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\begin{document}

\title{Hydrogeological control of the thermal regime of a sub-alpine headwater
stream}



\author[1]{Benjamin Roesky}%
\author[2]{Masaki Hayashi}%
\affil[1]{BGC Engineering Inc}%
\affil[2]{University of Calgary}%


\vspace{-1em}



  
  \date{June 18, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Stream thermal regimes are critical to the stability of freshwater
habitats. There is growing concern that climate change will result in
stream warming due to rising air temperatures, decreased shading in
forested areas due to wildfires, and changes in streamflow. Groundwater
plays an important role in controlling stream temperatures in mountain
headwaters, where it makes up a considerable portion of discharge. This
study investigated the controls on the thermal regime of a headwater
stream, and the surrounding groundwater processes, in a catchment on the
eastern slopes of the Canadian Rocky Mountains. Groundwater discharge to
the headwater spring is partially sourced by a seasonal lake. Spring,
stream, and lake temperature, water level, discharge and chemistry data
were used to build a conceptual model of the system. Meteorological data
was used to set up a stream temperature model. A tracer test was carried
out to estimate hyporheic exchange along the study reach. This study
presents a unique example of an indirectly lake-headed stream i.e.,
where the interaction of groundwater and lake water, and the hydraulic
gradient determine the resulting stream temperature. Energy balance of
the stream is mainly controlled by radiation. Sensible and latent heat
fluxes play a secondary role, but their effects generally cancel out.
Hyporheic exchange is present but plays only a minor role in the energy
balance. During snowfall events, the latent heat associated with melting
of direct snowfall onto the water surface was responsible for rapid
stream cooling. An increase in advective inputs from groundwater and
hillslope pathways did not result in observed cooling of stream water
during rainfall events. The results from this study will assist water
resource and fisheries managers in adapting to stream temperature
changes under a warming climate.%
\end{abstract}%



\sloppy


\textbf{Hydrogeological control of the thermal regime of a sub-alpine
headwater stream}

Benjamin Roesky and Masaki Hayashi

Department of Geoscience, University of Calgary

To be submitted to \emph{Hydrological Processes} (\textless{} 7500
words).

\textbf{Abstract} (\textless{} 300 words)

Stream thermal regimes are critical to the stability of freshwater
habitats. There is growing concern that climate change will result in
stream warming due to rising air temperatures, decreased shading in
forested areas due to wildfires, and changes in streamflow. Groundwater
plays an important role in controlling stream temperatures in mountain
headwaters, where it makes up a considerable portion of discharge. This
study investigated the controls on the thermal regime of a headwater
stream, and the surrounding groundwater processes, in a catchment on the
eastern slopes of the Canadian Rocky Mountains. Groundwater discharge to
the headwater spring is partially sourced by a seasonal lake. Spring,
stream, and lake temperature, water level, discharge and chemistry data
were used to build a conceptual model of the system. Meteorological data
was used to set up a stream temperature model. A tracer test was carried
out to estimate hyporheic exchange along the study reach. This study
presents a unique example of an indirectly lake-headed stream i.e.,
where the interaction of groundwater and lake water, and the hydraulic
gradient determine the resulting stream temperature. Energy balance of
the stream is mainly controlled by radiation. Sensible and latent heat
fluxes play a secondary role, but their effects generally cancel out.
Hyporheic exchange is present but plays only a minor role in the energy
balance. During snowfall events, the latent heat associated with melting
of direct snowfall onto the water surface was responsible for rapid
stream cooling. An increase in advective inputs from groundwater and
hillslope pathways did not result in observed cooling of stream water
during rainfall events. The results from this study will assist water
resource and fisheries managers in adapting to stream temperature
changes under a warming climate.

\textbf{Keywords} (eight required)

Stream temperature, alpine hydrology, energy balance, groundwater-stream
interaction, headwater spring, seasonal lake, hyporheic exchange,
Canadian Rockies

\textbf{1. Introduction}

The temperature of water plays a critical role in the stability of
various habitats including those of freshwater fish (Ebersole, Liss, \&
Frissell, 2001). The major energy fluxes that determine stream
temperatures are net shortwave and longwave radiation, sensible and
latent heat transfer, bed heat conduction, advection by groundwater, and
hyporheic exchange (Moore, Sutherland, Gomi, \& Dhakal, 2005). These can
be classified as exchanges occurring at either the air/water interface
or the streambed/water interface (Caissie, 2006). Energy-balance studies
have found that net streambed heat fluxes make up a greater fraction of
the total heat budget for smaller streams. In a catchment in New
Brunswick, Canada, the streambed heat flux accounted for 23 \% of the
total heat flux for a smaller stream compared to 12 \% for a larger
stream (Hebert, Caissie, Satish, \& El-Jabi, 2011). In a headwater
stream, in British Columbia, hyporheic exchange accounted for up to 25
\% that of net radiation during the period of the day with the greatest
warming rate (Moore et al., 2005a). However, the streambed heat fluxes
vary both spatially and temporally within the channel (Caissie \& Luce,
2017). Groundwater discharge results in summer stream cooling and winter
stream heating, acting as a buffer from thermal extremes (Hayashi \&
Rosenberry, 2002). Within the stream channel, patterns of seepage flux
are determined by channel profile and morphology, such as pool and
riffle sequences and cross-channel gradients (Gariglio, Tonina, \& Luce,
2013).

There is growing concern that climate change will result in stream
warming due to rising air temperatures, decreased shading in forested
areas due to wildfires, and changes in streamflow (Leach \& Moore,
2010). Long-term monitoring data have already shown stream temperature
increases over the last 30 years across the northwestern United States
(Isaak, Wollrab, Horan, \& Chandler, 2012). In mountain regions, changes
to flow regimes due to changing snowmelt dynamics (Bavay, Gr\selectlanguage{ngerman}ünewald, \&
Lehning, 2013), and rising groundwater temperatures must also be
considered (Kurylyk, MacQuarrie, \& McKenzie, 2014). Previous work has
revealed that groundwater, as distinguished from recent seasonal
precipitation and meltwater inputs, makes up an important fraction of
mountain headwater discharge (Hood \& Hayashi, 2015). Estimates vary
across catchments and seasons; up to 60 \% of streamflow, during early
snowmelt, was attributed to groundwater in a catchment in the Colorado
Rocky Mountains (Liu, Williams, \& Caine, 2004). In the Canadian
Rockies, a rock glacier spring contributed up to 50 \% of streamflow
during summer baseflow periods and up to 100 \% of streamflow over
winter (Harrington, Mozil, Hayashi, \& Bentley, 2018). The relative
position and size of alpine aquifers, including rock glacier; moraine;
talus; and alpine meadow, determine the groundwater storage-discharge
characteristics in these catchments (Hayashi, 2020).

There have been few studies on the effects of groundwater discharge on
the temporal and spatial variability in alpine thermal regimes.
Consequently, the impact of groundwater on ecosystems in these settings
is poorly understood (Brown, Milner, \& Hannah, 2007). The few existing
studies characterize the different source water contributions including
snowmelt, glacial icemelt and groundwater (Brown, Hannah, \& Milner,
2005). Groundwater-fed alpine streams exhibit greater streamflow
permanency (Brown, Hannah, \& Milner, 2006) and dampened diurnal
temperature variations (Constantz, 1998). Discrete groundwater
discharge, such as from a rock glacier spring, can mitigate the warming
effect of lake outflows, serving as a thermal refuge under a warming
climate (Harrington, Hayashi, \& Kurylyk, 2017).

Direct precipitation onto the stream surface is an advective component
of stream energy balance (Webb \& Zhang, 1997). However, most studies do
not include this flux, (e.g., Garner, Malcolm, Sadler, Millar, \&
Hannah, 2015; Harrington et al., 2017; Moore, Spittlehouse, \& Story,
2005) citing a study showing it to be negligible, even during heavy rain
(Evans, McGregor, \& Petts, 1998). However, there are evidences
indicating that stream temperatures do respond to precipitation events.
Brown and Hannah (2007) attribute observed temperature responses in an
alpine stream to `advected energy inputs, primarily from surface and
near-surface hillslope pathways and by groundwater, rather than direct
heat flux by falling precipitation'. The idea that precipitation results
in stream cooling due to the corresponding flow generation processes is
repeated elsewhere, where direct precipitation accounted for less than
1.2\% of the daily total heat flux and could not account for observed
cooling (Hebert et al., 2011). However, these studies did not consider
the effects of solid precipitation which could have a larger impact on
the energy balance. To our knowledge, Leach and Moore (2017) were the
first to demonstrate the role of channel-intercepted snowfall on stream
temperatures. Little work has been done to date to quantify the
processes that lead to observed stream temperature cooling during
precipitation events.

The aim of this study is to improve and quantify our understanding of
the processes controlling the thermal regimes of groundwater-fed
headwater streams in mountain regions. The three main study objectives
are:

\begin{enumerate}
\tightlist
\item
  Determine the spatial and temporal variability in groundwater
  discharge temperature to a sub-alpine stream and develop a conceptual
  model for the system.
\item
  Quantify the solid precipitation induced stream cooling processes to
  improve stream temperature models.
\item
  Characterize the downstream changes in the first-order stream channel
  by quantifying transient storage and increases in discharge.
\end{enumerate}

\textbf{2. Study Site}

The study is conducted at an unnamed headwater stream in a valley called
Hathataga (meaning huckleberry) by the local Stoney people (Crawler,
Labelle, Mark, \& Willie, 1987). Therefore, in this study the stream is
called Hathataga Creek. It is located in the Fortress Ski Area
(50°49'14'' N, 115°12'50'' W) in Alberta, on the eastern slopes of the
Canadian Rocky Mountains. The stream starts at a set of perennial outlet
springs (Gauging Station 1 (GS1); Figure 1B) and flows north until it
merges with Galatea Creek. The focus of this study is on an 850 m long
reach extending from the outlet springs to a previously installed stream
gauging station (GS4; Figure 1B).

A tarn, with no surface water outflows, is located at a higher elevation
to the south of the springs, separated by a moraine. The tarn, referred
to in this study as Hathataga Lake, forms following snowmelt and dries
up by late summer (Christensen, Hayashi, \& Bentley, 2020). As a result
of the hydraulic gradient, the springs drain the sub-catchment that
includes the tarn. This means that in summer months water flows from
Hathataga Lake to the springs.

The spring system consists of numerous discrete discharge points that
combine to form three spring branches (S1, S2 and S3) that merge just
above GS1. The location and presence of these transient discharge points
is dependent on the elevation of the water table. It is important to
distinguish between lake-headed streams and headwater streams as
downstream temperature gradients reflect source water temperature
(Mellina, Moore, Hinch, Macdonald, \& Pearson, 2002). Hathataga Creek is
indirectly lake-headed because there is no surface water connection to
Hathataga Lake. Another study at the site determined a travel time from
the lake to the spring system of approximately 4 hours, using a tracer
test (He, J., 2021). Given the horizontal distance of approximately 100
m the hydraulic conductivity of the moraine is on the order of 1 ×
10\textsuperscript{-2} m s\textsuperscript{-1}.

Elevations in the catchment range from 2034 m.a.s.l at the lower gauging
station (GS4) to 2900 m.a.s.l at the southern headwall. The catchment
has been divided into four sub-catchments (W1 to W4) (Figure 1A).

The bedrock underlying Hathataga Lake and the study reach consists of
recessive shales of the Jurassic Fernie Formation (McMechan, 2012). The
ridges between these valleys are made up of Paleozoic carbonates. The
Sulphur Mountain Thrust separates the Fernie Formation from the older,
more resistant carbonates that make up the headwall in the southern and
western part of the study catchment (Figure 1A).

Surficial sediments and the geomorphology of the area can be attributed
to the late Pleistocene and Holocene glaciations (Beierle, Smith, \&
Hills, 2003), which have resulted in the north facing cirque that can be
seen today, along with extensive moraine deposits surrounding Hathataga
Lake. Freeze-thaw weathering of the carbonate headwall has and continues
to contribute to steep talus cones. The coniferous tree line extends to
the base of these talus cones.

The outlet springs discharge at the base of the moraine north of the
lake. Stream geomorphology changes considerably downstream (Figure 2)
(Roesky, 2020). Flow is often turbulent passing through countless pools
and riffles. Between the outlet springs and GS2, the western stream
banks are shallow with numerous visible bank seeps. The eastern stream
banks are typically steeper, incised by 1 to 2 m, with bedrock only
occasionally outcropping. The hillslopes are mostly tree covered but
some segments are covered in alpine meadow on the western side.
Downstream of GS2 the stream gets progressively more incised, by up to
10 m, with increasing bedrock exposure on both sides (Figure 2). Stream
meanders also become more frequent.

\textbf{3. Methods}

\par\null

\emph{3.1 Stream discharge and temperature}

Stream discharge was manually measured bi-weekly (May-August) or monthly
(September-April) using a horizontal-axis current meter (Global Water,
FP101) and the velocity-area method (Dingman 2002, p. 609) with an
expected uncertainty of up to 9 \% (Hood, Roy, \& Hayashi, 2006). A
stage-discharge rating curve was developed at each of the four stream
gauging stations (GS1 to GS4; Figure 1) using at least ten measurements.
A root mean squared error below 0.015
m\textsuperscript{3}s\textsuperscript{-1} was obtained at all four
gauging stations with the largest errors occurring during the baseflow
period. Water levels were measured by pressure transducers (Solinst,
Levelogger). A continuous discharge record was computed by applying the
rating curves to the transducer data.

A number of different instruments were used to measure water
temperatures to reflect the spatial and temporal scales of interest.
Manual measurements were taken with a hand-held thermocouple thermometer
(Omega engineering, HH-25TC) during three spring temperature surveys and
for verifying continuous data. Temperature sensors (Maxime Integrated,
Ibuttons DS1921Z), coated in rubber (Plasti Dip) for waterproofing, were
used to measure longitudinal stream temperature profiles (T1 to T11),
spring branch temperatures (S1 to S3), and the temperature of the
Western tributary (T12). The thin rubber coating allowed the sensors to
reach thermal equilibrium in under 5-minutes. Each temperature sensor
was tied to a nail that was hammered into the streambed. A flat rock was
rested on each nail head to shield the sensor from solar radiation. The
pressure transducers (Solinst, Levelogger) also recorded temperatures in
the lake and at the stream gauging stations. Manufacturer-specified
accuracies are ±1°C and ±0.05°C for the \emph{Ibuttons}
and\emph{Leveloggers} respectively. The accuracy of the \emph{Ibuttons}
was improved to ±0.25°C following the method outlined in Johnson et al.
(2005). Sensors were calibrated in a constant temperature bath (VWR,
1157 Polyscience Refrigerated Circulator) over the range of temperatures
observed in the field. Streambed temperature was also monitored by
an\emph{Ibutton} , installed in P1 (Piezometer 1), 40 cm below the
streambed (Figure 1).

Snapshots of stream surface temperature were captured with a thermal
infrared camera (FLIR, E95). The manufacturer-listed accuracy is ± 2 °C
and the thermal sensitivity is 0.04 °C. A programmable emissivity of
0.96 was used along with measured relative humidity and air temperature.

\emph{3.2 Meteorological conditions}

The University of Saskatchewan had previously installed six automatic
weather stations (AWS) in the study catchment. In this work, AWS1
located in the meadow by the outlet springs was used (2084 m.a.s.l.). It
measured cumulative precipitation (Geonor, T-200B, with Alter wind
shield), air temperature and relative humidity (Rotronic, HC2-S3),
shortwave and longwave radiation (Kipp \& Zonen, CNR4) and wind speed
(R. M. Young, 05103).

Precipitation phase was determined using an air temperature threshold of
0 °C (Marks, Winstral. Reba, Pomeroy, \& Kumar, 2013). Below 0 °C
precipitation was classified as snow and above 0 °C as rain. However,
since the threshold is site specific (Marks et al., 2013) a time-lapse
camera (Wingscapes, TimelapseCam) was used to confirm the
classification. The camera was set up by the outlet springs to take
photos at 5-minute intervals. The images were then visually inspected to
see if snowfall was occurring or if it had accumulated on the ground.
This crude method assumes that snowfall does not melt within the
5-minute window, prior to image capture. Furthermore, when snowfall
occurred at night, we assume that melt did not occur until after
sunrise, due to low air temperatures. This method was suitable for our
purpose of qualitatively distinguishing between liquid and solid
precipitation.

\emph{3.3 Water and snow chemistry}

Water samples were collected weekly or bi-weekly at GS1, GS2, GS3 and
GS4, and at Hathataga Lake's north shore. Additional sampling included
the three spring branches (S1, S2 and S3) (see results below) on August
14 and September 26, 2019. All samples were filtered (0.45 \selectlanguage{greek}μ\selectlanguage{english}m) and
stored in 20-ml high-density polyethylene scintillation vials. A
`ball-in-funnel type collector' was used to collect liquid precipitation
(Prechsl, Gilgen, Kahmen, \& Buchmann, 2014). A table tennis ball was
placed in a funnel to help seal the sample bottle from evaporation and
debris. During rainfall, the ball could float which allowed collection.
Snow pits were dug to the ground surface, up to 1.5 m, and sampled at 20
cm intervals on March 27, April 23, May 8, 22, 29 and June 11, 2019. All
samples from a single pit were combined into a depth-integrated snowpack
sample, which was melted at room temperature and bottled. All samples
were refrigerated until analysis.

Samples were analyzed for stable isotope ratios, alkalinity and major
ion concentrations. Isotopes were analyzed using cavity-ringdown
spectroscopy (Los Gatos Research, Water Isotope Analyzer). The ratios
of\textsuperscript{18}O/\textsuperscript{16}O
and\textsuperscript{2}H/\textsuperscript{1}H were computed with
reference to the Vienna Standard Mean Ocean Water isotopic standard
(Coplen, 1995). Precision and accuracy as 1 standard deviation of lab
standards are 0.2 %0 for \textsuperscript{18}O and 1.0 %0 for
\textsuperscript{2}H. Alkalinity was determined using a
spectrophotometer (Gallery, Discrete Analyzer). An ion chromatograph
(Metrohm, 930 Compact IC Flex) was used for major ion analysis.

Electrical conductivity (EC) was measured manually using a handheld
meter (VWR International, Conductivity/Temperature Meter) for point
measurements and for verifying continuous data.

\emph{3.4 Tracer test}

A single uranine tracer experiment was performed on June 26, 2019 to
quantify transient storage between GS1 and GS2. Tracer concentration was
chosen based on a previous study by Lautz and Siegel (2007) with similar
flow conditions. A peristaltic pump (Solinst, 410) was set up at the top
of the reach to release 0.3 g L\textsuperscript{-1} of the fluorescent
dye, at 1.4 L min\textsuperscript{-1}, for a total of 27 minutes.
Fluorometers (Turner Designs, Cyclops-7F) were deployed at locations F1
and F2 (Figure 1), with shade caps, at the end of the reach and in the
stream near P4 (Figure 1). To obtain an accurate relationship between
sensor output voltage and dye concentration the fluorometers had
previously been calibrated in the laboratory with five concentration
standards: 0, 0.5, 4, 100 and 400 ppb of uranine. For the experiment,
the fluorometers were connected to dataloggers (Campbell Scientific,
CR1000) and set to take measurements at 5 second intervals. The
resulting breakthrough curves were then used to calculate total tracer
recovered to confirm complete mixing.

The one-dimensional transport model OTIS-P (Runkel, 1998) was used to
estimate the transient storage parameters, dispersion coefficient, and
stream cross sectional area (see electronic supplement for details)
assuming that the flow is at steady state and that uranine is a
conservative tracer (Smart \& Laidlaw, 1977). The steady-state
assumption was justified as there was a change in discharge of less than
6 \% at GS1 during the experiment.

\emph{3.5 Additional data}

Drive-point piezometers (1.9 cm inside diameter) were installed within
the second spring branch (P2), below AWS1 (P3), to the west of the
stream between GS1 and GS2 (P4) and in the lakebed (P5) (Figure 1).
Pressure transducers (In-Situ, MiniTroll, accuracy \textasciitilde{}1
mm) were placed in the piezometers to measure groundwater levels and
temperatures. Continuous water level data were verified bi-weekly with
manual water-level measurements. Lake water level was measured by a
pressure transducer (Solinst, Levelogger, accuracy \selectlanguage{ngerman}±0.3 cm), in a lake
stilling well. Stream dimension surveys were completed on June 26 and
August 2, 2019 whereby stream depth was recorded every 10 cm along the
width of the stream, at 24 separate transects. Twelve transects were
located between GS1 and GS2 at approximately 20 m intervals and the
remaining 12 transects were located at approximately 50 m intervals
between GS2 and GS4. The width of the transects ranged from 1.3 to 4.4
m.

\par\null

\emph{3.6 Stream temperature modeling}

Stream temperature data were analyzed using the one-dimensional heat
transfer model HFLUX (Glose, Lautz, \& Baker, 2017). The following
describes a model modification introduced in this study, while a brief
summary of HFLUX is presented in an electronic supplement.

In previous studies the direct precipitation flux has been calculated
using:\emph{q\textsubscript{p}} = 1.16
\emph{y\textsubscript{p}}(\emph{T\textsubscript{p}} --
\emph{T\textsubscript{w}} ) (1) where \emph{q\textsubscript{p}} is the
precipitation flux (W m\textsuperscript{-2}), \emph{y\textsubscript{p}}
is precipitation (mm h\textsuperscript{-1}), \emph{T\textsubscript{p}}
is precipitation temperature (°C), \emph{T\textsubscript{w}} is stream
temperature (°C), and 1.16 is a unit conversion factor including the
specific heat of liquid water (4.2 × 10\textsuperscript{3} J
kg\textsuperscript{-1}°C\textsuperscript{-1}) (Hebert et al., 2011;
Marcotte \& Duong, 1973). Precipitation temperature is assumed to be
equal to air temperature (Marcotte \& Duong, 1973).

At high elevation sites and in winter, precipitation often falls in the
solid state and melts in streams. To account for the latent heat of
fusion in the energy balance calculation, Equation (1) is modified in
this study as:\emph{q\textsubscript{p}} = 1.16
\emph{y\textsubscript{p}}(\emph{T\textsubscript{p}} --
\emph{T\textsubscript{w}} ) + 92.8\emph{y\textsubscript{p}} (2)

where the second term represents the effect of the latent heat of fusion
(= 3.34 × 10\textsuperscript{5} J kg\textsuperscript{-1} at 0 °C) and
unit conversion.

The HFLUX model was calibrated for 12:00 August 14 to 12:00 August 20,
2019, which included a snowfall event. The model was then validated for
12:00 August 20 to 12:00 August 26, 2019. Shading (\emph{SF} ),
groundwater temperature (\emph{T\textsubscript{L-gw}} ) and view to sky
coefficient (\emph{VTS} ) were estimated during the calibration process,
whilst considering field observations and aerial photographs, as the
parameters were not measured directly. Parameter estimation was carried
out using a nonlinear, multivariable optimization solver known as
fminunc (MathWorks, 2020a) which was integrated with the original code.
The objective function was set to minimize the root-mean-squared-error
(RMSE) between the measured and modeled stream temperatures.

\textbf{4. Results}

\emph{4.1 Stream discharge}

At the onset of snowmelt, in late May 2019, discharge increased rapidly
by an order of magnitude (Figure 3C). Streamflows were high from June 4
to July 8, after which levels receded. There were several peaks in
discharge corresponding to air temperature fluctuations (Figure 3B).
Discharge from GS2 and GS3 were combined to represent the combined
outflow from W2 and W3. Maxima of 0.24, 0.63 and 0.55
m\textsuperscript{3} s\textsuperscript{-1} were attained at GS1, GS2 +
GS3 and GS4, respectively. Discharge typically increased by 10 \% to 30
\% between GS1 and GS2, however during snowmelt this went up to 80 \%.
Diurnal discharge fluctuations, that became more pronounced downstream,
were likely caused by evapotranspiration because daily discharge minima
occurred between 14:00 and 15:00 and maxima occurred before sunrise.

Three spring temperature and location surveys were carried out during
the 2019 field season (Figure 4). On June 26, 25 discrete springs were
identified. By August 7, the number of springs was reduced to 16 and by
September 26 to seven. Not only did the number of springs decrease over
the season but the springs also moved northward to lower elevations,
corresponding with a decline in the water table. The highest elevation
spring was at 2086.3 m.a.s.l. on June 16 and at 2083.7 m.a.s.l. on
September 26.

Spring temperatures on June 26 ranged from 1.1 to 3.6 °C. On August 7,
temperatures increased to 2.1--7°C and on September 26 they decreased to
1.9--3.4°C (Figure 4). The warmest springs were initially concentrated
in the south-eastern part of the spring system but moved to the eastern
stream bank over the course of the season. On September 26, the warmest
spring was also the furthest north. Each of the three snapshots in
Figure 4 corresponds to different phases in Hathataga Lake's
hydroperiod. In (A) the lake water level (WL) was near its peak (2090.0
m.a.s.l., WL = 1.5 m), in (B) the lake temperature was near its peak
(2088.8 m.a.s.l., WL = 0.35 m), and in (C) the lake had dried up (2087.8
m.a.s.l., WL = -0.68 m). Note that WL is the water level with reference
to the lakebed.

\emph{4.2 Spring temperature}

The clusters of springs are grouped into three spring branches (S1, S2,
and S3 in Figure 4). Thermal infrared images of the spring area were
taken on August 14, 2019 at 12:15 to better visualise mixing of the
three spring branches (Figure 5). Water surface temperatures were
between 1.1 and 6.2°C. Distinguishable features include a cold side
spring (Figure 5A) and a sharp thermal boundary between water
originating from S1 and S2/S3. It can also be seen that GS1 is situated
on the warmer stream side which must be considered during interpretation
of the temperature data from the gauging station.

To better resolve the temporal variability, temperature sensors were
placed in each of the three spring branches from June 11 to October 17,
2019 (Figure 6). Data gaps were the result of sensors being exposed to
air (August) or full datalogger memory (July). Initial temperatures in
the spring branches were equal at \textasciitilde{}1.3°C but these
rapidly diverged at the onset of snowmelt (Figure 6). The maximum
recorded temperature in each spring branch was not reached
simultaneously: S2 reached its maximum on July 15 with temperatures
remaining high until late August. Temperatures at S1, on the other hand,
were rising during this time and reached a maximum on August 22. By
mid-September temperatures in S2 were back down to S3 levels. S1
temperatures had still not been reduced to S3 levels by October 17.
Diurnal variations are likely due to heating of spring water following
surface discharge. This is especially noticeable in S3 as it is the
longest spring branch above the temperature sensor.

The observed spatial and temporal variability in spring temperatures was
described above. Below, changes in spring temperature and discharge and
changes in lake temperature and water level are explored (Figure 7).
Note that stream temperature measured at GS1 was used, which was heavily
influenced by high temperature discharge (Figure 5A). Even though this
does not represent the spring system as a whole it captures the
relationship between the lake and springs satisfying the purpose of this
study. Additionally, water levels measured in P5 were used to include
days when water levels were below the lake stilling well. True lake
water levels were up to 5 cm higher than heads measured in the lake
piezometer due to the downward flux into the lakebed. The downward head
gradient beneath the lake accounts for the differences in readings
between the lake piezometer and stilling well. To capture both spring
snowmelt and the lake drying up, across two different seasons, the study
period extends from May 1 to October 1, 2018 and 2019.

During the 2018 season the water table under the lake rose to the
surface on May 18, after the onset of snowmelt. The maximum water level
was 1.8 m on June 24, coinciding with a maximum spring discharge of 0.31
m\textsuperscript{3} s\textsuperscript{-1} (Figure 7B). After this,
spring and lake temperatures increased rapidly until air temperatures
dropped on July 18 (Figure 7C). By August 15, the lake had dried up and
spring temperatures began to fall (Figure 7B and 7C). There are some key
distinctions between the 2018 and 2019 seasons. Snowmelt started two
weeks later in 2019 meaning that water levels reached the surface on May
31. Snowpack, measured at AWS1, prior to snowmelt was 60 cm deeper in
2018, however summer precipitation was greater in 2019. Also, the
maximum lake water level was 20 cm higher in 2018. Lastly, the lake
dried up later in 2019 and resurfaced following heavy precipitation on
September 2.

Prior to snowmelt in late May 2019, temperatures at GS1 remained steady
at \textasciitilde{}1.3°C (Figure 7F). In 2019, after the surface water
appeared in the lake, they continued rising rapidly during the following
four days to 1.47 m (Figure 7E). On June 4 stream and lake temperatures
reached seasonal lows of 0.9°C and 0.7°C, respectively. Daily average
lake temperature proceeded to rise to 4.4°C by June 13 (Figure 7F).
During this time, changes in lake water level and spring discharge
corresponded to fluctuations in air temperature (Figure 7D). For
example, in the first week of June daily average air temperature
decreased by 10°C, lake water level decreased by 0.5 m and spring
discharge decreased by 0.13 m\textsuperscript{3}
s\selectlanguage{english}\textsuperscript{-1}(Figure 7D, E, F). As air temperatures rose water
levels and spring discharge recovered.

Lake water level reached a maximum of 1.62 m on June 18, 2019 and stayed
high until mid-July when it began its downward trajectory (Figure 7E).
The decline in lake water levels coincided with a rapid increase in both
lake and stream temperatures (Figure 7F). By August 25, the lake had
dried up. However, the lake briefly appeared again following
precipitation on September 2, which was confirmed by a field visit on
September 4. This pattern was reflected in stream temperatures as a
decrease when lake water level was below the surface and an increase
when it resurfaced.

\emph{4.3 Chemical and isotopic composition}

As the snowpack started to melt in the catchment in late May 2019, the
alkalinity at GS1 briefly fell, and spring water became depleted in
deuterium (Figure 8E). This suggests the contribution of snowmelt water
to the springs through infiltration, as water levels were rising (Figure
8B). However, once water levels reached a maximum in the lake on June 4,
spring temperature and alkalinity began to increase, and isotopic
compositions became less negative (Figure 8D). This could be due to the
increased hydraulic gradients forcing pre-melt groundwater out at the
springs. After July 10, alkalinity decreased with falling water levels
(Figure 8).

Water samples were collected in the three spring branches and on the
north shore of Hathataga Lake between August 7 and 14, 2019; and
analyzed for alkalinity and major ions (Figure 9). The lake had an
alkalinity of 1.8 meq L\selectlanguage{english}\textsuperscript{-1}, which was most similar to
S1, the warmest spring branch, and most dissimilar to S3, the coldest
spring branch.

\emph{4.4 Stream temperature}

An example period (August 14--21, 2019) was chosen that included both a
rain and snowfall event, and captured daily stream temperature
variability, to model stream temperatures over a range of meteorological
conditions (Figure 10). The first precipitation event (PE1) was a
rainfall event and occurred on August 16 between 13:15 and 17:00 with a
maximum 15-minute intensity of 6.7 mm h\textsuperscript{-1} at 14:45 and
a total of 8.9 mm. The second event (PE2) was a snowfall event and
occurred between 22:45 on August 16 and 03:30 on August 17 with a
maximum intensity was 6.6 mm h\textsuperscript{-1} at 02:00 and a total
of 13.8 mm (Figure 10B).

During the six-day period, stream temperatures at 0 m (T1) remained
between 5.0 and 5.5 degC, whereas temperature variability became more
pronounced downstream (Figure 10C). T1 was located on the eastern side
of the creek at GS1 which meant that the temperature was more
representative of S1 (Figure 5A). For this reason, T2 was used as the
boundary condition in the HFLUX model (see below). Water temperatures
reached a maximum of 6.9 degC at 246 m (T4) and 9.6 degC at 809 m (T10) at
15:00 on August 19, coinciding with a maximum air temperature for the
period of 17.8 degC. A minimum air temperature of -1.4 degC was attained at
07:15 on August 17. This low did not correspond with stream temperature
lows, which occurred at 02:00 on August 17, during the snowfall event.
At this time water temperature was 2.9 degC at 246 m and 1.1 degC at 809 m
downstream. This meant a temperature drop during the snowfall event that
started at 22:45 of 2 degC and 3.5 degC, at T4 and T10 respectively (Figure
10C). During the rainfall event stream temperatures only fell by 0.5 degC
at 246 m and 0.8 degC at 809 m.

Groundwater levels in P2, located at the outlet springs, rose by 7 mm
during PE1 but no pronounced stream cooling was observed. During PE2
groundwater levels only rose by 1 mm (Figure 10D). The time-lapse camera
captured the accumulated snow melting after sunrise.

The temperatures simulated by the HFLUX model are shown in Figure 11A
for the original model and the modified model including the latent heat
of fusion (Eq. 2). During the snowfall event on August 17, the modified
model had a better match with observed temperature compared to the
original model. This resulted in a reduction in the overall RMSE between
measured and modelled stream temperatures along the study reach from
0.46 degC to 0.38 degC for August 17, and from 0.31degC to 0.29 degC for the
6-day period.

The energy fluxes computed by HFLUX is shown in Figure 11B, where
positive values correspond to an energy gain by stream and negative
values an energy loss. Net shortwave radiation was the major source of
energy with an average of 58.9 W m\textsuperscript{-2}. Net longwave
radiation and the sensible heat flux were mostly positive with averages
of 28.7 and 1.7 W m\textsuperscript{-2}, respectively. For most of the
period the latent heat flux was the major heat sink with an average of
-11.0 W m\textsuperscript{-2}. This was followed by bed conduction, the
smallest flux, with an average of -1.6 W m\textsuperscript{-2}. The
direct precipitation flux was mostly negligible as there was either no
precipitation or only liquid precipitation. However, the precipitation
flux became the dominant energy flux during the snowfall period,
reaching a minimum of -615.5 W m\textsuperscript{-2}, the single largest
flux during the 6-day period. The average total energy flux during the
period was 67.6 W m\textsuperscript{-2} resulting in a net increase in
water temperature downstream.

Hyporheic exchange was not included in the heat transfer equation (Eq.
S2-1) in HFLUX. Nevertheless, the stream temperature model had a
reasonably low RMSE. Therefore, it could be inferred that either little
hyporheic exchange was occurring in the system or that hyporheic
exchange had a negligible effect on stream temperatures in the channel.
With this in mind, a tracer test was used to quantify transient storage.

\emph{4.5 Dye tracer test}

Uranine dye was released continuously at GS1 during 10:53--11:20 on June
26, 2019, and it took 4 minutes for the tracer front to travel 152 m
downstream to F1, and 6.5 minutes to F2. A plateau concentration of
37-43 ppb was reached at F1 and 31-36 ppb at F2. The range in the
plateau concentrations measured at each fluorometer are attributed to an
inconsistent pumping rate. This is likely due to the battery not
providing a consistent voltage and the decreasing head difference
between the tracer solution and the stream which made pumping harder.

The breakthrough curves were analyzed using OTIS-P. A model was
generated in which both F1 and F2 were considered (Figure 12). A storage
zone area (\emph{A\textsubscript{s}} , Equation S1-2) of 0.11
m\textsuperscript{2} and 0.18 m\textsuperscript{2}, and an exchange
coefficient (\selectlanguage{greek}α, \selectlanguage{english}Equation S1-1 and S1-2) of
2.2\selectlanguage{ngerman}×10\textsuperscript{-4}s\textsuperscript{-1} and
\textsuperscript{}3.0×10\textsuperscript{-4} s\textsuperscript{-1} were
estimated for the respective sub-reaches. A dispersion coefficient of
1.2 m\textsuperscript{2} s\textsuperscript{-1} and 1.3
m\textsuperscript{2}s\textsuperscript{-1}, and stream cross sectional
area of 0.33 m\textsuperscript{2} and 0.36 m\textsuperscript{2} were
also estimated. The average stream cross sectional area from stream
survey measurements was 0.36 m\textsuperscript{2}. This means the
storage zone area was between one-third and one-quarter the stream cross
sectional area. The rate of longitudinal dispersion was comparable to
estimates by Haggard et al. (2001) where flow conditions were similar.
This was on the higher end of values reported in the literature (0.05 --
1.3 m\textsuperscript{2} s\textsuperscript{-1}) (Lautz \& Siegel, 2007).
The RMSE of the model was 0.93 ppb. The plateau concentrations were used
to account for tracer dilution. Discharge increased by 0.042
m\textsuperscript{3} s\textsuperscript{-1} or 25 \% between GS1 and GS2.
Discharge increases of 0.018 m\textsuperscript{3}
s\textsuperscript{-1}and 0.024 m\textsuperscript{3}
s\textsuperscript{-1} were determined for the respective sub-reaches.
Discharge obtained from the GS1 and GS2 rating curves showed an increase
of 28\% along the reach (Figure 3) which is similar to the estimates
obtained through tracer dilution. The average time that solutes spent in
the storage zone (\emph{t\textsubscript{s}} ) was 18 minutes suggesting
that transient storage represents storage in the hyporheic zone, which
can retain some solutes for 10-30 minutes, rather than stagnant side
channel. This is complemented by field observations of turbulent flow
with few stagnant pools.

Hyporheic exchange in the channel therefore did not have a noticeable
effect on stream temperatures and represented a negligible flux compared
to the energy fluxes included in the heat transfer equation (Equation
S2-1). Furthermore, hyporheic exchange is likely captured in part by the
bed conduction flux (Equation S2-11).

\textbf{5. Discussion}

\emph{5.1 Lake and spring thermal and hydrogeologic connectivity}

The headwater springs of Hathataga Creek is thermally influenced by the
seasonal body of water in the lake located upgradient of the springs,
resulting in a strong seasonality in the temperature of spring
discharge, which in turn affects the stream thermal regime (Figurer 13).
The spring has a steady temperature of \textasciitilde{}1.3 °C during
winter and early spring while the lake is covered by snow (Figure 7). As
the water table rises under the lake and forms the surface water body
after snowmelt, the lake becomes an effective absorber of shortwave
radiation. As a result, the lake water temperature rises, and so as the
temperature of S1 spring receiving the water sourced by the lake (Figure
13A). S2 and S3 springs receive less of lake-influenced groundwater but
more of the groundwater that bypasses the lake. This results in a
temperature contrast between S1 and S2/S3 (Figure 5). As the lake dries
out towards the end of the summer (Figure 13B), the spring temperature
decreases rapidly due to the loss of warm water from the lake.

The distinct thermal characteristics of lake-headed stream temperatures
have previously been described (Dripps \& Granger, 2013; Garrett, 2010;
Mellina et al., 2002). This study presents a unique example of an
indirectly lake-headed stream i.e., where the interaction of groundwater
and lake water, and the hydraulic gradient determine the resulting
stream temperature.

The processes taking place in this system have important implications
for the stream thermal regime under a changing climate. There have been
greater than average regional increases in mean air temperatures on the
eastern slopes of the Canadian Rockies. Warming of 2.6 °C has been
recorded at the Marmot Creek research basin, located 15 km north of the
Hathataga valley, since the 1960s (Harder, Pomeroy, \& Westbrook, 2015;
Fang \& Pomeroy, 2020). Typically, the concern is that this leads to
stream warming (Leach \& Moore, 2019). Higher summer air temperatures in
the Hathataga valley would lead to higher lake temperatures and
therefore even greater stream warming. Earlier snowmelt (Stewart, Cayan,
\& Dettinger, 2005) and a reduced snowpack (Mote, Hamlet, Clark, \&
Lettenmaier, 2005) have also been shown for the region. Reduced summer
streamflows would exacerbate stream warming. However, the duration of
the surface water in the lake would be shortened due to a reduced
snowpack. This in turn would reduce the time of warm groundwater
contribution to the springs, resulting in stream cooling. On the other
hand, summer precipitation has been increasing in the Canadian Rockies
(Harder et al., 2015). Increased summer precipitation could also impact
the lake's hydroperiod by increasing lake water levels and extending the
life of the lake. The frequency of mid-winter melts is also likely to
increase into the future (O'Neil, Prowse, Bonsal, \& Dibike, 2017). This
could cause a lake-spring connection in winter months. Climate change
will therefore impact the timing and magnitude of lake water levels,
which are an important control on stream temperatures.

This study illustrates the complex and non-linear nature of climate
change on surface water-groundwater interactions and the need to further
study the effects of both intermittent and non-intermittent alpine lakes
on stream thermal regimes.

\emph{5.2 Effects of direct precipitation on stream temperature in cold
regions}

Previous studies have concluded the direct precipitation heat flux to be
negligible (Evans et al., 1998) and observed stream cooling has been
attributed to the resulting flow generation processes (Brown \& Hannah,
2007). We began this study with the aim of quantifying these subsurface
flows to improve stream temperature models. However, we found that
direct precipitation made up a large component of the energy balance
during solid precipitation events (Figure 11B) consistent with the
findings of Leach and Moore (2017). Furthermore, Hathataga Creek did not
undergo any noticeable cooling during rainfall events. This suggested
that an increase in advective inputs, from groundwater and hillslope
pathways, did not play an important role in altering stream
temperatures.

The stream energy balance was dominated by shortwave radiation during
the day and longwave radiation at night (Figure 11B). The largest
temperature residuals occurred between 14:00 and 15:00 when measured
temperatures were up to 1.5 °C warmer than modelled ones. The
uncertainties in shortwave radiation came from estimates of shading.
This is attributed to shading values that were fixed in the model and
therefore did not change throughout the day. The radiation measurements
were taken in an open meadow. For most of the day the stream was well
shaded as captured by the shading estimates. However, in mid-afternoon
the position of the sun was such that it shone along the length of the
stream and shading estimates became erroneous. In future modelling
studies, shading and view to sky coefficient should be quantified in the
field using hemispherical images (Garner, Malcolm, Sadler, \& Hannah,
2017) or a densiometer (Gravelle \& Link, 2007).

Uncertainties in longwave radiation came from the assumption that canopy
surface temperature equals air temperature. In reality, longwave
radiation from surrounding vegetation (L\textsubscript{veg}, Equation
S2-5) is likely greater on sunny days when canopy temperature is greater
than air temperature (Pomeroy et al., 2009). The remaining fluxes were
relatively small in comparison. Uncertainties in the latent and sensible
heat flux came from meteorological measurements made at 3.45 m height
rather than 2 m. As a result, wind speed and the latent heat flux were
likely lower. Furthermore, measurements were made over the meadow rather
than the stream surface. It has been shown that wind speed is higher and
more variable at exposed regional weather stations compared to sheltered
microclimate sites (Benyahya, Caissie, El-Jabi, \& Satish, 2010). In
this study the stream surface is located in a topographic low relative
to the meadow. Therefore, wind speed was likely lower than measured.
During the snowfall event the direct precipitation flux was ten times
greater than other energy inputs.

The energy consumption caused by the melt of solid precipitation have
important implications for stream temperatures in alpine environments
and other cold regions. Equation 2, which describes this process, should
be considered in stream energy balance models. Without this flux,
parameter estimates from calibration would be less reliable to account
for the lower stream temperatures. In other mountain regions, such as
the Vernagtbach basin in Austria, there are years when solid
precipitation accounted for up to 70 percent of total precipitation
during the ablation season. During the same period, there were up to 50
days with snowfall (Escher-Vetter \& Siebers, 2007). In the Hathataga
catchment, solid precipitation accounted for 23 percent of total
precipitation from May to September 2019 with 20 days of snowfall.

This could also have important implications for the field of meteorology
where it is a challenge to determine precipitation phase. Greater than
expected temperature changes in small streams or of fluid in a
precipitation gauge (Geonor, T-200B) could be used as a proxy for
solid/liquid phase rather than using an air temperature threshold or
expensive laser-based sensors (Campbell Scientific, CS125). The
advantage of this method is that cooling associated with the latent heat
of fusion only occurs for solid precipitation, irrespective of air
temperature. This was especially relevant during summer hailstorms when
surface air temperatures were up to 10 °C but stream cooling was
observed.

\textbf{6. Conclusions}

Hathataga Creek is sourced by a spring complex located downgradient of a
seasonal lake, Hathataga Lake. It represents an example of
groundwater-fed headwater streams in mountain regions. The spring
complex consists of three separate springs having different thermal
regimes, which are strongly influenced by the hydroperiod of Hathataga
Lake. When the lake is dry, the temperatures of the three springs are
equal and controlled by groundwater temperature in the catchment.
However, once the lake forms, following snowmelt, the temperature of the
spring receiving lake-influenced groundwater rises compared to other
springs. During the summer months, lake water level and the lake energy
balance determine the magnitude and temperature of the water flux from
the lake to the springs. Climate change will likely result in changes to
the conditions that control the hydroperiod of the lake, namely the
depth of snowpack, the timing of snowmelt, amounts of summer
precipitation, and lake-atmosphere energy exchange. Therefore,
groundwater-lake water interactions must be considered when predicting
future stream temperatures in these settings.

The energy balance of the stream reach below the headwater springs was
mainly controlled by shortwave and longwave radiation. However, stream
temperature decreased rapidly during snowfall events due to direct entry
of snowfall onto the stream surface and subsequent melting. Stream
temperature models are improved when the latent heat flux associated
with the melting of direct snowfall are included. This process is
especially relevant in winter months and in cold regions where summer
snowfall and hailstorms are common. Tracer tests indicated substantial
effects of hyporheic exchange, but its effects on stream temperature was
negligible implying that energy exchange by hyporheic processes played
insignificant role in this particular setting.

Further case studies should be conducted on both seasonal and perennial
lakes to assess the effect of groundwater-lake water interactions on
stream temperatures downgradient. For the assessment of climate-change
impacts on headwater stream temperatures, it will be beneficial to use
physically-based catchment models including snow accumulation and melt,
energy balances of streams and lakes, and subsurface energy transfer
between streams and lake.

\textbf{Acknowledgement}

We thank Jesse He, Brandon Hill, Evan Sieben, and numerous others of
assistance with field work; Edwin Cey and Jason Leach for constructive
comments on an earlier draft, John Pomeroy and the University of
Saskatchewan's Cold Water Laboratory for sharing hydro-meteorological
data, and the Fortress Mountain Resort and the University of Calgary's
Biogeoscience Institute for logistical supports. Funding for this study
was provided by Canada First Research Excellence Fund (Global Water
Futures), Alberta Innovates (Water Innovation Program), Natural Sciences
and Engineering Research Council, and the Graduate Students Association
of the University of Calgary.\selectlanguage{english}
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