Modeling of solute transport in the unsaturated zone using HYDRUS-1D

Transcription

1 Examensarbete TVVR 12/52 Modeling of solute transport in the unsaturated zone using HYDRUS-1D Effects of and temporal variabilty in meteorological input data Alan Saifadeen Ruslana Gladnyeva Division of Water Resources Engineering Department of Building and Environmental Technology Lund University

2 Avdelningen för Teknisk Vattenresurslära TVVR-12/52 ISSN Modeling of solute transport in the unsaturated zone using HYDRUS-1D Effects of and temporal variabilty in meteorological input data Alan Saifadeen Ruslana Gladnyeva

3 I Abstract During the last several decades, the study of the movement of water and solutes in the unsaturated zone has become an issue of great significance due to profound effects of the physical and chemical processes occurring in this zone on the quality of both surface and subsurface waters. It is generally known that the precipitation and evaporation are the dominant controls on solutes transport into surface and ground waters. In this study, a general methodology has been developed to evaluate the effect of soil water, and temporal variability in precipitation and evaporation input data on the transport of solutes in soils. To achieve this goal, three objective functions were investigated, movement of center of mass of solutes, masses into groundwater, and depth to a limit concentration. A one-dimensional unsaturated transport model was used to simulate non-reactive transport of solutes. Simulations were conducted in HYDRUS-1D code using measured precipitation data for the period and potential evapotranspiration for three different geographic locations in Sweden (South, Middle, and North). In each location three different soil profiles (each 25 cm deep) were chosen. Modeling with HYDRUS-1D was performed using the period 1 st of March -25 th of September as simulation period. Simulations were run for the cases with and without for all three sites with different temporal variability of precipitation and evaporation input data. First, half-hourly precipitation and evaporation data were applied to simulate in the model, then hourly, 2 hours, 4 hours, and finally 24 hours. The results show that under nonhysteretic water flow solute migration is faster which in turn means an overestimation of the solute velocity. Analysis of the downward migration of the solutes indicates that the effect of is more pronounced in the coarse textured soils.results of the simulations also show that during study period, with the measured precipitation input data, there are small amounts of solutes leached into the groundwater. It is also found that the downward migration of solutes is deeper in Petisträsk compared to the other two sites. On the other hand, the transport of solutes in Norrköping is the slowest among the selected sites. The simulations show that a lower temporal resolution of the meteorlogical input data increases both underestimation of the downward movement of the solutes for non-hysteretic simulations and overestimation for hysteretic ones. Meanwhile, in most cases, this overestimation and underestimation rises with increasing hydraulic conductivity of the soil. Finally, the analysis of the results displays that the differences between hysteretic and non-hysteretic simulations are negligible when using daily input data. Consequently, we may recommend disregarding the effect of when using daily input data. Key words: HYDRUS-1D; Unsaturated zone; Soil water ; Solute transport; Temporal variability in precipitation.

4 II List of abbreviations and acronyms 1D 3D BC CDE COM E ET GL GW LC P R 2 SMHI WT One dimensional Three dimensional Boundary condition Advection-dispersion equation Centre of mass Evaporation Evapotranspiration Ground level Groundwater Limit concentration Precipitation Coefficient of determination in the simple linear regression Swedish Meteorological and Hydrological Institute Water table level

5 III Acknowledgements This study was made within the HYDROIMPACTS 2. project, financed by FORMAS. Rainfall data was supplied by SMHI. Thank you. We would also like to express sincere gratitude to our supervisor professor Magnus Persson for overall guidance and kind of support during the work with the thesis, especially for his help in creating the mathlab codes for averaging the meteorological data and center of mass calculations. Thanks to professor Cintia Bertacchi Uvo, the examiner of the thesis, for her valuable suggestions and comments about this work. Finally our thanks and gratitutes go to our families and friends for their support and endless encouragement.

6 IV Contents Abstract... I List of abbreviations and acronyms... II Acknowledgements... III 1 Introduction Background Objectives Study area Background Theory Water Flow in Unsaturated Zone Flow in single-porosity system Soil properties and unsaturated water flow Soil moisture characteristics Hydraulic conductivity in soil hydraulic properties Solute transport Materials and methods Introduction to HYDRUS-1D HYDRUS-1D model development Input data Meteorological data Soil hydraulic properties Contaminant sources Geometry information Time information Water flow Soil hydraulic property model Soil hydraulic parameters Flow boundary conditions Solutes transport General information Solute transport parameters... 23

7 V Solute transport boundary conditions Outputs Model limitations Data analysis Results and discussion Simulation scenarios Effect of Malmö Norrköping Petisträsk Effect of time resolution of the meteorological input data on Effect of Temporal variability in rainfall and evaporation Effect of geographic location Conclusions Recommendations and future work References Appendices Appendix A. Matlab codes for averaging the pecipitation Appendix B. Matlab codes for averaging potential evapotranspiration Appendix C. Calculation of contaminant concentrations Appendix D. Finding the centre of mass in a 11 vector of concentration values depth Appendix E. Grapghs to the depth of centre of mass, mass into groundwater,and depth to limit concentration against measured precipiations for all soils in Malmö, Norrköping, and Petisträsk with half hourly, 4-hourly, and daily meteoroligical input data... 66

8 1 1 Introduction 1.1 Background The zone between ground surface and groundwater table is defined as the unsaturated zone or the vadose zone which contains in addition to solid soil particles, air and water. The unsaturated zone acts as a filter for the aquifers by removing unwanted substances that might come from the ground surface such as hazardous wastes, fertilizers and pesticides. This is, could be attributed to the high contents of organic matters and clay, which motivates biological degradation, transformation of contaminants and sorption. Therefore, the vadose can be considered as a buffer zone protecting the groundwater. Thus, the hydrogeological properties of this zone are of great concern for the groundwater pollution (Selker, et al., 1999, Stephens, 1996). Many chemical and physical processes occur in the soil horizon. These processes are attributed to different soil phases, due to the existence of solid particles, water and air. In order to be able to model water and solute transport in the unsaturated zone and provide acceptable outputs concerning water and solute solution profiles, it is required to make some simplifications and assumptions due to the heterogeneous and complex nature of soil (Selker, et al., 1999). From hydrologic point of view, the transmission of water to aquifers, water on the surface, and atmosphere is greatly controlled by the processes in unsaturated zone. For these reasons the study and modeling of water flow and solutes transport in the unsaturated zone is becoming an issue of major concern,generally, in terms of water resources planning and management, and especially in terms of water quality management and groundwater contamination (Rumynin, 211). A large number of models have been developed during the past several decades to evaluate the the computations of water flow and solute transfer in the vadose zone. In general, they are either analytical or numerical models for predicting water and solute movement between the soil surface and the groundwater table. Amongst the most commonly used ones are the Richards equation for variably saturated flow, and the Fickian-based convection-dispersion equation (CDE) for solute transport (Šimůnek, et al., 29). These two equations are solved numerically using finite difference or finite element methods (Arampatzis, et al., 21, Šimůnek, et al., 29), which requires an iterative implicit technique (Damodhara Rao, et al., 26). HYDRUS is one of the computer codes which simulating water, heat, and solutes transport in one, two, and three dimensional variably saturated porous media on the basis of the finite

9 2 element method. The Richards s equation for variably-saturated water flow and advection-dispersion type equations (CDE) for heat and solute transport are solved deterministically (Šimůnek, et al., 29). In this study, HYDRUS-1D version 4.14 is used as a tool to simulate water and solute movement in the vadose zone to develop our understanding of downward movement of solutes under variable boundary conditions. The software is originaly developed and released by the United States. Salinity Laboratory in cooperation with the International Groundwater Modeling Center (IGWMC), the University of California Riverside, and PC-Progress, Inc. 1.2 Objectives The main aim of this research is to study water flow and solutes transport in the vadose zone in Sweden through investigating downward movement of the centre of mass of solutes and general patterns of concentration profiles. Specific objectives were set to achieve this goal, amongst which: Identifying the effect of on the movement of solutes for different kinds of soils in different geographic locations throughout Sweden; Examination of temporal variability in precipitation and implications of precipitation patterns on the downward movement of solutes in different types of soils in different geographic locations throughout Sweden. 1.3 Study area The study area is three sites Petisträsk, Norrköping and Malmö which are located in north-west, middlewest and south-east of Sweden, see Figure 1.1. The sites were chosen in different parts of Sweden to investigate the solute transport under different climatic conditions. Stochastic variability of precipitation is an important factor controlling temporal variability of the temporal patterns of solute movement in vadose zone. This in turn, determined by hydrologic filtering of precipitation variability in infiltration, storage, drainage and evapotranspiration (Harman, et al., 211). For each site the half-hourly measured precipitation data were obtained form SMHI weather stations and potential evapotranspiration was given as monthly data (Eriksson, 1981). The data were recorded during 13 years ( ).

10 3 Generally speaking about patterns of precipitation in Sweden, the summer is considered to be the season when the most rainfall occurs. However the period from Petisträsk Norrköping Malmö B C October to December is characterized by numerous days with continuous rain, while the larger amount of rainfall falls in the summer and this is due to great intensities of summer rainfalls (Raab and Vedin, 1995). Approximate distribution of precipitation during the years for the study sites is shown on the Figure 1.2. As data for Malmö, Norrköping and Petisträsk was not available, data from the closest weather stations: Lund, Linköping and Umeå is used. Mean annual precipitation for the period , for Lund (Malmö) is 655 mm, for Linköping (Norrköping) is 516 mm and for Umeå (Petisträsk) is 65 mm. While mean annual evapotranspiration for the period , for Lund (Malmö) is 5 mm, for Linköping (Norrköping) is 5 mm and for Umeå (Petisträsk) is 35 mm (Raab and Vedin, 1995). Figure 1.1: Map of Sweden with indicated study sites (Google_maps, 212)

11 4 a b Figure 1.2: Distribution of precipitation over the year for Lund (a), Linköping (b) and Umeå (c). Mean values Deep blue is rain and light blue is snow (Raab and Vedin, 1995). c

12 5 2 Background Theory Naturally surface water reaches groundwater in form of precipitation that fall down to the ground surface but also could be more artificial forms, for instance, irrigation, surface runoff, stream flow, lakes. Rainfall or irrigation may infiltrates to groundwater if their intensity is larger than the infiltration capacity of the soil (the maximum rate at which water absorbed by soil). Some precipitation or irrigation water may be intercepted by vegetation and then return to the atmosphere as evaporation from leave surfaces. Some infiltrated water may be taken up by plant roots and then given back to atmosphere as transpiration via leaves. The water that has not been lost through evapotranspiration (evaporation plus transpiration) has a chance to percolate downwards to a deeper vadose zone and eventually reach the groundwater table or saturated zone. If the groundwater table is shallow then groundwater may move upward to the root zone by vapor diffusion and by capillary rise. A schematic representation of the unsaturated zone is shown in Figure 2.1. Figure 2.1 Schematic of water fluxes and various hydrologic components in the vadose zone (Simunek and Genuchten, 26). Infiltration is considered to be an extremely complex process. It is a function of not only soil hydro physical properties (soil water retention and hydraulic conductivity) and rainfall characteristics (intensity and duration) but also controlled by initial water content, surface sealing and crusting, vegetation cover and ionic composition of infiltrated water. Solute infiltration occurs in vadose zone or unsaturated zone or zone of aeration. In this zone pores usually are partially saturated with water, and those ones which are not filled with water filled with air instead. However in vadose zone may exist some saturated zones, for

13 6 instance, perched water above impermeable soil layer (Simunek and Genuchten, 26). Vadose zone play incredibly important role in water and solute transport, because it functioning as: a storage medium, where biosphere has immediate access; a buffer zone, which controls and could prevent transport of contaminants downward to ground water; a living environment, where varies physical and chemical processes take place, which can isolate and slowdown exchange of contaminants with other environments (Nimmo, 26). 2.1 Water Flow in Unsaturated Zone Water flow in vadoze zone is usually described by a combination of continuity equation 2.1and Darcy Buckingham eq. 2.3,. The continuity equation 2.1 states that change in water content in a given volume of soil, because of spatial changes in water fluxes and possible sources and sinks within that volume of soil: 2.1 Where θ is the volumetric water content, [L 3 L 3 ], t is time [T], q is the volumetric flux density [LT 1 ], z i is the spatial coordinate [L], and S is a general sink orsource term [L 3 L 3 T 1 ], for example, root water uptake. Darcy (1856) made an experiment on the seepage of water through a pipe filled with sand. He proved that the flow rate Q through pipe filled with a sand was directly proportional to its cross-sectional area A and to the difference of hydraulic head h across the layer, and inversely proportional to the length of the pipe: 2.2 Where coefficient of proportionality K is a hydraulic conductivity, [LT -1 ]. Firstly Darcy s law was implemented to the partly saturated flow by Buckingham (197) and he found that in this case the hydraulic conductivity is a function of water content K=K(θ). This means that a small decrease in θ leads to a significant decrease in K. That is why for many soils the difference between hydraulic conductivities below and above water table might be great. Normally it is assumed that unsaturated flow has virtually vertical direction in contrast to saturated flow below the water table, which usually is horizontal or in parallel to impervious layers. This because at interface, where soils with different hydraulic conductivities are meet streamlines exhibit a pronounced refraction (Brutsaert, 25). Darcy s law was developed for an unsaturated medium:

14 7 2.3 Where h is hydraulic head and defined as: Combination of equations 2.3 and 2.1 and is called Richards equation and it describes vertical downward movement of water in unsaturated zone Where H is soil water pressure head relative to atmospheric pressure (H ). Richards equation is partially differential and highly non-linear as θ-h-k has a non-linear relationship in nature, which also indicates its strongly physically based origin. Moreover boundary conditions at a soil surface are changing irregularly. That is why it might be solved analytically only for limited boundary conditions. If relationships between θ-h-k are known, numerical solutions may solve the equation for various top boundary conditions (Dam, et al., 24). In this study solute transport was numerically simulated by HYDRUS-1D. The software uses modified Richards equation ( 2.6) and describes infiltration in vadose zone and modeling it as one dimensional vertical flow. 2.6 Where H is the water pressure head [L], α is the angle between the flow direction and the vertical axis (i.e., α = for vertical flow, 9 for horizontal flow, and < α < 9 for inclined flow), and K is the unsaturated hydraulic conductivity [LT -1 ] given by (Simunek, et al., 25). 2.7 where K r is the relative hydraulic conductivity [-] and K s the saturated hydraulic conductivity [LT -1 ] Flow in single-porosity system Water and solute movement in unsaturated zone was simulated by HYDRUS-1D using simple single porosity flow model (Figure 2.2). Single porosity model describes uniform flow in porous media while the other models are applied to simulate preferential flow or transport. In this case Richards equation and Fickianbased convection-dispersion equation for solute transport are solved for the entire flow domain.

15 8 Figure 2.2: Conceptual physical equilibrium model for water flow and solute transport in a single-porosity system (Simunek et al., 25). 2.2 Soil properties and unsaturated water flow Soil is a three-phase system; it consists of solid, liquid and gaseous phases which are distributed spatially. Solute movement in between these phases is controlled by physical, chemical and biological processes. Vadose zone is bounded by soil surface and joins with groundwater in capillary fringe. The main forces which are responsible for holding water in a soil are capillary and adsorptive forces. Water and its chemical content are changing because of infiltration of precipitation or irrigation, water uptake by plants and evaporation from soil surface (Parlange, et al., 26). Porosity of a soil [L 3 L -3 ] might be expressed as: 2.8 Where p b is a bulk density of the soil and p s is soil s particle density. From eq. 2.8 it is seen that soil porosity decreases when bulk density increases. Soil water content may be defined by mass, eq. 2.9, or by volume, eq. 2.1, but usually for numerous hydrological applications it is used in non-dimensional form, i.e. eq Where,, V w - water volume,[ L 3 ] V t - solid volume, [L 3 ], w is defined as the mass water content and ρ w is the specific density of water, ρ w 1 g/cm 3 Soil water content can be also expressed by the degree of saturation S [ ],

16 The volumetric water content varies between for dry soil to the saturated water content θ s, which supposed to be equal to the porosity if the soil were completely saturated. The degree of saturation ranges between one (soil completely filled with water) to zero (completely dry soil). By replacing porosity by θ s and subtracting residual water content θ r in eq. 2.11, effective saturation S e has been obtained By the way effective saturated water content normally does not reach 1% saturation of the pore space, due to air invasion (Parlange, et al., 26) Soil moisture characteristics The relationship between soil water suction, H, and the amount of water remaining in the soil or volumetric soil content (θ) resulting in function known as the moisture characteristic or retention curve in case of drying soil. It describes soil s ability to retain or release water. Figure 2.3 illustrates that the shape of the curve is connected with pore size distribution (Bouma, 1977). For sand the shape of the retention curve has a step form, for clay the retention curve, on the contrary, has a quite steep form. The mechanism of water retention differs with suction. Suction usually expressed by the soil water matric head (strictly negative) or soil suction (strictly positive). If suction is very low (higher moisture contents) water retention depends on capillary surface tension effects, and the last depends on pore size and soil structure (i.e. the aggregation of solid particles in soil). If suctions are higher (lower moisture contents) water retention influenced mainly adsorption, which depends on soil texture (i.e. the size distribution of solid particles in soil) and specific surface (i.e. surface area per unit of volume) of material. Clay particles have large specific surface compared to sand, because they are smaller and more flattened, when sand particles are bigger and more round. Due to this, clay soils have more fine pores and large adsorption which allow them to have greater water content at a given suction rather than sand (Ward and Robinson, 2b).

17 1 Figure 2.3: Soil moisture characteristics of different soil materials: 1-sand, 2-sandy loam, 3-silty clay loam, 4-clay (Bouma, 1977) One of the main limitations of using the retention curves is that the water content at a given suction depends not only on the value of that suction but also on moisture history of the soil (Ward and Robinson, 2b). The retentions curves will be different for drying and wetting soils: at a given matric pressure the water content for wetting soils will be less than for drying ones. Figure 2.4 shows typical example of hysteretic water retention in a soil. In HYDRUS-1D van Genuchten formula has been used to describe the water retention 2.13 Where, And 2.16

18 11 θ(ψ) soil water (retention), which is highly non-linear function of the pressure head, ψ;; θ r and θ s are residual and saturated volumetric water contents, respectively; n is empirical parameter related to the pore size distribution, that is reflected in the slope of water retention curve; α is an empirical parameter assumed to be related to the inverse of the air-entry suction, [L -1 ]; S e effective saturation [-]; K s hydraulic conductivity at natural saturation, [LT -1 ](Simunek, et al., 25) Hydraulic conductivity Another important hydraulic soil property that describes soil water movement is the relation between the soil s unsaturated hydraulic conductivity, K, and volumetric water content, θ. Hydraulic conductivity reflects the ability of porous medium to transfer the water. It may be expressed as: 2.17 Where k is intrinsic permeability; k rw (θ) is relative water permeability (the ratio of the unsaturated to the saturated water permeability) that varies from for completely dry soils to 1 for fully saturated soils; and μ w is the water viscosity. Where k is intrinsic permeability; k rw (θ) is relative water permeability (the ratio of the unsaturated to the saturated water permeability) that varies from for completely dry soils to 1 for fully saturated soils; and μ w is the water viscosity. Equation 2.17 demonstrates that hydraulic conductivity depends on size, shape of filled with water pores (Wang, 29) and how they are connected between each other, the flowing fluid (μ w and ρ w ) and water content of the soil (k rw (θ)). Hydraulic conductivity at or above saturation (h ) defined as hydraulic conductivity at natural saturation (K s ) (Simunek and Genuchten, 26). Fullness of pores with water is defined by or the history of the moisture state and its retention. Larger pores, which make greatest contribution to transfer water in soil, empty first when fluid content decreases. Left pores are smaller, and they have less ability to conduct water due to viscous frictions in them, which are much bigger compare to large pores. When fewer pores filled with water streamlines become more tortuous. Dry soil and small pores which are filled which in turn hindering the water flow as liquid transports through poorly conductive pore medium and it is simply adhering in form of films to soil particle. These factors reduce hydraulic conductivity greatly when soil goes from saturated to field-dry conditions. Other factors could also influence K, for instance, temperature as it affects fluid viscosity, microorganisms may reduce K, by constricting the pores (Nimmo, 26).

19 12 All previous means that the relation between K and θ is also a function of water and soil matrix properties, as well as relation between θ and H, and is strongly affected by water content and by (Parlange, et al., 26) in soil hydraulic properties A lot of studies were conducted recently to investigate the affect of and many of them showed that has an effect on unsaturated soil water movement and solute transport (Russo, et al., 1989, Yang, et al., 212, Lehmann, et al., 1998, Kool and Parker, 1987) as well as disregarding might leads to significant errors in prediction of solute movement and contaminant concentrations (Kool and Parker, 1987). The main factors which affect are the complexity of the pore space geometry, the presence of entrapped air, shrinking and swelling and the thermal gradients. There are many mechanisms by wich is propagated but the main ones are considered to be ink bottle and contact angle effects (Ward and Robinson, 2a). ink bottle effect implies that water drains the pore at a larger suction as larger suction is needed to enable the air to enter the narrow pore neck, than for filling the pore with water, as it is controlled by the lower curvature of the air-water interface in the wider pore itself. The contact angle affect implies that the contact angle of the solute interfaces is probably to be larger when the interface is advancing (wetting) than when it is receding (drying), so at a water content the suction will be greater for drying rather than for wetting (Ward and Robinson, 2a). However it is might be assumed that the contact angle is something that is not very understood as it is very difficult to measure (Nimmo, 26). The entrapped air affects. Some amount of air normally gets trapped in the form of bubbles enclosed by water, normally occupying approximately 1-3% of pore space. Thus maximum water content will be 7-9% of the total porosity when soil is drying. Though sometimes it could increase over time and become equal to porosity, because the soil might be saturated enough for all the air bubbles to dissolve (Nimmo, 26). Swelling and shrinkage. Wetting and drying maybe accompanied by swelling and shrinkage for fine grained clays (Ward and Robinson, 2a). This will lead to the changes in the pores geometry and bulk density of the medium so the water content will be different of the one prior to the swelling or shrinkage. As water is drained from the pores between flattened particles, the particles alignment

20 13 will become tighter and this will reduce the total volume. One may think that re-wetting may return particles on their original places but this not necessary so; resulting in a lower water content (Ward and Robinson, 2a). Thermal affects. Temperature affects the tension so it will have a great affect on retention relation. Increase of temperature means that less water will be held at a given matric pressure (Nimmo, 26). All this prove that is incredibly complex phenomena and many might neglect it for this reason. As it have been mentioned before the moisture characteristics curves are different for drying and wetting curves. The main drying curve describes the drying from the highest reproducible saturation degree to the residual water saturation. And the main wetting curve describes the wetting from the residual water content to the highest degree of saturation. Figure 2.4 shows a typical example of hysteretic water retention in a soil. Outer curves which start from very dry or wet conditions are called main drying or main wetting curves. Starting from a boundary wetting or drying curve, a sequence of wetting and drying cycles can be expressed by wetting and drying scanning curves (Lehmann, et al., 1998). Drying Wetting Figure 2.4: in the moisture characteristic (Bouma, 1977) HYDRUS-1D simulates by empirical model introduced by Scott, et al. (1983)which assumes that drying scanning curves are scaled from the main drying curve and wetting scanning curves from the main wetting curve. Both curves are described by eq using the parameter vectors θ d r, θ d s, θ d m, α d, n d and θ w r, θ w s, θ w m, α w, n w, where w and d mean wetting and drying respectively. The following restrictions are expected to hold in the applications of HYDRUS-1D: 2.18

21 14 This means that θ s d, α d,θ s w and α d are the only independent parameters for describing in soil moisture characteristics curve. It might also be assumed that there is a little in hydraulic conductivity, so K s d =K s w =K s and parameters: n, K s, α d, θ r, θ s w., hence the hysteretic retention curve is described by the 2.3 Solute transport HYDRUS-1D uses advection-dispersion equation to simulate solute transport in unsaturated zone. For inert, non-adsorbing solutes during one-dimensional water flow it has a form of 2.19 Where D =D(θ) is longitudinal dispersion coefficient. Combined solute and moisture transport equation will have a form 2.2 The majority of approximate solutions of the eq. 2.2 are based on the assumption that q and D near the front vary only slightly over the depth but are functions of time. In this case, the Eeq. 2.2 can be written as 2.21 The analytical solution of the advection dispersion is 2.22

22 15 3 Materials and methods 3.1 Introduction to HYDRUS-1D HYDRUS-1D is a computer software package which may be used for simulating water, heat, and solutes movement in one-dimensional variably saturated porous media. It can be also used to simulate carbon dioxide and major ion solute movement. Basically, the Richardss equation for variably-saturated water flow and advection-dispersion type equations (CDE) for heat and solute transport are solved numerically. To account for variability in the soil properties, many modifications are made to the flow equation, such as, a sink term to account for water uptake by plant roots, and dual-porosity type flow or dual-permeability type flow to account for non-equilibrium flow. The program can deal with different water flow and solutes transport boundary conditions (Šimůnek, et al., 29). In addition to HYDRUS computer code, the HYDRUS-1D software has an interactive graphics-based user interface module. Basically, the module consists of a project manager and a unit for pre processing and post processing. 3.2 HYDRUS-1D model development Input data Meteorological data Precipitation Precipitation and evapotranspiration during study period were given as input for time variable boundary conditions in HYDRUS-1D. The meteorological data for all the three sites under investigations (Loddeköpinge, Norrköping, and Petisträsk) were obtained from Swedish Metrological and Hydrological Institute (SMHI). Initially rainfall data were given in half-hourly time resolution. In order to investigate the effect of time resolution of the input on the model, half-hourly input was converted into 1, 2, 4 and 24 h input. The conversion was done by averaging the data, for more details see Appendix A. Potential Evapotranspiration Evapotranspiration was given as monthly data. Monthly data can give only hourly average values during a day which cannot give a good picture of reality, as evapotranspiration varying during the day and the season. For this study it was built a model which allowed calculating hourly ET with consideration of its

23 Diurnal variation of ET, % 16 diurnal variations (see Figure 3.1). The model was completed in a very simplified manner and it was assumed that: there is no ET during the night, 18: until 6:; ½ of the diurnal ET was during 8 hours, between 6: and 1:, and between 14: and 18:; ½ of diurnal ET occurred during 4 hours between 1: and 14: Hour of day Figure 3.1: Simplified model of a diurnal variation of evapotranspiration. In reality diurnal variations of ETn would probably have a look like in Figure 3.2; however, in terms of the study, which makes use of enormous amount of data, it was decided to simplify the curves, or in other words, to make the variation more even where it was possible, in order to ease the calculations. Figure 3.2: Penman-Monteith potential evapotranspiration as a function of time of day for (left) June and (right) December, calculated from hourly measurements at the Cefn-Brwyn automated weather station in the Wye catchment, Black dots and lines indicate means and standard deviations (Kirchner, 29). Conversion was done in an exact same way as for precipitation. The conversion codes for evapotranspiration and precipitation as well as diurnal variations of evaporation code were written in MATLAB, see Appendix B.

24 Soil hydraulic properties Investigation of coupled water and solute transport was done for different climatic conditions and for the soils with different physical properties. For this soil 1 (Persson and Berndtsson, 22), soil 2 (Zhang, 1991) and soil 3 have been chosen which are considered to be good representatives of typical Swedish agricultural soils. Three 25 cm deep multi layered soil profiles were used as input data for HYDRUS-1D for 3 sites of interest (Table 3.1). Table 3.1: Soil properties for study sites Depth, cm Sand, % Silt, % Clay, % Bulk density, g/cm 3 soil > soil > soil > Contaminant sources The top 5 cm of soil with area 1 m 2 with residual phase contamination extending to a depth of 2.5 m below ground surface was assumed to be contaminated with 1 g of non-volatile and non-reactive solute. 1 m 1 m Contaminant 5cm For the simulation of the solute transport by HYDRUS-1D the initial concentration in liquid phase (mass solute per volume of water) has been used as input to the model. The volume of water in.5 m 3 volume of dry soil was calculated from eq 2.1.

25 18 Volumetric water content for the soil was calculated according to van Genuchten formula, eq Van Genuchten hydrodynamic parameters θr and θs (Appendix C) were predicted by Hydrus-1D from the particle size distribution and bulk density of the soils (Table 3.1). Table 3.2: Soil hydraulic parameters obtained from Hydrus-1D, using the single porosity flow model Depth, cm θ r (v/v) θ s (v/v) α (1/m) n Ks (m/d) I Soil Soil Soil Following the initial liquid phase concentrations were obtained for different soil types: C soil 1 =23.2 mg/cm 3, C soil 2 =13.5 mg/cm 3 and C soil 3 =9.31 mg/cm 3, see (Appendix C) Main processes As shown in Figure 3.3, the main process dialog window contains the processes that can be simulated in HYDRUS such as water flow, solute and heat transport, root water uptake, and root growth. Only water flow and general solute transport options were selected and simulated in this research. Figure 3.3: The main process dialog window (HYDRUS-1D 29, user s manual)

26 Geometry information In HYDRUS-1D geometry of model can be defined. First, the number of soil types, the total depth of soil profile, and length units can be set under the geometry information dialog box. Then, finite element model can be constructed by subdividing each region into linear elements by means of soil profile graphical editor or soil profile summary dialog windows. In this study, three different kinds of soil profiles were used; Soil 1, Soil 2, and Soil 3. The total depth of each soil profile is 25 cm, representing the average depth of the unsaturated zone in Sweden, see section The finite element model was constructed by dividing the entire profile into 1 layers of the thickness of 2.5 cm. The detailed cross sections of one-dimensional models are shown in Figure 3.4. (a) (b) (c) Figure 3.4: shows cross-sections of the layered soils. (a) Soil 1 consists of four sub-layers. (b) Soil 2, consists of three sub-layers. (c) Soil 3, consists of three sub-layers. GL stands for ground level and WT stands for water table level Time information Under this section, time units, time discretization, and time-variable boundary conditions can be defined, see Figure 3.5. The unit of time was selected in hours and the period 1 st of March -25 th of September was used for simulation purposes (5 hours). In HYDRUS-1D code, the maximum number of time variable records is 1; therefore, 5 hours are chosen as simulation period, which consequently means having 1 records when using half hourly precipitation and evaporation input data. Meanwhile, the period 1 st

27 2 of March -25 th of September was selected due to the fact that a large amount of annual precipitation occurs in this period in Sweden. In addition, it is expected to have more infiltration because of unfrozen surfaces due to warmer weather, though the evaporation is higher during this period. Figure 3.5: Time information dialog window (HYDRUS-1D 29, user s manual) Water flow Soil hydraulic property model Within this command window, hydraulic model and can be defined. There are various hydraulic models that can be used as shown in Figure 3.6. In this research, van Genuchten-Mualem single porosity model was selected, first with, and then without.

28 21 Figure 3.6: Soil hydraulic property model window (HYDRUS1D 29, user s manual) Soil hydraulic parameters All the parameters needed for various soil hydraulic models are specified in this section, the water flow parameters dialog window is shown in Figure 3.7. The parameters needed are residual and saturated water contents, saturated hydraulic conductivity, pore connectivity parameter, and empirical coefficients Alpha and n. To predict the values of these parameters, HYDRUS-1D uses Rosetta DLL (Dynamically Linked Library), by Marcel Schaap (Šimůnek, et al., 29). The Rosetta model can be used to estimate water retention parameters according to van Genuchten (198), saturated hydraulic conductivity, and unsaturated hydraulic conductivity parameters according to van Genuchten (198) and Mualem (1976). To achieve this, the model uses a database of measured water retention and other properties for a wide variety of media. For a given a medium s particle-size distribution and other soil properties the model estimates a retention curve with good statistical comparability to known retention curves of other media with similar physical properties (Nimmo, 26). As the model uses basic more easily measured data, it is considered as a pedotransfer function model (PTFs) (Schaap, et al., 21).

29 22 Figure 3.7: Water flow parameters dialog window (HYDRUS-1D 29, user s manual) Percentage of sand, silt, and clay together with the bulk density for different soil layers were used to get values of all the parameters needed, see Table Flow boundary conditions Water flow boundary conditions are selected under this section. The window contains upper and lower boundaries. For 1D modeling purposes, it was assumed to have a constant pressure head at depth 25 cm (at the groundwater table) as a lower boundary condition and atmospheric boundary condition at the surface layer as an upper BC, see Figure 3.8. Figure 3.8: Water flow boundary conditions (HYDRUS1D 29, user s manual).

30 Solutes transport General information Under this pre-processing submenu, solute transport model, time weighting scheme, space weighting scheme, and some other parameters can be defined. The dialog window is shown in Figure 3.9. Figure 3.9: Solute transport window (HYDRUS1D 29, user s manual). For simulation purposes, equilibrium solute transport model is selected with Crank-Nicholson as time weight scheme and Galerkin finite elements as space weight scheme Solute transport parameters Solute transport parameters needed are Bulk density, longitudinal dispersivity, dimensionless fraction of adsorption sites, and immobile water content which set equal to zero when physical non-equilibrium is not considered. In addition to these parameters, some Solute Specific Parameters are needed such as Molecular diffusion coefficient in free water and Molecular diffusion coefficient in soil air which both were set equal to zero (Figure 3.1).

31 24 Figure 3.1: Solute transport parameters ((HYDRUS1D 29, user s manual) Solute transport boundary conditions For 1D modeling purposes, a concentration flux was used as an upper BC and Zero concentration gradient was assumed as a lower boundary condition with liquid phase concentrations as an initial condition. Figure 3.11 shows the detailed dialog window. Figure 3.11: Solute transport boundary conditions (HYDRUS1D 29, user s manual)

32 Outputs After HYDRUS-1D models have been prepared, simulations were performed to get the outputs. Generally, the HYDRUS code provides three different groups of output files, which are; T-level information, P-level information, and A-level information. Here, in this research, we made use of three different output files from these three groups, namely; D_INF.OUT file, which is from the P-level information group and used to find concentration profiles in the soil horizon at the end of the simulation period. Solute1.OUT file, this one is from the T-level information group and used to find the amount of solute leaching to the groundwater table at the end of the simulation period. T_LEVEL.OUT file, this file is also from the T-level information group and used to find the amount of net precipitation infiltrated to the soil Model limitations The study of the unsaturated zone is a complex work due to the heterogeneous nature of soil. Therefore, to be able to model movement of water and solutes, and in an attempt to achieve the aim and specific objectives of the study, some simplifications and limitations were made: Because of time limitations, only 13 years were simulated. In addition, the selected period for simulations (1 st of March-25 th of September) might not be the worst condition for downward migration of solutes in all the locations. It was assumed that the water-table is constant (25 cm below the ground surface) throughout the simulation period. The effect of root-water uptake was neglected. In order to make a comparison between the three selected sites concerning the effect of and time resolution of precipitation and evaporation input data, the soil profiles were kept the same in all the sites. A one-dimensional vertical movement was assumed and simulated in the model, though threedimensional flow representing more correctly the reality. However, the one-dimensional vertical movement is the dominant direction of flow in the unsaturated zone, in a large-scale field condition it could be seen as a simplification of the reality. But one should be aware that one-dimensional flow overestimates concentrations comparing to tree-dimensional spreading. A single porosity model was used to describe the uniform flow in the unsaturated porous media which neglects both the variability in the soil properties, and non-equilibrium flow.

33 26 Estimation of water retention was done with statistically calibrated pedotransfer function The Rosetta model. However it predicts water retention for a given soil from database of measured water retention for variety of porous media that is why it difficult to say how good the prediction is. If one would like to be more exact, then water retention measurements are needed. Simulations were conducted for the non-reactive solute transport. This might be an overestimation of the real downward migration of solutes. The input precipitation and evaporation data is another factor of uncertainty, especially the downscaling of the evapotranspiration input data. 3.3 Data analysis Three objective functions were used to achieve the aims of this research:depth of the centre of mass of solutes, depth to a limit concentration, and the amount of solute masses leached into the groundwater. To investigate the changes in the two depths, the concentrations across soil profiles were extracted from HYDRUS D_INF.OUT file. Then a MATLAB code (Appendix D) was used to get the variations during study period ( ) in these two depths across the soil profile. In addition, the masses to ground water were directly extracted from Solute1.OUT file.

34 27 4 Results and discussion 4.1 Simulation scenarios Effect of In this section the effect of on the downward movement of solutes in the three chosen sites in Sweden is evaluated. Only the results of half hourly input data are displayed and discussed, but the graphs of all the other time resolutions can be found in Appendix E Malmö During study period ( ) precipitation values vary between 243 mm and 577 mm in the selected period for simulations (1 st of March-24 th of September). The depth of COM against measured precipitations in all the three soil profiles (soil 1, soil 2, and soil 3), are displayed in three graphs (Figure 4.1). Red circular scatter dots represent the depth of COM when taking into account, and the depth to COM in non-hysteretic water system is shown by the green triangular dots. It is obvious that the depth of COM is deeper when neglecting in the soil water system in all the soil types. This is generally in agreement with a previous study conducted by Russo, et al. (1989), in which overestimated values of solute velocities have been noticed in transient flow models when neglecting. Pickens and Gillham (198) also reported that for a hypothetical case involving onedimensional transport of slug of water containing a nonreactive tracer during an infiltration-redistribution sequence in a vertical sand column, there is a lag in hysteretic concentration profiles compared to that of non-hysteretic case. This behavior could be due to the fact that under hysteretic conditions, only small changes in moisture content can be resulted from large changes in pressure head. In such a case, hysteretic simulations show slower changes than the non-hysteretic simulations (Bashir, et al., 29). On the other hand, the trend line is steeper when ignoring with higher R 2 value, which refers to more rapid response to the precipitation increase and stronger linear relationship between solute movement and precipitation.

35 Depth of COM (m) Depth of COM (m) Depth of COM (m) Depth of COM vs. precipetation- Malmö,.5h-soil 3 y =.143x R² =.9231 y =.117x R² = Prec. (cm) Linear () Linear () Depth of COM vs. precipetation- Malmö,.5h-soil 2 y =.25x R² =.9452 y =.15x R² = Prec. (cm) Linear () Linear () a 2. Depth of COM vs. precipetation- Malmö,.5h-soil 1 b 1.5 y =.36x R² = y =.3x R² = Linear () Prec. (cm) Linear () c Figure 4.1: Depth of COM of solutes versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the period , for both non-hysteretic (green trangular dots) and hysteretic (red circular dots) models. The relationship between depth of COM and precipitation in a specific soil type does not depend only on the amount of precipitation. One might expect that precipitation pattern could be another important factor, for instance. However, to demonstrate quantitatively the effect of precipitation increase on the downward migration of solutes, the maximum and minimum precipitations are applied in the trend line equations to get the corresponding depths to COM in all the soils. The precipitation is increased by a factor of more than 2 during study period, with this increase, the depth of COM is increased by a factor of 5 in soil 1 (for both hysteretic and non-hysteretic simulations), a factor of 5 in hysteretic soil 2 and 6 in nonhysteretic case, and a factor of 4 in hysteretic soil 3 and 5 in non-hysteretic case (Table 4.1).

36 29 Table 4.1: Variations in the depth of COM due to precipitation increase in meters for all the three soil types in Malmö, for the period , for both hysteretic and non-hysteretic soil waters. Soil 1 Soil 2 Soil 3 Precipitation (mm) When evaluating the effect of and comparing between different soil profiles, it is found that, on average, the depth of COM is deeper in non-hysteretic water system by 19% in soil 1, 26% in soil 2, and 8 % in soil 3 (Table 4.2). In other words, the differences decrease in fine textured soils compared to coarser ones (Parlange, et al., 26). Table 4.2: The average depths of COM in meters for all the three soil types in Malmö, for the period , for both hysteretic and non-hysteretic systems. Soil 1 Soil 2 Soil Another parameter which we are interested to investigate is the amount of solutes leaching into the ground water. As shown in Figure 4.2, the mass of solutes leached into the GW for all the soils in both soil water systems is zero until reaching a threshold precipitation value. The threshold value of precipitation is found to be around 45 mm in soil 1, and 57 mm in both soil 2 and soil 3. Beyond this threshold value there is some leaching, though the leaching masses are relatively small. The masses of solutes at the groundwater table can be seen in Table 4.3. Table 4.3: The masses of solutes into GW in mg/cm 3 for all the three soil types in Malmö, for the period , for both hysteretic and non-hysteretic soil waters. Soil 1 Soil 2 Soil 3 Precipitation (mm)