Coupled Cryo-Hydrogeological Modelling of Permafrost Dynamics at Umiujaq, Quebec, Canada

Coupled cryo-hydrogeological modelling of permafrost dynamics at Umiujaq, Quebec, Canada

Mémoire

Sophie Dagenais

Maîtrise interuniversitaire en sciences de la Terre - avec mémoire Maître ès sciences (M. Sc.)

Québec, Canada

Coupled Cryo-hydrogeological Modelling of Permafrost Dynamics at Umiujaq, Québec, Canada

Mémoire

Sophie Dagenais

Sous la direction de:

John Molson, directeur de recherche Jean-Michel Lemieux, codirecteur de recherche

Résumé

Un modèle numérique bidimensionnel a été développé afin d’évaluer l’impact de l’écoulement d’eau souterraine sur la dynamique du pergélisol dans un contexte de réchauffement climatique au Québec nordique. Le modèle conceptuel développé concerne une butte de pergélisol située dans la zone de pergélisol discontinu à proximité de la communauté Inuite d’Umiujaq, Nunavik, Québec. Le pergélisol s’est mis en place dans une unité gélive de silts marins qui se trouve au- dessus de deux unités de sédiments grossiers de sable et de gravier d’origine fluvio-glaciaire et glaciaire qui forment un aquifère confiné par l’unité de silts et le pergélisol où il y a un écoulement d’eau souterraine. Le code numérique HEATFLOW a été utilisé pour simuler l’écoulement d’eau souterraine couplé à la transmission de chaleur par conduction et advection le long d’une coupe 2D orientée dans la direction de l’écoulement de l’eau souterraine au droit de la butte de pergélisol étudiée. En premier lieu, le modèle a été étalonné manuellement à partir de profils de température mesurés dans la butte au cours des 10 dernières années à l’aide de câbles à thermistances et en tenant compte des flux de chaleur mesurés près de la surface du sol. En second lieu, une deuxième simulation a été réalisée en ne considérant que la transmission de chaleur par conduction et en négligeant ainsi l’écoulement d’eau souterraine. La comparaison entre ces deux simulations révèle le rôle important de l’écoulement d’eau souterraine sur la dynamique du pergélisol à Umiujaq. En effet, cet écoulement transporte l’eau plus chaude des zones de recharge vers l’aquifère confiné, ce qui contribue à réchauffer significativement le système en comparaison avec le cas sans écoulement. Une couche de pergélisol beaucoup plus mince est simulée lorsque l’écoulement d’eau souterraine est considéré dans la modélisation numérique. En outre, selon les résultats des simulations, l’énergie se dissipe le long de la ligne d’écoulement d’eau souterraine sous la base du pergélisol ce qui réduit sensiblement les températures du sol et de surface à proximité des zones de résurgence de l’eau souterraine le long d’un ruisseau en comparaison avec les zones de recharge. Finalement, en troisième lieu, le comportement futur du système simulé sous l’effet des changements climatiques est ensuite prédit en générant un scénario de réchauffement climatique selon une augmentation constante de la température de l’air et des précipitations. Les résultats des simulations suggèrent une dégradation du pergélisol par la base à un taux de 80 cm par année, et par le toit à un taux de 12 cm par année, jusqu’à la disparition complète du pergélisol dans le site d’étude d’ici 2040.

iii

Abstract

A 2D numerical model has been developed to assess the impacts of groundwater flow on permafrost dynamics under a warming climate in northern Québec. The conceptual model developed herein focuses on a small permafrost mound located in the discontinuous permafrost zone near the Inuit community of Umiujaq, Nunavik, Québec. At the study site, permafrost is found in marine silt overlying a deep confined sand and gravel aquifer with active groundwater flow. To better understand the cryo-hydrogeological system, the HEATFLOW numerical code was used to simulate coupled groundwater flow and heat transport by conduction and advection along a 2D cross-section through the permafrost mound and oriented along the assumed direction of groundwater flow. The model was first calibrated manually using temperature profiles in the permafrost mound measured along thermistor cables over the past 10 years and using observed heat fluxes near the ground surface. A second simulation was then performed assuming only conductive heat transfer and neglecting groundwater flow. A comparison between both simulations reveals the important role of groundwater flow on permafrost dynamics at the Umiujaq site. As groundwater flow brings warmer water from recharge areas into the deep confined aquifer, it contributes significantly to warming of the system relative to conduction alone, and significantly decreases permafrost thickness. However, the simulation showed that thermal energy is also lost along the flowpath below the permafrost base which induces a cooling in the discharge areas in comparison to the recharge areas. The future system behavior is then predicted by taking into account a climate change scenario based on increases in temperature and precipitation. The predictive simulation suggests that permafrost will thaw from the base at a rate of about 80 cm per year, and from the permafrost table at a rate of 12 cm per year, until completely thawed by about 2040.

Contents Résumé ...... iii

Abstract ...... iv

List of tables...... vii

List of figures ...... viii

Acknowledgments ...... xi

Avant-Propos ...... xiii

1 Introduction ...... 2

1.1 General context ...... 2

1.1.1 Review of current literature ...... 2 1.1.2 Motivation and Objectives ...... 5 1.1.3 Thesis structure ...... 6 1.2 Study site ...... 7

1.2.1 Location ...... 7 1.2.2 Geology and hydrogeology ...... 7 1.2.3 Climate ...... 10 1.3 Methodology ...... 10

1.3.1 Data ...... 10 1.3.2 Conceptual model ...... 22 2 Numerical model (Taken from Dagenais et al., 2018) ...... 29

Résumé ...... 30

Abstract ...... 31

2.1 Introduction ...... 32

2.2 Study site ...... 34

2.3 Meteorological and cryo-hydrogeological conditions ...... 36

2.3.1 Meteorological data ...... 36 2.3.2 Field instrumentation and data ...... 37 2.3.3 Hydrogeological data ...... 40 2.4 Numerical Model ...... 40

2.4.1 Theoretical approach ...... 40 2.4.2 Modelling strategy ...... 42 2.5 Conceptual and numerical site model ...... 42

2.5.1 Physical system ...... 42 2.5.2 Boundary conditions ...... 45 2.5.3 Initial conditions ...... 47 2.6 Numerical Simulations...... 48

2.6.1 Model Calibration ...... 48 2.6.2 Sensitivity analysis: Conductive heat transport ...... 55 2.6.3 Predicted permafrost thaw under future climate change...... 58 2.7 Conclusions ...... 60

3 General Conclusions ...... 62

Bibliography ...... 66

Appendix A: Coupled cryo-hydrogeological modelling of permafrost degradation at Umiujaq, Quebec Canada (Taken from Dagenais et al., 2017) ...... 72

Appendix B: Literature review ...... 81

Appendix C: Instrumentation and vegetation of the Tasiapik valley watershed ...... 84

Appendix D: Hydraulic conductivities measured in the Tasiapik valley ...... 85

List of tables

Table 1.1: Darcy fluxes assessed from hydraulic gradients and the FVPDM method for Sites 2, 5, and 3. 13

Table 1.2: Thermal conductivities measured with the thermal needle probe, water content and porosity of three soil samples. 15

Table 1.3: Assumed recharge rates according to the vegetation type and temperature difference between recharge water (Tq) and air temperature (Tair). 28

Table 2.1: Site instrumentation and measured variables. 38

Table 2.2: Physical and thermal properties of the different layers of the model (see Figure 2.1 and Figure 2.4 for layer stratigraphy). 43

Table 2.3: Assumed parameter values for the Umiujaq model. 44

Table 2.4: Heat exchange layer parameters according to topography and vegetation type. Topography symbols represent local high or local low topography along the cross-section from left to right. 47

vii

List of figures

Figure 1.1: Umiujaq site location on Hudson Bay and permafrost distribution in Nunavik, Quebec, Canada (adapted from Allard and Lemay 2012). Interpolated depth of the 0°C isotherm is from Lemieux et al. (2008). 8

Figure 1.2: Tasiapik valley watershed, location of groundwater wells from the Immatsiak network and location of the cross-sections A-A’ (well axis) and B-B’ (numerical model). The background image is from Google Earth 2018. 8

Figure 1.3: Cryo-hydrostratigraphic interpretative cross-section along the Tasiapik valley watershed (adapted from Fortier et. al. 2014). Note the horizontal scale of 1:10,000 and vertical exaggeration of 1:10. 9

Figure 1.4: Tasiapik valley watershed, permafrost mound and location of the instruments on the mound. Data from instruments that have been faded out on the mound picture are not presented in the current document. 11

Figure 1.5: Hydraulic heads in the groundwater wells at Site 3 and Site 5, from 2012 to 2017 (from the Solinst probes and manual measurements), and monthly precipitation measured at the SILA station. 12

Figure 1.6: Monthly recharge measured by Murray (2016) at Site 2 for the year 2014- 2015, for ground surfaces dominated by shrubs, spruce and lichen. 13

Figure 1.7: Subsurface temperatures measured using thermistor cables from 2002 to 2017 for the mid-winter period (January, February, March) in the left graphs and for the mid-summer period (July, August, September) in the right graphs, averaged over two years, located a) at the edge of the mound, and b) at the center of the mound (see locations in Figure 1.4). 16

Figure 1.8: Unfrozen water content and temperature in the unsaturated zone in summer and winter 2015 and 2017 from the moisture content and temperature monitoring arrays with a) and b) Water content and c) and d) Temperature, at the side of the mound (left column) and at the center of the mound (right column). 17

Figure 1.9: Water content as a function of time (2014 – 2017) from the moisture and temperature probes at 0.1 m and 1 m depths, at a) the center of the mound, and b) the side of the mound. 19

Figure 1.10: Photos of the permafrost mound from the Reconyx camera, and location of the snow poles a) in July 2017, and b) in February 2017. 20

Figure 1.11: Snowpack thickness on the permafrost mound in 2014-2015 for the snow poles identified in Figure 1.10. 20

viii

Figure 1.12: Heat flux measured at the center and the side of the mound at 8 cm depth from 2014 to 2015. 21

Figure 1.13: Temperatures at 10 cm depth from the HOBO temperature probes located at the center and beside the mound between 2014 and 2017 22

Figure 1.14: Conceptualized flow system along the cross-section B-B’ (Figure 1.2). 23

Figure 1.15: Watertable heads along the cuesta flowline calculated from the Dupuit equation 24

Figure 1.16: Input parameters of the heat transfer layer shown for the mid-summer and mid-winter periods with a) layer thickness and zone delimitation and b) heat flux and recharge rates in mm/year 25

Figure 1.17: Mean annual air temperatures recorded at Kuujjuarapik and Kuujjuaq and estimated temperatures at Umiujaq. The solid lines represent a 5-year moving average to reduce the variability and highlight the trends while the dots represent the mean annual air temperatures. The grey zones represent the warming periods. 27

Figure 2.1: Location of Umiujaq along the eastern coast of Hudson Bay and permafrost distribution in Nunavik, Québec, Canada (adapted from Allard and Lemay 2012). Interpolated depth of the 0°C isotherm is from Lemieux et al. (2008). 35

Figure 2.2: Tasiapik Valley watershed and 2D cryo-hydrogeologic model cross-section 35

Figure 2.3: Mean annual air temperatures (MAATs) at Kujjuarapik, Kujjuaq and Umiujaq, according to available data since 1926. The thick solid lines correspond to the five-year running average for each data set. The grey zones represent warming periods before and after a cooling period from 1950 to 1993. 37

Figure 2.4: a) Instrumentation of the permafrost mound (not to scale). b) Observed temperatures from the central thermistor cable (cable B) over time and MAATs from the Umiujaq-A station. The dashed lines are the interpolated depth of the permafrost table and extrapolated depth of the permafrost base. 39

Figure 2.5: Temperature-dependent functions assumed in the model for unfrozen water saturation (Wu) and relative permeability (kr). For simplicity, the kr function is shown only for a porosity of 0.35 (coarse sand). 45

Figure 2.6: Conceptualization of the 2D cryo-hydrogeological model showing a) groundwater flow boundary conditions and the intrinsic hydraulic conductivity distribution (unfrozen state; hydraulic conductivities vary with temperature; see Figure 2.5 for kr), and b) heat transport boundary conditions and initial temperature conditions assumed in the model. 45

Figure 2.7: Field data (solid colored lines) and simulation results (dashed lines) at the side (left column) and at the center of the permafrost mound (right column), showing: a) Subsurface temperatures measured in the field (thermistor cables A on left and B on right; see Figure 2.4a for location) averaged on a four-year basis for the mid-summer period (July, August, September) and model results averaged for the same mid-summer period from 2014-2017, b) Unfrozen water content (m3/m3) at a depth of 0.1 m, c) Ground temperatures at a depth of 0.1 m, and d) Heat flux at a depth of 0.08 m. 50

Figure 2.8: Simulated flow field at year 2017 from the calibrated model (Scenario 1) with coupled groundwater flow and heat transport: a) Hydraulic heads and streamtraces, b) Velocity magnitudes. 52

Figure 2.9: Simulated ground temperatures (in mid-summers of 1950, 1993, and 2017) as a function of depth and distance for: a) Scenario 1 with coupled groundwater flow and advective-conductive heat transport (the calibrated model), and b) Scenario 2 taking into account heat transfer by conduction without groundwater flow. The lower three figures are magnified to focus on the permafrost mound located from 300 to 350 m. The 0 °C isotherm is identified for comparison purposes. 53

Figure 2.10: Simulated ground temperatures in the central permafrost mound (at 337.5 m; see Profile B in Figure 2.4a and Figure 2.7b) as a function of depth and time: a) Scenario 1 with groundwater flow and advective-conductive heat transport, and b) Scenario 2 with thermal conduction only. 55

Figure 2.11: Simulated temperature distribution in mid-summer from 2017-2040 under the predictive climate change scenario and including groundwater flow. The simulation begins in 2017 with the calibrated advective-conductive heat transfer model. 59

Acknowledgments

I would like to express my sincere gratitude to all those persons and organizations involved in my research project for their support:

 John Molson, my supervisor, for all technical and moral support during the project. I would like to thank him particularly for his remarkable availability and his receptiveness to all my ideas and initiatives. I appreciated his way of seeing always more solutions than problems, giving me back the necessary motivation in critical stages of the project. I would also like to thank him for providing me the amazing opportunity to present my work in Paris to the Interfrost benchmark meeting. More than all, John has put his trust in me from the beginning and allowed me to work in the most optimal conditions, almost making the other students jealous!

 Jean-Michel Lemieux, my co-director, for his valuable advice and guidance throughout the whole process. I thank him for offering me a stimulating research environment, by questioning my work and always providing new motivating challenges. I’ve gained a lot of experience and valuable knowledge from him, both in the field and in research, and in the academic world.

 Richard Fortier, for his notable experience and rigor, which helped this project (and myself) to stay on the right track. His passion for geophysics and devotion for the Umiujaq project were truly inspiring and motivated me to give my best at every stage of the process. Throughout his thorough reviews and detailed comments, Richard pushed me to deliver high quality material and taught me the importance to always make my work «bullet proof ».

 René Therrien, for all the effort he put into the Umiujaq project and for reviewing my papers when needed. I’m also grateful to him for having so many international connections, which gave me the opportunity to connect with students from all over the globe and put life in our office.  The local Inuit community, especially the members including the president Ernest Tumic of the Anniturvik landholding corporation of Umiujaq, for giving us access to their land during the field experiments, and to the members of Park Tursujuk for their cooperation.

 Pierre Therrien for all the technical support he provided, his availability and ability to resolve all my technical problems with a touch of humor. He taught me that not only permafrost can be «Deep Freezed».  Jasmin Raymond for accepting to review this thesis, and for providing me access to the K2D pro thermal conductivity needle probe. A special thanks to his student Maria Isabelle for supervising me during the experiments at INRS-ETE.  All my field partners: Renaud Murray, for meticulously transferring his knowledge about the instruments and the study site, Marion Cochand for her great company in the bushes with the mosquitos, Pierre Jamin for his constant cheerfulness and creativity during those long days spent on the permafrost mound and Marie-Catherine Talbot Poulin for her involvement in the campaign logistics.  My office colleagues: Vinicius for making the working climate more enjoyable and for keeping alive all our plants, Jonathan Fortin for putting at our disposal a coffee machine and popcorn machine, Masoumeh Parkhizar for the great discussions we had between simulations.  Other students involved in the project, including Philippe Fortier for the detailed analysis of the snow pole photos to extract snow depth data, Britt Albers for the work in progress using my model and the general interest put into my project.

My project was financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), through a CGS M scholarship, through a Strategic Grant in partnership with the Ministère du Développement Durable, de l’Environnement et la Lutte contre les Changements Climatiques (MDDELCC) of Québec, and through a Discovery Grant to Dr. J. Molson. The northern scientific training program (NSTP) also financed part of the costs for my field work at Umiujaq in 2016 and 2017. The financial and logistical support of the Centre d’études nordiques, Université Laval, and especially its Director Dr. Najat Bhiry, is also greatly appreciated.

xii

Avant-Propos

This Master’s thesis includes 3 chapters. Chapter 2 of this Master’s thesis is a manuscript in the process of submission to Hydrogeology Journal of which I am the first and principal author. Since the paper content might be modified or updated during the submission process, referring to the final published version is thus recommended. My research project director Dr. John Molson and co-director Dr. Jean-Michel Lemieux are co-authors of this paper, as are professors Dr. Richard Fortier and Dr. René Therrien. I wrote the entire first draft of the paper and made all corrections and improvements in subsequent drafts. I also developed the numerical site model of coupled groundwater flow and heat transfer in a permafrost environment, which is the main subject of the study. Most of the data used for my research was collected at the study site near Umiujaq, Nunavik, during field campaigns in the summers of 2014-2017. With help from others, I collected data myself on the site during the summers of 2016 and 2017. Dr. Richard Fortier was the main investigator and organiser of these field campaigns with the help of Dr. Jean-Michel Lemieux. Dr. John Molson provided valuable support throughout the research period and was the principal reviewer of the paper and thesis. As co-authors, Dr. Jean-Michel Lemieux, Dr. Richard Fortier and Dr. René Therrien also reviewed the manuscript and provided valuable feedback. A paper presented at the 2017 Canadian Geotechnical Society-IAH conference in Ottawa (Dagenais et al., 2017) is included in Appendix A.

xiii

1 Introduction

In the context of the Quebec Government’s Climate Change Action Plan (2006-2012), the Ministère du Développement Durable, de l’Environnement et de la Lutte contre les Changements Climatiques (MDDELCC) of Québec has developed a Groundwater Monitoring Network (RSESQ) to investigate the impact of climate change on groundwater resources. As part of this initiative, a group of researchers from Université Laval in partnership with the Centre d’études nordiques (CEN) has been mandated to develop and maintain a sub-network of the RSESQ in northern Quebec where climate change impacts are occurring at a faster rate than in the south. A portion of this network, called Immatsiak, was implemented in 2012 near the Inuit village of Umiujaq along the east shore of Hudson Bay. Following the deployment of the Immatsiak network, researchers from Université Laval received a Strategic Grant in 2013 from the Natural Sciences and Engineering Research Council of Canada (NSERC) to further investigate the impacts of climate change on groundwater in the north. The main hypothesis of this major research project is that the water released from permafrost thaw, and subsequent increased aquifer recharge, could lead to a new resource of drinking water for northern communities and growing industries in the north, as groundwater is generally safer and more sustainable than surface water from rivers and lakes. The main research goal is to evaluate the present and future impacts of climate change on the groundwater system near Umiujaq and assess the potential of using groundwater as a new reliable resource of drinking water. The present thesis contributes to this broader project and through numerical modelling provides insights into the interaction between groundwater flow and permafrost dynamics.

1.1 General context

1.1.1 Review of current literature

Permafrost covers more than half of Canada’s territory, with depths varying from a few meters to a kilometer in the most northern areas (Zhang et. al., 2006). Considering the recent trend of global warming as observed at high latitudes, permafrost is currently degrading (Intergovernmental Panel on Climate Change IPCC, 2013), particularly in zones where permafrost is thinner and where ground temperatures are closer to 0 degrees (Sjöberg et al., 2015). Permafrost degradation can significantly modify hydrological, thermal and ecosystem dynamics at local and regional scales in northern regions. Considering observed permafrost thaw over the last few decades and its related impacts, there has

been a renewed interest in cryo-hydrogeological modelling. Until recently, permafrost degradation has been attributed to vertical conduction-dominated heat transfer, where ground temperatures are assumed to be controlled by surface temperature variations and the geothermal gradient. Active groundwater flow, however, can induce heat transfer by advection which can significantly modify the thermal regime in an otherwise conduction-dominated system (Kurylyk et al, 2014a).

Recent developments in coupled groundwater flow and heat transport models have allowed assessment of the role of groundwater flow in permafrost dynamics. Moreover, new insights have been gained into the potential impacts on sub-permafrost thaw in areas of high groundwater flow rates (Kurylyk et al., 2016). However, most recent cryo-hydrogeological studies have mainly focussed on changes in active layer thickness, groundwater discharge and on the general hydrogeological regime (Evans and Ge, 2017; Painter et al., 2016; Atchley et al., 2016; Frederick and Buffet, 2015; Jiang et al., 2012). Only a few studies have assessed the impact of sub-permafrost groundwater flow on permafrost thaw and even fewer have revealed the relative importance of advective heating relative to conduction alone. The most recent studies are briefly reviewed herein while a broader inventory is provided in Appendix B.

Rowland et al. (2011) studied the effect of groundwater flow through a high permeability gravel aquifer on sub-lake talik development using the 2D ARCHY model for coupled groundwater flow and heat transport. They found that it takes about 40% less time for permafrost to thaw under advective/conductive heat transfer versus conduction alone.

Mackenzie and Voss (2013) used the SUTRA-ICE model to investigate the contribution of groundwater flow on permafrost dynamics in an idealized continuous permafrost environment. According to their simulation results, advective heat flux accelerates thaw from both the permafrost table and base by a factor of 3 compared to conduction alone. They suggested that permafrost degradation contributes to enhancing groundwater flow, which acts as a positive feedback for further permafrost thaw. Thawing is more significant closer to recharge zones, and the contribution of advective heat transport decreases as groundwater cools along the flowpath towards discharge areas.

Wellman et al. (2013) used the SUTRA-ICE model to simulate sub-lake talik development at a hypothetical site of thick discontinuous permafrost overlying permeable sediments (K≈510-3 to 510-

4 m/s). They found that once an open talik develops, sub-lake groundwater flow increases significantly, enhancing the permafrost thaw rate due to advection and contributing to lateral expansion of the talik. Taliks were estimated to develop more than twice as fast with groundwater flow recharging or discharging through the lake.

Sjoberg et al. (2016) employed the Artic Terrestrial Simulator (ATS) model to understand the importance of groundwater flow on permafrost dynamics in sporadic permafrost environments, using data from a subarctic fen in northern Sweden. They found that permafrost thaw was strongly influenced by lateral groundwater flow in the peat and sand units (K≈510-3 to 510-5 m/s), especially during spring when hydraulic gradients were higher due to snowmelt and thawing of the active layer.

Luethi et al. (2016) investigated the role of non-conductive heat flux on intra-permafrost talik formation at the Ritigraben rock glacier in the Swiss Alps. Using a 1D snowpack model, they found that a contribution of advective heating by infiltrating water from snowmelt and rainfall, simulated as a heat source, was needed to reproduce observed talik formation at their field site.

On the other hand, a few studies have led to the conclusion that in some cases the contribution of groundwater flow to permafrost thaw is not significant. For instance, Bense et al. (2012) used the 2D numerical finite-element model FLEXPDE to simulate long-term permafrost degradation in an idealized sedimentary basin (K≈ 810-7 to 810-9 m/s) under a warming climate, in which groundwater flow is driven by topography. They found that advective heat flux induced by groundwater circulation did not contribute to accelerate permafrost degradation, unless extremely high and unrealistic flow rates were considered.

Kurylyk et al. (2016) used SUTRA to investigate the impact of groundwater flow on multi-decadal lateral permafrost thaw in a peat-wetland complex in the Northwest Territories, Canada. Surface processes modeled in 1D with NEST were applied as the upper boundary condition of the 3D coupled subsurface flow and heat transport model. At this site, groundwater flow occurred in a layer of silty clay (K=110-10 m/s) beside and below permafrost units which were overlaid by a 3 m thick organic layer. They concluded that this low-permeability silt-clay unit impedes groundwater flow thus limiting its contribution to permafrost thaw.

However, Bense et al.(2012) and Kurylik et al. (2016) have suggested that the contribution of heat advection could be important in regions where recharge is not limited to rainfall, where groundwater flow is strongly focussed (high gradients and/or soil permeability) or where geothermal heat flow anomalies occur. The effect of advective heat transfer could be even more important in discontinuous or sporadic permafrost areas since these environments are particularly vulnerable to climate warming, and where the sporadic permafrost is warmer and thinner than continuous permafrost (McClymont et al., 2013; Sjöberg et al., 2015; Kurylyk et al., 2016).

In addition to thermal conduction, when groundwater flow is significant, the energy required for permafrost thaw comes either from warm recharge water or deep geothermally warmed water (Mackenzie and Voss, 2013). Thus, groundwater flow can have an even greater impact on permafrost evolution close to recharge areas where relatively warm water is flowing from the surface towards permafrost units (Mackenzie and Voss, 2013).

1.1.2 Motivation and Objectives

Recent studies have revealed the potential contribution of groundwater flow to permafrost thaw due to transfer of heat by advection. Considering the current trend in climate warming, including faster thaw rates in northern areas, release of meltwater from permafrost bodies will also enhance groundwater flow, acting as a positive feedback to permafrost degradation. Understanding the role of groundwater flow in permafrost dynamics is thus crucial to help predict thaw rates and future behavior of permafrost under a warming climate.

Despite the recent advances in cryo-hydrogeological modelling, there is still a need to improve current models. In particular, most research to date has been focussed on the impacts of groundwater flow in the active layer, while new questions have arisen regarding potential impacts of groundwater flow on sub-permafrost thaw in areas with high groundwater flow. Also, most studies have been based on idealized field conditions that may not accurately represent local thermal and hydrogeological conditions and properties. The importance of integrating site-specific surface and subsurface thermal and hydrological properties for modelling the thermal regime of shallow and deep permafrost under a warming climate has been identified by Rasmussen (2018). Sites located in the discontinuous and sporadic permafrost zones are of particular interest because they are more vulnerable to increases in

air temperatures. Another limitation of current studies concerns the integration of surface processes into models of the subsurface thermal regime. Indeed, there is a need for models to more rigorously account for surface insulation due to snow cover and vegetation patterns (Mackenzie and Voss 2013; Kurylyk et al. 2014a; Atchley et al., 2016).

Therefore, the main objective of this project is to better understand the importance of groundwater flow on permafrost degradation by developing a numerical model of fully coupled groundwater flow and heat transfer by conduction and advection. This new insight will be based on field observations of an ice-rich permafrost mound near the Inuit community of Umiujaq, in northern Quebec, Canada. More specifically, this study focuses on permafrost dynamics at the scale of a single permafrost mound located in the discontinuous permafrost zone.

The secondary objectives of this study include: 1. Investigating the role of groundwater flow on permafrost thaw from both the permafrost table and base. 2. Integrating thermal and hydrological data and field observations to increase the accuracy of permafrost degradation predictions. 3. Improving the coupling of surface processes (snow, vegetation, air/ground heat transfer) with the subsurface regime.

1.1.3 Thesis structure

The following part of Chapter 1 describes the study site and presents details concerning the methodology, including a description of the relevant field data and their integration into the model. The second chapter takes the form of a manuscript from Dagenais et al. to be submitted to Hydrogeology Journal:

Dagenais S, Molson J, Lemieux J-M, Fortier R, Therrien R. (2018). Coupled cryo- hydrogeological modelling of permafrost dynamics at Umiujaq, Quebec, Canada, In submission: Hydrogeology Journal.

In Chapter 2, the numerical model is described in detail and the main results and conclusions are provided. The results are based on three different scenarios. The first (calibrated) scenario is used to

investigate the current thermal regime of permafrost at the study site, simulating the system with coupled groundwater flow and heat transport by conduction and advection. The second scenario is otherwise identical but considers a conduction-only (no groundwater flow) case. For the third scenario, predictions are made on the future behavior of permafrost under a constant increase in air temperature and precipitation, based on predictions of increased air temperature and precipitation from the ArcticNet IRIS (Integrated Regional Impact Study; Allard and Lemay, 2012) for the Umiujaq region. In the third and final chapter, Chapter 3, the research findings are summarized and general recommendations for future studies are formulated.

1.2 Study site

1.2.1 Location

The study site is located near the Inuit community of Umiujaq located just above the 56th parallel along the eastern coast of Hudson Bay (Figure 1.1). The site lies at the boundary between the discontinuous but widespread permafrost zone and the discontinuous but scattered zone. The field investigations were carried out in a small 2 km2 watershed in the Tasiapik Valley, delimited on the west side by a cuesta ridge and on the east side by the Umiujaq Hill (Figure 1.2). The valley is drained by a small stream that flows into Tasiujaq Lake. Ice-rich permafrost is found throughout the valley as small mounds called lithalsas, which are delineated in Figure 1.2. A total of nine groundwater wells located at seven different sites, which form part of the Immatsiak network, are distributed along the watershed’s north-south axis.

1.2.2 Geology and hydrogeology

At the end of the Wisconsinian period (~7600-7300 years ago), the Laurentide Ice-sheet covering North America had almost completely disappeared, causing bedrock erosion along weaknesses which, in the Umiujaq area, formed a landscape of valleys surrounded by cuestas culminating up to 250 m in height, as observed today. As the glacier retreated, all land below 270 m was submerged by the Tyrell Sea, connecting Lake Tasiujaq with Hudson Bay. Over the years, the Tyrell Sea deposited fine-grained deep sea sediments above glacial and fluvio-glacial coarse-grained sediments overlying the bedrock. During the period of Quaternary glacio-isostatic rebound, the land gradually emerged, deposits were eroded forming spurs and gullies, and vegetation spread over the land surface.

Permafrost developed in frost-susceptible deposits newly exposed to the cold climate (Fortier et. al., 2018), preferentially in zones of local high topography compared to those of low topography which remained more insulated from cold due to vegetation cover and snow accumulation. The topography of these ice-rich periglacial mounds is defined by initial erosion and further frost heaving due to the formation of segregated ice by cryosuction (Allard and Seguin, 1987). Today, permafrost mounds in the valley reach an elevation of between three to five meters above ground. A 2D cross-section extending from the north to south end of the watershed (orange line in Figure 1.2).

A A’

The bedrock is formed of arenites and arkosites of the Pachi Formation and subaerian basaltic flows of the Persillon formation. The bedrock is overlaid by 10-30 m of coarse sand and gravel forming a deep aquifer. In the lower part of the valley, the aquifer becomes confined due to the presence of a 20 meter thick overlying marine silt unit forming an aquitard. A surficial sand layer allows water runoff on top of the permafrost and silt unit, forming a shallow aquifer that completely drains during winter.

1.2.3 Climate

The local climate at Umiujaq is subarctic and characterized by long cold winters, short cool summers, and relatively low humidity and precipitation. Temperatures generally vary between 20°C in the summer and -30°C in winter. The watershed is located at the boundary separating shrub tundra and forest tundra. Lichen is present in areas of higher topography, such as permafrost mounds and well- drained terrain, while depressions are more commonly filled with shrubs. Mean annual precipitation measured between 2013 and 2016 is about 760 mm/year (Lemieux et al. 2018).

1.3 Methodology

The Umiujaq study site is now characterized by a wide variety of data which have been collected during field campaigns since 2000. The first part of the current project consisted of organising and analysing available data. The location of the cross-section could then be determined and the conceptual model drawn. Finally, the data were integrated into the conceptual and numerical model.

1.3.1 Data

The available data used for this study are listed below and illustrated in Figure 1.4: A. Hydraulic heads in groundwater wells from the Immatsiak network since 2012 B. Darcy fluxes measured with a tracer experiment in groundwater wells in 2016 C. Precipitation data at the SILA weather station since 2012 D. Recharge rates for different vegetation types in 2014-2015 (Murray 2016) E. Air temperatures and relative humidity from the Umiujaq-A Station located near the Umiujaq airport, since 1993 F. Air temperatures at Site 3 since 2012 G. Physical and thermal properties of different geological formations in the valley H. Temperature profiles in the permafrost mound since 2000 I. Unfrozen water content, snow depths, shallow heat fluxes and surface temperatures at the permafrost mound site since 2014

The above listed data will be presented in more detail in the following sections.

1.3.1.1 Hydraulic heads The Immatsiak network is composed of seven sites with nine groundwater wells which have been instrumented with water pressure probes (Solinst Levelogger, Model 3001). The hydraulic heads (relative to sea level) from 2012 to 2017 at the two wells closest to the studied permafrost mound, as well as monthly precipitation from the SILA station, are shown in Figure 1.5Erreur ! Source du renvoi introuvable.. Site 5 is located upstream relative to the studied permafrost mound, while Site 3 is located downstream. During the spring thaw (starting about mid-June), recharge begins and the water level gradually rises in the wells throughout the year until it reaches a peak in winter around January. A period of recession is then observed until the water level reaches its lowest point, usually in early June. Artesian conditions were observed at Site 3 during the winter 2015-2016, which is shown in Figure 1.5 as a static hydraulic head which corresponds to the elevation of the surface well casing. The slight increase of the hydraulic head above the elevation of the well casing at the end of the winter

period is due to the freezing of water within the upper part of the surface casing which allows a build- up of pressure.

Figure 1.5: Hydraulic heads in the groundwater wells at Site 3 and Site 5, from 2012 to 2017 (from the Solinst probes and manual measurements), and monthly precipitation measured at the SILA station.

1.3.1.2 Darcy flux Groundwater fluxes along the axis of the valley were first assessed indirectly with Darcy’s law, using head differences and distances between wells to calculate hydraulic gradients, and using hydraulic conductivities estimated from slug tests (Fortier et al., 2014). Tracer experiments were then also performed in summer 2016 using the Finite Volume Point Dilution Method (FVPDM) (Jamin et. al., 2018), providing direct measurements of Darcy fluxes in three wells. The measured Darcy fluxes are given in Table 1.1 for both methods.

In general, the Darcy fluxes assessed from the gradient method are much lower than from the FVPDM, except for Site 5 where it is only slightly lower. This could be due in part to the high margin of error associated with the gradient method considering the large spacing between wells and the uncertainty on the hydraulic conductivity values. Another hypothesis is that the wells may not be aligned with the main direction of local groundwater flow. Despite these differences, the Darcy fluxes obtained from the FVPDM are considered much more accurate than the gradient method since the FVPDM is a direct measurement (see Jamin et al. for details).

Table 1.1: Darcy fluxes assessed from hydraulic gradients and the FVPDM method for Sites 2, 5, and 3.

Ratio Based on hydraulic Based on FVPDM Hydraulic FVPDM/Gradient Piezometer gradients (2016) B experiments (2016) conductivity A method Darcy Flux Darcy Flux Uncertainty [m/s] [m/s] [m/s] [m/s] [ - ] -7 -6 -7 Site 2 (Pz2) 4.9  10-5 8.1  10 9.0  10 1.4  10 (1.5 %) 11 Site 5 (Pz6) 1.6  10-4 5.6  10-6 8.5  10-6 3.5  10-8 (0.4 %) 1.5 Site 3 (Pz4) 9.8  10-6 1.0  10-7 6.7  10-6 6.9  10-8 (1 %) 64 A Hydraulic conductivity was measured using slug tests (Fortier et al., 2014). B Hydraulic gradients were calculated with hydraulic heads measured at the time of the experiment.

1.3.1.3 Recharge Groundwater recharge was estimated by Murray (2016) using the Darcy method (Healy, 2010), which is based on the Darcy equation in the unsaturated zone:

휕ℎ 푞 = 퐾 [1.1] 푛푠 휕푧

where q is the Darcy flux (m/s), Kns is the unsaturated hydraulic conductivity (m/s), and 휕ℎ/휕푧 is the vertical hydraulic gradient. Four zones at Site 2 were instrumented to characterize hydraulic conductivities (Appendix C). The corresponding local recharge rate was calculated for three dominant vegetation types: lichen, spruce and shrubs. The recharge per vegetation type is shown in Figure 1.6.

Figure 1.6: Monthly recharge measured by Murray (2016) at Site 2 for the year 2014-2015, for ground surfaces dominated by shrubs, spruce and lichen.

1.3.1.4 Physical and thermal properties Different methods were used in 2014 to estimate hydraulic conductivity of the geological units found in the Tasiapik valley, including Guelph permeameter tests, slug tests in the Immatsiak wells and grain size analysis of various soil samples. Details concerning the methods are provided by Fortier et al. (2014) and the main results are presented in Appendix D.

Thermal conductivity at the study site was measured on undisturbed soil samples collected during the summer of 2016. Three samples of coarse sand, sandy silt and silt were respectively collected at 60, 20, and 60 cm depths in the active layer. The thermal conductivity was measured in the laboratory using a KD2Pro thermal conductivity meter (Decagon Devices) and a TR-1 sensor. The measurement range of the TR-1 sensor is from 0.10 to 4.00 W/(mK) with an accuracy of ±10%. The thermal conductivity of the original moist sample is first measured at room temperature (23 °C). A total of 9, 16 and 17 measurements were made, respectively, for samples 1 to 3, with a waiting time between each measurement of about one hour. Calibration was performed by comparing the experimental determination of the thermal conductivity of a standard material to its known value. The calibration factor is calculated with the following equation:

λ 퐶 = 푚푎푡푒푟푖푎푙 [1.2] λ푚푒푎푠푢푟푒푑

where 휆material is the known thermal conductivity of the calibration material, and 휆measured is the thermal conductivity of that material measured with the thermal needle probe apparatus. All thermal conductivities measured on the samples are then multiplied by this factor. The measured thermal conductivity of the wet sample is assumed equal to the mean of the conductivities of the different media (air, water, material). The thermal conductivity of the dry material is then obtained using equation 1.3:

λ푑푟푦 = (λ푤푒푡 − λ푤 ∗ 푆 ∗ 휃 − λ푎 ∗ (1 − 푆) ∗ 휃)/(1 − 휃) [1.3]

where λ푑푟푦, λ푤푒푡, λ푤, and λ푎 are the thermal conductivities respectively, of the dry material, wet material, water, and air, S is the saturation, and θ is the porosity. The saturation and porosity are calculated using dry weights and volumes of the different samples, assuming a solid density of 2600

kg/m3 and a liquid density of 1000 kg/m3. The estimated thermal conductivities, water content, and porosities of the samples are given in Table 1.2.

Table 1.2: Thermal conductivities measured with the thermal needle probe, water content and porosity of three soil samples.

No Sample Depth Thermal conductivity of solids Water Porosity (W/mK) content 1 Coarse sand 60 cm 3.04 28% 38% 2 Sandy silt 20 cm 2.76 20% 37% 3 Silt 60 cm 2.71 23% 30%

1.3.1.5 Temperature profiles Four thermistor cables were installed in the permafrost mound. The thermistors (44033RC Precision Epoxy NTC type) have a precision of ±0.1°C (Measurement Specialties Inc., 2008). Hourly readings and recording were obtained with a Campbell Scientific AM16/32 relay multiplexer and a Campbell Scientific CR10X Datalogger. The average temperature profiles for the thermistor cables located at the center of the mound and on the edge of the mound, from 2002 to 2017, are shown in Figure 1.7. The temperatures are averaged over two years in mid-summer (July, August, September) and mid- winter (January, February, March). Over the 15-year monitoring period, the interpolated active layer thickness increased from 2 meters in 2002 to nearly 4 meters in 2017. The extrapolated permafrost base reached a minimum depth of 19.7 m in 2009, but increased to 21 m in 2017. Based on the measured temperatures at the permafrost base, the geothermal heat fluxes between the permafrost and the deep aquifer vary between 0.2 and 0.7 W/m2.

1.3.1.6 Soil moisture and temperature probes The soil moisture and temperature of the unsaturated zone was monitored with Decagon 5TM probes which were installed at various depths in 2014 and connected to Decagon EM50 data loggers. Ten probes were installed both on the top and at the side of the mound in the silt unit. The unfrozen

3 3 (volumetric) water contents (m w/m total) and temperatures measured in the unsaturated zone are shown in Figure 1.8 for mid-summer and mid-winter 2015 and 2017, both at the side of the mound

(Figure 1.8a and Figure 1.8c) and on top of the mound (Figure 1.8b and Figure 1.8d). The accuracy for the measurement of volumetric water content varies from ±0.01 to ±0.02 m3/m3 while it is ±1°C for the temperature.

A general increase of the unfrozen water content and temperature in the unsaturated zone was observed between 2015 and 2017, especially during the mid-summer period. On top of the mound, which is more exposed to climate variations, temperatures are generally warmer in the summer and colder in the winter while unfrozen water content is generally lower than at the side of the mound. The variation of water content as a function of time on the top and the side of the mound for the shallow and deep probes is shown in Figure 1.9. The daily air temperature is illustrated by a pale gray line while a spline smoothing function used to reduce noise is shown by a dark gray line. At the center of the mound, significant seasonal variations are observed, with clear peaks around May consistent with the time where the temperature rises above 0 °C and the ground thaws. A delay of about 4 months occurs between the peaks observed at 0.1 m depth and those at 1 m depth. Beside the mound, the seasonal variations are attenuated, especially at a depth of 1 m where the water content remains around 0.3 throughout the whole year. The unfrozen water content generally remains higher at the side of the mound since water drains from the top of the mound and accumulates in the side depressions.

Figure 1.9: Water content as a function of time (2014 – 2017) from the moisture and temperature probes at 0.1 m and 1 m depths, at a) the center of the mound, and b) the side of the mound.

1.3.1.7 Snow cover Five snow poles were installed on the mound, as well as an automated camera (RECONYX PC800 HyperFire Professional Semi-Covert IR) which takes daily pictures of the snow poles at 10:00, 11:00, 12:00, 13:00 and 14:00. Examples of photos taken during summer (July) and winter (February) are shown in Figure 1.10 which also shows the location of the snow poles.

B A SP2 SP3 SP1

Figure 1.10: Photos of the permafrost mound from the Reconyx camera, and location of the snow poles a) in July 2017, and b) in February 2017.

The visible snow pole length was measured in each photo from summer 2014 to summer 2015, providing an estimate of snowpack distribution on and around the mound throughout the year. The assessed thicknesses of snow cover for the five poles are presented in Figure 1.11. The snow starts to

Figure 1.11: Snowpack thickness on the permafrost mound in 2014-2015 for the snow poles identified in Figure 1.10.

accumulate around November and melts completely by around May on the top of the mound, while it stays until June in the side depressions which are less exposed to wind and solar radiation. A maximum thickness of snow cover of about 1.6 m is reached at the end of March.

1.3.1.8 Heat flux Two Heat Flux Plates (HFPs) (Hukseflux HFP01SC) were installed in the center and the side of the mound at a depth of 8 cm. The plates are coupled with a pair of thermistors buried at depths of 2 cm and 6 cm which are connected to an automated datalogger system consisting of a Campbell Scientific AM16/32 relay multiplexer and a Campbell Scientific CR10X Datalogger. These HFPs generate a small voltage proportional to the temperature gradient measured between the thermistors, which is then divided by a sensitivity value to get heat flux values (W/m2). The sensitivity, provided for each plate on a calibration certificate, is entered in the datalogger system to allow self-calibration. The calibrated heat flux data, as well as air temperatures, are shown in Figure 1.12.

Figure 1.12: Heat flux measured at the center and the side of the mound at 8 cm depth from 2014 to 2015.

The heat flux varies between -1 and 2 W/m2 (negative values represent heat loss from the ground while positive values are heat gain). Negative heat fluxes are observed between November and June when the air temperature is lower than the ground surface. Heat fluxes on the top and the side of the mound are similar during the summer. The insulating effect of the thick snow cover on the side of the mound is clearly visible in winter where the heat flux is much lower on the side of the mound than on the top.

1.3.1.9 Surface temperature Ten surface temperature probes (HOBO Water Temperature Pro v2 connected to a U22-001 Data Logger) were buried 10 cm below the ground surface, recording a measurement every hour with an accuracy of ±0.21°C. Two probes, one located on the center of the mound and the other on the side of the mound, as well as the air temperatures, are presented in Figure 1.13.

Figure 1.13: Temperatures at 10 cm depth from the HOBO temperature probes located at the center and beside the mound between 2014 and 2017

Surface temperatures observed on top of the mound show large seasonal variations with temperatures reaching -20°C in the winter, while temperatures observed on the side of the mound are clearly affected by the insulating effect of snow cover with surface temperatures barely below the freezing point. Surface temperatures are similar in the summer at the two locations, due in part to the fact that both probes are located in zones where vegetation is very limited which does not provide a shade effect in summer.

1.3.2 Conceptual model

The conceptual model of the permafrost mound was developed in a 2D vertical section transverse to the valley, situated between the watershed boundaries (cross-section B-B’ in Figure 1.2). Lying approximately perpendicular to the axis containing the 9 wells of the Immatsiak network (cross- section A-A′ in Fig 1.2), the 2D model section is assumed to correspond to the main groundwater

flow directions toward the central stream. The 2D cross-section was extracted from the 3D geological model developed by Banville (2016), extending from ground surface to depths varying from 40 to 210 m (the bottom boundary is located at 40 m below sea-level). More details concerning the mesh, initial conditions and boundary conditions are provided in Chapter 2. The current section provides more details on how observed data were integrated into the model.

1.3.2.1 Flow system and flow boundaries The conceptual flow model is based on the hypothesis that groundwater flows from the cuesta towards the small stream, transverse to the orientation of the wells. Apparent fractures in the rock on the top of the cuesta and water seepage observed after rain events along the cuesta ridge are evidence that water infiltrates through the top fractures, flows below the ridge and recharges the deep sand aquifer at the base of the cuesta. Infiltration at the base of the cuesta is particularly focussed due to the presence of colluvium connected to the deep aquifer (Lemieux et. al., 2018). The conceptualized flow system is shown in Figure 1.14.

Figure 1.14: Conceptualized flow system along the cross-section B-B’ (Figure 1.2).

Based on temperature profiles located at the Umiujaq airport further along the back-slope of the cuesta, the depth to the permafrost in the cuesta is estimated to be about 20 m. Thus, groundwater is assumed to flow on top of the permafrost units and a 20 m deep unsaturated zone is assumed.

Considering the lack of data available on the left side of the cross-section, the Dupuit equation is used to estimate the watertable elevations (hydraulic head (h)) along the flow line through the cuesta (Dupuit 1863):

(ℎ2−ℎ2)푥 푤 ℎ2 = ℎ2 − 1 2 + (퐿 − 푥)푥 [1.4] 1 퐿 퐾

where h1 and h2 are the steady-state heads at the respective left and right limits of the flowline through

the cuesta, L is the distance between h1 and h2, K is the hydraulic conductivity of the aquifer, w is the

recharge and x is the distance along the flowpath (0 < x < L). Assuming h1 = 228 m, h2 = 94 m, with

-5 -9 K = 1×10 m/s and w = 6×10 m/s, the calculated heads are shown in Figure 1.15. The head h1 at the leftmost watertable point is fixed at 20 m below ground surface, while the rightmost bounding

head h2 corresponds to the ground surface elevation at the bottom of the cuesta. The remaining part of the watertable along the 2D section is assigned a transient recharge rate except for two fixed heads which correspond to observed surface water elevations along the cross-section, including the central stream. The flow system is assumed saturated.

Figure 1.15: Watertable heads along the cuesta flowline calculated from the Dupuit equation

1.3.2.1 Heat transport system and boundary conditions The top heat transport boundary corresponds to ground surface, which is represented using a heat transfer layer allowing spatially-variable thermal parameters along the longitudinal axis which control heat exchange between the ground and atmosphere. The exchange layer can incorporate ground surface conditions and mass and energy exchange processes, including snowpack, vegetation and heat

transfer across the air-ground interface. To handle spatial variation at the ground-atmosphere interface, the conceptual model for the Umiujaq site is divided into 7 zones according to vegetation type (lichen, bush or spruce) and topography (locally high or low). Net heat fluxes, layer thicknesses and recharge rates were assigned for each of the 7 zones and for each of the four seasons. These zones and associated parameters are presented in Figure 1.16 for summer and winter periods.

a) b)

Figure 1.16: Input parameters of the heat transfer layer shown for the mid-summer and mid-winter periods with a) layer thickness and zone delimitation and b) heat flux and recharge rates in mm/year

The ‘net’ heat flux is used to represent independent thermal fluxes that are not accounted for in the heat exchange layer based on the air-soil temperature gradient (ex. solar radiation). The thickness of the heat transfer layer is defined based on the estimated snow depths on the top and side of the studied mound.

1.3.2.2 Meteorological data

Past and present climate Considering that the simulations start in 1900 (see Chapter 2 for details) and no climatological data are available at Umiujaq for that time (the village was only founded in the early 1980’s), mean annual air temperatures (MAATs) were estimated based on data from Kuujjuarapik and Kuujjuaq. The air temperatures estimated at the study site for the period from 1900 to 2017 were based on 4 series of data:

Period 1 (1900-1925): A constant value equal to the MAAT estimated in 1926.

Period 2 (1926-1949): Temperatures recorded at Kuujjuarapik over this period were decreased by the mean difference between known MAATs at Kuujuarapik and Umiujaq between 1993 and 2017. The mean difference between the MAAT (1993-2017) at Umiujaq and Kuujjuarapik is 0.3°C. The MAAT at Umiujaq between 1926 and 1950 was then calculated by subtracting 0.3°C from the temperatures recorded at Kuujjuarapik.

Period 3 (1950-1992): A linear interpolation between air temperatures recorded at Kuujjuarapik and Kuujjuaq based on known MAATs between 1993 and 2017. Mean annual air temperatures, over the period 1993-2017, of -2.9°C, -3.2°C and -4.5°C were calculated respectively for Kuujjuarapik, Umiujaq and Kuujjuaq. A correlation was made between the 3 locations by calculating a differential ratio. The MAAT values at Umiujaq between 1950 and 1993 were then interpolated between values recorded at Kuujjuarapik and Kuujjuaq, proportionally to this ratio. Once the MAATs had been estimated over the entire simulation period, the daily mean temperatures for each year were then calculated with a cosine curve, oscillating around the estimated MAAT over a period of 365 days. The function amplitude was assumed constant over time and equal to 18°C, which corresponds to the mean half- difference between the maximum and minimum monthly temperatures recorded at all three locations.

Period 4 (1993-2017): Temperatures recorded at station Umiujaq A near the Umiujaq airport.

The resulting estimated MAATs at Umiujaq from 1900 to 2017 are shown in Figure 1.17. The solid lines represent a 5-year moving average.

Predicted climate Projected changes in climate variables over the Nunavik-Nunatsiavut region have been computed by the Ouranos research consortium (Allard and Lemay, 2012) based on the Canadian Regional Climate Model (CRCM) (Caya et al., 1995; Caya and Laprise, 1999; Plummer et al., 2006; Music and Caya, 2007). Ouranos applied the SRES A2 greenhouse gas increase scenario to project changes in various climate variables in the Nunavik-Nunatsiavut region, such as air temperatures, precipitation, degree- days of thawing and freezing, snow depth, etc. For the purpose of this study, only changes in air temperatures, as well as precipitation during winter (October to April) and summer (May to September), were considered. For the Umiujaq region, the study predicts a temperature increase of 4°C in winter and 1.7°C in summer, as well as a precipitation increase of 25%, between the 1971-2000 period (referred as the current climate conditions) and the 2041-2070 period.

Based on the temperature and precipitation increase projected by Ouranos (Allard and Lemay, 2012), a mean temperature increase of 0.09°C/year in winter and 0.02°C/year in summer was estimated for

the Umiujaq site between 2017 and 2050, as well as an annual precipitation increase of 0.5%. The calculated increments are applied in the model over each simulated year.

Recharge Based on the vegetation map from Provencher-Nolet (2014) (Appendix B), the percentage occupied by each vegetation type along the cross-section was assessed as follows: lichen (50%), shrubs (30%) and spruce (20%). Rock covered with vegetation is assumed to have the same recharge values as lichen, while lakes and road surfaces are assumed to have zero recharge. The year is divided into four periods starting with mid-summer (July, August, September). Monthly recharge values calculated by Murray (2016) were then summed over the respective periods and according to the vegetation type. The estimated total mean annual recharge, weighted according to vegetation cover along the cross-section, is about 300 mm/yr. The resulting values are presented in Table 1.3.

Table 1.3: Assumed recharge rates according to the vegetation type and temperature difference between recharge water (Tq) and air temperature (Tair).

Recharge (mm) Vegetation Type Weighted Total Tq - Tair /Period Lichen Bush Spruce (mm) (°C) Mid-summer 153 118 87 129 -2.0 Oct. – Dec. 123 78 60 97 -1.4 Mid-winter 1 1 6 2 0.0 Apr. – Jun. 65 119 78 72 -1.7 Total (mm/yr) 343 316 231 300 -

Rain water temperature varies throughout the year, being cooler than the air temperature during the summer. The temperature of recharge water can be estimated as the wet-bulb temperature, which can be calculated with Equation 1.5 (Stull, 2011), based on the dry-bulb temperature (air temperature) and relative humidity measured at Umiujaq:

−1 1⁄2 −1 3⁄2 −1 푇푞 = 푡푎푛 [0.15(푅퐻 + 8.31) ] + 푡푎푛 (푇 + 푅퐻) + 0.004(푅퐻) 푡푎푛 (0.02푅퐻) − 4.69 [1.5] where Tq is the recharge temperature, RH is the relative humidity in percent and T is the air temperature. The difference between air temperature and rain temperature is then averaged over the four seasons and applied in the model.

2 Numerical model (Taken from Dagenais et al., 2018)

Coupled cryo-hydrogeological modelling of permafrost dynamics at Umiujaq, Québec, Canada

S. Dagenais(1,2), J. Molson(1,2,*), J-M. Lemieux(1,2), R. Fortier(1,2), and R. Therrien(1,2) 1. Département de géologie et de génie géologique, 1065 avenue de la Médecine, Université Laval, Québec (Québec), Canada, G1V 0A6 2. Centre d’études nordiques, Université Laval, Québec (Québec), Canada, G1V 0A6. *Corresponding author

Reference: Dagenais S, Molson J, Lemieux J-M, Fortier R, Therrien R. (2018). Coupled cryo- hydrogeological modelling of permafrost dynamics at Umiujaq, Québec, Canada, In submission: Hydrogeology Journal.

Résumé

Un modèle numérique bidimensionnel de l’écoulement de l’eau souterraine, de la transmission de chaleur par conduction et advection, et du changement de phase qui prennent place dans un environnement pergélisolé a été développé pour une butte de pergélisol riche en glace dans la vallée Tasiapik à Umiujaq au Nunavik (Québec), Canada. La dégradation des buttes de pergélisol dans cette vallée située en zone de pergélisol discontinu a été attribuée à la tendance au réchauffement climatique observée au Nunavik au cours des deux dernières décennies. Les flux de chaleur à la base du pergélisol déterminés à partir des températures du sol mesurées avec des câbles à thermistances sont plus de dix fois supérieurs au gradient géothermique estimé dans la région. Un modèle numérique basé sur une coupe verticale extraite d’un modèle géologique tridimensionnel de la vallée a été produit. Ce modèle a été étalonné avec des profils de température et de flux de chaleur qui ont été mesurés dans la butte de pergélisol du site d’étude. Les simulations avec et sans écoulement d’eau souterraine ont montré que la transmission de chaleur par advection joue un rôle critique dans la dynamique du pergélisol et explique les flux de chaleur importants observés à la base du pergélisol. La transmission de chaleur par advection dans l’aquifère sous la base du pergélisol est à l’origine d’une augmentation des températures du sol en amont de la butte tandis que, dans la zone de résurgence en aval, l’eau souterraine après avoir perdu une partie de sa chaleur maintient le sol à des températures plus froides que celles résultant de la conduction thermique seule. En se basant sur un scénario de réchauffement climatique attendu dans la région d’ici 2050, selon les résultats de la simulation, le mollisol devrait s’épaissir et la base du pergélisol devrait se rapprocher de la surface d’environ 80 cm par année alors que le pergélisol devrait disparaître du site d’étude autour de 2040.

Mots clés: Écoulement d’eau souterraine, Pergélisol, Changements climatiques, Modélisation numérique, Nunavik

Abstract

A 2D cryo-hydrogeological numerical model of groundwater flow, coupled with advective-conductive heat transport with phase change in a permafrost environment, has been developed for an ice-rich permafrost mound in the Tasiapik Valley in Nunavik (Québec), Canada. Permafrost is thawing in this valley due to the trend of climate warming observed in Nunavik over the last two decades. Ground temperatures measured along thermistor cables in the permafrost mound show that permafrost degradation is occurring both at the permafrost table and base. Moreover, derived heat fluxes at the permafrost base are up to ten times higher than the expected geothermal heat flux. The numerical model, based on a vertical cross-section extracted from a 3D geological model of the valley, was first calibrated using observed temperatures and heat fluxes from the permafrost mound. Comparing simulations with and without groundwater flow, advective heat transport due to groundwater flow in the sub-permafrost aquifer is shown to play a critical role in permafrost dynamics and can explain the high apparent heat flux at the permafrost base. Advective heat transport leads to warmer subsurface temperatures in the recharge area while the cooled groundwater arriving in the downgradient discharge zone maintains cooler temperatures than those resulting from thermal conduction alone. Predictive simulations incorporating a regional climate change scenario suggest the active layer thickness will increase by about 12 cm/yr, while the depth to the permafrost base will decrease by about 80 cm per year. Permafrost within the valley is predicted to completely thaw by around 2040.

Keywords: Groundwater flow, Permafrost, Climate change, Numerical modelling, Nunavik

2.1 Introduction

Permafrost covers more than half of Canada’s territory, with depths varying from a few meters to over a kilometer in northern areas (Zhang et al., 2006). Due to its low hydraulic conductivity, permafrost acts as an impermeable or low-permeability barrier controlling aquifer recharge, water storage, and interactions between the ground surface and subsurface. As a consequence of the recent trends in global warming, many signs of permafrost degradation have already been observed around the globe (Allard et al., 2002; Intergovernmental Panel on Climate Change IPCC, 2013) which can have major impacts on groundwater dynamics and on the availability of groundwater as a source of drinking water.

Thawing of permafrost is expected to significantly modify a variety of hydrological, thermal and ecological systems at local and regional scales in northern regions (AMAP, 2017). In particular, enhanced infiltration through thawed ground and release of melt water from permafrost bodies are expected to increase rates of groundwater recharge and discharge, thus modifying groundwater flow systems and associated drainage networks. Since permafrost distribution is strongly influenced by the ground thermal regime, it becomes critical to understand the relevant heat transfer processes, not only by conduction but also by advection.

Until recently, permafrost degradation has been primarily attributed to vertical conduction-dominated heat transfer, neglecting the potential contribution of advective heat transfer from groundwater flow. Recent advances in coupled groundwater flow and heat transport modelling has led to new research investigating the role of groundwater flow in permafrost dynamics. However, the focus has mainly been limited to changes in active layer thickness, supra-permafrost groundwater flow, or groundwater discharge (Evans and Ge, 2017; Painter et al., 2016; Atchley et al., 2016; Frederick and Buffet, 2015; Frampton et al., 2013; Jiang et al., 2012). Only a few studies have assessed the impact of sub- permafrost groundwater flow on permafrost thaw and few have revealed the relative importance of advective heat transport versus conduction alone (Rowland et. al., 2011; de Grandpré et al., 2012; Mackenzie and Voss, 2013; Wellman et al., 2013). In addition, most of these studies are based on idealized hypothetical environments and do not attempt to simulate real field conditions. Access to reliable data on deep ground temperatures and sub-permafrost aquifers is challenging in permafrost environments and the lack of reliable data explains why only few studies have addressed the impact of groundwater flow on permafrost dynamics, as reviewed below.

Sjoberg et al. (2016) employed the Artic Terrestrial Simulator (Karra et al., 2014) to assess the importance of groundwater flow on permafrost dynamics in a sporadic permafrost environment, using data from a subarctic fen in northern Sweden. They found that permafrost thaw at their site is strongly influenced by lateral groundwater flow in shallow peat and sand units of relatively high hydraulic conductivity (K ≈ 510-3 to 510-5 m/s), especially during spring when hydraulic gradients are higher due to snowmelt and thawing of the active layer. In another study, Kurylyk et al. (2016) used the SUTRA 2D model (Voss and Provost, 2010; McKenzie et al., 2007) to investigate the impact of groundwater flow on multi-decadal lateral permafrost thaw in a peat-wetland complex in the Northwest Territories. They found that advective heat transport does not play a significant role at their site due to the low-permeability silt-clay unit which limits groundwater flow rates. At another site, Bense et al. (2012) reached a similar conclusion, although they suggested that the contribution of thermal advection could be important in regions where groundwater flow is strongly focussed due to high gradients and/or high soil permeability. Despite these recent advances in cryo-hydrogeological modelling, improvements are still needed in the understanding of field processes and in the development of coupled flow and heat transport models related to permafrost thaw (Ireson et al., 2013).

In this context, three important challenges have been identified which will be addressed herein:

1) Investigate the role of groundwater flow on permafrost thaw.

Since most studies which included advective heat transfer only addressed its role on permafrost dynamics in supra-permafrost aquifers, new insights are needed into potential impacts of groundwater flow in sub-permafrost aquifers. This is particularly true for regions of discontinuous and sporadic permafrost, where temperatures are close to 0 ºC and permafrost is thinner, making it more vulnerable to climate warming (McClymont et al., 2013; Sjöberg et al., 2016; Kurylyk et al., 2016).

2) Collecting and using field observations to improve model predictions of long-term permafrost thaw.

Most existing studies have been based on simplified conceptual models or idealized field conditions that may not represent realistic thermal and hydrogeological conditions. Indeed, the importance of

integrating site-specific thermal and hydrogeological properties of the active layer and permafrost for accurately simulating thermal dynamics in the context of a warming climate has recently been highlighted by Ireson et al. (2013), Rassmussen et al. (2018) and Kurylyk et al. (2016).

3) Integration of ground surface conditions along with mass and energy exchange processes in numerical models (including snowpack, vegetation, and heat transfer across the air/ground interface).

Most studies have neglected or oversimplified the impact of surface processes on subsurface thermal behavior. Indeed, the need for models to account for surface insulation and vegetation patterns has been well documented (Mackenzie and Voss, 2013; Kurylyk et al., 2014a; Atchley et al., 2016). For instance, accounting for variability in snow depth is crucial for accurately simulating ground surface temperatures, as well as for simulating permafrost thermal regimes (Allard and Séguin, 1987; Zhang, 2005; Painter et al., 2016; Rassmussen et al., 2018).

The main objective of this paper is to assess the role of groundwater flow on permafrost dynamics and thermal evolution using a numerical model of an ice-rich permafrost mound located in a discontinuous permafrost environment near the Inuit community of Umiujaq (Nunavik, Canada). The model is based on field observations of the permafrost mound including temperature profiles, heat flux measurements, hydraulic heads and groundwater flow measurements in piezometers close to the permafrost mound.

2.2 Study site

The village of Umiujaq is located along the eastern coast of Hudson Bay (56°N, 76°W), within the discontinuous permafrost zone (Allard and Seguin, 1987; Figure 2.1). The study site is within the Tasiapik Valley, delimited on the west side by a cuesta ridge and on the east side by the Umiujaq Hill, as shown in Figure 2.2. Lying within a 2 km2 watershed, the site is drained by a small stream which flows south towards Tasiujaq Lake. The regional climate is subarctic and characterized by long cold winters, short cool summers, and relatively low humidity and precipitation. Mean annual air temperatures oscillate around a mean of -3.6°C, from about -30 °C in winter to 20 °C in summer, while the mean annual precipitation for 2013-2016 is close to 760 mm (Lemieux et al., 2018).

Figure 2.1: Location of Umiujaq along the eastern coast Figure 2.2: Tasiapik Valley watershed and 2D cryo- of Hudson Bay and permafrost distribution in Nunavik, hydrogeologic model cross-section Québec, Canada (adapted from Allard and Lemay 2012). Interpolated depth of the 0°C isotherm is from Lemieux et al. (2008).

The stratigraphy of the study site is characterized from top to bottom by a thin deposit of littoral sands overlying a 20 m thick marine silt unit, and a 10-30 m thick sand and gravel deposit overlying the bedrock (Figure 2.2) (Fortier et al, 2018). Ice-rich permafrost is found in the silt unit. In the lower part of the valley, the layer of sand and gravel below the silt unit and permafrost forms a deep confined aquifer. Permafrost first aggraded during the period of glacio-isostatic rebound, when the frost- susceptible marine silt unit came in contact with the subarctic climate. Permafrost developed in the valley as raised periglacial landforms, known as lithalsas or permafrost mounds, due to frost heave and accumulation of segregation ice lenses within the soil (Fortier et. al. 2018).

In this study, a permafrost mound in the lower part of the valley with a diameter close to 30 m and a relative height above the surrounding ground of about 3-4 meters has been selected for detailed study. In the vicinity of the mound, snow cover and vegetation are highly variable, depending on the topography, drainage conditions, and wind exposure. From October to May, the mound top is sparsely covered with lichen and a thin snowpack (reaching a maximum thickness of 10 cm), while the side depressions are filled with shrubs of about 1 m high and a snowpack up to 1.6 m thick during mid- winter. The active layer thickness reaches approximately 4 m while the permafrost base reaches a depth of about 21 m below ground. The temperature is about -0.4 °C at a depth of 10 m.

Due to the trend of climate warming observed over the last 25 years throughout Nunavik, Québec, permafrost is currently degrading in this area (Buteau et al., 2004). Indeed, field observations, including subsurface temperature measurements collected over the past two decades, have clearly shown that permafrost is rapidly warming and thawing. Ground temperatures have been monitored at this site since 2001 with a thermistor array reaching 20.8 m deep within the permafrost mound and have been generally increasing over time. Heat fluxes between the confined aquifer and the base of permafrost have also been assessed from the temperature profiles. These heat fluxes are up to ten times higher than expected for the regional geothermal heat flux of 0.032 W/m2 (Mareschal and Jaupart, 2004). This very high apparent heat flux has been attributed to groundwater flow in the confined aquifer (Buteau et al., 2004). A finite volume point dilution test performed in a piezometer close to the studied permafrost mound in July 2016 (Jamin et al., 2018) showed that groundwater is flowing in the sand and gravel aquifer located beneath the permafrost mound with a Darcy flux of about 7.610-6 m/s.

2.3 Meteorological and cryo-hydrogeological conditions

2.3.1 Meteorological data

Long-term climatological records (air temperature, rain and snow precipitation, wind direction and snow depth) from two local meteorological stations are available at or near the Umiujaq site. The SILA station operated by the Centre d’études nordiques (CEN, Université Laval) since 1997 is located directly in the Tasiapik Valley while the Umiujaq-A station, operated by Environment Canada since 1993, is located close to the Umiujaq airport. Data from two other nearby stations operated by Environment Canada (Kuujjuarapik, 160 km south, and Kuujjuaq, 500 km north-east) were also used in this study to assess a time series of mean annual air temperature (MAAT) since 1926. The air

temperatures recorded in the three Inuit communities of Kuujjuarapik, Kuujjuaq and Umiujaq are summarized in Figure 2.3.

In Nunavik (Québec), available climate records can be divided into three main periods (delimited by dashed lines in Figure 2.3): 1) a warming period from 1926 (beginning of record) to 1950 where temperatures increased at a rate of 0.6 °C per decade, 2) a cooling period from 1950 to 1993 where temperatures decreased at a rate of about 0.25 °C per decade, and 3) a second warming period from 1993 until 2017 with a rate of 1.2 °C/decade. Precipitation measured at the SILA station with a snow- rain gauge is about 760 mm/year. The total mean annual aquifer recharge assessed by Murray (2016) using the Darcy equation, field measurements of suction in the unsaturated zone, and laboratory measurements of relative permeability, is about 210 mm/yr for the entire watershed.

2.3.2 Field instrumentation and data

During a field campaign in summer 2014, the permafrost mound was instrumented with various groundwater and heat monitoring devices, soil moisture and temperature probes, thermistor cables, heat-flux plates, and snow poles fitted with an automated camera. Superficial geological units of the site were also sampled in order to perform laboratory measurements of thermal conductivity. Details on the probes and associated measurements are provided inTable 2.1 Table 2.1 and instrument locations are shown in Figure 2.4a.

Table 2.1: Site instrumentation and measured variables. Variable Accuracy/ Time span Depths Probe Uncertainty (frequency) Soil moisture and temp. Center: 10 probes 0.1 - 2 m* ±0.01 - 0.02 m3/m3 2014-2017 (h) Decagon 5TM probes Side: 10 probes 0.1 - 1.0 m* ±1°C Heat flux Center : 1 plate 8 cm * ±3% 2014-2015 (h) Hukseflux HFP01SC plates: Side: 1 plate 8 cm*

Subsurface temperatures Center: ±0.1°C 2001-2015 (h) Thermistor cables 11 thermistors 2 - 21 m (B)* 2001-2009 (d) 10 thermistors 0 - 12 m Side: 2014-2015 (h) 20 thermistors 1-20 m 2001-2015 (d) 13 thermistors 1-13 m (A)* Thermal conductivity Coarse sand: 60 cm ±10% 2014 Thermal needle probe KD2 Pro Sandy silt: 20 cm Silt: 60 cm Surface temperatures 10 probes, 10 cm deep* ±0.21°C 2014-2017 (h) HOBO Water Temp. Pro V2 Snow depth 5 poles on center/side of the ±5 cm 2014-2017 Reconyx PC800 camera mound (5/day) *These instruments are shown in Figure 2.4a.

Data from the heat flux plates are only available for the year 2014-2015. Thermistor cables had already been installed during a previous field campaign, providing ground temperature records since 2001 from the surface down to the permafrost base (Buteau et al., 2004). Some thermistor cables were replaced during the field campaign in 2014. Thermal conductivities in three undisturbed soil samples were measured in the laboratory with a KD2 Pro Thermal Needle probe (Meter Environment Inc.), and were corrected to take into account the effect of temperature and moisture content. Based on the ground temperature records available for the studied permafrost mound, warming is occurring close to the surface with a significant increase in the active layer thickness from 2 m in 2001 to 4 m in 2017, which represents a mean thawing rate of 13 cm/year. (Figure 2.4b).

Close to the permafrost base, temperatures have been increasing from 2001 to 2010, although a recent decreasing trend has been observed up to 2017. A similar trend is observed in the mean annual air temperatures (MAATs) over the same period. Different responses are thus observed between the permafrost table, where the active layer depth has been generally increasing over the past decade, and the permafrost base, where temperatures have decreased over the past 7 years. This observation suggests that the thermal dynamics of the permafrost mound is controlled by different factors at its surface and at its base.

At Umiujaq, while the MAATs have been decreasing at a mean rate of 0.02 °C/year between 2012 and 2017, air temperatures averaged over the summer periods (July, August, September) have actually been increasing at a rate of 0.03°C/year. Since active layer thickness is generally controlled by the maximum temperature reached in the summer, increasing summer air temperatures due to climate change would therefore be the main cause for the increase in the active layer thickness (IPCC, 2007; Chen et al., 2003). Although to a lesser extent, the active layer thickness would also depend on changes in winter temperatures (Wu and Zhang, 2010). On the other hand, deeper in the system below the depth of zero annual amplitude, based on the observed annual variations of the subsurface temperatures, advective heat transfer due to groundwater flow within the confined aquifer is clearly contributing to increasing temperatures at the permafrost base.

The thermal response of groundwater to variations in air temperature is generally damped and delayed compared to the soil surface temperatures, and depends on many factors including the aquifer depth, flow rates and the thickness and types of overlying soil. Delays on the order of one year, for example, have been observed between shifts in air temperature and the thermal response of groundwater in shallow unconfined aquifers (Kurylyk et al., 2014b; Menberg, et. al., 2014). The temperature at the

permafrost base which is in contact with the aquifer and affected by groundwater flow would then be mainly controlled by the MAAT with a time delay, while the active layer thickness would be controlled by the maximum temperature reached during each summer.

2.3.3 Hydrogeological data

A network of 9 groundwater piezometers for monitoring the shallow and deep aquifers in the Tasiapik Valley (see Figure 2.1), along with 3 thermistor cables in non-permafrost environments, was installed during a drilling campaign in 2012 (see Fortier et al. (2018) for details). Two groundwater wells are located near the studied permafrost mound, one upstream and one downstream in the valley relative to the mound, allowing assessment of the local groundwater gradient. Darcy fluxes of 8.48106 and 6.6810-6 m/s (±1%) were respectively measured in these two wells from dilution tests performed in July 2016 (Jamin et al., 2018). Hydraulic conductivities of the different geological formations found at the study site were measured in 2014 using various methods, including infiltration tests with a Guelph permeameter, slug tests in the groundwater wells and grain size analyses of soil samples collected during the drilling campaign (Fortier et. al., 2014).

2.4 Numerical Model

2.4.1 Theoretical approach

In this study, the transient groundwater flow and heat transport equations were solved using the HEATFLOW finite element numerical model (Molson and Frind, 2018). The code takes into account density-dependent groundwater flow, phase change (freeze-thaw), latent and sensible heat, as well as the effect of temperature on water density and viscosity, thermal conductivity, heat capacity, unfrozen water content and relative permeability. HEATFLOW simulates a saturated flow system, including an option to consider a partially-saturated zone for heat transport. The code has been tested against other coupled groundwater flow and heat transport models including analytical solutions proposed by Lunardini (1985) and benchmarks from the INTERFROST consortium (Grenier et al., 2018; Rühaak et al., 2015). The model has also been successfully tested and applied in a number of field-scale heat storage, permafrost and freeze-thaw modelling studies (Shojae-Ghias et al., 2016 and 2018; Molson et al., 1992).

The HEATFLOW model solves a coupled set of temperature-dependent groundwater flow and heat transport equations. The general advection-dispersion equation for heat transport is expressed as:

  T CTo  θScρvTw w w i  λ  θScρD w w w ij   [2.1] xi  x i  x j  t

where θ is the porosity, Sw is the water saturation, cw is the specific heat of water (J/kg/K), ρw is the water density (kg/m³), 푣𝑖 is the mean linear groundwater flow velocity (m/s), 푇 is the ground temperature (C) (assuming local water-grain thermal equilibrium), 휆̅ is the apparent thermal conductivity of the bulk porous medium (J/m/s/K), Dij is the hydrodynamic dispersion coefficient

3 (m²/s), 퐶표 is the volumetric heat capacity of the porous medium (J/m /K), xi,j are the spatial coordinates (m), and t is time (s). In Equation 2.1, the heat capacity of the porous medium Co is defined by:

Sw Co S w c w  w   S i c i  i ()1   c s  s   i L  [2.2] T where L is the latent heat of water (J/kg) and the subscripts w, i and s represent the water, ice and solids, respectively. The bulk thermal conductivity is a function of the volumetric water, ice and solid fractions defined as:

2 λ θS λ  θS λ (1  θ ) λ  w w i i s  [2.3]

While the simulations account for the non-linear effects of temperature and ice fraction on the transient flow field and thermal parameters, several important assumptions have been made. The Umiujaq site model neglects, for example, cryo-suction as a porous medium freezes or soil consolidation as permafrost thaws. Both effects, however, are considered secondary with respect to the general hydrogeological and thermal behavior of the system. Based on low observed total dissolved solids concentrations in groundwater at the Umiujaq site (Cochand et al., 2018), water geochemistry

is also assumed uniform and dilute, thus effects of freezing-point depression with salinity are assumed negligible.

The numerical HEATFLOW model uses the Galerkin finite element approach with deformable isoparametric brick elements and a pre-conditioned conjugate gradient matrix solver. Picard iteration is applied to couple the flow and heat transport equations for which suitable convergence criteria are applied to the flow-transport coupling (representing maximum allowed head and temperature changes).

2.4.2 Modelling strategy

Starting from assumed initial temperature conditions in the year 1900, the HEATFLOW model was first run until 2017 and manually calibrated using temperature and heat flux data collected on the permafrost mound over the years 2001-2017. This approach allowed the model to first reach a pseudo steady-state condition by around 1920 at which time the observed mean annual air temperatures were applied and which was well before the calibration period of 2014-2017. Data from the study site, including air temperatures, thermal and hydraulic conductivities and snow depths, were used as model input while the surface heat exchange layer parameters were calibrated.

To highlight the role of advective heat transfer, a second simulation was performed assuming otherwise identical conditions but with no groundwater flow. Using a climate warming scenario derived from the ArticNet IRIS (Integrated Regional Impact Study; Allard and Lemay, 2012), the future system behavior was then predicted to the year 2040 by which time the permafrost had completely degraded.

2.5 Conceptual and numerical site model

2.5.1 Physical system

The 2D conceptual model of the Umiujaq site was developed in the vertical plane along the presumed direction of local groundwater flow, oriented along the valley cross-section and transverse to the main stream flowing through the center of the valley (Figure 2.1). Geology and hydrostratigraphic detail of the 2D model was derived from a 3D geological model of the valley developed from previous site investigations by Banville (2016) and Fortier et al. (2018).

The 2D model extends 650 m horizontally between the watershed boundaries, and varies in thickness from about 100 m near the center to 250 m at the boundaries. The base of the model is located 40 m below sea level. The mesh, adapted to conform to the topography and hydrostratigraphic interfaces, is formed of 81×54 deformed rectangular elements in the horizontal and vertical directions, respectively (Figure 2.1).

Physical parameters including thermal conductivities, hydraulic conductivities and porosity, were obtained from field or lab experiments. Unfrozen water content was assessed based on data from soil moisture probes. Where data were not available, values were obtained from the literature. The calibrated parameter values for each layer are summarized in Table 2.2.

Table 2.2: Physical and thermal properties of the different layers of the model (see Figure 2.1 and Figure 2.4 for layer stratigraphy).

Thermal Hydraulic conductivity B Porosity Saturation Layer conductivity K (m/s) θ (-) Sw (-) λ (J/m/s/K) Heat transfer layer 1.0 - 0.20 0.7 E Sand 3.0 A 1.010-5 0.30 C 1 Marine silt 2.7A 110-7 0.40 C 1 Coarse sand 3.0 A 1.510-4 0.35 C 1 Gravel 3.0 D 510-4 0.25 D 1 Fractured bedrock 3.0 D 310-5 0.30 D 1 Bedrock 2.0 F 110-9 D 0.1 D 1 A Thermal conductivity of the solids fraction, based on results from the thermal needle-probe lab test. B Based on grain size analyses and permeability tests on soil samples (Fortier et. al., 2014) C Assessed from lab experiments on soil samples collected from the permafrost mound. D Domenico and Schwartz (1997) E Water saturation in the unsaturated zone, based on data from the 5TM probes at 0.1 m depth. F Luckner and Schestakow (1991)

For all simulations, pre-defined empirical temperature-dependent functions for the unfrozen water

3 3 saturation (Wu , m w/m voids) and the relative permeability (kr) were assumed as defined in Equations 2.4 and 2.5, respectively (Molson and Frind, 2018):

(/)Tq2 Wu ( T ) (1  p )  e  p [2.4]

(1 Wu ( T )) kTr ( ) 10 [2.5] where p is the minimum unfrozen moisture content at low temperatures, and q and Ω are empirical constants which define the variations of the Wu and kr functions with T, respectively. These functions are assumed independent of groundwater chemistry. The parameters used in Equations 2.4 and 2.5, as well as the thermal properties for the solids, water and ice fractions, and convergence criteria for the non-linear coupling, are listed in Table 2.3. The specific temperature-dependent functions Wu and kr assumed in the current model are shown in Figure 2.5.

Table 2.3: Assumed parameter values for the Umiujaq model.

Model parameter Value Reference/comment Solids Specific heat 800 J/kg/K CRC Press (1980) Density 2630 kg/m3 (assuming dominant quartz minerals) Water Specific heat 4184 J/kg/K Density 1000 kg/m3 CRC Press (1980) Thermal conductivity 0.58 J/m/s/K at 10°C Latent heat 3.34105 J/kg Ice Specific heat 2108 J/kg/K CRC Press (1980) Density 920 kg/m3 Thermal conductivity 2.14 J/m/s/K

Convergence criteria Head 0.001 m Temperature 0.1 °C Free watertable 0.001 m

Specific storage 0

Unfrozen water saturation curve (Wu) p=0.2, q=2.0 Molson et al. (1992) Relative permeability function exponent for kr Ω=10 Grenier et al. (2018)

2.5.2 Boundary conditions

The boundary conditions for the flow and heat transport systems are shown in Figure 2.6a and b. a) b)

2.5.2.1 Flow system The top flow boundary represents the water table. Because of a lack of data along the first 200 m, where the water table is located within the fractured rock of the southern cuesta ridge, the Dupuit equation was used to estimate fixed-head water table elevations. Hydraulic heads based on field

measurements and observations are also imposed at two control points along the top boundary, including the main stream flowing through the valley. The imposed heads at these control points correspond to the surface water elevation under the assumption that the system is saturated. Otherwise, the water table is left free to move by applying an average local recharge of 300 mm/year, based on results from Murray (2016). The recharge varies over time as a function of the four seasons and varies in space following the percentage covered by each vegetation type (lichen, bush and spruce) along the cross-section. The left and right vertical boundaries correspond to the watershed boundaries and are thus considered symmetric (no-flow). The bottom boundary, within the sparsely fractured rock, is located about 50 m below the lower aquifer (thus about 2x the depth of the active flow zone), and is assumed impermeable.

2.5.2.2 Heat transport system A heat flux representing the local geothermal gradient (0.032 W/m2; Mareschal and Jaupart, 2004) is imposed across the bottom boundary while the left and right sides are assigned zero temperature- gradient conditions. Because these heat transport boundaries are also no-flow watershed boundaries, these zero-gradient conditions are equivalent to a zero heat flux condition. Along the top transport boundary representing ground surface, the HEATFLOW model allows the parameterization of a heat transfer layer and a corresponding temperature-dependent surface heat flux Ji defined by Equation 2.6 as:

λu Ji T air-( T s  q  c wρ w )  ( T q - T s )  J A [2.6] Bz

where λu and Bz are the thermal conductivity and thickness, respectively, of a conceptual surface heat transfer layer, Tair is the known transient air temperature (°C), Ts is the ground surface temperature

(°C) which is computed in the model, Tq is the temperature of the recharge water, and JA is a supplementary heat flux representing net solar radiation and evaporative heat loss which is mainly used as a calibration parameter. The term λu/Bz is also referred to as the heat exchange coefficient γ

2 (J/m /s/K) (Molson and Frind, 2018). The recharge temperature (Tq) was estimated as the wet-bulb temperature which is calculated based on air temperature and relative humidity measured at Umiujaq.

The conceptual surface heat exchange layer is typically used for model calibration and to handle the spatial heterogeneity of the surface along the longitudinal axis allowing variable snow cover and vegetation. In the model presented herein, calibrated values of the heat flux JA vary from about 3 to 30 W/m2. This heat flux is attenuated during the summer and winter in the topographic depressions on either side of the mounds due to the insulation effect of snow cover and the shade effect of vegetation, respectively. All parameters used in the heat exchange layer are provided in Table 2.4.

Table 2.4: Heat exchange layer parameters according to topography and vegetation type. Topography symbols represent local high or local low topography along the cross-section from left to right.

Topo. ( ( ) ( ) ( ) Variable Vegetation Lichen Lichen Bush Bush Bush Bush Spruce Zone 1 2 3 4 5 6 7 Surface heat flux Mid-summer 27 18 27 18 27 18 18 (W/m2) Oct. – Dec. 17 13 17 13 17 13 13 Mid-winter 3 11 3 11 3 11 11 Apr. – Jun. 19 13 19 13 19 13 13

Recharge rate Mid-summer 622 622 477 477 477 477 352 (mm/yr) Oct. – Dec. 499 499 317 317 317 317 244 Mid-winter 0 0 0 0 0 0 23 Apr. – Jun. 265 265 483 483 483 483 318

Exchange layer Mid-summer 15 15 15 15 15 15 22 thickness (cm) Oct. – Dec. 20 25 20 25 20 25 27 Mid-winter 25 135 25 135 25 135 32 Apr. – Jun. 17 91 17 91 17 91 24

2.5.3 Initial conditions

The initial hydraulic heads are assumed to closely follow surface elevations and are assumed uniform with depth. Since the simulated hydraulic heads rapidly equilibrate to the imposed boundary conditions, and quickly respond to transient recharge, the initial values of the hydraulic heads are much less important than the initial thermal state.

The initial temperature conditions were chosen to represent the estimated temperature and permafrost distribution in 1900 based on the geological history of northern Quebec as well as on local topography, snow cover, and vegetation distribution. Originally, permafrost had aggraded preferentially within the frost-susceptible marine unit in areas of higher elevation which had been exposed to the cold climate,

while depressions which had filled with insulating snow and vegetation remained free of permafrost. It is thought that historical permafrost extended not more than 30 meters deep (Allard and Séguin, 1987), which corresponds to the approximate depth of the marine silt unit. Considering that no temperatures were recorded in Umiujaq at the beginning of the century, estimated local mean average annual temperatures (MAATs) were used based on datasets from the villages of Kuujjuaq and Kuujjuarapik, about 500 km northeast and 160 km south of Umiujaq, respectively. The daily temperatures used as input in the model were then estimated with a cosine function oscillating around the MAAT with a period of 365 days and an amplitude of ±18°C.

The initial assumed temperature state representing the year 1900 is shown in Figure 2.6b. Two main permafrost mounds were emplaced within the unit of marine silt, each about 100 m wide and centered at 320 m and 550 m, respectively. These mounds are separated by an unfrozen zone (talik) below the central stream. Based on current field evidence and interpretations, two additional permafrost zones were also assumed present in 1900: a 150 m wide permafrost zone within the upper fractured rock of the southern cuesta ridge, and a smaller 30 m wide permafrost mound centered at about 250 m, located just south of the central permafrost mound. The permafrost is assumed to initially extend to the base of the marine silt unit with a uniform temperature of -0.5 °C, while the rest of the system is assumed to have an initial temperature of +1 °C.

Because the true initial conditions are unknown, this initial temperature state is acknowledged to be oversimplified. This initial state is nevertheless considered physically realistic, and is early enough in time such that it would not dominate the model calibration over 100 years later. The same conditions are used for comparing the simulation scenarios with and without flow.

2.6 Numerical Simulations

2.6.1 Model Calibration

Model calibration was performed assuming fully coupled groundwater flow and advective-conductive heat transfer. In the subsequent section, this calibration case is referred to as Scenario 1 in a comparison with an otherwise identical case (Scenario 2) but without flow, assuming conduction only.

Calibration was carried out manually by first modifying the heat exchange layer parameters, including the supplementary heat flux (JA), thermal conductivity, and unfrozen water saturation. The thermal conductivity, hydraulic conductivity, and porosities for each soil layer were then modified within a limited range of uncertainty to improve the calibration. During this iterative calibration process, the simulation results were compared with field data from the thermistor cable, soil moisture and temperature probes, as well as with the surface temperature probes and heat flux plates.

The simulation results after calibration are shown in Figure 2.7. Observed ground temperature profiles through the central permafrost mound and at the side of the mound are shown as 4-year averages in Figure 2.7a to show the general trends more clearly and to help reduce noise. Temperature profiles are only shown in mid-summer (average of July, August and September) to better delineate the variations in depths of the permafrost table and base over time, and because some field data were missing in winter months for certain years which would have led to overestimated mean annual average temperatures. The thermistor cable at the edge of the mound was not used for detailed calibration since it doesn’t reach the permafrost base. Due to malfunctions of a few thermistors along this cable starting in 2010, a new thermistor cable was installed during a field campaign in 2014. For this reason, no data are shown in Figure 2.7a (left column) between 2010 and 2013. The simulation results are shown by dashed blue lines at mid-summer for the most recent period from 2014 to 2017. The simulated temperature profiles at the edge of the central permafrost mound, (corresponding to thermistor cable A, left column) and in the center (corresponding to thermistor cable B, right column), are reasonably close to those observed (Figure 2.7a). Within the active layer, in both the observed and simulated summer profiles, the temperatures quickly decrease from the surface down to depths of 2- 4 m. The minimum ground temperatures vary between -0.2 and -3 ºC at depths of 2 to 4 m. Below 12 m, the ground temperatures increase as a function of depth with a gradient of about 0.13 ºC/m. The permafrost base is at a depth of 20-21 m. The high apparent heat flux observed from the temperature profile at the permafrost base is well reproduced by the model.

The unfrozen water content measured in the field from 2014 to 2017 at a depth of 0.1 m is significantly affected by annual variations, reaching a value close to zero when the ground freezes in winter, and varying from 0.2 to 0.3 in summer (Figure 2.7b). Sharp peaks are visible at the end of May when the ground thaws. While these peaks are less pronounced at the side of the mound due to the slower decrease in snow cover, the water content in summer is generally higher in the topographic depression at the mound side due to runoff and infiltration (Figure 2.7b). As part of the calibration, the mean total water saturation (frozen and unfrozen water) in the unsaturated zone was adjusted, while the space- and time-dependent fraction of frozen and unfrozen water is continuously updated by the model based on the simulated temperatures and Wu function. The corresponding simulated unfrozen water content provides a reasonable match to the observed annual variations, but there is no spring peak as observed with the probes.

The effect of thermal insulation in winter due to a thicker snow cover in the topographic depression at the mound side is evident in temperatures recorded at a depth of 0.1 m (Figure 2.7Erreur ! Source du renvoi introuvable.c). While the temperatures at the center of the mound (Fig 2.7c - right column) reach about -20 ºC in mid-winter, the corresponding temperatures at the mound side (Fig 2.7c - left column) are close to the freezing point. In summer, temperatures recorded at the mound top and side are similar, reaching about 10°C. The snow cover is thus an effective insulator, preventing heat loss in the winter and maintaining higher subsurface temperatures. The simulated ground temperatures at this 0.1m depth are close to those observed at both locations, which reflects the spatially and temporally-variable snow cover in the heat exchange layer of the model (Table 2.4).

Heat fluxes measured in 2014-2015 at 8 cm depth at the study site vary between 2 and -1 W/m2 (a positive heat flux reflects heat propagating into the ground). The insulating effect of snow cover reduces the heat flux at the mound side where it remains close to 0 W/m2 (Figure 2.7d). At the mound top, daily variations in heat flux are observed with values reaching -1 W/m2 which represents a net heat loss from the permafrost mound. Observed and simulated heat fluxes are on the same order of magnitude and are affected by similar trends, with a good match at the mound top but simulated fluxes were somewhat lower at the mound side compared to those observed. In general, the calibration is judged acceptable, considering the real system complexity and local scale characteristics that are not included in the model, and considering that only a one-year dataset was used. The overall calibration process showed that parameters of the heat transfer layer were the most sensitive, especially the

supplementary heat flux (JA) and the thermal conductivity. Parameters of the deeper soil layers generally showed a very low sensitivity compared to those of the near-surface layers.

2.6.1.1 Flow system Simulated hydraulic heads, streamtraces and velocity magnitudes from the model are shown in Figure 2.8a and Figure 2.8b. The hydraulic head distribution and streamtrace pattern reflects a complex groundwater flow system with recharge from across the ground surface from the left and right, with flow towards the small stream near the center. Streamtraces reflect the active flow field within the upper fractured rock at the left, being focussed into the lower sand and gravel aquifer below the permafrost and discharging at the surface in the stream. Despite the low permeability of the silt unit underlying the stream, the simulation produced a high rate of groundwater discharge into the stream, which is consistent with the observed stream baseflow. This clearly reveals the high contribution of groundwater flow to the mean flow rate in the stream during both summer and winter (Lemieux et al., 2018; Cochand et al., 2018). The high simulated velocities in the shallowest unconfined portion of the deep aquifer (where it is exposed at the surface) reflect the focused water infiltration at the base of the cuesta due to the presence of permeable colluvium. This infiltration is directly connected to the deeper part of the aquifer.

a) b)

Figure 2.8: Simulated flow field at year 2017 from the calibrated model (Scenario 1) with coupled groundwater flow and heat transport: a) Hydraulic heads and streamtraces, b) Velocity magnitudes.

Simulated groundwater Darcy fluxes in the gravel aquifer below the mound reach values from 3.5  10-7 to 1.75  10-6 m/s in 2017, while the measured Darcy flux was 6.68  10-6 m/s (Jamin et al., 2018). The higher fluxes measured in the field could be attributed to the presence of a groundwater flow component transverse to the cross-section, since the field tracer experiment did not reveal the flow

direction. Streamtraces are also visible in the shallow active layer where seasonal shallow groundwater flow also controls the permafrost dynamics.

2.6.1.2 Heat transport system The simulation results for Scenario 1, which included groundwater flow and advective-conductive heat transport, are shown in Figure 2.9a for three time snapshots: in 1950 (50 years after the beginning of the simulation period), 1993 (93 years), and 2017 (117 years).

Throughout the simulation period, permafrost thaw is occurring around and at the base of the two central permafrost mounds, especially in regions where groundwater flow is most active. More rapid degradation is observed on the left upgradient side of the central mound due to more significant inflow a) b)

of groundwater from the fractured rock layer. From 1950 to 2017, the left upgradient area becomes gradually warmer as warm recharge water infiltrates into the system and migrates downgradient along the dominant flowpath within the confined aquifer below the permafrost. Between 2015 and 2017, for example, the 2ºC temperature contour has migrated from 240 m to about 310 m, and by 2017 the leftmost permafrost mound has almost completely thawed (Fig 2.9a). The discharge zone below the stream (at about 420 m) is also warming over time, in part due to groundwater flow and advective heat transfer from the right (north) recharge area, although because of its more persistent permafrost cover, the contribution of advective heat transfer from the north is much less compared to inflow from the southern cuesta ridge. In addition, and as explained further below in the comparison conduction case, by the time groundwater reaches the discharge zone, it has already lost a significant amount of heat to the overlying permafrost.

Ground temperature variations within the central permafrost mound at x=337.5 m, as a function of depth and time, are given in Figure 2.9a. After equilibrating from the initial conditions over the first 50 years, ground temperatures clearly increase in time both above and below the permafrost mound. For example, from 1950 to 2017, the depth of the permafrost table increases from 1.2 to 2.2 m, while the depth of the permafrost base decreases from about 26.4 m to 19.3 m, reflecting the thermal impacts of groundwater flow within the active layer and within the deep aquifer below the permafrost. The simulated thawing rate at the permafrost base is two times greater over the period from 1993 to 2017 (1.5 m/decade) than between 1950 and 1993 (0.7 m/decade).

Figure 2.10: Simulated ground temperatures in the central permafrost mound (at 337.5 m; see Profile B in Figure 2.4a and Figure 2.7b) as a function of depth and time: a) Scenario 1 with groundwater flow and advective- conductive heat transport, and b) Scenario 2 with thermal conduction only.

2.6.2 Sensitivity analysis: Conductive heat transport

While the simulation results from the calibrated model clearly show the combined impacts of advective-conductive heat transfer on permafrost dynamics (Scenario 1), the contribution of each process was somewhat difficult to identify. A second scenario without groundwater flow (Scenario 2) is therefore provided for comparison in Figure 2.9b and 2.10. In neglecting groundwater flow in both the shallow active layer and within the confined aquifer below the permafrost, this second scenario serves to highlight the role of advective heat transfer on permafrost dynamics as simulated in Scenario 1. The comparison will also illustrate the effect of neglecting coupled groundwater flow and advective heat transport in numerical models which is a common approach in simulating permafrost dynamics (example: Mackenzie and Voss 2013; Wellman et al. 2013).

The simulated variations in ground temperature both in space and time for Scenarios 1 and 2 are provided in Figure 2.9 and 2.10. In comparison to the simulation case with groundwater flow (Scenario 1), the simulation results of Scenario 2 without groundwater flow show colder and warmer zones within the system, depending on their context within the flow system. In general, the permafrost mounds are colder and the permafrost base is deeper in Scenario 2 than in Scenario 1 since there is no advective heat transport component bringing warm recharge water into the deeper system. In the discharge area below the central stream, however, the subsurface in Scenario 2 is warmer than in Scenario 1. This non-intuitive behaviour is explained by the loss of heat along the sub-permafrost groundwater flowpath in Scenario 1. As heat is transferred from the flowing groundwater to the overlying colder permafrost, the permafrost mounds decrease in thickness, and the discharge area thus remains relatively cool. In Scenario 2, heat transfer by vertical conduction alone keeps the discharge area relatively warm since there is no inflowing cool groundwater discharging to the stream.

A similar effect was seen by Shojae-Ghias et al. (2016) in their numerical simulations of groundwater flow and permafrost thaw at Iqaluit, Nunavut, Canada. In their calibrated model, seasonally active groundwater flow in a supra-permafrost permeable zone leads to upgradient warming but downgradient cooling. As groundwater is cooling while flowing along the permafrost table, it maintains colder downgradient temperatures than without advective heat transfer, which attenuates the vertical conductive heat transfer from the ground surface and leads to a decrease in the depth to the permafrost table in the downgradient area. In their SUTRA model of an idealized discontinuous permafrost environment, Mackenzie and Voss (2013) also concluded that thawing of permafrost is more significant closer to recharge zones, and the contribution of advective heating decreases as groundwater cools along the flowpath towards the discharge areas.

This spatial variation in relative warming and cooling increases over time. Starting from identical initial temperature conditions in 1900, by 1950 the spatial extent of the permafrost mounds is clearly greater when groundwater flow is neglected (Figure 2.9b). The differences in temperature between the two scenarios increase over time where the permafrost mounds in 2017 in Scenario 2 are significantly larger and colder than in Scenario 1. Similarly, in the discharge zone in Scenario 2, warming increases over time.

A comparison of the changes in permafrost thickness at the center of the permafrost mound at distances from 300 to 350 m over time, for Scenarios 1 and 2 with and without groundwater flow (Figure 2.10a and 2.10b), respectively, provides added insights into the effect of groundwater flow on the thermal regime. In Scenario 2, ground temperatures slowly increase from the initial conditions towards an equilibrium vertical temperature gradient controlled by conduction between the geothermal heat flux from below and net heat loss across the ground surface (while seasonal heat loss and gain still occurs across the ground surface). By 1950, in Scenario 2, the depth of the permafrost base remains stable at depths on the order of 35-36 m, which is about 16 meters deeper than in Scenario 1. Thus, Scenario 1 with groundwater flow produces the most realistic permafrost thickness and the best match to the general subsurface thermal regime observed in the field.

For the studied permafrost mound at Umiujaq, the depth to the permafrost table is correlated with the maximum summer temperature. Although the MAAT has been decreasing over the last few years, the summer air temperatures were still increasing and the depth to the permafrost table was also accordingly increasing. However, in the model, the simulated depth to permafrost followed the MAAT: decreasing as the MAAT decreased. This can be explained by the fact that the model does not take into account the real seasonal variations in daily mean air temperature, including localized warming in summer, since a cosine curve of constant amplitude is imposed as the daily air temperature. In the model, decreasing the MAAT leads inevitably to decreasing summer temperatures and vice versa. At the permafrost base, ground temperatures recorded from the thermistor cable are correlated with trends in air temperature, with a decreasing depth to permafrost base from 2001 to 2010, and an increasing depth to permafrost base from 2010 to 2017. However, the simulated depth of the permafrost base in Scenario 1 only starts to significantly decrease around 2006, and keeps decreasing until the present, which reflects a delay of about 5 years between the imposed surface conditions and the deeper subsurface thermal regime. This delay could explain why the most recent cooling trend has not yet been reproduced by the model, or that such a delay is attenuating the thermal response of the subsurface to the MAAT.

2.6.3 Predicted permafrost thaw under future climate change

2.6.3.1 Climate change data Projected climate change scenarios over the Nunavik-Nunatsiavut region have been presented by Allard and Lemay (2012) in the ArcticNet Integrated Regional Impact Study based on the Canadian Regional Climate Model (CRCM) (Caya et al., 1995, Caya and Laprise, 1999, Plummer et al., 2006, Music and Caya, 2007). The A2 emission scenario was considered herein to project changes in various climate variables, including changes in air temperature and precipitation during winter (October to April) and summer (May to September). Using these climate change predictions for the Umiujaq study area over the time period from 2041-2070, we derived a temperature increase of 0.9 °C/decade in winter (October to April) and 0.2 °C/decade in summer (May to September), as well as a precipitation increase of 5%/decade. These temperature and precipitation increases were subsequently built into the surface boundary condition of the calibrated Umiujaq model and a future predictive scenario was run until complete permafrost thaw.

2.6.3.2 Simulation results The predictive climate change model was run from the initial conditions in 2017 (calibrated model with advection-conduction) until 2100. Simulation results are shown in Figure 2.11 for four snapshots in time: 2017, 2020, 2030, and 2040. Under the assumed conditions, the climate change scenario shows that the permafrost mound is expected to thaw both from the permafrost table at a mean average rate of 12 cm/year, and from the permafrost base at a mean average rate of 80 cm/year, until thaw is completed by about 2040. In this predictive simulation, a thin layer of soil still remains frozen until end of summer (see 2040 snapshot in Figure 2.11), but thaws completely every fall by about 2040 and thus is not considered permafrost. Degradation mainly occurs at the permafrost base and at the upgradient (left) part of the central permafrost mound and progresses in the direction of groundwater flow. The thaw rate increases even more rapidly during the last decade of the simulation.

Buteau et. al (2004) predicted thawing of the same permafrost mound under a constant increase in the MAAT of 0.05 °C/year, using a one-dimensional heat conduction model taking into account thaw settlement related to drainage of melt water. However, to recreate the high heat flux derived from the field geothermal profiles at the permafrost base, they had to impose an equivalent heat flux of 0.34 W/m2 at the lower boundary, which is 10 times higher than in the current calibrated model with groundwater flow, which was based on a heat flux determined by Mareschal and Jaupart (2004). Buteau et. al (2004) predicted a thaw rate from the permafrost table of 13 cm/year, and from the permafrost base at 5.8 cm/year. Both the simulation results of Buteau et al. (2004) and those presented herein predict similar thawing rates at the permafrost table. However, the predicted thaw rate at the permafrost base from the current advective-conductive heat transfer model is more than 10 times higher than that predicted by Buteau et al. (2004). Interestingly, a similar rate of 6.2 cm/year was predicted in the current model over the last few years of the Scenario 2 simulation which, as in the

Buteau et. al (2004) model, did not consider groundwater flow. The differences between the simulation results of these models with respect to thaw rates at the permafrost base can thus be attributed to the impacts of advective heat transfer.

2.7 Conclusions

Considering the current trend in climate warming observed at northern latitudes, the various heat transfer processes involved in permafrost dynamics must be better understood to allow prediction of future thaw behavior and its subsequent effects on land and infrastructure stability. By calibrating a coupled 2D numerical flow and heat transport model at the well-instrumented Umiujaq field site in Nunavik, Québec, Canada, heat transfer by advection due to groundwater flow, in addition to heat conduction, has been shown to play a critical role on permafrost dynamics. At the Umiujaq site in particular, seasonal groundwater flow in the active layer, as well as continuous flow in the deeper sub- permafrost aquifer, control the thermal regime of permafrost.

Calibration of the coupled groundwater flow and advection-conduction thermal transport model produced a reasonable match to the field data, including to observed temperature profiles and vertical heat fluxes. Neglecting heat transfer by advection due to groundwater flow in the active layer and in the sub-permafrost aquifer, and only considering heat transfer by conduction (Scenario 2), led to colder and thicker permafrost compared to the calibrated model (Scenario 1) and to field observations.

The impacts of groundwater flow on the spatial variation in ground temperature in cold regions depend on the hydrogeological context. Field observations of recharge areas at the Umiujaq study site suggest that groundwater flow transports warm water into the sub-permafrost aquifer. The perennially unfrozen ground below the permafrost base is therefore warmer and the permafrost is thinner than if heat transfer occurred by conduction alone. As the thermal energy transported by groundwater is lost along the flow path to the surrounding cooler medium, groundwater reaching the discharge areas is significantly colder than without such flow and associated heat losses. If groundwater flow is neglected in a model, simulated temperatures at groundwater discharge areas would therefore tend to be overestimated since conductive heat flux would not be attenuated by colder discharging groundwater. Conversely, neglecting groundwater flow would tend to under-predict temperatures in upgradient areas.

At the Umiujaq study site, where sub-permafrost groundwater flow is active and the recharge area is located close to the permafrost mounds, subsurface temperature variations along the deep aquifer are closely correlated to air temperature variations. Based on the simulation results, permafrost thaw is more rapid in upgradient or mid-gradient groundwater flow zones relative to downgradient zones. Under the assumed climate change scenario, permafrost at Umiujaq is expected to thaw from the base at a rate of 80 cm/year until completely thawed around 2040, in about 22 years, while Buteau had predicted a complete thaw by about 2150 without considering groundwater flow.

Although long-term monitoring data relative to both the thermal and hydrogeological regimes are available for the Umiujaq study site, the large number of independent variables in the model with often high uncertainties made the calibration process quite complex. The calibration generally showed a higher sensitivity for parameters from the near-surface layers, especially the heat transfer layer. Work is currently underway to perform a sensitivity analysis and automatic calibration with the PEST inverse calibration code (Doherty 2015, 2016) to identify the critical variables. Another limitation in the model is the assumption that groundwater flow only occurs along the simulated 2D cross-section, while the local flow direction at the study site is likely seasonally variable and could at times be oriented at slightly different angles. Three-dimensional simulations of flow and heat transport at the Umiujaq study site, including the effect of thaw settlement as suggested by Buteau et al. (2004), would improve the simulation results.

3 General Conclusions

The study presented herein is part of a broader project conducted by the groundwater research group at Université Laval, in partnership with the MDDELCC and the Centre d’études nordiques (CEN). The main purpose of this research project was to investigate the impacts of climate change on groundwater resources in the north. In particular, water released from permafrost thaw under a warming climate has been identified as a new and potentially more reliable source of drinking water than surface water for the Inuit communities and growing industries in the region of Nunavik and elsewhere in northern Canada. A better understanding of the interaction between groundwater flow and permafrost dynamics at the study site is one step to achieve this goal.

In this context of climate change and groundwater resources, a 2D numerical model of a cryo- hydrogeological flow system containing a small instrumented permafrost mound near Umiujaq has been developed. Calibration and predictive simulations of the model, which included coupled groundwater flow and heat transport, showed that groundwater flow plays a critical role in permafrost dynamics at the study site. A comparison between the simulation results and field observations has improved the understanding of the current permafrost thermal regime in this discontinuous permafrost region. The rapid thawing simulated at the study site has also provided insight into the potential increase in groundwater availability in the north over the next half-century.

In summary, the following conclusions were made from the simulations: 1. Calibration of the fully coupled groundwater flow and advective-conduction heat transfer model led to a good fit with the observed ground temperatures and heat flux data from the study site. 2. Groundwater flow in the sub-permafrost aquifer at the Umiujaq site can explain the observed high apparent heat flux at the permafrost base. 3. Neglecting groundwater flow in the model leads to slower thaw rates and thicker permafrost. 4. Close to the recharge areas, advective heat transfer by groundwater flow induces warmer ground temperatures and thinner permafrost than by conductive heat transfer alone. 5. Close to discharge areas, groundwater cooled by heat loss along the flow path induces cooler ground temperatures than by conductive heat transfer alone.

6. Permafrost is expected to thaw at the Umiujaq study site at rates of 12 and 80 cm per year at the permafrost table and base, respectively, until permafrost thaw is complete by around 2040.

Following analysis of the simulation results and taking a critical look at the current model, a few recommendations can be made to significantly improve the project’s outcomes.

1. Improve model accuracy Although a full manual calibration of the model has been completed, a sensitivity analysis and automatic calibration are still lacking. Work is currently underway to couple the HEATFLOW model with the PEST model in order to complete an inverse calibration and parameter sensitivity analysis, which is expected to reduce uncertainty of the model, provide improved predictions of permafrost behaviour under climate change, and help to identify critical field parameters which need further refinement.

2. More in-depth investigation into climate change impacts The calibrated model could be further applied to generate new predictions based on additional climate change scenarios. In particular, isolating the effect of predicted temperature increases compared to the effect of increases in precipitation, would allow a better understanding of their individual contributions. Integrating the effect of an increasing snowpack thickness would also provide more realistic predictions. Based on the simulation results presented herein, since groundwater is cooling significantly while flowing in the sub-permafrost aquifer, water in the discharge zone remains cool, even with climate warming. More investigations should be made by following the temperature evolution and energy balance along the flow path, from recharge to discharge, to monitor heat loss to the permafrost units. This would allow to better understand the effect of climate change on the thermal dynamics of groundwater and to extend the modelling approach to aquifers of different sizes and configurations in permafrost environments.

3. Extend the model to three dimensions Using a three-dimensional model would have been the best approach to simulate the complex structure and geometry of the system, but was beyond the scope of this study. The spatial distribution of the surface temperature probes, snow poles and thermistor arrays at the study site already allow a three-dimensional characterisation of thermal processes in and around the permafrost mound.

Additional modelling efforts should therefore be focussed on extending the current model to three- dimensions and increasing the spatial and temporal resolution if needed. This would allow accounting for groundwater flow components in multiple directions and to simulate thawing from both below and around the permafrost mound. However, true groundwater flow directions at the Umiujaq site remain uncertain.

4. Conduct further field investigations of the flow system A major strength of the model is that it relies on valuable thermal and hydrogeological data from the study site, allowing a more realistic representation of field conditions. Despite the wide availability of field data in this project, uncertainties remaining in certain variables represent an important limitation of the model. In particular, further investigations should be undertaken to better estimate the true direction of groundwater flow at the location of the permafrost mound. Permafrost thaw is strongly influenced by the direction of groundwater flow. Knowing the actual direction of flow in the aquifer would thus allow a better prediction of permafrost dynamics. The alignment of wells in the valley along the central stream provided a relatively poor estimation of groundwater flow rates and flow directions in the watershed. The tracer experiment completed in summer 2016 by Jamin et al. (2018) using the FVPDM approach to estimate Darcy fluxes was particularly useful. Further development of the FVPDM method (Jamin et al., 2018) to provide estimates of groundwater flow directions is currently underway and could be applied at the Umiujaq site in the near future. The spatial distribution of wells and the lack of data on the side of the cuesta also led to imposing some simplifications on the flow system in the model. Further hydrogeological investigations in the vicinity of the cuesta should be made to better estimate the water table elevation and recharge rate through the fractured rock.

5. Improve the HEATFLOW code The HEATFLOW model currently simulates a saturated flow system, including an option to consider a partially-saturated zone for heat transport. Eventually, the code could be developed to couple flow and heat transfer in the unsaturated zone to more rigorously investigate heat transfer processes due to recharge, including from snow melt, and to quantify the contribution to the total heat balance. This would allow a better representation of heat transfer occurring in the active layer within the perched aquifer at the study site, and would make the model more suitable for applying at different study sites. The code should also eventually take into account the effect of thaw settlement which has a significant

impact on permafrost thaw as shown by Buteau et al. (2004), and thus could help improve accuracy of the results.

Bibliography

Allard M, Seguin M-K (1987) The Holocene evolution of permafrost near the tree line, on the eastern coast of Hudson Bay (Northern Quebec). Canadian Journal of Earth Sciences 24: 2206–2222.

Allard M, Fortier R, Duguay C, Barrette N (2002) A trend of fast climate warming in northern Quebec since 1993. Impacts on permafrost and man-made infrastructures. American Geophysical Union, Fall Meeting, San Francisco.

Allard M, Lemay M (2012) Nunavik and Nunatsiavut: from science to policy: an integrated regional impact study (IRIS) of climate change and modernization. ArcticNet Inc., Quebec City, Canada, 303 p.

AMAP (2017) Snow, Water, Ice and Permafrost in the Arctic (SWIPA). Arctic Monitoring and Assessment Programme (AMAP), Oslo, Norway. xiv + 269 pp

Atchley AL, Coon ET, Painter SL, Harp DR, Wilson CJ (2016) Influences and interactions of inundation, peat, and snow on active layer thickness. Geophys. Res. Lett., 43, doi:10.1002/2016GL068550.

Banville D-R (2016) Modélisation cryohydrogéologique tridimensionnelle d’un bassin versant pergélisolé: une étude cryohydrogéophysique de proche surface en zone de pergélisol discontinu à Umiujaq au Québec Nordique. M.Sc. Thesis, Université Laval, 278 p.

Bense VF, Kooi H, Ferguson G, Read T (2012) Permafrost degradation as a control on hydrogeological regime shifts in a warming climate. J. Geophys. Res. Earth. Surf.117. doi:10.1029/2011JF002143

Bouwer H and Rice RC. (1976) A slug test method for determining hydraulic conductivity of unconfined aquifers with completely or partially penetrating wells, Water Resources Research, vol. 12, no. 3, pp. 423- 428.

Buteau S, Fortier R, Delisle G, Allard M (2004) Numerical simulation of the impacts of climate warming on a permafrost mound. Permafrost and Periglacial Processes, 15:41–57.

Caya D, Laprise R, Giguère M, Bergeron G, Blanchet JP, Stocks BJ, Boer GJ, McFarlane, NA (1995) Description of the Canadian regional climate model. Water, Air and Soil Pol., 82, 477-482.

Caya D, Laprise R (1999) A semi-implicit semi-Lagrangian regional climate model: The Canadian RCM. Mon. Wea. Rev., 127, 341–362, doi:https://doi.org/10.1175/1520-0493(1999)127<0341:ASISLR>2.0.CO;2.

Cochand M, Molson J, Barth JA-C, van Geldern R, Lemieux J-M, Fortier R, Therrien R (2018) Groundwater hydrogeochemistry in a discontinuous permafrost zone, Umiujaq, Québec, Canada, In submission: Hydrogeology J. (this issue).

Cooper HH, Bredehoeft JD and Papadopulos SS. (1967) Response of a finite-diameter well to an instantaneous charge of water, Water Resources Research, vol. 3, no. 1, pp. 263-269.

Liao C, Zhuang Q. (2017) Quantifying the Role of Permafrost Distribution in Groundwater and Surface Water Interactions Using a Three-Dimensional Hydrological Model, Arctic, Antarctic, and Alpine Research, 49:1, 81-100

Chen, W., Y. Zhang, J. Cihlar, S. L. Smith, and D. W. Riseborough (2003) Changes in soil temperature and active layer thickness during the twentieth century in a region in western Canada, J. Geophys. Res. , 108 (D22), 4696, doi:10.1029/2002JD003355.

CRC Press, (1980) Handbook of Chemistry & Physics, (Ed.: Weast, R.C.), CRC Press Inc.. de Grandpre I, Fortier D, Stephani E (2012) Degradation of permafrost beneath a road embankment enhanced by heat advected in groundwater. Can. J. Earth Sci. 49 (8), 953–962.

Doherty, J., 2015. Calibration and uncertainty analysis for complex environmental models. Watermark Numerical Computing, Brisbane, Australia. ISBN: 978-0-9943786-0-6.

Doherty, J., 2016. Model-independent Parameter Estimation User Manual Part I: PEST, SENSAN and Global Optimisers. Watermark Numerical Computing, Brisbane, Australia, 390.

Domenico P, Schwartz F (1998) Physical and Chemical Hydrogeology, 2nd Edition, John Wiley and Sons, doi: 10.1002/1099-1034(200004/06)35:23.0.CO;2-S, 528 p.

Dupuit, J. (1863) Études théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et à travers les terrains perméables, 2ème édition; Dunot, Paris.

Evans SG, Ge S (2017) Contrasting hydrogeologic responses to warming in permafrost and seasonally frozen ground hillslopes, Geophys. Res. Lett., 44, doi:10.1002/2016GL072009.

Endrizzi, S., S. Gruber, M. Dall’Amico, and R. Rignon. (2014) GEOtop 2.0: Simulating the combined energy and water balance at and below the land surface accounting for soil freezing, snow cover, and terrain effects. Geosci. Model Dev. 7:2831–2857. doi:10.5194/gmd-7-2831- 2014

Fortier R, Lemieux J-M, Talbot Poulin M-C, Banville D, Lévesque R, Molson J, Therrien R (2014) Hydrogéologie d’un bassin versant dans une vallée près d’Umiujaq, Rapport de la phase IIIb du projet de déploiement du réseau Immatsiak remis au MDDEFP, 259p.

Fortier, R, D Roy-Banville, R Lévesque, J-M Lemieux, J Molson, R Therrien, M Ouellet (2018), Development of a 3D cryohydrogeological model of a small watershed in a degrading permafrost environment in Umiujaq, Nunavik, Canada, In submission: Hydrogeology J. (this issue).

Frampton, A., and G. Destouni. (2015) Impacts of degrading permafrost on subsurface solute transport pathways and travel times. Water Resour. Res. 51:7680–7701. doi:10.1002/2014WR016689

Frampton A, Painter SL, Destouni G (2013) Permafrost degradation and subsurface flow changes caused by surface warming trends, Hydrogeology Journal, 21(1), 271–280.

Frederick JM, Buﬀett BA (2015), Eﬀects of submarine groundwater discharge on the present-day extent of relict submarine permafrost and gas hydrate stability on the Beaufort Sea continental shelf, J. Geophys. Res. Earth Surf., 120, 417–432, doi:10.1002/2014JF003349.

Ge, S., J.M. McKenzie, C. Voss, and Q. Wu. (2011) Exchange of groundwater and surface-water mediated by permafrost response to seasonal and long term air temperature variation. Geophys. Res. Lett. 38. doi:10.1029/2011GL047911

Guo D, Wang H and Wang A. (2017) Sensitivity of Historical Simulation of the Permafrost to Different Atmospheric Forcing Data Sets from 1979 to 2009, Journal of Geophysical Research: Atmospheres, 122, 22, (12,269-12,284), (2017).

Grenier C, Anbergen H, Bense V, Chanzy Q, Coon E, Collier N, Costard F, Ferry M, Frampton A, Frederick J, Holmen J, Jost A, Kokh S, Kurylyk B, McKenzie J, Molson J, Mouche E, Orgogozo L, Pannetier R, Rivière A, Roux N, Rühaak W, Scheidegger J, Selroos J-O, Therrien R, Vidstrand P, Voss C (2018) Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases, Advances in Water Resources, vol. 114, p196–218, https://doi.org/10.1016/j.advwatres.2018.02.001.

Healy, R. W. (2010) Estimating groundwater recharge, Cambridge University Press.

IPCC (2007) Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change Core Writing Team. In: Pachauri RK, Reisinger A (eds) IPCC, Geneva, Switzerland.

IPCC (2013) The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 1535 pp.

Ireson AM, van der Kamp G, Ferguson G, Nachshon U, Wheateret HS (2013) Hydrogeological processes in seasonally frozen northern latitudes: understanding, gaps and challenges. Hydrogeology Journal, 21(1):53- 66. https://doi.org/10.1007/s10040-012-0916-5

Jamin P, Cochand M, Dagenais S, Lemieux J-M, Fortier R, Molson J, Brouyère S, (2018) Direct measurement of groundwater flux in permafrost-impacted aquifers: an application of the finite volume point dilution method in Umiujaq (Nunavik, Canada), In submission: Hydrogeology J. (this issue).

Jiang Y, Zhuang Q, O'Donnell JA (2012) Modeling thermal dynamics of active layer soils and near-surface permafrost using a fully coupled water and heat transport model, J. Geophys. Res., 117, D11110, doi:10.1029/2012JD017512.

Karra S, Painter SL, Lichtner PC (2014) Three-phase numerical model for subsurface hydrology in permafrost- affected regions. The Cryosphere Discussions. 8, 149-185.

Kurylyk BL, MacQuarrie KTB, McKenzie JM (2014a), Climate change impacts on groundwater and soil temperatures in cold and temperate regions: Implications, mathematical theory, and emerging simulation tools, Earth-Sci. Rev., 138, 313–334, doi: 10.1016/j.earscirev.2014.06.006.

Kurylyk BL, MacQuarrie KTB, Voss CI. (2014b). Climate change impacts on the temperature and magnitude of groundwater discharge from shallow, unconfined aquifers. Water Resources Research, 50: 3253-3274

Kurylyk BL, Hayashi M, Quinton WL, McKenzie JM, Voss CI (2016) Inﬂuence of vertical and lateral heat transfer on permafrost thaw, peatland landscape transition, and groundwater ﬂow, Water Resour. Res., 52, 1286–1305, doi:10.1002/2015WR018057.

Lemieux J-M, Sudicky EA, Peltier WR, Tarasov L (2008) Simulating the impact of glaciations on continental groundwater flow systems: 1. Relevant processes and model formulation. J Geophys Res 113, F03017. doi:10.1029/2007JF000928

Lemieux J-M, Fortier R, Murray R, Dagenais S, Delottier H, Therrien R, Pryet A. and M Parhizkar (2018) Groundwater dynamics within a discontinuous permafrost watershed, Umiujaq, Nunavik, Canada. In submission: Hydrogeology J. (this issue).

Luckner L, Schestakow WM (1991) Migration Processes in the Soil and Groundwater Zone, Leipzig, Verlag für Grundstoffindustrie.

Luethi R., Phillips M, Lehning M (2016) Estimating non-conductive heat flow leading to intra-permafrost talik formation at Ritigraben rock glacier (Western Swiss Alps). Permafrost Periglac. Process., in press.

Lunardini VJ (1985) Freezing of soil with phase change occurring over a finite temperature difference. In 4th International Offshore Mechanics and Arctic Engineering Symposium, ASM.

Mareschal J-C, Jaupart C (2004) Variations of surface heat flow and lithospheric thermal structure beneath the North American craton, Earth and Planetary Science Letters, 223(1–2): 65–77. doi:10.1016/j.epsl.2004.04.002.

McKenzie JM, Voss CI, Siegel DI (2007) Groundwater flow with energy transport and water–ice phase change: numerical simulations, benchmarks, and application to freezing in peat bogs. Adv. Water Resour. 30 (4), 966–983.

McKenzie JM, Voss CI (2013) Permafrost thaw in a nested groundwater-flow system. Hydrogeol. J. 21 (1), 299–316.

McClymont, AF, Hayashi M, Bentley LR, Christensen BS (2013) Geophysical imaging and thermal modeling of subsurface morphology and thaw evolution of discontinuous permafrost, J. Geophys. Res.-Earth Surf., 118(3), 1826–1837. doi: 10.1002/jgrf.20114.

Measurement Specialties Inc., (2008) 44033RC Precision Epoxy NTC Thermistor. https://www.mouser.com/ds/2/418/44033-736515.pdf, (22 February 2008).

Menberg, K., P. Blum, B. L. Kurylyk, and P. Bayer (2014), Observed groundwater temperature response to recent climate change, Hydrol. Earth Syst. Sci. Discuss., 11, 3637–3673, doi: 10.5194/hessd-11-3637-2014.

Molson JW, Frind EO (2018) HEATFLOW-SMOKER: Density-dependent flow and advective-dispersive transport of thermal energy, mass or residence time, User Guide, U. Laval and U. Waterloo, 116pp.

Molson JW, Frind EO, Palmer C (1992) Thermal energy storage in an unconfined aquifer 2. Model development, validation and application, Water Resources Research, 28(10), 2857-2867.

Murray R (2016) Bilan hydrologique d’un bassin versant dans la région d’Umiujaq au Québec nordique, M.Sc. Thesis, Université Laval, 118 p.

Music B, Caya D (2007) Evaluation of the Hydrological Cycle over the Mississippi River Basin as Simulated by the Canadian Regional Climate Model (CRCM). J. Hydromet., 8(5), 969-988.

Painter SL, Coon ET, Atchley AL, Berndt M, Garimella R, Moulton JD, Svyatskiy D, Wilson CJ (2016) Integrated surface/subsurface permafrost thermal hydrology: Model formulation and proof-of-concept simulations, Water Resour. Res., 52, 6062–6077, doi:10.1002/ 2015WR018427.

Plummer DA, Caya D, Frigon A, Cote H, Giguere M, Paquin D, Biner S, Harvey R, de Elia R, (2006) Climate and climate change over North America as simulated by the Canadian RCM. J. Clim., 19(13), 3112-3132.

Provencher-Nolet, L. (2014) Détection de changements à court terme de la toundra arbustive à partir de photographies aériennes, Région d’Umiujaq, Nunavik (Québec, Canada), Maîtrise, Université du Québec & Institut National de la Recherche Scientifique.

Rasmussen, LH, Zhang, W, Hollesena J, Cable S, Christiansen, HH, Jansson P-E, Elberling B (2018) Modelling present and future permafrost thermal regimes in Northeast Greenland, Cold Regions Science and Technology (146) p199-213, Doi: 10.1016/j.coldregions.2017.10.011.

Rowland JC, Travis BJ, Wilson CJ (2011) The role of advective heat transport in talik development beneath lakes and ponds in discontinuous permafrost. Geophys. Res. Lett. 38 (17), L17504.

Rühaak W, Anbergen H, Grenier C, McKenzie J, Kurylyk BL, Molson J, Roux N, Sass I (2015) Benchmarking numerical freeze/thaw models, EGU General Assembly 2015, Division Energy, Resources & Environment, ERE, Energy Procedia, 76, 301-310, http://dx.doi.org/10.1016/j.egypro.2015.07.866.

Shojae-Ghias M, Therrien R, Molson J, Lemieux J-M (2016) Controls on permafrost thaw in a coupled groundwater flow and heat transport system: Iqaluit Airport, Nunavut, Canada, Hydrogeology Journal, http://dx.doi.org/10.1007/s10040-016-1515-7.

Shojae-Ghias M, Therrien R, Molson J, Lemieux J-M (2018) Numerical simulations of shallow groundwater flow and heat transport in a continuous permafrost setting under the impact of climate warming, In submission to: Canadian Geotechnical Journal.

Sjöberg, Y., Marklund, P., Pettersson, R., and Lyon, S. W. (2015) Geophysical mapping of palsa peatland permafrost, The Cryosphere, 9, 465-478, https://doi.org/10.5194/tc-9-465-2015.

Sjoberg Y, Coon E, Sannel ABK, Pannetier R, Harp D, Frampton A, Painter SL, Lyon SW (2016) Thermal effects of groundwater ﬂow through subarctic fens: A case study based on ﬁeld observations and numerical modeling, Water Resour. Res., 52, 1591–1606, doi:10.1002/2015WR017571.

Stull, R.B. (2011) Wet-Bulb Temperature from Relative Humidity and Air Temperature. Journal of Applied Meteorology and Climatology, 50 (11) 2267-2269.

Voss, CI, Provost AM (2010) SUTRA: A model for saturated–unsaturated variable-density ground-water flow with solute or energy transport. U.S. Geological Survey Water-Resources Investigations, U.S. Geological Survey, Reston, Virginia (260 pp.).

Wang, X.; Chen, R.; Yang, Y. (2017) Effects of Permafrost Degradation on the Hydrological Regime in the Source Regions of the Yangtze and Yellow Rivers, China. Water 2017, 9, 897.

Wellman TC, Voss CI, Walvoord MA (2013) Impacts of climate lake size, and supra and sub-permafrost groundwater flow on lake-talik evolution, Yukon Flats, Alaska (USA). 21 (1), 281–298.

Wu Q B and Zhang T J (2010) Changes in active layer thickness over the Qinghai-Tibetan Plateau from 1995 to 2007 J. Geophys. Res. 115 D09107

Zhang TJ (2005) Influence of the seasonal snow cover on the ground thermal regime: an overview. Rev. Geophys. 43 (4), RG4002.

Zhang, Y, Chen W, Riseborough DW (2006) Temporal and spatial changes of permafrost in Canada since the end of the Little Ice Age, J. Geophys. Res., 111, D22103, doi:10.1029/2006JD007284.

Zlotnik VA and McGuire VL. (1998) Multi-level slug tests in highly permeable formations, 1. Modification of the Springer-Gelhar (SG) model. Journal of Hydrology 204: 271–282.

Appendix A: Coupled cryo-hydrogeological modelling of permafrost degradation at Umiujaq, Quebec Canada (Taken from Dagenais et al., 2017)

Conference paper presented at GeoOttawa 2017

Reference: Dagenais S, Molson J, Lemieux J-M, Fortier R, Therrien R. (2018). Coupled cryo- hydrogeological modelling of permafrost degradation at Umiujaq, Québec, Canada, GeoOttawa 2017: 70th Canadian Geotechnical Conference and 9th Canadian Permafrost Conference, Canadian Geotech Soc, Quebec City, 1st-4th Oct. 2017

Coupled cryo-hydrogeological modelling of permafrost degradation at Umiujaq, Quebec Canada

S. Dagenais, J. Molson, J-M. Lemieux, R. Fortier, and R. Therrien Département de géologie et de génie géologique, Université Laval, Québec (Québec), Canada Centre d’études nordiques, Université Laval, Québec (Québec), Canada

ABSTRACT A two-dimensional numerical model based on field observations of permafrost mounds in the Tasiapik Valley, near Umiujaq, Nunavik, Québec, is developed to help understand the importance of groundwater flow on permafrost degradation. Coupled simulations of groundwater flow and heat transport around and beneath an ice-rich permafrost mound were completed in the vertical plane along the direction of local groundwater flow. The model includes transient density-dependent groundwater flow, advective-dispersive heat transport, latent heat and freeze-thaw feedback effects on the relative permeability. Simulations have shown that advective heat transport by groundwater flow plays a critical role in permafrost degradation and can explain the high apparent heat flux at the permafrost base.

RÉSUMÉ Un modèle numérique en deux dimensions basé sur des observations de buttes de pergélisol dans la vallée Tasiapik, près d’Umiujaq, Nunavik, Québec, est développé pour aider à comprendre l’importance de l’écoulement de l’eau souterraine sur la dégradation du pergélisol. Des simulations couplées de l’écoulement de l’eau souterraine et de la transmission de chaleur autour d’une butte de pergélisol riche en glace ont été complétées dans un plan vertical le long de la direction locale de l’écoulement. Le modèle prend en compte l’écoulement de l’eau souterraine, l’advection et la dispersion de chaleur, la chaleur latente et les effets du gel-dégel sur la perméabilité relative. Selon les résultats obtenus de la modélisation, l’advection de chaleur par l’écoulement de l’eau souterraine joue un rôle critique dans la dégradation du pergélisol et cela peut expliquer le flux de chaleur apparent élevé à la base de la butte.

1 INTRODUCTION

Complex permafrost dynamics depend on many coupled thermo-hydrological processes. Nevertheless, many existing studies on permafrost evolution in a changing climate do not take into account advective heat transport from groundwater flow or are based on idealized field conditions or hypothetical conceptual models (e.g. Riseborough et al. 2008; Zhang et al. 2008; Fortier et al. 2011). The main objective of this project is to understand the importance of groundwater flow on permafrost degradation by developing a numerical model based on field observations of an ice-rich permafrost mound located in the Tasiapik Valley near the Inuit community of Umiujaq, northern Quebec (Figure A.1).

1.1 Study site

The Umiujaq site is located within the discontinuous permafrost zone just above the 55th parallel. During the period of Quaternary glacio-isostatic rebound, permafrost mounds developed in fine-grained frost-susceptible marine deposits exposed to cold climate conditions (Fortier et. al., Figure A.1. Umiujaq site location on Hudson Bay and 2008). Those formations can also be called lithalsas, but permafrost distribution in Nunavik, Quebec, Canada the term ʺice-rich permafrost moundʺ will be used for (Allard and Lemay 2012). consistency with Fortier et al. (2008) who worked on the same study site. These mounds are currently found in a .Field observations within the study area, including shallow 20 m thick silty marine unit, overlying a 10-30 m subsurface temperature measurements collected over the thick sand and gravel deposit forming a confined aquifer past two decades, show that the permafrost table is found (Lemieux et al. 2016) at a mean depth of 2 m while the permafrost base reaches a depth of about 20 m (Figure A.2). Due to the trend of 73

Expected geothermal gradient

Figure A.3. Observed air and ground temperatures over time in a permafrost mound at the Umiujaq study site from Figure A.2. Observed ground temperature profiles within 2012 to 2015. a permafrost mound at the study site from 2001 to 2013. The dashed black line represents the expected geothermal gradient, assuming a heat flux of 0.032 W/m2 and a thermal conductivity of 2 J/m/s/K. climate warming observed over the last 25 years throughout Nunavik, Quebec, permafrost has been degrading in this area over time (Buteau et al., 2004). At Umiujaq, for example, evidence of rapid permafrost warming and thawing has been observed at the permafrost table and base (Figure A.2). These temperatures yield heat fluxes between the confined aquifer and the base of permafrost which are up to ten times higher than expected based on the regional geothermal heat flux of 0.032 W/m2 Figure A.4. Conceptual model of the study site, including (Mareschal and Jaupart 2004). stratigraphy and finite element mesh. Differences in heat flux have been attributed to expected to be more important within the underlying sand groundwater flow in the confined aquifer (Buteau et al. and gravel aquifer (Buteau et al., 2008). 2004). A finite volume dilution test performed in July 2016 Characteristic values of the physical and thermal (Jamin 2017) confirmed the presence of groundwater flow properties of the active layer and permafrost are provided beneath one of the mounds, with Darcy fluxes on the order in Table 1. These values were obtained from a field of 10-4 m/s. calorimetric method (Fortier et al. 1996) and were used by Buteau et al. (2004) for the development of a permafrost 1.2 Physical and thermal properties model with conductive heat transport. Values in Table 1 were used as a guideline for the definition of parameters in Field data characterizing the site’s hydrogeological and the top layers of the numerical model. thermal regimes were collected during field campaigns between 2000 and 2016. Variations in the air and ground Table 1. Physical model parameters. temperature in one of the mounds between 2012 and 2015 are given in Figure A.3. Active Parameter Permafrost The seasonal air temperatures currently oscillate Layer around a mean of -4 °C, extending from about -30 °C in the Volumetric water content [%] 22 - 42 40 - 75 winter to 20 °C in the summer (Figure A.3). A conceptual view of the soil and permafrost units found at the study site Volumetric ice content [%] 10 - 30 30 - 70 is presented in Figure A.4, representing a vertical cross- Porosity [%] 20 - 40 40 - 80 section aligned with the presumed directions of groundwater flow, transverse to the main central stream flowing through the valley. From ground surface, the 2 NUMERICAL SIMULATIONS sequence includes a surficial layer of sand, a marine silt layer containing permafrost, a confined sand and gravel In this study, the transient groundwater flow and heat aquifer, and bedrock (Banville, 2016). transport equations are solved using the HEATFLOW This cross-section was chosen because it contains a numerical model (Molson and Frind 2016). The code takes large instrumented permafrost mound (Figure A.4) located into account phase change (freeze-thaw), latent and in the lower part of the valley where groundwater flow is sensible heat, as well as the effect of temperature on water

density and viscosity, thermal conductivity, heat capacity, Over the past century, the climate in northern Quebec unfrozen water content and relative permeability. has changed significantly, with temperatures increasing most rapidly since 1993 (Allard et al., 2002). While 2.1 Governing equations historical climate data are not available for Umiujaq, air temperature data have been obtained from other villages The HEATFLOW model solves a coupled set of along the eastern shore of Hudson Bay, beginning from the temperature-dependent groundwater flow and heat early 1920’s (Fortier et al. 2011). Although a short cooling transport equations. The general advection-dispersion period was observed from 1965 to 1992, mean annual air heat transport equation is expressed as: temperatures have generally increased since the 1920’s. The simulations herein assume an annual increase of 0.02 °C/yr over the period 1900 – 1990.   T CTo  [1] Sw c w  w vT i     S w c w  w D ij   In this study, the conceptual model was used to x  x  x  t i i j recreate the estimated ground temperature conditions around 1990, before the more significant effects of global where θ is the porosity, Sw is the water saturation, cw is the warming were observed. Additional simulations will be specific heat of water (J/kg/K), ρw is the water density completed later using different flow conditions and warming (kg/m³), 푣𝑖 is the mean linear groundwater flow velocity scenarios to better understand the dynamics between (m/s), T is the ground temperature (C) (assuming local groundwater flow and heat transport, and to predict the future evolution of permafrost thawing. water-grain thermal equilibrium), 휆̅ is the apparent thermal A first simulation case (Scenario 1) was performed conductivity of the bulk porous medium (J/m/s/K), Dij is the under conductive heat transport only (without groundwater hydrodynamic dispersion coefficient (m²/s), 퐶표 is the 3 flow), while a second case (Scenario 2) includes coupled volumetric heat capacity of the porous medium (J/m /K), xi,j groundwater flow and advective-conductive heat transport. are the spatial coordinates (m), and t is time (s). In Equation The simulations were otherwise identical. In Scenario 2 1, the heat capacity of the porous medium Co is defined by: with groundwater flow, the system includes a saturated

zone with transient groundwater flow and heat transport,   S w [2] Co S w c w  w   S i c i  i (1   ) c s  s   i L and an upper unsaturated zone within the active layer with T  a simplified flow system representing mean steady-state

conditions (fluxes and water content), which is also coupled where L is the latent heat of water (J/kg) and the subscripts with transient heat transport. w, i and s represent the water, ice and solids, respectively. The main parameters used for the two simulation For the solids fraction, a specific heat (cs) of 800 J/kg/K and 3 cases, including hydraulic and thermal conductivities, a density (ρs) of 2630 kg/m were chosen, based on porosity and saturation for each layer, are presented in literature data (CRC Press, 1980). The remaining Table 2. The hydraulic conductivities as well as the flow parameters are defined as follows: cw =4184 J/kg/K,, 3 3 boundary conditions are shown in Figure A.5. ρw=1000 kg/m ,, ci=2108 J/kg/K,, and ρi,= 920 kg/m . The The top boundary of the flow domain represents the bulk thermal conductivity is a function of the volumetric water table. Because of a lack of data along the first 200 water, ice and solid fractions defined as: m, where the water table is located within the fractured

2 rock, the Dupuit equation was used to estimate the fixed- [3]  SSw  w   i  i (1   )  s head water table elevations.   Three hydraulic heads corresponding to surface water

elevations, estimated based on field measurements and The model has been successfully tested and applied in observations, are also imposed along the top boundary a number of permafrost modelling studies including (Figure A.5). The imposed 77 m head, for example, Shojae-Ghias et al. (2016) and Rühaak et al. (2015). While the simulations account for the non-linear effects of temperature and ice fraction on the transient flow field and thermal parameters, several important assumptions have been made. The model neglects, for example, cryosuction as a porous medium freezes or the effect of soil consolidation as permafrost thaws. Water composition is also assumed uniform.

2.2 Conceptual model and boundary conditions

Based on previous site investigations including those by Banville (2016) and Fortier et al. (2013), a 2D conceptual model was developed in the vertical plane along the direction of local groundwater flow at the mound site between the watershed boundaries. The mesh, adapted to Figure A.5. Groundwater flow boundary conditions and the conform to topography and to the hydrostratigraphic intrinsic hydraulic conductivity distribution (unfrozen state; interfaces, is formed of 81×54 (x,y) deformed rectangular hydraulic conductivities vary with temperature). elements in a domain measuring 650 x 250 m (Figure A.4). 75

Table 2. Physical and thermal properties of the different layers assumed in the model (see Figure A.4 and Figure A.5 for layer stratigraphy).

Hydraulic conductivity2 Porosity Saturation Thermal conductivity1 Layer K (m/s) θ (-) S (-) λ ( J/m/s/K) w KX KZ Heat transfer layer 3.0 - - 0.3 0.5 Sand 2.0 2x10-3 1x10-4 0.3 1 Marine silt 2.0 1x10-7 1x10-7 0.4 1 Coarse sand 2.0 1x10-3 1x10-4 0.35 1 Gravel 2.0 1x10-2 1x10-3 0.25 1 Fractured bedrock 3.0 2x10-5 2x10-6 0.05 1 Bedrock 3.0 1x10-9 1x10-9 0.05 1 1 The thermal conductivity of the solids fraction is based on results from a thermal needle-probe lab test. The values used for λwater and λice are respectively 0.58 and 2.14 J/m/s/K. 2The hydraulic conductivity values were chosen within a certain range estimated by Fortier et. al. (2014) on the basis of a grain size analysis made on soil samples for each unit. represents a small stream which intercepts water from the referred to as the heat exchange coefficient γ (J/m2/s/K) deep aquifer. (Molson and Frind 2016). Otherwise, the water table is left free to deform under a The conceptual heat exchange layer is typically used recharge of 60 mm/year, representative of the average for model calibration and to handle the spatial annual recharge estimated at the study site (Murray 2016). heterogeneity of the system along the longitudinal axis The left and right vertical boundaries correspond to the (snow cover, vegetation, etc). In the current model, watershed boundaries and are thus considered symmetric calibrated values of the exchange coefficient varied from (no-flow). The bottom boundary, within the sparsely 0.3 to 30 J/m2/s/K, being lowest during the winter in the fractured rock, is located about 50 m below the lower topographic depressions on either side of the mounds (due aquifer, and is assumed impermeable. to the insulation effect of snow cover). Water saturation The heat transport boundary conditions are shown in also increases towards the right boundary to simulate the Figure A.6. A heat flux representative of the geothermal presence of a thicker organic soil or vegetation layer. gradient in the area (0.032 W/m2) is imposed at the bottom The initial assumed temperature state representing the boundary while the left and right sides are assigned zero year 1900 is shown in Figure A.6. Two relatively large heat-flux (insulated) conditions. Along the top transport permafrost mounds were placed within the marine silt, boundary representing ground surface, the HEATFLOW separated by an unfrozen zone (talik) below the central model allows the parameterisation of a heat transfer layer, stream. The permafrost is assumed to extend to the base defined by: of the silt with a uniform temperature of -2.5°C, while the rest of the system is assumed to have an initial temperature λu [4] of +2°C. Ji T air  T s ( q  c wρ w )  ( T q  T s ) Bz Although the true initial conditions are unknown, this initial temperature state is acknowledged to be simplified. 2 where Ji is the thermal flux (W/m ), λu and Bz are the It will nevertheless be useful for comparing the simulation thermal conductivity and thickness, respectively, of a scenarios with and without flow, and to provide insight to conceptual surface heat transfer layer, Tair is the air facilitate model calibration. temperature (°C) (given), Ts is the surface aquifer All simulations assume given temperature-dependent temperature (°C) (computed by the model), and Tq is the functions for the unfrozen water content (Wu) and the temperature of the recharge water. The term λu/Bz is also relative permeability (kr), defined in Equations 5 and 6, Time (yr) respectively, as: Heat transfer layer ) 10

C  0 ( 2

r 0 1 2 3 4 ((/)) Tq [5] i -10

200 a Wu ( T ) (1  p )  e  p

T -20

)

(

l -2.5 C v and

l 100

N  (1 Wu ( T ))

f kT( ) 10 +2 C r [6]

N 0 0 100 200 300 400 500 600 where p is the terminal unfrozen moisture content at low Geothermal heat flux 0.032 W/m2 temperatures, q and Ω are empirical constants which define the curvature of the Wu and kr functions, respectively, and θ is the porosity. The chosen functions Figure A.6. Heat transport boundary conditions and initial for the current simulations are provided in Figure A.7 and temperature conditions assumed in the model.

are assumed independent of the groundwater chemistry. sand and gravel aquifer below the permafrost and See Molson and Frind (2016) for further details. discharging to the surface stream (Figure A.8b). Simulated groundwater flow velocities in the gravel aquifer below the mound in 1990 reach values from 1x10-5 to 1x10-4 m/s, 1 1 which is about 3 to 30 times lower than the value of 3x10-4 m/s measured in a field tracer experiment in 2016, 0.8 0.8 considering an estimated porosity of 0.3 (Jamin 2017). This

) apparent increase in flow rate between 1990 (simulated) 0.6 0.6 )

( Wu(T) ( and 2016 (observed) is consistent with the hypothesis of

k W 0.4 0.4 enhanced groundwater flow due to thawing of the mound

k r (T) during the intervening 26 years of climate warming. 0.2 0.2 The simulated temperature profiles and permafrost 0 0 thickness at the centre of the central mound over time, for -5 -4 -3 -2 -1 0 1 Temperature (C) Scenarios 1 and 2 (with and without groundwater flow), clearly illustrate the effect of the flow field on the thermal regime (Figure A.9). In Scenario 1 with only thermal Figure A.7. Temperature-dependent functions assumed in conduction (Figure A.9a), temperatures continually the model for the unfrozen moisture content (Wu) and the decrease from the initial condition towards an equilibrium relative permeability (kr), with p=0.2, q=2.0 and Ω = 10 temperature gradient controlled by conduction between the applied herein. For simplicity, the kr function is shown only geothermal heat flux from below and heat loss across the for a porosity of 0.35 (coarse sand). ground surface. By 1990, the permafrost base is over 40 m 2.3 Results deep, which is unrealistic, while the active layer is about 1 m thick. The two comparison simulations start at t=0 (year 1900) In Scenario 2 with groundwater flow (Figure A.9b), after and were run for 33,000 days (~90 years, to year 1990) equilibrating from the initial conditions over the first 20 with a maximum time step of 2 days. The results are shown years, temperatures increase in time both above and below at the full cross-section scale as well as at the local mound the permafrost mound. By 1990, the simulated permafrost scale. table has reached a depth of about 3-4 m, while the depth Hydraulic heads and velocities for the Scenario 2 case to the permafrost base decreases from about 30 m to about with groundwater flow are shown respectively in 25 m, reflecting the thermal impacts of groundwater flow Figures A.8a and A.8b. The hydraulic head distribution within the active layer and within the deep aquifer below reflects a complex groundwater flow system with recharge the permafrost base. from across the ground surface at the left and right, and With respect to the observed current thermal state, the with flow towards the small stream near the centre. Velocity simulated depth to the permafrost base in 1990 is magnitudes show dominant flow in the layers of higher considered reasonable, given the 25+ years of added effective hydraulic conductivities, including within the deep warming before reaching current conditions. However, the unfrozen sand and gravel aquifer. Streamtraces reflect the active flow field within the upper fractured rock at the left, extending into the lower a)

Figure A.8. Flow solution at year 1990 for Scenario 2 with groundwater flow: a) hydraulic heads and b) velocity Figure A.9. Simulated vertical temperature profiles in the magnitudes and streamtraces. The solid black line in central permafrost mound over time, comparing: a) Figure A.8a represents the location of the simulated Scenario 1 with thermal conduction only, and b) Scenario 2 vertical temperature profiles shown in Fig. A.9. with groundwater flow and heat transport. See Fig. 8a for profile location. 77

simulated thickness of the active layer in 1990 is already 1990, a small isolated permafrost mound remains in the somewhat greater than observed today. Additional centre of the section, about 90 m long and with a maximum simulations will include adjustments to the ground surface thickness of about 25 m, consistent with estimated thermal parameters to improve the calibration. conditions in 1990. The full temperature solution for the two scenarios, While the central permafrost mound in Scenario 2 has without groundwater flow (heat conduction only) and with significantly degraded by 1990, a large part of the marine flow, are shown in Figures A.10a and A.10b, respectively. silt unit to the right of the stream remains frozen (Figure In the first case (Scenario 1; Figure A.10a), under A.10b). This is primarily due to the less extensive recharge conductive heat transport only, the permafrost thickness area between the stream and the right-side watershed increases slowly over time as it approaches thermal boundary, compared to the recharge area left of the equilibrium. By the year 1990, the permafrost base has stream. Groundwater infiltration and flow rates are reached a depth of about 70 m while the unfrozen zones therefore relatively less on the right side of the model, and on either side of the central mound are maintained. The thawing rates are therefore slower. temperature at the base of the model below the central The current simulations extended only to 1990. A full mound decreases to about 0.5°C, while at the model base calibration with the Scenario 2 model to current conditions, near the left boundary it increases to about 2.5°C, since it including groundwater flow and the observed rapid is further below ground surface. increase in mean annual air temperatures since 1990, is In the second, more realistic case (Scenario 2), which underway. includes groundwater flow, significant warming is observed throughout the system (Figure A.10b). Thawing occurs around and beneath the initial two permafrost mounds, 3 CONCLUSIONS especially in regions where groundwater flow is most active. More rapid degradation is observed on the left side A preliminary 2D vertical cross-sectional cryo- of the central mound due to more significant inflow of hydrogeological model across the Tasiapik Valley near groundwater from the upgradient fractured rock layer. By Umiujaq, Quebec, has shown that groundwater flow plays 4b a) Scenario 1, No flow, thermal conduction only 4b b) Scenario 2, with groundwater flow Year 1990 Year 1990

200 200 Temp. (C) Temp. (C)

)

(

. . -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6

l l 100 100

0 C 0 C 0 0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Distance (m) Distance (m)

100 Year 1910 100 Year 1910

)

( ( 0 C

. . 0 C

v v 50 50

0 0 200 250 300 350 400 450 200 250 300 350 400 450

100 Year 1950 100 Year 1950

)

(

. . 0 C

v v 50 0 C 50

0 0 200 250 300 350 400 450 200 250 300 350 400 450

100 Year 1990 100 Year 1990

)

( ( 0 C

v v 50 50

E E 0 C

0 0 200 250 300 350 400 450 200 250 300 350 400 450 Distance (m) Distance (m) Figure A.10. Simulated temperatures (in mid-winter) after 10, 50 and 90 years for: a) Scenario 1 without groundwater flow (thermal conduction only) and b) Scenario 2 with coupled groundwater flow and advective-conductive heat transport. The 0°C isotherm is provided for comparison among the profiles.

a significant role in permafrost thaw at this site. By carrying Allard M. and Lemay M. 2012 Nunavik and Nunatsiavut: more heat energy from ground surface into the aquifer from science to policy: an integrated regional impact underlying the base of permafrost, groundwater infiltration study (IRIS) of climate change and modernization. leads to higher subsurface temperatures and more rapid ArcticNet, Quebec City, QC, 303 p. thawing at the permafrost base, compared to heat transfer Banville, D.-R. 2016. Modélisation cryohydrogéologique from thermal conduction alone. Shallow groundwater flow tridimensionnelle d’un bassin versant pergélisolé: une also induces more rapid permafrost thaw at the permafrost étude cryohydrogéophysique de proche surface en table while the no-flow simulation produces an zone de pergélisol discontinu à Umiujaq au Québec unrealistically deep permafrost layer. Nordique. M.Sc. Thesis, Université Laval, 278 p. Coupled groundwater flow and heat transport after 90 Buteau, S., Fortier, R., Delisle, G. and Allard, M. 2004. years resulted in a simulated depth of the base of Numerical simulation of the impacts of climate warming permafrost of about 25 m, compared to a depth of about 70 on a permafrost mound. Permafrost and Periglacial m if flow was neglected. This coupled groundwater flow Processes, 15:41–57. and heat transport simulation also showed that the CRC Press, 1980. Handbook of Chemistry & Physics, (Ed.: permafrost remains preferentially in the marine silt layer Weast, R.C.), CRC Press Inc.. due to its relatively low hydraulic conductivity. Persistent Domenico, P., and Schwartz, F. 1997. Physical and permafrost in the silt to the right side of the model is likely Chemical Hydrogeology, John Wiley and Sons, doi: due to lower groundwater fluxes in this area near the 10.1002/1099-1034(200004/06)35:23.0.CO;2-S, 528 p. watershed boundary. Fortier R., Allard M., and Sheriff F. 1996. Field estimation Thermal insulation of the subsurface from cold winter air of water-ice phase composition of permafrost samples temperatures also plays an important role in controlling the using a calorimetric method. Canadian Geotechnical thermal regime. This insulation effect is reproduced in the Journal 33(1): 355–362. model by a conceptual thermal exchange layer separating Fortier, R., LeBlanc, A.-M., Buteau, S., Allard, M. and the ground surface from the given air temperatures. This Calmels, F. 2008. Internal Structure and Conditions of layer is especially important within the topographic Permafrost Mounds at Umiujaq in Nunavik, Canada, depressions which have a deep winter snow cover keeping Inferred from Field Investigation and Electrical the subsurface free of permafrost. Resistivity Tomography. Canadian Journal of Earth Rising air temperatures due to climate change over the Sciences, Vol. 45, pp. 367-387. coming decades are expected to accelerate permafrost Fortier R., LeBlanc A.-M., and Wenbing, Y. 2011. Impacts thaw in this valley. Future climate change scenarios are of permafrost degradation on a road embankment at underway and will be completed using a fully calibrated Umiujaq in Nunavik (Quebec), Canada, Canadian model over the period 1990-2016, using the year 1990 Geotechnical Journal, 48(5): 720-740. doi: results presented here as the initial condition. 10.1139/t10-101. Fortier, R., Lemieux, J.-M., Therrien, R. and Molson, J. 2013. Campagne de forages pour l’installation de puits 4 ACKNOWLEDGEMENTS d’observation des eaux souterraines dans un petit bassin versant pergélisolé à Umiujaq, Rapport de la This project is supported by a Strategic Project Grant from phase III du projet de déploiement du réseau the Natural Sciences and Engineering Research Council of Immatsiak remis au MDDEFP, 89 p. Canada (R. Therrien, PI), as well as by NSERC Discovery Fortier, R., Lemieux, J-M., Talbot Poulin, M-C., Banville, D., Grants to the last four authors. We also thank the Ministère Lévesque, R., Molson, J. and Therrien, R. 2014. du Développement durable, de l’Environnement et de la Hydrogéologie d’un bassin versant dans une vallée Lutte contre les changements climatiques (MDDELCC), près d’Umiujaq, Rapport de la phase IIIb du projet de Quebec, and the Centre d’études nordiques at Université déploiement du réseau Immatsiak remis au MDDEFP, Laval for their logistical and financial support during the 259p.Jamin, P. 2017. Personal communication. field work at Umiujaq. Pierre Therrien of the Département Lemieux J-M., Fortier, R., Talbot-Poulin, M-C., Molson, J., de géologie et de génie géologique at Université Laval Therrien, R., Ouellet, M., Banville, D., Cochand, M. and provided valuable computational support. Murray, R., 2016. Groundwater occurrence in cold environments: Examples from Nunavik, Canada. Hydrog. J., http://dx.doi.org/10.1007/s10040-016- 5 REFERENCES 1411-1. Mareschal, J.-C. and Jaupart, C. 2004. Variations of Allard M., and Seguin M-K. 1987. The Holocene evolution surface heat flow and lithospheric thermal structure of permafrost near the tree line, on the eastern coast of beneath the North American craton, Earth and Hudson Bay (Northern Quebec). Canadian Journal of Planetary Science Letters, 223(1–2): 65–77. Earth Sciences 24: 2206–2222. doi:10.1016/j.epsl.2004.04.002. Allard, M., Fortier, R., Duguay, C. and Barrette, N. 2002b. Molson, J.W. and Frind, E.O. 2016. HEATFLOW- A trend of fast climate warming in northern Quebec SMOKER: Density-dependent flow and advective- since 1993. Impacts on permafrost and man-made dispersive transport of thermal energy, mass or infrastructures. American Geophysical Union, Fall residence time, User Guide, U. Laval and U. Waterloo, Meeting 2002. 116pp.

Murray, R. 2016. Bilan hydrologique d’un bassin versant dans la région d’Umiujaq au Québec nordique, M.Sc. Thesis, Université Laval, 118 p. Riseborough, D., Shiklomanov, N., Etzelmuller, B., Gruber, S. and Marchenko, S. 2008. Recent advances in permafrost modelling, Permafrost and Periglacial Processes. 19:137-156. Rühaak, W., Anbergen, H., Grenier, C., McKenzie, J., Kurylyk, B.L., Molson, J., Roux, N. and Sass, I. 2015. Benchmarking numerical freeze/thaw models, EGU General Assembly 2015, Division Energy, Resources & Environment, ERE, Energy Procedia, 76, 301-310, http://dx.doi.org/10.1016/j.egypro.2015.07.866. Shojae-Ghias, M., Therrien, R., Molson J. and Lemieux, J- M. 2016. Controls on permafrost thaw in a coupled groundwater flow and heat transport system: Iqaluit Airport, Nunavut, Canada, Hydrogeology Journal, http://dx.doi.org/10.1007/s10040-016-1515-7. Zhang, Y., Chen, W. and Riseborough, D.W. 2008. Disequilibrium response of permafrost thaw to climate warming in Canada over 1850–2100, Geophysical Research Letters, 35, L02502, doi:10.1029/2007GL032117 .

Appendix B: Literature review

Table A.1: Recent studies involving modelling of permafrost dynamics (in chronological order)

Main Author Goal Region PF Extent Model Model Dim. A B C D E F Type Size * * * * * * Physics- 1D Luethi et al. (2017) Intra-permafrost flow Swiss Alps Glacier Snowpack X X X X X based 1  20

Result: Advection dominance

GW discharge MODFLOW- FD 3D Liao et al. (2017) Tanana Flats Basin, Alaska Discontinuous X X GW/SW interaction USGS 500  500

Result: Permafrost influences flow regime

GW discharge Hypothetical high latt/alt 2D Evans et al. (2017) Continuous SUTRA FE X X X X ALT sites 220  250

Result: Increased ALT and discharge 1D and 2D Zhang et al. (2017) GW recharge Alpine China Isolated SHAW-DHM Empirical X X X X X 8000  6000 Result: Increased GW recharge and base flow

Painter et al. (2016) ALT, GW discharge Hypothetical Arctic tundra Discontinuous ATS FD 1D and 3D X X X X X

Result: Increased ALT (preliminary results) ALT, permafrost area, Guo et al. (2017) Northern Hemisphere All CLM - X X X X Historical (1900-2010) Result: Rate of surface and ALT decrease - Wang et al. (2017) GW discharge Yellow River, China Continuous - - X 600  100 km

Result: Increased winter discharge ratio, decreased Qmax/Qmin ratio

Rassmussen et al. Sensitivity of soil props. and Physics- 1D Zackenberg, Greenland Continuous CoupModel X X X X (2017) AL props. based 1  10 m

Result: Importance of in-situ soil parameter estimation

GW advec./cond. Tavvavuoma, North 1D and Sjoberg et al. (2016) Sporadic ATS FD X X X X X Lateral thawing Sweden 2D 10  5 m

Result: Advection importance

Peat-Plateau wetland NEST 1D and 3D Kurylyk et al. (2016) PF thaw Discontinuous FE X X X X X X Northwest Territories SUTRA 50  120  60

Result: PF thaw (Conduction dominance), enhanced GW flow 1D and 2D Atchley et al. (2016) Sensitivity of ALT Hypotethical Artic Continuous ATS FD X X X X

Result: Decreased ALT with peat increase, increased ALT with snow depth

Frederick and Buffet Beaufort shelf, Artic 2D ALT, GW discharge Continuous No name FV X X X X X (2015) Canada 150  1.5 km

Result: Importance of submarine GW discharge in evolution of permafrost Frampton and 2D GW/perm interact Physic- Destouni Hypothetical Discontinuous MarsFlo 30  100 X X X X PF thaw, Solute transport based (2013;2015) Result: Increased ALT and decreased seasonal variability

1D and 3D Endrizzi et al. (2014) Model description Hypothetical High alt/latt Geotop 2.0 FD X X X X X 120  160

Result: Relevance of GeoTop for permafrost thaw modeling

Mackenzie et al. 2D PF thaw Hypothetical Continuous SUTRA FE X X X X X (2013) 2000  5000

Result: Increased PF thaw

2D Bense et al. GW discharge Hypothetical Artic Continuous FlexPDE FD 200  1000 X X X X (2009;2012) Base and supra flow 600  10 000

Result: Increased GW discharge

2D Ge et al. (2011) ALT, PF temp, GW discharge Tibet plateau Continuous SUTRA FE X X X X X 200  250

Result: Increased ALT and increased discharge

Rowland et al. Effect of GW flow on sub- 2D Hypothetical Alaska Discontinuous ARCHY FD X X X (2011) lake talik dev. 200  60

Result: Increased PF thaw Discontinuous 1D Jiang et al. (2012) ALT Alaska and Hydrus FD X X X X X X 50 m continuous Result: Increased ALT

De Grand-pré et al. PF thaw under groundwater 2D Alaska Discontinuous Seep/W FE X X X (2012) flow 100  3 m

Result: Increased PF thaw

Wellman et al. 2D Talik formation, PF thaw Yukon Flats, Alaska Discontinuous SUTRA FE X X X X X X (2013) 500  1800

Result: Increased PF thaw * Contains an ‘X’ if the following criteria are considered in the study: A - Advective heat flux, B - Climate change, C - Coupled water/heat, D - Data from field, E - Surface processes, F - Surface/subsurface flow * Abbreviations: ALT (Active layer thickness), GW (Ground water), PF (Permafrost), SW (Surface water), FE (Finite-element), FD (Finite-difference), FV (Finite-volume)

Appendix C: Instrumentation and vegetation of the Tasiapik valley watershed

Figure B.1: Instrumentation and vegetation of the Tasiapik valley watershed. Adapted from Murray (2016) with vegetation data from Provencher - Nolet (2014)

Appendix D: Hydraulic conductivities measured in the Tasiapik valley

Table D.1: Hydraulic conductivity K estimated based on effective diameter d10 of analysed soil samples (Fortier et. al. 2014).

Hydraulic conductivity Number of Quaternary formation samples K max K min K median (m/s) (m/s) (m/s) Littoral and pre-littoral sediments (sand) - Mb 4 8.66  10-4 2.21  10-4 4.55  10-4 Intertidal sediments (sand) - Mi 3 2.55  10-4 7.26  10-6 7.36  10-6 Deep sea marine silt sediments (silt and sand) - Ma 21 2.98  10-5 4.13  10-8 1.18  10-7 Glacial outwash deposits (sand and gravel) - Gs 13 1.19  10-3 3.24  10-6 1.52  10-4 Frontal moraine sediments (sand, gravel) - GxT 3 1.83  10-3 2.82  10-4 5.03  10-4

Table D.2: Hydraulic conductivity measured with slug tests (Fortier et. al. 2014). Water level Screen K Piezo. Aquifer compared Analysis method Aquifer type penetration (m/s) to screen Pz 2 unconfined partial Above* Cooper et al. (1967) 4.9  10-5 Deposits (Mb) Bouwer and Rice Pz 3 unconfined complete Inside -5 Rock (basalt) (1976) 2.7  10 Deposits (GxT: 54%) Pz 4 confined partial Above Cooper et al. (1967) -6 9.9  10 Rock (arenite: 46%) Deposits (GxT et Zlotnik and McGuire Pz 6 confined* partial Above -4 Gs:81%) (1998) 1.6  10 Rock (arenite: 19%) Bouwer and Rice Deposits (GxT: 17%) Pz 8 unconfined partial Above * -4 (1976) 1.7  10 Rock (basalt: 83%) Deposits (Gs/GxT: 31%) Pz 9 unconfined partial Above * Cooper et al. (1967) -6 3.1  10 Rock (69%) *Determining conditions for the choice of analysis method

Table D.3: Hydraulic conductivities measured with the Guelph permeameter in the Tasiapik valley watershed (Fortier et. al. 2014).

K (m/s) Site Guelph Hazen (1982) PG_PDP 2.0  10 -04 7.3  10 -4 PG_GS_riv_Umi 1.1  10 -04 2.4  10 -4 PG_rav_N_E 3.2  10 -05 5.9  10 -5 PG_banc_emprunt_canal 2.1  10 -05 - PG_butte_sylvie_buteau_sable 2.6  10 -05 1.1  10 -4 PG_bord_de_route 5.0  10 -05 7.3  10 -5 PG_PBS1409 5.6  10 -05 - PG_PDL 3.0  10 -05 7.4  10 -4

Figure D.1: Location of the sites in the Tasiapik valley where the Guelph permeameter experiments were conducted (Fortier et. al., 2014).