Examensarbete
TVVR 12/5020
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
Division of Water Resources Engineering
Department of Building and Environmental Technology
Lund University
Avdelningen för Teknisk Vattenresurslära
TVVR-12/5020
ISSN-1101-9824
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
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 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 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 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 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
2
Introduction ............................................................................................................................................... 1
1.1
Background ........................................................................................................................................ 1
1.2
Objectives .......................................................................................................................................... 2
1.3
Study area .......................................................................................................................................... 2
Background Theory.................................................................................................................................... 5
2.1
Water Flow in Unsaturated Zone ...................................................................................................... 6
2.1.1
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
3
Flow in single-porosity system .................................................................................................. 7
Solute transport............................................................................................................................... 14
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
3.2.6
Outputs .................................................................................................................................... 25
3.2.7
Model limitations .................................................................................................................... 25
3.3
4
Solute transport boundary conditions ................................................................................ 24
Data analysis .................................................................................................................................... 26
Results and discussion ............................................................................................................................. 27
4.1
Simulation scenarios........................................................................................................................ 27
4.1.1
Effect of hysteresis .................................................................................................................. 27
4.1.1.1
Malmö ................................................................................................................................. 27
4.1.1.2
Norrköping ........................................................................................................................... 33
4.1.1.3
Petisträsk ............................................................................................................................. 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 Malmö, Norrköping, and Petisträsk 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 (Šimůnek,
et al., 2009). These two equations are solved numerically using finite difference or finite element methods
(Arampatzis, et al., 2001, Šimůnek, 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 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., 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 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., 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).
Petisträsk
C
Approximate distribution of precipitation during the
years 1961-1990 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 1961-1990, for Lund (Malmö)
is 655 mm, for Linköping (Norrköping) is 516 mm and for
Umeå (Petisträsk) is 650 mm. While mean annual
Norrköping
B
evapotranspiration for the period 1961-1990, for Lund
(Malmö) is 500 mm, for Linköping (Norrköping) is 500
mm and for Umeå (Petisträsk) is 350 mm (Raab and
Malmö
Figure ‎1.1: Map of Sweden with indicated study sites
(Google_maps, 2012)
Vedin, 1995).
4
b
a
c
Figure ‎1.2: Distribution of precipitation over the year for Lund (a), Linköping (b) and Umeå (c). Mean values 1961-1990. Deep
blue is rain and light blue is snow (Raab and Vedin, 1995).
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 θ is the volumetric water content, [L3L−3], t is time [T], q is the volumetric flux density [LT−1], zi is the
spatial coordinate [L], and S is a general sink orsource term [L3L−3T−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 (1907) 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, 2005). Darcy’s 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 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., 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], α is the angle between the flow direction and the vertical axis (i.e.,
α = 00 for vertical flow, 900 for horizontal flow, and 00 < α < 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 Fickianbased 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 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. ‎2.10, 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, [L3], w is defined as the mass water content and ρw is the
specific density of water, ρw≈1 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 θs, 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 θs and
subtracting residual water content θr 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 (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, 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
θ(ψ) – soil water (retention), which is highly non-linear function of the pressure head, ψ;; θr and θs 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]; 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
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; krw(θ) 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
μw is the water viscosity.
Where k is intrinsic permeability; krw(θ) 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
μw 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 (μw and ρw ) and water
content of the soil (krw(θ)). Hydraulic conductivity at or above saturation (h≥0) 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 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 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).
Drying
Wetting
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 θrd, θsd, θmd, αd, nd and
θrw, θsw, θmw, αw, 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
14
This means that θsd, αd ,θsw and αd 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=Ksw=Ks and
, hence the hysteretic retention curve is described by the
parameters: n, Ks, αd, θr, θsw.
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
‎2.20
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 advection–dispersion 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 (Šimůnek, 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
(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
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;

½ of the diurnal ET was during 8 hours, between 6:00 and 10:00, and between 14:00 and 18:00;

½ of diurnal ET occurred during 4 hours between 10:00 and 14:00.
Diurnal variation of ET, %
50
40
30
20
10
0
0 2 4 6 8 10 12 14 16 18 20 22
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, 1992–1996. 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.
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.
1m
1m
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 0.05 m 3 volume
of dry soil was calculated from eq ‎2.10.
18
Volumetric water content for the soil was calculated according to van Genuchten formula, eq. ‎2.13. 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
θr (v/v)
θs (v/v)
α (1/m)
n
Ks (m/d)
I
0.0388
0.372
0.0437
1.8178
5.01083
0.5
0.0341
0.3714
0.0383
1.4758
2.69542
0.5
0.0518
0.3974
0.021
1.4382
1.27167
0.5
Soil 1
0-20
Soil 2
0-20
Soil 3
0-120
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/cm3, 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, user’s 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, user’s 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, user’s 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 (Šimůnek, 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 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, 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, 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 ‎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, user’s 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, 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.
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, user’s 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, user’s 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 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.
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 Malmö
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 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., 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.
Depth of COM vs. precipetationMalmö, 0.5h-soil 3
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Depth of COM vs. precipetationMalmö, 0.5h-soil 2
1
y = 0.0143x - 0.2274
R² = 0.9231
y = 0.0117x - 0.1537
R² = 0.8549
Depth of COM (m)
Depth of COM (m)
28
0.8
y = 0.0205x - 0.3663
R² = 0.9452
0.6
0.4
y = 0.015x - 0.2421
R² = 0.865
0.2
0
15
25
35
No hys
Linear (No hys)
45
Prec. (cm)
55
15
65
With hys
Linear (With hys)
25
35
No hys
Linear (No hys)
a
Prec. (cm)
55
65
With hys
Linear (With hys)
b
2.0
Depth of COM (m)
45
Depth of COM vs. precipetationMalmö, 0.5h-soil 1
y = 0.036x - 0.573
R² = 0.8795
1.5
1.0
y = 0.03x - 0.4753
R² = 0.7948
0.5
0.0
15
25
35
45
55
65
Prec. (cm)
No hys
Linear (No hys)
With hys
Linear (With hys)
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 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 nonhysteretic case, and a factor of 4 in hysteretic soil 3 and 5 in non-hysteretic case (Table ‎4.1).
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 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Soil 2
Precipitation
(mm)
Hysteresis
243
0.2543
NO
hysteresis
0.3025
577
1.2557
1.5042
Soil 3
0.1227
NO
hysteresis
0.1323
0.6234
0.8166
Hysteresis
0.1308
NO
hysteresis
0.1204
0.5214
0.5977
Hysteresis
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 Malmö, for the period 1996-2008, for
both hysteretic and non-hysteretic systems.
Soil 1
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
0.6192
0.739
0.3033
0.381
0.2726
0.295
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.
3
Table ‎4.3: The masses of solutes into GW in mg/cm for all the three soil types in Malmö, for the period 1996-2008, for
both hysteretic and non-hysteretic soil waters.
Soil 1
Precipitation
(mm)
Hysteresis
450
577
0.002
0.164
NO
hysteresis
0.007
0.175
Soil 2
Hysteresis
0
0.00673
NO
hysteresis
0
0.0143
Soil 3
Hysteresis
0
0.00066
NO
hysteresis
0
0.0024
30
Mass into GW vs. precipetationMalmö, 0.5h-soil 3
Mass into GW mg/cm3
Mass into GW mg/cm3
0.0025
0.002
0.0015
0.001
0.0005
0
15
25
35
45
55
Mass into GW vs. precipetationMalmö, 0.5h-soil 2
0.015
0.01
0.005
0
65
15
prec. (cm)
No hys
25
35
45
55
65
prec. (cm)
No hys
With hys
b
Mass into GW, mg/cm3
a
With hys
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Mass into GW vs. precipetationMalmö, 0.5 h-soil 1
15
25
35
45
55
65
prec. (cm)
No hys
With hys
c
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.
31
3
Table ‎4.4: The average masses of solutes leached into the GW in mg/cm for all the three soil types in Malmö, for the
period 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Soil 2
NO
hysteresis
2.23E-02
Hysteresis
1.48E-02
Soil 3
Hysteresis
NO hysteresis
Hysteresis
5.18E-04
1.11E-03
5.05E-05
NO
hysteresis
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 Malmö, for the period
1996-2008, for both hysteretic and non-hysteretic simulations
Soil 1
Hysteresis
0.7538
2.25
NO
hysteresis
0.9753
2.3002
Soil 2
Hysteresis
0.6283
0.9016
NO
hysteresis
0.6508
1.0254
Soil 3
Hysteresis
0.5764
0.7758
NO
hysteresis
0.5501
0.8256
32
1
y = 0.0088x + 0.3832
0.9
R² = 0.6286
0.8
0.7
y = 0.0067x + 0.4444
0.6
R² = 0.5779
0.5
0.4
15.00 25.00 35.00 45.00 55.00 65.00
LC depth vs precipitation-Malmo, 0.5hsoil 2
Depth to LC (m)
Depth to LC (m)
LC depth vs precipitation-Malmo, 0.5hsoil 3
Precipitation, cm
with hysteresis
Linear (with hysteresis)
1.2
1.1
y = 0.0125x + 0.3824
1
R² = 0.6717
0.9
0.8
0.7
y = 0.0081x + 0.4976
0.6
R² = 0.5718
0.5
0.4
15.00 25.00 35.00 45.00 55.00 65.00
Precipitation, cm
with hysteresis
Linear (with hysteresis)
no hysteresis
Linear (no hysteresis)
a
no hysteresis
Linear (no hysteresis)
b
Depth to LC (m)
2.9
LC depth vs precipitation- Malmö,0.5hsoil 1
y = 0.0417x + 0.117
R² = 0.7496
2.4
1.9
1.4
y = 0.0398x + 0.0443
R² = 0.6402
0.9
0.4
15.00
25.00
35.00
45.00
55.00
65.00
Precipitation, cm
with hysteresis
no hysteresis
Linear (with hysteresis)
Linear (no hysteresis)
c
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 Malmö. 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 Malmö, for the period 1996-2008, for both
hysteretic and non-hysteretic soil waters.
Soil 1
Hysteresis
1.4931
NO
hysteresis
1.6352
Soil 2
Hysteresis
0.7919
NO
hysteresis
0.8394
Soil 3
Hysteresis
0.6897
NO
hysteresis
0.7048
33
4.1.1.2 Norrköping
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 Norrköping. 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 Mamlö and Petisträsk. 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.
Intensity cm/hr)
Half hourly precipitation-Norrkoping, 2003
a
1.5
1
0.5
0
Time
Intensity (cm/hr)
Half hourly precipitation -Norrkoping, 2006
b
2.5
2
1.5
1
0.5
0
Time
Figure ‎4.4: shows half hourly precipitations in 2003 (a) and 2006 (b) in Norrköping during 5000 hours of simulation.
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.
Deth of COM vs precipitation-Norrköping,
0.5h-soil 3
0.4
0.5
y = 0.009x - 0.0664
R² = 0.2391
0.3
Depth of COM (m)
Depth of COM (m)
0.5
0.2
y = 0.0059x + 0.0127
R² = 0.1697
0.1
0
20.00
25.00
30.00
35.00
40.00
45.00
y = 0.0157x - 0.2288
R² = 0.4542
0.4
0.3
0.2
y = 0.0116x - 0.137
R² = 0.307
0.1
0
20.00
25.00
30.00
35.00
40.00
45.00
Precipitation, cm
Precipitation, cm
with hysteresis
Linear (with hysteresis)
Deth of COM vs precipitation-Norrköping,
0.5h-soil 2
with hysteresis
Linear (with hysteresis)
no hysteresis
Linear (no hysteresis)
a
no hysteresis
Linear (no hysteresis)
b
Deth of COM vs precipitation-Norrköping,
0.5h-soil 1
Depth of COM (m)
1.2
1
0.8
y = 0.0407x - 0.7563
R² = 0.6049
0.6
y = 0.0304x - 0.5598
R² = 0.3141
0.4
0.2
0
20.00
25.00
30.00
35.00
40.00
45.00
Precipitation, cm
with hysteresis
Linear (with hysteresis)
no hysteresis
Linear (no hysteresis)
c
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 Norrköping, for the period 1996-2008, for both hysteretic and
non-hysteretic simulations are presented in Table ‎4.7.
35
Table ‎4.7: The maximum and minimum depths of COM in meters for all the three soil types in Norrköping, for the
period 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Soil 2
0.2787
NO
hysteresis
0.3745
0.8333
1.0043
Hysteresis
Soil 3
0.1887
NO
hysteresis
0.6774
0.4299
1.0012
Hysteresis
0.1721
NO
hysteresis
0.1863
0.3612
0.4044
Hysteresis
The precipitation varies between 288 mm and 409 mm in the selected simulation period (1 st 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 Norrköping, for the period 1996-2008,
for both hysteretic and non-hysteretic soil waters.
Soil 1
Hysteresis
0.4818
NO
hysteresis
0.6398
Soil 2
Hysteresis
0.2601
NO
hysteresis
0.3082
Soil 3
Hysteresis
0.2135
NO
hysteresis
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.
Mass into GW vs precipitation,
Norrkoping soil 3 0.5h
3.5E-10
3E-10
2.5E-10
2E-10
1.5E-10
1E-10
5E-11
0
20.00 25.00 30.00 35.00 40.00 45.00
Mass into the GW (mg/cm3)
Mass into the GW (mg/cm3)
36
Mass into GW vs precipitationNorrköping , 0.5h-soil 2
2.50E-05
2.00E-05
1.50E-05
1.00E-05
5.00E-06
0.00E+00
20.00 25.00 30.00 35.00 40.00 45.00
Precipitation, cm
with hysteresis
no hysteresis
Precipitation, cm
with hysteresis
no hysteresis
b
Mass into the GW (mg/cm3)
a
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
20.00
Mass into GW vs precipitationNorrköping , 0.5h-soil 1
25.00
30.00
35.00
40.00
45.00
Precipitation, cm
with hysteresis
no hysteresis
c
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).
3
Table ‎4.9: The average masses of solutes leached into the GW in mg/cm for all the three soil types in Norrköping, for
the period 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Hysteresis
3.34E-03
NO
hysteresis
6.83E-03
Soil 2
Hysteresis
3.647E-07
NO
hysteresis
1.771E-06
Soil 3
Hysteresis
3.465E-14
NO
hysteresis
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.
37
3
Table ‎4.10: The maximum masses of solutes into the GW in mg/cm for all the three soil types in Norrköping, for the
period 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Hysteresis
2.21E-02
Soil 2
NO
hysteresis
3.68E-02
Soil 3
NO
hysteresis
2.10E-05
Hysteresis
4.70E-06
NO
hysteresis
3.33E-10
Hysteresis
2.15E-13
4.1.1.3 Petisträsk
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 Petisträsk, 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 Petisträsk, for the
period 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Precipitation
(mm)
Hysteresis
27(96)
50(2004)
0.3638
1.3566
Soil 2
NO
hysteresis
0.4899
1.4537
Hysteresis
0.2024
0.8263
Soil 3
NO
hysteresis
0.2607
0.8525
Hysteresis
0.1832
0.6493
NO
hysteresis
0.1998
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 Petisträsk, for the period 1996-2008,
for both hysteretic and non-hysteretic soil waters.
Soil 1
Hysteresis
0.8285
NO
hysteresis
0.9607
Soil 2
Hysteresis
0.4511
NO
hysteresis
0.5071
Soil 3
Hysteresis
0.3813
NO
hysteresis
0.4025
38
Depth of COM vs. precipetationPetisträsk, 0.5h-soil 3
Depth of COM vs. precipetationPetisträsk, 0.5h-soil 2
Depth of COM (m)
Depth of COM (m)
0.75
y = 0.0158x - 0.1726
R² = 0.7754
0.6
0.45
0.3
y = 0.0143x - 0.1396
R² = 0.7358
0.15
0
15
25
35
45
Prec. (cm)
No hys
Linear (No hys)
0.9
0.75
0.6
0.45
0.3
0.15
0
y = 0.0203x - 0.2342
R² = 0.8266
y = 0.0189x - 0.2386
R² = 0.7733
15
55
25
35
45
55
Prec. (cm)
With hys
Linear (With hys)
No hys
Linear (No hys)
a
With hys
Linear (With hys)
b
Depth of COM vs. precipetationPetisträsk, 0.5h-soil 1
Depth of COM (m)
1.8
y = 0.0331x - 0.2455
R² = 0.8329
1.5
1.2
0.9
0.6
y = 0.0321x - 0.3464
R² = 0.7183
0.3
0
15
25
No hys
Linear (No hys)
35
Prec. (cm)
45
55
With hys
Linear (With hys)
c
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.
Mass into GW vs. precipetationPetisträsk, 0.5h-soil 3
1.8E-05
Mass into GW vs. precipetationPetisträsk, 0.5h-soil 2
0.0012
Mass into GW mg/cm3
Mass into GW mg/cm3
39
1.5E-05
1.2E-05
9E-06
6E-06
3E-06
0
15
25
35
prec. (cm)
No hys
45
0.0009
0.0006
0.0003
0
15
55
25
No hys
With hys
a
Mass into GW mg/cm3
35
prec. (cm)
45
55
With hys
b
0.18
Mass into GW vs. precipetationPetisträsk, 0.5h-soil 1
0.15
0.12
0.09
0.06
0.03
0
15
25
35
45
55
prec. (cm)
No hys
With hys
c
Figure ‎4.8: Mass into the GW versus measured precipitations in soil 1 (c), soil 2 (b), and soil 3 (a) for the period 19962008, 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.
3
Table ‎4.13: The average masses of solutes leached into GW in mg/cm for all the three soil types in Petisträsk, for the
period 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Hysteresis
2.86E-02
NO
hysteresis
4.76E-02
Soil 2
Hysteresis
5.13E-05
NO
hysteresis
2.33E-03
Soil 3
Hysteresis
7.25E-07
NO
hysteresis
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.
40
3
Table ‎4.14: The maximum masses of solutes leached into the GW in mg/cm for all the three soil types in Petisträsk,
for the period 1996-2008, for both hysteretic and non-hysteretic soil waters.
Soil 1
Hysteresis
9.59E-02
Soil 2
NO
hysteresis
1.47E-01
Soil 3
NO
hysteresis
9.59E-04
Hysteresis
3.12E-04
NO
hysteresis
1.51E-05
Hysteresis
9.40E-06
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 Malmö 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.
1.5
Depth of COM vs. precipetationMalmö, 24 h-soil 1
2
y = 0.036x - 0.573
R² = 0.8795
1
y = 0.03x - 0.4753
R² = 0.7948
0.5
0
15
25
35
45
Prec. (cm)
No hys
Linear (No hys)
55
65
With hys
Linear (With hys)
a
Depth of COM (m)
Depth of COM (m)
2
Depth of COM vs. precipetationMalmö, 0.5 h-soil 1
1.5
y = 0.0356x - 0.6305
R² = 0.8669
1
0.5
y = 0.0353x - 0.5945
R² = 0.8403
0
15
25
No hys
35
45
Prec. (cm)
Linear (No hys)
55
65
With hys
Linear (With hys)
b
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
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
(Malmö, Norrköping, and Petisträsk), for all the soils, for the period 1996-2008. The numbers between parentheses
are maximum and minimum precipitations during study period
Malmö (243-577)
Soil 1
Timestep
Half-hourly
input data
4-hourly
input data
Daily input
data
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
0.6192
0.739
0.3033
0.381
0.2726
0.295
0.6146
0.7248
0.3392
0.3940
0.2798
0.2927
0.6929
0.6693
0.3590
0.3628
0.2966
0.2872
Norrköping (288-409)
Soil 1
Timestep
Half-hourly
input data
4-hours
input data
Daily input
data
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
0.4818
0.6398
0.2601
0.3082
0.2135
0.2407
0.5500
0.6177
0.2763
0.3029
0.2377
0.2391
0.5329
0.5404
0.2752
0.2853
0.2338
0.2304
Petisträsk (270-500)
Soil 1
Timestep
Half-hourly
input data
4-hours
input data
Daily input
data
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
0.8285
0.9607
0.4511
0.5071
0.3813
0.4025
0.8559
0.9484
0.4561
0.5035
0.3804
0.3979
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
Malmö (243-577)
Soil 1
Timestep
Half-hourly
input data
4-hours
input data
Daily input
data
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
1
1.19
1
1.26
1
1.08
1
1.18
1
1.16
1
1.05
1
0.97
1
1.01
1
0.97
Norrköping (288-409)
Soil 1
Timestep
Half-hourly
input data
4-hours
input data
Daily input
data
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
1
1.33
1
1.18
1
1.13
1
1.12
1
1.10
1
1
1
1.01
1
1.04
1
0.99
Petisträsk (270-500)
Soil 1
Timestep
Half-hourly
input data
4-hours
input data
Daily input
data
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
Hysteresis
NO
hysteresis
1
1.16
1
1.12
1
1.06
1
1.11
1
1.10
1
1.05
1
1
1
1
1
1
4.1.2 Effect of Temporal variability in rainfall and evaporation
We started analyzing the effects of temporal averaging of precipitation and evaporation input data on the
downward movement of moisture and contaminants by the examination of three functions, COM, LC and
mass into groundwater of contaminant, for three soil types with and without effect of hysteresis and for
three sites of interest and how these functions are affected by averaging the input data.
43
For soil 1 in all sites solute movement was simulated with half hourly meteorological input as well as with
hourly, 2 hours, 4 hours and 24 hours which were obtained by averaging the half hourly data. For soil 2 and
soil 3 the simulations were done but only with half hourly, 4 hours and 24 hours inputs.
To be able to analyze the effect of temporal averaging of the meteorological data we took 0.5 hour input as
a base point, considering that the higher time resolution the more adequate outputs. This allowed us to
calculate the percentages of different time resolutions with regard to the base point for each year and later
compute the averages during the whole period for each soil type for each location. However, one may
question why higher time resolution input gives more adequate outputs. This was good explained by Wang
(2009) “the use of half hourly data is in itself an approximation that averages instantaneous rainfall
intensity even over shorter time intervals than half hourly, hourly, 2 hours, 4 hours and daily data do.
Hence the actual errors introduced by the reliance on daily meteorological data are higher”.
Investigating the migration of COM with different input, one can see that for all three locations the
averaged input seems to lead to the rising of underestimation of COM migration with increasing time step
and it is rising proportionally with hydraulic conductivity of soil in non-hysteretic model. The last evidencing
that contaminant transport in unsaturated zone is influenced to a large degree of the hydraulic properties
in unsaturated zone and its heterogeneity (Wang, 2009). For instance, in soil 3 even when using half hourly
short intense precipitations, the whole amount of water may not totally infiltrate due to low infiltration
capacity. This means small differences might occur when comparing half hourly results to daily ones in soil
3. Moreover, recent study by Wang (2009), seem to support this finding. It is worthwhile to notice that the
underestimation of COM migration is very small for 1, 2 and 4 hours time step, for all soil types, for all sites
and averagely do not exceed 1%. For 24 hours timestep the overestimation is also relatively small, 6.5% in
the average. The exception is Norrköping soil 1 with 24 hours time step where the underestimation is 17%,
see Table ‎4.17.
Table ‎4.17: Averaged depths of COM as a percentage of half hourly, during 1996-2008, without effect of hysteresis.
Timestep
Soil 1
0.5
1
2
4
24
1.00
1.00
0.99
0.98
0.89
Malmö
Soil 2
No hysteresis
1.00
0.99
0.95
Soil 3
Soil 1
1.00
1.00
0.98
1.00
1.00
0.99
0.96
0.83
Norrköping
Soil 2
No hysteresis
1.00
0.98
0.92
Soil 3
Soil 1
1.00
0.99
0.95
1.00
1.00
1.00
0.99
0.94
Petisträsk
Soil 2
No hysteresis
1.00
0.99
0.97
Soil 3
1.00
0.99
0.98
44
Comparing COM movement in hysteric and non-hysteric models, one may see that in many cases lower
input resolution leads, on a contrary, to the bigger overestimation of COM migration (Figure ‎4.10) It also
seems that the overestimation also raises with increasing hydraulic conductivity of the soil the same as for
non-hysteric model, but the overestimation is also quite small. For all cites, for all soils and for hourly time
step COM in average equals 2%; for 2 hours the overestimation does not exceed 5% in average; for 4 hours
the overestimation is 6% in average and for 24 is 11% (Table ‎4.18).
Center of mass, m
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.5
4
7.5
11
14.5
18
21.5
2007
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2008
Center of mass, m
Malmö, sand no hysteresis
1.6
Malmö, sand with hysteresis
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5
4
7.5
Timestep, hours
11 14.5 18 21.5
2007
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2008
Timestep, hours
Figure ‎4.10: Yearly contaminant migration for 1996-2008 years of simulations for soil 1, with and without effect of hysteresis,
Malmö, Sweden.
The reason why the COM is overestimated in hysteretic model when using daily input data compared to
half hourly is that the effect of the soil history disappear (variations in the soil moisture are neglected)
which in turn leads to deeper percolation. In other words, the hysteretic simulation results will be as that of
non-hysteretic case.
Table ‎4.18: Averaged depths of COM as a percentage of half hourly, during 1996-2008 years, with effect of hysteresis.
Timestep
0.5
1
2
4
24
Malmö
Soil 1
Soil 2
With hysteresis
1.00
1.00
0.98
0.97
1.00
1.11
1.13
1.18
Soil 3
1.00
1.04
1.09
Norrköping
Soil 1
Soil 2
With hysteresis
1.00
1.00
1.06
1.16
1.17
1.08
1.19
1.07
Soil 3
1.00
1.11
1.09
Petisträsk
Soil 1
Soil 2
With hysteresis
1.00
1.00
1.02
1.02
1.04
1.02
1.12
1.09
Soil 3
1.00
1.00
1.02
45
Analyzing how the temporal averaging the input data effects on the depth to LC one may see that for all
cites and all soil types in non-hysteretic model, the depth to LC is almost stable for hourly, 2 hours and 4
hours input. Though the depth to LC for 24 hours time step for all soil types, for all cites is slightly
underestimated by 2% in average. As in case with COM here we may also observe that it seems that the
depth to LC is more underestimated for coarse textured soils rather than for finer one, see Table ‎4.19.
Table ‎4.19: Averaged depths to LC as a percentage of half hourly, during 1996-2008 years, without effect of hysteresis.
Timestep
Soil 1
0.5
1
2
4
24
1.00
1.00
1.00
0.99
1.00
Malmö
Soil 2
No hysteresis
1.00
0.99
0.96
Soil 3
Soil 1
1.00
0.99
0.99
1.00
1.00
0.99
0.98
0.90
Norrköping
Soil 2
No hysteresis
1.00
0.99
0.98
Soil 3
Soil 1
1.00
0.99
0.99
1.00
1.00
1.00
0.99
0.96
Petisträsk
Soil 2
No hysteresis
1.00
1.00
0.99
Soil 3
1.00
1.00
1.00
For hysteretic case the depth to LC as the depth to COM is slightly overestimated and overestimation is also
rises with time step as well as with increasing hydraulic conductivity in the soil. Average overestimation of
depth to LC for all cites and for hourly timestep is 2%, for 2 hours time step it is stable, for 4 hours time
step 1% and for 24 hours time step is 3% (Table ‎4.20).
Table ‎4.20: Averaged depths to LC as a percentage of half hourly input, during 1997-2008 years, with effect of hysteresis.
Timestep
0.5
1
2
4
24
Malmö
Soil 1
Soil 2
With hysteresis
1.00
1.00
1.00
0.98
1.04
1.03
1.06
1.01
Soil 3
1.00
1.01
1.03
Norrköpink
Soil 1
Soil 2
With hysteresis
1.00
1.00
1.04
1.02
1.04
1.03
1.08
1.02
Soil 3
1.00
1.02
1.01
Petisträsk
Soil 1
Soil 2
With hysteresis
1.00
1.00
1.02
1.02
0.96
1.01
1.00
1.04
Soil 3
1.00
1.00
1.01
Investigating how much mass of the pollutant leaches into the groundwater with different timestep one
may notice that for all soil types and for all sites under non-hysteretic conditions the difference of the mass
of pollutant is increasing with a timestep. The pattern is unclear but it is clearly seen that for soils with
higher hydraulic conductivity the mass which reaches the ground table is less comparing to those which
have higher hydraulic conductivities. However the masses are very small, in average for soil 1 its 3.46*10-2
46
mg/cm3, for soil 2, 9.45*10-4 mg/cm3 and for soil 3, 8.75*10-5 mg/cm3, see Table ‎4.21 and Table ‎4.22
below.
Table ‎4.21: Averaged values of mass into groundwater as a percentage of half hourly input, during 1996-2008 years, without
effect of hysteresis
Timestep
Malmö
No hysteresis
Soil 1
Soil 2
Soil 3
Norrköping
No hysteresis
Soil 1
Soil 2
Soil 3
%
%
Soil 1
Petisträsk
No hysteresis
Soil 2
Soil 3
%
0.5
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1
0.94
-
-
0.93
-
-
0.98
-
-
2
0.84
-
-
0.84
-
-
0.95
-
-
4
24
0.62
0.53
1.06
2.03
1.30
17.30
0.55
0.14
1.47
511.69
1.39
27.52
0.84
0.50
0.77
0.50
0.73
0.57
Table ‎4.22: Averaged values of mass to groundwater, during 1996-2008 years, with hysteresis
Malmö
With hysteresys
Timestep
Soil 1
Soil 2
Norrköping
With hysteresys
Soil
3
Soil 1
%
1
1
2
4
24
1
1
3
4448
3496575960
1
504
338
1
122
54
1
27303
7900
3810
14393
Soil 2
%
1
3268
9389760
Petistrask
With hysteresys
Soil 3
Soil 2
Soil
3
1
10091
2774087
1
1
6
Soil 1
%
1
56964
226
1
3526162
1
22317102
169901355
Table ‎4.23 and Table ‎4.24 perform the averaged values of mass of pollutant to ground water as a
percentage of half hourly input data for 1996-2008 for all soil types and for all sites under hysteretic
conditions. It can be observed that the mass into ground water in all three cases is highly overestimated.
The tendency is not clear but we may say that the overestimation decreases with decreasing hydraulic
conductivity of the soil. One may see that 24 hours input data leads to greater overestimations comparing
to half hourly input especially for soil 1 and soil 2. However the masses of the contaminant which leached
to the ground water in all cases are very small even comparing to the those which were obtained from halfhourly input; for instance, for soil 1 for 3 sites with 24 hours input data the average mass of the
47
contaminant which reached the GW is 2.17*10-2 mg/cm3, for soil 2 is 9.79*10-4 mg/cm3 and for soil 3 is
9.96*10-5 mg/cm3.
3
Table ‎4.23: Averaged values of mass to groundwater, during 1996-2008 years, mg/cm , with hysteresis
Timestep
Malmö
Norrköping
Petisträsk
With hysteresys
With hysteresys
With hysteresys
Soil 1
Soil 2
Soil 3
average values
Soil 1
Soil 2
Soil 3
average values
2.65E-05 3.34E-03 3.65E-07
Soil 1
Soil 2
Soil 3
average values
3.47E14
0.5
1.48E-02
4.64E-04
2.86E-02 5.13E-05
7.25E-07
1
1.55E-02
-
-
4.58E-03
-
-
2.78E-02
-
-
2
1.50E-02
-
-
5.54E-03
-
3.10E-02
-
-
4
1.59E-02
5.04E-04
4.46E-05 7.56E-03 1.54E-06
24
1.81E-02
9.34E-04
9.93E-05 2.18E-03 1.00E-07
1.61E12
2.20E13
3.46E-02 4.61E-05
1.08E-07
4.49E-02 1.34E-04
7.61E-07
3
Table ‎4.24: Averaged values of mass to groundwater as a percentage of half hourly input, during 1996-2008 years, mg/cm ,
without effect of hysteresis
Malmö
No hysteresis
Timestep
Soil 1
Soil 2
Soil 3
average values
0.5
2.23E-02 1.11E-03 1.26E-04
1
2.22E-02
2
2.20E-02
4
2.14E-02 1.07E-03 1.16E-04
24
1.82E-02 9.10E-04 8.74E-05
Norrköping
No hysteresis
Soil 1
Soil 2
Soil 3
average values
6.83E-03 1.77E-06 2.57E-11
6.72E-03
6.56E-03
5.89E-03 1.41E-06 1.94E-11
3.15E-03 3.78E-07 1.54E-12
Petistrask
No hysteresis
Soil 1
Soil 2
Soil 3
average values
4.76E-02 1.79E-04 1.41E-06
4.74E-02
4.71E-02
4.58E-02 1.56E-04 5.11E-07
3.97E-02 1.04E-04 3.19E-07
4.1.3 Effect of geographic location
In Table ‎4.25, the average depths of COM in all the sites are presented. These results clearly demonstrate
that the depth of COM is deeper in Petisträsk compared to the other two sites. It can also be seen that the
lowest depths of COM occurred in Norrköping.
48
Table ‎4.25: The average depths of COM in meters in all the three sites (Malmö, Norrköping, and Petisträsk), for the
period 1996-2008, for both hysteretic and non-hysteretic systems. The numbers between parentheses are maximum
and minimum precipitations during study period.
Malmö (243-577)
Soil 1
Soil 2
NO
hysteresis
0.739
Hysteresis
0.6192
Soil 3
Hysteresis
NO hysteresis
Hysteresis
NO hysteresis
0.3033
0.381
0.2726
0.295
Norrköping (288-409)
Soil 1
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO hysteresis
Hysteresis
NO hysteresis
0.4818
0.6398
0.2601
0.3082
0.2135
0.2407
Petisträsk (270-500)
Soil 1
Soil 2
Soil 3
Hysteresis
NO
hysteresis
Hysteresis
NO hysteresis
Hysteresis
NO hysteresis
0.8285
0.9607
0.4511
0.5071
0.3813
0.4025
The average precipitations are 365, 343, and 365 mm in Malmö, Norrköping, and Petisträsk respectively.
The deeper migration of COM of solutes in Petisträsk could be, at least partially due to higher net
precipitation compared to the other two sites.
49
5 Conclusions
Water and solutes movement in the unsaturated zone is incredibly complex process due to the
heterogeneous nature of soil and variable atmospheric boundary conditions at both the soil surface over
short time periods. Despite all the simplifications which were made, HYDRUS-1D is a powerful tool to
simulate the movement of water and solutes in partially saturated porous media, since it can deal with
different water flow and solute transport boundary conditions. However, to be able to validate the model
performance, more data collection and measurements are needed which in turn means more cost-effective
sampling and analysis methodologies must be developed.
Results of the study show the following;

Generally, under non-hysteretic water flow, solute migration is faster which in turn refers to an
overestimation of the solute velocity, especially with high resolution input data.

Analysis of the downward migration of the solutes indicates that the effect of hysteresis is more
pronounced in the coarse textured soils

Generally, the leaching of solutes into the groundwater starts beyond some threshold precipitation
values, although even the maximum concentrations leached into the GW at the end of simulation
period are small, especially in Norrköping.

The results demonstrate that the concentration profiles of solutes in Norrköping and Malmö are
lagged behind that of Petisträsk, since the results show that the average depth of COM is deeper in
Petisträsk. It is also found that the lowest depths of COM occurred in Norrköping. This could be an
indication that the groundwater is more susceptible to contamination in Petisträsk and Malmö in
comparison to Norrköping. Though in the real conditions, there are many other key factors affecting
migration of contaminants from ground surface into the groundwater, for instance, land use,
topography, etc.

Lower time resolution of the input data leads to increasing both underestimation of the depth of
COM for non- hysteretic simulations and overestimation for hysteretic ones.

In most cases, overestimation and underestimation of the depth to COM is rising with increasing
hydraulic conductivity of the soil.

It is found that the differences between hysteretic and non-hysteretic simulations are very small
when using daily input data. Consequently, we may recommend neglecting the effect of hysteresis
when using daily input data.
50

Making a rough prediction of the migration of the depth to COM because of precipitation increase by
100 %, we may say that the depth to COM is dropped down below the GL by a factor of 5.
51
6 Recommendations and future work
Following are some proposed recommendations for this study.

Since in this study the simulations were conducted from 1996-2008 (13 years) which might not be
long enough to better find out and understand the tendency of the the downward migration of
solutes, it could be useful to extend the study period.

It might be also useful to try different simulation periods and compare between them to discover the
worst downward migration scenarios.

It could be interesting to simulate the movement of water and solutes using projected (modeled)
precipitation and evaporation input data during the same study period, and then comparing to the
simulations with measured data. This could be a useful tool when modeling for the future scenarios
using projected input data to see the impacts of the climate changes.

Finally, further investigation is required to evaluate the implications of precipitation pattern on the
solute transport.
52
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54
Appendices
Appendix A. Matlab codes for averaging the pecipitation
%from half hr to hourly prec (96-2008) measured
i=1:5000;
ph96cmh(i,1)=(p96cmh(2*i-1,1)+p96cmh(2*i,1))/2;
ph97cmh(i,1)=(p97cmh(2*i-1,1)+p97cmh(2*i,1))/2;
ph98cmh(i,1)=(p98cmh(2*i-1,1)+p98cmh(2*i,1))/2;
ph99cmh(i,1)=(p99cmh(2*i-1,1)+p99cmh(2*i,1))/2;
ph2000cmh(i,1)=(p2000cmh(2*i-1,1)+p2000cmh(2*i,1))/2;
ph2001cmh(i,1)=(p2001cmh(2*i-1,1)+p2001cmh(2*i,1))/2;
ph2002cmh(i,1)=(p2002cmh(2*i-1,1)+p2002cmh(2*i,1))/2;
ph2003cmh(i,1)=(p2003cmh(2*i-1,1)+p2003cmh(2*i,1))/2;
ph2004cmh(i,1)=(p2004cmh(2*i-1,1)+p2004cmh(2*i,1))/2;
ph2005cmh(i,1)=(p2005cmh(2*i-1,1)+p2005cmh(2*i,1))/2;
ph2006cmh(i,1)=(p2006cmh(2*i-1,1)+p2006cmh(2*i,1))/2;
ph2007cmh(i,1)=(p2007cmh(2*i-1,1)+p2007cmh(2*i,1))/2;
ph2008cmh(i,1)=(p2008cmh(2*i-1,1)+p2008cmh(2*i,1))/2;
%from hourly to 2 hr prec. (96-2008) measured
i=1:2500;
p2h96cmh(i,1)=(ph96cmh(2*i-1,1)+ph96cmh(2*i,1))/2;
p2h97cmh(i,1)=(ph97cmh(2*i-1,1)+ph97cmh(2*i,1))/2;
p2h98cmh(i,1)=(ph98cmh(2*i-1,1)+ph98cmh(2*i,1))/2;
p2h99cmh(i,1)=(ph99cmh(2*i-1,1)+ph99cmh(2*i,1))/2;
p2h2000cmh(i,1)=(ph2000cmh(2*i-1,1)+ph2000cmh(2*i,1))/2;
p2h2001cmh(i,1)=(ph2001cmh(2*i-1,1)+ph2001cmh(2*i,1))/2;
p2h2002cmh(i,1)=(ph2002cmh(2*i-1,1)+ph2002cmh(2*i,1))/2;
55
p2h2003cmh(i,1)=(ph2003cmh(2*i-1,1)+ph2003cmh(2*i,1))/2;
p2h2004cmh(i,1)=(ph2004cmh(2*i-1,1)+ph2004cmh(2*i,1))/2;
p2h2005cmh(i,1)=(ph2005cmh(2*i-1,1)+ph2005cmh(2*i,1))/2;
p2h2006cmh(i,1)=(ph2006cmh(2*i-1,1)+ph2006cmh(2*i,1))/2;
p2h2007cmh(i,1)=(ph2007cmh(2*i-1,1)+ph2007cmh(2*i,1))/2;
p2h2008cmh(i,1)=(ph2008cmh(2*i-1,1)+ph2008cmh(2*i,1))/2;
%from2 hr to 4 hr prec. (96-2008) measured
i=1:1250;
p4h96cmh(i,1)=(p2h96cmh(2*i-1,1)+p2h96cmh(2*i,1))/2;
p4h97cmh(i,1)=(p2h97cmh(2*i-1,1)+p2h97cmh(2*i,1))/2;
p4h98cmh(i,1)=(p2h98cmh(2*i-1,1)+p2h98cmh(2*i,1))/2;
p4h99cmh(i,1)=(p2h99cmh(2*i-1,1)+p2h99cmh(2*i,1))/2;
p4h2000cmh(i,1)=(p2h2000cmh(2*i-1,1)+p2h2000cmh(2*i,1))/2;
p4h2001cmh(i,1)=(p2h2001cmh(2*i-1,1)+p2h2001cmh(2*i,1))/2;
p4h2002cmh(i,1)=(p2h2002cmh(2*i-1,1)+p2h2002cmh(2*i,1))/2;
p4h2003cmh(i,1)=(p2h2003cmh(2*i-1,1)+p2h2003cmh(2*i,1))/2;
p4h2004cmh(i,1)=(p2h2004cmh(2*i-1,1)+p2h2004cmh(2*i,1))/2;
p4h2005cmh(i,1)=(p2h2005cmh(2*i-1,1)+p2h2005cmh(2*i,1))/2;
p4h2006cmh(i,1)=(p2h2006cmh(2*i-1,1)+p2h2006cmh(2*i,1))/2;
p4h2007cmh(i,1)=(p2h2007cmh(2*i-1,1)+p2h2007cmh(2*i,1))/2;
p4h2008cmh(i,1)=(p2h2008cmh(2*i-1,1)+p2h2008cmh(2*i,1))/2;
%from 4 hr to 24 hr prec. (96-2008) measured
i=1:208;
p24h96cmh(i,1)=(p4h96cmh(6*i-5,1)+p4h96cmh(6*i-4,1)+p4h96cmh(6*i3,1)+p4h96cmh(6*i-2,1)+p4h96cmh(6*i-1,1)+p4h96cmh(6*i,1))/6;
p24h97cmh(i,1)=(p4h97cmh(6*i-5,1)+p4h97cmh(6*i-4,1)+p4h97cmh(6*i-
56
3,1)+p4h97cmh(6*i-2,1)+p4h97cmh(6*i-1,1)+p4h97cmh(6*i,1))/6;
p24h98cmh(i,1)=(p4h98cmh(6*i-5,1)+p4h98cmh(6*i-4,1)+p4h98cmh(6*i3,1)+p4h98cmh(6*i-2,1)+p4h98cmh(6*i-1,1)+p4h98cmh(6*i,1))/6;
p24h99cmh(i,1)=(p4h99cmh(6*i-5,1)+p4h99cmh(6*i-4,1)+p4h99cmh(6*i3,1)+p4h99cmh(6*i-2,1)+p4h99cmh(6*i-1,1)+p4h99cmh(6*i,1))/6;
p24h2000cmh(i,1)=(p4h2000cmh(6*i-5,1)+p4h2000cmh(6*i-4,1)+p4h2000cmh(6*i3,1)+p4h2000cmh(6*i-2,1)+p4h2000cmh(6*i-1,1)+p4h2000cmh(6*i,1))/6;
p24h2001cmh(i,1)=(p4h2001cmh(6*i-5,1)+p4h2001cmh(6*i-4,1)+p4h2001cmh(6*i3,1)+p4h2001cmh(6*i-2,1)+p4h2001cmh(6*i-1,1)+p4h2001cmh(6*i,1))/6;
p24h2002cmh(i,1)=(p4h2002cmh(6*i-5,1)+p4h2002cmh(6*i-4,1)+p4h2002cmh(6*i3,1)+p4h2002cmh(6*i-2,1)+p4h2002cmh(6*i-1,1)+p4h2002cmh(6*i,1))/6;
p24h2003cmh(i,1)=(p4h2003cmh(6*i-5,1)+p4h2003cmh(6*i-4,1)+p4h2003cmh(6*i3,1)+p4h2003cmh(6*i-2,1)+p4h2003cmh(6*i-1,1)+p4h2003cmh(6*i,1))/6;
p24h2004cmh(i,1)=(p4h2004cmh(6*i-5,1)+p4h2004cmh(6*i-4,1)+p4h2004cmh(6*i3,1)+p4h2004cmh(6*i-2,1)+p4h2004cmh(6*i-1,1)+p4h2004cmh(6*i,1))/6;
p24h2005cmh(i,1)=(p4h2005cmh(6*i-5,1)+p4h2005cmh(6*i-4,1)+p4h2005cmh(6*i3,1)+p4h2005cmh(6*i-2,1)+p4h2005cmh(6*i-1,1)+p4h2005cmh(6*i,1))/6;
p24h2006cmh(i,1)=(p4h2006cmh(6*i-5,1)+p4h2006cmh(6*i-4,1)+p4h2006cmh(6*i3,1)+p4h2006cmh(6*i-2,1)+p4h2006cmh(6*i-1,1)+p4h2006cmh(6*i,1))/6;
p24h2007cmh(i,1)=(p4h2007cmh(6*i-5,1)+p4h2007cmh(6*i-4,1)+p4h2007cmh(6*i3,1)+p4h2007cmh(6*i-2,1)+p4h2007cmh(6*i-1,1)+p4h2007cmh(6*i,1))/6;
p24h2008cmh(i,1)=(p4h2008cmh(6*i-5,1)+p4h2008cmh(6*i-4,1)+p4h2008cmh(6*i3,1)+p4h2008cmh(6*i-2,1)+p4h2008cmh(6*i-1,1)+p4h2008cmh(6*i,1))/6;
57
Appendix B. Matlab codes for averaging potential evapotranspiration
%from hourly to half hour evaporation-mm/h
for i=1:5000
hi=i*2;
evahalfAR(hi-1:hi)=eva(hi/2);
end
%from hourly to 2 hour evaporation-cmh
for i=1:2500;
eva2h(i,1)=(evacm(2*i-1,1)+evacm(2*i,1))/2;
end
%from
2 hour to 4 hr evaporation-cmh
for i=1:1250;
eva4h(i,1)=(eva2h(2*i-1,1)+eva2h(2*i,1))/2; %#ok<*SAGROW>
end
58
%from 4 hr to 24 hr evaporation-cmh
for i=1:208;
eva24h(i,1)=(eva4h(6*i-5,1)+eva4h(6*i-4,1)+eva4h(6*i-3,1)+eva4h(6*i2,1)+eva4h(6*i-1,1)+eva4h(6*i,1))/6;
end
%montly evaporation Malmö
mar=22;
apr=64;
maj=108;
jun=132;
jul=130;
aug=104;
sep=62;
okt=28;
nov=12;
% from monthly to hourly evaporation
eva=zeros(1,6600);
for dag=0:274
if dag<30.1
eva(dag*24+1+6:dag*24+1+9)=mar/31/16;
eva(dag*24+1+10:dag*24+1+13)=mar/31/8;
eva(dag*24+1+14:dag*24+1+17)=mar/31/16;
elseif dag<60.1
59
eva(dag*24+1+6:dag*24+1+9)=apr/30/16;
eva(dag*24+1+10:dag*24+1+13)=apr/30/8;
eva(dag*24+1+14:dag*24+1+17)=apr/30/16;
elseif dag<91.1
eva(dag*24+1+6:dag*24+1+9)=maj/31/16;
eva(dag*24+1+10:dag*24+1+13)=maj/31/8;
eva(dag*24+1+14:dag*24+1+17)=maj/31/16;
elseif dag<121.1
eva(dag*24+1+6:dag*24+1+9)=jun/30/16;
eva(dag*24+1+10:dag*24+1+13)=jun/30/8;
eva(dag*24+1+14:dag*24+1+17)=jun/30/16;
elseif dag<152.1
eva(dag*24+1+6:dag*24+1+9)=jul/31/16;
eva(dag*24+1+10:dag*24+1+13)=jul/31/8;
eva(dag*24+1+14:dag*24+1+17)=jul/31/16;
elseif dag<183.1
eva(dag*24+1+6:dag*24+1+9)=aug/31/16;
eva(dag*24+1+10:dag*24+1+13)=aug/31/8;
eva(dag*24+1+14:dag*24+1+17)=aug/31/16;
elseif dag<213.1
eva(dag*24+1+6:dag*24+1+9)=sep/30/16;
eva(dag*24+1+10:dag*24+1+13)=sep/30/8;
eva(dag*24+1+14:dag*24+1+17)=sep/30/16;
elseif dag<244.1
eva(dag*24+1+6:dag*24+1+9)=okt/31/16;
eva(dag*24+1+10:dag*24+1+13)=okt/31/8;
eva(dag*24+1+14:dag*24+1+17)=okt/31/16;
elseif dag<274.1
60
eva(dag*24+1+6:dag*24+1+9)=nov/30/16;
eva(dag*24+1+10:dag*24+1+13)=nov/30/8;
eva(dag*24+1+14:dag*24+1+17)=nov/30/16;
end
end
%montly evaporation Petritrask
mar=8;
apr=20;
maj=75;
jun=120;
jul=110;
aug=74;
sep=32;
okt=8;
nov=1;
% from monthly to hourly evaporation
eva=zeros(1,6576);
for dag=0:274
if dag<30.1
eva(dag*24+1+6:dag*24+1+9)=mar/31/16;
eva(dag*24+1+10:dag*24+1+13)=mar/31/8;
eva(dag*24+1+14:dag*24+1+17)=mar/31/16;
elseif dag<60.1
eva(dag*24+1+6:dag*24+1+9)=apr/30/16;
eva(dag*24+1+10:dag*24+1+13)=apr/30/8;
eva(dag*24+1+14:dag*24+1+17)=apr/30/16;
61
elseif dag<91.1
eva(dag*24+1+6:dag*24+1+9)=maj/31/16;
eva(dag*24+1+10:dag*24+1+13)=maj/31/8;
eva(dag*24+1+14:dag*24+1+17)=maj/31/16;
elseif dag<121.1
eva(dag*24+1+6:dag*24+1+9)=jun/30/16;
eva(dag*24+1+10:dag*24+1+13)=jun/30/8;
eva(dag*24+1+14:dag*24+1+17)=jun/30/16;
elseif dag<152.1
eva(dag*24+1+6:dag*24+1+9)=jul/31/16;
eva(dag*24+1+10:dag*24+1+13)=jul/31/8;
eva(dag*24+1+14:dag*24+1+17)=jul/31/16;
elseif dag<183.1
eva(dag*24+1+6:dag*24+1+9)=aug/31/16;
eva(dag*24+1+10:dag*24+1+13)=aug/31/8;
eva(dag*24+1+14:dag*24+1+17)=aug/31/16;
elseif dag<213.1
eva(dag*24+1+6:dag*24+1+9)=sep/30/16;
eva(dag*24+1+10:dag*24+1+13)=sep/30/8;
eva(dag*24+1+14:dag*24+1+17)=sep/30/16;
elseif dag<244.1
eva(dag*24+1+6:dag*24+1+9)=okt/31/16;
eva(dag*24+1+10:dag*24+1+13)=okt/31/8;
eva(dag*24+1+14:dag*24+1+17)=okt/31/16;
elseif dag<274.1
eva(dag*24+1+6:dag*24+1+9)=nov/30/16;
eva(dag*24+1+10:dag*24+1+13)=nov/30/8;
eva(dag*24+1+14:dag*24+1+17)=nov/30/16;
62
end
end
%montly evaporation Norrköping
mar=20;
apr=53;
maj=104;
jun=139;
jul=127;
aug=95;
sep=48;
okt=17;
nov=3;
% from monthly to hourly evaporation
eva=zeros(1,6576);
for dag=0:274
if dag<30.1
eva(dag*24+1+6:dag*24+1+9)=mar/31/16;
eva(dag*24+1+10:dag*24+1+13)=mar/31/8;
eva(dag*24+1+14:dag*24+1+17)=mar/31/16;
elseif dag<60.1
eva(dag*24+1+6:dag*24+1+9)=apr/30/16;
eva(dag*24+1+10:dag*24+1+13)=apr/30/8;
eva(dag*24+1+14:dag*24+1+17)=apr/30/16;
elseif dag<91.1
eva(dag*24+1+6:dag*24+1+9)=maj/31/16;
63
eva(dag*24+1+10:dag*24+1+13)=maj/31/8;
eva(dag*24+1+14:dag*24+1+17)=maj/31/16;
elseif dag<121.1
eva(dag*24+1+6:dag*24+1+9)=jun/30/16;
eva(dag*24+1+10:dag*24+1+13)=jun/30/8;
eva(dag*24+1+14:dag*24+1+17)=jun/30/16;
elseif dag<152.1
eva(dag*24+1+6:dag*24+1+9)=jul/31/16;
eva(dag*24+1+10:dag*24+1+13)=jul/31/8;
eva(dag*24+1+14:dag*24+1+17)=jul/31/16;
elseif dag<183.1
eva(dag*24+1+6:dag*24+1+9)=aug/31/16;
eva(dag*24+1+10:dag*24+1+13)=aug/31/8;
eva(dag*24+1+14:dag*24+1+17)=aug/31/16;
elseif dag<213.1
eva(dag*24+1+6:dag*24+1+9)=sep/30/16;
eva(dag*24+1+10:dag*24+1+13)=sep/30/8;
eva(dag*24+1+14:dag*24+1+17)=sep/30/16;
elseif dag<244.1
eva(dag*24+1+6:dag*24+1+9)=okt/31/16;
eva(dag*24+1+10:dag*24+1+13)=okt/31/8;
eva(dag*24+1+14:dag*24+1+17)=okt/31/16;
elseif dag<274.1
eva(dag*24+1+6:dag*24+1+9)=nov/30/16;
eva(dag*24+1+10:dag*24+1+13)=nov/30/8;
eva(dag*24+1+14:dag*24+1+17)=nov/30/16;
end
64
Appendix C. Calculation of contaminant concentrations
For soil 1:
For soil 2:
For soil 3:
65
Appendix D. Finding the centre of mass in a 101 vector of concentration values
depth
summa=sum(c);
s=0;
i=1;
while s<(summa/2)
s=s+c(i);
i=i+1;
end
%linear interpolation
kvot=(s-summa/2)/c(i-1);
depth=(i-1)*0.025-kvot*0.025
%find where C is larger than limit
limit=0.2;
s=0;
i=55;
while c(i)>(limit)
i=i+1;
end
kvot=(c(i)-limit)/c(i-1);
largerthanlimit=(i)*0.025-kvot*0.025
66
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
1.5
1
0.5
30
45
Prec. (cm)
No hys
Linear (No hys)
0.4
0.2
60
With hys
Linear (With hys)
1.5
1
0.5
30
45
With hys
Linear (No hys)
Linear (With hys)
Depth of COM vs.
precipetation-Malmö, 4hsoil 2
0.8
0.6
0.4
0.2
No hys
Linear (No hys)
1
0.5
No hys
Linear (No hys)
Depth of COM (m)
1.5
30
45
Prec. (cm)
45
60
Prec. (cm)
No hys
Linear (No hys)
With hys
Linear (With hys)
60
With hys
Linear (With hys)
Depth of COM vs.
precipetation-Malmö, 4hsoil 3
0.6
0.4
0.2
15
30
45
60
Prec. (cm)
With hys
Linear (With hys)
Depth of COM vs.
precipetation-Malmö, 24hsoil 2
1
No hys
With hys
Linear (No hys)
Linear (With hys)
0.8
0.8
0.6
0.4
0.2
0
0
0.8
60
Depth of COM (m)
With hys
Linear (With hys)
30
30
45
Prec. (cm)
0
15
60
Depth of COM vs.
precipetation-Malmö, 24 hSoil 1
2
15
0.2
15
0
No hys
Linear (No hys)
0.4
60
No hys
1
0
30
45
Prec. (cm)
0.6
Prec. (cm)
Depth of COM vs.
precipetation-Malmö,4hSoil 1
15
Depth of COM vs.
precipetation-Malmö, 0.5hsoil 3
0.8
0
15
Depth of COM (m)
Depth od COM (m)
0.6
Depth of COM (m)
15
Depth of COM (m)
0.8
0
0
2
1
Depth of COM vs.
precipetation-Malmö, 0.5hsoil 2
Depth of COM (m)
Depth of COM vs.
precipetation-Malmö, 0.5 hsoil 1
2
Depth of COM (m)
Depth of COM (m)
E-1: Depth of COM versus precipitation for all soils in Malmö with half hourly, 4-hourly, and daily meteoroligical input data
Depth of COM vs.
precipetation-Malmö, 24hsoil 3
0.6
0.4
0.2
0
15
30
45
Prec. (cm)
60
No hys
With hys
Linear (No hys)
Linear (With hys)
15
30
45
60
Prec. (cm)
No hys
Linear (No hys)
With hys
Linear (With hys)
67
0.12
0.08
0.04
0
15
30
45
0.01
0.005
0
15
60
30
45
prec. (cm)
prec. (cm)
With hys
0.15
0.1
0.05
0
30
45
prec. (cm)
No hys
0.05
0
45
60
Prec. (cm)
No hys
With hys
0.0025
0.002
0.0015
0.001
0.0005
0
15
No hys
0.005
0
15
30
45
prec. (cm)
0.0015
0.001
0.0005
0
15
No hys
0.005
0
No hys
With hys
30
45
60
prec. (cm)
0.01
45
60
0.002
60
Mass into GW vs.
precipetation-Malmö, 24 hsoil 2
0.015
30
45
Mass into GW vs.
precipetation-Malmö, 4 hsoil 3
With hys
prec. (cm)
30
prec. (cm)
Mass into GW vs.
precipetation-Malmö, 4 hsoil 2
15
Mass into GW vs.
precipetation-Malmö, 0.5 hsoil 3
With hys
No hys
0.1
60
0.01
With hys
0.15
30
0.015
60
Mass into GW vs.
precipetation-Malmö, 24 h0.2
soil 1
15
Mass into GW (mg/cm3)
Mass into GW vs.
precipetation-Malmö, 4 hsoil 1
0.2
15
Masss into GW (mg/cm3
No hys
Mass into GW (mg/cm3)
Mass into GW (mg/cm3)
No hys
Mass into GW (mg/cm3)
0.16
Mass into GW (mg/cm3)
0.2
Mass into GW vs.
precipetation-Malmö, 0.5hsoil 2
0.015
60
With hys
Mass into GW (mg/cm3)
Mass into GW vs.
precipetation-Malmö, 0.5 hsoil 1
Mass into GW (mg/cm3)
Mass into GW, mg/cm3
E-2: Mass into GW versus precipitation for all soils in Malmö with half hourly, 4-hourly, and daily meteoroligical input data
With hys
Mass into GW vs.
precipetation-Malmö, 24 hsoil 3
0.0015
0.001
0.0005
0
15
No hys
30
45
prec. (cm)
With hys
60
68
E-3: Depth to LC versus precipitation for all soils in Malmö with half hourly, 4-hourly, and daily meteoroligical input data
2.4
1.9
1.4
0.9
0.4
15
30
45
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
60
LC depth vs precipitationMalmo, 0.5h-soil 2
Depth to LC (m)
2.9
Depth to LC (m)
Depth to LC (m)
LC depth vs precipitationMalmö,0.5h-soil 1
15
No hys
Linear (No hys)
1.9
1.4
0.4
45
15
30
15
Linear (With hys)
Linear (No hys)
With hys
Linear (With hys)
LC depth vs precipitationMalmo, 24h-soil 1
2.4
1.9
1.4
0.9
0.4
45
No hys
Linear (No hys)
45
60
No hys
Linear (With hys)
Linear (No hys)
1
0.9
0.8
0.7
0.6
0.5
0.4
15
Prec, (cm)
No hys
Linear (No hys)
30
60
60
With hys
No hys
Linear (With hys)
Linear (No hys)
1
0.9
0.8
0.7
0.6
0.5
0.4
LC depth vs precipitationMalmo, 24h-soil 3
15
30
Prec, (cm)
With hys
Linear (With hys)
45
Prec, (cm)
No hys
Linear (No hys)
45
60
With hys
60
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
30
45
LC depth vs precipitationMalmo, 4h-soil 3
LC depth vs precipitationMalmo, 24h-soil 2
15
30
Prec, (cm)
Depth to LC (m)
No hys
Depth to LC (m)
Depth to LC (m)
0.5
Prec, (cm)
Prec, (cm)
With hys
Linear (With hys)
0.6
60
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
60
With hys
30
0.7
LC depth vs precipitationMalmo, 4h-soil 2
0.9
15
45
Depth to LC (m)
2.4
2.9
30
With hys
Linear (With hys)
Depth to LC (m)
Depth to LC (m)
2.9
30
0.8
Prec, (cm)
LC depth vs precipitationMalmö, 4h-soil 1
15
LC depth vs precipitationMalmo, 0.5h-soil 3
0.4
Prec., cm
With hys
Linear (With hys)
1
0.9
No hys
Linear (No hys)
45
60
Prec, (cm)
With hys
Linear (With hys)
No hys
Linear (No hys)
69
0.6
0.5
0.4
0.2
35
25
45
Prec, (cm)
Linear (With hys)
Linear (No hys)
1
0.5
With hys
Linear (With hys)
Depth of COM (m)
No hys
35
Prec, (cm)
No hys
Linear (No hys)
Depth of COM vs
precipitation-Norrköping,
4h-soil 2
0.6
0.4
0.2
With hys
Linear (With hys)
Depth of COM vs
precipitation-Norrköping,
1.5
24h-soil 1
1
0.5
0
35
Prec, (cm)
With hys
Linear (With hys)
No hys
Linear (No hys)
35
Prec, (cm)
With hys
Linear (With hys)
45
No hys
Linear (No hys)
45
With hys
No hys
Linear (With hys)
Linear (No hys)
Depth of COM vs
precipitation-Norrköping,
4h-soil 3
0.6
0.4
0.2
45
Depth of COM vs
precipitation-Norrköping,
24h-soil 2
0.6
0.4
0.2
25
25
No hys
Linear (No hys)
0
25
35
Prec, (cm)
0
25
45
Depth of COM (m)
25
0.2
25
0
0
0.4
45
Prec, (cm)
With hys
Depth of COM vs
precipitation-Norrköping,
4h-soil 1
1.5
Depth of COM (m)
35
Depth of COM (m)
25
Depth of COM vs
precipitation-Norrköping,
0.5h-soil 3
0.6
0
0
0
Depth of COM (m)
Depth of COM (m)
1
Depth of COM vs
precipitation-Norrköping,
0.5h-soil 2
35
Prec, (cm)
45
With hys
No hys
Linear (With hys)
Linear (No hys)
35
Prec, (cm)
With hys
Linear (With hys)
Depth of COM (m)
1.5
Depth of COM vs
precipitation-Norrköping,
0.5h-soil 1
Depth of COM (m)
Depth of COM (m)
E-4: Depth of COM versus precipitation for all soils in Norrköping with half hourly, 4-hourly, and daily meteoroligical input data
45
No hys
Linear (No hys)
Depth of COM vs
precipitation-Norrköping,
0.6
24h-soil 3
0.4
0.2
0
25
35
Prec, (cm)
45
With hys
No hys
Linear (With hys)
Linear (No hys)
70
25
35
0E+00
25
45
Prec, (cm)
With hys
Mass into GW vs
precipitation-Norrkoping,
4h-soil 1
6E-02
4E-02
2E-02
0E+00
25
35
Prec, (cm)
With hys
Mass into GW, (mg/cm3)
2E-02
1E-02
35.00
45.00
Prec, (cm)
With hys
No hys
2E-10
0E+00
25
0E+00
35
Prec, (cm)
With hys
45
Prec, (cm)
With hys
0E+00
25
No hys
35
Prec, (cm)
With hys
0E+00
35
No hys
2E-10
No hys
5E-06
45
Mass into GW vs
precipitation-Norrkoping,
4h-soil 3
4E-10
45
Mass into GW vs
precipitation-Norrkoping,
24h-soil 2
1E-05
25
35
Prec, (cm)
With hys
1E-05
25
Mass into GW vs
precipitation-Norrkoping,
0.5h-soil 3
4E-10
No hys
2E-05
No hys
3E-02
45
Mass into GW vs
precipitation-Norrkoping,
4h-soil 2
3E-05
45
Mass into GW vs
precipitation-Norrkoping,
24h-soil 1
0E+00
25.00
Mass into GW, (mg/cm3)
No hys
Mass into GW, (mg/cm3)
Mass into GW, (mg/cm3)
With hys
35
Prec, (cm)
Mass into GW, (mg/cm3)
0E+00
2E-05
Mass into GW, (mg/cm3)
2E-02
Mass into GW vs
precipitation-Norrkoping,
0.5h-soil 2
4E-05
Mass into GW, (mg/cm3)
Mass into GW vs
precipitation-Norrkoping,
0.5h-soil 1
4E-02
Mass into GW, (mg/cm3)
Mass into GW, (mg/cm3)
E-5: Mass into GW versus precipitation for all soils in Norrköping with half hourly, 4-hourly, and daily meteoroligical input data
45
No hys
Mass into GW vs
precipitation-Norrkoping,
24h-soil 3
2E-11
1E-11
0E+00
25
35
45
Prec, (cm)
With hys
No hys
71
E-6: Depth to LC versus precipitation for all soils in Norrköping with half hourly, 4-hourly, and daily meteoroligical input data
LC depth vs precipitationNorrkoping, 0.5h-soil 1
LC depth vs precipitationNorrkoping, 0.5h-soil 2
1
0.4
0.8
0.4
25
35
Prec, (cm)
45
25
With hys
No hys
Linear (With hys)
Linear (No hys)
With hys
Linear (With hys)
LC depth vs precipitationNorrkoping, 4h-soil 1
1.2
25
1.2
LC depth vs precipitationNorrkoping, 4h-soil 2
0.8
0.8
1.2
35
45
25
Prec, (cm)
With hys
Linear (With hys)
No hys
Linear (No hys)
35
Prec, (cm)
With hys
Linear (With hys)
LC depth vs precipitationNorrkoping, 24h-soil 1
0.8
0.4
No hys
Linear (No hys)
0.8
35
45
Prec, (cm)
With hys
No hys
Linear (With hys)
Linear (No hys)
45
With hys
No hys
Linear (With hys)
Linear (No hys)
1.2
LC depth vs precipitationNorrkoping, 24h-soil 3
0.8
0.4
0.4
25
35
Prec, (cm)
Depth to LC (m)
1.2
LC depth vs precipitationNorrkoping, 4h-soil 3
25
LC depth vs precipitationNorrkoping, 24h-soil 2
Depth to LC (m)
1.6
No hys
Linear (No hys)
0.8
45
1.2
2
45
0.4
0.4
25
35
Prec, (cm)
With hys
Linear (With hys)
No hys
Linear (No hys)
Depth to LC (m)
1.6
2.4
0.4
45
2
0.4
Depth to LC (m)
35
0.8
Prec, (cm)
Depth to LC (m)
Depth to LC (m)
Depth to LC (m)
Depth to LC (m)
Depth to LC (m)
1.6
2.4
1.2
1.2
2.2
LC depth vs precipitationNorrkoping, 0.5h-soil 3
25
35
Prec, (cm)
With hys
Linear (With hys)
45
No hys
Linear (No hys)
25
35
Prec, (cm)
With hys
Linear (With hys)
45
No hys
Linear (No hys)
72
E-7: Depth of COM versus precipitation for all soils in petisträsk with half hourly, 4-hourly, and daily meteoroligical input data
0.8
0.4
0.8
0.4
0
0
With hys
Linear (No hys)
Linear (With hys)
Depth of COM vs.
precipetation-Petisträsk, 4hsoil 1
1.2
0.8
0.4
No hys
Linear (No hys)
0
55
With hys
Linear (With hys)
Depth of COM vs.
precipetation-Patisträsk, 4hsoil 2
1.2
0.8
0.4
55
Linear (With hys)
0.8
0.4
0
35
Prec. (cm)
No hys
Linear (No hys)
No hys
Linear (No hys)
With hys
Linear (With hys)
0.4
15
55
With hys
Linear (With hys)
0.8
0.4
0
55
With hys
Linear (With hys)
Depth of COM vs.
precipetation-Petisträsk, 4h0.8
soil 3
15
No hys
Linear (No hys)
35
Prec. (cm)
55
With hys
Linear (With hys)
35
Prec. (cm)
No hys
Linear (No hys)
Depth of COM vs.
precipetation-Patisträsk,
24h-soil 2
1.2
Depth of COM (m)
1.2
55
0
15
Depth of COM vs.
precipetation-Petisträsk, 24
h-Sand
35
Prec. (cm)
35
Prec. (cm)
No hys
Linear (No hys)
55
With hys
Linear (With hys)
Depth of COM vs.
precipetation-Petisträsk,
24h-soil 3
0.8
Depth of COM (m)
With hys
Linear (No hys)
15
0
15
0
35
Prec. (cm)
No hys
1.6
35
0.4
Prec. (cm)
No hys
15
Depth of COM (m)
15
55
Depth of COM (m)
35
Prec. (cm)
Depth of COM (m)
Depth of COM (m)
15
Depth of COM vs.
precipetation-Petisträsk,
0.5h-soil 3
0.8
Depth of COM (m)
1.2
1.6
Depth of COM vs.
precipetation-Patisträsk,
0.5h-soil 2
1.2
Depth of COM (m)
Depth of COM (m)
Depth of COM vs.
precipetation-Patisträsk,
0.5h-soil 1
1.6
0.4
0
15
No hys
Linear (No hys)
35
Prec. (cm)
55
With hys
Linear (With hys)
73
15
35
prec. (cm)
Mass into GW, mg/cm3
No hys
0.08
0.04
0
0.16
35
prec. (cm)
4E-04
0E+00
15
0.08
0.04
0
No hys
With hys
55
1E-03
35
prec. (cm)
0E+00
0E+00
35
45
prec. (cm)
With hys
55
35
prec. (cm)
55
With hys
Mass into GW vs.
precipetation-Petisträsk, 4hsoil 2
8E-06
4E-06
0E+00
15
With hys
4E-04
No hys
8E-06
No hys
55
8E-04
25
Mass into GW vs.
precipetation-Petisträsk,
0.5h-soil 2
15
25 35 45
prec. (cm)
No hys
Mass into GW vs.
precipetation-Petisträsk,
24h-soil 2
15
2E-05
With hys
No hys
0.12
55
8E-04
With hys
35
prec. (cm)
35
prec. (cm)
Mass into GW vs.
precipetation-Petisträsk, 4 h1E-03
soil 2
55
Mass into GW vs.
precipetation-Petisträsk,
24h-soil 1
15
15
No hys
0.12
No hys
0E+00
With hys
Mass into GW vs.
precipetation-Petisträsk, 4hsoil 1
0.16
15
Mass into GW, mg/cm3
55
4E-04
Mass into GW (mg/cm3)
0
8E-04
Mass into GW (mg/cm3)
0.04
1E-03
Mass into GW vs.
precipetation-Petisträsk,
0.5h-soil 2
Mass into GW (mg/cm3)
0.08
Mass into GW (mg/cm3)
0.12
Mass into GW (mg/cm3)
0.16
Mass into GW vs.
precipetation-Petisträsk,
0.5h-soil 1
Mass into GW (mg/cm3)
Mass into GW, mg/cm3
E-8: Mass into GW versus precipitation for all soils in Petisträsk with half hourly, 4-hourly, and daily meteoroligical input data
55
With hys
Mass into GW vs.
precipetation-Petisträsk,
24h-soil 2
2E-05
8E-06
0E+00
15
35
prec. (cm)
No hys
55
With hys
74
E-9: Depth to LC versus precipitation for all soils in Petisträsk with half hourly, 4-hourly, and daily meteoroligical input data
LC depth vs precipitationPetisträsk, 0.5h-soil 1
1.6
1.5
1.2
1.2
0.8
0.4
0.7
15
35
prec. (cm)
No hys
Linear (No hys)
15
55
With hys
Linear (With hys)
With hys
Linear (No hys)
Linear (With hys)
15
0.7
0.8
0.4
15
35
prec. (cm)
No hys
Linear (No hys)
55
15
With hys
Linear (With hys)
35
prec. (cm)
With hys
Linear (No hys)
Linear (With hys)
15
0.7
15
No hys
Linear (No hys)
35
prec. (cm)
55
With hys
Linear (With hys)
55
With hys
Linear (With hys)
LC depth vs precipitationPetisträsk, 24h-soil 3
1.2
Depth to LC (m)
1.5
35
prec. (cm)
No hys
Linear (No hys)
1.6
Depth to LC (m)
3.1
2.3
0.4
LC depth vs precipitationPetisträsk, 24h-soil 2
LC depth vs precipitationPetisträsk, 24h-soil 1
With hys
Linear (With hys)
0.8
55
No hys
55
LC depth vs precipitationPetisträsk, 4h-soil 3
1.2
Depth to LC (m)
Depth to LC (m)
1.5
1.2
35
prec. (cm)
No hys
Linear (No hys)
1.6
2.3
0.8
0.4
55
LC depth vs precipitationPetisträsk, 4h-soil 2
3.1
Depth to LC (m)
35
prec. (cm)
No hys
LC depth vs precipitationPetisträsk, 4h-soil 1
Depth to LC (m)
LC depth vs precipitationPetisträsk, 0.5h-soil 3
Depth to LC (m)
Depth to LC (m)
Depth to LC (m)
3.1
2.3
LC depth vs precipitationPetisträsk, 0.5h-soil 2
1.2
0.8
0.4
15
No hys
Linear (No hys)
35
prec. (cm)
55
With hys
Linear (With hys)
0.8
0.4
15
No hys
Linear (No hys)
35
prec. (cm)
55
With hys
Linear (With hys)