Phd Thesis, Université Laval, Quebec City, QC, Canada

Simulating surface water and groundwater ﬂow dynamics in tile-drained catchments

Thèse

Guillaume De Schepper

Doctorat interuniversitaire en Sciences de la Terre Philosophiæ doctor (Ph.D.)

Québec, Canada

Résumé

Pratique agricole répandue dans les champs sujets à l’accumulation d’eau en surface, le drainage souterrain améliore la productivité des cultures et réduit les risques de stagnation d’eau. La contribution signiﬁcative du drainage sur les bilans d’eau à l’échelle de bassins versants, et sur les problèmes de contamination dus à l’épandage d’engrais et de fertilisant, a régulièrement été soulignée. Les écoulements d’eau souterraine associés au drainage étant sou- vent inconnus, leur représentation par modélisation numérique reste un déﬁ majeur. Avant de considérer le transport d’espèces chimiques ou de sédiments, il est essentiel de simuler correctement les écoulements d’eau souterraine en milieu drainé. Dans cette perspective, le modèle HydroGeoSphere a été appliqué à deux bassins versants agricoles drainés du Danemark.

Un modèle de référence a été développé à l’échelle d’une parcelle dans le bassin versant de Lillebæk pour tester une série de concepts de drainage dans une zone drainée de 3.5 ha. Le but était de déﬁnir une méthode de modélisation adaptée aux réseaux de drainage complexes à grande échelle. Les simulations ont indiqué qu’une simpliﬁcation du réseau de drainage ou que l’utilisation d’un milieu équivalent sont donc des options appropriées pour éviter les maillages hautement discrétisés. Le calage des modèles reste cependant nécessaire.

Aﬁn de simuler les variations saisonnières des écoulements de drainage, un modèle a ensuite été créé à l’échelle du bassin versant de Fensholt, couvrant 6 km2 et comprenant deux réseaux de drainage complexes. Ces derniers ont été simpliﬁés en gardant les drains collecteurs princi- paux, comme suggéré par l’étude de Lillebæk. Un calage du modèle par rapport aux débits de drainage a été réalisé : les dynamiques d’écoulement ont été correctement simulées, avec une faible erreur de volumes cumulatifs drainés par rapport aux observations. Le cas de Fensholt a permis de valider les conclusions des tests de Lillebæk, ces résultats ouvrant des perspectives de modélisation du drainage lié à des questions de transport.

iii

Abstract

Tile drainage is a common agricultural management practice in plots prone to ponding issues. Drainage enhances crop productivity and reduces waterlogging risks. Studies over the last few decades have highlighted the significant contribution of subsurface drainage to catchments water balance and contamination issues related to manure or fertilizer application at the soil surface. Groundwater flow patterns associated with drainage are often unknown and their representation in numerical models, although powerful analysis tools, is still a major challenge. Before considering chemical species or sediment transport, an accurate water flow simulation is essential. The integrated fully-coupled hydrological HydroGeoSphere code was applied to two highly tile-drained agricultural catchments of Denmark (Lillebæk and Fensholt) in the present work.

A first model was developed at the field scale from the Lillebæk catchment. A reference model was set and various drainage concepts and boundary conditions were tested in a 3.5 ha tile-drained area to find a suitable option in terms of model performance and computing time for larger scale modeling of complex drainage networks. Simulations suggested that a simplification of the geometry of the drainage network or using an equivalent-medium layer are suitable options for avoiding highly discretized meshes, but further model calibration is required.

A catchment scale model was subsequently built in Fensholt, covering 6 km2 and including two complex drainage networks. The aim was to perform a year-round simulation accounting for variations in seasonal drainage flow. Both networks were simplified with the main collecting drains kept in the model, as suggested by the Lillebæk study. Calibration against hourly measured drainage discharge data was performed resulting in a good model performance. Drainage flow and flow dynamics were accurately simulated, with low cumulative error in drainage volume. The Fensholt case validated the Lillebæk test conclusions, allowing for further drainage modeling linked with transport issues.

v Contents

Résumé iii

Abstract v

Contents vi

List of Figures viii

List of Tables ix

Acknowledgments xiii

Preface xv

1 Introduction 1 1.1 Background and motivation ...... 1 1.2 Literature review ...... 4 1.2.1 Drainage deﬁnition and classiﬁcation ...... 4 1.2.2 Use of tile drainage ...... 6 1.2.3 Hydrology of drained areas ...... 8 1.2.4 Tile drainage modeling ...... 13 1.3 Research objectives ...... 20

2 Study sites 21 2.1 Lillebæk ...... 24 2.2 Norsminde and Fensholt ...... 25

3 Numerical model 27 3.1 Introduction ...... 27 3.2 Governing flow equations ...... 27 3.2.1 Subsurface flow ...... 27 3.2.2 Surface flow ...... 29 3.2.3 Drainage flow ...... 29 3.2.4 Coupling water flow ...... 30 3.2.5 Interception and evapotranspiration ...... 31 3.3 Discrete drains vs. Seepage nodes ...... 33 3.3.1 Steady-state simulations ...... 35 3.3.2 Transient simulations ...... 42

vi 4 Simulating coupled surface and subsurface water ﬂow in a tile-drained agricultural catchment 45 Abstract ...... 47 Résumé ...... 48 4.1 Introduction ...... 49 4.2 Methods ...... 53 4.2.1 Study area ...... 53 4.2.2 Numerical model ...... 55 4.2.3 Conceptual model ...... 56 4.2.4 Reference model ...... 58 4.2.5 Test models ...... 61 4.3 Results ...... 66 4.3.1 Reference model ...... 66 4.3.2 Test models ...... 72 4.3.3 Computational performance ...... 78 4.4 Discussion and conclusions ...... 79

5 Seasonal variations simulation of local scale tile drainage discharge in an agricultural catchment 83 Abstract ...... 85 Résumé ...... 86 5.1 Introduction ...... 87 5.2 Materials and methods ...... 89 5.2.1 Site description ...... 89 5.2.2 Numerical model ...... 90 5.2.3 Model conceptualization ...... 92 5.2.4 Heterogeneous vs. homogeneous models ...... 100 5.2.5 Calibration ...... 101 5.3 Results ...... 104 5.3.1 Water balance ...... 104 5.3.2 Drainage processes ...... 104 5.3.3 Drain ﬂow ...... 108 5.3.4 Hydraulic heads ...... 114 5.4 Discussion ...... 118 5.4.1 HydroGeoSphere model performance ...... 118 5.4.2 Drainage conceptualization ...... 119 5.4.3 Comparison of model codes (HydroGeoSphere vs. MIKE SHE) . . . 121 5.5 Conclusion ...... 123

6 Conclusions and perspectives 125

Bibliography 129

vii List of Figures

1.1 Classiﬁcation of agricultural drainage system types ...... 5 1.2 Conventional vs. controlled subsurface drainage systems ...... 9 1.3 Flow paths in a typical glacial till catchment of Denmark ...... 12

2.1 Location of the Lillebæk and Fensholt catchments ...... 22 2.2 Geological map of Denmark ...... 23 2.3 Lillebæk catchment topography ...... 24 2.4 Topography in the Fensholt and Norsminde catchments ...... 26

3.1 Simulation domain of the Fipps et al. (1986) verification example ...... 35 3.2 Verification example: vertical pressure head profiles of numerical and analytical solutions ...... 36 3.3 Verification example: hydraulic head distribution in the yz plane ...... 38 3.4 Verification example: hydraulic head distribution in 3D ...... 39 3.5 Verification example: hydraulic head in 3D and water flow pathways ...... 40 3.6 Verification example: discrete drain and seepage nodes hydrographs of the transient simulation ...... 43

4.1 Location of the Lillebæk catchment and modeling area ...... 54 4.2 2D meshes used for the Lillebæk reference and test simulations ...... 61 4.3 Lillebæk reference model hydrographs ...... 68 4.4 Lillebæk reference model saturation distribution in the clayey till ...... 69 4.5 Water table elevation in the Lillebæk reference and Test 2 model ...... 70 4.6 Drainage ﬂow hydrographs of the Lillebæk test models ...... 75 4.7 Drainage ﬂow hydrograph with daily precipitation applied in Lillebæk . . . . . 77

5.1 Location of the Fensholt and Norsminde catchments ...... 91 5.2 Fensholt 2D mesh with reﬁned nodes highlighted ...... 94 5.3 Geological units of the Fensholt heterogeneous model ...... 95 5.4 Cumulative corrected precipitation, corrected potential evapotranspiration, simulated evapotranspiration and simulated canopy interception in Fensholt . . 103 5.5 Observed and simulated drainage hydrographs in Fensholt with HydroGeoSphere 106 5.6 Pressure head distribution and depth to water table in AreaA and AreaB . . . 107 5.7 Observed and simulated cumulative drain ﬂow volumes in Fensholt ...... 109 5.8 Hydrographs produced by HydroGeoSphere and MIKE SHE for Fensholt . . . 113 5.9 Observed and simulated hydraulic head in piezometers of AreaA in Fensholt . . 116 5.10 Observed and simulated hydraulic head in piezometers of AreaB in Fensholt . . 117

viii List of Tables

1.1 Subsurface drainage indirect eﬀects on soils, streams or plants ...... 12 1.2 Non exhaustive list of models suitable for tile drainage modeling ...... 19

3.1 Verification example: pressure head values along the x = 15 m vertical profile . 37 3.2 Verification example: computational times and drainage volumes of the discrete drain and seepage node simulations ...... 41 3.3 Verification example: flux rate values compared to discrete drain and seepage nodes discharge rates ...... 42

4.1 Hydraulic properties of the Lillebæk reference model ...... 59 4.2 Lillebæk simulations convergence criteria ...... 60 4.3 List of Lillebæk simulations performed and their properties ...... 62 4.4 Hydraulic properties of the Lillebæk equivalent medium test ...... 63 4.5 Hydraulic properties for the Lillebæk dual-permeability test ...... 64 4.6 Drainage and overland ﬂow rates, and groundwater head values in Lillebæk . . 69 4.7 Water balance values of the Lillebæk simulations ...... 71 4.8 Mesh speciﬁcation and computational times for the Lillebæk simulations . . . . 77

5.1 Overland flow properties of the Fensholt model ...... 92 5.2 Hydraulic properties of the hydrofacies from the Fensholt heterogeneous geological model ...... 96 5.3 Hydraulic properties of the topsoil units from the Fensholt model ...... 97 5.4 Overland flow properties of the Fensholt model ...... 99 5.5 Performance criteria for measuring the Fensholt model efficiency ...... 102 5.6 Model performance criteria calculated over the calibration period in Fensholt . 111

Je vais par les sentiers Par les sentiers et sur les routes, Par delà la mer et plus loin, plus loin encore, (...) Devant moi s’avancent les Souﬄes des Aïeux. Birago Diop, Viatique

Acknowledgments

My special thanks go to my supervisor, Prof. René Therrien, for giving me the opportunity to step into the HydroGeoSphere world through this PhD work. The fulﬁllment of this work was made possible thanks to his guidance and wise advice. While giving my models a trained eye, he has kept me on track throughout my labor. And by his ﬂexibility, he gave me room for maneuver that has led me to interesting modeling challenges. I’m also grateful to René for giving me the chance to present our work at various international conferences.

I would like to gratefully thank Prof. Jens Christian Refsgaard, of the Geological Survey of Denmark and Greenland (GEUS), who has implemented and lead the NiCA Research Project, of which this thesis is part. We have had many valuable and fruitful discussions that were essential for the progress of my work. Our successful collaboration is due to his formidable knowledge and input on concepts we have developed for the Lillebæk and Fensholt models. I am also thankful to the occasion he gave me to join his friendly research team in Copenhagen for half a year.

From the Department of Hydrology at GEUS, my gratefulness goes especially to Anne Lausten Hansen for our Lillebæk collaboration and her helpful comments, data provided and warm welcome when I was there. She has always had a full involvement when answering my questions. I remember my ﬁrst steps in Copenhagen on a foggy Sunday morning with Anne and Britt Stenhøj Baun Christensen, who very kindly took me on a discovery walk through the city. I also deeply thank Xin He for his contribution, data and insightful comments during our Fensholt collaboration. I thank Lisbeth Flindt Jørgensen who perfectly organized our meetings in Denmark. I would also like to thank all the other members of this department for welcoming me as one of them. I would like to underline my gratitude to Charlotte Kjær- gaard and Bo Vangsø Iversen (Department of Agroecology, Aarhus University) for their data provided and details given about Fensholt.

Accurate runs of my models have been ensured by high quality meshes created by means of powerful scripts from Pierre Therrien, teaching and research coordinator at Université Laval. He has performed a considerable amount of work in the shadow of Master and PhD students while being available when the need was felt. He has contributed in many ways to our success and I am thankful to him for that.

xiii As Pierre has played an important role for me, so have colleagues and friends from the Depart- ment of Geology and Geological Engineering by continuously exchanging our experiences with HydroGeoSphere and sticking together in hard modeling times. Nelly Montcoudiol (geanre), Fabien Cochand (tu chiales), Tobias Graf (c’est l’optimal) and Jalil Hassaoui (on fait les choses) have been the motivating core from which advice, help and support have originated, together with lots of fun and relaxing times. Some visiting professors and researchers have helped me with their knowledge and input; I particularly think of Prof. Philip Brunner (Uni- versité de Neuchâtel, Switzerland), Tanguy Robert (AQUALE, Belgium), Samuel Wildemeer- sch (SPAQuE, Belgium), Oularé Sékouba (Université Félix Houphouët-Boigny, Ivory Coast), Christian Möck (Eawag, Switzerland) and Carlos Guevara (Leibniz Universität Hannover, Germany). Life at the department was made pleasant by their members with whom I enjoyed having discussions and sharing time. I especially thank my former oﬃcemates, that have not been named yet: Elham, Debora, Antoine, Arnaud, Donald, Jia, Karl, Nicolas and Olivier.

I thank Rob McLaren (Golder Associates Ltd., ON), Young-Jin Park and Hyoun-Tae Hwang (Aquanty Inc., ON) for their help, tips and sharing of their deep knowledge of HydroGeo- Sphere.

I give special regards to Prof. Philippe Renard (Université de Neuchâtel) who incited me to jump into this doctorate when finishing my masters under his supervision. His passion and involvement for the profession made me want to carry on in the research field. I also thank Andrea Borghi (Bundesamt für Landestopografie swisstopo, Switzerland), who completed his PhD in Neuchâtel under the supervision of Philippe Renard. I did learn a lot from you, especially how to keep motivated during a doctorate.

I would like to thank my family for their unwavering support since my very ﬁrst day in the geology ﬁeld. After putting a mountain range between us, this time was an ocean: my beloved Belgium is far from here, but their encouragement and strength always guided me throughout my work. I was also blessed with support originating from relatives in France and Switzerland. Last but not least, I deeply thank Virginie for her support and trust along the years, dispelling any doubt about the achievement of this work regardless of the ups and downs.

To all the friends who have crossed my path in Belgium, Switzerland, Canada, Denmark and Serbia to get to this point: thank you.

xiv Preface

The work presented in this thesis was fulﬁlled at the Department of Geology and Geological Engineering at Université Laval (Quebec City, Canada) under the supervision of Professor René Therrien. It was carried out in collaboration with the Department of Hydrology at the Geological Survey of Denmark and Greenland (GEUS) (Copenhagen, Denmark). Half a year of external research stay was spent at the Department of Hydrology at GEUS under the supervision of Prof. Jens Christian Refsgaard.

This work was ﬁnancially supported by the Danish Strategic Research Council through the NiCA Research Project’s Program Commission on Sustainable Energy and Environment under contract No. DSF 09-067260.

The first chapter of this manuscript provides an overview of the present PhD research background, state-of-the-art knowledge of the use of drainage systems and tile drainage modeling, and the research objectives. Following this, chapter 2 briefly describes both sites studied in this work. In chapter 3, governing flow equations used in models developed for both study sites are defined. In addition, a simple tile drainage verification example was run to document the differences observed in simulated water flow from a discrete drain and from drainage sink nodes. Chapter 4 is a research paper published in Journal of Hydrology (De Schepper et al., 2015) entitled «Simulating coupled surface and subsurface water flow in a tile-drained agricultural catchment ». In this article, various concepts were tested for describing tile drainage in numerical models. Chapter 5 is a paper that was submitted to Water Resources Research on October 16, 2015. Its title is «Seasonal variations simulation of local scale tile drainage discharge in an agricultural catchment ». Here, tile drainage flow was run over a year-round simulation with two complex drainage networks. The last chapter concludes this work, dis- cusses perspectives and provides insight on potential future research in the field of tile drainage modeling.

Chapter 1

Introduction

1.1 Background and motivation

Agricultural production needs have lead to widespread use of tile drainage under humid climatic conditions over the last few decades. Tile drainage is used worldwide in agricultural lands for reducing flooding risks, for removing unwanted excess water from the top soil, for enhancing crop yields, for land reclamation to expand crop areas and, in some cases, for reducing or controlling the salinity of soils (Hoffman and Durnford, 1999). Tile drains are usually found in low permeability clayey to silty soils. Such pipes buried underground act as shortcuts in the water cycle: water is captured, channeled and discharged to local streams in extremely short times, compared to its natural residence time in soils. In addition, macropores or fractures generate even faster water flow as they are preferential flow pathways. This often comes with nutrient and pesticide transport through the soils to the drains (Šimůnek et al., 2003). In the drains, soil particle transport occurs in addition to solute transport, which regularly leads to clogging issues (e.g. Chapman et al., 2001).

Nutrient contamination of groundwater and surface water is a widely known threat to water resources. The presence of such compounds in discharge waters has also been shown to lead to significant eutrophication of surface water, accompanied by deterioration of water quality, and what is referred to as dead zones due to algal blooms in estuaries and coastal waters (Blann et al., 2009). This promotes algal productivity leading to depletion of oxygen in waters (Grant and Blicher-Mathiesen, 2004), all of which causes significant changes to local conditions. The intensification of agricultural practices in Europe since the late 1970’s goes

1 hand in hand with an increase in nitrate concentrations in groundwater and surface water bodies (Iversen et al., 1998). In Denmark, tile drainage is commonly used in agricultural areas (Olesen, 2009); related nutrient contamination issues are thus of major concern (Kronvang et al., 1996).

Particular attention is paid to these issues within the NiCA Project1, of which the present PhD work is part. The NiCA Project focuses on nitrate reduction within geologically heterogeneous catchments in Denmark. The main aim of the project is to use and develop tools for estimating nitrate reduction rates in the saturated and unsaturated zones under agricultural crops. The starting hypothesis of the project is that a good prediction of nitrate reduction in the soil relies on an appropriate characterization of geological heterogeneity. The setting- up of the NiCA Project has been done in response to the Water Framework Directive of the European Parliament and the European Council. By means of this directive, published and adopted in December 2000, the European Commission expects the European Member States to implement a water management strategy and to reach a good quality for their water bodies (groundwater, surface and coastal waters). In the NiCA case, the Nitrates Directive 91/676/EEC (European Commission, 2008) is the most important one. It requires, among others, reducing the impact of nutrient loads from agricultural crops on groundwater, surface and coastal waters. A report published by the Geological Survey of Denmark and Greenland (GEUS) (Ernstsen et al., 2006) presents a national scale nitrate reduction map and shows that two-thirds of the nitrate leached from the soil surface is being reduced before reaching the coastal waters. It is known that nitrate reduction processes may occur in the saturated zone of clayey tills in Denmark (e.g. Hansen et al., 2008), and that these processes are affected by geological heterogeneities at small scales. In addition to this nitrate reduction map, a tool has recently been developed for estimating nitrogen risk in Danish catchments based on nitrogen leaching and retention data (Blicher-Mathiesen et al., 2014). Even though such tools are of prime importance, they are not precise enough to distinguish vulnerable areas at catchment or ﬁeld scales. One of the main objectives of the NiCA project is therefore to develop methods and knowledge at smaller scales. A comprehensive description of this project has been provided by Refsgaard et al. (2014).

Numerous studies have shown the signiﬁcant impact of subsurface drainage on groundwater

1Oﬃcial website: http://www.nitrat.dk

2 and surface water flow patterns by mean of numerical models at the field scale to catchment scale (e.g. Rozemeijer et al., 2010). Such studies usually present results of groundwater flow models only (Purkey et al., 2004), coupled modeling approaches of a groundwater flow and overland water flow model (Kim and Delleur, 1997; Maalim and Melesse, 2013; Hansen et al., 2013), or even groundwater and drainage water flow models coupled by means of an external module (Henine et al., 2014). Water exchange processes occur between the subsurface body, the surface domain and drainage pipes. Yet few models have been developed with a fully coupled scheme, having the ability of simulating tile drainage flow in a variably saturated subsurface domain fully coupled to the surface domain, even if they are promising tools for understanding and quantifying tile-drained catchments dynamics. In the framework of the NiCA project, such modeling capabilities were needed and the HydroGeoSphere code (Therrien et al., 2010) was chosen for exploring its potential in the project context.

3 1.2 Literature review

1.2.1 Drainage deﬁnition and classiﬁcation

Tile drainage is one of the various techniques used in agricultural drainage systems. The intended effect of using such systems is to improve water runoff and to avoid ponding at the land surface. Drainage systems are artificial and installed for ensuring agricultural production needs. They can be installed at the land surface (surface drainage systems) or underground (subsurface drainage systems) (Figure 1.1). In both cases, they consist of two main components (Oosterbaan, 1994): a field drainage system, which aims at lowering the water table in the field, and a main drainage system, also known as a collector system, used for conducting water out of the field to an outlet.

Surface field drainage systems are divided into regular and checked systems, in both of which water flow is driven by gravity. Surface regular drainage systems are generally made of ditches or trenches used in bedded land (flat) or graded land (sloping) for drying the land surface. Surface checked systems are used in basins and terraces having water flow control bunds that are typically found in submerged fields (e.g. rice-growing terraces).

Subsurface field drainage systems are differentiated into conventional and controlled systems (see Figure 1.2). Conventional drainage systems are composed of a simple drainage network without any complementary equipment. Controlled drainage is a drainage technique in which the network has additional equipment (pit, tank, flashboard riser, drop log, etc.) in order to control drainage flow (Evans et al., 1991, 1995). Both systems drain water by gravity but, by using controlled drainage, the global drainage outflow of a field may be reduced by up to 30 % in comparison to conventional drainage. In the case of controlled systems, drainage may be performed by pumping water in a series of vertical wells.

As they are located at the surface, surface drainage systems allow for faster water ﬂow than subsurface drains, which have thus slower response to rainfall events (Robinson, 1990). In either case, water is routed by collector drains to an outlet that is an open-ditch surrounding ﬁelds or a local stream. Before reaching the outlet, collector drains direct water to disposal drains (surface drainage systems) or to deep main drains (subsurface drains), and then to the outlet or to disposal drains. Disposal drains act here as temporary storage drains.

4 One should note here that natural drainage systems exist too, such as caves, root holes, fractures, etc. Drains are also installed in other hydrologic environments for avoiding ﬂoods, such as in urban areas (Maršálek and Sztruhár, 1994) or even sports ﬁelds (Adams, 1986).

Graded land Regular systems Surface drainage Bedded land systems (by gravity) Bunded basins Checked systems Bunded terraces

FIELD DRAINAGE Subsurface drains SYSTEMS (tiles, pipes, moles, (INTERNAL ) Conventional ditches, channels) systems Subsoiling (deep ploughing) Subsurface drainage systems (by gravity or Subsurface drains pumped) (gravity ﬂow with controlled structures) Controlled systems Well drainage (pumped)

Deep collectors using pipes or ditches Deep main drains (for subsurface drainage) MAIN DRAINAGE SYSTEMS Outlet (EXTERNAL ) Shallow collectors using channels or ditches Disposal drains (for surface drainage)

Figure 1.1: Classification of agricultural drainage system types. Black solid lines depict the classification in itself, while blue arrows indicate a transfer of water from one drainage network component to another. Modified from Oosterbaan (1994).

5 1.2.2 Use of tile drainage

Tile drainage systems are generally found in the Northern Hemisphere, mostly in North Amer- ica and Europe, but they are also used in other regions such as China, India or Egypt (Nijland et al., 2005). The northern European countries usually have a large proportion of subsurface drained agricultural lands, with the Netherlands having the highest percentage of drained fields in the region (about 65 % of the total fields) (Robinson and Rycroft, 1999), whereas southern European countries seem to have less than 10 to 20 % of the cropland equipped with subsurface drainage systems. This marked difference highlights the presence of glacial till deposits in the topmost soils of northern Europe which, combined with spatial climatic variations (rain, temperature and evaporation distribution), cause longer waterlogging periods (Green, 1980). An exception to this statement is Hungary with 73 % of agricultural fields that are drained (Goudie, 2013). This country is part of the Pannonian Basin that is dominated by fine lake and deltaic deposits (Juhász et al., 1997).

Besides its application to arable land, tile drainage is also used in peatlands found in northern Europe and North America (Baldock et al., 1984; Hillman, 1992). By lowering the water table, subsurface drainage enhances soil aeration in peat soils, which is essential for the forestry industry in boreal regions of Fennoscandian and North-American countries (Rothwell et al., 1996). Extraction of peat is another application linked with peatlands drainage. Tile drainage is also commonly associated with irrigation systems for proper water management in arid and semi-arid regions (e.g. Mohanty et al., 1998). In such regions, where high evapotranspiration rates are observed, controlled drainage is preferred to conventional drainage so that the water table level is kept at a desired level allowing suﬃcient soil moisture content for plant uptake in the root zone (Ayars et al., 2006). Another purpose of subsurface drainage in arid areas is to control the salinity of soils (Skaggs et al., 1994). As evapotranspiration is high, residual salt precipitates at the soil surface or in the root zone. Inﬁltrating water through the soil surface and leaching through the root zone may thus dissolve salt and transport it in drainage pipes, resulting in contamination of surface water (Tedeschi et al., 2001).

In North America, it is estimated that about 43 million ha of land in the United States, mostly in the Corn Belt region (Zucker and Brown, 1998), and 8 million ha in Canada are tile-drained (Skaggs et al., 1994; Madramootoo et al., 2007). Tile drainage is a common practice in forested peatlands in Alberta (Rothwell et al., 1996) and in Ontario (Payandeh,

6 1973) to ensure tree growth. Subsurface drainage is also encountered in agricultural ﬁelds of eastern Canadian provinces (Madramootoo et al., 2007), mainly in Ontario (Whiteley and Ghate, 1979; Irwin and Bryant, 1986) and Québec (Natho-Jina et al., 1987; Simard et al., 1995; Elmi et al., 2004).

In some cases, tile drainage likely induces enhanced migration of certain chemical species and contamination of downstream water bodies such as streams, lakes and marine waters. Nutrient and pesticide transport can lead to freshwater and coastal water contamination, threatening local ecosystems (Blann et al., 2009). Serious eutrophication and hypoxia issues have been reported worldwide, for example, in the Gulf of Mexico (Rabalais et al., 2001), the Baltic Sea (Larsson et al., 1985), the North Sea (Howarth et al., 1996), coastal waters of Southern Japan (Suzuki, 2001) and the Black Sea (Mee, 1992). Other environmental issues have also been reported such as trout spawning beds ﬁlling with sediments or drying waterfowl habitat in Ontario (Irwin and Bryant, 1986) and even bacterial contamination (Escherichia coli) of surface water bodies due to manure application in tile-drained areas (Stratton et al., 2004).

In Denmark, about 50 % of agricultural lands are tile-drained (Olesen, 2009). Irrigation systems, likely combined with subsurface drainage systems, are present in 17 % of the Danish agricultural lands and they are only used temporarily (eﬀective irrigation is less than 17 %) (Baldock et al., 2000).

7 1.2.3 Hydrology of drained areas

Surface drainage systems, as defined in Figure 1.1, are installed in flat areas where high precipitation rates are observed in combination with a low infiltration capacity of soils, leading to water ponding at the surface. When shallow water tables are observed, subsurface drainage systems are typically installed in low hydraulic conductivity soils (Oosterbaan, 1994). If needed, both drainage systems may work simultaneously as a preventive measure when high waterlogging risks are encountered.

When considering the water cycle in an agricultural environment, tile drainage may not be the first component that comes to mind. Precipitation, evapotranspiration, stream flow, runoff and groundwater flow are usually the main components considered (Gordon et al., 2008). Irrigation may be another key part of the hydrologic cycle in some cases (Tedeschi et al., 2001), but it often goes hand in hand with subsurface drainage. An appropriate balance between irrigation and drainage is needed to control water transfer from the land surface to the drains. Limited drainage induces high watertables and soil salinization. On the other hand, too intense drainage can critically lower the water table and may result in salt dissolution and mobilization in drainage waters. Drainage flow salinity is therefore likely proportional to the water table depth: the deeper the water table, the higher the salinity of the water discharged by drains (Christen and Skehan, 2001).

According to common practice, tile drainage pipes are usually buried from 1 to 2 m below the soil surface and the horizontal spacing is about 20 to 50 m between each pipe (Burton, 2010). These values may vary depending on speciﬁc local conditions such as hydraulic properties of soils or precipitation rates (Brooks and Corey, 1964b; Randall and Goss, 2008).

Water management systems such as tile drains have an impact on water flow and water quality at the field scale, but impacts may also be significant at the catchment scale (Carlier et al., 2007). At the field scale, tile drainage flow is affected by horizontal drain spacing, the shape of the drainage network and the soil properties. At the catchment scale, drainage flow is influenced by the spatial disposition of the fields within the catchment, and therefore by the spatial arrangement of the entire collecting network, as well as the drainage capacity of the network (Robinson and Rycroft, 1999). As defined by Yue (2010), drainage flow can be separated in two parts: a lateral flow component, for which water flows to pipes and

8 Water table Drainage outlet

CONVENTIONAL DRAINAGE

Control structure Water table Drainage outlet

CONTROLLED DRAINAGE

Figure 1.2: Conventional versus controlled subsurface drainage systems, and their associated conceptual ﬂow paths. Modiﬁed from Zucker and Brown (1998).

originates from the surrounding media, and the actual drainage flow in the drains. Lateral flow intensity determines the drainage network efficiency, and it depends on several factors, namely soil hydraulic conductivity, drain diameter, perforation frequency along the pipes, etc.

When tile drains are found in clay-dominated soils (>35 %), additional drainage structures may be created by digging subsurface channels with a ripper blade combined to a cylindrical foot and an expander (Filipović et al., 2014). This is called mole drainage. It helps maintain a low water table when tile drainage systems action is not sufficient and it allows greater lateral flow to tile drains. While creating mole drains, ripper blades induce the formation of vertical cracks in which preferential water flow occurs towards the underlying mole drains (Leeds-Harrison et al., 1982). Tile and mole drains are non conductive under unsaturated conditions because positive pressure must occur before water can start flowing into them (Stormont and Zhou, 2005).

As pointed out here, tile drainage avoids water storage in soils and discharges water to local streams, acting as a shortcut in the hydrologic cycle. A non-exhaustive insight of indirect eﬀects related to subsurface drainage is listed in Table 1.1 (Schothorst, 1978; Konyha et al.,

9 1992; Oosterbaan, 1994; Uusitalo et al., 2001; Rudy, 2004; Blann et al., 2009).

Despite their widespread use, tile drainage systems can’t be designed based on established rules. Designing such networks is highly dependent on local factors such as soil structure, topography and crop rotation (Sheler, 2013). As drainage systems usually discharge in local streams, tile-drained areas likely induce higher flow peaks in downstream surface waters during heavy rainfall events (Wiskow and van der Ploeg, 2003). However, as mentioned in Table 1.1, it appears from the literature that both reductions and increases of downstream peak discharge in surface waters are observed in tile-drained areas. This issue has been documented and discussed for decades (Robinson and Rycroft, 1999). In general, low permeability drained soils seem to have a positive effect by reducing downstream peak discharge (Robinson, 1990; Skaggs et al., 1994). On the other hand, more permeable drained soils tend to increase downstream peak discharge leading in some cases to flooding events (Robinson, 1990; Wiskow and van der Ploeg, 2003). Robinson and Rycroft (1999) add a shade to this statement by remarking that, in areas where shallow water table levels are found, peak discharge rates appear to be decreased compared to the initial water table, prior to the drainage network installation. During drainage, higher water storage capacity of soils is gained and therefore water infiltrates and runoff decreases. Whereas with a deep initial water table level, tile drainage shortcuts the infiltrating water after a rainfall event and discharges water in local streams resulting in increased surface water peaks intensity. Both increases and decreases in discharge peaks have been observed in agricultural catchments as well as in forest peatlands (Mustonen and Seuna, 1971; Heikurainen et al., 1978; Christen and Skehan, 2001; Holden et al., 2004; Deasy et al., 2009).

The extension of tile-drained areas is known to be proportional to drainage flow rates; the larger the drainage network, the higher the drainage flow rate (King et al., 2014). Yet, this observation may be site-specific and the authors mention that detailed comprehension of all the hydrological processes that occur in tile-drained areas is still a major knowledge gap.

Water flow patterns in a typical Danish tile-drained catchment are shown in Figure 1.3. A part of the infiltrating water is drained and exported to surface water bodies with a very short residence time in the underground due to fast turbulent flow in the drainage pipes. The remaining water recharges local, regional or deep aquifers by following natural flow pathways and discharges in surface or coastal waters. Nitrate transport is often associated with these

10 water ﬂow patterns. It is transported from the soil surface or the root zone to the drains and aquifers. When reaching the drains, nitrate is usually transported as a conservative chemical species favored by oxic conditions, as shown by the oxidized zone. A reduced zone is found deeper, usually in the saturated zone. Denitriﬁcation occurs when reaching the saturated zone, that is delimited by the redox interface (Hansen, 2006); nitrate is transported and reduced as it becomes a reactive chemical species (Hansen, 2014). Nitrate reduction results in nitrogen loss from the system through gas mainly under its N2 forms (Korom, 1992; Appelo and Postma, 2005). When discharged in stream waters, unreduced nitrate causes severe contamination issues (e.g. Blann et al., 2009).

11 Table 1.1: Subsurface drainage indirect eﬀects on soils, streams or plants.

Positive effects Negative effects Increased aeration of the soil Increased risks of drought Reduction of downstream peak discharge ∗ Increase of downstream peak discharge ∗ Stabilized soil structure Soil subsidence in peat soils Higher availability of nitrogen in the soil Decomposition of organic matter Higher crop production Erosion of soils Better workability of the soil Acidification of potential acid sulphate soils Earlier planting dates Surface water loading with sediments Decrease of chemical species in soils Downstream surface water contamination Chemical species are typically nitrate, phosphorous, salt, some pesticides, etc.

∗ Reduction or increase of downstream peak discharge rates depend on local hydrologic conditions. See discussion above.

Figure 1.3: Flow paths in a typical glacial till catchment of Denmark and associated redox interface. Modiﬁed from Hinsby et al. (2008).

12 1.2.4 Tile drainage modeling

Several numerical models have been developed to simulate hydrological processes related to subsurface drainage. They have been used to demonstrate that tile drainage networks have a key impact on groundwater and surface water flow as well as chemical species transport and erosion (Gärdenäs et al., 2006; Kiesel et al., 2010; Rozemeijer et al., 2010; Warsta et al., 2013). Numerical models have also demonstrated reliable predictive abilities when used in conjunction with in situ monitoring systems (Tim, 1996). Representing discrete tile drains in a model requires information on the location and depth of the individual drains that constitute the drainage network, but which is often unavailable. Discretizing complex drainage networks may also lead to extremely dense computational meshes causing potentially very long simulation times. As a result, the representation of complex tile drainage networks in models is often simplified and drains are simulated as high conductivity layers (e.g. Carluer and de Marsily, 2004; Rozemeijer et al., 2010), open cylinders with a seepage face boundary condition (e.g. Lin et al., 1997; Akay et al., 2008), or represented as nodal sinks (e.g. Gärdenäs et al., 2006) for which subsurface water fluxes are estimated from mass balance equations (Purkey et al., 2004). The simplification is also considered by authors (e.g. Morrison, 2014) because drainage networks are rarely mapped in detail and information on location, spacing, diameter and orientation of drains is lacking.

Alongside Richards’ equation, which is commonly solved by models for describing variably- saturated subsurface water flow (see Table 1.2), subsurface drainage water flow has usually been simulated using three different spacing formulas under steady-state conditions:

– the Hooghoudt equation that characterizes steady flow in regular parallel tile networks with constant recharge in flat lands (Hooghoudt, 1940); – the Kirkham equation developed for calculating drainage flow in a ponding context (Kirkham, 1949); – the Ernst equation used in drained layered profiles (Ernst, 1956).

The Hooghoudt formula considers radial water flow under and towards the drains, and horizontal water flow above these. The Ernst equation takes radial flow into account above and below the drains as total flow. By combining both expressions, a generalized form of the Hooghoudt equation has been developed so that both radial and horizontal flow to drains

13 are calculated (van Beers, 1976). The generalized Hooghoudt equation is referred to in the literature as shown in Table 1.2.

When transient drainage water flow is considered, the Boussinesq equations (Boussinesq, 1872) may be applied but its inherent non-linearity makes it difficult to solve. Even when these equations are linearized (van Schilfgaarde, 1963), their use is restricted to analytical solutions. More recently a powerful analytical solution was developed for calculating transient flow to a single drain (Cooke et al., 2000). Yet, numerical solutions are usually preferred. Fipps et al. (1986) were amongst the first authors to consider subsurface drains as boundary conditions represented in a 2D numerical solution. Based on this study, MacQuarrie and Sudicky (1996) developed a one-dimensional drainage flow equation for drains in three-dimensional variably saturated models. Nowadays, one-, two- and three-dimensional numerical codes are available with a wide variety of applications for tile drainage simulations.

One-dimensional models

Depending on the specific simulation needs for a given tile drainage application, models have focused on simulating hydrological processes at different scales and dimensions. For example, comprehensive one-dimensional models such as SWAP (Kroes et al., 2008), formerly known as SWATR (Feddes et al., 1978), or DRAINMOD (Skaggs, 1978) have been widely used for simulating vertical water flow and solute transport through the saturated and unsaturated zones. SWAP represents tile drains as nodal sinks while DRAINMOD solves the Kirkham’s or Hooghoudt’s equations for 1D drains (Youssef et al., 2005). DRAINMOD can simulate nutrient dynamics in drained soils in relation to local agricultural and climatic conditions. Sheler (2013) provides detailed information and comparison of these codes. Other models have integrated the tile drainage algorithms from DRAINMOD into other groundwater flow models. For example, the ADAPT model (Warld et al., 1988) couples the root-zone model GLEAMS (Leonard et al., 1987) to DRAINMOD. Ale et al. (2013) document the performance of both ADAPT and DRAINMOD. In another example, the DRAIN-WARF model (Dayyani et al., 2010) links DRAINMOD to the shallow groundwater flow model WARMF (Chen et al., 2001) and uses a distributed parameters approach for simulating freezing and thawing in tile-drained environments. Other examples of 1D models include SaltMod, which simulates salinity variation in soil moisture, groundwater and drainage water (Oosterbaan, 2002), and

14 ANSWERS, which simulates water ﬂow in the unsaturated zone only at the ﬁeld scale with the Brooks-Corey model (Brooks and Corey, 1964a) accounting for soil erosion (Beasley et al., 1980).

Two-dimensional models

Models have been developed for two-dimensional simulations, such as MHYDAS-DRAIN (Tiemeyer et al., 2007), a two-dimensional spatially distributed model for simulating field scale water flow in drained lowlands. Tile drains are defined by their depth, slope, diameter and spacing and where drainage water flow is assumed to originate from the soil matrix and macropores. At a larger scale, AnnAGNPS (Binger and Theurer, 2001) solves Hooghoudt’s equation for tile drains in 2D agricultural watersheds. The model is mainly applied to evaluate water quality related to crop rotation. SIDRA is another deterministic model that simulates water fluxes through the saturated zone by solving Boussinesq’s equation (Lesaffre and Zimmer, 1988). It can incorporate subsurface drains as discrete drains at the bottom of a conductive layer that is located at the boundary with a low permeability unit. SIDRA can compute drainage flow rates and hydraulic heads at mid-distance between two parallel drains. PESTDRAIN (Branger et al., 2009) has been later developed by coupling SIDRA to the unsaturated and surface flow model SIRUP (Kao et al., 1998) and to the pesticides transport model SILASOL. Another example of a 2D model that simulates unsaturated and saturated water flow is ANTHROPOG (Carluer and de Marsily, 2004), which represents drains as a high-permeability porous medium.

When creating catchment scale models, it may be relevant to work with the representative elementary watershed concept, which is included in the physically-based semi-distributed THREW model (Tian et al., 2008, 2006). A storage-discharge relation regulates tile drainage flow in drains as drainage flow rate values are proportional to the height of the water table above the drains (Li et al., 2010). The physically-based, semi-distributed and process-oriented SWAT model (Arnold et al., 1998) uses a method similar to the representative elementary watershed concept of THREW by dividing the simulation domain in hydrologic response units to simulate water flow, solute transport and sediment transport in agricultural catchments, accounting for crop use rotation. Du et al. (2005) improved SWAT with respect to the simulation of tile drainage water flow by including a simple tile flow equation to the original

15 SWAT model.

Another approach for simulating subsurface drainage is to assume that drained plots are interconnected by ﬁlled pipes for which the Richards’ equation is solved, which is used in the 2D physically-based catchment model CATFLOW (Maurer, 1997; Klaus and Zehe, 2011).

Three-dimensional models

A smaller number of three-dimensional models have been developed to simulate tile drainage. The finite-difference flow model MODFLOW represents drains as individual sinks that are active when the water table is higher than the elevation of the drain (McDonald and Har- baugh, 1988). The volumetric flow rate out of the subsurface into the drain is computed with Darcy’s law and requires that the conductance of the drain is specified. The FLUSH model was developed for simulating 3D hydrological processes in tile-drained clayey fields (Warsta et al., 2013). FLUSH treats macropores and drains as local sinks, with macropores being coupled to tile drains and the soil matrix. Furthermore, FLUSH considers additional cracks created in a clayey matrix resulting from decreased matrix water saturation produced by drainage. Subsurface drains are defined in FLUSH as water sinks and cannot represent a source of water. In contrast, the HYDRUS model allows drains located in the saturated zone to represent pressure head sinks as well as sink/source terms when the surrounding matrix becomes unsaturated (Šimůnek et al., 2006). HYDRUS simulates 2D or 3D water flow and solute transport in variably-saturated porous media and can also represent a system consisting of macropores and porous matrix with a dual-permeability approach (Akay et al., 2008). In the 3D integrated catchment model MIKE-SHE/MIKE 11 (Refsgaard and Storm, 1995) tile drainage is also accounted for as a sink where drainage is generated when the water table is above the drain level. The drainage water is then routed either downhill or to the nearest stream. The original version of MIKE-SHE/MIKE 11 coupled groundwater flow, surface water flow, unsaturated flow and evapotranspiration. A macropore option was added by Christiansen et al. (2004).

Few models have a limited application to arid tile-drained areas where salinity is to be taken into account as they have been developed only for simulating density-dependent groundwater ﬂow and transport. SUTRA (Voss and Provost, 2010) is one of those models. It treats drains only as sink nodes in a subsurface domain governed by the Darcy equation. In FEMWATER

16 (Lin et al., 1997), Richards’ equation is solved for groundwater ﬂow with drains being given a seepage boundary condition. In both codes, overland ﬂow is not considered.

All the models mentioned in the previous paragraphs are listed in Table 1.2. This is a non exhaustive list; models that are commonly used for simulating tile-drained environments were considered, but some others may be suitable for similar aims. HydroGeoSphere is added for comparison purposes to the other models, details about the model and governing equations are given in chapter 3.

Tile drainage modeling with HydroGeoSphere

The first authors to simulate tile drainage were MacQuarrie and Sudicky (1996), using FRAC3DVS (Therrien and Sudicky, 1996) from which HydroGeoSphere originated. They have contributed to the implementation of tile drainage in the code by developing a one- dimensional flow equation for drains in three-dimensional variably saturated media that is equivalent to an open channel flow equation. Subsurface drains were superimposed onto the porous medium by using a common node coupling approach in a theoretical model having a single pipe.

Rozemeijer et al. (2010) created a field scale model with a few parallel drains discharging in an open ditch, accounting for subsurface, surface and tile drainage water flow. The authors emphasized the action of drains at an experimental area of their study area, by including discrete pipes. However, when simulating water flow for the whole field, drainage water flow was represented as a high conductivity layer, which is defined as an equivalent medium (Carlier et al., 2007).

Yue (2010) developed a tile drainage module that removes the pressure continuity assumption between subsurface and drain common nodes. In this approach, the Preissman slot method (Cunge and Wegner, 1964) was used for modeling 1D free surface or pressurized transient flow in the drains. A flux boundary condition was applied at the outlet by a hypothetical diffusive wave flow between the drain outlet and adjacent water. As a result, water flux exchange between a drain outlet and the surface domain was made workable. In addition, resistance adjustment factors were introduced for lateral flow exchange between the soil and the pipes to get rid of the mesh size effects along drains.

17 Modeling of drainage water ﬂow accompanied by solute transport was studied by Frey et al. (2012) in a two-dimensional model simulating liquid manure transport to a single drain in a macroporous silt loam soil. This study showed the importance of including a dual-permeability medium when considering fast transport through soils with macropores for accurate simulation results.

Spatial scale of tile drainage models

The models listed in Table 1.2 cover a wide range of applications, depending on the modelers’ interest in the description of specific physical processes. Since most were developed for field or crop-scale applications, drainage dynamics are usually well represented at those scales in the literature (e.g. Warsta et al., 2013; Kroes et al., 2008). At larger scales (subcatchment to catchment scale), drainage is generally simplified (e.g. Hansen et al., 2013; Carluer and de Marsily, 2004). Modeling subsurface drainage effects on groundwater flow and surface water flow dynamics at the catchment scale is still a major challenge. Catchment scale modeling is essential to investigate the entire water cycle in catchments dominated by tile drainage flow. Yet, no guideline states the best tile drainage modeling approach to account for detailed physical processes at large scale while avoiding too dense mesh. Modelers must often choose a balance between the level of discretization of model meshes and the associated simulation time. Hansen et al. (2013) are one of the few authors that mention scaling issues regarding tile drainage modeling. In their study, groundwater flow dynamics simulated at the scale of drainage networks produced results that were not precise enough for small-scale model calibration purposes. Nevertheless, these authors did not define a minimum representative scale at which accurate drainage flow results could be expected. It is believed that such issues are site specific and can rarely be defined with a general rule.

18 Table 1.2: Non exhaustive list of models suitable for tile drainage modeling. Each model is given its dimension (Dim.) and scale (F = ﬁeld, C = catchment) application. Surface, Sub- surface and Drain domains show governing equations (plain text) or waterbalance parameters (in italics).

Model Dim. Scale Overland Subsurface Drain Reference AnnAGNPS 2D C Curve number∗ Darcy Hooghoudt Binger and Theurer (2001) ANSWERS 1D F - Brooks-Corey Hooghoudt Bouraoui et al. (1997) CATFLOW 2D F Saint-Venant Richards Richards Maurer (1997) DRAINMOD 1D F - Richards Hooghoudt/Kirkham Skaggs (1978) FEMWATER 3D F - Richards Seepage Lin et al. (1997) FLUSH 3D F Saint-Venant Richards Sink Warsta et al. (2013) HydroGeoSphere 3D Any Saint-Venant Richards Hazen-Williams Therrien et al. (2010) HYDRUS 3D Any - Richards Sink/Source Šimůnek et al. (2006) MHYDAS-DRAIN 2D F Hortonian ﬂow Reservoir Hooghoudt Tiemeyer et al. (2007) MIKE SHE/MIKE 11 3D Any Saint-Venant Richards Sink Refsgaard and Storm (1995) MODFLOW 3D Any - Darcy Sink McDonald and Harbaugh (1988) PESTDRAIN 2D F Reservoir Boussinesq Boussinesq Branger et al. (2009) SaltMod 1D F Waterbalance equation for the three domains Oosterbaan (2002) SUTRA 3D Any - Darcy Sink Voss and Provost (2010) SWAP 1D F Reservoir Richards Hooghoudt Kroes et al. (2008) SWAT 2D C Curve number∗ Storage Sink Arnold et al. (1998)

∗ The curve number values for surface runoﬀ are calculated based on Soil Conservation Service curves developed by the U.S. Department of Agriculture (1972).

19 1.3 Research objectives

This research was undertaken to extend knowledge and understanding of water dynamics in heterogeneous clayey till soils under tile drainage conditions. A field-scale model that couples subsurface water flow to surface and drainage water flow was developed for the Lillebæk catchment. A coupled surface and subsurface flow model of the Fensholt subcatchment was also built. Drainage flow was not coupled to the subsurface in this model; discrete drains were rather represented by seepage nodes to eliminate numerical issues.

Specific objectives for application to the Lillebæk area were to test various concepts for simulating field scale drainage water flow, and to highlight the best suited concepts for field scale or larger scale modeling in terms of simulation time, mesh refinement and degree of precision in the processes described.

In the Fensholt case, one of the objectives was to use and validate suggested options highlighted in Lillebæk for accurate drainage ﬂow modeling at large scale. A simpliﬁed version of two drainage network were therefore included in a catchment scale model. Instead of focusing on a short-term precipitation event, such as in the Lillebæk case, investigating drainage response to seasonal climate variations was selected. Another objective was to compare results from a model run of Fensholt by means of HydroGeoSphere with results from a larger scale model developed with MIKE SHE.

20 Chapter 2

Study sites

Two study areas have been investigated in Denmark: the 4.7 km2 Lillebæk catchment and the 6 km2 Fensholt catchment that is located in the larger Norsminde catchment (100 km2). Within these catchments, land use is dominated by agriculture (Figure 2.1, grain crops) and agricultural plots are commonly tile-drained, which implies that stream discharge is dominated by drainage discharge. Both catchments are found in glacial landscapes originating from the Weichsel and Saale glaciations (Houmark-Nielsen and Kjær, 2003). Highly heterogeneous clayey to silty till geological materials are found in the shallow subsurface (Knutsson, 2008) (Figure 2.2). Sand lenses of various extension and sand layers of glaciofluvial origin may be included in the till units or found deeper. In Denmark, these sandy units, together with glaciofluvial gravel units, represent at least 50 % of the groundwater resources (Kelstrup et al., 1982). They are connected to the surrounding clayey till layers which are usually fractured allowing preferential water flow (Fredericia, 1990; Klint and Gravesen, 1999; Nilsson et al., 2003). As aquitards show high bulk hydraulic conductivities, they are therefore of prime importance when considering aquifer recharge. At the national scale, groundwater recharge is known to vary from 15 - 60 mm year−1 in eastern Denmark to 170 - 193 mm year−1 in western Denmark (Jacobsen, 1995). Groundwater recharge is tied to the yearly average precipitation variation that is on average from less than 600 mm in eastern Denmark to 900 mm in western Denmark (Kronvang et al., 1993).

21 N Norsminde 0.0 1.25 2.5 km

Sweden

0 100 200 Germany km

Lillebæk 0.0 0.5 1.0 km

Legend

Agriculture Urban/Settlement Horticulture Road Polyculture Industrial area Forest Technical area Grass Sports facilities Peatland Recreation area Sand Graveyard Lake Mining Sea Stream Wetland Catchment boundary Salt marsh Lillebæk model area Fensholt 0.0 0.5 1.0 2.0 km

Figure 2.1: Location of the Lillebæk catchment and the Fensholt catchment, that is included in the Norsminde catchment, with associated land use maps from Nielsen et al. (2000).

22 Bornholm

Norsminde

Lillebæk

0 25 50 100 km

Legend

Post-glacial eolian sand Outwash plains Post-glacial freshwater peat Marsh Post-glacial marine sand and clay Beach ridges Glacial melt water sand and gravel Older marine deposits Glacial melt water clay Pre-Quaternary Sandy till and gravel Lakes Clayey till

Figure 2.2: Geological map of Denmark (Schack Pedersen, 2011), with the Lillebæk and Norsminde catchments locations highlighted.

23 2.1 Lillebæk

The Lillebæk catchment is located on the southeastern shore of Fyn island. The topography in Lillebæk gently slopes toward the southeast and varies from 50 to 60 meters above mean sea level (mamsl) to a few meters above sea level along the coast (Figure 2.3). A tile-drained plot was chosen in this catchment to build a model that covers 3.5 ha comprising an irregular drainage network made of 5 main collecting drains and 15 secondary drains. The Lillebæk catchment has to date been well characterized (Hansen, 2010) as it is part of the Danish Agricultural Watershed Monitoring Program LOOP, established in 1989 as part of the Danish aquatic environment action plan (Grant et al., 2007). In the context of the LOOP-program, the Lillebæk catchment has been monitored in detail for several years to investigate nitrate issues at the catchment scale (Rasmussen, 1996).

Model area

Elevation [mamsl] 93

0 N 0 250 500 1000 m

Figure 2.3: Lillebæk catchment topography and highlighted model area (red line).

24 2.2 Norsminde and Fensholt

The Norsminde catchment is located on the east coast of Jutland. This catchment shows high topographical variations from about 100 mamsl in the western part to low elevations in the eastern part; the western part being characterized by hilly terrains while the eastern part is dominated by low-lands, divided by a Wechselian glacial melt water valley (Figure 2.4). The catchment outlet is the Normsinde Fjord, a 2 km2 estuary located northeast of the catchment, in which the catchment surface waters discharge through the Odder and Rævs rivers. The area of interest for our model is the Fensholt subcatchment, located in the western hilly land. This area is highly tile-drained with well mapped drains. Two complex and dense tile drainage networks, covering 34 ha and 28 ha, respectively made of 199 and 95 drain pipes, were targeted for our model.

25 Elevation Norsminde [mamsl] Fjord 173

Fensholt

N 0 1.25 2.5 5 km

Figure 2.4: Topography in the Norsminde catchment, with the Fensholt subcatchment highlighted.

26 Chapter 3

Numerical model

3.1 Introduction

HydroGeoSphere is a fully integrated, physically-based three-dimensional numerical model able to simulate subsurface, surface and drainage water ﬂow, solute and heat transport (Ther- rien et al., 2010). A brief overview of the governing ﬂow equations is presented here. Hy- droGeoSphere is the numerical model of choice for the tile-drainage studies of the Lillebæk and Norsminde catchments. The reader is referred to Therrien et al. (2010) and Brunner and Simmons (2012) for a comprehensive model description.

3.2 Governing ﬂow equations

In HydroGeoSphere, water flow is described in three-dimensional subsurface porous media, two-dimensional water flow is considered at the surface and in fractures, and one-dimensional flow occurs in features such as wells and drain pipes. Coupling water flow in such domains, by taking complex physical processes into account (such as variably-saturated flow, evapotranspiration or runoff), requires solving non-linear equations.

3.2.1 Subsurface ﬂow

HydroGeoSphere applies a modified form of Richards’ equation to describe subsurface flow driven by gravity and capillary forces in porous media. Water flow in discrete fractures or dual continua can be simulated and are fully coupled to the subsurface porous media by a

27 volumetric ﬂuid exchange rate factor. The general form of Richards’ equation for 3D transient subsurface water ﬂow in a variably-saturated porous medium is given by:

∂ − ∇ · (w q) + Γ ± Q = w (θ S ) (3.1) m ext m ∂t s w X where wm is the volumetric fraction of the total porosity occupied by the porous medium [-],

Γext is an exchange ﬂux term between the subsurface domain and another domain (i.e. surface or drain) [LT−1], Q is the volumetric ﬂow rate per unit volume of the medium representing −1 external sources and sinks [LT ], θs is the saturated water content [-], Sw is the water saturation [-].

The Darcy ﬂux q [LT−1] is:

q = −K · kr∇ (ψ + z) (3.2)

−1 where K is the hydraulic conductivity tensor [LT ], kr is the relative permeability of the medium [-], ψ is the pressure head [L] and z is the elevation [L].

In equation (3.1), the storage term on the right-hand side is deﬁned as the sum of a com- pressibility eﬀect term in the saturated zone and a saturation change term in the unsaturated zone (Cooley, 1971; Neuman, 1973). It gives then:

∂ ∂h ∂S (θ S ) ≈ S S + θ w (3.3) ∂t s w w S ∂t s ∂t

where SS is the speciﬁc storage coeﬃcient [-].

Under variably-saturated conditions in the subsurface domain, the unsaturated zone can be characterized in HydroGeoSphere by the van Genuchten (1980) or Brooks and Corey (1964a) models for identifying relations between head, saturation and relative permeability. Subsurface and surface ﬂow are described using non-linear equations that are discretized with the control volume ﬁnite element method and linearized by means of the Newton-Raphson iterative method (Huyakorn and Pinder, 1983).

28 3.2.2 Surface ﬂow

Surface flow is solved by a 2D diffusion wave approximation of the Saint-Venant equations for unsteady surface water flow (Barré de Saint-Venant, 1871). This diffusion wave equation originates from the simplification of two-dimensional Saint-Venant mass balance equations and a momentum equation for the x-direction and y-direction respectively. The general diffusion wave equation for surface water flow is:

∂φ h − ∇ · (d q ) − d Γ ± Q = o o (3.4) o o o o o ∂t

−1 where do is the depth of flow [L], Γo is an exchange flux term [LT ], Qo is a volumetric −1 flow rate per unit area representing external sources and sinks [LT ], ho is the water surface elevation [L], φo is the surface flow domain porosity [-] and qo is the surface water flow flux given by Manning’s equation:

2/3 do qo = − · k ∇ (d + z ) (3.5) nΦ1/2 ro o o where n is the Manning roughness coeﬃcient [TL−1/3], Φ is the surface water gradient [-], kro is a relative permeability factor [-] and zo is the elevation [L].

3.2.3 Drainage ﬂow

The general water ﬂow along one-dimensional features, such as tile drains, is described as follows: ∂h q Q = −C · A · (R )p · p (3.6) 1D f H ∂s

2 where C is a proportionality constant [-], Af is the area of ﬂow in a pipe [L ], RH is the hydraulic radius [L] (calculated by dividing the area of ﬂow and the wetted perimeter of the pipe), hp is the hydraulic head in the pipe [L], s is the distance along the pipe’s axis [L], p and q are exponent factors.

When considering tile drainage, the Hazen-Williams empirical equation (Williams and Hazen, 1905) is used for describing water ﬂow depending on head loss along pipes due to friction of

29 water ﬂowing in them:

∂h 0.54 Q = −k · C · A · (R )0.63 · p (3.7) 1D HW f H ∂s

0.37 where k is a unit conversion factor (0.849 m /s) and CHW is the Hazen-Williams roughness coeﬃcient [-].

3.2.4 Coupling water ﬂow

As shown in equations (3.1) and (3.4), water exchange terms are involved for expressing exchanges between model domains (i.e. subsurface, surface and drains). Those terms can be determined by two different approaches: the dual node approach and the common node approach. The dual node approach is based on a Darcy flux transfer between two domains separated by a thin porous medium holder of the water exchange. The common node approach assumes hydraulic head continuity between two domains, corresponding to a superposition principle (Therrien and Sudicky, 1996). In our case, the dual node approach is chosen for coupling of subsurface and surface flows. Coupling of groundwater flow and tile drainage flow also uses a dual node approach, as does the flow coupling for a porous medium with a second continuum.

Governing equations for coupled groundwater (pm) and surface water ﬂow (olf) are:

(ho − h) Γpm→olf = − (kr)exch(pm,olf) Kexch(pm,olf) (3.8) lexch(pm,olf)

∂dv = −∇¯ · d ¯q + Q∂ (¯x − ¯x ) + Γ → (3.9) ∂t o o o pm olf

where dv is the volume depth [L], ¯x − ¯xo is the node position [L], (kr)exch, Kexch and lexch are the relative permeability, saturated hydraulic conductivity and the coupling length for ﬂuid exchange.

Coupled groundwater (pm) and drainage water ﬂow (d) is expressed by:

(hd − h) Γd→pm = −2πrdKexch(pm,d) (3.10) lexch(pm,d)

30 0.54 ∂ 0.63 ∂hd 2 ∂hd k · C · A · (R ) · + Q δ (s − s ) + Γ → = πr S (3.11) ∂s HW f H ∂s d c d pm d sp ∂t ! where rd is the drain radius [L]. Equation 3.10 accounts for pressurization in drainage pipes that induces leakage of water to the surrounding porous medium.

3.2.5 Interception and evapotranspiration

When applying a potential evapotranspiration boundary condition at the surface of a model, HydroGeoSphere simulates interception by vegetation or buildings and actual evapotranspiration by plants.

Interception is a storage factor that is proportional to the type of land cover (vegetation or buildings) and, when vegetation is considered, its seasonal development stage. Rain is intercepted and stored, where latter mentioned water becomes available for depletion by Max evaporation. The interception varies from 0 to Sint , which is deﬁned as the maximum interception storage capacity [L] and calculated as follows (Kristensen and Jensen, 1975):

Max Sint = cint · LAI (3.12)

where cint is the canopy storage parameter [L] and LAI is the leaf area index [-].

Evapotransporation is considered as a combination of transpiration by plants and evaporation.

Transpiration (Tp) is calculated based on the model developed by Kristensen and Jensen (1975):

Tp = f1 (LAI) · f2 (θ) · RDF · (Ep − Ecan) (3.13)

where f1 (LAI) is a function of leaf area index [-] , f2 (θ) is a function of moisture content

(θ) [-], RDF is a root distribution function [-], Ep is the reference evapotranspiration [L] and

Ecan is the evaporation by vegetation [L].

The ﬁrst three dimensionless factors of equation (3.13) are deﬁned by the following equations:

f1 (LAI) = max {0, min [1, (C2 + C1LAI)]} (3.14)

31 where C1 and C2 are ﬁtting parameters [-].

0 for 0 ≤ θ ≤ θwp  − C3  θfc θ 1 − for θwp ≤ θ ≤ θfc  θfc−θwp   h i f (θ) =  (3.15) 2 1 for θfc ≤ θ ≤ θo   C3 θan−θ 1 − − for θo ≤ θ ≤ θan  θan θo   h i 0 for θ ≤ θ  an    where θwp is the moisture content at the wilting point [-], θfc is the moisture content at ﬁeld capacity [-], θo is the moisture content at the oxic limit [-] and θan is the moisture content at the anoxic limit [-].

′ z2 ′ ′ z′ rF (z ) dz RDF = 1 (3.16) RLr ′ ′ 0 rF (z ) dz R ′ 3 −1 ′ where rF (z ) is a root extraction function [L T ], z is the depth coordinate from the soil surface [L] and Lr is the eﬀective root length [L].

Evaporation (Es) occurs at the soil surface and along a prescribed depth (Bsoil) in the subsurface domain. It is calculated with the following formulation:

∗ Es = α · (Ep − Ecan) · [1 − f1 (LAI)] · EDF (Bsoil) (3.17)

where EDF is an evaporation distribution function limiting evaporation from the soil surface ∗ to the Bsoil depth, and α is a wetness factor [-] calculated as follows:

− θ θe2 for θ ≤ θ ≤ θ θe1−θe2 e2 e1  ∗  α = 1 for θ > θe1 (3.18)   0 for θ < θ  e2   

32 3.3 Discrete drains vs. Seepage nodes

From the preliminary models created in Lillebæk and Fensholt, it appeared that the Hazen- Williams drainage equation (equation 3.7) may induce some numerical issues. In hummocky terrains of Fensholt, results showed an undesired increased drainage eﬀect, which didn’t show up in the gently sloping Lillebæk case. Hydraulic gradients simulated within the pipes of a drainage network are smaller than those calculated in the surrounding porous media. Hy- draulic heads therefore show very little variations along the pipes, whereas the hydraulic head for each node in the discrete drains should be equal to its elevation. A zero pressure head value would therefore be calculated, which is physically closer to what is generally observed in tile drainage systems: drainage occurs when the groundwater table rises above the drain elevation with water ﬂowing from saturated soils into the drains (Warsta et al., 2013).

An alternative option to model drainage flow had to be investigated. The two-dimensional steady-state flow example created by Fipps et al. (1986) and numerically tested with Hydro- GeoSphere by MacQuarrie and Sudicky (1996) in a three-dimensional configuration was used here. Note here that MacQuarrie and Sudicky (1996) used a one-dimensional drainage flow equation that differs slightly from the Hazen-Williams equation. The drainage formulation in HydroGeoSphere was recently modified so that the actual Hazen-Williams equation is solved.

A 3D benchmark model of sandy loam domain having a hydraulic conductivity of 1.5 × 10−5 m s−1 was built to verify the simulation approach. The domain ranges from 0 to 30 m in the x and y direction, covering an area of 900 m2, and from 0 to 3 m in the z direction (Figure 3.1). The top boundary of the domain is assigned a 3 m prescribed head boundary condition, while the lateral and bottom boundaries are impermeable.

Two set-ups were then tested. First, a single discrete drain (diameter = 0.0216 m) was implemented in the model, located at x = 15 m, z = 2 m and ranges in the y direction from y = 1 m to y = 29 m. A critical depth boundary condition was applied at the outlet of the drain (x = 15 m, y = 1 m and z = 2 m) allowing free drainage. This set-up couples the drain to the subsurface domain with a dual-node approach and solves the Hazen-Williams equation. A second set-up was considered by replacing the drain segments by nodes being given a seepage boundary condition. This is physically suitable for drainage simulation purposes as seepage nodes are given a zero pressure head condition when the water table rises above the nodes’

33 elevation (Therrien et al., 2010), allowing free drainage to occur by acting as sink nodes. On the other hand, if the water table drops below the seepage nodes elevation, a no-ﬂow boundary condition is applied to these nodes and drainage stops.

Regarding the spatial dicretization of the model domain, a nodal spacing of 0.5 m was set in the x direction, 1.0 m in the y direction and 0.2 m in the z direction. Following MacQuarrie and Sudicky (1996) model set-up, the grid was reﬁned in the y direction between y = 14 m to y = 16 m with decreasing nodal spacing from y = 14 m to 15 m (minimum nodal spacing = 0.05 m) and increasing nodal spacing from y = 15 m to 16 m. In the z direction, nodal spacing decreases from z = 1.8 m to z = 2.0 m (minimum nodal spacing = 0.05 m) and increases from z = 2.0 m to z = 2.2 m. In total, the model has 53 878 nodes and 49 140 elements. Simulations were run for a period of 100 000 sec, which corresponds to 27 h 46 min 40 sec.

34 3.3.1 Steady-state simulations

Conventional drainage under steady-state flow conditions was simulated in both set-ups. The numerical results were compared to the drainage analytical solution developed by Kirkham (1949). In Figure 3.2, the vertical profile displayed at x = 22 m shows the same results from the discrete drain and seepage cases, and they coincide with the analytical solution. At x = 15 m, the seepage drainage simulation shows pressure head values, in the near vicinity of the drain, that are closer to the analytical solution than the discrete drain values. This behavior was seen along the entire profile as well (Table 3.1).

Prescribed head boundary (H = 3 m) 3 m

2 m Drain (r = 0.0108 m)

K = 1.5 E-5 m/s Impermeable boundary z = 0 m x = 0 m 15 m 30 m Figure 3.1: Simulation domain of the Fipps et al. (1986) example used as a veriﬁcation example. The domain ranges in the y direction from 0 to 30 m. Modiﬁed from MacQuarrie and Sudicky (1996).

35 3.0

2.5

2.0

1.5

1.0 Analytical (x = 22 m) Numerical (x = 22 m) Elevation above datum [m] Analytical (x = 15 m) 0.5 Numerical, seepage (x = 15 m) Numerical, discrete drain (x = 15 m)

0.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Pressure head [m]

Figure 3.2: Numerical and analytical solutions for pressure head along vertical profiles at x = 15 m and x = 22 m. The discrete drain and seepage node set-ups are displayed. At x = 22 m, seepage and discrete drain numerical solutions coincide; they are displayed under a single joint vertical profile. Modified from MacQuarrie and Sudicky (1996).

36 Table 3.1: Pressure head values along the x = 15 m vertical proﬁle for the discrete drain and seepage node numerical solutions, compared to the Kirkham (1949) analytical solution.

Pressure head [m] Elevation [m] Analytical Seepage nodes Discrete drain 30.0 0.000 0.000 0.000 2.95 0.030 0.030 0.031 2.75 0.149 0.150 0.156 2.55 0.259 0.260 0.272 2.35 0.342 0.348 0.366 2.15 0.316 0.372 0.401 2.05 0.181 0.260 0.302 2.00 ∼0.01 0.000 0.061 1.95 0.285 0.337 0.380 1.89 0.464 0.538 0.573 1.82 0.678 0.696 0.726 1.73 0.837 0.846 0.872 1.63 0.997 1.000 1.023 1.50 1.152 1.166 1.186 1.35 1.326 1.350 1.368 1.17 1.535 1.558 1.574 0.97 1.767 1.780 1.795 0.77 1.997 1.996 2.010 0.57 2.203 2.207 2.220 0.37 2.409 2.414 2.426 0.17 2.615 2.618 2.630 0.00 2.795 2.794 2.806

37 Cross-sections in the yz plane at x = 15 m (Figure 3.3) show groundwater heads above and below the drain in the discrete drain model (Figure 3.3a) and in the seepage nodes model (Figure 3.3b). Both profiles look similar although slight differences can be seen. The seepage nodes profile is perfectly symmetric in the y direction, with a hydraulic head value of 2.0 m at the drain elevation (thin dark blue line from y = 1 m to 29 m), where the pressure head is equal to 0.0 m. On the other hand, the discrete drain profile is asymmetric due to a small hydraulic head gradient along the drain from its upstream end (y = 29 m) to its outlet (y = 1 m). A zero pressure head is calculated at the outlet of the drain but positive values are simulated in the upstream part, inducing the asymmetry seen below the drain in the hydraulic head distribution.

Hydraulic head [m]

2.0 2.2 2.5 2.8 3.0 a)

Figure 3.3: Hydraulic head distribution in the yz plane at x = 15 m in the discrete drain (a) and the seepage nodes model (b) models.

38 Figure 3.4 shows the hydraulic head distribution in the 3D domain for the discrete drain (Figure 3.4a) and seepage nodes (Figure 3.4b) cases. Lateral hydraulic head values appear to be equivalent in both cases. The symmetry differences observed in Figure 3.3 are also seen here along the cross-sections at y = 4 m, 13 m and 22 m (Figure 3.4a). Nevertheless, the lateral drainage flow patterns, as defined by Yue (2010), exposed in 2D vertical sections in Figure 3.5 with the associated hydraulic head distribution, appear to be similar in both simulations.

a) Discrete drain

b) Seepage nodes

Hydraulic head [m]

2.0 2.2 2.5 2.8 3.0 Figure 3.4: Hydraulic head distribution in the 3D domain for the discrete drain (a) and the seepage nodes examples (b). Three cross-sections are displayed at y = 4 m, 13 m and 22 m.

39 a) Discrete drain

b) Seepage nodes

Hydraulic head [m]

2.0 2.2 2.5 2.8 3.0 Figure 3.5: Hydraulic head distribution in the 3D domain for the discrete drain (a) and the seepage nodes examples (b), with associated water ﬂow pathways.

40 In terms of computational performances, both simulations were run in serial mode using a 3.70 Gb RAM computer with 1 CPU core at 2.60 GHz. The discrete drain simulation ran in 2 h 31 min and the seepage nodes simulation in 37 min (Table 3.2). About 77 300 m3 of water was drained during the both simulations, thereby validating the use of the seepage nodes option as a drainage boundary condition.

With this verification example, the seepage drainage option appears to be suitable for simulating lateral drainage water flow, i.e. water flow in the porous medium towards the drains. However, for this simulation option, the physical properties of the pipe were not specified and pipe flow and drainage routing, with potential pressurized flow, were not considered. Drainage flow was mainly driven by the resistance from the porous medium here.

Table 3.2: Computational times and drainage volumes of the discrete drain and seepage node steady-state and transient simulations. All simulations were run using a 3.70 Gb RAM computer with 1 CPU core at 2.60 GHz.

Discrete drain Seepage nodes Computational time Steady-state 2 h 31 min 37 min Transient state 3 d 21 h 19 min 11 h 13 min Drainage volume Steady-state 77 300 m3 77 302 m3 Transient state 47 322 m3 47 331 m3

41 3.3.2 Transient simulations

The seepage drainage option test was also conducted with a transient simulation. The model set-up was quite similar to the steady-state test, except the top boundary condition that was modified. A time-varying flux was applied at the top nodes during a period of 100 000 s, as shown in Table 3.3. The initial flux value applied (8.59 × 10−4 m s−1) is equivalent to the flux induced by the steady-state case prescribed head boundary condition.

In Figure 3.6, the discrete drain and seepage nodes options show similar response to varying flux: both drainage discharge hydrographs are superimposed. Yet, Table 3.3 shows discharge rates for both set-ups with the seepage nodes option having a little time-lag (of about 150 s) in response to varying flux values, while the discrete drain option doesn’t show any time- lag. This difference is not noticeable in Figure 3.6 and it doesn’t affect the total drainage volume, as seen in Table 3.2 (discrete drain = 47 322 m3, seepage nodes = 47 331 m3), since the discrete drain and seepage nodes options roughly drain the same amount of water during the simulation. The seepage nodes time-lag issue is therefore believed to be numerical rather than conceptual and doesn’t affect the drainage results significantly.

Computational times were much longer than the steady-state simulations, with 3 d 21 h 19 min for the discrete drain case and 11 h 13 min for the seepage nodes case (Table 3.2).

Table 3.3: Flux rate values applied at the Fipps et al. (1986) domain during transient simulations compared to discrete drain and seepage nodes discharge rates. Positive ﬂux values reveal water entering the simulation domain while negative discharge values indicate water leaving the domain.

Time [s] Flux [m s−1] Discrete drain [m3 s−1] Seepage nodes [m3 s−1] 09 8.5 × 10−4 −7.73 × 10−1 −7.73 × 10−1 12 500 8.59 × 10−4 −7.73 × 10−1 −7.73 × 10−1 25 000 4.29 × 10−4 −3.86 × 10−1 −3.87 × 10−1 37 500 4.29 × 10−4 −3.86 × 10−1 −3.86 × 10−1 50 000 2.15 × 10−4 −1.93 × 10−1 −1.99 × 10−1 62 500 2.15 × 10−4 −1.93 × 10−1 −1.93 × 10−1 75 000 4.29 × 10−4 −3.86 × 10−1 −3.79 × 10−1 87 500 4.29 × 10−4 −3.86 × 10−1 −3.86 × 10−1 90 000 8.59 × 10−4 −7.73 × 10−1 −7.64 × 10−1 100 000 8.59 × 10−4 −7.73 × 10−1 −7.73 × 10−1

42 iue36 iceedanadseaendshdorps(dr hydrographs nodes seepage and drain Discrete 3.6: Figure ta.(96 aei rnin iuain oprdt h ievrigflxboundary flux time-varying the in). to (flux domain compared simulation simulation, the of transient top a the at in applied case condition (1986) al. et Flux in [m/s]

Drainage discharge [m³/s] 2.0 x10 4.0 x10 6.0 x10 8.0 x10 1.0 x10 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.0 -4 -4 -4 -4 -3 0.0 2.0 x10 4 4.0 x10 4 Time [s] 6.0 x10 4 iaedshre fteFipps the of discharge) ainage Seepage nodes Discrete drain Flux in 8.0 x10 4 1.0 x10 43 5

Chapter 4

Simulating coupled surface and subsurface water ﬂow in a tile-drained agricultural catchment

Simulation des écoulements couplés de surface et souterrains dans un bassin versant agricole drainé

G. De Schepper, R. Therrien Department of Geology and Geological Engineering, Université Laval Quebec City, Canada

J. C. Refsgaard, A. L. Hansen Department of Hydrology, Geological Survey of Denmark and Greenland Copenhagen, Denmark

Reference: G. De Schepper, R. Therrien, J. C. Refsgaard, and A. L. Hansen (2015). Simulating coupled surface and subsurface water ﬂow in a tile-drained agricultural catchment. J. Hydrol., 521, 374 – 388. doi:10.1016/j.jhydrol.2014.12.035

Abstract

The impact of shallow tile drainage networks on groundwater flow patterns, and associated transport of chemical species or sediment particles, needs to be quantified to evaluate the effects of agricultural management on water resources. A current challenge is to represent tile drainage networks in numerical models at the scale of a catchment for which accurate simulation and reproduction of subsurface drainage water dynamics are essential. This study investigates the applicability of various tile drainage modeling concepts by comparing their results to a reference model. The models were set up for a 3.5 hectare regularly monitored tile-drained area located in the clayey till Lillebæk catchment in Denmark, where the main input of water to the streams originates from subsurface drainage. Several simulations helped identify the most efficient way of modeling tile-drained areas using the integrated surface water and groundwater HydroGeoSphere code, which also simulates one-dimensional water flow in tile drains. The aim was also to provide insight on the design of larger scale models of complex tile drainage systems, for which computational time can become very large. A reference model that simulated coupled surface flow, groundwater flow and flow in tile drains was set up and showed a rapid response in drain outflow when precipitation is applied. A series of additional simulations were performed to test the influence of flow boundary conditions, temporal resolution of precipitation data, conceptual representations of clay tills and drains, as well as spatial discretization of the mesh. For larger scale models, the simulations suggest that a simplification of the geometry of the drainage network is a suitable option for avoiding highly discretized meshes. Representing the drainage network by a high-conductivity porous medium layer reproduces outflow simulated by the reference model. This approach greatly reduces the mesh complexity and simulation time and thus represents an alternative to a discrete representation of drains at the field scale, but specifying the hydraulic properties of the layer requires calibration against observed drain discharge.

47 Résumé

L’impact des réseaux de drainage agricole sur les écoulements souterrains, associés au transport d’espèces chimiques ou de particules sédimentaires, doit être quantifié pour évaluer les effets de la gestion agricole sur les ressources en eau. La représentation des réseaux de drainage souterrain dans les modèles numériques à l’échelle d’un bassin versant reste essentielle pour simuler correctement les dynamiques d’écoulement de drainage. Cette étude examine l’applicabilité de divers concepts de modélisation de drainage en comparant leurs résultats à un modèle de référence. Les modèles ont été construits sur base d’une parcelle drainée de 3.5 hectare régulièrement contrôlée située dans le bassin versant de Lillebæk (Danemark), dont le sous-sol est majoritairement constitué de till argileux et où les cours d’eau sont majoritairement alimentés par les eaux de drainage. Plusieurs simulations ont permis d’identifier la manière la plus efficace de modéliser des parcelles drainées à l’aide du code HydroGeoSphere intégrant écoulements de surface et écoulements souterrains, et capable aussi de simuler les écoulements de drainage unidimensionnels. Le but était aussi de donner un aperÃ§u de la conception de modèles à plus grande échelle de systèmes de drainage complexes, pour lesquels les temps de calcul peuvent devenir très importants. Un modèle de référence qui simule les écoulements couplés de surface, souterrains et de drainage a été créé et a montré une réponse rapide du drainage lorsque des précipitations ont été imposées. Une série de simulations ad- ditionnelles ont été réalisées pour tester l’influence des conditions aux limites d’écoulement, de la résolution temporelle des données de précipitation, de la représentation conceptuelle des tills argileux et des drains, tout comme la discrétisation du maillage. Pour les modèles à plus grande échelle, les simulations suggèrent qu’une simplification de la géométrie du réseau de drainage est une option pertinente pour éviter les maillages trop fins. Représenter le réseau de drainage par une couche à haute conductivité hydraulique reproduit correctement les débits de drainage du modèle de référence. Cette approche réduit considérablement la complexité du maillage et le temps de simulation, et elle représente donc une alternative à une représen- tation discrète de drains à l’échelle d’un champ, mais un calage du modèle par rapport aux débits de drainage observés est nécessaire.

48 4.1 Introduction

Subsurface drainage is a common agricultural practice in humid climates and is designed to lower the water table to prevent waterlogging and flooding and to maintain agricultural crop productivity. In addition, drainage systems are used for land reclamation to expand crop areas. Such systems, added with control structures, are also found in semi-arid to arid regions where they are used to reduce or control the salinity of the root zone and soils by maintaining a shallow water table depth (Hoffman and Durnford, 1999; Ayars et al., 2006). Tile drainage networks are typically installed in low hydraulic conductivity soils, such as clays or silty clays. Macropores or fractures located in these soils are preferential flow pathways that can generate fast water flow and advection-dominant solute transport to the drains (Šimůnek et al., 2003). While overland flow decreases during drainage, nutrients, pesticides and even soil particles are transported through the tile drains. Nutrient transport leads to surface and coastal water contamination, eutrophication and hypoxia issues, threatening local ecosystems (Blann et al., 2009).

As stated by Warsta et al. (2013), proper nutrient transport quantification relies on water movement quantification. When considering water balance at the crop or catchment scale, field data collection is needed for quantifying rainfall, drainage flow or stream flow. However, field data typically only gives information on the amount of water that flows at a drainage system outlet, while the physical processes controlling water flow upstream of the outlet are difficult to measure, even if it has been demonstrated that drainage water flow intensity is tied to the area of land that is actually drained (King et al., 2014). Precise water flow/routing separation could be measured, for example, by adding flowmeters at each contributing pipe of the network, but that would imply arduous equipment installation and excessive costs. In addition, it would disturb farmers work when plowing fields and thus disturb the object of the study. Numerical models are therefore considered as necessary tools to characterize drainage water flow in and around the entire drainage network, including their interactions with the surrounding porous media.

Several numerical models have been developed to simulate hydrological processes related to the drainage of clayey soils. These models have demonstrated that tile drainage networks have a key impact on groundwater and surface water ﬂow as well as on chemical species transport

49 and erosion (Gärdenäs et al., 2006; Kiesel et al., 2010; Rozemeijer et al., 2010; Warsta et al., 2013). Numerical models have also demonstrated reliable predictive abilities when used in conjunction with in situ monitoring systems (Tim, 1996). Representing discrete tile drains in a model requires information on the location and depth of the individual drains that constitute the drainage network, which is often unavailable. Discretizing complex drainage networks may also lead to extremely dense computational meshes and potentially very long simulation times. As a result, the representation of complex tile drain networks in models is often simpliﬁed and drains are simulated as high conductivity layers (e.g. Carluer and de Marsily, 2004; Rozemeijer et al., 2010), open cylinders with a seepage face boundary condition (e.g. Akay et al., 2008), or represented as nodal sinks (e.g. Gärdenäs et al., 2006) for which subsurface water ﬂuxes are estimated from mass balance equations (Purkey et al., 2004).

Depending on the specific simulation needs for a given tile drainage application, models have focused on simulating hydrological processes at different scales. For example, comprehensive one-dimensional models such as SWAP (Kroes and van Dam, 2003) or DRAINMOD (Skaggs, 1978) have been widely used for simulating vertical water flow and solute transport through the saturated and unsaturated zones. Few models have been developed for two-dimensional simulations, such as MHYDAS-DRAIN (Tiemeyer et al., 2007), a two-dimensional spatially distributed model for simulating field-scale water flow in drained lowlands, where tile drains are defined by their depth, slope, diameter and spacing and where drainage water flow is assumed to originate from the soil matrix and macropores. At a larger scale, AnnAGNPS (Binger and Theurer, 2001), which is an annualized version of the single-event agricultural model AGNPS, solves Hooghoudt’s equation for tile drains in 2D agricultural watersheds. The model is mainly applied to evaluate water quality related to crop rotation. SIDRA is another deterministic model that simulates water fluxes through the saturated zone by solving Boussinesq’s equation (Lesaffre and Zimmer, 1988). SIDRA can incorporate subsurface drains as discrete drains at the bottom of a conductive layer that is located at the boundary with a low permeability unit, and can compute drainage flow rates and hydraulic heads at mid- distance between two parallel drains. PESTDRAIN (Branger et al., 2009) was later developed by coupling SIDRA to the unsaturated and surface flow model SIRUP (Kao et al., 1998) and to the pesticide transport model SILASOL. Another example of a 2D model that simulates unsaturated and saturated water flow is ANTHROPOG (Carluer and de Marsily, 2004),

50 which represents drains as a high-permeability porous medium.When creating catchment scale models, the representative elementary watershed concept is used in the physically-based, semi- distributed and process-oriented SWAT model (Arnold et al., 1998) by dividing the simulation domain in hydrologic response units to simulate water flow, solute transport and sediment transport in agricultural catchments. Du et al. (2005) improved SWAT with respect to the simulation of tile drainage water flow by including a simple tile flow equation to the original SWAT model.

A number of three-dimensional models have been developed to simulate tile drainage. The finite-difference flow model MODFLOW represents drains as individual sinks that are active when the water table is higher than the elevation of the drain (McDonald and Harbaugh, 1988). The volumetric flow rate out of the subsurface into the drain is computed with Darcy’s law and requires that the conductance of the drain be specified. The FLUSH model was developed for simulating 3D hydrological processes in drained clay soils (Warsta et al., 2013). FLUSH treats macropores and drains as local sinks, with macropores being coupled to tile drains and the soil matrix. Furthermore, FLUSH considers additional cracks created in a clayey matrix resulting from decreased matrix water saturation produced by drainage. Sub- surface drains are defined in FLUSH as water sinks and cannot represent a source of water. In contrast, the HYDRUS model allows drains located in the saturated zone to represent pressure head sinks as well as sink/source terms when the surrounding matrix becomes unsaturated (Šimůnek et al., 2006). In the 3D integrated catchment model MIKE-SHE/MIKE 11 (Refsgaard and Storm, 1995) tile drainage is also accounted for as a sink where drainage is generated when the water table is above the drain level. The drainage water is then routed either downhill or to the nearest stream. Another approach for simulating subsurface drainage is to assume that drained plots are interconnected by pipes, which is used in the 3D physically-based catchment model CATFLOW (Klaus and Zehe, 2011; Maurer, 1997).

MacQuarrie and Sudicky (1996) simulated 3D variably-saturated flow in a porous medium coupled with one-dimensional channel flow into tile drains. They represent tile drains with one-dimensional finite elements that are superimposed onto three-dimensional elements representing the subsurface. Continuity of fluid pressure is assumed for nodes that belong to both one-dimensional tile drain elements and three-dimensional subsurface elements, which allows for water exchange between the drains and the surface. Drains can therefore act as

51 either sources or sinks in the model. MacQuarrie and Sudicky (1996) used an earlier version of the coupled surface and subsurface HydroGeoSphere model (Therrien et al., 2010) that only simulated subsurface flow. The same approach described in MacQuarrie and Sudicky (1996) to couple one-dimensional flow into tile drains to three-dimensional subsurface flow is used in HydroGeoSphere, which can further couple tile drain and subsurface flow to two-dimensional surface flow. Rozemeijer et al. (2010) used HydroGeoSphere for coupled surface and subsurface flow simulations but represented drains as equivalent-medium high conductivity layers in a 3D model to test an experimental tile drainage network in a Dutch agricultural subcatchment. Yue (2010) extended the approach developed by MacQuarrie and Sudicky (1996) to simulate tile drains in HydroGeoSphere by removing the assumption of pressure continuity at common drain and subsurface nodes, introducing resistance along the drain to compute lateral flow, using the Preissmann slot method to combine free surface and pressurized flow and allow for a flux boundary condition at the drain outlet.

In this study, results from various models were compared to identify an appropriate combination of model properties, with respect to simulation time, process description and mesh refinement, to determine the most efficient model set-up to accurately simulate tile drainage. We have applied the HydroGeoSphere model (Therrien et al., 2010) to simulate coupled surface and subsurface flow in a tile-drained plot in the agricultural Lillebæk catchment in Denmark. Previous work on the Lillebæk catchment has highlighted the significant impact of tile drainage on surface water flow (Kronvang et al., 2003; Hansen et al., 2013). That work suggests that a coupled surface and subsurface flow modeling approach that can also account for flow into a complex tile drain network, such as provided by HydroGeoSphere, would be well-suited for the catchment. To our knowledge, such a modeling approach has not been documented before.

52 4.2 Methods

4.2.1 Study area

The study area is a tile-drained agricultural plot of the Lillebæk catchment, which is located on the island of Fyn in Denmark (Figure 4.1). The catchment is dominated by agricultural land and its surface elevation varies between a maximum of 50 to 60 mamsl (meters above mean sea level) to sea level elevation along the coast. Groundwater levels, stream discharge, drainage discharge and nutrient ﬂuxes in the catchment are regularly monitored within the Danish Agricultural Watershed Monitoring Program LOOP, established in 1989 as part of the Danish Action Plan for the Environment (Grant et al., 2007).

The regional landscape and near-surface geology have been shaped by several ice advances and retreats associated with the Weichsel and the Saale glaciations (Houmark-Nielsen and Kjær, 2003). Horizontal to subhorizontal Quaternary glacial and interglacial deposits lay unconformably on Paleogene limestones (Danian) and marls (Selandian), which dip gently towards the southwest (Gravesen and Nyegaard, 1989). The total thickness of the Quaternary deposits varies between 30 m and 60 m. They consist of an upper clayey till from the Weichsel glaciation that overlies a sand unit, which in turn overlies a clayey till from the Saale glaciation. The upper till provides confinement for the sand unit, which is the regional aquifer. The upper till also contains complex fracture and macro-pore networks that can create vertical preferential water flow and mass transport pathways between the surface and the underlying sand (Rasmussen, 1996; Klint and Gravesen, 1999; Klint, 2001; Nilsson et al., 2001). Fractures and macropores form a well-connected network and they have been shown to be hydraulically active along their total vertical extent (Nilsson et al., 2003). In addition to vertical fractures and macropores, the tills at the site also contain horizontal sand lenses. Depending on their extent, these lenses may be interconnected, for example through vertical fractures, which can lead to fast water flow and contaminant transport (Kessler et al., 2012).

The average precipitation recorded in the Lillebæk catchment from 1990 to 2004 was about 839 mm/year (Hansen et al., 2013). The years 1996 and 2003 have been among the driest for that period, with an average precipitation of 600 mm/year, while 1994 was the wettest year with an annual precipitation of about 1100 mm/year. It is estimated that a third of the yearly precipitation inﬁltrates into the soil and the recharge for the regional sandy aquifer is

53 estimated at 150 mm/year (Grant et al., 2000).

Most agricultural soils are tile drained in the catchment and, as a result, surface water flow is highly influenced by drainage flow. Tile drainage discharge has been regularly measured at the outlet of the drainage network in Lillebæk. Water flowing in the drains discharges into a collector well and water fluxes are measured with a 30◦ Thompson weir combined to a water pressure transducer and a datalogger (Hedeselskabet, 1989). Manual water levels in the collector are regularly monitored to validate these measurements. The drainage discharge is continuously monitored but only daily discharge rates are recorded and available.

a) b) Sweden

Copenhagen

Lillebæk

0 50 100 200 Germany km

c) 32 m

7 m Land use Lillebæk catchment Stream Model area Piped stream

Urban/Settlement Forest Road Peatbog Agriculture Inland marsh Grass Surface water Natural grassland Sea

Figure 4.1: Location of the Lillebæk catchment (55◦ 7’ N, 10◦ 44’ E) (a), shown with local land use and surface streams (b). The model area located within the catchment is highlighted in red, with the drainage network illustrated (c).

54 4.2.2 Numerical model

Coupled 2D surface and 3D subsurface flow at the study site, along with 1D flow in individual tile drains, was simulated with HydroGeoSphere, which is a fully-integrated three-dimensional surface/subsurface water flow, solute and heat transport model (Therrien et al., 2010; Brunner and Simmons, 2012). The governing equation for three-dimensional variably-saturated flow in the subsurface is the following form of Richards’ equation:

∂ ∇ · k K · ∇h + Qδ (x − x ) + Γ = (θ S ) (4.1) r 0 ext ∂t s w X where kr is the relative permeability of the porous medium, K is the hydraulic conductivity tensor [L T−1], h is the hydraulic head [L], Q is source or sink term that represents an external 3 −1 −3 volumetric applied per unit volume [L T L ] at location x0, θs is the saturated water content and Sw is the porous medium volumetric saturation. In equation 4.1, the term Γext represents volumetric ﬂuid exchange per unit volume [L3 T−1 L−3] with either the surface ﬂow domain or the tile drains.

Depth-integrated surface water ﬂow is described by the following diﬀusion wave approximation: ∂d ∇ · (d K ) · ∇h + Q δ (x − x ) + Γ d = v (4.2) o o 0 o 0 o o ∂t

where ∇ is the two-dimensional gradient operator, do is the depth of surface water ﬂow [L],

Ko is a surface conductance that can be described, for example, with Manning’s formula, Qo is a source or sink term that represents an external volumetric exchange term applied per 3 −1 −3 unit volume [L T L ] at location x0, and dv is the equivalent volume depth of water [L] for depth of flow do in the presence of microtopography and surface obstructions. The term 3 −1 −3 Γo represents volumetric fluid exchange per unit volume [L T L ] with the subsurface domain. This exchange is described by a first-order fluid flux term that depends on the subsurface hydraulic head and depth of flow.

Fluid ﬂow in tile drains can be represented with one-dimensional line elements where ﬂow along the element axis (s) is described by the following equation:

∂ ∂ − (Q ) + Q δ (s − s ) + A Γ = (A ) (4.3) ∂s 1D w p f 1D ∂t f

55 −3 where Q1D is the volumetric water flux along the drain [L T ] defined as Q1D = Af q1D −1 2 , where q1D is the linear velocity [L T ] averaged over cross-section Af [L ], and Qw is the volumetric flow rate in and out of the tile drain at location s = sp. The term Γ1D represents the volumetric fluid exchange per unit volume [L3 T−1 L−3] with the subsurface domain. Similarly, for the fluid exchange between the surface and subsurface, that exchange is described by a first-order fluid flux term that depends on subsurface hydraulic head and depth of flow in the tile drains.

Equation 4.3 represents the general form used in HydroGeoSphere to represent ﬂow along one- dimensional features such as wells, surface channels, pipes or tile drains. The volumetric ﬂow rate along these one-dimensional elements is represented by the following general equation:

∂h q Q = −C · A · (R )p · w (4.4) 1D f H ∂s

where C is a proportionality constant, RH is the hydraulic radius and p and q are exponents. For the tile drain simulations presented here, parameters were chosen such that equation 4.4 corresponded to the Hazen-Williams empirical equation for pipe ﬂow.

All governing ﬂow equations in HydroGeoSphere are discretized with the control volume ﬁnite element method and the iterative Newton-Raphson method is used to solve the resulting systems of discretized non-linear equations. Further details of the governing equations and solution methodology are presented in Therrien et al. (2010).

4.2.3 Conceptual model

The exact location of most drains in the Lillebæk catchment is unknown but five small tile drain sectors have been mapped and monitored as part of the LOOP program (Grant et al., 2007). One such sector was selected for this study. The sector, which covers 3.5 ha, contains a drainage network of irregular shape consisting of 5 main drains and 15 secondary drains with a diameter of 0.1 m (Figure 4.1). A conceptual model for water flow was defined for this sector to support the numerical simulations of coupled 2D surface and 3D subsurface flow along with one-dimensional flow in the tile drain network. The conceptual model, described below, served as the reference model for a series of simulations designed to investigate different conceptual and numerical representations of the tile drainage network, as well as different boundary

56 conditions. These other simulations, which represent variations of the reference model, are also described in this section.

The lateral boundaries of the sector considered in the conceptual model, and highlighted in Figure 4.1, are assumed to correspond to the area of influence of the drainage network. Although Hansen et al. (2013) indicate that there is likely lateral flow in the regional sand aquifer across these lateral boundaries, they are assumed here to be no-flow boundaries for the conceptual model. The impact of lateral flow in the sand aquifer was assessed in one of the simulations described below. The top of the domain corresponds to ground surface while the bottom corresponds to the bottom of the sand aquifer, which overlies the lower clay till. The bottom boundary is assumed to be a no-flow boundary. The geological units considered in the model are the top soil, the upper clay till unit, and the sand aquifer. The upper clay till is further divided into two sub-units, the A/B horizon and the C horizon, according to their distinct hydraulic properties. There are no surface water bodies on the domain considered and any water flow occurring at ground surface is assumed to exit at the point of lowest ground surface elevation.

To assess the impact of the tile drainage network on surface and subsurface ﬂow dynamics, precipitation over a 4 day period, from 25 February 2002 to 1 March 2002, was considered. Daily precipitation data for this period for the Lillebæk station were provided by the Danish Meteorological Institute (DMI). However, we preferred to use hourly precipitation data to provide a ﬁner temporal resolution of the drain response to the rainfall input. In the absence of hourly data at the Lillebæk station, we used temporal precipitation patterns from the nearby Årslev weather station to infer hourly precipitation at Lillebæk, assuming that the hourly precipitation pattern was similar at both locations. The Årslev station is located about 25 km north-west of the Lillebæk catchment and records hourly precipitation. For the 4 day period, the hourly precipitation at the Årslev station was calculated as a percentage of the total daily precipitation. This hourly percentage was then applied to the recorded daily precipitation at Lillebæk to provide discrete hourly values, which represents precipitation input at ground surface for the model. The period considered is in winter and evapotranspiration is therefore equal to zero.

57 4.2.4 Reference model

The model area for the study site, shown in Figure 4.1c, was first discretized horizontally with a triangular finite element mesh using the method described in Käser et al. (2014). This method allows to automatically refine the mesh in areas with larger surface topography gradients, compared to flat areas, which is better suited for surface flow simulations. Automatic refinement is also possible near linear features such as tile drains or rivers. For the study site, the 2D triangular mesh was refined along the drains and the lateral boundaries of the model, as illustrated in Figure 4.2a. The length of the 1D elements representing tile drains was equal to 2 m. The resulting triangular mesh, which represents the domain where the surface water flow equation is solved, contains 5370 nodes and 10 383 elements. The hydraulic properties of the surface flow domain are taken from (Hansen et al., 2013) and are assumed uniform (Table 4.1). A critical depth boundary condition is applied at the lowest elevation of the surface domain to allow outflow of surface water.

The 2D triangular mesh was duplicated in the third dimension, from ground surface down to the bottom of the sandy aquifer to form 3D triangular prism elements. A total of 10 layers of 3D elements with variable thicknesses were thus generated to discretize the top soil and the two sub-units that form the upper clayey till, while the sandy aquifer was discretized with one layer of elements. The 3D mesh thus contained 64 440 nodes and 114 213 triangular prism elements. The nodes at the top of the mesh represent ground surface, which gently slopes towards the southeast with elevations ranging from 29 to 23 mamsl. The elevation of the nodes at the top of the mesh was interpolated from a digital elevation model that has a grid size of 1.6 m. The thickness of the top soil was assumed to be uniform and equal to 0.2 m while the thicknesses of the two upper till units were assumed equal to 2.0 m and 0.8 m for the A/B and C horizons, respectively (Table 4.1). The elevation of the top and bottom boundaries of the sandy aquifer were interpolated from a geological model set up for the Lillebæk catchment by Hansen (2010) on a 50 m grid. The resulting total thickness of the sandy layer in the model varies between 30 m and 35 m.

The hydraulic properties of the four different geological units are shown in Table 4.1. Each unit is assumed to be homogeneous with hydraulic conductivity and specific storage values taken from Hansen et al. (2013) and also based on infiltration tests (Nilsson et al., 2001). A vertical to horizontal anisotropy ratio of 10 is assumed for the hydraulic conductivity of the

58 Table 4.1: Hydraulic properties of the reference model for the subsurface units, surface ﬂow domain and tile drains.

Domain Unit Parameter Value −1 −6 Horizontal hydraulic conductivity Kh [m s ] 2.2 × 10 −1 −5 Vertical hydraulic conductivity Kv [m s ] 2.2 × 10 Top soil −3 Specific storage Ss [-] 1.0 × 10 Thickness [m] 0.2 Horizontal hydraulic conductivity K [m s−1] 3.8 × 10−6 Clayey till h Vertical hydraulic conductivity K [m s−1] 3.8 × 10−5 (A/B hori- v Specific storage S [-] 1.0 × 10−3 zons) s Subsurface Thickness [m] 2.0 −1 −8 Horizontal hydraulic conductivity Kh [m s ] 3.8 × 10 −1 −8 Clayey till Vertical hydraulic conductivity Kv [m s ] 1.9 × 10 −3 (C horizon) Specific storage Ss [-] 1.0 × 10 Thickness [m] 0.8 −1 −6 Horizontal hydraulic conductivity Kh [m s ] 4.6 × 10 −1 −7 Vertical hydraulic conductivity Kv [m s ] 4.6 × 10 Sandy aquifer −3 Specific storage Ss [-] 2.0 × 10 Thickness [m] 30 to 35 Manning roughness coefficient [m1/3 s−1] 10 Surface Rill storage height [m] 1.0 × 10−3 Obstruction storage height [m] 1.0 × 10−3 Tile drains Diameter [m] 0.1

top soil and clay tills to account for the presence of macropores and vertical fractures (Nilsson et al., 2003). The unsaturated hydraulic properties of the top soil and clayey till units were described with the van Genuchten functions (van Genuchten, 1980), with a residual saturation equal to 0.164 and van Genuchten parameters α and β equal to 2.3 m−1 and 1.26, respectively. These values were obtained with the ROSETTA pedotransfer model (Schaap et al., 2001) by calibrating van Genuchten’s curves based on grain size analysis on soil samples from the Lillebæk catchment. The calibration process and the van Genuchten parameter values were given by Hansen et al. (2014).

When constructing the 3D mesh, one layer of nodes was located at a depth of 1 m below ground surface, which is the assumed depth of the tile drains for the study site. Nodes belonging to that layer, and whose position corresponds to that of the network shown in Figure 4.1c, were selected to construct the drainage network with one-dimensional elements.

59 The trace of the network is visible when inspecting the mesh shown in Figure 4.2a, which has been reﬁned close to the drains. The tile drains, which were represented in the model by discrete 1D linear elements, were assumed to have a diameter of 0.1 m (Table 4.1). A critical depth boundary condition is applied at the outlet of the drainage network to allow water to ﬂow out of the simulation domain.

For all simulations described below, hourly precipitation for the 4 day period described previously was applied at the top of the surface domain. A challenge in coupled surface and subsurface flow simulations is to specify initial conditions that are in equilibrium with the prescribed boundary condition before precipitation is applied (Ajami et al., 2014). To define the initial conditions, a preliminary simulation was conducted where the model domain was initially fully saturated and then allowed to drain, without precipitation, for a sufficiently long period (100 years in this case) to reach steady-state flow conditions for the prescribed boundary conditions, excluding precipitations. The simulations were then started for the 4 day period and the model was run for another 3 month period without any rainfall to analyze the response of the drains to the 4 day period and to let the model reach quasi steady-state again. Very low convergence criteria were specified for the Newton-Raphson iterations to keep the mass balance error as low as possible (Table 4.2). Adaptive time stepping was used for adjusting time steps according to the variation in saturation during each simulation (Therrien et al., 2010).

Table 4.2: Convergence criteria for the Newton-Raphson iteration and the ﬂow matrix solver.

Criterion Value Newton-Raphson absolute convergence criterion [m] 1.0 × 10−20 Newton-Raphson residual convergence criterion [-] 5.0 × 10−7 Iterative ﬂow matrix solver convergence criterion [m] 1.0 × 10−13

60 4.2.5 Test models

A series of test models, based on the reference model, were developed to investigate the impact of some of the assumptions of the conceptual model. This section describes the test models, which are also listed in Table 4.3. For some of these test models, parameters were adjusted during the simulations to reproduce the model output from the reference model. These adjustments are commented below.

(a) (b) (c)

(d) (e) (f)

100 m

Figure 4.2: a) 2D triangular mesh created to discretize the domain shown in Figure 4.1c and used for the reference model and tests 1 -4, b) coaser mesh, with 5 m discretization for tile drains, used for test 5, c) finer mesh, with 1 m discretization for tile drains, used for test 6, d) mesh for a simplified network (test 7), e) mesh used for the simulation with a drainage layer (test 2) where the drainage network is shown but was not discretized, f) location of the outflow boundary nodes of the drainage layer for test 2.

Test 1

The ﬁrst test was set up by modifying the drainage boundary condition at the drainage network outlet, where a prescribed hydraulic head was speciﬁed instead of a channel critical

61 Table 4.3: Tests performed on the reference model (Ref.) illustrating the type of representation for the drains (Drain type), the boundary condition at the drain outlet (Drains BC), the lateral ﬂow boundary condition along the aquifer layer (Lateral BC), the time interval for precipitation (Precip.) and the conceptual model for the subsurface (Porous media).

Lateral BC Test n◦ Drain type Drains BC Precip. Porous media (aquifer) Ref. discrete channel no flow hourly single 1 discrete fixed head no flow hourly single equivalent 2 - no flow hourly single medium 3 discrete channel fixed head hourly single 4 discrete channel no flow hourly dual 5 discrete channel no flow hourly single 6 discrete channel no flow hourly single 7 discrete channel no flow hourly single 8 discrete channel no flow daily single

depth boundary condition. The prescribed hydraulic head was equal to the elevation of the drain at the outlet, which is a boundary condition often used to represent drains. For example, in MODFLOW, a high prescribed value for the drain conductance will produce a hydraulic head at the drain cell equal to the drain elevation. This situation corresponds to a very efficient drain that always maintains the water table lower or equal to its elevation. The goal of this first test was thus to compare results for both types of boundary conditions and to observe potential differences in water outflow values.

Test 2

For this test, the discrete drainage network was not discretized with one-dimensional elements but rather represented as an equivalent porous medium by introducing a high hydraulic conductivity layer having a thickness of 0.1 m, which corresponds to the drains diameter. This layer is assumed to be present over the whole simulation domain. Including such a conceptual drainage layer greatly simplifies the mesh since individual drains are no longer discretized (Figure 4.2e). The layer was given properties of a typical sand to gravel material (Table 4.4). Hydraulic conductivities were initially defined with an anisotropy factor of 10 in the horizontal direction, but were subsequently modified for reproducing the simulated drainage discharge from the reference model. Values shown in Table 4.4 are the adjusted

62 ones.

To simulate outﬂow from the drainage layer, all nodes belonging to that layer that are located at the downstream boundary of the domain were assigned prescribed hydraulic heads equal to their elevation. Those nodes are shown in Figure 4.2f. Other types of boundaries were tested for these nodes, such as a seepage face, but the prescribed heads were best suited here.

Table 4.4: Hydraulic properties of the equivalent porous medium layer used to represent the drainage network (Test 2).

Parameter Value Reference −1 −2 Horizontal hydraulic conductivity Kh [m s ] 1.0 × 10 Assumed, manually adjusted −1 −5 Vertical hydraulic conductivity Kv [m s ] 1.0 × 10 Assumed, manually adjusted −5 Speciﬁc storage Ss [-] 1.0 × 10 Assumed Residual saturation Sr [-] 0.045 Carsel and Parrish (1988) van Genuchten parameter α [m−1] 1.45 Carsel and Parrish (1988) van Genuchten parameter n [-] 2.68 Carsel and Parrish (1988)

Test 3

For this simulation, the lateral boundaries of the domain were modified to account for regional flow in the sandy aquifer. The no-flow lateral boundaries in the sandy aquifer were thus changed to prescribed hydraulic heads, with values taken from the model developed by Hansen et al. (2013). These hydraulic heads were assumed to remain constant during the simulated 4 day-precipitation event.

Test 4

Nutrient transport is a current issue in the Lillebæk catchment and future work will likely focus on nutrient transport modelling. In this case, a dual continuum approach might be more appropriate than a single continuum approach to account for transport and preferential water flow in fractured and macropore bearing clayey tills (Rosenbom et al., 2009). Although a discrete fracture modeling approach is the most efficient way of simulating water flux through fractured clayey till aquitards (Jørgensen et al., 2004), there is no data on fracture length, spacing, density and orientation for our study area. Efficiency of a dual-permeability model

63 using HydroGeoSphere and its ability to accurately simulate nutrient transport in macroporous soils has been demonstrated by Frey et al. (2012). We have consequently decided to apply a similar conceptual model here.

Macropores have been observed in the A horizon of the upper clay till in Lillebæk, as well as in the top soil, while the B horizon mostly contains fractures (Nilsson et al., 2003). Both horizons were therefore defined as dual-permeability media for this simulation, with one medium representing the clay matrix and another medium representing either the system of macropores for horizon A and the top soil or fractures for horizon B (Table 4.5). Properties of the interface between the matrix and both the macropores and fractured media, which control fluid exchange between the media, are assumed to be similar to those of the clay matrix, which is the approach used by Gerke and van Genuchten (1993). Volume fractions for the dual-permeability medium were assumed equal to 55 % for the matrix and 45 % for the macropores and fractures. Although the actual volume fractions of matrix and macropores/fractures are unknown; it is likely that the volume fraction for macropores and fractures is lower than the value assumed here. Furthermore, those volume fractions were selected to also fit the drainage outflow hydrograph simulated with the reference model.

Table 4.5: Hydraulic properties for the dual-permeability simulation (Test 4).

Medium Parameter Value Reference Hydraulic conductivity K [m s−1] 7.0 × 10−9 Nilsson et al. (2003) −3 Matrix Specific storage Ss [-] 1.0 × 10 Assumed (A/B hori- Residual saturation Sr [-] 0.10 Estimated from Yates et al. (1992) zons) van Genuchten parameter α [m−1] 1.5 Estimated from Yates et al. (1992) van Genuchten parameter n [-] 1.25 Estimated from Yates et al. (1992) −1 −5 Horizontal hydraulic conductivity Kh [m s ] 1.0 × 10 Estimated from Nilsson et al. (2003) −1 −3 Vertical hydraulic conductivity Kv [m s ] 1.0 × 10 Assumed −3 Macropores Specific storage Ss [-] 1.0 × 10 Assumed (A horizon) Residual saturation Sr [-] 0.01 Rosenbom et al. (2009) van Genuchten parameter α [m−1] 10 Gerke and van Genuchten (1993) van Genuchten parameter n [-] 2.0 Gerke and van Genuchten (1993) −1 −7 Horizontal hydraulic conductivity Kh [m s ] 3.8 × 10 Estimated from Hansen et al. (2013) −1 −5 Vertical hydraulic conductivity Kv [m s ] 3.8 × 10 Estimated from Hansen et al. (2013) −3 Fractures Specific storage Ss [-] 1.0 × 10 Assumed (B horizon) Residual saturation Sr [-] 0.01 Rosenbom et al. (2009) van Genuchten parameter α [m−1] 4.687 Rosenbom et al. (2009) van Genuchten parameter n [-] 2.297 Rosenbom et al. (2009) Matrix volume fraction [-] 0.55 Assumed, manually adjusted

64 Tests 5, 6 and 7

The representation of discrete drains in a numerical model can greatly increase the number of nodes, as illustrated by the mesh in Figure 4.2a, and thus increase simulation times. Models developed for catchments larger than that considered here can potentially lead to extremely large meshes and make simulation impractical. It is therefore useful to investigate the impact of the level of discretization of drains on flow dynamics, which was done here for Tests 5 to 7. The reference model had 2 m elements along discrete drains. For Test 5, a coarser mesh was created with 5 m elements along drain segments (Figure 4.2b) while a finer mesh was created for Test 6 with 1 m elements along drain segments (Figure 4.2c). For another simulation, Test 7, the drainage network was simplified by retaining only the 5 main drains, which reduces the number of nodes (Figure 4.2d). This last simulation aimed at assessing the effective contribution of the main drains to the total water outflow.

Test 8

This simulation aimed at comparing the impact of using the original daily precipitation data as opposed to the hourly precipitation data used in the reference model. The simulated drainage outflow rates were also compared to the measured daily outflow rates to evaluate the representativeness of this model. Since this model was not calibrated, this comparison remains qualitative. However, the total volume of water flowing through the drains could be evaluated for both the reference model and this Test 8 model to assess any differences in the amount of water stored in the subsurface following precipitation.

65 4.3 Results

In this section, results from the reference model are ﬁrst presented followed by a comparison of simulated hydrographs and water balance between the reference model and the various test models.

4.3.1 Reference model

The applied precipitation for the 4-day period shows three main peaks within the ﬁrst 24 hours (Figure 4.3). The highest precipitation intensity of 7.9 mm h−1 corresponds to the second peak. The simulated drainage discharge shows that the drainage system quickly responds to precipitation, with drainage ﬂow peaks reached 50 to 60 minutes after precipitation peak values are applied to the model surface (Figure 4.3).

The generated overland flow hydrograph also contains three peaks but their intensities vary more than that of the drainage system. The first peak in overland flow only seems to be influenced by the second half of the first precipitation peak, meaning that during the first half of the peak all the water is infiltrating and either flowing through the unsaturated zone to the drains or recharging the aquifer. The second overland flow peak has a maximum water flow rate value that is almost twice as high as the drainage peak value (Table 4.6). For this specific period in the simulation, the drainage water flow capacity may thus be exceeded inducing pipe pressurization issues in some pipes of the drainage network.

The overland flow values for the third peak are lower than that of drainage flow. Secondary precipitation peaks after day 86 (after 2 days of simulation) produce drainage flow but don’t lead to generation of overland flow, as shown in Figure 4.3. This figure also shows that the recession for drainage is slower than for overland flow, with drainage flow rates gradually decreasing to zero over a few days after the rainfall event, whereas overland flow rates show an abrupt decrease to zero. At the outlet of the drainage network, the hydraulic head is 17 cm higher at the second peak than it is initially before the first peak (Table 4.6).

As a full simulation including evapotranspiration is outside the scope of the present study and, as hourly observed discharge data are not available, we aim at simulating plausible hydrographs that reﬂect the hydrological regime and allow realistic studies of numerical issues related to alternative model conceptualizations rather than matching the observed hydrograph

66 perfectly. Furthermore, the flows and water balance of such a small catchment are to a large extent governed by boundary fluxes that are unknown. Therefore we have not attempted to calibrate our model against observed discharge. Figure 4.3 shows that the simulated discharges are somewhat higher than the observed ones, and analyses of the total water flows during the four day period reveal that the model simulates about 50 % more runoff than observed, indicating that the model dynamics are slightly more flashy than the observations. But altogether, the pattern of response is reasonable and the simulated hydrographs reflect the observations sufficiently well to serve the purpose of our study.

The total water balance for the simulation period is displayed in Table 4.7. The total water outflow is higher than precipitation and the amount of water stored in the porous medium therefore decreases as the simulation progresses. All precipitation water is thus flowing out through the drains or at the soil surface while, before the start of precipitation, no water originating from precipitation is flowing through the drains. Because the initial head distribution corresponds to a quasi steady-state, the outflow at the drain outlet during the transient simulation is not exactly equal to zero but its value is very small compared to the magnitude of precipitation. This background outflow was also observed for most of the test models, except for tests 3 and 4 for which no background outflow is observed. Outflow from the drains corresponds to 78.7 % of the total water outflow for the model. Outflowing water also originates from the soil matrix.

The saturation distribution in the glacial clayey till unit, shown in Figure 4.4 where the sandy aquifer layer has been masked, shows that tile drainage leads to a quick drop in saturations during and after the precipitation event. The impact of drainage is clearly seen in the downstream part of the model, which is almost fully saturated during the event (ﬁrst and second peaks). Low saturations are observed around the drains in an otherwise saturated surrounding environment. The upstream part shows lower saturation values than the downstream part, however in the part of the model having no drains a high saturation lens distinctly appears at the ﬁrst peak and persists to the end of the event. The steady-state snapshot taken before the event shows that the water table is initially below the drainage system. The water table rises at the end of the event (day 89) but remains mostly below the drains.

The initial baseﬂow value, which is very close to 0 m3 s−1 and corresponds to a pseudo steady- state, is reached again shortly after the event.

67 Figure 4.3: Hydrographs of drainage discharge at the network outlet and overland ﬂow at the surface outlet and applied hourly precipitation at ground surface for the 4-day simulation. Observed daily drainage ﬂow data results are also presented.

68 Table 4.6: For each model, computed maximum drainage (Qmax drains) and overland (Qmax surface) ﬂow rates at second peak, and computed hydraulic heads at the outlet of the drainage network just before the rainfall event (Hout init) and for the second peak (Hout peak).

3 −1 3 −1 Test Qmax drains [m s ]Qmax surface [m s ]Hout init [m]Hout peak [m] Ref. 2.30 × 10−2 4.41 × 10−2 22.63 22.80 1 2.39 × 10−2 4.31 × 10−2 22.63 22.63 2 2.23 × 10−2 4.64 × 10−2 22.63 22.80 3 2.27 × 10−2 4.18 × 10−2 20.83 22.80 4 1.79 × 10−2 5.08 × 10−2 22.63 22.71 5 2.47 × 10−2 4.25 × 10−2 22.63 22.81 6 2.22 × 10−2 4.47 × 10−2 22.63 22.80 7 1.30 × 10−2 5.50 × 10−2 22.63 22.74 8 7.63 × 10−3 2.63 × 10−3 22.63 22.71

Figure 4.4: Saturation distribution in the clayey till for steady-state conditions (before the precipitation event), at the time of the ﬁrst precipitation peak, at the time of the second peak and at the end of the 4-day simulation. The black lines across the sections show the drainage network.

69 a) b)

c) d)

Figure 4.5: Water table elevation (WT), expressed in mamsl, of the reference (a) and test 2 (b) models at peak 2 (day 85.3). Water table elevation after the three main peaks, displayed at day 86, is also shown for the reference (c) and Test 2 (d) models. The black lines are the pipes constituting the drainage network. Coordinates are ETRS 89 / UTM Zone 32 N coordinates.

70 Table 4.7: Global water balance for each model illustrating the total precipitation amount (Ptot), the total water outflow amount (Vout), the total drainage outflow (Vdrains), the total overland outflow (Vsurface), the corresponding storage to/from the matrix (Stor.) and the total water mass balance. Positive Stor. values reveal water storage in the porous medium while negative values show water released by the porous medium.

Vdrains [mm] Vsurface [mm] Mass balance Test Ptot [mm]Vout [mm] Stor. [mm] Amount [mm] % of Vout Amount [mm] % of Vout Amount [mm] Error [%] Ref. 41.4 42.8 33.7 78.7 9.1 21.3 −0.8 −0.6 0.1 1 41.4 44.5 35.6 80.0 8.9 20.0 −2.1 −1.0 0.3 2 41.4 45.1 37.4 82.9 7.7 17.1 −2.4 −1.3 0.3 3 41.4 24.1 16.4 68.0 7.7 32.0 0.0a 0.0 0.0 4 41.4 31.5 23.9 75.9 7.6 24.1 9.5 0.4 0.01 5 41.4 42.5 33.3 78.4 9.2 21.6 0.4 −0.7 0.4 6 41.4 42.3 33.7 79.7 8.6 20.3 0.2 −0.7 0.3 7 41.4 42.2 27.3 64.7 14.9 35.3 −0.1 −0.7 0.3 8 41.4 40.3 35.8 88.8 4.5 11.2 1.6 −0.5 0.8

a The storage value for Test 3 doesn’t account for the outﬂow induced by the prescribed head aquifer boundary condition. 71 4.3.2 Test models

Test 1: drainage ﬁxed head boundary condition

Modifying the boundary condition at the outlet of the drainage network produces a hydrograph similar to the reference hydrograph (Figure 4.6a). Compared to the reference model, the second peak is slightly higher (+4 %) while the first and third ones are close to the reference. Recession after the peaks is identical to that of the reference model. While the highest peak for drainage is slightly higher than that of the reference model, the maximum simulated overland flow rate is lower (−2 %, see Table 4.6) and the total overland outflow is slightly lower than the reference (−2 %, see Table 4.7). In addition, this first test produces an increase in the total volume of water drained compared to the reference model (+5 %) and the soil matrix contribution (storage) is higher (+162 %). The total mass balance error is a bit higher than that of the reference model (+0.2 %). Finally, because of the fixed head boundary condition, no hydraulic head changes are observed at the outlet of the drainage network from the beginning of the rainfall event and the second peak (Table 4.6).

Test 2: equivalent medium as drainage layer

The model (Test 2) that represents the drainage network as a single drainage layer, using an equivalent porous medium approach, reproduced almost exactly the outflow hydrograph of the reference model. Since the hydrograph for Test 2 cannot be distinguished from that of the reference model, it is not shown in Figure 4.6. From a conceptual perspective, the outflow hydrograph is not for a single location, such as the outlet of the drainage network as is the case for the reference model, but a series of nodes that correspond to the outlet of the drainage layer (as shown in Figure 4.2f). That outlet corresponds to a vertical face having a thickness of 0.1 m and a length slightly larger than 100 m where hydraulic heads are prescribed, which explains why no change in hydraulic head is seen (Table 4.6). Although the total outflow is similar to that of the reference model, the equivalent porous medium model produces spatial distributions of hydraulic head and saturation that are different from those produced by the reference model. However, when looking at Figure 4.5, it appears that the water table elevation calculated by the Test 2 model (Figure 4.5b and Figure 4.5d) doesn’t show extreme differences from the reference model water table elevation (Figure 4.5a and Figure 4.5c). The highest peak intensity for drainage is slightly lower than that of the reference model (−3 %),

72 but the maximum overland ﬂow rate at peak 2 is higher than for the reference (+5 %, see Table 4.6). This model produces more intense overland ﬂow peaks but the overall amount of surface water is lower than for the reference (−15 %, see Table 4.7). This test also produces water storage unlike the reference (+200 %) and the total mass balance error is a bit higher than the reference model (+0.2 %).

Test 3: aquifer layer prescribed head boundary condition

Compared to the reference model, the drainage outflow caused by the first precipitation peak during day 84 is delayed and lower, while the drainage outflow for the other two precipitation peaks at day 85 is similar. The model also produces faster drainage recession, with outflow rates becoming zero after the first precipitation and third precipitation peaks. Furthermore, outflow drainage remains equal to zero after day 86 since the water table remains below the location of the drains for that period.

The sum of drainage and overland outflow for this model is much lower than that of the reference (−44 %, see Table 4.7). The model also produces less drainage outflow and surface outflow (−51 % and −15 % respectively). A feature of this model is that there is no change in the amount of water stored in the matrix (storage = 0 mm). The total mass balance error is also somewhat higher than the reference (+0.2 %). Finally, the second precipitation peak produces higher overland flow rate than drain outflow (Table 4.6), suggesting pipe pressurization, and the initial groundwater head at the outlet is much lower than the reference (about 1.60 m lower), while the peak head value is the same.

The lateral boundaries for the underlying sandy aquifer were assumed to be no-flow boundaries for the reference model, although there is evidence of horizontal water flow in the sandy aquifer across these boundaries (Hansen et al., 2013). For the Lillebæk catchment, observed lateral inflow into the sandy aquifer should ideally be included in the model, since it influences the drainage outflow. However, assigning the inflow boundary for the Lillebæk model, or for similar catchment models, is a challenge since lateral flow rates in aquifers are generally unknown. Specifying a constant head as was done here remains an approximation since it assumes that other boundary conditions, such as rainfall, do not affect the hydraulic heads at the aquifer boundary.

73 Test 4: clayey till dual permeability medium

The dual-permeability model produces lower peaks for drainage outflow compared to the reference model (Figure 4.6a). Peaks appear less smooth than the other cases. Even if dual media are taken into account here, this model shows a similar peak time lag simulated of 57 min than the reference case (Figure 4.6a). Since lower peaks are observed on the hydrograph, the maximum drainage outflow value (−22 %) and the hydraulic head at the outlet at peak 2 (9 cm lower, see Table 4.6) and the total drainage outflow volume (−29 %, see Table 4.7) are much lower than for the reference model. The total volume of overland flow for this simulation is lower than for the reference model and the maximum overland flow rate is higher. Less overland flow is generated and drainage is less effective. This model shows a significant increase in the water stored for the total simulation period, meaning that some part of the total water flowing through the model is stored in the soil matrix. It is also the model with the lowest mass balance error.

Tests 5, 6 and 7: mesh refinement and simplification influences

Simulations for models 5 and 6 produced similar drainage hydrographs at the outlet of the network (Figure 4.6b). The simulation with the coarser mesh (Test 5) produces peaks that are slightly larger than those produced by the reference model (+7 %). Test 6 shows a second peak that is slightly lower than that of the reference model (−3 %). The mass balance shows that the total outflow for the coarser mesh model is slightly lower than for the reference model (−0.7 %, see Table 4.7), but the mass balance error is higher (+0.3 %). A lower contribution of drainage and a slightly higher contribution of overland flow are observed (−1 % and +1 % respectively). For the finer mesh (test 6), the water balance for drain outflow is similar to the reference model but overland flow is smaller (−5 %). In both cases, storage values are positive and the total error is higher (+ +0.2 %, see Table 4.7). The main difference caused by the different levels of discretization used for Tests 5 and 6 is thus lower overland flow produced by the finer mesh. Additionally, the overland outflow peak for test 6 is higher than for the reference model while it is lower for Test 5 (+1 % and −4 % respectively, see Table 4.6). Although the maximum drainage flow rates are observed for different mesh refinements, the hydraulic heads at the outlet remain similar (Table 4.6).

The simulation for a simpliﬁed drainage network (Test 7) results in a lower drainage outﬂow

74 Figure 4.6: Outﬂow hydrographs of the drainage network for a) the reference model and tests 1, 3 and 4 and b) the reference model and models with reﬁned meshes along the drains (5 to 7). Precipitation is also plotted for comparison purpose.

75 ( −19 %), as illustrated by the lower intensity of the peaks in the hydrograph (Figure 4.6b) and a higher contribution to overland flow than for the reference model (+64 %, see Table 4.7). The water released by the matrix storage is also lower for this case (storage = −0.1 mm). The maximum water flow rate variations calculated by the model for drainage and overland flow are emphasized as the drainage value is lower than the reference (−43 %) and the overland flow is higher (+25 %). Lower drainage flow rates imply a lower hydraulic head at the outlet of the network during the rainfall event (6 cm lower) while the initial head is equal to the reference model initial head value.

Test 8: daily precipitation

The daily precipitation time series, shown in Figure 4.7, has only one main peak. When daily precipitation is applied, the simulated drainage curve shows a distinct response of drains to the infiltrating rain and even shows a tendency to reach plateaus for each daily precipitation value (Figure 4.7). The simulated drainage discharge rates are higher than the observed ones, but the temporal trend for both drainage curves is similar and shows a distinct response to rainfall. Comparison of Figure 4.3 and Figure 4.6 shows that the maximum discharge rates at the outlet of the network are smaller than those computed for the reference model, although the total volumetric outflow is similar. Those lower discharge rates, which can be viewed as mean rates for a 24-hour period, are also associated with a smaller difference in hydraulic head at the network outlet (9 cm difference), even though the initial value is the same as in the reference model. The water mass balance for this test shows a slightly lower water amount exported with 88.8 % flowing out through the drains while water is stored in the matrix (1.6 mm). The total mass balance error is the highest of all models (0.8 %).

76 Figure 4.7: Calculated and observed drainage discharge hydrographs and daily precipitation values applied to the model. Precipitation values originate from data measured daily at 6 am, this explains the short time-lag for the precipitation curve.

Table 4.8: Mesh speciﬁcation and computational times for the reference and test models. Each simulation was run using a 3.39 Gb RAM computer with 8 CPU cores at 3.40 GHz.

Test Description Nodes Elements Computing time Time steps Ref. Critical depth drainage 64 440 114 213 2 h 40 min 206 1 Prescribed head drainage 64 440 114 213 1 h 12 min 275 2 Equivalent medium 21 564 35 618 15 min 529 3 Aquifer prescribed head 64 440 114 213 1 h 37 min 529 4 Clay till dual-permeability 64 440 114 213 13 h 35 min 6674 5 Coarse mesh 30 012 51 095 21 min 435 6 Fine mesh 139 020 250 888 6 h 2 min 449 7 Simpliﬁed network 47 112 82 445 50 min 350 8 Daily precipitation 64 440 114 213 50 min 518

77 4.3.3 Computational performance

All simulations were run using a 3.39 Gb RAM computer with 8 CPU cores at 3.40 GHz and with the parallelized version of HydroGeoSphere (Hwang, 2012; Hwang et al., 2014). One of the objectives of testing diﬀerent models was to investigate computational aspects, in particular the simulation time and the number of time steps required for the simulation. Both results are found in Table 4.8 for the various models. The total number of time steps required for the simulation varies because a variable time stepping option was used in Hydro- GeoSphere. As a result, the number of time steps, and the time step size, required to reach a similar convergence criteria for the Newton-Raphson iteration can vary from one simulation to another.

The reference model and the Tests 1, 3, 4 and 8 had the same mesh but the total simulation time varied. Specifying a prescribed hydraulic head boundary at the drainage outlet for the ﬁrst test reduced the simulation time by more than half compared to the reference model. The equivalent medium drainage layer model (test 2) had the mesh with the fewer elements and nodes and was the fastest model. Changing the aquifer lateral boundary conditions from no ﬂow to prescribed head (test 3) also speeds up the simulation compared to the reference model but more time steps are taken by the model. On the other hand, the dual-permeability model (test 4) greatly increased the total simulation time, which was 13 h 35 min, as well as required a much larger number of time steps for the simulation.

Models 5 to 7 used meshes that were different from that of the reference model, which influenced the total simulation time, in addition to the variations made to the model compared to the reference model. A coarser mesh along the drains (test 5) reduced by more than half the number of nodes and elements and decreased the total simulation by a factor of 10. The finer mesh had the opposite effect, with a longer simulation time. A simpler drainage network (test 7) also shortened the total time needed for a model run as the model has fewer elements. Finally, applying daily precipitation data (test 8) also greatly reduced the total simulation time compared to the reference model, even if more time steps were taken by the model.

78 4.4 Discussion and conclusions

The simulations presented here suggest that, in the context of tile drainage, a fully coupled subsurface, surface and drainage model allows for a more realistic representation of the ﬂow dynamics.

However, simulation time and data availability remain major challenges. For example, if drains are only partially mapped within a catchment and their location, orientation, and length are unknown, using an equivalent medium layer for representing drainage remains a valid option. Creating an equivalent medium layer is also appropriate to avoid dense meshes and therefore exceedingly long simulation times. A similar drain representation has been successfully applied in real cases (e.g. Rozemeijer et al., 2010) and provides considerable advantages in simplifying the model mesh and avoiding internal boundary conditions. Carlier et al. (2007) have developed a method for calculating equivalent medium parameters based on the drainage network geometry. They have applied it at the field scale on a drainage network made of parallel pipes located at regular intervals. Defining the equivalent layer properties with this method did not seem feasible in our case as the drainage network is irregular and most of the drains do not show a parallel pattern. The equivalent medium hydraulic parameters were therefore defined by modifying the model properties to reproduce the reference model drainage outflow values. On the other hand, such a model ideally requires calibration against drainage observation data to reproduce the water budget at the field or catchment scale.

Using HydroGeoSphere, Frey et al. (2012) have shown that a dual-permeability representation of the subsurface is required to simulate nutrient transport in low-permeability macroporous soils. Tile drainage is commonly used in agricultural environments, where transport of chemical species or even sediment particles is often a key modeling issue. The conceptual model to represent that tile-drained material, for example an equivalent porous medium or a dual- permeability medium, should therefore be carefully chosen.

The temporal resolution of precipitation data applied in the model can significantly affect flow dynamics. Using hourly datasets instead of daily datasets produced more pronounced drainage peaks, suggesting that a higher rainfall frequency should be used when possible.

Although a coupled surface, subsurface and tile drain ﬂow model is suggested as the preferred

79 one, the various models tested here also show the influence of other model parameters on drainage outflow, such as choice of boundary conditions and mesh size. Even though we have been focusing on the subsurface drainage network in the clayey till unit, setting lateral fixed head boundary conditions to the underlying sandy aquifer layer improves the drainage simulation. Depending on the need of further transport simulations, using a dual-permeability representation of the low-permeability clayey till may be required for better representation of matrix diffusion and advective transport through macropores. When constructing larger scale models, simplifying the drainage network also simplifies the mesh and reduces simulation times, but model calibration against observation data is needed to adequately represent drainage.

As pointed out by Koch et al. (2013), proper flow modeling of tile drained areas should include discrete tile drainage systems. At field scale, our simulations showed that discrete pipes are the most relevant concept to be chosen for modeling proper drainage flow dynamics. However, a representation of the whole drainage network in a model may lead to very long and perhaps impractical simulation times. Simplifying the drainage network, as tested here by taking into account the main collecting pipes of the network, represents an alternative for fast computing times.

When performing simulations at larger scales, one would need to include various drainage areas made of numerous pipes in a model. The need of modeling drainage flow originating from such areas may be restrained by highly discretized meshes. In such a case, the network simplification option is a suitable option for simulating drainage flow. In addition to reducing simulation time, it allows modelers to avoid creating dense and complex meshes. Another recommended concept to avoid dense meshes is to represent drainage networks by an equivalent high-conductivity porous medium layer, as adopted by Rozemeijer et al. (2010). Nevertheless, with both options, calibration is needed against observed drainage flow rate data to ensure proper calculations of water volumes involved in drainage.

Even if no transport simulation was performed here, it is believed that the most relevant concept to envisage, in terms of appropriate physical processes simulated, is creating a dual permeability model with discrete drains so that preferential ﬂow and transport pathways are taken into account.

80 In any case, the heterogeneity of tile-drained clayey tills can greatly influence groundwater flow dynamics as well as tile drainage. We are currently developing a larger scale model to simulate seasonal variations in tile drainage outflow, where heterogeneities of the clayey tills will be represented in greater detail, as investigated in the NiCA research project (Refsgaard et al., 2014), which this study is part of. This project focuses on nitrate reduction within geologically heterogeneous agricultural catchments. In the light of this project framework, more realistic simulated water flow patterns in heterogeneous tile-drained field are required, which is the cornerstone of potential nutrient transport modeling through subsurface drained soils. Although each case is unique, we would argue that some of the key conclusions are generic and apply to many tile drained areas, namely that a simplified mesh may be adequate for simulating the flow dynamics at the drain outlet, while a detailed mesh and probably a dual permeability concept are recommended for detailed studies of contaminant transport.

Chapter 5

Seasonal variations simulation of local scale tile drainage discharge in an agricultural catchment

Modélisation des variations saisonnières du drainage souterrain dans un bassin versant agricole

G. De Schepper, R. Therrien Department of Geology and Geological Engineering, Université Laval Quebec City, Canada

J. C. Refsgaard, X. He Department of Hydrology, Geological Survey of Denmark and Greenland Copenhagen, Denmark

C. Kjærgaard, B. V. Iversen Department of Agroecology, University of Aarhus Aarhus, Denmark

Submitted to Water Resources Research, October 16, 2015.

Abstract

Seasonal variations of tile drainage discharge were simulated in the 6 km2 Fensholt catchment, Denmark, with the coupled surface and subsurface HydroGeoSphere model. The catchment subsurface is represented in the model by 3 m of topsoil and clay, underlain by a heterogeneous distribution of sand and clay units. Two subsurface drainage networks were represented as nodal sinks. A stochastic distribution of the heterogeneous units was generated and their hydraulic properties were adjusted to reproduce drainage discharge for one of the two drainage networks and validated with drainage discharge for the other. Simulation results were compared to those of another model for which the heterogeneous sand and clay units were replaced by a homogeneous unit, whose hydraulic conductivity was the mean value of the heterogeneous model. With the homogeneous model, drainage dynamics were well simulated but drainage discharge was less accurate than the heterogeneous model. Results were also compared to those a larger scale model created with the MIKE SHE code, built with the same heterogeneous model. HydroGeoSphere and MIKE SHE generated drainage discharge that was significantly different, with better simulated groundwater dynamics data produced by HydroGeoSphere. Nodal sinks in HydroGeoSphere reproduced drain flow peaks more accurately. Calibration against drainage discharge data suggests that drain flow is controlled primarily by geological heterogeneities included in the model and, to a lesser extent, by the nature of the soil units located between the drains and the ground surface.

85 Résumé

Les variations saisonnières du drainage agricole ont été simulées dans le bassin versant de Fensholt (6 km2) au Danemark, à l’aide du modèle hydrologique couplé de surface et subsurface HydroGeoSphere. Le modèle de subsurface de Fensholt est représenté par 3 m de terre arable et d’argile sous lesquels une distribution hétérogène d’unités de sable et d’argile est présente. Deux réseaux de drainage ont été représentés par des pertes nodales alignées. Un modèle stochastique des unités hétérogènes a été utilisé et leurs propriétés hydrauliques ont été calées pour reproduire les débits de drainage de l’un des réseaux de drainage et valider les écoulements observés dans le second. Les résultats de simulation ont été comparés à ceux d’un autre modèle pour lequel les unités hétérogènes de sable et d’argile ont été remplacées par une unité homogène, dont la conductivité hydraulique a la valeur moyenne des unités hétérogènes. Les dynamiques d’écoulement de drainage ont été correctement simulées avec le modèle homogène, mais les débits de drainage étaient moins précis que ceux du modèle hétérogène. Les résultats ont aussi été comparés à ceux d’un modèle créé à plus grande échelle avec MIKE SHE, construit sur base de la même distribution stochastique. Hydro- GeoSphere et MIKE SHE ont généré des débits de drainage sensiblement diﬀérents, avec des dynamiques d’écoulement souterrain mieux simulées par HydroGeoSphere. Les pertes nodales d’HydroGeoSphere ont reproduit les pics de drainage plus précisément. Le calage des résul- tats par rapport aux données de débit de drainage indiquent que les écoulements de drainage sont contrôlés principalement par les hétérogénéités géologiques inclues dans le modèle, et, dans une moindre mesure, par la nature des unités de sol situées entre les drains et la surface du sol.

86 5.1 Introduction

Tile drainage influences surface water and groundwater flow patterns at the field and catchment scales and can also contribute to nutrient transport to surface water (Stenberg et al., 2012). The impact of tile drainage on water resources has been quantified for temperate climates, where subsurface drainage of fine-textured soils is common for agricultural lands (Schilling et al., 2012), as well as for arid and semi-arid climates where tile drainage is generally associated with irrigation (Ayars et al., 2006). For example, King et al. (2014) showed that 45 % of the total discharge at the outlet of a catchment in Ohio, USA, for example, originated from tile drainage. Tile drainage varied temporally during a year, with drainage occurring on average 75 % of the time and full pipe flow occurring for only 2 to 4 days. Larger drained areas have shown higher drainage water volumes throughout the year. Increases in baseflow at catchment outlets have also been reported in tile-drained catchments (Schilling and Libra, 2003).

Some numerical models have been specifically developed for drainage simulations (e.g. Kroes and van Dam, 2003; Tiemeyer et al., 2007), while others include drainage as one component of the entire hydrologic cycle (e.g. Refsgaard and Storm, 1995; Šimůnek et al., 2006). Drainage has mostly been simulated for time scales ranging from a few weeks (Boivin et al., 2006), a few days (Rozemeijer et al., 2010; De Schepper et al., 2015) to a few hours (Frey et al., 2012). Among the simulations that have focused on seasonal variations over one or more years, such as those observed by King et al. (2014), most were with 1D models, such as DRAIN-WARMF (Dayyani et al., 2010) and ANSWERS (Bouraoui et al., 1997), or 2D models, such as SWAT (Du et al., 2005; Koch et al., 2013), M-2D (Abbaspour et al., 2001), MHYDAS-DRAIN (Tiemeyer et al., 2007) and THREW (Li et al., 2010). These 1D and 2D models generally produced good correlation between yearly simulated and observed drainage discharge. Although 3D models are considered more accurate than 2D or 1D models to simulate groundwater flow and tile drainage dynamics (Koch et al., 2013; Moriasi et al., 2009), they are not as widely used. In one example, unsaturated soil properties were estimated at the catchment scale by 3D inverse modeling with the MODHMS model (Vrugt et al., 2004). Al- though the uncertainty associated to calibrated parameters was large, the simulated drainage discharge was close to the observed discharge. Warsta et al. (2013) have developed the FLUSH model to simulate coupled 2D overland flow, 3D subsurface flow and subsurface transport of

87 sediments, including erosion, with drains represented as local sinks. With the model, Warsta et al. (2013) reproduced drainage discharge and seasonal variations in overland ﬂow at the ﬁeld scale.

The objective of the present study was to simulate local scale seasonal variations of subsurface drainage discharge in an agricultural catchment, located in Fensholt, Denmark. Field investigations have showed that tile drainage is a significant component of streamflow in the catchment (Nilsson, 2013) and that it can also contribute to rapid transport of nutrients, including nitrates, to streams. Tile drainage dynamics must be quantified to establish reg- ulations for nitrogen applications that minimize nitrate release to groundwater and surface water (Refsgaard et al., 2014). The HydroGeoSphere model (Therrien et al., 2010) has been used here to simulate fully coupled 3D subsurface flow, 2D overland flow and drainage flow in 1D linear drain elements. Although simulations focused on the catchment scale, individual drainage was represented explicitly in the model to simulation the impact of drainage networks on local scale groundwater flow. The novelty of the work presented here is the simulation of the seasonal variability of tile drainage discharge with a fully-coupled surface water and groundwater flow model.

88 5.2 Materials and methods

5.2.1 Site description

The Fensholt catchment covers an area of 6 km2 located within the larger Norsminde catchment (100 km2), about 15 km south of the city of Aarhus on the east coast of Jutland, Denmark (Figure 5.1). The average annual precipitation in the Norsminde catchment for the 1990-2013 period is 870 mm, with annual values that ranged from a maximum value of 925 mm in 2012 to a minimum of 700 mm in 2013.

Surface elevation in the Norsminde catchment varies from more than 100 meters above mean sea level (mamsl) in the western part to sea level in the eastern part. The western part, where the Fensholt catchment is located, is characterized by hilly terrains and the eastern part is dominated by lowlands. Agricultural land covers 78.3 % of the catchment. Forests cover 9.7 % of the territory, urban areas and roads cover 6.9 %, and wetlands and peatlands cover the remaining 5.1 %. The catchment outlet is the Norsminde Fjord, a 2 km2 estuary located to the northeast. The main stream in the Fensholt catchment is the Stampemølle Bæk (Figure 5.1), which ﬂows from west to east and discharges in the Odder River. A few tributaries are present along the main stream.

The Norsminde catchment is located in the Norwegian-Danish Basin structural unit that was formed during Permian rift tectonics and reactivated later during the Miocene (Japsen et al., 2007; Rasmussen et al., 2010). In the Fensholt catchment, Miocene deposits are located on top of Paleogene ﬁne-grained marine marls and clays. The only Miocene deposits in the region are Early Miocene marine clay and deltaic to coastal-plain sand, whose total thickness is 40 m (Rasmussen et al., 2010). Middle and Upper Miocene were eroded following a late Neogene exhumation (Japsen et al., 2007). The resulting hiatus is followed by heterogeneous Quaternary clayey and sandy glacial deposits. These Quaternary deposits mainly consist of a clay matrix that surrounds sand lenses of variable extent. The clayey deposits are of glaciolacustrine origin and show clay to clayey till facies, whereas sandy units are glacioﬂuvial (He et al., 2014). In the Fensholt catchment, the thickness of the Quaternary glacial sequence varies from up to 30 m on hilltops to about 15 m along the Stampemølle Bæk.

In the area, Quaternary sand lenses form local aquifers while the Miocene sand and gravel deltaic deposits correspond to regional aquifers (Knutsson, 2008). Hydraulic head data and

89 stream ﬂow monitoring at the stream discharge station (SD, Figure 5.1c) show that a local sandy aquifer recharges the Stampemølle Bæk (Nilsson, 2013).

The Fensholt catchment is heavily tile-drained, as indicated by the available mapped tile drainage networks (Figure 5.1c). We focused on two complex and dense tile drainage networks (Drainage areas A and B). Drainage area A (AreaA) covers 34 ha and contains 199 pipes. Drainage area B (AreaB) contains 95 pipes and covers 28 ha. The outlets of both networks (Figure 5.1c, StA and StB) discharge into a tributary of the Stampemølle Bæk, whose flow is dominated by tile drainage. Drainage discharge is monitored on an hourly basis at drainage stations StA and StB, as part of a larger monitoring project1, with bidirectional battery- operated electromagnetic flowmeters connected to both drainage networks outlets: stainless steel electrodes measure water flow with a ±0.5 mm s−1 accuracy (Windgassen, 2006). A comparison of data from the catchment stream discharge station (SD) with that from the drainage stations suggests that about 74 % of the Fensholt catchment discharge originates from tile drains. Shallow piezometers (Figure 5.1c, Pz1 to Pz8), which are 2 m deep, have been installed in the drainage areas to regularly monitor groundwater levels.

5.2.2 Numerical model

The HydroGeoSphere model (Therrien et al., 2010) simulates fully-coupled variably-saturated subsurface flow, overland flow and drainage flow. Richards’ equation is used to describe three- dimensional variably-saturated flow in the subsurface and 2D surface flow is represented by the diffusion wave approximation. The model uses the control volume finite element method for discretizing the governing flow equations and the Newton-Raphson iteration method is applied to solve the discretized non-linear equations. HydroGeoSphere uses the model developed by Kristensen and Jensen (1975) for calculating actual evapotranspiration based on potential evapotranspiration. Details on governing equations and their implementation in HydroGeoSphere are given by (Therrien et al., 2010). The model capabilities are discussed in the comprehensive review by Brunner and Simmons (2012) and specific developments related to tile drainage modeling have been documented by De Schepper et al. (2015).

1IDRÆN Project: www.idraen.dk

90 Norsminde Fjord Drainage area B Norsminde Sweden

Fensholt Odder River StB Aarhus Stampemølle Bæk

Norsminde Copenhagen Drainage area A

StA

0 50 100 200 0 2.5 5 Germany km km

SD Stream Elevation Drain pipe (mamsl) N Drainage catchment 175 Drainage station Stream discharge station 0 0 750 1500 m

Figure 5.1: Location of (a) the Norsminde catchment in Denmark (55◦ 58’ N, 10◦ 8’ E), (b) the Fensholt catchment within the Norsminde catchment, (c) a zoom-in on the Fensholt catchment showing topography (1.6 m digital elevation model), mapped drainage networks, drainage discharge measurement stations (StA and StB) with their respective drainage areas and stream discharge station on the Stampemølle Bæk stream at the outlet of the catchment (SD). Eight observation piezometers are located in the two drainage areas (Pz1 to Pz8). 91 5.2.3 Model conceptualization

Surface domain

To represent the surface flow domain, the surface of the catchment was discretized with the automated 2D triangular mesh construction method documented by Käser et al. (2014). The mesh was refined along the drains and streams by specifying a mean inter-nodal distance of 25 m (Figure 5.2). The mesh was also refined in areas where the surface slope is greater than 9 %. The edges forming the triangular elements range from 6 m long. The refined 2D triangular mesh contained 5843 nodes and 11 431 triangular elements.

The elevation of each node in the 2D mesh was interpolated from a digital elevation model with a 1.6 m grid size. Overland flow properties representative of agricultural land were assigned to the surface of the model (Table 5.1), with Manning roughness coefficients assumed to be isotropic. The coupling length included in the term describing first-order water exchange flux between surface and subsurface was assumed uniform and equal to that used by Goderniaux et al. (2009). Rill storage and obstruction storage height values were taken from Cochand (2014).

Table 5.1: Overland ﬂow properties applied to the surface domain (agricultural land).

Parameter Value Source Manning roughness coeﬃcient n [m1/3 s−1] 3.0 × 10−1 Li et al. (2008) −3 Rill storage height Hd [m] 5.0 × 10 Cochand (2014) −2 Obstruction storage height Ho [m] 3.0 × 10 Cochand (2014) −2 Coupling length Lc [m] 1.0 × 10 Goderniaux et al. (2009)

Subsurface domain

To generate the 3D mesh for the subsurface domain, the 2D mesh was replicated in the third dimension from the ground surface down to a depth of 20 m. A total of 18 layers of 3D triangular prism elements were generated (Figure 5.3a) and the total number of nodes and elements in the 3D mesh were 111 017 and 205 758, respectively. The ﬁrst 3 meters below ground surface were discretized with 9 layers of variable thicknesses to represent the top soil, a clayey till unit and both drainage networks, with a ﬁner discretization close to the drain

92 depth (Figure 5.3c). The 9 remaining layers extend from 3 m to 20 m below ground surface and have a thickness of 2 m, except for a 1 m layer located between depths of 3 m and 4 m. These layers correspond to Miocene sand and clay and Quaternary sand and clay. He et al. (2014) further divides the Quaternary sequence into two groups: glacial sand and clay, and tectonic sand and clay of glaciotectonic origin.

A spatially-variable distribution of the Miocene and Quaternary sand and clay units was used here, based on the work of He et al. (2014). They generated 10 stochastic realizations of their spatial distribution for the entire Norsminde catchment on a 20 × 20 × 2 m grid. Those realizations were conditioned with borehole observations and airborne geophysical data. Each realization was then used as input for 10 diﬀerent hydrological models. From hydrological validation tests, He et al. (2014) identiﬁed the realization that performed best, which we selected here to assign subsurface properties between depths of 3 m and 20 m (Figure 5.3). That best realization is referred here as the ’heterogeneous geological model’. The distribution of geological units in the model is illustrated on Figure 5.3. The hydraulic properties of the sand and clay units below a depth of 3 m were given by He et al. (2015) and are shown in Table 5.2 as initial values.

Directly above the geological units assigned according to the He et al. (2014) model, a clayey till unit was specified over the entire model area between depths of 3.0 m and 1.5 m. Three soil horizons were then specified between a depth of 1.5 m and ground surface. The C horizon is assumed located between depths of 1.5 m and 0.7 m, the B horizon is assumed to be from 0.7 m and 0.3 m and the A horizon is the uppermost layer, from an assumed depth of 0.3 m to ground surface. The hydraulic properties of each unit located between ground surface and a depth of 3 m are listed in Table 5.3. The van Genuchten functions (van Genuchten, 1980) were used to describe the unsaturated hydraulic properties of all units in the first three meters.

93 AreaB Drainage area Drain nodes Stream nodes AreaA Topography nodes

0 375 750 m

Figure 5.2: 2D mesh with reﬁned nodes highlighted for both drainage areas, rivers and topography areas where the surface slope is greater than 9 %.

94 Geological units A’ a) Soil A horizon (0.0 to -0.3 m) c) 3 m B horizon (-0.3 to -0.7 m) A C horizon (-0.7 to -1.5 m) Clayey till (-1.5 to -3.0 m)

Stochastic model 17 m Glacial sand Glacial clay Vertical exaggeration: x 10 Tectonic sand b) ’ A A Tectonic clay Miocene sand Miocene clay

Figure 5.3: (a) Geological units in the heterogeneous model, (b) vertical cross-section through the model, (c), a zoom on this section in the zone where drainage areas of interest are located. The vertical exaggeration for all ﬁgures is 10 x. 95 Table 5.2: Hydraulic properties of the hydrofacies located below a depth of 3 m and deﬁned following the heterogeneous geological model of He et al. (2014). Initial values were those from He et al. (2015) and calibrated values were obtained manually.

Hydrofacies Parameter Initial value Calibrated value −1 −4 −6 Horizontal hydraulic conductivity Kh [m s ] 4.17 × 10 2.0 × 10 Glacial −1 −5 −7 Vertical hydraulic conductivity Kv [m s ] 4.17 × 10 2.0 × 10 sand −5 Specific storage Ss [-] 5.0 × 10 - −1 −8 −8 Horizontal hydraulic conductivity Kh [m s ] 2.54 × 10 1.0 × 10 −1 −9 −9 Glacial clay Vertical hydraulic conductivity Kv [m s ] 2.54 × 10 1.0 × 10 −5 Specific storage Ss [-] 5.0 × 10 - −1 −6 −6 Horizontal hydraulic conductivity Kh [m s ] 7.2 × 10 2.0 × 10 Tectonic −1 −7 −7 Vertical hydraulic conductivity Kv [m s ] 7.2 × 10 2.0 × 10 sand −5 Specific storage Ss [-] 5.0 × 10 - −1 −7 −8 Horizontal hydraulic conductivity Kh [m s ] 4.6 × 10 1.0 × 10 Tectonic −1 −8 −9 Vertical hydraulic conductivity Kv [m s ] 4.6 × 10 1.0 × 10 clay −5 Specific storage Ss [-] 5.0 × 10 - −1 −4 −6 Horizontal hydraulic conductivity Kh [m s ] 3.3 × 10 2.0 × 10 Miocene −1 −5 −7 Vertical hydraulic conductivity Kv [m s ] 3.3 × 10 2.0 × 10 sand −5 Specific storage Ss [-] 5.0 × 10 - −1 −8 −8 Horizontal hydraulic conductivity Kh [m s ] 5.4 × 10 1.0 × 10 Miocene −1 −9 −9 Vertical hydraulic conductivity Kv [m s ] 5.4 × 10 1.0 × 10 clay −5 Specific storage Ss [-] 5.0 × 10 -

96 Table 5.3: Hydraulic properties of the topsoil units (A, B and C horizons) and clayey till unit. Initial values were taken from the associated literature sources.

Unit Parameter Initial value Calibrated value Source −1 −8 −5 Horizontal hydraulic conductivity Kh [m s ] 8.9 × 10 1.0 × 10 He et al. (2015) −1 −9 −6 Vertical hydraulic conductivity Kv [m s ] 8.9 × 10 1.0 × 10 He et al. (2015) −5 Specific storage Ss [-] 1.0 × 10 - He et al. (2015) A horizon Residual saturation Sr [-] 0.083 - Iversen et al. (2011) van Genuchten parameter α [m−1] 0.52 - Iversen et al. (2011) van Genuchten parameter n [-] 1.51 - Iversen et al. (2011) Thickness [m] 0.3 - - −1 −8 −5 Horizontal hydraulic conductivity Kh [m s ] 8.9 × 10 1.0 × 10 He et al. (2015) −1 −9 −6 Vertical hydraulic conductivity Kv [m s ] 8.9 × 10 1.0 × 10 He et al. (2015) −5 Specific storage Ss [-] 1.0 × 10 - He et al. (2015) B horizon Residual saturation Sr [-] 0.078 - Iversen et al. (2011) van Genuchten parameter α [m−1] 0.80 - Iversen et al. (2011) van Genuchten parameter n [-] 1.45 - Iversen et al. (2011) Thickness [m] 0.4 - - −1 −8 −6 Horizontal hydraulic conductivity Kh [m s ] 8.9 × 10 4.0 × 10 He et al. (2015) −1 −9 −7 Vertical hydraulic conductivity Kv [m s ] 8.9 × 10 4.0 × 10 He et al. (2015) −5 Specific storage Ss [-] 1.0 × 10 - He et al. (2015) C horizon Residual saturation Sr [-] 0.099 - Iversen et al. (2011) van Genuchten parameter α [m−1] 0.98 - Iversen et al. (2011) van Genuchten parameter n [-] 1.41 - Iversen et al. (2011) Thickness [m] 0.8 - - −1 −8 −6 Horizontal hydraulic conductivity Kh [m s ] 8.9 × 10 1.0 × 10 He et al. (2015) −1 −9 −7 Vertical hydraulic conductivity Kv [m s ] 8.9 × 10 1.0 × 10 He et al. (2015) −5 Specific storage Ss [-] 1.0 × 10 - He et al. (2015) Clayey till Residual saturation Sr [-] 0.099 - Iversen et al. (2011) van Genuchten parameter α [m−1] 0.98 - Iversen et al. (2011) van Genuchten parameter n [-] 1.41 - Iversen et al. (2011) Thickness [m] 1.5 - -

97 Tile drains

Two tile drainage networks, areas A and B (Figure 5.1c), were included in the model. The number of drains in each network was however reduced to decrease simulation times. The network in area A was thus represented with 14 drains while 8 drains were retained for area B (Figure 5.2). Although the geometry of the drainage network was simpliﬁed, the main drainage paths were represented in the model. De Schepper et al. (2015) show that, if the main drainage paths are retained in a model, the drainage network can be simpliﬁed for large-scale simulations, providing that the model is calibrated.

Although tile drains can be discretized with 1D line elements and fluid flow along drains can be simulated in HydroGeoSphere, drain were represented here as seepage nodes to reduce computational times. The seepage nodes were located 1 m below ground surface and their spatial distribution was specified to represent the drainage network (Figure 5.2). Drainage area A was discretized with 203 seepage nodes, while drainage area B contained 86 nodes (Figure 5.2).

With the seepage node option, the pressure head at a seepage node is set to zero during a time step if there is fluid flow from the subsurface to the drain, and a no flow boundary is assigned in the opposite case, when the pressure head at a seepage node is negative. Drainage therefore occurs only when the water table rises above the drain node elevation. The drainage water is not routed to the stream but it is summed up during simulation to compare to observed drainage. A simulation of the verification example presented in MacQuarrie and Sudicky (1996) shows that the seepage node representation of drains provides results similar to those for a model where drains are represented as 1D line elements.

Climate data

The period selected for the simulations is from July July 23, 2012 to July 24, 2013. Pre- cipitations for this period were extracted from 10 km grid raster datasets provided by the Danish Meteorological Institute (DMI), and were applied at the surface domain as a daily ﬂux boundary condition during the ﬁrst 96 days. From day 97 until day 366, daily precipitations were disaggregated into hourly precipitations according to rainfall measurements at a weather station located south of Fensholt, in the Norsminde catchment. Corrections were applied to the raw rainfall measurements following recommendations from Stisen et al. (2012).

98 The daily potential evapotranspiration (PET) was estimated from reference evapotranspiration data calculated on a 20 × 20 km with the Makkink equation for the Denmark landmass (Scharling, 1999). Compared to PET calculated with the Penman-Monteith equation, the Makkink equation overestimates evapotranspiration for western Denmark, compared to the eastern Denmark reference (Detlefsen and Plauborg, 2001). A correction factor of 0.95 was therefore applied to PET to account for this overestimation (Refsgaard et al., 2011; Stisen et al., 2012). The resulting potential evapotranspiration was applied to surface domain of the model.

To calculate actual evapotranspiration, agricultural land evapotranspiration properties, which are predominantly winter wheat, were assigned to the top layer elements (Table 5.4). Root depth (Lr) values are taken from Børgesen et al. (2013). Evaporation depths were estimated based on recommendations for Danish soils given by Kristensen and Jensen (1975). The transpiration fitting parameters (C1, C2 and C3) and the canopy interception (cint) were defined based on Li et al. (2008). Measured soil moisture values at pF 4.2 and pF 2 were used for defining the wilting point (θwp) and field capacity (θfc) limiting saturations respectively (Børgesen and Schaap, 2005). Leaf Area Index values were adapted from Børgesen et al. (2013) and varied seasonally.

Table 5.4: Evapotranspiration properties applied to the surface layer (winter wheat). Leaf Area Index values are linearly interpolated between the periods shown here.

Parameter Value Source

Root depth Lr [m] 1.6 Refsgaard et al. (2011) Evaporation depth Le [m] 0.2 Default value Transpiration fitting parameter C1 [-] 0.31 Kristensen and Jensen (1975) Transpiration fitting parameter C2 [-] 0.15 Kristensen and Jensen (1975) Transpiration fitting parameter C3 [-] 5.9 Kristensen and Jensen (1975) Wilting point θwp [-] 0.18 Iversen et al. (2011) Field capacity θfc [-] 0.69 Iversen et al. (2011) Leaf Area Index (from 01/11 to 10/04 [-] 1.0 Børgesen et al. (2013) Leaf Area Index (from 30/04 to 09/06 [-] 5.0 Børgesen et al. (2013) Leaf Area Index (from 23/07 to 17/07 [-] 0.0 Børgesen et al. (2013) Canopy interception cint [mm] 0.05 Default value

99 Boundary conditions

A critical depth boundary condition was assigned to the surface domain at the outlet of the Fensholt catchment (see SD, Figure 5.1c). The lateral boundaries were assumed to be groundwater divides, corresponding to no-ﬂow boundaries.

De Schepper et al. (2015) have showed that, for similar shallow systems that are not bounded by a low-permeability geological unit, deeper flow should be accounted for. In the Fensholt model, the bottom boundary was set at 20 m below ground surface and does not correspond to a low-permeability boundary. The regional MIKE SHE model developed for the Norsminde catchment for the 2000-2003 period (He et al., 2015) suggests that there is a downward flow component in Fensholt at that depth, with little annual variation. A downward flux value of 0.11 mm d−1 was applied at the bottom boundary of the model, which corresponds to the average value simulated by He et al. (2015).

Simulation parameters

For the iterative solution of the non-linear ﬂow equations, the Newton-Raphson absolute and residual convergence criteria were set to 1.0 × 10−4 m and 1.0 × 10−4, respectively. A maximum variation of 0.05 in saturation between successive timesteps was used for the adaptive time stepping strategy used in HydroGeoSphere (Therrien et al., 2010). In addition, time steps were limited to a maximum of 1 hour. The model was run with the parallelized version of the code (Hwang, 2012; Hwang et al., 2014) on a 3.39 Gb RAM computer with 4 CPU cores at 3.40 GHz.

5.2.4 Heterogeneous vs. homogeneous models

The results presented here are for various versions of the numerical model. The ﬁrst version corresponds to the initial heterogeneous model for which the distribution of sand and clay between depths of 3 m and 20 m was generated stochastically and their hydraulic conductivities were calibrated against stream discharge for the entire Norsminde catchment by He et al. (2015). A second version corresponds to the same heterogeneous spatial distribution of sand and clay but for which the hydraulic conductivities were modiﬁed to reproduce the drainage discharge at Fensholt. This second version is the calibrated heterogeneous model. In addition to the two heterogeneous models, results from a third model are presented, where

100 the heterogeneous distribution of sand and clay is replaced with a homogeneous unit whose properties are those of the clayey till horizon (Table 5.3, calibrated values).

The equations solved by coupled surface and subsurface ﬂow models are non-linear. Direct steady-state solutions are not possible and transient simulations are therefore required. Since initial conditions are usually unknown, a model spin-up is necessary to ensure that they don’t impact the simulation results. Each model (initial heterogeneous, calibrated heterogeneous and homogeneous) was therefore ﬁrst run with fully saturated initial conditions during an entire year by applying precipitation and evapotranspiration datasets. The resulting hydraulic head distribution was then used as initial hydraulic heads for the targeted yearly simulations.

5.2.5 Calibration

The heterogeneous model was calibrated manually by trial and error to reproduce observations for drainage area A. The hydraulic conductivities of all geological units were modiﬁed, using a single value for all sand units and another value for all clay units, while keeping the vertical anisotropy factor, Kv / Kh equal to 0.1 (Table 5.2). Hydraulic properties of A, B, C horizons and the upper till layer were also adjusted, while initial values were used for all the other parameters (Table 5.3). During calibration, simulated drainage water ﬂuxes were most sensitive to the hydraulic conductivity of the C horizon and the clayey till units (Table 5.3).

The ﬁrst 96 days of simulation were not considered for calibration as only daily precipitation data were applied to the model before day 96, while hourly drainage discharge measurements were available. From day 97 until the end of the simulation, hourly precipitation data were applied, which was appropriate for calibration.

Three performance criteria were calculated for the calibrated heterogeneous, initial heterogeneous and homogeneous models (Table 5.5). The coefficient of determination r2 was first calculated, which estimates the correlation of observed and simulated data points. Another common criterion is the Nash-Sutcliffe efficiency coefficient NSE (Nash and Sutcliffe, 1970), which evaluates the model performance against the mean of the observed values if it was used for prediction. Even if r2 and NSE are widely used, they are known to be very sensitive to higher values as they are calculated from squared values of differences between observed and simulated data points (Krause et al., 2005). They were therefore calculated based on weekly-averaged drainage discharge values. Finally, a cumulative volumetric error factor was

101 calculated based on cumulative drainage volumes over the entire simulated year, as seen in Figure 5.4.

The model was calibrated for drainage area A by focusing on matching simulated and observed graphical plots, as advised by Bennett et al. (2013) for ﬂashy systems, and on the related total volumetric error. Drainage measurements in area B were not used for calibration and hence served as a proxy basin validation test (Klemeš, 1986) showing the model reliability areas for which it has not been calibrated (blind test).

Table 5.5: Performance criteria for measuring the Fensholt model efficiency, where n is the number of data points, QO and QS are observed and simulated drainage flow values, QO and Q S are observed and simulated mean drainage flow values, VO and VS are observed and simulated drainage volumes.

Criterion name Formula Range 2 n − − (QO,i QO)(QS,i QS ) Coefficient of determination r2 i=1 (0, 1) n 2 n 2  Q −Q Q −Q  i=P1 ( O,i O) i=1 ( S,i S )   qP qP n − 2 i=1 (QO,i QS,i) Nash-Sutcliffe coefficient NSE 1 − 2 (-∞, 1) n − (QO,i QO) P i=1 n P − n i=1 VS,i i=1 VO,i Volumetric Error VE n (-∞, ∞) =1 VO,i P i P P

102 PET SET

Fall

Figure 5.4: Cumulative corrected precipitation (Precipitation), corrected potential evapotranspiration (PET), simulated evapotranspiration (SET) and simulated canopy interception over the simulated year with the calibrated heterogeneous model (23/07/2012 - 24/07/2013).

103 5.3 Results

Results from the model calibration (AreaA) and model validation (AreaB) are presented here. The calibrated heterogeneous model results are compared with results from the Norsminde catchment model developed with MIKE SHE by He et al. (2015).

5.3.1 Water balance

The same precipitation and evapotranspiration datasets were applied to each of the models, heterogeneous and homogeneous, for the simulated period (23/7/2012 to 24/7/2013). Cumu- lative corrected precipitation, corrected potential evapotranspiration and simulated evapotranspiration are shown in Figure 5.4. In addition, this figure shows the cumulative simulated canopy interception amount that is part of the simulated evapotranspiration. The total precipitation amount (715 mm) reflects a dry simulation period compared to the annual average. Figure 5.4 shows that the first two months (end of summer) were wet, with about 150 mm of rainfall, while the second half of winter and beginning of spring were exceptionally dry, with very little rainfall. A major rainfall event occurred in the spring, around day 305, with about 50 of precipitation in a very short time. The last simulated month (beginning of summer 2013) was also dry. Both PET and SET curves show that evapotranspiration was mainly effective during spring and summer.

5.3.2 Drainage processes

The simulated hydrographs with the heterogeneous calibrated model for the entire year and for periods with major peak flow (Figure 5.5), from days 96 to 230, provided a good match with observations, except that peak intensities for AreaB were about one third lower than for AreaA. This difference is probably due to the difference in density of drains, and by extension of drain nodes, in both drainage areas (Figure 5.2) since a simplified drainage network induces lower drainage discharge values (De Schepper et al., 2015). The drain node difference in both networks was reflected during the simulation with more effective drainage for AreaA than for AreaB (Figure 5.6).

Also shown in Figure 5.6 are 2D snapshots of the depth to water table in the area of interest before and during a rainfall event in late fall at days 143 and 147 (zoom-in in Figure 5.5). In addition, a 3D close-up view of AreaA is displayed with cross-sections showing pressure head

104 distributions in the soil units (from 0.0 to 3.0 m depth). The depth to water table color scale highlights that the water table was below the drain depths (1.0 m) before the drainage peak. The water table between drains was lower for AreaA than for AreaB. Pressure heads were generally negative along drains in AreaA before the peak. At day 147, drain nodes were still active, even if it was not easily seen in the 2D depth to water table plot, with lower pressure head values in their vicinity. The water table was not lowered below the drain depth, while drainage peaks were matching and correctly simulated as seen in Figure 5.5. Yet, some peaks were simulated before day 147 due to applied precipitation data deviation.

105 106

Figure 5.5: Observed and simulated drainage ﬂow for drainage areas A and B for the initial and calibrated HydroGeoSphere models and for the homogeneous model for the one-year simulation (23/7/2012 to 24/7/2013). Observed data were measured at drainage stations StA and StB. A zoom-in on the period of interest highlighted in Figure 5.6 is shown on the right-hand side. Fensholt catchment AreaB Drainage areas Elevation in mamsl Pz5 97

95 Pz6 Pz8 91 Pz7 AreaA 87 Pz1

87 83 87 83

Pz2

87 83 79 83 75 Pz4 79 71 75 Pz3 75 79

71 71 67 67

Pressure head Depth to water table

a) day 143 c) day 143

Pressure Depth to head [m] water table [m] 0.0 0.0

0.5 -0.5 Drain nodes 1.0 -1.0

1.5 -1.5

2.0 b) day 147 d) day 147 -2.0

2.5 -2.5

3.0 -3.0

Figure 5.6: (a, b) Pressure head distribution along vertical cross-sections in DrainA for the calibrated heterogeneous model (0.0 to 3.0 m depth), (c, d) depth to water table for both AreaA and AreaB. Targeted output times were selected before a drainage peak (a, c - day 143) and at maximum peak ﬂow (b, d - day 147). At the top, the topography is displayed in Fensholt and in the area of interest with piezometer locations.

107 5.3.3 Drain ﬂow

Initial heterogeneous model

For the initial heterogeneous model, no drainage peak flows are simulated for both drainage areas although various flashy peaks were observed during the simulation period (Figure 5.5). In AreaA, the simulated low flow is slightly overestimated compared to observed data during fall and winter (from day 85 to 230), while it is underestimated for the same period in AreaB. In the spring, little drainage flow was produced around day 265 while flow was greater during the major rainfall event at day 304 in AreaA (Figure 5.7). During the same rainfall event, drainage discharge also occurred in AreaB, but it was less intense than for AreaA at the same period. No significant drainage flow was simulated before day 60 in AreaA and day 85 in AreaB.

As no peaks were simulated with the initial heterogeneous model, the cumulative drainage curves (Figure 5.7) reveal a markedly lower total drainage volume, expressed in mm, in both drainage areas compared to the observed discharge volume. The yearly simulated drainage discharge volumes of AreaA and AreaB amounted to 155 mm and 114 mm, respectively, while measured values were 265 mm and 308 mm, which demonstrates a major water deﬁcit in the simulation.

The water deficit highlighted in the total amount of drained water is clearly seen in the volumetric error (VE) values that were −41 % for AreaA and −63 % for AreaB (Table 5.6). The coefficient of determination (r2) for AreaA was 0.70 and 0.63 for AreaB. The Nash- Sutcliffe coefficient (NSE) was 0.49 for AreaA and 0.14 for AreaB. Thus the coefficients demonstrated a poorer performance of the model for drainage area B than for drainage area A.

108 Figure 5.7: Observed and simulated cumulative drain ﬂow equivalent height, expressed in mm, for drainage areas A and B. Simulated curves are displayed for the initial and calibrated heterogeneous models, the homogeneous model, and for the MIKE SHE model.

Calibrated heterogeneous model

The heterogeneous calibrated model hydrograph of AreaA showed several ﬂashy peaks that coincide with the observed drainage trend (Figure 5.5). Simulated peaks are generally higher than the observed peaks. Drainage discharge in dry periods was adequately simulated, with decreasing drainage values after peaks that are closer to the observed values than the initial heterogeneous model results. Nevertheless, simulated drainage discharge during drawdown periods was slightly higher than what was measured in Fensholt between days 130 and 210.

109 The simulated drain ﬂow peaks are more frequent and greater than those observed. In addition, little drainage was simulated around day 330 during a short rainfall event. In total, about 42 peaks were simulated, while 29 were observed. The simulated cumulative drainage curve is closely corresponding to the observed one (Figure 5.7), with a total amount of 275 mm of simulated drainage discharge. The associated volumetric error is 4 % (Table 5.6).

In drainage area B (Figure 5.5), no significant drainage was simulated before day 80. After- wards, drainage peaks were simulated with the same frequency as in AreaA but they were less intense, while low flow was still accurately simulated. Simulated drainage flowrates lower than the measured rates induced a total cumulative drain flow amount of 245 mm for AreaB (Figure 5.7), which is much lower than the observed value (308 mm). The volumetric error is consequently much higher than in AreaA (−20 %).

In addition to the volumetric error, the NSE was also larger for AreaA (0.84) than for AreaB (0.73), and they were the highest of all models (Table 5.6). The r2 criterion showed similar values for both drainage areas (0.77 for AreaB against 0.84 for AreaA). These criteria suggest better performance of the model in AreaA compared to AreaB, conﬁrming the good calibration against AreaA drainage discharge.

The annual drainage discharge from AreaA and AreaB, expressed as precipitation fractions, were close to observed values. The ﬁeld data showed drainage discharge recovery values from precipitation of 37 % in AreaA and 43 % in AreaB. The associated simulated values for the calibrated heterogeneous model were 38 % and 34 %, respectively.

Homogeneous model

The homogeneous model produced the highest drainage peaks of all models for AreaA (Fig- ure 5.5). The model simulated most peaks that were observed, but they were flashier than what was observed. Nevertheless, the first peaks right after day 60 and the peaks between days 250 and 300 were very low, compared to the calibrated model simulation results. The homogeneous hydraulic conductivity values were higher than that for the calibrated heterogeneous clay units and slightly lower than that of the sand units. In addition, hydraulic conductivity values were lower than the calibrated A, B and C horizon. These lower hydraulic conductivity values made the water table drop faster during dry periods due to drainage, with simulated low flow in between peaks that is lower than observed low flow and lower than low flow of the

110 other models.

Similarly to the heterogeneous calibrated model, no significant drainage discharge was simulated before day 80 for AreaB, where simulated drainage was generally lower compared to AreaA. However, in contrast to drainage area A, some peaks were simulated between days 250 and 300. Surprisingly, a series of significant drainage peaks were simulated around day 330, while they were of minor importance in AreaA. As AreaB is located further upstream compared to AreaA, one would expect a similar trend in AreaA between days 325 and 345, but this was not the case. This last group of peaks allowed the homogeneous model to have total drainage discharge volumes that very closely resembled field measurements (Figure 5.7), with a simulation of 312 mm compared to the measured 308 mm in AreaB. The similar curve for AreaA showed a larger difference between simulated and observed total drainage discharge (297 mm and 265 mm, respectively). The volumetric error was therefore 1 % in AreaB and 12 % in AreaA. The r2 criterion was equal to 0.81 for AreaA and 0.73 for AreaB and the computed NSE is 0.78 for AreaA and 0.72 for AreaB.

Table 5.6: Model performance criteria calculated over the calibration period (from day 96 to 366, i.e. 28/10/2012 to 24/07/2013) based on weekly averaged discharge values.

Ideal Initial Calibrated Homogeneous MIKE SHE Criterion value AreaA AreaB AreaA AreaB AreaA AreaB AreaA AreaB r2 [-] 1 0.70 0.63 0.84 0.77 0.81 0.73 0.89 0.79 NSE [-] 1 0.49 0.14 0.84 0.73 0.78 0.72 0.79 0.54 VE [%] 0 −41 −63 4 −20 12 1 −37 −52

111 MIKE SHE model

The MIKE SHE model of Norsminde was calibrated for the 2000 to 2003 period (He et al., 2015), while our simulations are for the 23/7/2012 to 24/7/2013 period. In MIKE SHE, a uniform horizontal mesh size equal to 100 × 100 m was used. In terms of drainage conceptualization, both models treated drain flow the same way: drainage sinks were active as soon as the water table rose higher than the drain elevation. But, in MIKE SHE, drainage sink conditions were applied at all cells, because the distance between the drain pipes is less than the grid size. The HydroGeoSphere model, which has a spatial resolution finer than the drainage network, represented drainpipe locations at some of the HydroGeoSphere nodes, while the other nodes were able so simulate the water table between drain pipes. Another main difference between both models is the output data frequency: HydroGeoSphere had hourly results and MIKE SHE had daily. The hydrofacies properties of the MIKE SHE model were the same as the initial heterogeneous model was created in HydroGeoSphere and are listed in Table 5.2 and Table 5.3 (initial values).

Figure 5.8 shows the observed and simulated drain flow hydrographs for AreaA and AreaB for the calibrated HydroGeoSphere heterogeneous model and the MIKE SHE model. Similarly to the HydroGeoSphere initial heterogeneous model, the MIKE SHE model produces low drain flow values but the main peak dynamics were correctly calculated. In addition, faster drawdown and lower drainage discharge during dry periods were simulated. Both MIKE SHE hydrographs looked almost similar aside from the first substantial drainage values that were calculated earlier for AreaA (day 61) than for AreaB (day 82). The last day of significant drainage was day 222 for both areas. None of the peaks observed and simulated by Hy- droGeoSphere after day 222 were reproduced by MIKE SHE. In AreaB, prior to and after the fall/winter drainage period, zero drain flow values were simulated. In AreaA, a minimum value of 1.0 × 10−2 mm d−1 was observed outside of the drainage period. The series of drainage peaks observed between days 60 and 82, represented a challenge to both models, as they were neither simulated by HydroGeoSphere nor by MIKE SHE, probably due to climate data uncertainty since the same precipitation data were applied to both models.

As for the initial heterogeneous model, the MIKE SHE model results induced a major water deﬁcit in the total cumulative drained water amount, with VE values of −37 % for AreaA and −52 % for AreaB. High r2 values were calculated (0.89 in AreaA and 0.79 in AreaB), but

112 they were not validated by NSE calculations (0.79 and 0.54, respectively), though expressing good performance in AreaA results.

Figure 5.8: Observed and simulated drainage ﬂow in drainage areas A and B from 23/7/2012 to 24/7/2013, with HydroGeoSphere data from the calibrated heterogeneous model and MIKE SHE data from the Norsminde catchment scale model developed by He et al. (2015).

113 5.3.4 Hydraulic heads

Figure 5.9 and Figure 5.10 show hydraulic heads simulated with the MIKE SHE and calibrated HydroGeoSphere models for piezometers Pz1 to Pz9 results, along with measured values. During the dry season (e.g. day 32) hydraulic heads for some piezometers were below the elevation of the drains, while hydraulics heads were mostly above the drain elevations for all piezometers during the wet season.

Beyond dry periods, simulated hydraulic heads by HydroGeoSphere tend to reach maximum constant values in all piezometers, highlighting that drainage limits the rise of the water table. In AreaA (Figure 5.9), simulated hydraulic heads for Pz4 are about 0.5 m lower than the observed heads during the period of active drainage (from day 61 to 225). Before and after this period, Pz4 was mostly dry with occasional ﬂashy water table rises. The simulated water table at Pz2 is lower than the drain elevation and much lower than most of the observations, except the one at day 137 that matched the simulated hydrograph. The active drainage period for Pz2 was from day 82 to 218. For Pz3, the active period was from day 61 to 218, with some short dry periods in between. In the spring, some rapid water table rises were observed, similar to Pz4. The Pz1 active drainage period was quite sporadic, with numerous dry periods, probably because Pz1 is located in the most upstream part of the drainage area.

Plots showing the depth to the water table (Figure 5.6) illustrate hydraulic head variations in AreaA. Pz1 was the only dry piezometer at day 143 with the water table being lower than −1.5 m and it was about −0.8 m at day 147. During this period, the water table at Pz2 and Pz4 was slightly lower than the drain depth. At Pz3, the water table was located between 0.5 and 0.75 m below ground surface.

The simulated head values in AreaB were mostly higher than drain elevations when piezometers were not dry (Figure 5.10). In addition, simulated heads were generally higher than the observed ones, with few observed data points matching the simulated curves. Pz5 had a shallow water table during fall and winter. In Pz6, high hydraulic head values were simulated until day 227. The wet period was slightly shorter in Pz7, where it lasted until day 218, but a few hydraulic head losses were simulated. A fast water table rise was simulated at day 263, matching the last observation point, which was also simulated in Pz8. Pz8 had the longest period of high simulated hydraulic heads, from day 82 to 230. Simulated values

114 higher than ground surface might have produced overland flow at the surface, but no water accumulation was noticed after inspection of the model surface domain. As Pz8 is located in the most downstream part of AreaB, it suggests insufficient drainage in the upstream part and an oversimplification of the drainage network in the model. Including more drains in the network, with more drainage nodes in AreaB, would probably lead to lower hydraulic head values in Pz8 and in the other piezometers.

The MIKE SHE results in AreaA showed simulated hydraulic heads that were above drain elevations in Pz2 to Pz4, and even above the soil surface in Pz2. In Pz1, they were close to the observed data and to the HydroGeoSphere results. Similar trends were simulated during fall and winter in Pz1 to Pz3, while Pz4 had registered a shorter and higher hydraulic head rising period from day 90 to 200. It was similarly simulated in AreaB at Pz5, Pz7 and Pz8 from day 60 to 200. Hydraulic head values in Pz5 to Pz7 were below the drain elevation during the entire simulation and were even lower than the bottom of piezometers Pz5 and Pz6. Simulated heads were close to observed ones only for Pz8.

The major difference between HydroGeoSphere and MIKE SHE results relates to for flow dynamics, with HydroGeoSphere producing relatively flashy changes in hydraulic heads while MIKE SHE produced slowly varying hydraulic heads. This difference may be due to i) the differences between the 3D Richards’ equation in HydroGeoSphere and the 1D Richards’ equation coupled with groundwater flow in MIKE SHE, ii) differences in spatial discretization, and iii) drainage conceptualization differences in the codes. Nodes in HydroGeoSphere, along with finer mesh discretization, probably allowed for finer drainage flow simulation and enhanced lateral drainage flow, as seen with better peak flow simulated in HydroGeoSphere.

115 Figure 5.9: Observed and simulated hydraulic heads in piezometers of drainage area A (Pz1 to Pz4) for the one-year simulation (23/07/2012 - 24/07/2013). The dashed data line was taken from the calibrated heterogeneous model in HydroGeoSphere. The solid line was from a MIKE SHE simulation for the Norsminde catchment, after He et al. (2015). The HydroGeoSphere data were plotted when the water table had risen above the elevation of the piezometer bottom. Ground surface and drain elevations are also presented.

116 Figure 5.10: Observed and simulated hydraulic head in piezometers of drainage area B (Pz5 to Pz8) for the one-year simulation (23/07/2012 - 24/07/2013). The dashed data line was taken from the calibrated heterogeneous model in HydroGeoSphere. The solid line was from a MIKE SHE simulation for the Norsminde catchment, after He et al. (2015). The HydroGeoSphere data were plotted only when the water table had risen above the elevation of the piezometer bottom. Ground surface and drain elevations are also presented.

117 5.4 Discussion

5.4.1 HydroGeoSphere model performance

The heterogeneous model was calibrated manually against drainage discharge in AreaA by only varying the hydraulic conductivity values. The flow dynamics for AreaA were correctly simulated and the total volumetric error was 4 %. However, the model could not be validated with AreaB observations since the total volumetric error was larger, equal to 20 %, and the simulated drainage peaks were about one third of the observed drain flow peak intensity from AreaA, for which more drains were retained in the simplified network representation. Denser drainage networks usually drain significantly more water (Henine et al., 2014; De Schepper et al., 2015). As a result, the water table simulated in AreaB was generally shallower than in AreaA.

The simulated water table in piezometers for both drainage areas was above the bottom of the piezometer filter primarily in the fall and winter. In the spring, simulated water table was lower than the filter bottom of the piezometers except for some rapid rises. Observed hydraulic heads varied over time but simulated hydraulic heads showed less variability. In the models presented here, only matrix flow was simulated in the porous media towards the drains, although field evidence shows the presence of macropores and fractures in the topsoil and clayey matrix. Sand lenses, macropores and fractures have been shown to be major preferential water flow pathways for near surface deposits in Danish soils (Jørgensen et al., 2004; Kessler et al., 2012). A more detailed representation of these heterogeneities in the model could have improved the reproduction of the temporal variability of observed hydraulic heads. However, adding them would require extensively refined meshes and would greatly increase simulation times (Blessent et al., 2009).

Drainage discharge observations from catchments in North America showed rapid response to precipitation during wet periods, in winter, and very little or no drainage discharge during summer (Eastman et al., 2010; Williams et al., 2015). This trend was also highlighted in the calibrated heterogeneous model of Fensholt. For AreaA, few drain flow peaks were simulated before day 60 (late-summer) while significant drainage response was simulated in fall and winter. The simulated temporal drainage pattern was similar to that observed. In AreaB, a few low-intensity peak flows were measured in late-summer, but none was simulated. Simulated

118 drainage for this drainage area is consistent with observations from Williams et al. (2015), but the ﬁeld data expressed rapid drainage response also before day 60. A heavy rainfall event in late-spring (day 304) was clearly registered in both observed and simulated hydrographs. It appeared after a long dry period, but the intensity of the event resulted in a fast water table rise and consecutively signiﬁcant drainage occurred.

The heterogeneous calibrated model had the highest performance criteria of all models, especially in the drainage area of interest (AreaA). The NSE coefficient for drainage discharge in AreaA was 0.84, indicating good model performance in that area. By calibrating their model against cumulative monthly and daily drainage discharge, Green et al. (2006) obtained 0.9 and 0.5 NSE values. Yet, in Fensholt, the NSE coefficient was 0.73 in AreaB. Drainage calibration was mostly sensitive to the clayey till and C horizon units, which were assumed homogeneous over the entire model area, with a vertical anisotropy factor equal to 0.1. Drainage flow appears to be governed by the entire hydrogeological system, suggesting that a good representation of drainage is not possible without an appropriate conceptualization of surrounding and lower porous media properties. Finer peak flow calculations and better performance criteria were reported for the heterogeneous calibrated model compared to the heterogeneous initial model.

The NSE coeﬃcient of 0.73 obtained for AreaB is slightly less than for the calibrated AreaA. But the AreaB validation test reﬂects the performance that can be expected for areas that have not been calibrated, and as such the result is very encouraging. On this basis we can expect the model to have predictive capabilities for the remaining part of the Fensholt catchment.

5.4.2 Drainage conceptualization

No discrete drains were therefore in our model since they were rather represented as sink nodes aligned along the actual drains. Lateral flow was only simulated towards drain nodes, as defined by Yue (2010). Even though HydroGeoSphere provides an integrated drainage module coupled to the subsurface domain, with pipe flow and drainage routing capabilities, they were not included in the simulations. In addition, the physical characteristics of drainage pipes were not accounted for, such as pipe diameter, drain resistance factors or progressive clogging of pipes. Even if drains have a resistance factor that varies with drain clogging (van der Velde et al., 2010), the resistance from the surrounding porous medium drives drainage

119 ﬂow (Yue, 2010), as illustrated by the initial and calibrated heterogeneous models.

While some authors regularly observed pipe pressurization (Henine et al., 2014), others observed that full pipe flow occurred for only 2 to 5 days during a year (King et al., 2014). Both studies considered conventional drainage networks, without any drain flow control structure. Causes of pressurized flow are numerous. They are either of internal origin (obstruction due to soil erosion) or of external origin: modified drainage design (additional drains added to a network), channeling surface flow through tile drains or flooding at land surface where a drainage outlet is located. King et al. (2014) observed both actual full pipeflow at the outlet from upstream drains and from flooding due to heavy rainfall events. Henine et al. (2014) simulated such conditions and demonstrated that pressurization leads to head loss along drains and backflow from pipes to the surrounding porous medium.

In Fensholt, satisfactory results were obtained with the calibrated heterogeneous model in terms of drainage discharge compared to field measurements. The seepage boundary condition applied at drain nodes had no drainage design limitation (i.e. pipe diameter) accounting for full pipe flow and backflow. Hydraulic head values higher than the soil surface simulated close to the outlet of Drain B (in Pz8) may create surface runoff. Simplifying a network artificially increases drain spacing, which enhances surface runoff as less water is conducted through subsurface drains.

Instead of using drainage sink nodes, if discrete drains were implemented in the model and coupled to the subsurface domain while solving the Hazen-Williams equation, simulation times would have increased because smaller time-steps are generally required to solve pipe ﬂow. Coupling pipes to the surrounding porous media would have allowed water routed in the drains to ﬂow back from the pipes to the porous media. Water would have been exported from the model when reaching drainage networks outlets only (StA and StB), with water being routed in the drains before the outlet allowing for water exchanges along the pipes. With the sink nodes option, water leaves the simulation domain as soon as it reaches the drains.

120 5.4.3 Comparison of model codes (HydroGeoSphere vs. MIKE SHE)

The MIKE SHE model covered the entire Norsminde catchment with 2D rectangular elements whose lateral size was 100 m. The HydroGeoSphere model focused on the smaller-scale Fen- sholt catchment and represented ground surface with triangular prism elements whose edges varied in length from 6 to 150 m. Both models used the same geological structure and hydraulic properties but produced very different results. The spatial scale and discretization level used in integrated hydrological models were previously demonstrated to influence simulation results (Blöschl and Sivapalan, 1995; Blessent et al., 2009). In MIKE SHE, Refsgaard (1997) and Vázquez et al. (2002) highlighted the dependency of effective hydraulic parameters on grid resolution. Refsgaard (1997) also stated that changing a model’s spatial scale and grid resolution requires that calibration should be repeated to ensure appropriate hydraulic properties. Similar conclusions were reached with HydroGeoSphere (Sciuto and Diekkrüger, 2010).

These authors indicated also that results were less sensitive to upscaling hydraulic parameters in a model compared to changing the spatial scale. This lower sensitivity was validated by our homogeneous model, whose results were closer to those of the calibrated heterogeneous model than its initial version. The hydraulic conductivity of the clayey till in the calibrated homogeneous model was higher than that of the topsoil units and the heterogeneous clay units, and they were equivalent to that of the heterogeneous sand units. The volumetric error for the homogeneous error was small, 1 % for AreaB and 12 % for AreaA. Nevertheless, AreaB had a series of peaks in late-spring that were neither simulated in AreaA nor observed (Figure 5.5, around day 330) but that were counted in the total volumetric error. This was probably due to missing local heterogeneous units that were present in the heterogeneous model. The NSE of the homogeneous model showed a good performance in AreaA (0.78), while being 0.79 in the MIKE SHE model. Both models had similar performances in terms of drainage discharge, suggesting that heterogeneous parameterization of the geology in HydroGeoSphere was needed, especially as both drainage networks of interest were conceptually simplified (De Schepper et al., 2015). Even by keeping all the actual pipes in the model, the simulated drain flow would have resulted in a similar hydrograph trend; the hydraulic conductivities were limiting factors in peak flow.

In addition, evaluating model performance based on volumetric error, NSE or r2 was demon-

121 strated here not to be suﬃcient. A good volumetric error may conceal average NSE or r2 coeﬃcient values, and vice versa. It is therefore essential to combine several criteria for assessing model performance.

Along with spatial discretization differences, transferring parameters calibrated with a given code to another (i.e. from MIKE SHE to HydroGeoSphere) may have had an impact on results. Both solved similar equations in the surface and subsurface domains and treated drains as sinks. However, drains in HydroGeoSphere were conceptualized as sink nodes, which is physically closer to reality than drainage sinks applied at elements in MIKE SHE. Further- more, the MIKE SHE model was calibrated against stream discharge. Drainage discharge in AreaA was targeted in the calibration process with HydroGeoSphere. The drain node approach in HydroGeoSphere assumes that water entering the drains leaves the domain without being discharged in the subsurface domain or at the land surface, which is generally observed in the field. In MIKE SHE, drained water was routed downhill and was locally contributed to stream discharge. Calibration against stream discharge was thus not feasible with Hy- droGeoSphere. It might be relevant to consider this issue since Hansen et al. (2013) stated that combining catchment discharge calibration with drainage discharge calibration should allow for better simulated results. The same authors warned about scaling issues leading to low simulation performance due to drainage areas being too small with respect to larger heterogeneous geological bodies in their MIKE SHE model. In Fensholt, the drain flow calibration performed correctly with HydroGeoSphere, but it was hardly conceivable to define a rule assessing the tile drainage network scale under which geological heterogeneities had little impact on drain flow calibration.

122 5.5 Conclusion

A 6 km2 fully coupled saturated-unsaturated-overland flow model was developed to simulate local scale seasonal tile drainage discharge over a one-year period with the numerical model HydroGeoSphere. Seepage nodes were specified as sinks for simulating tile drainage, which gave satisfactory results in terms of drain flow and lateral groundwater flow dynamics towards drains. With the existing version of the code, seepage nodes represent an alternative to representing tile drains with 1D line elements, which is prone to convergence difficulties in hilly terrains. The model, which was based on a heterogeneous geological conceptualization of the glacial till area, was calibrated against hourly drainage discharge data for a 34 ha drainage area. Subsequently, it was validated against drainage data from another 28 ha drainage area as well as observed groundwater head data from the two subareas. The model performed well against the independent validation data suggesting a sufficient predictive capability for areas where it was not calibrated.

The hydraulic properties of the subsurface plays a major role in determining groundwater dynamics related to lateral drain ﬂow and the volume of water that was actually captured by the drains. Calibration of hydraulic parameters for geological units (sediment facies) was of prime importance in improving the simulation of drainage discharge.

The HydroGeoSphere results were compared to results produced with a larger scale MIKE SHE model. Both models used the same climate data as well as the same conceptualization of geology, soil and vegetation. Drainage was also conceptualized as sinks in both models, but HydroGeoSphere used triangular elements with side lengths of 6 m in the drain areas and drain nodes were only assigned at the location of the main pipes allowing to resolve the change of ground water table between drain pipes, whereas the large scale MIKE SHE model with a discretization of 100 × 100 m contained drains in all elements and was not able to resolve the dynamics around the individual drain pipes. This conceptual difference, together with a full 3D Richards’ equation in HydroGeoSphere compared to a coupled 1D unsaturated and 3D saturated flow description in MIKE SHE, lead to a better description of the flow dynamics around the drains produced by HydroGeoSphere.

123

Chapter 6

Conclusions and perspectives

This PhD research aimed at simulating tile drainage water flow and associated shallow groundwater flow dynamics for complex irregular subsurface drainage networks at various spatial scales (from plot to catchment) and for different time scales (from a rainfall event to an entire year). Simulating drainage flow in subsurface networks with fully-coupled 3D groundwater flow, surface water flow and drain flow models under variably saturated conditions is a major challenge. Depending on the desired degree of accuracy for simulated physical drainage processes, the representation of complex drainage networks or their simplification shows slightly different simulated drain flow dynamics in between actual drains. Including discrete 1D linear pipes provides accurate results but may lead to extremely long computational times. Upscaling from plot-scale to catchment-scale requires simplified drainage networks to maintain reasonable simulation times while ensuring accurate simulated drain flow dynamics, but the balance between these two is difficult to define and is site-specific.

A field-scale model was built in the Lillebæk catchment. Various drainage modeling concepts were tested to investigate the most efficient way, in terms of data handling and model runtime, to simulate small scale tile drainage in a fully coupled subsurface, surface and drainage model. The degree of mesh refinement and temporal resolution of rainfall data applied to a model were also tested and were shown to significantly influence the model computing time and drain flow dynamics. Accounting for drainage in models requires that discrete drains be considered but may result in very dense meshes. A promising alternative to keep discrete drains and decrease the computational burden by using coarser meshes was to simplify the drainage network so that the main collecting pipes are represented in the model.

125 This simplification approach was selected to create a larger scale model of the Fensholt subcatchment including two complex drainage networks. Seepage nodes were applied as sinks for simulating tile drainage to overcome numerical issues that may occur with the current Hydro- GeoSphere verson in hilly terrains. Even if the Hazen-Williams equation was consequently not solved in drains, good results from the seepage nodes were reported in terms of drain flow dynamics and associated groundwater flow. The model was calibrated against discharge data from a 34 ha drainage area (AreaA) and was validated with data from another 28 ha drainage area (AreaB). The simulations suggested that calibrating a model against data from a specific area is sufficient so that uncalibrated areas elsewhere within the same catchment give satisfactory results, demonstrating promising predictive capabilities of the model.

Warsta (2011) and Yue (2010) both recommended the development of sophisticated mesh generation tools that are suitable for tile drainage modeling purposes. In the present work, the Triangle mesh generator (Shewchuk, 1996) was used with a mesh refinement and relaxation algorithm based on Python scripts created by Therrien (2012) that respects the Delaunay criteria (Delaunay, 1934). This mesh creation and refinement method was documented by Käser et al. (2014), and was exclusively applied to the Lillebæk and Fensholt cases. This mesh generator was powerful enough to create meshes with varying degrees of refinement for simulations at the field or catchment scale with appropriate mesh refinement along drains and with .

In both catchments investigated, the models allowed for a realistic physical representation of drainage dynamics linked with shallow groundwater flow and overland flow. They were demonstrated to be powerful tools on which subsequent reliable analysis could be expected. Even though several studies were conducted recently to quantify tile drainage water flow with on-field measurements (e.g. King et al., 2014) or numerical models (e.g. Rozemeijer et al., 2010), properly reproducing and quantifying groundwater flow patterns associated with tile drainage remains a major challenge.

126 Perspectives for future research on tile drainage modeling include:

1. Further development of the drainage module in HydroGeoSphere is needed to solve the Hazen-Williams equation for drainage modeling in sloping terrains. The results of this work suﬀered numerical issues, but they were not severe. Since the model was able to converge, it is believed that the equation needs testing to tune one of the equation terms and correctly generate drain ﬂow with zero pressure head values calculated along drainage pipes.

2. Once the updated form of the drainage equation is up and running, adding an exchange term ensuring coupling between a drainage network outlet and a discharge node at the surface domain should be considered. Having such a feature would allow for a better physical representation of drainage and stream discharge. In the present state of the model, drainage water is removed from the model, whereas it should contribute to stream ﬂow or supply ﬁltering wetlands at the surface (e.g. Kovačić et al., 2000).

3. Further physically-based improvements of the code could be done by developing progressive clogging of pipes related to tile drainage. Clogging is a common physical process observed in clayey tile-drained fields due to soil erosion and sediment transport (Turtola et al., 2007; Øygarden et al., 1997). In addition to obstructing drains, sediment loading leads to temporal variations of pipe entrance resistance (van der Velde et al., 2010). Pressurized flow is then favored (Henine et al., 2014), inducing head loss and leakage along the drains while water is routed downstream. For now, drains are assumed to be fully effective when tile drainage is active in HydroGeoSphere, each pipe being empty and partially filled with water.

4. In Fensholt, manual calibration of the model with few adjusted parameters showed good performance regarding simulated and observed drainage discharge. Nevertheless, it is believed that an automatic calibration approach with tools such as PEST (Doherty, 2005) would produce more accurate results. Using PEST would probably help facilitate calibration of models with data from multiple drainage networks. The choice of manual vs. automatic calibration is determined by computational performance of numerical models as automatic calibrations might be more time-consuming. Future improvements in computational power will likely improve inverse modeling applications.

127 5. After calibration, a validation period is usually chosen for testing a model’s predictive capabilities (Refsgaard, 1997). Focusing on a speciﬁc season or short-term period may not be suﬃcient for this purpose. As mentioned by Williams et al. (2015) and King et al. (2014), tile drainage discharge is highly dependent on climate conditions. A validation period could then be run with longer than one year time series, as was done with the Norsminde model of He et al. (2015). Avoiding biased predictions is a major challenge for solute transport modeling, especially when tile drainage models are used for decision-making linked to agricultural management of fertilizer application.

6. Finally, the next step to consider is simulating solute transport for investigating, among others, nitrate contamination issues. Since this type of contamination is diﬀuse, simplifying drainage networks in models, such as in the Fensholt case, is not believed to be appropriate for nitrate transport simulations since a part of nitrate would not be transported through missing drains. Including discrete drains in models should therefore be considered for ensuring accurate mass transport.

128 Bibliography

Abbaspour, K. C., Kohler, A., Šimůnek, J., Fritsch, M., and Schulin, R. (2001). Application of a two-dimensional model to simulate ﬂow and transport in a macroporous agricultural soil with tile drains. Eur. J. Soil Sci., 52(3):433–447. doi:10.1046/j.1365-2389.2001.00389.x.

Adams, W. A. (1986). Practical aspects of sportsﬁeld drainage. Soil Use Manage., 2(2):51–54. doi:10.1111/j.1475-2743.1986.tb00679.x.

Ajami, H., McCabe, M. F., Evans, J. P., and Stisen, S. (2014). Assessing the impact of model spin-up on surface water-groundwater interactions using an integrated hydrologic model. Water Resour. Res., 50(3):2636–2656. doi:10.1002/2013WR014258.

Akay, O., Fox, G. A., and Šimůnek, J. (2008). Numerical simulation of ﬂow dynamics during macropore-subsurface drain interactions using HYDRUS. Vadose Zone J., 7(3):909–918. doi:10.2136/vzj2007.01488.

Ale, S., Gowda, P. H., Mulla, D. J., Moriasi, D. N., and Youssef, N. A. (2013). Com- parison of the performances of DRAINMOD-NII and ADAPT models in simulating nitrate losses from subsurface drainage systems. Agric. Water Manage., 129:21–30. doi:10.1016/j.agwat.2013.07.008.

Appelo, C. A. J. and Postma, D. (2005). Geochemistry, groundwater and pollution, 2nd Edition. A.A. Balkema Publishers, Leiden, The Netherlands. 672 p.

Arnold, J. G., Srinivasan, R., Muttiah, R. S., and Williams, J. R. (1998). Large-area hydrologic modeling and assessment: Part I. Model development. J. Am. Water Resour. Assoc., 34(1):73–89. doi:10.1111/j.1752-1688.1998.tb05961.x.

Ayars, J. E., Christen, E. W., and Hornbuckle, J. W. (2006). Controlled drainage for improved water management in arid regions irrigated agriculture. Agric. Water Manage., 86(1-2):128– 139. doi:10.1016/j.agwat.2006.07.004.

Baldock, D., Caraveli, H., Dwyer, J., S. Einschütz, Petersen, J. E., Sumpsi-Vinas, J., and Varela-Ortega, C. (2000). The environmental impacts of irrigation in the European Union. A report to the Environment Directorate of the European Commission, Institute

129 for European Environmental Policy, in association with the Polytechnical University of Madrid and the University of Athens, London, United Kingdom. 138 p. Available at: ec.europa.eu/environment/agriculture/pdf/irrigation.pdf.

Baldock, D., Mermet, L., Mustin, M., Kelly, P. W., and Hermans, B. (1984). Wetland drainage in Europe: The eﬀects of agricultural policy in four EEC countries. Institute for European Environmental Policy, London, Great Britain. 166 p.

Barré de Saint-Venant, A.-J.-C. (1871). Théorie et équations générales du mouvement non permanent des eaux courantes (in French). Comptes rendus des séances de l’Académie des Sciences, 73:147–154.

Beasley, D. B., Huggins, L. F., and Monke, E. J. (1980). ANSWERS: A model for watershed planning. T. ASAE, 23(4):938–944. doi:10.13031/2013.34692.

Bennett, N. D., Croke, B. F. W., Guariso, G., Guillaume, J. H. A., Hamilton, S. H., Jake- man, A. J., Marsili-Libelli, S., Newham, L. T. H., Norton, J. P., Perrin, C., Pierce, S. A., Robson, B., Seppelt, R., Voinov, A. A., Fath, B. D., and Andreassian, V. (2013). Char- acterising performance of environmental models. Environ. Model. Softw., 40(1-2):1–20. doi:10.1016/j.envsoft.2012.09.011.

Binger, R. L. and Theurer, F. D. (2001). AGNPS98: A suite of water quality models for watershed use. In Proceedings of the Sediment Monitoring, Modeling and Managing: 7th Federal Interagency Sedimentation Conference, pages 25–29, Reno, NV, USA.

Blann, K. L., Anderson, J. L., Sands, G. R., and Vondracek, B. (2009). Eﬀects of agricultural drainage on aquatic ecosystems: A review. Crit. Rev. Env. Sci. Tec., 39(11):909–1001. doi:10.1080/10643380801977966.

Blessent, D., Therrien, R., and MacQuarrie, K. (2009). Coupling geological and numerical models to simulate groundwater ﬂow and contaminant transport in fractured media. Comput. Geosci., 35(9):1897–1906. doi:10.1016/j.cageo.2008.12.008.

Blicher-Mathiesen, G., Andersen, H. E., Carstensen, J., Børgesen, C. D., Hasler, B., and Windolf, J. (2014). Mapping of nitrogen risk areas. Agric. Ecosyst. Environ., 195:149–160. doi:10.1016/j.agee.2014.06.004.

Blöschl, G. and Sivapalan, M. (1995). Scales issues in hydrological modeling: A review. Hydrol. Processes, 9(3-4):251–290. doi:10.1002/hyp.3360090305.

Børgesen, C. D., Jensen, P. N., Blicher-Mathiesen, G., and Schelde, K. (2013). Udviklingen i kvælstofudvaskning og næringsstofoverskud fra Dansk landbrug for perioden 2007-2011 (in Danish). DCA Rapport Nr. 031, Danish Centre for Food and Agriculture, Aarhus Univer- sity, Tjele, Denmark. Available at: pure.au.dk/portal/ﬁles/68362856/dcarapporten31.pdf.

130 Børgesen, C. D. and Schaap, M. G. (2005). Point and parameter pedotransfer functions for water retention predictions for Danish soils. Geoderma, 127(1-2):154–167. doi:10.1016/j.geoderma.2004.11.025.

Boivin, A., Šimůnek, J., Schiavon, M., and van Genuchten, M. T. (2006). Comparison of pesticide transport processes in three tile-drained ﬁeld soils using HYDRUS-2D. Vadose Zone J., 5(3):838–849. doi:10.2136/vzj2005.0089.

Bouraoui, F., Vachaud, G., Haverkamp, R., and Normand, B. (1997). A distributed physical approach for surface-subsurface water transport modeling in agricultural watersheds. J. Hydrol., 203(1-4):79–92. doi:10.1016/S0022-1694(97)00085-1.

Boussinesq, M. J. (1872). Théorie des ondes et des remous qui se propagent le long d’un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond (in French). J. Math. Pures Appl., 17:55–108. Available at: eudml.org/doc/234248.

Branger, F., Tournebize, J., Carluer, N., Kao, C., Braud, I., and Vauclin, M. (2009). A sim- pliﬁed modelling approach for pesticide transport in a tile-drained ﬁeld: The PESTDRAIN model. Agric. Water Manage., 96(3):415–428. doi:10.1016/j.agwat.2008.09.005.

Brooks, R. H. and Corey, A. T. (1964a). Hydraulic properties of porous media. Hydrology papers no. 3, Colorado State University, Fort Collins, CO, USA.

Brooks, R. H. and Corey, A. T. (1964b). Hydraulic properties of porous media and their relation to drainage design. T. ASAE, 7(1):26–28. doi:10.13031/2013.40684.

Brunner, P. and Simmons, C. T. (2012). HydroGeoSphere: A fully integrated, physically based hydrological model. Ground Water, 50(2):170–176. doi:10.1111/j.1745-6584.2011.00882.x.

Burton, M. (2010). Irrigation management: Principles and practices. CABI, Wallingford, United Kingdom. 375 p.

Carlier, J. P., Kao, C., and Ginzburg, I. (2007). Field-scale modeling of subsurface tile-drained soils using an equivalent-medium approach. J. Hydrol., 341(1-2):105–115. doi:10.1016/j.jhydrol.2007.05.006.

Carluer, N. and de Marsily, G. (2004). Assessment and modelling of the inﬂuence of man-made networks on the hydrology of a small watershed: Implications for fast ﬂow components, water quality and landscape management. J. Hydrol., 285(1-4):76–95. doi:10.1016/j.jhydrol.2003.08.008.

Carsel, R. F. and Parrish, R. S. (1988). Developing joint probability distributions of soil water retention characteristics. Water Resour. Res., 24(5):755–769. doi:10.1029/WR024i005p00755.

131 Chapman, A. S., Foster, I. D. L., Lees, J. A., Hodgkinson, R. A., and Jackson, R. H. (2001). Particulate phosphorus transport by sub-surface drainage from agricultural land in the UK. Environmental signiﬁcance at the catchment and national scale. Sci. Total Environ., 266(1-3):95–102. doi:10.1016/S0048-9697(00)00734-8.

Chen, C. W., Herr, J., and Weintraub, L. H. Z. (2001). Watershed Analysis Risk Management Framework: Update one, A decision support system for watershed analysis and total maximum daily load calculation, allocation and implementation. Technical Report No. 1005181, EPRI, Palo Alto, CA, USA.

Christen, E. W. and Skehan, D. (2001). Design and management of subsurface horizontal drainage to reduce salt loads. J. Irrig. Drain Eng., 127(3):148–155. doi:10.1061/(ASCE)0733-9437(2001)127:3(148).

Christiansen, J. S., Thorsen, M., Clausen, T., Hansen, S., and Refsgaard, J. C. (2004). Modelling of macropore ﬂow and transport processes at catchment scale. J. Hydrol., 299(1- 2):136–158. doi:10.1016/j.jhydrol.2004.04.029.

Cochand, F. (2014). Impact des changements climatiques et du développement ur- bain sur les ressources en eau du bassin versant de la Rivière Saint-Charles (in French). PhD thesis, Université Laval, Quebec City, QC, Canada. Available at: www.theses.ulaval.ca/2014/31183/31183.pdf.

Cooke, R. A., Badiger, S., and Garcia, A. M. (2000). Drainage equations for random and irregular tile drainage systems. Agr. Water Manage., 48(3):207–224. doi:10.1016/S0378-3774(00)00136-0.

Cooley, R. L. (1971). A finite difference method for unsteady flow in variably saturated porous media: Application to a single pumping well. Water Resour. Res., 7(6):1607–1625. doi:10.1029/WR007i006p01607.

Cunge, J. A. and Wegner, M. (1964). Intégration numérique des équations d’ écoulement de Barré de Saint-Venant par un schéma implicite de diﬀérences ﬁnies (in French). La Houille Blanche, 1:33–39. doi:10.1051/lhb/1964002.

Dayyani, S., Prasher, S. O., Madani, A., and Madramootoo, C. A. (2010). Develop- ment of DRAIN-WARMF model to simulate ﬂow and nitrogen transport in a tile- drained agricultural watershed in Eastern Canada. Agric. Water Manage., 98(1):55–68. doi:10.1016/j.agwat.2010.07.012.

De Schepper, G., Therrien, R., Refsgaard, J. C., and Hansen, A. L. (2015). Simulating coupled surface and subsurface water ﬂow in a tile-drained agricultural catchment. J. Hydrol., 521:374–388. doi:10.1016/j.jhydrol.2014.12.035.

132 Deasy, C., Brazier, R. E., Heathwaite, A. L., and Hodgkinson, R. (2009). Pathways of runoﬀ and sediment transfer in small agricultural catchments. Hydrol. Process., 23(9):1349–1358. doi:10.1002/hyp.7257.

Delaunay, B. (1934). Sur la sphère vide. A la mémoire de Georges Voronoï (in French). Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskii i Estestvenyka Nauk, 6:793–800. Available at: mi.mathnet.ru/eng/izv4937.

Detlefsen, N. and Plauborg, F. (2001). Reevaluation of methods for calculating reference evapotranspiration - potential evapotranspiration. Technical report, The Danish Institute of Agricultural Sciences, Foulum, Denmark.

Doherty, J. (2005). PEST: Model-independent parameter estimation. User manual, 5th Ed. Technical report, Watermark Numerical Computing, Brisbane, Qld, Australia. Available at: www.pesthomepage.org.

Du, B., Arnold, J. G., Saleh, A., and Jaynes, D. B. (2005). Development and application of SWAT to landscapes with tiles and potholes. T. ASAE, 48(3):1121–1133. doi:10.13031/2013.18522.

Eastman, M., Gollamudi, A., Stampﬂi, N., Madramootoo, C. A., and Sarangi, A. (2010). Comparative evaluation of phosphorus losses from subsurface and naturally drained agricultural ﬁelds in the Pike River watershed of Quebec, Canada. Agric. Water Manage., 97(5):596–604. doi:10.1016/j.agwat.2009.11.010.

Elmi, A. A., Madramootoo, C. A., Egeh, M., and Hamel, C. (2004). Water and fertilizer nitrogen management to minimize nitrate pollution from a cropped soil in southwestern Quebec, Canada. Water Air Soil Poll., 151(1-4):117–134. doi:10.1023/B:WATE.0000009910.25539.75.

Ernst, L. F. (1956). Calculation of the steady ﬂow of groundwater in vertical cross sections. Neth. J. Agr. Sci., 4:126–131.

Ernstsen, V., Højberg, A. L., Jacobsen, P. R., von Platen, F., Tougarard, L., Hansen, J. R., Blicher-Mathiesen, G., Bøgestrand, J., and Børgesen, C. D. (2006). Beregning af nitrat- reduktionsfaktorer for zonen mellem rodzonen og frem til vandløb. Data og metode for 1. generationskortet (in Danish). Rapport 2006/93, Geological Survey of Denmark and Greenland (GEUS), Copenhagen, Denmark.

European Commission (2008). Groundwater protection in Europe. The new Groundwater Directive: Consolidating the EU Regulatory Framework. Technical report, European Com- mission, Luxembourg, Luxembourg. 35 p. doi:10.2779/84304.

133 Evans, R. O., Skaggs, R. W., and Gilliam, J. W. (1991). Controlled drainage management guidelines for improving drainage water quality. North Carolina Cooperative Extension Service Bulletin, Raleigh, NC, USA. No. AG-443.

Evans, R. O., Skaggs, R. W., and Gilliam, J. W. (1995). Controlled versus conventional drainage eﬀects on water quality. J. Irrig. Drain. Eng., 121(4):271–276. doi:10.1061/(ASCE)0733-9437(1995)121:4(271).

Feddes, R. A., Kowalik, P. J., and Zaradny, H. (1978). Simulation of ﬁeld water use and crop yield. First edition, Centre for Agricultural Publishing and Documentation, Wageningen, The Netherlands. 189 p.

Filipović, V., Kochem Mallmann, F. J., Coquet, Y., and Šimůnek, J. (2014). Numerical simulation of water ﬂow in tile and mole drainage systems. Agric. Water Manage., 146:105– 114. doi:10.1016/j.agwat.2014.07.020.

Fipps, G., Skaggs, R. W., and Nieber, J. L. (1986). Drains as a boundary condition in ﬁnite elements. Water Resour. Res., 22(11):1613–1621. doi:10.1029/WR022i011p01613.

Fredericia, J. (1990). Saturated hydraulic conductivity of clayey tills and the role of fractures. Nord. Hydrol., 21(2):119–132. doi:10.2166/nh.1990.009.

Frey, S. K., Rudolph, D. L., Lapen, D. R., and Ball Coelho, B. R. (2012). Viscosity dependent dual-permeability modeling of liquid manure movement in layered, macroporous, tile drained soil. Water Resour. Res., 48(6):W00L11. doi:10.1029/2011WR010809.

Gärdenäs, A. I., Šimůnek, J., Jarvis, N., and van Genuchten, M. T. (2006). Two-dimensional modelling of preferential water ﬂow and pesticide transport from a tile-drained ﬁeld. J. Hydrol., 329(3-4):647–660. doi:10.1016/j.jhydrol.2006.03.021.

Gerke, H. H. and van Genuchten, M. T. (1993). A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour. Res., 29(2):305–319. doi:10.1029/92WR02339.

Goderniaux, P., Brouyère, S., Fowler, H. J., Blenkinsop, S., Therrien, R., Orban, P., and Dassargues, A. (2009). Large scale surface-subsurface hydrological model to assess climate change impacts on groundwater reserves. J. Hydrol., 373(1-2):122–138. doi:10.1016/j.jhydrol.2009.04.017.

Gordon, L. J., Peterson, G. D., and Bennett, E. M. (2008). Agricultural modiﬁca- tions of hydrological ﬂows create ecological surprises. Trends Ecol. Evol., 23(4):211–219. doi:10.1016/j.tree.2007.11.011.

Goudie, A. (2013). The human impact on the natural environment: Past, present and future. Cambridge University Press, Cambridge, MA, USA, 7th edition. 422 p.

134 Grant, R. and Blicher-Mathiesen, G. (2004). Danish policy measures to reduce diﬀuse nitrogen emissions from agriculture to the aquatic environment. Water Sci. Technol., 49(3):91–100.

Grant, R., Blicher-Mathiesen, G., Jørgensen, J. O., Kloppenborg-Skrumsager, B., Kronvang, B., Jensen, P. G., and Rasmussen, P. (2000). Landovervågningsoplande 1999: NOVA 2003 (in Danish). Technical Report No. 334, National Environmental Research Institute of Denmark, Aarhus University, Aarhus, Denmark. 147 p.

Grant, R., Blicher-Mathiesen, G., Pedersen, L. E., Jensen, P. G., Madsen, I., Hansen, B., Brüsch, W., and Thorling, L. (2007). Landovervågningsoplande 2006 (in Danish). Tech- nical Report No. 640, NOVANA Program, National Environmental Research Institute of Denmark, Aarhus University, Aarhus, Denmark. 126 p.

Gravesen, P. and Nyegaard, P. (1989). Hydrogeologisk kortlægning Lillebæk - Vandmiljø- planens Overvågningsprogram Landovervågningsoplande LOOP4 (in Danish). Technical report, Geological Survey of Denmark and Greenland, Copenhagen, Denmark.

Green, C. H., Tomer, M. D., Di Luzio, M., and Arnold, J. G. (2006). Hydrologic evaluation of the soil and water assessment tool for a large tile-drained watershed in Iowa. T. ASABE, 49(2):413–422. doi:10.13031/2013.20415.

Green, F. H. W. (1980). Current ﬁeld drainage in northern and western europe. J. Environ. Manage., 10(2):149–153.

Hansen, A. L. (2010). Modelling of ﬂow and nitrate transport from root zone to stream system in Lillebæk catchment. Master’s thesis, Department of Geography and Geology, University of Copenhagen, Copenhagen, Denmark. Available at: www.nitrat.dk.

Hansen, A. L. (2014). Spatially distributed nitrate reduction potential in the saturated zone in till areas: Challenges and uncertainty assessment. PhD thesis, Department of Geosciences and Natural Resource Management, University of Copenhagen, Copenhagen, Denmark. Available at: rex.kb.dk/KGL01009018301.

Hansen, A. L., Ernstsen, V., Refsgaard, J. C., He, X., Therrien, R., and Jensen, K. H. (2014). Factors controlling the depth of the redox-interface in a Danish till area. Unpublished paper.

Hansen, A. L., Refsgaard, J. C., B.Christensen, B. S., and Jensen, K. H. (2013). Importance of including small-scale tile drain discharge in the calibration of a coupled groundwater-surface water catchment model. Water Resour. Res., 49(1):585–603. doi:10.1029/2011WR011783.

Hansen, J. R. (2006). Nitrate modelling at catchment scale. PhD thesis, Geological Survey of Denmark and Greenland (GEUS), Copenhagen, Denmark.

135 Hansen, J. R., Ernstsen, V., Refsgaard, J. C., and Hansen, S. (2008). Field scale heterogeneity of redox conditions in till-upscaling to a catchment nitrate model. Hydrogeol. J., 16(7):1251– 1266. doi:10.1007/s10040-008-0330-1.

He, X., Højberg, A. L., Jørgensen, F., Schamper, C., and Refsgaard, J. C. (2015). Assessing hydrological predictive uncertainty using stochastically generated geological models. Hydrol. Process., 29(19):4293–4311. doi:10.1002/hyp.10488.

He, X., Koch, J., Sonneborg, T. O., Jørgensen, F., Schamper, C., and Refsgaard, J. C. (2014). Transition probability-based stochastic geological modeling using airborne geophysical data and borehole data. Water Resour. Res., 50(4):3147–3169. doi:10.1002/2013WR014593.

Hedeselskabet (1989). Landovervågningsoplandet Lillebæk, L00P4. Aﬂeveringsrapport (in Danish). Technical report, Hydrometriske Undersøgelser, Hedeselskabet. August 1989.

Heikurainen, L., Kenttaines, K., and Liane, J. (1978). The environmental eﬀects of forest drainage. SUO, 29(3-4):49–58.

Henine, H., Nédélec, Y., and Ribstein, P. (2014). Coupled modelling of the eﬀect of overpressure on water discharge in a tile drainage system. J. Hydrol., 511:39–48. doi:10.1016/j.jhydrol.2013.12.016.

Hillman, G. R. (1992). Some hydrological eﬀects of peatland drainage in Alberta’s boreal forest. Can. J. For. Res., 22(11):1588–1596. doi:10.1139/x92-211.

Hinsby, K., de Melo, M. T. C., and Dahl, M. (2008). European case studies supporting the derivation of natural background levels and groundwater threshold values for the protection of dependent ecosystems and human health. Sci. Total Environ., 401(1-3):1–20. doi:10.1016/j.scitotenv.2008.03.018.

Hoﬀman, G. J. and Durnford, D. S. (1999). Drainage design for salinity control. In Skaggs, R. and van Schilfgaarde, J., editors, Agricultural drainage, pages 579–614, Madison, WI, USA. American Society of Agronomy.

Holden, J., Chapman, P. J., and Labadz, J. C. (2004). Artiﬁcial drainage of peatlands: Hydro- logical and hydrochemical process and wetlands restoration. Prog. Phys. Geog., 28(1):95– 123. doi:10.1191/0309133304pp403ra.

Hooghoudt, S. B. (1940). Algemene beschouwing van het probleem van de detailontwatering en de inﬁltratie door middel van parallel loopende drains, greppels, slooten en kanalen (in Dutch). In Bijdragen tot de kennis van eenige natuurkundige grootheden van den grond, number 7, Bodemkundig Instituut te Groningen, Groningen, The Netherlands.

Houmark-Nielsen, M. and Kjær, K. H. (2003). Southwest Scandinavia, 40-15 kyr BP: Palaeo- geography and environmental change. J. Quat. Sci., 18(8):769–786. doi:10.1002/jqs.802.

136 Howarth, R. W., Billen, G., Swaney, D., Townsend, A., Jaworski, N., Lajtha, K., Downing, J. A., Elmgren, R., Caraco, N., Jordan, T., Berendse, F., Freney, J., Kudeyarov, V., Murdoch, P., and Zhao-Liang, Z. (1996). Regional nitrogen budgets and riverine N and P ﬂuxes for the drainage to the North Atlantic Ocean: Natural and human inﬂuences. Biogeochemistry, 35(1):75–139. doi:10.1007/BF02179825.

Huyakorn, P. S. and Pinder, G. F. (1983). Computational methods in subsurface ﬂow. Aca- demic Press, New York, NY, USA, third edition. 473 p.

Hwang, H.-T. (2012). Development of a parallel computational framework to solve ﬂow and transport in integrated surface-subsurface hydrologic systems. PhD thesis, University of Waterloo, Waterloo, ON, Canada. Available at: hdl.handle.net/10012/6612.

Hwang, H.-T., Park, Y.-J., Sudicky, E. A., and Forsyth, P. A. (2014). A parallel computational framework to solve ﬂow and transport in integrated surface-subsurface hydrologic systems. Environ. Model. Softw., 61:39–58. doi:10.1016/j.envsoft.2014.06.024.

Irwin, R. W. and Bryant, G. (1986). Eﬀect of subsurface drain discharge on streamﬂow. In Smith, K. V. H. and Rycroft, D. W., editors, Hydraulic design in water resources engineering: Land drainage, pages 233–242. Springer, Berlin, Germany.

Iversen, B. V., Børgesen, C. D., Lægdsmand, M., Greve, M. H., Heckrath, G., and Kjærgaard, C. (2011). Risk predicting of macropore ﬂow using pedotransfer functions, textural maps, and modeling. Vadose Zone J., 10(4):1185–1195. doi:10.2136/vzj2010.0140.

Iversen, T. M., Grant, R., and Nielsen, K. (1998). Nitrogen enrichment of European inland and marine waters with special attention to Danish policy measures. Environ. Pollut., 102(1):771–780. doi:10.1016/S0269-7491(98)80111-5.

Jacobsen, O. S. (1995). Grundvandsovervågning 1995 (in Danish). Technical report, Geolog- ical Survey of Denmark and Greenland (GEUS), Copenhagen, Denmark. 64 p.

Japsen, P., Green, P. F., Nielsen, L. H., Rasmussen, E. S., and Bidstrup, T. (2007). Mesozoic-Cenozoic exhumation events in the eastern North Sea Basin: A multi-disciplinary study based on palaeothermal, palaeoburial, stratigraphic and seismic data. Basin Res., 19(4):451–490. doi:10.1111/j.1365-2117.2007.00329.x.

Jørgensen, P. R., McKay, L. D., and Kistrup, J. P. (2004). Aquifer vulnerabil- ity to pesticide migration through till aquitards. Ground Water, 42(6):841–855. doi:10.1111/j.1745-6584.2004.t01-3-.x.

Juhász, E., Kovács, L. O., Muller, P., Tóth-Makk, A., Phillips, L., and Lantos, M. (1997). Climatically driven sedimentary cycles in the Late Miocene sediments of the Pannonian Basin, Hungary. Tectonophysics, 282(1–4):257–276. doi:10.1016/S0040-1951(97)00222-9.

137 Kao, C., Nédélec, Y., and Zimmer, D. (1998). Surface runoﬀ mechanisms and modeling in subsurface drained ﬁelds. In Brown, L., editor, 7th Annual Drainage Symposium: Drainage in the 21st Century, Food production and environment, pages 258–266, Orlando, FL, USA.

Käser, D., Graf, T., Cochand, F., McLaren, R. G., Therrien, R., and Brunner, P. (2014). Channel representation in physically-based models coupling groundwater and surface water: Pitfalls and how to avoid them. Ground Water, 52(6):827–836. doi:10.1111/gwat.12143.

Kelstrup, N., Bækgaard, A., and Andersen, L. J. (1982). Grundvandsressourcer i Danmark. kommisionen for de Europæiske Fællesskaber (EEC) (in Danish). Technical report, Th. Schæfer Druckerei GmBH, Hannover, Germany. 74 p.

Kessler, T. C., Klint, K. E. S., Nilsson, B., and Bjerg, P. L. (2012). Characterization of sand lenses embedded in tills. Quat. Sci. Rev., 53:55–71. doi:10.1016/j.quascirev.2012.08.011.

Kiesel, J., Fohrer, N., Schmalz, B., and White, M. J. (2010). Incorporating landscape depres- sions and tile drainages of a northern German lowland catchment into a semi-distributed model. Hydrol. Process., 24(11):1472–1486. doi:10.1002/hyp.7607.

Kim, S. and Delleur, J. W. (1997). Sensitivity analysis of extended TOPMODEL for agricultural watersheds equipped with tile drains. Hydrol. Process., 11(9):1243–1261. doi:10.1002/(SICI)1099-1085(199707)11:9<1243::AID-HYP555>3.0.CO;2-0.

King, K. W., Fausey, N. R., and Williams, M. R. (2014). Eﬀect of subsurface drainage on streamﬂow in an agricultural headwater watershed. J. Hydrol., 519(Part A):483–445. doi:10.1016/j.jhydrol.2014.07.035.

Kirkham, D. (1949). Flow of ponded water into drain tubes in soil overlying an impervious layer. EOS, Trans. Amer. Geophys. Union, 30(3):369–385. doi:10.1029/TR030i003p00369.

Klaus, J. and Zehe, E. (2011). A novel explicit approach to model bromide and pesticide transport in connected soil structures. Hydrol. Earth Syst. Sci., 15(7):2127–2144. doi:10.5194/hess-15-2127-2011.

Klemeš, V. (1986). Operational testing of hydrological simulation models. Hydrol. Sci. J., 31(1):13–24. doi:10.1080/02626668609491024.

Klint, K. E. S. (2001). Fractures in glacigenic diamict deposits: Origin and distribution. PhD thesis, Geological Survey of Denmark and Greenland, Copenhagen, Denmark.

Klint, K. E. S. and Gravesen, P. (1999). Fractures and biopores in Weichselian clayey till aquitards at Flakkebjerg, Denmark. Nord. Hydrol., 30(4-5):267–284. doi:10.2166/nh.1999.015.

Knutsson, G. (2008). Hydrogeology in the Nordic Countries. Episodes, 33(1):148–154.

138 Koch, S., Bauwe, A., and Lennartz, B. (2013). Application of the SWAT model for a tile- drained lowland catchment in North-Eastern Germany on subbasin scale. Water Resourc. Manag., 27(3):791–805. doi:10.1007/s11269-012-0215-x.

Konyha, K., Skaggs, R., and Gilliam, J. (1992). Eﬀects of drainage and water-management practices on hydrology. J. Irrig. Drain. Eng., 118(5):807–819. doi:10.1061/(ASCE)0733-9437(1992)118:5(807).

Korom, S. F. (1992). Natural denitriﬁcation in the saturated zone: A review. Water Resour. Res., 28(6):1657–1668. doi:10.1029/92WR00252.

Kovačić, D. A., David, M. B., Gentry, L. E., Starks, K. M., and Cooke, R. A. (2000). Eﬀectiveness of constructed wetlands in reducing nitrogen and phosphorus from agricultural tile drainage. J. Environ. Qual., 29(4):1262–1274. doi:10.2134/jeq2000.00472425002900040033x.

Krause, P., Boyle, D. P., and Bäse, F. (2005). Comparison of diﬀerent eﬃciency criteria for hydrological model assessment. Adv. Geosci., 5:89–97. doi:10.5194/adgeo-5-89-2005.

Kristensen, K. J. and Jensen, S. E. (1975). A model for estimating actual evapotranspiration from potential evapotranspiration. Nord. Hydrol., 6(3):170–188. doi:10.2166/nh.1975.012.

Kroes, J. G. and van Dam, J. C. (2003). Reference manual SWAP version 3.0.3. Alterra Report No. 773, Alterra Research Institute, Wageningen, The Netherlands. Available at: swap.alterra.nl/References.htm.

Kroes, J. G., van Dam, J. C., Groenendijk, P., Hendriks, R. F. A., and Jacobs, C. M. J. (2008). SWAP version 3.2. Theory description and user manual. Alterra Report No. 1649, Alterra Research Institute, Wageningen, The Netherlands. 262 p. Available at: swap.alterra.nl/References.htm.

Kronvang, B., Ærtebjerg, G., Grant, R., Kristensen, P., Hovmand, M., and Kirkegaard, J. (1993). Nationwide monitoring of nutrients and their ecological eﬀects: State of the Danish aquatic environment. Ambio, 22(4):176–187.

Kronvang, B., Græsbøll, P., Larsen, S. E., Svendsen, L. M., and Andersen, H. E. (1996). Diﬀuse nutrient losses in denmark. Water Sci. Tech., 33(4-5):81–88. doi:10.1016/0273-1223(96)00217-X.

Kronvang, B., Iversen, H., Vejrup, K., Mogensen, B. B., Hansen, A.-M., and Hansen, L. (2003). Pesticides in streams and subsurface drainage water within two arable catchments in Denmark: Pesticide application, concentration, transport and fate. Pesti- cide Research Nr. 69, Danish Environmental Protection Agency, Copenhagen, Denmark. www2.mst.dk/Udgiv/publications/2003/87-7972-951-7/pdf/87-7972-952-5.pdf.

139 Larsson, U., Elmgren, R., and Wulﬀ, F. (1985). Eutrophication and the Baltic Sea: Causes and consequences. Ambio, 14(1):9–14.

Leeds-Harrison, P., Spoor, G., and Godwin, R. J. (1982). Water ﬂow to mole drains. J. Agric.Eng. Res., 27(2):81–91. doi:10.1016/0021-8634(82)90095-6.

Leonard, R. A., Knisel, W. G., and Still, D. A. (1987). GLEAMS: Groundwater Loading Eﬀects of Agricultural Management Systems. T. ASAE, 30(5):1403–1418. doi:10.13031/2013.30578.

Lesaﬀre, B. and Zimmer, D. (1988). Subsurface drainage peak ﬂows in shallow soil. J. Irrig. Drain Eng., 114(3):387–406. doi:10.1061/(ASCE)0733-9437(1988)114:3(387).

Li, H., Sivapalan, M., Tian, F., and Liu, D. (2010). Water and nutrient balances in a large tile-drained agricultural catchment: A distributed modeling study. Hydrol. Earth Syst. Sci., 14(11):2259–2275. doi:10.5194/hess-14-2259-2010.

Li, Q., Unger, A. J. A., Sudicky, E. A., Kassenaar, D., Wexler, E. J., and Shikaze, S. (2008). Simulating the multi-seasonal response of a large-scale watershed with a 3D physically- based hydrologic model. J. Hydrol., 357(3-4):317–336. doi:10.1016/j.jhydrol.2008.05.024.

Lin, H. C., Richards, D. R., Yeh, G. T., Cheng, J. R., Cheng, H. P., and Jones, N. L. (1997). FEMWATER: A three-dimensional ﬁnite element computer model for simulating density- dependent ﬂow and transport in variably saturated media. Technical Report CHL-97-12, Waterways Experiment Station, U.S. Army Corps of Engineers, Vicksburg, MS, USA. 143 p. Available at: homepage.usask.ca/ mjr347/gwres/femwref.pdf.

Maalim, F. K. and Melesse, A. M. (2013). Modelling the impacts of subsurface drainage on surface runoﬀ and sediment yield in the Le Sueur Watershed, Minnesota, USA. Hydrolog. Sci. J., 58(3):570–586. doi:10.1080/02626667.2013.774088.

MacQuarrie, K. T. B. and Sudicky, E. A. (1996). On the incorporation of drains into three- dimensional variably saturated groundwater ﬂow models. Water Resour. Res., 32(2):477– 482. doi:10.1029/95WR03404.

Madramootoo, C. A., Johnston, W. R., Ayars, J. E., Evans, R. O., and Fausey, N. R. (2007). Agricultural drainage management, quality and disposal issues in North America. Irrig. and Drain., 56(S1):S35–S45. doi:10.1002/ird.343.

Maršálek, J. and Sztruhár, D. (1994). Urban drainage: Review of contemporary approaches. Water Sci. Technol., 29(1-2):1–10.

Maurer, T. (1997). Physikalisch begründete, zeitkontinuierliche modellierung des wassertrans- ports in kleinen ländlichen einzugsgebieten (in German). PhD thesis, Mitteilungen Inst.

140 f. Hydrologie u. Wasserwirtschaft, University of Karlsruhe, Karlsruhe, Germany. Available at: nbn-resolving.org/urn:nbn:de:swb:90-AAA657972.

McDonald, M. G. and Harbaugh, A. W. (1988). A modular three-dimensional finite-difference ground-water flow model. Book 6, Chapter A1, Techniques of Water-Resources Investiga- tions, USGS, Denver, CO, USA.

Mee, L. D. (1992). The Black Sea in crisis: A need for concerted international action. Ambio, 21(4):278–286.

Mohanty, B. P., Bowman, R. S., Hendrickx, J. M. H., Šimůnek, J., and van Genuchten, M. T. (1998). Preferential transport of nitrate to a tile drain in an intermittent-ﬂood-irrigated ﬁeld: Model development and experimental evaluation. Water Resour. Res., 34(5):1061– 1076. doi:10.1029/98WR00294.

Moriasi, D. N., Arnold, J. G., Vazquez-Amábile, G. G., Engel, B. A., and Rossi, C. G. (2009). Incorporation of a new shallow water table depth algorithm into SWAT2005. T. ASABE, 52(3):771–784. doi:10.13031/2013.27398.

Morrison, A. K. (2014). Limitations on the study of tile drainage using a distributed parameter hydrologic model and stable isotopes. Master’s thesis, Department of Geolog- ical and Atmospheric Sciences, Iowa State University, Ames, IA, USA. Available at: lib.dr.iastate.edu/etd/13659.

Mustonen, S. E. and Seuna, P. (1971). Inﬂuence of forest draining on the hydrology of peatlands. Publ. No. 2, National Board of Waters, Water Research Institute, Helsinki, Finland.

Nash, J. E. and Sutcliﬀe, J. V. (1970). River ﬂow forecasting through conceptual models, Part I - A discussion of principles. J. Hydrol., 10(3):282–290. doi:10.1016/0022-1694(70)90255-6.

Natho-Jina, S., Prasher, S. O., Madramootoo, C. A., and Broughton, R. S. (1987). Mea- surements and analysis of runoﬀ from subsurface drained farmlands. Can. Agr. Eng., 29(2):123–130.

Neuman, S. P. (1973). Saturated-unsaturated seepage by ﬁnite elements. J. Hydraul. Div. Am. Soc. Civ. Eng., 99(12):2233–2250.

Nielsen, K., Stjernholm, M., Østergaard Olsen, B., Müller-Wohlfeil, D.-I., Madsen, I., Kjeldgaard, A., Groom, G., Hansen, H. S., Rolev, A. M., Hermansen, B., Skov-Petersen, H., Johannsen, V. K., Hvidberg, M., Jensen, J. E., Bacher, V., and Larsen, H. (2000). Areal Informations Systemet - AIS (in Danish). Technical report, Danmarks Miljøundersøgelser, Miljø- og Energiministeriet, Denmark.

141 Nijland, H. J., Croon, F. W., and Ritzema, H. P. (2005). Subsurface drainage practices: Guidelines for the implementation, operation and maintenance of subsurface pipe drainage systems. ILRI Publication No. 60, Alterra, Wageninen, The Netherlands. 608 p. Available at: edepot.wur.nl/264729.

Nilsson, B. (2013). Exchange of nitrate in the transition zone between groundwater and stream water in the norsminde catchment. Nica technical note, unpublished report, Geo- logical Survey of Denmark and Greenland (GEUS), Copenhagen, Denmark. Available at: www.nitrat.dk.

Nilsson, B., Harrar, W. G., Brüsch, W., Vosgerau, H., and Bojesen, O. (2003). Results of a forced-gradient tracer test to explain glyphosat occurence in a fractured till. Unpublished paper.

Nilsson, B., Sidle, R. C., Klint, K. E., Bøggild, C. E., and Broholm, K. (2001). Mass transport and scale-dependent hydraulic tests in a heterogeneous glacial till-sandy aquifer system. J. Hydrol., 243(3-4):162–179. doi:10.1016/S0022-1694(00)00416-9.

Olesen, S. E. (2009). Kortlægning af potentielt dræningsbehov på landbrugsarealer opdelt efter landskabselementer, geologi, jordklasse, geologisk region samt høj/lavbund (in Dan- ish). DJF Internal Report No. 21, Faculty of Agricultural Sciences, University of Aarhus, Aarhus, Denmark. 31 p. Available at: web.agrsci.dk/djfpublikation/djfpdf/intrma21.pdf.

Oosterbaan, R. J. (1994). Agricultural drainage criteria. In Ritzema, H. P., editor, Drainage Principles and Applications. International Institute for Land Reclamation and Improve- ment, Wageningen, The Netherlands.

Oosterbaan, R. J. (2002). SaltMod. Description of principles, user manual and examples of application. Technical report, International Institute for Land Re- clmatation and Improvement, Wageningen, The Netherlands. 77 p. Available at: www.waterlog.info/pdf/saltmod.pdf.

Øygarden, L., Kværner, J., and Jenssen, P. D. (1997). Soil erosion via preferential ﬂow to drainage systems in clay soils. Geoderma, 76(1-2):65–86. doi:10.1016/S0016-7061(96)00099-7.

Payandeh, B. (1973). Analysis of a forest drainage experiment in northern Ontario. I. Growth analysis. Can. J. For. Res., 3(3):387–389. doi:10.1139/x73-057.

Purkey, D. R., Wallender, W. W., Fogg, G. E., and Sivakumar, B. (2004). Describing near surface, transient ﬂow processes in unconﬁned aquifers below irrigated lands: Model application in the Western San Joaquin Valley, California. J. Irrig. Drain Eng., 130(6):451–459. doi:10.1061/(ASCE)0733-9437(2004)130:6(451).

142 Rabalais, N. N., Turner, R. E., and Wiseman, W. J. (2001). Hypoxia in the Gulf of Mexico. J. Environ. Qual., 30(2):320–329. doi:10.2134/jeq2001.302320x.

Randall, G. W. and Goss, M. J. (2008). Nitrate losses to surface water through subsurface, tile drainage. In Hatﬁeld, J. L. and Follett, R. F., editors, Nitrogen in the environment: Sources, problems, and management, pages 145–175. Elsevier Academic Press, San Diego, CA, USA, Second edition. doi:10.1016/B978-0-12-374347-3.00006-8.

Rasmussen, E. S., Dybkjær, K., and Piasecki, S. (2010). Lithostratigraphy of the Upper Oligocene-Miocene succession of Denmark. Geol. Surv. Den. Greenl. Bull., 22:92. Available at: www.geus.dk/publications/bull/nr22/index-uk.htm.

Rasmussen, P. (1996). Monitoring shallow groundwater quality in agricultural watersheds in Denmark. Environ. Geol., 27(4):309–319. doi:10.1007/BF00766700.

Refsgaard, J. C. (1997). Parameterisation, calibration and validation of distributed hydrological models. J. Hydrol., 198(1-4):69–97. doi:10.1016/S0022-1694(96)03329-X.

Refsgaard, J. C., Auken, E., Bamberg, C. A., Christensen, B. S. B., Clausen, T., Dalgaard, E., Eﬀersø, F., Ernstsen, V., Gertz, F., Hansen, A. L., He, X., Jacobsen, B. H., Jensen, K. H., Jørgensen, F., Jørgensen, L. F., Koch, J., Nilsson, B., Petersen, C., De Schepper, G., Schamper, C., Sørensen, K. I., Therrien, R., Thirup, C., and Viezzoli, A. (2014). Nitrate reduction in geologically heterogeneous catchments: A framework for assessing the scale of predictive capability of hydrological models. Sci. Total Environ., 468/469:1278–1288. doi:10.1016/j.scitotenv.2013.07.042.

Refsgaard, J. C., Stisen, S., Højberg, A. L., Olsen, M., Henriksen, H. J., Børgesen, C. D., Vejen, F., Kern-Hansen, C., and Blicher-Mathiasen, G. (2011). Water balance in Denmark: Guide to quantiﬁcation of water balances based on hydrological data for the period 1990- 2010. Report 2011/77, Geological Survey of Denmark and Greenland (GEUS), Copenhagen, Denmark.

Refsgaard, J. C. and Storm, B. (1995). MIKE SHE. In Singh, V. P., editor, Computer Models of Watershed Hydrology, pages 806–846, Water Resource Publications, CO, USA.

Robinson, M. (1990). Impact of improved land drainage on river ﬂows. Report No. 113, Institute of Hydrology, Wallingford, Oxon, United Kingdom. 226 p. Available at: nora.nerc.ac.uk/id/eprint/7349.

Robinson, M. and Rycroft, D. W. (1999). The impact of drainage on streamﬂow. In Skaggs, R. W. and van Schilfgaarde, J., editors, Agricultural drainage, pages 767–800. American Society of Agronomy, Madison, WI, USA.

143 Rosenbom, A. E., Therrien, R., Refsgaard, J. C., Jensen, K. H., Ernsten, V., and Klint, K. E. (2009). Numerical analysis of water and solute transport in variably-saturated fractured clayey till. J. Contam. Hydrol., 104(1-4):137–152. doi:10.1016/j.jconhyd.2008.09.001.

Rothwell, R. L., Sillins, U., and Hillman, G. R. (1996). The eﬀect of drainage on sub- strate water content at several forested alberta peatlands. Can. J. For. Res., 26(1):53–62. doi:10.1139/x26-006.

Rozemeijer, J. C., van der Velde, Y., McLaren, R. G., van Geer, F. C., Broers, H. P., and Bierkens, M. F. P. (2010). Integrated modeling of groundwater-surface water interactions in a tile-drained agricultural ﬁeld: The importance of directly measured ﬂow route contributions. Water Resour. Res., 46(11):W11537. doi:10.1029/2010WR009155.

Rudy, H. (2004). Environmental impacts of agricultural drains. Technical report, Ontario Ministry of Agriculture and Food, Guelph, ON, Canada.

Schaap, M. G., Leij, F. J., and van Genuchten, M. T. (2001). ROSETTA: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol., 251(3-4):163–176. doi:10.1016/S0022-1694(01)00466-8.

Schack Pedersen, S. A. (2011). Geologisk kort over de overﬂadenære jordater (Jordartskort 1:200.000, Version 2) (in Danish). GEUS Rapport 2011/19, Geological Survey of Denmark and Greenland (GEUS), Copenhagen, Denmark.

Scharling, M. (1999). CLIMATEGRID - DENMARK: Precipitation, air temperature and potential evapotranspiration. Technical Report 99-12, Danish Meteorological Institute, Copenhagen, Denmark.

Schilling, K. E., Jindal, P., Basu, N. B., and Helmers, M. J. (2012). Impact of artiﬁcial subsurface drainage on groundwater travel times and baseﬂow discharge in an agricultural watershed, Iowa (USA). Hydrol. Process., 26(20):3092–3100. doi:10.1002/hyp.8337.

Schilling, K. E. and Libra, R. D. (2003). Increased baseﬂow in Iowa over the second half of the 20th Century. J. Am. Water Resour. Assoc., 39(4):851–860. doi:10.1111/j.1752-1688.2003.tb04410.x.

Schothorst, C. J. (1978). Het zakkingsproces bij ontwatering van de westelijke veenweide gronden (in Dutch). Landbouwkundig Tijdschrift, 6:167–175.

Sciuto, G. and Diekkrüger, B. (2010). Inﬂuence of soil heterogeneity and spatial discretization on catchment water balance modeling. Vadoze Zone J., 9(4):955–969. doi:10.2136/vzj2009.0166.

144 Sheler, R. J. (2013). The impact of agricultural drainage systems on hydrologic re- sponses. Master’s thesis, University of Iowa, Iowa City, IA, USA. Available at: ir.uiowa.edu/etd/2630.

Shewchuk, J. R. (1996). Triangle: Engineering a 2D quality mesh generator and Delaunay tri- angulator. In Selected papers from the Workshop on Applied Computational Geormetry, To- wards Geometric Engineering, pages 203–222, London, United Kingdom. Springer-Verlag. Available at: dl.acm.org/citation.cfm?id=645908.673287.

Simard, R. R., Cluis, D., Gangbazo, G., and Beauchemin, S. (1995). Phosphorous status of forest and agricultural soils from a watershed of high animal density. J. Environ. Qual., 24(5):1010–1017. doi:10.2134/jeq1995.00472425002400050033x.

Šimůnek, J., Jarvis, N. J., van Genuchten, M. T., and Gärdenäs, A. (2003). Review and comparison of models for describing non-equilibrium and preferential ﬂow and transport in the vadose zone. J. Hydrol., 272(1-4):14–35. doi:10.1016/s0022-1694(02)00252-4.

Šimůnek, J., van Genuchten, M. T., and Šejna, M. (2006). The HYDRUS software package for simulating two- and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Technical Manual, Version 1.0, PC Progress, Prague, Czech Republic. 213 p. Available at: www.pc-progress.com/en/Default.aspx?Downloads.

Skaggs, R. W. (1978). A water management model for shallow water table soils. Technical Re- port No. 134, Water Resources Research Institute, NC State University, Raleigh, NC, USA. Available at: repository.lib.ncsu.edu/dr/bitstream/1840.4/1618/1/NC-WRRI-134.pdf.

Skaggs, R. W., Brevé, M. A., and Gilliam, J. W. (1994). Hydrologic and water quality impacts of agricultural drainage. Crit. Rev. Env. Sci. Tec., 24(1):1–32. doi:10.1080/10643389409388459.

Stenberg, M., Ulén, B., Söderström, M., Roland, B., Delin, K., and Helander, C. A. (2012). Tile drain losses of nitrogen and phosphorus from ﬁelds under integrated and organic crop rotations. A four-year study on a clay soil in southwest Sweden. Sci. Total Environ., 434:79–89. doi:10.1016/j.scitotenv.2011.12.039.

Stisen, S., Højberg, A. L., Troldborg, L., Refsgaard, J. C., Christensen, B. S. B., Olsen, M., and Henriksen, H. J. (2012). On the importance of appropriate precipitation gauge catch correction for hydrological modelling at mid to high latitudes. Hydrol. Earth Syst. Sci., 16:4157–4176. doi:10.5194/hess-16-4157-2012.

Stormont, J. C. and Zhou, S. (2005). Impact of unsaturated ﬂow on pavement edgedrain performance. J. Transp. Eng., 131(1):46–53. doi:10.1061/(ASCE)0733-947X(2005)131:1(46).

145 Stratton, G. W., Madani, A., Gordon, R. J., Sharples, K., Coulter, T., and Thiagarajan, A. (2004). Bacterial quality of surface and subsurface drainage water from manured ﬁelds. T. ASABE, (701P0304):197–205. doi:10.13031/2013.15725.

Suzuki, T. (2001). Oxygen-deﬁcient waters along the Japanese coast and their eﬀects upon the estuarine ecosystem. J. Environ. Qual., 30(2):291–302. doi:10.2134/jeq2001.302291x.

Tedeschi, A., Beltrán, A., and Araguésa, R. (2001). Irrigation management and hydrosalinity balance in a semi-arid area of the middle Ebro River Basin (Spain). Agr. Water Manage., 49(1):31–50. doi:10.1016/S0378-3774(00)00117-7.

Therrien, P. (2012). 3D mesh generation and reﬁnement as a function of the topographic slope: A step by step tutorial. Technical report, Department of Geology and Geological Engineering, Université Laval, Quebec City, QC, Canada. 55 p.

Therrien, R., McLaren, R. G., Sudicky, E. A., and Park, Y.-J. (2010). HydroGeo- Sphere: A three-dimensional numerical model describing fully-integrated subsurface and surface ﬂow and solute transport. Groundwater Simulations Group. 453 p. Available at: www.ggl.ulaval.ca/ﬁleadmin/ggl/documents/rtherrien/hydrogeosphere.pdf.

Therrien, R. and Sudicky, E. A. (1996). Three-dimensional analysis of variably-saturated ﬂow and solute transport in discretely-fractured porous media. J. Contam. Hydrol., 23(1-2):1– 44. doi:10.1016/0169-7722(95)00088-7.

Tian, F., Hu, H., and Lei, Z. (2008). Thermodynamic watershed hydrological model (THModel): Constitutive relationship. Sci. China, Ser. E: Tech. Sci., 51(9):1353–1369. doi:10.1007/s11431-008-0147-0.

Tian, F., Hu, H., Lei, Z., and Sivapalan, M. (2006). Extension of the Representative Elemen- tary Watershed approach for cold regions via explicit treatment of energy related processes. Hydrol. Earth Syst. Sci., 10(5):619–644. doi:10.5194/hess-10-619-2006.

Tiemeyer, B., Moussa, R., Lennartz, B., and Voltz, M. (2007). MHYDAS-DRAIN: A spatially distributed model for small, artiﬁcially drained lowland catchments. Ecol. Model., 209(1):2– 20. doi:10.1016/j.ecolmodel.2007.07.003.

Tim, U. S. (1996). Coupling vadose zone models with GIS: Emerging trends and potential bot- tlenecks. J. Environ. Qual., 25(3):535–544. doi:10.2134/jeq1996.00472425002500030019x.

Turtola, E., Alakukku, L., and Uusitalo, R. (2007). Surface runoff, subsurface drainflow and soil erosion as affected by tillage in a clayey Finnish soil. Agric. Food Sci., 16(4):332–351.

U.S. Department of Agriculture (1972). National Engineering Handbook. USDA Soil Conservation Service, Washington D.C., USA. Available at: www.nrcs.usda.gov/wps/portal/nrcs/detailfull/national/water/?cid=stelprdb1043063.

146 Uusitalo, R., Turtolaa, E., Kauppilab, T., and Liljaa, T. (2001). Particulate phosphorus and sediment in surface runoff and drainflow from clayey soils. J. Environ. Qual., 30(2):589–595. doi:10.2134/jeq2001.302589x. van Beers, W. F. J. (1976). Computing drain spacing. Bull. No. 15, International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands. 47 p. van der Velde, Y., Rozemeijer, J. C., De Rooij, G. H., Van Geer, F. C., and Broers, H. P. (2010). Field scale measurements for separation of catchment discharge into flow route contributions. Vadose Zone J., 9(1):25–35. doi:10.2136/vzj2008.0141. van Genuchten, M. T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil. Sci. Soc. Am., 44(5):892–898. doi:10.2136/sssaj1980.03615995004400050002x. van Schilfgaarde, J. (1963). Design of tile drainage for falling water tables. J. Irrig. and Drain. Div., 89(2):1–12.

Vázquez, R. F., Feyen, L., Feyen, J., and Refsgaard, J. C. (2002). Eﬀect of grid size on eﬀective parameters and model performance of the MIKE-SHE code. Hydrol. Process., 16(2):355–372. doi:10.1002/hyp.334.

Voss, C. I. and Provost, A. M. (2010). SUTRA, A model for saturated-unsaturated variable- density ground-water ﬂow with solute or energy transport. Water-resources investigations report 02-4231, U.S. Geological Survey, Reston, VA, USA. 291 p.

Vrugt, J. A., Schoups, G., Hopmans, J. W., Young, C., Wallender, W. W., Harter, T., and Bouten, W. (2004). Inverse modeling of large-scale spatially distributed vadose zone properties using global optimization. Water Resour. Res., 40(6):W06503. doi:10.1029/2003WR002706.

Warld, A. D., Alexander, C. A., Fausey, N. R., and Dorsey, J. D. (1988). The ADAPT agricultural drainage and pesticide transport model. In Modeling Agricultural, Forest and Rangeland Hydrology: Proceedings of the 1988 International Symposium, pages 129–141, American Society of Agricultural Engineers, St. Joseph, MI, USA.

Warsta, L. (2011). Modelling water flow and soil erosion in clayey, subsurface drained agricultural fields. PhD thesis, Department of Civil and Environmental Engineering, Aalto University, Espoo, Finland. Available at: lib.tkk.fi/Diss/2011/isbn9789526042893/.

Warsta, L., Karvonen, T., Koivusalo, H., Paasonen-Kivekäs, M., and Taskinen, A. (2013). Simulation of water balance in a clayey, subsurface drained agricultural ﬁeld with three- dimensional FLUSH model. J. Hydrol., 476:395–409. doi:10.1016/j.jhydrol.2012.10.053.

147 Whiteley, H. R. and Ghate, S. R. (1979). Sources and amounts of overland runoﬀ from rain on three small Ontario agricultural watersheds. Can. Agr. Eng., 21(1):1–8.

Williams, G. S. and Hazen, A. (1905). Hydraulic tables: Showing the loss of head due to the friction of water ﬂowing in pipes, aqueducts, sewers, etc. and the discharge over weirs. John Wiley and Sons, New York, NY, USA, ﬁrst edition. 96 p.

Williams, M. R., King, K. W., and Fausey, N. R. (2015). Contribution of tile drains to basin discharge and nitrogen export in a headwater agricultural watershed. Agric. Water Manage., 158:42–50. doi:10.1016/j.agwat.2015.04.009.

Windgassen, H. (2006). Municipal water metering - The electromagnetic solution. World Pumps, 483:26–29. doi:10.1016/S0262-1762(06)71176-2.

Wiskow, E. and van der Ploeg, R. R. (2003). Calculation of drain spacings for optimal rainstorm ﬂood control. J. Hydrol., 272(1-4):163–174. doi:10.1016/S0022-1694(02)00262-7.

Yates, S. R., van Genuchten, M. T., Leij, F. J., and Warrick, W. (1992). Analysis of measured, predicted, and estimated hydraulic conductivity using the retc computer program. Soil Sci. Soc. Am. J., 56(2):347–354. doi:10.2136/sssaj1992.03615995005600020003x.

Youssef, M. A., Skaggs, R. W., Chescheir, G. M., and Gilliam, J. W. (2005). Field evaluation of a model for predicting nitrogen losses from drained lands. J. Environ. Qual., 35(6):2026– 2042. doi:10.2134/jeq2005.0249.

Yue, F. (2010). Fully-coupled physically-based approach for modeling conventional and man- aged subsurface drainage. PhD thesis, University of Illinois at Urbana-Champaign, Cham- paign, IL, USA. Available at: hdl.handle.net/2142/16124.

Zucker, L. A. and Brown, L. C. (1998). Agricultural drainage: Water quality impacts and subsurface drainage studies in the Midwest. Ohio State University Extension Bulletin No. 871, Ohio State University, Columbus, OH, USA. Available at: ohioline.osu.edu/b871.

148