Modeling of Solute Transport in the Unsaturated Zone Using HYDRUS-1D

Modeling of solute transport in the

unsaturated zone using HYDRUS-1D

Effects of hysteresis and temporal variabilty in meteorological

input data

___________________________________________________________________

Alan Saifadeen

Ruslana Gladnyeva

Examensarbete

TVVR 12/5020

Division of Water Resources Engineering

Department of Building and Environmental Technology

Lund University

Modeling of solute transport in the unsaturated zone using

HYDRUS-1D

Effects of hysteresis and temporal variabilty in meteorological input data

Alan Saifadeen

Ruslana Gladnyeva

Avdelningen fr Teknisk Vattenresurslra

TVVR-12/5020

ISSN-1101-9824

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

hysteresis, 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 1996-2008 and potential

evapotranspiration for three different geographic locations in Sweden (South, Middle, and North). In each

location three different soil profiles (each 250 cm deep) were chosen. Modeling with HYDRUS-1D was

performed using the period 1st of March -25th of September as simulation period. Simulations were run for

the cases with and without hysteresis 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 non-

hysteretic 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 hysteresis 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 Petistrsk compared to the other two

sites. On the other hand, the transport of solutes in Norrkping 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 hysteresis when using daily input data.

Key words: HYDRUS-1D; Unsaturated zone; Soil water hysteresis; Solute transport; Temporal variability in

precipitation.

II

List of abbreviations and acronyms

1D One dimensional

3D Three dimensional

BC Boundary condition

CDE Advection-dispersion equation

COM Centre of mass

E Evaporation

ET Evapotranspiration

GL Ground level

GW Groundwater

LC Limit concentration

P Precipitation

R2 Coefficient of determination in the simple linear regression

SMHI Swedish Meteorological and Hydrological Institute

WT Water table level

III

Acknowledgements

This study was made within the HYDROIMPACTS 2.0 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.

IV

Contents Abstract .............................................................................................................................................................. I

List of abbreviations and acronyms ................................................................................................................... II

Acknowledgements .......................................................................................................................................... III

1 Introduction ............................................................................................................................................... 1

1.1 Background ........................................................................................................................................ 1

1.2 Objectives .......................................................................................................................................... 2

1.3 Study area .......................................................................................................................................... 2

2 Background Theory.................................................................................................................................... 5

2.1 Water Flow in Unsaturated Zone ...................................................................................................... 6

2.1.1 Flow in single-porosity system .................................................................................................. 7

2.2 Soil properties and unsaturated water flow ..................................................................................... 8

2.2.1 Soil moisture characteristics...................................................................................................... 9

2.2.2 Hydraulic conductivity ............................................................................................................. 11

2.2.3 Hysteresis in soil hydraulic properties ..................................................................................... 12

2.3 Solute transport ............................................................................................................................... 14

3 Materials and methods ........................................................................................................................... 15

3.1 Introduction to HYDRUS-1D ............................................................................................................ 15

3.2 HYDRUS-1D model development .................................................................................................... 15

3.2.1 Input data ................................................................................................................................ 15

3.2.1.1 Meteorological data ............................................................................................................ 15

3.2.1.2 Soil hydraulic properties ...................................................................................................... 17

3.2.1.3 Contaminant sources ........................................................................................................... 17

3.2.2 Geometry information ............................................................................................................. 19

3.2.3 Time information ..................................................................................................................... 19

3.2.4 Water flow ............................................................................................................................... 20

3.2.4.1 Soil hydraulic property model ............................................................................................. 20

3.2.4.2 Soil hydraulic parameters .................................................................................................... 21

3.2.4.3 Flow boundary conditions ................................................................................................... 22

3.2.5 Solutes transport ..................................................................................................................... 23

3.2.5.1 General information ............................................................................................................ 23

3.2.5.2 Solute transport parameters ............................................................................................... 23

V

3.2.5.3 Solute transport boundary conditions ................................................................................ 24

3.2.6 Outputs .................................................................................................................................... 25

3.2.7 Model limitations .................................................................................................................... 25

3.3 Data analysis .................................................................................................................................... 26

4 Results and discussion ............................................................................................................................. 27

4.1 Simulation scenarios ........................................................................................................................ 27

4.1.1 Effect of hysteresis .................................................................................................................. 27

4.1.1.1 Malm ................................................................................................................................. 27

4.1.1.2 Norrkping ........................................................................................................................... 33

4.1.1.3 Petistrsk ............................................................................................................................. 37

4.1.1.4 Effect of time resolution of the meteorological input data on hysteresis .......................... 40

4.1.2 Effect of Temporal variability in rainfall and evaporation....................................................... 42

4.1.3 Effect of geographic location ................................................................................................... 47

5 Conclusions .............................................................................................................................................. 49

6 Recommendations and future work........................................................................................................ 51

References ....................................................................................................................................................... 52

Appendices ...................................................................................................................................................... 54

Appendix A. Matlab codes for averaging the pecipitation .......................................................................... 54

Appendix B. Matlab codes for averaging potential evapotranspiration ..................................................... 57

Appendix C. Calculation of contaminant concentrations ............................................................................ 64

Appendix D. Finding the centre of mass in a 101 vector of concentration values depth ........................... 65

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 Malm, Norrkping, and Petistrsk with half

hourly, 4-hourly, and daily meteoroligical input data ................................................................................. 66

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, 2011).

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 (imnek,

et al., 2009). These two equations are solved numerically using finite difference or finite element methods

(Arampatzis, et al., 2001, imnek, et al., 2009), which requires an iterative implicit technique (Damodhara

Rao, et al., 2006). 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

2

element method. The Richardss equation for variably-saturated water flow and advection-dispersion type

equations (CDE) for heat and solute transport are solved deterministically (imnek, et al., 2009).

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 hysteresis 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 Petistrsk, Norrkping and Malm which are located in north-west, middle-

west 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., 2011).

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 (1996-2008).

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

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 1961-1990 for the study sites is shown on the

Figure 1.2. As data for Malm, Norrkping and Petistrsk

was not available, data from the closest weather stations:

Lund, Linkping and Ume is used. Mean annual

precipitation for the period 1961-1990, for Lund (Malm)

is 655 mm, for Linkping (Norrkping) is 516 mm and for

Ume (Petistrsk) is 650 mm. While mean annual

evapotranspiration for the period 1961-1990, for Lund

(Malm) is 500 mm, for Linkping (Norrkping) is 500

mm and for Ume (Petistrsk) is 350 mm (Raab and

Vedin, 1995).

Petistrsk

Norrkping

Malm

Figure 1.1: Map of Sweden with indicated study sites (Google_maps, 2012)

B

C

4

Figure 1.2: Distribution of precipitation over the year for Lund (a), Linkping (b) and Ume (c). Mean values 1961-1990. Deep blue is rain and light blue is snow (Raab and Vedin, 1995).

a b

c

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, 2006).

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

6

instance, perched water above impermeable soil layer (Simunek and Genuchten, 2006). 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, 2006).

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 is the volumetric water content, [L3L3], t is time [T], q is the volumetric flux density [LT1], zi is the

spatial coordinate [L], and S is a general sink orsource term [L3L3T1], 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 Darcys law was implemented to the partly saturated flow by Buckingham (1907) and he found that

in this case the hydraulic conductivity is a function of water content K=K(). This means that a small

decrease in 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, 2005). Darcys law was developed for an unsaturated medium:

7

2.3

Where h is hydraulic head and defined as:

2.4

Combination of equations 2.3 and 2.1 and is called Richards equation and it describes vertical downward

movement of water in unsaturated zone

2.5

Where H is soil water pressure head relative to atmospheric pressure (H 0).

Richards equation is partially differential and highly non-linear as -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 -H-K are known, numerical solutions may solve the equation for

various top boundary conditions (Dam, et al., 2004).

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], is the angle between the flow direction and the vertical axis (i.e.,

= 00 for vertical flow, 900 for horizontal flow, and 00 < < 900 for inclined flow), and K is the unsaturated

hydraulic conductivity [LT-1] given by (Simunek, et al., 2005).

2.7

where Kr is the relative hydraulic conductivity [-] and Ks the saturated hydraulic conductivity [LT-1].

2.1.1 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 Fickian-

based convection-dispersion equation for solute transport are solved for the entire flow domain.

8

Figure 2.2: Conceptual physical equilibrium model for water flow and solute transport in a single-porosity system (Simunek et al., 2005).

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., 2006).

Porosity of a soil [L3L-3] might be expressed as:

2.8

Where pb is a bulk density of the soil and ps is soils 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. 2.10, but usually for numerous

hydrological applications it is used in non-dimensional form, i.e. eq. 2.10

2.9

2.10

Where, , Vw - water volume,[ L3] Vt - solid volume, [L

3], w is defined as the mass water content and w is the

specific density of water, w1 g/cm3

Soil water content can be also expressed by the degree of saturation S [],

9

2.11

The volumetric water content varies between 0 for dry soil to the saturated water content 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 s and

subtracting residual water content r in eq.2.11, effective saturation Se has been obtained.

2.12

By the way effective saturated water content normally does not reach 100% saturation of the pore space,

due to air invasion (Parlange, et al., 2006).

2.2.1 Soil moisture characteristics

The relationship between soil water suction , H, and the amount of water remaining in the soil or

volumetric soil content () resulting in function known as the moisture characteristic or retention curve in

case of drying soil. It describes soils 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, 2000b).

10

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,

2000b). 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,

2.14

2.15

And

2.16

11

() soil water (retention), which is highly non-linear function of the pressure head, ;; r and 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; is an empirical parameter

assumed to be related to the inverse of the air-entry suction, [L-1]; Se effective saturation [-]; Ks hydraulic

conductivity at natural saturation, [LT-1 ](Simunek, et al., 2005).

2.2.2 Hydraulic conductivity

Another important hydraulic soil property that describes soil water movement is the relation between the

soils unsaturated hydraulic conductivity, K, and volumetric water content, . Hydraulic conductivity reflects

the ability of porous medium to transfer the water. It may be expressed as:

2.17

Where k is intrinsic permeability; krw() is relative water permeability (the ratio of the unsaturated to the

saturated water permeability) that varies from 0 for completely dry soils to 1 for fully saturated soils; and

w is the water viscosity.

Where k is intrinsic permeability; krw() is relative water permeability (the ratio of the unsaturated to the

saturated water permeability) that varies from 0 for completely dry soils to 1 for fully saturated soils; and

w is the water viscosity.

Equation 2.17 demonstrates that hydraulic conductivity depends on size, shape of filled with water pores

(Wang, 2009) and how they are connected between each other, the flowing fluid (w and w ) and water

content of the soil (krw()). Hydraulic conductivity at or above saturation (h0) defined as hydraulic

conductivity at natural saturation (Ks) (Simunek and Genuchten, 2006).

Fullness of pores with water is defined by hysteresis 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, 2006).

12

All previous means that the relation between K and is also a function of water and soil matrix properties,

as well as relation between and H, and is strongly affected by water content and by hysteresis (Parlange,

et al., 2006).

2.2.3 Hysteresis in soil hydraulic properties

A lot of studies were conducted recently to investigate the affect of hysteresis and many of them showed

that hysteresis has an effect on unsaturated soil water movement and solute transport (Russo, et al., 1989,

Yang, et al., 2012, Lehmann, et al., 1998, Kool and Parker, 1987) as well as disregarding hysteresis might

leads to significant errors in prediction of solute movement and contaminant concentrations (Kool and

Parker, 1987).

The main factors which affect hysteresis 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

hysteresis is propagated but the main ones are considered to be ink bottle and contact angle effects

(Ward and Robinson, 2000a).

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, 2000a).

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, 2006).

The entrapped air affects. Some amount of air normally gets trapped in the form of bubbles

enclosed by water, normally occupying approximately 10-30% of pore space. Thus maximum water

content will be 70-90% 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, 2006).

Swelling and shrinkage. Wetting and drying maybe accompanied by swelling and shrinkage for fine

grained clays (Ward and Robinson, 2000a). 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

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, 2000a).

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,

2006).

All this prove that hysteresis 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).

Figure 2.4: Hysteresis in the moisture characteristic (Bouma, 1977)

HYDRUS-1D simulates hysteresis 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. 2.13 using the parameter vectors rd, s

d, md, d, nd and

rw, s

w, mw, w, nw, where w and d mean wetting and drying respectively. The following restrictions are

expected to hold in the applications of HYDRUS-1D:

2.18

Drying

Wetting

14

This means that sd, d ,s

w and d are the only independent parameters for describing hysteresis in soil

moisture characteristics curve. It might also be assumed that there is a little hysteresis in hydraulic

conductivity, so Ksd=Ks

w=Ks and , hence the hysteretic retention curve is described by the

parameters: n, Ks, d, r, s

w.

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() is longitudinal dispersion coefficient. Combined solute and moisture transport equation will

have a form

2.20

The majority of approximate solutions of the eq. 2.20 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. 2.20 can be written as

2.21

The analytical solution of the advectiondispersion is

2.22

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 (imnek, et al., 2009).

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

3.2.1 Input data

3.2.1.1 Meteorological data

Precipitation

Precipitation and evapotranspiration during study period 1996-2008 were given as input for time variable

boundary conditions in HYDRUS-1D. The meteorological data for all the three sites under investigations

(Loddekpinge, Norrkping, and Petistrsk) 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

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, 18:00 until 6:00;

of the diurnal ET was during 8 hours, between 6:00 and 10:00, and between 14:00 and 18:00;

of diurnal ET occurred during 4 hours between 10:00 and 14:00.

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, 19921996. Black dots and lines indicate means and standard deviations (Kirchner, 2009).

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.

0

10

20

30

40

50

0 2 4 6 8 10 12 14 16 18 20 22

Diu

rnal

var

iati

on

of

ET, %

Hour of day

17

3.2.1.2 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, 2002), soil 2 (Zhang, 1991)

and soil 3 have been chosen which are considered to be good representatives of typical Swedish

agricultural soils. Three 250 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/cm3

soil 1

0-20 80 16.5 3.5 1.53

20-45 78.8 18.3 2.9 1.55

45-70 84.3 11.8 3.9 1.55

>70 93.4 4.8 1.8 1.56

soil 2

0-20 68.0 27.2 4.8 1.48

20-150 58.15 32.99 8.86 1.48

>150 40.5 44.6 14.9 1.65

soil 3

0-120 59.0 25.6 15.4 1.45

120-150 36.9 32.8 30.3 1.50

>150 35.3 36.5 28.2 1.60

3.2.1.3 Contaminant sources

The top 5 cm of soil with area 1 m2 with residual phase contamination extending to a depth of 2.5 m below

ground surface was assumed to be contaminated with 100 g of non-volatile and non-reactive solute.

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 0.05 m3 volume

of dry soil was calculated from eq 2.10.

Contaminant

1 m

1 m

5cm

18

Volumetric water content for the soil was calculated according to van Genuchten formula, eq. 2.13. Van

Genuchten hydrodynamic parameters r and s (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 r (v/v) s (v/v) (1/m) n Ks (m/d) I

Soil 1

0-20 0.0388 0.372 0.0437 1.8178 5.01083 0.5

Soil 2

0-20 0.0341 0.3714 0.0383 1.4758 2.69542 0.5

Soil 3

0-120 0.0518 0.3974 0.021 1.4382 1.27167 0.5

Following the initial liquid phase concentrations were obtained for different soil types: Csoil 1=23.2 mg/cm3,

Csoil 2 =13.5 mg/cm3 and Csoil 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 2009, users manual)

19

3.2.2 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 250 cm, representing the average depth of the unsaturated zone in Sweden, see section

3.3.1. The finite element model was constructed by dividing the entire profile into 100 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.

3.2.3 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 1st of March -25th of September was

used for simulation purposes (5000 hours). In HYDRUS-1D code, the maximum number of time variable

records is 10000; therefore, 5000 hours are chosen as simulation period, which consequently means having

10000 records when using half hourly precipitation and evaporation input data. Meanwhile, the period 1st

20

of March -25th 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 2009, users manual)

3.2.4 Water flow

3.2.4.1 Soil hydraulic property model

Within this command window, hydraulic model and hysteresis 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 hysteresis, and then without hysteresis.

21

Figure 3.6: Soil hydraulic property model window (HYDRUS1D 2009, users manual)

3.2.4.2 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 (imnek, et al., 2009). The Rosetta model can be used to estimate water

retention parameters according to van Genuchten (1980), saturated hydraulic conductivity, and

unsaturated hydraulic conductivity parameters according to van Genuchten (1980) 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 mediums 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, 2006). As the model uses basic more easily measured data, it is

considered as a pedotransfer function model (PTFs) (Schaap, et al., 2001).

22

Figure 3.7: Water flow parameters dialog window (HYDRUS-1D 2009, users 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 3.1.

3.2.4.3 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 250 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 2009, users manual).

23

3.2.5 Solutes transport

3.2.5.1 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 2009, users 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.

3.2.5.2 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 3.10).

24

Figure 3.10: Solute transport parameters ((HYDRUS1D 2009, users manual)

3.2.5.3 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 2009, users manual)

25

3.2.6 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;

NOD_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.

3.2.7 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 (1st of March-25th 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 (250 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 hysteresis

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 three-

dimensional 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.

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 NOD_INF.OUT file. Then a MATLAB code (Appendix D) was used to get the variations during study

period (1996-2008) in these two depths across the soil profile. In addition, the masses to ground water

were directly extracted from Solute1.OUT file.

27

4 Results and discussion

4.1 Simulation scenarios

4.1.1 Effect of hysteresis

In this section the effect of hysteresis 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.

4.1.1.1 Malm

During study period (1996-2008) precipitation values vary between 243 mm and 577 mm in the selected

period for simulations (1st of March-24th 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 hysteresis, 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 hysteresis 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

hysteresis. Pickens and Gillham (1980) also reported that for a hypothetical case involving one-

dimensional 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., 2009).

On the other hand, the trend line is steeper when ignoring hysteresis with higher R2 value, which refers to

more rapid response to the precipitation increase and stronger linear relationship between solute

movement and precipitation.

28

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 1996-2008, 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 non-

hysteretic case, and a factor of 4 in hysteretic soil 3 and 5 in non-hysteretic case (Table 4.1).

y = 0.0143x - 0.2274 R = 0.9231

y = 0.0117x - 0.1537 R = 0.8549

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

15 25 35 45 55 65

De

pth

of

CO

M (

m)

Prec. (cm)

Depth of COM vs. precipetation-Malm, 0.5h-soil 3

No hys With hys Linear (No hys) Linear (With hys)

y = 0.0205x - 0.3663 R = 0.9452

y = 0.015x - 0.2421 R = 0.865

0

0.2

0.4

0.6

0.8

1

15 25 35 45 55 65

De

pth

of

CO

M (

m)

Prec. (cm)



y = 0.036x - 0.573 R = 0.8795

y = 0.03x - 0.4753 R = 0.7948

0.0

0.5

1.0

1.5

2.0

15 25 35 45 55 65

De

pth

of

CO

M (

m)

Prec. (cm)



a b

c

29

Table 4.1: Variations in the depth of COM due to precipitation increase in meters for all the three soil types in Malm, for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.

Precipitation (mm)

Soil 1 Soil 2 Soil 3

Hysteresis NO

hysteresis Hysteresis

NO hysteresis

Hysteresis NO

hysteresis

243 0.2543 0.3025 0.1227 0.1323 0.1308 0.1204

577 1.2557 1.5042 0.6234 0.8166 0.5214 0.5977

When evaluating the effect of hysteresis 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., 2006).

Table 4.2: The average depths of COM in meters for all the three soil types in Malm, for the period 1996-2008, for both hysteretic and non-hysteretic systems.

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 450 mm in soil 1, and 570 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/cm3 for all the three soil types in Malm, for the period 1996-2008, for

both hysteretic and non-hysteretic soil waters.

Precipitation (mm)


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

450 0.002 0.007 0 0 0 0

577 0.164 0.175 0.00673 0.0143 0.00066 0.0024


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

0.6192 0.739 0.3033 0.381 0.2726 0.295

30

Figure 4.2: Scatter plot of masses into GW versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the

period 1996-2008, for both non-hysteretic (green triangular dots) and hysteretic (red circular dots) simulations.

Generally the leaching of solutes is less in hysteretic case (Table 4.3 and Table 4.4), which in turn indicates

more retardation of solute transport relative to the movement predicted if the soil water system is

considered as non-hysteretic (Russo, et al., 1989, Henry, et al., 2002).

It is well known that the downward migration of solutes in fine soils is slower compared to coarse textured

soils due to lower hydraulic conductivity in finer ones. This means that the amount of solutes leaching into

the ground water in the soil 2 and soil 3 is less than that of soil 1(Table 4.4). It can be seen that the

relationship between mass into GW and precipitation is not linear, though it shows a linear response after

the threshold value in soil 1. It can also be noticed that leaching occurs at the highest precipitation value in

soil 2 and soil 3 during study period; therefore, the trend is not clear beyond this value.

0

0.0005

0.001

0.0015

0.002

0.0025

15 25 35 45 55 65

Mas

s in

to G

W m

g/cm

3

prec. (cm)

Mass into GW vs. precipetation-Malm, 0.5h-soil 3

No hys With hys

0

0.005

0.01

0.015

15 25 35 45 55 65

Mas

s in

to G

W m

g/cm

3

prec. (cm)

Mass into GW vs. precipetation-Malm, 0.5h-soil 2

No hys With hys

0 0.02 0.04 0.06 0.08

0.1 0.12 0.14 0.16 0.18

0.2

15 25 35 45 55 65

Mas

s in

to G

W, m

g/cm

3

prec. (cm)

Mass into GW vs. precipetation-Malm, 0.5 h-soil 1

No hys With hys

a b

c

31

Table 4.4: The average masses of solutes leached into the GW in mg/cm3 for all the three soil types in Malm, for the

period 1996-2008, for both hysteretic and non-hysteretic soil waters.


Hysteresis NO

hysteresis Hysteresis NO hysteresis Hysteresis

NO hysteresis

1.48E-02 2.23E-02 5.18E-04 1.11E-03 5.05E-05 1.81E-04

Since under current precipitation values there is little or no leaching of solutes into the GW, It could be

useful to evaluate the variations in the depth to LC. Figure 4.3 shows variations in the depth of LC against

precipitation, as mentioned in section 3.3 that the limit value was set to 0.2 mg/cm3. The maximum and

minimum values of depth to LC are presented in Table 4.5. It is evident that the depth to this limit value is

deeper without hysteresis. The variations in the depth of LC due to precipitation increase do not give a

strong linear response, where the R2 values are relatively low for both water systems in all the soil profiles.

This could be due to the fact that the precipitation is considered as the only independent variable in the

simple linear regression while there are many other factors affecting downward movement of solutes,

though precipitation is the dominant one. On the other hand, a non-linear (decreasing) tendency is more

obvious beyond 450 mm of precipitation in all the three soils. These findings illustrate the complex nature

of water and solute movement in the unsaturated zone.

Table 4.5: The maximum and minimum depths to LC in meters for all the three soil types in Malm, for the period 1996-2008, for both hysteretic and non-hysteretic simulations


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

0.7538 0.9753 0.6283 0.6508 0.5764 0.5501

2.25 2.3002 0.9016 1.0254 0.7758 0.8256

32

Figure 4.3: The depth to the LC versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the period 1996-2008, for both non-hysteretic (green triangular dots) and hysteretic (red circular dots) simulations

Table 4.6 gives the average depths to LC for all the soils in Malm. Once again, the effect of hysteresis in

different soil types is investigated. The depth of LC is found to be deeper in non-hysteretic model by 10% in

soil 1, 6% in soil 2, and 2% in soil 3. It is clear that the effect is more pronounced in coarse soil (soil 1) than

in the finer soils (soil 2 and soil 3) (Parlange, et al., 2006).

Table 4.6: The average depths to LC in meters for all the three soil types in Malm, for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

1.4931 1.6352 0.7919 0.8394 0.6897 0.7048

y = 0.0067x + 0.4444 R = 0.5779

y = 0.0088x + 0.3832 R = 0.6286

0.4

0.5

0.6

0.7

0.8

0.9

1

15.00 25.00 35.00 45.00 55.00 65.00

De

pth

to

LC

(m

)

Precipitation, cm

LC depth vs precipitation-Malmo, 0.5h-soil 3

with hysteresis no hysteresis Linear (with hysteresis) Linear (no hysteresis)

y = 0.0081x + 0.4976 R = 0.5718

y = 0.0125x + 0.3824 R = 0.6717

0.4 0.5 0.6 0.7 0.8 0.9

1 1.1 1.2

15.00 25.00 35.00 45.00 55.00 65.00

De

pth

to

LC

(m

)

Precipitation, cm

LC depth vs precipitation-Malmo, 0.5h-soil 2

with hysteresis no hysteresis

Linear (with hysteresis) Linear (no hysteresis)

y = 0.0398x + 0.0443 R = 0.6402

y = 0.0417x + 0.117 R = 0.7496

0.4

0.9

1.4

1.9

2.4

2.9

15.00 25.00 35.00 45.00 55.00 65.00

De

pth

to

LC

(m

)

Precipitation, cm

LC depth vs precipitation- Malm,0.5h-soil 1



a

c

b

33

4.1.1.2 Norrkping

To investigate the effects of hysteresis on the transport process of solutes in this location, the same soil

profiles were used in the model, but using measured precipitation in Norrkping. In this part only the depth

of COM and masses leached into the ground water are presented and discussed, but the graphs of the

depth to LC can be found in Appendix E.

The depth of COM versus measured precipitation plots of Figure 4.5 show a different pattern compared to

the same soil profiles in Maml and Petistrsk. The relationship between precipitation and depth of COM is

unclear (non-linear). This could be attributed, at least partially, to the precipitation pattern. For this reason,

two years (2003 and 2006) are selected to investigate the effect of precipitation pattern for soil 1 for the

hysteretic simulation case. These two years are chosen because the difference in precipitation between

them is very small (34.44 cm in 2003 and 34.99 cm in 2006), but the difference in depth to COM is relatively

big (0.2787 m in 2003 and 0.8861 m in 2006). As evident from Figure 4.4, more intense precipitations were

occurred in 2006 compared to 2003. The intensity exceeded 1.5 cm/hr at 6 rainfall occasions in 2006 while

in 2003 there are no such intensities, and 1.0 cm/hr precipitations exceeded at 12 occasions in 2006 while

only 4 times in 2003.

Figure 4.4: shows half hourly precipitations in 2003 (a) and 2006 (b) in Norrkping during 5000 hours of simulation.

0

0.5

1

1.5

Inte

nsi

ty c

m/h

r)

Time

Half hourly precipitation-Norrkoping, 2003

0 0.5

1 1.5

2 2.5

Inte

nsi

ty (

cm/h

r)

Time

Half hourly precipitation -Norrkoping, 2006

a

b

34

However, to better understand the implications of precipitation pattern in all the sites on the downward

movement of water and solutes, more investigation is required.

Figure 4.5: The depth of COM versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the period 1996-2008, for both non-hysteretic (green triangular dots) and hysteretic (red circular dots) simulations.

To quantitatively illustrate the effect of hysteresis in soil profiles, The maximum and minimum, depths of

COM in meters for all the three soil types in Norrkping, for the period 1996-2008, for both hysteretic and

non-hysteretic simulations are presented in Table 4.7.

y = 0.0059x + 0.0127 R = 0.1697

y = 0.009x - 0.0664 R = 0.2391

0

0.1

0.2

0.3

0.4

0.5

20.00 25.00 30.00 35.00 40.00 45.00

De

pth

of

CO

M (

m)

Precipitation, cm

Deth of COM vs precipitation-Norrkping, 0.5h-soil 3


y = 0.0116x - 0.137 R = 0.307

y = 0.0157x - 0.2288 R = 0.4542

0

0.1

0.2

0.3

0.4

0.5

20.00 25.00 30.00 35.00 40.00 45.00

De

pth

of

CO

M (

m)

Precipitation, cm




y = 0.0304x - 0.5598 R = 0.3141

y = 0.0407x - 0.7563 R = 0.6049

0

0.2

0.4

0.6

0.8

1

1.2

20.00 25.00 30.00 35.00 40.00 45.00

De

pth

of

CO

M (

m)

Precipitation, cm



a b

c

35

Table 4.7: The maximum and minimum depths of COM in meters for all the three soil types in Norrkping, for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

0.2787 0.3745 0.1887 0.6774 0.1721 0.1863

0.8333 1.0043 0.4299 1.0012 0.3612 0.4044

The precipitation varies between 288 mm and 409 mm in the selected simulation period (1st of March-25th

of September) during 13 years of study period. The relationship between COM and precipitation is not

deterministic; therefore, the minimum depth of COM does not necessarily correspond to the minimum

precipitation.

However, an evaluation of the effect of hysteresis on the downward migration of solutes is done by a

comparing the average depth of COM in all the soils (Table 4.8).

Table 4.8: The average depths of COM in meters for all the three soil types in Norrkping, for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

0.4818 0.6398 0.2601 0.3082 0.2135 0.2407

It is found that the depth of COM is deeper in non-hysteretic system by 33% in soil 1, 18% in soil 2, and 13%

in soil 3. This indicates that the differences are most pronounced in coarse textured soils (Parlange, et al.,

2006, Ward and Robinson, 2000a).

One can observe that the leaching masses are very small in this site, but still there are very small masses

seeping into the GW beyond some threshold precipitation value especially in soil 1. It can be noticed from

Figure 4.6 that the threshold precipitation is around 350 mm in all the soil types. However, the leaching

masses are different among soil types with different patterns beyond the threshold precipitation value. For

the soil 1, an unclear pattern is dominant beyond the threshold value despite a decreasing trend after the

peak mass. On the other hand, in the other two soils there is almost no leaching under current precipitation

values, though there are some small masses leached into the GW at 350 mm of precipitation.

36

Figure 4.6: Masses into GW versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the period 1996-2008, for both non-hysteretic (green triangular dots) and hysteretic (red circular dots) simulations.

Regarding the effect of hysteresis, it is obvious that leaching is higher in non-hysteretic simulations in all

the soil types (Table 4.9 and Table 4.10).

Table 4.9: The average masses of solutes leached into the GW in mg/cm3 for all the three soil types in Norrkping, for

the period 1996-2008, for both hysteretic and non-hysteretic soil waters.


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

3.34E-03 6.83E-03 3.647E-07 1.771E-06 3.465E-14 2.567E-11

As mentioned previously that the solute concentrations at the groundwater table at the end of the the

simulation period are very small, the maximum masses are presented below in Table 4.10.

0

5E-11

1E-10

1.5E-10

2E-10

2.5E-10

3E-10

3.5E-10

20.00 25.00 30.00 35.00 40.00 45.00

Mas

s in

to t

he

GW

(m

g/cm

3 )

Precipitation, cm

Mass into GW vs precipitation, Norrkoping soil 3 0.5h


0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

20.00 25.00 30.00 35.00 40.00 45.00

Mas

s in

to t

he

GW

(m

g/cm

3)

Precipitation, cm

Mass into GW vs precipitation- Norrkping , 0.5h-soil 2


0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

20.00 25.00 30.00 35.00 40.00 45.00

Mas

s in

to t

he

GW

(m

g/cm

3 )

Precipitation, cm

Mass into GW vs precipitation- Norrkping , 0.5h-soil 1


a b

c

37

Table 4.10: The maximum masses of solutes into the GW in mg/cm3 for all the three soil types in Norrkping, for the



Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

2.21E-02 3.68E-02 4.70E-06 2.10E-05 2.15E-13 3.33E-10

4.1.1.3 Petistrsk

Figure 4.7 gives an overview of the depth of COM plotted against measured precipitations in all the three

soil profiles (soil 1, soil 2, and soil 3) in this site. In all the three soil types the depth to COM is deeper when

neglecting hysteresis. However, the differences decrease in soil 3 and soil 2 compared to soil 1.

In Petistrsk, precipitation varies between 270 mm and 500 mm during study period (1996-2008). In the

soil 1, the depth of COM varies between 0.3638 m and 1.3566 m in hysteretic water system, and between

0.4899 m to 1.4537 m in non- hysteretic one (Table 4.11).

Table 4.11: The maximum and minimum depths of COM in meters for all the three soil types in Petistrsk, for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.

Precipitation (mm)


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

27(96) 0.3638 0.4899 0.2024 0.2607 0.1832 0.1998

50(2004) 1.3566 1.4537 0.8263 0.8525 0.6493 0.7022

When comparing between different soil types, on average, the depth of COM is deeper in non-hysteretic

system by 16% in soil 1, 12% in soil 2, and 6% in soil 3 (Table 4.12). From this comparison , one can conclude

that the effect of hysteresis decreases in fine textured soils compared to coarser ones (Parlange, et al.,

2006, Ward and Robinson, 2000a).

Table 4.12: The average depths of COM in meters for all the three soil types in Petistrsk, for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

0.8285 0.9607 0.4511 0.5071 0.3813 0.4025

38

Figure 4.7: The depth of centre of mass of solutes versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the period 1996-2008, for both non-hysteretic (green triangular dots) and hysteretic (red circular dots) simulations.

It is apparent from Figure 4.8 that the leaching of solutes again occurs beyond a threshold precipitation

value in all the soil types. It is found that the threshold value is around 370 mm in both soil 1 and soil 2, and

around 405 mm in soil 3. However, the pattern beyond the threshold value is different among the soil

types. For the soil 1, the leaching is increasing almost linearly with increasing precipitation, but in the other

two soil types, even with increasing precipitation, a decreasing trend in the masses leached into the GW

could be seen after peak values.

y = 0.0158x - 0.1726 R = 0.7754

y = 0.0143x - 0.1396 R = 0.7358

0

0.15

0.3

0.45

0.6

0.75

15 25 35 45 55

De

pth

of

CO

M (

m)

Prec. (cm)

Depth of COM vs. precipetation- Petistrsk, 0.5h-soil 3

No hys With hys

Linear (No hys) Linear (With hys)

y = 0.0203x - 0.2342 R = 0.8266

y = 0.0189x - 0.2386 R = 0.7733

0

0.15

0.3

0.45

0.6

0.75

0.9

15 25 35 45 55

De

pth

of

CO

M (

m)

Prec. (cm)

Depth of COM vs. precipetation-

Petistrsk, 0.5h-soil 2

No hys With hys


y = 0.0331x - 0.2455 R = 0.8329

y = 0.0321x - 0.3464 R = 0.7183

0

0.3

0.6

0.9

1.2

1.5

1.8

15 25 35 45 55

De

pth

of

CO

M (

m)

Prec. (cm)

Depth of COM vs. precipetation- Petistrsk, 0.5h-soil 1

No hys With hys


a b

c

39

Figure 4.8: Mass into the GW versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the period 1996-

2008, for both non-hysteretic (green triangular dots) and hysteretic (red circular dots) simulations.

Though the leaching masses are small, but still they are higher in non-hysteretic simulations. The average

concentration of solutes at the groundwater table can be seen below in Table 4.13.

Table 4.13: The average masses of solutes leached into GW in mg/cm3 for all the three soil types in Petistrsk, for the



Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

2.86E-02 4.76E-02 5.13E-05 2.33E-03 7.25E-07 1.41E-06

The maximum masses seeped into the GW in all the soil types in this site are presented below in Table 4.14.

0

3E-06

6E-06

9E-06

1.2E-05

1.5E-05

1.8E-05

15 25 35 45 55

Mas

s in

to G

W m

g/cm

3

prec. (cm)

Mass into GW vs. precipetation-Petistrsk, 0.5h-soil 3

No hys With hys

0

0.0003

0.0006

0.0009

0.0012

15 25 35 45 55

Mas

s in

to G

W m

g/cm

3

prec. (cm)

Mass into GW vs. precipetation- Petistrsk, 0.5h-soil 2

No hys With hys

0

0.03

0.06

0.09

0.12

0.15

0.18

15 25 35 45 55

Mas

s in

to G

W m

g/cm

3

prec. (cm)

Mass into GW vs. precipetation- Petistrsk, 0.5h-soil 1

No hys With hys

a b

c

40

Table 4.14: The maximum masses of solutes leached into the GW in mg/cm3 for all the three soil types in Petistrsk,

for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

9.59E-02 1.47E-01 3.12E-04 9.59E-04 9.40E-06 1.51E-05

4.1.1.4 Effect of time resolution of the meteorological input data on hysteresis

The importance of time resolution of the input data on hysteresis is illustrated by investigating the depth of

COM in all the three sites for the three soil profiles under investigation (Table 4.15). Shown are the average

depths to COM with half hourly, 4-hourly, and daily input data during study period. The results show that

the differences between hysteretic and non-hysteretic simulations decrease with decreasing time

resolution of the input data. In Table 4.16, the average depth of COM in non-hysteretic simulations are

compared to hysteretic case, it seems that the differences between hysteretic and non-hysteretic

simulations are disappeared when using daily input data. Figure 4.9 shows the depth of COM against

precipitation in soil 1 in Malm for only half hourly and daily input data, but the graphs for all the other

time resolutions for all soil profiles in the three sites are presented in Appendix E.

Figure 4.9: Shows the effect of input data resolution on hysteresis, half hourly data (a) compared to daily data (b)

It is expected to have less variation in the soil moisture when using averaged daily input data. In other

words, the effect of moisture history of the soil will be vanished over short time periods (hours), which play

an important role when finding water content at a specific suction. This means that the effect of hysteresis

y = 0.036x - 0.573 R = 0.8795

y = 0.03x - 0.4753 R = 0.7948

0

0.5

1

1.5

2

15 25 35 45 55 65

De

pth

of

CO

M (

m)

Prec. (cm)

Depth of COM vs. precipetation-Malm, 0.5 h-soil 1

No hys With hys


y = 0.0356x - 0.6305 R = 0.8669

y = 0.0353x - 0.5945 R = 0.8403

0

0.5

1

1.5

2

15 25 35 45 55 65

De

pth

of

CO

M (

m)

Prec. (cm)

Depth of COM vs. precipetation-Malm, 24 h-soil 1

No hys With hys


a b

41

will not be that important, since the mechanism of hysteresis is more pronounced over short time periods

(hours).

Table 4.15: The average depths of COM in meters with half hourly, 4-hourly, and daily input data in all the three sites (Malm, Norrkping, and Petistrsk), for all the soils, for the period 1996-2008. The numbers between parentheses are maximum and minimum precipitations during study period

Timestep

Malm (243-577)


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

Half-hourly input data

0.6192 0.739 0.3033 0.381 0.2726 0.295

4-hourly input data

0.6146 0.7248 0.3392 0.3940 0.2798 0.2927

Daily input data

0.6929 0.6693 0.3590 0.3628 0.2966 0.2872

Norrkping (288-409)

Timestep Soil 1 Soil 2 Soil 3

Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis


0.4818 0.6398 0.2601 0.3082 0.2135 0.2407

4-hours input data

0.5500 0.6177 0.2763 0.3029 0.2377 0.2391

Daily input data

0.5329 0.5404 0.2752 0.2853 0.2338 0.2304

Petistrsk (270-500)


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis


0.8285 0.9607 0.4511 0.5071 0.3813 0.4025

4-hours input data

0.8559 0.9484 0.4561 0.5035 0.3804 0.3979

Daily input

data 0.9111 0.9080 0.4927 0.4906 0.3917 0.3933

42

Table 4.16: Average depth of COM in non-hysteretic simulations compared to average depth of COM in hysteretic simulations

Timestep

Malm (243-577)


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis


1 1.19 1 1.26 1 1.08

4-hours input data

1 1.18 1 1.16 1 1.05

Daily input data

1 0.97 1 1.01 1 0.97

Norrkping (288-409)


Hysteresis NO


NO hysteresis

Hysteresis NO

hysteresis

Documents

Modeling of Solute Transport in the Unsaturated Zone Using HYDRUS-1D