We discuss the various performance aspects of parallelizing our transient global-scale groundwater model at 30′′ resolution (30arcsec; °1/41km at the Equator) on large distributed memory parallel clusters. This model, referred to as GLOBGM, is the successor of our 5′ (5arcmin; °1/410km at the Equator) PCR-GLOBWB 2 (PCRaster Global Water Balance model) groundwater model, based on MODFLOW having two model layers. The current version of GLOBGM (v1.0) used in this study also has two model layers, is uncalibrated, and uses available 30′′ PCR-GLOBWB data. Increasing the model resolution from 5′ to 30′′ creates challenges, including increased runtime, memory usage, and data storage that exceed the capacity of a single computer. We show that our parallelization tackles these problems with relatively low parallel hardware requirements to meet the needs of users or modelers who do not have exclusive access to hundreds or thousands of nodes within a supercomputer. For our simulation, we use unstructured grids and a prototype version of MODFLOW 6 that we have parallelized using the message-passing interface. We construct independent unstructured grids with a total of 278 million active cells to cancel all redundant sea and land cells, while satisfying all necessary boundary conditions, and distribute them over three continental-scale groundwater models (168 million - Afro-Eurasia; 77 million - the Americas; 16 million - Australia) and one remaining model for the smaller islands (17 million). Each of the four groundwater models is partitioned into multiple non-overlapping submodels that are tightly coupled within the MODFLOW linear solver, where each submodel is uniquely assigned to one processor core, and associated submodel data are written in parallel during the pre-processing, using data tiles. For balancing the parallel workload in advance, we apply the widely used METIS graph partitioner in two ways: it is straightforwardly applied to all (lateral) model grid cells, and it is applied in an area-based manner to HydroBASINS catchments that are assigned to submodels for pre-sorting to a future coupling with surface water. We consider an experiment for simulating the years 1958-2015 with daily time steps and monthly input, including a 20-year spin-up, on the Dutch national supercomputer Snellius. Given that the serial simulation would require °1/44.5 months of runtime, we set a hypothetical target of a maximum of 16h of simulation runtime. We show that 12 nodes (32 cores per node; 384 cores in total) are sufficient to achieve this target, resulting in a speedup of 138 for the largest Afro-Eurasia model when using 7 nodes (224 cores) in parallel. A limited evaluation of the model output using the United States Geological Survey (USGS) National Water Information System (NWIS) head observations for the contiguous United States was conducted. This showed that increasing the resolution from 5′ to 30′′ results in a significant improvement with GLOBGM for the steady-state simulation when compared to the 5′ PCR-GLOBWB groundwater model. However, results for the transient simulation are quite similar, and there is much room for improvement. Monthly and multi-year total terrestrial water storage anomalies derived from the GLOBGM and PCR-GLOBWB models, however, compared favorably with observations from the GRACE satellite. For the next versions of GLOBGM, further improvements require a more detailed (hydro)geological schematization and better information on the locations, depths, and pumping rates of abstraction wells.

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A significant increase in surface water salinization in low-lying deltas is expected globally due to saline groundwater exfiltration driven by rising sea levels and decreasing freshwater availability. Sustaining fresh water-dependent agriculture in such areas will entail an increased demand for fresh water flushing. Unfortunately, the flushing of surface water is not operationally optimised and results in excessive use of scarce freshwater. To meet the increased demand for flushing, while minimizing the need for diverted freshwater, new operational designs are required. This paper presents a novel network model based approach that uses De Saint Venant (SV) and Advection Dispersion (AD) equations to optimize multiple objectives on water level and salinity control using a Nonlinear Model Predictive Control (NMPC). The resulting NMPC problem is solved with a receding horizon implementation, where the nonlinear program (NLP) at each iteration is solved using state-of-the-art large scale interior point solver (IPOPT). We evaluate the performance of the proposed approach and compare it to the traditional fixed flushing for a representative Dutch polder. Firstly, the approach is shown to be capable of controlling the water level and salinity level in the polder. Secondly, the results highlight that the network of canals, which were originally made for drainage, could not be made sufficiently fresh with current intake capacity. A simple design approach was used to identify appropriate new capacities for two of the gates that allow optimal flushing to guarantee the required water level and salinity constraints.

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The Nile Delta Aquifer (NDA) is threatened by salt water intrusion (SWI). This article demonstrates an approach for identifying critical salinity concentration zones using a three-dimensional (3D) variable-density groundwater flow model in the NDA. An innovative procedure is presented for the delineation of salinity concentration in 2010 by testing different simulation periods. The results confirm the presence of saline groundwater caused by SWI in the north of the NDA. In addition, certain regions in the east and southwest of the NDA show increased salinity concentration levels, possibly due to excessive groundwater extraction and dissolution of marine fractured limestone and shale that form the bedrock underlying the aquifer. The research shows that the NDA is still not in a state of dynamic equilibrium. The modeling instrument can be used for simulating future scenarios of SWI to provide a sustainable adaptation plan for groundwater resource.

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Worldwide, delta areas are under stress due to climate change. With rising sea
levels and decreasing freshwater availability, surface water salinization due to
groundwater exfiltration is expected to increase in these low-lying areas. To
counteract surface water salinization, freshwater diverted from rivers is used to flush agricultural ditches. In this paper, we demonstrate a Model Predictive Control (MPC) scheme to control salinity and water levels in a water course while minimizing freshwater usage. A state space description of the discretized De Saint Venant and advection-dispersion equations for water and salt transport, respectively, is used as the internal model of the controller. The developed MPC scheme is tested using groundwater exfiltration data from two different representative Dutch polders. The tests demonstrate that water levels and salinity concentrations can successfully be controlled within set limits while minimizing the freshwater used.@en

We present a systematic approach for salinity sensor placement in a polder network, where the objective is to estimate the unmeasured salinity levels in the main polder channels. We formulate this problem as optimization of the estimated salinity levels using root mean square error (RMSE) as the "goodness of fit" measure. Starting from a hydrodynamic and salt transport model of the Lissertocht catchment (a low-lying polder in the Netherlands), we use principal component analysis (PCA) to produce a low-order PCA model of the salinity distribution in the catchment. This model captures most of the relevant salinity dynamics and is capable of reconstructing the spatial and temporal salinity variation of the catchment. Just using three principal components (explaining 93% of the variance of the dataset) for the low-order PCA model, three optimally placed sensors with a greedy algorithm make the placement robust for modeling and measurement errors. The performance of the sensor placement for salinity reconstruction is evaluated against the detailed hydrodynamic and salt transport model and is shown to be close to the global optimum found by an exhaustive search with a RMSE of 82.2 mg/L.@en

Whether a coastal area is suitable for beach nourishments and can induce a growth in fresh groundwater resources depends on the appropriateness of the intended site for beach nourishments, and the attainable growth in fresh groundwater resources. In this study we presume that all eroding sandy beaches are suitable for large beach nourishments, and focus on the impact of these nourishments on fresh groundwater in various coastal settings. The growth in fresh groundwater resources – as a consequence of the construction of a beach nourishment – was quantified with 2-D variable-density groundwater models, for a global range in geological parameters and hydrological processes. Our simulation results suggest that large beach nourishments will likely lead to a (temporary) increase of fresh groundwater resources in most settings. However, for a substantial growth in fresh groundwater, the coastal site should receive sufficient groundwater recharge, consist of sediment with a low to medium hydraulic conductivity, and be subject to a limited number of land-surface inundations. Our global analysis shows that 17% of shorelines may consist of erosive sandy beaches, and of these sites 50% have a high potential suitability. This shows a considerable potential worldwide to combine coastal protection with an increase in fresh groundwater resources.@en

As Egypt's population increases, the demand for fresh groundwater extraction will intensify. Consequently, the groundwater quality will deteriorate, including an increase in salinization. On the other hand, salinization caused by saltwater intrusion in the coastal Nile Delta Aquifer (NDA) is also threatening the groundwater resources. The aim of this article is to assess the situation in 2010 (since this is when most data is sufficiently available) regarding the available fresh groundwater resources and to evaluate future salinization in the NDA using a 3D variable-density groundwater flow model coupled with salt transport that was developed with SEAWAT. This is achieved by examining six future scenarios that combine two driving forces: increased extraction and sea level rise (SLR). Given the prognosis of the intergovernmental panel on climate change (IPCC), the scenarios are used to assess the impact of groundwater extraction versus SLR on the seawater intrusion in the Delta and evaluate their contributions to increased groundwater salinization. The results show that groundwater extraction has a greater impact on salinization of the NDA than SLR, while the two factors combined cause the largest reduction of available fresh groundwater resources. The significant findings of this research are the determination of the groundwater volumes of fresh water, brackish, light brackish and saline water in the NDA as a whole and in each governorate and the identification of the governorates that are most vulnerable to salinization. It is highly recommended that the results of this analysis are considered in future mitigation and/or adaptation plans.

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For a large beach nourishment called the Sand Engine – constructed in 2011 at the Dutch coast – we have examined the impact of coastal forcing (i.e. natural processes that drive coastal hydro- and morphodynamics) and groundwater
recharge on the growth of a fresh groundwater lens between 2011 and 2016. Measurements of the morphological change and the tidal dynamics at the study site were incorporated in a calibrated three-dimensional and variabledensity
groundwater model of the study area. Simulations with this model showed that the detailed incorporation of both the local hydro- and morphodynamics and the actual recharge rate can result in a reliable reconstruction of the growth in fresh groundwater resources. In contrast, the neglect of tidal dynamics, land-surface inundations, and morphological changes in model simulations can result in considerable overestimations of the volume of fresh groundwater. In particular, wave runup and coinciding coastal erosion during storm surges limit the growth in fresh groundwater resources in dynamic coastal environments, and should be considered at potential nourishment sites to delineate the area that is vulnerable to salinization.@en

Saline groundwater exfiltration to surface water increases the surface water salinization and degrades the surface water quality in low-lying deltaic areas. The use of surface water will be less appropriate for agricultural, industrial and drinking water production due to salinization, and therefore, freshwater diverted from river is used for flushing canals and ditches in these areas. Current water management strategies for flushing control in low lying polders have to be revised due to expecting negative effects of climate change, sea level increase and decreasing fresh water availability. Model predictive control (MPC) is a powerful control option which is increasingly used by operational water managers for managing water systems. The explicit consideration of constraints and multi-objective management are important features of MPC. In this study, a MPC scheme is developed and tested for combined salinity and water level control of a polder ditch. Saline groundwater exfiltration flux and concentration is modelled and used as known disturbances for the MPC scheme by using Rapid Saline Groundwater Exfiltration Model (RSGEM). The developed control scheme is tested on a test case using real data from a Dutch polder affected by high saline groundwater exfiltration to observe the performance of the controller for a real scenario. Simulation results show that MPC can increase the operational efficiency of flushing operations significantly.@en

A benchmark problem involving the rotating movement of three immiscible fluids is proposed for verifying the density-dependent flow component of groundwater flow codes. The problem consists of a two-dimensional strip in the vertical plane filled with three fluids of different densities separated by interfaces. Initially, the interfaces between the fluids make a 45°angle with the horizontal. Over time, the fluids rotate to the stable position whereby the interfaces are horizontal; all flow is caused by density differences. Two cases of the problem are presented, one resulting in a symmetric flow field and one resulting in an asymmetric flow field. An exact analytical solution for the initial flow field is presented by application of the vortex theory and complex variables. Numerical results are obtained using three variable-density groundwater flow codes (SWI, MOCDENS3D, and SEAWAT). Initial horizontal velocities of the interfaces, as simulated by the three codes, compare well with the exact solution. The three codes are used to simulate the positions of the interfaces at two times; the three codes produce nearly identical results. The agreement between the results is evidence that the specific rotational behavior predicted by the models is correct. It also shows that the proposed problem may be used to benchmark variable-density codes. It is concluded that the three models can be used to model accurately the movement of interfaces between immiscible fluids, and have little or no numerical dispersion.@en