities and ecological relevance [J].Ecological Modelling1994,75-76:299-308.
[31] ALLEN MT P P, DEJONG TM. Using L-systems for modeling source-sink interactions,architecture and physiology of growing trees: the L-PEACH model [J]. New Phytologist,2005,166(3):869-80.
[32] MZ KANG P H C, AM LIE MATHIEU, V RONIQUE LETORT, RUI QI, ZHI GANGZHAN. A Functional-Structural Plant Model--Theories and Its Applications in Agronomy[M]. Crop Modeling and Decision Support2009:148-60.
[33] SS ANAPALLI L R A, L. MA, D.J. TIMLIN, C.O. STOCKLE, K.J. BOOTE, G.HOOGENBOOM. Current water deficit stress simulations in selected agricultural systemsimulation models [M]. Response of crops to limited water: understanding and modelingwater stress effects on plant growth processes. L.R. Ahuja, V.R. Reddy, S.A. Saseendran, Q.Yu (Eds.).2008:1–38.
[34] T. HOWELL J M. Relationship of dry matter production of field crops to water consumtion[M]. in "Les besoins en eau des cultures, Paris", Paris: INRA Editions,1984.
[35] MAILHOL J-C O A, RUELLE P. Sorghum and Sunflower Evapotranspiration and Yieldfrom Simulated Leaf Area Index [J]. Agricultural Water Management,1997,35:167-82.
[36] KHALEDIAN MR M J-C, RUELLE P, ROSIQUE P. Adapting PILOTE Model for Waterand Yield Management under Direct Seeding System: The Case of Corn and Durum Wheat ina Mediterranean Context [J]. Agricultural Water Management,2009,96:757-70.
[37] CLAUSNITZER V, HOPMANS J W. Simultaneous modeling of transient three-dimensionalroot growth and soil water flow [J]. plant and Soil,1994,164(2):299-314.
[38] HEERAMAN D A H J W, CLAUSNITZER V. Three dimensional imaging of plant roots insitu with X-ray computed tomography [J]. Plant and Soil,1997,189(2):167-79.
[39] SOMMA F H J W, CLAUSNITZER V. Transient three-dimensional modeling of soil waterand solute transport with simultaneous root growth, root water and nutrient uptake [J]. Plantand Soil,1998,202(2):281-93.
[40]金明现王.玉米根系生长及向水性的模拟[J].植物学报,1996,38(5):384-90.
[41] JP LYNCH K L N, ROBERT D. DAVIS AND ANDREI G. JABLOKOW. SimRoot:modelling and visualization of root systems [J]. Plant and Soil,1997,188(1):139-51.
[42] TSUTSUMI D, KOSUGI K, MIZUYAMA T. Root-System Development andWater-Extraction Model Considering Hydrotropism [J]. Soil Sci Soc Am J,2003,67:387-401.
[43] DANIEL LEITNER S K, GERNOT BODNER, ANDREA SCHNEPF. A dynamic rootsystem growth model based on L-Systems:Tropisms and coupling to nutrient uptake fromsoil [J]. Plant and Soil,2010,332(1-2):177-92.
[44] DAUZAT J, RAPIDEL B, BERGER A. Simulation of leaf transpiration and sap flow invirtual plants_model description and application to a coffee plantation in Costa Rica [J].Agricultural and Forest Meteorology,2001,109(2):143-60.
[45] CHENU K, CHAPMAN S C, HAMMER G L, et al. Short‐term responses of leaf growthrate to water deficit scale up to whole‐plant and crop levels: an integrated modellingapproach in maize [J]. Plant, Cell&Environment,2008,31(3):378-91.
[46] SILVA D D, FAVREAU R, AUZMENDI I, et al. Linking water stress effects on carbonpartitioning by introducing a xylem circuit into L-PEACH [J]. Annals of Botany2011,108(6):1135-45.
[47] WU L, REFFYE P D, HU B-G, et al. A water supply optimization problem for plant growthbased on GreenLab model [M]. In: Kamgnia E, Philippe B, Slimani Y, editors.7èmeColloque Africain sur la Recherche en Informatique. Mammamet, Tunisia: INRIA.2004:194-207.
[48] SONG Y B C, HANAN J. Architectural analysis and modeling of maize growth anddevelopment under water stress [M].5th International Workshop on Functional StructuralPlant Models (FSPM07), Napier New Zealand.2007:4-10.
[49] PAGLIS C M P, R. G. VON Maize yield and blooming date simulation by usingCERES-Maize model [J]. Ciência e Agrotecnologia,2009,33(2):509-16.
[50] FOURNIER C, ANDRIEU B. A3D architectural and process-based model of maizedevelopment [J]. Annals of Botany,1998,81:233-50.
[51]郭焱李.玉米冠层学描述与三维重建研究[J].应用生态学报,1999,10(1):1-6.
[52] WANG XP G Y, WANG XY, MA YT, LI BG. Estimating photosynthetically active radiationdistribution in maize canopies by a three-dimensional incident radiation model. FunctionalPlant Biology [J]. Functional Plant Biology,2008,35(9-10):867-75.
[53]马韫韬，文美平，李保国，王锡平，郭焱.基于器官尺度虚拟玉米冠层直射光分布的快速计算模型[J].农业工程学报,2007,23(10):151-5.
[54] MA YT W M, GUO Y, LI BG,COURNEDE PH,DE REFFYE P. Parameter optimization andfield validation of the functional-structural model GREENLAB for maize at differentpopulation densities [J]. annals of Botany,2008,101:1185-94.
[55] BIRCH C J, THORNBY, DAVID, ADKINS, STEVE, ANDRIEU, BRUNO,, HANAN J.Architectural modelling of maize under water stress [M]. In Animal Production Science.6thTriennial Conference of the Maize Association of Australia, Griffith, NSW.2006:335-41.
[56] FOURNIER C, ANDRIEU B. ADEL-maize: an L-system based model for the integration ofgrowth processes from the organ to the canopy. Application to regulation of morphogenesisby light availability [J]. Agronomie,1999,19:313-27.
[57] YOUHONG SONG C B, JIM HANAN. Analysis of maize canopy development underwater stress and incorporation into the ADEL-Maize model [J]. Functional Plant Biology2008,35(10):925–35
[58] DROUET J-L, PAG S L. GRAAL: a model of GRowth, Architecture and carbon ALlocationduring the vegetative phase of the whole maize plant:: Model description andparameterisation [J]. Ecological Modelling,2003,165(2-3):147-73.
[59]管建慧,刘克礼,郭新宇.玉米根系构型的研究进展[J].玉米科学,2006,14(6):162-6.
[60] DIGGLE A J. Rootmap A model in three-dimensional coordinates of the growth and structureof fibrous root systems [J]. Plant and Soil,1988,105(2):169-78.
[61] PAG S L, JORDAN M O, PICARD D. A simulation model of the three-dimensionalarchitecture of the maize root system [J]. Plant and Soil,1989,119(1):147-54.
[62] BERNTSON G. Modelling root architecture: are there tradeoffs between efficiency andpotential of resource acquisition?[J]. New Phytologist,1994,127(3):483-93.
[63]冯斌,杨培岭.植物根系的分形及计算机模拟[J].中国农业大学学报,2000,5(2):96-9.
[64] A. H. FITTER T R S, M. L. HARVEY, G. W. WILSON. Architectural analysis of plant rootsystems1. Architectural correlates of exploitation efficiency [J]. New Phytologist,1991,118(3):375-82.
[65]邓旭阳，郭新宇.玉米根系集合造型研究[J].工程图学学报，,2004,4:62-6.
[66]张吴平.三维根系功能-结构模型的构建与根区土壤水分运动的模拟[D].北京;中国农业大学,博士学位论文,2006.
[67] HOCHHOLDINGER F. The maize root system: morphology, anatomy, and genetics [J].Handbook of Maize: Its Biology2009):145-60.
[68]宋有洪.玉米生长的生理生态功能与形态结构并行模拟模型[D].北京;中国农业大学,博士学位论文,2003.
[69] HONERT T H V D. Water transPort in PlantS as a catenary [J]. Discuss Faraday Soc,1948,3:146-53.
[70] NEUMANN H H, THURTELL G W. Stevenson K. In situ measurements of leaf waterpotential and resistance to water flow [J]. Can J plant Sci,1974,54:175-84.
[71] WALLACE J S, BISCOE P V. Water relations of w inter wheat,4. hydraulic resistance andcapacitance in the soil-plant system [J]. J Agric Sci Cambridge,1983,100:591-600.
[72]刘文兆.土壤-植物系统水分运移过程的阻容电模拟[J].生态学报,2005,25(11):2947-53.
[73] HERZOG K M H R, THUM R. Diurnal changes in the radius of a subalpine Norway sprucestem: their relation to the sap flow and their use to estimate transpiration [J]. Trees,1995,10:94-101.
[74] PER M KI M. E N, S SEVANTO, H ILVESNIEMI, E SIIVOLA, P HARI,T VESALA. Treestem diameter variations and transpiration in Scots pine: an analysis using a dynamic sap flowmodel [J]. Tree Physiology,2001,21:889-97.
[75] ZWEIFEL R I H, H SLER R. Link between diurnal stem radius changes and tree waterrelations [J]. Tree Physiology,2001,21:869-87.
[76] STEPPE K D P D, LEMEUR R, VANROLLEGHEM PA. A mathematical model linking treesap flow dynamics to daily stem diameter fluctuations and radial stem growth [J]. TreePhysiology,2005,26:257-73.
[77] DAUDET F A, A.LACOINTE, RE J P G A, et al. Generalized MuKnch Coupling betweenSugar and Water Fluxes for Modelling Carbon Allocation as A4ected by Water Status [J]. Jtheor Biol2002,214:481-98.
[78] SCHEPPER V D, STEPPE K. Development and verification of a water and sugar transportmodel using measured stem diameter variations [J]. J Exp Bot,2010,61(8):2083-99.
[79] GARDNER W R. Dynamic aspects of water availability to plants [J]. Soil Science,1960,89(2):63-73.
[80] MOLZ F J. Water transport in the soil-root system: Transient analysis [J]. WATERRESOURCES RESEARCH,1976,12(4):805-8.
[81]罗远培李.根土系统与作物水氮资源利用效率[M].北京:中国农业科技出版社,1996.
[82]杨培岭郝.植物根系吸水模型的发展动态[J].中国农业大学学报,1999,2(2):1-10.
[83]邵明安，杨文治，李玉山.植物根系吸收土壤水分的数学模型[J].土壤学报,1987,24(4):295-304.
[84] GREEN S R, I. VOGELER, B.E. CLOTHIER, T.M. MILLS, C. VAN DEN DIJSSEL.Modelling water uptake by a mature apple tree [J]. Aust J Soil Res,2003,41:365-80.
[85] KEESE K E, B.R. SCANLON, R.C. REEDY. Assessing controls on diffuse groundwaterrecharge using unsaturated flow modeling.[J]. Water Resour Res,2005,41:12.
[86] LI K Y, R. DE JONG, M.T. COE, N. RAMANKUTTY. Root-water-uptake based upon a newwater stress reduction and an asymptotic root distribution function.[J]. Earth Interact,2006,10:1-22.
[87] IM NEK J, M.H. VAN GENUCHTEN, M. EJNA. The HYDRUS-1D software packagefor simulating the one-dimensional movement of water, heat and multiple solutes invariably-saturated media, version3.0[M]. HY-DRUS Software Series1. Dep. ofEnvironmental Sciences, Univ. of Cali-fornia, Riverside.2005.
[88] BRAUD I, N. VARADO, A. OLIOSO. Comparison of root water uptake modules using eitherthe surface energy balance or potential transpiration [J]. J Hydrol,2005,301:267-86.
[89] SKAGGS T H, GENUCHTEN M T V, SHOUSE P J, et al. Macroscopic approaches to rootwater uptake as a function ofwater and salinity stress [J]. Agricultural Water Management,2006,86(1-2):140-9.
[90] LIER Q D J V, DAM J C V, METSELAAR K, et al. Macroscopic root water uptakedistribution using a matric flux potential approach [J]. Soil Science Society of America2008,7(3):1065-78.
[91] LIER Q D J V, DAM J C V, METSELAAR K. Root water extraction under combined waterand osmotic stress [J]. Soil Science Society of America Journal,2009,73(3):862-75.
[92]傅承新，丁炳扬.植物学[M].浙江大学出版社,2002.
[93] PALLAS B, LOI C, COURN DE A C P H, et al. Comparison of three approaches to modelgrapevine organogenesis in conditions of fluctuating temperature, solar radiation and soilwater content [J]. annals of Botany,2011,107(5):729-45.
[94] JARVIS P G. The interpretation of the variations in water potential and stomatal conductancefound in canopies in the field.[M]. Philosophical Transactions of the Royal Society, London,Ser. B.1976:593-610.
[95] COWAN I R, FARQUHAR G D. Stomatal function i n relation t o leaf metabolism andenvironment [M]. In Integration of Activity in the Higher Plant, D.H. Jennings, Editor.1977,Cambridge Univ. Press,Cambridge: U. K,1977.
[96] CHUNFANG WEI M T T, ERNST STEUDLE. Direct Measurement of Xylem Pressure inLeaves of IntactMaize Plants. A Test of the Cohesion-Tension Theory TakingHydraulicArchitecture into Consideration [J]. Plant Physiology,1999,121:1191-205.
[97] CLAPP R B, HORNBERGER G M. Empirical equations forsome soil hydraulic properties [J].Water Resour Res,1978,14:601-4.
[98] AMOS B, WALTERS D T. Maize Root Biomass and Net Rhizodeposited Carbon: AnAnalysis of the Literature [J]. Soil Sci Soc Am J,2006,70:1489-503.
[99] JURGENFRENSCH, ERNSTSTEUDLE. Axial and Radial Hydraulic Resistance to Roots ofMaize [J]. Plant Physiol,1989,91:719-26.
[100] LE ROUX X L A, ESCOBAR-GUTIERREZ A, LE DIZES S. Carbon-based models ofindividual tree growth: A critical appraisal [J]. Annal Forest Science,2001,58(5):469-506.
[101] EVERS J B, VOS J, X.YIN, et al. Simulation of wheat growth and development based onorgan-level photosynthesis and assimilate allocation [J]. ournal of Experimental Botany,2010,61(8):2203–16.
[102] HEUVELINK E. Dry matter partitioning in tomato: validation ofa dynamic simulation model[J]. Annals of Botany,1996,77:71-80.
[103] SONG Y, C.J. BIRCH, J. HANAN. Maize canopy production under contrasted water regimes[J]. Annals of Applied Biology,2010,157(1):111-23.
[104] SINCLAIR T R. Theoretical Analysis of Soil and Plant Traits Influencing Daily Plant WaterFlux on Drying Soils [J]. Agronomy Journal,2005,97(7):1148-52.
[105] FITTER A H, STICKLAND T S. Architecture analysis of plan troot system [J]. NewPhytologist,1992,121:243-8.
[106] ROSE D A. The description of growth of root system [J]. plant and Soil,1983,75:405-15.
[107]赵春江,王功明,郭新宇, et al.基于交互式骨架模型的玉米根系三维可视化研究[J].农业工程学报,2007,23(9):1-6.
[108] DELFEENA EAPEN M A L B, GEORGINA PONCE, MAR′A E. CAMPOS,GLADYSI.CASSAB. Hydrotropism: root growth responses to water [J]. Trends in Plant Science,2005,10(1):44-9.
[109] J. IMUNEK K H, M.T.V. GENUCHTEN. The SWMS3D Code for Simulating Water Flowand Solute Transport in Three-Dimensional Variably-Saturated Media [M]. S. Laboratory(Ed.), U.S. Department of Agriculture, Riverside, CA,1995.
[110] HERKELRATH WN M E, GARDNER WR. Water uptake by Plants: I and II [J]. Soil Sci SocAm J1977,41(1033-1043):
[111] TAKAHASHI H M Y, FUJII N. Hormonal interaction during root tropic growth:hydrotropism versus gravitropism [J]. Plant Mol Biol,2009,29:489-502.
[112]平晓燕,周广胜,孙敬松.植物光合产物分配及其影响因子研究进展[J].植物生态学报,2010,34(1):100-11.
[113] E REFFYE P H F, BLAISE F, BARTH L MY D, DAUZAT J,AUCLAIR D. A modelsimulating above-and below-ground tree architecture with agroforestry applications [J].Agroforest Syst,1995,30:175-97.
[114] BLAISE F F T, STOKES A, DE REFFYE P. A modelsimul a ting interac tions betwe e nplant shoot an rootarchitecture in a non-homogen eous environment [M]. In:Stokes A (ed)Proc. Int. Conf.“The Supporting Roots ofTrees and Woody Plants: Form, Function andPhysiology”,Bordeaux,20–24July,1998, Series:‘Developments in plantand soil sciences.2000:61-76.
[115]赵星.虚拟植物生长中几个问题的研究[D];中国科学院自动化研究所,博士后学位论文,2003.
[116]吕游，杨克俭.树木冠层与根系统一建模研究[J].计算机与数字工程,2007,35(10):44-5：65.
[117] MICHEL G NARD J D, NICOL S FRANCK, FRAN OISE LESCOURRET, NICOLASMOITRIER, PHILIPPE VAAST， GILLES VERCAMBRE. Carbon allocation in fruit trees:from theory to modelling [J]. trees,2008,22(3):269-82.
[118] GUO Y, FOURCAUD T, JAEGER M, et al. Plant growth and architectural modelling and itsapplications [J]. Annals of Botany,2011,107(5):723-7.
[119]郑国清，段韶芬，阎书波，吕冰清.玉米叶龄与器官发育模拟模型[J].玉米科学2003,11(4):63-6.
[120] SALAH H B H, TARDIEU1F. Quantitative analysis of the combined effects of temperature,evaporative demand and light on leaf elongation rate in well-watered field andlaboratory-grown maize plants [J]. J Exp Bot,1996,47(11):1689-98.
[121] ROBERTSON M J. relations between internode elongation plant height and leaf appearancein maize [J]. Field Crops Research,1994,38(3):135-45.
[122] SONG Y, BIRCH C, QU S, et al. Analysis and Modelling of the Effects of Water Stress onMaize Growth and Yield in Dryland Conditions [J]. Plant Production Science,2010,13(2):199-208.
[2] VOS J, EVERS B, BUCK-SORLIN G H, et al. Functional–structural plant modelling: a newversatile tool in crop science [J]. Journal of Experimental Botany2010,61(8):2101-15.
[3]曹宏鑫,石春林,金之庆.植物形态结构模拟与可视化研究进展[J].中国农业科学,2008,41(3):669-77.
[4] HANAN J, PRUSINKIEWICZ P. Foreword: studying plants with functional–structuralmodels [J]. Functional Plant Biology,2008,35:1-3.
[5] SHAO H B, CHU L Y, JALEEL C A, et al. Water-deficit stress-induced anatomical changesin higher plants [J]. Comptes Rendus Biologies,2008,331(3):215-25.
[6]屈洪春.虚拟植物智能生理引擎及关键技术研究[D].重庆;重庆大学,博士学位论文,2009.
[7]刘骥.植物生长模拟与可视化研究[D].重庆;重庆大学,博士学位论文,2009.
[8]曾令秋.虚拟植物器官生长和变形技术研究[D].重庆;重庆大学,博士学位论文,2009.
[9]郭焱,李保国.虚拟植物的研究进展[J].科学通报,2001,46(1):1-4.
[10] MATHIEU A, COURN DE P H, LETORT V, et al. A dynamic model of plant growth withinteractions between development and functional mechanisms to study plant structuralplasticity related to trophic competition [J]. Annals of Botany,2009,103(8):1173-86.
[11] DU N, GUO W, ZHANG X, et al. Morphological and physiological responses of Vitexnegundo L. var. heterophylla (Franch.) Rehd. to drought stress [J]. Acta PhysiologiaePlantarum,2010,32(5):839-48.
[12] F RODRIGUEZ M B, JL GUZMAN. A virtual course on automation of agricultural systems[J]. IntJEngngEd,2006,22(6):1197-210.
[13] WIT C T D. Photosynthesis of leaf canopies [M]. Agricultural Reseach Report. WageningenUniversity.1965.
[14] DUNCAN W G L R S, WILLIAMS W A, HANAU R. A model for simulating photosynthesisin plant communities [J]. Hilgardia1967,38:181-205.
[15]谢云，KINIRYJR.国外作物生长模型发展综述[J].作物学报,2002,28(2):190-5.
[16] BARNSLEY M.F. D S. Iterated function systems and global construction of fractals [J].Proceedings of the Royal Society of London,Series A,Mathematical and Physical Sciences,1985,1817(399):243-75.
[17] MICHAEL F.BARNSLEY J H E, DOUGLAS P.HARDIN. Recurrent iterated functionsystems [J]. Constructive Approximation,1989,5:3-31.
[18] P.PRUSINKIEWICZ M H. Automata language and iterated function systems [M]. FractalModeling in3D Computer Graphics and Imagery. ACM SIGGRAPH.1991:115-43.
[19] P.DE REFFYE C E, J.FRANCON,M.JAEGER,C.PUECH. Plant models faithful to botanicalstructure and development [J]. Computer Graphics,1988,22(4):151-8.
[20] WILLIAM T.REEVES R B. Approximate and probabilistic algorithms for shading andrendering structured particle systems [J]. Computer Graphics,1985,19(3):313-22.
[21] LINDENMAYER. Mathematical models for celluar interaction in development,Part I Part II[J]. Journal of Theoretical Biology,1968,18:280-315.
[22] P.PRUSINKIEWICZ, J.HANNAN. Lindenmayer Systems,fractals,and plants [M]. NewYork:Springer-Verlag.1990:25-30.
[23] P.PRUSINKIEWICZ R K, B.LANE. The L+C plant modelling language [M].Functional-Structural Plant Modelling in Crop Production,J.Vos et al.(eds.),Springer,2007.
[24] HONDA H. Description of the form of trees by the parameters of the tree-like body: effects ofthe branching angle and the branch length on the shape of the tree-like body [J]. Journal ofTheoretical Biology1971,31:331-8.
[25] HACKETT C. A model of the extension and branching of a semihal root of barley, and its usein studying relations between root dimensions. I. The model [J]. Australian Journal of Botany,1972,25:669-79.
[26] FISHER J B. A quantitative analysis of terminalia branch [M]. In: Tomlinson (ed). TropicalTrees as Living Systems. New York: Cambridge University Press,1978.
[27] PERTTUNEN J N E, MARTIN J, LECHOWICZ, SIEV NEN R, MESSIER C. Application ofthe functional-structural tree model Lignum to sugar maple saplings (acer saccharum Mmarsh)growing in forest gaps [J]. Annals of Botany2001,88(3):471-81.
[28] YAN H P K M Z, DE REFFYE P, DINGKUHN M. A dynamic architectural plant modelsimulating resource-dependent growth [J]. Annals of Botany,2004,93:591-602.
[29] GUO Y M Y T, ZHAN Z G, LI B G, DINGKUHN M, LUQUET D, DE REFFYE P.Parameter optimization and field validation of the functional–structural model GREENLABfor maize [J]. Annals of Botany,2006,97:217-30.
[30] KURTH W. Morphological models of plant growth: possibilities and ecological relevance [J].Ecological Modelling1994,75-76:299-308.
[31] ALLEN MT P P, DEJONG TM. Using L-systems for modeling source-sink interactions,architecture and physiology of growing trees: the L-PEACH model [J]. New Phytologist,2005,166(3):869-80.
[32] MZ KANG P H C, AM LIE MATHIEU, V RONIQUE LETORT, RUI QI, ZHI GANGZHAN. A Functional-Structural Plant Model--Theories and Its Applications in Agronomy[M]. Crop Modeling and Decision Support2009:148-60.
[33] SS ANAPALLI L R A, L. MA, D.J. TIMLIN, C.O. STOCKLE, K.J. BOOTE, G.HOOGENBOOM. Current water deficit stress simulations in selected agricultural systemsimulation models [M]. Response of crops to limited water: understanding and modelingwater stress effects on plant growth processes. L.R. Ahuja, V.R. Reddy, S.A. Saseendran, Q.Yu (Eds.).2008:1–38.
[34] T. HOWELL J M. Relationship of dry matter production of field crops to water consumtion[M]. in "Les besoins en eau des cultures, Paris", Paris: INRA Editions,1984.
[35] MAILHOL J-C O A, RUELLE P. Sorghum and Sunflower Evapotranspiration and Yieldfrom Simulated Leaf Area Index [J]. Agricultural Water Management,1997,35:167-82.
[36] KHALEDIAN MR M J-C, RUELLE P, ROSIQUE P. Adapting PILOTE Model for Waterand Yield Management under Direct Seeding System: The Case of Corn and Durum Wheat ina Mediterranean Context [J]. Agricultural Water Management,2009,96:757-70.
[37] CLAUSNITZER V, HOPMANS J W. Simultaneous modeling of transient three-dimensionalroot growth and soil water flow [J]. plant and Soil,1994,164(2):299-314.
[38] HEERAMAN D A H J W, CLAUSNITZER V. Three dimensional imaging of plant roots insitu with X-ray computed tomography [J]. Plant and Soil,1997,189(2):167-79.
[39] SOMMA F H J W, CLAUSNITZER V. Transient three-dimensional modeling of soil waterand solute transport with simultaneous root growth, root water and nutrient uptake [J]. Plantand Soil,1998,202(2):281-93.
[40]金明现王.玉米根系生长及向水性的模拟[J].植物学报,1996,38(5):384-90.
[41] JP LYNCH K L N, ROBERT D. DAVIS AND ANDREI G. JABLOKOW. SimRoot:modelling and visualization of root systems [J]. Plant and Soil,1997,188(1):139-51.
[42] TSUTSUMI D, KOSUGI K, MIZUYAMA T. Root-System Development andWater-Extraction Model Considering Hydrotropism [J]. Soil Sci Soc Am J,2003,67:387-401.
[43] DANIEL LEITNER S K, GERNOT BODNER, ANDREA SCHNEPF. A dynamic rootsystem growth model based on L-Systems:Tropisms and coupling to nutrient uptake fromsoil [J]. Plant and Soil,2010,332(1-2):177-92.
[44] DAUZAT J, RAPIDEL B, BERGER A. Simulation of leaf transpiration and sap flow invirtual plants_model description and application to a coffee plantation in Costa Rica [J].Agricultural and Forest Meteorology,2001,109(2):143-60.
[45] CHENU K, CHAPMAN S C, HAMMER G L, et al. Short‐term responses of leaf growthrate to water deficit scale up to whole‐plant and crop levels: an integrated modellingapproach in maize [J]. Plant, Cell&Environment,2008,31(3):378-91.
[46] SILVA D D, FAVREAU R, AUZMENDI I, et al. Linking water stress effects on carbonpartitioning by introducing a xylem circuit into L-PEACH [J]. Annals of Botany2011,108(6):1135-45.
[47] WU L, REFFYE P D, HU B-G, et al. A water supply optimization problem for plant growthbased on GreenLab model [M]. In: Kamgnia E, Philippe B, Slimani Y, editors.7èmeColloque Africain sur la Recherche en Informatique. Mammamet, Tunisia: INRIA.2004:194-207.
[48] SONG Y B C, HANAN J. Architectural analysis and modeling of maize growth anddevelopment under water stress [M].5th International Workshop on Functional StructuralPlant Models (FSPM07), Napier New Zealand.2007:4-10.
[49] PAGLIS C M P, R. G. VON Maize yield and blooming date simulation by usingCERES-Maize model [J]. Ciência e Agrotecnologia,2009,33(2):509-16.
[50] FOURNIER C, ANDRIEU B. A3D architectural and process-based model of maizedevelopment [J]. Annals of Botany,1998,81:233-50.
[51]郭焱李.玉米冠层学描述与三维重建研究[J].应用生态学报,1999,10(1):1-6.
[52] WANG XP G Y, WANG XY, MA YT, LI BG. Estimating photosynthetically active radiationdistribution in maize canopies by a three-dimensional incident radiation model. FunctionalPlant Biology [J]. Functional Plant Biology,2008,35(9-10):867-75.
[53]马韫韬，文美平，李保国，王锡平，郭焱.基于器官尺度虚拟玉米冠层直射光分布的快速计算模型[J].农业工程学报,2007,23(10):151-5.
[54] MA YT W M, GUO Y, LI BG,COURNEDE PH,DE REFFYE P. Parameter optimization andfield validation of the functional-structural model GREENLAB for maize at differentpopulation densities [J]. annals of Botany,2008,101:1185-94.
[55] BIRCH C J, THORNBY, DAVID, ADKINS, STEVE, ANDRIEU, BRUNO,, HANAN J.Architectural modelling of maize under water stress [M]. In Animal Production Science.6thTriennial Conference of the Maize Association of Australia, Griffith, NSW.2006:335-41.
[56] FOURNIER C, ANDRIEU B. ADEL-maize: an L-system based model for the integration ofgrowth processes from the organ to the canopy. Application to regulation of morphogenesisby light availability [J]. Agronomie,1999,19:313-27.
[57] YOUHONG SONG C B, JIM HANAN. Analysis of maize canopy development underwater stress and incorporation into the ADEL-Maize model [J]. Functional Plant Biology2008,35(10):925–35
[58] DROUET J-L, PAG S L. GRAAL: a model of GRowth, Architecture and carbon ALlocationduring the vegetative phase of the whole maize plant:: Model description andparameterisation [J]. Ecological Modelling,2003,165(2-3):147-73.
[59]管建慧,刘克礼,郭新宇.玉米根系构型的研究进展[J].玉米科学,2006,14(6):162-6.
[60] DIGGLE A J. Rootmap A model in three-dimensional coordinates of the growth and structureof fibrous root systems [J]. Plant and Soil,1988,105(2):169-78.
[61] PAG S L, JORDAN M O, PICARD D. A simulation model of the three-dimensionalarchitecture of the maize root system [J]. Plant and Soil,1989,119(1):147-54.
[62] BERNTSON G. Modelling root architecture: are there tradeoffs between efficiency andpotential of resource acquisition?[J]. New Phytologist,1994,127(3):483-93.
[63]冯斌,杨培岭.植物根系的分形及计算机模拟[J].中国农业大学学报,2000,5(2):96-9.
[64] A. H. FITTER T R S, M. L. HARVEY, G. W. WILSON. Architectural analysis of plant rootsystems1. Architectural correlates of exploitation efficiency [J]. New Phytologist,1991,118(3):375-82.
[65]邓旭阳，郭新宇.玉米根系集合造型研究[J].工程图学学报，,2004,4:62-6.
[66]张吴平.三维根系功能-结构模型的构建与根区土壤水分运动的模拟[D].北京;中国农业大学,博士学位论文,2006.
[67] HOCHHOLDINGER F. The maize root system: morphology, anatomy, and genetics [J].Handbook of Maize: Its Biology2009):145-60.
[68]宋有洪.玉米生长的生理生态功能与形态结构并行模拟模型[D].北京;中国农业大学,博士学位论文,2003.
[69] HONERT T H V D. Water transPort in PlantS as a catenary [J]. Discuss Faraday Soc,1948,3:146-53.
[70] NEUMANN H H, THURTELL G W. Stevenson K. In situ measurements of leaf waterpotential and resistance to water flow [J]. Can J plant Sci,1974,54:175-84.
[71] WALLACE J S, BISCOE P V. Water relations of w inter wheat,4. hydraulic resistance andcapacitance in the soil-plant system [J]. J Agric Sci Cambridge,1983,100:591-600.
[72]刘文兆.土壤-植物系统水分运移过程的阻容电模拟[J].生态学报,2005,25(11):2947-53.
[73] HERZOG K M H R, THUM R. Diurnal changes in the radius of a subalpine Norway sprucestem: their relation to the sap flow and their use to estimate transpiration [J]. Trees,1995,10:94-101.
[74] PER M KI M. E N, S SEVANTO, H ILVESNIEMI, E SIIVOLA, P HARI,T VESALA. Treestem diameter variations and transpiration in Scots pine: an analysis using a dynamic sap flowmodel [J]. Tree Physiology,2001,21:889-97.
[75] ZWEIFEL R I H, H SLER R. Link between diurnal stem radius changes and tree waterrelations [J]. Tree Physiology,2001,21:869-87.
[76] STEPPE K D P D, LEMEUR R, VANROLLEGHEM PA. A mathematical model linking treesap flow dynamics to daily stem diameter fluctuations and radial stem growth [J]. TreePhysiology,2005,26:257-73.
[77] DAUDET F A, A.LACOINTE, RE J P G A, et al. Generalized MuKnch Coupling betweenSugar and Water Fluxes for Modelling Carbon Allocation as A4ected by Water Status [J]. Jtheor Biol2002,214:481-98.
[78] SCHEPPER V D, STEPPE K. Development and verification of a water and sugar transportmodel using measured stem diameter variations [J]. J Exp Bot,2010,61(8):2083-99.
[79] GARDNER W R. Dynamic aspects of water availability to plants [J]. Soil Science,1960,89(2):63-73.
[80] MOLZ F J. Water transport in the soil-root system: Transient analysis [J]. WATERRESOURCES RESEARCH,1976,12(4):805-8.
[81]罗远培李.根土系统与作物水氮资源利用效率[M].北京:中国农业科技出版社,1996.
[82]杨培岭郝.植物根系吸水模型的发展动态[J].中国农业大学学报,1999,2(2):1-10.
[83]邵明安，杨文治，李玉山.植物根系吸收土壤水分的数学模型[J].土壤学报,1987,24(4):295-304.
[84] GREEN S R, I. VOGELER, B.E. CLOTHIER, T.M. MILLS, C. VAN DEN DIJSSEL.Modelling water uptake by a mature apple tree [J]. Aust J Soil Res,2003,41:365-80.
[85] KEESE K E, B.R. SCANLON, R.C. REEDY. Assessing controls on diffuse groundwaterrecharge using unsaturated flow modeling.[J]. Water Resour Res,2005,41:12.
[86] LI K Y, R. DE JONG, M.T. COE, N. RAMANKUTTY. Root-water-uptake based upon a newwater stress reduction and an asymptotic root distribution function.[J]. Earth Interact,2006,10:1-22.
[87] IM NEK J, M.H. VAN GENUCHTEN, M. EJNA. The HYDRUS-1D software packagefor simulating the one-dimensional movement of water, heat and multiple solutes invariably-saturated media, version3.0[M]. HY-DRUS Software Series1. Dep. ofEnvironmental Sciences, Univ. of Cali-fornia, Riverside.2005.
[88] BRAUD I, N. VARADO, A. OLIOSO. Comparison of root water uptake modules using eitherthe surface energy balance or potential transpiration [J]. J Hydrol,2005,301:267-86.
[89] SKAGGS T H, GENUCHTEN M T V, SHOUSE P J, et al. Macroscopic approaches to rootwater uptake as a function ofwater and salinity stress [J]. Agricultural Water Management,2006,86(1-2):140-9.
[90] LIER Q D J V, DAM J C V, METSELAAR K, et al. Macroscopic root water uptakedistribution using a matric flux potential approach [J]. Soil Science Society of America2008,7(3):1065-78.
[91] LIER Q D J V, DAM J C V, METSELAAR K. Root water extraction under combined waterand osmotic stress [J]. Soil Science Society of America Journal,2009,73(3):862-75.
[92]傅承新，丁炳扬.植物学[M].浙江大学出版社,2002.
[93] PALLAS B, LOI C, COURN DE A C P H, et al. Comparison of three approaches to modelgrapevine organogenesis in conditions of fluctuating temperature, solar radiation and soilwater content [J]. annals of Botany,2011,107(5):729-45.
[94] JARVIS P G. The interpretation of the variations in water potential and stomatal conductancefound in canopies in the field.[M]. Philosophical Transactions of the Royal Society, London,Ser. B.1976:593-610.
[95] COWAN I R, FARQUHAR G D. Stomatal function i n relation t o leaf metabolism andenvironment [M]. In Integration of Activity in the Higher Plant, D.H. Jennings, Editor.1977,Cambridge Univ. Press,Cambridge: U. K,1977.
[96] CHUNFANG WEI M T T, ERNST STEUDLE. Direct Measurement of Xylem Pressure inLeaves of IntactMaize Plants. A Test of the Cohesion-Tension Theory TakingHydraulicArchitecture into Consideration [J]. Plant Physiology,1999,121:1191-205.
[97] CLAPP R B, HORNBERGER G M. Empirical equations forsome soil hydraulic properties [J].Water Resour Res,1978,14:601-4.
[98] AMOS B, WALTERS D T. Maize Root Biomass and Net Rhizodeposited Carbon: AnAnalysis of the Literature [J]. Soil Sci Soc Am J,2006,70:1489-503.
[99] JURGENFRENSCH, ERNSTSTEUDLE. Axial and Radial Hydraulic Resistance to Roots ofMaize [J]. Plant Physiol,1989,91:719-26.
[100] LE ROUX X L A, ESCOBAR-GUTIERREZ A, LE DIZES S. Carbon-based models ofindividual tree growth: A critical appraisal [J]. Annal Forest Science,2001,58(5):469-506.
[101] EVERS J B, VOS J, X.YIN, et al. Simulation of wheat growth and development based onorgan-level photosynthesis and assimilate allocation [J]. ournal of Experimental Botany,2010,61(8):2203–16.
[102] HEUVELINK E. Dry matter partitioning in tomato: validation ofa dynamic simulation model[J]. Annals of Botany,1996,77:71-80.
[103] SONG Y, C.J. BIRCH, J. HANAN. Maize canopy production under contrasted water regimes[J]. Annals of Applied Biology,2010,157(1):111-23.
[104] SINCLAIR T R. Theoretical Analysis of Soil and Plant Traits Influencing Daily Plant WaterFlux on Drying Soils [J]. Agronomy Journal,2005,97(7):1148-52.
[105] FITTER A H, STICKLAND T S. Architecture analysis of plan troot system [J]. NewPhytologist,1992,121:243-8.
[106] ROSE D A. The description of growth of root system [J]. plant and Soil,1983,75:405-15.
[107]赵春江,王功明,郭新宇, et al.基于交互式骨架模型的玉米根系三维可视化研究[J].农业工程学报,2007,23(9):1-6.
[108] DELFEENA EAPEN M A L B, GEORGINA PONCE, MAR′A E. CAMPOS,GLADYSI.CASSAB. Hydrotropism: root growth responses to water [J]. Trends in Plant Science,2005,10(1):44-9.
[109] J. IMUNEK K H, M.T.V. GENUCHTEN. The SWMS3D Code for Simulating Water Flowand Solute Transport in Three-Dimensional Variably-Saturated Media [M]. S. Laboratory(Ed.), U.S. Department of Agriculture, Riverside, CA,1995.
[110] HERKELRATH WN M E, GARDNER WR. Water uptake by Plants: I and II [J]. Soil Sci SocAm J1977,41(1033-1043):
[111] TAKAHASHI H M Y, FUJII N. Hormonal interaction during root tropic growth:hydrotropism versus gravitropism [J]. Plant Mol Biol,2009,29:489-502.
[112]平晓燕,周广胜,孙敬松.植物光合产物分配及其影响因子研究进展[J].植物生态学报,2010,34(1):100-11.
[113] E REFFYE P H F, BLAISE F, BARTH L MY D, DAUZAT J,AUCLAIR D. A modelsimulating above-and below-ground tree architecture with agroforestry applications [J].Agroforest Syst,1995,30:175-97.
[114] BLAISE F F T, STOKES A, DE REFFYE P. A modelsimul a ting interac tions betwe e nplant shoot an rootarchitecture in a non-homogen eous environment [M]. In:Stokes A (ed)Proc. Int. Conf.“The Supporting Roots ofTrees and Woody Plants: Form, Function andPhysiology”,Bordeaux,20–24July,1998, Series:‘Developments in plantand soil sciences.2000:61-76.
[115]赵星.虚拟植物生长中几个问题的研究[D];中国科学院自动化研究所,博士后学位论文,2003.
[116]吕游，杨克俭.树木冠层与根系统一建模研究[J].计算机与数字工程,2007,35(10):44-5：65.
[117] MICHEL G NARD J D, NICOL S FRANCK, FRAN OISE LESCOURRET, NICOLASMOITRIER, PHILIPPE VAAST， GILLES VERCAMBRE. Carbon allocation in fruit trees:from theory to modelling [J]. trees,2008,22(3):269-82.
[118] GUO Y, FOURCAUD T, JAEGER M, et al. Plant growth and architectural modelling and itsapplications [J]. Annals of Botany,2011,107(5):723-7.
[119]郑国清，段韶芬，阎书波，吕冰清.玉米叶龄与器官发育模拟模型[J].玉米科学2003,11(4):63-6.
[120] SALAH H B H, TARDIEU1F. Quantitative analysis of the combined effects of temperature,evaporative demand and light on leaf elongation rate in well-watered field andlaboratory-grown maize plants [J]. J Exp Bot,1996,47(11):1689-98.
[121] ROBERTSON M J. relations between internode elongation plant height and leaf appearancein maize [J]. Field Crops Research,1994,38(3):135-45.
[122] SONG Y, BIRCH C, QU S, et al. Analysis and Modelling of the Effects of Water Stress onMaize Growth and Yield in Dryland Conditions [J]. Plant Production Science,2010,13(2):199-208.