Real-Time Management and Control of Groundwater Flow Field and Quality

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Doctoral Thesis

Real-time management and control of groundwater flow field and quality

Author(s): Marti, Beatrice S.

Publication Date: 2014

Permanent Link: https://doi.org/10.3929/ethz-a-010263985

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ETH Library DISS. ETH NO. 22017

REAL-TIME MANAGEMENT AND CONTROL OF GROUNDWATER FLOW FIELD AND QUALITY

A thesis submitted to attain the degree of

DOCTOR OF SCIENCES of ETH ZURICH

(Dr. sc. ETH Zurich)

presented by

BEATRICE SABINE MARTI

MSc ETH in Environmental Engineering

born 10. July 1984 citizen of Beromünster

accepted on the recommendation of

Prof. Dr. Wolfgang Kinzelbach Prof. Dr. Harrie-Jan Hendricks Franssen Prof. Dr. Dennis McLaughlin

2014

PhD Thesis

Real-time management and control of groundwater ﬂow ﬁeld and quality

Beatrice Sabine Marti

Acknowledgements

I thank my supervisor Prof. Dr. Wolfgang Kinzelbach for his valuable and experi- enced input and for making this PhD thesis possible. Prof. Dr. Fritz Stauﬀer I thank for leading me to supervise Bachelor and Master students, a task which I immensely enjoyed. Dr. Gero Bauser I thank for supervising my project thesis and for leading me to this PhD thesis. Dr. Hans-Peter Kaiser from the Zurich water works I thank for the excellent cooperation which included data and information exchange. I further thank Dr. Uli Kuhlmann and Michael Balmer from TK Consult AG for their help with the modelling software. Prof. Dr. Harrie-Jan Hendricks Franssen I thank for reviewing this thesis and answering questions about the real-time model and his former PhD student Dr. Wolfgang Kurtz for valuable discussions on the Hardhof and for the implementation of the 3D real-time heat transport model which I was allowed to use for this thesis. Further I thank Prof. Dr. Dennis McLaughlin for the fruitful discussions on real-time control and for reviewing my thesis. I further thank the members of the GWH research group for their feedback on parts on my thesis and of course for the distraction they provided during breaks. I super- vised several Bachelor, project and Master thesis’s and I want to thank the students for their excellent cooperation and the interesting discussions. Last but not least I want to thank my family and friends for their support, especially I thank my mother Evelyne for supporting me during my studies and my husband Roland for being there.

Abstract

Real-time control is a powerful tool for steering complex and dynamical systems into the desired direction. Parallel to the increase in computational capacity and the availability of measurements in real-time, real-time control has become interesting for management of environmental systems that are under pressure. One such system is the Hardhof well field in Zurich, Switzerland. The location within the city boundaries and downstream of contaminated sites make its water quality vulnerable to multiple threats, some of which have to be controlled on a daily basis. This thesis analyses the real-time control in operation at the Hardhof well field. The efficacy of the real-time flow model as well as the real-time control of the flow field was confirmed. Although the existing optimal control, that is computed with a genetic algorithm, performs well, the routine is time consuming and its understanding requires extensive expert knowledge. As an alternative, an expert system control was designed for the well field. Compared to the historically applied management, the expert system was able to reduce the risk of potentially polluted water reaching the drinking water production wells to a similar level as the optimal control currently in place at least during the analysed time period. The result was achieved in a fraction of the time needed for the optimal control and the algorithm of the expert system is intuitively understandable. The disadvantage of the expert system control is that, contrary to the genetic algorithm, it is not able to automatically adjust to new boundary conditions that were not included in the knowledge base of the design phase. Further, the method of ensemble control was applied to the 2D flow model of the Hardhof well field. It includes the ensemble information that is already available from the real-time modelling in the control routine. Results show a considerable improvement of the resilience of the control with regard to extreme events compared to traditional deterministic and stochastic control methods. It could further be shown that the feedback from the model update which the control receives as an input from the real-time model enhances the performance of the control substantial- ly. The ensemble control further allows the characterization of the risk to draw city water which is not possible with the control currently in operation at the Hardhof. Last but not least the threat of rising groundwater temperatures in the well field was addressed. A temperature control routine was coupled to the 3D-heat transport model of the Hardhof. A one year simulation of 3D heat transport showed that sea- sonally, the abstraction rates in the well field can be re-distributed to decrease the temperature in the drinking water produced by 1 to 2 ◦C. Long term simulations with the 2D heat transport model revealed a seasonal cold water bubble in the center of the well field where a further drinking water production well could be constructed to pump colder water.

iii

Zusammenfassung

Echtzeitsteuerung ist eine wertvolle Methode zur Regelung komplexer und dynami- scher Systeme. Parallel mit der Steigerung der Rechenkapazität und der vermehrten Verfügbarkeit von Messungen in Echtzeit, ist die Echtzeitsteuerung auch für das Management von Umweltsystemen unter Stress interessant geworden. Das Grund- wasserwerk Hardhof in Zürich ist ein solches System. Seine Position inmitten der Stadt Zürich im Unterstrom von belasteten Standorten ist die Quelle für eine Viel- zahl von Bedrohungen für die Grundwasserqualität. Einige von diesen Bedrohungen müssen täglich unter Kontrolle gebracht werden. Diese Doktorarbeit untersucht das Echtzeitmodell und die Echtzeitsteuerung, die derzeit im Hardhof in Betrieb sind. Die Eﬃzienz des Echtzeit-Strömungsmodells so- wie der Echtzeitsteuerung des Fliessfeldes wurden bestätigt. Obwohl die bestehende Echtzeitsteuerung, die mit einem genetischen Algorithmus optimiert wird, gut ab- schneidet, ist sie zeitintensiv in der Berechnung und eine spezialisierte Ausbildung ist zum Verständnis des Algorithmus nötig. Als Alternative wurde deshalb eine Steue- rung mit einem Experten System entworfen. Die Expertensteuerung reduziert den Stadtwasseranteil im Vergleich zum historischen Management des Brunnenfeldes auf ein ähnlich tiefes Niveau wie die optimale Steuerung, die im Hardhof zur Zeit ver- wendet wird. Dieses Resultat wird in einem Bruchteil der Zeit erziehlt, die für die optimale Steuerung nötig ist. Zudem ist der Algorithmus der Expertensteuerung in- tuitiv verständlich. Der Nachteil der Expertensteuerung ist, dass sie im Gegensatz zur optimalen Steuerung, nicht fähig ist, sich an neue Randbedingungen, die nicht in der Designphase miteinbezogen wurden, anzupassen. Des weiteren wird die Methode der Ensemblesteuerung auf ein 2D Strömungsmodell des Hardhofs angewandt. Diese Steuerung berücksichtigt die Information, die im En- semble des Echtzeitmodells bereits zur Verfügung steht. Die Resultate zeigen eine Verbesserung der Belastbarkeit der Steuerung im Bezug auf Extremereignisse gegen- über den traditionellen deterministischen und stochastischen Steuerungsmethoden. Es kann zudem gezeigt werden, dass die Rückkopplung vom realen System auf die Steuerung, welche mit der Echtzeitmodellierung erreicht wird, eine signiﬁkante Ver- besserung der Steuerung zur Folge hat. Ein weiterer Vorteil der Ensemblesteuerung gegenüber der aktuell am Hardhof laufenden Steuerung ist, dass das Risiko poten- tiell verschmutztes Wasser zu pumpen charakterisiert werden kann. Zu guter letzt werden die steigenden Grundwassertemperaturen angesprochen. Eine Temperatursteuerung wurde an ein 3D Wärmetransportmodell des Hardhofs gekop- pelt. In einer Simulation über ein Jahr konnte gezeigt werden, dass durch Neuvertei- len der Entnahmeraten in den Herbstmonaten die Trinkwassertemperatur um 1 bis 2 ◦C gesenkt werden kann. Langzeitsimulationen mit einem 2D Wärmetransport- modells des Hardhofs deckten zudem das saisonale Auftreten einer Kaltwasserbla- se inmitten des Hardhofs auf. Eine weitere Reduktion der Trinkwassertemperatur v könnte durch saisonales Pumpen aus dieser Kaltwasserblase erreicht werden.

vi Contents

1 Introduction1

2 Hydrogeology, well field operation and data5 2.1 Hydrogeology of the Limmat valley aquifer...... 5 2.2 Development of the Hardhof well field...... 5 2.3 Operation of the Hardhof well field...... 7 2.4 The concept of city water ...... 10 2.5 The data...... 11

3 Deterministic models 17 3.1 Flow model...... 18 3.1.1 Time dependent boundary conditions...... 19 3.1.2 Initial conditions...... 22 3.1.3 Calibration of parameters...... 22 3.2 Heat transport model...... 23 3.2.1 3D heat transport model...... 23 3.2.2 2D heat transport model...... 25 3.2.3 Time dependent boundary conditions...... 26 3.2.4 Initial conditions...... 27 3.2.5 Heat transport parameters...... 27 3.3 Comparison of the deterministic models...... 27 3.3.1 Flow simulation...... 28 3.3.2 Tracer test simulation...... 30 3.3.3 Heat transport simulation...... 33 3.3.4 Conclusion...... 35

4 Real-time models 37 4.1 Theoretical background...... 38 4.2 Review of the 3D real-time model...... 40 4.2.1 Implementation of the 3D real-time model...... 40 4.2.2 The boundary conditions...... 41 4.2.3 The initial parameter set...... 43 4.2.4 Evaluation of prediction of hydraulic heads...... 43 4.2.5 Evaluation of parameter updates...... 45 4.2.6 Conclusions...... 46 4.3 The 2D real-time model...... 47 4.3.1 Implementation of the 2D real-time model...... 48 4.3.2 The boundary conditions...... 48 4.3.3 The ensembles...... 49 vii 4.3.4 Evaluation of prediction of hydraulic heads...... 53 4.3.5 Evaluation of parameter updates...... 55 4.3.6 Conclusions...... 56

5 Real-time control of the Hardhof well field 57 5.1 Introduction to real-time control of non-linear systems...... 57 5.2 Lessons learned from current control schemes...... 59 5.3 Expert system control...... 63 5.3.1 Introduction...... 63 5.3.2 Method...... 64 5.3.3 Results...... 67 5.3.4 Conclusions...... 72 5.4 Optimal control of 2D flow field...... 72 5.4.1 Method...... 73 5.4.2 Results and Discussion...... 83 5.4.3 Conclusion...... 86 5.5 Temperature Control...... 87 5.5.1 Method...... 88 5.5.2 Results...... 92 5.5.3 Discussion...... 92 5.5.4 Conclusion...... 95

6 Conclusions 97

Bibliography 101

7 Appendix 109

Curriculum vitae 111

viii List of Figures

1.1 Hardhof: Schematic overview...... 2 1.2 Temperature over time in well A...... 3

2.1 The Limmat valley aquifer...... 6 2.2 Side view of horizontal filter well...... 7 2.3 Inside well D...... 7 2.4 Pressure valve to the horizontal filter tubes...... 7 2.5 Map of the artificial recharge infrastructure...... 9 2.6 Extension of the Herdern landfill...... 11 2.7 Electrical conductivity in the Herdern area...... 12 2.8 Observation locations...... 13 2.9 Detail of measurement locations in the east...... 14 2.10 Detail of measurement locations in the west...... 14 2.11 Detail of measurement locations in the hardhof area...... 15

3.1 The model grid...... 17 3.2 Overview over 3D-model boundary conditions...... 20 3.3 Leakage zones...... 23 3.4 K-values of 1-layer calibration...... 24 3.5 K-values of 2-layer calibration, upper layer...... 24 3.6 K-values of 2-layer calibration, lower layer...... 24 3.7 Comparison of head simulations...... 29 3.8 Detail drawing of basin 2 and well C...... 30 3.9 Detail drawing of tracer experiment area...... 31 3.10 Comparison of tracer test simulations...... 33 3.11 Inﬂuence of porosity on tracer test simulation...... 34 3.12 Comparison of temperature simulations...... 35 3.13 Comparison of temperature simulations at horizontal wells...... 36

4.1 Illustration of the real-time modelling procedure...... 40 4.2 River discharge 2011...... 41 4.3 Pumping rates 2011...... 42 4.4 Recharge rates 2011...... 42 4.5 Leakage initial ensemble...... 43 4.6 MAE 2011...... 44 4.7 hP3241 2011...... 44 4.8 leakage 2011...... 45 4.9 Average initial K-values...... 46 4.10 Average updated K-values...... 46 4.11 Structure of the 2D real-time model...... 48 ix 4.12 River discharge 2006-2011...... 48 4.13 Pumping rates 2006-2011...... 49 4.14 Recharge rates 2006-2011...... 50 4.15 Initial head distribution...... 50 4.16 Average initial K-values...... 51 4.17 Realization no 13 of K-values...... 51 4.18 Ensemble of leakage factors...... 51 4.19 Fixed head ensemble for 2006 to 2011...... 52 4.20 Areal recharge ensemble for 2006 to 2011...... 52 4.21 Ensembles of abstraction rates for 2006 to 2011...... 53 4.22 Ensembles of inﬁltration rates for 2006 to 2011...... 53 4.23 River head ensemble for 2006 to 2011...... 53 4.24 MAE 2006/2007...... 54 4.25 P3241 2006/2007...... 54 4.26 P3241 2011...... 55 4.27 leakage 2006/2007...... 56 4.28 Average initial K-values...... 56 4.29 Average updated K-values...... 56

5.1 Model predictive control schematic...... 58 5.2 Percentage of city water...... 60 5.3 Electrical conductivity in well C and river Limmat...... 60 5.4 Suggested and applied infiltration basin 2...... 61 5.5 Suggested and applied infiltration infiltration wells...... 61 5.6 Suggested and applied infiltration-abstraction ratio...... 62 5.7 Overview over Hardhof well field...... 64 5.8 ES control flow...... 66 5.9 ES fraction of city water...... 70 5.11 ES path lines on day 515...... 70 5.10 ES particle path lines...... 71 5.12 Probability of failure schematic...... 73 5.13 Locations of control node points...... 75 5.14 General algorithm of the routine for computing the nonlinear objective function...... 78 5.15 Effect of goal function components...... 79 5.16 Pareto front...... 80 5.17 Sensitivity of goal function...... 80 5.18 General algorithm of the real-time control model...... 81 5.19 General algorithm of the Call control routine...... 82 5.20 Deterministic vs. ensemble control...... 83 5.21 Deterministic vs. ensemble control...... 84 5.22 Gradients offline control, May 5...... 86 5.23 Gradients online control, May 5...... 87 5.24 Gradients offline control, June 28...... 88 5.25 Gradients online control, June 28...... 89 5.26 Minimization of the mixed water temperature...... 90 5.27 Fixed head boundary condition for 3D heat transport simulation... 90 x 5.28 River stage boundary condition for 3D heat transport simulation... 91 5.29 Areal recharge for 3D heat transport simulation...... 91 5.30 Abstraction rates for 3D heat transport simulation...... 91 5.31 Infiltration rates for 3D heat transport simulation...... 92 5.32 Boundary temperatures for 3D heat transport simulation...... 92 5.33 Temperature distribution with and without management...... 93 5.34 Mixed temperature with and without management...... 93 5.35 Temperature distribution October 9, 2008...... 94

List of Tables

2.1 Capacity of infrastructure...... 8

3.1 Model overview...... 18 3.2 Calibrated leakage values...... 23 3.3 Solute and heat transport analogy...... 25 3.4 Heat transport parameter values of 2D model...... 27 3.5 Heat transport parameter values of 3D model...... 28 3.6 Filtered length of the observation bores...... 31

5.1 ES classiﬁcation...... 67 5.2 ES Inﬁltration scheme...... 69 5.3 Goal function weights...... 77

7.1 Overview Hardhof literature...... 110

xiii

List of Abbreviations a.s.l. Above sea level AWEL Cantonal office for waste, water, energy, and air (Amt für Abfall, Wasser, Energie und Luft) b.g.s. Below ground surface CSTR Continuous stirred tank reactor DOC Dissolved organic carbon EC Electrical conductivity EnKF Ensemble Kalman filter ES Expert System HACCP Hazard analysis and critical control point. A conceptual approach to prevent hazards in food production processes. ID Identifier I/O Input/Output KF Kalman filter lhs Latin hypercube sampling MAE Mean absolute error Nap Naphtionate np Node pair std Standard deviation TCE Tetrachloroethene

xv List of Symbols

αEnKF Weighting matrix for parameter updating

αL Longitudinal dispersivity [L]

αT Transversal dispersivity [L] C Concentration [M L−3] −2 −1 −1 CA Volumetric heat capacity of the aquifer [M T L K ] c Concentration [M L−3] −2 −1 −1 CW Volumetric heat capacity of water [M T L K ] 2 −1 Dh Hydrodynamic dispersion tensor [L T ] 2 −1 Dt Thermal dispersion and diﬀusion tensor [L T ] η Dynamic viscosity [M L−1 T−1] g Head gradient [L] g Acceleration by gravity [L T−2] γ Heat capacity ratio [–]

H Mapping matrix [NO × NS] K Hydraulic conductivity [L T−1]

Kgain Kalman gain [NS × NO] 2 −1 Kperm Permeability [L T ] krel Relative Permeability, scaling factor [–] L log10 leakage coefficient −1 λC Decay rate [T ] 2 −3 λt,eff Effective thermal conductivity of the variably saturated aquifer [M L T ] 2 −3 λt,sat Thermal conductivity of the saturated soil [M L T ] lVG Van Genuchten parameter [–] m Aquifer thickness [L] mVG Van Genuchten constant [–] n Porosity [–]

NO Number of measurement locations np Pore size index [–]

NR Number of realizations

NS Number of states

P Cross-covariance matrix of state replicates [NS × NS] p Pressure [m T−2 L−1] −1 −2 pc Capillary pressure [M L T ] −1 −2 pe Water entry pressure [M L T ] −1 −3 Pt Heat production per unit volume [M L T ] xvi q Source/sink term [T−1] Q Discharge rate [L3 T−1]

R Cross-covariance matrix of measurement errors [NO × NO] ρ Water density [M L−3]

Rt Thermal retardation factor

S0p Specific storage coefficient [–] se Effective saturation [–]

Sr Saturation [–]

Sres Residual saturation [–]

Ss Maximum saturation [–] T Temperature [◦ C], temperature diﬀerences in [◦ K] t Time [T] τ Residence time [T] t Time t v Darcy-velocity or speciﬁc discharge, the discharge rate through a unit area [L T−1] V Volume [L3] − Xt State matrix of time t [NS x NR] + Xt Updated state matrix of time t [NS × NR] Y log10 hydraulic conductivity

Yt State observation matrix of time t [NO x NR] z Elevation [L]

T0 Surface temperature [K]

xvii List of SPRING attributes

GLEI Nodes with equal potential or equal concentration or temperature LEKN Nodal leakage [L2 T−1] LERA Line-leakage [L T−1] QKON Mass ﬂux [M T−1]

xviii Chapter 1

Introduction

Optimization tools have successfully been applied to groundwater management for several decades. Comprehensive reviews on the subject have been made for example by Gorelick [33] and by Ahlfeld and Muligan [1]. The basis of a reliable groundwater management decision is an accurate prediction of the model states (e.g. hydraulic heads) which - themselves - are subject to various decision variables (e.g. abstraction rates). Accurate predictions, however, - especially of dynamic systems - can only be computed with carefully calibrated models. Nowadays, model parameters can be estimated with state of the art software (e.g. Doherty [17]). However, due to the heterogeneity of natural aquifers as well as the eventual non-uniqueness of model calibration the parameter uncertainty of distributed groundwater models is still a challenge to producing reliable predictions that can be used for management decisions ( Carrera et al. [12]). One way to improve the accuracy of model predictions is to take into account new measurements of states continuously as they become available over time. Such data assimilation techniques allow the decision maker to automatically update a distributed model with measured data in real-time which enhances the data base for the decision process. In this thesis the focus lies on the real-time control of the Hardhof well field. The Hardhof well field produces about 15 % [61] of the drinking water demand of the greater Zurich area, Switzerland. The rest of the water demand is covered with lake and spring water. Drinking water is produced in 4 large horizontal wells (Wells A, B, C, and D in Figure 1.1). The well field is mainly recharged through 3 infiltration basins and 12 infiltration wells as well as by leakage from the river Limmat. The water for the artificial recharge is produced in river bank filtration wells along the river Limmat. In the Swiss law, drinking water is treated as foodstuff [16]. The Zurich water works are therefore obliged to follow the principles of the hazard analysis and critical control point concept (HACCP), a conceptual approach to prevent hazards in food production processes. The following hazards have been identified for the drinking water produced in the Hardhof well field [37]: (i) Chemical pollution of the river Limmat, (ii) flood in the river Limmat and microbiological contamination of the river bed filtrate, (iii) temperature increase of the river bank filtrate leading to higher groundwater temperatures (see Figure 1.2). High groundwater temperatures are a problem in the drinking water distribution system: bacterial growth rates in the distribution network increase with higher temperatures and a disinfectant becomes necessary if high temperatures prevail over a prolonged time period [63]. However, disinfectants may produce noxious by-products which are not desired in the drinking water [71]. 2

To the pressure zones N L imm at r iver Weir A B Recharge Horizontal I wells basins D C II River bank filtration (vertical wells) III Infiltration wells S 7-12 Infiltration wells S 1-6 Herdern

Hans-PeterHighway A1 Kaiser -Chlorinated solvents Hans-Peter Kaiser -Organic material -High salt contents & el. Conductivity

Figure 1.1: A schematic overview over the Hardhof well field. Drinking water is produced in the four horizontal wells A, B, C, and D and pumped to three different pressure zones (illustrated with the green, red and lilac arrows going out of the drinking water distribution center). Vertical wells along the river Limmat produce river bank filtrate which is infiltrated into the aquifer through the slow sand filtration basins 1, 2, and 3 and through the infiltration wells 1 to 12. South of the highway lies the former waste dump (Herdern) of the city of Zurich.

Further, warm water has a stale taste which is not desired by the consumer. (iv) Storage and transport of hazardous goods immediately south of the well field (e.g. mineral oil), (v) Leakage of heavy metals and salts from the waste dump Herdern immediately south of the well field, (vi) Leakage of chlorinated hydrocarbons from contaminated sites in the west of the well field, and (vii) Leakage of waste water from sewer lines in the proximity of the well field Apart from the continuous observation of the river and groundwater quality, the following measures are taken to manage these threats: In case of pollution of the river Limmat, points (i) and (ii), the river bank filtration wells and the horizontal wells are shut down. All the threats from the south of the well field (points (iv), (v), and partially (vi) and (vii)) are coped with by maintaining a hydraulic barrier along the south of the well field. The artificial recharge infrastructure not only serves to increase the capacity of the well field, but also forms an underground water mountain which leads potentially polluted water from upstream past the drinking water wells. Due to its strong interaction with the river Limmat and the daily changing abstraction rates, the flow field in the Hardhof area is very dynamic. For the maintenance of the hydraulic barrier, the infiltration rates of the 3 basins and the 12 infiltration wells therefore have to be adjusted on a daily basis for optimal protection. In a cooperation with the Zurich water works and the private consultant company TK Consult AG, the Institute of Environmental Engineering at ETH Zurich developed an operational real-time model and control [44]. Two control schemes have been designed by Bauser et al., i.e. a hydraulic gradient based control [7] and a stream Chapter 1 Introduction 3

Figure 1.2: The average and the maximum temperatures in the horizontal drinking water production well A show a rising trend over the past 30 years. (Figure source: Courtesy of H.-P. Kaiser, Zurich water works.) line based control [8], the latter of which is currently applied in the Hardhof well field. Up to now, there is no management strategy for the increasing temperatures of the river bank water. The real-time flow model shows an excellent performance. It was recently extended to include heat transport in a PhD thesis by Wolfgang Kurtz [53]. However, the real- time control has the following weaknesses: There is no constraint on the groundwater level in the Hardhof area. In order to minimize the inflow of potentially polluted water from the south, the infiltration rates are set high by the control which can lead to high groundwater tables in the Hardhof area such that pumps have to be employed to keep the cellars of buildings dry. Further, the control currently in place at the Hardhof well field is based on stream lines that are calculated on a quasi-stationary flow field. The flow field of a given day is frozen and particle path lines are tracked backward for 200 days until their origin either in the river, the infiltration wells and basins, or elsewhere can be determined. This is a conservative method since the flow field never stays the same for 200 days. It thus produces an infiltration excess. Further, the control routine up to now does not take into account the stochastic information of the flow field which is available from the ensemble-based real-time model. Within the scope of this thesis, the performance of the currently operating real-time model and control routine in the Hardhof was analysed. Further, an Expert System control for the Hardhof well field, originally elaborated under the supervision of Gero Bauser [6], was refined and compared to the stream-line control by Bauser et al. [8]. Further, a 2D flow and heat transport-model was coupled to the data assimilation routine described by Evensen [25] and a real-time optimization routine taking into account additional constraints and stochastic information on the flow field was implemented. Finally, a management scheme for periods with warm temperatures was devised. 4

The following chapters refer to the modelling part: Chapter 2 summarizes the basic information about the Limmat valley aquifer in general, the Hardhof well field specifically and the available data and time series. Chapter 3 presents a review of the flow and heat transport model. Chapter 4 explains the real-time model used in this work as the basis of the real-time management. In chapter 5, the real-time control for the Hardhof well field developed in this PhD thesis is presented. Concluding remarks are made in Chapter 6. Chapter 2

Hydrogeology, well ﬁeld operation and data

2.1 Hydrogeology of the Limmat valley aquifer

The Limmat valley was probably formed in the beginning of the pleistocene period 2.5 · 106 years ago [68]. During the last glaciation the valley was filled with glacial deposits. Kempf et al. [50] explain the complex succession of deposits of gravel, sand, and loam as sediments from glacial rivers which were occasionally overrun by the glacier. The aquifer material is characterized by a high hydraulic conductivity (K) and prominent thickness (m) in the south-east. Both, hydraulic conductivity and thickness, generally decrease towards the western part of the aquifer (Figure 2.1). However, the aquifer is characterized by highly variable thickness and the presence of narrow channels [50]. Estimates of hydraulic conductivities have been obtained by pumping tests and local flowmeter tests. While the regional pumping tests show high hydraulic conductivities −2.5 m of about 10 s , the local flowmeter tests reveal strong vertical heterogeneity in −1 −6 m the decimetre range from 10 to 10 s .

2.2 Development of the Hardhof well ﬁeld

The Hardhof well field was opened in 1934 with a capacity of 56’000 m3 d−1 [50]. At that time, it was located outside the city boundaries in the fields and close to the river Limmat. Zurich saw a rapid growth in population and consequently in water demand in the following decades. Therefore, the water works built a second water plant in the 1950s supplying lake water. Also the capacity of the Hardhof well field was extended in the 1970s. Today, a city like Zurich would probably rely on lake water only. But it was the time of the cold war and the threat of a nuclear war was pending. Groundwater is one of the safest drinking water resources even in war times, so precautions were taken to be able to supply the greater city area with safe drinking water for two weeks even if a worst case event would occur. The capacity of the well field was extended by the construction of four large horizontal wells with a total capacity of 150’000 m3 d−1 (Wells A, B, C, and D in Figure 1.1 on page2). In order to avoid excessive drawdown of the groundwater table, 3 artificial recharge basins (basins 1, 2, and 3 in Figure 1.1) were installed 6 2.2 Development of the Hardhof well field

Figure 2.1: An extract of the groundwater map of the Limmat valley. The Limmat valley aquifer extends from the moraine front north of lake Zurich (in the bottom right corner of the figure) to the north and west. The darker blue the colour the larger the thickness of the aquifer. The brown color denotes shallow saturated areas. Blue arrows indicate the main flow direction perpendicular to the head contours (in dark blue). The four red dots mark the drinking water production wells of the Hardhof well field. The magenta coloured area in the bottom left corner of the figure is a different kind of aquifer and not relevant in this study. Map retrieved from maps.zh.ch on July 23, 2013.

south of the wells. A further advantage of the artificial recharge is the formation of a hydraulic barrier against inflow of groundwater from the south west of the well field. In the late 19th century, an old clay pit straight south of the well field was used as a household waste dump. After 1904, incineration clinker and building rubble was deposited there before the pit was closed and railway lines were built on top of it. More on the waste dump and its consequences for the Hardhof well field can be found in chapter 2.4 on page 10. In later years, the vertical infiltration wells S 1-6 and S 7-12 were constructed to improve the hydraulic barrier. The artificial recharge is fed with river bank filtrate from 19 vertical wells along the river Limmat. The river bank filtrate, contrary to the river water, is almost free of suspended solids and very well suited for artificial groundwater recharge. To complete or replace the river bank filtrate in times of need (i.e. during constructions or shut down of the river bank filtration wells or increased demand for infiltration), a river water treatment plant has been constructed. This is, however, only a backup to the groundwater well field. Chapter 2 Hydrogeology, well field operation and data 7

2.3 Operation of the Hardhof well ﬁeld

The horizontal wells

The horizontal filter wells consists of a chamber of 3 m in diameter (see Figure 2.3). In 20 to 25 m depth of this chamber, 10 to 40 m long horizontal filter pipes extend into the porous medium. They are separated from the central chamber by valves (Figure 2.4). When these valves are open, groundwater flows through the filter pipes and is collected in the chamber. When the pumps are not operated, the water table in the chamber corresponds to the groundwater table. In the central chamber, 3 pumps convey the drinking water to the water distribution centre where it is pumped into the water supply network of the city of Zurich. The amount of water pumped from the four horizontal wells is determined by the number of pumps (1, 2 or 3) that are operated and by the duration each of these pumps is operated. The normal operation scheme for the horizon- Figure 2.2: Drawing of a side view tal drinking water wells is 0-1-1-2 which means of a horizontal filter well. that in one well, no pump is active, in two wells one pump is active, and in the fourth well 2 pumps are operated. One pump has a maximum capacity of 14’400 m3 d−1. The pumping capacities of the Hardhof

Figure 2.3: A photo of three pipes which are Figure 2.4: Pressure valves on the connected to three pumps that can be oper- horizontal ﬁlter tubes. Picture ated in each of the horizontal drinking water taken during the renovation of well wells (here in well D). Picture taken during the D in December 13, 2011. renovation of well D in December 13, 2011. 8 2.3 Operation of the Hardhof well ﬁeld

Table 2.1: The maximum capacities of the drinking water production infrastructure of the Hardhof well field. Infrastructure Max [m3 d−1] Horizontal filter well 43’200 Infiltration wells S 1-6 each 4’600 Infiltration wells S 7-12 average 4’730 Infiltration basins 1-3 each 30’000 River bank filtration wells total 115’000

infrastructure are summarized in Table 2.1 on page8. In order to guarantee the same average utilization time and thus wear of all pumps, the scheme rotates over the available 12 pumps in the four drinking water wells. The horizontal wells are generally operated during the night hours. This is done to ﬁll the reservoirs at night for the higher drinking water consumption during the day and to utilize the lower electricity prize during the night. An average of 20’000 to 25’000 m3 d−1 is thus produced. In the central chamber of each drinking water production well, several water quality parameters are measured continuously. These are water temperature, oxygen concentration, turbidity, and electrical conductivity (EC).

The artiﬁcial recharge network

The network plan of the artificial recharge infrastructure is given in Figure 2.5. River bank filtrate is pumped in 19 vertical wells. Two groups of 6 wells are located below the weir (see Figure 1.1 on page2 for the location of the weir in the river Limmat). They are connected to a collection chamber with siphons. Water is pumped to the artificial recharge network from this collection chamber, therefore only the collective water production in all 12 wells below the weir is known. Water quality measures such as temperature and electrical conductivity are collected in each of the two siphon conduits leading to the collection chamber. So temperature and electrical conductivity of the mixed water from 6 wells only is known at any time. North of the weir, 7 vertical wells pump river bank filtrate, their individual water production is known individually. 4 of these wells (wells 332, 333, 335, and 336) are connected to a heat exchanger with which the office building of the Zurich water works is climatized. In 2 of these 7 wells, temperature and electrical conductivity are measured. One of them is well 330, the other is well 336. The allowed production rate of the river bank filtration wells is 115’000 m3 d−1 [66]. However, in the past years, only about 60’000 to 80’000 m3 d−1 have been produced at low and high groundwater tables respectively (supporting information of Bauser et al. [7]). All the river filtrate is collected in one conduit where temperature and electrical conductivity are measured, immediately after the merging of both flows. From this conduit, water is then distributed to the individual recharge infrastructures. First, a branch supplies the infiltration wells S 1 to S 6. The water is aerated by cascading Chapter 2 Hydrogeology, well field operation and data 9 Basin 1 Basin 2 Basin 3 Heat exchanger 329 329 330 331 332 333 335 336 Infiltration basins

Collecting Collecting chamber Eastern siphon conduct Infiltration wells Collecting chamber Flow measurementFlow measurement Temperature Western Western siphon conduct 306 308 309 310 311 312 306 308 309 310 311 316 317 318 329 322 324 S S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S12 S 9 S10 S11

River bank filtration filtration wells

Figure 2.5: Simplified technical map of the artificial recharge infrastructure. 10 2.4 The concept of city water over steps and is then collected in a chamber from where it is conveyed to the 6 infiltration wells. The infiltration in the individual wells takes place with a free water table (from the chamber) depending on the capacity of the individual wells. Another branch leads to the three infiltration basins. The basins are operated with a free water table as well. The water is aerated by dropping over steps before ponding up to a maximum of 3 m above the slow sand filters. The basins have a filter area of 3800 to 4000 m2 with the vertical structure of typical slow sand filters (as described for example in Ellis and Wood [21]). The newer infiltration wells S 7 to S 12 are fed through another distribution chamber. The amounts of water going to well S 7, to wells S 8 to S 10, and to wells S 11 and S 12 are determined with overfall weirs installed at fixed heights. The flow contributions of these 3 well groups therefore are fixed at 14 %, 50 %, and 36 % respectively. The infiltration capacities of the individual wells are not known. However, pumping tests suggest a high variability of the potential infiltration rates, especially in the eastern part of the Hardhof area [87]. Recharge rates are collected for wells S 1 to S 6 collectively, for wells S 7 to S 12 collectively and for each infiltration basin individually. No further temperature and electrical conductivity measurements are available in the individual infiltration infrastructures. The one taken just after the collection of the water coming from the river bank filtration wells is the one used for characterizing the recharge water.

2.4 The concept of city water

Already in the late 70s when the capacity of the well field was increased, it was found that with increasing pumping activity, the groundwater quality in the Hardhof well field became more vulnerable to inflowing leachates from the former Herdern waste dump south of the well field [77]. For simplification, we call the area south and upstream of the well field area the city area and the groundwater flowing below the city area city water. For a modernization of the rail tracks that now lie on top of the former waste dump Herdern, the site was investigated thoroughly [28]. The extension of the artificial fill is shown in Figure 2.6. Only the areas with a dark shade are filled with household waste, the lighter shaded areas are filled with building rubble, clinker from the waste incineration plant, and excavated material. Most of the fill lies above the average groundwater table, during high water tables however, part of it gets inundated which is undesirable since it may lead to increased leaching of salts and heavy metals into the groundwater. Increased concentrations of sulphate, ammonium, boron, DOC (dissolved organic carbon), and electrical conductivity have been measured in the Herdern area and in plumes to the north-west of the former waste dump [28]. Also TCE (Tetra- chloroethene) was measured in the study by Geologisches Büro Dr. Heinrich Jäckli AG [28], however, this contamination seems not to stem from the Herdern site but from further upstream towards the city center. TCE is a solvent and is widely used in dry cleaning. Of the above mentioned parameters, electrical conductivity can be measured continuously at a comparatively low cost. The electrical conductivity of water increases with increasing ion concentration. It therefore is a sum parameter Chapter 2 Hydrogeology, well field operation and data 11

Figure 2.6: The Herdern landfill was used as waste dump for the city of Zurich until the first waste incineration plant was put into operation in 1904 [23]. The area with the darkest shade is mainly filled with houshold wastes from before 1904. The lighter shaded areas are filled with building rubble, clinker and excavated material. Figure from Geologisches Büro Dr. Heinrich Jäckli AG [28]. for the ion concentration in the water. It does not, however, give information about the individual salt components in the water [48]. Since electrical conductivity measurements are temperature dependent, all values are corrected for 20◦C. Electrical conductivities found in the Herdern area amount to up to 600 µS cm−1 at 20◦C whereas about 150 to up to 300 µS cm−1 at 20◦C are measured in the river Limmat. Electrical conductivity in the Hardhof area is typically below 300 µS cm−1 at 20◦C. Kaiser [48] found, that conductivity values can be used to estimate the origin of the drinking water in the horizontal wells. Electrical conductivity is hence used by the Zurich water works to characterize city water.

2.5 The data

Piezometric head and temperature

The amount and quality of data available for the Limmat valley aquifer in general and the Hardhof well ﬁeld in particular is excellent. The observation network has grown with the number of production and inﬁltration wells over the years. A data base, the so called data ware house, of the Zurich water works stores measurements 12 2.5 The data

Figure 2.7: Interpolated measurements of electrical conductivity in the Herdern area. Figure retrieved from Geologisches Büro Dr. Heinrich Jäckli AG [28]. in minute intervals. For modelling however, we receive aggregated or averaged daily values. Among the former are pumping rates and precipitation, among the latter are piezometric head, temperature, electrical conductivity, and river stages. The plausibility of the data is checked prior to using them for the modelling of the Hardhof well ﬁeld. All head and temperature measurement devices are revised and calibrated every 6 months by the Zurich water works. Figure 2.8 shows the 86 locations of bores where piezometric heads (blue) or heads and temperatures (red) are measured continuously. Figures 2.9, 2.10, and 2.11 show details of Figure 2.8 including the bore IDs. The groundwater table shows yearly variations of half a meter to two meters. The closer the observation point is to the river, the higher are the variations. Following the discharges in the rivers Limmat and Sihl, the ground water tables are generally high in spring and summer and low in winter with lag times according to the distance of the measurement location to the rivers.

Natural areal recharge and soil temperature

Daily precipitation as well as air and soil temperature measurements are available from the station Reckenholz (a MeteoSwiss station about 10 km north of the Hard- hof) and since 2007, air temperature measurements are available from the Hardhof area (operated by the Zurich water works). Climatic data such as wind speed, sun shine duration, and radiation are available from the Reckenholz station.

River discharge and temperature

The most important contributions to the recharge of the aquifer are due to leakage from the rivers Limmat and Sihl (which are located at or close to the northern Chapter 2 Hydrogeology, well ﬁeld operation and data 13

Head Head and Temperature 251 000 Recharge Infrastructure

250 000

249 000

248 000

247 000 677 000 678 000 679 000 680 000 681 000 682 000 683 000 Figure 2.8: Locations of piezometric head measurements (blue dots) and head and temperature measurements (red dots). The black dots denote the locations of the horizontal drinking water wells. All green dots refer to the artificial recharge infrastructure (river bank filtration wells in the north and artificial recharge infrastructure in the south). and eastern aquifer boundaries respectively). Discharge in both rivers as well as temperature is measured continuously by the cantonal office for waste, water, energy, and air (AWEL http://www.awel.zh.ch/). Discharge predictions for up to 3 days are available. The river Limmat has an average discharge of 70 m3 s−1 and peak flows of up to 300 m3 s−1. The temperatures vary between 4 ◦ C and 25 ◦ C. The river Sihl has an average discharge of 6 m3 s−1 with peak flows of up to 70 m3 s−1. The temperature of the river Sihl displays a very similar regime as the river Limmat with the same temperature range. 14 2.5 The data

3612 3404

249 000 3607

3610 248 500 3606 516 3609 3621 3603 248 000 3624 53

3605 3601 247 500 425

247 000

680 000 680 500 681 000 681 500 682 000 682 500 683 000 Figure 2.9: Detail of Figure 2.8. The map shows the IDs of the observation bores in the east of the model area. Only piezometric heads are measured in this area.

3335 250 000 3534 3317 3526 3522 249 500 3332 3315 3304 3311 3306 3326 3327 249 000 3313 3307 3322 3321 3325 3244 251 000 3347 3243 3432 D 3346 C

250 500 3431 3421 3423 250 000 3422

249 500

3425 249 000 678 000 678 500 679 000 679 500 680 000 680 500 678 000 678 500 679 000 679 500 Figure 2.10: Detail of Figure 2.8. The map shows the IDs of the observation bores in the west of the model area. Chapter 2 Hydrogeology, well ﬁeld operation and data 15

250 400 Head 3522 Head and Temperature 250 300 Recharge Infrastructure 330 3301 3137 250 200 3304 3135 3306 3134 3132 3511 3131 3146 336 250 100 3145 3141 3121 3322 3143 250 000 3122 3321 3507 3251 3244 3123 A 3117 249 900 3347 3118 3254 3243 3124 3110 S6 3342 3501 3240 3120 B 3343 S5 3222 3113 3112 249 800 D 3232 3241 S4 3101 3346 3344 C 3111 S3 S7 3231 3201 3102 249 700 S2 S9 S10 3221 3216 3234 3224 S11 S1 3257 3238 S12 3258 S8 3247 3239 3423 3259 3402 249 600 3421 3407 3417 3408 3409 249 500 3422 3403

679 400 679 600 679 800 680 000 680 200 680 400 680 600 Figure 2.11: Detail of Figure 2.8. The map shows the IDs of the observation bores in the Hardhof area.

Chapter 3

Deterministic models

The basis for the real-time control is a numerical model that simulates the physical processes in the Hardhof area with sufficient accuracy. From previous works, a 2D [19] and a 3D-model [46] of the upper Limmat valley aquifer are available. The following chapter presents both models and compares them under different flow and transport scenarios. Both models are implemented in the groundwater flow and transport modelling software SPRING [51]. They display the same number of nodes (7198) and elements (14003) in the first layer (see Figure 3.1). The element sizes are 50 m far away

0 0.5 1km River bank filtration wells

Horizontal wells

Recharge basins

Recharge wells River Limmat

River Sihl

Figure 3.1: Top view on the model grid. The first layer of all models discussed here displays the same grid. from the Hardhof area and 30 m in the Hardhof area. The resolution goes down to 18 3.1 Flow model about 1 m around the wells and infiltration basins. The 3D-model has a vertical grid resolution of 1.67 m which results in up to 26 layers, depending on the aquifer thickness. This resolution results in 173’599 elements in the 3D-model [44]. The 2D-model consists of one layer in the vertical direction with a thickness depending on the actual aquifer thickness [19]. In the first section of this chapter, the implementation of the groundwater flow equation in SPRING is described. Further, the implementation of the boundary and initial conditions and the calibration of the model parameters are explained. The second section focuses on the heat transport model, giving details on its implementation in SPRING. In the third section, the performance of the models is compared with respect to their ability to reproduce measurements of piezometric head, temperature, and tracer concentration. Table 3.1 gives an overview over the different models discussed.

Table 3.1: Overview over the diﬀerent deterministic models and parameter sets used in the sections of this thesis. Some of the parameter sets were only used for comparison with the calibrated ones (i.e. 1-layer, split, see section 3.3 on page 27). The parameter sets are described in section 3.1.3 on page 22.

Dimension Parameter set ﬂow heat solute 1-layer 4.2, 5.2, 5.3 - - 3D 1-layer, split - - - 2-layer - 5.5 -

2D - 4.3, 5.4 - -

3.1 Flow model

The following Equation 3.1 describes variably saturated propagation of pressure in a porous medium. In words, the equation expresses the balance between variably saturated storage changes and flows on one side and sources and sinks on the other side. SPRING [15] solves this equation for hydraulic heads at all model grid nodes with a finite element method [51]. ∂S ∂p ∂p K · k S · ρ · S + n · ρ · r +n·S · −∇· ρ · perm rel (∇p + ρ · g · ∇z) = q r 0p ∂p ∂t r ∂t η (3.1) Chapter 3 Deterministic models 19 with: Sr Saturation [–] ρ Water density [M L−3] S0p Specific storage coefficient [–] n Porosity [–] p Pressure [M T−2 L−1] t Time [T] 2 −1 Kperm Permeability [L T ] η Dynamic viscosity [M L−1 T−1] g Acceleration by gravity [L T−2] krel Relative permeability, scaling factor [–] z Elevation [L] q Source/sink term [T−1]

For variably saturated computations of ﬂow the relative saturation and relative permeability are computed following Van Genuchten [79][51]:

1−np np n pc p Sr = Sres + (Ss − Sres) · 1 + (3.2) pe mVG 2 lVG 1/mVG krel = (Se) · 1 − 1 − (Se) (3.3)

Sr − Sres Se = (3.4) Ss − Sres with: Sres Residual saturation [–] Ss Maximum saturation [–] −1 −2 pc Capillary pressure [M L T ] −1 −2 pe Water entry pressure [M L T ] np Pore size index [–] Se Eﬀective saturation [–] lVG Van Genuchten parameter lVG = 0.5 [–] −1 mVG Van Genuchten constant mVG = 1 − np [–]

3.1.1 Time dependent boundary conditions

All time dependent boundary conditions (see Figure 3.2 are fed to the models in daily time steps.

River-aquifer interaction

The software FLORIS [30], which solves the 1D Saint-Venant equations, was used to interpolate the river water level at each node of the numerical model in a time- varying simulation from January 2004 to August 2005 [22]. A quadratic function with three parameters was ﬁtted to the head-discharge-curves thus obtained for every node. Using these three parameters, the river water level at each node and 20 3.1 Flow model

Transient fixed head

Leakage from rivers

Areal Recharge

Lateral inflow

0 1 2 km

Figure 3.2: 3D-view of the 3D-groundwater flow model that was used for the real- time application in the Hardhof well field. The vertical coordinate is exaggerated by a factor of 20. for each river discharge is computed. The rivers are modelled as two lines of leakage nodes. Leakage is implemented in SPRING in three ways, two of which were applied in the present study. One is with line-leakage (LERA) and the other with nodal leakage (LEKN). The leakage flux between one river node and the corresponding groundwater node is thus expressed as in Equation 3.5[51].

Qleakage = LEKN · (hriver − hgroundwater) = LERA · l · (hriver − hgroundwater) (3.5)

Where l is the river length attributed to a given leakage node and h refers to the water level in the river and in the groundwater, respectively. The nodal leakage represents a reduced hydraulic conductivity through the river bed as given in Equation 3.6.

kd LEKN = · l · br (3.6) d kd being the reduced hydraulic conductivity of the river bed with thickness d. l being the length of the river stretch attributed to a given node and br the wetted perimeter of the river bed. Calibration of leakage values was performed using 5 zones of line leakage values (LERA). These calibrations were done under isothermal conditions, however, En- geler et al. [22] showed a significant improvement of the model performance when the leakage term was adapted to the daily river temperature. Further, Weber [85] looked at the influence of the river bed profile on the river-aquifer interaction and found that the approach described above to model the river with two lines of leakage nodes is appropriate. von Liechtenstein [80] looked at the river-aquifer interaction using measurements of temperature and electrical conductivity as tracers. Her find- Chapter 3 Deterministic models 21 ings confirmed the calibrated leakage values of Engeler et al. [22] in the Hardhof area.

Fixed head boundary

The western outflow boundary is given by a head measurement of the Cantonal Office for Waste, Water, Energy, and Air (AWEL). The measurement is attributed to all nodes of the western boundary as a fixed head. This is an approximation but since the outflow boundary is far away from the Hardhof area, it is a sufficiently good approximation.

Areal recharge

Based on the climate data, the daily areal recharge to the Limmat valley aquifer from precipitation is computed by a water balance with the evapotranspiration evaluated by the Penman-Monteith equation [3]. It was assumed in previous studies, that 84 % of the urban surface area is sealed and drains to the sewer system [19], [22],and [44]. So only a fraction of the approximately 1000 mm precipitation per year contributes to the areal recharge. The recharge is attributed to the ﬁrst model layer. In the 3D-models, the Van Genuchten equations [79] are solved. However, due to the small amount of areal recharge and the coarse resolution of the grid in the vertical direction, areal recharge is modelled only roughly.

Lateral inﬂow

In the 3D-model, lateral inflow is modelled at the south-east end of the aquifer where the river Sihl enters the model domain. At this location, the Limmat valley aquifer is connected to the Sihl-valley aquifer through a narrow channel. In the 2D-model, lateral inflows were neglected because they had little influence on the flow field in the proximity of the Hardhof area.

Abstraction and inﬁltration

Infiltration as well as abstraction wells are implemented as point sources and sinks respectively. That means, the pumping rates are attributed to a single node. In order to account for longer screened sections in the wells, the SPRING attribute GLEI was used on all nodes along the screened sections of the wells. The GLEI attribute forces the solver to yield the same potential (and the same concentration or temperature as an option for transport simulations) for all nodes belonging to one GLEI-group. In the 3D-model, the horizontal wells are implemented as areas of equal potential (using GLEI) in the layers where the actual filter pipes are located (i.e. in 20 to 25 m depth). The areas of equal potential correspond to circles with the radius the filter legs extend from the central bore. In a Master project work, Manuel Hartmann compared the modelling of the horizontal wells with the above described GLEI 22 3.1 Flow model attribute to a more detailed version where the individual filter legs were modelled and to an analytical solution presented in Hantush and Papadopulos [39]. His thesis shows, that the above described GLEI version is sufficiently accurate to compute the drawdown in the Hardhof area [40]. Like the wells, the recharge basins are modelled as point sources with the attribute GLEI to distribute the recharge over the area of the recharge basins. In the 2D-flow model, the wells are implemented as point sinks and the horizontal wells and the infiltration basins as point sinks surrounded by GLEI areas which lie all in the same layer.

3.1.2 Initial conditions

The initial conditions of the head ﬁeld correspond to the water table interpolated from the measurements at the ﬁrst time step to be simulated. For some simulations, a spin up period is computed. In these cases the initial conditions correspond to the ones computed at the last time step of the spin up period.

3.1.3 Calibration of parameters

For the same grid and boundary conditions, two sets of hydraulic conductivities and leakage factors of the 3D model exist, namely the 1-layer and the 2-layer calibration. The names refer to the number of vertical layers used for the zonation of the K-values. In the 1-layer calibration, all vertically overlying elements display the same hydraulic conductivities, imitating a 2D-calibration, whereas in the 2-layer calibration, the upper 10 layers or 17 m of the model are more conductive than the lower layers. Transient inverse modelling was used in both cases, using a pilot point approach implemented in the software SPRING. Further, the calibration periods in both cases are May/June 2004 and July/August 2005, two periods representative of the hydraulic regime of the Hardhof area. Marti et al. [58] refers to the 1-layer calibration whereas Kurtz et al. [52] and Huber et al. [46] refer to the 2-layer calibration. The two parameter sets are compared in detail in section 3.3. Engeler et al. [22] used a combination of the 1-layer K-values and the leakage values from the 2-layer calibration. The 3D-heat transport simulations described hereafter use the parameter set from the 2-layer calibration. The real-time model and control application period of 2011 discussed in this thesis was based on the parameter set from the 1-layer calibration. Leakage coefficients were calibrated for 5 zones (see Figure 3.3). Zone 5 corresponds to the river Sihl, zone 4 corresponds to the river Limmat within the city. Zone 3 is adjacent to the Hardhof area. It is separated from zone 2 by the Höngg weir. Zone 1 is the last river stretch in the model area that reaches down to the suburb of Schlieren. Table 3.2 lists the leakage values calibrated with the 1-layer and the 2-layer settings. The only major difference between the leakage values is in zone 4. Figure 3.4 shows the K-values from the 1-layer calibration. The figure shows the K-values in layer 5. However, all layers are attributed the same K-values. The white areas within the model boundary are impermeable. Chapter 3 Deterministic models 23

Zone 1 Zone 2 Zone 3

Zone 4

Zone 5

0 1 2 km

Figure 3.3: Zones used for the calibration of leakage coeﬃcients.

Table 3.2: The leakage values calibrated with the 1-layer calibration and with the 2-layer calibration in [10−5 m/s]. Zone 1-layer 2-layer 1 4 3 2 84 110 3 8 13 4 0.04 4 5 0.5 0.4

Figures 3.5 and 3.6 ﬁnally show the K-values from the 2-layer calibration in layer 5 (6.7 m depth) and layer 11 (17 m depth) respectively.

3.2 Heat transport model

3.2.1 3D heat transport model

Heat transport is only implemented in SPRING for 3D-models. The software uses a split operator approach developed by Ch. König [51] for solving the fully coupled ﬂow and transport equations. The 3D-heat transport equation balances heat storage on one side with conductive and convective heat transport plus a source/sink term on the other side (Equation 3.7).

∂T Pt = ∇ · (Dt · ∇T ) − γ · ∇ · (v · T ) + (3.7) ∂t CA 24 3.2 Heat transport model

Figure 3.4: K-values obtained from the 1-layer calibration.

Figure 3.5: K-values obtained from the Figure 3.6: K-values obtained from the upper layer of the 2-layer calibration. lower layer of the 2-layer calibration. with: T Temperature [◦ K] t Time [T] 2 −1 Dt Thermal dispersion and diﬀusion tensor [L T ] λt,sat Dt,L = + γ · αL · v CA λt,sat Dt,T = + γ · αT · v CA 2 −3 λt,sat Thermal conductivity of the saturated soil [M L T ] −2 −1 −1 CA Volumetric heat capacity of the aquifer [M T L K ] γ Thermal capacity ratio γ = CW /CA [–] −2 −1 −1 CW Volumetric heat capacity of water [M T L K ] αL Longitudinal dispersivity [L] αT Transversal dispersivity [L] v Darcy-velocity [L T−1] The 3D heat transport model, including time dependent boundary conditions as Chapter 3 Deterministic models 25 well as heat transport parameters used in this thesis was implemented and kindly provided by Kurtz et al. [52].

3.2.2 2D heat transport model

For the 2D-model, a work-around via the analogy between the solute and heat transport equations has been used to make heat transport simulations possible [73]. This work-around has been implemented within the scope of a master project thesis by the two Master students, Raphael Looser and Stephan Kammerer [57]. The 2D-heat transport equation as in Stauﬀer et al. [73] (Equation 3.8) is obtained by averaging the 3D-heat transport equation (Equation 3.7) over the thickness of the aquifer.

∂T Pt λt,eﬀ · (T − Tsurface) = ∇ · (Dt · ∇T ) − γ · ∇ · (v · T ) + − (3.8) ∂t m · CA m · CA · (f + m/2)

In this equation, the heat flux from the earth surface to the aquifer is computed through the average of the thermal conductivities of the saturated and the unsaturated soil λt,eff. The temperature difference (T − Tsurface) from the earth surface to the average depth of the aquifer is relevant. That is the depth to the water table f plus half the aquifer thickness m. Equation 3.8 can be compared to the 2D-solute transport equation (Equation 3.9) which can be solved in SPRING.

∂C 1 PC = ∇ · (Dh · ∇C) − · ∇ · (v · C) + − λC · C (3.9) ∂t n m · n The correspondence between the parameters of the two equations is given in Ta- ble 3.3. The solute transport implementation in SPRING only features either a

Table 3.3: The comparison between the parameters of the solute transport equation and the heat transport equation (Table adapted from Stauffer et al. [73]). Solute transport Heat transport Solute concentration C ≥ 0 Temperature T ≥ 0 Hydrodynamic dispersion tensor Dh Thermal dispersion tensor Dt Inverse porosity 1/n Thermal capacity ratio γ = CW /CA Source/sink term PC /(n · m) Thermal source/sink term Pt/(CA · m) Decay coefficient λC Thermal flux coefficient λt,eff/(CA · m · (f + m/2)) concentration dependent source or a sink term but not both at the same time. However, the net heat flux from and to the surface is negative in winter when the aquifer temperature is higher than the surface temperature and positive in summer when the aquifer temperature is lower than the surface temperature. The surface heat flux therefore was implemented by splitting it into two parts: One of linear degradation within the aquifer and one of an average equivalent heat flux from the top. When the surface temperature is higher than the groundwater temperature, the summed fluxes are positive, meaning that the groundwater is heated up. If on the other hand the surface temperature is lower than the groundwater temperature, 26 3.2 Heat transport model the summed fluxes are negative indicating a cooling down of the groundwater. For details on the implementation see section 3.2.3.

3.2.3 Time dependent boundary conditions

River water temperature

The same measured river water temperature for all river node points of the rivers Limmat and Sihl is implemented as ﬁxed temperature in the 2D and in the 3D models. The river temperature is measured at the Hardturm station operated by FOEN (Swiss Federal Oﬃce of the Environment).

Soil temperature

Soil temperature is measured at 20 cm depth in the Reckenholz meteo station. This temperature is used for the top boundary condition in both the 2D and the 3D model. Whereas in the 3D model, the surface temperature is a fixed boundary temperature, a work-around for the surface heat flux had to be devised for the 2D model. In the 2D model, the net heat exchange between aquifer and soil surface was separated in heat production (heat flux from the surface to the aquifer) and a decay (sink of heat when the surface temperature is below the aquifer temperature). The heat loss is modelled with the equivalent thermal flux coefficient (Equation 3.10).

λt,eﬀ λC = (3.10) CA · m · (f + m/2)

Only one value for λC can be fed to the numerical model. However, aquifer thickness and depth to the groundwater table vary throughout the model area. In the present case, the average decay rate over the model area is used. Therefore the average aquifer thickness m was used. The thermal flux coefficient is constant over time. The heat production is modelled as a mass production rate (Equation 3.11). It is computed outside of SPRING and implemented with the attribute QKON in SPRING. Pt · n T0 PC = where Pt = λt,eff · (3.11) CA f + m/2 QKON is attributed to each node of the model grid. The heat production therefore has to be adapted to take into account the variable patch sizes belonging to a given node in the finite element grid Apatch (Equation 3.12). It is further adapted to the actual thickness of the aquifer at a given node i (mi). This means it is not strictly consistent with the heat loss in the aquifer which is too high in shallow parts of the model and too low in areas with large aquifer thickness.

mi QKON = PC · Apatch · (3.12) m Chapter 3 Deterministic models 27

Areal recharge temperature

In the 3D model, the areal recharge is attributed the soil temperature. In the 2D model, convective heat ﬂux from areal recharge is implemented as areal recharge with a given concentration (equivalent soil temperature).

Artiﬁcial recharge temperature

For the artificial recharge a temperature measurement in the pipe leading to the artificial recharge infrastructure is used in both the 2D and the 3D models (see figure 2.5 on page9 for the measurement location).

3.2.4 Initial conditions

Heat transport is considerably slower than the propagation of pressure. Therefore, a spin-up period of 0.5 to 1 year has been computed to obtain an initial condition for all simulations. The exact duration of the spin-up period is stated when simulations are described here after.

3.2.5 Heat transport parameters

The parameters of the isothermal flow field calibrations have been used to model heat transport (described in section 3.1 on pages 18 ff). Literature values have been taken for the heat transport parameters of the 2D model. A summary of the values used are given in table 3.4 for the 2D model and in table 3.5 for the 3D model.

Table 3.4: Values of heat transport parameters of the 2D model (Looser and Kam- merer [57]). Parameter name Value Unit Source m Mean aquifer thickness 17.5 m computed f Mean depth to aquifer 4.4 m computed −1 −1 λt,sat Thermal conductivity of saturated soil 2.7 W m K after [73] −1 −1 λt,usat Thermal conductivity of unsaturated soil 1.8 W m K after [73] 6 −3 −1 CA Speciﬁc heat capacity of aquifer 2.6·10 J m K after [73] 6 −3 −1 CW Speciﬁc heat capacity of water 4.2·10 J m K after [73] n Equivalent porosity (n = CA/CW ) 0.62 – computed

3.3 Comparison of the deterministic models

In order to gain a better understanding of the models and parameter sets available for the Hardhof well ﬁeld, a simple benchmarking has been done where ﬂow, heat and (with the 3D model) solute transport were simulated over the same historical 28 3.3 Comparison of the deterministic models

Table 3.5: Values of heat transport parameters of the 3D model. The values are taken from the 3D heat transport model kindly provided by Wolfgang Kurtz of the research center Jülich, Germany [53]. Parameter name Value Unit −1 −1 CW Specific heat capacity of water 4192 J kg K −1 −1 λW Thermal conductivity of water 0.587 W m K −3 ρW Density of water at reference temperature 1000 kg m S Specific storage coefficient 3.3·10−4 - −1 −1 CA Specific heat capacity of soil 800 J kg K −1 −1 λS Thermal conductivity of soil 3.5 W m K −3 ρS Density of soil 2600 kg m n Porosity 0.15 - time period. The results of these simulations are discussed in the following section.

The 1-layer, split parameter set Flowmeter measurements in basins 2 and 3 [62] and along the south of the well field [87] show a difference in hydraulic conductivity between the upper 10 m and the lower part of the aquifer and possibly the presence of a layer with reduced hydraulic conductivity between both. The newer 2-layer calibration, however, has the boundary between the more conductive and the less conductive lower layer at about 17 m. In order to test whether the level of the boundary between higher and lower hydraulic conductivity influences the simulation results, the 1-layer parameter field was split into two layers: a more conductive layer in the upper 10 m and a lower conducive lower layer down to the bottom of the aquifer. The splitting of layers was done in a way that keeps the vertical average hydraulic conductivity constant. The conductivity of the upper layer was increased by a factor of 2. The conductivity of the lower layer was decreased by a factor of 2 weighted by the number of layers in the lower zone divided by the number of layers in the upper layer.

3.3.1 Flow simulation

The flow simulations were run for the year 2006. The time dependent boundary conditions that were applied to this period can be viewed in figures 4.12 to 4.14 in section 4.3.2 on page 48 ff. Figure 3.7 shows results of the head time series at the observation locations in the Hardhof area where also temperature measurements are available. Contrary to the 2D simulations, the additional abstraction rates during construction periods in May/June and September and the tracer test in November are not implemented in the three 3D simulations (1-layer, 2-layer, and 1-layer, split). This explains the inability of the 3D simulations to reproduce the measurements in the above mentioned periods. Other dynamics such as the reaction to high water levels in the river Limmat in June and September are well represented by all four models. Chapter 3 Deterministic models 29

Figure 3.7: Flow simulations of the year 2006. 3D simulations with the 1-layer (black), the 2-layer (dark blue), and the 1-layer split (light blue) parameter sets. Further the results of the 2D simulation are shown (in green), as are the measurements (in red).

Excluding the construction periods which were not implemented in the 3D models, all models perform similarly well with regard to the dynamics. All 3D simulations were done with exactly the same initial and boundary conditions. Only the hydraulic conductivities and leakage values were changed between the simulations. Generally, the 2-layer model performs best of the 3D models. Not only the dynamics of the observed time series can be reproduced but also the absolute groundwater level. It is worth noting that the simulations with the 1-layer parameters lie up to 0.5 m higher than the others. It is possible that the lateral inflows used as boundary conditions in the calibration of the 2-layer parameter set and applied as boundary conditions in these simulations, were not the same as used in the calibration of the 1-layer parameter set and therefore lead to too high groundwater tables with the 1-layer parameter set. Simulations performed by Manuela Mauchle, a master project student, applying the time dependent leakage coefficient suggested by Engeler et al. [22] to the 2-layer parameter set did not increase the goodness of fit between measured and observed data [60]. Adapting the leakage value to changes of temperature in the warm season increased the river-aquifer interaction which, in the case of the 1-layer calibration, lowers the groundwater table in the Hardhof area. A desired effect seeing it is generally too high in the Hardhof area. Lowering of the water table during the warm summer month however does not improve the simulations with the 2-layer parameter set. 30 3.3 Comparison of the deterministic models

3.3.2 Tracer test simulation

In order to gain a better insight into the hydro-geology of the Hardhof well field, several tracer tests have been carried out in November/December 2006. The Zurich water works appointed the private geology consultancy office Dr. Lorenz Wyssling AG to investigate the flow paths from basin 2 to the drinking water wells C and D under steady state flow conditions. A detailed description of the general conditions and the procedure of the tracer test can be taken from the report of Wyssling AG [88]. In this work, the effect of model parameters and concentration boundary conditions on the interpretation of the tracer tests by simulations is looked at. The following questions are to be answered in the section to follow: • Can the tracer experiment of 2006 be reproduced with the current parameter sets of the 3D-flow model? • How sensitive is the model result to changes in the porosity? Note: Decreasing the aquifer dispersivity leads to a similar result as decreasing the porosity: The break–through curve is narrowed down and the peak arrives earlier. However, for numerical reasons further reduction of the dispersivity was not possible.

The tracer experiment

The tracer transport between basin 2 and well C is of paramount interest since basin 2 is supposed to shield well C from the inﬂow of water from the south of the well ﬁeld.

Figure 3.8 shows a drawing of the top and side views of basin 2 and well C. Well C, as the other drinking water production wells A, B, and D, consists of a vertical bore with a radius of 3 m and two layers of horizontal filter legs of about 30 m length each which extend from the main bore. Basin 2 features one bore in each of its four corners. The bores are not depicted in figure 3.8 because their ineffi- Figure 3.8: Top and side view of basin 2 and well C. ciency to transport water to deeper aquifer layers has been demonstrated with flow meter tests [62]. They are not taken into account in the tracer test simulations. In this work we try to gain insight into the parameters of the flow and transport equations mainly in the area between basin 2 and well C. The well field was operated at steady state. Abstraction took place only in wells C and D, with 18’720 m3d−1 each. Sodium-naphthionate (Nap) was used as a tracer. Chapter 3 Deterministic models 31

Figure 3.9: Top view on the area of the tracer experiment with the observation bores in red. The observation bores are labelled with numbers. Three numbers indicate bores with ﬁltered pipes in diﬀer- ent depths close to each other (i.e. 3222, 3228, 3229 and 3224, 3238, 3239). Tracer concentrations were also measured in the two pumping wells C and D, marked with black stars here.

The tracer is degradable in sun-light and shows very little but irreversible sorption in loamy soils [54]. 3 kg naphthionate was mixed in the inflow of basin 2. Samples were taken in wells C and D. Further, tracer concentrations were measured in piezometers around basin 2 and 3241 north-west of well C (see figure 3.9). Only in piezometer 3241 tracer concentrations were found. The bore is screened from 5 to 20 m below ground surface. Table 3.6 summarizes the depth of the screened section in each observation bore. Wells C and D pump water in two layers of horizontal filter pipes at 378.5 and 379.5 m a.s.l.. Figure 3.10 on page 33 shows the measured concentrations over time in the observation locations wells C and D and bore 3241 in red. The fact, that no Nap (nor any other tracer) was measured in the other bores close to basin 2 suggests the presence of a channel-like structure with high hydraulic conductivity connecting basin 2 and bore 3241. The shape of the break through curves of bore 3241 and well D show features of a typical advective diffusive tracer transport in homogeneous soil.

Table 3.6: Depth of the screened pipe segment in each of the observation locations. The maximum measured concentration is given in the third column. Bore ID Depth of ﬁlter Max. conc. measured [m b.g.s.][mg m−3] 3241 5.5–20.5 70 3222 18.2–21.2 0 3228 10.7–11.6 0 3229 2.8–7.3 0 3224 18.7–23.9 0 3238 13.8–14.6 0 3239 8.6–9.3 0 well C 19–20 19 well D 20–21 1

The break–through curve of well C on the other hand shows a typical tailing behaviour. The break–through curve has two parts: A fast peak and a slow tail with 32 3.3 Comparison of the deterministic models a distinct bend between the two parts of the curve. The fast pathway leads through the upper, more conductive aquifer layer and only a short way through the lower layer. The slower pathway travels directly down into the lower, less conductive layer and from there to the well and produces the tail of the break–through curve.

The boundary concentration

The total inﬁltrated water in one day is larger than the volume of basin 2. Thus, the tracer concentration cannot be set constant. Basin 2 can be modelled as an ideal ∗ −1 continuously stirred tank reactor with an inlet concentration cin of 0 mg l . The model is derived from the concentration mass balance over the basin: dc∗ · V = c∗ · Q − c∗ · Q dt in dc∗ Q 1 ⇔ = −c∗ · = −c∗ · (3.13) dt V τ where Q is the ﬂow through the basin, V is the volume of the basin, c∗ is the tracer concentration in the basin, and τ is the mean residence time of the water in the basin. ∗ refers to the ideal model concentrations. ∗ ∗ By integration of c over time t from the initial concentration c0 to the current concentration c∗ at time t, the boundary concentration as a function of time can be computed as follows: t ∗ ∗ − τ c (t) = c0 · e (3.14) Wyssling’s report states, that a maximum of 85 % of the added Naphthionate could be recovered [88]. The rest is probably lost by irreversible sorption [54]. The tracer mass added to basin 2 can therefore be reduced to M = 0.85 · 3000 g = 2550 g since we do not account for sorption in the solute transport model. From Wyssling’s report [88] it is visible, that the water level in basin 2 was at about 1 m. The vol- 3 ∗ ume V of basin 2 therefore was around 3750 m , the initial concentration c0 about 680 mg m−3, and the mean residence time τ about 0.2 d (5 h). The time step size for boundary conditions of the simulations is one day. The boundary concentrations therefore have been discretized in homogeneous daily concentrations c(ti to ti+1) by integration of the model equation 3.14 over intervals of one day each.

Z ti+1 1 t 1 ti ti+1 ∗ − τ ∗ − τ − τ c(ti to ti+1) = · c0 · e dt = · c0 ∗ τ · e − e (3.15) ti+1 − ti ti ti+1 − ti

Thus, for day 1, a boundary concentration of 258 mg m−3 is computed.

Results and discussion

Figure 3.10 shows the results of the tracer test simulations with the 3D model using the 1-layer and the 2-layer parameter sets (2-layer and 1-layer split). The fit for the wells C and D is better than for the observation point 3241 because several stream lines come together in the well and errors are averaged out whereas only Chapter 3 Deterministic models 33 one stream line goes through an observation point. The differences between the different parameter sets are small though the 3-dimensional parameter sets yield better results in piezometer 3241.

Figure 3.10: Solute transport simulations of the tracer test in November 2006. 3D simulations with the 1-layer (black), the 2-layer (dark blue), and the 1-layer split (light blue) parameter sets. The measurements are given in red.

Generally, the concentrations, especially in well C, are overestimated. The bend in the break–through curve of well C can not be reproduced with any of the models. One explanation could be that the vertical anisotropy is underestimated in all the models. Figure 3.11 shows the inﬂuence of changes in porosity on the break through curves. The simulations were performed with the 1-layer split parameter set which had a default porosity of 0.2. Decreasing the porosity narrows the width of the break through curves and shifts the arrival times of the maximum concentration to smaller concentrations. A relatively high porosity of 0.2 seems to produce the best ﬁt between the measured and modelled break–through curves.

3.3.3 Heat transport simulation

The heat transport simulations were run for the year 2006. The time dependent boundary conditions that were used in this time period can be viewed in ﬁgures 5.27 to 5.32 in section 5.5 on page 87 ﬀ. Figure 3.12 shows results of the temperature time series at the temperature observation locations in the Hardhof. No spin-up periods have been used in these simulations. Taking into account that wrong initial conditions lead to a wrong level of the temperature curves (generally too high for the 3D models), the dynamics of the temperature curves can still be represented 34 3.3 Comparison of the deterministic models

Figure 3.11: Solute transport simulations of the tracer test in November 2006. Influence of porosity on the tracer test simulation. fairly well with all 3D models. All models overestimate the yearly temperature cycle however. In the 2D model it becomes evident from the piezometers far away from the river Limmat that the temperatures are not in equilibrium. One could get rid of this effect by applying a spin-up period of 1 year as has been shown by the master students Looser and Kammerer [57] and Mauchle [60]. Figure 3.13 shows the temperature curves in the horizontal filter wells. Taking into account only the second half of the simulation period in order to avoid the effect of possibly wrong initial conditions, the fit between the measured and modelled temperatures in the pumping wells is good. The 2D model overestimates the influence of the river Limmat in well A. This could probably be improved by including temperature observations in the model calibration. This has not been done up to recently due to the requirement of large computational resources necessary for the calibration of a fully coupled flow and transport model. Such a calibration is currently under way. All 3D models produce very similar temperature time series in the horizontal wells. Differences are only visible in well A which can be explained with differences in the leakage values. The 2D model performs better for wells B, C and D than the 3D models. For wells C and D, the explanation is that the construction periods in the first half of 2006 and the tracer experiment in November 2006 are implemented in the boundary conditions of the 2D model but not in the 3D models. These construction periods were not documented in the log file received from the water works and therefore were not implemented in the model boundary condition. Only recent deeper research into the reasons for model deviation from the measurements in cer- tain time periods revealed the construction periods for which the abstraction rates had to be estimated. Parameters of the river-aquifer-interaction could be respon- Chapter 3 Deterministic models 35

Figure 3.12: Heat transport simulations of the year 2006. 3D simulations with the 1-layer (black), the 2-layer (dark blue), and the 1-layer split (light blue) parameter sets. Further the results of the 2D simulation are shown (in green), as are the measurements (in red). sible explain the discrepancies in well B and for the overestimation of temperature extremes of the 2D model in well A.

3.3.4 Conclusion

Of all the 2D and 3D models, the 3D model with the 2-layer parameter produces the best data ﬁt for the simulated time period. As Manuela Mauchle could show in her thesis, the 2-layer model averaged over the depth of the aquifer also performs well with the 2D temperature model [60]. 36 3.3 Comparison of the deterministic models

Figure 3.13: Results of the heat transport simulations of the year 2006 at the horizontal ﬁlter wells. 3D simulations with the 1-layer (black), the 2-layer (dark blue), and the 1-layer split (light blue) parameter sets. Further the results of the 2D simulation are shown (in green), as are the measurements (in red). Chapter 4

Real-time models

We design models to be able to predict the behaviour of more or less complex real systems subject to disturbances. Traditionally, the parameters of these models are calibrated against measurements of system variables (e.g. hydraulic head, temperature or concentration). However, measurements cost money and time, both of which are generally limited resources. Therefore, often only the reaction of the system to a limited range of possible disturbances can be measured and used for parameter calibration. This leads to the possibility that the model cannot reproduce the correct system behaviour if the disturbances are out of the range the model was calibrated with. Another drawback of traditional calibration of groundwater model parameters is that it assumes that the parameters are constant over time. This has been found to be an insufficient assumption for dynamic groundwater systems where river-aquifer interaction plays an important role (e.g. [19], [47], and [52]). Important dynamic processes determining the river-aquifer interaction are often neglected in groundwater flow models [86]. For example, a flood erodes the river bed, flushing away the clogging layer which reduces the water flux between river and underlying aquifer [41]. Periods of low flow on the other hand can enhance biomass growth and lead to clogging [76]. Furthermore, it has been found that parameters describing river-aquifer interactions not only vary in time, but are highly heterogeneous in space (several orders of magnitude) [11], [52]. Another important parameter, the hydraulic conductivity of the aquifer, does not change significantly over time but generally only few measurements are available and the translation of these measurements to a numerical model grid is not evident [12]. Current state of the art parameter estimation provides stochastic information about the parameter fit or even allows the estimation of a set of equally likely parameters [18]. The use of this information for state prediction lies at hand: Not only one prediction of the model states but an ensemble of equally likely predictions can be produced. These can, for example, be the basis for more robust management decisions. Furthermore, new measurements become available as the system is observed over time. These can be used to update estimated parameters. Tools for optimal model predictions when measurements are available have been developed in control engineering science already decades ago. Rudolf E. Kalman [49] first described the method for optimal predictions of linear systems, a method which was later named the Kalman filter (KF). Evensen [24] introduced the Ensemble Kalman filter (EnKF) for large numbers of state variables. The Ensemble Kalman filter is a Monte Carlo approximation of the Kalman filter. It allows the estimation 38 4.1 Theoretical background of the state covariance matrix on the basis of an ensemble of equally likely model predictions [9] whereas the traditional Kalman filter necessitates the deduction of the covariance matrix by computing the covariances between all of a large number of state variables. Hendricks Franssen and Kinzelbach [42] first adapted the Ensemble Kalman filter to a groundwater flow system. They not only used it for the prediction of the hydraulic heads in the model area, but also for updating the model parameters in the aug- mented state vector approach. A comparison to Monte Carlo-type inverse modelling showed that parameter estimation with the Ensemble Kalman filter produced similar error statistics but was significantly more efficient in computation [43]. Thus, taking advantage of measurements becoming available in real-time and coupling the groundwater model to the Ensemble Kalman filter proves an excellent means to produce reliable characterisations of the model states. In section 1 of this chapter, the application of the Ensemble Kalman filter for real- time groundwater flow modelling is introduced. A review of the application of the 3D-real-time model in the operation of the Hardhof well field is given in section 2. The Ensemble Kalman filter is then coupled to the 2D-model with stochastic time dependent boundary conditions. This 2D-real-time model is described in the third section.

4.1 Theoretical background

The EnKF has been concisely summarized in an article by Geir Evensen [25] which can be considered an EnKF reference paper. The parameter update with EnKF as implemented by Hendricks-Franssen et al. [44] works in two steps as follows.

Step 1 : Predictions of states − Computation of the states of the current time step Xt with the numerical model − and measurement of the current states Yt. Xt is a matrix of size [number of states (NS) × number of realizations (NR)]. The vector of states is composed of hydraulic heads at each model node point. Optionally, also concentrations or temperatures as well as parameters such as log10 hydraulic conductivities in every model element or log10 leakage factors in every river leakage node can be appended to the state matrix. Yt is a matrix of size [number of measurement locations (NO) × NR]. The general procedure for non-linear models M is to propagate each replicate of the state ensemble to the next time step. That is, a prediction of the states of the time step t is produced based on the model states of the previous time step t − ∆t and disturbances Ut (see Equation 4.1).

− + Xt = M Xt−∆t,Ut (4.1)

The superscripts − and + denote the predicted and updated states respectively. Usually, only one single measurement per observation location is available so the measurement is perturbed with a predeﬁned Gaussian sampling error. Chapter 4 Real-time models 39

Step 2 : Updating of the current states. The Kalman gain Kgain [NS × NO] is computed from the cross-covariances between the state replicates P [NS × NS] and between the measurement errors R [NO × NO]. H [NO × NS] is a matrix that maps the observation locations to the model nodes. P Kgain = (4.2) HP + R The Kalman gain is a measure of how much we trust the model compared to the observations. If the measurements are very accurate R approaches 0 and Kgain approaches 1. If on the other hand the model is much more trustworthy than the observations (P <<< R), Kgain approaches 0. The modelled states are subsequently updated according to Equation 4.3.

+ − − Xt = Xt + αEnKF · Kgain · HXt − Yt (4.3)

Thus, for very accurate measurements, as Kgain approaches 1, the modelled states are corrected with the difference between the modelled and measured states. If the model is more accurate than the measurements and Kgain is close to zero, the modelled states are hardly corrected. αEnKF is a damping factor that takes values between 0 and 1. It defines which states are updated to what amount. Only the parameter updates are damped (αEnKF = 0.1). For state updates, αEnKF is 1. Hendricks Franssen and Kinzelbach [42] found that using the damping parameter reduced problems stemming from filter inbreeding.

Filter inbreeding

Filter inbreeding is caused by overparametrization of the model or a small ensemble size. It shows in the filter becoming over-confident on the model which leads to a reduction of the cross-covariance between the modelled state replicates. If, with filter inbreeding, the bandwidth of the state replicates does not cover at least part of the measurement replicates, the filter is no longer able to update the model states with these measurements. There are several methods to counteract filter inbreeding. The most obvious one is to not underestimate the model error by choosing an adequate ensemble size with a realistic spread. Apart from that, there are empirical methods to correct for filter inbreeding. One is the introduction of the above mentioned damping factor αEnKF, where parameters are updated with a different factor than the model states. Other possibilities of improving filter performance may be distance dependent filtering [45], [38] and covariance inflation [4], [5]. 40 4.2 Review of the 3D real-time model

4.2 Review of the 3D real-time model implemented at the Hardhof well ﬁeld

The real-time model as presented in Hendricks Franssen et al. [44] has been running on-line at the Hardhof well ﬁeld throughout the years up to now. In this section, the year 2011 is looked at in detail. Hereafter, only a brief summary of the implementation of the real-time model is given. Details on the modelling part can be found in Hendricks Franssen et al. [44]. The following section analyses the on-line model’s performance during the application phase 2011 and summarizes the lessons learned.

4.2.1 Implementation of the 3D real-time model

This section is essentially a summary from Hendricks Franssen et al. [44]. The deterministic 3D-groundwater flow model described in section 3.1 on page 3.1 is used to compute the predictions of the model states. The commercial SPRING software [15] is coupled to the Ensemble Kalman filter (EnKF) through a model interface programmed by the engineering company TK Consult AG. The EnKF software is called EnKF3d-SPRING and was programmed in C/C++ by Harrie-Jan Hendricks Franssen [44]. The off-line simulations were done on a 32bit Linux operating system. The calibrated 1 layer parameter set (log10 hydraulic conductivity Y and log10 leakage coefficient L) plus a set of 99 stochastic realizations were fed to the EnKF. The Y -Ensembles were computed based on a semi-variogram which was estimated from measurements. The L-Ensembles are computed from the calibrated parameters plus a normally distributed perturbation. For details on the calibration or how the realizations were obtained refer to Hendricks Franssen et al. [44]. These ensembles are assumed to represent the range of probable realities and form the initial parameter sets of the real-time model. All boundary conditions are deterministic, e.g. the same measured pumping rates are fed to all replicates of the ensemble.

Measurement noise True system

Sensors

Measurement errors

Z t U t

+ - X + X t−1 X t Ensemble t Model update

Figure 4.1: Illustration of the real-time modelling procedure. Depending on whether or not an update was made the previous time step, the modelled or updated states of the previous time steps are fed as initial conditions to the model. Chapter 4 Real-time models 41

The real-time model is run on a daily basis. At time t − 1, the updated states of the + previous prediction time step Xt−1 are used as the initial conditions. The predicted demand for drinking water for the next day determines the abstraction rates for the next day t. Predictions of river discharge for time t are available and fed to the model. Thus, the deterministic model produces a prediction of the states for − time t: Xt . Head and parameter updates were made daily whereby the damping factor αEnKF was 1 for updating the states and 0.1 for updating the parameters. An illustration of the updating procedure is given in Figure 4.1. The real-time model was started in January 2011. The year 2011 is looked at in this section though the real-time model continues to run at the Hardhof well ﬁeld until the present.

4.2.2 The boundary conditions

As described in section 3.1 on pages 18 ﬀ, the deterministic model underlying the real-time model is subject to time varying boundary conditions. The boundary conditions applied in the on-line model in the year 2011 from January to November are described below.

River discharge

The discharge in the rivers Limmat and Sihl is given in Figure 4.2. High flows in summer alternate with low flows in winter. It is noticeable here that normally, the river Sihl only contributes a small fraction of the Limmat discharge. However, there is one event, in the second half of June 2011, where an important precipitation event in the catchment of the river Sihl caused a narrow peak in the discharge of the river Limmat. The catchment of the river Sihl is notorious for very local but strong precipitation events (thunder storms), causing floods with a large transport capacity for debris and dead wood. Flooding from the river Sihl is one of the major natural hazards for downtown Zurich.

Figure 4.2: Time series of discharge of the rivers Limmat and Sihl for the year 2011. 42 4.2 Review of the 3D real-time model

Abstraction and inﬁltration

The year 2011 is a typical year for abstraction (upper graph in Figure 4.3) except for well B which is turned oﬀ most of the year due to renovation of the well. Also the inﬁltration rates over both years are typical (lower graph in Figure 4.3).

Figure 4.3: Time series of abstraction rates in the horizontal filter wells A to D (upper figure) and actual infiltration rates in basins 1 to 3 and in the infiltration wells S1 to S12 for the year 2011.

Areal recharge and lateral inﬂow

Only little areal recharge has been computed for 2011. The lateral inﬂow only takes place when areal recharge is larger than zero. This is an approximation. Lateral inﬂow stems from recharge that occurs on the hill slopes north and south of the model area. The slopes in the north are part of the city and display a similar recharge pattern as the model area. The slopes on the south are mainly covered by forest. More recharge is likely to occur in this area than in the model area. These recharge events are neglected here.

Figure 4.4: Time series of areal recharge rates for the year 2011. Chapter 4 Real-time models 43

4.2.3 The initial parameter set

The 1-layer parameter set (section 3.1.3 on page 22) was used. Hendricks Franssen et al. [44] describe how they estimated the initial ensemble of hydraulic conductivities based on the geostatistical analysis of pumping tests and ﬂow meter tests. Figure 4.5 shows the initial ensemble of leakage values in the 5 leakage zones. The values show a spread of about 1.5 log-units. The log10(K)-values have an average standard deviation of 0.6.

4.2.4 Evaluation of prediction of hydraulic heads

The on-line model, where states and parameters are updated, shows a signiﬁcantly better ﬁt with the observations than the deterministic model, which was computed as a conventional forward run without updates. Figure 4.6 shows the evolution of the mean absolute error (MAE) between modelled and measured observations over the year 2011. The MAE of a given time step has been computed from the summed error over all head observation points in the model area (see Equation 4.4).

NO N 1 X XR Figure 4.5: Initial leak- MAE = |yi,j − (hi · xj)| (4.4) age ensembles in the 5 NRNO i=1 j=1 leakage zones for the year where the index i denotes rows and the index j denotes 2011. columns. The small letters y, h, and x denote scalars, row, or column vectors of the measurement matrix, the mapping matrix and the state matrix respectively, depending on the indices. With both models, the absolute errors in the Hardhof area are smaller than in the east of the model area, where the maximum errors are found. The minimum absolute errors range in the millimeter scale whereas the maximal absolute errors range from 0.5 m to 8 m in the on-line model and from 2 m to 8 m in the deterministic model. The large errors in the east of the model area stem from a huge construction site at the Zurich main railway station that was not taken into account by the model. There, the groundwater table had to be controlled for the construction of railway tracks running underground below the river Sihl and the groundwater table. It was found that neglecting the drawdown at the construction site had little inﬂuence on the performance of the model in the Hardhof area. Generally, the deterministic model is not able to follow the yearly cycle of hydraulic head measurements very well. The ﬁt between simulation and observation is best during the summer months (parameters were also calibrated during warm periods, see Section 3.1.3 on page 22). The deterministic model has trouble simulating the draw down of the groundwater table during periods with high abstraction rates, i.e. 44 4.2 Review of the 3D real-time model

February and March 2011, whereas the on-line model is able to capture the dynamics of the hydraulic head measurements. In November 2011, the large abstraction rates are compensated with large infiltration rates (contrary to the previous two periods). The drawdown around the drinking water production wells therefore is less pronounced and the on-line model is able to capture the evolution of the water table at the observation points. In May 2011, the river Limmat features a flow peak after a prolonged low flow period. This flood event causes the on-line model to overshoot the hydraulic head observations, especially in the locations close to the river.

Figure 4.6: Mean absolute error (MAE) of the on-line model and the deterministic model over the year 2011.

Figure 4.7 shows a representative example of hydraulic head time series computed with the on-line model (with state and parameter updating) and with the deterministic model (no updating) for observation point 3241 located in the middle of the Hardhof well ﬁeld (see Figure 2.10 on page 14).

Figure 4.7: Hydraulic head time series of piezometer 3241 in the center of the Hardhof well ﬁeld.

The deterministic model has a few weaknesses which makes it difficult to reproduce the dynamics of the measurements. The 1-layer parameter set was used. The model Chapter 4 Real-time models 45 probably underestimates the vertical anisotropy in the Hardhof area. A further reason for the inadequacy of the deterministic model may be that the temperature dependence of the leakage-factors as stated by Engeler et al. [22] and the enhanced river-aquifer interaction due to an increase in the wetted perimeter and the flushing of the clogging layer in the river bed during high flow periods were neglected. It should of course be considered that the piezometer 3241 is just one of many piezometers and that overall the deterministic model is performing well as seen from the MAE.

4.2.5 Evaluation of parameter updates

Leakage coeﬃcients

The variation of leakage coefficients over time is given in Figure 4.8. The real- time model was restarted in January 2011 with the calibrated parameter set. The locations of the different leakage zones in the model area is given in Figure 3.3 on page 23. The calibrated leakage coefficient in zone 3, where a fair amount of data

Figure 4.8: Leakage time series for the year 2011. is available for calibration and which is also most influenced by pumping in the Hardhof area, seems to be representative for this area. The value remains more or less constant during the updating period 2011. This can not be said for the other parameters. As the leakage value in zone 1 increases, the value in zone 2 decreases in January. In February, the leakage in zone 2 increases but the one in zone 1 decreases. The leakage coefficients of zones 1 and 2 may be correlated. Indeed, only few head measurements are available in the downstream region, in particular close to zone 1, such that updates of parameters may be non-unique. A similar effect is seen for the two upstream leakage zones 4 and 5. The water that does not infiltrate from the river Sihl has to come from the river Limmat and vice versa. The average initial leakage coefficient of all 5 zones amounts to 10−4.6 m/s = 2.5 · 10−5 m/s whereas after updating, the average leakage coefficient increased to 10−4.3 m/s = 5 · 10−5 m/s. No immediate reaction of the leakage values to floods in the rivers Limmat and Sihl can be detected. Kurtz et al. [52] showed that it may take several months for the 46 4.2 Review of the 3D real-time model leakage values to adapt to new hydraulic conditions of the river bed under the same updating conditions as applied here.

Hydraulic conductivity

Also hydraulic conductivities in all elements of the model were updated. Figure 4.9 shows the spatial distribution of the ensemble average of 100 replicates of log10 conductivity values in layer 5 at 6.7 m depth below soil surface. The average of the ensemble of the hydraulic conductivity ﬁeld in the same layer after one year of updating with the updating scheme described above is given in Figure 4.10. All layers look similar therefore only one is shown here.

Figure 4.10: Average of the hydraulic Figure 4.9: Average of the initial hy- conductivity ensemble after 1 year up- draulic conductivity ensemble. dating.

The heterogeneity of the hydraulic conductivity values has increased considerably through the updating procedure. The ﬁeld gets patchy and some values get unreal- istically high. While the minimum and maximum values in the average of the initial ensemble range from 10−3.04 = 9.1 · 10−4 to 10−1.91 = 1.2 · 10−2 m/s, the updated ensemble features values in the range between 10−5.82 = 1.5 · 10−6 and 10+0.87 = 7.4 m/s in layer 5 (which is representative for all layers). However, the average hydraulic conductivity over the whole model area changes only little through the updating period: from 10−2.67 = 2.1 · 10−3 m/s in the initial ensemble to 10−2.76 = 1.7 · 10−3 m/s in the updated ensemble.

4.2.6 Conclusions

Generally, the on-line model shows an excellent performance when it comes to the prediction of hydraulic heads. Contrary to the conventional forward simulation, real-rime modelling with state and parameter updating allows a prediction of highly dynamic head time series which is accurate enough for use in the real-time control of the ﬂow ﬁeld. Chapter 4 Real-time models 47

However, there are pitfalls to state and parameter updating with the Ensemble Kalman filter. For one, the ensemble needs to be fairly large (at least one hundred replicates) to allow for stable matrix arithmetic and to avoid filter inbreeding. Such large ensembles slow down the simulation considerably. Further, the EnKF assumes that the conceptual model (grid resolution, boundary condition types, etc.) is per- fect (no error source). The ensemble of states and parameters needs to reflect the actual uncertainty of the system state and parameters. For the states this can be estimated fairly well. For the parameters K and the leakage coefficients this is very difficult. The EnKF is sensitive to initial ensembles. And last but not least, there are no physical boundaries to the parameter updates as for example Wang et al. [84] criticise. This is why the resulting updated parameter fields become patchy with areas of unphysically high parameter values right next to very low values. It remains to be seen, whether joint updating of states and parameters is advanta- geous to the additional modelling of known processes as for example the temperature dependence of the river-aquifer interaction or the increased leakage flux during high river water tables. Doubts are permitted especially since the Ensemble Kalman filter is not able to immediately react to sudden changes in the parameter values as has been shown by Kurtz et al. [52]. The deterministic model and thus also the on-line model could still be improved. Engeler et al. [22] for example found a significant reduction of the head residuals when including temperature dependent leakage fluxes into their deterministic model. Automatic temperature correction of the leakage values was implemented as an option in the parallelised version EnKF3d-SPRING developed by Kurtz et al. [53].

4.3 The 2D real-time model

The 3D real-time model presented in the previous section (section 4.2 on page 40) is accurate enough for the control of the flow field. However, its computation time is considerable. The propagation of 100 replicates through one time step takes approximately 30 minutes. This is not too long for the operation in the water works since they only need to compute one time step per day. However, in order to design an optimal control routine, the model should be as fast as possible because most optimizers require multiple model calls. So, for the optimization of the infiltration rates in one time step, 200 iterations may easily be required for the optimizer to reach a stop criterion, leading to over 4 days optimization time for the 3D real- time model. Further, the control routine should not be devised for one time step but for a longer time period featuring the most important hydraulic conditions in the Hardhof area. That means even if only control over a time period of 10 days is optimized, the simulation time amounts to over 40 days! Therefore, a faster 2D model has been coupled to an Ensemble Kalman filter in Matlab [59] for the intended ensemble based control. The procedure as well as the validation of the 2D model are presented below. 48 4.3 The 2D real-time model

4.3.1 Implementation of the 2D real-time model

Matlab [59] was used to program the model-EnKF-interface. EnKF was imple- X 0, U t - mented after Evensen [25]. The model I/O X t−1, U t was adapted from EnKF3d-SPRING de- MATLAB SPRING - scribed in the section 4.2. For each time X t step, Matlab writes the initial and bound- EnKF ary conditions to the SPRING model files, runs the simulation in SPRING, and reads Figure 4.11: Conceptual set-up of the the results back to Matlab. All reads and 2D real-time model. writes are done from hard disk. See figure 4.11 for an illustration of the interaction between Matlab and SPRING. Whereas in the 3D real-time model described in section 4.2 state and parameter updates were made on a daily basis, only states were updated daily in the 2D real-time model. The parameters K and leakage were updated every 10th day with a damping factor of 0.1. In addition, covariance matrix inflation as applied in Kurtz et al. [52] was used on the states in the 2D real-time model.

4.3.2 The boundary conditions

As described in section 3.1 on pages 18 ﬀ, the deterministic model underlying the real-time model is subject to time variant boundary conditions. The boundary conditions applied in the 2D oﬀ-line model in the years 2006 to 2011 are described below.

River discharge

The discharge in the rivers Limmat and Sihl is given in Figure 4.12. Generally, high ﬂows in summer alternate with low ﬂows in winter. From these river discharge data, the river water tables at all river nodes of the model are computed using previously computed quadratic interpolation functions (see section 3.1.1 on page 19 for details).

Figure 4.12: Time series of discharge of the rivers Limmat and Sihl for the years 2006 to 2011. Chapter 4 Real-time models 49

Abstraction and inﬁltration

Wells C and D were shut oﬀ during a major construction in the Hardhof area in 2008 and 2009 (upper graph in Figure 4.13). Additional wells were operated to lower the groundwater table in the Hardhof area. These, however, could not be implemented in the model because the exact locations of the pumps, the pumping rates, and the duration of the individual pumping periods are not available. Two periods of construction and pumping during a steady-state tracer test in 2006 could be accounted for by increasing the pumping in wells C and D by the documented amounts. The inﬁltration rates over the years 2006 to 2011 are given in the lower graph in Figure 4.13.

Figure 4.13: Time series of abstraction rates in the horizontal filter wells A to D (upper figure) and infiltration rates in basins 1 to 3 and in the infiltration wells S1 to S12 for the years 2006 to 2011.

Areal recharge and lateral inﬂow

Areal recharge is computed with evapotranspiration according to the Penman-Monteith method [3] using climate data from the Swiss meteo station Reckenholz (For details see section 3.1.1 on page 21).

4.3.3 The ensembles

The ensembles are created in Matlab. Realistic measurement errors are estimated for initial and boundary conditions. For each input, 49 realizations are drawn from a normal or from a Log-normal distribution with the observed value as mean and an estimated standard deviation. Latin hypercube sampling (lhs) according to the method of Stein [74] was used. Budiman Minasny of the University of Sydney 50 4.3 The 2D real-time model

Figure 4.14: Time series of areal recharge rates for the years 2006 to 2011. provided the Matlab routine for the lhs method via the Mathworks ﬁle exchange network1. The measured boundary conditions and the calibrated parameter set present one additional realization. Therefore a total of 50 realizations is simulated at each time step. Generally, two types of errors are taken into account. One concerns a systematic error where the whole time series might be measured too high or too low. The other concerns point measurement errors. Both errors are assumed to be mutually independent and therefore may be added up linearly. The exact procedures are given below.

Initial heads

Only the heads of the first time step are perturbed. All following head ensembles are computed with the distributed groundwater flow model. An error of 10 cm is estimated for both, the distribution of the initial head field and for the hydraulic heads at each model node. That is, the groundwater table might be on average higher or lower than the interpolated one and each node might show a higher or lower hydraulic head than estimated. In Figure 4.15 realization 1 of the initial heads is shown. Figure 4.15: Initial head distribution.

Hydraulic conductivities

The errors of the hydraulic conductivity values are assumed to be log-normally distributed. The variance of the ensemble used in Hendricks Franssen et al. [44] was also used here. It had to be reduced for numerical stability of the 2D-model by 0.2 log-units. Further, the variance of the ensemble was reduced in the Hardhof area where a high density of conductivity observations is available and thus the K-values

1http://www.mathworks.ch/matlabcentral/fileexchange/4352-latin-hypercube-sampling, retrieved October 29, 2013. Chapter 4 Real-time models 51 are better known. In order to balance the reduced variance from the 3D model, the entire K-ﬁeld is assumed to have a systematic error of 0.3 log-unit meaning that the average K-ﬁeld may be higher or lower than in the ensemble provided by Hendricks Franssen et al. [44]. Figures 4.16 and 4.17 show the K-values of realizations 1 and 13.

Figure 4.16: Average of the initial hy- Figure 4.17: Realization number 13 of draulic conductivity ensemble of the 2D- the initial hydraulic conductivity ensem- model. ble of the 2D-model.

Leakage coeﬃcients

The errors of the leakage coeﬃcients are assumed to be log-normally distributed. The ensemble from Hendricks Franssen et al. [44] was used but, as for the hydraulic conductivities, the variance of the ensemble had to be reduced for the 2D model (see ﬁgure 4.18). In this case, the variance was reduced by 1 log-unit and the bias was set to zero.

Figure 4.18: Ensemble of zonal leakage factors used for the real-time simulations of the years 2006 to 2011. The color code corresponds to the one in Figure 3.3 on page 23 where the locations of the 5 leakage zones in the model grid are shown. 52 4.3 The 2D real-time model

Fixed potential

A hydraulic head measurement is used as a ﬁxed potential at the outﬂow boundary. It has an estimated measurement error of 5 cm. The measurement error was estimated based on the documentation of the half-yearly calibrations of the measurement devices used by the water works. Although the observation location is operated by the Canton of Zurich and not by the water works, the same measurement error as for the water works observation locations is assumed for simplicity reasons. Figure 4.19 shows the resulting ensemble of 50 replicates used for the 2D simulations.

Figure 4.19: Ensemble of ﬁxed heads at the outﬂow boundary for the years 2006 to 2011. The black line denotes the measurement and the gray lines constitute the stochastic realizations.

Areal recharge

Recharge events are drawn from a Poisson distribution with a λ-value of 1.6 ·10−4. Further, a 50 % compounded error is assumed originating from the computation of the areal recharge from the climate data yielding the following ensemble for the areal recharge (see ﬁgure 4.20).

Figure 4.20: Ensemble of areal recharge for the years 2006 to 2011. The black line denotes the mean and the gray lines constitute the 49 stochastic replicates. For illustration, one day with areal recharge is zoomed in on (blue box).

Pumping rates

A measurement error of 5 % for the individual pumping rates and a bias of 20 % for the flow measurements are assumed. Figures 4.21 and 4.22 show the ensembles for the abstraction and infiltration rates. The infiltration wells S 1-6 were not operated in that time period. Chapter 4 Real-time models 53

Figure 4.21: Ensembles of abstraction rates for the years 2006 to 2011. The dark lines denote the measured values and the light lines in the same color constitute the stochastic replicates.

Figure 4.22: Ensembles of inﬁltration rates for the years 2006 to 2011. The dark lines denote the measured values and the light lines in the same color constitute the stochastic replicates.

River head data

The interpolated river head data are assumed to have an error of 5 cm (see ﬁgure 4.23 for the river water level at a river node in the Hardhof area).

Figure 4.23: Ensemble of river head data at model node no. 750 for the years 2006 to 2011. The black line denotes the mean and the gray lines constitute the ensemble.

4.3.4 Evaluation of prediction of hydraulic heads

Figure 4.24 shows the mean absolute error (MAE) of the real-time model and the deterministic model over time. The formula for the computation of MAE is given in equation 4.4 on page 43. 54 4.3 The 2D real-time model

Figure 4.24: Mean absolute error (MAE) of the real-time model and the deterministic model over the years 2006 and 2007.

For both, the real-time and the deterministic model, the model errors are larger in the year 2006 than in the year 2007. This can be explained by the fact, that the pumping regime in 2007 was much more regular than in the year 2006. The generally larger MAE in the 2D models than in the 3D models mainly stems from the observation points far away from the Hardhof which are not reproduced well with the 2D model. However, the 2D model displays a very good performance in the Hardhof area. As for the 3D real-time model, the time series of modelled and observed head at location 3241 are shown (ﬁgure 4.25).

Figure 4.25: Head time series at point 3241 computed with the real-time model and the deterministic model over the years 2006 and 2007.

Both, the deterministic and the real-time model are very accurate during the year 2007. Contrary to the 3D real-time model (section 4.2) the 2D real-time model does not significantly improve the 2D-deterministic model as was seen in the 3D real-time model . This is on one hand due to the already good performance of the deterministic model and on the other hand due to a probably sub-optimal tuning of the filter inbreeding correction. If the filter inbreeding correction is insufficient, the covariance matrix of the model contains small values compared to the measurement uncertainties, leading to a narrowing of the state prediction ensemble. Thus, EnKF trusts the model more than it should compared to the observations and it hardly updates the model predictions. The performance of the real-time model could probably be improved considerably by reviewing the filter inbreeding correction. Figure 4.26 shows the same time period as figure 4.7 on page 44 that was computed Chapter 4 Real-time models 55 with the 3D model. Contrary to the 3D deterministic model, the 2D deterministic model is able to reproduce a lot of the yearly head dynamics at observation point 3241. This can be partly explained with the use of slightly different parameter sets in the 3D model and in the 2D model. The leakage factors of the 2D model are higher than those in the 3D model. The hydraulic conductivities are the same in both models. Another influence on the dynamics of the models is the implementation of the infiltration and abstraction rates. In the 3D model, the artificial recharge through the basins is implemented in the first layer of the model. The infiltration from the injection wells, the abstractions in the horizontal drinking water wells and the river bank filtration wells are implemented in the layers which correspond to the filtered depth of the wells. Due to the neglecting of 3D effects in the hydraulic conductivity field in the 3D model (except for a 10-fold reduction of the vertical hydraulic conductivity), the head dynamics in the Hardhof can therefore be underestimated. In the 2D model, all infiltration and abstraction is distributed over the entire aquifer depth which increases the head dynamics in many Hardhof observation points.

Figure 4.26: Head time series at point 3241 computed with the real-time model and the deterministic model over the year 2011.

4.3.5 Evaluation of parameter updates

Figure 4.27 shows the updated leakage values over time for the 2D real-time model run in 2006 through 2007. The leakage values are averaged in each of the 5 leakage zones. Significant changes are only made in the first few updating steps. It seems that the initial leakage values are slightly too high for the 2D model. Figure 4.28 shows the average initial K-values whereas figure 4.29 shows the average of the updated K-values (after 2 years of updating). The general pattern is the same in the initial field and in the updated field: The hydraulic conductivity in the east is lower than in the west in both fields. However, in the updated K-field, the area of increased conductivity has become more conductive and has shifted to the north. 56 4.3 The 2D real-time model

Figure 4.27: Leakage time series for the years 2006 and 2007 computed with the 2D real-time model.

Figure 4.29: Average of the hydraulic Figure 4.28: Average of the initial hy- conductivity ensemble after 2 years up- draulic conductivity ensemble. dating.

4.3.6 Conclusions

Though the real-time model adapts the parameters, its performance is not significantly better than the deterministic model if the boundary conditions are well known (as in the year 2007). There is still a considerable distance to observations where a higher weighting of observed values would improve the real-time model. Generally the filter is overconficent of the accuracy of the model. This deficiency can probably be improved by reviewing the parameters of the filter inbreeding correction. Chapter 5

Real-time control of the Hardhof well ﬁeld

5.1 Introduction to real-time control of non-linear systems

Dynamic systems, be it the trajectory of a bicycle or the distribution of valuable water among various shareholders, need steering and correction of the steering in real-time. The steering of a bicycle is a classical example for real-time control: A bicycle rider can determine a trajectory before starting it. However, he has to constantly correct the balance of the cycle using his weight and the handle bar. He is doing real-time control of the bicycle-rider system. Similarly complex but on a different level is the second example: Resources like drinking water are highly under pressure in densely populated areas as for example the Swiss midland. Various shareholders compete for these resources within short distances in space and time. This results in highly dynamic systems which need to be managed in real-time. However, only in recent years have measurement devices which are able to transfer data in real-time become available at reasonable cost. Therefore real-time management has only recently become a valid option for the control of environmental systems. In the following chapter the real-time control of an aquifer, the Hardhof well field, is presented. A control influences a system such that the output of that system follows a given reference signal [36]. A control is optimal when no improvement of the system output with respect to the reference signal can be achieved. For linear systems having only one input signal and one output signal, optimal controls can be derived analytically [36]. However, things get more complicated for non-linear systems with multiple input and output signals. The Hardhof well field for example is a non-linear system with multiple in- and outputs. The infiltration rates of several artificial recharge infrastructures (system inputs) have to be managed at the same time as the hydraulic barrier has to be maintained south of the well field (system output). The hydraulic barrier can be controlled at one single location or, better, at several locations along the south of the well field. Non-linearity may also be found in the system itself: An aquifer may be a variably saturated groundwater body making the groundwater flow equation non-linear. Another part of the non-linearity can arise in the evaluation of the control criterion. But more on this later in this chapter. 58 5.1 Introduction to real-time control of non-linear systems

One way to deal with such systems is model predictive control [34] in which the reaction of the system to a given control is simulated with a model. Figure 5.1 shows the schematic procedure for a model predictive control where measurements of the system output provide a feedback to the control loop.

ε ũ ̃y t−1 System t

Y t

X - X + Model t EnKF t

u t−1 Control

Figure 5.1: Overview over a model predictive control scheme as applied in this study.

− The model produces an ensemble of probable system outputs Xt based on the given disturbance ut−1 and ensembles of initial conditions and boundary conditions. The control routine uses an optimizer to find the optimal values for ut−1 which requires several iterations, i.e. model runs. Once the predefined stop criterion of the optimizer is met, the disturbances ut−1 are applied to the real system. Based on the forcing u˜t−1 (e.g. infiltration rates), the system produces the output y˜t (e.g. hydraulic heads). ut−1 and u˜t−1 are not necessarily the same: unknown disturbances influence the actual input to the system. The output can be measured at discrete locations which implies measurement error ε with known distribution. Sampling from this distribution yields a given number of replicates of y˜t which are stored in the matrix Yt. The ensemble Kalman filter then combines measurements and model + predictions to produce updated model predictions Xt . While some groundwater systems only need seasonal management (i.e. aquifers, which are sparsely used or where the effect of short-term non-optimality of the management has little effect on the quantity that needs to be controlled), others are highly dynamic and require more frequent decisions. The Hardhof aquifer is such a system. The well field lies close to the river Limmat which has a major influence on the groundwater flow field as well as the groundwater quality. Further, abstraction rates are adapted on a daily basis, depending on the predicted drinking water demand. Therefore, also the conditions for the hydraulic barrier change on a daily basis and the infiltration has to be adapted accordingly. Gero Bauser designed the first management strategies for the Hardhof well field [6]. In the following, a review of the performance of Bausers control in the Hardhof well field is given. Then, new control strategies which were designed within the scope of this thesis are presented and discussed. Chapter 5 Real-time control of the Hardhof well field 59

5.2 Lessons learned from current control schemes

A real-time control, developed by Bauser et al. [8] has been operational with the 3D real-time model, developed by Hendricks Franssen et al. [44] (described in section 4.2) over the year 2011. This section summarizes the method applied by Bauser et al. [8] for the real-time control and reviews its performance during the application period in 2011.

Method of stream line based control

For details on the method the reader is asked to refer to Bauser et al. [8]. Basis of the control is the 3D real-time model by Hendricks Franssen et al. [44] described in section 4.2 on page 40 ff. Bauser et al. [8] optimize the infiltration rates in the 3 basins, one infiltration well group (S 1-6) and the wells S 7, S 8-10 and S 11- 12 on a daily basis. The goal of the control is to minimize the percentage of city water by maintaining a hydraulic barrier along the south of the well field while not infiltrating excessively. In order to do that, they freeze the flow field and trace 1350 virtual particles from each of the 4 horizontal drinking water wells (A to D) back along the flow field for 200 days. If the particle path lines cross a boundary line (along the southern lane of the highway south of the well field), the water transported in the streamline following the particle path line is assumed to produce potentially contaminated city water. The number or stream lines crossing the boundary line is weighted with the abstraction rate in the well the particle started from and allows to compute the amount of city water pumped. The percentage of city water (%s) in the horizontal wells has been shown to correlate well with the electrical conductivity measurements in the same wells [7], [6]. A fuzzy logic rule set was used as the rule base for the control. Each infiltration infrastructure is assigned an infiltration rate on the basis of a function parameter that is determined with a genetic algorithm and by the percentage of city water. The goal function of the optimization is to minimize a weighted sum of the infiltration rates and the squared difference between the simulated percentage of city water and a pre-defined reference value for the percentage of city water.

Results from on-line application 2011 and discussion

Figure 5.2 shows the simulated percentage of city water (%s) during the year 2011 and the respective electrical conductivity (EC) measurement in well C. The computed percentage of city water is very low (< 1 %). The general decrease of EC in Figure 5.2 happens over several months and can not be attributed to the changed management. Figure 5.3 shows the development of the electrical conductivities in the river Limmat and in well C over the year. The curves are parallel most of the year except for the summer months and for the EC peaks in well C in October and November. During these times well C can be assumed to receive more city water than in the winter months. This is partly conﬁrmed with the increased percentage of city water in July and November. This seasonality of the EC measurement, however, is not reproduced by the percentage of city water. During the bank ﬁltration, 60 5.2 Lessons learned from current control schemes the dissolved ion concentration increases due to a reduction of the redox potential. This process is neglected in the patricle tracking method applied by Bauser et al.

Figure 5.2: Percentage of city water during the application period 2011 and the electrical conductivity. Both measurements are taken in well C.

Figure 5.3: Electrical conductivity measured in well C and in the river Limmat in the year 2011.

Well C was operated regularly during the year 2011, except for two periods with increased abstraction rates in mid March and in the end of November. It was turned off for a few days in the first half of November (see figure 4.3 on page 42). The peaks of abstraction rates in March and November are reflected in an increased fraction of city water in well C in the same time periods. However, the increase is tempo- rary since the increased abstraction can be covered with an increase in infiltration (figure 4.3) which leads to a decrease in both, electrical conductivity and %s in the second half of March and in November. During high flow periods, i.e. in July (figure 4.2 on page 41), electrical conductivity goes down whereas %s goes up. This could be an indication, that the model overestimates the inflow of city water during high flow periods. Further events of figure 5.2 are difficult to interpret. It is not possible to explain the sudden increase of %s in mid May with the measured data. Nor can the peak in the EC measurement in well C end of October be explained. Figures 5.4 and 5.5 illustrate the infiltration rates suggested by the real-time control Chapter 5 Real-time control of the Hardhof well field 61 algorithm and the actually applied infiltration rates in the two main recharge infrastructures for well C (Basin 2 and the infiltration wells S 7-12). Here, the infiltration in wells S 1-6 is zero so the graph in figure 5.5 shows only the infiltration in wells S 7-12. Technically, the separation of the infiltration wells S 7-12 in smaller groups is not possible. Only the total inflow to the wells can be controlled. The distribution between the wells is fixed by an overflow and by their respective infiltration capacities. Therefore the infiltration in the 6 wells S 7-12 is summed up.

Figure 5.4: Suggested and applied inﬁltration rates in basin 2 during the year 2011.

Figure 5.5: Suggested and applied inﬁltration rates in the inﬁltration wells S 7-12 during the year 2011.

The focus of the infiltration lies on the infiltration wells S 7-12. Their strategic location between the basins and between the drinking water wells and the city area (see figure 1.1 on page2) explains their importance. The comparison of figure 5.2 to figures 5.4 and 5.5 shows that the suggested infiltration rates for basin 2 and the infiltration wells S 7-12 follow the computed percentage of city water in well C. Further, the applied infiltration rates in basin 2 follow the suggested rates parallelly. This is not the case for the applied infiltration rates in the infiltration wells S 7-12. In mid April or in August for example, the applied infiltration rates were increased instead of decreased as the management model suggested. There is no apparent explanation to the increase of the infiltration rates in August visible from the available data. Of course it has to be noted that the model suggests considerably high infiltration rates which could not be realised. Once the 62 5.2 Lessons learned from current control schemes suggested rates decrease the recommended infiltration rate is followed. The actual infiltration in the Hardhof well field is subject to several constraints which were not included in the control developed by Bauser [6]. The load on the slow sand filtration basins should be as constant as possible or at least the basin should not run dry such that the filter cake (the biologically active clogging layer that forms at the surface of the filter) can fulfil its function. Further, the maximum possible infiltration rate of the basins depends on the filter age. With increasing operating time, the filter gets clogged and the infiltration capacity decreases up to a point where the filter bed has to be renewed. A similar clogging occurs in the infiltration wells. The operator therefore should be able to limit the upper bounds of the infiltration infrastructures manually. A further constraint of the infiltration rates is the danger of water logging in the Hardhof area. High infiltration rates as they are suggested by the real-time controls developed by Bauser [6] lead to an excessive rise of the groundwater table in the Hardhof area. Figure 5.6 shows the suggested and applied ratio of total infiltration rate over total abstraction rate (infiltration-abstraction ratio, iar) in the Hardhof area (only abstractions in the horizontal drinking water wells are accounted for, not the river bank filtration wells). Generally, the iar of both the suggested and the applied management are similar. In the case of mid September, where the infiltration-abstraction ratio is above 12, the abstraction rates were very low (see Figure 4.3 on page 42). In this special case, such a high ratio is feasible and even makes sense over a short time period in order to keep a constant load on the infiltration infrastructures.

Figure 5.6: Suggested and applied ratio between total inﬁltration rate and total abstraction rate in the Hardhof well ﬁeld.

Conclusion or "lessons learned"

The control developed by Bauser [6] showed excellent performance under controlled conditions (assuming the Hardhof operators are able to follow the suggested infiltration rates to the point). However, it fails when additional constraints to the infiltration rates as time-variant maximum infiltration capacities or constraints on the water level in the Hardhof area become relevant. By including these constraints the Hardhof operators should be able to follow the suggested infiltration rates more Chapter 5 Real-time control of the Hardhof well field 63 closely. Satisfying more constraints however, will probably reduce the ability of a control to minimize the inflow of city water to the well field to as low a level as shown by Bauser [6].

5.3 Expert system control

The content of this section is based on a publication by Marti et al. in the journal Water Science and Technology: Water Supply[58].

5.3.1 Introduction

Groundwater is the most important drinking water resource in Switzerland. The natural reservoirs typically lie in valleys and are mainly fed by infiltrating water from rivers. However, also the major part of the Swiss population lives in valleys close to rivers. Thus, the pressure on the quality of the drinking water resource is high. Industrial sites, transportation lines for hazardous materials, sewage lines, and old waste disposal sites result in a high potential for groundwater contamination and constitute a considerable challenge for well field operation. In this paper we present the methodology for the design of an expert system (ES) for real-time well field management and apply it to a case study: Hardhof well field in Zurich, Switzerland. Well field management became popular in the 1980ies with the optimization of pump and treat schemes in groundwater remediation (e.g. [33], [32]). The solutions to the optimization problems were obtained analytically for simple groundwater flow con- figurations. However, these analytical solutions are not applicable to general groundwater flow problems with complex geometry. Alternative management strategies for reservoirs have been proposed for synthetic problems (e.g. Gordon et al. [31]). The first successful applications of real-time management of underground reservoirs have been implemented in the oil industry (e.g. Saputelli et al. [67]). With the increasing availability of online measurements of hydraulic head and water quality indicators, real-time management of groundwater becomes relevant (e.g. [7], [14]).

Site description

The well field is fed directly by the river Limmat in the north and west. In the south, it is artificially recharged with river bank filtrate in 3 infiltration basins and 12 infiltration wells (Figure 1). Through this recharge, the capacity of the well field is increased and a hydraulic barrier against potentially contaminated water from the former waste disposal site Herdern is formed. The dimension of the solute plume spreading from the Herdern site westwards was determined by Geologisches Büro Dr. Heinrich Jäckli AG [28]. In 2001, Kaiser analysed the origin of the water drawn in the four horizontal wells [48]. Based on these studies the water in the four drinking water wells can be assigned either to river bank filtrate (low electrical conductivity (EC) close to the one of the river Limmat) or to city water (groundwater coming from below the city area and possibly passing through the Herdern site, characterized by 64 5.3 Expert system control elevated EC). A detailed description of the Hardhof well field including technical data can be found in Bauser et al. [7]. Central to this well field is that the drinking

Figure 5.7: Overview over the Hardhof well field. River bank filtrate is drawn in 19 bank filtration pumps and recharged to the aquifer through 3 infiltration basins (I, II, and III) and 12 infiltration wells (S1 to S12). Drinking water is drawn in the four horizontal wells A, B, C, and D and pumped to the different pressure zones of the drinking water distribution network of the city of Zurich. water quality is not only influenced by pumping rates in the production wells but to a considerable part by the artificial recharge. Although ES may be applied for the management of any well field this work focuses on well fields heavily influenced by artificial recharge. For this study daily measurements of hydraulic head in 85 locations are available for the years 1992 to 2011. The locations of the piezometers are given in Huber et al. [46]. Furthermore, the daily pumping rates of all wells and basins as well as daily discharge data of the rivers Limmat and Sihl, precipitation and climate data are given.

5.3.2 Method

An Expert System (ES) is a collection of logic rules mimicking expert knowledge. It is a widely applied decision support system (e.g. [70]). The principal layout of an ES follows a tree of if-then-relationships, leading from a given situation to a decision. The algorithm follows human reasoning and therefore it is intuitive and easy to understand. In order to establish the if-then-relationships, a knowledge base has to be built. In our case, this is done by analysing the daily time series of model input and output data. For the design of the ES we proceed in four steps: • Phase 1: Modelling the well field. • Phase 2: Building of the knowledge base; expert knowledge is gathered, the control and actuating variables that influence the control variable are determined. Chapter 5 Real-time control of the Hardhof well field 65

• Phase 3: Setting up of the rule base of the ES; the knowledge is organized in a set of if-then-relationships leading from a given situation to a decision. • Phase 4: Identifying parameters and adjusting the rule base; The ES is itera- tively calibrated on the design period and validated on a new set of data.

Phase 1: Modelling the well ﬁeld

The design of a new management strategy often cannot be done in the real well field because flawless operation of the well field cannot be guaranteed during the design phase. Therefore, a model of the well field is needed which reproduces the relevant processes of the real well field with an appropriate accuracy over the management horizon. In the present case, the drinking water quality has to be maintained at an appropriate level. The relevant information for management is the distribution of hydraulic head in the aquifer and the quality of the water in the four drinking water wells. The management horizon in this case study is one day. The well field is modelled with a transient 3-dimensional finite element groundwater flow model (SPRING 3.4, delta h [15]). The model was calibrated with a modified pilot point method similar to Alcolea et al. [2]. Because of computational constraints (large number of nodes) and the large uncertainty of the input data for solute transport (i.e. the initial and boundary conditions), fully coupled flow and solute transport modelling for the Lim- mat valley aquifer at sufficient speed is still a challenge up to now. Bauser et al. [7] therefore implemented a particle tracking tool which they coupled to the groundwater flow model to verify the origin of the water in the drinking water wells. Particles are tracked back from the four horizontal wells along a quasi-steady-state flow field until they either pass the virtual boundary between Hardhof and city area (along Highway A1 in Figure 1) or it is clear that the particle path lines do not lead to the city area (i.e., when they reach a control boundary, e.g., the river bank). Thus Bauser et al. [7] were able to compute the fraction of water in each well coming from the city area, hereafter called fraction of city water. They further showed that the fraction of city water can be used as an indicator for water quality in the drinking water wells. A detailed description of the particle tracking tool is given in Bauser [6]. More details on the model can be found in Hendricks Franssen et al. [44]. We use their deterministic central model in the present study.

Phase 2: Building of the knowledge base

A throughout process oriented understanding of the system was necessary for the modelling of the system. In this phase now the knowledge about the system is organized in a control oriented manner: The control variable as well as the relevant disturbances are determined. In the case of well field management the control variable can be the produced water quality or the pumping rates in the wells. In this work we focus on the drinking water quality. Relevant disturbances with regard to drinking water quality in a well field are processes which dominate the flow field (i.e. recharge and abstraction of groundwater) or sources of pollution (e.g., periodicity or threshold behaviour). In order to be controllable, the disturbances have to be 66 5.3 Expert system control known. Unknown or minor disturbances are treated as uncertainties of the model. Figure 5.8 shows the concept of the control oriented system description where Σ denotes the model of the system to be managed. The simulated water quality (the output of the model Σ) is fed back to the input of the ES. We will refer to it as the feedback variable. Already, the major sources and sinks of the system are known from phase 1, the

Figure 5.8: Concept of the control loop. Σ denotes the model of the system to be managed. Note that the simulated water quality is fed back to the input of the ES. modelling of the system. Delay times between the disturbances and the control variable may be found through the analysis of Pearson’s cross-correlation between each major disturbance and the control variable. The delay times of the system should be veriﬁed for example with an estimation of travel times in the aquifer and taken into account in the input of the ES.

Phase 3: Setting up of rule base

In order to cope with the multiple inputs to the ES we propose to combine the impacts of the disturbances and the feed back variable on the simulated water quality in one artificial variable. This variable contains the information about how probable a reduced water quality in the current management horizon is. First, each of the i = 1,...,N disturbances and the feedback variable are attributed a weight wi. As a first guess this weight corresponds to the maximum of Pearson’s cross-correlation. The weight wi accounts for the relative impact of the input variable i to the ES on the output of the model. The following steps are accomplished for each management horizon: • For a first guess the input variables are classified approximately according to their 30th, 60th, and 90th percentile and attributed a value vi. For example invalid measurements are classified as “no measurement” and attributed the value 0. Values below the 30th percentile are classified as low and attributed the value 1. See Table 5.1 for an overview of the classes and the corresponding values. • The values of the input variables are then multiplied with the weights of the P variables and summed up over all input variables (wi · vi). The resulting value is a measure for the probability of an impairment of the drinking water quality in the given time step. • The resulting value is again classified into low, medium, high, and extreme and an infiltration scheme is attributed. The infiltration scheme determines the Chapter 5 Real-time control of the Hardhof well field 67

amount of artificial recharge and (if necessary) its distribution to the artificial recharge infrastructure(s). For the determination of the infiltration scheme expert knowledge again plays a central role. The artificial recharge modifies the flow field of the groundwater and the expert has to understand in which way it has to be changed in order to maintain an appropriate water quality.

Table 5.1: The values of the classes and the initial and adjusted parameters of the ES.

Initial guess Adjusted values Class Value QC (t) frC (t − 1) hL(t − 14) QC (t) frC (t − 1) hL(t − 14) [-] [m3/d] [-] [m a.s.l.] [m3/d] [-] [m a.s.l.] No value 0000 ≤00’000 ≤0 ≤395.0 ≤00’000 ≤0 ≤396.0 Low 0001 ≤02’500 ≤0.05 ≥398.9 ≤02’500 ≤0.05 ≥398.9 Medium 0010 ≤06’500 ≤0.10 ≥398.4 ≤06’500 ≤0.10 ≥398.5 High0100 ≤12’000 ≤0.20 ≥398.2 ≤10’000 ≤0.20 ≥398.3 Extreme 1000 >12’000 >0.20 <398.2 >10’000 >0.20 <398.3 Weight w 00-<0.5<0.8<0.2<1<0.8<0.8

Phase 4: Identiﬁcation of parameters

The well ﬁeld management is now simulated with the ES management and the parameters of the ES (weights, values of the classes) are adapted manually where needed. If the calibration of the ES is satisfactory, a validation period is simulated.

5.3.3 Results

An expert system was designed according to the methodology described above to manage the water quality in the Hardhof well field. The simulation of the well field management is based on historical data. The following paragraphs describe the design phases 2 to 4 (phase 1, the modelling of the well field, is described in detail in Bauser et al. [7], Hendricks Franssen et al. [44], and in section 4.2).

Phase 2: Building of the knowledge base

The goal of the ES is to maintain a high water quality in the Hardhof well field by adapting the amount and distribution of water infiltrated in basins I to III and in the injection wells S1 to S12. Due to its location close to the southern boundary of the well field, well C is the most vulnerable one to withdraw city water. This is confirmed by the measurement of EC in the drinking water wells, with the highest values in well C. For the ES, we thus only use the fraction of city water in well C frC from the model output. For the decision about the infiltration scheme of the next time step the fraction of city water of time step t − 1 is fed back to the input of the ES. The desired water quality is zero percent of city water in well C. In this study we assume that the Herdern deposit constitutes a constant source of 68 5.3 Expert system control pollution. Therefore, we can concentrate on the flow field as the major influence on the quality of the drinking water. The factors influencing the flow field are the recharge and the abstraction from the aquifer. The major abstractions in the Hardhof area are effected by the Zurich water works. The rates are determined by the demand of the city of Zurich and regarded as known disturbances in this work. So is the distribution of the abstraction in the four drinking water wells. Recharge has two important components in the Hardhof area: the infiltration from the river Limmat and the artificial recharge. The rate of infiltration from the river depends strongly on the water level in the river (hL). The water level can be determined on a daily basis but it cannot be influenced by the Zurich water works, it is therefore a known disturbance. The artificial recharge in the Hardhof area is determined by the Zurich water works. It can be used by the management to act on the system in order to maintain an appropriate drinking water quality. The degrees of freedom for the management can be reduced from 12 + 3 (12 injection wells + 3 recharge basins) to 6 because the 12 injection wells cannot be operated individually but in the following groups: group 1 contains S1 to S6, group 2 corresponds to well S7, group 3 contains S8, S9, and S10, and group 4 contains S11 and S12. Group 1 lies downstream of the well field and is never operated. The cross-correlation analysis between EC measurements in the river Limmat, the horizontal wells, the infiltration infrastructures, and a representative piezometer in the city revealed the typical lag times (in days) between the measurement locations. The following disturbance variables were found to have the highest correlation with EC in well C on a given day t: Abstraction in well C on day t, QC (t), fraction of city water in well C on day t − 1, frC (t − 1), and water level of the river Limmat on day t − 14, hL(t − 14). The corresponding correlations between the input variables and the water quality measure are given in Table 5.1 on page 67 in the form of the weights w of the variables (initial guess). The lag times correspond to the average travel times of the water found with tracer tests (e.g. [48]).

Phase 3: Setting up of rule base

In phase 2, two known disturbances and one feedback variable were identified and their influence on the water quality was estimated (initial guess of the weights wi in Table 5.1 on page 67). The initial estimates of the boundaries between the classes for each ES input variable are determined based on the cumulative frequency distributions of daily values from 2004 of each variable (Table 5.1). The initial estimate for the infiltration scheme is given in Table 5.2. The infiltration focuses on injection well groups 2, 3, and 4 and basins I, II, and III. An exemplary path through the ES algorithm for the computation of the infiltration scheme of day t could look like this (the numbers refer to the initial guess of the parameters of the ES): The river water level on day t-14 was below 397 m a.s.l. It is therefore classified as low and attributed the value 1. This value is multiplied with the weight 0.2 yielding 0.2. Then, the abstraction rate of day t is classified as high, attributed the value 100, multiplied with the corresponding weight of 0.8 (yielding 80), and summed up with the result of the previous decision (yielding 80 + 0.2 = 80.2). The same procedure is repeated for the fraction of city water in well C on Chapter 5 Real-time control of the Hardhof well field 69

Table 5.2: Inﬁltration scheme for the initial and the adjusted parameters of the ES. The daily total abstraction rate is multiplied by the factor f and distributed between the basins and the injection wells with the rations given for each class. Among the basins and the injection well groups the inﬁltration rate is further distributed according to the ratios given here below.

Initial guess Adjusted values Low Medium High Extreme Low Medium High Extreme Factor f 1 1 1.3 1.5 1 1.2 1.2 1.5 Basins:wells 2:1 2:1 1:1 1:2 2:1 1:1 1:1 1:2 B I:II:III 1:2:2 1:6:4 1:6:4 1:6:5 1:2:2 1:6:4 1:6:4 1:6:5 Group 2:3:4 1:3:2 1:4:2 1:4:2 1:4:2 1:3:2 1:4:2 1:6:2 2:4:2

day t − 1. The resulting value is again classified. The class is usually higher or the same as the highest classified input variable. A classification to low means that the danger of attracting city water into the well is low and less infiltration is needed in order to maintain the hydraulic barrier. In order not to allow a depletion of the aquifer, the minimum total infiltration rate is set equal to 1 - 1.5 times the total abstraction rate in the Hardhof well field on a given day, depending on the classification of the infiltration scheme (Qinfiltration = f · Qabstraction, with f[1, 1.5], Table 5.2).

Phase 4: Identiﬁcation of parameters

The ES management is now simulated with historical data of the year 2004. Iter- atively, the parameters of the ES are tuned in order to reduce the fraction of city water in the drinking water wells. In this process, the visualizations of particle path lines for selected days are consulted. A significant reproduction of the fraction of city water is achieved after 3 iterations. A first validation period in January 2005 however exhibits a very low groundwater table which never occurred during 2004 and where the ES management does not perform satisfactorily. The phases 2 to 4 are completed again with an extended knowledge base from Jan- uary 1992 to January 2005. Although the statistics of the prolonged time series change, the delays between the input variables and the water quality remain the same. After 3 iterations of manual parameter tuning the water quality computed with the ES management between January 2004 and February 2005 was again improved considerably compared to the historical management scheme (Figure 5.9). The final adjusted parameters of the ES are given in Tables 2 and 3. The weights of the adjusted parameter set do not refer to the statistics of the knowledge base any more but have a very similar weight. As an alternative to the correlations, the input variables of the ES could be given the same weight as an initial guess. Figure 4 shows the particle path lines before (on the left) and after the tuning of the parameters (on the right). On the right side of Figure 4 no particle path lines computed with the ES management cross the boundary line between Hardhof area and city area whereas this is not the case in the left hand figure. Accordingly also 70 5.3 Expert system control

2.0 ES validation 1.5 hist 1.0 well B [%] fraction of 0.5 city water in

0 Jan04 Apr04 Jul04 Oct04 Jan05 Apr05 Jul05

40 ES validation 30 hist 20 well C [%] fraction of 10 city water in

0 Jan04 Apr04 Jul04 Oct04 Jan05 Arp05 Jul05

20 ES validation 15 hist 10 fraction of well D [%] 5 city water in

0 Jan04 Apr04 Jul04 Oct04 Jan05 Apr05 Jul05

Figure 5.9: Fraction of city water of the calibration and validation period of the ES with the extended knowledge base. The validation period starts on February 1, 2005 and is marked with a vertical line. The fraction of city water in well A is zero at all times for the historical as well as for the ES management. The fraction of city water in the drinking water wells computed with the historical management (hist) are given in gray. the fraction of city water is smaller after the tuning of the parameters than before the tuning of the parameters. The figure further shows the particle path lines of the historical management where the fraction of city water was elevated (also reflected in the elevated EC measurement). Compared to the historical management, the infiltration rate in basin III was increased by a factor of 2 using the adjusted ES. While with the historical management scheme, less water was infiltrated than abstracted for several days before May 4, 2004 (path lines for this day are depicted in Figure 4), the ES management infiltrates 50 % more water than is abstracted during the same period and thus succeeds in maintaining the fraction of city water at a low level (see Figure 5.9).

The validation period was prolonged to 8 months from February to August 2005. The ES with the enlarged knowledge base and tuned parameters performed well during the validation phase (Fig- ure 5.9). Except for two peaks of 3 % of city water in well D in June 2004 and June 2005, all peaks of city water in the Figure 5.11: Particle path lines from well drinking water wells are reduced signiﬁ- D on simulated day 515, beginning of June cantly with the ES management scheme. 2005. The two peaks are caused by particle path lines crossing the boundary line twice Chapter 5 Real-time control of the Hardhof well ﬁeld 71

Figure 5.10: Particle path lines on May 4, 2004 (simulation day number 124) for the initial parameters (dark gray in the left figure) and the iterated final parameters (dark gray in the right figure). The light gray lines were computed with the historical well field operation. The black line south of the well field describes the boundary between Hardhof and city water area.

(see Figure 5.11). Even though the path lines pass through potentially contaminated city area, the water quality in the well is not endangered since the water originates from one of the injection wells of the water works. The fraction of city water could be reduced by increasing the infiltration rates. This is not recommendable however because excessive infiltration could lead to water logging in the Hardhof area. The ES management holds the comparison with the optimal control presented in Bauser [6]. Even though the infiltration scheme found with the ES is not optimal, it nevertheless reduces the amount of city water in the drinking water wells to an acceptable level with a reasonable simulation time. That means, no iterative model runs are needed for the ES management, only a deterministic model prediction on which the particle path line analysis is based on.

Applicability to other settings

The design procedure of the ES presented here may be applied to an arbitrary well field management problem, given the problem has a solution. The essential limitation of the ES is the knowledge base. The management can only get as good as the knowledge base is extensive. If essential processes influencing the well field are unknown the application of the presented method yields unreasonable results. A drawback of the ES is the need for manual adjustment of the parameters. The procedure is tedious and prone to conceptual errors (i.e. if the understanding of the system is not profound enough). A periodic updating of the knowledge base and the parameters of the ES with the newest data is recommendable if the management is applied in a real well field. The implementation of the ES in a real well field is assumed to be straight forward because the rule base is intuitively understandable without background knowledge in control engineering which enhances the acceptance among the professionals operating the well fields. 72 5.4 Optimal control of 2D flow field

Model uncertainty and unknown disturbances

In the presented methodology we do not consider model uncertainties and unknown disturbances. However, the model is assumed to yield a conservative estimate of the water quality [7]. So we base the management decision on a cautious estimate of the fraction of city water in the wells.

5.3.4 Conclusions

In this chapter, the methodology for the design of an ES for well field management is presented. The applicability of the method was demonstrated in a study of the Hardhof well field. It was shown that, given the main processes influencing the well field are known, the ES is an efficient alternative to the fully-fledged optimization approach. We propose periodic updating of the knowledge base and the parameters of the ES to newly available data in order to maintain a good performance of the ES. Although the ES management is not optimal, it is close to optimal as shows the comparison with Bauser et al. [7] and Bauser [6]. Furthermore it features a small computation time and a simple, intuitive structure which are key advantages for the implementation in a well field.

5.4 Optimal control of 2D ﬂow ﬁeld

The control routines designed for the Hardhof well field up to now all operate on the basis of the deterministic model, although the information from a whole ensemble of predictions is available [7], [6], [8], [58]. The potential of taking advantage of available stochastic information for the control of groundwater systems is obvious. Already Fisher Atwood and Gorelick [26], Wagner and Gorelick [82], Freeze and Gorelick [27], and Ahlfeld and Muligan [1] have described the problem of stochastic control of groundwater systems and possible solutions. The most common solution applied is to optimize not for the mean of a decision variable but for the mean plus/minus some function of the standard deviation of the decision variable [81]. This function is usually constant in time and based on an a priori known distribution of the control variable and can be viewed as a safety margin [33]. Alternatively to the optimization with a safety margin, chance constraints can be implemented in the problem formulation. Thereby a specified small probability of failure of the controlled objective is tolerated in order to achieve feasibility of the problem while including uncertainty of model parameters or constraints [13], [69]. However, in groundwater systems, this method can only be applied to linear (or linearized) problem formulations [78], [29], [75]. Further, these management models often involve heuristics which are not strictly optimal [20]. An alternative to computationally intensive distributed groundwater models are emulation models. They are widely applied in management of surface water systems [72]. A simple example of an emulation model is a response matrix approach (e.g. Peña-Haro et al. [65]). More recently, reduced-order modelling has been ap- Chapter 5 Real-time control of the Hardhof well field 73 plied to groundwater systems [55]. Lin and McLaughlin [56] used a reduced-order model to emulate the fully distributed groundwater flow model and compared traditional control schemes with an ensemble control routine coupled to an EnKF updating scheme, where the information from the entire ensemble was used as basis for the control decision. The goal of the real-time ensemble control as compared to the deterministic control is to achieve a better characterization of the reality by narrowing down the distribution of the modelled decision variable and to obtain a more robust decision by taking into account the entire ensemble information (see figure 5.12 for an illustration). Lin and McLaughlin [56] found a significant improvement for the real-time ensemble control as opposed to the traditional control. y t i

In this chapter an ensemble control for s

n Ensemble control the hydraulic barrier in the Hardhof e D area is presented. Essentially, the concept of the real-time control formu- lated by Lin and McLaughlin [56] is followed. However, for the emulation of the 2D groundwater flow model, a linearization was used instead of a Deterministic control reduced-order model. The goal is to improve the robustness of the control by narrowing down the distribution of 0 Gradient possible gradients south of the well Figure 5.12: Effect of ensemble control vs. field and to reduce the number of real- deterministic control. The density function izations that produce negative gradi- of the gradients is narrowed down and the ents. The control model is described mean is shifted to positive gradients. Fur- and the difference between determin- ther the area of below the curve on the neg- istic control with and without safety ative side of the gradient axis is smaller for margin and ensemble control is evalu- the ensemble control than for the determin- ated. Further, the effect of state and istic control. parameter updating on the control is looked at.

5.4.1 Method

The management model

A typical management model consists of one or several control variables, constraints, and disturbances. The control variables are the ones that the manager can influence to steer the system in the desired direction. In the present case these are the infiltration rates in the 3 infiltration basins and the 2 infiltration well groups S 1-6 and S 7-12. The control variables are not to be confused with the controlled variables. Contrary to the first, the later cannot directly be influenced by the manager. The controlled variables are the variables describing the systems’ response to disturbances and changes in the control variables. They serve as a measure of success or failure of the control. In the present case, the hydraulic gradient south of the well field needs to be maintained in a way to avoid the inflow of city water. Therefore 74 5.4 Optimal control of 2D flow field the hydraulic heads in the south of the well field are chosen as the controlled variables. Typically the values of multiple controlled variables have to be aggregated into one single value which is part of the goal function that the optimizer attempts to minimize. Next to control variables and controlled variables, the management model further features disturbances. Disturbances are variables that influence the system but cannot be influenced by the manager. In the present example abstraction rates in the Hardhof well field are treated as disturbances because they are given by the drinking water demand of the city of Zurich. Further, river water levels and areal recharge rates are treated as disturbances. Control as well as controlled variables are subject to constraints. These can be hard constraints, meaning boundaries that cannot be violated within the bounds of physical laws (e.g. minimum and maximum infiltration rates that are given by the infrastructure in place), or soft constraints. Soft boundaries can be violated by the optimizer. They are implemented in the goal function by the use of penalty functions. To use soft constraints where physically possible is one way to deal with infeasible control problems. In the present example, a soft constraint for the hydraulic heads south of the well field has been implemented because it is not possible to maintain the hydraulic barrier for all realizations of the real-time model at all times. Therefore, a management model with hard constraints on the hydraulic heads would be infeasible in some time steps. In the case of infeasibility the optimizer routine does not find a solution to the control problem. The implementation as soft constraints with according penalties when the constraints are not met allows the optimizer to always find a solution that minimizes the soft constraint violation. The soft constraints and how they are combined in the goal function is described in detail here below. The control variables x are the infiltration rates in the 3 infiltration basins and the 2 infiltration well groups S 1-6 and S 7-12, yielding a degree of freedom of 5 for the control. x therefore is a 5-dimensional vector. The infiltration rates are subject to hard constraints (i.e. minimum and maximum infiltration rates) and to the following soft constraints. • The sum of the infiltration rates x should not exceed the sum of the abstraction rates Qabstraction by more than a factor of 1.5 in order to avoid high costs and flooding (equation 5.1).

5 4 X X fα = | xi − 1.5 · Qabstration,j| (5.1) i=1 j=1

The factor 1.5 is based on experience from work by Bauser et al. [7], [6], [8] and Marti et al. [58]. A sensitivity analysis of the factor with regard to the performance of the control with the given weights (see table 5.3 on page 77) showed that a factor of 1.5 yields the best results. The first column in figure 5.15 on page 79 illustrates the effect of this goal function component on infiltration rates (top row). If only this goal function component is active, the optimizer regulates the infiltration rate to be exactly 1.5 times the abstraction rates. Chapter 5 Real-time control of the Hardhof well field 75

• The infiltration rates should be such that the risk of inflow of city water is minimized. The risk to draw city water is computed from the hydraulic head gradients gi,r at i = 1,. . . ,7 control node pairs (np, see figure 5.13) for realization number r = 1 in the deterministic control case or over all realizations in the ensemble control case. In the case of deterministic control, the predicted

Figure 5.13: The locations of the control node points np 1 to np 7 and the additional node pair np 8 which was not used for the control but during the analysis of the results.

head gradients computed with the deterministic model (realization 1) g1 are used for the control. However, from the prediction step, the ensemble of gradients is known and the standard deviation of the gradient ensemble can be computed for every time step. This is a safety margin approach. The factor of 0.3 was chosen heuristically in order to produce similar risks to draw city water with the deterministic control and with the ensemble control. The risk is composed of the failure count times the amount by which the gradient is negative (see equation 5.2). In the deterministic control case the failure count is computed as follows: If the gradient plus 0.3 times the standard deviation is negative the control decision produces a failure.  deterministic control:  if g1 − 0.3 · std(g) < 0; risknpi = 1 · |g|;    risknpi : ensemble control: (5.2)  for all realizations do:   if g < 0; failure count + = 1 · |g|;  i npi  failure countnpi risknpi = ; NR For ensemble control, the gradients of all realizations are tested and the failures for a given node pair are summed up. The risk of a given node pair to draw 76 5.4 Optimal control of 2D ﬂow ﬁeld

city water is then the fraction between the failure count and the number of realizations. The optimizer computes gradients along the surface of the goal function. It is therefore of advantage to implement a goal function which is continuously increasing or decreasing. This is one reason to use the risk to draw city water instead of the failure count directly. The failure count as a function of the inﬁltration rates is not continuous whereas the risk is. The further advantage of the risk as opposed to the failure count is that realizations producing a large negative gradient which therefore present a higher threat to the drinking water quality are weighted more than gradients which are close to zero. The risk has to be aggregated since the applied optimization routine MATLAB fmincon only takes one-dimensional goal functions. Here, the maximum risk from the 7 control node pairs is chosen (see equation 5.3).

fβ = max risknpi (5.3) i

Figure 5.15 shows the effect of this goal function component on the infiltration rates, the risk to draw city water, and the groundwater level in the Hardhof in the second column of the figure. The risk to draw city water can be minimized by increasing the infiltration rates and, as a result, allowing higher groundwater levels in the Hardhof. • The infiltration rates should not change much between two time steps to allow the well field to be operated as stably as possible (equation 5.4).

5 5 X X fγ = | xi(t) − xi(t − 1)| (5.4) i=1 i=1

Figure 5.15 shows that the infiltration rate is kept constant at the initial value if only this goal function component is active. • The infiltration should not raise the groundwater level above a given level (here 397 m a.s.l.) in order to avoid water logging of buildings in the Hardhof. A linear combination of a linear function and an error function describes the function for this soft constraint (equation 5.5). The water level at observation point 3145 is used to control the groundwater level in the Hardhof area as the water works have coupled their warning system to the stage of that observation location. 0.5 maxh(hP 3145,r) − 397 fδ = · max(hP 3145,r) − 393 +0.25· 1 + erf √ 399 − 393 h 0.4 (5.5) Figure 5.15 demonstrates that the groundwater level can be kept low with this fourth goal function component. However, this happens at the cost of low infiltration rates and a high risk to draw city water. These soft constraints are implemented as linear combinations in the goal function f. f = α · fα + β · fβ + γ · fγ + δ · fδ (5.6) Chapter 5 Real-time control of the Hardhof well field 77

The non-linear control problem is given by the following equation: minx f(x), subject to 0 ≤ x ≤ xmax. The algorithm that does the computation of the goal function value is given in ﬁgure 5.14 (Note: objective function and goal function are hereafter used interchangeably).

A weighting of the diﬀerent soft constraints is needed. For example, depending on the risk vs. cost preference of the decision maker, soft constraints fα and fβ above can be weighted diﬀerently.

Figure 5.16 on page 80 shows the Pareto front that opens between the summed risk to draw city water and the infiltration-abstraction ratio (iar) that is obtained by varying the weights α or β while keeping the other weights of the goal function constant. A low risk to draw city water can be achieved by increasing the weight of β, however, this also increases the iar meaning higher infiltration rates compared to abstraction rates. On the other hand the infiltration rates can be kept low at the cost of a higher risk to draw city water by increasing the weight of α. In the current setting, the weights for α, β, γ, and δ are not all constant over time. In order to have β, the weight for the risk to draw city water, and δ, the weight for the groundwater level, approximately on the same level as the other constraints, they are multiplied by the sum of the initial infiltration rates xi,0 (table 5.3).

Table 5.3: Weights for the diﬀerent components of the goal function. Name α β γ δ P5 P5 Weight 2 50 · i=1 xi,0 2 3 · i=1 xi,0

The sensitivities of the goal function components with regard to the weights α and β are given in ﬁgure 5.17. In the 2-dimensional plots, f is not necessarily at a minimum with the chosen weights. The weights are, however, suitable for the minimization of the risk to draw city water which was the main goal in this study.

Coupling of the management model to the simulation model

The management model described above was implemented in Matlab [59] and coupled to the 2D real-time groundwater flow model described in section 4.3 on page 47. In a first step, the initial and historical boundary conditions are read into Matlab and, optionally, new ensembles can be generated from this data by using latin hypercube sampling. The initial and boundary conditions of the real-time model are described in section 4.3 on page 47 ff. The deterministic model underlying the real- time model is described in section 3.1 on page 18 ff. The procedure of the real-time control for a given time step (1 day) is described in the following. The algorithm is given in figure ??. 1. Linearisation of model prediction with SPRING. Matlab writes the SPRING [15] model and the input files for the time dependent boundary conditions and calls the SPRING sitra routine as an external function. The sitra routine computes non-stationary flow and transport in 2 or 3 spatial dimensions. The model 78 5.4 Optimal control of 2D flow field

Algorithm 1: Routine for computing the nonlinear objective function. Data: Current inﬁltration rates. Result: According value of objective function. // The objective function is computed in each iteration of the optimizer fmincon. 1 Compute the linear response of the gradients at 7 control node points for the given inﬁltration rates; // Compute the first goal function component: The difference between infiltration and abstraction rate. 5 P5 2 fα = |sumi=1xi − 1.5 · j=1 Qj|; // Compute the second goal function component: The risk to draw city water. 3 if deterministic control then 4 for each control node point do 5 if gradient + 0.3· std < 0 then 6 risknpi = |gradient|; 7 end 8 end 9 else if ensemble control then 10 for each control node point do 11 for each realizatino do 12 if gradient < 0 then 13 failure count + = |gradient|; 14 end 15 end 16 risknpi = failure count / number of realizations; 17 end 18 end // Compute the third goal function component: The change of infiltration rates over time. P5 P5 19 fγ = | i=1 xi(t) − i=1 xi(t − 1)|; // Compute the fourth goal function component: A penalty for the groundwater level in the Hardhof. max (h )−397 f = 0.5 · (max (h ) − 393) + 0.25 · 1 + erf h P√3145,r 20 δ 399−393 h P 3145,r 0.4 ; // Compute the goal function value 21 f = α · fα + β · max risknpi + γ · fγ + δ · fδ;

Figure 5.14: General algorithm of the routine for computing the nonlinear objective function. Chapter 5 Real-time control of the Hardhof well ﬁeld 79

Figure 5.15: The effects of the 4 goal function components on the infiltration rates, the risk to draw city water and on the groundwater level in the Hardhof. Each column indicates which goal function component is active. E.g. in the first column labelled with α only the first goal function component is active. The rows show the summed infiltration and abstraction rates (top row), the risk to draw city water (middle row) and the groundwater level in the Hardhof (bottom row).

prediction is computed for all realizations of the real-time model. This process is parallelized in Matlab. The SPRING model is run multiple times to produce linear response functions for each infiltration infrastructure. The linearisation functions are computed for each realization of the ensemble in the case of ensemble control and for the average model in the case of deterministic control. Also these computations can be run in parallel on several processors. 2. Optimization of the infiltration rates based on the linearised model in Matlab. The linear response functions are used as the basis for the model predictive control. The linearisation is justifiable: The 2D model is very close to linear with little loss to accuracy. Further the acceleration of the optimization with the linearised model is considerable compared to the optimization with the full distributed model. Algorithm3 (figure ??) describes the linearisation of the model and the optimization of the infiltration rates as implemented in Matlab. 3. Model prediction with SPRING based on the optimized infiltration rates. At the end of the optimization, the model prediction is repeated with the distributed model. 4. Sampling of truth from the model prediction. One predetermined realization of the model prediction is used as the measurement of the truth. This step is necessary in offline computations as no true measurements are available. 80 5.4 Optimal control of 2D flow field

Figure 5.16: The Pareto front obtained from varying the two weights α (blue) and β (red). The default values used for the management simulations are given in black color. The indicated values for β are multiplied with the sum of the initial inﬁltration rates, this has been left out in the graph for space reasons.

Figure 5.17: The sensitivity of the control with regard to the two weights α and β. f is the goal function value, mean(risk) stands for the average risk to draw city water over all 7 control node pairs and is weighted with β. iar stands for the infiltration- abstraction-ratio and is weighted with α. max(hP ) stands for the highest water level in observation point 3145 in all realizations and is weighted with δ. And dQi is the difference between the sum of the infiltration rates in two subsequent time steps. It stands for the stability of the infiltration rate over time and is weighted by γ.

An estimated sampling error of 5 cm is used to generate an ensemble of the measurements. 5. Udpating of states and parameters with EnKF. The updating is done with the measurement of the truth. Heads are updated at every time step, parameters as hydraulic conductivities and leakage factors are updated every 10th Chapter 5 Real-time control of the Hardhof well ﬁeld 81

Algorithm 2: General algorithm of the real-time control model. Data: Initial and boundary conditions as well as a parameter set have to prepared in a matrix format before the start of the simulation. Further, a numerical groundwater ﬂow model in Spring needs to be available. Various options can be set in a separate parameter ﬁle. Result: Simulated head time series interpolated at the observation points for each time step and realization. // Initialization of system and model. 1 Read in initial and boundary conditions; 2 Setting up of the numerical model; 3 for each time step do // Linearisation of the model prediction and optimization of infiltration rates based on linearized model predictions. 4 Call control; // Computation of model prediction using the optimal infiltration rates. 5 Compute model prediction; // Sampling of measurements from a given realization and updating of the model with EnKF. 6 Update the model; 7 end

Figure 5.18: General algorithm of the real-time control model.

time step. A detailed description of the updating procedure can be found in section 4.3 on page 47 ﬀ. Note that the sampling of the measurement and the update of the model prediction are preparatory for the next time step in the present algorithm. In the on-line application of the real-time model, observations become available only the next day. There, the real-time control routine starts with the model update prior to the optimizer. This can be done very easily in this implementation by moving the Update the model routine in algorithm2 (ﬁgure ??) in front of the Call control routine.

If not stated diﬀerently realization 13, a replicate with low hydraulic conductivities (see ﬁgure 4.17 on page 51) representing a worst case scenario, was used as reality. Some results are compared to simulations done with realization 47 as reality, a replicate with high hydraulic conductivity in the Hardhof area.

The optimizer

The management routine minimizes a goal function with the Matlab routine fmincon using the interior point method. The interior point method implemented in Matlab closely follows the algorithm presented by Waltz et al. [83]. This section roughly summarizes the literature by Waltz et al. [83] and Nocedal and Wright [64]. 82 5.4 Optimal control of 2D ﬂow ﬁeld

Algorithm 3: General algorithm of the Call control routine. Data: Initial and boundary conditions of a given time step. 1 Initialization; 2 for each control variable do 3 Linarisation of the numerical model; 4 if deterministic control then 5 Compute linear response of average model. 6 else if ensemble control then 7 Compute linear response of each realization. 8 end // Call optimizer with nonlinear objective function 9 fmincon(); 10 Store optimized inﬁltration values; 11 end

Figure 5.19: General algorithm of the Call control routine.

The interior-point method transforms an original optimization problem (equation 5.7) into a sequence of sub-problems using barrier functions (equation 5.8).

min f(x) , subject to h(x) = 0, g(x) ≤ 0 (5.7) x

m X min f(x) − µ ln(si) , subject to h(x) = 0, g(x) + s = 0 (5.8) x,s i=1 Where s > 0 is the slack variable that transforms an inequality constraint into an equality constraint and µ > 0 is the barrier parameter which ensures the approaching of an optimal solution with decreasing µ. The barrier function can be derived with the ﬁrst-order necessary conditions for optimality. For details the reader is refered to Nocedal and Wright [64]. fmincon then attempts to solve the Karush-Kuhn-Tucker (KKT) conditions 5.9 with a direct step.

 2      ∇xxL(x, s, λh, λg; µ) 0 Jh(x) 0 dx ∇xL(x, s, λh, λg; µ) −1  0 S Λg Jg(x) I  dx  ∇sL(x, s, λh, λg; µ)     = −    Jh(x) 0 0 0  dh   h(x)  Jg(x) 0 0 0 dg g(x) + s (5.9) With the Lagrangian function deﬁned as

m X T T L(x, s, λh, λg; µ) = f(x) − µ ln(si) + λh h(x) + λg g(x) (5.10) i=1

λ is the Lagrangian multiplier. S and Λg denote the diagonal matrices with values s and λg respectively. J denotes the Jacobian matrix. The new iterates are given + by x = x + αxdx (accordingly for s, λg, and λh) whereby the step length αx is computed in two stages using a backtracking line search (for details refer to Waltz Chapter 5 Real-time control of the Hardhof well field 83 et al. [83]). If the Jacobian of the constraint functions is non-convex or if the Hessian of the Lagrangian function or the Jacobian of the constraint functions associated with the sequence of sub-problems display rank deficiencies, the algorithm switches to a conjugate gradient method using a trust region approximated with a quadratic function. The algorithm is thereby able to reach convergence efficiently even in the presence of non-convexity or matrix rank deficiency. Details on the line step algorithm can be found in Waltz et al. [83]. The trust region steps are described in Byrd et al. [10]. Note that the interior point algorithm used here is a local optimizer. It is therefore possible that it gets stuck in a local optimum and does not find the global optimum of the optimization problem. This does not seem to be problematic in the present case. The optimization has produced the same optimal infiltration rates for a wide variety of initial values. Further note that fmincon accepts a vector of control variables but returns one single goal function value. It is therefore suitable for multiple input single output control systems.

5.4.2 Results and Discussion

Figure 5.20 shows results for deterministic offline (no updates of states and parameters) and online (with updates of states and parameters) and ensemble offline and online control with realization number 13 as reality. Realization 13 features low hydraulic conductivity in the south of the well field (compare figure 4.17 on page 51) which makes it a difficult case for the control of the hydraulic barrier. The high hydraulic conductivity south of the well field leads to a higher groundwater table south of the well field than for average hydraulic conductivities. In order to maintain the hydraulic barrier, more water has to be infiltrated in the infiltration infrastructure of the Harfhof.

Figure 5.20: Deterministic (det) offline and online vs. ensemble (en) offline and online control. The reality in this simulation was realization number 13 featuring below average hydraulic conductivities in the south of the well field. 84 5.4 Optimal control of 2D flow field

The risk to draw city water can be reduced best by the ensemble online control. However, the low risk of city water comes at the cost of high infiltration rates. De- terministic online control and ensemble offline control achieve similar results with regard to the average risk but the deterministic online control reaches the result with lower infiltration rates and subsequently a lower groundwater table in observation location 3145. For both deterministic and ensemble control, the switching from offline to online mode allows well field operation at a lower risk without increase of the infiltration rates. The feedback achieved by the real-time model with the updating of states and parameters is more important than the choice between the control including the full ensemble information (ensemble control) or control based on the deterministic model and taking into account a safety margin. The same simulations as above were repeated with realization number 47 as reality (figure 5.21). The results are similar as for the low conductivity reality. Both deterministic and ensemble control are robust with regard to the reality assumed for the real-time control. Also in these simulations the cost for lower risks is achieved by an increase of infiltration in the ensemble control schemes. The deterministic online control has difficulty reducing the risk in the lower control node pairs (np 6 and np 7) whereas the real-time model has trouble updating the parameter field fast enough to reality 47. The updating frequency of the parameters is 10 days and heavy damping is applied leading to slow changes in parameter values.

Figure 5.21: Deterministic oﬄine and online vs. ensemble oﬄine and online control. The reality in this simulation was realization number 47 featuring above-average hydraulic conductivities in the Hardhof area.

Figure 5.22 shows the gradients of 8 node pairs south of the well field (see figure 5.13) for 3 offline simulations on May 5, a day with high abstraction rates. The optimizer tries to improve the control node pair with the highest risk of failure. Most of the time, this is one of the node pairs in the west of the well field, node pairs 6 and 7. The node pairs in the west of the well field are also those which show a clear improvement when passing from deterministic control without safety margin, to deterministic control with safety margin, and finally ensemble control. Without updates of states and parameters, the deterministic control with safety Chapter 5 Real-time control of the Hardhof well field 85 margin shows a narrower distribution of head gradients (i.e. a higher accuracy of prediction) than the ensemble control but the ensemble control yields a lower risk of failure. The ensemble control achieves this result by increasing the infiltration rates, as mentioned above, and thereby shifting the gradient distribution to more positive values. However, this happens at the cost of high infiltration rates and a generally higher groundwater table in the Hardhof area. The deterministic control with safety margin performs worse than the deterministic control without safety margin at the control nodes in the east of the well field (np 1 to 4). Already in the previous time steps, the deterministic control with safety margin fails in the western most control node pairs. Throughout the simulation period up to May 5, the goal function value is higher for the deterministic control without safety margin than with safety margin. The main contribution to the increase of the goal function value is fα, which is a function of the difference between infiltration and abstraction rates. The contribution of the risk of city water changes comparatively little between the two simulations. It is slightly higher in the case with safety margin. The higher goal function value for deterministic control without safety margin leads to a higher infiltration rate in basin 1 for the case with safety margin and thus to a reduction in the risk to draw city water. This slight difference in the contributions to the goal function can decide whether or not a control fails. This example emphasizes the sensitivity of the control to the weighting of the goal function components for the case where no feedback from the real system through state and parameter updating is used to stabilize the control system. Comparison of figure 5.22 and figure 5.23 emphasises the influence of the feedback between groundwater system and control. The kernel density curves are generally narrower in the online simulation than in the offline simulation. The difference between deterministic online control without and with safety margin is a matter of the safety margin: The density curve is shifted to the right (towards more positive gradients). This is in contrast to the deterministic control where the safety margin performed significantly better with regard to the western control node pairs than the deterministic control without safety margin. The distribution of the head gradients is not the same for every time step. Fig- ures 5.24 and 5.25 show the gradient distributions for June 28, a day with typical boundary conditions after the event with high abstraction rates in the beginning of May (figures 5.22 and 5.23). Compared to the gradients produced with the offline control simulations, the online control simulations produced even narrower gradient distributions than for May 5 (figure 5.23). Whereas all online control models produced negative gradients in May 5, during typical operation conditions only the ensemble control is able to maintain the hydraulic barrier. Contrary to the deterministic controls, the ensemble control is able to recover from the extreme event and produce positive gradients at most node pairs. The use of the ensemble information makes the control less vulnerable to discrepancies between reality and model because it is likely that the truth lies somewhere within the ensemble. For the deterministic control, truth and model may differ considerably, even with updating of states and parameters. This makes it impossible for the control to determine infiltration rates which satisfy both, truth and model. 86 5.4 Optimal control of 2D flow field

Figure 5.22: Kernel density plots of the gradients at 8 node pairs along the south of the well field with deterministic offline control without safety margin (black), deterministic offline control with a safety margin of 0.3 standard deviations (blue), and ensemble offline control (red). The gradients were drawn for May 5. Minimum (line on the left), mode (fat line), and maximum (line on the right) gradients as well as the gradients of the individual realizations (pale color) are drawn on the negative y-axis.

5.4.3 Conclusion

The strength of using feedback for control is demonstrated. The controls operating with updates of states and parameters display a narrower distribution of head gradients and achieve a lower risk to draw city water with less infiltration than the controls operating on the simple forward runs. Further it can be shown, that for this problem setting, the ensemble control has an advantage over the deterministic control. It produces less risk to draw city water, however, at the cost of higher infiltration rates. The control is sensitive to the weighting of the goal function components. It is for the water works to decide which of the four soft constraints is most important and to choose the weights accordingly. If, under the current weighting, the level of infiltration rates and the level of the groundwater are considered more important than the risk to draw city water or if a risk to draw city water below 6 % is considered acceptable, deterministic control may be favoured over ensemble control because the computation time needed for deterministic control is considerably smaller than Chapter 5 Real-time control of the Hardhof well field 87

Figure 5.23: The kernel densities of the gradients at the control node pairs when the online model is active and ensures the feedback loop between the groundwater system and the control. Deterministic online control without safety margin (black), deterministic online control with safety margin (blue), and ensemble online control (red). The gradients are drawn for May 5. Minimum (line on the left), mode (fat line), and maximum (line on the right) gradients as well as the gradients of the individual realizations (pale color) are drawn on the negative y-axis. for ensemble control. However, for the problem at hand where daily decisions are required, both methods are fast enough to produce optimal inﬁltration rates for the next day.

5.5 Temperature Control

The rising extremes of temperatures in the river Limmat and consequently in the wells that are close to the river are one of the threats to the drinking water quality that have to be addressed. It is not possible to significantly reduce the temperature in a single well because the inflowing water temperature cannot be changed significantly by modifying the pumping regime. However, small changes in temperature in the individual drinking water wells may well affect the temperature of the mixed water of all four wells. Thus, a very simple idea for controlling the temperature in the pumped drinking 88 5.5 Temperature Control

Figure 5.24: Kernel density plots of the gradients at 8 node pairs along the south of the well field with deterministic offline control without safety margin (black), deterministic offline control with a safety margin of 0.3 standard deviations, and ensemble offline control. The gradients were drawn for June 28. Minimum, mode, and maximum gradients as well as the gradients of the individual realizations are drawn on the negative y-axis. water is to pump the needed amount of water from the coldest wells. Thus, the temperature in the mixed water from all four horizontal wells can be reduced. The following chapter shows the effect of such a redistribution of abstraction rates to the coldest wells.

5.5.1 Method

The heat transport model (described in section 3.2 on page 23) with the 2-layer parameter set (see section 3.1.3 on page 22) was used to simulate heat transport in the year 2006. A routine was programmed in C and coupled to the existing paraEnKF- 3dSPRING provided by Wolfgang Kurtz and Harrie-Jan Hendricks Franssen of the Forschungszentrum Jülich. However, contrary to the works published by Kurtz and Hendricks Franssen (e.g. [52], [44]), in the present case paraEnKF3dSPRING was not run with an ensemble of parameters and initial conditions but with the deterministic model. The routine re-distributes the abstraction rates of the 4 horizontal wells as soon as a threshold temperature, in the present case 16 ◦C, is reached in Chapter 5 Real-time control of the Hardhof well ﬁeld 89

Figure 5.25: The kernel densities of the gradients at the control node pairs when the online model is active and ensures the feedback loop between the groundwater system and the control. Deterministic online control without safety margin (black), deterministic online control with safety margin (blue), and ensemble online control (red). The gradients are drawn for June 28. Minimum, mode, and maximum gradients as well as the gradients of the individual realizations are drawn on the negative y-axis. one of the wells (see ﬁgure 5.26). The temperatures are elevated only during the autumn months. This control is therefore switched on only during a few months of the year.

The algorithm is an optimization routine that minimizes the mixed water temperature while satisfying the following constraints on the abstraction rates: The sum of the abstraction rates before and after the optimization have to be the same and the abstraction rates in each well have to be larger than 0 and smaller than the maximum pumping capacity of the given well. The re-distribution of the abstraction rates is essentially done by looking for the coldest well and pumping as much of the drinking water demand from that well according to its capacity. If the drinking water demand is larger than the maximum pumping capacity of one well, the surplus demand is distributed to the second coldest well and so forth. Only temperature was optimized in this example. The inﬁltration rates were not optimized. Therefore, with this method, the hydraulic barrier may not be optimal. The control horizon in this example is 1 day. The algorithm is an optimal feed for- 90 5.5 Temperature Control

Algorithm 4: Minimization of the mixed water temperature. Result: Re-distributes the abstraction rates such that the temperature of the mixed drinking water is minimized. 1 for each time step do 2 Test temperature of each horizontal well; 3 if Temperature in one of the wells > threshold temperature then 4 min Tmixed subject to constraints on the abstraction rates.; 5 end 6 end

Figure 5.26: Minimization of the mixed water temperature. ward control. The control system is linear and therefore no model predictive control hast to be applied. Further, no feedback from the real groundwater system is taken into account. That means that no updates of the modelled temperatures are made in this example. However, when applied to the real groundwater system, model updates can improve the accuracy of the model prediction as discussed for the flow model in section 4.2 and shown by Kurtz et al. [53]. Finally, the pumping rates optimized for the temperature control were fed to the 2D flow model and a particle tracking routine (geoneu, a package of SPRING) was run on both scenarios - with and without tempearture management - to analyze the effect of the temperature control on the content of city water in the drinking water wells.

Time dependent boundary conditions

Figure 5.27 shows the ﬁxed head at the outﬂow boundary for the simulation period of the year 2006. It essentially follows the river stages as can be seen from the comparison with Figure 5.28 below.

Figure 5.27: The ﬁxed head boundary condition for the year 2006.

As an example, the river water level at node 723 in the Hardhof area is shown in ﬁgure 5.28. The river water levels correlate with the river discharge given in Figure 4.12 on page 48. Figure 5.29 shows the areal recharge from precipitation in the model area. Contrary to the 2D model (see Figure 4.14 on page 50) where only few recharge events are modelled, the 3D model for 2006 contains more recharge events. This is due to the fact that precipitation was available from the Hardhof area for the year 2006. For the longer time series used in the 2D model, precipitation data from the Reckenholz Chapter 5 Real-time control of the Hardhof well ﬁeld 91

Figure 5.28: The river level at node 723 in the Hardhof area for the year 2006. meteo station were used.

Figure 5.29: The areal recharge in the model area for the year 2006.

The abstraction rates in the four horizontal drinking water wells for the year 2006 are given in ﬁgure 5.30. The abstraction rates used in this example are not corrected for the construction periods and the tracer test.

Figure 5.30: The daily abstraction rates in the four horizontal drinking water wells for the year 2006.

The infiltration rates in the four horizontal drinking water wells for the year 2006 are given in figure 5.31. Figure 5.32 shows the temperature boundary conditions applied in the 3D heat transport simulation, namely the soil temperature used for the advective heat flux from areal recharge as well as for the diffusive heat flux by heat conduction, the river water temperature mainly relevant for advective transport, and the temperature of the water that is fed to the artificial recharge infrastructures.

Initial conditions

The heat transport simulation was started with historical boundary conditions on January 1, 2006, and run till December 31, 2006. The period from January to 92 5.5 Temperature Control

Figure 5.31: The daily inﬁltration rates in the three recharge basins and the 12 inﬁltration wells Si for the year 2006.

Figure 5.32: The boundary temperatures applied to the 3D heat transport model during the year 2006.

May 2006 was used as spin up period and the second part of the year, from June to December, was used for the management simulation. The 2-layer parameter set (described in section refsubsec:ﬂowmodelparameterestimation on page 22) was used.

5.5.2 Results

Figure 5.33 shows the distribution of temperature in the groundwater at 17 m depth (the level of the abstraction wells C and D) on December 7 2006. The optimizer takes advantage of the cold plume reaching well B and pumps the entire drinking water demand from well B whereas without the optimizer, groundwater is pumped in the two wells C and D. The temperature of the mixed water without and with temperature management is given in ﬁgure 5.34. It is possible to reduce the temperature of the mixed water by 0.5 to 1 ◦C. This is not a lot given that the water works would like to keep the temperature of the drinking water below 16 ◦C and it remains - in this example - above 17 ◦C even with re-distribution of the pumping rates.

5.5.3 Discussion

A heat front propagates through the aquifer at a slower speed than an ideal tracer front. The factor by which it is slowed down is called the thermal retardation factor and is computed as shown in equation 5.11. (The equation is taken from Stauﬀer et al. [73], the parameter values are given in table 3.5 on page 28.) Note that Chapter 5 Real-time control of the Hardhof well ﬁeld 93

Figure 5.33: Temperature distribution in ◦C in the groundwater on December 7 2006 at 17 m depth without (left) and with (right) re-distribution of the abstraction rates.

Figure 5.34: Temperature of the mixed drinking water without and with distribution of the abstraction rates. equation 5.11 is only valid for homogeneous aquifers. For heterogeneous aquifers, the thermal retardation factor may well be 1 or even lower than 1 due to preferential ﬂow paths. J CA 800 kg·K Rt = = = 1.27 (5.11) n · C J W 0.15 · 4192 kg·K

Heat transport is further influenced by lenses of low hydraulic or thermal conductivity in the aquifer material (though not as much as solute transport). Which makes heat transport more sensitive to the hydraulic conductivity distribution than flow simulations. Whereas pressure waves propagate quickly around lenses with reduced 94 5.5 Temperature Control hydraulic conductivity, heat fronts have to travel around and through such lenses. Altogether, heat transport simulations pose a considerably larger challenge to the modeller and the computational resources available than flow simulations. This has an effect on the possible applications of management and optimizing strategies on heat transport models: Algorithms that necessitate many iterations of model runs for example are not suitable. Further, the simulation period used for the design of the control should be short since many model runs are usually necessary during the development of the control algorithm. However (as for model calibration problems), this may hamper the effectivity of the control if the design period is not chosen wisely (including relevant system disturbances). The challenges met by the development of a temperature control presented here led to the conclusion that a faster heat transport model is needed for the design of a control. As a result, the 2D heat transport model was developed in cooperation with the Master students Raphael Looser and Stephan Kammerer [57]. Long term simulations with the 2D heat transport model done by Manuela Mauchle [60] revealed a seasonal cold water bubble between the existing drinking water wells and the river Limmat (see figure 5.35). One solution to further reduce the temperature of the produced drinking water may be the construction of a further production well in the area where the cold water bubble appears in autumn and to pump drinking water from that new well.

Figure 5.35: Modelled temperature distribution on October 9, 2008. Figure source: Mauchle [60]

The particle tracking on the 2D simulation with the historical pumping and with the pumping scheme from the temperature control showed a slight improvement from 3 m3/s city water without temperature control (corresponding to 10 % city water) to 2 m3/s city water with temperature control (corresponding to 7 % city water). A significant improvement of the amount of city water pumped can be noted in well C where the maximum percentages pumped were reduced from 47 % without Chapter 5 Real-time control of the Hardhof well field 95 temperature control to 32 % with temperature control. No significant improvement of the fraction of city water can be noted in the other drinking water wells. Please not that these numbers for the percentage of city water cannot be directly compared to the ones computed with the method from Bauser et al. A different algorithm was used here and applied to a 2D flow model, not a 3D flow model as in Bauser et al.

5.5.4 Conclusion

It is possible to reduce the temperature of the drinking water produced in the Hard- hof well field by re-distributing the daily drinking water demand to the coldest production wells. The effect on the temperature however is limited to 0.5 to 1 ◦C. Other engineering solutions like the construction of a further production well in the area where cold water is found during the autumn months may further reduce the temperature of the drinking water produced in the Hardhof well field. The experience from the simulations presented above emphasised the importance of fast models for the design of control algorithms. The time demand for the 3D heat transport simulation is considerable and does not allow the design of a temperature management based on the distributed model. A way out could be the use of a 2D heat transport model, at the cost of a loss of accuracy where 3D effects are relevant, or the use of a surrogate model.

Chapter 6

Conclusions

Summary of the results

All models used in this study are able to reproduce the dynamics of the flow field. Also the tracer experiment could be modelled with sufficiently accurate results with the existing 3D models. The heat transport is best modelled with the 3D models. The most suitable parameter set for flow, tracer and heat transport is the one featuring two layers with different hydraulic conductivities. A re-calibration of the 2D heat transport model using several years of temperature as well as head data to estimate hydraulic conductivities and leakage factors is computationally feasible nowadays and should be done before management of heat transport is implemented with the 2D model. The real-time flow model and the real-time control of the flow field that are currently in place in the well field generally display a good performance. The updated flow field has sufficient accuracy for the real-time control. The real-time control that is currently operated in the Hardhof well field is able to maintain a very low percentage of city water in the drinking water wells. In day to day operation deficiencies are observed such as too high water tables in piezometer 3145 and early clogging of basin 2 which is used more often than foreseen leading to an early ageing of the infiltration infrastructure. An expert system control was introduced as an alternative to the currently in place real-time control, based on an optimization with a genetic algorithm. Contrary to the optimal control, the expert system is intuitively understandable and does not require specific background knowledge in control engineering. It further only takes a fraction of the computation time of the optimal control but achieves similar fractions of city water. Its disadvantage compared to the optimal control is that it is not able to automatically adapt its rule base to new boundary conditions that were not included during the design phase of the expert system. The rule base and the decision rules of the expert system have to be re-evaluated periodically (every time new boundary conditions arise) to ensure a reliable operation of the management. An ensemble control tool was coupled to a 2D real-time flow model. The advantage of the ensemble control is that it takes into account the stochastic information available from the real-time model. The ensemble control was compared to a deterministic control where the control decision is based on the average of the ensemble produced by the real-time model and to a deterministic control with a safety margin which depends on the width of the ensemble. Further, the ensemble and deterministic real- 98 time controls were compared to feed-forward controls where no updating of modelled states and parameters was performed. The results show a clear advantage of the real-time control over the feed-forward only control: The resulting ensembles are narrower and the control decision is more precise. The main difference between the deterministic control with and without safety margin is essentially the safety margin. The performance of the control can be improved with a safety margin, however, this causes higher infiltration rates and therefore higher operation costs. For similar costs, the ensemble real-time control performs better and should be favoured over deterministic control. The resilience of the control with regard to extreme boundary conditions is higher for the ensemble control than for the deterministic controls, at least as long as the truth lies within the ensemble. Although state and parameter updating is performed, the deterministic controls struggle if the truth differs from the model. This may be improved with a better tuned updating of the 2D real-time model. Last but not least the threat of rising groundwater temperatures in the well field was addressed. The drinking water temperature rises above a threshold temperature during the autumn months. A temperature management tool was coupled to a 3D heat transport model in order to reduce the drinking water temperature while it is above the threshold temperature. This is done by re-distributing the abstraction rates to the coldest wells. The drinking water temperature can thus be reduced by 1 to 2 ◦C. This control can be added to the presented flow field controls. Steering for colder water in autumn leads to higher abstraction rates in wells C and D which in turn entails a higher risk to draw city water in these wells and subsequently higher infiltration rates in the surrounding infiltration infrastructure. This has the positive side effect of partially withholding city water from the drinking water wells. A further decrease of the drinking water temperature could be achieved by the construction of a fifth drinking water well in the center of the Hardhof well field where a seasonal cold bubble was identified in long term simulations with the 2D heat transport model.

Own contribution to the research

Within the scope of this thesis the existing models of the Limmat valley aquifer were benchmarked in section 3.3 and the performance of the existing real-time model and control were assessed in sections 4.2 and 5.2. Further, 3 innovative control systems were designed and applied to a case study site, the Hardhof well field in Zurich, Switzerland. As a first step an expert system control was designed based on the analysis of the historical management and compared to an optimal control routine. In a second step a 2D real-time model was implemented and coupled to Matlab. An optimizer determines the infiltration rates at every time step using the entire ensemble information available from the real-time model. It could be demonstrated that the control decision thus becomes more robust with regard to model errors than if it is solely based on the average of the ensemble prediction. The third control involves the heat management of the Hardhof well field. It was demonstrated, that the redistribution of abstraction rates to the coldest wells yields limited cooling of the drinking water. However, possible locations of further drinking water wells could Chapter 6 Conclusions 99 be identified based on long term heat transport simulations.

Future work

The present study focuses on the application of real-time control to the Hardhof well field. Several interesting subjects could not be addressed within the scope of this thesis but their study would be of considerable scientific and societal use. One of them is to prove the applicability of the real-time model to other aquifer types in Switzerland. One major limitation of why the huge potential of real-time modelling has not yet found a wider application in the consulting industry is the limited number of application examples. In addition, open questions like the economic cost and benefit of a real-time model compared to a conventional model have not been addressed in research up to now which further hinders the ready implementation in practice. A further open point is a benchmarking of different optimizers, including global optimizers, for the present control problem. Optimizers have their specific strengths and weaknesses and may be more or less suitable for highly non-linear control problems as the 2D real-time control problem presented in section 5.4. The characteristics of the optimizers are generally well known from publications with standardized optimization problems. However, the control problem presented here is unique and new and (comparably) not well characterized. In the present study, possible channels of increased or decreased hydraulic conductivity have not been modelled. However, the presence of such channels in the Hardhof area is considered a fact. It would be interesting to evaluate the influence of modified initial hydraulic conductivity ensembles incorporating characteristic features on the performance of the real-time model and real-time control. Long term optimization of heat transport were not possible due to computational constraints. With increasing computational capacities these will be possible in future years. Already now, the need to optimize heat transport in urban aquifers such as the upper Limmat valley aquifer is evident. An ever increasing density of tunnels, underground parkings, and shallow heat exchangers increase the average groundwater temperature by several degrees. A careful management of additional heat inputs to the aquifer is needed to maintain the quality of the resource for drinking water purposes. As an alternative to the fully distributed heat transport model, a fast surrogate model could be designed. Surrogate models find a wide application in surface water management [72] but, to the author’s knowledge, have not been used in heat transport management problems in well fields. A last open issue is whether or not the increasing pressure on the ground heat resource can be coped with under the existing regulations or whether they have to be adapted. The Swiss federal law allows a maximum temperature change of 3 degrees relative to the naturally prevalent temperature for shallow heat exchangers. How- ever, the law does not specify the naturally prevalent temperature in more detail. Currently, the heat emission from tunnels and underground parkings does not fall under the federal regulation of water protection [35]. Does this view still make sense in times of increasing pressure on aquifer heat resources? Already with limited computational power, the natural and human induced heat fluxes in an aquifer can be 100 assessed and the above question be addressed. Bibliography

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Appendix 110

Table 7.1: Overview over the Zurich water works internal reports, plans, and proﬁles that were available for this work. Bereich Typ Titel Jahr Autor

Limmat Plan Übersichtsplan der Limmat von Zürichsee zur Wipkinger- 1953 Büro für Wasserkraftanla- brücke gen der Stadt Zürich Profil Längenprofil der Limmat vom Zürichsee zur Wipkingerbrücke 1953 Büro für Wasserkraftanla- gen der Stadt Zürich Bericht Kraftwerk Höngg. Schwebstoffablagerungen im Stauraum der 1993 Ingenieurbüro für bauliche Limmat Anlagen Profil Längenprofil Kraftwerk Höngg 1998 Büro für Wasserkraftanla- gen der Stadt Zürich Plan Konzessionsstrecke Kraftwerk Höngg 1998 EWZ Hardhof Diverses Konzessionsbedingungen, Auszug aus dem Protokoll des 1981 WVZ1 Regierunsrates des Kantons Zürich Bericht Grundwasserwerk Hardhof, Konzessionspumpversuch, Schutz- 1989 WVZ1, ETH2, Wyssling3 zonen, Betriebskonzept Plan Transportleitung Hardhof-Lyren, Situation 1:2500 1989 Jäckli4 Plan Transportleitung Hardhof-Lyren, Längsprofil 1:2500/250 1989 Jäckli4 Bericht Neugestaltung der Schutzzonen im Gebiet Hardegg rechts der 1991 Wyssling3 Limmat Bericht Abstell- und Unterhaltsanlage SBB Zürich-Herdern, Hauptun- 1992 Jäckli4 tersuchung Umweltverträglichkeit, Teilbericht Hydrogeologie Bericht Jahresbericht über die Grundwasserspiegelschwankungen 1994, 1995 Jäckli4 Auszug Bericht Jahresbericht über die Grundwasserspiegelschwankungen 1995, 1996 Jäckli4 Auszug Bericht Hydrogeologischer Baubefund 1998 Wyssling3 Plan Schluckbrunnen S7-S12, Geologisches Profil 1:1000/100 (Aus- 1998 Wyssling3 führungsplan) Plan FEHLT! 1998 Electrowatt5 Plan übersichtsplan, Längenprofil Stollen Limmattal (Hardhof nach 1998 Electrowatt5 Lyren) Plan übersichtsplan, Profile/Querschnitte Stollen Limmattal (Hard- 1998 Electrowatt5 hof nach Lyren) Plan übersichtsplan, Aufsicht Stollen Limmattal (Hardhof nach 1998 Electrowatt5 Lyren) Plan Höhenlage des GW-Stauers, Variante hoch 1989 WVZ1, ETH2, Wyssling3 Plan Höhenlage des GW-Stauers, Variante tief 1989 WVZ1, ETH2, Wyssling3 Bericht Ausbau der Wasserversorgung Zürich, Gesamtkonzept und 1999 WVZ1 Ausführung der Projekte Bericht Grundwasserströmungen im Hardhof, Tracerversuche 2001 WVZ1 2000/2001 Profil Piezometer Bohrprofile und Filterstrecken 2005 WVZ1 Bericht Markierversuch 2006, Hydrogeologische Befunde und Konse- 2006 Wyssling3 quenzen für das GW Modell Hardhof Bericht Die Uferfiltration im Grundwasserwerk Hardhof 2006 WVZ1 Diverses Warnwerte für Grundwasserstand im Hardhof 2011 WVZ1 Brunnen Profil Filterbrunnen 306, 308–312, 314, 316, 317, 320, 324, 326, 328– 1975 Jäckli4 333, 335, 336 Bericht HFB A, Dokumentation der Pumpversuche 1976 WVZ1 Plan Fassungsstränge Horizontalbrunnen A 1976 Electrowatt5 Plan Fassungsstränge Horizontalbrunnen B 1976 Electrowatt5 Plan Fassungsstränge Horizontalbrunnen C, digital Plan Fassungsstränge Horizontalbrunnen D 1977 Electrowatt5 Plan Längenprofil Heberleitung Fischerweg 1977 Electrowatt5 Anreicherung Plan Anreicherungsbecken, Schluckbrunnen 1977 Electrowatt5 Bericht Limmatwasseraufbereitung Hardhof, projektierte Schluck- 1995 Wyssling3 brunnen (7-12). Resultate der hydrogeologischen Untersuchun- gen zur optimalen Plazierung der Schluckbrunnen Plan Limmatwasseraufbereitung Hardhof, projektierte Schluck- 1995 Wyssling3 brunnen, Geolog. Profil Profil Limmatwasseraufbereitung Hardhof, projektierte Schluck- 1995 Wyssling3 brunnen, Bohrprotokolle Profil Limmatwasseraufbereitung Hardhof, projektierte Schluck- 1995 Wyssling3 brunnen, Flowmetermessungen Profil Geologische Brunnenprofile S7 bis S12 1998 Wyssling3 Tabelle GWFörderung, Anreicherung mit Uferfiltrat 1998 WVZ1 Plan Anreicherungsanlagen, elektro-hydraulisches Betriebsschema 1999 WVZ1 Darstellung Anreicherungsanlagen, Auszug 2000 WVZ1 Messung Wasserverteilung in Schluckbrunnen 7-12 2006 WVZ1 Messung Verteilung Wasser Vertikalfilterbrunnen 306-324, Vgl. mit 3D 2006 WVZ1 Modell City Piezom. Profil Dokumentation Grundwasser-Messstellen 1993 WVZ1 Notizen Mappe mit Piezometer City (36xx), Koordinaten, Wasser- ?? stände Modell Bericht Grundwasseranreicherung Zürich City, Grundwassermodell 1984 WVZ1, Electrowatt5, Jäckli4 Generell Bericht überbauung Hardturm-Areal, Pfingsweidstrasse Zürich, 2007 Jäckli4 Hydrogeologische Beurteilung der geplanten Grundwasser- Wärmenutzung 1 WVZ refers to the Zurich water works. 2 ETH refers to the ETH Zurich. 3 Wyssling refers to the geology consultancy company Dr. Lorenz Wyssling AG. 4 Jäckli refers to the geology consultancy company Dr. Heinrich Jäckli AG. 4 Elektrowatt refers to the consultancy company Elektrowatt Infra AG. Curriculum vitae

Beatrice Sabine Marti

Date of birth: July 10, 1984 Nationality: Swiss marti @ ifu.baug.ethz.ch

Education

10/2010 – 06/2014 Ph.D. studies at ETH Zurich, Switzerland, Institute of Envi- ronmental Engineering, Thesis: "Real-time management and control of groundwater flow field and quality" (Supervisor: Prof. Dr. Wolfgang Kinzelbach) 09/2008 – 06/2010 Master studies in Environmental Engineering at ETH Zurich, Switzerland, Degree: MSc ETH Env. Eng.; Master thesis: "Bioelectrochemical removal of sulfur from source-separated urine" (Supervisor: Dr. Kai Udert and Prof. Dr. E. Morgenroth) 09/2005 – 6/2008 Bachelor studies in Environmental Engineering at ETH Zurich, Switzerland, Degree: BSc ETH Env. Eng.; Bachelor thesis: "Membrane processes in drinking water purification" (Supervisor: Dr. Wouter Pronk and Prof. Dr. W. Guyer) 06/2003 Maturität (university entrance examination) at Kantonsschule Trogen, Switzerland.

Journal Publications

B. S. Marti, G. Bauser, F. Stauﬀer, U. Kuhlmann, H.-P. Kaiser, and W. Kinzelbach (2012). An expert system for real-time well ﬁeld management. Water Science and Technology: Water Supply,12(5), pp 699–706, doi:10.2166/ws.2012.021

Conference contributions

1. B. Marti, D. McLaughlin, W. Kinzelbach, H.-P. Kaiser: "Ensemble control of the Hardhof well field under constraints", EGU, Vienna, Austria, April 8-13, 2013 111 2. B. S. Marti: "Echtzeitmodell - Beispiel Hardhof" (invited talk), SGH Jahresta- gung - Grundwassermonitoring, Sierre, Switzerland, May 4-5, 2012 3. B. S. Marti, H.-P. Kaiser, U. Kuhlmann, H.-J. Hendricks Franssen, W. Kinzel- bach: "Application of a groundwater flow model for real-time well field management - lessons learned", EGU, Vienna, Austria, April 22-27, 2012 4. B. S. Marti, G. Bauser, F. Stauffer, U. Kuhlmann, H.-P. Kaiser, W. Kinzel- bach: "An Expert System for well field management", IWRM, Dresden, Ger- many, October 12-13, 2011 5. B. S. Marti, G. Bauser, U. Kuhlmann, H.-P. Kaiser, F. Stauffer, W. Kinzel- bach: "Management of temperature in an urban well field", ModelCare, Leipzig, Germany, September 18-22, 2011