Density Dependent Groundwater Flow at the Island of Texel, the Netherlands

DENSITY DEPENDENT GROUNDWATER FLOW AT THE ISLAND OF TEXEL, THE NETHERLANDS

Gualbert H.P. OUDE ESSINK University of Utrecht; Inst. of Earth Sciences; Centre of Hydrology (ICHU); Dept. of Geophysics; P.O. Box 80021; 3508 TA Utrecht; The Netherlands; [email protected]

ABSTRACT

Salt water intrusion is investigated at Texel, which is a Wadden island in the northern part of The Netherlands with a surface area of approximately 130 km2. In this coastal groundwater system of Quatenary deposits, salinisation of the upper layers is taking place. At present, brackish water already occurs close to the surface of the low-lying polder areas at the eastern part of the island. Freshwater occurs up to –50 m M.S.L. in the sand-dune area at the western part. Density dependent groundwater flow in this system is modelled in three-dimensions by MOCDENS3D. The model is dimensioned 20 km by 29 km by 302 m depth, whereas about 125,000 active elements and one million particles simulate groundwater flow and salt transport during 500 years. The salinity in the top layer as well as the salt load at the surface of the polders will increase substantially during the next centuries. In addition, a relative sea level rise of 0.75 meter per century definitely intensifies the salinisation process, causing a further increase in salt load in the polders. As such, the increased salinisation of the top layer will affect the surface water system from an ecological as well as a socio-economical point of view.

INTRODUCTION The lowest phreatic water levels can be measured in the so-called Prins Texel is the biggest Dutch Wadden Hendrik polder, with levels as low as island in the North Sea. It is often –2.0 m N.A.P.1 In addition, a dune called Holland in a nutshell (figure area called De Hooge Berg, which is 1a). The population of the island is situated in the southern part of the about 13,000, whereas in island in the polder area summertime, the number of people Dijkmanshuizen, has a phreatic can be as high as 60,000. A sand- water level of some +4.75 m N.A.P. dune area is present at the western The nature reserve ‘De Slufter’ in the side of the island, with phreatic water northwestern part of the island is a levels up to 4 metres above mean tidal salt-marsh. sea level. At the eastern side, four 1 low-lying polder areas with controlled N.A.P. stands for Normaal Amsterdams Peil. It water levels are present (figure 1b). roughly equals Mean Sea Level and is the reference level in The Netherlands. m Phreatic water level [m]: k

< -4 m M.S.L. 0 . 0 -2.50 -4 - -2 - e -1.50

e 5 -2 - 0 nz . 2

e - -1.50 d - 0 - 2 Island of d -1.25 a 0

Texel . 2 -10 W s 5 -1.25 - - 10-20 -1.00 5 . element De Slufter -1.00 7 -

20-40 - ve -0.75 cti

>40 0 . 1. Eijerland -0.75 0 ina a - 1

- -0.50 Se 5 North Sea . rth -0.50 2 -

1 0.00 Amsterdam - No 2. Waal en Burg/

0 0.00 . Het Noorden - 5 0.50 1 - 0.50

Den Haag 5 lowest point: . 3. Dijkmanshuizen/ - 7 1.00 1 - -6.7 m M.S.L. a De Schans Rotterdam e 1.00 0 -

ar .

1.50

0 De Hooge Berg

e 2

Germany - n sea 1.50

u - d 5 .

- 4. Prins Hendrik 2.00

2 d

2 ts - n polder 2.00

a - S

0 3.00 . 5 2 Belgium - 3.00 ive elemen - 4.00 5 .

7 inact

2 4.00 - - 0 25 50 75 100 km 6.50 highest point: 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 km a. +322 m M.S.L. b.

Figure 1: a. map of The Netherlands: position of the island of Texel and ground surface of the Netherlands; b. map of the island of Texel: position of the four polder areas and sand-dune area as well as phreatic water level in the top aquifer at –0.75 m N.A.P.

First, the computer code, which is by the MODFLOW module used to simulate variable density (McDonald and Harbaugh, 1988; flow in this groundwater system, is Harbaugh and McDonald, 1996). summarised. Second, the model of The advection-dispersion equation, Texel will be designed, based on which simulates the solute transport, subsoil parameters, model is solved by the MOC module using parameters and boundary the method of characteristics conditions. The numerical results of (Konikow and Bredehoeft, 1978; two scenarios of sea level rise are Konikow et al., 1996). Advective discussed in the next section, and transport of solutes is modelled by finally, some conclusions are drawn. means of the method of particle tracking and dispersive transport by means of the finite difference CHARACTERISTICS OF THE method. A so-called freshwater head NUMERICAL MODEL If is introduced to take into account differences in density in the MOCDENS3D (Oude Essink, 1998), calculation of the head: which is the three-dimensional p computer code MOC3D (Konikow et I f z (1) al.,1996) but adapted for density U g differences, is used to simulate the f transient groundwater system as it where If is the freshwater head [L], occurs on the island of Texel. The Uf is the reference density, usually groundwater flow equation is solved the density of fresh groundwater at reference chloride concentration C0 convergence criterion for the [M L-3], p is the pressure [M L-1 T-2], groundwater flow equation and z is the elevation head [L]. See (freshwater head) is equal to 10-5 m. Oude Essink (1998, 1999, 2000) for The total simulation time is 500 a detailed description of the years. adaptation of MODFLOW to density differences. A linear equation of The groundwater system consists of state couples groundwater flow and permeable aquifers, intersected by solute transport: loamy aquitards and aquitards of U (C) U [1 E (C C )] (2) clayey and peat composite. The f C 0 system can be divided into six main where U(C) is the density of -3 subsystems. The top subsystem groundwater [M L ], C is the chloride (from 0 m to –22 m N.A.P.) and the -3 concentration [M L ], and EC is the second subsystem (from –22 m to – volumetric concentration expansion 62 m N.A.P.) have hydraulic gradient [L3 M-1]. MOCDENS3D conductivities kx of approximately 5 takes into account hydrodynamic m/d and 30 m/d, respectively. The dispersion. For a conservative solute third subsystem is an aquitard of 10 as chloride, the molecular diffusion m thickness and has hydraulic for porous media is taken equal to conductivities k which varies from -9 2 x 10 m /s. 0.01 to 1 m/d. The fourth subsystem (from –72 m to –102 m N.A.P.) and For the numerical computations the fifth subsystem (from –102 m to – following parameters are applied. 202 m N.A.P.) have hydraulic The groundwater system consists of conductivities kx of some 30 m/d and a 3D grid of 20.0 km by 29.0 km by only 2 m/d, respectively. The lowest 302 m depth. Each element is 250 m subsystem, number six, has a by 250 m long. In vertical direction hydraulic conductivity kx of the thickness of the elements varies approximately 10 m/d to 30 m/d. from 1.5 m at the top layer to 20 m Note that the first, second and fourth over the deepest ten layers. The grid subsystems are intersected by contains 213440 elements: nx=80, aquitards. ny=116, nz=23, where ni denotes the number of elements in the i direction. The following subsoil parameters are Due to the rugged coastline of the assumed: the anisotropy ratio kz/kx system and the irregular shape of equals 0.4 for all layers. The the impervious hydrogeologic base, effective porosity ne is 0.35. The only 58.8 % of the elements longitudinal dispersivity DL is set (125,554 out of 213,440) is equal to 2 m, while the ratio of considered as active elements. Each transversal to longitudinal element contains eight particles to dispersivity is 0.1. Note that no solve the advection term of the numerical 'Peclet' problems occurred solute transport equation. As such, during the simulations (Oude Essink some one million particles are used and Boekelman, 1996). On the initially. The flow time step 't to applied time scale, the specific recalculate the groundwater flow -1 storativity Ss [L ] can be set to zero. equation equals one year. The

The bottom of the system as well as corresponding density of that saline the vertical sea-side borders are groundwater equals 1024.1 kg/m3. considered to be no-flux boundaries. At the top of the system, the mean DISCUSSION sea level is –0.10 m N.A.P. and is constant in time in case of no sea Numerical simulation of the period level rise2. A number of low-lying 1990-2000 AD areas is present in the system with a total area of approximately 124 km2. Density dependent groundwater flow The phreatic water level in the polder is not only determined by head areas differs significantly, varying differences but also by density from –2.05 m to +4.75 m N.A.P. (De differences. Variable density Hooge Berg) (figure 1b), and is kept groundwater flow simulated with a constant in time. Small fluctuations in numerical model is very sensitive to the phreatic water level are the accuracy of the initial density neglected. The constant natural distribution. As such, the initial groundwater recharge equals 1 chloride concentration, which is mm/d in the sand-dune area. linearly related to the initial density by equation 2, must accurately be At the initial situation (1990 AD), the inserted in each active element. hydrogeologic system contains Though the initial chloride saline, brackish as well as fresh distribution in this Texel case is groundwater. The salinity increases based on about hundred with depth, whereas freshwater measurements of chloride, errors lenses exist at the sand-dune areas can easily occur, mainly because of at the western side of the island, up a lack of enough data. Therefore, to some –50 m N.A.P. A freshwater artificial inversions of fresh and lens of some fifty metres thickness saline groundwater can easily occur has evolved at the sandy hill De in the numerical model, though they Hooge Berg. The volumetric do not exist in reality. These ten concentration expansion gradient EC years of simulation, from 1990 to is 1.34 x 10-6 l/mg Cl-. Saline 2000 AD, are used to smooth out groundwater in the lower layers does unwanted, unrealistic density not exceed 18000 mg Cl-/l, as sea dependent groundwater flow, which water that intruded the groundwater was caused by the numerical system has been mixed with water discretisation of the initial density from the river Rhine. The distribution.

Salt water intrusion during the period 2000-2500 AD 2 Note that in reality, the mean sea level in eastern direction towards the Waddenzee is probably somewhat higher over a few hundreds At the year 2000 AD, the chloride of meters. The reason is that at low tide, the piezometric head in the phreatic aquifer of this concentration is already high in the tidal foreland outside the dike cannot follow the four polder areas (figure 2). At the relatively rapid tidal surface water fluctuations hill ‘De Hooge Berg’, fresh (Lebbe, pers. comm., 2000). It will be retarded which results in a higher low tide level of the sea, and thus in a higher mean sea level.

m m

k k

0 0

. . 0 2000 AD 0 2200 AD

5 5

. .

2 2

- -

0 0

. .

5 5

- -

5 5

. .

7 7 - elements De Slufter - De Slufter

0 tive 0

. .

0 1. Eijerland 0 1. Eijerland

1 1

- inac - inactive elements

Sea

5 5 . h Sea .

2 2 th

1 1

- - Nort 2. Waal en Burg/ Nor 2. Waal en Burg/

0 0

. .

5 Het Noorden 5 Het Noorden

1 1

- -

5 5

. .

7 7

1 3. Dijkmanshuizen/ 1 3. Dijkmanshuizen/

- -

a De Schans a De Schans

e e

0 0

. .

0 ar 0 ar

2 De Hooge Berg 2 De Hooge Berg

- -

e e n

n sea sea

u u

d d

2 - - 4. Prins Hendrik 4. Prins Hendrik

-22.5 - d

d ts n

n polder polder

a a

S S ments

-25.0 ele - ive

t 5

ac 7

-27.5 in - inactive elemen

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 km 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 km Concentration [mg Cl -/l] 0 50 150 300 1000 2500 5000 7500 10000 12500 15000 ------50 150 300 1000 2500 5000 7500 10000 12500 15000 18630

Figure 2: Chloride concentration in the top layer at –0.75 m N.A.P. for the years 2000 and 2200 AD. No sea level rise is simulated. groundwater occurs up to some –45 layer increases, especially in the m M.S.L. Fresh water from the sand- areas close to the coastline. dunes flows towards the sea as well as towards the low-lying polder Effect of sea level rise on salt areas. In these low-lying areas, water intrusion during the next seepage is quite high (up to some 500 years 2.1 mm/day at the western side of the Prins Hendrik polder, see figure According to the Intergovernmental 3a). In addition, the salt load is high Panel of Climate Change (IPCC) too, with values up to some 95,000 Second Assessment Report (Warrick kg/ha/year in the same polder area et al., 1996), a sea level rise of 0.49 (figure 4a). m is to be expected for the year 2100, with an uncertainty range from The salinisation of the groundwater 0.20 to 0.86 m. This rate is 2 to 5 flow system of the island of Texel is times the rate experienced over the visualised in figure 2. It shows the last century. Two scenarios of sea change in chloride concentration in level variation are considered for the the top layer at the years 2000 AD next millenium: no sea level rise and and 2200 AD. The level of sea is a sea level rise of 0.75 m per kept constant during these two century. This figure includes land hundred years. The salinity in the top m

0 0 2000 AD 2200 AD

5 ements

l . . De Slufter

7 7 De Slufter elements

- ve e ti tive

. . ac 1. Eijerland ac 1. Eijerland

0 0 in in

- Sea

5 5

2 2

orth Sea 1

- - N 2. Waal en Burg/ North 2. Waal en Burg/

. . Het Noorden Het Noorden

1 1

. . 3. Dijkmanshuizen/

7 7 3. Dijkmanshuizen/

- - a a De Schans De Schans

e e

0 ar

. . ar

0 0 De Hooge Berg De Hooge Berg

- n

n sea sea

u d

5 d

. -

- 4. Prins Hendrik 4. Prins Hendrik

d d

- -22.5 n

n polder polder

S S ments 0 e . 5 elements

el 2

- -25.0 e

7 inactiv

inactive 2

-27.5 -

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 km 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 km seepage (-) and infiltration (+) [mm/day]: -3.50 -1.50 -1.00 -0.75 -0.50 -0.25 -0.10 0.00 0.10 0.25 0.75 ------1.50 -1.00 -0.75 -0.50 -0.25 -0.10 0.00 0.10 0.25 0.75 1.20 Figure 3: Seepage through the top layer at –0.75 m N.A.P. for the years 2000 and 2200 AD. Sea level rise is 0.75 meter per century. Seepage (figure 3) as well as the salt subsidence caused by groundwater load (figure 4) at –0.75 m N.A.P. for recovery, the compaction and the years 2000 AD and 2200 AD shrinkage of clay, and the oxidation increase because of the salinisation of peat. in the subsoil. Sea water, with a high content of chloride, is attracted by Figure 5 shows the change in the polder areas, as the phreatic chloride concentration in the top water level in these areas is low layer at –0.75 m N.A.P. for the sea relative to the level of the sea. level rise scenario at two moments in time: 200 years (2200 AD) and 500 In figure 6, the seepage in the four years (2500 AD) after 2000 AD. different polder areas is given as a During the next centuries, the salinity function of time. As can be seen, in the groundwater system will seepage quantities increases which increase very serious when the sea will probably has its effect of the level rises 0.75 m/c. By comparing capacity of the pumping stations in the figures 2b and 5a, the effect on the polder areas. Their capacity the chloride concentration in the top should be increased because e.g. in layer of a sea level rise relative to no two hundred years, the seepage sea level rise can be seen: the quantity is about doubled in all four salinity increases rapidly. areas.

. 0 2000 AD 0 2200 AD

2 2

5 5

- nts -

me ements le

. De Slufter . De Slufter

- tive e

0 0 1. Eijerland . 1. Eijerland . inactive el

0 inac 0

1 1

- -

2 2

1 1 North Sea

- North Sea 2. Waal en Burg/ - 2. Waal en Burg/

0 Het Noorden

. Het Noorden

1 1

. 3. Dijkmanshuizen/ . 3. Dijkmanshuizen/

1 a

- a De Schans - De Schans

e e

0 ar 0

. De Hooge Berg De Hooge Berg

0 0

2 n

n sea sea

d -

5 - 4. Prins Hendrik

4. Prins Hendrik . d

2 d

2 n n polder

-22.5

polder -

S S

0 . elements 5

-25.0 ve elements - ive ti t c

5 . inac ina 7

-27.5

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 km 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 km Salt load (+) [kg/ha/year]: -50000 -2500 -500 -100 0 500 1000 2500 5000 10000 30000 >90000 ------2500 -500 -100 0 500 1000 2500 5000 10000 30000 90000

Figure 4: Salt load (in kg/ha/year) in the top layer at –0.75 m N.A.P. for the years 2000 and 2200 AD. Sea level rise is 0.75 meter per century.

The salt load as a function of time Numerical computations show that demonstrates that the effect of sea salt water intrusion is severe level rise is substantial in all four low- because the polder areas with low lying polder areas of the island of phreatic water levels are situated Texel. The increase in salt load will very close to the sea. In case of a be enormous due to the sea level relative sea level rise of 0.75 m per rise of 0.75 m per century. This will century, the increase in salinity is definitely affect environmental enormous. A doubling of the present aspects. A doubling of the salt load seepage quantities can be is probably already reached within established within two centuries in all (only) one century in the polder four polder areas. Moreover, the salt areas Eijerland and Dijksmanhuizen. load will probably be doubled in two polder areas within only one century. CONCLUSIONS This will definitely affect environmental, as well socio- The computer code MOCDENS3D ecomonis aspects of the island of can be used to simulate density Texel. dependent groundwater flow in three dimensions at an island of the size of Texel, 130 km2 by 300 m thick.

0 2200 AD 0 2500 AD

- s - nt

7 7 elements De Slufter

eleme - De Slufter e ive

t 0

0 1. Eijerland 0 1. Eijerland

1 inactiv

- inac - Sea

. . th

- - Nor North Sea 2. Waal en Burg/ 2. Waal en Burg/

5 Het Noorden Het Noorden 5

7 7 3. Dijkmanshuizen/

3. Dijkmanshuizen/ 1

a De Schans a De Schans e

ar 0

2 De Hooge Berg

- De Hooge Berg e

e n

n sea sea

u u

. d

d -

2 4. Prins Hendrik - 4. Prins Hendrik

2 d

-22.5

d - ts

n polder

n polder nts a a

. S S

-25.0 eleme - e

2 inactive elemen

-27.5 inactiv -

Figure 5: Chloride concentration in the top layer at –0.75 m N.A.P. for the years 2200 and 2500 AD. Sea level rise is 0.75 m per century.

1. Eijerland 2. Waal en Burg 40000 25000 sea level rise=+0.75 m/century 20000 30000

3 slr=+0.75 m/c 15000 20000 10000 sea level rise=0 m/century slr=0 m/c Seepage [m /day] [m Seepage 10000 5000

0 0 2000 2100 2200 2300 2400 2500 2000 2100 2200 2300 2400 2500 Time [year] Time [year] 3. Dijkmanshuizen 4. Prins Hendrik polder 40000 25000

30000 20000 slr=+0.75 m/c slr=+0.75 m/c 3 15000 20000 slr=0 m/c 10000 slr=0 m/c 10000 Seepage [m /day] 5000

0 0 2000 2100 2200 2300 2400 2500 2000 2100 2200 2300 2400 2500 Time [year] Time [year]

Figure 6: Seepage (in m3/day) through the top layer at –0.75 m N.A.P. of the four polder areas as a function of 500 years. 1. Eijerland 2. Waal en Burg 200000 100000

] sea level rise=+0.75 m/century

r slr=+0.75 m/c a

e 150000 75000 y /

l C 100000 50000 n o t [

d slr=0 m/c a 50000 25000 o l

sea level rise=0 m/century t l a

S 0 0 2000 2100 2200 2300 2400 2500 2000 2100 2200 2300 2400 2500 Time [year] Time [year] 3. Dijkmanshuizen 4. Prins Hendrik polder 200000 ] r a e

y 150000

/ slr=+0.75 m/c

- slr=+0.75 m/c

l C

n 100000 o t [

d a

o 50000 l

slr=0 m/c

t slr=0 m/c l a

S 0 2000 2100 2200 2300 2400 2500 2000 2100 2200 2300 2400 2500 Time [year] Time [year]

Figure 7: Salt load (in ton Cl-/year) through the top layer at –0.75 m N.A.P. of the four polder areas as a function of 500 years.

ACKNOWLEDGEMENT difference ground-water flow model; U.S.G.S. Techniques of Water-Resources Investigations, Book 6, Chapter A1, 586 p. The author wishes to thank Jeroen OUDE ESSINK, G.H.P. (1998). MOC3D Tempelaars and Arco van Vugt (of adapted to simulate 3D density-dependent the consultancy bureau Witteveen & groundwater flow; Proc. MODFLOW'98 Bos, the Netherlands) for the Conf., Golden, Colorado, USA, 291-303. preparation of the input files OUDE ESSINK, G.H.P. (1999). Simulating density dependent groundwater flow: the (especially subsoil parameters) for adapted MOC3D; Proc. 15th Salt Water the numerical model. Intrusion Meeting, Ghent, Belgium, May 1998, 69-79. REFERENCES OUDE ESSINK, G.H.P. (2000). Salt Water Intrusion in a Three-dimensional HARBAUGH, A.W. and M.G. MCDONALD. Groundwater System in The Netherlands: a (1996). User's documentation for the Numerical Study; submitted to Transport in U.S.G.S. modular finite-difference ground- Porous Media. water flow model; U.S.G.S. Open-File OUDE ESSINK, G.H.P. and R.H. Report 96-485, 56 p. BOEKELMAN. (1996). Problems with large- KONIKOW, L.F. and J.D. BREDEHOEFT. scale modelling of salt water intrusion in 3D; (1978). Computer model of two-dimensional Proc. 14th Salt Water Intrusion Meeting, solute transport and dispersion in ground Malmö, Sweden, June 1996, 16-31. water; U.S.G.S. Tech. of Water-Resources WARRICK , R.A., J. OERLEMANS, P. Investigations, Book 7, Chapter C2, 90 p. WOODWORTH, M.F. MEIER and C. Le KONIKOW, L.F., D.J. GOODE and G.Z. PROVOST, C. (1996). Changes in sea level, HORNBERGER. (1996). A three- in: Climate Change 1995: The Science of dimensional method-of-characteristics Climate, edited by J.T. Houghton, L.G. Meira solute-transport model (MOC3D); U.S.G.S. Filho and B.A. Callander, Contribution of Water-Resources Investigations Report 96- Working Group I to the Second Assessment 4267, 87 p. Report of the Intergovernmental Panel of MCDONALD, M.G. and A.W. HARBAUGH. Climate Change, Cambridge Uni. Press, (1988). A modular three-dimensional finite- Cambridge, 359-405.