The importance of coupled modelling of variably saturated groundwater flow-heat transport for assessing river–aquifer interactions

Journal of Hydrology 397 (2011) 295–305

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The importance of coupled modelling of variably saturated groundwater flow-heat transport for assessing river–aquifer interactions I. Engeler a, H.J. Hendricks Franssen a,c, R. Müller b, F. Stauffer a,⇑ a

Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland Water Supply of Zurich (WVZ), Hardhof 9, 8023 Zurich, Switzerland c Agrosphere, IBG-3, Forschungszentrum Juelich GmbH, 52425 Juelich, Germany b

a r t i c l e

i n f o

Article history: Received 22 December 2009 Received in revised form 23 November 2010 Accepted 9 December 2010 Available online 14 December 2010 This manuscript was handled by P. Baveye, Editor-in-Chief Keywords: Groundwater hydrology River–aquifer interaction Groundwater flow model Leakage coefficient Temporally variable leakage coefficient Coupled flow and heat transport

s u m m a r y This paper focuses on the role of heat transport in river–aquifer interactions for the study area Hardhof located in the Limmat valley within the city of Zurich (Switzerland). On site there are drinking water production facilities of Zurich water supply, which pump groundwater and infiltrate bank filtration water from river Limmat. The artificial recharge by basins and by wells creates a hydraulic barrier against the potentially contaminated groundwater flow from the city. A three-dimensional finite element model of the coupled variably saturated groundwater flow and heat transport was developed. The hydraulic conductivity of the aquifer and the leakage coefficient of the riverbed were calibrated for isothermal conditions by inverse modelling, using the pilot point method. River–aquifer interaction was modelled using a leakage concept. Coupling was considered by temperature-dependent values for hydraulic conductivity and for leakage coefficients. The quality of the coupled model was tested with the help of head and temperature measurements. Good correspondence between simulated and measured temperatures was found for the three pumping wells and seven piezometers. However, deviations were observed for one pumping well and two piezometers, which are situated in an area, where zones with important hydrogeological heterogeneity are expected. A comparison of simulation results with isothermal leakage coefficients with those of temperature-dependent leakage coefficients shows that the temperature dependence is able to reduce the head residuals close to the river by up to 30%. The largest improvements are found in the zone, where the river stage is considerably higher than the groundwater level, which is in correspondence with the expectations. Additional analyses also showed that the linear leakage concept cannot reproduce the seepage flux in a downstream section during flood events. It was found that infiltration is enhanced during flood events, which is attributed to additional infiltration areas. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction In most groundwater models, the interaction between surface water and groundwater plays a more or less important role. The seepage flux between rivers and aquifers is influenced by various factors. Obviously, the river stage is of particular importance, as it affects the hydraulic gradient between river and aquifer. Either there is a hydraulic gradient from the river to the groundwater, which causes infiltrating conditions, or contrariwise groundwater exfiltrates into the river. These relations are shown in Fig. 1. At a given location, infiltration and exfiltration may alternate over time, related with temporal changes of the groundwater level and (especially) the river stage. Usually, the riverbed has a smaller hydraulic conductivity than the underlying or adjacent aquifer. This is re-

⇑ Corresponding author. Tel.: +41 44 633 30 79; fax: +41 44 633 10 61. E-mail address: [email protected] (F. Stauffer). 0022-1694/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2010.12.007

lated with colmation processes that cause the development of a clogging layer. Moreover, clogging is typically stronger for infiltrating conditions than for exfiltrating ones. The river stage may also influence the riverbed dynamics (e.g., Kollet and Zlotnik, 2007). Typically, higher stages produce higher shear stress on the riverbed and therefore, clogging of riverbed can be temporally reduced or inverted. But effective stress of newly deposited sediments during flood events can also reduce hydraulic conductivity (Springer et al., 1999). Furthermore, it is possible that more sediment is transported from upper reaches than flushed away. This is especially true for impounded river sections. Sedimentation and erosion effects might also depend on the peak discharge (e.g., Blaschke et al., 2003). Further factors of influence mentioned in the literature are the hydrogeological situation in the vicinity of the river (e.g., Bruen and Osman, 2004) and the biological activity as well as the geochemical conditions (e.g., Sophocleous, 2002). Wiese and Nützmann (2009) describe the role of geochemical conditions and the unsaturated zone beneath surface water bodies. The

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River water level Head

-3 Kmean = 5 x 10 ms-1

Riverbed with hydraulic conductivity Krb and thickness drb River Saturated zone of aquifer with hydraulic conductivity K Unsaturated zone Fig. 1. Schematic representation of the river–aquifer interaction in case of saturated conditions below the river bed, which is the basis for the leakage concept.

hydrogeological controls that lead to an unsaturated zone and a disconnection between surface water and groundwater were examined for rivers by Brunner et al. (2009). The implications of disconnection on modeling and management of surface water groundwater systems were discussed by Brunner et al. (2010). Temperature is also expected to influence seepage rates, not only because temperature influences aquatic habitats, but also hydraulic conductivity. As hydraulic conductivity is related to water density and dynamic viscosity, higher seepage rates are expected for higher temperatures (e.g., Constantz et al., 1994; Constantz, 1998), either on diurnal or on seasonal basis. Doppler et al. (2007) found strong evidence that the head residuals of an isothermally calibrated groundwater flow model close to a river were strongly influenced by the temperature dependence of the leakage coefficient. Boano et al. (2009) discuss an exchange mechanism between the in-stream and the hyporheic zones due to density gradients. These density gradients are caused by concentration and/or temperature gradients. Several research articles are available, which take in account temperature in numerical modelling (e.g., Brookfield et al., 2009; Hidalgo et al., 2009). However, the main focus usually lies in the propagation of thermal plumes. An overview of heat transport in groundwater with focus on its use as a tracer is given by Anderson (2005). If heat transport is used as a tracer for the determination of infiltration rates using temperature measurements (e.g., Constantz, 2008), the leakage coefficient is generally not of main concern. Temperature measurements can also be used to determine the leakage coefficient if river water temperature is clearly different from groundwater temperature (e.g., Vogt et al., 2010). However, these works do not consider the temperature-dependence of the leakage coefficient. The importance of the temperature dependence of the leakage coefficient (or hydraulic conductivity) for infiltration fluxes was stressed by Constantz and Murphy (1991) and Jaynes (1990). From much earlier work the importance of the dependence is in fact already known. Rorabaugh (1947) found for the Ohio river that the streambed leakage was relatively constant over the year, specifically demonstrating that when in the winter the stage is high and the temperature is low versus in the summer when the stage is low and the temperature is high, these factors offset to create relatively constant leakage throughout the year. Ronan et al. (1998) showed that daily variations in infiltration from a stream could be attributed to temperature dependent hydraulic conductivity. Constantz et al. (2003) fitted temperature dependent hydraulic conductivities of a streambed based on bromide and heat tracer tests. Although some works point to the importance of considering temperature dependent leakage coefficients the topic is in general neglected by groundwater modellers.

This paper is based on the work of Doppler et al. (2007), who interpreted transient head residuals as a partial consequence of temperature-dependent leakage coefficients. They used twodimensional groundwater flow modelling and model calibration to assess the importance of temperature-dependent leakage coefficients on groundwater heads for the Hardhof study area in the city of Zurich (Switzerland), which will also be the subject of this study. In this paper three-dimensional coupled groundwater flow and heat transport simulations were performed in order to more deeply investigate the importance of the temperature-dependence of the hydraulic parameters on river–aquifer interactions. The river–aquifer interaction is also modelled using a leakage concept. Accordingly, the leakage coefficient is conceived as the hydraulic conductivity of the riverbed divided by its thickness. We will compare simulations, where the seepage rate is modelled using an isothermal (i.e., constant) leakage coefficient and using temperature-dependent (variable) leakage coefficients. The hydraulic conductivity of the aquifer is always modelled in a coupled (temperature-dependent) manner. In both cases, an isothermally calibrated groundwater model is used as the basis for the simulations. First, the coupled groundwater flow and heat transport model is tested against measured groundwater temperatures, in order to check whether the model is able to adequately represent heat transport. Afterwards, the head residuals of the coupled and uncoupled simulations are compared. The head residuals are further analyzed with respect to the role of flood events. Doppler et al. (2007) found that a major flood event in 1999 increased the leakage coefficient considerably. Here, an additional analysis is presented for a further simulation period with another major flood event. In summary, this work investigates temporal variations of leakage coefficients related with the temperature dependence of the leakage coefficient and flood events. The aim is to determine whether fully coupled flow-heat transport simulations with temperature dependent material properties (leakage coefficient and hydraulic conductivity) give better results than simulations where temperature dependence is not considered. It investigates for a practical case whether it can be important to consider the temperature dependence in hydrogeological simulation studies. Alternatively, although it is of course known that material properties are temperature-dependent, it could be for practical purposes (hydrogeological simulation studies) irrelevant. 2. Theory Variably saturated groundwater flow will be considered, which is governed by (e.g., Bear, 1979):

I. Engeler et al. / Journal of Hydrology 397 (2011) 295–305

    @S @p qkkr ðSÞ r SqSop þ qn ðrp þ qg rzÞ ¼ w @p @t l

ð1Þ

where S is saturation [–], q is water density [M L3], Sop is the specific storativity with respect to pressure [L T2 M1], n is porosity [–], p is pressure [M L1 T2], t is time [T], k is permeability [L2], kr is relative permeability [–], l is dynamic viscosity [M L1 T1], g the gravitational acceleration [L T2], z is the elevation with respect to a reference [L], w represents sources (recharge) and sinks (abstraction) [M L3 T1] and the Nabla operator [L1] is three-dimensional referring to spatial coordinates x. In this equation, the interaction between river and aquifer is accounted for by the local seepage flux q, by means of a boundary condition. For the modelling of the seepage flux between surfacewater and groundwater, the common linear leakage concept is adopted. Therefore, the leakage rate is a linear function of the difference Dh between the river stage and the groundwater head if the groundwater table is above the river bottom (e.g., Kinzelbach, 1986). Otherwise, for unsaturated conditions below the riverbed, which means that the groundwater table is below the riverbed level, the difference between river stage and pressure head is taken. Darcy’s law applied to a unit area of the riverbed yields

q ¼ K rb

Dh drb

ð2Þ

where q is the specific leakage rate [L T1], Krb the hydraulic conductivity [L T1] of the riverbed, drb is the thickness of the riverbed [L]. The quotient of the hydraulic conductivity and the thickness of the riverbed is the leakage coefficient with l = Krb/drb. As the riverbed has usually a lower hydraulic conductivity than the underlying or adjacent aquifer, the riverbed controls the leakage rate. A major difficulty is the determination of the leakage coefficient. There are seepage meters, which measure the infiltration flux (Murdoch and Kelly, 2003). Due to the spatial heterogeneity of the riverbed and the surrounding hydrogeological settings, a local seepage measurement is expected to give only local information. For example, even in regions where infiltration prevails, local groundwater exfiltration may occur (Brunke and Gonser, 1997). Furthermore, the exchange flux is affected by the river geometry and the river flow direction with respect to the groundwater flow (e.g., Woessner, 2000). The usual way to estimate leakage coefficients is by model calibration using head data. Such a method is a good choice for this work, due to the available dense network of monitoring. The temperature-dependence of the leakage coefficient can be related to the dependence of viscosity on temperature by the following empirical relationship:

lðTÞ ¼ 2:414  105  10ð247:8=ðT140ÞÞ

ð3Þ 1

1

where l is the dynamic viscosity of water [M L T ] at temperature T [H] in Kelvin. Thus the temperature dependence of leakage is apparent from the following relation (Muskat, 1937):

KðTÞ ¼

kqg lðTÞ

ð4Þ

For the definitions of the parameters see Eq. (1) and the text below of it. Both water density and dynamic viscosity are temperaturedependent. But whereas water density varies little as function of temperature, viscosity variations are more important. According to Eq. (3), dynamic viscosity would change almost by a factor of 1.7 if temperature drops from 25 °C to 4 °C (possible temperature range at our field site) compared to a density difference of less than 1%. It was postulated by Doppler et al. (2007) that an important part of the head residuals could be explained by temperature-

297

dependent leakage coefficients. Therefore, heat transport is simulated in a coupled manner together with the variably saturated groundwater flow. Heat transport is governed by (de Marsily, 1986):

@T Cf ¼ Dt r2 T  r  ðv TÞ þ Pt @t Cm

ð5Þ

were Dt [L2 T1] is the thermal diffusion and dispersion tensor, Cf [L2 T2 H1] is the specific heat capacity of water, Cm [L2 T2 H1] the average heat capacity of the porous medium, v [L T1] the specific flux vector, and Pt [H T1] is the thermal source/sink term. The terms in this equation can be variable in space and time, as will be specified in Section 4. 3. Site description The modelled aquifer is located in the upper Limmat valley within the city of Zurich (Switzerland). It contains mainly sandy gravel, debris from river Sihl (which is located on the SouthEastern side of the aquifer) and moraine material (Kempf et al., 1986). The mean hydraulic conductivity is of the order of 5  103 ms1. The variable thickness of the aquifer (up to 70 m) and its heterogeneous structure including small channels and lenses with high and low hydraulic conductivities caused by changing river courses are typical characteristics. The natural slope of the groundwater table varies between 0.1% and 0.6%. In general, it is steeper towards the Eastern part. In the Hardhof area, the flow gradient is strongly influenced by groundwater pumping and recharge (Doppler et al., 2007). Otherwise, the groundwater flow is from the East to the West, following the general topography. Due to the widely sealed soil surface within the Hardhof area, recharge from precipitation is significantly reduced. As a consequence, the main source of groundwater is infiltrating water from river Limmat. Hence the interaction between surface water and groundwater is of special importance. River Limmat is located in the Northern part of the modelled area. It is fed by Lake Zurich. The lake’s water level is controlled by a weir located at Platzspitz in the North-Eastern part of the model area. A second weir – the Hoengg weir – is located close to the Hardhof area. Therefore, part of the river section in the Hardhof area is impounded. River Sihl borders the aquifer on the Eastern side and joins the Limmat at Platzspitz. It forms the South-Eastern boundary of the study area. See also Fig. 2 for a sketch of the position of the rivers and weirs. Long-time mean discharge rates of the rivers are 95.8 m3 s1 (Limmat) and 6.8 m3 s1 (Sihl, Swiss Federal Office for the Environment (FOEN)). Especially the flood discharge of river Sihl can be a multiple of the long-time mean, since there is no retention similar to Lake Zurich, which dampens flood peaks of river Limmat. The aquifer is bounded to the North and South by moraines of the Kaeferberg and of the Uetliberg respectively. There is some lateral inflow from these hills. The largest inflow occurs from the South (Uetliberg) and in particular close to river Sihl. Lake Zurich has no direct connection to the aquifer. The Hardhof area contains important groundwater pumping and infiltration facilities run by Zurich Water Supply (Fig. 2): Four horizontal wells pump approximately 12% of the drinking water supply of the region of Zurich. Water is pumped by 19 bank filtration wells located along river Limmat, and this water is infiltrated in three recharge basins and 12 infiltration wells located on the Southern and Western side of the Hardhof area. This artificial groundwater recharge creates a hydraulic barrier, which should prevent the pumping of potentially contaminated water from the city area or the close-by highway. Potential contamination is present as diffuse pollution in the subsurface below the city and in one principal contaminated site.

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0

500 1000 m

7

N 4

3

5

6 2

1

1 A

3135

B

3317

C

D

Lake Zurich

2 River Sihl

1

3 River Limmat 4 Model domain

2

5 Platzspitz weir

3

6 Uetliberg 7 Kaeferberg

0

Bank filtration wells Recharge wells Production wells A to D

Roads River Limmat Recharge basins 1 to 3

100

200 m

Höngg weir Piezometers

Fig. 2. Model area and Hardhof site. Indicated are also the rivers and weirs.

The yearly fluctuations of averaged daily temperatures of the rivers Limmat and Sihl are in the range of about 4 °C in February/ March up to 25 °C in July/August (peak values can outreach these boundaries). Groundwater recharge has a strong impact on heat transport in the Hardhof area. Since the infiltration facilities are located in the vicinity of the pumping wells, the increased temperature amplitude is not smoothed out by long flow distances and has a major effect on the temperature of the pumped drinking water. The soil temperature at 20 cm depth has a range of about 2 °C in winter to up to 23 °C in summer. The amplitude is similar to the one of the river, but the average is about 2 K lower. Furthermore, there are lateral inflows with unknown temperature. Considering the comparatively small rates and the long flow distances, we assume that their influence on the energy dynamics of the Hardhof area is of minor importance.

4. Model A three-dimensional finite element model for variably saturated groundwater flow and heat transport of the study area was developed using the software SPRING (delta h, Witten, Germany). In an earlier work, analyses were made with a two-dimensional flow model (Doppler et al., 2007). The extended three-dimensional model not only allows an improved representation of flows close to the river, but also the simulation of coupled flow and heat transport over the depth of the aquifer including a comparison with temperature measurements.

The model boundaries on the Northern, Southern and Eastern sides correspond to the natural aquifer boundaries. There is no direct contact with Lake Zurich. On the Western boundary, a prescribed, but temporally variable, head boundary condition is established using the head measurement in a piezometer at this boundary. The basic numerical grid consists of triangular finite elements with a typical size of 50 m. In the Hardhof area (where the pumping and infiltration facilities are located) the grid is refined to 30 m in general and close to the wells and basins down to 1 m. In the vertical direction the aquifer is divided into 25 layers of 1.6 m maximum thickness each. Moreover, only in small areas the aquifer depth is larger than 40 m, often it is only 20 m. The model is discretized into 173,599 finite elements. The incorporation of the unsaturated zone in our model allows an approximately correct timing of recharge events at the groundwater table. Unsaturated parameters were estimated. However, due to the relatively coarse discretization, the precision of unsaturated flow calculations is limited. This is acceptable since the recharge rate is small compared with the infiltration rate from the river and the artificial recharge rates. Actual evapotranspiration was calculated with an external soil water balance model according to the FAO method (Allen et al. (1998, Eq. (85))) and the net recharge rate was applied on the surface elements of the model. Actual evapotranspiration was calculated by determining potential evapotranspiration with the help of the Penmann–Monteith equation according a scheme as proposed by Allen et al. (1998) and applying a correction for soil-limited evapotranspiration on the basis of a water balance model. The necessary data for calculating

I. Engeler et al. / Journal of Hydrology 397 (2011) 295–305

potential evapotranspiration were obtained from measurements at the meteorological station of Zurich-Affoltern, which are checked and quality controlled by Meteoswiss. In this study the FAO method for calculating actual evapotranspiration was applied (Allen et al., 1998). Precipitation measurements and the calculated actual evapotranspiration yield the estimated net recharge rate. The groundwater table is in general at least 5 m below the soil surface and therefore the mentioned water balance method is well-suited to estimate recharge in this area. Only 15% of the calculated value was used as recharge for the groundwater flow model, since most of the surface is sealed in the model area. The lateral inflow at the Southern model boundary was calculated using the recharge rate time series, as the lateral inflow mainly originates from precipitation on the lateral hill-slopes. It implies that the lateral inflow has exactly the same temporal distribution as the calculated recharge. The amount of lateral inflow is a function of the recharge, and was determined (with different values for three different zones) on the basis of model runs. In general, lateral inflow and also recharge only play a minor role in the overall water balance of the area. The courses of river Sihl and river Limmat proceed mostly along the Eastern and Northern model boundaries. The interaction between river and aquifer is accomplished with the help of two lines of nodal points along the river shores in approximately 60 m of distance with the help of nodal point-related leakage coefficients. The grid between these two leakage lines is also refined. Alternatively, it was tested to what extent simulation results are affected by moving these lines by 10 m towards the river centre. The sensitivity with respect to moving the leakage lines was found to be limited. The calculated groundwater heads in the boreholes changed only in the cm range and do not impact the results in this study concerning river–aquifer interaction. The software FLORIS (VAW, ETH Zurich) was used for calculating transient stages in and along the rivers Limmat and Sihl. The one-dimensional hydraulic model uses as input cross-sectional river profiles and dam locations, together with measured daily average values of river discharge rate and river stages. The hydraulic model yielded daily averages of the river water level for each river discretization point in the period January 2004 to August 2005. Quadratic regression equations were derived for each discretization point along the river in order to estimate the water levels as a function of the river discharge at each leakage node for the complete period from August 2005 to October 2007. It is further assumed that the shape of the riverbed did not vary over time. The estimated river stages were calculated on a daily basis. Pumping and infiltration rates of the wells and basins operated by Zurich Water Supply were available on a daily basis as well. The hydraulic conductivity and the leakage coefficient were calibrated for isothermal conditions by transient inverse modelling taken into account time series of head measurements from 87 piezometers. Two calibration periods were chosen: May/June 2004 and July/August 2005. These periods were selected because they are characterized by very different hydrological conditions, including a minor and a major flood, elevated water abstraction and also typical mean conditions. A pilot point based approach (de Marsily, 1978) including a regularization term (Alcolea et al., 2006) was used. The vertical hydraulic conductivity is everywhere 1/10th of the horizontal hydraulic conductivity. The CPU-intensity of the calculations did not allow an inverse conditioning of multiple equally likely hydraulic conductivity fields with the help of transient head data, as proposed by Hendricks Franssen et al. (1999), nor its additional conditioning on transport data (Hendricks Franssen et al., 2003). Nevertheless, this would have been preferable as the full posterior distribution of the parameter uncertainty would have been determined. The leakage coefficient was optimized for five zones, whereas the hydraulic conductivity was calibrated with the help of pilot points. The number of pilot points

299

used for the three-dimensional calibration was limited as the CPUintensity of the calculations did not allow for many more pilot points. For the definition of the leakage zones and the location of the pilot points, geological considerations were also taken into account. The calibrated model was able to well reproduce the heads in general. However, the head residuals close to river Limmat showed a seasonal cycle, which can again be attributed to the temperature dependence of the leakage coefficient as in Doppler et al. (2007). Details of the calibration procedure can be found in Doppler et al. (2007) and Hendricks Franssen et al. (2011). A Multi-Gaussian model was adapted for the spatial distribution of hydraulic conductivities. It is well known that MultiGaussian models are not able to reproduce connectivity of extreme hydraulic conductivity values (Gomez-Hernandez and Wen, 1998). Moreover, calibration does in general not allow detecting these non-Multi-Gaussian features, if a Multi-Gaussian model was adapted (Kerrou et al., 2008). Moreover, the relatively limited amount of pilot points further complicated the detection of small-scale variability and connectivity. Therefore, the spatial heterogeneity of the geology cannot be reproduced to the full extent by the calibrated model. This holds in particular true for the Southern Hardhof area, where it is believed that small channels with high permeability alternate with poorly permeable layers (Geologisches Büro and Lorenz Wyssling, 2006). Moreover, for the leakage coefficient a high degree of variability is expected, which is replaced in this model by constant values for certain zones. Details of the calibration can be found in Doppler et al. (2007) and Hendricks Franssen et al. (2011). In order to investigate the role of heat transport on river–aquifer interaction, a heat transport model was established, which is fully coupled to the flow model. It was assumed that the default leakage coefficients, obtained from the isothermal calibration, corresponded to a river water temperature of 17.5 °C. This is the average river water temperature over the calibration period. The temperature-dependent leakage coefficient as function of the river water temperature is then obtained as:

lðTÞ ¼

lðT ¼ 17:5  CÞ lðT ¼ 17:5  CÞ lðTÞ

For heat transport simulations, transient input data are required. Measurements of the river water temperature were used to assign water temperature to the leakage nodes and the correction of the leakage coefficient. Soil surface temperature measurements are used as upper boundary condition and exert a strong influence on the temperature of the infiltrating water from precipitation. The temperature of the infiltration water in the basins and wells was measured on a daily basis. Furthermore, a constant mean annual temperature of 12 °C is assumed for the lateral inflows. The thermal transport parameters are assumed spatially constant. For the solid matrix the specific heat capacity is set to 800 J/kgK and the heat conductance for the matrix in saturated conditions is 3.5 W/mK. The heat transport calculations were also used to test the coupled groundwater flow and heat transport model. For that purpose, temperature measurements in eight boreholes and the four pumping wells were used. Simulations, where the leakage coefficient is temperature-dependent, are compared with simulations, where the leakage coefficient is isothermal. Simulations start in January 2004 and end in October 2007. The time step for simulating heat transport was 90 s and determined on the basis of the Courant criterion. The time step of the flow model was 900 s. As the transient input data are available on a daily basis, the model simulations do not take into account that the pumping wells are operating in reality only 8 h per day. This may lead to small local and temporal deviations. As the model output and measurements are compared on the basis of daily averages,

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it is expected that this simplification does not affect much the results of the study. Furthermore, additional simulations with spatially variable leakage coefficients were carried out. In total eight stochastic realisations of spatially variable leakage coefficients were generated with the variance r2ln l ¼ 1:0 and a correlation length of the logleakage coefficient of 40 m. The arithmetic mean was similar for the eight stochastic realisations, being for each of the five zones equal to the calibrated leakage coefficient. 5. Results and discussion 5.1. Heat transport model In order to test the accuracy of the coupled flow and heat transport model, the simulated groundwater temperature in the four pumping wells A, B, C and D and nine piezometers are compared with measurements. Except for well C, more than 90% of the simulated temperatures are in a bandwidth of plus or minus two K (Table 1). For pumping well C and two piezometers (Piezometer 3224 next to basin 2 and piezometer 3257 in the Southwest of basin 3) only bad agreement is achieved. The results for fully coupled flow and heat transport simulations and simulations where the leakage coefficients are isothermal only show small deviations. This indicates that for the considered locations and temperature range, the full coupling of flow and heat transport does not strongly influence the results. The larger deviations observed at well C and the area South of it confirm the presumption that there exists important hydrogeological heterogeneity in the Southern part of the Hardhof area, which is not known precisely enough. The lack of a sufficient number of pilot points in the calibration

Table 1 Average of absolute head residuals (simulation-measurement) in the horizontal pumping wells and the percentage of absolute deviations below certain thresholds.

Average abs. head residuals [°C] Abs. deviation < 1 °C [% of residuals] Abs. deviation < 1.5 °C [% of residuals] Abs. deviation < 2 °C [% of residuals]

A

B

C

D

0.9045 69

1.0259 53

1.241 43

0.9158 58

85

69

67

83

91

94

75

96

397

and the assumption of Multi-Gaussianity hampered the detection of these more complex heterogeneous structures. In general the model tends to underestimate the temperature. The mean simulated temperature in the four pumping wells is 0.44 K lower than the measured values. A possible explanation for this could be too low temperatures for the upper soil layer in our model. Data originate from measurements at the meteorological station in Zurich located approximately 100 m higher than the top ground surface at the aquifer’s position. Therefore, it seems to be reasonable that soil temperature is underestimated by about 0.5 K. The soil temperature affects the groundwater temperature by heat diffusion and also by means of the infiltrating water. Its impact will, however, be much smaller close to the river as groundwater temperature is dominated there by the infiltrating river water. 5.2. The role of heat transport in river–aquifer interaction Now we will compare fully coupled simulations with simulations where the leakage coefficient is not temperature-dependent. Here simulated heads for these two versions are compared with measurements. Hydraulic head residuals are calculated, which are defined as simulated minus measured head. In Fig. 3 the measured and calculated heads of piezometer 3135 (upstream Hoengg weir) and in Fig. 4 the corresponding residual and temperature time series are shown. Comparing the calculated heads using the two different leakage coefficients, the residuals are significantly reduced in the case of temperature-dependent leakage coefficients mainly during winter season. It is shown in Table 2 that river temperature and the head residuals exhibit a strong negative correlation in case of isothermal leakage coefficients and a reduced correlation in case of temperature-dependent leakage coefficients. Considering both the negative correlation and the residual time series, it is obvious that head residuals are larger for lower temperatures. The trend of generally larger head residuals during winter can be explained by the fact that the model is calibrated for two periods in late spring and summer. Mean river water temperature during these periods was 17.5 °C. These results show that for measurements close to the river it is important to take the effects into account that the leakage coefficients are temperature-dependent. Even if other reasons cannot be excluded as an explanation of the residual’s seasonal cycle, there is strong support for a temperature-dependent leakage coefficient as postulated by Doppler et al. (2007). It is possible to obtain

Isothermal leakage−coeff. Temperature−dependent leakage−coeff. Measurement

Head [m]

396.5

396

395.5

395

394.5 Jan04

May04

Oct04

Mar05

Aug05 Jan06 Time [month]

Jun06

Nov06

Apr07

Sep07

Fig. 3. Hydraulic head values at piezometer No. 3135 (upstream Hoengg weir, at approximately 15 m distance from river shore, see also Fig. 2). Represented are the measured hydraulic head, calculated head on the basis of isothermal leakage coefficients and simulated head on the basis of temperature-dependent leakage coefficients.

301

1.5

25

1

20

0.5

15

0

10

−0.5

Temperature [°C]

Head residuals [m]

I. Engeler et al. / Journal of Hydrology 397 (2011) 295–305

5 Isothermal leakage−coeff. Temperature−dependent leakage−coeff. Temperature river Limmat

−1 Jan04

0 May04

Oct04

Mar05

Aug05 Jan06 Time [month]

Jun06

Nov06

Apr07

Sep07

Fig. 4. Head residuals (calculated–measured) at piezometer No. 3135; for calculations on the basis of isothermal leakage coefficients and temperature-dependent leakage coefficients. The river water temperature is also shown.

Table 2 Correlation coefficients of head residuals and water temperature for piezometer Nos. 3306 and 3304 downstream of the Hoengg weir and the other piezometers upstream of the Hoengg weir. Simulations with temperature-dependent (var.) leakage coefficients and isothermal (const.) leakage coefficients. Piezometer

3306

3304

3301

3137

3135

3134

3122

R const. leak. R var. leak.

0.177

0.030

0.641

0.604

0.668

0.721

0.370

0.255

0.206

0.170

0.306

0.311

0.291

0.060

slightly better results with isothermally calibrated leakage coefficients, if the calibration is carried out for conditions which are close to the average conditions (i.e., for a river water temperature around 12.8 °C (average over the period 2004–2007) instead of 17.5 °C). This could be achieved by using as calibration periods late winter in combination with late summer. However, this does not change the main problem that we point to: better results are obtained for fully coupled flow-heat transport simulations with temperature-dependent leakage coefficients. Doppler et al. (2007) observed a seasonal cycle of the head residuals mainly upstream of the Hoengg weir, where the hydraulic difference between river stage and groundwater head is larger than downstream the weir. The head difference is 2.0 m in piezometer 3135 in January 2005, whereas it is only 0.1 m in piezometer 3307 (see Fig. 2 for the position of these locations). The same effect was found in this study. With increasing head difference, the effect of temperature-dependence grows, whereas the improvements in the model are minor if the head difference is small. These findings are in agreement with Eq. (2). Figs. 5 and 6 show the interpolated head residuals for isothermal leakage coefficients (Fig. 5) and with temperature-dependent leakage coefficients (Fig. 6). The difference between the situation upstream and downstream Hoengg weir is clearly visible. In this study, temperature-dependence of hydraulic conductivity and the leakage coefficient is analyzed only with regard to the physical water properties (mainly water viscosity). There are other riverbed parameters, which are also potentially temperaturedependent or show a seasonal cycle and which might influence the seepage rates. Brunke and Gonser (1997) mention the physical, chemical and biological clogging mechanisms, where the latter might be temperature-dependent due to higher biological activity. According to the correlation coefficient shown in Table 2, temperature-dependent hydraulic conductivity and leakage coefficients

reduce the correlation of the head residuals with temperature, but not completely. Wiese and Nützmann (2009) state that the unsaturated zone below the surface water zone and the biogeochemical processes are important for the seepage flux in their study. However, presuming that higher temperature favours biological clogging, this would cause contrary effects in our case and would lead to even larger head residuals during winter season. Nevertheless, seasonal effects of sedimentation / erosion combined with biogeochemical processes cannot be excluded. An alternative explanation for the cyclicity of head residuals could be a wrong representation of recharge rate in the model, for example because of a poor characterization of actual evapotranspiration. However, this is a very unlikely explanation of the observed cyclicity. We would expect this cyclicity especially in areas further away from the river and other boundaries. Close to the river hydraulic head values are strongly controlled by the rivers stage and the leakage values. The spatial pattern of the cyclicity that we found is exactly the opposite: no cycle in most of the study area, except for a zone close to the river. We discard an erroneous representation of recharge as an explanation for the observed cyclicity in the model residuals. 5.3. Dependence of head residuals on river discharge and pumping management The temperature dependence of the leakage coefficient only partly explains the head residuals. Therefore, also the influence of the river discharge rate and river stage was investigated. For extreme discharge rates (flood events), the head residuals for a piezometer in the Western part of Hardhof downstream of the Hoengg weir are strongly negative (i.e., the measured heads are much higher than the simulated heads, Fig. 7). This means that the leakage flux is underestimated by the model. Two possible causes, which could explain this effect, are: – The leakage concept as implemented in the model calculates leakage rates corresponding to a constant flow through the area of the riverbed. This area is a function of the river stage related to the cross-sectional profile of the river. For the case of extreme floods, the assumption of a constant riverbed area does not hold and deviates significantly from reality. However, after the flood event, this error vanishes again. The cross-sectional area (wetted perimeter) could in principle be included in the leakage

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Head residuals [m] -2.0 - -1.5 -1.5 - -1.0 -1.0 - -0.5 -0.5 - 0.0

3317

0.0 - 0.5 0.5 - 1.0 1.0 - 1.5 1.5 - 2.0 2.0 - 2.5

3301 3306 3304 3137 3325

3122

3251

3117

3241 3257

N

0 125 250

3224 3407

3102 3402

500 Meters

Fig. 5. Interpolated head residuals (calculated–measured) in the Hardhof area at the 1st of March 2006 for simulation with isothermal leakage coefficients.

coefficient. The hydraulic conductivity of the additional area (which is flooded during the extreme event only) might be very different from the leakage coefficient for the main riverbed. Part of the downstream section of river Limmat was renaturalized, which allows the flooding of larger areas than upstream of the Hoengg weir. – The riverbed may change due to higher shear stress during flood events. The colmation layer would be thinner during such events. This would imply that the leakage coefficient would increase and the seepage flux would be larger than expected. The underestimation of infiltration during flood events of the model was already described by Doppler et al. (2007). The effect can be confirmed also for temperature-dependent hydraulic parameters, and additional floods, which were not analyzed by Doppler et al. (2007), as shown in Fig. 7. This is in principle also in agreement with Rushton and Tomlinson (1979), who postulate a non-linear leakage coefficient. A further effect visible in Fig. 7 is the flood event in August 2005, which leads to a positive shift in the head residuals. A similar effect was already observed by Doppler et al. (2007) for the flood event in 1999, but in the opposite direction. Note that the corresponding piezometer in Fig. 7 is located downstream of the Hoengg weir and therefore outside of the impounded river section, while the negative shift was observed for the piezometers upstream of the Hoengg weir within the impounded river section. A positive shift means that the leakage rate decreases in reality compared to the model. Doppler et al. (2007) found that the leakage coefficient increased after the major flood

of 1999 in the area upstream of the Hoengg weir. In this context one has to consider the flow discharge fractions of river Sihl and river Limmat during the flood events. During the flood of 2005, the overall discharge rate reached a peak value of 407 m3 s1 with a relatively large part coming from river Sihl (157 m3 s1). During the flood of 1999, the total discharge rate had a peak value of 490 m3 s1 with a smaller fraction from river Sihl (128 m3 s1) (Swiss Federal Office for the Environment (FOEN)). Also in their duration the two flood events differed considerably: In 1999 the discharge was strongly increased during more than one month compared to less than two weeks in 2005 (Swiss Federal Office for the Environment (FOEN)). Finally, the floods were generated by different mechanisms. The 1999 flood was related with snow melting combined with frequent rainfalls, whereas the 2005 flood was caused by intensive summer precipitation. Taking into account that almost all the sediment is brought in by river Sihl, and given the mechanisms that triggered the floods, the differences in the long-term effects can be attributed to different sediment loadings. The importance of accounting for sediment transport from upper reaches is also in correspondence with the findings of Blaschke et al. (2003) for river Danube, where differing effects on the leakage coefficient have been observed for large and small flood events. The operation management influences the residuals as well. The rates of pumping and infiltration can be significantly different from one day to the next. The management (bank filtration wells) can create local drawdown and therefore higher hydraulic gradients from river to groundwater. Still we could not find a clear

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Head residuals [m] -2.0 - -1.5 -1.5 - -1.0 -1.0 - -0.5 -0.5 - 0.0

3317

0.0 - 0.5 0.5 - 1.0 1.0 - 1.5 1.5 - 2.0 2.0 - 2.5

3301 3306 3304 3137 3122

3251

3325

3117

3241 3257

0 125 250

N

3224 3407

3102 3402

500 Meters

Fig. 6. Interpolated head residuals (simulated–measured) in the Hardhof area at the 1st of March 2006 for simulation with temperature-dependent leakage coefficients.

1

350

0

300

−0.5

250

−1

200

−1.5

150

−2

100

−2.5 −3 Jan04

River discharge [m3s−1]

Head residuals [m]

0.5

400 Head residuals Discharge river Limmat

50

May04

Oct04

Mar05

Aug05 Jan06 Time [month]

Jun06

Nov06

Apr07

Sep07

Fig. 7. Head residuals (calculated–measured) downstream the Hoengg weir at piezometer No. 3317 and discharge rate of river Limmat.

correlation of the residuals with the different management operations considering the complete period. 5.4. Discussion All these results show that the leakage coefficient can vary over time. We anticipate that in certain situations, especially in case of

pumping close to rivers, and especially in case of larger head gradients between river and aquifer, it is relevant to take into account that the leakage coefficient is temperature-dependent. This occurs for example for rivers, which have an unsaturated zone below the riverbed, as often is the case in arid regions. Infiltration from the river will vary as a function of temperature, and if the river only carries a small amount of water, also diurnal fluctuations in

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infiltration rate (due to diurnal temperature variations) might be of importance. It is expected that infiltration increases during the day, which could reduce the discharge rate of such (small) rivers. This decrease could be erroneously attributed to evapotranspiration. It is also important to take into account that during flooding, the area, where infiltration can occur, is increased. This can be taken into account in principle, but the leakage coefficient for the newly inundated area has to be calibrated as well. This could be done with the help of historical flood data and measured heads. Finally, it is not easy to predict how floods will modify the riverbed and how this will affect the leakage coefficients. Therefore, it is important to recalibrate the leakage coefficients in real-time. Hendricks Franssen and Kinzelbach (2008, 2009) proposed a Ensemble Kalman Filter method for this, and Hendricks Franssen et al. (2011) showed how the leakage coefficient can be adapted and re-calibrated in real-time with the help of measured data for the same aquifer. The results of the eight stochastic realisations with spatially variable leakage coefficients showed sensitivity with respect to the spatial variability of the leakage coefficient and also indicated that spatial variability has to be included as a possible explanation for the remaining head residuals. Additional analyses with different scenarios would be necessary in order to further explore the role of spatial variability on leakage. Given the CPU-intensity of the coupled simulations and the need to explore different scenarios and to process a large number of stochastic realisations, this was not possible in the context of this work. It will be the subject of future investigations. 6. Conclusions With our study we demonstrated that modelling seepage with strong river–aquifer interaction using temperature-dependent leakage coefficients can improve the simulation accuracy compared to simulations with isothermal leakage coefficients. At certain locations in the study area close to the river, the head residuals are decreased by about 30% if the temperature dependence of the leakage is taking into account. Major improvements are achieved upstream the Hoengg weir in the study area, where the river water level is always above the groundwater head, whereas downstream of the weir this difference is smaller or even inverted. According to the leakage concept as formulated in Eq. (2), the leakage coefficient is multiplied with the hydraulic difference between the river water level and groundwater head. Therefore, it is coherent that the impact of temperature-dependent leakage coefficients is higher upstream. The correlation coefficients (between head residuals and river water temperature) confirmed those findings, since they show only weak correlation of head residuals with river temperature downstream the Hoengg weir and stronger negative correlation upstream. A further limitation of a constant leakage coefficient pointed out in this study was the reproduction of the seepage during flood events. The model underestimates the seepage rates significantly during these extreme events. Since the underestimation is particularly present in areas, where neighbourhood areas of the riverbed can be flooded, it is potentially related with enhanced infiltration due to the larger infiltration areas. Also the hydraulic conductivity of the riverbed might be increased because of the removal of sediments due to increased shear stress during floods. After the flood of August 2005, a sudden increase of the head in the Western part of the model area was noticed. Doppler et al. (2007) observed an opposite shift in 1999 in the Eastern part of the model area, which corresponds to the impounded river section. We attribute this phenomenon to differing sedimentation events and also to differing sedimentation/erosion processes in the downstream and the upstream river sections.

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