Density-dependent Groundwater Flow Research Articles

Island hydrogeology in the tropics: Constraining a 3D variable-density groundwater flow and solute transport model with geophysics

Saltwater intrusion is the greatest risk to coastal community water supplies where they are dependent on fresh groundwater as the main source of supply. For small, fractured bedrock island aquifers, the fresh groundwater lens dynamics and transition zone geometry are complex. This study investigated the impacts of projected increases in groundwater pumping on a fresh groundwater lens to evaluate changes to the lens geometry and localized up-coning from the deeper, more saline aquifers beneath a small bedrock island in the tropics. A combination of traditional hydrogeological datasets and an airborne electromagnetic survey were used to develop a three-dimensional density-dependent groundwater flow and solute transport model using the SEAWAT code. This investigation represents one of very few studies that have taken such an approach. The model was calibrated using observed groundwater hydraulic heads and chloride concentration data, and calculated chloride values based on bulk conductivity measurements determined from inverted geophysical data. A staged calibration approach was adopted, firstly assessing the time-average lens extent and geometry, and secondly considering the seasonal groundwater level response. In the calibration, the geophysical data helped constrain the lens geometry in the absence of hydraulic head and chloride data. The calibrated model was used to test scenarios where groundwater pumping rates were increased above the current demand of 452 m3 d−1, showing that the lens is likely to be stable, i.e., its available storage is not expected to contract excessively, for extraction rates of up to 3,000 m3 d−1. The combined use of geophysical data and a numerical modeling approach was advantageous in investigating the lens characteristics. It also demonstrated how these techniques can be used together to evaluate coastal water resources and to manage water supply risks for coastal communities. The study demonstrated that the freshwater lens can likely support the freshwater demands of the remote community, and is a preferred option compared with high-cost and more complicated options such as seawater desalination and managed aquifer recharge.

Saltwater intrusion management in shallow and deep coastal aquifers for high aridity regions

Study regionThe current study was applied on two extensive and important regional aquifers: the first is the shallow aquifer of Gaza coastal aquifer (GCA), Palestine and the second is the deep aquifer of the Nile Delta (NDA), Egypt. The two sites are suffering from high stress water resource and contamination by saltwater intrusion (SWI). SWI is natural phenomena that damage the fresh groundwater in two sites and increase the aquifer. Shallow and deep aquifer plays a natural role for keeping the quality of freshwater from SWI in costal aquifers. This study aims to compare different methods for aquifer protection from SWI by analyzing their efficiency using numerical groundwater models in the two sites. Study focusThe finite difference for density dependent groundwater flow model SEAWAT was used on two sites to investigate the extension of SWI without management (base case) and the four methods to control SWI. The numerical models were calibrated for the base case using the other studies and field data to simulate the intrusion in GCA and NDA. The investigated four methods focused on (1) subsurface physical barriers of Cut-off walls), (2) subsurface physical barriers of subsurface dams, (3) the hydraulic method including Treatment and Recharge of collected wastewater, Abstraction and Desalination of low salinity by brackish water, and (4) the land reclamation using earth fill method. New hydrological insights for the regionThe simulated results indicated for the base cases that the intrusion salt mass (NaCl) reached 6068 × 103 kg for GCA and 8863 × 1010 kg for NDA. Moreover, the percentage of aquifer salt mass was decreased and reached 17.60%;, 23.30%; 7.85% and 6.20% in for shallow aquifer while it reached 2.05%; 0.90%; 5.30% and 0.80% in deep aquifer for the physical subsurface dam of cut-off wall, subsurface dam, hydraulic method and land reclamation technique respectively. On the other side the control methods in shallow aquifers is more effective than the deep one. The subsurface barriers and land fill method isn’t effective for deep aquifer while the hydraulic of TRAD method has a positive effect on SWI in shallow and deep aquifers. The current study could be carried out around the world in different coastal hydrological groundwater thickness using the effective method to increase the mitigation of SWI and increase the fresh groundwater resources in coastal aquifers.

Identification of management options to mitigate seawater intrusion in an overexploited multi-layered coastal aquifer by integrated rainfall–runoff, surface water and density-dependent groundwater flow modeling

Identification of management options to mitigate seawater intrusion in an overexploited multi-layered coastal aquifer by integrated rainfall–runoff, surface water and density-dependent groundwater flow modeling

The influence of connected heterogeneity on groundwater flow and salinity distributions in coastal volcanic aquifers

Geological heterogeneity is a key factor affecting rates and patterns of groundwater flow and the evolution of salinity distributions in coastal aquifers. The hydrogeologic systems of volcanic aquifers are characterized by lava flows that can form connected geologic structures in the subsurface. Surface-based geostatistical techniques were adopted to generate geologically-realistic, statistically equivalent model realizations of a hydrogeologic system based on that of the Big Island of Hawaii (conduit models). The density-dependent groundwater flow and solute transport code SEAWAT was used to perform 3D simulations to investigate subsurface flow and salt transport through these random realizations. Statistically equivalent geological systems generated with sequential indicator simulation (SIS) and equivalent homogeneous systems were also simulated for comparison. Simulation results show that conduit realizations tend to have more complex salinity distributions with larger mixing zones for which the center of mass is farther offshore compared to homogeneous and SIS realizations. The zone of groundwater discharge is also farther offshore than for homogeneous and SIS models, with higher point fluxes of both fresh and saline water and greater spatial variability. This highlights the importance of the geometry of geologic features in coastal groundwater flow and solute transport processes in highly heterogeneous aquifers. It also points to the importance of preferential flow, with implications for both coastal groundwater resource management and solute fluxes to the ocean.

Development of an efficient conjunctive meta-model-based decision-making framework for saltwater intrusion management in coastal aquifers

This paper presents an integrated framework for management of aquifers threatened by saltwater intrusion (SI). In this framework, SEAWAT model is used for simulating the density dependent groundwater flow. Three meta-models based on the artificial neural network (ANN), M5 tree and random subspaces model (RSM) are developed, as surrogate models for SEAWAT to accurately simulate the groundwater response to different pumping and recharge scenarios. Various patterns of recharge to and discharge from aquifer are used to generate a database for training the mentioned surrogate models. To decrease the number of training parameters, the aquifer area is divided into different zones using k-means clustering technique (KMC). Additionally, a conjunctive model (CM) using a combination of the three surrogate models is proposed to enhance the accuracy of the simulation. It is then integrated with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) with the objectives of maximizing pumping rates and minimizing SI length. Next, the socially optimal scenarios are selected from the obtained Pareto-front using the Nash bargaining theory. The performance of the proposed model is evaluated by applying it to the Kahak aquifer, Iran, which is subjected to SI. The results show that the conjunctive model using KMC technique predicts SI length with a comparable accuracy and results in 95% reduction in runtime compared to a simulation-optimization (SO) model.

Multi-objective Freshwater Management in Coastal Aquifers Under Uncertainty in Hydraulic Parameters

This paper proposes a novel stochastic framework for groundwater quantity and quality management in aquifers threatened by saltwater intrusion. In this methodology, a finite difference SEAWAT code is linked with an optimization model to solve density-dependent groundwater flow equations considering different patterns of pumping rates. To reduce the computational time of the simulation–optimization process especially when there are a high number of decision variables, a modular evolutionary polynomial regression (MEPR) model is developed and coupled with the optimization algorithm. The info-gap theory is utilized to evaluate the robustness of optimal scenarios incorporating the uncertainty of hydraulic conductivity (k) of the heterogeneous aquifer. For each management scenario proposed by the simulation–optimization model, values of robustness and opportuneness indices are computed based on utility functions of different agricultural sectors. The results of applying the proposed method to the Qom aquifer in Iran show that coupling MEPR model with the simulation–optimization model considering the uncertainty of the aquifer parameter k could provide a reliable management scenario with a comparatively low computational cost.

Rebuttal to \u201cThe case of the Biscayne Bay and aquifer near Miami, Florida: density-driven flow of seawater or gravitationally driven discharge of deep saline groundwater?\u201d by Weyer (Environ Earth Sci 2018, 77:1\u201316)

A recent paper by Weyer (Environ Earth Sci 2018, 77:1–16) challenges the widely accepted interpretation of groundwater heads and salinities in the coastal Biscayne aquifer near Miami, Florida, USA. Weyer (2018) suggests that the body of saltwater that underlies fresh groundwater just inland of the coast is not a recirculating wedge of seawater, but results instead from upward migration of deep saline groundwater driven by regional flow. Perhaps more significantly, Weyer (2018) also asserts that established hydrologic theory is fundamentally incorrect with respect to buoyancy. Instead of acting along the direction of gravity (that is, vertically), Weyer (2018) claims, buoyancy acts instead along the direction of the pressure gradient. As a result, Weyer (2018) considers currently available density-dependent groundwater flow and transport modeling codes, and the analyses based on them, to be in error. In this rebuttal, we clarify the inaccuracies in the main points of Weyer’s (2018) paper. First, we explain that Weyer (2018) has misinterpreted observed equivalent freshwater heads in the Biscayne aquifer and that his alternative hypothesis concerning the source of the saltwater does not explain the observed salinities. Then, we review the established theory of buoyancy to identify the problem with Weyer’s (2018) alternative theory. Finally, we present theory and cite successful benchmark simulations to affirm the suitability of currently available codes for modeling density-dependent groundwater flow and transport.

Long-time resistivity monitoring of a freshwater/saltwater transition zone using the vertical electrode system SAMOS

In September 2009 two newly developed vertical electrode systems were installed in boreholes in the water catchment areas Waterdelle and Ostland at the North Sea island Borkum to monitor possible changes of the transition zone between the freshwater lens and the underlying saltwater. The vertical electrode systems, which were both installed between 44 m and 65 m below ground level, are used for geoelectrical multi-electrode measurements carried out automatically several times per day; the measurements are still ongoing. The whole system consisting of a vertical electrode system in a borehole and the measuring unit at ground level is called SAMOS (Saltwater Monitoring System).At both locations the data show a clear resistivity decrease that indicates the transition zone between freshwater and saltwater. The depth of the transition zone as well as the kind of resistivity decrease is very stable since 2010.Temporal changes are visible if single depths are considered. In 2015 Miriam Ibenthal used a vertical 2D density-dependent groundwater flow model to explain the long-term resistivity measurements and showed that the temporal changes at CLIWAT 2 (Ostland) could be explained by variations of the groundwater level, changing groundwater recharge rates and changing pumping rates of the nearby located drinking water supply wells.

English

A numerical model of variable-density groundwater flow and miscible salt transport is applied to investigate the extent of seawater intrusion in coastal aquifer of Ras El-Hekma, northwestern coast, Egypt. The SEAWAT 2000 code is used to solve the density-dependent groundwater flow and solute transport governing equations. Seventeen groundwater samples were collected in 2015 for routine chemical analysis and water level monitoring were carried out and interpreted. The model was calibrated using data measured for heads (m) and TDS (mg/L) in 2009 compared with data collected in 2015. Three scenarios of pumping and fourth scenarios of sea level rise by 0.5 m were applied. The results of three scenarios of pumping revealed that there was a general trend of drawdown in water table (~5 m) of observed wells located at about 1 to 1.5 km from the coast at the end of 20 years of simulation. At the same time there was replenishment from rainfall and surface runoff caused a water table rise in some observed wells that were located inland. For the proposed fourth scenario of sea level rise, the seawater/freshwater interface will migrate more inland (0.5 to 2 km) than its current position. The result of the numerical model shows a transgression of seawater inland and along the coast. The model and chemical results recommend a decrease in pumping to the drilled wells should not exceed 40 m3/day in order to avoid further seawater intrusion along the coast and upwelling of deep saline groundwater with continuous monitoring of the groundwater level and salinity measurements in north coast of Mediterranean Sea. Key words: Seawater intrusion, groundwater modeling, SEAWAT code, Ras El-Hekma, Egypt.

Development of a discrete‐continuum VDFST‐CFP numerical model for simulating seawater intrusion to a coastal karst aquifer with a conduit system

AbstractA hybrid discrete‐continuum numerical model, Variable‐Density Flow and Solute Transport—Conduit Flow Process (VDFST‐CFP), is developed to simulate seawater intrusion to a coastal karst aquifer with a conduit network. The Darcy‐Weisbach equation is applied to simulate the nonlaminar groundwater flow in the conduit system that is conceptualized as pipes, while the Darcy equation is used for laminar groundwater flow in the continuum porous medium. Density‐dependent groundwater flow with appropriate additional density terms in the conduit is analytically derived. The flow and transport equations are coupled, and numerically solved by the finite difference method with an implicit iteration procedure. Two synthetic benchmarks are developed to compare the VDFST‐CFP model results with other numerical models, such as the variable‐density SEAWAT, constant‐density continuum MODFLOW/MT3DMS, and constant‐density discrete‐continuum CFPv2/UMT3D models. The VDFST‐CFP model compares reasonably well with the other model results in both conduit and porous medium domains, and well describes water and salt exchange between the two systems. Under turbulent flow conditions within the conduit, the Darcy‐Weisbach equation calculates the flow rate more accurately without overestimation by the Darcy equation. Sensitivity analysis indicates that conduit diameter, friction factor, matrix hydraulic conductivity, and effective medium porosity are important parameters in the VDFST‐CFP model. The pros and cons of the VDFST‐CFP model are discussed, including the model assumptions and simplifications, limitations of the discrete‐continuum modeling method, and the convergence criteria. In general, the newly developed VDFST‐CFP model provides a new numerical modeling method for simulating seawater intrusion in a coastal karst aquifer with conduits.

Saltwater intrusion in an irrigated agricultural area: combining density-dependent modeling and geophysical methods

Saltwater intrusion is one of the most important water quality problems in coastal aquifers, especially in areas with increased water demands. Geophysical techniques can provide a non-invasive and cost-effective approach for determining the geometrical characteristics of an aquifer and for guiding the saltwater intrusion modeling process and in turn reducing the model’s inherent uncertainty. In this work, the above concept was applied in the Tympaki basin in Heraklion, Greece. The transient electromagnetic method was used to obtain an accurate 3-D geomodel (bedrock geometry and fault detection) of the basin. This, in turn, was used to guide the construction of a density-dependent groundwater flow and transport simulation model. The results show significant advancement of the saltwater intrusion front in the northern part of the study area, while the phenomenon is less pronounced in the central and southern parts. This is mainly attributed to the combined effect of the fault in the northern part of the basin, the uplifted Neogene deposits in the central part and the freshwater inflow from the Festos corridor in the southern part.

Validity and slopes of the linear equation of state for natural brines in salt lake systems

Many density-dependent groundwater flow simulations rely on a linear equation of state that relates the fluid density to the total dissolved solute content (TDS). This approach ignores non-linear volume of mixing effects, as well as the impact of any chemical reactions. These effects can be considered by using geochemical codes that implement algorithms that calculate the density of a fluid based on the concentration of individual solute species. While in principle such algorithms could be used in-lieu of a linear equation of state in a groundwater model, the computational overhead is such that the use of a more simplified equation of state is preferred. This requires that the assumption of linearity as well as the appropriate value of the linear slope have to be determined. Here, published density measurements of 7 chemically-distinct salt lake brines are compared with densities calculated by PHREEQC-3, confirming the applicability of PHREEQC’s algorithm to salt lake brines, as well as to seawater brines and artificial brines from laboratory experiments. Further, calculations with PHREEQC-3 are used to assess the impact of mineral precipitation reactions during evaporative concentration. Results show that the density–TDS relationship is essentially linear over a wide concentration range, and that slopes range between 0.64 and 0.75, with the upper end of the range applying to Na–CO3–Cl brines and the lower end to Na–Cl brines. Mineral precipitation of highly-soluble evaporate minerals such as halite and trona limit TDS, and may lead to considerable errors in coupled flow simulations based on a linear equation of state at high concentrations. Misrepresentation of the slope may lead to an error of up to 20% in the calculated length of the brine nose bordering a salt lake, or of the Rayleigh number, which indicates if a density stratification is stable or not.

Recommendations of Controlling Saltwater Intrusion in an Inland Aquifer for Drinking-Water Supply at a Certain Waterworks Site in Berlin (Germany)

Saltwater intrusion is a widespread contamination problem of continuing great practical interest in many coastal and inland aquifers all over the world. Therefore, it is highly desirable to properly manage groundwater resources for drinking-water supply by controlling saltwater intrusion. This paper proposes to provide two recommendations of controlling saltwater intrusion in an inland aquifer for drinking-water supply at a certain waterworks site in Berlin (Germany) on the basis of the validated source of saltwater intrusion as well as pumping optimization, using a density-dependent groundwater flow and solute transport model. In terms of pumping-rate reduction, the optimal pumping rate was validated for eliminating the effect of saltwater intrusion. Without consideration of scenario conditions, its value could be set 1.39 × 10−2 m3/s (50 m3/h) or 5.56 × 10−3 m3/s (20 m3/h), if the requirement of drinking water palatability were good or excellent, respectively. With regard to pumping-pattern rearrangement, the well construction was modified to access bank filtration for eliminating the effect of saltwater intrusion.

Saltwater Upconing Below a Pumping Well in an Inland Aquifer: a Theoretical Modeling Study on Testing Different Scenarios of Deep Saline-Groundwater Pathways

To date, studies on the geological conditions in inland aquifers leading to pathways for upwelling deep saline groundwater due to pumping have not been published yet. Therefore, this paper conducted a theoretical modeling study to raise two hypotheses about deep saline-groundwater pathways leading to saltwater upconing below a pumping well in an inland aquifer based on the field situation at the Beelitzhof waterworks in southwestern Berlin (Germany), defined as follows: (1) there are windows in the Rupelian clay caused by glacial erosion, where their locations are uncertain, and (2) there are no windows in the clay, but the clay is partially thinned out but not completely removed by glacial erosion, so salt can merely come through the clay upward by diffusion and eventually accumulate on its top. These hypotheses were tested to demonstrate the impact of the lateral distance between windows in the clay and the well, as well as salt diffusion through the clay depending on its thickness on saltwater intrusion in the pumping well, respectively, using a density-dependent groundwater flow and solute transport model. Hypothesis 1 was validated with four scenarios that windows could occur in the clay at the site, and their locations under some conditions could significantly cause saltwater intrusion, while hypothesis 2 could be excluded, because salt diffusion through the clay with thickness greater than 1 m at the site was not able to cause saltwater intrusion.

Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach

A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater–groundwater circulations in the swash and surf zones of the beach, which induced a large seawater–groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies.

A Modelling Study of Seawater Intrusion in the Liao Dong Bay Coastal Plain, China

To investigate the extent of seawater intrusion in the Liao Dong Bay coastal plain, China, a numerical model for variable-density groundwater flow and miscible salt transport was developed. The SEAWAT code was used to solve the density-dependent groundwater flow and solute transport governing equations. The simulation was conducted for 55 months from October, 2004 to April, 2009. The numerical model was calibrated by the hydraulic heads measured in April, 2009. Using the calibrated model and the same hydrogeological conditions in 2004, the extent of seawater intrusion prediction was conducted for the next 40 years. The results show that the extent of seawater intrusion area will increase in all geologic layers with nearly 6.2 km in the upper Quaternary aquifer and 4.3 km in lower Quaternary aquifer for 40 years. In the Minhuazhen group aquifer, the maximum speed of seawater intrusion is 62.2 m/yr. Therefore, some protection of the freshwater aquifer from seawater intrusion in the Liao Dong Bay coastal plain is imperative.

A semi-analytical solution for saltwater intrusion with a very narrow transition zone

The Henry saltwater intrusion problem provides a semi-analytical solution that is largely used for benchmarking density-dependent groundwater flow models. The major drawback of this problem arises from the high dispersion value used by Henry (represented by the dimensionless parameter b = 0.1). Finding a stable semi-analytical solution for small values of b is challenging due to the low convergence of the corresponding nonlinear system. In this work, an accurate semi-analytical solution is developed in the case of a very narrow transition zone corresponding to b = 0.005. About 6,330 terms are used in the Fourier series to accurately represent the solution. The resolution of the corresponding highly nonlinear system is made possible by the modified Powell hybrid algorithm due to the analytical evaluation of the Jacobian, which drastically reduces the computational time. The new test problem is also investigated numerically using different numerical methods and different mesh sizes to show its high worthiness, compared to the standard Henry problem, for benchmarking density driven flow codes.

An evaluation of the relative importance of the effects of climate change and groundwater extraction on seawater intrusion in coastal aquifers in Atlantic Canada

To investigate the relative importance of projected sea-level rise, climate change effects on recharge, and groundwater extraction on seawater intrusion in important coastal aquifers in Atlantic Canada, a three-dimensional numerical model of density-dependent groundwater flow coupled with solute transport was developed for the Richibucto region of New Brunswick. The model was used, with an efficient 2k factorial design approach, to perform simulations for the period 2011–2100. The results of the factorial analyses indicate that the relative importance of the three factors investigated varies depending on the model location considered. The effect of declining recharge is most significant at shallow to intermediate depths along the freshwater–seawater transition zone, while the effect of increasing pumping rates dominates at a location relatively close to the well field. The effect of sea-level rise is shown to be significant only at the much deeper inland toe of the transition zone. The spatial variation in importance is related to how different model boundary conditions influence freshwater flow at the different locations within the model domain. This investigation indicates that sea-level rise has the least significant effect (of the three factors considered) on future seawater intrusion in sandstone aquifers in the Richibucto region.

On the effective hydraulic conductivity and macrodispersivity for density-dependent groundwater flow

In this paper, semi-analytical expressions of the effective hydraulic conductivity (\(K^{E})\) and macrodispersivity (\(\alpha ^{E})\) for 3D steady-state density-dependent groundwater flow are derived using a stationary spectral method. Based on the derived expressions, we present the dependence of \(K^{E}\) and \(\alpha ^{E}\) on the density of fluid under different dispersivity and spatial correlation scale of hydraulic conductivity. The results show that the horizontal \(K^{E}\) and \(\alpha ^{E}\) are not affected by density-induced flow. However, due to gravitational instability of the fluid induced by density contrasts, both vertical \(K^{E}\) and \(\alpha ^{E}\) are found to be reduced slightly when the density factor (\(\gamma \)) is less than 0.01, whereas significant decreases occur when \(\gamma \) exceeds 0.01. Of note, the variation of \(K^{E}\) and \(\alpha ^{E}\) is more significant when local dispersivity is small and the correlation scale of hydraulic conductivity is large.

Freshwater lens formation below juvenile dunes on a barrier island (Spiekeroog, Northwest Germany)

Morphodynamic changes of barrier islands and the consequences for underlying freshwater reservoirs are of major interest for coastal environments and drinking water supply in coastal areas. Here, a geomorphological and hydrological reconstruction of dune formation on a barrier island and their freshwater reservoirs is presented. The aim was to provide an integrated analysis of the co-evolution of dunes and freshwater resources during the development of a barrier island. The study area is the eastern part of Spiekeroog Island, the so-called ‘Ostplate’, at the Northwest German coast, that expanded significantly in the last 360 years due to coastal land reclamation. The first dune growth was initiated in the 1940s at the newly formed sand flat, and dune freshening started around 1970. Pore water measurements in November 2011, March and August 2012 confirm the existence of freshwater below the dune area and indicate a landward movement of the freshwater–saltwater interface in winter and a seaward movement in summer, respectively, in response to storms and corresponding coastal flooding. A density-dependent groundwater flow model was used to estimate the present thickness and shape of the lenses as well as to reconstruct the evolution of the freshwater reservoirs. The simulations suggest an asymmetric lens shape with a freshwater discharge “tube” below the beach to the sea and an extended brackish transition zone below the salt marsh area towards the tidal flat. The simulation results also indicate that the freshwater reservoirs are still in a stage of development (after 40 years of simulation time) and are estimated to reach steady-state after about 300–500 years under the given conditions without taking into account possible impacts of climate change.