Content uploaded by Attila Galsa
Author content
All content in this area was uploaded by Attila Galsa on Apr 11, 2022
Content may be subject to copyright.
Journal of Hydrology 609 (2022) 127695
Available online 9 March 2022
0022-1694/© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
nc-nd/4.0/).
Research papers
Interaction of basin-scale topography- and salinity-driven groundwater
ow in synthetic and real hydrogeological systems
Attila Galsa
a
,
*
, ´
Ad´
am T´
oth
b
, M´
ark Szij´
art´
o
a
, Daniele Pedretti
c
, Judit M´
adl-Sz˝
onyi
b
a
Department of Geophysics and Space Science, Institute of Geography and Earth Sciences, ELTE E¨
otv¨
os Lor´
and University, Budapest, Hungary
b
J´
ozsef and Erzs´
ebet T´
oth Endowed Hydrogeology Chair, Department of Geology, Institute of Geography and Earth Sciences, ELTE E¨
otv¨
os Lor´
and University, Budapest,
Hungary
c
Dipartimento di Scienze della Terra “A. Desio”, Universit`
a degli Studi di Milano, Milan, Italy
ARTICLE INFO
This manuscript was handled by C. Corradini,
Editor-in-Chief
Keywords:
Mixed topohaline convection
Salinity-driven groundwater ow
Topography-driven groundwater ow
Numerical modelling
ABSTRACT
Salinization of groundwater has endangered e.g. drinking water supply, agricultural cultivation, groundwater-
dependent ecosystems, geothermal energy supply, thermal and hydrocarbon well production to a rising de-
gree. In order to investigate the problem of coupled topography- and salinity-driven groundwater ow on a
basin-scale, a systematic simulation set has been carried out in a synthetic numerical model. Detailed sensitivity
analysis was completed to reveal the effect of the salinity, permeability, permeability heterogeneity and
anisotropy, mechanical dispersivity and water table head on the salt concentration eld and the ow pattern. It
was established that a saline dome with slow inner convection formed beneath the discharge zone in the base
model due to the topography-driven regional fresh groundwater ow. An increase in the salinity or the
anisotropy or decrease in the water table variation weakens the role of the forced convection driven by the
topography, thus facilitating the formation of a saline, dense, sluggish layer in the deepest zone of the basin. In
the studied parameter range, the variation in permeability and dispersivity affects the shape of the saltwater
dome to less degree. However, the decrease in permeability and/or the increase in dispersivity advantage the
homogenization of the salt concentration within the saline zone and strengthen the coupling between the salt-
water and freshwater zone by growing the relative role of diffusion and transverse dispersion, respectively. The
interaction of the topography-driven forced and salinity driven free convection was investigated along a real
hydrological section in Hungary. Simulation elucidated the fresh, brackish and saline character of the water
sampled the different hydrostratigraphic units by revealing the connection between the topography-driven upper
siliciclastic aquifer and the lower conned karstic aquifer through faults in high-salinity clayey aquitard. The
current study improves the understanding of the interaction between the topography-driven forced and the
salinity-driven free convection, i.e. topohaline convection, especially in basin-scale groundwater ow systems.
1. Introduction
Hydrogeological problems that we have to solve in practical tasks
often refer to complex systems, but our solutions are necessarily
simplied. Unfortunately, it means that we neglect many effects and
processes and, on the contrary, put in the focus what we think is sig-
nicant. To exclude these uncertainties and better understand some
physical uid ow processes and their interactions, we started a sys-
tematic analysis of superimposed uid driving forces and their impacts
on basin-scale ow patterns. We have already examined the combina-
tion of topography and thermal buoyancy that drive groundwater ow
in a theoretical basin to better understand the inuencing factors and
the consequences of the interaction (Szij´
art´
o et al., 2019). The lesson
learnt from this systematic theoretical analysis, we applied to a real
hydrogeological system focusing on these driving forces (Szij´
art´
o et al.,
2021). In this paper, we continue the analysis with the interactions of
topography and salinity as driving forces of uids on basin-scale ow
systems and demonstrate it for an actual hydrogeological situation
without trying to extend the problem to any other driving force.
The importance and understanding of salt transport processes in
groundwater ow systems has developed parallel to the increasing
natural resource demands of humankind. In coastal environments, the
rising number and yield of wells producing freshwater entail the sub-
surface transgression of sea water and subsequent deterioration of water
* Corresponding author.
E-mail address: attila.galsa@ttk.elte.hu (A. Galsa).
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
https://doi.org/10.1016/j.jhydrol.2022.127695
Received 12 May 2021; Received in revised form 16 February 2022; Accepted 4 March 2022
Journal of Hydrology 609 (2022) 127695
2
quality has become a daily problem of inhabitants living near the
coastlines (e.g. Barlow and Reichard, 2010; Werner et al., 2013; Hussain
et al., 2019). In an inland environment, salinization triggered by
groundwater overexploitation and pumping deeper and more saline
reserves gives difculties for agriculture, drinking water supply and the
groundwater-dependent ecosystem protection (e.g. Jalali, 2007; Rodrí-
guez-Rodríguez and Benavente, 2008; Herbert et al., 2015; McFarlane
et al., 2017; Payen et al., 2016; Schuler et al., 2018; Singh, 2020).
Interaction of salt and fresh groundwater can lead to carbonate disso-
lution resulting in permeability increase and extended reservoirs for
hydrocarbon and thermal water production (Dublyansky, 1995; Kamb-
esis and Coke, 2013; He et al., 2017; Zhang et al., 2020a; Smith et al.,
2021). On the other hand, it can trigger sinkhole development causing
serious environmental problems and damage (Oz et al., 2016; Karaki
et al., 2019). The long-term negative impact of salinization on aquifers
may be exacerbated by the effects of climate change (Havril et al., 2018),
e.g. in terms of sea level rising or change in intensity–duration–fre-
quency of precipitation events (e.g. De Paola et al., 2014; Sun et al.,
2019). In addition, lithium recovery from brine attempts to satisfy the
increasing requirements of the battery industry (e.g. Kesler et al., 2012;
Marazuela et al., 2018; García-Gil et al., 2019).
Dissolved solids content increases the water density; hence it affects
the groundwater ow driven by buoyancy force. Nield (1968) analyti-
cally determined the conditions of the onset of haline convection in a
homogeneous, horizontal innite porous layer, and Van Dam et al.
(2009) uncovered the rst eld documentation of precipitation-induced
saltwater ngering as a manifestation of natural free convection in a
porous medium. However, the water table elevation varies from place to
place, thus the topography-driven groundwater ow is always present in
the upper part of the terrestrial basins (T´
oth, 2009). Therefore, it also
acts in these terrestrial environments with elevated dissolved solid
content. Consequently, these cases require mathematical models (typi-
cally, numerical models) to evaluate the coupled effects of topography-
and salinity-driven groundwater ow.
The concept of coupled topography- and salinity-driven groundwater
ow has been adopted to explain the high salt content of the submarine
groundwater discharge (SGD) on a local scale (Konikow et al., 2013),
and to elucidate the variability and the distance of SGD in a heteroge-
neous coastal volcanic aquifer near the Big Island of Hawaii, USA
(Kreyns et al., 2020). Duffy and Al-Hassan (1988) revealed the
groundwater circulation in a homogeneous medium as a balance be-
tween the rainwater recharge in surrounding mountains and the salt-
water counter ow beneath the playa in the Great Basin, Utah, USA. The
two-dimensional, homogeneous and isotropic numerical model was
recalculated using multicomponent reactive transport simulations to
infer the evolution of the evaporite precipitation and brine composition
(Hamann et al., 2015). Topography-driven forced and salinity-driven
free convection processes were modelled in a simple geological envi-
ronment to trace the brine inltration beneath a saline disposal basin in
Australia (Simmons and Narayan, 1997). Zhang et al. (2020b) presented
a sensitivity analysis to study the effect of the salinity, the hydraulic
conductivity and the dispersivity on the positions of stagnation points
and the hierarchy of the groundwater ow system. However, it seems
from the published papers that topography effects are examined on a
local scale or for simple basins, but they are commonly neglected.
Therefore, some of the models remained oversimplied in terms of
omittance of variations in topography and water table.
Although numerical models are acknowledged tools to quantify the
interaction of topography- and salinity-driven groundwater ow,
several questions are still unresolved regarding the sensitivity of these
models to the key parameters feeding the governing equations. Small
variations in critical parameters, such as relative density differences due
to salinity, variations of intrinsic permeability, anisotropy and me-
chanical dispersivity or change in water table amplitude may generate
great deviations in model outputs. As such, given the ubiquitously
difcult aquifer characterization that renders model parameterization
always uncertain, high sensitivity to model parameters can create high
uncertainty in the decisions to be made about the water management of
an aquifer. While disentangling the model response to the input pa-
rameters is therefore of the uppermost importance, this task is in turn
severely complicated by the computational burden required to resolve
the nonlinear fully coupled density-dependent groundwater ow
equations.
The main aim of this paper is to investigate, through detailed nu-
merical modelling, how the interaction of topography-driven forced and
salinity-driven free convection and the different model parameters in-
uence the salt concentration and groundwater ow pattern at basin-
scales and thus how the decisions made from the model responses
may vary depending on the model sensitivity. Other uid driving forces,
e.g. temperature difference, compaction, compression, were neglected
in order to focus on and highlight the interaction of topography- and
salinity-driven regional groundwater ow and systematically examine
the effects of this interaction rstly. Once the processes and phenomena
are comprehensively understood and synthesized, other uid driving
processes can also be coupled. Therefore, in the rst part of the paper, a
two-dimensional, synthetic simulation set is presented, where the effect
of salinity (dissolved solid content), permeability, depth-dependence
and anisotropy of permeability, dispersivity and water table amplitude
is qualied and quantied systematically by monitoring parameters, e.g.
the Darcy ux and the salt concentration for both the entire basin and
the fresh/saltwater zones. In the second part, the mixed topohaline
convection simulation is carried out to demonstrate its effect in a real
environment, along a hydrogeological section in Hungary based on
M´
adl-Sz˝
onyi et al. (2019). The fundamental goal is to reveal the evo-
lution of marine-origin pore water and to explain the formation of the
fresh-, brackish and saltwater saturated units on a basin scale.
2. Materials and methods
2.1. Model development
The solution of the combined topography- and salinity-driven
groundwater ow requires the coupled handling of the continuity
equation (1), the Darcy’s Law (2) and the mass transport equation (3)
governing the mass conservation, the momentum conservation and the
transport of the dissolved solid matter by advection, molecular diffusion
and mechanical dispersion, respectively (Delgado, 2012; Nield and
Bejan, 2017),
Φ
∂ρ
w
∂
t+ ∇(
ρ
wq) = 0(1)
q= − k
μ
[∇p−
ρ
wg](2)
Φ
∂
c
∂
t= − q∇c+ ∇ DdiffI+Ddisp ∇c(3)
where q, p and c denote the unknown Darcy ux, the pressure and the
dissolved salt concentration, while Φ, k,
μ
, g, D
diff
, D
disp
, t and I are the
porosity, the diagonal permeability tensor, the dynamic viscosity of the
water, the gravitational acceleration, the molecular diffusion, the me-
chanical dispersion, the time and the identity matrix, respectively. The
parameters of the base model are summarized in Table 1. The salinity-
dependence of the viscosity was neglected in the course of the simula-
tion, the dispersion tensor was dened by the longitudinal and the
transverse dispersivity,
α
L
and
α
T
, respectively. The transverse dis-
persivity was afxed to the longitudinal one,
α
T
=
α
L
/10. The salt con-
tent was characterized by the non-dimensional concentration ranging
between c =0 and 1 to focus on the density variation of the water. A
simple linear relation was supposed between the water density and the
concentration (e.g. Duffy and Al-Hassan 1988, Nield and Bejan 2017),
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
3
ρ
w=
ρ
0(1+βc)(4)
where
ρ
0
=1000 kg/m
3
is the freshwater density and β denotes the
relative density difference between freshwater (c =0) and saltwater (c
=1).
A simple two-dimensional numerical model was built to reveal the
physical background of salinity transport. The basin-scale model is
characterized with a length of L =40 km and a mean depth of d =5 km
(Fig. 1) to test the outcomes of synthetic simulations for a real hydro-
geological system. The boundary conditions for the ow were no-ow
along the sidewalls and the bottom, while the regional groundwater
ow was driven by a cosinusoid water table (e.g. Domenico and Pal-
ciauskas, 1973; Wang et al., 2015; Zhang et al., 2018),
zwt(x) = − A⋅cos
π
x
L(5)
with an amplitude of A =50 m, where x denotes the horizontal coor-
dinate. The water table, z
wt
corresponds to the top of the model domain.
No-ux boundary conditions for the concentration were prescribed
along the sidewalls, while the concentration was xed along the hori-
zontal boundaries. It was c =1 at the bottom and c =0 on the surface,
thus diffusive and dispersive ux was allowed across the horizontal
boundaries. The former represents salinity inux from a deep imper-
vious formation, and the latter symbolizes e.g. the freshwater inltration
and the salt precipitation from the groundwater. The initial condition for
the ow was obtained from Eqs. (1)–(2) with reference water density
(Fig. 1.a), and the initial condition for the concentration was calculated
from Eq. (3) without the advection term (q =0), which is the solution of
the diffuse problem resulting in linear vertical concentration prole
(Fig. 1.b).
The coupled problem (Eq. (1)–(3)) was solved by COMSOL Multi-
physics v4.2, a nite element numerical software package (Zimmer-
mann, 2006. The model domain was discretized by triangle elements
with a maximum size of 100 m and 8 boundary layer elements were used
to minimize the inaccuracy due to the weak resolution of the high
gradient zones. Thus, the mesh consisted of 57,159 nite elements for
the base model, which varied between 56,880–80,023 as the water table
amplitude was changed from 0 m to 500 m. The pressure and the con-
centration were discretized within the elements by quadratic and linear
polynomials, respectively. Simulations were run until models reached
the stationary solution, which required typically 1 Myr, ranging from
0.5 to 50 Myr (e.g. for low permeability, high permeability anisotropy or
slight water table amplitude). Initial time steps were increased expo-
nentially to 1000 yr to stabilize the transition effects, after that the
maximum time step was xed as 100 yr. Simulations were run on an
Intel Workstation with 24 cores, requiring approx. 1–2 days CPU time
and 4 GB memory for one model. Before the synthetic simulation set, the
coupled model was expansively tested and conrmed in a horizontal and
inclined layer, and solutions were compared with the analytical and
numerical results of Weatherill et al. (2004). Tests resulted in perfect
accordance focusing on the onset (critical Rayleigh number) and the
form (transition from multi- to unicellular convection) of free haline
convection.
Table 1
Parameters of the base model.
Description Symbol Value Unit
Porosity Φ 0.1 1
Reference water density
ρ
0
1000 kg/m
3
Dynamic viscosity of the water
μ
10
-3
Pa s
Molecular diffusion D
diff
10
-9
m
2
/s
Relative density difference β 0.01 1
Horizontal permeability of the matrix k
x
10
-12
m
2
Factor of depth-dependent permeability γ 1 1
Permeability anisotropy coefcient
ε
1 1
Longitudinal dispersivity
α
L
0 m
Transverse dispersivity
α
T
0 m
Water level amplitude A 50 m
Fig. 1. Boundary and initial conditions for (a) the ow (blue) and (b) the salt concentration (green) in the base model (Table 1). (a) Streamlines of the Darcy ux
(white) are magnitude controlled, red arrows illustrate the ow direction. (b) Isocontour of c =0.5 (black line) represents the boundary between the saltwater and
the freshwater zone. The model length is 40 km, the average model depth is 5 km, the vertical exaggeration is 1.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
4
2.2. Model parameterization
Firstly, we systematically investigated the effect of the following
relevant parameters (Table 2) resulting in 56 time-dependent models:.
1. the relative density difference due to salinity, β;
2. the permeability, k;
3. the factor of depth-dependence of permeability, γ;
4. the permeability anisotropy,
ε
;
5. the mechanical dispersivity,
α
L
and
α
T
; and
6. the water level amplitude, A.
The six selected parameters are usually uncertain given the limited
characterization and exhibit strong scale dependency. For instance, the
salinity of groundwaters may vary both in time and space. In Hungary, it
is typical that the salt concentration increases with depth owing to the
deep, marine sedimentary environment, while salinity is lower in
shallow strata complexes due to lacustrine sedimentation and the
intense meteoric water inltration (e.g. Vars´
anyi and ´
O.Kov´
acs, 2009;
Szocs et al., 2013). In general, the groundwater salinity can vary from
0 to even 40% including fresh, brackish, saline and brine waters
(Deming, 2002). In this paper, the effect of salinity on the water density
is parameterized by a factor of β, which presents the relative density
increase of the water. The aquifer permeability (or hydraulic conduc-
tivity) can vary over several orders of magnitude in relatively short
spatial scales to the effects of geological heterogeneity (Sanchez-Vila
et al., 2006; Pedretti et al., 2016; Liu et al., 2016). One of the most
common heterogeneities of permeability is its pressure-dependence
(Ehrenberg and Nadeau, 2005). Permeability decreasing exponentially
with depth was dened by
k(z) = k0explnγ⋅z
d(6)
to characterize the pressure-dependence of the permeability (Jiang et al.
2009; Jiang et al., 2011), where k
0
denotes the surface permeability and
z is the vertical coordinate pointing upwards. Anisotropy also controls
the time evolution of ow and transport patterns in aquifers and de-
pends on the nature and connectivity of the hydrogeological bodies
(Cirpka et al., 2015; Pedretti et al., 2014). In siliciclastic sedimentary
basins, where the sub-horizontal aquifer and aquitard layers alternate,
the effective hydraulic conductivity strongly depends on the ow di-
rection. The horizontal permeability, in such environments, can exceed
the vertical permeability by several orders of magnitude (e.g. Galsa,
1997; Hoque and Burgess, 2020). Mechanical dispersion is present in the
subsurface both in microscopic scale (grain size) and local scale (e.g.
quasi-impermeable zones, lens). In aquifers (e.g. fractured media, sili-
ciclastic and uvial sediments), the longitudinal dispersivity is scale-
dependent (Gao et al., 2012) and varies within a wide range (Gelhar
et al., 1992; Schulze-Makuch, 2005; Vanderborght and Vereecken,
2007). The variation of the water level inuences both the ow pattern
and the salinity of the groundwater as one of the main driving forces (e.
g. T´
oth, 2009).
The inuence of forming dense, saline zone/layer on the concen-
tration eld and the ow pattern was studied both qualitatively and
quantitatively. Monitoring parameters were dened to characterize the
groundwater ow system by the average Darcy ux (q
av
), concentration
(c
av
), hydraulic head (h
av
), as well as the relative area (A
s
, A
f
), the Darcy
ux (q
s
, q
f
) and the concentration (c
s
, c
f
) computed for both the saltwater
(subscript s) and the freshwater (subscript f) zone. The salt- and fresh-
water zones were separated by an arbitrary boundary of the solute
content of c =0.5. After the synthetic numerical simulations, the
topography- and salinity-driven groundwater ow model was applied
along a 2D hydrogeological section in Hungary taking into consideration
the outcome of the synthetic model runs.
3. Synthetic model results
3.1. Effect of relative density difference
As a rst step, the effect of density increase due to salinity on the
concentration eld and the ow pattern was studied. The results show
that the saltwater is swept out from the basin by the topography-driven
groundwater ow, when β =0, i.e. the water density is independent of
the salt content (Fig. 2.a). A shrank zone beneath the discharge area can
survive the regional freshwater circulation near the stagnation point
(see e.g. An et al., 2015). Even though the saltwater is denser by only
1%, an extended saline zone (c ≥0.5, contoured by a black line) forms
beneath the discharge area in the base model (Fig. 2.b, Table 1). The
concentration distribution within the saline zone is rather diffuse sug-
gesting that there is no intense inner ow. As the salt content (i.e. water
density due to salinity) increases, a dense layer evolves right above the
model bottom (Fig. 2.d–g), which consequently reduces the diffuse
transport from the base below resulting in an average concentration
decrease in the basin.
Fig. 3 illustrates how the dense, saline zone modies the regional,
unidirectional ow pattern. When the concentration-dependence of the
water density is neglected (Fig. 3.a), the Darcy ux eld is equivalent to
the solution of the simple Darcy ow (see Fig. 1.a). When the water
density is not neglected (Fig. 3.b–d), the ow eld strongly depends on
the presence of the saline zone. The most striking inuence of the saline
zone on the ow pattern is that the topography-driven regional ow is
suppressed, but the magnitude of the Darcy ux is not affected by the
saline dome. On the other hand, slow circulation forms within the
saltwater domain. This sluggish inner convection has opposite vorticity
compared to the regional groundwater ow. The pattern of the inner
convection depends strongly on the saline content, as measured by β.
The higher the salinity contrast with the freshwater, the more pro-
nounced the recirculation zone. Note that β =3% produces an inner
convection zone about two times more extended compared to β =1%.
The model is therefore highly sensitive to limited salinity changes.
The given problem of topography- and salinity-driven groundwater
ow tends towards a stationary solution, which is plotted against the
relative density difference, β (Fig. 4). As the water density increases (see
Eq. (4)) from β =0 to 0.2, the domain-averaged Darcy ux (q
av
) is
reduced by 43% (Fig. 4.a). The domain-averaged concentration (c
av
)
shows a non-monotonic character with a maximum at about β =2–3%
(Fig. 4.b), when a considerable saltwater zone forms beneath the
discharge area (Fig. 2.c). At a lower value of β, the salt content cannot
resist the topography-driven groundwater ow, while at a higher value
of β a thin, dense salty layer evolves in the deepest part of the basin. The
domain-averaged hydraulic head (h
av
) becomes more negative owing to
the increasing water density (Fig. 4.c).
The specic behaviour of the saltwater and freshwater zone sepa-
rated by the arbitrary isocontour of c =0.5 was also investigated. As β
increases, the relative area of the dense, saline zone (A
s
, the area normed
by the total area of the basin) shrinks, apart from the model of β =0,
when the saltwater is swept out from the basin (Fig. 2.a and 4.d). On the
contrary, the relative area of the complementary freshwater zone, A
f
(also normed by the total area of the basin) increases in the same way as
A
s
decreases. Fig. 4.e illustrates that the inner convective velocity of the
saltwater zone (q
s
) is lower up to about two orders of magnitude
Table 2
Studied parameters.
Description Symbol Value Unit
Relative density difference β 0–0.2 1
Matrix permeability k 10
-14
–10
-12
m
2
Factor of depth-dependent permeability γ 1–100 1
Permeability anisotropy coefcient
ε
1–1000 1
Longitudinal dispersivity
α
L
(=10
α
T
) 0–100 m
Water level amplitude A 0–500 m
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
5
compared to the velocity of the freshwater zone (q
f
), which remains
quite constant (q
f
≈2⋅10
-8
m/s). Specically, the minimum saltwater
velocity of q
s
=3⋅10
-10
m/s was found when β =2%, i.e. at the peak of
maximum domain-averaged concentration, c
av
. This point also corre-
sponds to the lowest average concentration of the dense zone (c
s
≈0.65)
(Fig. 4.f), when an extended saltwater dome with thick transition zone
forms beneath the discharge zone (Fig. 2.c).
Fig. 2. Stationary solution of salt concentration at different relative density differences, β =0–20%. Other parameters are dened in the base model (Table 1). Black
isocontour of c =0.5 represents the boundary of the saltwater and the freshwater zones.
Fig. 3. Darcy ux for different relative density differences due to salinity at t =100 kyr. Streamlines (white – not magnitude controlled) and arrows (red –
normalized) represent the ow direction.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
6
3.2. Effect of permeability
3.2.1. Permeability in a homogeneous and isotropic medium
The role of rock permeability on the salinity was investigated using
the base model (Table 1), while the permeability (horizontal and ver-
tical) was decreased from k =10
–12
m
2
to 10
–14
m
2
. Fig. 5 illustrates that
the change in permeability has no drastic inuence on the salt concen-
tration eld. By decreasing the permeability, the ow linearly slows
down (Fig. 6.a), according to Eq. (2). When the Darcy ux is reduced in
the freshwater zone, the diffusion ux across the boundary of the salt-
and freshwater zones is retained. Lower diffusion ux from the saltwater
zone results in higher salt content (Fig. 6.b) and a more homogeneous
concentration eld (Fig. 5.a–d). As the average salt content increases,
the hydraulic head decreases due to the enhanced water density (Fig. 6.
c).
Decreasing the permeability from k =10
-13
m
2
to 10
-14
m
2
, the
diffusion ux becomes commensurable to the order of advection, thus
the diffusion zone between the salt- and freshwater thickens (Fig. 5.d–g).
A thickening diffusion zone appears above the model bottom, as well.
While the change in permeability by two orders of magnitude drives an
equal reduction in the average Darcy ux, the maximum of the diffusion
ux reduces by only a factor of 5, specically from 8⋅10
-11
to 1.4⋅10
-
11
m/s.
The permeability reduction inuences the Darcy ux of the saltwater
and freshwater zones in a different manner (Fig. 6.e). The ow slows
down in both zones, but the gradient of the Darcy ux curve is higher for
the freshwater zone than the saltwater zone (i.e. dq
f
/dk >dq
s
/dk),
consequently, the difference in the Darcy ux decreases to one order of
magnitude. The effect of two processes appears both in the concentra-
tion and the relative area curves (Fig. 6.d and f). The homogenization (in
the cases of k =10
-12
–10
-13
m
2
) increases the salt content and the area of
the saline zone. Then the diffusion zone thickening (in the cases of k =
10
-13
–10
-14
m
2
) hinders the rate of the area growth, and it leads to a
slight concentration decrease within the saltwater zone. Nevertheless,
the average salt content of the basin shows a slight increase (Fig. 6.b)
owing to the slowing down regional groundwater ow.
3.2.2. Permeability heterogeneity
Owing to the increasing pressure, the permeability shows a decrease
downwards both in carbonates and sandstones, which is frequently
Fig. 4. Stationary solutions of the monitoring parameters plotted against the relative density contrast, β. (a) The average Darcy ux, (b) the average salt concen-
tration and (c) the average hydraulic head. (d) The relative area, (e) the Darcy ux and (f) the concentration averaged for the saltwater (red) and the freshwater
(blue) zones.
Fig. 5. Stationary solution of salt concentration at different permeability of the matrix, k =10
–12
–10
-14
m
2
. Other parameters are dened in the base model (Table 1).
Black isocontour of c =0.5 represents the boundary of the saltwater and the freshwater zones.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
7
approximated by an exponential trend. In Eq. (6) γ represents the factor
of the permeability decay, that is the ratio of the surface and bottom
permeability. Fig. S1 (Supplementary material) illustrates the effect of γ
on the concentration eld within the interval of γ =1–100. Increasing γ
has a very similar inuence on salinity as decreasing permeability in the
previous part. When the permeability decreases with depth by a factor of
1–10 (Fig. S1.a–d), a homogenization occurs in the saltwater zone due to
the lower Darcy ux in the freshwater zone (Fig. S2.e in Supplementary
material) and the reduced diffusion ux across the boundary of the salt-
and freshwater zones. The only difference between Fig. 5 and Fig. S1 is
that the homogenization evolves not in the whole saltwater dome, but it
has a depth-dependence (γ >1). This process results in a considerable
increase in average concentration (Fig. S2.b), the area and the concen-
tration of the saltwater zone (Fig. S2.d and f).
Decreasing permeability with depth by 1–2 orders of magnitude (γ =
10–100) brings forward another phenomenon (Fig. S1.d–g). The Darcy
ux decrease with depth is so pronounced that the diffusion approxi-
mates the advection in the mass transport, thus a diffusion zone forms
between the fresh- and saltwater zones, as well as along the bottom
boundary. It enhances the salinity in the freshwater zone (Fig. S2.f).
Because of the depth-dependent permeability, the diffusion zone thins
upwards, and in the near-surface region, the intense ow effectively
erodes the top of the saltwater dome. Consequently, a slight reduction
can be observed in the average concentration (Fig. S2.b), the area and
the concentration of the saltwater dome (Fig. S2.d and f). Depth-
dependent permeability induces a continuous Darcy ux and hydrau-
lic head decrease in the whole basin (Fig. S2.a and c), however, the ow
slows down less in the freshwater zone, which occupies the shallower
zones of the basin (Fig. S2.e).
3.2.3. Permeability anisotropy
The permeability anisotropy coefcient, which is the ratio of the
horizontal to vertical permeability, was varied ranging between
ε
=
1–1000, while the value of the horizontal permeability was xed, k
x
=
10
-12
m
2
. Weakening the vertical permeability leads to slower ow
which extends the simulation time. For models, where 2 Myr was not
enough to reach the stationary solution, and the variation of the moni-
toring parameters was very slow, a steady-state solution was calculated
from the end of the time-depending solution.
It was found that the anisotropy strongly modies the shape of the
saltwater zone. Fig. 7 displays the stationary solution of the salt con-
centration at different permeability anisotropies. As the anisotropy in-
creases from
ε
=1 to 50 (Fig. 7.a–d), the boundary between the salt- and
the freshwater zones changes from convex to concave, since the
groundwater ow becomes constrained to shallower zones. Growing the
anisotropy beyond the value of
ε
=100, the penetration of the regional
groundwater ow decreases, and a sluggish layer evolves in the deep
part of the basin. In the case of
ε
=1000, this sluggish zone becomes
thicker (approx. 1.5–2 km). The concentration in the salt layer shows a
diffuse pattern indicating that there is no relevant advective mass
transport.
Monitoring parameters point out the dichotomy of the effect of
anisotropy. As
ε
increases, the average Darcy ux decreases with an
increasing gradient (Fig. 8.a). The change in the morphology of the
saltwater dome (
ε
=1–50) is reected in a slight decrease of the average
concentration and the relative area of the saline zone (Fig. 8.b and d).
Within this interval, the Darcy ux in the saltwater zone is nearly con-
stant. At higher anisotropy values (
ε
≥50) the topography-driven fresh
groundwater does not reach the bottom of the basin, which facilitates
the formation of the deep, saline, sluggish, dense layer above the bot-
tom. This thickening layer enhances the average salt content (Fig. 8.b),
which results in a relevant head decrease (Fig. 8.c). The size of the saline
zone increases (Fig. 8.d), and the Darcy ux decreases steeply (Fig. 8.e).
As a result of the appearance of the diffuse transition across the salt- and
freshwater boundary, the salt content of the freshwater zone grows
(Fig. 8.f).
3.3. Effect of dispersivity
Longitudinal dispersivity was raised from the value of the base
model,
α
L
=0 to 100 m (Fig. 9), meanwhile the transverse dispersivity
varied together with
α
L
as
α
T
=
α
L
/10. Even though the longitudinal
dispersivity is only
α
L
=1 m, the concentration distribution within the
saline dome becomes more homogeneous (Fig. 9.b). By increasing
α
L
to
10 m, the salt content is getting higher owing to (1) the enhanced lon-
gitudinal dispersion of inner convection within the saltwater zone, and
(2) the higher transverse dispersion across the bottom below the saline
dome (Fig. 9.a–e). As the dispersivity was increased further (
α
L
=
10–100 m), the boundary separating the salt- and the freshwater zone
thickens due to the incremented transverse dispersion. In addition, a
Fig. 6. Stationary solutions of the monitoring parameters plotted against the matrix permeability, k. (a) The average Darcy ux, (b) the average salt concentration
and (c) the average hydraulic head. (d) The relative area, (e) the Darcy ux and (f) the concentration averaged for the saltwater (red) and the freshwater (blue) zones.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
8
thin salty layer evolves along the bottom of the model beneath the
freshwater zone. Mechanical dispersion facilitates the solute content
mixing both within and between the zones, and consequently, it en-
hances salt transport. The surface Sherwood number (Weatherill et al.,
2004) increases from 146 to 1410 within the range of
α
L
=0–100 m.
Fig. 10 quanties the above-mentioned processes. Within the inter-
val of
α
L
=0–10 m, the saltwater zone enlarges from A
s
=20% to 30%
(Fig. 10.d), its solute content increases by dispersive mixing (Fig. 10.f),
and the ow intensies due to the stronger linkage between the salt
dome and the topography-driven freshwater zone (Fig. 10.e). The
broadening salt dome reduces the average Darcy ux of the basin ow
by approx. 10% (Fig. 10.a), enhances the average salt content consid-
erably (Fig. 10.b), which results in lower hydraulic heads (Fig. 10.c).
When the longitudinal dispersivity is ranged from
α
L
=10 to 100 m,
there is no such a signicant variation in the monitoring parameters. As
the transition zone thickens due to the effective transverse dispersion
ux (between the salt- and freshwater zones, and along the bottom of the
basin), the Darcy ux difference and the solute content difference
between the two zones moderate (Fig. 10.e and f).
3.4. Effect of water table amplitude
The inuence of topography-driven groundwater ow can be
directly stimulated by the water table gradient. In the synthetic model,
the amplitude of the water table was varied between A =0 and 500 m to
observe the modication of the saltwater zone. In the models where the
amplitude was higher than that of the base model (A >50 m), the
regional groundwater ow was intense enough to press the saline dome
to the left side (Fig. 11.e–g). The saline zone shrank toward the stag-
nation point and its density increased to be able to resist the regional
freshwater ow. For lower water table amplitudes (A <50 m) the
topography-driven ow weakens, thus the saline zone tends to pervade
the deeper part of the basin to form a dense, saline layer (Fig. 11.a–c). It
is worth noting when the amplitude is approx. A =10 m, the
topography-driven groundwater ow is weak enough to press the saline
dome to the discharge zone, but strong enough to advect the brackish
Fig. 7. Stationary solution of salt concentration at different permeability anisotropy,
ε
=1–1000. Other parameters are dened in the base model (Table 1). Black
isocontour of c =0.5 represents the boundary of the saltwater and the freshwater zones.
Fig. 8. Stationary solutions of the monitoring parameters plotted against the permeability anisotropy,
ε
. (a) The average Darcy ux, (b) the average salt concen-
tration and (c) the average hydraulic head. (d) The relative area, (e) the Darcy ux and (f) the concentration averaged for the saltwater (red) and the freshwater
(blue) zones. The end of the time-dependent solution is denoted by diamond, the stationary solution computed from the end of the time-dependent solution is
denoted by a circle.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
9
water from the model (Fig. 11.b). As a result, the size of the saline zone is
reduced. At A =1 m, the regional ow is weak, which results in a nearly
diffuse density-based layering (Fig. 11.a).
Stationary numerical solutions show a linear relationship between
the average Darcy ux and the water table head, following Darcy’s law
formulated in Eq. (2) (Fig. 12.a). The more intense the regional ow is,
the lower the average salt concentration in the basin is noticed (Fig. 12.
b), and lower salt content causes higher hydraulic heads (Fig. 12.c).
Hydraulic head higher than zero is the consequence of that the area
dominated by recharge is enhanced, while the area dominated by
discharge is reduced. At A =50 m the relative area of the zone having h
>0 is 50.3%, while it is 53.1% at A =500 m. As the water table
amplitude decreases, the average head becomes more negative, for the
model of A =1 m, only 15.1% of the model domain is characterized by a
hydraulic head higher than zero.
Decreasing water table amplitude eventuates in that the Darcy ux is
reduced both in the fresh- and the saltwater zone (Fig. 12.e). The ow
within the saline zone is slower by 1–2 orders of magnitude. The Darcy
ux in the model without water table variation (A =0) tends to zero,
therefore it is not displayed in Fig. 12.e. The size of the saline zone in-
creases by weakening the topography-driven ow (A), and it converges
to A
s
=A
f
=0.5 at A =0 (diffuse solution) in Fig. 12.d. However, a local
extremum appears in the curves near A =10 m, where a transition exists
in the morphology of the saltwater zone, and the saline dome transforms
into a deep, saline layer. The salt content of the freshwater zone is
practically zero if A >50 m, the regional ow sweeps out the saltwater
from the topography-dominated groundwater zone (Fig. 12.f). Since the
salt content of the saline zone increases by A, a sharp boundary evolves
between the two zones in the absence of mechanical dispersion (Fig. 11.
g). On the contrary, reducing A the concentration of the two zones
converge to the diffuse solution, c
s
=0.75 and c
f
=0.25.
Fig. 9. Stationary solution of salt concentration at different longitudinal dispersivity,
α
L
=0–100 m. Transverse dispersivity is
α
T
=
α
L
/10, other parameters are
dened in the base model (Table 1). Black isocontour of c =0.5 represents the boundary of the saltwater and the freshwater zones.
Fig. 10. Stationary solutions of the monitoring parameters plotted against the longitudinal dispersivity,
α
L
. (a) The average Darcy ux, (b) the average salt con-
centration and (c) the average hydraulic head. (d) The relative area, (e) the Darcy ux and (f) the concentration averaged for the saltwater (red) and the freshwater
(blue) zones.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
10
4. Demonstration in a realistic environment
A two-dimensional section was selected to demonstrate the interac-
tion of topography- and salinity-driven groundwater ows in a real
hydrological environment in Hungary. The area was extensively inves-
tigated by M´
adln´
e Sz˝
onyi et al. (2018), M´
adl-Sz˝
onyi et al. (2019) and
M´
adln´
e Sz˝
onyi (2020) studying the geological and structural settings,
hydrostratigraphy, examining the hydrocarbon and hydrogeological
systems, analysing pressure and salinity data from wells etc. in detail. In
addition, a two-dimensional numerical simulation was carried out tak-
ing into the consideration only the effect of topography and the advec-
tive heat transport (M´
adl-Sz˝
onyi et al., 2019). Therefore, in this part,
only the most relevant information is summarized, which is necessary to
elucidate the background of the numerical ow and transport simulation
and time-variation of salinity.
Fig. 13 illustrates the location of the section in the NW part of the
Great Hungarian Plain crossing the G¨
od¨
oll˝
o Hills from SW to NE direc-
tion in Hungary. The section length is 48.5 km, the depth of the model
varies between 3590 and 3625 m depending on the water table topog-
raphy. The geology of the area was grouped into ve hydrostratigraphic
units (HsU) complemented by the original pore uid content (Table 3):
the karstied Triassic carbonate (HsU1); the Eocene limestone (HsU2);
the clayey Oligocene aquitard (HsU3); the siliciclastic Miocene aquifer-
aquitard group (HsU4) and the undifferentiated Upper Miocene-
Pliocene-Quaternary group (HsU5) (M´
adln´
e Sz˝
onyi, 2020). In the
hydrostratigraphic division, HsU1 and HsU5 are considered as the main
aquifers, and HsU3 represents the main aquitard based on geological
and hydrogeological descriptions and evaluation of pumping test data
(Rman and T´
oth, 2011; Garamhegyi et al., 2020). The hydrostrati-
graphic section of the study area and the location of faults are originally
based on seismic interpretation of MOL Plc. (M´
adln´
e Sz˝
onyi et al.,
2013).
The most signicant difference between the present model and the
model of M´
adl-Sz˝
onyi et al. (2019) is that the evolution of the salinity is
taken into account here following Eq. (4). Since most hydrostratigraphic
units were deposited in a marine environment, we simplied the real
Fig. 11. Stationary solution of salt concentration at different water table amplitudes, A =0–500 m. Other parameters are dened in the base model (Table 1). Black
isocontour of c =0.5 represents the boundary of the saltwater and the freshwater zones.
Fig. 12. Stationary solutions of the monitoring parameters plotted against the water table amplitude, A. (a) The average Darcy ux, (b) the average salt concen-
tration and (c) the average hydraulic head. (d) The relative area, (e) the Darcy ux and (f) the concentration averaged for the saltwater (red) and the freshwater
(blue) zones. (e) The values of q
s
and q
f
at A =0 tend to be zero, thus they are not marked in the logarithmic scale.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
11
situation and the initial condition for salt concentration was c =1 in
each unit at a relative density difference of β =3% (TDS of approx.
40,000 mg/l). The boundary conditions for the ow are a linearized
surface water table with a maximum elevation of 125 m at x =20 km
representing the G¨
od¨
oll˝
o Hills (Fig. 14.a). Along the left and right
boundary of the model the head is xed at 100 m and 90 m, respectively,
showing the ow-through character of the model. The model is closed
from below by a no-ow boundary. Boundary conditions for the salt
Fig. 13. The location of the study area: (a) Hungary in Europe, (b) the topography of the Pannonian Basin and the broad vicinity of the study area (Horv´
ath et al.,
2006) and (c) the topography and the outcrops of Mesozoic carbonates with the simulated hydrogeological cross-section in EOV coordinate system (National
Hungarian Grid in meter unit).
Table 3
Description and model parameters of the hydrostratigraphic units, faults based on M´
adl-Sz˝
onyi et al. (2019).
Hydrostratigraphic
units
Age Mean
depth [m]
Sedimentary
environment
Pore uid Horizontal hydraulic
conductivity [m/s]
Porosity
[1]
Anisotropy
[1]
HsU5 Upper Miocene-
Pliocene-Quaternary
530 undifferentiated
siliciclastics
from brackish to
meteoric
10
-5
0.15 100
HsU4 Miocene 1480 undifferentiated siliciclastic
carbonate
marine 10
-6
0.08 100
HsU3 Oligocene 1990 deep water shale marine 10
-9
0.05 100
HsU2 Eocene-Oligocene 2430 siliciclastic carbonate with
karstication
marine &
meteoric
10
-6
0.2 100
HsU1 Paleozoic-Triassic-
Jurassic
3000 fractured, karstied marine
carbonate
marine 10
-5
0.2 10
Faults – – – – 10
-5
0.1 1
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
12
concentration are c =0 on the surface, knowing that the study area is a
recharge zone, while the bottom boundary is no-ux, representing the
impervious base rock. Along the side walls c =0 in HsU4 and HsU5,
where the freshwater outow dominates, and c =0.1 in HsU1–HsU3
units, which have no direct connection to meteoric waters. Faults are
implicated in the model as domains with an average aperture of 10 m
and characterized with hydrogeological parameters listed in Table 3.
Additional modications were made compared to the model of M´
adl-
Sz˝
onyi et al. (2019). Mechanical dispersion was introduced due to the
coupled topography- and salinity-driven problem. Based on the former
synthetic model results, the value of the longitudinal dispersivity was
dened as
α
L
=100 m and the transverse dispersivity was
α
T
=10 m. In
order to handle the effective molecular diffusion in porous medium D
eff
,
the Bruggeman model was used (Wu et al., 2019), that is D
eff
=Φ
3/2
D
diff
.
Using additional thermal well hydraulic data, the horizontal hydraulic
conductivity of HsU1 and HsU2 was reduced by one order of magnitude.
Also, the values of anisotropic coefcients were increased from
ε
=10 to
100 in units HsU2–HsU5, where the layered siliciclastic sediments
effectively retard the vertical groundwater ow (e.g. Galsa, 1997; Rman
and T´
oth, 2011; Hoque and Burgess, 2020).
The evolution of the salt concentration is presented for four different
time steps up to the maximum simulation time of 1 Myr (Fig. 14.b–e).
Only 1 kyr is enough for the meteoric water to displace the saltwater in
the upper part of HsU5. After 10 kyr, saltwater is swept out from HsU5
and the upper part of HsU4. Dense, salty plumes descend from the clayey
HsU3 aquitard into the karstied HsU1 at x =3–10 km, where the
aquitard is the thinnest (Fig. 14.c). The faults at x≈6 and 34 km, where
the salt content decrease appears rstly, facilitate the hydraulic
connection between the aquifers above and below HsU3. After 100 kyr
HsU4 and HsU5 are fully saturated by freshwater, while HsU1 is satu-
rated by brackish water owing through this domain from SW to NE
(Fig. 14.d). Small-scaled salty downwellings are noticeable in HsU2,
directly below the Oligocene aquitard (HsU3). After 1 Myr a consider-
able part of the original salt content has already been preserved in the
lower part of HsU3, however, the salinity of the layer has not been
uniform (Fig. 14.e). The concentration is higher in the zones, which are
thicker and are far from the hydraulically conductive faults. If the saline
water reaches a fault or the boundary of HsU3 by diffusion, it will be
effectively advected and displaced by fresh/brackish groundwater.
Fig. 14.f emphasizes that HsU4 and HsU5 are dominated by topography-
driven meteoric groundwater ow, while HsU1 and HsU2 are prevailed
by brackish through-ow. However, the upper and lower units are not
perfectly separated, because the two groundwater types communicate
through faults and the thin parts of the HsU3 aquitard. Finally, we note
that a hydraulic head maximum (120–125 m) can be noticed in the
surroundings of the topographic divide, G¨
od¨
oll˝
o Hills (x =20 km)
(Fig. 14g). On the other hand, distinctive head minima appear in the
lower part of HsU3 correlating with the salt content. Within these zones,
even a 100 m head decrease is present compared to the freshwater zone.
5. Interpretation and discussion
5.1. Synthetic scenarios
Based on the synthetic simulations, it was established that a salt-
water zone evolves beneath the discharge zone as a result of a dynamic
Fig. 14. (a) The horizontal hydraulic conductivity (K
x
) of the hydrostratigraphic units and the location of faults (magenta) with the boundary conditions for the ow
(blue) and the salt concentration (green). Concentration distribution along the section at (b) t =1 kyr, (c) t =10 kyr, (d) t =100 kyr and (e) t =1 Myr. (f) The Darcy
ux magnitude and (g) the hydraulic head eld at t =1 Myr. (f) Normalized black arrows illustrate the ow direction. Vertical exaggeration is 1.5.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
13
equilibrium between the negative buoyancy force of saltwater and the
topography-driven fresh groundwater ow. The size and shape of the
saline zone depend on the studied parameters. In general, if the effect of
salinity becomes dominant, the saltwater zone forms a dense, salty layer
in the deeper part of the basin. If the salinity-driven buoyancy prevails
against the regional ow, the salt concentration tends to the diffuse
distribution without advective solute content transport. This is the case,
when the relative density contrast (β ≥10%, Fig. 2.d–g) and the
permeability anisotropy (
ε
≥100, Fig. 7.e–g) are enhanced or the water
table amplitude is reduced (A ≤5 m, Fig. 11.a–b). However, if the
topography-driven groundwater ow becomes dominant, the saltwater
zone shrinks, and it is pressed toward the stagnation point beneath the
discharge zone. The diffusion from below is not sufcient to maintain an
extended saline zone against the regional ow. This solution is obtained
from the simulations by decreasing the salinity (β <1%, Fig. 2.a) or by
increasing the water table amplitude (A >200 m, Fig. 11.g).
Monitoring parameters quantify the effects of studied parameters on
Darcy ux, the salt concentration and the hydraulic head etc. computed
for the entire basin and/or the salt- and freshwater zone. Besides, they
highlight the modications in the extent and morphology of the salt-
water zone (saline zone to layer at
ε
=100, Fig. 8.b–d), or the transition
from advection- to diffusion-dominated mass transport system (at A =
10 m, Fig. 12.b and d). Darcy ux values averaged for the different zones
indicate that sluggish circulation occurs within the saltwater zone. The
ow in the saline zone is slower by approx. 1–2 orders of magnitude, but
q
s
and q
f
seem not to be independent of each other. The diffusion
mechanism is supposed to couple these two zones. Near the zone
boundaries, the diffusive ux is high due to the large concentration
gradient, and the salt content in the saline zone decreases resulting in
buoyancy force and upward motion being parallel to the regional
groundwater ow (Fig. 3). We note that this weak linkage can be
overtaken by small-scale heterogeneities within the saltwater zone,
which can lead to more complex inner convection (Fig. S3 in Supple-
mentary material).
In the studied parameter interval, the variation of permeability and
dispersivity do not cause relevant modications in the shape of the sa-
line water zone. It is worth mentioning that qualitatively, the perme-
ability decrease and the dispersivity increase affect the structure of the
saline zone in a similar way. First, the salt content increases by ho-
mogenization (Fig. 5.a–d and Fig. 9.a–d), then it decreases by thickening
the transition between the two zones (Fig. 5.e–g and. Fig. 9.e–h). The
latter process can be attributed to the increase of the relative effect of
diffusion (reducing the permeability retains the role of advection) and to
the amplication of transverse dispersion. Both phenomena strengthen
the coupling between the two zones, as it is supported by the fact that
the difference between q
f
and q
s
decreases from 2 to 1 orders of
magnitude (Fig. 6.e and Fig. 10.e). The effect of the permeability
decreasing exponentially with depth is very similar to the case of
permeability decrease, but its inuence weakens toward the surface.
Dimensionless numbers facilitate the simultaneous interpretation of
the effects of different model parameters on the behavior of the
groundwater ow system. Sherwood number (Sh) describes the ratio of
the surface concentration ux and the concentration ux due to purely
diffusion. It means that the larger the value of Sh, the stronger the role of
advection/convection in the solute transport. P´
eclet number (Pe) ex-
presses the convective transport (i.e. q
av
, the average Darcy ux in
simulations) compared to diffusion and dispersive solute transport,
Pe =qavd
Ddiff +
α
Lqav
.(7)
Both the diffusive and dispersive uxes are used in the denominator
since both hinder the convection (e.g. Simmons and Narayan, 1997).
Fig. 15.a shows the Sherwood number plotted against the P´
eclet
number for each synthetic simulation. Increasing salinity (β) retains the
ow slightly and reduces the surface solute ux by almost one order of
magnitude. Decreasing permeability in the homogeneous (k), the depth-
dependent (γ) and the anisotropic (
ε
) models slow down the ow and
lessens the surface concentration ux. When the effective permeability
decreases with depth (γ,
ε
), where the salt content is higher, a reduction
in Sh is more pronounced. Although the dispersivity (
α
L
) decreases Pe
(by enhancing the denominator of (7)), Sh increases owing to the
stronger coupling between the salt- and freshwater zones by higher
transverse dispersion. Higher water table amplitude (A) intensies the
advective transport and raises the surface concentration ux. While
lower water table amplitude decreases both Pe and Sh, and drives the
system toward the thin saline layer and then toward the diffusion state.
In the most numerical solutions, a dense, sluggish, saline dome forms
beneath the discharge zone, but decreasing the water table amplitude
(A) or increasing permeability anisotropy (
ε
) and salinity (β), the system
transforms into a thin layer or a diffusion regime (solid symbols).
Szij´
art´
o et al. (2019) dened a modied P´
eclet number to separate
the effect of thermal buoyancy from the total convective Darcy ux in
synthetic groundwater ow models driven by mixed thermal convec-
tion. In this paper, we reinterpreted the former denition, because (1)
advection competes with molecular diffusion and mechanical dispersion
(instead of thermal diffusion), and (2) the haline convection retards the
ow in the studied models. Thus, the modied P´
eclet number is
Pe*=(qadv −qav)d
Ddiff +
α
Lqav
(8)
using the difference between the advective (q
adv
) and the total convec-
tive (q
av
) Darcy ux. Advective Darcy ux was calculated for each
simulation at β =0, that is the negative buoyancy force of salinity was
Fig. 15. (a) Sherwood number (Sh) plotted against the P´
eclet number (Pe) calculated for each synthetic simulation. The saline layer/diffusion regime is separated
from the saline dome regime by shading. (b) Non-dimensional numbers obtained from the P´
eclet number and the modied P´
eclet number (Pe*) calculated for each
synthetic simulation. The studied model parameters are denoted by different symbols in (b) and their extremums are labelled. The intersection of dashed lines shows
the base model (Table 1).
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
14
neglected.
The relation between the topography-driven and the buoyancy-
driven groundwater ow is elucidated in Fig. 15.b, where Pe +Pe* is
proportional to the advective Darcy ux and Pe/(Pe +Pe*) shows the
ratio of the total convective and advective Darcy ux (see Eq. (7) and
(8)). When the salinity does not inuence the ow (β =0), the advective
(q
adv
) and convective ux (q
av
) are identical, Pe/(Pe +Pe*) =1. The
increase in salinity retains the regional groundwater ow, e.g. the
convective Darcy ux at a value of β =0.2 is reduced by 43%. The
decrease of permeability in a homogeneous medium (k) and the increase
in mechanical dispersion (
α
L
) similarly affect the convective ux (see
Figs. 5 and 9). Decrease in k and increase in
α
L
considerably reduce the
advective transport compared to diffusion and dispersion (Pe +Pe*),
respectively, but these effects moderate the convective ow relative to
the base model by only some percent. Effective permeability decreasing
with depth (γ,
ε
) slows down the ow and lessens the role of salinity-
induced buoyancy force, as Pe/(Pe +Pe*) tends to 1. Increasing the
water table amplitude (A) strengthens the advective ux and weakens
the inuence of salinity on the ow. On the other hand, decreasing water
table amplitude accentuates the negative buoyancy force, as, for
instance, the convective ux at A =1 m is reduced to 23%.
Zhang et al. (2020b) noted that the increase of salinity retards the
nested groundwater ow intensity — analogously to our ndings —,
although their hierarchical synthetic models have different boundary
conditions. Qualitatively, a similar brine zone with counter-rotating
inner convection forms beneath playas, as an interaction between the
freshwater inltration in the surrounding mountains and the redis-
solution of evaporites in playas both on regional (Duffy and Al-Hassan,
1988) and on a local scale (Hamann et al., 2015). However, in these
models, the saltwater recharge across the surface destabilizes the system
and stimulates the groundwater ow, while in our models, the salt
transport occurs from below, which stabilizes the system and hinders the
groundwater ow. At the same time, the dispersive ux through the
boundary of the salt- and freshwater zones appears in both simulations.
The transverse dispersion between the two zones enhances the coupling
between the ow systems by decoupling the ow from the salt transport,
as was concluded by Wen et al. (2018), who investigated the role of
dispersion on CO
2
storage in deep saline aquifers.
In an examined realistic hydrogeological situation (β =2.5%, k
x
=
10
-12
m
2
,
ε
=100,
α
L
=100 m and A =50 m) a thin saline layer (approx.
17,500–35,000 mg/l) formed due to the high anisotropy coefcient and
it occupied the lower 7.6% of the basin (lower 380 m). The average TDS
content of the saline layer and the topography-driven upper zone was
26,100 mg/l and 1,240 mg/l, respectively. The brackish character of the
upper zone is explained by the large value of transverse dispersivity,
α
T
=10 m, which enhanced the salinity ux into the freshwater zone. The
maximum TDS content near the surface approximates only 630 mg/l in
the leftmost part of the discharge zone, however, this value reaches
4000 mg/l at a depth of 200 m, which can seriously deteriorate the
quality of the water in case of drinking and irrigation utilization. The
Darcy ux in the upper zone (q
f
≈6.8⋅10
-9
m/s) is higher than that in the
saline, sluggish layer by a factor of approx. 110. The average water
density in the saline water layer is 1018 kg/m
3
resulting in a 50 m hy-
draulic head decrease in the entire layer.
5.2. Realistic scenario
Numerical modelling of the studied hydrogeological section illus-
trates that the high salt content trapped in the clayey Oligocene aquitard
(HsU3) can survive over 1 Myr. Based on samples of hydrocarbon and
thermal wells, high TDS content in the Oligocene aquitard
(30,000–50,000 mg/l) and brackish pore water observed in Triassic
carbonates (1,000–10,000 mg/l) (M´
adl-Sz˝
onyi et al., 2019) agree with
the numerical model results (Fig. 14.e). The elevated TDS content ex-
plains the hydraulic head decit measured in HsU3, and it is in harmony
with the nding, that the thicker HsU3, the lower the hydraulic head.
However, higher salt content cannot elucidate the “underpressure”
(M´
adl-Sz˝
onyi et al., 2015), which might be the result of decompaction
and insufcient groundwater replenishment due to the uplifting of
G¨
od¨
oll˝
o Hills, which started 3–4 Myr ago (Ruszkiczay-Rüdiger et al.,
2007).
During the last 3–4 Myr, G¨
od¨
oll˝
o Hills became a topographic divide,
which facilitated the signicance of a topography-driven groundwater
ow system. Since the entire section is a recharge area, the upper
Neogene and Quaternary units (HsU4 and HsU5) are characterized by
low TDS. Based on data evaluation, the fractured and conned Triassic
carbonate is likely to be in connection with unconned carbonate on the
western side of Danube River (Fig. 13.c), so it is part of the Buda
Thermal Karst (BTK) system (M´
adl-Sz˝
onyi and T´
oth, 2015; Szij´
art´
o
et al., 2021). However, the connection and isolation are tectonically
inuenced, thus it can differ from place to place (M´
adln´
e Sz˝
onyi, 2020).
Brackish pore water in HsU1 and HsU2 can be the consequence of the
meteoric water inltration in the unconned part of BTK, the hydraulic
connection between the unconned and conned carbonates and the
weak saltwater leakage from HsU3. Based on the numerical simulation,
the linkage between the topography-driven fresh groundwater (HsU4
and HsU5) and the compositionally mixed brackish karst water (HsU1
and HsU2) is plausible through faults and the thinnest parts of the
Oligocene aquitard (HsU3).
These simulations, like each numerical or conceptual model, include
simplications and have limitations, which can modify the outcomes.
(1) One of them is that source/sink terms (precipitation and dissolution
of salts (e.g. V´
asquez et al., 2013; Hamann et al., 2015), evaporite for-
mation etc.) are not built into the simulations, however, the exit of the
salt content is allowed through the upper boundary of the synthetic
model by diffusion. However, it is supposed that these local-scale pro-
cesses cannot considerably change the received basin-scale ow pattern.
(2) Although equivalent porous media (EPM) approximation can be
accepted in the karstied carbonates on basin-scale (e.g. Long et al.,
1982; Scanlon et al., 2003; M´
adl-Sz˝
onyi and T´
oth, 2015), the effect of
relevant hydraulically conductive faults was taken into account (Berre
et al., 2019). (3) For the sake of simplicity, the effect of thermal buoy-
ancy was neglected in the simulations, which might be another impor-
tant factor in deep, karstied, basin-scale carbonate systems (e.g. Havril
et al., 2016; Szij´
art´
o et al., 2019, 2021). However, a recent study showed
that in the presence of topography-driven groundwater ow advective
heat transport exists, but free thermal convection might occur only at
higher Rayleigh numbers (Szij´
art´
o et al. 2019). For the purposes of this
paper, omittance of buoyancy due to temperature differences can be an
acceptable assumption. The fully coupled solutions (topography plus
salinity plus temperature) indicate a plausible perspective of further
simulations. Nevertheless, a preliminary simulation was completed
along the hydrogeological section crossing G¨
od¨
oll˝
o Hills in order to ash
the process of topothermohaline convection, where the ow pattern and
the salt concentration is controlled by both the water table topography
and the buoyancy force due to the temperature and the salinity variation
(Supplementary material). As a working hypothesis for further simula-
tions, it can be established that owing to the elevated geothermal
gradient characterizing the area, thermal convection formed in the deep,
partly conned karstied aquifers (HSU1 and HSU2), which intensied
the ow, strengthened the hydrodynamic connection between the upper
(HSU4 and HSU5) and lower aquifers, and facilitated the saltwater
drainage from the clayey Oligocene aquitard (HSU3) (Fig. S4 in Sup-
plementary material). (4) In both the synthetic simulations and the case
study, the upper boundary condition for the ow was a simple cosinu-
soid or a linear hydraulic head. However, local variations in the
topography and the water table can disturb the ow pattern and the
salinity eld, as well. A hierarchically nested groundwater system could
induce a more complex distribution of the salt concentration and the
temperature (Zhang et al., 2020b; An et al., 2015). In general, higher
salinity and surface heat ux are expected in the regional discharge area
rather than in local discharge/recharge areas. The lowest salinity and
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
15
heat ux are probable in regional recharge zones. Nonetheless, the
formation of time-dependent thermal buoyancy, which strongly de-
pends on the physical and geometrical model parameters (Szij´
art´
o et al.,
2019), is able to modulate or even overwrite the above-mentioned
simplied consideration resulting in a complex nested system where
the ow, the salinity and the heat vary in time and space.
6. Conclusions
Interaction of topography- and salinity-driven groundwater ow was
systematically investigated in synthetic two-dimensional, basin-scale
numerical models and then in a realistic scenario based on the
siliciclastic-carbonate basin in Hungary.
It was established in the synthetic analyses, that the effect of
increasing water density due to salinity and decreasing water table
amplitude on the saltwater distribution is similar. The rst enhances the
buoyancy-driven free convection, while the second reduces the
topography-driven forced convection. Thus, the numerical solutions
trend from a topography-dominated regional freshwater system towards
a diffusion-dominated layered system. The increase of permeability
anisotropy shows similar progress towards the formation of a dense,
saline layer in the deeper part of the basin. In the studied parameter
domain, both the decrease of permeability and the increase of dis-
persivity extinguish the relative role of advection by enhancing the
diffusion or dispersion, respectively. The two phenomena strengthen the
coupling between the fresh- and saltwater zone.
Based on the synthetic simulation set, the coupled topography- and
salinity-driven model was applied along a 2D hydrogeological section in
Hungary. After 100 kyr, the original marine pore water is outplaced
from both the upper siliciclastic aquifers by topography-driven meteoric
freshwater and the lower karstied carbonates by the brackish
groundwater through-ow. However, the marine-origin pore water in
the middle aquitard can survive over 1 Myr resulting in a signicant
head minimum. The connection between the upper and lower pervious
units are revealed by the presence of conductive faults, while the
connection between the clayey cover and conned carbonates is repre-
sented by dense, saline nger-like downwellings.
The current study improves the understanding of the interaction
between the topography-driven forced and the salinity-driven free
convection, especially in basin-scale groundwater ow systems. On the
one hand, the sensitivity analysis of the synthetic models highlights the
role of the most important model parameters inuencing the coupled
ow system. On the other hand, the phenomenon of mixed convection
was investigated and proved along a simplied 2D hydrogeological
section in Hungary to demonstrate the mixing of fresh, brackish and
saline water. Nevertheless, the combined topography- and salinity-
driven groundwater ow plays an important role in the Atacama salt
at aquifer, Chile (Tejeda et al., 2003; V´
asquez et al., 2013), in the
surroundings of playas in Pilot Valley, USA (Duffy and Al-Hassan, 1988;
Fan et al., 1997), below saline disposal basins in the Murray–Darling
Basin, Australia (Simmons and Narayan, 1997), in the salt accumulation
in the beach of Bon Secour National Wildlife Refuge, USA (Geng and
Boufadel, 2015) etc. Therefore, the results of the study can be used with
the necessary adaptations in further terrestrial hydrogeological envi-
ronments as well.
CRediT authorship contribution statement
Attila Galsa: Methodology, Validation, Investigation, Writing –
original draft, Writing – review & editing. ´
Ad´
am T´
oth: Data curation,
Supervision, Writing – review & editing, Funding acquisition. M´
ark
Szij´
art´
o: Visualization, Supervision, Writing – review & editing, Fund-
ing acquisition. Daniele Pedretti: Supervision, Funding acquisition.
Judit M´
adl-Sz˝
onyi: Data curation, Conceptualization, Writing – review
& editing, Supervision, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgements
Authors are grateful to the anonymous reviewers for the instructive
comments and inspiring suggestions. This research is part of a project
that has received funding from the European Union’s Horizon 2020
research and innovation program under grant agreement No 810980.
The project was supported by the ÚNKP-19-3 and ÚNKP-19-4 New Na-
tional Excellence Program of the Ministry for Innovation and Technol-
ogy, by the Hungarian Scientic Research Fund (K 129279), by the
J´
anos Bolyai Research Scholarship of the Hungarian Academy of Sci-
ences and by the ÚNKP-21-4 New National Excellence Program of the
Ministry for Innovation and Technology from the source of the National
Research, Development and Innovation Fund. The paper was prepared
with the professional support of the Doctoral Student Scholarship Pro-
gram of the Co-operative Doctoral Program of the Ministry of Innovation
and Technology nanced from the National Research, Development and
Innovation Fund.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.jhydrol.2022.127695.
References
An, R., Jiang, X.-W., Wang, J.-Z., Wan, L., Wang, X.-S., Li, H., 2015. A theoretical analysis
of basin-scale groundwater temperature distribution. Hydrogeol. J. 23 (2), 397–404.
https://doi.org/10.1007/s10040-014-1197-y.
Barlow, P.M., Reichard, E.G., 2010. Saltwater intrusion in coastal regions of North
America. Hydrogeol. J. 18, 247–260. https://doi.org/10.1007/s10040-009-0514-3.
Berre, I., Doster, F., Keilegavlen, E., 2019. Flow in fractured porous media: A review of
conceptual models and discretization approaches. Transp. Porous Media 130,
215–236. https://doi.org/10.1007/s11242-018-1171-6.
Cirpka, O.A., Chiogna, G., Rolle, M., Bellin, A., 2015. Transverse mixing in three-
dimensional nonstationary anisotropic heterogeneous porous media. Water Resour.
Res. 51, 241–260. https://doi.org/10.1002/2014WR015331.
De Paola, F., Giugni, M., Topa, M.E., Bucchignani, E., 2014. Intensity-Duration-
Frequency (IDF) rainfall curves, for data series and climate projection in African
cities. SpringerPlus 3, 133. https://doi.org/10.1186/2193-1801-3-133.
Delgado, J.M.P.Q., 2012. Heat and Mass Transfer in Porous Media. Springer, Berlin,
Heidelberg, p. 266.
Deming, D., 2002. Introduction to Hydrogeology. McGraw Hill, New York, pp. 480,
ISBN-10: 0072326220.
Domenico, P.A., Palciauskas, V.V., 1973. Theoretical analysis of forced convective heat
transfer in regional ground-water ow. GSA Bull. 84 (12), 3803–3814. https://doi.
org/10.1130/0016-7606.
Dublyansky, Y.V., 1995. Speleogenetic history of the Hungarian hydrothermal karst.
Environ. Geol. 25, 24–35. https://doi.org/10.1007/BF01061827.
Duffy, C.J., Al-Hassan, S., 1988. Groundwater circulation in a closed desert basin:
topographic scaling and climatic forcing. Water Resour. Res. 24 (10), 1675–1688.
https://doi.org/10.1029/WR024i010p01675.
Ehrenberg, S.N., Nadeau, P.H., 2005. Sandstone vs. carbonate petroleum reservoirs: A
global perspective on porosity-depth and porosity-permeability relationships. AAPG
Bull. 89 (4), 435–445. https://doi.org/10.1306/11230404071.
Fan, Y., Duffy, C.J., Oliver Jr, D.S., 1997. Density-driven groundwater ow in closed
desert basins: eld investigations and numerical experiments. J. Hydrology 196,
139–184. https://doi.org/10.1016/S0022-1694(96)03292-1.
Galsa, A., 1997. Modelling of groundwater ow along a section in the Great Hungarian
Plain using hydraulic heads measured in wells (in Hungarian with English abstract).
Magyar Geozika 38 (4), 245–256. http://epa.oszk.hu/03400/03436/00151/pdf/
EPA03436_magyar_geozika_1997_04_245-256.pdf.
Gao, G., Zhan, H., Feng, S., Fu, B., Huang, G., 2012. A mobile–immobile model with an
asymptotic scale-dependent dispersion function. J. Hydrology 424–425, 172–183.
https://doi.org/10.1016/j.jhydrol.2011.12.041.
Garamhegyi, T., Sz´
ekely, F., Carrillo-Rivera, J.J., M´
adl-Sz˝
onyi, J., 2020. Revision of
archive recovery tests using analytical and numerical methods on thermal water
wells in sandstone and fractured carbonate aquifers in the vicinity of Budapest.
Hungary. Environmental Earth Science. 79, 129. https://doi.org/10.1007/s12665-
020-8835-6.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
16
García-Gil, A., V´
azquez-Su˜
n´
e, E., Ayora, C., Tore, C., Henríquez, ´
A., Y´
a˜
nez, J., 2019.
Impacts of the transient skin effect during brine extraction operations in a crystalline
halite aquifer, J. Hydrology, 577, paper: 123912, 10.1016/j.jhydrol.2019.123912.
Gelhar, L.W., Welty, C., Rehfeldt, K.R., 1992. A critical review of data on eld-scale
dispersion in aquifers. Water Resour. Res. 28 (7), 1955–1974. https://doi.org/
10.1029/92WR00607.
Geng, X., Boufadel, M.C., 2015. Impacts of evaporation on subsurface ow and salt
accumulation in a tidally inuenced beach. Water Resour. Res. 51, 5547–5565.
https://doi.org/10.1002/2015WR016886.
Hamann, E., Post, V., Kohfahl, C., Prommer, H., Simmons, C.T., 2015. Numerical
investigation of coupled density-driven ow and hydrogeochemical processes below
playas. Water Resour. Res. 51, 9338–9352. https://doi.org/10.1002/
2015WR017833.
Havril, T., Molson, J.W., M´
adl-Sz˝
onyi, J., 2016. Evolution of uid ow and heat
distribution over geological time scales at the margin of unconned and conned
carbonate sequences - A numerical investigation based on the Buda Thermal Karst
analogue. Mar. Pet. Geol. 78, 738–749. https://doi.org/10.1016/j.
marpetgeo.2016.10.001.
Havril, T., T´
oth, ´
A., Molson, J.W., Galsa, A., M´
adl-Sz˝
onyi, J., 2018. Impacts of predicted
climate change on groundwater ow systems: Can wetlands disappear due to
recharge reduction? J. Hydrol. 563, 1169–1180. https://doi.org/10.1016/j.
jhydrol.2017.09.020.
He, Z., Ding, Q., Wo, Y., Zhang, J., Fan, M., Yue, X., 2017. Experiment of carbonate
dissolution: implication for high quality carbonate reservoir formation in deep and
ultradeep basins. Geouids, 2017, paper: 8439259, 10.1155/2017/8439259.
Herbert, E.R., Boon, P., Burgin, A.J., Neubauer, S.C., Franklin, R.B., Ard´
on, M.,
Hopfensperger, K.N., Lamers, L.P.M., Gell, P., 2015. A global perspective on wetland
salinization: ecological consequences of a growing threat to freshwater wetlands.
Ecosphere 6 (10), paper: 206. https://doi.org/10.1890/ES14-00534.1.
Hoque, M.A., Burgess, W.G., 2020. Representing heterogeneity of uvio-deltaic aquifers
in models of groundwater ow and solute transport: A multi-model investigation in
the Bengal Basin. J. Hydrology, 590, paper: 125507, 10.1016/j.
jhydrol.2020.125507.
Horv´
ath, F., Bada, G., Windhoffer, G., Csontos, L., Dombr´
adi, E., D¨
ov´
enyi, P., Fodor, L.,
Grenerczy, G.y., Síkhegyi, F., Sza´
an, P., Sz´
ekely, B., Tim´
ar, G., T´
oth, L., T´
oth, T.,
2006. Atlas of the present-day geodynamics of the Pannonian basin: Euroconform
maps with explanatory text (in Hungarian with English abstract). Magyar Geozika
47 (4), 133–137. http://epa.niif.hu/03400/03436/00186/pdf/EPA03436_magyar_
geozika_2006_04_133-137.pdf.
Hussain, M.S., Abd-Elhamid, H.F., Javadi, A.A., Sherif, M.M., 2019. Management of
Seawater Intrusion in Coastal Aquifers: A Review. Water, 11 (12), paper: 2467,
10.3390/w11122467.
Jalali, M., 2007. Salinization of groundwater in arid and semi-arid zones: an example
from Tajarak, western Iran. Environ. Geol. 52, 1133–1149. https://doi.org/10.1007/
s00254-006-0551-3.
Jiang, X-W., Wan, L., Wang, X-S., Ge, S., Liu, J., 2009. Effect of exponential decay in
hydraulic conductivity with depth on regional groundwater ow. Geophys. Res.
Lett., 36 (24), paper: L24402, 10.1029/2009GL041251.
Jiang, X-W., Wang, X-S., Wan, L., Ge, S., 2011. An analytical study on stagnation points
in nested ow systems in basins with depth-decaying hydraulic conductivity. Water
Resour. Res., 47 (1), paper: W01512, 10.1029/2010WR009346.
Kambesis, P.N., Coke, J.G., 2013. Overview of the Controls on Eogenetic Cave and Karst
Development in Quintana Roo, Mexico. In: Coastal Karst Landforms (ed. Lace, M.J.,
Mylroie, J.E.). Springer, Dordrecht, 347–373, ISBN: 978-94-007-5016-6, 10.1007/
978-94-007-5016-6_16.
Karaki, N.A., Fiaschi, S., Paenen, K., Al-Awabdeh, M., Closson, D., 2019. Exposure of
tourism development to salt karst hazards along the Jordanian Dead Sea shore.
Hydrol. Earth Syst. Sci. 23, 2111–2127. https://doi.org/10.5194/hess-23-2111-
2019.
Kesler, S.E., Gruber, P.W., Medina, P.A:, Keoleian, G.A., Everson, M.P., Wallington, T.J.,
2012. Global lithium resources: Relative importance of pegmatite, brine and other
deposits. Ore Geol. Rev., 48, 55–69, 10.1016/j.oregeorev.2012.05.006.
Konikow, L.F., Akhavan, M., Langevin, C.D., Michael, H.A., Sawyer, A.H., 2013.
Seawater circulation in sediments driven by interactions between seabed topography
and uid density. Water Resour. Res. 49, 1386–1399. https://doi.org/10.1002/
wrcr.20121.
Kreyns, P., Geng, X., Michael, H.A., 2020. The inuence of connected heterogeneity on
groundwater ow and salinity distributions in coastal volcanic aquifers. J.
Hydrology, 586, paper: 124863, 10.1016/j.jhydrol.2020.124863.
Liu, R., Li, B., Jiang, Y., Huang, N., 2016. Review: Mathematical expressions for
estimating equivalent permeability of rock fracture networks. Hydrogeol. J. 24,
1623–1649. https://doi.org/10.1007/s10040-016-1441-8.
Long, J.C.S., Remer, J.S., Wilson, C.R., Witherspoon, P.A., 1982. Porous media
equivalents for networks of discontinuous fractures. Water Resour. Res. 18 (3),
645–658. https://doi.org/10.1029/WR018i003p00645.
M´
adln´
e Sz˝
onyi, J., 2020. Pattern of groundwater ow at the boundary of unconned and
conned carbonate systems on the example of Buda Thermal Karst and its
surroundings (in Hungarian). DSc Thesis, pp. 150, https://scholar.google.com/
scholar?q=Pattern%20of%20Groundwater%20Flow%20at%20the%20Boundary%
20of%20Unconned%20and%20Conned%20Carbonate%20Systems%20on%
20the%20Example%20of%20Buda%20Thermal%20Karst%20and%20its%
20Surroundings.
M´
adln´
e Sz˝
onyi, J., Czauner, B., Er˝
oss, A., Simon, S., 2013. Karbon´
atos ´
es Csatlakoz´
o
Üled´
ekes Medenceterületek Fluidumdinamikai ¨
Osszefügg´
eseinek Vizsg´
alata a
Sz´
enhidrog´
en Kutat´
as Hat´
ekonys´
ag´
anak Javít´
asa ´
Erdek´
eben a Paleog´
en-medenc´
eben
– Z´
ar´
ojelent´
es. Investigation of uid-dynamic connection of carbonate and adjoining
basin in hydrocarbon exploration purposes – Final Report. Hungarian Oil Company,
Budapest.
M´
adln´
e Sz˝
onyi, J., Er˝
oss, A., Havril, T., Poros, Zs., Gy˝
ori, O., T´
oth, ´
A., Csoma, A., Ronchi,
P., Mindszenty, A., 2018. Fluids, ow systems and their minerological imprints in
the Buda Thermal Karst (in Hungarian with English abstract). F¨
oldtani K¨
ozl¨
ony, 148
(2), 75–96, 10.23928/foldt.kozl.2018.148.1.75.
M´
adl-Sz˝
onyi, J., Czauner, B., Iv´
an, V., T´
oth, ´
A., Simon, S.z., Er˝
oss, A., Bodor, P.,
Havril, T., Boncz, L., S˝
oreg, V., 2019. Conned carbonates? – regional-scale
hydraulic interaction or isolation? Mar. Pet. Geol. 107, 591–612. https://doi.org/
10.1016/j.marpetgeo.2017.06.006.
M´
adl-Sz˝
onyi, J., Pulay, E., T´
oth, ´
A., Bodor, P., 2015. Regional underpressure: a factor of
uncertainty in the geothermal exploration of deep carbonates, G¨
od¨
oll˝
o Region,
Hungary. Environ. Earth Sci. 74 (12), 7523–7538. https://doi.org/10.1007/s12665-
015-4608-z.
M´
adl-Sz˝
onyi, J., T´
oth, ´
A., 2015. Basin-scale conceptual groundwater ow model for an
unconned and conned thick carbonate region. Hydrogeol. J. 23, 1359–1380.
https://doi.org/10.1007/s10040-015-1274-x.
Marazuela, M.A., V´
azquez-Su˜
n´
e, E., Custodio, E., Palma, T., García-Gil, A., Ayora, C.,
2018. 3D mapping, hydrodynamics and modelling of the freshwater-brine mixing
zone in salt ats similar to the Salar de Atacama (Chile). J. Hydrology 561, 223–235.
https://doi.org/10.1016/j.jhydrol.2018.04.010.
McFarlane, D.J., George, R.J., Barrett-Lennard, E.G., Gilfedder, M., 2017. Salinity in
dryland agricultural systems: Challenges and opportunities. In: Innovations in
Dryland Agriculture (ed. Farooq, M., Siddique, K.H.M.). Springer International
Publishing, 521–547, ISBN: 978-3-319-47928-6, 10.1007/978-3-319-47928-6_19.
Nield, D.A., 1968. Onset of thermohaline convection in a porous medium. Water Resour.
Res. 4 (3), 553–560. https://doi.org/10.1029/WR004i003p00553.
Nield, D.A., Bejan, A., 2017. Convection in Porous Media, 5th ed. Springer Int, p. 988.
Oz, I., Eyal, S., Yoseph, Y., Ittai, G., Elad, L., Haim, G., 2016. Salt dissolution and sinkhole
formation: Results of laboratory experiments. J. Geophys. Res. Earth Surf. 121,
1746–1762. https://doi.org/10.1002/2016JF003902.
Payen, S., Basset-Mens, C., Nú˜
nez, M., Follain, S., Grünberger, O., Marlet, S., Perret, S.,
Roux, P., 2016. Salinisation impacts in life cycle assessment: a review of challenges
and options towards their consistent integration. Int. J. Life Cycle Assess. 21,
577–594. https://doi.org/10.1007/s11367-016-1040-x.
Pedretti, D., Russian, A., Sanchez-Vila, X., Dentz, M., 2016. Scale dependence of the
hydraulic properties of a fractured aquifer estimated using transfer functions. Water
Resour. Res. 52, 5008–5024. https://doi.org/10.1002/2016WR018660.
Pedretti, D., Fern`
andez-Garcia, D., Sanchez-Vila, X., Bolster, D., Benson, D.A., 2014.
Apparent directional mass-transfer capacity coefcients in three-dimensional
anisotropic heterogeneous aquifers under radial convergent transport. Water Resour.
Res. 50, 1205–1224. https://doi.org/10.1002/2013WR014578.
Rman, N., T´
oth, Gy., 2011. T-JAM Vízf¨
oldtani koncepcion´
alis modell (in Hungarian), pp.
25.
Rodríguez-Rodríguez, M., Benavente, J., 2008. Denition of wetland typology for hydro-
morphological elements within the WFD. A case study from southern Spain. Water
Resour. Manage. 22, 797–821. https://doi.org/10.1007/s11269-007-9193-9.
Ruszkiczay-Rüdiger, Z., Fodor, L.I., Horv´
ath, E., 2007. Neotectonics and quaternary
landscape evolution of the G¨
od¨
oll˝
o Hills, Central Pannonian Basin. Hungary. Global .
Planet. Change 58 (1), 181–196. https://doi.org/10.1016/j.gloplacha.2007.02.010.
Sanchez-Vila, X., Guadagnini, A., Carrera, J., 2006. Representative hydraulic
conductivities in saturated groundwater ow. Rev. Geophys., 44, paper: RG3002,
10.1029/2005RG000169.
Scanlon, B.R., Mace, R.E., Barrett, M.E., Smith, B., 2003. Can we simulate regional
groundwater ow in a karst system using equivalent porous media models? Case
study, Barton Springs Edwards aquifer, USA. J. Hydrology 276, 137–158. https://
doi.org/10.1016/S0022-1694(03)00064-7.
Schuler, M.S., Ca˜
nedo-Argüelles, M., Hintz, W.D., Dyack, B., Birk, S., Relyea, R.A., 2018.
Regulations are needed to protect freshwater ecosystems from salinization.
Philosophical Transactions of the Royal Society B, Biological Sciences, 374, paper:
20180019, 10.1098/rstb.2018.0019.
Schulze-Makuch, D., 2005. Longitudinal dispersivity data and implications for scaling
behavior. Groundwater 43 (3), 443–456. https://doi.org/10.1111/j.1745-
6584.2005.0051.x.
Simmons, C.T., Narayan, K.A., 1997. Mixed convection processes below a saline disposal
basin. J. Hydrology 194, 263–285. https://doi.org/10.1016/S0022-1694(96)03204-
0.
Singh, A., 2020. Salinization and drainage problems of agricultural land. Irrig. Drain. 69
(4), 844–853. https://doi.org/10.1002/ird.2477.
Smith, M.E., Wynn, J.G., Scharping, R.J., Moore, E.W., Garey, J.R., Onac, B.P., 2021.
Source of saline groundwater on tidally inuenced blue holes on San Salvador
Island, Bahamas. Hydrogeol. J. 29, 429–441. https://doi.org/10.1007/s10040-020-
02266-z.
Sun, Y., Wendi, D., Kim, D.E., Liong, S.-Y., 2019. Deriving intensity–duration–frequency
(IDF) curves using downscaled in situ rainfall assimilated with remote sensing data.
Geosci. Lett. 6, 17. https://doi.org/10.1186/s40562-019-0147-x.
Szij´
art´
o, M., Galsa, A., T´
oth, ´
A., M´
adl-Sz˝
onyi, J., 2019. Numerical investigation of the
combined effect of forced and free thermal convection in synthetic groundwater
basins. J. Hydrol. 572, 364–379. https://doi.org/10.1016/j.jhydrol.2019.03.003.
Szij´
art´
o, M., Galsa, A., T´
oth, ´
A., M´
adl-Sz˝
onyi, J., 2021. Numerical analysis of the
potential for mixed thermal convection in the Buda Thermal Karst, Hungary. J.
Hydrology: Regional Studies, 34, paper: 100783, 10.1016/j.ejrh.2021.100783.
Szocs, T., Rman, N., Süveges, M., Palcsu, L., T´
oth, G.y., Lapanje, A., 2013. The
application of isotope and chemical analyses in managing transboundary
groundwater resources. Appl. Geochem. 32, 95–107. https://doi.org/10.1016/j.
apgeochem.2012.10.006.
A. Galsa et al.
Journal of Hydrology 609 (2022) 127695
17
Tejeda, I., Cienfuegos, R., Mu˜
noz, J.F., Dur´
an, M., 2003. Numerical modeling of saline
intrusion in Salar de Atacama. J. Hydrol. Eng. 8 (1), 25–34. https://doi.org/
10.1061/(ASCE)1084-0699(2003)8:1(25).
T´
oth, J., 2009. Gravitational Systems of Groundwater Flow: Theory, Evaluation,
Utilization. Cambridge University Press, United Kingdom, p. 297.
Van Dam, R.L., Simmons, C.T., Hyndman, D.W., Wood, W.W., 2009. Natural free
convection in porous media: First eld documentation in groundwater. Geophys.
Res. Lett., 36, paper: LL11403, 10.1029/2008GL036906.
Vanderborght, J., Vereecken, H., 2007. Review of dispersivities for transport modeling in
soils. Vadose Zone J. 6 (1), 29–52. https://doi.org/10.2136/vzj2006.0096.
Vars´
anyi, I., ´
O.Kov´
acs, L., 2009. Origin, chemical and isotopic evolution of formation
water in geopressured zones in the Pannonian Basin, Hungary. Chem. Geol. 264
(1–4), 187–196. https://doi.org/10.1016/j.chemgeo.2009.03.006.
V´
asquez, C., Ortiz, C., Su´
arez, F., Mu˜
noz, J.F., 2013. Modeling ow and reactive
transport to explain mineral zoning in the Atacama salt at aquifer, Chile. J. Hydrol.
490, 114–125. https://doi.org/10.1016/j.jhydrol.2013.03.028.
Wang, J.-Z., Jiang, X.-W., Wan, L., W¨
orman, A., Wang, H., Wang, X.-S., Li, H., 2015. An
analytical study on artesian ow conditions in unconned-aquifer drainage basins.
Water Resour. Res. 51 (10), 8658–8667. https://doi.org/10.1002/2015WR017104.
Weatherill, D., Simmons, C.T., Voss, C.I., Robinson, N.I., 2004. Testing density-
dependent groundwater models: two-dimensional steady state unstable convection
in innite, nite and inclined porous layers. Adv. Water Resour. 27, 547–562.
https://doi.org/10.1016/j.advwatres.2004.01.003.
Wen, B., Chang, K. W., Hesse, M.A., 2018. Rayleigh-Darcy convection with
hydrodynamic dispersion. Phys. Rev. Fluids, 3, paper: 123801, 10.1103/
PhysRevFluids.3.123801.
Werner, A.D., Bakker, M., Post, V.E.A., Vandenbohede, A., Lu, C., Ataie-Ashtiani, B.,
Simmons, C.T., Barry, D.A., 2013. Seawater intrusion processes, investigation and
management: Recent advances and future challenges. Adv. Water Resour. 51, 3–26.
https://doi.org/10.1016/j.advwatres.2012.03.004.
Wu, H., Fang, W.-Z., Kang, Q., Tao, W.-Q., Qiao, R., 2019. Predicting effective diffusivity
of porous media from images by deep learning. Sci. Rep. 9, 20387. https://doi.org/
10.1038/s41598-019-56309-x.
Zhang, J., Zhou, J., Fu, L., Li, H., Lou, D., 2020a. Karstication of Ordovician carbonate
reservoirs in Huanghua depression and its control factors. Carbonates Evaporites 35,
paper: 42. https://doi.org/10.1007/s13146-020-00572-x.
Zhang, X., Jiao, J.J., Li, H., Luo, X., Kuang, X., 2020b. Effects of downward intrusion of
saline water on nested groundwater ow systems. Water Resour. Res., 56, paper:
e2020WR028377, 10.1029/2020WR028377.
Zhang, Z.-Y., Jiang, X.-W., Wang, X.-S., Wan, L., Wang, J.-Z., 2018. A numerical study on
the occurrence of owing wells in the discharge area of basins due to the upward
hydraulic gradient induced wellbore ow. Hydrol. Process. 32 (11), 1682–1694.
https://doi.org/10.1002/hyp.11623.
Zimmermann, W.B.J., 2006. Multiphysics Modeling With Finite Element Methods. World
Scientic Publishing Company, Singapore, p. 422.
A. Galsa et al.
