Horizontal and Temporal Variability of Transport Processes in Lakes

HORIZONTAL AND TEMPORAL VARIABILITY OF TRANSPORT PROCESSES IN LAKES

Alexander LeBaron Forrest

B.Eng. & Soc., McMaster University, 2002 B.Sc., McMaster University, 2002 M.A.Sc., University of British Columbia, 2004

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

The Faculty of Graduate Studies

(Civil Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

(Vancouver)

August 2011

Abstract

This work examines the three dimensional nature of three important physical transport processes in lakes: (1) convection generated from a negative surface buoyancy flux; (2) transport resulting from rotational adjustment; and, (3) underflow fate during episodic wind stirring. Vertical and horizontal temperature gradients were characterized using a combination of traditional (moorings and vertical profilers) and novel techniques (an Autonomous Underwater Vehicle) at two sites; Pavilion Lake, British Columbia, Canada and Lake Thingvallavatn, Iceland. The former site is a relatively small (5 km2), temperate lake, with comparatively low snow cover that allows solar radiation to be the dominant energy flux to the system during late winter months. Analysis of water temperature distribution in surface waters during summer and winter enabled convective patterns resulting from a negative surface buoyancy flux to be inferred. In addition to previously studied physical transport phenomena, this work has revealed the existence of a cyclonic eddy under winter ice cover in Pavilion Lake, consistent with the internal Rossby radius of deformation, extending down to ~ 14 m below the ice surface and rotating with an azimuthal speed of ~ 3 cm s-1 (as predicted by equations of cyclogeostrophic flow). Horizontal temperature transects beneath the eddy revealed temperature fluctuations associated with 1 – 2 m vertical displacements in the region 5 m directly below the eddy and are thought to be an undocumented source of mass transport. The latter field site was an embayment of a larger (88 km2) subarctic lake with a groundwater inflow that propagates through the embayment as a negatively buoyant underflow. Surface wind shear events entrain the underflow into the overlying lake water. This entrainment alters the characteristics and the ultimate fate of the underflow in the lake. Calculated entrainment of the underflow and entrainment calculated from the bulk Richardson number are in close agreement. Measurements made during these studies not only elucidated details of the three dimensional nature of known transport mechanisms but also revealed previously undiscovered modes of mass transport associated with wintertime lake hydrodynamics.

Preface

While all of the research presented herein represents original work on behalf of the author, several collaborators have contributed during the editorial process, which have helped guide the creation of this final product. A long list of people also participated in each of the field deployments that helped to ensure successful operations.

Chapter 2 is based on fieldwork conducted in Pavilion Lake, British Columbia, Canada in both the summer of 2006 and the winter of 2007 by Alexander Forrest and Dr. Bernard Laval. During both deployments, I was responsible for all logistics, experimental field design, data collection, and post-processing. Dr. Bernard Laval and Dr. Roger Pieters provided guidance during the drafting of the original manuscript with Dr. Darlene S.S. Lim, the other collaborator on this work, contributing to the final editorial process. A version of this chapter has been published; Forrest, A.L., Laval, B.E., Pieters, R., and Lim, D.S.S. 2008. Convectively driven transport in temperate lakes. Limnol. Oceanogr. 53(5, part 2), 2321–2332.

Chapter 3 is a return to Pavilion Lake, BC, in the winter of 2008, by Alexander Forrest and Dr. Bernard Laval. Once again, I was responsible for all aspects of the project with Dr. Bernard Laval and Dr. Roger Pieters providing guidance during the drafting of the original manuscript and Dr. Darlene Lim, the other collaborator on this work, contributing to the final editorial process. Initial results have been published as Forrest, A.L., Laval, B.E. and Pieters, R. 2009. Under-ice convection in a temperate lake. International Association of Hydraulic Engineering and Research (IAHR). Vancouver, BC, Canada. 8 pages. The more detailed analysis presented in Chapter 3 of this thesis is in the process of being submitted.

Chapter 4 represents collaboration between Alexander Forrest, Dr. Hrund Andradóttir, and Dr. Bernard Laval during the winter of 2009 at Lake Thingvallavatn, Iceland. For this project, I was responsible for all aspects of the project, except for the measurements taken with an Aquadopp ADV, which were provided by Dr. Hrund Andradóttir. Initial results have been published as Andradóttir H.Ó., Forrest A.L., and Laval B.E. 2009. Fate of groundwater inflow in Lake Thingvallavatn during early spring ice-breakup, Proceedings of the 13th International Workshop

iii

on Physical Processes in Natural Waters, Sept 1 – 4, Palermo, Italy. This previous work was written equally by myself and Dr. Hrund Andradóttir. I was responsible for drafting of this chapter that has been accepted for publication to the Journal of Aquatic Sciences.

In addition to the scientific advances that have been made in this work, I have been responsible for, or coauthored, several manuscripts in an effort to document the engineering lessons learnt during the course of my PhD studies:

Forrest, A.L. and B.E. Laval. (2007). Charting lacustrine environments with UBC-GAVIA. AUV Science in Extreme Environments, Scott Polar Research Institute, Cambridge, UK. 7 pages.

Forrest, A.L. and B.E. Laval. (2007). Seasonal thermal structure of Pavilion Lake. AUV Science in Extreme Environments, Scott Polar Research Institute, Cambridge, UK. 7 pages.

Forrest, A.L., H. Bohm, B.E. Laval., E. Magnusson, E., R. Yeo, and M.J. Doble. (2007). Investigation of under-ice thermal structure: Small AUV deployment in Pavilion Lake, BC, Canada. Oceans 2007 IEEE/MTS. Vancouver BC, Canada. 9 pages.

Doble, M.J., P. Wadhams, A.L. Forrest, and B.E. Laval. (2008). AUV deployment through ice: two years of Arctic experience. Cold Regions Science and Technology. 56: 90 – 97.

Forrest, A.L., B.E. Laval, M.J. Doble, E.J. Magnusson, and R. Yeo. (2008). AUV measurements of under-ice thermal structure. Oceans 2008 IEEE/MTS. Quebec City, PQ, Canada. 10 pages.

Forrest, A.L. and B.E. Laval. (2009). From oceans to lakes - applying new tools in limnology. Journal of Ocean Technology. 4(1): 36 – 45.

Crees, T., C. Kaminski, J. Ferguson, J.M. Laframboise, A.L. Forrest, J. Williams, E. MacNeil, D. Hopkins, and R. Pederson. 2010. UNCLOS under ice survey - An historic AUV deployment in the Canadian high arctic. Oceans 2010 IEEE/MTS. Seattle, WA, USA. 8 pages.

As part of my involvement with different research groups over the course of my PhD studies, I have also been involved with authoring, or coauthoring, other works:

Lim, D.S.S., B.E. Laval, G.F. Slater, D. Antoniades, A.L. Forrest, W. Pike, R. Pieters, M. Saffari, D. Reid, D. Schulze-Makuch, D. Andersen, and C.P. McKay. (2009). Limnology of Pavilion Lake, B. C., Canada - Characterization of a microbialite forming environment. Fundamental and Applied Limnology. 173(4): 329 – 351.

Forrest, A.L., B.E. Laval, D.S.S. Lim, D.R. Williams, A.C. Trembanis, M.M. Marinova, R. Shepard, A.L. Brady, G.F. Slater, M.L. Gernhardt, and C.P. McKay. (2009). Performance evaluation of underwater platforms in the context of space exploration. Planetary and Space Science. 58(4): 706 – 716.

Lim, D.S.S., G.L. Warman, M.L. Gernhardt, C.P. McKay, T. Fong, M.M. Marinova, A.F. Davila, D. Andersen, A.L. Brady, Z. Cardman, B. Cowie, M.D. Delaney, A.G. Fairén, A.L. Forrest, J. Heaton, B.E. Laval, R. Arnold, P. Nuytten, G. Osinski, M. Reay, D. Reid, D. Schulze- Makuch, R. Shepard, G.F. Slater, and D. Williams. (2010). Scientific field training for human planetary exploration. Planetary and Space Science. 58(6): 920 – 930.

Table of Contents

Abstract ...... ii Preface...... iii Table of Contents ...... vi List of Tables...... viii List of Figures ...... ix Acknowledgements...... x Dedication ...... xi 1 Introduction...... 1 1.1 Review of Relevant Limnology...... 3 1.1.1 Convection Driven by a Negative Buoyancy Flux...... 3 1.1.2 Transport Resulting from Rotational Adjustment...... 6 1.1.3 Negatively Buoyant Underflows...... 8 1.2 Autonomous Underwater Vehicles...... 9 1.3 Previous Work at the Study Sites...... 12 1.4 Work Objectives...... 13 2 Convectively Driven Transport in a Temperate Lake...... 14 2.1 Introduction ...... 14 2.2 Methods ...... 15 2.2.1 Site Description...... 15 2.2.2 Data Collection ...... 16 2.3 Summertime Campaign (Cooling Heat Flux)...... 18 2.3.1 Summertime Observations...... 18 2.3.2 Surface Layer Heat Budget...... 23 2.3.3 Convective Motion...... 24 2.3.4 Intrusion Propagation...... 25 2.4 Wintertime Campaign (Radiative Heat Flux)...... 27 2.4.1 Wintertime Observations...... 28 2.4.2 Surface Heat Flux ...... 33 2.4.3 Convective Motion...... 35 2.5 Conclusions...... 36 3 A Cyclonic Eddy in an Ice-Covered Lake ...... 39 3.1 Introduction ...... 39 3.2 Methods ...... 40 3.2.1 Site Description...... 40 3.2.2 Data Collection ...... 40 3.3 Observations ...... 43 3.3.1 Observed Eddy Characteristics...... 44 3.3.2 Observed Eddy Evolution...... 48

3.4 Discussion ...... 51 3.4.1 Eddy Behavior ...... 51 3.4.2 Beneath the Eddy...... 55 3.4.3 Eddy Erosion...... 58 3.5 Summary and Conclusions ...... 59 4 Preconditioning of an Underflow During Ice-Breakup in a Subarctic Lake ...... 61 4.1 Introduction ...... 61 4.2 Methodology...... 63 4.2.1 Site Description...... 63 4.2.2 Field Measurements...... 64 4.2.3 Net Thermodynamic Flux from Bulk Aerodynamic Formulae...... 66 4.3 Results...... 67 4.3.1 Ice Cover Erosion and Break-up...... 67 4.3.2 Inflow Characterization...... 68 4.3.3 Observed Water Column Response to Dominant Wind Regimes ...... 70 4.3.4 Vertical Characterization of the Underflow...... 72 4.3.5 Horizontal Characterization of the Underflow...... 74 4.4 Discussion ...... 78 4.4.1 Weak Wind-Forcing ...... 79 4.4.2 Strong Wind-Forcing ...... 82 4.5 Conclusions...... 85 5 Conclusions ...... 87 5.1 Research Summary ...... 87 5.2 Contributions and Recommendations...... 89 5.2.1 Autonomous Underwater Vehicles ...... 89 5.2.2 Convection Associated with a Negative Buoyancy Flux...... 90 5.2.3 Motion Resulting from Rotational Adjustment...... 91 5.2.4 Negatively Buoyant Underflow Modified Through Wind-Stirring ...... 93 Bibliography ...... 95 Appendices...... 105 Appendix A: Differential Solar Heating ...... 105 Appendix B: Entrainment Prediction...... 109 Appendix C: UBC-Gavia AUV Description ...... 111 Appendix D: Vehicle Deployments...... 120

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List of Tables

Table 2.1: Lake and ice characteristics at three stations in the Central Basin...... 30 Table 3.1: Summary of transects and profiles collected during the field deployment...... 43

viii

List of Figures

Figure 1.1: Typical four-layer stratification associated with radiatively driven convection ...... 5 Figure 1.2: Conceptual illustration of under-ice submerged rotating eddies...... 7 Figure 1.3: Conceptual illustration of an unsteady, negatively buoyant underflow...... 9 Figure 1.4: Schematic of UBC-Gavia...... 11

Figure 2.1: Bathymetry of Pavilion Lake with location in British Columbia, Canada...... 16 Figure 2.2: Meteorological measurements during the summertime campaign...... 19 Figure 2.3: Bin-averaged vertical temperature profiles ...... 20 Figure 2.4: Horizontal temperature transects in the surface mixed layer ...... 21 Figure 2.5: Horizontal temperature transects at the depth of the thermocline...... 22 Figure 2.6: Meteorological measurements during the wintertime campaign ...... 29 Figure 2.7: Vertical temperature profiles on three separate winter days ...... 31 Figure 2.8: Horizontal temperature measurements at the depth of the surface layer ...... 32 Figure 2.9: Horizontal temperature measurements at 6.20 m depth in the convective layer...... 33 Figure 2.10: Horizontal temperature measurements at 17.00 m depth in the convective layer.... 34

Figure 3.1: Bathymetry of Pavilion Lake with location in British Columbia, Canada...... 41 Figure 3.2: Temperature collected by the AUV using a horizontal lawnmower survey ...... 45 Figure 3.3: Horizontal transects at four depths along and across the Central Basin ...... 46 Figure 3.4: Observed temperature composite from five repetitions of 0.75 m transect ...... 47 Figure 3.5: Vertical CTD profile survey collect on 22 Feb 2008 ...... 48 Figure 3.6: Temporal evolution of horizontal temperature transects in the CL...... 49 Figure 3.7: Daily solar irradiance and observed water temperature time series...... 50 Figure 3.8: Solutions to the cyclogeostrophic flow equation for a specified density field...... 53 Figure 3.9: Along basin horizontal temperature measurements with the CL and the QL ...... 56 Figure 3.10: Multiple horizontal temperature measurements collected at 14.28 m...... 57 Figure 3.11: Summary illustration of the observed and proposed processes...... 59

Figure 4.1: Location of Silfra Bay shown relative Lake Thingvallavatn, Iceland...... 65 Figure 4.2: Position of ice cover on Silfra Bay approximated from field observations ...... 68 Figure 4.3: Observed meteorological forcing and water column response ...... 69 Figure 4.4: Bin-averaged temperature profiles taken at the deep and shallow mooring lines...... 72 Figure 4.5: Temperature contours from a CTD transect at 10:00 hrs, 24 Feb 2009...... 73 Figure 4.6: Vertical temperature profiles in Silfra Bay and the main body of the lake...... 75 Figure 4.7: Horizontal temperature profiles collected at a 2 m constant depth ...... 76 Figure 4.8: Horizontal temperature profiles collected at a 2 m constant altitude...... 78 Figure 4.9: Illustration of a 2D model of an idealized underflow system ...... 80 Figure 4.10: Predicted mixing periods based on water column mixing energy...... 84

Acknowledgements

Over the course of this work, I have encountered many wonderful people around the world who have encouraged me to achieve more than I had ever planned. First and foremost I need to thank Bernard Laval, my supervisor, for never hesitating to support me in all my endeavors. Secondly, over the course of my research, the entire crew of talented scientists and engineers who work at Pavilion Lake have become an integral part of my research no matter how far afield I go. A special recognition must be made to Darlene Lim, Chris McKay, Dale Andersen, Donnie Reid, David Williams, and Geoff Mullins who challenged me to explore in different directions. I also need to thank Val Schmidt, Nicole Raineault, and Adam Skarke, and especially their director, Art Trembanis, from the Coastal Sediments, Hydrodynamics, & Engineering Lab at the University of Delaware, who dreams as large as I do. The welcome that I received in Iceland, especially by Hrund Andradóttir and Pasquale Amendola (University of Iceland) and Einar Sæmundsen (Thingvellir National Park Service), is the only reason that the research there was possible at all. Similarly, without the efforts of Geoff Schladow, marion wittmann, and Brant Allen (Tahoe Environmental Research Center), it would not have been possible to achieve all that we did in Lake Tahoe. A special thanks also goes to Steve McPhail, Ken Collins, and Maaten Furlong, amongst many others from the Autosub group at the National Oceanographic Centre whose efforts to put AUVs under-ice never ceases to inspire. Those people who share my polar obsession including Martin Doble, (Laboratoire d’Oceanographie de Villefranche), Chris Roper (Roper Resources), and Jeremy Wilkinson (Scottish Association for Marine Science), deserve special note, as, without them, I would have never made it to such remote corners of the world. I would also like to thank the teams from International Submarine Engineering, Defence Research and Development Canada, Memorial University and Natural Resources Canada, with special notice to James Ferguson, Chris Kaminski, Tristan Crees, Gina Miller, Ron Verrall, Jeff Williams, Richard Pederson, Peter King, and Ron Lewis who helped redefine the role AUVs can play in Arctic exploration. Finally I would like to say how proud I am to be one of the ‘Gaviators’; Bernard Laval, Harry Bohm, Richard Yeo, Eggert Magnusson, Brian McFadden, Weston Pike, Val Schmidt, Nicole Rainault, Larry Kost, Claudine Fortier, Art Trembanis, and Andrew Hamilton. I can only hope to share adventures with them again in the future.

Dedication

for my wife and our families

1 Introduction

Mixing and transport in lakes is primarily driven by fluxes of mass, heat and mechanical energy through the free surface, inflows, or outflows. This work characterizes the three dimensional, time evolving nature of three important physical transport processes as they occur in two different lakes: (1) convection generated from a negative surface buoyancy flux; (2) transport resulting from rotational adjustment; and, (3) mixing induced by underflow propagation.

In open-water, away from inflows, wind shear and thermodynamic fluxes at the free surface are the primary drivers of mixing (Imberger, 1998). The energy imparted by wind shear will result in top down stirring of the water column (Findikakis and Law, 1999). When wind shear is absent, surface cooling drives convection in the surface layer (Lei and Patterson, 2006). In ice-covered conditions, the water column is effectively isolated from wind shear and warming of the ice- water interface through solar volumetric heating is one of the main sources of near-surface convection (Farmer, 1975). Vertical temperature gradients in the water column result from this radiatively driven convection (Mironov et al., 2002). Horizontal temperature gradients will result from spatial variations in volumetric heating (i.e., different levels of light attenuation in a heterogeneous ice cover; Bengtsson, 1986b).

Unlike open-water conditions where wind stirring mixes horizontal temperature gradients on timescales of hours to days, under ice-cover density anomalies potentially endure for timescales of days to months (Chao and Shaw, 1998). These longer timescales allow sufficient time for density anomalies to respond to rotational adjustment without becoming mixed into the background stratification. Although eddy formation from rotational adjustment has been studied under sea-ice (Manley and Hunkins, 1985), this constitutes a previously unobserved mass transport process under lake-ice.

In both summer and winter, stratification in the vicinity of inflows will be controlled by the buoyancy flux associated with the inflow. Depending on the sign of the buoyancy flux, lake inflows initially form overflows or underflows (Carmack et al., 1979). Underflows will propagate downslope, while entraining ambient water, to the point of neutral buoyancy. At this

1 1: Introduction point, the underflow will either form an intrusion into the ambient stratification or, if denser than the ambient stratification, continue flowing downslope as controlled by the bathymetry (Wells and Wettlaufer, 2007). Surface driven wind mixing will modify underflow behavior in those regions where depths are sufficiently small that wind stirring can entrain the underflow into the overlying water.

These physical transport processes vary on spatial scales from small (1 mm) to basin-scale (> 1 km) and timescales from seconds to years. Studies of these processes generally characterize vertical variability well; however, the associated horizontal variability has been less comprehensively studied. The ability to characterize horizontal and vertical gradients to the same resolution is logistically challenging using surface-based techniques. This work focuses on integrating observations of both vertical and horizontal temperature variability to characterize the three-dimensional, time evolving nature of basin-scale lake processes. Temporal and vertical variability were measured using traditional instrumentation (moorings and profilers) and horizontal variability was measured using an Autonomous Underwater Vehicle (AUV) as a data collection platform. This work examines waters that are both open and ice-covered. An AUV allows measurements to be made in open-water conditions that would otherwise be challenging, and measurements to be made under-ice that would otherwise be impossible.

Section 1.1 of this chapter provides an overview of the physical processes that are relevant to this work. As the AUV is a relatively novel data collection platform and influences the sampling methodology, it is described in detail in Section 1.2. A review of previous studies conducted at the study sites is given in Section 1.3. The objectives of this study are presented in Section 1.4. Chapter 2 describes the investigation of convectively driven transport in Pavilion Lake, British Columbia, Canada during evening cooling in the summer of 2006 and afternoon radiative heating in the winter of 2007. Chapter 3 describes a follow-up study in the winter of 2008, which highlights the role rotational adjustment plays under ice as a cyclonic eddy is described. To our knowledge, this is the first eddy under lake-ice to be observed and characterized. Chapter 4 explores inflow propagation in Lake Thingvallavatn, Iceland in the winter of 2009; a location where incoming groundwater forms a significant underflow into the lake. Underflow response to

2 1: Introduction the two dominant wind regimes was described through a series of measurements made during the spring ice-cover break-up.

1.1 Review of Relevant Limnology

Each of the subsequent chapters of this work explores new insights that arise from combining measurements of horizontal and vertical water column variability. This combination allows the three-dimensional, time evolving nature of physical transport processes to be better characterized. This section reviews the processes studied in each of the subsequent chapters: (1) convection associated with a negative surface buoyancy flux, (2) transport resulting from rotational adjustment, and (3) mixing induced by underflow propagation. The first and last of these processes are well-studied phenomena in lakes and observations presented in this work contribute to the knowledge of the associated three-dimensional structure. In contrast, motion associated with rotational adjustment has, to our knowledge, never been documented under lake ice.

1.1.1 Convection Driven by a Negative Buoyancy Flux

Above the temperature of maximum density, convection in freshwater lakes occurs during periods of surface heat loss (Wells and Sherman, 2001). The surface layer of lakes is defined as the portion of the water column, directly below the free surface, influenced by surface conditions. This layer is generally separated from underlying, hypolimnetic waters by a region of increasing density referred to as the metalimnion. Many have described this thermal structure in detail (Imberger, 1985; Monismith et al., 1990; Saggio and Imberger, 2001). During periods of surface wind shear away from inflows, surface wind stress is the dominant mechanism by which momentum and turbulent kinetic energy is provided to the system (Imberger, 1985). During periods where wind shear is absent, surface buoyancy flux controls mixing of the surface layer (Lei and Patterson, 2002).

The dynamics of the surface layer have been extensively studied in both the field (Imberger and Parker, 1985; Imberger and Hamblin, 1982; Monismith, 1985) and modeled using numerical techniques (Horsch and Stefan, 1988; Horsch et al., 1994; Lei and Patterson, 2006). Convection

3 1: Introduction resulting from both a uniform and differential surface heat flux has been studied extensively (e.g. Monismith et al., 1990) and has shown motion to be associated with gravitational instabilities in the form of convective plumes and density currents (Horsch and Stefan, 1988). Work in this field has modeled the various characteristics of these instabilities (e.g. entrainment, velocity, etc.; Wells and Wettlaufer, 2005). With the development of techniques that better resolve horizontal variability, plumes and density currents can now be characterized in an unprecedented way (Fer et al., 2002c).

Below the temperature of maximum density, the absorption of shortwave radiation directly below the ice surface creates a negative buoyancy flux. This flux results in gravitational instabilities, which drive convective motion in the water column (Mironov et al., 2002). At the onset of these instabilities, the typical inverse stratification associated with winter ice cover will initially be sharpened (Pieters and Lawrence, 2009) before forming the following four-layer structure (Figure 1.1): a stably stratified diffusive surface layer (SL) in direct contact with the underside of the ice; a well-mixed convective layer (CL) that deepens and warms with added heat input; an entrainment layer (EL) from which underlying fluid is mixed into the CL; and, a weakly stratified quiescent layer (QL) that continues to the bottom (Jonas et al., 2003).

As solar radiation penetrates the SL, gravitational instabilities will form at the top of the CL. These instabilities will descend as convective plumes with velocities of 1 – 10 mm s-1 (Mironov et al., 2002). These plumes will descend to the bottom of the CL, on a timescale of several minutes, where water from the QL will be entrained through penetrative convection. Through this process, the CL will deepen over time while concurrently warming at a rate of 0.025 – 0.25 ºC d-1 (Mironov et al, 2002; Jonas et al., 2003). When solar radiative forcing ceases at sunset, these motions will slowly come to a halt before starting up again during the next day.

Radiatively driven convection has been observed in the field and modeled in laboratory and numerical studies. Barnes and Hobbie (1960) were the first to report on radiatively driven convection as a physical transport process in ice-covered lakes. Farmer (1975) then made the first systematic field observations of this process in Babine Lake, Canada. Using a variety of field techniques, the temporal evolution of the thermal structure was described and compared

4 1: Introduction

Figure 1.1: Typical four-layer stratification (SL, CL, EL and QL) associated with radiatively driven convection (Pavilion Lake, BC, Canada on 18 Feb 2007). Bottom of profile represents lake depth. with a time-dependent mixed-layer model (Farmer, 1975). This thermal structure was further examined in the late spring of 1994 and 1995 in a series of studies in Lake Vendyurskoe and Lake Rindozero (Bengtsson and Svensson, 1996; Malm et al., 1997). Convective overturning was not observed in these studies as the water column was almost at the temperature of maximum density, and a slight conductivity stratification was sufficient to stabilize the system (Malm et al., 1997).

All of these studies used a combination of vertical profiling and moorings to measure temperature, conductivity, or velocity within the water column. The next evolution in instrumentation was the direct measurement of temperature microstructure, which led to estimates of the turbulent kinetic energy (TKE) dissipation rate (Jonas et al., 2003). The majority of under-ice studies to date have been based on vertical profiling techniques, either at a single

5 1: Introduction mooring location (Jonas et al., 2003) or a small number of locations along horizontal transects (Bengtsson, 1996).

Many laboratory studies have examined the problem of boundary-driven convection from distributed heat sources (Park and Whitehead, 1998) as would be associated with radiatively driven convection; few studies have described systems at or below the temperature of maximum density (Myrup et al., 1970; Ivey and Hamblin, 1989). A number of numerical studies have modeled radiatively driven convection using the mixed layer model of Farmer (1975) or some variation thereof (Patterson and Hamblin, 1988; Bengtsson, 1996). Most recently, a large-eddy simulation model was applied to simulate radiatively driven convection in the CL. This model was then coupled to a simple mixed layer model to predict layer growth (Mironov et al., 2002).

1.1.2 Transport Resulting from Rotational Adjustment

In oceans, density anomalies associated with salinity gradients may give rise to eddy formation through rotational adjustment. Under sea-ice, Chao and Shaw (1996) suggested eddies form from density anomalies resulting from shallow brine or freshening sources beneath the ice surface. These sources generally result from differential heat flux at the ice / water interface. Differential surface heating or cooling will create localized areas of ice melt (freshwater generation) or ice formation (brine generation; Smith et al., 2002). Under certain conditions, a shallow axisymmetric brine source produces a shallow cyclone and underlying anticyclone pairing. With an ice cover, the shear between the water and the ice damps the top eddy while leaving the submerged one intact. Conversely, a freshening source will generate an opposite rotation pairing (Chao and Shaw, 1998). Figure 1.2 provides a conceptual schematic of under-ice submerged rotating eddies.

Deviations of isohalines from the horizontal provide the driving force for eddy formation and maintenance. Since fresher waters rise and spread, rather than more saline waters sinking, Chao and Shaw (1998) found that the associated eddy pair was shallower and weaker for freshwater formation than for brine rejection sources of comparable strength. The observed horizontal length scale of these eddies have been found from Arctic field data to be equivalent to the Rossby radius (Timmermans et al., 2008).

6 1: Introduction

Figure 1.2: Conceptual illustration of submerged oceanic eddies under ice in the absence of currents. The dashed contours represent the region underneath the ice cover where sources of fresher or more saline waters are being applied and dashed-dot lines represent isohalines.

Since, even in open water, field studies of rotational phenomena tend to be quite complex (Kirillin et al., 2008), work to date has generally been in a laboratory. For example, Fernando et al. (1991) studied the effects of rotation and convective turbulence using a uniformly distributed heat source along the bottom of a rotating table in homogenous fluid. It was several years later that the compounding effects of stratification (Ivey et al., 1995; Levy and Fernando, 2002) and differential heating (Condie and Griffiths, 1989; Park and Whitehead, 1998) were investigated.

Using an evenly distributed heat source, and both homogenous and stratified fluids, Coates and Ivey (1997) examined the effects of varying rotation rates on eddy formation. The multiple eddies that formed spun with an equal distribution of cyclonic and anti-cyclonic rotation. Narimousa (1998) generated eddies using a localized circular region of destabilizing flux in a rotating tank with a localized saline water source. Similar to earlier work, the formation of multiple eddies was observed near the source of the negative buoyancy flux; however, over time, a much larger single eddy, approximately the same size as the source itself, formed and continued to spread both radially and vertically. This was proposed as one of to be one of the formation mechanisms of the deep-sea chimneys that are seen in the Arctic Ocean (Wadhams et al., 2004; Spall et al., 2008).

7 1: Introduction

1.1.3 Negatively Buoyant Underflows

Inflow propagation depends primarily on the density of the inflow relative to the density of the ambient water column. The density contrast between the two waters will result in the inflow being either positively or negatively buoyant. Negatively buoyant water will propagate until such depth, known as the intrusion depth, where the ambient water is of greater or equal density (Wells and Wettlaufer, 2007; Fer et al., 2002a). In cases where such a depth does not exist, the generated underflow will continue to a depth controlled by the bathymetry (Dallimore et al., 2001).

Figure 1.3 provides a schematic of a typical unsteady, density underflow (i.e., a leading front is illustrated) with an underflow of thickness, hu, moving at a constant velocity, u, as indicated.

Underflow thickness increases along the bed through entrainment (E = dhu/dx; as indicated by the dotted line) of overlying water into the underflow. Ellison and Turner (1959), and a number of studies since then, have shown that hu increases linearly as a function of distance downslope (Dallimore et al., 2001; Gu et al., 1996; Cenedese et al., 2003). This entrainment of overlying fluid into the underflow has a velocity, known as the entrainment velocity, w, associated with it.

Several authors have developed empirical models (Fischer et al., 1979), analytical solutions (Jirka, 2007) and numerical approximations (Jirka, 2003) to describe these flows in both summer and winter months (Fischer et al., 1979; Carmack et al., 1979). Several laboratory (Ellison and Turner, 1959; Hallworth et al., 1996) and numerical studies (Hetland, 2005; Rueda and MacIntyre, 2009) have examined the associated flow dynamics. A great deal of this research has focused on examining mixing induced by the underflow and the related entrainment.

Density underflows also arise from negatively buoyant convective plumes in the surface layer. These plumes will initially descend to the lakebed where they will form density currents that will begin propagating downslope as a density underflow (Horsch and Stefan, 1988). These underflows will undergo the same evolution as those generated from riverine inputs. If the underflow does not penetrate the thermocline and flow to depth, it will form an intrusion (Wells and Wettlaufer, 2007). This process will continue until the density contrast between the two

8 1: Introduction

Figure 1.3: Conceptual illustration of an unsteady, negatively buoyant underflow for a point source into a water body. layers is reduced to the point where intrusion does occur and is a function of the width of the basin, the density contrast between layers, and the buoyancy flux associated with the underflow.

1.2 Autonomous Underwater Vehicles

Autonomous Underwater Vehicles (AUVs) are tetherless unmanned submersibles, preprogrammed to execute a series of commands with minimal to no surface communications (i.e., limited operator input). As operations are untethered, AUVs are increasingly being used in environments that would be challenging to reach with traditional research vessels (e.g. under-ice; Hayes and Morrison, 2002). Another advantage of operating untethered is that, once below the surface, AUVs are decoupled from both surface and ship motion. Decoupling the data collection platform from surface influence can significantly improve the collected data quality.

The use of AUVs, as both scientific and survey platforms, is becoming more widespread as the technology becomes increasingly robust. Applications can be roughly divided between commercial, military, and academic sectors. The first of these, primarily the offshore oil

9 1: Introduction industry, is concerned with seabed surveys and pipeline tracking (Evans et al., 2003) whereas military involvement with AUVs has been almost entirely concentrated on port protection and mine countermeasures (Bovio et al., 2006). Academic applications tackle a diversity of issues from tracking harmful algal blooms (Robbins et al., 2006), to mapping deep sea vents (Yoerger et al., 2007), to space analogue research (Forrest et al., 2009).

From the perspective of limnology and oceanography (either biological, chemical or physical), one of the strengths of AUVs as platforms is the ability to sample horizontal variability in the water column to a vertical position tolerance not easily obtained by any other means. A combination of horizontal (AUV), vertical (traditional profilers), and temporal (traditional moorings) sampling techniques allows the three-dimensional, time-evolving nature of complex scalar fields in the water column to be characterized in a fashion that has previously not been possible. This is particularly relevant in ice-covered systems, as these are generally under-studied as a result of logistical and sampling challenges.

While several AUV-based studies have focused on ocean settings (e.g. Ramos et al., 2007; Statham et al., 2005), little application, with some notable exceptions (e.g. Laval et al., 2000a, Fong and Jones, 2006), has been seen in lakes. Although there have been a few scientific under- ice deployments (Ferguson et al., 1999; Wadhams et al., 2002; Hayes and Morrison, 2002; Brierly et al., 2003; McEwan et al., 2005; Nicholls et al., 2006) no studies were made under lake ice prior to the work presented here.

A focus of this work was to use UBC-Gavia (Figure 1.4), a Gavia-class AUV, as a data collection platform for high-resolution, horizontal temperature measurements using a SBE49 Fastcat Conductivity-Temperature-Depth (CTD) profiler. As illustrated, the SBE49 Fastcat CTD is positioned on top of the vehicle with the sampling intake aft of the nose of the AUV by 3 cm. Given the intake position, the sampled water is likely to be undisturbed during normal vehicle operation. Typical cruising speeds of the vehicle during the various campaigns varied from 1.2 – 1.6 m s-1. At the 16 Hz sampling frequency of the CTD, this works out to an 8 – 10 cm along

10 1: Introduction

SBE49 Fastcat CTD

Figure 1.4: Schematic of UBC-Gavia with on-board modules and SBE49 Fastcat CTD labeled. track resolution. In addition to the SBE49 Fastcat CTD, UBC-Gavia was also equipped with an additional suite of instrumentation described in Appendix C. Although these additional instruments were not used in this work, they were used for the additional vehicle deployments described in Appendix D.

Mission planning involves a series of depths and waypoints being programmed into the control software that the vehicle then follows. While there are several vehicle navigation modes for horizontal positioning (Appendix C), all rely on some form of dead-reckoning as GPS reception is not possible underwater. Dead-reckoning on this vehicle has a position error of 1 – 2 % by distance traveled. Surfacing approximately every 1000 m was designed into the AUV mission planning in order to reset this position error through reacquiring new GPS positions.

In the vertical, two vehicle operation modes are used in this work: constant depth and constant altitude (height above bottom). Vertical positioning in the water column is determined using real- time pressure data in constant depth mode and real-time altitude data in constant altitude mode. The first of these uses an onboard pressure sensor independent of the CTD whereas the second uses altitude estimates from the Acoustic Doppler Current Profiler (ADCP) module. CTD pressure data collected during constant depth mission is typically offset from the programmed depth set point. In post-processing, the mean and standard deviation are calculated from CTD pressure data to estimate a bound for the 95 % confidence interval. In a similar fashion, the 95% confidence interval bounding the altitude data was determined. The vehicle’s ability to maintain its vertical set point, as quantified by these 95% confidence interval bounds, was significantly better for constant depth (± 5 cm) than for constant altitude missions (± 20 cm). Temperature

11 1: Introduction measurements associated with the pressure data outside of these bounds were discarded. Scales for temperature variations associated with vertical vehicle motion within the background thermal stratification were calculated for constant depth missions and are presented in each of the following chapters.

1.3 Previous Work at the Study Sites

Two study sites are presented in this work; Pavilion Lake, British Columbia, Canada and Lake Thingvallavatn, Iceland. Pavilion Lake is located in central British Columbia in a limestone valley known as Marble Canyon. This is a 5 km2, predominantly groundwater fed, ultra- oligotrophic, dimictic lake that is part of an ongoing series of studies on growth processes of organosedimentary structures known as microbialites located at multiple depths along the lake bottom (Laval et al., 2000b; Lim et al., 2009; Brady et al., 2009). As part of these studies, significant effort has been spent characterizing seasonal variations of the physical environment (Lim et al., 2009). In recent years, this lake has also been designated a space analogue research site by the Canadian Space Agency, which has resulted in additional research questions around space exploration (Forrest et al., 2009; Lim et al., 2010). The focus of many of these questions has been the examination of physical transport problems during the summer months using multiple data collection platforms (e.g. AUV and manned submersible).

Lake Thingvallavatn, located in southwest Iceland, is one of the country's largest (83 km2) and deepest lakes, with a mean depth of 34 m and maximum depth of 114 m. Adalsteinsson et al. (1992) estimated that ~ 90% of its 100 m3 s-1 average discharge enters the lake as underwater springs, which are predominantly fed by melt water runoff from the Langjokull and Thorisjokull glaciers. This water percolates through basaltic glacial deposits and lavas before entering the northern shore of the lake through a series of underwater cracks (Adalsteinsson et al., 1992; Saemundsson, 1992). Although a major, multi-discipline study was undertaken in the late 1980s examining the chemistry, biology and physics of the lake (Adalsteinsson et al., 1992) the majority of studies since then have investigated the native arctic charr and stickleback fish stock found in the lake (Malmquist, 1992; Olafsdottir et al., 2006). Researchers have also examined the

12 1: Introduction role of phytoplankton (Jonasson, 1992) and zooplankton (Lindegaard, 1992) in biomass distribution and energy flow within the lake and how this is related to fish stock distribution.

1.4 Work Objectives

This work uses a combination of horizontal and vertical sampling techniques to explore the three dimensional nature of physical transport processes. The processes explored include: (1) convection resulting from a negative surface buoyancy flux in both summer and winter (Chapter 2); (2) transport under-ice resulting from rotational adjustment (Chapter 3); and, (3) underflow fate through periodic wind stirring (Chapter 4). While Chapters 2 and 4 examine processes that have been described in other studies, new insights are provided through the use of horizontal sampling. The presence of a submerged, cyclonic eddy discussed in Chapter 3, is, to our knowledge, the first such field observation ever made in a lake.

2 Convectively Driven Transport in a Temperate Lake1

2.1 Introduction

Above the temperature of maximum density, convection in freshwater lakes occurs during periods of surface heat loss, which result in vertical mixing that can erode the diurnal thermocline (Imberger, 1985; Lei and Patterson, 2006). Seasonally, autumnal cooling erodes the seasonal thermocline (Fer et al., 2002b; Wells and Wettlaufer, 2007). Below the temperature of maximum density and under ice-cover, convection occurs during periods of shortwave radiative heating (Farmer, 1975; Mironov et al., 2002; Ellis et al., 1991). Volumetric heating of the water will result in the warming and deepening of the mixed layer. The rate at which this warming takes place is related to the ice cover characteristics, which modulate the amount of through-ice solar penetration (Jonas et al., 2003).

Basin-scale convection resulting from uniform heat flux has been well studied, as it is important in controlling lake stratification (Imberger, 1985; Fer et al., 2002a; Jonas et al., 2003). Studies have also examined transport resulting from differential heat flux (Fer et al., 2002b; Monismith et al., 1990). These studies have focused on the convection associated with differential heat flux with particular attention to shallow, near-shore regions of lakes. These regions have been demonstrated to have higher heating and cooling rates than adjacent deeper waters (Fer et al., 2002b). These higher rates result in the formation of both turbulent convective plumes and density currents in the near-shore region. A limitation to these studies is that conventional instrumentation is largely designed for vertical, rather than horizontal, sampling and is unable to highly resolve horizontal variability on short timescales.

1A version of Chapter 2 has been published. Forrest, A.L., B.E. Laval, R. Pieters, and D.S.S. Lim. (2008) Convectively driven transport in temperate lakes. Limnology and Oceanography, 53(5, part 2), 2321 – 2332.

14 2: Convectively Driven Transport

Horizontal variability in the water column is characterized in this study using an Autonomous Underwater Vehicle (AUV) as a data collection platform. Within the past decade, AUVs have seen increased application in physical oceanography with examples including: shallow hydrographic surveys of Narragansett Bay, Rhode Island (Levine et al., 1997); a survey of coastal fronts in Haro Strait, British Columbia (Nadis, 1997); deep water hydrographic and current measurements in the Strait of Sicily (Stansfield et al., 2001); turbulence gradient measurements (Thorpe et al., 2002); water renewal in hypoxic sea lochs (Overnell et al., 2002); and, AUV-based acoustic Doppler current profiler (ADCP) flow field measurement (Fong and Jones, 2006). To date, there are few examples of this technology being applied to limnology and none to under-ice limnology. Some examples of freshwater work include: flow field prediction in tidally forced lakes (Fong and Jones, 2006); internal waves in a small lake (Laval et al., 2000a); and, gravity currents associated with littoral cooling (Fer et al., 2002b).

This work details investigations of the horizontal temperature variability within the upper waters of a temperate lake in both summer and winter. Horizontal temperature measurements were made using UBC-Gavia, a small Gavia-class AUV. The next section describes the study site, the AUV, and additional instrumentation. Sections 2.3 and 2.4 describe mixing during the field campaigns in summer 2006 and winter 2007, respectively. Studying convection in the surface waters in both summer and winter is important as mass transport resulting from a destabilizing heat flux will control vertical stratification of the water column in temperate lakes during periods of little to no surface wind shear. This condition is sometimes present during periods of low wind in the summer and is typical with winter ice cover.

2.2 Methods

2.2.1 Site Description

Pavilion Lake is a 5 km2 temperate lake located in central British Columbia in a limestone valley known as Marble Canyon (Figure 2.1a). Pavilion Lake has three basins (North, Central, and South Basins) orientated along the longitudinal axis of the lake joined by sills 6 – 10 m deep.

15 2: Convectively Driven Transport

Figure 2.1: (a) Bathymetry of Pavilion Lake with British Columbia location inset (filled circle – location of meteorological station). Contours represent 20 m intervals with maximum depth of 61 m in the Central Basin. The area outlined with a dashed line is enlarged in (panels b and c): (b) summertime AUV transects (solid lines): transect in mixed layer (2.12 m depth) on left and transect along the thermocline (7.02 m depth) on right (filled inverted triangle – location of vertical CTD profiling); and, (c) Wintertime AUV transect (solid line) for all depths (open square – point of launch and recovery; open inverted triangle – site of vertical CTD profiling; X – locations of ice profiling Stations H1 – H3 indicated from north to south).

This lake is primarily groundwater fed with no year round surface inflows and a single regulated outflow at the top end of the North Basin. AUV-based work presented in this study was conducted in the Central Basin at the widest point of the lake. This work is part of a series of studies examining this relatively deep (maximum recorded depth of 61 m) freshwater lake, which has evidence of macro-scale growth of organosedimentary structures known as microbialites (Laval et al., 2000b).

2.2.2 Data Collection

The investigation was divided into two campaigns: summer (08 – 09 Aug 2006) and winter (21 – 22 Feb 2007). The primary focus of these campaigns was to characterize the horizontal temperature variability using UBC-Gavia. In the summer campaign, UBC-Gavia cycled twelve times along 500 m, constant-depth, transects in the surface mixed layer (2.12 m depth) and above

16 2: Convectively Driven Transport the seasonal thermocline (7.02 m depth; Figure 2.1b). In the winter campaign, 300 m transects were conducted in the stratified surface layer (0.50 m depth), and the convectively mixed layer (6.20 and 17.00 m depth; Figure 2.1c). During both campaigns, a tolerance of 10 cm (i.e., ± 5 cm away from the mean AUV depth determined in post-processing) was used; data points associated with depths exceeding this tolerance are not reported.

Horizontal temperature transects were collected with a Seabird Electronics SBE-49 Conductivity-Temperature-Depth (CTD) profiler mounted on UBC-Gavia. As configured for this deployment, the vehicle was approximately 2.4 m in length, 0.2 in diameter, and 55 kg dry weight in air. Although the maximum velocity of the vehicle is approximately 3 m s-1, a cruising speed of 1.6 m s-1 was selected for an along track resolution of ~ 10 cm. The vehicle navigated using a combined RDI Workhorse Navigator Doppler velocity log (DVL) and a Kearfott inertial navigation system (INS). As the water column depths exceeded the range of the DVL (> 30 m), periodic surface intervals (i.e., vehicle surfacing with zero thrust) were required to reset accumulated position error with new GPS fixes. As these surface intervals are not possible under ice, mission lengths were reduced from 12 km (summer) to 3 km (winter). Vertical temperature profiles were collected with a Seabird SBE19plus CTD profiler (vertical resolution ~ 20 cm). These profiles were collected continuously during the vehicle deployment at a fixed location along the mission transects (Figure 2.1b – filled inverted triangle; Figure 2.1c – open inverted triangle).

During both campaigns, meteorological data (wind speed and direction, air temperature, relative humidity, and incoming shortwave solar radiation) were measured with a Campbell Scientific CR1000 weather station. This station was positioned on the shoreline at a point near the sill separating the North and Central Basins (Figure 2.1a). Wind parameters were sampled every 10 seconds and then averaged every 15 minutes. All other parameters were averaged over 30 minute intervals. During the summer campaign, the surface water temperature (estimated using the average temperature values from CTD casts during the testing period) was used with the meteorological data to estimate the surface heat flux using bulk aerodynamic formula. In this estimation, near-neutral stability of the atmosphere above the lake surface was assumed (i.e.,

17 2: Convectively Driven Transport

za/Lo < 0.5; where za is the measurement height above the water surface and Lo is the Monin- Obukhov length in the atmospheric boundary layer). Calculation of the bulk transfer coefficients associated with the bulk aerodynamic formulae was solved iteratively to estimate the latent and sensible heat flux (Launiainen 1995; Launiainen and Cheng, 1998; Heikinheimo et al. 1999).

During the winter campaign, three ice profiles were collected on 25 Feb 2007, 3 days after the AUV sampling, at the approximate beginning (Station H1), middle (Station H2), and end (Station H3) of the AUV transect in the Central Basin (Figure 2.1c). Depths of white and black ice were recorded for each profile. No precipitation was recorded in the three-day interval between AUV and ice sampling. Samples of the white and black ice were collected in polyethylene bags, melted at room temperature, and then transferred to sample bottles. These samples were then measured for conductivity using a Guildline Portasal. Vertical temperature profiles were collected from each of these three holes.

2.3 Summertime Campaign (Cooling Heat Flux)

Over the course of the summertime campaign, a series of horizontal temperature transects were collected in the epilimnion and above the seasonal thermocline. In the epilimnion, a horizontal temperature gradient was observed to gradually weaken during evening cooling. Measurements along the thermocline suggest the propagation of an intruding density current. Detailed observations are summarized in Section 2.3.1. Section 2.3.2 presents a heat budget for the observed cooling of the surface mixed layer. The negative buoyancy flux associated with this cooling is responsible for thermal instabilities that take the form of convective plumes and density currents discussed in Section 2.3.3.

2.3.1 Summertime Observations

Figure 2.2 summarizes the observed weather conditions from 08 – 11 Aug 2006, including the AUV sampling period on 09 Aug 2006 (grayed-out). A peak wind speed of ~ 5 m s-1 was observed prior to the sampling period, while wind speed ranged from 1 – 2 m s-1 during the

18 2: Convectively Driven Transport

Figure 2.2: Meteorological measurements during the summertime campaign: (a) wind speed; (b) wind direction (0 and 360º represent north); (c) air temperature; (d) relative humidity; (e) incident shortwave radiation. Grayed period indicates time of AUV deployment on 09 Aug 2006. sampling period (Figure 2.2a). Wind direction was generally from the southeast until the sampling period when the wind was from the west (Figure 2.2b). Temperature, humidity, and shortwave radiation (Figure 2.2c – e) all show warm, dry days leading up to the sampling period and then cloudy, more humid conditions the following day.

Between 20:00 hrs and 23:30 hrs on 09 Aug 2006, 138 consecutive vertical CTD profiles were collected at a location in the approximate center of the AUV track (Figure 2.1b – filled inverted triangle). During this time, the AUV was collecting horizontal temperature transects at two constant depths (Figure 2.3 – dashed-dot lines). Figure 2.3 shows the average temperature of all casts with the two dotted lines representing the standard deviation of temperature along the profile. The seasonal thermocline depth (where ∂T ∂z is a maximum) was 8.40 m. The

19 2: Convectively Driven Transport

Figure 2.3: Bin-averaged temperature profiles: solid line – average temperature over testing period on 09 Aug 2006 (n = 138, bin size = 0.5 m); dotted lines – twice the standard deviation of averaged temperature profiles; dashed-dot lines at 2.12 and 7.02 m depths indicate shallow and deep AUV transect depths respectively; and, h is the depth of the surface mixed layer.

-1 depth of the surface mixed layer, h, defined here as the depth where ∂T ∂z < 0.1 ºC m is 4.9 m (Figure 2.3).

During the data collection period, temperature measurements were made along twelve consecutive return transects at the shallow (2.12 m) depth while outbound and the deep (7.02 m) depth while inbound. Temperature measurements made using the AUV will be affected by vertical vehicle motion within the water column stratification. The mean vertical temperature gradient at the depth of the shallow and deep AUV transects was 0.002 ºC m-1 and 1.0 ºC m-1. Combining these mean vertical temperature gradients with the ± 5 cm tolerance about the mean AUV depth, estimates for temperature changes associated with vertical displacements of the AUV are 2 x 10-4 and 0.10 ºC for the shallow and deep transects, respectively.

20 2: Convectively Driven Transport

Figure 2.4: Horizontal temperature transects in the surface mixed layer (2.12 m) on 09 Aug 2006. The first run (~ 20:00 hrs) is shown at the bottom of the figure and the last run (~ 23:30 hrs) at the top with a transect repeat interval of ~ 15 min. Each profile is offset by 0.05 ºC for display purposes. The reference point is defined as the point where the mission was executed on the initial leg (i.e., northeast side of the initial transect).

Figure 2.4 shows temperature measured along each of the horizontal transects in the surface mixed layer. In the first transect, temperature ranged from 19.05 ºC at the near end to 19.15 ºC at the far end of the transect. By the end of the profiling 3.5 hours later, the average along-track temperature was reduced to 18.95 ± 0.01 ºC (range represents one standard deviation of temperature measurements along final transect). Temperature fluctuations are observed along all transects. As the magnitude of these fluctuations is greater than 2 x 10-4 ºC (i.e., attributed to vehicle motion), they are taken to be evidence of water motion.

Figure 2.5 shows the temperature measured along the deep horizontal transects. Observed temperature fluctuations, especially evident in transects 3, 7, and 8 between 100 and 200 m, have

21 2: Convectively Driven Transport magnitudes from 0.1 – 0.2 ºC. As these magnitudes are similar to those attributable to vehicle motion in the vertical stratification, it is difficult to categorize these fluctuations. Decreases in temperature greater than 0.50 ºC (i.e., clearly not attributed to vehicle motion) were observed along the latter half of the transects. This cooler water is first observed in transect 5 at 640 m (21:45 hrs) and propagates to 570 m by the final transect at 23:15 hrs. Based on these observations, a mean progression rate of this cooler water over the test period is calculated to be 0.013 m s-1 (Figure 2.5 – solid line).

Figure 2.5: Horizontal temperature transects at the base of the surface mixed layer (7.02 m) on 09 Aug 2006. The first run (~ 20:00 hrs) shown at the bottom of the figure and the last run (~ 23:30 hrs) at the top with a transect repeat interval of ~ 15 min. Each profile is offset by 0.75 ºC for display purposes. The reference point is defined as the point where the mission was executed on the initial leg (i.e., the northeast corner of the initial transect).

22 2: Convectively Driven Transport

2.3.2 Surface Layer Heat Budget

The shallow temperature transects (Figure 2.4) show the surface layer cooling by 0.1 – 0.2 ºC, depending on location, over the course of the sampling period. The heat flux required to account for the observed cooling of the surface mixed layer ( H˜ ) can be estimated by vertically integrating the change in heat content (Monismith et al., 1990):

∂ T H˜ = −ρ C h (2.1) w p ∂t

-3 where ρw is water density assumed to be 1000 kg m , Cp is the specific heat of water (4182 J kg-1 K-1), h is the depth of the surface layer (4.9 m), and T is the layer average temperature. Positive fluxes represent heat lost from the water to the atmosphere. Three different values of were estimated using a time average of from the consecutive vertical CTD profiles at 275 m (-1.77 x 10-5 ºC s-1), and horizontal CTD profiles at 100 m (-1.44 x 10-5 ºC s-1) and 500 m along the mission track (-1.77 x 10-5 ºC s-1). Using these estimates of , surface heat flux estimates of 362, 295, and 362 W m-2 were calculated using Equation 2.1.

These surface heat flux estimates are now compared to the surface heat flux calculated from the measured meteorological data (Figure 2.2). During the evening of 09 Aug 2006, average values for the ambient air temperature, wind speed, and relative humidity were taken as 19.20 ºC, 4.35 m s-1, and 40 %. As all vertical and horizontal profiling was conducted after sunset under a clear sky, both cloud cover and shortwave radiation were considered negligible for these calculations. Using the average surface water temperature of 19.00 ºC, as observed in the vertical profiles (Figure 2.3), an iterative solution of the bulk aerodynamic formulae was used to estimate latent (190 W m-2) and sensible heat fluxes (-2 W m-2) (Launiainen, 1995; Launiainen and Cheng, 1998; Heikinheimo et al., 1999). A value of net longwave radiation (80 W m-2) was calculated using empirical formulae (Tenn. Valley Auth., 1972). Summing each of these fluxes, the net surface heat flux rate was approximated to be 268 W m-2, which is consistent with the calculated change in heat content.

23 2: Convectively Driven Transport

2.3.3 Convective Motion

Surface heat flux will create a negative surface buoyancy flux where is the buoyancy parameter defined as with the gravitational constant and α the coefficient of thermal expansion (Wells and Sherman, 2001). This flux will decrease background stratification until, given sufficient time, the formation of thermal instabilities will result. As the dimensionless Rayleigh number ( Ra = gβΔT ⋅ H 3 υα ) for this system is O(1013), and orders of magnitude greater than the critical Rayleigh number of ~ 650 for a free-surface boundary, Rayleigh-BÈnard convection is not expected (Lei and Patterson, 2002). Instead, generated thermal instabilities will initially take the form of convective sinking plumes. The resulting convective motion initially breaks up any residual daytime circulation patterns, promotes vertical mixing, and may eventually lead to density current formation and propagation.

At steady state, convective plumes will fall as quickly as they are replaced by rising water. These convective plumes will have associated horizontal length and vertical velocity scales. Horizontal length scales associated with these plumes can be estimated through a closer examination of the temperature fluctuations evident throughout each of the shallow horizontal temperature transects (Figure 2.4). As the magnitude of the observed temperature fluctuations exceed what is attributable to vertical vehicle motion, the fluctuations are thought to be associated with convective plumes.

Horizontal transects in the surface layer show temperature variability over a broad range of length scales. Large-scale, persistent features (e.g. the broad temperature decrease then increase from 400 m – 600 m in transects 5 – 9 of Figure 2.4) are likely not associated with convective plumes. In order to isolate horizontal length scales associated with convective motion, temperature along the horizontal transect was high pass filtered using a wavenumber cut-off of (50 m)-1. Horizontal length scales of the convective plumes were then estimated by measuring the width of the temperature anomalies that exceed one standard deviation of the filtered data. The estimated mean length scale for all twelve transects in the surface layer was (3.5 ± 2.9) m, where the error represents one standard deviation from the mean pressure data collected while

24 2: Convectively Driven Transport the AUV was on transect. This is in reasonable agreement with measurements of horizontal length scales of 5 m made by Thorpe et al. (1999) during both summer and winter.

A vertical velocity scale for these convective plumes is given by (Ward, 1990):

(2.2)

Using the average for the three estimated values in the previous section yields B = -1.57 x 10-7 2 -3 -1 m s and vp ~ 9 mm s . This velocity scale is used to calculate a time of ~ 9 minutes for these convective plumes to vertically traverse the surface mixed layer depth (4.9 m). The lack of coherence in the temperature fluctuations between transects (Figure 2.4) is therefore expected since the transect repeat time of 15 – 17 min was larger than the timescale of the convective motion.

Penetrative convection may result when convective plumes reach the seasonal thermocline. When the lakebed is shallower than the seasonal thermocline, convection cools the water more than occurs offshore and there is the potential for density currents to form. These density currents would propagate along the lakebed to the depth of the thermocline where they will either form an intrusion along the thermocline or continue penetrating into the underlying denser water (Horsch and Stefan, 1988; Monismith et al., 1990).

2.3.4 Intrusion Propagation

The cooler water initially observed in transect 5 of Figure 2.5 is theorized to be the front of a density current forced by differential heating in the lake shallows, propagating as an intrusion along the thermocline. Observations of the onset of these cooler temperatures is consistent with the theoretical estimate of timing onset based on the theory of density current formation. Direct sun was off the lake by ~ 20:00 hrs on 09 Aug 2006 and the onset of the cooler temperatures associated with the front was first observed at ~ 21:45 hrs, giving an observed onset time of 105 minutes after sun-off. Density currents generated in the shallows of the western shore of Pavilion Lake will propagate orthogonal to the shoreline and intersect the AUV transect line at an angle of

25 2: Convectively Driven Transport approximately 45º. As a result of this geometry, the observed mean progression rate is faster than the true speed of the propagating front. Using the observed, along-transect component of front observed velocity of 0.013 m s-1, the front velocity is estimated to be 0.007 m s-1. The last point of the AUV transect is 150 – 170 m off shore, and the density current front could propagate from the shore to this point in 360 – 405 minutes. This is inconsistent with the first observation of the cooler water along the transect 105 minutes after sun down indicating that the estimated velocity is actually being under predicted. That said, bottom velocities before the point of detachment have been observed to range from 0.03 – 0.07 m s-1 (Wuest et al., 2005). To the knowledge of the authors, intrusion velocities mid water column, arising from density currents resulting from differential currents, have not been directly measured in the field. Further study would be required to explain the observed intrusion velocity.

In two-layer stratification, density currents will form an intrusion if they are less dense than the lower layer or will continue flowing downslope to intrude at the base. Conditions required for density currents to penetrate the density interface between the two layers have been experimentally quantified using a Richardson number defined on buoyancy flux (Ching et al., 1993; Wells and Wettlaufer, 2007):

(2.3) where h = 4.9 m is the depth of the interface, L is the width of the basin, is the reduced gravity of the interface with , , and being the associated densities of the surface layer, bottom layer and reference density respectively. Wells and Wettlaufer (2007) demonstrated that density currents will penetrate the stratification for values of less than a critical value of 27. This critical value of was shown to be only weakly related to slope angle (Wells and Wettlaufer, 2007).

A value for can be calculated using the observed characteristics of the water column. Using

= 998.435 (T = 19 ºC) kg m-3, = 999.728 (T = 10 ºC) kg m-3 and of 1000 kg m-3, is calculated to be 0.0126 m s-2. Using the mean basin width, L, of 500 m and the average value of

26 2: Convectively Driven Transport

B of -1.57 x 10-7 m2 s-3 calculated above, a value of was estimated to be 34. Although this predicted value is greater, it is close to the critical of 27 required for interface penetration (Wells and Wettlaufer, 2007) implying that, over time, penetration may eventually occur. It should be noted that T = 10 ºC is a conservative estimate of the bottom layer temperature. Colder temperatures would generate larger estimates of which would predict increased resistance to bottom layer penetration.

In cases where the density current does not initially penetrate the stratified interface (i.e., > 27), the surface layer evolves by the filling box mechanism (Baines and Turner, 1969; Wells and Wettlaufer, 2005). Over time, intruding density currents will reduce until a critical value is reached during which the density current increasingly penetrates the thermocline and underlying fluid. The time scale, , required for to reach this point is given by (Wells and Wettlaufer, 2007):

(2.4)

The calculated Ri = 34 and estimated basin width of 500 m provide a value for of ~ 23 ( ρ )initial hours. As this time estimate greatly exceeds the nighttime cooling period of ~ 10 hours, complete penetration of the seasonal thermocline is unlikely. Longer cooling periods, reduced density contrasts between layers, or an increased buoyancy flux would all potentially result in increased penetration of the thermocline.

2.4 Wintertime Campaign (Radiative Heat Flux)

Over the course of the wintertime campaign, vertical temperature profiles have the four-layer structure typically associated with radiatively driven convection. A series of successive horizontal temperature transects in the surface (SL) and convective layer (CL) suggest evidence of convective motion resulting from daytime heating. Detailed observations are summarized in

27 2: Convectively Driven Transport

Section 2.4.1. Section 2.4.2 demonstrates solar heating of the water column is sufficient to drive convection in the CL. Section 2.4.3 discusses how this convection may be responsible for temperature patterns observed in the horizontal transects.

2.4.1 Wintertime Observations

Figure 2.6 summarizes the observed weather conditions from 21 – 23 Feb 2007, which includes the AUV sampling periods (grayed out) on the evenings of 21 and 22 Feb 2007. Peak wind speeds of 6 – 7 m s-1 were observed to be blowing from the north for large portions of the two- day period but had dropped to 1 – 2 m s-1 from the west and east respectively for the two sampling periods (Figure 2.6a and b). Air temperature was generally just below freezing except for brief periods of daytime heating (Figure 2.6c). Afternoon heating was qualitatively associated with drier air (Figure 2.6d) and peak solar radiation values of 300 – 500 W m-2.

Significant variability was observed in snow cover across the Central Basin during the field campaign, as the surface was heavily wind scoured. Wind scouring resulted in snow being absent at the three stations where ice profiles were collected on 25 Feb 2007 in the Central Basin near the start, middle, and end of the AUV transect (Stations H1, H2, and H3; Figure 2.1c). Measured ice characteristics are summarized in Table 2.1 and show considerable differences between the three different stations. Station H2 had the greatest white ice, least black ice, and thinnest total ice cover. Field observations of ice cracks over the entire Central Basin provide further evidence of horizontal variability of the ice cover. The conductivity of the white ice at Station H2 was considerably less than observed at Stations H1 and H3, suggesting this site has the highest proportion of snow in the ice. The specific conductivity of the black ice decreases from Station H1 – H3. These values are all within range of published values for freshwater lakes (Pieters and Lawrence, 2009).

Over the course of an eight-day field campaign, vertical temperature profiles were collected at Station H2. Profiles collected on 18, 22, and 25 Feb 2007 show evidence of a similar four-layer structure: first, a stably stratified surface layer (SL); second, a convectively mixed layer (CL); third, an interfacial entrainment layer (EL); and, fourth, a quiescent layer going to depth (QL).

28 2: Convectively Driven Transport

Figure 2.6: Meteorological measurements during the wintertime campaign: (a) wind speed; (b) wind direction (0 and 360º represent north); (c) air temperature; (d) relative humidity; (e) incident shortwave radiation. Grayed periods represent the times of AUV deployment on two separate days.

This vertical structure is consistent with the thermal structure associated with radiatively driven convection (Farmer, 1975; Mironov et al., 2002; Jonas et al., 2003). As observed in this study (Figure 2.7 – inset) and elsewhere (Farmer 1975; Malm et al. 1997), radiatively driven convection will have a twofold effect in the CL: the CL will deepen over time and the overall temperature of the CL will increase. An average deepening rate ( = 0.57 m d-1) and a warming rate ( = 0.015 ºC d-1) of the CL was observed over the study period.

The three depths of the horizontal temperature measurements are indicated with dashed-dot lines in Figure 2.7. During the two data collection periods, five consecutive horizontal temperature transects were collected at each of following three depths: the shallow depth (0.50 m) 21:30 – 21:05 hrs, 21 Feb 2007; the medium depth (6.20 m) 16:45 – 17:20 hrs, 22 Feb 2007; and the

29 2: Convectively Driven Transport

Table 2.1: Lake and ice characteristics at three stations in the Central Basin

Central basin (H1)1 Central basin (H2)1 Central basin (H3)1 White ice depth (m) 0.04 0.19 0.07 Black ice depth (m) 0.46 0.21 0.46 Total ice depth (m) 0.50 0.40 0.53 White ice C252 (µS cm-1)3 178 63.6 161 Black ice C25 (µS cm-1)3 86.2 69.9 36.4 Notes: 1. H1, H2, and H3 are the three sampling sites along the AUV transect at the beginning, middle, and end of the AUV transect. 2. C25 refers to specific conductivity (i.e., electrical conductivity normalized to 25ºC). 3. Specific conductivity measured from samples with the Guideline Portasal. deep depth (17.00 m) 16:45 – 17:20 hrs, 22 Feb 2007. The mean vertical temperature gradient, calculated at these three depths for the two different sampling days, was 0.85, 0.001, and 0.001ºC m-1. Combining these mean vertical temperature gradients with the ± 5 cm tolerance of the mean AUV depth, estimates for temperature changes associated with vertical displacements of the AUV are 8.5 x 10-2, 1 x 10-4, and 1 x 10-4 ºC for the three transect depths.

All five horizontal temperature transects in the SL on 21 Feb 2007 show water temperature at the lake center ~ 0.5 ºC cooler than the surrounding waters (Figure 2.8). This cooler water remains at the same location along the transect (100 – 300 m) throughout the 35 minute sampling period. Temperature fluctuations of up to ~ 0.15 ºC with a horizontal length scale of 2 – 5 m are evident in the data. These fluctuations are nearly double the temperature changes attributable to vehicle motion. As the vehicle was intermittently hitting the ice surface during data collection, it is unclear if vehicle motion is driving these fluctuations or if they are evidence of water column motion. As it is not possible to determine one way or another, they will not be discussed further.

Horizontal temperature transects within the CL on 22 Feb 2007 are shown in Figure 2.9 (6.20 m depth) and Figure 2.10 (17.00 m depth). In both of these figures, the data shows the evolution of a basin-scale, warmer water mass in the same region (150 – 250 m from the reference point) as the cooler water observed the previous day in the SL (Figure 2.8). In the initial transects of Figure 2.9 and Figure 2.10 the temperature across the basin was roughly uniform; (2.127 ± 0.003) ºC at 6.20 m depth and (2.145 ± 0.018) ºC at 17.00 m depth (range represents one

30 2: Convectively Driven Transport

Figure 2.7: Vertical temperature profiles on three separate days during the wintertime campaign demonstrating an evolving four-layer structure: surface layer (SL); convectively-mixed layer (CL); entrainment layer (EL); quiescent layer (QL) (inset – detail of the dashed line rectangular outlined area). standard deviation of temperature measurements along initial transect). These values agree closely with the mean temperature of the CL of (2.122 ± 0.002) ºC as measured in the vertical profile collected at ~ 14:00 hrs the same day. As the vertical and horizontal temperature measurements are in agreement, the observed warming of the CL (Figure 2.7) is not thought to be the result of the observed basin-scale temperature anomaly. This anomaly progressively increases in temperature to a maximum of ~ 0.05 ºC at 6.20 m depth and ~ 0.10 ºC at 17.00 m depth. In the final transect at both depths, the amplitude of the temperature anomaly starts to decrease. As sampling was in the early evening (~ 50 minutes after sun down), this decrease in temperature could be evidence of convective motion spin down.

In addition to the observed basin-scale temperature anomaly, temperature fluctuations of much shorter length scales were also observed. At 6.20 m depth, along-transect temperature

31 2: Convectively Driven Transport

Figure 2.8: Horizontal temperature measurements at the depth of the surface layer (0.50 ± 0.05 m) on 21 Feb 2007. First run (~ 20:30 hrs) shown on bottom and final run (~ 21:05 hrs) on top yielding a transect repeat interval of ~ 7 min. Each profile is offset by 0.25 ºC for display purposes. The reference point is defined as the point where the mission was executed on the initial leg (i.e., the northeast corner of the initial transect). fluctuations of up to ~ 0.02 ºC were observed. As the magnitude of these fluctuations is nearly two orders of magnitude greater than what is attributable to vehicle motion, they most likely related to water column motion. In addition, these fluctuations seem to occur primarily in the region of the warm temperature anomaly indicating a possible correlation. In contrast, at 17.00 m depth, temperature fluctuations of up to ~ 0.05 ºC were observed along the entire transect.

32 2: Convectively Driven Transport

Figure 2.9: Horizontal temperature measurements at 6.20 m depth in the convective layer on 22 Feb 2007. Initial run (~ 16:45 h) shown on bottom and final run (~ 17:20 h) on top with a transect repeat interval of ~ 7 min. Each profile is offset by 0.05 ºC for display purposes. The reference point is defined as the point where the mission was executed on the initial leg (i.e., the northeast corner of the initial transect). Position of the vertical CTD profiles 120 m from the reference point as indicated (solid vertical line).

2.4.2 Surface Heat Flux

As mentioned in the observations, vertical temperature profiles (Figure 2.7) demonstrate a thermal structure consistent with radiatively driven convection. Ice cover will attenuate the amount of solar radiation entering the water column. Launiainen and Cheng (1998) accounted for the decay of incident solar radiation in the ice column to estimate the surface radiation flux at the ice-water interface:

(2.5)

33 2: Convectively Driven Transport

Figure 2.10: Horizontal temperature measurements at 17 m depth in the convective layer on 22 Feb, 2007. Initial run (~ 16:45 hrs) shown on bottom and final run (~ 17:20 hrs) on top with a transect repeat interval of ~ 7 min. Each profile is offset by 0.10 ºC for display purposes. The reference point is defined as the point where the mission was executed on the initial leg (i.e., the northeast corner of the initial transect). Position of the vertical CTD profiles 120 m from the reference point as indicated (solid vertical line). where the surface albedo, , was selected as 0.3 for the ice surface, is the incident solar radiation, and and are the extinction coefficient and ice thickness. The extinction of solar radiation in ice is highly dependent on the wavelength of the incident light, ice characteristics, and atmospheric conditions. Following the procedure of Launiainen and Cheng (1998), values of 17.1 and 1.6 m-1 were selected for the white ice for the upper 10 cm and lower ice column respectively. Similarly, values of 8.4 and 1.5 m-1 were selected for the black ice for the upper 10 cm and lower ice column respectively.

-2 A minimum value of 10 W m for I 0 , the time-averaged radiation flux at the ice-water interface, has been proposed as the minimum value required for under-ice convection to be initiated

34 2: Convectively Driven Transport

(Kelley, 1997; Malm et al., 1997). Using this value in Equation 2.5, and the observed ice conditions, the minimum solar radiation required for water motion is 175 W m-2 at Station H2. On 22 Feb 2007, surface irradiance exceeded this value from 10:30 – 16:30 hrs, suggesting that during the field campaign there was sufficient solar radiation for 8 hours per day to drive under- ice convection across the basin. This prediction of convection is consistent with the well- developed CL, which the vertical profiles (Figure 2.7) showed to warm throughout the study period.

A region was observed between ~ 150 – 250 m across both transect depths within the CL (Figure 2.9 and Figure 2.10) and was shown to increase in temperature over the 35 minutes that the AUV transects were being collected. This thermal pattern does not match the across-basin trend estimated for I 0 . It is unclear what could cause the observed patterns to develop and begin to dissipate on the observed 35 minute timescale. As discussed in the next chapter, a similar basin- scale temperature anomaly was observed in 2008. As this pattern was observed to be stable over the entire sampling campaign in 2008 and the CL was much less developed, the dominant physical transport processes are thought to differ between 2007 and 2008.

2.4.3 Convective Motion

As observed in the vertical temperature profiles (Figure 2.7), the negative buoyancy flux associated with daytime heating will result in the CL deepening and warming over time. Both the observed deepening and warming of the CL are the direct result of convective cells redistributing heat within the CL and entraining water from the underlying EL (Mironov et al., 2002). These convective cells will continue in the CL until the associated energy is dissipated by friction. The time scale, , to dissipate these convective cells is given by the ratio of turbulent kinetic energy to the rate of turbulent kinetic energy dissipation (Kelley, 1997):

(2.6)

35 2: Convectively Driven Transport

where Cz is an empirical coefficient assumed to be 0.6, h is the thickness of the CL, and the other values have been listed previously. It should be noted that the use of is a conservative simplification, as solar radiation will also be attenuated in the SL. This is acceptable only in the limit where the depth of the CL far exceeds the depth of the SL (Mironov et al., 2002), as is the case here. Using this simplification and the CL thickness (average h = 20 m during the testing period), the amount of time required to halt the water motion resulting from radiatively driven convection, , is estimated to be ~ 1 hour.

From this predicted time scale, motion should continue through short interruptions of surface forcing (e.g. scattered clouds) but not through the night. As the SL was sampled ~ 4 hours after sundown on 21 Feb 2007, evidence of motion was not expected in Figure 2.8. In contrast, sampling on 22 Feb 2007 (medium and deep transects) was just after sun down leading to the hypothesis that, temperature fluctuations associated with residual motion are likely still present. Similar to the summer campaign, the horizontal temperature fluctuations in the CL (Figure 2.9 and Figure 2.10) are hypothesized to be direct observations of convective motion. At 17.00 m depth, these fluctuations are potentially compounded by interaction with the underlying stratified fluid; Kelley (1997) proposed that convective motion in the CL could potentially generate internal waves at the layer interface. For this reason, the transects from 6.20 m depth were used to determine length scales associated with convective cells. Temperature data was high-pass filtered with a wavenumber cut-off of (50 m)-1, and horizontal length scales of the convective plumes were estimated by measuring the width of the temperature anomalies that exceed one standard deviation of the filtered data. The estimated mean length scale for all five transects at this depth was (5.9 ± 3.3) m, where the error represents one standard deviation. This length scale is comparable to the length scales observed during the summer campaign and those observed by Thorpe et al. (1999) in Lake Geneva during both summer and winter.

2.5 Conclusions

This work presents field observations of the thermal structure formed by convection forced by a net heat flux in two environments relatively free of surface wind shear: (1) summer, nighttime

36 2: Convectively Driven Transport cooling of the epilimnion resulting from temperature differential between the water and the air; and, (2) mid-winter, under-ice, volumetric heating of the surface waters beneath the ice surface resulting from penetrating solar radiation. Observations from both campaigns indicate that the surface heat flux generated a negative buoyancy flux, resulting in convective motion within the surface mixed layer of the lake.

During the summer, repeated horizontal temperature measurements made by an AUV demonstrate horizontal temperature gradients in the epilimnion and cooler water intruding along the thermocline. Estimated cooling rates from repeated horizontal temperature transects and vertical temperature profiling were consistent with fluxes estimated from meteorological data. Observations of cooler water, proposed to be the intrusion of a density current along the seasonal thermocline, were made. It was theorized that differential nighttime cooling of near-shore water was driving the formation of these bottom-following density-currents. This mechanism is a potentially important physical phenomenon driving the transport of nutrients and minerals from the littoral to pelagic regions of this lake.

During the winter, as water temperature was below the temperature of maximum density, radiative heating rather than surface cooling drives under-ice convection. The evolving four layer structure observed over the test period agrees well with the thermal structure associated with radiatively driven convection. Radiative heat flux through the ice is shown to be sufficient to drive under-ice convection; a hypothesis supported by both the observed deepening and warming of the CL during the test period. Horizontal temperature transects within the CL show temperature fluctuations with associated length scales similar to those observed during the summer campaign. Horizontal temperature transects also show a cold water anomaly O(100 m) wide within the SL and above a warm water anomaly of similar width within the CL. This warm anomaly in the CL was observed to develop from a nearly homogeneous background to a maximum temperature anomaly of 0.1ºC and begin to decay within 35 minutes. As the temperature anomaly was not coincident with solar forcing estimated for the three stations, it cannot be definitively shown to directly result from ice cover variability. The rapid growth and

37 2: Convectively Driven Transport decay of the anomaly described here distinguishes it from the persistent anomaly presented in the next chapter that is shown to be in a rotational balance.

While traditional limnological methods are useful for bulk characterization, this work explored previously unresolved physical dynamics of the mixed layer of a temperate lake in conditions relatively free of surface wind shear that would have been difficult to quantify during summer months and impossible under winter ice cover without the use of an AUV platform.

3 A Cyclonic Eddy in an Ice-Covered Lake1

3.1 Introduction

Eddies have long been investigated beneath sea-ice (Newton et al., 1974; Spall et al., 2008). They have been observed to: (1) have a radius on the order of the internal Rossby radius (Timmermans et al., 2008); (2) persist for a time scale on the order of months to years (Wadhams et al., 2004); (3) display horizontal density differences as a result of lateral salinity gradients (Manley and Hunkins, 1985); and, (4) play an important role in mixing and vertical heat transfer in the ice-covered surface layer (Ou and Gordon, 1998). In lakes, eddies have been observed during open-water conditions (Kirillin et al., 2008; Emery and Csanady, 1973; Schwab et al., 1995; Akitomo et al., 2004); however, to our knowledge, eddies have not been observed under lake ice.

In late winter / early spring lake stratification under lake ice is often dominated by solar radiative heating of the upper waters beneath the ice surface (Farmer, 1975; Mironov et al., 2002). Below the temperature of maximum density, heating results in warmer, denser water that drives convection. Such, convection has been identified as the dominant form of vertical transport in many temperate lakes until ice-off occurs (Jakkila et al., 2009; Stefanovic and Stefan, 2002). During this time period radiative heating forms a well-mixed layer in the upper part of the water column (Farmer, 1975).

In this chapter, we present observations of an eddy in an ice-covered, temperate lake, which were made possible through the use of an Autonomous Underwater Vehicle (AUV). The eddy persisted for the duration of the six-day field study from 18 – 23 Feb 2008. The next section describes the study site, AUV, and additional instrumentation. Section 3.3 describes observations

1A version of Chapter 3 has been published. Forrest, A.L., Laval, B.E. and Pieters, R. 2009. Under-ice convection in a temperate lake. International Association of Hydraulic Engineering and Research (IAHR). Vancouver, BC, Canada. 8 pages.

39 3: A Cyclonic Eddy in an Ice-Covered Lake made within and below the eddy. In Section 3.4, the velocity structure is estimated by assuming that the observed density gradients are in cyclogeostrophic balance with both the centripetal and Coriolis accelerations. Transport in the underlying water resulting from the eddy is also considered. The existence of such an eddy has potential implications for both horizontal and vertical transport in ice-covered lakes.

3.2 Methods

3.2.1 Site Description

Pavilion Lake is located in Marble Canyon, a limestone valley at the south end of the Marble Range in central British Columbia, Canada (Figure 3.1). Compared to other regions in British Columbia, the range surrounding Pavilion Lake is relatively dry, receiving a low snow pack (less than 30 cm per year), and has an average air temperature of -6.5 ºC in February. Ice-on generally occurs by late December, with the ice thickness reaching 40 – 60 cm; ice-off occurs in late March to early April (Lim et al., 2009). The lake is divided into three main basins (North, Central and South) connected by sills 6 – 10 m deep. Pavilion Lake has an area of 5 km2 and a maximum depth of 61 m in the central basin. The lake is predominately groundwater fed, with regulated outflow from the north end.

This site has been extensively studied in the past decade, focusing on the growth of organosedimentary structures on the lake bottom known as microbialites (Laval et al., 2000b; Lim et al., 2009; Brady et al., 2009 and 2010). Over the course of these studies, few observations have been made during winter months. For example, Chapter 2 of this work presents a study of radiatively driven convection beneath the ice in February 2007. In this previous study, significant but transitory horizontal variation in temperature was observed across the Central Basin. This variation was of sufficient interest to form the basis of the field campaign described in this work.

3.2.2 Data Collection

The field campaign for this study was conducted from 18 – 23 Feb 2008 using an Autonomous Underwater Vehicle (AUV) along with a Conductivity-Temperature-Depth (CTD) profiler,

40 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.1: Bathymetry of Pavilion Lake with location in British Columbia, Canada provided in inset. Inverted filled triangle marks location of the meteorological station and thermistor mooring. The dashed box gives the study area with the boundaries of the box at the approximate sill locations in the lake. temperature chain and meteorological station. The AUV, UBC-Gavia, as configured for this deployment, was 2.4 m in length, 0.2 m in diameter and 55 kg dry weight in air. This AUV has a maximum cruising speed of ~ 3.0 m s-1; however, a speed of ~ 1.4 m s-1 was selected to provide better along-track resolution. The vehicle was programmed to run at constant depth and data was filtered to remove measurements outside the specified depth tolerance of ± 5 cm. Vehicle navigation was based on a combination of dead-reckoning aided by a two-buoy, acoustic long baseline (LBL) system, which enabled multiple transects to be collected under ice without needing the vehicle to resurface for position corrections. Instead, the LBL system was used for lateral position corrections of 2 – 4 m, estimated in post-processing using the triangulated LBL ranges. These position corrections were made approximately once per transect.

A variety of AUV missions were run to sample temperature horizontally. Example missions were designed to: (1) sample along a selected line track at 5 m (going out), 15 m (return), 10 m (going out) and 20 m (return); (2) sample at 15 m depth repeatedly for a 2 – 4 hours duration; and, (3)

41 3: A Cyclonic Eddy in an Ice-Covered Lake collect a lawnmower pattern of transects at 5 m depth using a spatial offset of 50 m. The majority of the associated mission transects ran across the Central Basin; however, four transects were also collected along the major axis of the Central Basin. Table 3.1 provides a summary of the missions run.

Temperature along horizontal transects was measured using a Seabird Electronics SBE49 CTD (resolution and accuracy of 0.0001 ºC and 0.005 ºC) mounted on the AUV. The CTD sampled at a frequency of 16 Hz, and with the selected AUV cruising speed of ~ 1.5 m s-1, provides an along track spatial resolution of ~ 10 cm.

Vertical temperature profiles were collected with a Seabird Electronics SBE19plus (same temperature resolution and accuracy) from a series of holes in the ice cover. Auger holes were drilled at 11 stations across the Central Basin from which one profile per station was collected on 22 Feb 2008 to a depth of 35 m. No profile was collected from Station 11 due to insufficient water depth. Lowering this instrument at a rate of ~ 0.8 m s-1, and sampling at 4 Hz, the vertical resolution was ~ 20 cm.

A time series of temperature was collected at Station 6 for the duration of the campaign by hanging a thermistor chain from the ice. This chain consisted of seventeen RBR TR-1050 single channel temperature loggers (resolution and accuracy of 0.002 ºC and 5 x 10-5 ºC). These loggers were placed at 2 m intervals from 1 to 35 m depth and temperature was sampled at 1 Hz.

In addition to the vertical temperature profiles, snow and ice depths were measured at each station (including Station 11). Just before the auger broke through to water, as the holes were being drilled, ice chips were collected in polyethylene bags. These samples were melted at room temperature, and then transferred to sample bottles for conductivity analysis using a Guildline Portasal.

Meteorological data (wind speed and direction, air temperature, incoming photosynthetic active radiation (PAR), and relative humidity) were measured using an Onset weather station on the ice at Station 6. All meteorological parameters were sampled every 10 s at a height of 2.4 m for the

42 3: A Cyclonic Eddy in an Ice-Covered Lake

Table 3.1: Summary of transects and profiles collected during the field deployment.

Date Time Description of Observations 18 Feb 2008 22:00 – 00:30 hrs Across-basin AUV transects at 0.33, 4.47 and 14.45 m 19 Feb 2008 14:00 – 16:30 hrs Across-basin AUV transects at 4.58 and 14.68 m 19 Feb 2008 22:00 – 01:30 hrs Across-basin AUV transects at 4.58 and 14.68 m 20 Feb 2008 11:30 – 14:30 hrs Across-basin AUV transects at 4.75 and 9.75 m, Figure 3.6 Across-basin AUV transects at 14.20 and 19.07 m 20 Feb 2008 18:30 – 21:00 hrs Across-basin AUV transects at 4.75 and 9.75 m, Figure 3.6 Across-basin AUV transects at 14.20 and 19.07 m Across-basin AUV transects at 0.75 m, Figure 3.4 21 Feb 2008 14:00 – 18:00 hrs Across and along-basin AUV transects 4.36, 9.27, 14.20, and 19.07 m, Figure 3.3 Figure 3.9 Across-basin AUV transects at 0.75 m, Figure 3.4 22 Feb 2008 14:00 – 15:30 hrs Multiple across-basin AUV transects at 14.28 m 22 Feb 2008 16:00 – 17:00 hrs AUV horizontal lawnmower at 4.29 m, Figure 3.2 CTD profiles and ice samples at 10 across-basin stations 23 Feb 2008 10:30 – 14:15 hrs Multiple across-basin AUV transects at 14.28 m, Figure 3.10

duration of the field campaign; wind speed and direction was averaged and recorded every 15 min, while all other variables were averaged every 30 min intervals.

This meteorological data was used to determine the four main heat flux components at the air-ice interface: net shortwave irradiance, SW, net longwave radiation, LW, sensible, H, and, latent heat, λE . SW was calculated by converting the measured PAR at the weather station, using a scaling factor of PAR SW = 0.47 (Papaioannou et al., 1993). Longwave, sensible, and latent heat flux from the ice surface were calculated using the bulk aerodynamic formulae. These components were calculated using the method of Launiainen and Cheng (1998). In this analysis, the surface temperature of the snow or ice was assumed to be air temperature. Launainen (1995) and Andreas (2002) provide an extensive overview of this analysis.

3.3 Observations

During the study period, a high-pressure weather system over Pavilion Lake resulted in clear and sunny conditions. The lake surface was covered with ~ 0.5 m of black ice with 0 to 10 cm snow, which allowed good penetration of sunlight through the ice. Throughout the study, the water

43 3: A Cyclonic Eddy in an Ice-Covered Lake column below the ice was reverse stratified in a similar four-layer structure as observed in the previous chapter:

• Stratified Layer (SL), from the bottom of the ice to 2 m depth, in which the temperature increases from the freezing point at the ice to ~ 2.3 ºC at 2 m;

• Convective Layer (CL), or nearly convective layer, from 2 – 10 m depth, in which the temperature is relatively uniform around 2.3 ºC;

• Entrainment Layer (EL), from 10 – 14 m depth, in which the temperature increases from 2.3 to 3.6 ºC; and,

• Quiescent Layer (QL), below 14 m depth, with a temperature of about 3.6 ºC.

Sunlight penetrating through snow, ice and the SL warms the top of the CL. This solar irradiance can result in a negative buoyancy flux in the CL (Farmer, 1975). During this study, evidence of radiatively driven convection was only able to be inferred on the west side of the basin through the presence of a well-formed CL. In the central region of the basin, a different convective mechanism was observed. To describe this mechanism, the one horizontal ‘lawnmower’ survey collected by the AUV is shown first. This survey is followed by a presentation of the horizontal transects along and across the Central Basin (Table 3.1), CTD profiles and moored data.

3.3.1 Observed Eddy Characteristics

The lawnmower survey of the Central Basin was undertaken with the AUV at a constant depth of 4.29 ± 0.05 m to examine horizontal variations in temperature. Near the center of the basin, a circular region was observed ~ 220 m across with a temperature of 0.4 ºC less than the surrounding region (Figure 3.2). As will be outlined in following sections, this circular thermal anomaly is proposed to be evidence of an under-ice eddy.

On 21 Feb 2008, transects were collected at four depths, 4.36, 9.27, 14.20 and 19.07 m. These depths were selected to sample all of the layers other than the SL. The total of eight transects, four along (southeast to northwest) and four across (northeast to southwest) the Central Basin, were run as two separate missions rather than single line runs. The intersection of these two sets

44 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.2: Contours of temperature collected by the AUV using a horizontal lawnmower survey at a constant depth of 4.29 m on 22 Feb 2008 with the eddy core at ~ 2.0 ºC and the surrounding water at ~ 2.4 ºC. The survey consisted of sixteen legs, with approximately 50 m spacing, across the basin (scale marked as shown). of transects were serendipitously near the approximate center of the eddy (Figure 3.3 inset – star). The two missions were close together in time (~ 45 min) to provide a synoptic view of temperature. Contours of measured temperatures are shown in Figure 3.3. These contours reveal a roughly cylindrical thermal structure extending down to a depth of ~ 14 m. The observed radius in the along lake transect (Figure 3.3b) is slightly smaller, which, as Figure 3.2 is symmetrical, suggests that the along lake transect was slightly off the eddy center. At 4.36 m, the temperature within the eddy was reduced by 0.4 ºC, while at 9.27 m and 14.20 m the temperature in the eddy was increased by 0.8 ºC and 0.2 ºC respectively. Note the contouring program interpolates the temperatures between the four sampling depths.

Horizontal variations in temperature across the lake were also observed in the stratified layer (SL) ~ 25 cm below the underside of the ice. On 20 Feb 2008 and 21 Feb 2008, five horizontal

45 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.3: Horizontal transects within 5 cm of prescribed depths (4.36, 9.27, 14.20 and 19.07 m) (a) across and (b) along the basin on from 15:00 to 18:00 hrs on 21 Feb 2008. Data was 15 m bin averaged. The locations of these measurements are marked with horizontal lines. Inset shows position of the across and along basin transects. The transects intersect at 0 m in (a) and (b). Distances along the transect are referenced to the center of the eddy as indicated in the inset by a star (positive values are to the northeast). profiles were collected at a depth of 0.75 ± 0.05 m (~ 0.25 m below the ice). At this depth, the AUV had difficulty maintaining its set point so close to the ice. As a result of this poor vehicle performance, many blocks of data were outside the specified depth tolerance. These blocks were removed and a composite of all runs, rather than individual transects, is shown in Figure 3.4. At this depth, the temperature in the eddy was observed to be approximately 0.15 ºC cooler than the surrounding water.

Vertical CTD profiles were collected at ten stations spaced 50 m apart (Figure 3.5a). Positions of these stations follow the across-basin AUV transect run on the same day (Figure 3.5 inset – line). The convective layer (CL) showed three distinct stratification regions across the lake: (1) the

46 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.4: Observed temperature composite from five horizontal transects (inset) at 0.75 ± 0.05 m depth (SL) on 20 Feb 2008 and 21 Feb 2008. Distances along the transect is referenced to the center of the eddy as indicated in the inset by a star (positive values are to the northeast). northeast side of the lake (Stations 1 and 2) is weakly stratified (0.068 ºC m-1) between 2 – 10 m; (2) the central region (Stations 3 – 6) is more strongly stratified (0.108 ºC m-1) between 2 – 7 m; and, (3) the southwest side of the lake (Stations 7 – 10) is nearly isothermal (0.002 ºC m-1) between 2 – 10 m. These regions are consistent with observations from Figure 3.3 and Figure 3.4 with the eddy extending from near the surface to a lower boundary at the base of the CL (14 m depth). The estimated height, H, of the eddy is 14 m. In Figure 3.5b, profiles from Stations 1, 5, and 10, selected as representative of the three regions, are overlain. These three profiles show the eddy center to be ~ 0.5 ºC cooler from 2 to 8 m and ~ 1.0 ºC warmer from 8 to 14 m than the surrounding water. Note that the CL was not fully developed (i.e. still weakly stratified) except on the west side of the lake (Stations 6 – 10).

47 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.5: (a) Vertical CTD profiles collected at Stations 1 – 10 on 22 Feb 2008. The CL (from 2 to 10 m) shows three distinct regimes: moderately stratified (Stations 1 – 2, dashed lines); weakly stratified (Stations 7 – 10, dot-dashed lines); and strongly stratified (Station 3 – 6, inside the eddy, solid lines). The temperature profiles are offset by 0.5 ºC for display purposes. Note that the first 3 m of the profile collected at Station 8 was removed as the pump was blocked with ice. (b) Profiles from each of the three regions; Station 1 (dashed line), Station 5 (solid line), and Station 10 (dot-dashed line). Inset shows the location of the transect line, Station 1 (circle), Station 5 (square), Station 10 (inverted triangle), and eddy center (star).

3.3.2 Observed Eddy Evolution

In order to characterize the temporal evolution of the eddy over one day, two sets of horizontal transects were collected in the morning and evening of 20 Feb 2008 in (1) the upper (4.75 m) and (2) the lower (9.75 m) part of the CL (Figure 3.6). Both the morning and evening data show the same thermal structure as seen in Figure 3.3 with the eddy colder in the upper part of the CL (4.75 m) and warmer in the lower part of the CL (9.75 m; Figure 3.6 – as indicated). At the southwest side of the transect, the temperature at both depths are roughly equal, consistent with small vertical temperature gradients typical of the CL observed on the southwest side of the

48 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.6: Horizontal profiles in the upper CL (4.75 m, cooler profiles) and the lower CL (9.75 m, warmer profiles) on 20 Feb 2008 from 10:45 – 13:30 hrs (solid lines) and 18:30 – 21:00 hrs (dashed lines). Data was 10 m bin averaged. The inset shows the location of the transect. Distances along the transect are referenced to the center of the eddy as indicated in the inset by a star (positive values are to the northeast). The solid vertical line marks the position of the thermistor mooring, as marked in the inset by a square. basin (Figure 3.5). Small changes in temperature were noted from morning to evening. For example, at 9.75 m depth, the eddy becomes less symmetric over the course of the day. At the edges of the eddy, the horizontal gradients in temperature at both depths (4.75 and 9.75 m) are much greater than in the eddy core and any changes in eddy size, shape or position would result in significant shifts in the temperature at these edges.

The thermistor chain was positioned directly on the southwest edge of the eddy ~ 60 m from the eddy center (Figure 3.6 – solid vertical line). The temperature record from 18 – 23 Feb 2008 shows a relatively constant temperature gradient between 1 and 7 m (Figure 3.7b) depths with the largest gradient measured in the top three meters of the water column. At these depths,

49 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.7: (a) One hour, bin-averaged solar irradiance 2 m above the ice surface with positive flux values representing heat gained by the lake, and (b) five minute, bin-averaged observed temperature measured at the position of the thermistor chain (Figure 3.1). Each trace represents the record from one thermistor at indicated depth (right axis). Note that the profiles between 13 and 19 m have a 0.2 ºC temperature offset between each record to prevent them from overlying on each other. Periods of rapid temperature decreases (> 0.25 ºC) at 11 m depth are grayed out, rapid increase in (> 0.5 ºC) at 9 m depth is circled, and periods of coherence between records collected at 13 – 19 m depth are also circled. particularly at 3 m, warming within the temperature record appears qualitatively correlated with the incident sunlight at the surface (Figure 3.7a). At the 9 m depth, the largest change was observed at 15:15 on 19 Feb 2008 when the temperature increased from 2.7 ºC to 3.3 ºC in ~ 2 hours where it then remained stable for 3 hours before returning to the cooler temperatures (Figure 3.7b - circled). Increases in temperature at this depth are suggestive of lateral movement of the eddy to the west. At the 11 m depth, decreases in temperature from the apparent stable temperature of 3.6 ºC to temperatures below 3.25 ºC in less than two hours were observed in the

50 3: A Cyclonic Eddy in an Ice-Covered Lake

temperature record. Three such events are grayed out in Figure 3.7 as they also indicate potential eddy movement. It is also interesting to note the coherence in the temperature records from the 13 – 19 m depth as indicated at 05:00 hrs on 20 Feb 2010 and 20:00 hrs on 22 Feb 2010 (Figure 3.7b – circled).

Evidence of the eddy was observed each day between 18 – 23 Feb 2008 (Table 3.1). Collected measurements suggest that the eddy center was undergoing small lateral translations while the apparent radius remained relatively constant. The center of the eddy, measured at ~ 5 m depth, was located at -20.7 m (18 Feb 2008), -36.8 m (19 Feb 2008), -14.8 m (20 Feb 2008), 0 m (21 Feb 2008), and 43.8 m (22 Feb 2008) across the lake (x-axis of Figure 3.3). Eddy radius at this depth, defined as where the temperature was 0.1 ºC less than the surrounding water, was 108, 100, 110, 110, and 100 m for each of these five days. This implies that the structure of the eddy is remaining stable while moving across the lake. The eddy was likely moving along the lake as well although insufficient points were measured along the basin to quantify this movement. Note that displacements of 50 m along the lake, approximately half the radius, will reduce the apparent radius across the lake by only ~ 15 m, close to the observed variation in radius.

3.4 Discussion

In the previous section, observations of a relatively stationary, three-dimensional thermal anomaly were detailed over the course of the six-day field campaign. Subsequent discussion will focus on the behavior and implications of this eddy.

3.4.1 Eddy Behavior

To begin, a time scale for the evolution of the observed horizontal density field in the absence of rotation can be estimated as the time to establish an exchange flow. Such a flow would cause the

1 2 eddy core to spread and double in size in Tdouble = r c, where r = 110 m is the radius, c = (g'⋅h) ,

g' is the reduced gravity, g'= g⋅ Δρ ρ0 , and h = 8 m is assumed to be the CL depth. The observed horizontal temperature change through the eddy at 9.75 m in this study is 3.55 ºC at the eddy center and 2.50 ºC in the surrounding waters (Figure 3.6). Using these temperatures and an -3 -4 -2 assumed reference density, ρ0, of 1000 kg m , g' = 1.6 x 10 m s and Tdouble is ~ 50 minutes.

51 3: A Cyclonic Eddy in an Ice-Covered Lake

The adjustment time of a rotating, stratified fluid to changes in forcing scales with the Ekman

2 number, E, which is defined as E = υ ( f ⋅ H ) where υ is the viscosity of the fluid and H = 14 m is the height of the eddy (Greenspan and Howard, 1963). Within the weakly stratified eddy, viscosity is proposed to be close to molecular viscosity. Taking υ as 10-6 m2 s-1, E ~ 10-5. For E −1 << 1 the adjustment time scales as T = (E1 2 ⋅ f ) , giving an adjustment timescale on the order of 15 days for the observed eddy. That the eddy was observed relatively unchanged over several days suggests that the observed horizontal pressure gradient is in balance with rotational forces. Rotational eddies have been described for open water conditions in small (Kirillin et al., 2008) and large (Akitomo et al., 2004) lakes but not, to our knowledge, under lake-ice. The observations presented in the previous section are similar to observations of eddies under sea-ice (Chao and Shaw, 1998; Timmermans et al., 2008). These eddies have horizontal scales on the order of, or less than, the internal Rossby radius of deformation ( R = c f ), where c is defined above and f is the Coriolis frequency. At a latitude of 51 ºN, f = 1.13 x 10-4 s-1, and using the same value of c as above (Figure 3.5 – Stations 7 – 10) gives R ~ 315 m, a value of the same order of magnitude, but nearly three times greater than the observed radius. As discussed below, the discrepancy suggests that centripetal acceleration, as well as Coriolis, is balancing a horizontal pressure gradient associated with the observed density field (i.e., an internal cyclogeostrophic balance).

Combining the across-basin temperature data from the horizontal transects of 21 Feb 2008 (Figure 3.3) and the vertical profiles of 22 Feb 2008 (Figure 3.5) provides a higher level of detail than either individual dataset. Using 30 m horizontal bins and 0.5 m vertical bins, these two datasets were interpolated to a common grid (Figure 3.8a). Irregular data in the surface layer on the west side of the transect were removed as shown in the upper left corner of the plot in Figure 3.8a. Density was calculated using the state equation of Chen and Millero (1986) (Figure 3.8b). Using cylindrical coordinates, a steady, inviscid force balance (normalized by mass) in the radial direction including centripetal, Coriolis and pressure gradient forces (i.e., a cyclogeostrophic force balance) is given by:

52 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.8: Contour plots of: (a) the observed temperature across the eddy; (b) density minus a reference density of 1000 kg m-3 (c) pressure gradient force (d) azimuthal velocity calculated from Equation 3.1 with cyclonic motion positive. White arrows in (a) indicate the depth of the horizontal temperature profiles from 21 Feb 2008 (Figure 3.3) and the vertical temperature profiles from 22 Feb 2008 (Figure 3.5). Distances along the transect are referenced to the center of the eddy as in Figure 3.3 (positive values are to the northeast).

53 3: A Cyclonic Eddy in an Ice-Covered Lake

2 u 1 ∂ p θ + f ⋅u − ⋅ = 0 (3.1) r θ ρ ∂r 0

where uθ is the azimuthal velocity, r is the radial direction with the origin at the eddy center, and p is the pressure. Making the hydrostatic approximation, taking the vertical coordinate (z) increasing downwards, and assuming no horizontal pressure gradient at the surface, the pressure field can be derived from the observed density field by integrating Equation 3.2 from the surface downwards (Figure 3.8c).

∂p ∂z = ρ⋅ g (3.2)

The calculated velocity field (Figure 3.8d) shows the eddy rotating cyclonically with a maximum -1 azimuthal velocity, umax = 3 cm s between 6 – 8 m depth. With a cyclonic eddy centripetal and Coriolis forces are oriented radially outwards and oppose the inwards pressure gradient. Assuming no horizontal pressure gradient at the surface imposes zero velocity at the surface. Moving downwards along the eddy edge, the radial pressure gradient increases in magnitude and the cyclonic velocity increases (Figure 3.8d) until about 7.5 m depth. Below this, the radial pressure gradient decreases in magnitude until velocity approaches zero at the bottom of the eddy (Figure 3.8d). The non-zero velocities beneath the eddy at 15 m depth are likely a result of problems of the combined dataset and not a reasonable prediction of the cyclogeostrophic balance. Results, qualitatively similar to Figure 3.8d, are found if the level of no horizontal pressure gradient (i.e., equivalent to a level of no motion) is taken at 15 m depth and the pressure field is derived by integrating Equation 3.2 upwards.

Relative magnitude of the centripetal and Coriolis forces can be found by calculating the ratio of scales for these forces (i.e., the Rossby number). The azimuthal velocity of the eddy, along with

the observed radius of 110 m, can be used to calculate a Rossby number, Ro = umax (r ⋅ f ) = 2.4 associated with the eddy. This implies the centripetal force is twice as large as the Coriolis force for the balance given in Equation 3.1. This validates the inclusion of the centripetal acceleration rather than a simply geostrophic balance (i.e., thermal wind). The Rossby number for this eddy

54 3: A Cyclonic Eddy in an Ice-Covered Lake is nearly twice that estimated for anticyclonic eddies found under sea-ice (e.g. Timmermans et al., 2008).

3.4.2 Beneath the Eddy

Beyond transporting water laterally in the upper water column, an eddy may also act as a transport mechanism to the underlying waters. This is suggested by temperature variations observed in the region directly below the eddy at 14.27 m and 19.07 m from 21 Feb 2008 (Figure 3.9 – grayed out). These variations ranged in magnitude from 0.02 – 0.1 ºC and are qualitatively well-correlated between the two depths. This is similar to the temperature coherence observed in the temperature records from the thermistor chain from 13 – 19 m (Figure 3.7b – circled). This correlation is particularly evident at a distance of 50 – 100 m to either side of the eddy center. Vertical vehicle motion was ruled out as an explanation for these temperature variations. Combining the mean vertical temperature gradients with the ±5 cm of the mean AUV depth, scales for temperature changes associated with AUV movements were estimated to be (1.7 ± 0.7) x 10-3 ºC, an order of magnitude lower than observed temperature variations.

To expand on these observations, a series of horizontal across-lake transects were run at a constant depth of 14.28 m on 23 Feb 2008. At the AUV cruising speed, a single across-basin transect took ~ 4 minutes to complete. In the 3.75 hour sampling period, 53 transects were completed. At the AUV depth of 14.28 m, transects were expected to be either in the EL in the areas surrounding the eddy or the QL in the region directly below the base of the eddy. Temperature measurements revealed evidence of water movement in two regions: within the EL at the southwest side of the transect (-250 m and beyond), and within the QL directly below the eddy (Figure 3.10 – grayed out). Temperature variations measured in the QL directly below the eddy were 0.04 – 0.07 ºC in magnitude, had a positive bias, and often displayed a coherency between runs. For example, the peak in temperature at -75 m (Figure 3.10 – circled) persists for the first 12 profiles or about 50 minutes. A similar pattern was observed in 12 horizontal profiles collected at 14.28 m on 22 Feb 2008 (not shown). As this implied motion was consistent on both days indicates it is directly associated with the eddy. Given the vertical stratification (Figure 3.5), vertical displacements of the water column of 1 – 2 m are required to explain the majority of the

55 3: A Cyclonic Eddy in an Ice-Covered Lake

Figure 3.9: Along basin horizontal temperature measurements collected at the base of the convective layer (14.27 m depth; dash-dot line) and in the quiescent layer (19.07 m depth; solid line) within a 0.05 m tolerance of the depth setpoint on 21 Feb 2008. The gray region represents the area located directly beneath the eddy. Distances along the transect are referenced to the center of the eddy as indicated in the inset by a star (positive values are to the southeast). temperature variations. As the overlying fluid is necessarily cooler, the observed positive bias is thought to be indicative of upwelling of the underlying fluid. These displacements were also observed to persist for timescales of nearly an hour and extend down to at a depth of ~ 20 m. The depth to which these displacements propagated is not known due to a lack of horizontal temperature data below 20 m.

Evidence of movement was also observed in the EL at -250 m and beyond in Figure 3.10. Unlike the temperature fluctuations in the QL, which were present in all transects, temperature fluctuations were only present in transects after ~ 11:15 hrs. By the end of the horizontal profiling at ~ 14:15 hrs, evidence of water movement was present to a distance of ~ 250 m away from the eddy center. Although the observed temperature variations were of similar magnitude as the region below the eddy (0.05 – 0.10 ºC), they were not coherent between runs and had a

56 3: A Cyclonic Eddy in an Ice-Covered Lake negative bias suggestive of downwelling of the overlying fluid. This downwelling likely occurs as a result of convective plumes resulting from radiatively driven convection. Solar volumetric heating will result in a destabilizing buoyancy flux at the top of the CL. Below the temperature of maximum density, this flux will result in convective plumes that are both warmer and denser than the surrounding water at the same depth. As plumes form, they will result in penetrative convection, which, in turn causes the CL to deepen and warm over time (Mironov et al., 2002). Evidence of this convection within the QL and EL will necessarily be cooler water as water is being brought down from the CL.

Figure 3.10: Horizontal temperature measurements collected at 14.28 m on 23 Feb 2008 and bin- averaged at 3 m. The first run (10:27 hrs) is shown at the bottom of the figure and the last run (14:13 hrs) at the top with a transect repeat interval of ~ 4 min. Each profile is offset by 0.05 ºC for display purposes. The positively biased temperature measurements lie directly below the region beneath the eddy (grayed out region). Front progression is shown moving from left to right by the straight line reaching a minimum distance to the eddy of ~ 150 m. Distances along the transect are referenced to the center of the eddy as indicated in the inset by a star (positive values are to the northeast).

57 3: A Cyclonic Eddy in an Ice-Covered Lake

3.4.3 Eddy Erosion

Penetrative convection resulting from convective plumes will not only change the characteristics of the CL but will result in direct erosion of the eddy. As an example, changes seen Figure 3.6 shows evidence of eddy sidewall erosion where the region just to the southwest of the thermistor chain drops from 2.8 to 2.5 ºC between the two sets of horizontal profiling separated by five hours on 20 Feb 2008. This and other similar decreases in temperature were observed in the thermistor mooring record throughout the study period. Decreases in temperature in the thermistor mooring record, from an apparent stable temperature of 3.6 ºC, were observed at 11 m depth on 18, 20, and 21 Feb 2008 (Figure 3.7b – grayed regions). The fact that each of these drops in temperature took place during daytime hours indicates that solar forcing is likely driving penetrative convection at these times. On 18 and 20 Feb 2008, the temperature decreased rapidly and then recovered within 2 – 4 hours. On 21 Feb 2008, the temperature continued to decrease to 2.9 ºC before increasing during the late evening. Temperatures decreased again in the early morning of 22 Feb 2008 before increasing again in the later afternoon on 23 Feb 2008 and recovering back to 3.6 ºC on the evening of 23 Feb 2008. It is not clear what forced this longer duration temperature pattern; however, the concurrent warming in the temperature records from 1 – 7 m depth suggest that the dynamics of the eddy are changing (i.e., undergoing lateral translations). Assuming that lateral translation results in these longer duration trends, this mechanism would also explain the increase in temperature observed at the 9 m depth in Figure 3.7b at 15:15 hrs on 19 Feb 2008.

Gradual warming of the CL will also contribute to eddy erosion as lateral density differences and associated pressure gradients will become less significant over time. This will indirectly lead to eddy erosion as the predicted cyclogeostrophic velocities will decrease proportional to the decreases in lateral density differences. Unlike rotational eddies that persist in the ocean for timescales on the order of months or years (Wadhams et al., 2002), the observed eddy will necessarily collapse by spring overturn at the latest.

58 3: A Cyclonic Eddy in an Ice-Covered Lake

3.5 Summary and Conclusions

A conceptual illustration of the observed eddy described in this work is provided in Figure 3.11. The density in the top half of eddy was less than surrounding waters and the density in the bottom half of the eddy was higher than surrounding waters as illustrated by the isopycnals (Figure 3.11 – dashed lines). Assuming these pressure gradients are balanced by centripetal and Coriolis forces, the eddy is predicted to be rotating in a cyclonic fashion with maximum azimuthal speeds of ~ 3 cm s-1. Location and depth of the eddy were observed to be relatively stable over the six-day period of the field deployment from 18 – 23 Feb 2008 with the observed radius and position of the eddy center remaining relatively constant.

Figure 3.11: Schematic of the observed eddy with direction of predicted rotation indicated. Solar heating (indicated by vertical arrows) began forming the radiatively driven convection within the water column (SL – surface layer, CL – convective layer, EL – entrainment layer, and QL – quiescent layer). Top-down convective mixing may have driven some erosion of the eddy from the west. Fluctuations were observed below the eddy, at the top of the QL. Dashed lines indicate isopycnals associated with the eddy and the stratified fluid response in the QL.

59 3: A Cyclonic Eddy in an Ice-Covered Lake

This observed eddy has a number of potential effects on the under-ice mixing dynamics in the lake. First, the eddy contributes to lateral mass transport in the CL. Second, in addition to this lateral mass transfer in the CL, the eddy is a potential source of mixing at the base of the eddy, within the top of the QL (Figure 3.11). The vertical displacement of the stratified fluid in the region below the eddy, in response to perturbations of the QL, is an undocumented source of mass transport at these depths during the winter months and is poorly understood. Concurrent to these processes, radiatively driven convection is eroding the entrainment layer and possibly sides of the eddy. This top-down vertical mixing will also contribute to transport in the lake. Note that overall heating of the CL outside of the eddy will be a factor in eddy spin down, as lateral temperature gradients become less significant. This mixing would be concurrent with top-down vertical mixing associated with radiatively driven convective circulation.

Overall, the existence of this cyclonic eddy under lake ice represents a complex combination of conditions, surface forcing, and background stratification. Further study would be required to identify the key mechanisms driving the formation and maintenance of the eddy that could not be addressed with the data collected in this study.

4 Preconditioning of an Underflow During Ice- Breakup in a Subarctic Lake1

4.1 Introduction

Negatively buoyant underflows result from higher density water flowing into receiving waters of lower density. In lakes, these density differences are often driven by turbidity (Rueda and MacIntyre, 2010), salinity (Dallimore et al., 2001), or temperature (Fischer and Smith, 1983). In all cases, the inflow will push forward along the surface until its momentum is reduced and the flow becomes buoyancy driven. The location where the denser fluid plunges below the ambient waters is known as the plunge point. The resulting density current will move downslope and reach a normal state in which it has a constant velocity and an entrainment rate proportional to the bulk Richardson number (Ellison and Turner, 1959; Simpson, 1997). This current will continue to flow downslope until reaching either the lake bottom or the intrusion depth associated with the density of the inflow. The intrusion depth is the depth at which the underflow has the same density as the surrounding water and the underflow will separate from the bottom and form a horizontally spreading intrusion (Britter and Linden, 1980; Wells and Wettlaufer, 2007).

Field studies of underflows in lakes (e.g. Fischer and Smith, 1983; Dallimore et al., 2001) have been conducted during summer months far more often than winter. With some exceptions (e.g. Miller and Aiken, 1996), studies of inflow propagation in winter have been focused on ice- covered temperate, rather than Arctic or subarctic, lakes. During winter at these latitudes, water temperatures are below the temperature of maximum density and surface inflows, often being slightly colder than the ice-covered lake water, will tend to form positively buoyant overflows

1 A version of Chapter 4 has been published in Andradóttir H.Ó., Forrest A.L., and Laval B.E. 2009. Fate of groundwater inflow in Lake Thingvallavatn during early spring ice-breakup. Proceedings of the 13th International Workshop on Physical Processes in Natural Waters, Sept 1-4, Palermo, Italy. The detailed analysis provided in this chapter has been accepted for publication in the Journal of Aquatic Sciences.

61 4: Wind Preconditioning of an Underflow

(Bengtsson, 1986a). Below the temperature of maximum density, negatively buoyant underflows will form if the source waters are more turbid (Rueda and MacIntyre. 2010), more saline, or, as is the case here, warmer than the lake water (e.g. a ground water source).

At high latitudes in winter, negative net heat flux will tend to result in a positive buoyancy flux (Jakkila et al., 2009) and wind stirring will be the dominant surface mixing mechanism. During ice break-up, the water column will be intermittently isolated from wind stirring by transitory ice cover. It is assumed in this work that the presence of land-fast ice-cover will isolate the water column from wind stirring. Thus, underflows will generally be undisturbed by surface processes during periods of weak wind forcing and/or the presence of ice cover (e.g. Carmack et al., 1979). Strong wind-forcing across open water will drive top-down deepening of the wind-mixed surface layer (Imberger and Parker, 1985). It is hypothesized in this work that during strong wind- forcing, shallow underflows will be entrained into overlying water (e.g. Morillo et al., 2008). Changing climate conditions are reducing ice cover duration on lakes (Weyhenmeyer et al., 2004). As a result, the water column will be more frequently exposed to periods of strong wind- forcing. This will potentially increase the mixing of underflows propagating across shallow regions and thereby alter the ultimate fate and distribution of these source waters in the lake.

This work reports observations of the propagation of a negatively buoyant underflow in a bay of a subarctic lake subject to wind-forcing and ice-cover interactions during ice break-up. Section 4.2 outlines the site and instrumentation associated with this study. Field observations in Section 4.3 highlight the presence of two dominant wind regimes, weak (either low wind speed or the presence of shorefast ice cover) and strong (high wind speed and no ice cover) wind-forcing. Section 4.4 discusses underflow response to these two wind regimes. In the weak wind-forcing regime, the plunge point, underflow velocities and entrainment rate are described. In the strong wind-forcing regime, the discussion includes how underflow characteristics are modified through weakening of the vertical stratification by wind mixing. This is the first known example of direct field measurements of a negatively buoyant underflow in a lake with variable ice-cover.

62 4: Wind Preconditioning of an Underflow

4.2 Methodology

4.2.1 Site Description

Lake Thingvallavatn, a subarctic lake located in southwest Iceland, is one of the country's largest (83 km2) and deepest lakes with a 34 m and a 114 m mean and maximum depth (Figure 4.1 – 3 filled star) and a total volume of 2.9 km (Adalsteinsson et al., 1992). From 1951 – 1990, Lake Thingvallavatn was predictably ice-covered from January through April (Adalsteinsson et al., 1992). In the winters of 2002 – 2008, ice cover has demonstrated large spatial and temporal variability during the 5-week average frozen period; for two of these years, Lake Thingvallavatn has been observed to be ice-free (Sveinbjornsson, 2009). Silfra Bay, the study site on the lake (Figure 4.1), has an areal extent of 1.5 km2 and slopes at a fairly constant grade to a maximum depth of 10 – 12 m at the mouth of the bay (Figure 4.1 – star). The width of the bay is relatively constant at 500 m before it starts to widen at the northern extent of the 10 m isobath. Shallow Silfra Bay is important from a hydrological point of view, as it contains the lake's largest inflow (~ 32 m3 s-1). In Silfra Bay, groundwater percolates to the surface through a series of rifts that form a network of parallel channels upstream of the lake, eventually merging into a single channel (Figure 4.1 – circle). This channel, with an estimated width and depth of 10 m and 30 m, initially enters the lake before terminating abruptly. At the channel termination, the inflow upwells into the overlying water, ~ 1 m deep, before flowing out into the lake (Figure 4.1 – inverted triangle). This is referred to hereafter as the Silfra inflow. The comparatively smaller Oxara River surface inflow (~ 3 m3 s-1) enters Silfra Bay just north of the Silfra inflow (Figure 4.1 – triangle). Other large groundwater sources exist along the lake margin, particularly along the northern and eastern shores. Combined with the Silfra inflow, these groundwater sources account for nearly 90% (~ 97 m3 s-1; Vatnaskil, 2000) of the mid-winter inflow discharge from the lake.

During winter months, the main body of Lake Thingvallavatn is generally isothermal between 0.8 – 1.4 ºC. Source water of the Silfra inflow percolates through the underlying rock and has historically been found to have a near-constant, year-round temperature (~ 3.3 ºC) and conductivity (~ 71 µS cm-1) (Adalsteinsson et al., 1992). This inflow conductivity is very close

63 4: Wind Preconditioning of an Underflow to that of the ambient lake water of (65 – 70 µS cm-1) (Lindegaard, 1992) and as such salinity will not significantly affect density. Since Silfra source water is warmer than the lake water, colder than the temperature of maximum density, it is expected to form a negatively buoyant underflow. At 0.3 ± 0.1 º C (Andradottir et al., 2009) the Oxara River is slightly cooler than the lake water and is expected to form a positively buoyant overflow.

While the Oxara River does not contribute significantly to the physical mixing within Silfra Bay, as a result of the comparative flow rate, this river has historically been responsible for the delta formation at the head of the bay that consists of characteristically red sand and gravel. Filtering this red wavelength from aerial imagery, the delta and near-shore (2 – 3 m depth) regions of the bay are clearly delineated (Figure 4.1 – dark grey). The orientation of the groundwater flow (Figure 4.1 – arrow) beyond the channel termination (Figure 4.1 – inverted triangle) is inferred to follow a southwest bearing between the delta to the north and the near-shore region on the southeast side of the bay.

4.2.2 Field Measurements

The field campaign for this study was conducted from 18 – 28 Feb 2009 using a wide array of instrumentation. On 19 Feb 2009, two rows of three thermistor moorings were deployed near the ice edge, roughly along the 2 m (~ 450 m from source inflow; Stations 4 – 6 in Figure 4.1 – diamonds; shallow water mooring line) and 5 m bathymetric contours (~ 600 m from source inflow; Stations 1 – 3 in Figure 4.1 – diamonds; deep water mooring line). RBR TR-1050 single channel temperature loggers (resolution < 5 x 10-5 ºC, accuracy ± 0.002 ºC, and a 3 sec time constant) were placed at 0.5 – 1 m depth intervals from the bottom recording at a 1 sec sampling interval. The topmost loggers for each of the thermistor chains were located within 1 m of the water surface and measurements were assumed to be surface temperatures.

Two RBR XR-420 dual channel temperature/conductivity loggers (temperature resolution, accuracy, and time constant same as a TR1050, conductivity resolution and accuracy of 0.01 and ± 3 µS cm-1 respectively) were installed at the lowest point of Stations 1 and 2 (0.5 m above the

64 4: Wind Preconditioning of an Underflow

Figure 4.1: Silfra Bay shown relative to Lake Thingvallavatn (inset) and the deepest location of the lake (filled star). Relative positions in Silfra Bay of moorings (diamonds labeled with station numbers), source water measurements (circle), meteorological measurements (square), assumed location of submerged Silfra inflow channel termination (inverted triangle), Oxara River inflow (triangle), and assumed mouth of Silfra Bay (star) are indicated. Parallel lines show the out and back constant depth AUV transects under-ice run on 20 Feb 2009 (dash-dot) and constant altitude AUV transects run on 25 Feb 2009 (solid). Solid arrow indicates inferred direction of the incoming groundwater inflow. Isobaths in meters were generated from depth soundings generated from AUV bottom-tracking. lakebed) sampling at a 5 sec interval. In total, there were six sensors at each of the stations along the deep water mooring line and two at the stations along the shallow water mooring line. An additional XR-420 was installed in the main channel of the Silfra inflow upstream of the lake (Figure 4.1 – circle) to monitor upstream conditions.

Water velocities above the lakebed were monitored over a 2.5 day period at Station 2 at 0.2 m depth intervals using a Nortek Aquadopp Acoustic Doppler Velocimeter (ADV). Velocity measurements were averaged at a 10 min interval and then low-pass filtered to remove sub-

65 4: Wind Preconditioning of an Underflow hourly variations. This instrument provided sufficient signal strength to yield reliable readings within the first 4 m from the bottom of the total 5.2 m water column depth. The acoustic signal readings at 1.6 – 2 m above bottom additionally showed interference with the stationary vertical tether used to deploy the instrument. In this study, values at this depth were discarded and bridged via linear interpolation with adjacent cells.

Daily vertical temperature profiles were taken at Stations 1 to 6 using a Seabird Electronics SBE- 19plus conductivity-temperature-depth (CTD) profiler (temperature resolution and accuracy of < 0.0001 ºC and ± 0.005 ºC). Additional casts were made at various locations in the open water and along the leading edge of the ice cover. The locations of these profiles, measured with a GPS, were used as the basis for mapping the ice cover during the field study. Horizontal temperature transects were collected with a Seabird Electronics SBE 49 CTD (temperature resolution and accuracy of < 0.0001 ºC and ± 0.005 ºC) mounted on UBC-Gavia, a Gavia-class Autonomous Underwater Vehicle (AUV). AUV transects were designed to run in the region of Station 2 at constant depths (Figure 4.1 – dash dot lines) and altitudes (Figure 4.1 – solid lines) with data within ± 10 cm of the control set point retained.

As configured for this deployment, UBC-Gavia was 2.4 m in length, 0.2 m in diameter and 55 kg dry weight in air. Unlike standard, untethered operating conditions, a 3 mm monofilament line (deployed at the vehicle cruising speed of ~ 1.4 m s-1) was used for the under-ice missions (Doble et al., 2009). Although limiting the length of transect, the line was used as a backup for AUV retrieval as the ice was too thin (~ 10 cm thick) to safely deploy directly, yet too thick to break through with the deployment boat.

4.2.3 Net Thermodynamic Flux from Bulk Aerodynamic Formulae

Meteorological data (air temperature, photosynthetically active radiation (PAR), relative humidity, wind speed and direction) were measured using an Onset weather station (Figure 4.1 – square) at a height of 1.7 m and averaged over a 5 min interval. Using these data, and the measured surface water temperatures, it is possible to estimate the four main heat flux components; net shortwave irradiance (SW), net longwave radiation (LW), sensible heat (H), and

66 4: Wind Preconditioning of an Underflow latent heat ( ). Positive flux values represent heat gained by the lake. SW was calculated by converting the measured PAR at the weather station, using a scaling factor of

(Papaioannou et al., 1993) and then correcting for the surface albedo, α (Launiainen and Cheng, 1998). Continuous cloud cover was assumed in the calculation of the remaining three components using bulk aerodynamic formulae (Launiainen and Cheng, 1998). For continuous cloud cover, a maximum decrease in the net surface heat flux of 20 – 30 % was estimated as compared to clear sky conditions. Stability of the air above the lake was assumed to be near neutral when iteratively solving the universal functions (Launiainen, 1995; Launiainen and Cheng, 1998; Heikinheimo et al., 1999).

4.3 Results

4.3.1 Ice Cover Erosion and Break-up

During the first three days of the field study (18 – 21 Feb 2009), ice covered the majority of Silfra Bay and the portion of Lake Thingvallavatn that could be visually observed from the study site (Figure 4.2a). This ice cover was extremely rotten, unable to support people, and the leading edge receded slowly during these first three days of weak southerly winds. A strong westerly wind event (>10 m s-1) during the latter half of 21 Feb 2009 initiated movement of the ice cover to the east side of the lake (Figure 4.2a), leading to its eventual total breakup. Highly variable winds, generally from the northwest, drove the remaining ice, no longer shorefast, out into the main body of the lake on 22 Feb 2009. Easterly winds on 22 Feb 2009 pushed the ice edge back onto the western shores later on 22 Feb 2009 (Figure 4.2b) and then into Silfra Bay on 23 Feb 2009. This ice then remained in the bay for a 24-hour period ending on 24 Feb 2009 (Figure 4.2c). Each change in wind direction resulted in the accumulation of ice along the shoreline and a decrease in overall ice cover on the lake. On 25 Feb 2009, small mobile ice pans were present (not shown) prior to the ice cover disappearing altogether by the end of 26 Feb 2009, 4 days after break-up had initiated.

67 4: Wind Preconditioning of an Underflow

Figure 4.2: Position of ice cover on Silfra Bay approximated from field observations. Ice cover is illustrated from 18 – 24 Feb 2009 (ice cover is white, open water is hatched, and dark grey represents near-shore or delta regions): (a) receding leading ice edge from 18 – 21 Feb 2009; (b) position of ice on western shore on 22 Feb 2009; and, (c) movement of a large, triangular pan of ice into the bay on 23 Feb 2009 with the rest of the ice cover behind, followed by departure of the ice cover on 24 Feb 2009. For the remainder of the study, the observable portion of the lake was free of ice.

4.3.2 Inflow Characterization

Temperature measurements of the Silfra inflow, as monitored in the main channel upstream of the lake (Figure 4.1 – circle), had an average value over the study period of 3.31 ± 0.02 ºC. No significant differences were observed between measurements of specific conductivity of the Silfra inflow (at the same location) and the ambient waters. Both waters were ~ 71 µS cm-1. As the specific conductivities of the two waters were so similar, specific conductivity could not be used as a tracer of the Silfra inflow. As a spot check of inflow velocity, ADV measurements were made on 18 Feb 2009, at the same location as the temperature measurements of the Silfra inflow (Andradottir et al., 2009). Uniform velocity measurements of 11 ± 5 cm s-1 were measured in the channel center over a 1 hour time period at 0.2 m depth intervals within 3 m of the surface. Using the previously mentioned channel width and depth estimates of 10 m and 30 m, a volumetric discharge of ~ 30 m3 s-1 was calculated. This field estimation validates a discharge estimate of 32.4 m3 s-1 generated using data from Vatnaskil (2000). Subsequent

68 4: Wind Preconditioning of an Underflow

Figure 4.3: Ice cover and meteorological measurements (panels a – e) made during the field campaign; (a) ice cover over moorings indicated in black, (b) wind speed [m s-1], (c) wind direction (0º represents from north) [º], (d) air temperature [ºC], and (e) calculated net heat flux [W m-2]. Wind directions associated with wind speed greater than 5 m s-1 are circled in the wind direction subplot. Panels f – h show one-hour, bin-averaged water temperature at the three deep-water stations (corresponding to Stations 1 – 3 respectively) clearly displaying weakly (grayed out) and strongly stratified periods at all three stations. Arrows indicate onset of events where the water column is mixed at one of the stations. Panels i and j show low pass filtered ADV measurements from 22 – 24 Feb 2009: (i) water speed along major axis (positive towards the SW), (j) water speed along minor axis (positive towards the NW).

69 4: Wind Preconditioning of an Underflow calculations assume the volumetric discharge of the Silfra inflow to be constant at this latter value.

4.3.3 Observed Water Column Response to Dominant Wind Regimes

Figure 4.3 summarizes the weather conditions, water temperature at the deep mooring line, and water velocity from 20 – 27 Feb 2009. Periods when the majority of Silfra Bay was ice-covered are blacked out in Figure 4.3a. During the study period, the embayment was exposed to varied winds with peak velocities of ~ 8 m s-1 on 21 Feb 2009 (Figure 4.3b). We define periods of strong wind-forcing when wind speed exceeds 5 m s-1 and periods of weak wind-forcing when wind speed is less than 5 m s-1. Wind directions associated with strong wind-forcing are circled (Figure 4.3c). Apart from the initial event on 21 Feb 2009, wind direction associated with strong wind-forcing was typically from the northeast (Figure 4.3c). Air temperature was generally above freezing until 25 Feb 2009 and below freezing thereafter (Figure 4.3d). There was a net loss of heat through the bay surface except for periods around mid-day (Figure 4.3e). Except for 23 Feb 2009, strong wind-forcing was also observed to be associated with higher surface heat loss.

Changing meteorological conditions over the study period led to variability in the measured water temperature at each of the three deep-water stations (Figure 4.3 f – h). For large potions of the study, the temperature record at all three stations show similar inverse thermal stratification: near-surface water influenced by atmospheric conditions at ~ 1.0 ºC; and, a warmer underflow with temperatures up to 3.0 ºC. Exceptions to this were when the water column is weakly stratified at all three stations. We define periods of weak stratification, grayed-out in Figure 4.3 and henceforth referred to as ‘mixing events’, as those times when the measured difference between the top and bottom thermistors, averaged across the three deep-water moorings, was less than 0.3 ºC. These mixing events are associated with strong wind-forcing and represent ~ 40 % of the sampling duration. One notable exception when strong wind-forcing failed to create a mixing event is 24 Feb 2009 when the presence of ice inhibited wind stirring.

There are many instances of stratification varying between stations (e.g. fully mixed at one station and stratified at others), which potentially result from baroclinic response to changing

70 4: Wind Preconditioning of an Underflow wind forcing, rotational effects, or lateral internal tilting of the underflow due to transverse winds. Two longer period events occurred on 21 Feb 2009 and 24 Feb 2009 (duration of 4 and 6 hours respectively; highlighted by arrows in Figure 4.3f – h) and represent about 5% of the observation period; however, most of these events are short lived (i.e., < 1 hour). The remainder of the temperature record shows evidence of the underflow (i.e. strong stratification) at all three deep-water stations and is associated with weak wind forcing. Most of the temperature record can be categorized as being either strongly stratified during periods of weak wind-forcing (55% of the time) or weakly stratified during periods of strong wind-forcing (40% of the time). Even during these periods, it should be noted that temperatures will vary between stations (Figure 4.3f – h). This work focuses on characterizing these two most prevalent periods and neglects any transverse variability.

Figure 4.3i and j summarize water velocity measurements made using the ADV at Station 2 from

12:00 hrs, 22 Feb 2009 to 20:00 hrs, 24 Feb 2009. The ADV data collection period was characterized by very low wind speeds (< 1 m s-1) except from 12:00 – 18:00 hrs on 23 Feb 2009 and 12:00 – 20:00 hrs on 24 Feb 2009 when wind speed increased to ~ 5 m s-1 (Figure 4.3b). The period of increased wind speed on 23 Feb 2009 was coincident with an ice pan moving into the bay at ~ 13:00 hrs (Figure 4.2c). This ice cover effectively isolated the water column during the period of strong wind-forcing on 24 Feb 2009 until the ice left the bay. Hourly averaged, measured horizontal water speed near the surface (1 – 2.8 m) showed a dominant flow to the northeast (3 – 5 cm s-1) although flow reversal was observed during the mixing event on 23 Feb 2009. Below the surface layer, water was flowing to the southwest at a measured water speed of 4.8 ± 0.5 cm s-1 in the mid-water column (2 – 3 m depth) and then 6.5 ± 0.7 cm s-1 in the bottom 2.5 m (2.8 – 5.2 m depth). The measured direction of the bottom flow matches the southwest orientation of the inferred channel from the aerial imagery (Figure 4.1 – arrow), and the surface waters were observed to flow in a counter-direction for the majority of the study period. Underflow direction appears to reverse during the high (> 5 m s-1) wind event at 15:00 hrs, 24 Feb 2009. This wind event was responsible for the ice cover disappearing completely.

In summary, water temperature and velocity measurements suggest the Silfra inflow forms a persistent underflow within Silfra Bay. This underflow is periodically mixed vertically in the

71 4: Wind Preconditioning of an Underflow water column when strong wind-forcing events occur. When these events occur, changes in the underflow characteristics will result.

4.3.4 Vertical Characterization of the Underflow

Vertical temperature profiles at the shallow mooring line, collected from 12:00 – 13:00 hrs 22 Feb 2009 during weak wind forcing (Figure 4.4), show temperature differences > 1.0 ºC in both the vertical and horizontal. In contrast, temperature profiles at the deep mooring line have comparatively little lateral variability (< 0.1 ºC) near the surface and showing temperature variations of > 0.5 ºC at the western station in the 3 – 4 m thick warmer underflow. Underflow thickness, du, is defined as the height from the bottom to where the temperature is 0.1 ºC above the mid-depth layer temperature (defined as depths where !T !z approaches zero). Using this definition, a value for du of 3.4 m was calculated for Station 2. These vertical temperature

Figure 4.4: Bin-averaged temperature profiles taken between 12:00 – 13:00 hrs 22 Feb 2009 (bin size = 0.2 m) at the deep mooring line (dashed line is Station 1, solid line is Station 2, dash-dot line is Station 3) and shallow mooring line (solid lines show Stations 4 – 6 as indicated). du is marked for Station 2 where it is defined as to the temperature 0.1 ºC above ambient lake temperature. Locations are shown in inset (filled diamonds) with open water hatched.

72 4: Wind Preconditioning of an Underflow profiles suggest that the underflow is not yet evenly distributed across the width of the bay at the shallow water mooring line, but is uniformly distributed across the bay at the deep water mooring line.

A transect of vertical temperature profiles was collected during a period of weak wind-forcing at 10:00 hrs on 24 Feb 2009 around the western edge of the ice pan (Figure 4.5 – inset). This transect clearly shows the underflow propagating out to a distance of 1.5 km from the source inflow where it is expected to extend well beyond. Underflow thickness, du, is marked in two of the profiles as they are used in the later discussion of entrainment. The predicted plunge point, derived in a latter section, is indicated with a solid line between the two mooring lines. The position of this point indicates, as did the profiles in Figure 4.4, the inflow establishing a negatively buoyant underflow upstream of the deep water mooring line.

Figure 4.5: Temperature contours from a CTD transect at 10:00 hrs, 24 Feb 2009 (locations shown in inset) showing the gravity-driven, groundwater underflow into Silfra Bay. Depths of CTD measurements as shown and locations of profiles shown in inset (filled circles) with open water hatched. Point at which transect crosses deep water mooring line indicated in inset (filled diamond). Predicted plunge point indicated with a solid line and underflow thicknesses, du, using the previous definition, as indicated at 800 and 1310 m along transect.

73 4: Wind Preconditioning of an Underflow

In addition to temperature profiles within Silfra Bay showing vertical stratification, evidence of the underflow extended into the main body of the lake. Figure 4.6 shows two vertical temperature profiles, one taken at the mouth of Silfra Bay (Figure 4.6 inset; ~ 1.5 km from Silfra inflow) on 24 Feb 2009 and the other taken in the main body of the lake (Figure 4.6 inset; ~ 2.5 km from Silfra inflow) on 26 Feb 2009. Both profiles were collected during similar atmospheric conditions and show similar thermal stratification as observed in Figure 4.3. du was observed to increase from 3.5 m at the mouth of Silfra Bay to 4.2 m in the main body of the lake. These observations are consistent with theory that predicts linear underflow growth through the entrainment of overlying cooler ambient lake water during downslope propagation. During weak wind-forcing, the underflow had a maximum temperature of 2.75 ºC at the mouth of the bay and 1.75 ºC in the main body of the lake (Figure 4.6). During strong wind-forcing, a much weaker although still present, near-bottom temperature signal was measured. For example, underflow temperature at the mouth of the bay was ~ 1.6 ºC on 25 Feb 2009. This profile during strong wind-forcing shows that wind is mixing the underflow in water as deep as the mouth of Silfra Bay (~ 10 m).

4.3.5 Horizontal Characterization of the Underflow

Horizontal temperature transects were used to characterize behavior of the underflow beneath the ice cover. Figure 4.7a shows two horizontal temperature transects collected beneath the ice at a constant depth of (2.0 ± 0.1) m on 20 Feb 2009 (position of AUV transects shown in inset). During the transects, Silfra Bay was ice-free from the shore to ~ 660 m and was judged to be ice- covered over the rest of the lake from shoreline observations (Figure 4.7a and inset). From the depth of the AUV relative to the ambient stratification (Figure 4.7b), measurements were expected to be at, or just below, the upper boundary of underflow. It should be noted that these horizontal transects were ~ 0.5 ºC warmer than at the same depth in the vertical profiles collected on 22 Feb 2009 (Figure 4.4) in the same weak forcing condition. This lower temperature is attributed to the strong wind-forcing event on 21 Feb 2009.

Temperature measurements made using the AUV will be affected by vertical vehicle motion within the water column stratification. The mean vertical temperature gradient at the depth of the

74 4: Wind Preconditioning of an Underflow

Figure 4.6: Vertical temperature profiles collected at the mouth of Silfra Bay (1.5 km from the source inflow; 13 m total depth – 10:30 hrs 24 Feb 2009) and in the main body of the lake (2.5 km from the source inflow; 32 m total depth – 10:30 hrs 26 Feb 2009) during weak wind-forcing and a single profile collected at the mouth of Silfra Bay (1.5 km from the source inflow; 11 m total depth – 10:30 hrs 25 Feb 2009) during strong wind-forcing (locations shown in inset).

Underflow thickness, du, marked in each of the weak wind-forcing profiles with the lake bottom hatched in all three profiles.

AUV transects was 0.2 ºC m-1, as determined from the vertical profile (Figure 4.7b). Combining the mean vertical temperature gradients with the ± 5 cm tolerance about the mean AUV depth, an estimate for temperature changes associated with vertical displacements of the AUV was 0.02 ºC. As the observed along-track temperature fluctuations were an order of magnitude greater than this, they are not attributable to vehicle motion.

Although exceptions were observed when the temperature would decrease by up to 0.2 ºC (e.g. Figure 4.7a – 750 and 830 m in the western transect), the overall trend in the western transect was for the temperature to increase proportional to the distance from the Silfra inflow source.

75 4: Wind Preconditioning of an Underflow

Figure 4.7: (a) Horizontal temperature profiles collected at a 2 m constant depth (± 10 cm) under ice cover from 11:00 – 12:00 hrs on 20 Feb 2009. These profiles are shown as a function of the lateral distance from the source inflow (solid and dashed lines represent 50 cm and 10 m horizontal bin averages) with the approximate position of the ice-edge indicated with a solid line. The eastern and western profiles have a lateral separation of 50 m going from open water (hatched) to the ice (inset). (b) Bin averaged (0.2 m bins) vertical temperature profile collected late afternoon 19 Feb 2009 at Station 3 (inset – diamond). Both wind periods were characterized by weak wind-forcing. Relative position of the AUV is shown within the vertical stratification.

Temperature along the eastern transect was observed to increase over the first 125 m then decrease in the final 50 m. Other than these trends, little along-track temperature variability was observed in open water (maximum deviation from the 10 m lateral bin average of ~ 0.03 ºC) between 620 and 670 m from the source inflow. In contrast, relatively large along-track temperature variability was observed under the ice cover (beyond 670 m; maximum deviation from the 10 m lateral bin average of ~ 0.38 ºC). Temperature along the two transects (Figure 4.7a) was offset by 0.05 – 0.1 ºC (lateral separation of 50 m) even though they were less than 5 minutes apart. This offset between the two transects is potentially explained by the lateral variability in temperature observed in the three stations (Figure 4.3f – h) later that same day.

76 4: Wind Preconditioning of an Underflow

These constant depth temperature transects demonstrate two different aspects of the nature of the underflow. First, increasing temperatures are indicative of an increasing proportion of the underflow being sampled with increasing distance from source even as the overall temperature of the underflow is decreasing. Second, greater along-track temperature variability indicates active vertical mixing. It should be noted that the along-track variability was likely not the result of radiatively driven convection (e.g. Farmer, 1975) as the calculated average solar irradiance below the ice for 20 Feb 2009 was calculated to be 3 W m-2 using the methods of Launiainen and Cheng (1998). This estimated value is well below the minimum value of 10 W m-2 required for convective plume formation under ice (Kelley, 1997).

Horizontal temperature measurements were also collected on 25 Feb 2009. In contrast to the previous constant depth transects, these transects were at a constant altitude of (2.1 ± 0.2) m from bottom (Figure 4.8a). The mean vertical temperature gradient, ~ 50 m from the starting point of the transect, at the initial depth of the AUV was 0.04 ºC m-1 (Figure 4.8b). Combining the mean vertical temperature gradients with the ± 20 cm tolerance about the mean AUV altitude, an estimate for temperature changes associated with vertical displacements of the AUV was 0.008 ºC. Though AUV depth increased by 2 m over the length of the mission, this estimate is assumed to remain valid for the entire transect.

As shown, the temperature record in both transects initially increases (575 – 625 m) then decreases in temperature in a non-linear fashion from 625 – 690 m. Beyond 690 m, both temperature records decrease linearly with slopes of -3.9 x 10-4 ºC m-1 and -2.1 x 10-4 ºC m-1 for the eastern and western transects. A 0.075 ºC offset is observed in the linear portion of both transects, which, similar to the constant transects (Figure 4.7) indicates lateral variability. In contrast to the constant depth transects, the constant altitude transects were conducted during a period of relatively strong wind (3 – 5 m s-1) resulting in colder temperatures and weaker vertical stratification. A collection period with lower wind speed (e.g. 24 Feb 2009) would have been

77 4: Wind Preconditioning of an Underflow

Figure 4.8: (a) Two temperature profiles collected at a 2.1 m constant altitude (± 20 cm) from 10:00 – 10:15 hrs on 25 Feb 2009 (track locations shown in inset). These profiles are shown as a function of the lateral distance from the source inflow (western transect – solid line; eastern transect – dashed line). Linear regressions (solid bold lines) of the linear portions of each transect are overlain. (b) Bin averaged (0.2 m bins) vertical temperature profile collected at 10:00 hrs on 25 Feb 2009 at Station 2 (inset – diamond). Relative initial position of the AUV is shown within the vertical stratification. preferred to directly estimate entrainment into the underflow (see Appendix B), but we were unsuccessful in completing constant altitude missions during a low wind period.

4.4 Discussion

From observations of both atmospheric forcing and water column response (Figure 4.3), we define two dominant regimes: (1) a weak wind-forcing regime characterized by low wind speed (< 5 m s-1) or ice cover; and strong stratification; and, (2) a strong wind-forcing regime

78 4: Wind Preconditioning of an Underflow characterized by high wind speed and weak stratification. In the following discussion, properties of the underflow during weak wind-forcing are compared with established relationships. Subsequently, a comparison of wind stirring to underflow buoyancy flux is used to predict when top-down mixing processes are sufficient to homogenize the water column.

4.4.1 Weak Wind-Forcing

Empirical relationships use inflow and ambient conditions to predict the distance between source inflows and their associated plunge point, Lp. The relative densities and inlet conditions are accounted for using the densimetric inflow Froude number defined as where U0 is the initial velocity, h0 the upstream inflow depth (recall the termination of the Silfra rift is submerged in ~ 1 m of water and 10 m wide) and is the reduced gravity. When Fr0

> 1, Lp, the distance to the point of initial water column stratification, known as the plunge point, can be estimated using (Hauenstein and Dracos, 1984)

(4.1)

where S0 is the constant bottom slope and b0 represents the width of the groundwater inflow. As inflow velocity information was unavailable, the measured underflow speed of 6.5 cm s-1 at

Station 2 on 24 Feb 2009 was used as a first approximation for U0. Based on the measured Silfra inflow and ambient water temperatures of 3.31 and 1.2 ºC, g' and Fr0 were calculated to be 5.9 x -4 -2 10 m s and 2.7 respectively, thus satisfying the Fr0 constraint for use of Equation 4.1.

Estimating S0 in the region between the shallow water and deep water mooring lines at 0.004 m/m, Lp was determined to be ~ 525 m. This value corresponds to a distance between the two mooring lines (Figure 4.5 – solid line) and is consistent with the observations described in Section 4.3.4.

Bulk velocity associated with the underflow was estimated by applying heat and mass balances to the bay approximated as a box with two-layer stratification. This two-layer system is assumed to be at steady state, with a single source inflow, an underflow, and an overflow returning an ambient lake temperature (Figure 4.9). The deep water mooring line was assumed to be the open

79 4: Wind Preconditioning of an Underflow

Figure 4.9: Illustration of a 2D model of an idealized underflow system (not drawn to same scale as Figure 4.5 with underflow discharge, Qu, and returning ambient flow, Qr, both with representative temperatures (Tu, Tr) and depths (du, dr) and moving with associated velocities

(Uu, Ur). As the underflow entrains ambient fluid, it will grow linearly (as shown by the deviation from the dotted line). Inflow conditions (Q0, T0), boundary conditions at the deep water mooring line (Tub, dub) are defined in addition to the overall height of the water column, H. boundary through which the underflow exits and the overflow returns. The underflow boundary temperature, Tub, and depth, dub, are shown at the deep water mooring line as a reference point for further discussion. In a two-layer approximation, fluid exiting the system via the underflow with thickness du, velocity Uu, and temperature Tu. will necessarily be replaced by return overlying fluid of depth dr, velocity Ur, and temperature Tr. In the process, returning overflow is entrained into the underflow resulting in du growing linearly as a function of the distance away from the source (shown by the deviation from the dotted line in Figure 4.9).

The overflow temperature will also be modified by surface heat flux, which has to be accounted for in the heat balance of the system. An ice-free condition was assumed for the calculation of surface heat flux, which, for the period of 06:00 – 12:00 hrs on 24 Feb 2009 was ~ -50 W m-2.

80 4: Wind Preconditioning of an Underflow

This is a conservative estimate, as a greater surface heat loss would occur with open water than through ice cover (Launiainen and Cheng, 1998). As previously discussed, groundwater inflow 3 -1 was assumed to be Q0 = 32.4 m s (Vatnaskil, 2000) and T0 = 3.3 ºC (as measured). Underflow thickness, du, for the same period was calculated at (2.4 ± 0.2) m from time-averaged temperature measured at the three deepwater moorings. Average total water depth, H, was measured at (4.7 ±

0.6) m, and dr = H – du = (2.3 ± 0.8) m. Overflow and underflow temperatures were averaged from the three deepwater moorings. Inputting the above values into a heat and mass balance -1 results in predicted velocities Ur and Uu of ~ 3 and ~ 5 cm s . These values agree well with water speed measurements made during this time period (Figure 4.3i). Using the bay width of 500 m, the approximate width at the deep water mooring line, these velocities correspond to estimated volumetric flow rates of 35 and 60 m3 s-1, respectively. It should be noted that the influence of surface heat flux on these calculations of velocity was estimated to be ~ 5 % and is thus considered to be of secondary importance.

Underflow entrainment has been estimated from both laboratory (Ellison and Turner, 1959) and field (Dallimore et al., 2001; Fischer and Smith, 1983) studies. These studies have shown that underflows quickly reach a steady normal state for a constant slope angle, α, where the bulk Richardson number, , and the volumetric entrainment rate, E, are constant. A value of 2.8 x 10-3 was calculated for E using Equation 4.2 based on observed underflow thicknesses, du, in the two indicated profiles (Figure 4.5) and their distances away from the inflow source in the bay on 24 Feb 2010 (Ellison and Turner, 1959).

(4.2)

Cenedese et al. (2004) and Dallimore et al. (2001) provide a good overview of various studies that examine multiple different types of negatively buoyant underflows. At slope angles similar to those found here, a number of field and lab studies have observed a relationship between E and Ri (e.g. Dallimore et al., 2001). Given the underflow conditions in this study, Ri is calculated to be 0.5. Fitting this value to the curve developed by Dallimore et al. (2001), E is in the range of 2 – 8 x 10-3. Stefanovic and Stefan (2002) calculated a value for E of 8 x 10-3 for density

81 4: Wind Preconditioning of an Underflow currents resulting from differential heating in an ice-covered lake (Ri = 0.17). These estimates of entrainment are consistent with those calculated for this work using Equation 4.2.

A negatively buoyant underflow will propagate downslope until it reaches a point of neutral buoyancy with the ambient fluid. At this depth, called the intrusion depth, the underflow will separate from the bottom boundary to form a horizontally spreading intrusion (e.g. Fer et al., 2002a; Wells and Wettlaufer, 2007). In our case, assuming the ambient lake temperature is constant at 1.2 ºC (recall Figure 4.6), the underflow is not expected to reach neutral buoyancy with ambient water and will run downslope until the deepest part of the lake is reached at a range of ~ 8 km away from the source inflow (Figure 4.1 – inset). As the underflow propagates through the lake, it will be diluted through entrainment of the overlying layer. As will be shown in the next section, stirring resulting from increased wind will result in the underflow being further diluted as it traverses Silfra Bay.

4.4.2 Strong Wind-Forcing

As discussed in the previous section, underflow dynamics during the weak wind-forcing regime are controlled through a balance between gravity and entrainment of the overlying waters. Entrainment of ambient water into the underflow, driven by turbulence generated by the underflow itself, will increase the thickness of the underflow and correspondingly decrease its temperature proportional to the distance from the source inflow. In contrast, stirring caused by moderate to strong winds will contribute significantly to the dilution of the underflow as it traverses the relatively shallow Silfra Bay. As the bay becomes well-mixed, groundwater will no longer propagate as far or as deep into the lake as during weak wind-forcing.

During strong wind-forcing, a threshold will be reached where the net TKE production by wind stirring will overcome the buoyancy flux of the underflow. Above this threshold, the water column will become completely mixed. These time periods were predicted by comparing the calculated net TKE production over a given time interval (Es) to the energy required to mix the water column, Em. Mixing of the water column is expected when Es is greater than Em. Em was calculated using a formulation similar to that used by MacIntyre et al. (1999) in their calculation of the stability number (zg is the centroid height):

82 4: Wind Preconditioning of an Underflow

(4.3)

-2 Em = 1.0 kJ m was determined by averaging the temperature profiles generated from the three deep-water moorings at 10:00 hrs on 24 Feb 2009. During this time period, stratification was strong (i.e. during the weak wind-forcing regime). We use the formulation proposed by

Findikakis and Law (1999) to estimate Es over a time interval :

(4.4)

where ρa is the air density, parameters Cs, Co, and Cu are empirical constants and is the mean wind speed at 10 m above the water surface. The time interval ( ) is taken to be the underflow hydraulic residence time from the Silfra inflow source to the deep water mooring line. Using the measured underflow velocity this value is calculated to be ~ 4 hours. Values for Cs and Co of 0.2 and 0.02 were selected based on the analysis provided by Tucker and Green (1977) and subsequently Findikakis and Law (1999). The value for Cu was estimated from the following equation (Findikakis and Law 1999):

(4.5)

As shown in , there is good correlation between those times when mixing is predicted (i.e. Es >

Em; circles on Figure 4.10a) and those times when mixing events were observed at the deep water mooring lines (grayed out regions from Figure 4.3 and Figure 4.10). Recall that these grayed out regions were determined when the average temperature difference between the top and bottom thermistors (Figure 4.10b) at the three deep water moorings was less than 0.3 °C. Note that periods of strong wind stirring are generally associated with a negative heat flux (Figure 4.3), which will stabilize the water column. However, the comparison in Figure 4.10 above demonstrates that wind stirring is sufficient to mix the water column at the deep water mooring line.

In order to confirm that wind-stirring is sufficient to mix the water column in water deeper than the deep water mooring line, Em was calculated using profiles collected during periods of weak

83 4: Wind Preconditioning of an Underflow

-2 Figure 4.10: (a) Es (kJ m ) over the testing period at 1-hour intervals with circled values greater -2 than the threshold for water column mixing at the deep water mooring line (Em = 1 kJ m ) and -2 threshold for water column mixing at the mouth of the bay (Em = 5 kJ m ). (b) Concurrent temperature differences between top and bottom thermistors at Stations 1 (solid line), 2 (dotted line) and 3 (dashed line) show periods of mixing ( ) (grayed out as with Figure 4.3) and periods of stratification ( ). wind-forcing at the mouth of the bay and the main body of the lake (24 and 26 Feb 2009; Figure -2 4.6). These profiles give Em = 5.0 and 50.0 kJ m for the mouth and main respectively. At the mouth of the bay these values predict complete mixing on 21 Feb 2009 and only briefly on 25 Feb 2009 (Figure 4.10). This latter prediction is consistent with the profile measured during strong wind-forcing on 25 Feb 2009 (Figure 4.6). Complete mixing is not predicted to occur at 32 m depth in the main body of the lake.

The linear portions of the constant altitude temperature transects (Figure 4.8) are suggestive of simple underflow entrainment as described for weak wind-forcing regime; however, these transects occurred during the strong wind-forcing period (10:00 – 10:15 hrs on 25 Feb 2009; Figure 4.10) and the vertical profiles from Figure 4.6 and Figure 4.8 show that the bay is weakly-

84 4: Wind Preconditioning of an Underflow stratified out to the mouth during the time that these transects were collected. Thus the vertical stratification in the vicinity of the transects is weak and two-layer underflow entrainment theory cannot be used to characterize the constant altitude temperature data. The observed along-track linear decrease in temperature is more likely due to vertical mixing of the underflow into a proportionately deeper column of lake water. As a point of comparison, the vertical average of the temperature profile at the start of the transect on 25 Feb 2009 (Figure 4.8b) is 1.51 ºC, which is similar to the average of 1.66 ºC of a profile at a similar location the day before (Figure 4.5) during weak wind-forcing. This suggests that heat is nearly conserved, though redistributed vertically by the wind stirring. Extending this argument, consider the average temperature of 1.40 ºC of a profile conducted at the mouth of the bay during the weak wind conditions of 24 Feb 2009 (Figure 4.6). An average horizontal temperature gradient of vertically averaged temperature can be calculated as the difference of the vertically averaged temperature of the two profiles conducted on the same day as the transects (i.e., 25 Feb 2009) divided by their horizontal separation of ~ 1000 m. A calculated mean temperature gradient of -2.6 x 10-4 ºC m-1 compares well with the observed linear gradients of -3.9 ºC m-1 and -2.1 x 10-4 ºC m-1.

In summary, during the strong wind-forcing regime, wind-stirring will result in a large portion of Silfra Bay being vertically mixed (or the entire bay during strongest winds) as compared to periods of weak wind-forcing where an underflow was measured. As observed in this study, this mixing of the underflow with lake water reduces the temperature of the underflow. This will have implications on the eventual fate of the underflow. Observed periods of mixing are predicted to occur when TKE production by wind stirring integrated over the underflow hydraulic residence time in the bay exceeds the potential energy associated with the stratification. Field observations of weak stratification were in close agreement with predictions of complete mixing.

4.5 Conclusions

In this work, a combination of moorings, vertical and horizontal temperature profiling was used to characterize a negatively buoyant underflow in the Silfra Bay region of Lake Thingvallavatn. Underflow characteristics were modified through wind forcing. Although this forcing

85 4: Wind Preconditioning of an Underflow demonstrated significant variability during the period of ice break-up, two dominant regimes were identified and the associated water column response was examined; (1) weak wind-forcing (either through low wind speeds or ice cover), and (2) strong wind-forcing (high wind speeds and no ice cover). Relatively uniform vertical stratification associated with weak wind-forcing accounted for ~ 55 % of the sampling record whereas the water column was generally well- mixed during strong wind forcing events and comprised an additional 40 %. The small remainder of the temperature record was spatially complex with varying stratification between stations.

During periods of weak wind-forcing a clearly defined warm underflow, with temperatures up to 3.0 ºC, was observed underlying the ambient lake water at ~ 1.2 ºC. Vertical profiles indicate this underflow propagates into the main body of the lake. In this work, mass and energy budgets were developed to characterize this underflow. Good correlation between predicted and measured velocities was found, leading to the conclusion that the two-layer model was a reasonable approximation of this system during periods of weak wind-forcing. The evaluated entrainment rate of this underflow within Silfra Bay is in relatively close agreement with other studies on this subject. Assuming ambient lake temperature is isothermal, the underflow will likely reach the deepest part of the lake ~ 8 km from the source inflow, as opposed to forming a mid-water intrusion. The underflow is a likely transport mechanism for groundwater to the bottom of the lake during long periods of ice cover (historically 2 – 3 months in Lake Thingvallavatn).

During periods of strong wind-forcing, the underflow is well-mixed by wind stirring as it traverses Silfra Bay. These time periods were successfully predicted by estimating when the TKE production by wind stirring integrated over the underflow hydraulic residence time in the bay exceeded the potential energy associated with the stratification. In recent years, Lake Thingvallavatn has been increasingly subject to ice-free periods that are thought to directly result from global climate change. This means that the water column is increasingly subject to strong wind-forcing periods during the winter months, and subsequent mixing of the water column during episodic winter wind-storm events, which is historically not the case. Predicting behavior of the underflow is necessary to understand the evolving pathways of groundwater inflow into the lake.

5 Conclusions

5.1 Research Summary

This work examines three important physical transport processes in lakes: (1) convection associated with a negative buoyancy flux; (2) motion generated through rotational adjustment; and, (3) negatively buoyant underflow fate as it is modified through episodic wind-stirring. These processes were investigated using a combination of horizontal and vertical sampling techniques, which allowed the associated three-dimensional, time evolving nature to be characterized in a previously unexplored manner.

Convection associated with a negative buoyancy flux was explored in both the summer of 2006 and the winter of 2007 in Pavilion Lake, British Columbia (Chapter 2). This flux resulted from cooling of the epilimnion during the summer campaign and warming of the surface layer of the water under ice resulting from penetrative solar radiation during the winter campaign. In both cases, this generated flux drove convective motion within the surface mixed layer of the lake. Temperature measurements, made in both the epilimnion and along the thermocline during the summer campaign, suggest the presence of convective plumes and density currents acting as a source of mass transport. Both the calculated Richardson number and the observed mean frontal velocity suggest that the formed density current is forming an intrusion along the seasonal thermocline. During the winter campaign, vertical and horizontal temperature measurements, made in the near-surface waters of the lake during the winter campaign, suggest an active convection layer from ~ 2 – 20 m depth. Although previous studies have observed this convective layer, this work characterizes significant horizontal variability across the basin. Shorter length scale temperature fluctuations of ~ 6 m were observed that were thought to be related to surface driven convective plumes. A longer length scale temperature anomaly of O(100) m was also observed that appeared unrelated to surface forcing. This observed anomaly was shown to evolve over a time scale of 30 minutes. This time scale is too short for the associated density anomaly to undergo rotational adjustment, in contrast to the temperature

87 5: Conclusions anomaly investigated in the subsequent year that was shown to be stable for a series of consecutive days.

In the absence of other physical transport processes, and given sufficient time and space, rotational adjustment will drive motion under lake-ice through eddy formation. Field observations of a submerged, cyclonic eddy during the winter field campaign of 2008 in Pavilion Lake, British Columbia (Chapter 3), are a previously unobserved transport mechanism in ice- covered lakes. Shown to be relatively stable for the six-day field campaign, this eddy must have formed after ice-on (early January) and dissipated before or during ice-off (late March). An estimated time scale for the spindown of this eddy was calculated to be 15 days. The maximum predicted azimuthal velocity of ~ 3 cm s-1 was calculated using the equations for cyclogeostrophic flow. Measurements made directly below the base of the eddy indicate temperature fluctuations that imply vertical displacement of up to 2 m that has previously not been documented. The existence of such eddies will result in lateral transport in the well-mixed layer and may induce vertical transport in the underlying quiescent layer. Both of these modes of physical transport are previously undocumented in ice-covered lakes.

Negatively buoyant underflows have been extensively studied during summer but significantly less so during winter stratification and rarely in ice covered environments. This work explored the fate of an underflow as it traverses a shallow embayment in Lake Thingvallavatn, Iceland during seasonal ice break up (Chapter 4). Strong stratification of the water column was observed during periods of weak wind-forcing (low winds or ice cover) that comprised ~ 55 % of the study period. Underflow velocity was successfully predicted using mass and heat balances applied to a two-layer approximation of the bay. Entrainment into the underflow from vertical profiles is in reasonable agreement with theory. Conversely, weak stratification was observed during periods of strong wind-forcing that comprised ~ 40 % of the study period. This study successfully predicted periods of weak stratification based on the energy required to mix the water column. The ultimate fate of the underflow will depend on surface forcing conditions as it traverses the bay. Understanding the dynamics of the underflow, and how it relates to wind shear, is important for understanding physical mass transport in lakes with similar inflows. This is particularly relevant for those systems susceptible to the effects of climate change (e.g. Arctic

88 5: Conclusions and sub-Arctic) as changing temperatures will potentially reduce the yearly period of time that they are ice-covered, thereby exposing them more frequently to wind-stirring during winter months.

New insights of these physical mass transport processes provided in this study contribute to the understanding of the associated three-dimensional variability and temporal evolution. As shown in this work with the observations of a submerged eddy, such studies are necessary for understanding the associated mixing of known transport processes and identifying the mixing dynamics of new ones.

5.2 Contributions and Recommendations

5.2.1 Autonomous Underwater Vehicles

The use of an AUV as a data collection platform, like the use of all new technologies in research, is a double-edged sword. High precision measurements of scalars within the water column (e.g. temperature) with little vertical motion allow horizontal variability to be characterized in an unprecedented way. As shown in this work, this characterization generates new insights to studied transport processes and potentially contributes to understanding previously unidentified dynamics. On the other hand, the use of a mobile platform requires significant time for technique development. One must reconsider traditional sampling strategies, develop new data processing techniques, and be able to interpret the biases that are inherent to mobile platforms.

One of the greatest challenges encountered in this work was vehicle reliability, which often resulted in large dataset gaps. Unlike surveys of features that are relatively invariable in time (i.e., benthic features, bathymetry, etc.), studies of physical transport processes are highly time dependent and thus susceptible to these data gaps. While high lateral resolution data provides key information to understanding these transport processes, all effort should be made to minimize vehicle downtime. The amount of downtime is directly related to the resources dedicated to the project (e.g. equipment, people, time, etc.). The deployments detailed in this work were generally limited to myself and sometimes one other person directly working with the AUV. While this was sufficient, it is recommended for future work to have a minimum of 2 – 3

89 5: Conclusions people directly involved in the field with additional technical software and hardware support available as needed. In terms of the study of physical transport processes, the current stage of AUV development is more useful for providing information on shorter timescale (minutes to hours) rather than long term monitoring programs (weeks to months). If long term monitoring programs were required, as is often proposed, a strategy for vehicle deployment would be required in order to measure characteristics of the desired physical transport phenomena. Elements to be incorporated into such a strategy would include time for vehicle engineering, time for data download, time to charge, etc. All of these elements include resource allocation, which is critical in the initial planning stages of a deployment.

AUV technology is in its infancy and, as demonstrated by the many applications detailed here (Appendix D), there is no end to directions that it could be taken. From the perspective of this work, the most exciting of these challenges are applications under-ice. Due to the limited number of applications to date, every deployment, either in lake or ocean, is pioneering. Under-ice environments are some of the most challenging for AUV exploration resulting from the fact that, unlike open water conditions, there really is no ‘fail-safe’. If a vehicle aborts during its mission there is a very real probability of permanent loss. Additionally, there are many engineering challenges for deployment, navigation, and recovery that are unique to ice-covered systems. A partial list of these challenges include: deploying through a small ice hole (i.e., insufficient room to dive); navigating without the ability to reacquire new position fixes; and, recovery back the point of deployment smaller than the associated position error. New techniques to address each of these challenges were developed as part of this work that contribute to making AUV technologies, as a whole, more robust.

5.2.2 Convection Associated with a Negative Buoyancy Flux

Convective motion associated with a negative surface buoyancy flux was investigated in both the summer and winter field studies (Chapter 2). This motion was observed to take the form of convective plumes that resulted in mixing in the surface waters of the lake and density currents that form along the near-shore regions of the lake. The mean horizontal length scale estimated for these plumes was (3.5 ± 2.9) m for the summer campaign and (5.9 ± 3.3) m during the winter

90 5: Conclusions campaign. These scales are in agreement with other studies (Thorpe et al., 1999). Field observations of density current propagation along the seasonal thermocline allows penetration into the underlying fluid to be better understood.

Recommendations for future research include conducting numerical and laboratory experiments in both unbounded (e.g. deep water) and bounded environments (e.g. shoaling near-shore regions). The study of unbounded environments would determine if the measured horizontal length scales of the convective plumes measured in this study are appropriate for the various field conditions studied. The study of bounded environments would help determine when density current formation is likely to occur. Knowledge of density current formation would allow future field experiments to be better designed to characterize the associated flows (e.g. entrainment rates, vertical velocities, etc.).

While negative buoyancy flux has been extensively studied in the summer, horizontal motion associated with radiatively driven convection under ice is poorly understood. This work has shown that there is much more lateral variability than previously documented. This study was limited by the fact that conditions were only observed on two days with similar surface forcing. The next step would be to create a monitoring program over the course of the spring warming cycle (i.e., January – March) to examine variation of the water column response to different surface forcings. While horizontal transects would play a key role in such a study, they should be used in less of an exploratory manner and more on a repeated monitoring schedule (e.g. same transects repeated daily). Additional emphasis should be placed on more traditional data collection methods (e.g. vertical profilers, moorings, etc.) for water column measurements. In addition, a closer examination of lateral variability of the surface forcings (e.g. ice column characteristics, snow cover, topographic shading, etc.) should be evaluated throughout the monitoring program.

5.2.3 Motion Resulting from Rotational Adjustment

In relative quiescent conditions (e.g. under-ice), density anomalies that form in the water column will potentially remain stable for time scales of days to weeks. As these anomalies are not quickly mixed into the ambient stratification, they will be subject to rotational adjustment. While

91 5: Conclusions rotational adjustment has been a proposed transport mechanism in ice-covered lakes, this study presents the first detailed observations of the thermal structure associated with a submerged, under lake-ice eddy (Chapter 3). Integration of the horizontal and vertical measurements allowed the thermal structure of this eddy to be sufficiently resolved to apply a cyclogeostrophic balance and predict the associated velocity field. This synoptic view would have been challenging with either the horizontal or the vertical profiling techniques alone.

After observing and describing an under-ice eddy in this work, two questions arise: (1) what is the origin of this eddy and (2) why does this eddy remain stable over six days, approximately half of the decay timescale? While neither of these questions is answered in the present work, a few of the possible processes that may play a role include: (1) salt exclusion during ice formation (Pieters and Lawrence, 2009); (2) sediment heat flux (Welch and Bergmann, 1985); (3) inflow propagation (Bengtsson, 1996); and, (4) differential surface heating (Mironov et al., 2002). Horizontal variation in solar forcing was considered (Appendix A) but the predicted differential heating was contrary to that required to drive the formation and maintenance of the observed eddy. Further investigation should numerically model the system to determine mechanisms that drive formation, maintenance, and decay of this structure (e.g. Huttula et al., 2010). Such studies would also help identify the extent of the stratified fluid response below the eddy that was measured in this work. The existence of eddies under lake-ice is an exciting new field of study in fluid mechanics that is poorly understood at the moment.

Future field studies could also help identify eddy formation processes by initially using traditional sampling methods. This work would be complemented through the use of numerical models to identify both lakes and associated time periods where submerged eddies are potentially occurring. Once eddies have been identified, more detailed field studies would use both horizontal transects and vertical profiling to fully characterize both the eddy itself and the surrounding regions to the side and below the eddy. The best strategy for vertical profiling would be to identify sampling locations that could be returned to at a regular time interval (e.g. daily). Similarly, depths of horizontal transects need to be initially identified and then repeated continuously at fixed intervals. Both of these strategies would better resolve the eddy behavior that was only possible to be inferred in this study. Key to these future studies would be the use of

92 5: Conclusions velocity measurements to validate water velocities that were only inferred from horizontal density gradients in this work.

5.2.4 Negatively Buoyant Underflow Modified Through Wind-Stirring

Conditions often arise where an inflow forms a negatively buoyant underflow that propagates downslope (Chapter 4). In regions where surface wind shear provides sufficient energy to entrain the underflow into the overlying surface water, the characteristics of the underflow will change significantly (e.g. velocity, entrainment, etc.). This study examined the two dominant regimes of an underflow response to variable wind forcing. Significant challenges were addressed during this work as measurements were made during spring ice breakup; a period of extremely dynamic forcing conditions.

While the two dominant underflow responses comprised nearly 95 % of the study period, non- uniform responses were observed across the basin during the remainder of the time. Poorly understood, these responses were shown to endure for up to several hours. It is recommended that future work explore these transient conditions, as it is unclear whether they play a secondary role in the dominant underflow responses. It is suggested that these studies take the form of further fieldwork coupled with numerical analysis. Specific recommendations include deploying moorings from the depth of the estimated plunge point of the inflow and then far out into the main body of the lake. These moorings would ideally have instrumentation to directly measure the vertical and horizontal components of water velocity associated with the underflow. These moorings would then allow the underflow to be characterized farther out into the main body of the lake without additional confounding factors associated with the plunge zone. These moorings could then act as the boundaries of horizontal transects at constant depth and altitude to be collected under various forcing conditions.

The ability of an AUV to collect data at a constant altitude is one of the potential strengths of this platform for underflow studies. Although not fully exploited in this work, as constant altitude transects were only collected during a relatively well-mixed period, it is possible to derive underflow entrainment. The developed technique is presented (Appendix B), which could be applied to any scalar measured by the vehicle. Although non-conservative, temperature data

93 5: Conclusions collected during a well-mixed period in this work, is presented as a case study. Future work would ideally use the developed technique with a conservative scalar (e.g. salinity) instead.

The lateral variability observed in this study could also be better characterized by collecting multiple transects at regular spacing between these two mooring lines. Ideally, these stations could also form part of a long-term monitoring program to explore the seasonal variability of underflow behavior. Studying the complex nature of the dynamics associated with this process, and all processes detailed in this work, allows the scientific community to better understand the seasonal variability of physical mass transport in lakes.

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104

Appendices

Appendix A: Differential Solar Heating

In Chapter 3 differential solar heating across the surface of the lake was proposed as a possible mechanism for the maintenance of the eddy. Such differential heating will result from both topographic shading and local ice conditions. The subsequent discussion presents an analysis that considers each of these in turn and then estimates the combined effect on the lake. The techniques presented should be included in future research where possible eddies exist.

For six days prior and during the field campaign, an extended period of high pressure was observed. This high pressure system resulted in clear skies with air temperature above freezing during the day and below freezing at night. The observed solar irradiance on the ice surface at Station 5 (Figure A.1) had surface irradiance values peaking at ~ 500 W m-2 on 22 Feb 2009 with a daily average value of ~ 100 W m-2. The amount of sunlight that the water column receives will depend on topographic shading and local ice conditions.

The surrounding mountains shade various sections of Pavilion Lake throughout the day. To assess shading effects a digital elevation model (DEM) with a 10 m grid size was created using ArcGIS 10. Assuming clear sky conditions, this model was used to calculate the total global solar radiation (direct and diffuse) across the lake surface for February 2008 (Burrough and McDonnell, 1998). Model predictions were then calibrated against the field measurements and time averaged. The results show significant differential heating across the Central Basin; the northeast side of the Central Basin (Station 1) is predicted to receive ~ 20 % more daily average surface irradiance as the southwest side (Station 11; Figure A.1). It is also interesting to note the position of the eddy (outlined in white) relative to the isopleths of daily average solar surface irradiance in the middle of the Central Basin.

In addition to topographic shading, local snow and ice cover conditions will result in variable light attenuation. Snow and ice characteristics at all eleven stations across the lake are shown in Table A.1. No white ice was observed in this survey and snow levels were generally low (4.6 ±

105 Appendix A: Differential Solar Heating

Figure A.1: Daily average solar surface irradiance [W m-2] on the ice surface of the Central Basin based on shading by topography of Pavilion Lake for the month of February 2008. The position of the eddy is outlined in white and circles mark the CTD and ice column profiling stations.

3.2 cm) although higher on the southwest side of the basin. These observed conditions were significantly different than the previous year that was characterized by a significant fraction of white ice and almost no snow as shown in the previous chapter. The mean ice thickness, 50.5 ± 4.3 cm, was shown to be relatively constant over most of the basin except for the southwest side of the basin (Station 11) where it was ~ 10 cm thinner. The mean conductivity of the ice 5.9 ± 2.2 µS cm-1 (Table A.1) also suggests that the properties of the black ice being homogeneous across the basin.

Attenuation of incoming solar radiation depends on cloud conditions, snow and ice thickness and type of ice present. Each of these variables will affect the selection of light attenuation coefficients; a more detailed discussion can be found in Launiainen and Cheng (1998). Following their procedure, an attenuation coefficient of 15 m-1 was used for snow, 8.4 m-1 was

106 Appendix A: Differential Solar Heating

Table A.1: Across basin ice characteristics along the southwest / northeast transect that is also associated with the CTD profile survey shown in Figure A.1.

Station 11* 10 9 8 7 6 5 4 3 2 1 Distance† -390 -305 -250 -200 -150 -105 -55 0 50 95 145 (m) Snow 10 9 7 5.5 4.5 5.5 2 0 2 3 2 Depth (cm) White Ice 0 0 0 0 0 0 0 0 0 0 0 (cm) Black Ice 41 46 47 55 54 52 52 52 52 55 50 (cm) Total 51 55 54 60.5 58.5 57.5 54 52 54 58 52 Depth (cm)

Is, Solar 79 88 92 94 97 98 99 100 100 101 101 Irradiance (W m-2) ‡

I0, Solar 2.0 2.2 2.7 2.8 3.1 3.0 4.1 11.5 4.1 3.7 4.3 Flux (W m-2)||

C25 of Ice - - 7.9 3.1 5.1 5.5 2.4 5.7 6.7 8.0 9.1 Samples (µS cm-1) * Station 11 is on the same transect as the vertical profile survey (position indicated in Figure A.1) but no CTD profile was taken at this location.

† Distance is measured as length from the center of the eddy with Station 1 and Station 11 on the northeast and southwest sides of the transect respectively.

‡ Daily average solar irradiance, IS, at each of the stations as using a DEM of Pavilion Lake to estimate effects of topographic shading.

|| Daily average solar flux beneath ice surface, I0, estimated using the modeled solar irradiance and measured ice conditions at each of the stations. used for the black ice in the upper 10 cm, and 1.5 m-1 for the remainder of the ice column. Note different values would have been selected had white ice been present. Using these light attenuation coefficients, the ice and snow thickness for each station, and the daily average values estimated with topographic shading, the surface radiation at the ice-water interface, I0, for each of the stations was calculated (Table A.1). The combined effect of the topographic shading, increased snow, but decreased ice thickness to the southwest, is that daily average I0 is estimated

107 Appendix A: Differential Solar Heating to be approximately half on the southwest than the northeast side of the basin. The combined effect of topographic shading and local snow and ice conditions indicates that the water column beneath the ice is experiencing differential solar heating, with maximum heating near the eddy core.

Volumetric heating associated with this differential solar input will result in lateral variability in density; however, the predicted pattern (Table A.1) with maximal heating near the lake center decreasing shoreward is opposite to that required to explain the pattern of stratification associated with the eddy. This discrepancy would suggest that differential heating is not the primary forcing mechanism maintaining the eddy while an unidentified process is.

108

Appendix B: Entrainment Prediction

In Chapter 4, it is hypothesized that entrainment predictions could be made from the linear portions of the constant altitude horizontal transects within the underflow and oriented along the direction of the underflow; however, it was not possible to do this analysis as the only time period in which constant altitude missions were successfully completed within the underflow were during a well-mixed period. That said, the subsequent discussion presents an analysis that could be applied to constant altitude scalar data of an underflow in a constant width channel using a conservative tracer.

Entrainment can be estimated using an adaptation of the energy balance of the underflow. Assuming heat energy to be conserved in the underflow, and using the definition of energy resulting from temperature change, the ratio of the flow rate can be expressed as the inverse ratio of the change in temperature between the layers

(B.3)

where Tx is the underflow temperature measured anywhere along the transect, Qx is the sum of the underflow flow rate at the deep water mooring line boundary (Qub) and the entrained flow rates (Qe) anywhere along the x-coordinate. By definition of the normal underflow state (Ellison and Turner, 1959; Dallimore et al., 2001), Uu remains constant even as du increases. If the width, W, is also assumed to be constant, the ratio of the flow rates is substituted with the ratio of underflow heights . Substituting this into Equation B.3, du can be written as a function of Tx:

dub ⋅(Tub − Tr ) du = (B.4) (Tx − Tr )

Combining Equations B.2 and B.4 gives E as a function of Tx:

109 Appendix B: Entrainment Prediction

dub ⋅(Tub − Tr ) dTx E = − ⋅ (B.5) 2 dx (Tx − Tr )

As a demonstrative example, we will use the derived slopes from the linear portions of the constant altitude transects in Figure 4.8 (Chapter 4). Applying all temperatures from the constant altitude mission for Tx and dTx dx , as measured along the linear portions of the transects, along with dub, Tub, and Tr of 2.4 m, 1.55 ºC and 1.2 ºC respectively (as estimated from thermistor chain data from Station 2), the mean E for the western and eastern transects was estimated to be 1.3 x 10-3 and 2.8 x 10-3.

There are limitations to our approach of using temperature as a tracer for estimating entrainment; however, this approach could be applied to other field sites with more standard tracers (e.g. salinity). Furthermore, this approach would be made more robust through better estimations of the associated flow rates of the different layers rather than using the assumptions of constant width and velocity as was done here. Addressing these issues may demonstrate that the use of such data could provide valid estimates of entrainment.

110

Appendix C: UBC-Gavia AUV Description

One of the strengths of UBC-Gavia is its modularity. Gavia vehicles were one of the first AUVs on the market to have this attribute, although it is becoming increasingly available (e.g. new REMUS vehicles now have similar modularity). The Gavia vehicle can interchange modules depending on the specific mission requirements and availability of different units. The main components of the vehicle (as shown in Figure C.1) are the: nose module, battery module, ADCP module, buoyancy module, control module, and propulsion module. Each of the scientific instruments and additional devices required for navigation are indicated directly on the vehicle (A – I).

B I D F

G A

C E H

Figure C.1: Schematic of UBC-Gavia. The on-board modules are labeled and the scientific and navigation instrumentation include: A - Forward collision-avoidance sonar; B - SBE49 FastCat CTD; C - High resolution digital camera with strobe light; D - Upward looking 1200kHz RDI ADCP; E - Downward looking 1200 kHz RDI ADCP with Doppler Velocity Log (DVL) functionality; F - WET Labs BB3TM backscatter meter; G - Imagenex 220 / 990 kHz sidescan sonar; H - Acoustic modem; and, I - Communications tower.

As detailed in each of the chapters of this thesis, results presented in this work are based primarily on the temperature data collected with the Seabird SBE 49TM Conductivity- Temperature-Depth (CTD) recorder (B). The scientific payload onboard UBC-Gavia also includes several other instruments: (C) a high frame-rate digital camera with a 1 W LED strobe array; (D – E) an upward and downward facing 1200 kHz, RDI Workhorse NavigatorTM Acoustic Doppler Current Profiler (ADCP); (F) a WET Labs BB3TM backscatter meter; and, (G)

111 Appendix C: Vehicle Description an ImagenexTM dual-frequency (220/990 kHz) sidescan sonar. The backscatter meter measures optical backscatter on red, green and blue wavelengths. All sensor data is recorded internally in raw form. In post-processing this data is adjusted to a single sampling frequency and georeferenced using the AUV navigation data.

C.1 Nose Module

The nose module contains two components; an obstacle avoidance system (OAS) in the nose fairing and a camera system, which includes the sensor and the lens. The OAS is a 675 kHz Imagenex Model 852 Ultra-Miniature Echo Sounder that has a pencil-beam shaped sonar with a 10º beam width that has an adjustable gain and resolution. If multiple detections of an object are made within the 50 m range of the echo sounder, vehicle propulsion will be halted and then, if repeated hits continue to be made, the vehicle control software will command reverse propulsion. After a fixed timeout period, the vehicle will restart the mission and continue on the previous settings unless an overall timeout has been reached and the mission is aborted. The performance of the OAS tends to be quite inconsistent where, although it is detecting the bottom, the vehicle will often hit, as the command to halt is not executed soon enough. Another scenario that is often encountered is that the vehicle would fail to dive from the surface, as the OAS would detect entrained air in the waves as an obstacle. This could only be avoided by turning down the gain of the instrument but, in doing so, would make the OAS less sensitive to objects on the bottom. Finally, the OAS had difficulty detecting objects on the water surface (e.g. boat keels), which meant that great care had to be taken to avoid hitting the chase boat.

In addition to the OAS, the nose module contains a camera that is pointed down through a viewport at the underside of the module. The camera is a Scorpion 20SO model, from Point Grey Research using a Sony 1/1.8” ICX274 Charge Coupled Device (CCD) sensor. This camera has gain capabilities from 0 – 25 dB, shutter speed range from 0.110 µs to 70 ms a signal to noise ratio of 57 dB, and a rated power consumption of 3.5 W. Although gain, aperture and exposure can all be set to fully automatic, they were generally hard coded in the control software before the beginning of each mission as the automatic setting would generate images that were generally underexposed in low light environments. For low light environments, there is an associated strobe array that is separated from the lens by ~ 1.2 m in the standard configuration of

112 Appendix C: Vehicle Description the vehicle. This 1 W, LED strobe is synchronized with the camera and provides adequate light for images to a vehicle altitude of 2 – 3 m, the standard operating altitude set point for image gathering missions. Ideally, more light would be desired (i.e., 5 W or higher); however, due to the physical configuration of the lights within the strobe, it was not possible to upgrade without a major redesign of the strobe. Camera focus would also have to be manually set, generally before each major deployment. It was noticed that after transport handling, the lens would generally lose its focus. Manufacturer’s specifications quote an image resolution of 1628 x 1236 pixels but, due to a limitation with the onboard processer, recorded images were constrained to 800 x 600 pixels.

C.2 Battery Module

Lithium-ion rechargeable batteries (6 stacks – 1 kWh each) are stored in the battery module and supply power to the vehicle. With all onboard instrumentation operating, the battery life endurance is expected to be 6 – 8 hours. At typical cruising speeds of this vehicle, this gives an operating range of 22 – 29 km. There is also a small emergency battery stack found in this module used to start the vehicle and maintain emergency status for ~ 72 hours after the main battery stacks have been depleted. During emergency status, the communication subsystems (GPS and satellite phone) will turn on for a period of 10 minutes out of every hour get a position fix and broadcast the estimated location.

Two things should be noted about the vehicle battery maintenance: the charging cycle and the vehicle start up. When the batteries are fully depleted and the AUV is put on charge, the amperage draw on the charger will initially be ~ 3 A before stepping up to ~ 6 A after the first hour and then 9 – 10 A after about 2 hours. This will then gradually start dropping down until the batteries are fully charged. The amperage draw at this point will be between 0.3 – 0.6 A although a value anywhere below 1 A is a trickle charge and the main stacks are fully charged. It should be noted that the emergency batteries never begin charging until the trickle charge has started. This is important to be aware of if the main batteries are being used in heavy charge-use cycle (e.g. continuous daily operations). To actually start the vehicle, the power management uses the emergency batteries as a starter for the main power stack, using Stack 4 for initial startup. If there are any issues with either Stack 4 (e.g. communications with the PCB board) or the

113 Appendix C: Vehicle Description emergency batteries themselves, the vehicle won’t start up. The strategy, if this is encountered, is to charge the emergency batteries or to change the location of the battery stack on the PCB board if needed. The other option is to charge the emergency batteries directly using a 14 V power source for ~ 15 minutes. Disconnecting the emergency battery leads from the PCB board and then connecting directly to the power source does this. It should be noted however that this should only be done as a last result as it involves a fair bit of work to isolate the power leads.

C.3 ADCP Module

Dead-reckoning is calculated using directional information from the internal magneto-inductive electronic compass and tilt sensors, depth information from the pressure sensor in the control module and speed information from one of two sources: the calculated speed based on the propeller speed (much less accurate) or the measured velocity from the downward facing 1200 kHz, RDI Workhorse Navigator, Acoustic Doppler Current Profiler (ADCP). The ADCP provides reliable navigational data when the Doppler velocity log (DVL) is within range (~ 30 m) of the bottom (i.e., bottom tracking is established). At greater altitudes from the bottom, the water velocity can be measured directly with the ADCP and can, theoretically, provide more accurate data than the propeller speed. To date, this has shown not to be the case and the propeller speed is still used for dead-reckoning in deep water.

The ADCP module is equipped with two 1200 kHz ADCP units; one directed upwards and one downwards. Water column velocities can also be recorded although the functional range of 15 m is significantly less than the bottom tracking range. To date, although measurements have been made at majority of the deployments, this data has never been used. Encountered software problems prevented data from being recorded at the locations where this data would have been useful (e.g. in the submerged eddy and the underflow). When data was being recorded in lakes, the expected velocities (e.g. < 1 cm s-1) are significantly less than can be reliably recorded with this instrument (Fong and Jones, 2006). The science objectives of those deployments where velocities were higher (e.g. ocean environments) were not water column measurements.

114 Appendix C: Vehicle Description

C.4 Buoyancy Module

The original intention of the designers of the vehicle was to have all the buoyancy internal to the vehicle. While this worked well for saltwater systems, the floatation was found not to be sufficient for freshwater systems. The buoyancy module was designed for UBC-Gavia to provide extra floatation. This module is essentially void space within the vehicle with a rigid shell. While this approach is somewhat simplistic for this need, it has indirectly benefited operations, particularly under-ice, in two ways: (1) storage space inside the vehicle, and (2) space on the vehicle to add on additional external payload. One of the under-ice recovery systems tested extensively for both this system and larger AUV applications (i.e., an ISE Explorer class vehicle) was the use of a 457 kHz commercial avalanche beacon commonly carried by skiers. This was fitted inside the buoyancy module and then located with a secondary unit held on the top of the ice. When the vehicle was directly beneath lake-ice (~ 50 cm thick), this would work well to a range of ~ 30 m for fine-scale localization. When tested under sea-ice (~ 2 m thick), this range was reduced down to ~ 3 m range and so was deemed not to be overly useful for sea-ice applications. Having extra space on the outside of the vehicle also proved to be useful for additional sensors. While the long-term intention is to make this module into a new permanent payload, it is now possible to simply ‘strap-on’ new sensors for trial deployments. For example, during the Ellesmere Island deployment in 2008 (see Appendix D), a TriOS Ramses radiometer was strapped onto the outside of the vehicle. While this was not a self-contained recording device, it had a 50 m cable that was used for the deployment that allowed for continuous recording of the results. Another example is that two undergraduate UBC Engineering Physics final year projects (in 2009 and 2010) have worked on the design and build of a water sampler that could be fitted to this module and used to collect 50 mL water samples at multiple water depths. Trial deployments in Pavilion Lake have proven their successful operation.

One of the disadvantages of using a buoyancy module is that it moves the center of buoyancy relative to the center of gravity of the vehicle. As such, attitude control of UBC-Gavia is generally shown to have decreased stability as compared to a vehicle not similarly equipped. Initial efforts to increase the stability were to add internal weight although was generally unsuccessful. The strategy used instead was to bolt external weights that could be added directly

115 Appendix C: Vehicle Description to any module on the vehicle. The was further refined in 2008 when another undergraduate Engineering Physics final year project designed external buoyancy control modules for the battery and propulsion modules. These worked so well that they have been used on every deployment since.

C.5 INS Module

For many of the deployments, the ADCP module was replaced with an Inertial Navigation System (INS) coupled with a DVL. When the DVL was in range of the bottom, this was a significantly better position estimator (0.1 % drift by distance traveled as compared to 2 – 5 % using dead-reckoning using propeller speed to determine speed over ground). It should be noted, that, in deep water applications (i.e. no DVL lock) the navigation error associated with the INS will accumulate faster than it will with regular dead reckoning. While not required for the standard scientific payload, the GeoswathTM multibeam sonar requires the higher positioning accuracy associated with the INS to produce reliable results as it needs to sync with the PPS signal being generated by the GPS receiver that is also passed to the INS in addition to the attitude provided by the INS which is used in post-processing of the data. In deep water (i.e. >30 m) under-ice, the DVL was also used to generate a speed over ‘ground’ by inverting the vehicle and tracking the ice-surface. While this worked well under sea-ice, it showed poor performance under lake-ice as it is suspected that the surface was too smooth to track properly. Future applications are looking at changing the functionality of the upwards pointing ADCP to also include DVL functionality in order to avoid conducting the missions in an inverted mode. This is preferred as, in inverted flight, it is difficult to maintain communications with the vehicle while it is on the surface as the communications tower is submerged.

While working well at lower latitudes, problems with initial INS alignment were expected at higher latitudes (> 70º). This results from the fact that the heading prediction the INS uses is increasingly unstable at higher latitudes and so heading alignment becomes proportionally harder during the alignment phase. Initial alignment of the INS is achieved using two methods; (1) a moving base alignment (fixed error) or, (2) a stationary alignment (fixed time). Standard operating protocol for UBC-Gavia, with an INS/DVL module onboard, is to perform the moving base alignment. Position drift was high (~ 20 m min-1) once the alignment was complete,

116 Appendix C: Vehicle Description however, and appeared to be randomly oriented. A stationary alignment, with an increased alignment time, gave better results with initially minimal drift. Drift after even a very short, tethered, mission was similar to that seen with the moving base alignment, however. Reviewing the navigation logs, the system appeared to perform well for the first 2 – 3 minutes of a run before significant position jumps and drift began to occur. It was therefore necessary to perform a new alignment after every mission and this significantly slowed down operations.

C.6 Control Module

The Control Module contains most of the navigation and processing components of the AUV. Navigation is done through multiple modes: by global positioning system (GPS) (SBAS/WAAS enabled) when the AUV is at the surface; dead-reckoning when submerged; or, acoustic long baseline (LBL) positioning when submerged and multiple LBL transponders are present. Depth set points will be achieved using data being fed by the onboard pressure sensor. The AUV has a navigational error propagation algorithm that will halt a mission if an adjustable threshold value is attained. Although reset with every new GPS fix, this can be problematic if there is a high degree of washover when the vehicle surfaces. An alternative to dead reckoning is the use of the LBL system. The AUV triangulates itself via communications with two, preset LinkQuestTM UWM2000H transponders located at fixed GPS locations in the water column and a two-way acoustic modem that is located on board. Although this is a much more accurate navigational system there is a trade-off in functional range. The two transponders are optimally placed 800 m apart halfway down in the water column. These then represent one side of a box in which the vehicle can operate.

Work has been done on trying to combine the LBL location with INS dead reckoning in order to maintain a relative position for under sea-ice deployments where the surface can be concurrently drifting (up to 10 km day-1) and rotating (2 – 3º day-1). Not successfully implemented during any of the deployments, a new technique was developed instead. This method was homing using a minimization of range to a single LBL beacon lowered in a receiving net at the end of a given mission. This would allow the vehicle to be returned to the deployment hole while continuously knowing it’s absolute position throughout the entirety of the mission (provided the INS drift was

117 Appendix C: Vehicle Description still low). This was successfully implemented during the winter deployment in Pavilion Lake, 2008 but hasn’t been tested since. Future missions will hopefully refine this technique further.

There are four modes of communication with the vehicle: a wireless LAN; an IridiumTM satellite link; the previously mentioned two-way acoustic modem; and, a direct LAN connection. Both the wireless and IridiumTM links are located in the communications tower. The majority of communication and mission profile updates is conducted via the wireless LAN (11 mbps) and then the data transfer is generally conducted through the direct LAN connection (100 mbps). This is because the direct LAN connection needs to be activated through the wireless and file size is generally insignificant for mission files but not so for the collected data (especially sidescan, image and multibeam data). Due to maximum packet size, the refresh rate for the acoustic modem is only 1 Hz. In addition, communications through the acoustic modem is limited due to the time to ping the LBL transponders. With the current software configuration, the refresh rate is approximately once per minute. For this reason, the communication with the acoustic modem has only been used to triangulate the position of the vehicle from the surface on those occasions when it grounded. If the vehicle surfaces and it is out of wireless range, backup communications send a text message through the IridiumTM satellite link giving a position and status update.

The Control Module also carries the majority of the scientific payload including the CTD, the optical backscatter unit, and the sidescan sonar. Each of these instruments record at different acoustic and sampling frequencies, which, generally, do not conflict with each other. The exception to this is the sidescan sonar, which will often record acoustic noise from the acoustic modem, the LBL returns, and the propulsion module. Efforts have been made to minimize this interference but it still persists. For those missions where sidescan sonar data is the primary focus, the practice that is used with UBC-Gavia is to simply not use the acoustic modem.

C.7 Propulsion Module

The propulsion unit is a hydrofoil with the control surfaces placed in a 'X'-configuration aft of the propeller. Analysis of vehicle performance has shown that this configuration provides marginally better maneuverability than the more commonly seen cruciform arrangement (Butler

118 Appendix C: Vehicle Description and Black, 1997). The four control surfaces have independent servomotors in order to maintain some control if one were to become damaged. A disadvantage of this arrangement is, in very calm water conditions, the vehicle will sometimes have difficulty diving, as there is not enough ability to pitch the vehicle down while it is on the surface. When this problem was encountered, the technique used several times was to generate a wake with the chase boat that would allow the control surfaces of the vehicle to become submerged and have enough authority to dive the AUV. The problem with this was that, if the vehicle were to temporarily halt mid-mission, it wouldn’t be able to submerge itself again. It should also be noted that if the vehicle is ballasted too light, and is unable to submerge, it will spiral to the right on the surface in circles ~ 20 m in radius due to the right hand torque of the propeller.

In the five years of deploying the vehicle, the majority of failures have been generally associated with the propulsion module and specifically with the Maxon servomotors that drive the control surfaces. Although not calculated directly, the mean time between failures (MTBF) was ~ 2 years for these motors and so it is highly recommended to have spares on hand (or a spare nozzle all together) in the event of a failure. While unclear what is causing the failure, it appears to be the encoders on the servomotors that are failing and the only solution are to completely replace them. It has been suggested that these motors are undersized for this application and should be redesigned all together. If repairs are being conducted on this module, it is also important to note to use thread locker on each of the screw connectors. As a result of all the moving parts, the screws will back themselves off periodically causing performance failure. Another frequently encountered problem are the serial connectors to each of the four PCB boards controlling the servomotors. As a result of the design, these frequently disconnect themselves during shipping and transport and result in zero movement of the control surface. The final failure that has been observed is the rupture main drive shaft seal, which is characterized by a leaking white emulsification of oil and water from the propeller. While the vehicle will continue operating normally, this should be replaced immediately as continued leaking will result in the connectors on the drive motor corroding and needing a complete replacement. The MTBF for the shaft seal is ~ 3 years although it has been suggested that it should be replaced every 2 years.

119

Appendix D: Vehicle Deployments

In addition to the operations detailed in this work, during the course of my PhD studies the vehicle was involved in a number of deployments worldwide. These are detailed below to provide examples of the types of operations that can conducted with this, and similar styled, vehicles. As shown in the subsequent discussion, applications are varied. A common theme to most of this work is that none of the applications tend to be ‘conventional’ AUV deployments (i.e., benthic mapping or military operations). AUV technologies are still in their infancy and so diverse applications, as outlined, emphasize the strength and versatility of these vehicles as data collection platforms.

D.1 Vancouver, BC, Canada, 2006

When the vehicle was first purchased in 2006, it was deployed at four different locations in and around the Vancouver area in 2006 and 2007: (1) Sasamat Lake, Port Moody, BC; (2) Loon Lake, Maple Ridge, BC; (3) Levette Lake, Squamish, BC; and, (4) English Bay, Vancouver, BC. The focus of these deployments was conducting a full-systems shakedown of the vehicle before taking it further afield. Sasamat Lake was selected due to its relative proximity to Vancouver and was used to examine the performance and accuracy of the navigation systems. Putting out surface moorings at fixed locations, and measuring the targeting accuracy of the vehicle when it surfaced, was part of the conducted tests. Also tested was the performance of the internal compass, which, initially, was badly calibrated and had to be corrected in the firmware code. Loon Lake was selected as previous work had been conducted here with an AUV (Laval et al., 2000) to test the performance of the Seabird SBE49 CTD. At low conductivity ranges (< 1000 µS cm-1), conductivity measurements were not self-similar on ascent and descent. Several tests, suggested by Seabird, were conducted during this time period and, although performance was improved, the issue was never fully resolved. Levette Lake and English Bay were both full system shakedowns.

120 Appendix D: Vehicle Deployments

D.2 Loch Etive, Scotland, UK, 2006

In November 2006, UBC-Gavia was taken to Loch Etive, Scotland, UK, in association with the Scottish Association for Marine Science (SAMS) and funded by Collaborative Autosub Science in Extreme Environments (CASEE), with the objective of optimizing the performance of a fixed buoyancy vehicle in a highly stratified estuary. Not a true freshwater system, Loch Etive has been identified as the sea loch with the largest freshwater input in Scotland with 2 – 6 meters of fresh (~ 5 ppt) water over salt (~ 25 ppt) water. For reference, this system is conveniently divided into an upper (145 m maximum depth) and lower (70 m maximum depth) basin, separated by a sill of 13 m depth that roughly bisects the loch. The purpose of this work was to prepare for deployments in ice-covered lakes that display a high degree of stratification (e.g. perennially ice- covered lakes in the McMurdo Dry Valleys, Antarctica). The secondary objective was to measure the internal waves that are generated from the sill separating the upper and lower basins. During spring tides, a 20 m amplitude baroclinic wave propagates at a speed of 0.2 m s-1 until the energy is dissipated at the head of the loch.

After satisfying the primary objective on the initial day of testing, through a combination of dive control and ballasting, a number of secondary scientific missions were planned: (1) studying deep-water renewal events; (2) measuring baroclinic waves; and, (3) estimating riverine discharges into the loch (e.g. the River Awe). Logistical and operational problems prevented the completion of these three studies (the most successful being the study of baroclinic waves) although gathered results provided initial data for the design of future studies. The high degree of versatility and adaptability demonstrated in this work is one of the benefits of working with man- portable AUVs as compared to larger ship-based vehicles.

D.3 Pickering, ON, Canada, 2007

In September 2007, in conjunction with the University of Waterloo, UBC-Gavia was involved with a study at Ontario Power Generation's Pickering Nuclear Generation Station (OPG - PNGS) outfall. Located on the shore of Lake Ontario in Pickering, ON (~ 40 km east of Toronto), OPG- PNGS generates as much as 120 m3 d-1 of warm water that is allowed to be as much as 5 ºC greater than ambient lake water temperature split between two outfalls. Ongoing studies in the area are investigating the lifecycle of dreissenid (zebra) mussels and Cladophora, filamentous

121 Appendix D: Vehicle Deployments green algae dominant in the Great Lakes. These algae were a major problem in the heyday of eutrophication (1960 – 1970s) but were not prevalent until the advent of zebra mussels in the late 1990s. The three proposed mechanisms for the re-introduction of this species are: (1) improved water clarity; (2) facilitation of phosphorus (P) transport; and, (3) particle transport and resuspension. In and around the OPG-PNGS, this poses a serious problem as the Cladophora, growing in large mats attached to lake bottom, detach in late fall and blind the intake screens of the plant. Immediately east of OPG-PNGS is the City of Pickering (COP) Wastewater Treatment Plant (WWTP) and a creek that are theorized to be potential sources of phosphorous and sediment.

The study conducted by UBC-Gavia was to collect benthic imagery at one of the OPG-PNGS outfalls and of the WWTP to investigate the distribution of the Cladophora mats. Onboard sensors gathered concurrent measurements of the optical and physical properties (temperature and conductivity) of the water column to see if a causal relationship existed. Similar in approach to what could be done with a diver-led study or point sampling with a drop camera from a boat, the use of AUVs allows a much broader areal coverage in a much shorter duration of time. UBC- Gavia mission design was for grid patterns to be followed in both the outfall plumes of the OPG- PNGS and the WWTP at a working altitude (depth from the lake bed) of 2 – 3 m. These missions were extended out to 25 m water depth (approximate working boundary of ongoing studies). Images gathered during these missions were generally able to resolve features in the sediment and distributions of both the zebra mussels and the Cladophora demonstrating AUVs as a stable platform for collecting high-resolution data for the assessment of ecosystem dynamics. It was noted however that the positional error of the vehicle was increased while operating directly in the plume outfall as a result of increased water velocities (~ 3% error by distance traveled underwater). Deployments in high-energy systems (e.g. rivers, outfalls, etc.) should be planned carefully in order to maximize AUV performance.

D.4 Bonaire, Netherland Dutch Antilles, 2008

In January 2008, UBC was involved with a NOAA Oceans Expedition, lead by the University of Delaware, in Bonaire, Netherland Dutch Antilles. The objective of the deployment was to survey the health of the coral reef in the near-shore regions (0 – 50 m depth) as a follow-up to a survey

122 Appendix D: Vehicle Deployments that was conducted nearly two decades before. In addition, surveys were conducted in the deeper waters (down to 200 m depth) as they had not been examined in the original study. Relevant collected data using UBC-Gavia was the benthic imagery and sidescan sonar surveys. One of the challenges encountered in this study was the extremely steep slope (> 30º) that is characteristic of the near-shore regions of the island. What was found was that, from 0 – 25 m depth, the slope was quite shallow (< 5º) and collected data clearly showed coral formations to a high level of detail. The slope would then drop off quickly in two shelf breaks down to ~ 100 m where it would level off slightly as it continued down to depths greater than 1000 m within a few km of shore. A number of lessons were learnt including how to optimize AUV performance for steep- walled conditions and the angles of ascent and descent of the vehicle. Key in this was collecting images on the diving profile and returning to the surface at a greater altitude. This allowed for good quality images to be collected and prevented the vehicle from getting caught in the bottom sediment. Even with that lesson learnt, the vehicle became lost at sea for a period of 24 hours that was theorized to result from entanglement with old dive lines that had been deserted on the seabed. Although recovered, several lessons were learnt that night on the available emergency backup systems on board the vehicle.

In addition to the state of the reefs study that was the primary focus, there was secondary focus on two other studies. The first of these was an examination of near-shore differential heating. This was done in a region, known to the local diving community as ‘The Invisibles’, that was relatively shallow to an offshore distance of 1.5 km before dropping off to deeper depths. Repeated transects were run from the early morning until early afternoon during the initial daytime heating. Although this is still undergoing continued analysis, it was shown that the littoral zone heats significantly faster than the off-shore region and it has been suggested by others (e.g. Monismith et al., 2006) to act as a path of nutrient flux to the reef community. It should be noted that the conductivity hysteresis problems encountered with the CTD in freshwater were not observed here. It is the current theory that the problem is related to very low conductivities in combination with vehicle performance. This is an issue that is still trying to be resolved. The final study that was conducted with UBC-Gavia was a one-day study in Lac Bay on the west shore of the island investigating using benthic imagery to differentiate species of macrophytes (eel grass and turtle grass) in shallow waters. Performance of the vehicle was

123 Appendix D: Vehicle Deployments intermittent in these shallow waters as the OAS kept trying to abort the mission as it was too close to the bottom and when it observed wave action. From collected images from the portions of the transects that were run, it was possible to clearly delineated different marine macrophytes.

D.5 Ellesmere Island, NU, Canada, 2008

In late April 2008, UBC-Gavia was deployed just north of the Canadian Forces Station Alert in Jolliffe Bay, Lincoln Sea off directly off the coast of Ellesmere Island, NU. This was part of the European DAMOCLES (Developing Arctic Modelling and Observation Capabilities for Long- term Environmental Studies) program to use multibeam swath bathymetry to measure sea-ice thickness. This would then be compared with coincident measurements of snow and ice thickness and snow and ice freeboard using a helicopter-borne electromagnetic induction system (HEM) and a scanning laser profilometer mounted on a Twin Otter aircraft. The goal of these deployments was to increase the understanding of the freeboard-draft-thickness relation in advance of space-based ice thickness determination. As all of the work was conducted on a 3 mm string, measurements were only taken within a 400 m radius of the deployment hole and operating depth was less than 50 m. Of the many engineering obstacles faced during this deployment, one of the most challenging was operation of the vehicle in inverted flight. This mode of operation was required as the swath bathymetry SONAR module, rented for this application, had a downward orientation only. Inverted flight was achieved by repositioning all of the external ballast on the top of the vehicle and then making firmware changes as the horizontal reference frame of the vehicle had been rotated by 135° (i.e. x = -y) when inverted. These software changes were initially tested in Pavilion Lake during the under-ice operations in 2007 and 2008.

Secondary objectives of this study were to; (1) examine the under-ice thermal structure beneath first-year and multi-year ice, and (2) study light conditions at 2 m depth beneath the ice surface and compare it to the ice and snow thickness conditions. Significant lateral variability was discovered in temperature using the onboard CTD between the two different ice regimes in the surface layer although the salinity signal was relatively homogenous. This was thought to result from the interaction between the sea-ice surface and the observed tidal signal. In the region of the multi-year ice, significant ice keels were present (> 20 m deep) that would result in mixing of

124 Appendix D: Vehicle Deployments the surface layer whereas the relatively smooth and thin (~ 2 m deep) first year ice would cause less mixing. Although light data was successfully collected on the final day of operations, this is still undergoing analysis to try and remove the influence of the vehicle performance. This was a common problem encountered in all of the deployments; due to the tether, vehicle performance influencing the collected dataset. In each deployment, significant post-processing time is focused on either removing the introduced biases to the dataset or quantifying what these effects are.

D.6 Orka Voe, Shetland Islands, Scotland, UK, 2008

One of the primary sectors driving the development of AUV technology is oil and gas. This is founded on both the need for exploration for site development and maintenance and inspection of existing pipeline networks. In April 2008, UBC-Gavia was involved with a pipeline inspection in Orka Voe, Shetland Islands, Scotland, UK. At this location, several large pipelines make landfall from oilrigs located in the North Sea where they are then routed to the large Sullom Voe refinery. Oil companies are mandated to inspect these pipelines at fixed time intervals (generally between 3 – 5 years) using traditional sidescan sonar surveys and ROV inspections for pipeline movement or damage. One of the challenges with standard, ship-based survey techniques is that they are unable to come close to where these pipes make landfall and so are required to conduct diver-based surveys. In contrast to these larger boats, small, man-portable AUVs are able to be deployed from shore and can survey these regions that were previously only accessible to diver support.

The project in Orka Voe covered a relatively small area (<1.5 km2) where the pipes made landfall out to a distance approximately 3 km offshore. The primary objective was to gather sidescan imagery from both sides of the three pipelines at this location. If the pipeline had lifted since the previous survey, it would be possible to observe in the sidescan sonar data results. The secondary objective was to collect multibeam swath data to examine if any discrepancies with the available charts. While both objectives were met at the end of six days, this deployment highlighted the challenges of planning operations around the littoral zone in places that are prone to inclement weather. Originally, the mission had been planned for two days but was significantly delayed by weather and sea-state. Cresting waves, minimum height of 1 m, were

125 Appendix D: Vehicle Deployments encountered almost every day. While not as significant for ship-based deployments, these prevented most shore-based launches.

D.7 Baku, Azerbaijan, 2009

While most of these extra deployments were conducted using UBC-Gavia, it should also be noted that the skillset developed in using this vehicle is extremely specialized and is currently in high demand for a variety of AUV applications. An example of this is a short contract that was conducted in Baku, Azerbaijan. At this location, an oil and gas company had hired a survey group to conduct AUV surveys of a shallow harbor where the oil jackets are docked near Baku. Although the company that won the bid had the necessary equipment, they didn’t have the necessary personnel and so contracted out mission operations. The objectives of this study were to conduct a multibeam survey of the harbor (average depth between 2 – 5 m) and the channel (~ 5 – 10 m) out to the deeper waters approximately 5 km off shore. This was survey was required on a frequent interval to chart any hidden obstacles and to see if the bed had changed as a result of dredging or other harbor operation. The other objective of this study was to test and implement a pipe-tracking algorithm that had recently been added to the control software of the vehicle. While the first of the objectives was met within the first three days of operations, the pipe-tracking algorithm resulted in significantly reduced vehicle performance. Although it performed well when the pipe was on the surface of the sea-bed, it would often lose track when the pipe became buried, as was often the case. This operation highlighted the need to fully test new developments before implementing them in front of clients.

D.8 Lake Tahoe, NV, USA, 2009

In August 2009, UBC collaborated with the University of California Davis and the University of Delaware to conduct a full lake survey of Lake Tahoe to chart out the extent of the invasive species Corbicula fluminea. Commonly known as the Asian clam, this freshwater bivalve has been slowly spreading throughout the lake since its introduction in 2004. A new image- processing algorithm was written to analyze each photo collected and count the dead clam matter present on the lakebed. This was found to work and highlighted the adaptability of the instrument as a data collection platform. It was also hypothesized that filamentous algae prospers in regions where clams are present. To test this, a new optical backscattering unit that measured colored

126 Appendix D: Vehicle Deployments dissolved organic matter (CDOM), turbidity, and chlorophyll-a, was installed in order to detect algae through a theoretical elevation in levels of CDOM in the water column.

Two types of missions were run during this deployment; along-shore and across-shore deployments. The former was down to examine the overall spatial distribution and the latter was run to quantify the depth distribution of clam presence. In total, nearly 200 km of mission track were run over the 10-day deployment of which nearly 120 km were spent running along the 5 m isobath. While this was certainly challenging for the operators, all of the missions were run at night to standardize the light conditions in the images, all of the objectives of the study were not only met but also exceeded. One of the significant challenges of this deployment was the steep slopes (> 15º) in the regions of interest for image collection. The optimization of vehicle performance for every given location is a non-trivial process that should be built into the time estimate required for every deployment.

D.9 Tasman Bay, New Zealand, 2010

In January 2010, two missions were conducted in New Zealand in conjunction with the University of Delaware, the University of Waikato, and the Cawthron Institute. The first of these was a study of the hydrothermal vents located in the freshwater Lake Rotoiti located on the North Island. These vents submerged approximately 120 m down, release positively buoyant warm water, which entrains gas to the lake surface. The original mission design was to dive to into these plumes and measure the temperature differences. It was quickly determined that this was not possible due to the resolution of the thermistor on board and the fact that the thermal signal was too quickly dissipated into the water column. The gas bubbles in the water column could be ‘seen’ in the multibeam data. From this, it was possible to reconstruct a three dimensional image of the bubble plume. These observations are unique, as, although plumes have been observed in the ocean before, they have never before been seen in lake systems before.

The second deployment was located in the Tasman Bay on the South Island where a benthic nepheloid layer (BNL) is commonly observed at the level of the seafloor; particularly during summer stratification. Understanding the role of this layer is critical for scallop recruitment and productivity in the bay; two critical elements for the scallop industry based in this area. Both

127 Appendix D: Vehicle Deployments

AUV, and more traditional, surveys were used to examine patterns in the BNL and see how these relate to a large river discharge which is known to be a significant source of nutrients and plankton into Tasman Bay. Although the AUV surveys provide an interesting new perspective on lateral heterogeneity of both this system, and all the systems described, it is only through the combination of these surveys with more traditional techniques (vertical profilers, ship tows, moorings, etc.) that it is really possible to build up a three-dimensional model of any of the problems described in this work.

D.10 Pavilion Lake, BC, Canada, 2006 – 2010

Throughout all of the deployments that were previously described, UBC-Gavia was involved with the space science and exploration goals of Pavilion Lake Research Project. Used as an analogue for unmanned robotic vehicles (e.g. Mars rovers), missions were designed each year with the targeted goal of learning techniques to improve operations (e.g. human robotic interface, data visualization, etc), while concurrently trying to achieve specific scientific goals. The combination of these two objectives add to the overall fidelity of the analogue and allow more scientific groups to learn from a single experiment. The three experiments that were chosen were to (1) map out the central abyssal plain of the lake, (2) search for springs with a conductivity tracer, and (3) examine a salinity layer at the bottom of the lake. Each of these met specific goals of the overall project. Each of these objectives were selected as the pilots of the manned submersibles, concurrently deployed, either ranked the objective a lower priority (as in the case of the first experiment) or were unable to measure the subtle differences required for the other two experiments. One of the most important lessons to emphasize is that the tool should always be selected based on the problem rather than the reverse situation, which is often the case.

128