MODELING PHOSPHORUS TRANSPORT IN SOIL AND WATER by Joumana Abou Nahra Department of Bioresource Engineering McGill University, Montreal Submitted August 2006 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Doctor of Philosophy Joumana S. Abou Nahra, 2006 iABSTRACT Joumana Abou Nahra Doctor of PhilosophyBioresource Engineering Modeling Phosphorus Transport in Soil and Water Themainobjectiveofthisprojectwastoinvestigateandmodel phosphorus (P) transport in soil column studies. A model named HYDRUS-NICA wasdeveloped,bycouplingahydrologicalandtransportmodel(HYDRUS-1D model)withanaqueouschemicalmodel(non-idealcompetitiveadsorption NICA),toimprovethepredictionsofPtransportinsoilandwater.The HYDRUS-NICAmodelwasdevelopedbyreplacingthenon-linearempirical (Freundlich andLangmuir) equations of the HYDRUS-1Dmodel with the NICA model equations. The numerical accuracy of the HYDRUS-NICA model was then evaluated by comparing the relative errors produced by the HYDRUS-NICA and HYDRUS-1Dmodels.Theresultsshowedthatthenumericalschemesofthe HYDRUS-NICA code are stable. The ability of the NICAmodel to describe phosphate (PO4) adsorption to soilparticleswastestedusingsoilscollectedfromagriculturalfieldsinsouthern Quebec.ThesurfacechargeandPO4adsorptioncapacityofthesesoilswere measured. Results were used to estimate the NICA model parameters using a non-linearfittingfunction.TheNICAmodelaccuratelydescribedthesurfacecharge of these soils and the PO4 adsorption processes. TheHYDRUS-1DmodelwasappliedtosimulatewaterflowandPO4 transportinre-constructedsoilcolumnexperiments.TheHYDRUS-1Dmodel wascalibratedbasedonphysicalandchemicalparametersthatwereestimated fromdifferentexperiments.Overall,theHYDRUS-1Dmodelsuccessfully simulatedthewaterflowinthecolumns;however,itoverestimatedthefinal adsorbed PO4 concentrations in the soil. The discrepancies in the results suggested iithattheHYDRUS-1Dmodelcouldnotaccountforthedifferencesinthesoil structurefoundinthecolumns,orthattheFreundlichisothermcouldnot adequately describe PO4 adsorption. TheHYDRUS-NICAmodelwascalibratedandvalidatedwithresults fromre-packedcolumnexperiments.Thesimulatedresultswerethencompared with results obtained by the HYDRUS-1D model. The overall goodness-of-fit for the HYDRUS-1D model simulations was classified as poor. The HYDRUS-NICA model improved significantly the prediction of PO4 transport, with the coefficient of modeling efficiency values being close to unity, and the coefficient of residual mass values being close to zero. The HYDRUS-NICA model can be used as a tool to improve the prediction of PO4 transport at the field scale. iiiRSUM Joumana Abou Nahra Doctorat en gnie Gnie des bioressources Modlisation du transport du phosphore dans le sol et leau Lobjectifprincipaldecetterecherchetaitdedcrireetdemodliserle transport du phosphore (P) dans des essais de colonnes de sol. Dans ce cadre, un modlemathmatiqueatconupourtudierletransportduPdanslessols, dans des conditions de saturation variables. Ce modle vise dpasser les limites imposesparlesmodlesdetransportduPexistants,encouplantunmodle chimiqueaqueux(lemodleNICA)unmodlehydrologique(lemodle HYDRUS-1D).LemodleHYDRUS-NICAatdveloppenremplaantles quationsdadsorptionnon-linaire(FreundlichetLangmuir)dumodle HYDRUS-1DparlesquationsdumodleNICA.Lefficacitnumriquedu modleatvalueencomparantleserreursrelativesproduitesparlemodle HYDRUS-NICAetcellesproduitesparlemodleHYDRUS-1D.Lesrsultats ont prouv que les analyses numriques du code de HYDRUS-NICA sont stables. LacapacitdumodleNICAdcrirel'adsorptiondesphosphates(PO4) surlesparticulesdesolatvalueenutilisantdessolsprlevsdansdes champsagricolesdusudduQubec(Canada).Pourcefaire,unecaractrisation physico-chimiquedessolsslectionnsadabordteffectue.Lesrsultatsde cesexpriencesontservilestimationdesparamtresetlacalibrationdu modle NICA. Unefois calibr, ce dernier a dcrit ladsorption des PO4 dansles sols de manire trs satisfaisante. Lemodle HYDRUS-1D v.3.00 a t utilis pour tudierlcoulement de l'eau et le transport des PO4 dans les sols. Des expriences physiques et chimiques ontdabordtmenespourestimerlesparamtresexigsparlemodle HYDRUS-1D.Parlasuite,desessaisdecolonnesunidimensionnelsontt effectusavecdessolsnonremanispourvaliderlemodleHYDRUS-1D.En ivmoyenne,lemodleaestimlacomposante pertes dubilanhydriquedune maniresatisfaisanteparrapportauxrsultatsexprimentaux,tandisqueles concentrations de PO4 adsorbs ont t surestimes. La corrlation faible entre les rsultatssimulsetmesurspourletransportdesPO4porteconclurequele modle HYDRUS-1D est incapable de tenir compte de la structure htrogne du soldescolonnesdesolnonremaniet/ouquel'isothermedeFreundlichnepeut pas dcrire avec justice l'adsorption des PO4 sur les particules de sol. LemodleHYDRUS-NICAatcalibretvalidpartirdedonnes obtenuesdessaisdecolonnesunidimensionnelsavecdeschantillonsdesol homognes.Lesrsultatssimulsaveclemodlemodifionttcomparsaux rsultatsobtenusaveclemodleHYDRUS-1D.Engnral,lafiabilitdes simulationsdumodleHYDRUS-1Dtaitconsidrecommefaible.Lemodle HYDRUS-NICA a dmontr une meilleure capacit dcrire le transport des PO4 danslescolonnesdesolhomognes,avecuncoefficientdefficacitde modlisationprsdel'unit,etlecoefficientdes cartscumulsprsdezro.Le modle HYDRUS-NICA pourrait donc tre utilis comme outil pour amliorer la prdiction du transport des PO4 dans le sol et leau sur le terrain. vACKNOWLEDGMENTS I wish to acknowledge the financial support provided by Le Fonds Qubcois delaRecherchesurlaNatureetlesTechnologies(FQRNT).Iwouldliketothank mysupervisor,Dr.ChandraMadramootoo,forhisguidance,hisfinancialsupport, and his understanding during the pastfewyears, especially duringthetough periods ofmyPh.D.Aspecialthank-youtoDr.WilliamHendershotforhisscientific guidanceandhispatienceforalwayswillingtoansweranyquestion;complexor trivial.AspecialthanksaswelltoHlneLalandeforherinvaluablehelp,and patience in the laboratory. I would like to thank Mr. Peter Enright for always willing toprovidetechnicaladviceandassistance.Thanksarealsoduetomycommittee members,Dr.KokandDr.Ghoshal,fortheirinsightfulinputintothisresearch.I would like to thank Dr. Thomas Wihler and Dr. Timothy Rennie for their suggestions onimprovingthecomputationalmodelinginvolvedinthisresearch.Furthermore,I wouldliketoacknowledgethevaluableadviceofDr.Jirkaimnekinthe development of the model for this research. I would like to thank all of my fellow graduate students during the five years of my Ph.D. for their friendship and support. I would like to specifically thank Dr. A. Sarangiand Mr. Baldur Bujatzeckfor theirinspiring ideas and their motivation, Ms. YaqiongHuforherassistanceinthelaboratorywithgreatenthusiasm,andMr. Michel Baraer and Mr. Nicolas Stmpfli for their help with the French version of my abstract.Aspecialwordofgratitudetoallthesummerstudents;theywereofgreat helpinthefieldandthelaboratoryespeciallyMr.KentonOlivierre,Ms.Meghan Bischel, and Ms. Genevive Leroux.I wouldlike to thankas well all the staffat the BraceCentre,andmorespecificallyMs.BanoMehdiforherassistanceinthe laboratories and Ms. Wendy Ouelletteforhervaluable help regarding administration matters at McGill. IespeciallythankmyfamilyinLebanon;mymother,Sophie,forher unconditional love, support, and devotion; my sister, Julie, for being a great example tofollow;andmyaunt,Latife,forbelievinginmydreams.Thankyouforalways being there for me; this thesis is as much yours as it is mine. viTABLE OF CONTENTS ABSTRACT.................................................................................................................. i RSUM..................................................................................................................... iii ACKNOWLEDGMENTS.............................................................................................v TABLE OF CONTENTS.............................................................................................vi LIST OF TABLES.......................................................................................................xi LIST OF FIGURES.................................................................................................. xiii LIST OF ABBREVIATIONS....................................................................................xiv NOMENCLATURE....................................................................................................xv CONTRIBUTION TO AUTHORS ..............................................................................1 CHAPTER 1: General Introduction ............................................................................2 1.1BACKGROUND ................................................................................. 2 1.2HYPOTHESIS..................................................................................... 3 1.3OBJECTIVES...................................................................................... 5 1.4SCOPE................................................................................................. 5 1.5THESIS OUTLINE.............................................................................. 6 CHAPTER 2: Literature Review..................................................................................7 2.1INTRODUCTION................................................................................ 7 2.2THE CHEMISTRY OF PHOSPHORUS.............................................. 8 2.3THE PHOSPHORUS CYCLE.............................................................. 9 2.4EQUILIBRIUM-BASED ADSORPTION MODELS ......................... 11 2.5THE NICA MODEL.......................................................................... 13 2.6THE WATER CYCLE....................................................................... 14 2.7PHOSPHOROUS TRANSPORT AND PATHWAYS........................ 15 2.8SUB-SURFACE WATER FLOW...................................................... 16 2.9SOLUTE TRANSPORT .................................................................... 19 2.10TRANSPORT MODELS FOR SUB-SURFACE RUNOFF................ 20 2.11NUMERICAL MODELS IN USE AND THEIR APPLICATIONS.... 21 2.11.1The LEACH Model .................................................................... 21 2.11.2The SWAP Model ...................................................................... 22 vii2.11.3The VS2DT Model ..................................................................... 22 2.11.4The HYDRUS Model ................................................................. 23 2.12CONCLUSIONS................................................................................ 26 CONNECTING TEXT TO CHAPTER 3 ..................................................................29 CHAPTER 3: The Development of the HYDRUS-NICA Model ...............................30 ABSTRACT.................................................................................................. 30 3.1INTRODUCTION.............................................................................. 31 3.2THE CONCEPTUAL MODEL.......................................................... 33 3.2.1Objective .................................................................................... 33 3.2.2Model Description...................................................................... 33 3.2.3Assumptions and Assertions of the Model .................................. 34 3.3THE REPRESENTATIONAL MODEL............................................. 35 3.3.1Water Module............................................................................. 35 3.3.2Solute Module ............................................................................ 37 3.3.3Chemical Module ....................................................................... 38 3.4THE COMPUTATIONAL MODEL .................................................. 42 3.4.1Model Development ................................................................... 42 3.4.2Code Modification...................................................................... 42 3.4.3Numerical Schemes .................................................................... 43 3.5CODE VERIFICATION.................................................................... 44 3.5.1Verification of Water Flow and Solute Transport........................ 44 3.5.2Problem Description................................................................... 46 3.5.3Results........................................................................................ 47 3.6CONCLUSIONS................................................................................ 48 CONNECTING TEXT TO CHAPTER 4 ..................................................................55 CHAPTER 4: Modeling Phosphate Adsorption to the Soil: Application of the Non-Ideal Competitive Adsorption Model .........................................................................56 ABSTRACT.................................................................................................. 56 4.1INTRODUCTION.............................................................................. 56 4.2MATERIAL AND METHODS.......................................................... 59 4.2.1Sample Collection and Preparation ............................................. 59 4.2.2Soil Chemical Analysis............................................................... 60 viii4.2.3Back Titration Experiment.......................................................... 60 4.2.4Batch Adsorption Experiment..................................................... 61 4.2.5Estimation of Free Phosphate Concentrations ............................. 62 4.2.6Modeling Phosphate Adsorption................................................. 62 4.3RESULTS AND DISCUSSION......................................................... 68 4.3.1Soil Chemical Properties ............................................................ 68 4.3.2Surface Charge Data................................................................... 69 4.3.3Phosphate Adsorption................................................................. 70 4.3.4Modeling Phosphate Adsorption................................................. 71 4.4CONCLUSIONS................................................................................ 74 CONNECTING TEXT TO CHAPTER 5 ..................................................................79 CHAPTER 5: Modeling Phosphorus Transport in Re-constructed Soil Columns Using the HYDRUS-1D Model: I. Parameter Estimation..........................................80 ABSTRACT.................................................................................................. 80 5.1INTRODUCTION.............................................................................. 81 5.2METHODOLOGY............................................................................. 82 5.2.1Overview of the HYDRUS-1D Model (ver.3.00) ........................ 82 5.2.2Site Description and Sampling.................................................... 84 5.2.3Chemical Properties.................................................................... 85 5.2.4Physical Properties ..................................................................... 85 5.2.5Estimation of the Soil Hydraulic Parameters............................... 86 5.2.6Estimation of the Adsorption Parameters .................................... 87 5.2.7Re-constructed Column Leaching Experiments........................... 88 5.3RESULTS AND DISCUSSION......................................................... 90 5.3.1Soil Physical Properties .............................................................. 90 5.3.2Estimation of the Soil Hydraulic Parameters............................... 91 5.3.3Estimation of the Adsorption Parameters .................................... 92 5.3.4Re-constructed Column Leaching Experiments........................... 93 5.4CONCLUSIONS................................................................................ 95 CONNECTING TEXT TO CHAPTER 6 ................................................................101 CHAPTER 6: Modeling Phosphorus Transport in Re-constructed Soil Columns Using the HYDRUS-1D Model: II. Calibration and Validation..............................102 ixABSTRACT................................................................................................ 102 6.1INTRODUCTION............................................................................ 103 6.2METHODOLOGY........................................................................... 104 6.2.1Sensitivity Analysis .................................................................. 104 6.2.2Calibration................................................................................ 105 6.2.3Boundary and Initial Conditions ............................................... 107 6.2.4Statistical Analysis ................................................................... 108 6.3RESULTS AND DISCUSSION....................................................... 109 6.3.1Sensitivity Analysis .................................................................. 109 6.3.2Calibration................................................................................ 110 6.3.3Validation................................................................................. 111 6.4CONCLUSIONS.............................................................................. 115 CONNECTING TEXT TO CHAPTER 7 ................................................................121 CHAPTER 7: Modeling Phosphate Transport in Re-packed Soil Columns using the HYDRUS-1D and HYDRUS-NICA Models. ............................................................122 ABSTRACT................................................................................................ 122 7.1INTRODUCTION............................................................................ 123 7.2MATERIALS AND METHODS...................................................... 125 7.2.1Re-packed Column Leaching Experiments ............................... 125 7.2.2The HYDRUS-1D and HYDRUS-NICA Models...................... 127 7.2.3Simulations............................................................................... 128 7.2.4Calibration................................................................................ 129 7.2.5Assessment of Model Performance ........................................... 131 7.3RESULTS AND DISCUSSION....................................................... 133 7.3.1Re-packed Column Leaching Experiments ............................... 133 7.3.2Sensitivity analysis for HYDRUS-NICA model........................ 134 7.3.3Calibration................................................................................ 135 7.3.4Model Evaluation ..................................................................... 137 7.4CONCLUSIONS.............................................................................. 140 CHAPTER 8: General Summary and Conclusions .................................................148 8.1GENERAL SUMMARY AND CONCLUSIONS............................. 148 x8.2RECOMMENDATIONS FOR FUTURE RESEARCH.................... 151 CHAPTER 9: Contributions to Knowledge .............................................................152 REFERENCES .........................................................................................................153 Appendix A.................................................................................................................169 Appendix B.................................................................................................................174 Appendix C.................................................................................................................197 xiLIST OF TABLES Table 2.1: Summary of Four Models: HYDRUS_2D, SWAP, VS2DT and LEACHM........................................................................................ 28 Table 3.1: Modeling Steps for Richards Equation............................................. 50 Table 3.2: Input Parameters and Values for the Code Verification ..................... 50 Table 3.3: Results of the Code Verification........................................................ 51 Table 3.4: Results from the Convergence Test ................................................... 52 Table 4.1: General Scheme of Parameter Estimation and Validation of the NICA Model............................................................................................... 75 Table 4.2: Chemical Properties of the Soils........................................................ 75 Table 4.3: Optimized Surface Charge Parameters and Goodness of Fit for the NICA Model...................................................................................................... 76 Table 4.4: Optimized PO4 Adsorption Parameters and Goodness of Fit for the NICA Model .................................................................................... 76 Table 5.1: Parameters Required to Calibrate the HYDRUS-1D Model............... 96 Table 5.2: Cores Needed for the Different Experiments ..................................... 97 Table 5.3: Soil Chemical Characteristics............................................................ 97 Table 5.4: Soil Physical Properties..................................................................... 97 Table 5.5: Optimized Soil Hydraulic Parameters................................................ 98 Table 5.6: Optimized Freundlich Adsorption Isotherm Parameters..................... 98 Table 5.7: Final Soil Characteristics................................................................... 98 Table 6.1: Outline Followed to Test the Sensitivity of the HYDRUS-1D Model to these Parameters............................................................................. 117 Table 6.2: The Estimated Parameters Required to Calibrate the HYDRUS-1D Model............................................................................................. 117 Table 6.3: Initial (IC) and boundary (BC) Conditions for Water Flow and Solute Transport........................................................................................ 118 Table 6.4: Calibrated Parameters Used in HYDRUS-1D Simulations .............. 118 Table 6.5: Modeling Criteria Used in the HYDRUS-1D Simulations ............... 118 xiiTable 6.6: Mass Balance Output from the HYDRUS-1D Model for Both Columns....................................................................................................... 119 Table 6.7: Comparison Between Simulated and Measured Results................... 119 Table 7.1: Selected Soil Chemical Properties ................................................... 142 Table 7.2: Phosphorus Soil Analysis Based on Mehlich-III Extractions ........... 142 Table 7.3: Results of the Sensitivity Analysis for the HYDRUS-NICA Model. 142 Table 7.4: Calibrated Parameters Used in HYDRUS-1D Model Simulations ... 143 Table 7.5: Initial and Calibrated Estimates of PO4 Adsorption Parameters for the NICA Model .................................................................................. 143 Table 7.6: Evaluation of the HYDRUS-1D and HYDRUS-NICA Models Performances.................................................................................. 144 xiiiLIST OF FIGURES Figure 2.1: Phosphorus Cycle ............................................................................ 11 Figure 3.1: The Framework of the Model........................................................... 53 Figure 3.2: The Framework of the Water Module .............................................. 53 Figure 3.3: The Framework of the Solute Module.............................................. 53 Figure 3.4: The Framework of the Chemical Module ......................................... 54 Figure 3.5: Water Bottom Flux with Time ......................................................... 54 Figure 4.1: Variable Surface Charge of Samples 5 (a) and 3 (b) ......................... 77 Figure 4.2: Adsorption of PO4 in Soil Samples 1 (a) and 2 (b) ........................... 77 Figure 4.3: Validation of the NICA model Using Soil Samples 3(a), 11 (b), and 8 (c) .................................................................................................... 78 Figure 5.1: Schematic Drawing of the Columns ................................................. 99 Figure 5.2: Validation of the Freundlich Equation Using samples 6 (a) and 9 (b)....................................................................................................... 100 Figure 6.1: Sensitivity Results for Parameters: Ksat (a), Ci(x) (b), and (c)....... 120 Figure 6.2: Measured Volumetric Water Content (VWC) for Column 1 for all Three depths................................................................................... 120 Figure 7.1: Experimental Set-up for Each Column........................................... 145 Figure 7.2: Concentration of PO4 in Leachates................................................. 146 Figure 7.3: Electrical Conductivity of Leachates.............................................. 146 Figure 7.4: pH of Leachates............................................................................. 146 Figure 7.5: Comparison Between Measured and Simulated Outflow PO4 Concentration from the Re-packed Soil Columns under Treatment 2....................................................................................................... 147 xivLIST OF ABBREVIATIONS ADEAdvection-Dispersion Equation AECAnion Exchange Capacity CECCation Exchange Capacity CMECoefficient of Modeling Efficiency CRMCoefficient of Residual Mass DDLDiffused Double Layer ECElectric Conductivity FORTRANProgramming Language HDPEHigh-Density Poly-Ethylene HYDRUS-1DSoftware package for simulating One-Dimensional Movement of Water, Heat, and Multiple Solutes KH2PO4 Potassium Phosphate KClPotassium Chloride LEACHMLeaching Estimation and Chemical Model NICANon-Ideal Competitive Adsorption NPKNitrogen-Phosphorus-Potassium NPSNon-Point Source Pollution OMOrganic Matter PPhosphorus PO4Phosphate P. Sat.Phosphorus Saturation Index PSAParticle Size Analysis rLinear Correlation Coefficient R2Coefficient of Determination RRetardation Factor RMSERoot Mean Square Error SCMSurface Complexation Model SCSSoil Conservation Service SWAPSoil-Water-Atmosphere-Plant Model VS2DT Variably Saturated 2D Flow and Transport ZPCZero Point Charge xvNOMENCLATURE inverse of the pore entry value empirical parameter shape fitting adsorption parameter rcrelative error for solute rwrelative error for water water content rresidual water content s saturated water content bbulk density turtuosity cconcentration in solution Ciinitial concentration dttime increment dxspace increment D1wdispersion coefficient DLlongitudinal dispersivity Dwmolecular diffusion coefficient ETopotential evapotranspiration rate hwater pressure head kdequilibrium adsorption coefficient Kunsaturated hydraulic conductivity Ksatsaturated hydraulic conductivity Ki median affinity constant for component i* KPO4median affinity constant for component PO4* KOH median affinity constant for component OH* lpore-connectivity parameter npore size distribution index nOHnon-ideality behaviour of component OH* nPO4non-ideality behaviour of component PO4* pHmeasure of (H+) in solution pOHmeasure of (OH-) in solution Pipedicted value Oi masured valueOmaverage of measured values pintrinsic heterogeneity of the soil surface* qvolumetric flux density Qmaxtotal number of available proton binding sites* Qvvariable surface charge* Rtresult value for using the test parameter value Rb result value for using the base parameter value sconcentration adsorbed Ssink term Se effective moisture content ttime coordinate vseepage velocity x, zvertical spatial coordinate c/cportion of PO4 adsorbed to the soil to PO4 soluble in solution *subscripts 1 and 2represent the two types of binding sites (low pH and high pH) to describe PO4 adsorption in the NICA model1CONTRIBUTION TO AUTHORS Allthemanuscriptsinthisthesis(Chapters3,4,5,6,and7)havebeen authoredbyJoumanaAbouNahra,Dr.ChandraMadramootoo,andDr.William Hendershot. Joumana Abou Nahra is the first author for all the manuscripts in this thesis.Shedesignedandcarriedoutthedifferentcomputationalandlaboratory experiments, did the data analysis, and wrote the manuscripts. Professor Chandra Madramootoo, research supervisor, is the first co-author for all the manuscripts in thisthesis.Hisroleincludedsupervisoryguidance,funding,andmany constructivecommentsintheexperimentalprotocolsandinreviewingthe manuscripts.ProfessorWilliamHendershot,professorattheNaturalResource SciencesDepartmentatMcGillUniversity,isthesecondco-authorforallthe manuscriptsin this thesis. His contributionsincluded guidance on several aspects oftheexperimentalwork,valuablesuggestionsabouttheresearch,and constructive inputs while reviewing the manuscripts. 2CHAPTER 1: General Introduction 1.1BACKGROUND Degradationoffreshwaterquality,bothsurfacewaterandgroundwater, havemainlybeenattributedtomismanagement.Thenatureofwaterpollution could be biological, chemical, physical, or a combination of these. The sources of pollutioninriversvaryandincludemunicipalwaste(effluentsfromtreatment plants),industrialdischarges(wastewaterdischarges,airemissions,andsolid wastedisposal),agriculturalloading,aquacultureandfisheriesenhancement activities, forest management practices, and atmospheric transport and deposition. These different types of pollution have drastically increased the supply ofmicro-organisms (bacteria and parasites), nutrients such as nitrogen, phosphorus, copper, magnesium,iron,andotherhazardouscompoundstofreshwaterecosystems. Municipalandindustrialeffluentscanbeeasilycontrolledandrestrictedat their end of the pipe source. Whereas agricultural effluents pose a serious risk because they contribute to the pollution from non-point sources, and are difficult to detect andmanage(USEPA,2003).InsouthernQuebec(Canada),non-pointsource (NPS)pollutionfromagriculturalwatershedshighlycontributestowater degradationinriversandlakes.NPSpollution,fromthesewatersheds,ispartly duetoelevatedconcentrationsofphosphorus(P)asaresultofcontinuous applicationoffertilizers.Theseelevatedconcentrationsaregreater than0.03mg L-1 in fresh waterways and aquatic systems, exceeding provincial norms (MENV, 2006). Therefore, P can be classified as a contaminant. Phosphorusposesamajorenvironmentalproblemduetoitshigh contribution to eutrophication of fresh water bodies. Eutrophication is a condition of an aquatic ecosystem where high nutrient concentrations, such as nitrogen and phosphorus,stimulatealgalblooms,degradingthewaterqualityintheseaquatic ecosystems(RitterandShirmohammadi,2001).Phosphorus,bynature,strongly adsorbstothesoilformingstablebondswiththesoilfunctionalgroup(Sposito, 31982).ThesoilactsasasinkthattrapsPmoleculesfoundinthesoilsolution (Sharpley et al., 1981; 1984). As a result, it was believed that P transport through thesubsurfacerunoffandmatrixflowwasnegligible,andPlossfromthefield wasmainlyrestrictedtosurfacerunoff.Recentresearchhasshownthata considerableloadofPinfreshwaterbodiesisattributedtosubsurfacerunoff fromartificiallydrainedfields,especiallyinsouthernQuebec(Enrightand Madramootoo, 2003; Simard, 2005). The reason behind these contradicting results isthatunderintensifiedapplicationofinorganicP, theequilibriumofthesesoils in fixing P shifts causing an increase in P desorption, and as a result an increase in Pconcentrationinsolutionisobserved.Consequently,theseelevatedP concentrations in solution get transported down the soil profile bymatrixflow or subsurface runoff (Sharpley, 1995b). Furthermore, P could be transported as well down thesoilprofilethroughmacroporeflow,especiallyinclayeysoils(Stamm etal.,1998;Hoodaetal.1999).Accordingly,water-qualitymonitoringstations have been established on four fields in southern Quebec since 2001 to quantify P transport through subsurface and surface runoffin tile drainedfields (Gollamudi, 2006).However,theresultsobtainedfromthesestationsdonotprovide information on the transport pathway and mechanisms of P in the soil profile. To improve the understanding of P transport and behaviour in the soil profile through subsurface runoff or matrix flow, this research aims at modeling P transport in the subsurface through matrix flow under variably saturated soil conditions. The main objectiveistodescribethedistributionandthemechanismsofP transportinthe soil profile. 1.2HYPOTHESIS Severalhydrologicalmodelshavebeendeveloped tosimulatewaterflow andcontaminanttransportinthesoil-waterenvironment.Thesemodelsinclude SWAP(Kroesetal.,1999),VS2DT(Lappalaetal.,1993),andHYDRUS-1D (imneketal.,2005),yettheyarenotspecializedindescribingthemechanism ofPadsorptionandtransportinthesoil;theyportrayPadsorptionthrough 4empiricalmodelsandresultininadequatepredictionofthePadsorptionand transport (Sparks, 2003). To improve the prediction of P transport in the soil and water,Iproposetocoupleachemicalaqueousmodelwithahydrological-transport model to dynamically predict P transport in the soil profile. For this research, the HYDRUS-1D (ver.3.00) model (imnek et al. 2005) wasappliedtosimulateP transportinthesoil-waterenvironment.HYDRUS-1D utilizesstable numerical solutions;it utilizesfinite difference to integrate in time finiteelementanalysistointegrateinspace,whichtakescareofirregularly shapedboundariesandfluctuatingboundaryconditions.Furthermore,the HYDRUS-1Dmodelhasbeensuccessfullyappliedtosimulatewaterflowand solutetransportinseveralagriculturalfields(Pangetal.,2000;Ventrellaetal., 2000).However,theHYDRUS-1Dmodelutilizestheempiricalmodels (Langmuir and Freundlich isotherms) to describe nutrient/P adsorption to the soil. Thedisadvantageofempiricalmodelsisthattheyprovideparametersthatare onlyappropriatetoconditionsunderwhichtheexperimentwasconducted;their applicationconstitutesessentiallyacurvefittingprocedure,andtheestimated parameters are unknown function of the soil pH and ionic strength of the solution. (GoldbergandSposito,1984).Asanalternative,thenon-idealcompetitive adsorption(NICA)modelwasproposedtodescribePadsorptionontothesoil particles. The NICA model (Koopal et al., 1994) represents an improvement over otherempiricalmodelsofadsorption.Itdescribestheadsorptionofdissolved substances, in relation to the competitive non-ideal behaviour of other substances inthesoilaqueoussolution,whileconsideringthepHandtheionicstrength. Therefore,bycouplingtheNICA(chemical)modelwiththeHYDRUS-1D (transport)model,itshouldimprovetheestimationofPtransportinthesoil throughmatrixflow,andpresentPtransportinthesoilinadynamicand mechanistic manner. 51.3OBJECTIVES ThisresearchsmainaimsaretotestthecapabilityoftheHYDRUS-1D modelinmodelingPtransportinthesoil,andtodevelopamodel,namedthe HYDRUS-NICAmodel,toovercomelimitationsofcurrentsoilPmodels.The HYDRUS-NICAmodelisadynamic,mechanistic,distributed,one-dimensional modeltoportrayPdistributionandtransportalongthesoilprofile.Thismodel will serve as a tool to depict P transport in the soil-water environment. The main objectives of this study were to: 1.Design and build the HYDRUS-NICA model, and verify its code. 2.Conductphysicalandchemicalexperimentstoestimateandderivethe different parameters needed by the HYDRUS-1D model and by the NICA model. 3.CalibrateandvalidatetheNICAmodelinmodelingPadsorptiontothe soil. 4.CalibratetheHYDRUS-1DandHYDRUS-NICAmodelsbasedonthe experimental results. 5.Conductre-constructedsoilcolumnexperiments,andusetheresultsto validate the HYDRUS-1D model. 6.Conductre-packedcolumnexperiments,andusetheseresultstovalidate both the HYDRUS-NICA and HYDRUS-1D models. 1.4SCOPE Themodelwillbevalidatedandcalibratedwithresultsobtainedfrom laboratoryexperiments.Parametersneededbythemodelwillbeestimated independentlyfromphysicalandchemicalexperiments(adsorptionandtitration experiments). The model will be validated against results obtained from re-packed andre-constructedsoilcolumnexperiments.Thesecolumnexperimentswill simulate thetransportandreactionprocessesofPundersteady-stateandvaiably saturatedconsitions,respectively.Thesoilstestedinalltheexperimentsare 6sampledfromafieldlocatedinsouthernQuebec(Canada),onthePikeRiver watershed, near the town of Bedford. The field covers an area of approximately 8 ha.ThePikeRiverisconsideredasub-watershedoftheRichelieuRiverandis oneoftheprimarytributariesthatdrainintotheMissisquoiRiver.Itsdrainage basin covers an area of 629 km2 (Caumartin and Vincent, 1994). 1.5THESIS OUTLINE Thisthesishasbeenwrittenasaseriesofmanuscripts,eachcontributing totheobjectivesstatedabove.Chapter2presentsaliteraturereviewonthe chemistry of P, chemical adsorption models, hydrology and contaminant transport pathways,andwaterqualityandsolutetransportmodels.Afterwhich,five sequentialmanuscriptsarepresented.Chapter3,thefirstmanuscript,describes themethodologyofdevelopingtheHYDRUS-NICAmodelanditscode verification.Chapter4investigatestheabilityoftheNICAmodelinmodelingP adsorptiontothesoil.Chapter5estimatestheparametersrequiredbythe HYDRUS-1DmodeltomodelPtransportinundisturbedsoilcolumns.The following, Chapter 6, calibrates and validates the HYDRUS-1D model to model P transportinundisturbedsoilcolumns.Chapter7examinestheabilityofthe HYDRUS-NICAmodelinsimulatingPtransportinre-packedsoilcolumns. Chapter8,summarizesthesignificantresultsattained,andprovides recommendationsandsuggestionsforfuturestudiesbasedontheconclusions drawnfromthisthesis.Thefinalchapter,Chapter9,presentsthedifferent contributions to the knowledge acquired by this study. 7CHAPTER 2: Literature Review 2.1INTRODUCTION Theuseofcomputermodelstopredictphosphorus(P)contaminationin surfaceandsubsurfacewatersrequiresaninclusivedescriptionofPinputs, dynamics,transport,andlossesfromthesoil-waterenvironment(Haygarthand Sharpley, 2000). Thus, the mainfocus will on P behaviourin soil and water, and itsconsequenceoftheenevironment.ThesignificanceofPpollutionfrom agricultural non-point sources (NPS) to surface waters has been an environmental concernforresearchersandinvestigatorsinthepastdecades,duetoits contributiontoeutrophication,makingthewaterunsuitablefordrinking, industrial,recreationaluses,andforfisheries(SharplyandMenzel,1987). Eutrophicationisaprocessinwhichawaterbodybecomesrichindissolved nutrients, often leading to algal blooms, low dissolved oxygen, and changes in the compositionofplantsandanimalswithinthewaterbody.EvenlowlevelsofP (0.01mgL-1)indrinkingwaterposeseriouslong-termeffectsonhumanhealth (WHO, 2004). Furthermore, P concentrationsinmajor riversin southern Quebec exceedwaterqualitynorms(>0.03mgL-1)(MENV,2006;GirouxandTran, 1996).Thisismainlyaresultoftheshifttowardsintensifiedandspecialized agriculture(MENV,2006),theincreaseinapplicationoforganicandinorganic nitrogen and P, including manure disposal on land to increase crop productivity. It hasbeenbelievedthatPismainlylostfromthefieldbysurfacerunoffandsoil erosion(Gollamudi,2006;Simard,2005).Howeverrecentstudieshaveshown that a considerable portion of total P added to the field is lost through sub-surface runoff(Simsetal.,1998).Monitoringstationswereinstalledtosurveywater quality from tile drained fields in southern Quebec. Results have shown that more than 40% of total Plost from thefieldis through subsurface runoff of tile drains fields (Simard, 2005; Gollamudi, 2006). These results indicate that P transport in 8sub-surface runoffis significant, but the transport pathway andmechanismisnot very clear. As a result, the emphasis of this study is on P transport through subsurface runoff.ThischapterpresentsthemajoraspectsofPchemistry,transport,and modeling in the soil-water environment. First, it provides a review of P chemistry andbehaviourwithinthesoilenvironment.Second,itintroducesthedifferent chemicalmodelsestablishedtodescribePadsorptionphenomena.Third,it describesthehydrologyandsolutetransportprocessesinthesoil-water environment.Andfinally,itpresentsadiscussionofvariouswaterquality transportmodels,andtheirapplicabilityinpredictingtransportofPthrough matrix flow. 2.2THE CHEMISTRY OF PHOSPHORUS Phosphorusisoneoftheessentialnutrientsneededforcropgrowth;itis thesecondkeyplantnutrient(MillerandDonahue,1990).Phosphorusexistsin organicandinorganicformswithinthesoil.MajorsourcesofinorganicPin agricultural fields are inorganic fertilizers, while the main sources of organic P are animalmanure. Phosphorus interacts with soil particles inits exchangeable form, knownasorthophosphate(McBride,1994).Thedifferentformsof orthophosphoric acid that can exist in the soil solution are H3PO4, H2PO4-1, HPO4-2, and PO4-3. The availability of the different forms is dependent on pH; however, at the pH of the soil, PO4-3 has the strongest binding affinity to the soil (McBride, 1994).OrganicPformsincluderelativelylabilephospholipids,inositolsand fulvic acids, and the more resilient forms are humic acids. The different phosphate (PO4) anions in solution are attracted to positively charged sites, on the surface of soil particles, according to the soil anion exchange capacity(AEC).SoilsthatdeveloppositivechargesaresoilsrichinFe,Al,Ca oxide minerals, and layers of silicates; these positive charges can occur as well on the edges of broken octahedral sheets. The AEC of various hydroxide minerals is dependentonthepHandelectrolyteconcentrationsofthesurroundingmedium, 9which might lead to a competition among different anions in the soil solution. The pHdependentchargesarisefromassociationsanddisassociationsofpotential determining ions OH-/H+. It all depends on the zero point charge (ZPC) of the soil. The ZPC is the pH at which the soilhas no charge. For exampleif the pH isless than the ZPC then soil particles will develop positive charges on their surface and vice versa (Tan, 1998). Phosphate(PO4)anionscanalsoadsorbto thesurfaceofthesoilparticle throughspecificadsorptionreactions(non-electrostaticforces)and/orprecipitate inthesoilaggregates(Evangelou,1998).Sposito(1989)definesPO4specific adsorptionasinner-spheresurfacecomplexation,andTan(1998)definesitas ligandexchangeorchemisorption.Thespecificadsorptionreactionisthe formation of covalent bonds in mono-dentate complexes, between the PO4 anions insolutionandthesoilmetalcomplexes,whiledisplacingOH-groupsonthe surfaceofthesoilparticle(GoldbergandSposito,1984;1985).Inacidic conditions, PO4 anions form covalent bonds with Fe+3, Al+3, and Mn+2 complexes, andwhileinbasicsoilstheyformbondswithCa+2complexes.Inaddition,PO4 adsorption(retention)canoccurinclaymineralsthathavehydroxylsurfaces. Ryden and Syers (1977) defined the PO4 precipitation process as more-physically adsorbedP,wherethePO4anionsdiffusefurtherintothesoilstructureforming bi-dentateandbi-nuclearcomplexes,renderingthemmoreinsolubleandthe reactiontendstobeirreversible(Tan,1998;GoldbergandSposito,1985). These anionsarereferredtoasthePO4anionsthatcannotbeextractedbydiluteacid (Tan, 1998). The process of PO4 precipitation is considered to be slow. 2.3THE PHOSPHORUS CYCLE ThePcycle,asindicatedbyFigure2.1,describestheinteractionsand transformations of P taking place in an array of physical, chemical, and biological processestodeterminethedifferentformsofP,theiravailabilityfortheplant uptake,andtheirtransportinsurfaceandrunoffand/orleaching(Ritterand Shirmohammadi,2001).AccordingtoFigure2.1,themajorsourcesofPinthe 10soilareinorganicfertilizersdirectlyappliedtothefield,andorganicfertilizers introducedasplantresidues,animalmanure,municipalandindustrialwaste,and rockweathering.Phosphorusislostfromthesoilthroughplantuptake,leaching intothevadosezoneandgroundwater,and/orsurfacerun-offandsoilerosion. However,P,inthesoil-watersolution,canexistinseveralforms:dissolvedin solution(labile),adsorbedtothesoilfunctionalgroups(activeinorganicP), precipitated(stableinorganicP),freshorganicP(freshlyadded),andstable organicP(Matthews,1998).TheconcentrationandtherateatwhichPis transformedfromoneformtoanotherarehighlycomplex,andaremainlya functionofthesoilproperties,climateconditions,andlanduseandits management. Yet, the different forms of P in the soil are not in discrete entities, as intergrades and dynamic transformations occur continuously between the different availableformstomaintainequilibriumconditions(Sharpley,1995a). Themajor transformationprocessesofPinthesoilare:mineralizationandimmobilization, precipitationanddissolution,andadsorptionanddesorption.Weathering, mineralization,anddesorptionincreasePavailabilityinsolution,while immobilization,precipitation,andadsorptiondecreasePavailabilityinsolution. MineralizationisthemicrobialconversionoforganicPtoPO4ionsavailableto theplants,whileimmobilizationoccurswhenmicrobesconsumefreshplant residues and transform PO4 ionsinto organic P. Precipitationis theincorporation ofPmoleculesintothesolidphasethroughstrongbonds,whileweathering involves the slow conversion of naturally P-rich mineral soil to P available to the plant. The adsorption process is the fixation (chemisorption) of the PO4 ions onto the soil surface and is characterized as a fast process, while the desorption process isthereleaseoftheseadsorbedPO4ionsbackinsolutionandisusuallyamuch slowerprocess.Therelationbetweentheadsorptionanddesorptionprocessis controlledbyanequilibriumconstant.AstheconcentrationofPO4increasesin thesoilsolution,thePO4ionsspontaneouslyadsorbtosoilchargedsurfacesto restore the equilibrium. In the same way, if the concentration of PO4 in solution is depleted,theadsorbedPO4ionstothesoilsurfacedissolvebackintosolution accordingtotheequilibriumconstant(Tan,1998;Lindsay,1979).However, 11underacontinuousincreaseofPO4ionsinsolution,theadditionalPO4ionsare lessstronglyboundtothesoilresultinginahigherequilibriumofPO4 concentrationinsolution.Consequently,theseelevatedPO4concentrations becomemorepronetobeleacheddownintothesoilprofilethroughinfiltrating water (Sharpley, 1995b). Therefore, it is vital to understand the dynamics between thesourceandthesinkpassingthroughanequilibriumstate,soastolimitand control P impacts on the environment (Ritter and Shirmohammadi, 2001; Jones et al., 1984). Figure 2.1: Phosphorus Cycle 2.4EQUILIBRIUM-BASED ADSORPTION MODELS Adsorptionanddesorptionareamongthemostimportantchemical processesinsoilsaffectingPtransportandcontaminationinfreshwater ecosystems(JohnsonandCole,1980).Therefore,quantifyingtheratioofP concentrationadsorbedtothesoil,toPconcentrationinsoilsolution,isa mandatory step for modeling P transport. Phosphorus behaviour in soilshas been extensivelydescribedbyadsorptionequilibriummodelswhichincludeempirical models and double-layer models. These models describe the relationship between FERTILIZERSOIL SOLUTIONPACTIVElabile INORGANIC PSTABLE INORGANIC P FRESH ORGANIC P STABLE ORGANIC P fastslow 123PLANT UPTAKESURFACE RUNOFF LEACHING1: Adsorption/Desorption; 2: Precipitation/Dissolution; 3: Immobilization 12thedissolvedconcentrationsofachemicalcomponent(sorbate)insolution,and theadsorbedquantityofthesamechemicalcomponentbythesoilaggregates (sorbant)atequilibriumforaconstantpressureandtemperature(Evangelou, 1998).Theempiricalmodels,whichincludetheFreundlichandLangmuir equations, describe P adsorption on a macroscopic level; they do not describe the mechanism of P adsorption. The main disadvantage of these equations is that they assumethesurfaceofthesoilparticlesisandtheyarenotabletopredictthe maximumadsorptivecapacityofthesoilparticles(Sparks,2003).Thedouble layermodelsincludesthediffusedouble-layer,Stern,andsurfacecomplexation models.Thediffusedouble-layer(DDL)modelwasdevelopedbyGouy(1910) andChapman(1913)basedonthetheoryofelectricaldiffuseddoublelayer created by the charged surfaces of the soil surface. The DDL describes adsorption processesbyassumingthatthesurfaceofthesoilparticleisnegativelycharged, andthatthecounterionsaremostlyconcentratednearthesurface,anddecrease exponentially with increased distance from the surface. Stern modified the Gouy-Chapman model by identifying a neutral layer (Stern layer) separating the surface chargefromthecounterions.Bothmodelsshowedanumberofproblemsin describingadsorptionreactionatthesoilsurface.Theyfailedtodescribethe distributionofionsadjacent to thesurfaceofthesoilparticle,andtheyassumed that the charge surface of the soil to be platy-shape and extremely large, knowing that the soil particles are complex in shape and vary in size (Sparks, 2003). DuetolimitationsoftheGouy-ChapmanandSternDDLmodels,the surfacecomplexationmodels(SCM)wereintroducedtodescribethereactionof aqueous species with surface functional groups of the soil particle surfaces, based onthermodynamicsproperties(Sparks,1999).AccordingtoEvangelou(1998), SCMs are considered to be advanced approaches. They quantify the distribution of ions in the soil, based on the molecular descriptions of the electric double layer that develops around the soil surfaces, in relation to experimental adsorption data. Surfacecomplexationmodelsincludefivebasicmodels.Themaindifference amongthesefivemodelsisinthewaytheydescribethespatialdistributionof chargespresentwithinthesolid-liquidphaseofthediffuseddoublelayer(Bolt 13andvanRiemsdijk,1986).Acomprehensivedescriptionforallfivemodelshas been presented by Goldberg (1998). These SCM models have generally been used to describe the pH dependent adsorption of metals and anions at moderate to high surface loadings (Tadanier et al., 2000). They define the surface species, chemical reactions,andmassandchargebalances,tobuildupaseriesofreactionswith relatedcharacteristics.Basedonthesefamiliesofreactions,theymathematically calculate the values of thermodynamic properties for the soil surfaces such as the activitycoefficientsandequilibriumconstants(Goldberg,1998).TheSCM representsanimprovementoverotherempiricalmodelsofadsorption;therate-sorption coefficient they provide take into account the soil texture, the pH, and the nature of aqueous speciesinvolved (Koretsky, 2000). However, the conditions to whichSCMareappliedarelimitedandtheylacksimplicitytoapplytoany system (McBride, 1997). 2.5THE NICA MODEL Anewaqueouschemicalmodel,thenon-idealcompetitiveadsorption (NICA)model,isintroducedtodescribeadsorptionofionstoheterogeneous surfaces of the soil particles. The NICA model (Koopal et al., 1994) describes the specificadsorptionofionsontochargedsurfaces, ofthesoilsurfaces,inrelation toothercompetingdissolvedionsinsolution,whiletakingintoaccountthepH andtheionicstrengthofthesolution.TheNICAmodelconsidersacontinuous distribution of the heterogeneous surface charge, where the overall non-ideality is dividedintointrinsicheterogeneity(specifictothebindingsurface)andion-specificnon-ideality.TheNICAmodelwasoriginallydevelopedtodescribethe adsorption ofmetalions onto organic and humic substances. The NICAmodelis athermodynamicallyconsistentcompetitivebindingmodelforheterogeneous systemsandcomponentspecificbindingstoichiometry;thederivationofNICA equation is fairly simple (Koopal et al., 2001). Kinniburgh et al. (1996) combined the NICA model with a Donnan-type model to take into account the non-specific bindingofelectrolyteions,toproducetheNICA-Donnanmodel.Themodified 14versioncoulddescribebothspecificandnon-specificadsorption.The NICA and NICA-Donnanmodelshavebeensuccessfullyappliedtodescribemetal adsorptionto organicmatter.Benedettietal.(1995)discussedtheapplicationof theNICAmodeltodescribemetalionbindingbyhumicsubstances.TheNICA modelprovidedagooddescriptionoftheadsorptionofH,Ca,Cd,andCuonto purifiedpeathumicacid(PPHA)overawiderangeoffreemetalion concentration.Similarly,Kinniburghetal.(1999)proved that theNICA-Donnan modelprovidesagoodfitfor thebindingofH, Ca,Cd,Cu,andPboverawide rangeofpHandfreemetalconcentrations.Milneetal.(2001)derivedageneric NICA-Donnanmodelparameterdatabaseforprotonadsorptionbyhumic substancesbasedon49datasets.Koopaletal.(2001)furtherprovedthatthe NICA-Donnanmodelgivesgoodresultsfor thedescriptionofmetalionbinding ontoPPHA.Finally,consideringthecomplexityofbothsystems,andthe similaritybetweenthenatureofmetalbindingtohumicsubstancesandPO4 adsorption to soils (they both form strong covalent inner sphere complexes to the chargedsurfaces they adsorb to), the NICAmodel shouldbesuitable to describe PO4 adsorption onto the soil particles. 2.6THE WATER CYCLE The hydrological cycle provides a model for understanding the global water system. Moisture content is lost from the earth to the atmosphere through evaporation of water bodies and transpiration of plants. The evaporated water condenses in the atmosphere to form clouds. Due to circulating winds and gravity, the clouds release the water back to the earth in the form of precipitation: rain or snow. As water reaches the ground level, it is intercepted by the plant canopy, flows overland, and infiltrates into the soil profile to emerge into surface runoff, subsurface runoff, and/or deep percolation into the groundwater. As a result, the earth preserves the mass balance of water (Viessman and Lewis, 1995) Thedifferentcomponentsofthewatercyclearequitewellestablished; identifyingthemillustratesthedifferentpathwaysofcontaminanttransportto 15fresh water bodies. Therefore, the processes that affect the transport of P to fresh watersareoverlandflow,subsurfaceandsurfacerunoff,anddeeppercolation. Subsurfacerunoffanddeeppercolationinvolvebothverticalandlateralflow. Since this study is concentrated on studying P transport in the subsurface layers of thesoil,thefollowingdiscussionwillincludeonlythedifferentpathwaysofP transport through subsurface runoff. 2.7PHOSPHOROUS TRANSPORT AND PATHWAYS In order to model the transport of P from the soil matrix to the waterways, the mechanisms, pathways, and forms in which P is mobilized must be defined to set the basics of this study (Haygarth and Sharpley, 2000). The different forms of P foundin the soil-water pathways havebeen discussedin the previous sections. The threemechanisms or processesby which Pis transferredinto waterways are dissolution,incidental,andphysicaltransfer.Dissolutionisaprocess that occurs atthemicro-level(withinthesoilaggregates)likeleaching,mineralization,and sorption/desorption.Physicalprocessestakeplaceonthemacro-level,andare definedasphysicaldisplacementorentrainmentofcolloids.While,incidental processesfallinbetween;theseareshort-termtransfersofP,mostoftensoon after application of fertilizers, as a result of an effective (high intensity) rainfall. Hydrological transfer pathways are complex to classify because a range of spatialscales(slopeandfield)ofwaterflow,aswellasvariationsintheplane (soilprofile)andtimescaleofflowareconsidered.Althoughleachingis commonlyusedtodescribetheverticalmovementofwaterthroughthesoil profile, it is important to highlight that leaching is not a pathway but a process. A surrogatetermtodescribetheverticalmovementofwaterismatrixflow. Furthermore,runoffisusedtodescribethelateralmovementofwateroveror below the soil surface, which causes the short-term increase in water levels at the outlet of the field and/or watershed (Haygarth and Sharpley, 2000). 162.8SUB-SURFACE WATER FLOW 2.8.1Matrix Flow Soil is defined as a porous medium: a solid material enclosing inter-related porespaces.Thepercolationoffluidswithinaporousmediaispossiblethrough the inter-related pore spaces (Daugherty et al., 1985). Water can flow through the soilporousmediaunderbothsaturatedandunsaturatedconditions.Therateand volumeofwaterbeingdisplacedthroughthesoilprofileisaffectedbythe percentage of moisture saturation in the soil (Warrick, 2002). Water content found within these pores can be divided into three categories: drainage or surplus water, plant-available or capillary water, and non-available water. Non-available water is the hygroscopic water heldby the soil at conditionsbelow the permanent wilting point(lessthan-15bars).Drainablewateristheamountofwater thatisableto drainduetogravity(greaterthan-1/3bar).Theplant-availablewaterliesin between the permanent wilting point and field capacity; the water retained by the soil due to capillary forces. Therearetwofundamentalphysicalpropertiesofthesoilthatdescribe waterflowandretentionbythesoil:porosityandhydraulicconductivityofthe soil(Warrick,2002;Hillel1998).Thehydraulicconductivity(K)measuresthe soils ability to transmit water, and is determined from the pore-size distribution of the soil (volume and continuity of conducting pores), and the saturated hydraulic conductivity (Ksat). According to Darcys Law, under laminar flow conditions in a saturatedhomogenousporesystem,thevelocityofwaterflowingwithinthesoil particlesisafunctionofhydraulicconductivity,porosity,andporehydraulic gradient.Yetunderunsaturatedconditions,largerporesdrainmorereadilythan smallerones,whichindicatethat thehydraulicconductivity(K)ismuchsmaller than in saturated conditions, and is represented as a function of the pressure head orwatercontent.Richards(1931)developedawaterflowequationinporous mediaundervariablysaturatedconditionsbasedonDarcysLawandthe continuitytheory,whereheincludedasourceandsinkaspecttothecontinuity equationsincethewatercontentandpressureheadchangewithtime(Warrick, 172002). Richards equationmaybe expressedin three standard forms: the h-based form, the -based form, and the mixed form. The mixed form expresses water flux in terms of both the pressure head h and themoisture content . Thisformis the most direct mathematical expression of the physics of unsaturated flow, because it representsthehydraulicconductivityasafunctionofthemoisturecontentas opposed to the hydraulic head. The term K (h) in Richards equation is not a direct representative of the underlying physics, but is rather a description the water filled pores which facilitate the movement of water through a porous media (Celia et al., 1990; de Vasconcellos and Amorim, 2001). SolutionsforRichardsnon-linearpartialdifferentialequationrequirethe specification of initial and boundary conditions. The initial conditions specify the initial condition of the flow in the system, while the boundary conditions regulate the domain to be studied, and connects with the areas outside the domain (Zheng andBennett,2002).Non-linearpartialdifferentialequationsareeithersolved analyticallyornumerically.Analyticalmethodsyieldexactsolutionstothe governingdifferentialequations,whilenumericalmethodsapproximatethe differentialequationswithasetofalgebraicequations.Typically,numerical solutionsareusedtosolveunsaturatedflowequationsbecauseoftheirnon-linearity. De Vasconcellos and Amorim (2001) modeled Richards equation using itsmixedform:theyusedfinitedifferencetechniqueswithbackwardEulertime marching coupled with modified Picards method. Results showed that the model is able to handle short duration infiltration. Theusualdescriptionofsoil-watermovementinunsaturatedzones ignorestheeffectofairbyassumingthatairisdisplacedwithoutviscous resistance.Yet,thisisnotthecaseifairflowishinderedbythepresenceofa shallowwater table,whereanimpermeablelayerisobserved(Allen,1986). The coupledmovementofairandwaterhasbeenmodeledinunsaturatedzones throughatwo-phaseflowapproach.ToumaandVauclin(1986)ranan experimental andnumerical analysis of two-phase flowin the vadose zone. They concludedthatwhenairisabletoescapeinadvanceofthewaterfront,aone-phasemodelseemsadequatetomodelinfiltration.Butifaircanonlyescape 18throughthesurface,thenentrappedairparticlesaheadofthewaterfrontcauses severereductionininfiltrationrates,andatwo-phaseflowapproachshouldbe used.CeliaandBenning(1992)presentedanumericalalgorithmformodelinga two-phaseflowinaporousmedia,basedonamodifiedPicardslinearization. Results showed that air phase advection shouldbe considered when dealing with contaminant transport in unsaturated zones. 2.8.2Preferential flow Incontrasttomatrixflow,preferentialflowdoesnotpermeatetheentire porousnetworkofthesoilmatrix,butmovesthroughdistinctivepathwaysthat constituteonlyafractionofthesoilsvolume(Hillel,1998).Thesepathways includecavitiesandfissureswhichareeitherformedfromdryingandwetting conditionsinclayeysoils,biologically(earthworms,ants,androdents),orby decaying roots. As water infiltrates through the soil, it tends to flow through these macroporeswithoutflowingthroughallthemicroporesinthesoilprofile. Preferentialflowhasaseriousimpactonthemovementofsolutesinthesoil. Hoodaetal.(1999)conductedastudyonPlossindrainflow,fromintensively managed grassland soils, and concluded that significant amounts of P losses could occur through preferential flow in a field. Severalmodelshavebeendevelopedtosimulatesoluteandnutrient transport processes (Steenhuis et al., 1994; Shalitand Steenhuis, 1996; Stamm et al., 1998; Villholth and Jensen, 1998). Steenhuis et al. (1994) developed a simple physically-based two-layer model, in which sorption and desorption processes are separated.Themodelwastestedonthree-independentdatasets,andresults showedthatthemodelprovidesagoodframeworkforpredictingsolute concentrationsinpreferentialflow.ShalitandSteenhuius(1996)modifiedthe modeldevelopedbySteenhuisetal.(1994)totakeintoaccountanon-uniform distributionofsoluteinthesurfacelayerinhighflowrateevents.Theirresults showedthatonlyafractionoftheupperlayercontributestotheflowin macroporesduringhighflowrateperiods.Stammetal.(1998)studied preferentialtransportofdissolvedreactivePindrainedgrasslandsoils.The 19discharge-concentrationcurvesdevelopedduringthisstudyprovedthatPwas transportedthroughpreferentialflowpathsfromthesurfacetothedrains. Furthermore,McGechanetal.(2005)adapted theMACROmodel(Jarvis,1994) tostudythethrough-soiltransportofPtosurfacewatersfromlivestock agriculturalfields. The MACROmodel has the most comprehensive treatment of macropore flow, and has mainly been applied to study pesticide movement in the soil.McGechanetal.(2005)concludedthatelevatedPlossesoccurfrom livestock farming areas through macropore flow. 2.9SOLUTE TRANSPORT Generally, hydrodynamic and abiotic processes mainly affect contaminant andsolutetransportmovementdownthesoilprofile.Hydrodynamicprocesses, suchasadvection-dispersionandpreferentialflow,affectthepollutanttransport byimpactingtheflowofwaterintothesubsurface.Abioticprocesses,suchas adsorption,precipitationanddissolution,affecttheirtransportbycausing reactionsbetweenthecontaminantandthefixedsoilmatrix,orbyalteringthe form and concentration of the contaminant (Knox et. al, 1993). The transport of a solute within the soil porous media throughmatrixflow water is simulated using thegeneralpartialdifferentialcalledtheadvection-dispersionequation(ADE) (Warrick,2002).Threeprocessesaffectthechangeofsoluteconcentrationwith time:advection,hydrodynamicdispersion,andadsorption.Hydrodynamic dispersion(dispersionanddiffusion)isamolecularscaleprocess,whichcauses spreadingduetotheconcentrationgradientandrandommotion.Advection represents the movement of a contaminant with the flowing water according to its seepagevelocity(Bedientetal.,1999).Adsorptionisregardedasaretardation process,andisdefinedastheinteractionofthedissolvedcontaminantwiththe surfacechargesofsoilparticles.ThesolutionoftheADEisusually simultaneously coupled with the soil water flow equation (Richards Equation), as well as with adsorption models. A finite difference numerical scheme was adapted 20to solve these equations. Good fits were obtained when compared with laboratory results when the soil had high and low water content. 2.10TRANSPORT MODELS FOR SUB-SURFACE RUNOFF Modelingwaterflowinvariablysaturatedconditionsisessentialfor assessing solute (contaminant) transport in the subsurfacelayers of the soil. Two differentmodeling concepts exist for simulatingwater flowinhomogeneous soil profiles:waterbalancemodelsandnumericalmodels.Thewaterbalancemodels includetheHELP,andDRAINMODmodels.Saturatedandunsaturatedflowin thewaterbalancemodelsiscalculatedbasedonDarcyslaw.Whileunder unsaturatedconditions,thesaturatedhydraulicconductivityisreplacedbythe unsaturatedhydraulicconductivity,determinedbyanalyticalsoilhydraulic functionslikeCampbells(1974)equation.TheHELPmodel(Schroederetal., 1994;GogolevandDelaney,P.1998)wasdevelopedtosimulatelandfill hydrologicprocessesandtotesttheeffectivenessoflandfilldesigns. DRAINMOD (Skaggs, 1980-2002; Fernandez et al., 1997) predicts the effects of drainageandassociatedwatermanagementpracticesonwatertabledepths,the soilwaterregime,andcropyields.DRAINMODanalyticallysolvestheGreen-Amptequationtosimulateinfiltration,andHooghoudtsequationtosimulate flowinto the drains;both equationsare derivedfrom Darcyslaw, and subjected to different boundary conditions. These models utilize several assumptions which allowforspeeding-upthecomputationprocess,butmayproduceinadequate resultsundersomeconditions(Gogolev,2002).Forexample,theHELPmodel assumesconstantpressureheadinthesoillayersbeingstudied,whichisa reasonable assumption for moisture contents above field capacity.The numerical models are usually based on Richards equation for water flow in porous media, and solve the advection-dispersion equation simultaneously forsolutetransport.ThesemodelsincludeLEACHM(HutsonandWagenet, 1992), SWAP (Kroes et al., 1999), VS2DT (Lappala et al., 1993), and HYDRUS-1D/2D (imnek et al., 1998); Table 2.1 presents a detailed comparison between 21thesefourmodels.Throughouttheliteratureexamined,theRichardsequation-based models are the most theoretically proven to represent flow processes in the porousmediummorerealisticallythanwater-balancemodels(API,1996), especiallyinnear-surface water flow conditions (Scanlon et al., 2002). However, large-scaleapplicationsofRichardsequation-basedmodelstohighly heterogeneous soils withvariable hydraulic properties can be extremely difficult; theintegrationoftheRichardsequationrequirespowerfullcomputerswith significant capacity, and needs more time to run. 2.11NUMERICAL MODELS IN USE AND THEIR APPLICATIONS 2.11.1The LEACH Model TheLEACHM(LeachingEstimationAndChemistryModel)(Hutson andWagenet,1992)isacomprehensive,deterministic-mechanistic,one-dimensionalfinitedifferencemodelusedforthepredictionofwaterandsolute movement,transformation,plantuptakeandchemicalreactionsinunsaturated zones. LEACHM is not designed to describe surface runoff and erosion, although itestimatesrunoffusingprofilehydrologyandtheSoilConservationService (SCS) curve number procedure. Transport of a dissolved chemical contaminant is simulatedusingthegeneralADE.LEACHMreflectsonsorption/desorptionof thechemicalpartitioning(phosphorusandnitrogen)usingtheempiricalnon-linearFreundlich-Langmuirisothermsapproach(Hutson,2000).LEACHM utilizes finite difference analysis to solve the governing equation in both time and space. LEACHM was evaluated to predict drainage in zero-tension pan lysimeters, andbromide(Br-)leachingincornfields(Jemisonetal.,1994).TheLEACHM overestimatedBr-leachingbutadequatelysimulatedwaterthroughmatrixflow. Webb and Lilburne (2000) used the LEACHM model to evaluate the relative risk ofgroundwatercontaminationbypesticideleaching,associatedwithsoilsin SouthIsland,NewZealand.Simulationswererunfor2yearswith2crops (spring-sownwheatandpotatoes),and2pesticides(MCPAandmetalaxyl). 22ResultsshowedthatLEACHMsimulationshadgreatlyoverestimatedthe retardation of pesticides through sandy gravel substrates, overlying many aquifers from alluvium in New Zealand. These results further showed that c the LEACHM model that it is not able to simulate contaminant transport over a depth of 2 m. 2.11.2The SWAP Model TheSWAPmodel(Soil-Water-Atmosphere-Plant)(Kroesetal.,1999; 2000; Department of Water Resources, WageningenAgricultural University)is a one dimensional model that simulates water flow, solute transport, heat flow, and crop growth in the soil-air-plant environment. Furthermore, the SWAP model has thecapabilityofsimulatingpreferentialflow,adsorption,anddecomposition processesofnutrientsandpesticides(vanDametal.,1997).SWAPsolvesthe differentgoverningequationsusingimplicitfinitedifferencenumericalanalysis. Sarwaretal.(2000)andSarwarandFeddes(2000)used the transientsimulation model,SWAP,toevaluatedrainageparameterdesignsforadrainageprojectin Pakistan. SWAP was calibrated and applied to two sample fields. Results showed a close approximation exists between the simulated and measured flow data up to 1.0 m in depth. Furthermore, SWAP proved to be a valuable tool for the design of drainagesystemsintermsofcropyieldandsoilsalinity.Droogersetal.(2000) usedSWAPinaninnovativewaybyextendingitsnormalpointbehaviourtoa distributedapproach,inordertoanalyzewaterbalancesonawatershedscale. Results showed that when the SWAPmodelis appliedin a distributed manner,it servesasausefultooltoanalyzeallthecomponentsofthewaterbalancefora whole irrigation system. 2.11.3The VS2DT Model The VS2DT (Variably Saturated 2D Flow and Transport) (Lappala et al., 1993;U.S.GeologicalSurvey)modelconsidersvariablysaturated,two-dimensional,isothermalconditionstosimulateflowandtransportundersteady-state and transient-state conditions. It uses finite difference techniques with a fully 23implicitschemetosolveRichardsEquationandADEatsubsequenttimesteps (Shawetal.,2001).TheVS2DTmodelhasbeenextensivelyverifiedfor groundwater flow and chemical transport using analytical solutions (Healy, 1990). VS2DT has been modified to include boundary conditions imposed by pipe drains inallthreemodesofoperation;conventionaldrainage,controlleddrainage,and subirrigation(Munsteretal.,1994).Itwasfurthermodifiedtoincludethe transport of multiple chemicals (Munster et al., 1996). Results, from both studies, showedthatVS2DTisanextremelyusefultoolinassessingtheeffectsofwater tablemanagementonthechemicalsandnutrientsintiledrainedfields.Chakka andMuster(1997)developedanewmethodologyforVS2DTtosimulate preferentialflowandaquifer-riverinteractionsontheBrazosRiverfloodplain, Texas.WilkisonandBlevins(1999)appliedtheVS2DTmodeltostudythe transport ofnitrogenfertilizerwithintheunsaturatedzones.Theresultsfromthe simulations showed that nitrogen transport from the field is subject to both matrix andpreferentialflow.Shawetal.(2001)utilizedtheVS2DTmodeltoevaluate hydraulicpropertiesofsoilswithdifferencesintheoverlyingsandyandloamy horizontextures.Hydrologicalmodeling,withtheVS2DTmodel,provedtobe beneficialinevaluatingtheflowpathwaysalongaheterogeneousprofile,in relationtothesoilhydraulicconditions,developingmoreefficientirrigation strategies. 2.11.4The HYDRUS Model HYDRUS(imneketal.,1998;2005;U.S.SalinityLaboratory, USDA/ARS,Riverside,California)isanumericalmodelforsimulatingwater-flowandsolutetransportinvariablysaturatedsoils,underbothsteady-stateand transientconditions.Water-flowandsolute-transportaredescribedbasedon Richardsequationandadvection-dispersionequation,respectively.The governingdifferentialequationsaresolvedusingtheGalerkin-typelinearfinite element technique applied to a network of triangular elements. Integration in time isperformedusingthebackwardfinitedifferenceschemeforbothsaturatedand 24unsaturated conditions (Rassam and Cook, 2002). All of these techniques provide satblesolutionsfor thegoverningequationagoodinterfacebetweenunsaturated andsaturatedconditions.Finiteelementtechniquesprovidetablesolutionfor irregular boundaries and time-dependent boundaries, andfinite differences, using theCrank-NicholsonScheme,minimizeserrorproductionwhenintegratingover smalltimeincrements.TheHYDRUSmodelexistsinoneandtwodimensional form: HYDRUS-1D and HYDRUS-2D, respectively (imnek et al., 2005); both versions utilize the same governing equations and principles. The only difference isthattheHYDRUS-2Dmodelintegratesthegoverningequationsintwo dimensions.However,throughouttheliterature,theHYDRUS-2Dmodelis mainlyappliedunderfieldconditions,whileHYDRUS-1Dmodelisappliedto study water flow and solute transport in one dimensioninlaboratory columns. In thisstudy,Ptransportwasstudiedonlyinsoilcolumns;therefore,theone-dimensional version (HYDRUS-1D) of the HYDRUS model was used. HYDRUS-2DwasappliedbyBen-GalandDudley(2003)tosimulateP movement and P distribution patterns under continuous application of P fertilizer, fromasubsurfacepointsourceemitter.Bothsimulatedandexperimentalresults showedthatanincreaseinPuptakebytheplants,andgreaterPmobility,was observedundercontinuousapplicationsofwaterandfertilizerasopposedto intermittentapplications.However,Ben-GalandDudley(2003)concludedthat theLangmuirisotherm,providedwithintheHYDRUS-2Dmodel,isinadequate for describing P sorption. It assumes instantaneous equilibrium with the solid and solutioninterfaces.RassamandCook(2002)modeledwater-flowandsolute-transport in acid sulphate soil of tile drained fields using the HYDRUS-2D model. They concluded that numericalmodeling, employed by the HYDRUS-2D model, providedaneffectivetoolinunderstandingthemechanismsinvolvedinsucha complex system, and hence was a valuable management tool. Mailhol et al. (2001) studied theimpact offertilization practices on nitrogen leaching underirrigation, throughbothfieldexperimentsandnumericalmodeling(HYDRUS-2D).The simulation results from the HYDRUS-2D model were in agreement with the field 25results;thenitrogenleachingisnotsignificantundertheareaofstudy,andthe yield was not affected under high irrigations rates. Moreover,Pangetal.(2000)usedtheHYDRUS-2Dmodeltosimulate water and solute (pesticide) movement in variable saturated soil conditions, and in groundwateruptoadepthof10m.Themodelsimulatedwellthewater distribution along the soil profile, but it performed better with less heterogeneous soils.Withrespecttothepesticidetransport,HYDRUS-2Dprovidedsimilar resultstothemeasuredresultsfromthefield,inbothunsaturatedandsaturated conditions. De Vos et al. (2002) studied themovement of chloridein tile drained Dutch reclaimed fields using HYDRUS-2D and field experiments. Their aim was toanalyzetheoriginofchlorideconcentrationsinthedrains.HYDRUS-2D provided a good description of the dynamics of water flow and solute transport in two dimensions. Oztekin (2002) studied drain flow into subsurface drainage pipes foralayeredsoilprofileinNorthCentralOhio(USA)usingtheHYDRUS-2D model.TheresultssimulatedbythefiniteelementHYDRUS-2Dmodel,werein agreementwiththeresultsobtainedtheempiricalequation,Kirkham-Hooghoudt equation, for water table elevations below 70 cm. Persicanietal.(1996)appliedtheHYDRUS-2Dtosimualateatrazine mobilityintwoalluvialsoilsinnorthernItaly.Theirresultsshowedthat HYDRUSdidsimulatesuccessfullyatrazinemobilityinthefield;nevertheless, theywereabletoimprovetheirresultwhentheycalibratedtheiradsorption equilibrium constant (kd) with field conditions. Ventrella et al. (2000) applied the HYDRUS-1DmodeltosimulatewaterchlorinetransportinfinetexturedItalian soilssubjecttoafluctuatingsalinegroundwatertable.Theyconcludedthatthe HYDRUS-1Dmodelisveryusefulforanalyzingrelativelycomplexflowand solutetransportprocessesatthefieldscale.However,Phillips(2006) investigatedtheabilityoftheHYDRUS-2Dmodelinsimulatingthe transportofreactivechemicalslikepotassiuminundisturbedsoilcolumns. TheresultsshowedthattheHYDRUSmodelwassuccessfulinsimulating waterflowbutitwasnotveryconclusivewithregardtoreactivesolute transport.Phillips(2006)recommendedmoreinvestigationintotheability 26of the HYDRUS model in predicting the transport of reactive chemicals in the soil-water environment. 2.12CONCLUSIONS Theneedtodevelopwaterqualitymodelscameaboutwhentheproblem of NPS pollution was highlighted in the late 1970s, with the Clean Water Act and its successive amendments. This act brought attention to many researchers of the necessityinresearchinganddevelopingwaterqualitymodels.NPSpollutionis oneofthemainproblemsofglobalconcern.Agriculturalpracticesarenow acknowledged as one of the main contributors of NPS pollutant including P to the pollution of fresh water bodies (Corwin et al., 1999). Furthermore, P, classified as a non-point source pollutant, has become a major concern to researchers due to its contributiontoeutrophicationofaquaticecosystems.Advancedinformation technologiesmustbeappliedtosolvemultidisciplinaryproblemsofNPS pollution.ThecombinationofchemicalandtransportmodelstosimulateP transport in sub-surface runoff presents a promising solution. However, choosing thepropergoverningequationsforwaterflow,solutetransport,andchemical relationsfortheconditionsandprocessestakingplaceinthesoil-water environment,isacrucialstep.TheNICAmodelisadynamicaqueouschemical modelthatcouldprovideagooddescriptionofPO4adsorptionontothesoil.It provides an advantage over other adsorption models, since it describes adsorption ofaspecificioninrelationto otherspeciesinsolution, thepH,and theaqueous solution ionic strength. Thesub-surfacewaterflowandsolutetransportmodels,describedinthe literatureabove,arefairlywelldocumentedandhavebeentestedagainstfield conditions.LEACHMproved tobemorelimitedto thevadosezone,anditdoes notprovideagoodinterfacebetweenunsaturatedandsaturatedconditions.The VS2DTmodelhasbeensuccessfullyappliedtodescribepesticidetransport.Yet the solution, provided by the VS2DT model, is very sensitive to initial conditions oftheproblemandtomeshdiscretization(Healy,1990).TheSWAPmodelwas 27betteradaptedtosimulatewaterflowthansolutetransport.Ithasbeen successfullyappliedtoirrigationschedulingandwaterbudgeting.However,the SWAPmodelisbetteradaptedtoconditionsintheNetherlandsandinEurope. Furthermore,theHYDRUSmodelhasbeensuccessfullyappliedtosimulate waterflowandrelativelyreasonabletosimulatenutrienttransportonseveral agriculturalfields.TheHYDRUSmodelutilizesthefiniteelementnumerical techniquestosolvethegoverningequationsinspace,andthefinitedifference technique to integrate the governing equationsintime. Thesenumerical schemes offer stable numerical solutions to deal with timedependent boundary conditions andvariablysaturatedconditions.Inaddition,theHYDRUScodeautomatically adjusts the time step to satisfy Courants number. The HYDRUS model considers both linear and nonlinear types of ion adsorption onto the soil particles, which are factoredintothecontaminanttransportequation.Theseadsorptionequationsare foundinmostmodelsdiscussedaboveaswell;theyprovidemorereseanable predictionswithrespecttosolublenutrientthanstronglyadsorbedones.In conclusion,theHYDRUSmodelprovidesstablesolutionstowaterflowina variablysaturatedporousmediuminbothundisturbedandhomegenizedsoils, however,itsabilitytosimulatePtransportinsoilandwaterwillbefurther investigated in this study. 28Table 2.1: Summary of Four Models: HYDRUS_2D, SWAP, VS2DT and LEACHM HYDRUS1D/2D SWAP (SWATRE) VS2DT LEACHM Authors imnek et al., 2005 Kroes et al., 1999 Lappala et al., 1993 Hutson and Wagenet, 1992 Developer USDA/USSL Riverside, California Wageningen Agricultural University U.S. Geological Survey Flinders University of South Australia Numerical Method FE-space FD-time implicit FD Implicit FD-time Central FD-space FD-space FD-time Dimension 1/2D 1D 2D 1D Sat/Unsat ! ! ! ! Plant Uptake ! ! ! ! van Genuchten, 1980 van Genuchten, 1980 Brooks & Correy, 1964 Campbell (1974) Brooks & Correy, 1964 Mualem, 1976 Campbell, 1974 K-h- van Genuchten, 1980 %silt-clay-sand %silt-clay-sand %silt-clay-sand %silt-clay-sand Ksat, PSA, b, Se, Ksatv, Ksath, PSA, b Ksat hor, PSA, b, Se Ksat, b, Se s, r, , n s, r, , n s, r, , n s, r, , n Parameters L, T (2D), D*, L, T (2D), Dw L, T (2D), Dw climate; N; and P data Adsorption Linear/ Non-linear Non-linear Linear Non-linear Language FORTRAN FORTRAN FORTRAN FORTRAN Phosphorus/Irrigation Snow drainage/sub irrigation Bromide Nitrogen/fertilization Thawing and freezing Nitrogen leaching Nitrate Leaching Hydrology/drainage Drainage Effect of WTM Phosphorus Chloride Transport Lateral flow in sandy soils Pesticide Virus Transport Pesticide Transport Surfactant Transport Application Pesticide Transport Output Graphical / ASCII files ASCII files ASCII files ASCII files 29CONNECTING TEXT TO CHAPTER 3 Thischapterisamanuscriptawaitingtobepublishedin2006.The manuscript is co-authored by my supervisor Dr. C.A. Madramootoo and Dr. W.H. Hendershot,ProfessorattheNaturalResourceSciencesDepartmentofMcGill University. All literature cited in this chapter is listed in the reference at the end of this thesis. Chapter 3 covers the development of the HYDRUS-NICA model designed to simulate the transport of phosphorus in the soil-water environment. As stated in Chapter1,theproposedmodelaimsatcoveringthelimitationsofothersoilP models;hence,improvingthepredictionofPinthesoil-waterenvironment.A completedescriptionofthecomputationaldevelopmentoftheHYDRUS-NICA model,anditscodeverificationispresented.Thisisthetopicofthefollowing article. 30CHAPTER 3: The Development of the HYDRUS-NICA Model Joumana Abou Nohra, Chandra Madramootoo, and William Hendershot ABSTRACT AmodelnamedHYDRUS-NICAwasdevelopedbycouplingahydrological model (the HYDRUS-1D model) with an aqueous chemicalmodel (the NICAmodel) to improvethesimulationofphosphorus(P)transportinthesoil-waterenvironment.The empiricalnon-linearadsorptionequationsoftheHYDRUS-1Dmodelwerereplacedby thenon-idealcompetitiveadsorption(NICA)model.ThehypothesisistheNICAmodel providesanimprovement overempiricalmodel;itdescribestheadsorptionofdissolved substanceslikePto thesoilinrelationto thedifferentcompetingsubstancesinthesoil aqueoussolution,whiletakingintoaccountthepHandtheionicstrength.Thisstudy presents the different stages that were followed in developing the HYDRUS-NICA model: the conceptual, representational, and computationalmodels. This studyfurther describes theverificationproceduresconductedonthedevelopedcodeoftheHYDRUS-NICA model.Verificationofthecodewasbasedoncomparingtheaccuracyofthenumerical schemes of both the HYDRUS-NICA and HYDRUS-1D (HYDRUS) models. Numerical accuracywasevaluatedbasedontherelativeerrorproducedfromthewaterflowand solutetransportatspecifiedtimeandspaceincrements.Theresultsshowedthaterrors producedbytheHYDRUS-NICAmodelforwaterflowandPtransportareslightly higher than the HYDRUS model for the same conditions; however, on average they were lessthantwopercent(withintheacceptablerange).Thus,itwasconcludedthatthe solutionsofHYDRUS-NICAmodeldidconvergeataproperrate,andconfirmedthat modifications to the HYDRUS computer code have been implemented correctly. Keywords: HYDRUS model, Richards equation, Advection-Dispersion Equation, NICA model, code verification 313.1INTRODUCTION Thedevelopmentofamodelanditscomponentsencompassesfivedistinctive stages:aconceptualmodel,representationalmodel,computationalmodel,code verification,andmodelvalidation.However,thefirstthreestagesarehighlylinked (Ewing,2002).Theconceptualmodeldescribesthedifferentphysicalprocessestobe modeled,anddefinesthe objectives,assumptionsandassertionstobeconsideredbythe model.Therepresentationalmodeltranslatestheprocessesdescribedbytheconceptual model into mathematical relationships. The computational model encodes the formulated mathematicalequationswithinacomputerprogram.Equationsaresolvedbasedonthe assumptionsandconditionsstatedintheconceptualmodel.Oncethecomputational modeliscomplete,itscodeisverifiedtoensurethedesiredresults(ParrottandKok, 2000). Finally the model is run under real-time conditions to simulate different scenarios. Theresultsobtainedarevalidatedagainstmeasureddata toinvestigatetheproximityof themodelpredictionstoreality.Modelvalidationincludestwoadditionalsteps: calibrationandsensitivityanalysis.Theseanalysesaresignificantinunderstandinghow the model varies as a function of theinput data and the model parameters (Saltelli et al., 2000). Themainpurposeofthisstudyistodevelopanumericalmodeltoimprovethe predictionofphosphorus(P)transport,andPadsorptionprocessesinthesoil-water environment,undervariablysaturatedconditions.Asproposed,themodelcouplesan aqueous chemical model, the NICA model (Koopal et al., 1994), with a hydrological and solute transport model, the HYDRUS-1D model (imnek et al., 1998). The NICA model is anon-ideal competitive adsorption (NICA)model;introducinga newmethodologyin dynamicallypredictingPadsorptioninsoilsolutions.NICAdescribestheadsorptionof solublesubstancesbytakingintoaccountthecompetitivenon-idealbehaviourofthe different substancesin the soil aqueous solution,while considering the pH and theionic strength. The NICAmodel presents an advantage over the empiricalmodels (Freundlich andLangmuiradsorptionisotherms)andthesurfacecomplexationmodels(SCM)(a diffused doublelayer (DDL)model). Empiricalmodels have been used to determine the quantity/intensityrelationshipbetweenphosphatesfoundinsolutionandthesoilsolid 32phase (Bache and Williams, 1971). These isotherm models describe adsorption data on a macroscopic level; they do not describe the mechanisms of adsorption (Sparks, 2003). On theotherhand,SCMaremechanisticchemicalmodelsandrepresentanimprovement overtheempiricalmodelsofadsorption.Therate-sorptioncoefficienttheyprovide depends on soil texture, the nature of aqueous species involved, and is less dependent on thesystemsvariables,suchaspHandtheconcentrationoftheaqueousspecies (Koretsky,2000).However,SCMrequirenumerousparametersandlacksimplicity. AccordingtoMcBride(1997),theDDLtheoryanditsmodifications,failstomeetthe two criteria for an acceptance of a theory: conformity with experimental observations and simplicity.TheDDLmodelsprovideasatifactoryfittoexperimentaldataonlyundera very limited range of conditions, and require a substantial number of parameter for every solute being studied.TheHYDRUS-1Dmodel(imneketal.,1998)isaphysicallybasednumerical modelfor simulating water-flow, heat, and multiple solutes transport in one-dimensional variably saturated soils, under both steady state and transient conditions. The HYDRUS-1DmodelsolvestheRichardsEquationtosimulatewaterflow,andtheAdvection-DispersionEquation(ADE)tosimulatesolutetransportinporousmedia,witha Windowsinterface.Severalphysically-basednumericalmodelsfoundintheliterature utilizethesegoverningequations,likeSWAP(Kroesetal.,1999),LEACHM(Hutson andWagenet,1992),andVS2DT(GogolevandDelaney,1999)models.However,the HYDRUS-1Dmodelutilizesfiniteelementnumericaltechniquestosolvethegoverning equations in space and the finite difference technique to integrate the governing equations intime.Thesenumericalschemesofferstablenumericalsolution;theyallowthemodel totakeintoaccountdifferenttypesofboundaryconditions,toprovideagoodinterface betweensaturatedandunsaturedconditions,andtointegrateoversmalltimeandspace increments (Rassam and Cook, 2002; imnek et al., 2005) ThischapterpresentsthedifferentstepsinvolvedincouplingtheHYDRUS-1D modelwiththeNICAmodel:theHYDRUS-NICAmodel.Themainobjectivesofthis studywere:1)todeveloptheconceptualandrepresentationalmodelsoftheHYDRUS-NICAmodel,2)tobuilditscomputationalmodel,and3)toverifyitscode.The HYDRUS-NICAmodel, as developedin this chapter, willbe calibrated and validated in 33Chapter7;itwillbetestedagainstrealtimeconditionsusingexperimentallymeasured results. 3.2THE CONCEPTUAL MODEL 3.2.1Objective Themainobjectiveofthemodelistoestimatethe time-depthdistributionofthe moisturecontentandpressureheadinanactivesoilprofile,andthetime-depth distribution of P concentration in an active soil profile. 3.2.2Model Description The HYDRUS-NICA model is based on the distributed approach that will be used to portray the spatial and temporal variability of P in one-dimension, vertically down the soil profile. The HYDRUS-NICA model is composed of three main modules: a chemical module,watermodule,andsolutemodule(Figure3.1).Thechemicalmoduleprovides the solute module with the ratio of P adsorbed to P in solution (s/c); it is necessary to determine the retardation factor (R) of P in the soil. In the case of P, the retardation factor determines the portion of Pin solution that gets adsorbed to the charged surfaces on the soilparticles,andgetsretardedfrombeingtransportedthoughmatrixflow.Thewater module provides the solute module with the seepage velocity of water in the soil porous mediawhichisnecessarytodeterminetheadvectionanddispersiontransportofP throughmatrixflow.Basedontheoutputofthechemicalandthewatermodules,the solute module can determine concentration of P in the soil solution, at the different space (dx)andtime(dt)increments.ThechemicalmodelwasbasedontheNICAmodel (Koopal et al., 1994), and the water and solute modules were based on the HYDRUS-1D code(imneketal1998)withouttheWindowsinterface.TheHYDRUS-1D (HYDRUS)sourceisacombinationoftheSWMS_2Dsourcecodedevelopedby imneketal.(1992)tosimulatewaterflowandsolutetransportinatwo-dimensional variablysaturatedmedia,andtheUNSATCHEMsourcecodedevelopedbyimneket 34al.(1993)tosimulateone-dimensionalvariablysaturatedwaterflow,heattransport, carbon dioxide production and transport. AversionofthesourcecodeoftheHYDRUS model,suppliedbyDr.JirkaimnekoftheU.S.SoilSalinity Laboratory,wasusedin this study. 3.2.3Assumptions and Assertions of the Model The following assumptions and assertions are considered by the HYDRUS-NICA model: 1.OnlytheadsorptionanddesorptionprocessesfromthePcycleareconsideredin the chemicalmodel. The rates of dissolution andprecipitation processes are very small and extend over a large period of time. Thus they are considered negligible as compared to the instantaneous adsorption and desorption processes (Laiti et al., 1996). 2.TheformofP,consideredbytheHYDRUS-NICAmodel,isPO4-3(PO4)or orthophosphoricacid;PO4anionshavethestrongestbindingcapacityto thesoil functional groups at the pH of the soil, naturallyoccurringin the field (McBride, 1994). 3.OrganicsourcesofPwithinthesoilarenotincludedasspeciesinthechemical module.Consequently,thecompetitionoforganicanionswithPO4adsorption sites will not be considered either. 4.Complexations of PO4 ions with background ions are not considered. 5.The nature of P adsorption onto the soil surface functional groups is considered to be non-linear. 6.Both steady-state and transient boundary conditions are considered. 7.The model simulates water flow under variably saturated conditions. 8.Onlyone-phaseflowisconsidered.Airandwatervapourflowwillnotbe modeled. 359.Themo