Simultaneous estimation of soil hydraulic and solute transport parameters from transient infiltration experiments

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<ul><li><p>Simultaneous estimation of soil hydraulic and solute transportparameters from transient infiltration experiments</p><p>M. Inoue a, J. Simunek b,*, S. Shiozawa c, J.W. Hopmans d</p><p>a Arid Land Research Center, Tottori University, Hamasaka 1390, Tottori 680, Japanb US Salinity Laboratory, USDA-ARS, 450 W. Big Springs Dr., Riverside, CA 92507, USA</p><p>c Institute of Agricultural and Forest Engineering, University of Tsukuba, Tsukuba, Japand Hydrology Program, Department LAWR, 123 Veihmeyer Hall, University of California, Davis, CA 95616, USA</p><p>Received 6 October 1999; received in revised form 10 February 2000; accepted 11 February 2000</p><p>Abstract</p><p>Estimation of soil hydraulic and solute transport parameters is important to provide input parameters for numerical models</p><p>simulating transient water flow and solute transport in the vadose zone. The LevenbergMarquardt optimization algorithm in</p><p>combination with the HYDRUS-1D numerical code was used to inversely estimate unsaturated soil-hydraulic and solute transport</p><p>parameters from transient matric pressure head, apparent electrical conductivity, and euent flux measurements. A 30 cm long soil</p><p>column with an internal diameter of 5 cm was used for infiltration experiments in a coarse-textured soil. Infiltration experiments</p><p>were carried out with both increasing and decreasing solute concentrations following a sudden increase in the infiltration rate.</p><p>Matric pressure heads and solute concentrations were measured using automated mini-tensiometers and four-electrode sensors,</p><p>respectively. The simultaneous estimation results were compared with independently measured soil water retention, unsaturated</p><p>hydraulic conductivity, and solute dispersion data obtained from steady-state water flow experiments. The optimized values cor-</p><p>responded well with those measured independently within the range of experimental data. The information contained in the ap-</p><p>parent electrical conductivity (which integrates information about both water flow and solute transport) proved to be very useful for</p><p>the simultaneous estimation of soil hydraulic and solute transport parameters. 2000 Elsevier Science Ltd. All rights reserved.</p><p>Keywords: Four-electrode sensor; Bulk soil electrical conductivity; Hydraulic conductivity; Soil water retention curve; Dispersivity</p><p>1. Introduction</p><p>In arid and semiarid regions that are characterized byhigh air temperatures and low precipitation rates, saltsaccumulation at or near the soil surface is common. Soilsalinization in irrigated agriculture may be acceleratedby the presence of high groundwater table when, forexample, deep drainage is reduced because of low sub-soil permeability. The combined eects of waterloggingand salinization may cause a significant decrease of ag-ricultural productivity of irrigated lands [17]. When areliable drainage system is present, salts can be removedfrom the root zone by leaching using excess irrigationwater. Such practices can be conveniently described</p><p>using models that simulate simultaneously water flowand solute transport processes [22].</p><p>Computer models based on numerical solutions ofthe flow and solute transport equations are increasinglybeing used for a wide range of applications in soil andwater management. Model predictions depend largelyon the accuracy of available model input parameters.Soil hydraulic parameters, characterizing the water re-tention and permeability properties, and transport andchemical parameters aecting the rate of spreading ofchemicals and their distribution between solid and liquidphases are the most important input variables for suchmodels.</p><p>The use of parameter estimation techniques for de-termining soil hydraulic properties is well established[2,8]. The approach has been widely used for variouslaboratory and field experiments. Among others, lab-oratory experiments include one-step [7,30] and multi-step [1,31] outflow experiments, upward flux or headcontrolled infiltration [3], the evaporation method</p><p>Advances in Water Resources 23 (2000) 677688</p><p>www.elsevier.com/locate/advwatres</p><p>* Corresponding author. Tel.: +1-909-369-4865; fax: +1-909-342-</p><p>4964.</p><p>E-mail addresses: mainoue@center.tottori-u.ac.jp (M. Inoue), jsi-</p><p>munek@ussl.ars.usda.gov (J. Simunek), shiozawa@sakura.cc.tsukuba.</p><p>ac.jp (S. Shiozawa), jwhopmans@ucdavis.edu (J.W. Hopmans).</p><p>0309-1708/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 3 0 9 - 1 7 0 8 ( 0 0 ) 0 0 0 1 1 - 7</p></li><li><p>[20,24], and infiltration followed by redistribution [25].In separate lines of research, solute transport parametersare often obtained from column experiments assumingsteady-state water flow [15], and using parameter esti-mation codes such as CFITIM [33] or CXTFIT [29] forfitting analytical solutions of the transport equation toexperimental breakthrough curves. Solute transportparameters for conditions for which no analytical solu-tions exist, such as for nonlinear adsorption, can beobtained using numerical solutions [10,25]. The aboveparameter estimation eorts for water flow and solutetransport have remained relatively disjoint. Althoughthere are numerous studies that combined estimation offlow and transport parameters for groundwater flowproblems [12,27,34], only a very few studies have usedcombined transient variably-saturated water flow andsolute transport experiments for simultaneous estima-tion of soil hydraulic and solute transport parameters[13].</p><p>Dierent strategies in combined estimation of waterflow and solute transport parameters can be followed.Only water flow information (matric pressure headsand/or fluxes) can be used first to estimate soil hydraulicparameters, followed with estimation of transportparameters using only transport information (concen-trations). Combined water flow and transport informa-tion can be used to estimate sequentially soil hydraulicand solute transport parameters. Finally, combinedwater flow and transport information can be used tosimultaneously estimate both soil hydraulic and solutetransport parameters. The last approach is the mostbeneficial since it uses crossover eects between statevariables and parameters [27] and it takes advantage ofthe whole information, because concentrations are afunction of water flow [12]. Misra and Parker [13]showed that simultaneous estimation of hydraulic andtransport properties yields smaller estimation errors formodel parameters than sequential inversion of hydraulicproperties from water content and matric pressure headdata followed by inversion of transport properties fromconcentration data.</p><p>The main motive for the simultaneous estimation ofwater flow and solute transport parameters in ground-water studies is to use the most information availableand to decrease parameter uncertainty. In soil studies,this is accompanied by the motive to avoid carrying outrepeated experiments on the same sample. That is, re-peated experiments on the same or identically-packedsoil columns most likely will aect the magnitude of flowand transport parameters. Moreover, the presentedtransient flow and transport experiments are more re-alistic than those requiring steady state. The combineduse of transient flow and transport data for estimationof the soil hydraulic and solute transport parameters canalso result in substantial time-savings as compared tosteady-state methods.</p><p>Excellent tools have been developed over the years toanalyze transient flow experiments such as ONESTEP[6], SFIT [9], and HYDRUS-1D [23]. Some programsare designed for specific experiments only (e.g., ONE-STEP [6]), while others are more versatile (e.g., SFIT [9],HYDRUS-1D [23]). Of the above codes, only HY-DRUS-1D allows simultaneous inversion of soil hy-draulic and solute transport parameters, includingsituations involving linear and nonlinear solute trans-port during either steady-state or transient water flow.</p><p>The objective of this study is to determine soil hy-draulic and solute transport parameters of a Tottoridune sand using various steady-state and transient waterflow and solute transport laboratory column exper-iments. The transient and steady-state tests involve in-filtration at dierent rates. Parameters determined usingdierent analytical and parameter estimation ap-proaches will be compared. We also discuss the appli-cation and calibration of a four-electrode sensor tomeasure the bulk soil electrical conductivity. Themeasured bulk soil electrical conductivity is a variablethat integrates information on both water flow andsolute transport and can thus be beneficially used toestimate simultaneously soil hydraulic and solutetransport parameters. We show that the measured bulksoil electrical conductivity is especially advantageouswhen used for the simultaneous estimation of soil hy-draulic and solute transport parameters.</p><p>2. Theory</p><p>2.1. Water flow</p><p>Variably-saturated water flow in porous media isusually described using the Richards equation</p><p>ohhot o</p><p>ozKh oh</p><p>oz</p><p> Kh</p><p>; 1</p><p>where t is time and z is depth (positive upward), and hand h denote the volumetric water content and the soilwater matric pressure head, respectively. The Richardsequation can be solved numerically when the initial andboundary conditions are prescribed and two constitutiverelations, i.e., the soil water retention, h(h), and hy-draulic conductivity, K(h), functions, are specified. Thesoil water retention curve in this study is described usingthe van Genuchten analytical expression [32]</p><p>Seh hh hrhs hr 1</p><p>1 jahjnm : 2</p><p>The hydraulic conductivity function is described usingthe capillary model of Mualem [14] as applied to the vanGenuchten function [32]</p><p>Kh KsSe 1 1 S1=me m2: 3</p><p>678 M. Inoue et al. / Advances in Water Resources 23 (2000) 677688</p></li><li><p>In Eqs. (2) and (3), hr and hs denote the residual andsaturated volumetric water contents, respectively; Se iseective saturation, Ks the saturated hydraulic conduc-tivity, a pore connectivity coecient, and a, n and m( 1 ) 1/n) are empirical coecients.</p><p>2.2. Solute transport</p><p>Solute transport in variably-saturated porous mediais described using the convectiondispersion equation</p><p>oRhCot o</p><p>ozhD</p><p>oCoz</p><p> ovhC</p><p>oz; 4</p><p>where C is the solute concentration, R the retardationfactor, D the eective dispersion coecient, and v is thepore water velocity. The retardation factor R and thedispersion coecient D are defined as</p><p>R 1 qbKdh</p><p>; 5</p><p>D kjvj; 6where Kd is the linear adsorption distribution coecient,qb the bulk density, and k is the longitudinal dispersiv-ity. Eq. (6) assumes that molecular diusion is insignif-icant relative to dispersion.</p><p>2.3. Initial and boundary conditions</p><p>The initial condition for each infiltration experimentwas obtained by establishing steady-state downwardinfiltration with a constant water flux and a constantsolute concentration. Then, at some time t ti, bothmatric pressure head and solution concentration wereconstant with depth</p><p>hz; ti hi;Cz; ti Ci:</p><p>7</p><p>The upper boundary conditions (z 0) for the infiltra-tion experiments are given by</p><p> K ohoz</p><p> 1 qtopt;</p><p> hD oCoz qC qtoptCtopt;</p><p>8</p><p>where qtop and Ctop are, respectively, water flux andsolute concentration applied at the soil surface.</p><p>A zero matric pressure head gradient (free drainage,q)K) and a zero concentration gradient are used asthe lower boundary conditions (at z)L) for waterflow and solute transport, respectively,</p><p>ohoz</p><p> zL 0;</p><p>oCoz</p><p> zL 0:</p><p>9</p><p>The water flow and solute transport equations subject toinitial and boundary conditions were solved numericallyusing the HYDRUS-1D code [23].</p><p>2.4. Parameter optimization</p><p>The general approach of parameter estimation in-volves the minimization of a merit, goal or objectivefunction that considers all deviations between the mea-sured and simulated data, with the simulated resultscontrolled by the adjustable parameters to be optimized[26]. The objective function OF(b) for the transient flowexperiments is given by</p><p>OFb WhXN1i1</p><p>hmti hoti; b2</p><p> WqXN2i1</p><p>qmti qoti; b2; 10</p><p>where Wh, and Wq are normalization factors for matricpressure head and flow rate, respectively, with eachfactor being inversely proportional to their measure-ment variance; N1, and N2 the number of observationsfor matric pressure head and flux, respectively; and b isthe vector of optimized parameters. The subscripts mand o refer to the measured and optimized values. Theweighted least-squares estimator of Eq. (10) is a maxi-mum-likelihood estimator as long as the weights containthe measurement error information of particularmeasurements.</p><p>The objective function for the transport part of thetransient experiments is given by</p><p>OFb WECXN3i1ECa;mti ECa;oti; b2; 11</p><p>where ECa is the bulk electrical conductivity, WEC itsnormalization factor, and N3 is the number of electricalconductivity measurements. The objective function forsimultaneous optimization of soil hydraulic and solutetransport parameters combines objective functionsEqs. (10) and (11).</p><p>The LevenbergMarquardt method [11,27,34] (as in-corporated in the HYDRUS-1D code [23]) was used tominimize the objective function OF(b). The parametervector b includes the parameters a, n, hr, hs, Ks, l, and k.Each inverse problem was restarted several times withdierent initial estimates of optimized parameters andthe run with the lowest value of the objective functionwas assumed to represent the global minimum. The soilbulk electrical conductivity, ECa, was calculated in theHYDRUS-1D code from calculated values of the solu-tion electrical conductivity, ECw, and the water content,h (see Section 3.1).</p><p>M. Inoue et al. / Advances in Water Resources 23 (2000) 677688 679</p></li><li><p>3. Materials and methods</p><p>3.1. Electrical conductivity measurements</p><p>Nondestructive methods for direct measurement ofsoil salinity include buried porous electrical conductivitysensors, four-electrode probe systems, electromagneticinduction sensors, and time domain reflectometry sys-tems [16,18]. These methods all measure the bulk soilsolute concentration rather than the solution concen-tration of individual ions [19]. The four-electrode probeis used for measurement of solute concentrations whenrapid measurements are needed; this method is wellsuited for measuring both water flow and solute trans-port variables simultaneously during transient infiltra-tion and/or evaporation. The main disadvantage of thefour-electrode sensor is that soil-specific calibration isrequired.</p><p>The four-electrode sensor developed for this study isdescribed in detail by Shiozawa et al. [21]. The sensorconsists of four stainless steel rods of 1 mm outside di-ameter, which are inserted parallel in the center of anacrylic cylinder ring of 20 mm length and 50 mm insidediameter (Fig. 1). The two inner and two outer stainlesssteel rods are spaced 8 and 16 mm, respectively.</p><p>The ratio of the electric current (I) flowing throughthe outer electrodes to the voltage dierence (V2) be-tween the two inner electrodes is measured. The ratio I/V2 is inversely proportional to the electrical resistance ofthe measured medium, or proportional to its electricalconductivity (EC). The magnitude of the electric current(I) through the two outer electrodes i...</p></li></ul>

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