Department of Pesticide Regulation

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1 Department of Petiide Regulation Mary-Ann Warmerdam Diretor M E M O R A N D U M Arnold Shwarzenegger Governor TO: Randy Segawa Environmental Program Manager I Environmental Monitoring Branh FROM: Frank Spurlok, Reearh Sientit III Original igned by Environmental Monitoring Branh Rik Bergin, Environmental Sientit Environmental Monitoring Branh Ata Tuli, Environmental Sientit Environmental Monitoring Branh Brue Johnon, Reearh Sientit III Environmental Monitoring Branh Original igned by Original igned by Original igned by DATE: SUBJECT: FUMIGANT TRANSPORT MODELING USING HYDRUS: 4. DEVELOPMENT AND TESTING OF MODIFICATIONS TO ENHANCE FUMIGANT FIELD SIMULATIONS ABSTRACT Several modifiation to the HYDRUS1D and HYDRUS2/3D model were propoed by Department of Petiide Regulation (DPR ) Air and Ground Water Group to enhane imulation of fumigant vadoe zone tranport. The modifiation were implemented by the model primary author, Dr. Jirka Šimůnek, and inluded variou hange to input/output data and file format, temperature dependene of the tagnant urfae boundary layer, ability to imulate tarp removal mid-imulation, ability to imulate inorporated appliation mid-imulation, and implementation of dual volatilization boundary ondition at the oil urfae. The peifi modifiation and DPR ubequent teting of their omputational integrity are doumented in thi report. In ummary, while a few programming error were initially found and repaired, the teting reult reported herein for the final modifiation verion indiate the modified ode work a expeted and ontain no known error. The very mall deviation between the unmodified and modified model verion oberved in ome ae were attributable to numerial error a i ommon with finite element model I Street P.O. Box 4015 Saramento, California A Department of the California Environmental Protetion Ageny

2 Page 2 I. INTRODUCTION DPR ha been evaluating the ue of HYDRUS1D and HYDRUS2/3D model (Šimůnek et al., 2006; Šimůnek et al. 2009) for imulating pot-appliation fumigant volatilization from oil. Previou DPR report have invetigated potential error in imulated volatilization ariing from ue of inaurate pedotranfer funtion to etimate oil hydrauli parameter (Spurlok, 2008), evaluated HYDRUS1D and HYDRUS2/3D numerial algorithm for both the ga phae diffuion/orption proe within oil and firt-order ma tranfer urfae volatilization proe at the oil urfae (Spurlok, 2009), and onduted enitivity analyi of model output to fumigant phyial-hemial propertie (Spurlok, 2010). The HYDRUS model have been widely ued for imulating a variety of vadoe zone tranport problem (< However, there are unique apet to imulating pot-appliation fumigant volatilization a ompared to other type of tranport problem. For example, in California many fumigant/appliation method ombination require ue of a plati film over the oil ( tarp ) for a peified period after appliation. In the HYDRUS model, a tarp i imulated uing a tagnant boundary layer at the oil urfae. The thikne of the boundary layer i hoen to provide a ma tranfer reitane at the oil urfae equivalent to that of tarp (Spurlok, 2010). However, tarp permeabilitie to fumigant are often highly temperature dependent (Paperniek, 2006), in part ontributing to diurnal inreae and dereae in fumigant flux. The urrent verion of HYDRUS1D and HYDRUS2/3D do not have the apability to imulate thi temperature dependene. Thi limit their ability to aurately imulate fumigant diurnal flux dynami. To addre thi and other limitation, DPR ontrated with the primary HYDRUS developer, Dr. Jirka Šimůnek, to implement everal modifiation to the urrent HYDRUS model, thereby improving their ability to imulate fumigant volatilization from oil. Thee inluded: 1. Modifiation: Simulation of temperature-dependent variable boundary layer thikne. The temperature dependene i deribed uing an Arrheniu-type relationhip imilar to other HYDRUS temperature-dependent variable. Purpoe: To allow imulation of temperature dependent tarp permeability. Program: HYDRUS1-D and HYDRUS2/3D 2. Modifiation: Automatially reate text output file of nodal total, diolved, olid, and ga phae onentration; and water ontent and temperature. Purpoe: To allow more onvenient invere parameter etimation uing 3rd party oftware uh a PEST (< PEST i a flexible nonlinear parameter etimation program, and alo ha the ability to allow Monte Carlo imulation. Program: HYDRUS1-D and HYDRUS2/3D.

3 Page 3 3. Modifiation: Speifiation of Total (diolved plu orbed plu ga-phae) initial nodal onentration a oppoed to only diolved onentration a in urrent HYDRUS program. Purpoe: Provide a muh more onvenient method of peifying initial ondition. Program: HYDRUS2/3D. 4. Modifiation: Inlude the ability to model mid-imulation inorporated petiide appliation. Thi might inlude, for intane, oil inorporation of an herbiide (0 7.5 m) or broadat injetion of a fumigant (depth m). Purpoe: Thi apability i needed by DPR ground water group for ertain modeling enario. Program: HYDRUS1-D and HYDRUS2/3D. 5. Modifiation: Inlude the Moldrup Water Linear Redution Model (WLR) a an option for deribing the effet of ga-phae tortuoity on diffuion. Purpoe: Thi modifiation provide the more reent WLR model a an alternative to the onventional Millington-Quirk tortuoity model. The WLR model ha been reported to provide better predition than many other model (Werner et al., 2004). Program: HYDRUS2/3D. 6. Modifiation: Inlude the ability to model mid-imulation pot-appliation tarp-utting (removal). Purpoe: Thi modifiation provide additional apability to imulate flux under atual ue pratie. Program: HYDRUS1-D and HYDRUS2/3D. 7. Modifiation: provide the ability to imulate two different volatilization boundary ondition at the oil urfae (e.g. tarped and untarped). Purpoe: Thi modifiation will allow imulation of tarped bed fumigant appliation where only a portion of the field i tarped. Program: HYDRUS2/3D. Additional modifiation may be implemented in the future. The purpoe of thi report i doument the omputational teting of the modifiation lited above. II. OVERVIEW The modifiation to the HYDRUS1D and HYDRUS2/3D model were teted in two phae. The objetive of Phae 1 teting wa to verify that when the modified model were run without any of the new feature, they gave the ame reult a the exiting unmodified model. Deviation between the unmodified and modified model in thoe enario would indiate that inadvertent error were introdued during modifiation of the program ode. The mot urrent unmodified model verion ued in Phae 1 teting were HYDRUS1D ver and HYDRUS2/3D ver (Standard 2D verion). Phae 2 model teting wa onduted to evaluate the atual modifiation to the program ode. A variety of approahe were ued in Phae 2 depending on the partiular modifiation. Thee are explained below under Phae 2 teting.

4 Page 4 Note that in the following diuion, lower ae t indiate unit of time, while upper ae T indiate unit of temperature. III. PHASE 1 TESTS A. HYDRUS1D Two of the HYDRUS author, Dr. Jirka Šimůnek and Rien van Genuhten, preented a HYDRUS oure to DPR in Saramento in June In that oure they provided everal example HYDRUS1D fumigant modeling projet to demontrate model feature. Thee projet were fumig1, fumig1a, fumig2, fumig3, fumig4, and fumig4a. The projet erved a the bai of Phae 1 teting here to evaluate the omputational integrity of the modified HYDRUS1D relative to the unmodified model. The projet are available for download from the HYDRUS web ite at < and are deribed in detail in < Eah projet i baed on a fumigant broadat appliation enario with the fumigant initially evenly ditributed between the m depth. The imulation time wa 21 day in all ae. Other feature of the fumig1 fumig4 enario are given in Table 1. Table 1. Charateriti of HYDRUS1D projet ued in Phae 1 teting imulation enario harateriti init. on. peified a aqueou on (M L wat ) y n y y y y init. on. peified a total on (M L oil ) n y n n n n heat tranport and temperature dependene of n n n n y y Henry law and degradation oeffiient preene of tarp n n y n n y pot-appliation water appliation n n n y n n Variable ompared: The variable that were ompared were the 21d (end-of-imulation) nodal water ontent, temperature and fumigant aqueou onentration; 0 21 d flux time erie, and 21d umulative flux. fung1 fumg1a fumig2 fumig3 fumig4 fumig4a

5 Page 5 Output file ued: BALANCE.OUT umulative flux and ma balane data NOD_INF.out nodal water ontent, nodal fumigant water onentration olute1.out flux time erie Conluion: No direpanie between the unmodified and modified model output were evident. For example, projet fumig1a, fumig3, and fumig4a inlude all of the harateriti in Table 1, and end of imulation nodal oil-water ontent, oil temperature, fumigant liquid phae onentration and umulative flux were idential for the modified and unmodified model verion. The fumigant flux time erie were alo idential (e.g. Figure 1). Figure 1. HYDRUS1D projet fumig4a flux time erie for modified and unmodified verion of HYDRUS1D Variable unmodified model * t modified model * t2 flux (M/ L^2 t) time (d) B. HYDRUS2/3D Projet ued in teting: The Phae 1 modeling enario ued for HYDRUS2/3D wa a uburfae line oure tarped fumigant appliation baed on HYDRUS tutorial 3.05 (< Water, olute and heat tranport were imulated, and temperature dependene of the ga phae diffuion oeffiient, Henry law ontant and 1t order degradation oeffiient were alo

6 Page 6 onidered. A pule of fumigant wa applied with water for 0.2 day from a 20 m deep, 1 m radiu dripper to the 100 m deep x 75 m wide modeling domain. The upper urfae of the tranport domain wa ubjet to a 500 m boundary layer to imulate the preene of a tarp and the duration of the imulation wa 7 d. Variable ompared: 7d (end-of-imulation) nodal water ontent, temperature and aqueou fumigant onentration; and 7d umulative fumigant flux. Output file ued: on1.txt, temp.txt, th.txt exported text file of nodal aqueou fumigant onentration, temperature and water ontent, repetively olute1.out fumigant flux time erie, umulative flux Conluion: Program output ompared well. Simulated fumigant flux from the two program wa nearly idential (Figure 2). Perent differene in nodal onentration, temperature and water ontent were alulated a: un mod ified output mod ified output [1] perent differene = x 100 un mod ified output Aro all node in the tranport domain, perent differene in aqueou fumigant onentration, temperature, and water ontent were in the range of 0.32% to % (Table 2). The mall differene in end of imulation nodal water ontent, temperature and fumigant aqueou phae onentration were attributable to mall differene in numerial error between the two program. The umulative flux of the modified model wa 0.33% greater than the unmodified model, while end of imulation relative fumigant ma balane error were 0.44%and 0.70% for the unmodified and modified imulation, repetively. No ubtantial differene between modified and unmodified model verion were evident.

7 Page 7 Figure 2. HYDRUS2/3D phae 1 omparion of modified and unmodified model Variable unmodified model modified model flux (M/(L t)) time Table 2. End-of-imulation perent differene (Eq. 1) in nodal water ontent, temperature and fumigant aqueou onentration between modified and unmodified HYDRUS2/3D model (N= 1079 node). IV. PHASE 2 TESTS A. HYDRUS1D Nodal variable minimum median maximum water ontent -1.2E E-04 0 temperature -6.8E E-04 onentration.2e-01.1e e New output file NOD_INF_C.out A uburfae line oure tarped fumigant appliation imilar to that ued in Phae 1 teting wa run uing both the modified and unmodified program. Heat tranport and temperature dependene were not imulated in thi example o a to implify ga phae onentration alulation. End of imulation nodal onentration in NOD_INF_C.out were ompared to alulation baed on end of imulation nodal liquid onentration in the unmodified HYDRUS1-D output file NOD_INF.out. Calulation formulae are given in appendix 1. The output were nearly idential, indiating the NOD_INF_C.out i alulating nodal onentration orretly; the perent differene for eah nodal onentration wa in the range of % to 0.044% (Table 3).

8 Page 8 Table 3. End-of-imulation perent differene (Eq. 1) between imulated and hand-alulated nodal onentration for Phae 2 teting of new output file, NOD_INF_C.out (N=1079 node). Variable minimum median maximum liquid onentration -4.3E E E-02 olid onentration -4.1E E E-02 ga onentration -4.2E E E-02 ma in liquid phae -5.2E E E-02 ma in olid phae -4.4E E E-02 ma in ga phae.7e E E-02 total ma -4.5E E E Temperature dependene of the tagnant urfae boundary layer In the HYDRUS program, the flux J (M L -2 t -1 ) at any given time i alulated a: Dg [2] J = C g d( T ) where D g i the ga phae diffuion oeffiient (L 2 t -1 ) and d(t) i a funtion giving the temperature dependent boundary layer thikne (L). Eq. [2] aume that the onentration ditant from the oil urfae (i.e. at the top of the boundary layer) i zero. The funtion d(t) i given by: Ea 1 1 [3] d( T ) = dref exp[ ( )] R Tref T where d ref i the boundary layer thikne at the referene temperature T ref = K, E a i the ativation energy (joule mol -1 ), R i the ga ontant (= joule mol -1 ) and T i the temperature (K). Finally, when the HYDRUS ine wave oil urfae temperature model i ued, the temperature T at any time t i given by: 2π t 7π [4] T( t ) = T0 + A in( ) p 12 where T 0 i the mean oil urfae temperature (degree entigrade), p i the period (typially =1 day) and A i the amplitude of the ine wave in degree. The performane of the temperature dependent boundary layer option wa evaluated by imulating volatilization from a oil olumn at an initial uniform fumigant onentration, and invoking the ine wave temperature model at the oil urfae. Eq. 2-4 were ued in onjuntion with the HYDRUS1D predited ga phae onentration at the oil urfae (C g, eq. 2) to alulate flux at peifi time tep. The alulated fluxe agreed well with the HYDRUS imulated fluxe (Fig. 3). Although mall, perent differene between modeled and hand

9 Page 9 alulated reult are not hown. The modeled reult are an average baed on two value due to the Crank-Niholon numeri olution heme (J. Šimůnek, peronal ommuniation). Thu, at leat a portion of any deviation between modeled and hand alulated reult are due to averaging. Figure 3. Tet of temperature dependent boundary layer option. Calulated v. imulated flux for HYDRUS 1-D. Diurnal variation in flux due to boundary layer temperature dependene Variable modeled alulated flux (M/L^2 t) time Mid-imulation tarp removal at peified time The tarp removal option wa teted uing the fumig4a projet by diretly omparing end of imulation nodal water ontent, temperature and aqueou fumigant onentration, and umulative flux time erie obtained from the unmodified program and the modified program. For the modified program, tarp removal wa peified at 7d. The total imulation time wa 21d. For the unmodified program (no tarp removal option), a 7d tarped appliation wa firt imulated. End of imulation nodal water ontent, temperature and fumigant onentration were then ued a initial ondition for a eond 14d untarped imulation. The umulative flux time erie were nearly idential (Figure 4), with perent differene in total 21d umulative fluxe of 0.7%. End of imulation nodal water ontent, temperature and aqueou phae fumigant onentration of the two model verion ompared favorably (Table 4).

10 Page 10 Figure 4. Cumulative flux time erie for modified and unmodified HYDRUS1D imulation of projet fumig4a with tarp utting imulated at day 7. Cumulative flux (M L^-2) unmodified HYDRUS1D - Seond portion imulation without tarp. unmodified HYDRUS1D - End of firt imulation ued a Firt portion imulation with tarp initial ondition for eond imulation Variable modified * time unmodified * time2 modified HYDRUS1D w/ tarp utting at day Time (d) Table 4. End-of-imulation perent differene (Eq. 1) in nodal water ontent, temperature and fumigant aqueou onentration for Phae 2 teting of tarp-utting option uing projet fumig4a (N= 150 node). Nodal variable minimum median maximum water ontent temperature 0 5.0E E-01 onentration -6.1E E E Mid-imulation appliation at a peified time and loation in profile The mid-imulation appliation option wa teted uing the fumig1a projet (Table 1) a a bai for further modifiation. A imilar teting proedure to the mid-imulation tarp removal wa employed: three eparate projet were reated, a 7d, 14d, and 21d imulation. The unmodified 7d imulation final nodal water ontent were ued a initial ondition for the unmodified 14d projet. The modified 21d imulation wa onduted with a mid-imulation appliation peified at 7 day, equal to the ma applied at the tart of the 14d imulation. The final nodal olute onentration of the 14d imulation (unmodified) and 21d imulation (modified) were ompared. The reulting final nodal total onentration were eentially idential (Figure 5), with perent differene around for all onentration (Table 5).

11 Page 11 Figure 5. Final total onentration for modified and unmodified HYDRUS1D imulation of projet fumig1a with a mid-imulation appliation. 6.00E-04 Ma (M/L^3) 5.00E E E E-04 Modified 21d Unmodified 14d 1.00E E Depth (m) Table 5. End-of-imulation perent differene (Eq. 1) in nodal onentration utilizing the mid-imulation appliation modifiation in HYDRUS1D (N = 150 node). B. HYDRUS2\3D Variable minimum median maximum liquid onentration -2.6E E E-01 olid onentration -2.6E E E-01 ga onentration -2.6E E E-01 ma in liquid phae.0e e e-01 ma in olid phae -2.6E E E-01 ma in ga phae -2.5E E E-02 total ma -2.7E E E New output file NOD_INF_C.out The proedure for omparing the new nodal onentration in the modified HYDRUS2/3D program to the unmodified program wa the ame a in the HYDRUS1D teting of NOD_INF_C.out. The modeling enario wa the uburfae line oure tarped fumigant appliation ued for the HYDRUS2/3D Phae 1 teting. Final nodal onentration from the modified program NOD_INF_C.out file were ompared to final nodal onentration, hand

12 Page 12 alulated from liquid onentration, in the unmodified HYDRUS2/3D output. The two et of reult were imilar, with differene at a fration of a perent (Table 6). Table 6. End-of-imulation perent differene (Eq. 1) in nodal onentration for Phae 2 teting of new output file, NOD_INF_C.out, in HYDRUS2D/3D (N=1079 node). Variable minimum median maximum liquid onentration -4.9E E E-03 olid onentration -4.7E E E-03 ga onentration -4.9E E E-03 ma in liquid phae.3e E E-02 ma in olid phae -4.5E E E-03 ma in ga phae -2.3E E E-02 total ma -1.5E E E Speifiation of initial nodal onentration on total onentration bai The ame uburfae line oure modeling enario wa ued to ompare peifiation of initial onentration in term of liquid onentration to total onentration, where total onentration = liquid phae + olid phae + ga phae olute, expreed a ma olute/volume bulk oil. The two initial ondition peifiation method yielded idential total- and phae peifi olute onentration. 3. Temperature dependene of the tagnant urfae boundary layer The teting method for the HYDRUS2/3D temperature dependent boundary layer option wa idential to that ued for HYDRUS1-D (etion IV.A.2., above). In hort, flux from a retangular tranport domain with ontant initial uniform fumigant oil onentration wa alulated at different time from imulated oil urfae nodal onentration from HYDRUS2/3D, the oil urfae temperature a a (ine) funtion of time, alulated boundary layer thikne a a funtion of time and the peified diffuion oeffiient (Eq. 2 4). Similar to reult for the temperature dependent boundary ondition tet in HYDRUS1-D, it evident that flux baed on modeled and hand alulated boundary layer thiknee are eentially idential (Figure 6).

13 Page 13 Figure 6. Tet of temperature dependent boundary layer option. Calulated v. imulated flux for HYDRUS2/3D. Diurnal variation in flux due to boundary layer temperature dependene. 50 Variable modeled alulated 40 flux [M/( L^2 t)] time Mid-imulation tarp removal at peified time The Phae 2 tet of the HYDRUS2/3D tarp utting option followed the ame proedure a in the HYDRUS1D tet of that ame option: The unmodified program wa run for even day with a tarp, and the reultant nodal water ontent, temperature and fumigant onentration were ued a initial ondition for a eond 14d imulation without tarping. The modeling enario onited of a retangular tranport domain with a ontant initial fumigant onentration in oil at the m depth. The preene of a tarp wa imulated uing a tagnant urfae boundary layer d = 500 m. At the time of tarp removal, the modified HYDRUS2/3D program hange d bak to a value appropriate for a bare oil urfae (i.e. d = 0.5 m). The umulative flux time erie were nearly idential (Figure 7), with perent differene in total 21d umulative fluxe of 0.7%. End of imulation nodal water ontent, temperature and aqueou phae fumigant onentration of the two model verion ompared favorably (Table 7).

14 Page 14 Figure 7. Cumulative flux time erie for modified and unmodified HYDRUS2/3D imulation of projet fumig4a with tarp utting imulated at day unmodified HYDRUS2/3D - Firt portion imulation with tarp unmodified HYDRUS2/3D - Seond imulation without tarp. End of firt imulation ued a initial ondition for eond. umulative flux (M L^-1) modified HYDRUS2/3D w/ tarp utting at day 7 Variable unmodified mod_um_flux model modified model um_flux Time (d) Table 7. End-of-imulation perent differene (Eq. 1) in nodal water ontent, temperature and fumigant aqueou onentration for Phae 1 teting uing projet fumig3a (N= 1079 node). Nodal variable minimum median maximum water ontent -8.5E E-06 temperature -1.0E E-06 onentration -9.3E E Alternative formulation of ga phae tortuoity Diffuive tranport of a ga in oil depend on the volume fration of air-filled pore, the geometry of thoe pore and their interonnetedne. The latter two harateriti are deribed in vadoe tranport model by the ga phae tortuoity τ g (0 < τ g < 1). The net effet of τ g in model uh a HYDRUS i to diretly ale (redue) the effetive ga phae diffuion oeffiient by a fator of τ g. Conequently, the effetive diffuion oeffiient D eff (=τ g * D g ) i atually ued in internal model alulation when tortuoity i onidered. While mot model ue a Millington Quirk (1961) type model to alulate τ g from air-filled poroity a v and aturated

15 Page 15 water ontent θ (e.g. Šimůnek, 2006), Moldrup and o-worker introdued a Water Linear Redution Model (WLR) a an alternative (Moldrup et al., 2006) av [5] τ g = θ Implementation of the WLR model wa teted in HYDRUS2/3D uing two imulation of diffuive tranport only for an initial plug of olute in the enter of a long horizontal olumn (Figure 8). The WLR model wa ued in the firt imulation with θ = 0.400, a v = and D g = 300. Thi yielded a WLR tortuoity fator of and D eff = The eond imulation did not inlude either tortuoity model, and that imulation ued a aled ga phae diffuion oeffiient D g = D eff, 1t imulation = The reult were eentially idential (Figure 9), demontrating orret implementation of the WLR tortuoity model. Figure 8. Diffuion inide an infinite olumn with initial olute ditribution: on = C 0, w < x < w; = 0 otherwie. Boundary ondition for all boundarie: water zero flux, olute zero flux. x -w w 0 Figure 9. End-of-imulation liquid olute ditribution for the Moldrup WLR tortuoity model and a imulation without tortuoity but idential D eff a the firt ae Variable No_Tortuoity Moldrup Conentration x (m)

16 Page Mid-imulation appliation at a peified time and loation in profile A imilar proedure to the HYDRUS1D teting of mid-imulation appliation wa ued in teting the HYDRUS2D/3D verion of the ame option. The end of imulation nodal water ontent of an unmodified 7day run were ued a the initial ondition of an unmodified 14d run. The output of a modified 21d imulation, with a mid-imulation appliation at 7 day equal to the ma applied at the tart of the 14d imulation, wa ompared to the output of an unmodified 14d imulation (Figure 10). Nodal onentration of both imulation were analogou to one another, with perent differene everal order of magnitude below one (Table 8). Figure 10. Final total onentration for modified and unmodified HYDRUS2D/3D imulation with a mid-imulation appliation. Note that node number in HYDRUS2/3D are aigned during the meh generation tep and do not neearily diplay any obviou geometri onfiguration, leading to unuual ditribution of onentration a a funtion of node number. One hundred fifty of 232 total node hown above for larity. Table 8. End-of-imulation perent differene (Eq. 1) in nodal onentration utilizing the midimulation appliation modifiation in HYDRUS2D/3D (N=232 node). Variable minimum median maximum ConL -8.8E E E+00 ConS -6.1E E-03.2E-03 ConG -6.1E E-03.2E-03 MaL -9.5E E E+00 MaS -1.0E E E+00 MaG -6.3E E E+00 TotalMa -1.0E E E+00

17 Page Implementation of two different volatilization boundary ondition at oil urfae In HYDRUS2/3D, the volatile olute boundary ondition (BC) imulate volatilization a a firt-order ma tranfer proe through a tagnant boundary layer at the oil urfae. The rate of diffuion i proportional to the onentration differene between the top and bottom of the boundary layer, and inverely proportional to the depth of a tagnant boundary layer d. The boundary layer depth i adjutable and provide ma tranfer reitane at the urfae. To imulate the preene of a tarp, an equivalent d i hoen to repreent the ma tranfer reitane of the tarp (Spurlok, 2010). To imulate volatilization from a bare oil urfae, d = 0.5 m i typially aumed (Jury et al. 1983, Simunek et al., 2006). The unmodified HYDRUS2/3D verion only allow peifiation of a ingle volatilization boundary ondition, i.e. for all node where volatilization i imulated, a ingle ma tranfer reitane mut be ued. Thi hortoming prevent realiti imulation of ertain enario uh a tarped bed appliation (Figure 11). Figure 11. Example of bedded tarp fumigant appliation where hallow fumigant hank appliation are immediately followed by the bed haping/tarping proe. hank appliation tarped bed, d=600 untarped furrow, d=0.5 m HYDRUS2/3D wa modified to remedy thi hortoming. The modified verion now allow two different volatile olute BC to be peified at the oil urfae. The firt volatilization ondition i a before, where a tagnant boundary layer of uer-defined depth i peified. Thi volatilization BC i peified for node where the water flow BC i Atmopheri. The eond volatilization BC i a bare-oil volatilization BC where the tagnant boundary layer thikne i ontant = 0.5m. The eond BC may be peified only for node in whih the water flow BC i variable flux 1.

18 Page 18 The performane of thi BC wa invetigated uing a modeling enario oniting of a retangular tranport domain with a ontant initial fumigant onentration at the 20-40m depth. There were 19 node aro the upper boundary. Unlike the previou modeling omparion, it wa not poible to devie a imulation with the unmodified verion of Hydru2/3D whih would mimi the omputation of the modified Hydru2/3D for the implementation of two different volatilization boundary ondition at oil urfae. Therefore, intead of a modified to unmodified omparion, a erie of imulation wa onduted to hek for the oniteny of ditributed veru lumped untarped area veru tarped urfae fration. Thirteen imulation were performed uing different nodal ombination of the two volatilization BC (Figure 12). Simulation 1 and 8 (Figure 12) both imulated bare ground emiion uing d = 0.5 m at all node. In 1, the water flow boundary ondition wa atmopheri, o thi imulation orreponded to the volatilization BC a it ha previouly been implemented. In imulation 8, the water flow boundary ondition wa variable flux 1, o that imulation utilized only the modifiation. The total flux in the two ae were eentially equal (Figure 12), demontrating the equivalene of the bare ground volatilization BC for the two ae. Figure 12. Invetigation of modified HYDRUS2/3D volatilization boundary ondition. For untarped node, boundary layer depth = 0.5 m; for tarped node, boundary layer depth d = 600 m. Flux ratio = (ma fumigant volatilized at end of imulation/total initial appliation). In the remaining imulation, the effet on flux of number of untarped node, and onfiguration of thoe node were invetigated. The onfiguration entered refer to imulation 3 and 8 13, where the untarped node are adjaent and entered on the urfae. The onfiguration ditributed refer to imulation 3 8 where the untarped node are evenly paed aro the urfae. It apparent that even when a mall fration of the urfae i untarped, large inreae in flux relative to the tarped ae may be oberved (f. imulation 2 4). imulation# 1 nodal volatility boundary ondition at top of tranport domain no. untarped node 19 fration urfae untarped tarped area flux --- untarped area flux 2795 total flux ratio untarped atmopheri BC tarped atmopheri BC untarped variable flux BC

19 Page 19 In addition, the ditribution, a well a amount, of untarped area influene flux ratio (Figure 13). The higher fluxe oberved for the ditributed onfiguration are attributable to horter mean diffuion pathway for fumigant moleule at the urfae. Figure 14 how how the modified boundary ondition affet fumigant oil onentration aro the urfae uing imulation 4. Finally, Figure 15 i an illutrative example of the dual volatilization boundary ondition for a bedded tarp appliation, where the bed portion of the field i overed by a tarp and the furrow are untarped. The diurnal flutuation in umulative flux reult from temperature dependene of D g, Henry ontant and tarp permeability. Figure 13. Flux ratio v fration urfae area untarped for ditributed and entered untarped nodal onfiguration (Figure 12) flux ratio Variable entered onfiguration * C1 ditributed onfiguration * C fration urfae area untarped Figure 14. End of imulation fumigant ditribution for 3 ditributed untarped node (ae 4, Figure 12).

20 Page 20 Figure 15. Illutrative example of dual volatilization boundary ondition imulation for bedded tarp appliation. Immediately after fumigant injetion, bed i haped and tarped. In umulative flux plot, the atmopheri olute flux i the umulative flux through the tarped region (delineated by the white line), while the variable boundary flux 1 i the umulative flux through the (untarped) furrow. Note olor onentration ale i different for eah piture. t = 0 day t = 2 day t = 5 day t = 8 day Cumulative Atmopheri Solute Flux t = 21 day Cumulative Variable Boundary Flux Time [day] Time [day] V. CONCLUSION Baed on the teting onduted, the modified HYDRUS1-D and HYDRUS2/3D program perform a expeted. No error were evident in the modified program.

21 Page 21 VI. REFERENCES Jury, W. A., W. F. Spener, and W. J. Farmer, Behavior aement model for trae organi in oil, I. Model deription, J. Environ. Qual., 12, , Millington, R.J. and J.P. Quirk Tranport in porou media. p In F.A. Van Beren et. Al (ed). Tran. 7th International Congre of Soil Siene, Vol. 1, Madion, WI, Aug Amterdam, The Netherland. Millington, R.J. and J.P. Quirk Permeability of porou olid. Trana. Faraday So. 57: Moldrup, P., T. Oleen, J. Gamt, P. Shjonning, T. Yamaguhi, and D.E. Rolton Prediiting the ga diffuion oeffiient in repaked oil: Water-indued linear redution model. Soil Si. So. Am. J. 64: Papiernik, S. and S.R. Yate Effet of Environmental Condition on the Permeability of High Denity Polyethylene Film To Fumigant Vapor. Environ. Si. Tehnol. 36: Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuhten The HYDRUS-1D Software Pakage for Simulating the One-Dimenional Movement of Water, Heat, and Multiple Solute in Variably-Saturated Media. Uer Manual verion Available at: < Šimůnek, J., M. Th. van Genuhten and M. Šejna The HYDRUS Software Pakage for Simulating the Two- and Three-Dimenional Movement of Water, Heat, and Multiple Solute in Variably-Saturated Media. Tehnial Manual. verion 1. Available at: < Spurlok, F Fumigant Tranport Modeling Uing HYDRUS: Etimation of Soil Hydrauli Parameter Uing Pedotranfer Funtion. Augut 14, 2008 memorandum to: R. Segawa. Available at: < Spurlok, F Fumigant Tranport Modeling Uing Hydru: 2. Comparion of Model Simulation to Analytial Solution of Fik Seond Law of Diffuion. Available at: < Spurlok, F Fumigant Tranport Modeling Uing Hydru: 3. Fumigant Tranport Modeling Uing Hydru: 3. Seletion, Temperature Dependene and Senitivity Analyi of Fumigant Phyiohemial Propertie. Available at: < Werner, D., P. Grathwohl, and P. Höhener, Review of field method for the determination of the tortuoity and effetive ga-phae diffuivity in the vadoe zone, Vadoe Zone J., 3, , 2004.

22 APPENDIX 1 DOCUMENTATION FOR MODIFIED FEATURES

23 Appendix 1 page 2of 17 HYDRUS-1D and HYDRUS (2D/3D) Modifiation to Simulate and Analyze the Tranport of Fumigant Jiří Šimůnek Department of Environmental Siene Univerity of California Riveride Riveride, CA Agreement No 09-C0078 Department of Petiide Regulation Environmental Monitoring Brah 1001 I Street 4th Floor Saramento, CA 95814

24 Appendix 1 page 3of 17 Appendix Content: 1. New Output File Nod_inf_.out 2. Total Initial Nodal Conentration 3. Temperature Dependene of the Stagnant Surfae Boundary Layer 4. Tarp Removal at a Speified Time 5. Alternative Formulation for the Ga Phae Tortuoity 6. Appliation of a Fumigant at a Speified Time and Loation 7. Two Different Volatilization Boundary Condition at the Soil Surfae 8. Referene 9. HYDRUS-1D and HYDRUS (2D/3D) Tet Example 10. The Fumigant.in Input File

25 Appendix 1 page 4of New Output File Nod_inf_.out A new output file (Nod_inf_.out) i reated by both HYDRUS-1D and HYDRUS (2D/3D), whih ontain nodal oordinate, water ontent, temperature, and variou form of onentration (i.e., liquid, olid, gaeou, and total). Below i an example of one time-level from thi file. The file ontain the following variable: Node x,z Wat ConL ConS ConG Node Number x- and z-oordinate 3 Water Content [L L ] Liquid phae onentration [M L ] -1 Solid phae onentration [M M ] Ga phae onentration [M L ] MaL Ma in the liquid phae, S l [M L ] MaS MaG Ma in the olid phae, S [M L ] Ma in the ga phae, S g [M L ] TotalMa Total Ma, S=S l +S +S g [ML ] Temper Temperature [ o C] Subript w,, a, and refer to water, ontaminant, air, and oil. w a w Time: Node z Wat ConL ConS ConG MaL MaS MaG TotalMa Temper [L] [M_/L_w^3] [M_/M_] [M_/L_a^3] [M_/L_^3] [M_/L_^3] [M_/L_^3] [M_/L_^3] [C] E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E end

26 Appendix 1 page 5of 17 The table below deribe how variou variable are alulated. Liquid phae onentration [M L ] Solute ma in the liquid phae, [M L ] S l Ga phae onentration [M L ] a w Solute ma in the ga phae, S g [ML ] Solid phae onentration -1 [M M ] Solute ma in the olid phae, S [M L ] Total olute ma, S=S l +S +S g [M L ] Equilibrium model Mobile-immobile model θ + θ θ + θ m m im im m im θ mθ m imθ im K H K Ha K H K Ha K D K D [ fm + (1 f ) im ] ρ KD K [ f (1 f ) ] Two-ite orption model + θ θ K H K Ha f K k ρ D m + im ( fekd ) e D Two-kineti ite model na na k k k ρ + ( k k ρ ) a m im θ θ m θ im K D 3 air ontent [L L ] a liquid phae onentration [M L ] liquid phae onentration in the mobile phae[m L ] liquid phae onentration in the immobile phae[m L ] 3 water ontent [L L ] w 3 water ontent in the mobile phae [L L ] 3 water ontent in the immobile phae [L L ] 3-1 ditribution (orption) oeffiient [LwM ] K H Henry' law ontant [-] S l olute ma in the liquid phae [M L ] S S g S k 1 k olute ma in the olid phae [M L ] ma in the ga phae [M L ] total olute ma, S=S l +S +S g [M L ] -1 olid phae onentration [M M ] -1 olid phae onentration on kineti orption ite [M M ] -1 olid phae onentration on firt kineti orption ite [M M ] w w w w w

27 Appendix 1 page 6of 17 2 k -1 olid phae onentration on eond kineti orption ite [MM ] f fration of orption ite in ontat with mobile water [-] f e fration of orption ite with equilibrium orption [-] ρ bulk denity [M L ]

28 Appendix 1 page 7of Total Initial Nodal Conentration Solute tranport initial ondition an be peified either in term of the liquid onentration [ML ; ma of olute/volume of water] or in term of the total onentration S [ML ; ma of olute/volume of oil]. The liquid phae onentration i in the latter ae alulated for linear orption a follow: S = θ + ρ + a g = θ + ρk + a K = ( θ + ρk + a K ) v D v H D v H S (1) = θ + ρk + a K D v H and for nonlinear orption by finding a root of the following nonlinear equation: β ρkd S = θ + ρ + a v g = θ + + avk H β 1+ η For the two kineti orption ite model (only a linear ae i implemented, i.e., without bloking) the ditribution oeffiient k for i aumed to be defined a: K θk (2) a D = (3) ρkd Rather than peifying diretly onentration in the nonequilibrium phae, the nonequilibrium phae onentration an be peified to be initially at equilibrium with equilibrium phae onentration. In uh ae, the immobile water ontent onentration will be et equal to the mobile water ontent onentration for the dual poroity model. The orbed onentration at the kineti orption ite will be et equal to: for the linear orption and: = (1 f ) K D (4) ρkd = (1 f ) 1 + η for the nonlinear orption. For the two kineti orption ite model, the orbed onentration are et equal to: θk ρk β β (5) a = (6) where k a and k d are the attahment and detahment oeffiient, repetively. Thee option an be eleted from the new etion (Initial Condition) of the Solute Tranport - General Information dialog window (ee below). d

29 Appendix 1 page 8of 17

30 Appendix 1 page 9of Temperature Dependene of the Stagnant Surfae Boundary Layer Temperature dependene of the thikne of the tagnant urfae boundary layer (i.e., a urfae boundary layer through whih volatile olute diolve to the atmophere) wa implemented in a imilar way a for all other tranport and reation parameter uing the Arrheniu equation [Stumm and Morgan, 1981]. After ome modifiation, thi equation an be expreed in the general A A Ea( T - Tr ) a T = a r exp A A RuT T r (7) where a r and a T are the value of the oeffiient (the thikne of the tagnant urfae boundary layer) being onidered at a referene abolute temperature T r A and abolute temperature T A, repetively; R u i the univeral ga ontant, and E a [ML 2 T -2 M -1 ] i the ativation energy of the partiular reation or proe being modeled. In both HYDRUS-1D and HYDRUS (2D/3D), the ativation energy of thi fator i entered at the following loation in the Temperature Dependent Solute Tranport and Reation parameter dialog window (ee below).

31 Appendix 1 page 10of Tarp Removal at a Speified Time In the modified omputational module imulating tranport of fumigant, the Pule Duration variable i ued intead to repreent the "Time of Tarp Removal". The variable i peified in the "Solute Tranport - General Information" dialog window at the following loation in the HYDRUS-1D (left figure below) and HYDRUS (2D/3D) (right figure below) HYDRUS-1D HYDRUS (2D/3D) After the tarp i removed, the tagnant boundary layer i aumed to have a ontant thikne of d = 0.5 m. The Fumigant.in input file need to be in the projet folder and the lfumig variable ha to be et to.true. for thi option to be ative.

32 Appendix 1 page 11of Alternative Formulation for the Ga Phae Tortuoity Alternative relationhip are available in verion 4.05 of HYDRUS-1D and higher to deribe tortuoity oeffiient in both phae. Moldrup et al. [2000] uggeted the following formulation for alulating the tortuoity fator in the gaeou phae for ieved and repaked oil: a τ g = θ Thi formulation wa found to provide uperior predition of everal poroity-baed relationhip by Werner et al. [2004]. Similarly, Moldrup et al. [1997] uggeted an alternative relationhip for alulating the tortuoity oeffiient in the liquid phae: θ τ w = 0.66 θ The Millington-Quirk [1961] tortuoity model are expeted to perform well for and (ine they were derived auming randomly ditributed partile of equal ize) while Modrup tortuoity model are expeted to perform better aro oil type. 1.5 v 8 / 3

33 Appendix 1 page 12of Appliation of a Fumigant at a Speified Time and Loation Fumigant an be applied during the imulation at a eleted time uing the Fumigant.in input file (ee Appendix B at the end of thi report), whih need to be plaed in the projet folder. For thi option to beome ative, both lfumig (ativate the tranport of fumigant) and laddf (appliation of fumigant during the imulation) variable have to be et to.true.. One need to additionally peify the time when a fumigant i applied (taddf [T]), the ma of the applied fumigant (FumMa, in [M L -2 ] or [M L -1 ] in HYDRUS-1D and HYDRUS (2D/3D), repetively), and the loation of fumigant appliation. In HYDRUS-1D one need to peify the upper (zaddft) and lower (zaddfb) depth of the appliation, in HYDRUS (2D/3D) one need to peify the upper (zaddft) and lower (zaddfb) depth and the left (zaddfl) and right (zaddfr) ide of the appliation. HYDRUS then analye water and air ontent in a partiular domain and peifie uh a liquid onentration o that the total applied ma orrepond with the peified appliation ma (FumMa). Any exiting ma of fumigant preent in the oil profile during the new appliation i taken into aount during thee alulation.

34 Appendix 1 page 13of Two Different Volatilization Boundary Condition at the Soil Surfae Two different volatilization boundary ondition (a in the figure below) tarped bed, boundary layer d = d(temp) hank injetion untarped furrow, boundary layer d =0.5 m an be ued in the new verion of HYDRUS (2D/3D) a follow. One need to ue the "Speial Boundary Condition Option", whih allow the "Time-Variable Flux 1" boundary to be treated the ame way a the "Atmopheri" boundary (in term of water flow) (hekbox "treat the timevariable flux boundary ondition a atmopheri, i.e., with limited preure head).

35 Appendix 1 page 14of 17 Uing thi option one an have two eparate boundary ondition at the oil urfae, whih are both treated a Atmopheri boundarie. Thee two boundarie on the urfae an then have either the ame or different fluxe, but they are both treated a Atmopheri boundarie. Uer an apply the "Volatile BC" for olute tranport on both of them, and treat the one part (the Atmopheri boundary) a having the tarp, and the eond part (the Time-Variable Flux 1 boundary ) a not having the tarp (i.e., with d=0.5 m).

36 Appendix 1 page 15of Referene: Jury, W. A., W. F. Spener, and W. J. Farmer, Behavior aement model for trae organi in oil, I. Model deription, J. Environ. Qual., 12, , Millington, R. J., and J. M. Quirk, Permeability of porou olid, Tran. Faraday So., 57, , Moldrup, P., T. Oleen, D. E. Rolton, and T. Yamaguhi, Modeling diffuion and reation in oil: VII. Prediting ga and ion diffuivity in unditurbed and ieved oil, Soil Si., 162(9), , Moldrup, P., T. Oleen, J. Gamt, P. Shjønning, T. Yamaguhi, and D. E. Rolton, Prediting the ga diffuion oeffiient in repaked oil: water-indued linear redution model, Soil Si. So. Am. J., 64, , Šimůnek, J., M. Th. van Genuhten, and M. Šejna, The HYDRUS-1D oftware pakage for imulating the one-dimenional movement of water, heat, and multiple olute in variablyaturated media. Verion 3.0, HYDRUS Software Serie 1, Department of Environmental Siene, Univerity of California Riveride, Riveride, CA, 270 pp., Šimůnek, J., M. Th. van Genuhten, and M. Šejna, The HYDRUS Software Pakage for Simulating Two- and Three-Dimenional Movement of Water, Heat, and Multiple Solute in Variably-Saturated Media, Tehnial Manual, Verion 1.0, PC Progre, Prague, Czeh Republi, pp. 241, 2006a. Šimůnek, J., M. Šejna, and M. Th. van Genuhten, The HYDRUS Software Pakage for Simulating Two- and Three-Dimenional Movement of Water, Heat, and Multiple Solute in Variably-Saturated Media, Uer Manual, Verion 1.0, PC Progre, Prague, Czeh Republi, pp. 161, 2006b. Stumm, W., and J. J. Morgan, Aquati Chemitry: An Introdution Emphaizing Chemial Equilibria in Natural Water, John Wiley & Son, New York, NY, Werner, D., P. Grathwohl, and P. Höhener, Review of field method for the determination of the tortuoity and effetive ga-phae diffuivity in the vadoe zone, Vadoe Zone J., 3, , 2004.

37 Appendix 1 page 16of HYDRUS-1D and HYDRUS (2D/3D) Tet Example HYDRUS-1D example: HYDRUS-1D example that were ued during the HYDRUS oure in Saramento in June 2008 were expanded to demontrate new apabilitie. Currently, there are the following HYDRUS-1D example of inreaing omplexity. Name Fumig1 Fumig1a Fumig2 Fumig3 Fumig4 Fumig4a Fumig5 Fumig6 Fumig6a Deription No tarp, the initial ondition given in liquid onentration No tarp, the initial ondition given in total onentration S Surfae tarp, the initial ondition given in liquid onentration No tarp, the initial ondition given in liquid onentration, irrigation No tarp, the initial ondition given in liquid onentration, heat tranport, effet of temperature Surfae tarp, the initial ondition given in liquid onentration, heat tranport, effet of temperature Surfae tarp removed at a ertain time, the initial ondition given in liquid onentration, heat tranport, effet of temperature Surfae tarp removed at a ertain time, initially no fumigant in the oil profile, heat tranport, effet of temperature, fumigant applied at a ertain time Surfae tarp removed at a ertain time, the initial ondition given in liquid onentration, heat tranport, effet of temperature, fumigant applied at a ertain time (i.e., two appliation - initially and at a ertain time). HYDRUS-2D example: HYDRUS (2D/3D) two-dimenional example that were ued during the HYDRUS oure in Saramento in June 2008 were expanded to demontrate new apabilitie. Currently, there are the following two-dimenional HYDRUS example of inreaing omplexity. Name Deription Fumig1 Impermeable tarp (infinite reitane), the initial ondition given in liquid onentration Fumig2 No tarp (no reitane), the initial ondition given in liquid onentration Fumig3 Surfae tarp (finite reitane), the initial ondition given in liquid onentration Fumig4 No tarp (no reitane), the initial ondition given in liquid onentration, urfae irrigation Fumig5 Surfae tarp removed at a ertain time, the initial ondition given in liquid onentration, heat tranport, effet of temperature Fumig6 Surfae tarp removed at a ertain time, initially no fumigant in the oil profile, heat tranport, effet of temperature, part of the urfae i untarped Fumig7 Surfae tarp removed at a ertain time, the initial ondition given in liquid onentration, heat tranport, effet of temperature, fumigant applied at a ertain time (i.e., two appliation - initially and at a ertain time).

38 Appendix 1 page 17of The Fumigant.in Input File The Input file Fumigant.in (in HYDRUS-1D), whih initiate everal new option for the fumigant tranport (tarp removal, fumigant appliation during imulation) ha to be loated in the folder with the orreponding projet: *** BLOCK X: FUMIGANT INFORMATION ************************************** Fumigant (lfumig) t Additional Appliation (laddf) t Appliation Time (taddf) Additional Ma (FumMa) Appl. Top (zaddft) Appl.Bottom (zaddfb) *** END OF INPUT FILE 'FUMIGANT.IN' ************************************ lfumig: =t: if new fumigant option are ued, i.e., a) tarp removal, b) additional fumigant appliation, or ) new output file. =f: if regular HYDRUS i to be ued. laddf =t: additional fumigant appliation at a ertain time =f: no additional fumigant appliation taddf time of additional fumigant appliation [T] FumMa ma of applied fumigant [M L -2 ] zaddft z-oordinate (poitive) of the top of additional fumigant appliation [L] zaddfb z-oordinate (poitive) of the bottom of additional fumigant appliation [L] The Input file Fumigant.in (in HYDRUS (2D/3D)), whih initiate everal new option for the fumigant tranport (tarp removal, fumigant appliation during imulation) ha to be loated in the folder with the orreponding projet: *** BLOCK X: FUMIGANT INFORMATION ************************************** Fumigant (lfumig) t Additional Appliation (laddf) t Appliation Time (taddf) Additional Ma (FumMa) Appl. Left (xaddfl) Appl.Right (xaddfr) Appl. Top (zaddft) Appl.Bottom (zaddfb) *** END OF INPUT FILE 'FUMIGANT.IN' ************************************ lfumig: =t: if new fumigant option are ued, i.e., a) tarp removal, b) additional fumigant appliation, or ) new output file. =f: if regular HYDRUS i to be ued. laddf =t: additional fumigant appliation at a ertain time =f: no additional fumigant appliation taddf time of additional fumigant appliation [T] FumMa ma of applied fumigant [M L -1 ] xaddfl x-oordinate of the left ide of the zone of additional fumigant appliation [L] xaddfr x-oordinate of the right ide of the zone of additional fumigant appliation [L] zaddft z-oordinate of the top of additional fumigant appliation [L] zaddfb z-oordinate of the bottom of additional fumigant appliation [L]