2.1. Northern Rhine Delta Basin (NDB) System Description
The Rhine river splits into several branches just upstream of the city of Arnhem (Figure 1
). The distribution of the discharge over the branches can be controlled to a limited extent by a weir near the city of Arnhem. On average, two thirds of the river flow is directed to the Waal branch, while the Lek receives some 10–15% of the cross border flow of the Rhine. The allocation of the river flow along the Lek river can be controlled by three weirs (see Figure 1
The Rhine–Meuse delta is situated in the western part of the country. Here, the Rhine branches connect with the Meuse river, before flowing into the North Sea through two major outlets. The southern outlet is controlled by sluices (Haringvliet), and the northern outlet is an open shipping channel (Rotterdam Waterway). Sea water enters the estuary through this northern channel.
The western part of the Lek (area of interest; see Figure 1
) is a tidal branch of the river Rhine with an open connection to the sea. The discharge is controlled by a weir (Hagestein). During periods of low discharge on the Rhine (below 1500 m3
/s), the Lek receives a minimal net discharge of 1–10 m3
/s. The drinking water inlets under study are situated at two different locations along the downstream section of the Lek, Kinderdijk and Bergambacht (Figure 2
, Table 1
). Close to Streefkerk, a third location is planned in the near future. At all locations, the type of inlet is river bank filtration: the water is extracted at 40–50 m below surface [6
]. Additionally, at Bergambacht, there is an open water intake.
The mouth of the Lek, just downstream from the intake at Kinderdijk, is situated approximately 42 km from the North Sea. Salt intrusion in the mouth of the Lek commonly occurs during low river flows and high seawater levels. However, it is expected that salinization of the Lek rapidly decays in upstream direction, although few measurement data exist to date to support this view. A typical example of salinization of the mouth of the Lek is presented in Figure 3
, showing the situation in the second half of 2018 when a severe hydrological drought occurred in the Rhine river catchment.
Calculations show [7
] that the tidal excursion—the distance a water particle travels during a tidal cycle [8
]—at the Lek is 6 to 7 km from the mouth under average tidal conditions. This distance increases during spring tide and can reach up to 14 km during storm surges. This implies that the inlet at Kinderdijk is situated within reach of the average tidal excursion. The intake locations at Streefkerk and Bergambacht which are situated more upstream (Figure 2
) will only face salinization during storm surges or through mixing processes causing longitudinal dispersion.
The sea is not the only source of salt in the Lek. On the freshwater side, the Rhine carries a salt load as well. The chloride concentration of the Rhine river can be described by the relationship C(t) = Cb
/Q(t), where Cb
is the background chloride concentration and Lc
is the chloride load. In [9
], estimates for Cc
were derived from measurements in 2007–2008 (Lc
= 60 kg/s; Cb
= 47 mg/L). Using these estimates, the typical chloride concentration for low discharges (800–1500 m3
/s) ranges from 90 to 125 mg/L. A more recent estimate of this riverine chloride concentration (i.e., the combination of background chloride concentration and chloride load), based on the year 2011, results in a range of 97–141 mg/L.
For assessing the impact of climate change on salinization of the Lek and the effectiveness of mitigation measures, preferably long time series are calculated in which a large set of variations in conditions like river discharge, tide and wind conditions occur. To date, this can only be carried out with 1D models, which are a commonly applied for hydrodynamic calculations in river studies [10
]. Therefore, a 1D hydrodynamic model of the Rhine–Meuse estuary was used to describe the transport of water and salt. This Northern Delta Basin (NDB) model is part of the Dutch National Water Model (NWM), a set of hydraulic and hydrological models and tools set up to support the national fresh water policy [11
]. With the NWM model, the hydrology and water distribution throughout The Netherlands can be calculated [12
]. From this, boundary conditions are extracted for the nested and more detailed NDB model [13
The NDB model is setup in the SOBEK-RE modelling suite, a one-dimensional open-channel dynamic numerical modelling system [16
]. Salt transport in the NDB is modelled by a 1D longitudinal advection-dispersion formulation. The advective part describes the distribution of salt along with the 1D motion of the water. Other processes contributing to the distribution of salt that, due to limited dimensions and spatial scale, cannot be resolved by the model are described by the dispersion coefficient. This covers 3D mixing processes like gravitation, circulation and Taylor shear dispersion. Within SOBEK-RE, the dispersion coefficient is estimated by the adjusted version of the Thatcher–Harleman equation [17
The current version of the NDB model (NDB1_1_0) was setup in 2003 [20
] and recalibrated in 2005 [21
]. Due to its relative long distance from the mouth of the estuary, the river Lek has as yet not been vulnerable to salinization, except for its mouth at Kinderdijk. As a consequence, little data is available and calibration of the NDB model has never focused on the Lek. Only recently, a range for the longitudinal dispersion coefficients was estimated for this part of the Rhine estuary [7
], based on an analytic expression for salt dispersion in combination with system knowledge and branch characteristics. An overview of the obtained values is given in Table 2
. It shows that the estimate for the dispersion coefficient varies with conditions, like discharge, salinity gradient and location within the estuary. However, the adjusted Thatcher–Harleman formulation in the NDB model is not able to capture this behavior. Therefore, in this study a range of fixed values was used, depending on the minimum upstream discharge at Hagestein (the most right column in Table 2
The minimum value used in this study is the average of the estimates for a discharge of 2 m3/s, i.e., 55 m2/s. For higher upstream discharges, the dispersion coefficient shows a variation with location along the Lek. The aim of this study is to assess the impact of increasing the upstream discharge on this river branch. To prevent overestimation of the effect of the measure, the dispersion values used were based on the average estimates for the most downstream location (Kinderdijk) and the highest gradient in chloride concentration (∆C = 500 mg Cl/L).
To assess the impact of this approach, sensitivity calculations have been carried out for an 8-year period. For the reference case, the range of D
= 25–80 m2
/s has been explored, which coincides with the full range estimated in Table 2
. For the case with a minimum discharge of 20 m3
/s, the range has been extended from 90 m2
/s towards the lowest value estimated in Table 2
= 25 m2
/s), since D
= 90 m2
/s is expected to be a conservative estimate for the dispersion coefficient, based on typical hydrodynamic and salinity gradient conditions at Kinderdijk. In practice, the dispersion coefficient further upstream of Kinderdijk will be lower.
The results of this sensitivity analysis are shown in Figure 4
, in which the 365-day moving average of chloride at Streefkerk is given for the minimum and the 20 m3
/s discharge cases. It shows that the range of the dispersion coefficient is relevant to the results, but that the effect of the upstream discharge is larger, provided the difference in upstream discharge is sufficiently large (some tens of cubic meter per seconds).
The model setup was validated against observed chloride concentrations at Kinderdijk, available for the period 2001–2011 (no observations were available for the other two locations). Figure 5
illustrates the behavior of the model; it describes the overall variations reasonably well. The model is able to reproduce sudden salinization events due to sea water intrusion. However, the magnitude of the peaks is underestimated.
This general model performance can also be observed from Figure 6
, where the 365-day moving average is plotted for the observed and modelled chloride concentrations at Kinderdijk. The averaged chloride concentration is underestimated for years with a substantial impact of seawater intrusion, like the year 2003.
From this validation, and in line with previous findings [22
], it can be concluded that the model is well able to capture salinization events, but that exact variations differ and the influence of sea water intrusion is underestimated. As variations in chloride concentration in the Lek vary between about 50 mg Cl/L up to over 3500 mg Cl/L, estimating exact exceedance durations of a threshold of 150 mg Cl/L requires a very high accuracy of the model. The validation shows that this accuracy cannot be achieved with this basin wide 1D model. In addition, the limited representation of the physical processes relevant for salinity intrusion in 1D poses an uncertainty on the predictability with changing conditions such as sea level rise. However, a global indication on the amount and duration of exceedance in current and future climate can be obtained. The model can therefore be used to carry out a first-order assessment of the vulnerability of the inlet locations to salinization and of the risk reduction that can be achieved by reallocating the available water over the Rhine branches. However, it should not be used in an operational water management context, where more precise estimates are required for a day to day balancing of the freshwater allocation to the Lek and the salinization potential of the intake locations.
2.3. Climate Projection
The climate projection used in this study is the Wh-dry scenario for the Rhine river catchment [1
]. This scenario is part of the KNMI’14 climate scenarios [23
]—a regionalized interpretation of the AR5 climate projections—and serves as the worst case scenario from a fresh water supply perspective. The Wh-dry scenario projects a change in meteorological conditions (precipitation and evapotranspiration) in The Netherlands, impacting the intake and outlet discharges from the river Lek. Furthermore, the Wh-dry scenario projects for 2050 a sea level rise of 40 cm relative to 1995. The Wh-dry scenario projects a strong reduction in summer precipitation in the Rhine catchment by 17% in 2050 [1
] and leads to a longer duration and severity of low Rhine river discharges entering The Netherlands. For example, the long term mean annual lowest seven-day flow drops from 1010 m3
/s in current conditions to 825 m3
/s in 2050 in Wh-dry conditions, and the number of days with a flow below 1000 m3
/s doubles from 23 to 46 [2
To assess the potential impact of climate change under the Wh-dry scenario on salt water intrusion, the NDB model was rerun with adjusted boundary conditions according to the Wh-dry scenario. The 50-year time series of future river discharges and lateral discharges and intakes has been taken from the National Water Model as used in the context of the Delta Program fresh water supply. The projected sea level rise of 40 cm by 2050 has been added to the marine boundary condition of the model thereby copying the variability of tides and storm surges as historically occurred over the 1961–2011 period.