SPATIAL AND TEMPORAL PATTERNS OF TEMPERATURE
IN THE HORSEFLY RIVER
by
Moshi Arthur Charnell
B.Sc., The University ofVictoria, 1998

THESIS SUBMITTED IN PARTIAL FULFILMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
ill

NATURAL RESOURCES AND ENVIRONMENTAL STUDIES

© Moshi Charnell, 2001
THE UNIVERSITY OF NORTHERN BRITISH COLUMBIA
November 2001

UNIVEf-tSITY Or

All rights reserved. This work may not be reproduced
in whole or in part, by photocopy or other means,
without the permission of the author.

RTH

BRJTISH COLUMBIA
LIBRARY
Prince George, BC

ABSTRACT

Water temperature influences the ecology of a stream. Management practices, such as dear-cutting
and land clearing for agriculture, have been associated with increases in the expected summer stream
temperature at a variety of spatial and temporal scales in other systems.

As a result, landscape

disturbances within the Horsefly River's Watershed would be expected to change the ecology of the
Horsefly River. The major difference between this study and most other studies is that the Horsefly
Watershed (-2300 km~ is at least five times larger than watersheds studied previously.
This study assessed the temporal patterns of stream temperature by evaluating trends in the Horsefly
River's weekly water temperature near the Horsefly Townsite from July 1 to September 30 over a 45year period (1955 - 1999).

Possible trends in ground and ground water temperatures within the

Horsefly Watershed were also evaluated.

Assessing the influence of landscape disturbances on the

Horsefly River's temperature near the Horsefly Townsite were inferred from a high spatial and
temporal resolution environmental survey conducted within the Horsefly Watershed from July 1 to
September 30, 2000.
Weekly averages of daily the stream temperature statistics (maximum, average, minimum, range) were
decomposed into a meteorological component (weekly air temperature), a hydrological component
(weekly stream discharge) and a yearly trend component using multiple linear regression analysis.
There were discernible yearly trends in the Horsefly River's temperature near the Horsefly Townsite
that were independent of the meteorological and hydrological components. There was also a potential
trend in ground and ground water temperature (0.033 oC/year) within the Horsefly Watershed.

The high-resolution environmental survey suggested that most (-95%) of the recent (post 1955)
landscape disturbances did not affect the Horsefly River's water temperature near the Horsefly
Townsite.

As well, the trends in the weekly averaged daily stream temperature statistics could be
11

explained by the potential increasing trend in ground and ground water temperature. All the results
from this research are consistent with the hypothesis:

annual changes in the Horsefly River's

temperature near the Horsefly Townsite from 1955 to 1999 were a direct consequence of climate
warming and not likely related to landscape disturbances within the Horsefly Watershed. Management
of the Horsefly River should consider trends in long-term climate change as an indicator for changes
in the ecology of the river.

111

TABLE OF CONENTS
ABS1'RACf ....................................................................................................................................................................... ii
TABLE OF CONENTS ............................................................................................................................................... iv
LIST OF TABLES ........................................................................................................................................................... v
LIST OF FIGURES ....................................................................................................................................................... vi
ACKOWLEDGEMENTS ......................................................................................................................................... viii
1 IN'TRODUCTION .................................................................................................................................................. 1
1.1
Research Objectives ................................................................................................................................... 3
1.2
Literature Review ........................................................................................................................................ 3
1.2.1 Horsefly Watershed ............................................................................................................................ 9
1.2.1.1 Environmental Conditions of the Horsefly Watershed ............................................... 10
1.2.1.2 Historical Disturbances within the Horsefly Watershed .............................................. 21
2 METHODS .............................................................................................................................................................. 23
2.1
Defining the Horsefly Watershed ........................................................................................................ 23
2.2
Historic Stream Temperature Data ..................................................................................................... 25
2.3
Meteorological and Hydrological Data............................................................................................... 26
2.4
Snow Pack Data ........................................................................................................................................ 31
2.5
MOELP Air/Stream Temperature Data ........................................................................................... 33
2.6
Summer 2000 Survey ............................................................................................................................... 35
2.7
Multiple Linear Regression Analysis ................................................................................................... 39
3 RESULTS .................................................................................................................................................................. 47
3.1
Descriptive Analysis of the Summer 2000 Spatial Variability ...................................................... SO
3.2
Multiple Linear Regression Analysis of the Historic Stream Temperature .............................. 52
3.2.1 Partitioning the Variance of Stream Temperature ................................................................... 60
3.2.2 Stream Temperature's Associations with Air Temperature .................................................. 66
3.2.3 Stream Temperature's Associations with Stream Discharge ................................................ 71
3.2.4 Stream Temperature's Associations with the Yearly Trend Variable ................................. 76
4 DISCUSSION ......................................................................................................................................................... 83
5 CONCLUSION ...................................................................................................................................................... 92
6 LITERATURE CITED ........................................................................................................................................ 93

1V

LIST OF TABLES
Table 2-1 --- Environment Canada Oimate Stations in the vicinity of the Horsefly Townsite
that provided data for this study .......................................................................................................... 28
Table 2-2 --- Environment Canada Hydrologic Stations that provided data for this study.................... 30
Table 2-3 --- MOELP snow survey locations that provide data for this study ............................................. 32
Table 2-4--- MOELP air/ stream temperature monitoring locations that are within the
1-Iorsefly Watershed ................................................................................................................................. 34
Table 2-5 ---Summer 2000 stream temperature survey locations .................................................................... 36
Table 3-1 ---Simple correlation coefficients and the correlation indexes for the weekly
averaged daily air temperature statistics from Quesnel Airport associated with the
climate stations that were within 10 km of the Horsefly Townsite ............................................ 53
Table 3-2--- Simple correlation coefficients and the correlation indexes for weekly averaged
daily stream temperature statistics from Horsefly Townsite associated with weekly
averaged daily air temperature statistics from Quesnel Airport.................................................. 54
Table 3-3 ---Dates where non-linear bias was observed in the multiple linear regression
analyses along with the type of bias ..................................................................................................... 55
Table 3-4--- Dates where the Durban-Watson statistic indicated that there was significant
serial autocorrelation in the multiple linear regression model... ................................................... 59

v

LIST OF FIGURES
Figure 1-1 --- Map of British Columbia with reference to Horsefly and other cities .................................... 2
Figure 1-2 ---Map of features in the Horsefly area............................................................................................... 10
Figure 1-3 ---Locations of the data monitoring locations used to summarise environmental
conditions in the Horsefly area ............................................................................................................. 12
Figure 1-4 --- Box plots of the daily maximum air temperature at Horsefly Lake/ Grohs Lake
for each day between July 1 and September 30 ............................................................................... 13
Figure 1-5 ---Box plots of the daily minimum air temperature at Horsefly Lake/ Grohs Lake
for each day between July 1 and September 30............................................................................... 14
Figure 1-6--- Box plots of the daily air temperature range at Horsefly Lake/ Grohs Lake for
each day between July 1 and September 30...................................................................................... 15
Figure 1-7 --- Box plots of the total daily precipitation at Horsefly Lake / Grohs Lake for each
day between July 1 and September 30................................................................................................ 16
Figure 1-8--- Box plots of the daily average stream discharge at Horsefly River above
McKinley Creek for each day between July 1 and September 30............................................... 17
Figure 1-9 --- Box plots of the daily maximum stream temperature at Horsefly River near
Horsefly Townsite for each day between July 1 and September 30........................................... 18
Figure 1-10 --- Box plots of the daily minimum stream temperature at Horsefly River near
Horsefly Townsite for each day between July 1 and September 30........................................... 19
Figure 1-11 --- Box plots of the daily stream temperature range at Horsefly River near Horsefly
Townsite for each day between July 1 and September 30............................................................ 20
Figure 1-12--- Recorded forested area that has been used for forestry activities and/or has
been disturbed by fire in the Horsefly Watershed .......................................................................... 22
Figure 2-1 ---Horsefly Watershed boundary .......................................................................................................... 25
Figure 2-2--- Map of the Environment Canada climate stations that were within 10 km of the
Horsefly Townsite .................................................................................................................................... 29
Figure 2-3 ---Map of the Environment Canada stream discharge monitoring locations that
were within the Horsefly River Watershed ....................................................................................... 31
Figure 2-4--- Map ofMOELP snow/water equivalent monitoring locations that are within the
Horsefly Watershed................................................................................................................................. 33
Figure 2-5--- Map ofMOELP air/stream temperature monitoring locations that are within the
Horsefly Watershed ................................................................................................................................. 35
Figure 2-6--- Summer 2000 environmental survey locations. Refer to Table 2-5 for
descriptions of each location ................................................................................................................. 38
Figure 3-1 --- Yearly averaged air temperature at Quesnel Airport against year with a linear
trend line ..................................................................................................................................................... 49
Figure 3-2--- Yearly averaged air temperture at Horsefly Lake/ Grohs Lake against year
with a linear tread line ............................................................................................................................. 50
Figure 3-3 --- Average stream temperature for the week centred on July 24 plotted against the
distance upstream from the Horsefly Townsite .............................................................................. 52
Figure 3-4--- Residuals from the multiple linear regression analysis of weekly averaged daily
stream temperature range for week centred on August 3 plotted against weekly
averaged stream discharge ...................................................................................................................... 56

Vi

Figure 3-5 ---Residuals from the multiple linear regression analysis of weekly averaged daily
maximum stream temperature for week centred on July 15 plotted against weekly
averaged stream discharge...................................................................................................................... 57
Figure 3-6 --- Estimates from the multiple linear regression analysis of weekly averaged stream
temperature range for week centred on August 3 plotted against weekly averaged
daily stream temperature range ............................................................................................................. 58
Figure 3-7 --- Residuals from the multiple linear regression analysis of weekly averaged daily
minimum stream temperature for week centred on July 31 plotted against the
yearly trend variable................................................................................................................................. 60
Figure 3-8 --- Partitioned variance in weekly averaged daily maximum stream temperature as a
result of the multiple linear regression models ................................................................................. 63
Figure 3-9--- Partitioned variance in weekly averaged daily minimum stream temperature as a
result of the multiple linear regression models ................................................................................. 64
Figure 3-10 --- Partitioned variance in weekly averaged stream temperature as a result of the
multiple linear regression models ......................................................................................................... 65
Figure 3-11 --- Partitioned variance in weekly averaged daily stream temperature range as a
result of the multiple linear regression models ................................................................................. 66
Figure 3-12--- Associations weekly averaged daily maximum stream temperature had with
weekly averaged air temperature.......................................................................................................... 68
Figure 3-13 --- Associations weekly averaged daily minimum stream temperature had with
weekly averaged air temperature .......................................................................................................... 69
Figure 3-14 --- Associations weekly averaged stream temperature had with weekly averaged air
temperature................................................................................................................................................ 70
Figure 3-15 --- Associations weekly averaged daily stream temperature range had with weekly
averaged daily air temperature range ................................................................................................... 71
Figure 3-16 --- Associations weekly averaged daily maximum stream temperature had with
weekly averaged stream discharge ........................................................................................................ 73
Figure 3-1 7 --- Associations weekly averaged daily minimum stream temperature had with
weekly averaged stream discharge........................................................................................................ 74
Figure 3-18 --- Associations weekly averaged stream temperature had with weekly averaged
stream discharge ....................................................................................................................................... 75
Figure 3-19 --- Associations weekly averaged daily stream temperature range had with weekly
averaged stream discharge...................................................................................................................... 76
Figure 3-20 --- Associations weekly averaged daily maximum stream temperature had with the
yearly trend variable ................................................................................................................................. 79
Figure 3-21 --- Associations weekly averaged daily minimum stream temperature had with the
yearly trend variable ................................................................................................................................. 80
Figure 3-22 --- Associations weekly averaged stream temperature had with the yearly trend
variable as a result. .................................................................................................................................... 81
Figure 3-23 ---Associations weekly averaged daily stream temperature range had with the
yearly trend variable................................................................................................................................. 82

Vtl

I

ACKOWLEDGEMENTS
Throughout the development of my thesis there have been many persons whose participation were
vital. Initially, and most importantly, was the financial support provided by Riverside Forest Products
(Riverside), Williams Lake Division. This support was administered under the direction of Philippe
Theriault and Gordon Chipman from Riverside; Ellen Petticrew, Chris Hawkins and Brian Guy from
the University of Northern British Columbia (UNBQ; and Pat Teti from the Ministry of Forests
(MOF), Williams Lake District In addition, financial support was provided by the FRBC - Slocan
Endowed Chair of Mi.xedwood Ecology and Management, Chris Hawkins. With support from these
people and the organizations they represent, the conception, development and completion of this
thesis were possible.
My thesis was data intensive and thanks go to the people who supplied data and those who assisted me
in collecting, compiling, and analyzing data. Using spatial data supplied by Riverside and MOF
together with technical assistance from Roger Wbeate, Scott Emmons and Robert Legg (UNBC's
Geographic Information Systems (GIS) Gurus), I was able to build a picture of the Horsefly
Watershed and design the a sampling survey. Incorporating my survey design with an existing Ministry
of Environment, Lands and Parks (MOELP), survey required data and field assistance from Rob
Dolighan, MOELP. Performing the environmental survey required further assistance from Riverside,
equipment provided by Mark Shrimpton and Peter Jackson from UNBC and labour from Kirstin
Campbell, who experienced some harsh conditions during the removal of all the field equipment.
Historical environmental surveys were key to my analysis and many peoples' foresight should be
acknowledged. These people work or worked within the International Pacific Salmon Commission
and Environment Canada and I assure them that their data was appreciated and put to good use.
Organizing and analyzing these data required the statistical expertise of Dieter Ayers and technical
support from Jean Wang, Patrick Mann and Peter Jackson. The GIS Lab and the High Performance
Computing Facility at UNBC were my homes away from home and I thank the other residents for
being such great company.
I would like to thank my supervising committee for treating me like I was a colleague. We approach
this research as a team and this made for an enjoyable research environment Chris Hawkins, Peter
Jackson, Mark Shrimpton, Steve Dewhurst, Gord Chipman and Pierre Beaudry are good people and
deserve my thanks. I would also like to thank my external supervisor, Steve MacDonald from Simon
Fraser University for his valuable comments on my thesis. His interest in my thesis topic made the
research more worthy.
Finally I would like to thank my dear friends Kevin Fort, Dieter Ayers and Kirstin Campbell for their
personal support. Sometimes the only thing that can clear your mind is a casual conversation with a
close personal friend.

V111

I

1

INTRODUCTION

The Horsefly River, located m the central interior of British Columbia (Figure 1-1), is important
habitat for seven fish species valued for both commercial and recreational use (Rob Dolighan 1, pers.
comm.). The Horsefly River Watershed is also important to the local tourism, agriculture, mining, and
forest industries.
Water temperature influences the ecology of a stream as it is the pnmary determinant of all
biochemical and physiological processes and has profound effects on animal behaviour (Patton, 1973;
Barton et al., 1985; Holtby, 1988; Johnson and Jones, 2000).

As a consequence, temperature will

determine habitat utilization of aquatic organisms including fish (Brown, 1970; Patton, 1973; Ringer
and Hall, 1975; Lynch et al., 1984; Davies and Nelson, 1994). According to historical records, the
Quesnel water system, of which the Horsefly River is a part, held the largest sockeye salmon

(Oncori!JnchtJS nerka) population for the Fraser River Valley in the early part of the 20th century and the
Horsefly River was apparently the primary spawning area for this fishery (Goodlad, 1956). In the
1960's, the International Pacific Salmon Commission expressed concern about the high temperatures
in the Horsefly River (Goodman, 1966; Vernon, 1966). As a result a cool water siphon was installed,
which drains the bottom of McKinley Lake and is activated during salmon spawning periods with high
stream temperature (Bell, 1963).

1

Rob Dolighan, September, 1999, Fisheries Biologist, Ministry of the Environment, Land and Parks
(MOELP), Rob.Dolighan@gems5.gov.bc.ca
1

Figure 1-1 ---Map of British Columbia with reference to Horsefly and other cities.

Landscape disturbances, such as clear-cut logging and land clearing for agriculture, have been
associated with increases in the expected summer stream temperature at a variety of spatial and
temporal scales within other study areas (Levno and Rothacher, 1967; Brown, 1970; Feller, 1981; Swift,
1982; Rishel et al., 1982; Lynch et al., 1984; Fowler et al., 1987; 1-Ioltby, 1988; Brownlee et al., 1988;
Beschta and Taylor, 1988; 1-Iosteder, 1991; Johnson, and Jones, 2000). The principal cause of this
temperature increase is attributed to an increase in a stream's exposure to direct solar radiation through
riparian vegetation removal (Barton et al., 1985; Beschta and Taylor, 1988; Sinokrot and Stefan, 1993).
The effect of landscape disturbances on stream temperature may therefore be an important issue in
fisheries management for the Horsefly River Watershed.

2

1.1

Research Objectives

Although there are many inter-relationships in watershed management (Meehan, 1991), this research
investigated on the temporal patterns of the Horsefly River's temperature near the Horsefly Townsite
and the possible effect of landscape disturbances and/ or climate warming on these patterns for the
summer (July 1 to September 30).

Temporal patterns of stream temperature were assessed by

evaluating trends in the Horsefly River's weekly water temperature near the Horsefly Townsite from
July 1 to September 30 over a 45-year period (1955 - 1999). Possible trends in snow accumulation and
ground and ground water temperatures within the Horsefly Watershed were also evaluated.

The

influence of landscape disturbances on the Horsefly River's temperature near the Horsefly Townsite
were inferred from a high spatial and temporal resolution environmental survey conducted within the
Horsefly Watershed from July 1 to September 30,2000.
1.2

Literature Review

Many studies have addressed the impact of landscape disturbances on stream temperature. Most of
the researchers focused on summer stream temperature, but some researchers have considered other
times of the year (Feller, 1981; Swift, 1982; Lynch et al., 1984; Holtby, 1988; Stefan and Sinokrot,
1993). Stream heating, cooling and the resulting temperature are a consequence of the interactions of
stream water with its environment.

Factors which have been considered influential on stream

temperature within a reach are: advection from upstream inflow; groundwater exchange and
precipitation; the absorption of short-wave and long-wave radiation; the emission of long-wave
radiation; evaporation and condensation; convection at the air-water interface; conduction with the
streambed; and the least significant, fluid friction (Brown, 1969; Hewlett and Fortson, 1982; Theurer et

al., 1984; Adams and Sullivan, 1989; Sullivan et al., 1990; Sinokrot and Stefan, 1993; Johnson and
Jones, 2000). If these factors can be accounted for, temperature at the downstream cross-section of a
reach should be predictable.

3

Studies of summer stream temperature can be divided into stream reach studies and watershed studies.
Stream reach studies are at the smaller end of the spatial scale and are capable of resolving impacts on
stream temperature at high (hourly and daily) temporal resolution (Brown, 1969; Patton, 1973; Barton
et al, 1985; Brownlee, 1988; Sullivan et al., 1990; Rashin and Graber, 1992; Davies and Nelson, 1994).
Watershed studies, in contrast, often consider larger spatial scales. The impacts on stream temperature
are resolved at low (weekly, monthly and yearly) temporal resolution (Levno and Rothacher, 1967;
Brown and Krygier, 1970; Feller, 1981; Hewlett and Fortson, 1982; Theurer et al., 1984; Lynch et al.,
1984; Fowler et al., 1987; Holtby, 1988; Beschta and Taylor, 1988;Johnson and Jones, 2000).
Many stream temperature statistics have been used to describe the temperature of a stream. Forest
practice regulations are primarily concerned with maximum stream temperatures (Caldwell et al., 1991)
and most studies have focused on statistics based on the daily maximum stream temperature. The
following is a short list of stream temperature statistics that have been used to describe the relationship
between landscape disturbances and/ or climate warming and stream temperature: daily maximum
(Burton and Likens, 1973; Brownlee et al., 1988; Gu et al., 1998), daily minimum (Burton and Likens,
1973; Brownlee et al., 1988), daily average (Gu et al., 1998), daily range (Feller, 1981; Brownlee et al.,
1988), 5-day averaged daily maximum (Bettinger and Johnson, 1998), weekly maximum (Levno and
Rothacher, 1967; Barton et al., 1985), weekly average (Stefan and Sinokrot, 1993), weekly averaged
daily maximum (Zwieniecki and Newton, 1999), monthly average (Goodman, 1966), monthly
averaged daily maximum (Levno and Rothacher, 1969; Brown and Krygier, 1970), yearly maximum
(Brown and Krygier, 1970; Feller, 1981; Caldwell et al., 1991 ), yearly maximum daily range (Feller,
1981), and the average daily maximum of the 10 warmest days of the year (Beschta and Taylor, 1988).
Relating the results between studies of stream temperature for different temperature statistics seemed
to be an impractical task. For example, a change in a daily average does not imply that a monthly
average has changed and a change in a monthly average does not imply that a particular daily average

4

has changed.

Therefore, it was proposed that, in general, landscape disturbances and/ or climate

warming affect stream temperature at a variety of time scales.
The maJOr direct causal link between landscape disturbances and changes in summer stream
temperature is universally accepted to be the loss of riparian vegetation (Levno and Rothacher, 1967;
Brown, 1970; Patton, 1973; Holtby, 1988; Larson and Larson, 1996).

The reduction in riparian

vegetation increases a stream's exposure to solar radiation, thereby increasing the amount of energy
received by the stream and resulting in increased stream temperature.

By prescribing adjacent

streamside buffers strips, in which there is minimal forest removal, the impact of human induced
landscape disturbances on stream temperature can be reduced (Hewlett and Fortson, 1982; Auble,
1991; Osborne and Kovacic, 1993; Davies and Nelson, 1994). Designing buffer strips that maintain

aquatic ecosystem integrity while allowing development activities have been approached using an
assortment of site-specific factors, such as elevation, stream size and groundwater inflow. (Sullivan et

al., 1990; Rashin and Graber, 1992; Osborn and Kovacic, 1993; Anonymous, 1995; Larson and
Larson, 1996).
Other causal links between landscape disturbances and stream temperature, which have been
hypothesised, are the general loss of vegetative ground cover and the construction of roads and ditches
(Hewlett and Fortson, 1982; Beschta and Taylor, 1988; Johnson and Jones, 2000). A loss of ground
cover will expose the ground to more solar radiation and may result in an increase in shallow ground
water temperature (Heath and Trainer, 1968; Taniguchi et al., 1999b; Johnson and Jones, 2000). This
heated shallow ground water may flow into a stream and cause an increase in stream temperature
(Patton, 1973; Hewlett and Fortson, 1982). Also a loss of vegetation will reduce evapotranspiration,
thereby increasing ground water levels and possibly creating surface water flow which may be exposed
to solar radiation (Brown, 1970; Lynch et al., 1984; Chamberlin et al., 1991). Roads and ditches may
impede the flow of cool groundwater into a stream or bring the groundwater to the surface thereby
5

exposing it to direct solar radiation (Beschta and Taylor, 1988; Furniss et al., 1991). The magnitude of
these possible effects varies with environmental and physical conditions as well as when and where the
effect is measured (Barton et al., 1985; Theurer et al., 1984; Beschta and Taylor, 1988; Adams and
Sullivan, 1989; Zwieniecki and Newton, 1999).
Forests generally recover from disturbances so that the effect of vegetation removal on stream
temperature diminishes as the forests return to pre-disturbance conditions (Auble, 1991).

Smaller

streams have returned to pre-disturbance conditions within 6 years due to fast growing shrubs that can
shade these streams quickly (Brown and Krygier, 1970; Feller, 1981). Pre-disturbance conditions for
watersheds with larger streams have been assumed or shown to re-occur between 15 and 30 years
(Beschta and Taylor, 1988; Hostetler, 1991; Johnson and Jones, 2000). Recovery in terms of stream
temperature is not only dependent on the surrounding growing conditions and the vegetation species,
but also the streams' characteristics such as width and orientation.
The recovery of stream temperature to changes has a spatial and temporal dependency. An induced
change in stream temperature at a location is transmitted downstream and this temperature signal will
deteriorate over time (Burton and Likens, 1973; Beschta and Taylor, 1988; Stefan and Sinokrot, 1993;
Zwieniecki and Newton, 1999). It has been hypothesised that each stream has its own temperature
signature reflecting its specific environment and flow conditions (Zwieniecki and Newton, 1999). This
temperature signature is a curved increase in stream temperature that is a function of stream distance
from the headwaters.

An induced change in stream temperature will return to the stream's

temperature signature as the change is transmitted downstream and the deterioration of this induced
temperature change has an exponential decay rate as the water flows downstream (Ibeurer et al., 1984;
Adams and Sullivan, 1989).
Theoretically, there is a tendency for daily average stream temperature to converge to daily average air
temperature as water flows downstream (Ibeurer et al., 1984; Adams and Sullivan, 1989; Sinokrot and
6

Stefan, 1993; Zwieniecki and Newton, 1999).

Under the assumption of steady state flow, this

condition is called the equilibrium condition or thermal equilibrium. A stream in thermal equilibrium
has very little thermal memory and is only reacting to a very localized environment and as a result
upstream disturbances in the temperature signature are virtually undetectable (Adams and Sullivan,
1989).
Climate warming may cause increases in stream temperature (Stefan and Sinokrot, 1993; Amell, 1996;
Pilgrim, et al, 1998; Foreman et al., 2001 ). The effect of climate change has been examined through
the direct association air temperature has with stream temperature. An increase in air temperature
across years implies an increase in stream temperature for the same period (daily, weekly, monthly,
yearly) (Stefan and Sinokrot, 1993; Amell, 1996; Pilgrim, et al, 1998). There is evidence that variations
in climate produce changes in ground and ground water temperatures (Pollack and Chapman, 1993;
Taniguchi et al., 1999a) and as a consequence may change stream temperature, but a review of the
literature did not find a direct relationship between trends found in ground and ground water
temperatures induced by climate change and trends in stream temperature.
Environmental variables that have been used to describe stream temperature patterns include: air
temperature, stream discharge, radiation, ground water exchange, wind, humidity and characteristics of
the stream channel and surrounding landscape (Brown and Krygier, 1970; Theurer et al., 1984;
Gulliver and Stefan, 1986; Beschta and Taylor, 1988; Adams and Sullivan, 1989; Mackey and Berries,
1991; Stefan and Preud'homme, 1993; Davies and Nelson, 1994). Air temperature is highly correlated
with stream temperature and has been used as a predictor for stream temperature (Goodman, 1966;
Mackey and Berrie 1991; Stefan and Preud'homme, 1993). Although there is very little heat exchange
or generation at the air/water interface (Brown, 1969; Beschta and Taylor, 1988), both factors have
similar daily and seasonal temperature patterns in response to solar radiation (Adams and Sullivan,
1989).

As a result, air temperature has been used to explain variation in stream temperature that

7

cannot be explained by changes in landscape characteristics (Brown, 1969; Theurer et al., 1984; Holtby,
1988; Hosteder, 1991; Rashin and Graber, 1992; Johnson and Jones, 2000). Air temperature can be
used as an indicator for regional climate conditions and has been considered independent of local
landscape disturbances (Beschta and Taylor, 1988; Johnson and Jones, 2000).
Air temperature has also been used as an indicator for ground or ground water temperature (Oke,

1987; Adams and Sullivan, 1989). Under the assumption of no annual trend in air temperature, the
ground and ground water temperature five metres below the surface is nearly a steady constant with a
value that is near the yearly averaged air temperature (Adams and Sullivan, 1989). An implication of
the possible association between yearly averaged air temperature and ground water temperature is that
any detectable long-term trends in yearly averaged air temperature maybe mimicked in ground and
ground water temperatures (Pollack and Chapman, 1993; Taniguchi et aL, 1999a). Annual variation in
air temperature is dampened as the heat is transmitted into the ground (Heath and Trainer, 1968;

Pollack and Chapman, 1993).
Stream discharge has been shown to have an inverse (Goodman, 1966; Brown, 1969; Hockey et al,
1982; Barton et al, 1985) or direct negative (Theurer et al., 1984; Holtby, 1988; Hosteder, 1991)
association with stream temperature along a stream during the summer months. Both associations
state that an increase in stream discharge is associated with a decrease in stream temperature. Stream
discharge is a variable that can be controlled through direct management (dams, weirs, siphons, etc.)
and it has been proposed that stream temperature could be managed through the regulation of stream
discharge (Gu et al., 1998). Releasing water from reservoirs during periods of low stream discharge
may reduce or maintain stream temperature (Foreman et al., 2001).

Stream temperature is a complex physical phenomenon that varies with space and time. Empirical
approaches have been used to account for variation in stream temperature and have defined the
variation that can be associated with changes in the landscape by removing the variation that cannot be
8

associated with the landscape (Beschta and Taylor, 1988; Hosteder, 1991). Air temperature and stream
discharge have been used to explain variation in stream temperature and have been considered fairly
independent of small changes in the landscape (Fowler et al., 1987; Beschta and Taylor, 1988). An
empirical approach for describing spatial and temporal patterns of stream temperature may be
appropriate.
1.2.1

Horsefly Watershed

The Horsefly River enters the main arm of Quesnel Lake from the south (Figure 1-2) and contributes
the majority of the lake's inflow with a mean annual discharge of 30 m 3 / s. The main river system is
approximately 98 km in length and originates in the Quesnel Highlands. A 10 m high waterfall, Black
Canyon Falls, located 55 km from Quesnel Lake obstructs further upstream movement for migrating
fish and another waterfall located in the Upper Horsefly River obstructs movement of resident fish.
For the purposes of this study, the Horsefly Watershed will be the area drained above the Horsefly
Townsite (Figure 1-3). This area covers approximately 2300 km2 with an elevation range from about
700 m to 2500 m.

The following biogeoclimatic zones are represented in the watershed: Alpine

Tundra (A1), Engelmann Spruce - Subalpine Fir (ESSF), Interior Cedar- Hemlock (ICH), Sub Boreal Spruce (SBS) and Sub - Boreal Pine Spruce (SBPS) (MacKinnon et al., 1992). The Horsefly
River above the Horsefly Townsite has a general east-west orientation and most of its major tributaries
drain south to north. The eastern tributaries are predominandy fed by melting snow, whereas the
western tributaries drain wedands and lakes.

9

Historic Stream
Temperature
Monitoring
Location

10

0

10

20 Kilometers

~~~~

Figure 1-2 --- Map of features in the Horsefly area.

1.2.1.1

Environmental Conditions of the Horsefly Watershed

For interior British Columbia, the Horsefly area has an extensive history of au: temperature,
precipitation, stream discharge and stream temperature data collection and a good inventory of historic
land-use. The climate station, Horsefly Lake / Grohs Lake (Figure 1-3), recorded data from July 1 to
September 30 for the years 1950-61, 83, 84, and 1987-1999. The daily maximum air temperature
(Figure 1-4) at this station peaked around 25 oc in late July; declined until the beginning of September
and then was replaced with noisy oscillations.

The daily minimum air temperature (Figure 1-5)

exhibited a similar pattern except that the initial increase was shallower, the peak was around 9 oc
possibly a few weeks later than the peak in daily maximum air temperature and the oscillations were
n01sy. The daily air temperature range (Figure 1-6) exhibited no trend across the season and had a
10

general range of 17 oc. Daily total precipitation (Figure 1-7) exhibited periodicity with an approximate
interval of two weeks. For most of the days the median was zero and the largest precipitation events
occurred in August and the precipitation events in late September were sporadic.
The stream discharge station, Horsefly River above McKinley Creek (Figure 1-3), recorded data during
July 1 to September 30 for the years 1955-58, and 1964-1999. The daily average stream discharge
(Figure 1-8) at this station had a well-defined decay that started the season around 45 m 3I s and ended
the season around 10 m 3I s. There was also a general decay in the variability of daily average stream
discharge until around mid-August. After mid-August this variability had a slight increase until the
beginning of September and afterwards there was a slight decrease. Using the few years of stream
discharge data (1945-59) recorded on the Horsefly River at Horsefly, which was recorded at the same
location as the historic stream temperature (Figure 1-3), it was estimated that there was a 40% increase
in stream discharge between these sites. This site also exhibited a very similar seasonal pattern to
Horsefly River above McKinley Creek.
The stream temperature station, Horsefly River near Horsefly Townsite (Figure 1-3), generally
recorded data during July 1 to September 30 for the years 1946, 1953-90 and 1995-1999. Each of the
three stream temperature statistics, daily maximum (Figure 1-9) and minimum (Figure 1-1 0) stream
temperature and daily stream temperature range (Figure 1-11), had prominent patterns from July 1 to
September 30. The daily maximum stream temperature during the period rose from 13 oc in early July
to a peak of 18 oc in mid-August and decreased to 10 oc at the end of September. The daily minimum
stream temperature had a similar pattern that started and ended the period at 11 oc and 8 oc
respectively with a peak of 14 oc that occurred two weeks earlier than the peak in the daily maximum
stream temperature. The pattern of daily stream temperature range was also apparent in its variability.
This pattern started and ended at 2 oc with a peak of 3 oc in mid-August The variability in daily
stream temperature range also increased then decreased with the highest variation in August.
11

10

~~~~

0

10

20 Kilometers

Figure 1-3 ---Locations of the data monitoring locations used to summarise environmental
conditions in the Horsefly area. The Horsefly Watershed Boundary is indicated by the dark solid
line.

12

35 . -------------------------------------------------------,

30 -

()

25

0

~

:J

iii

20

Qj

a.

E
Q)
t,_

15

<(

E
:J
E
·x
m
:2

10
5

Jul 1

Jul8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-4 ---Box plots of the daily maximum air temperature at Horsefly Lake/ Gruhs Lake for
each day between July 1 and September 30. Displayed are the medians (bars), inter-quartile ranges
(boxes), either the 1.5 times the inter-quartile ranges or the data minimums/ maximums (whiskers)
and outliers (points).

13

20 . -------------------------------------------------------,

15 -

0

~

10

0

~

::s

n;

Q;
a.
E
Q)

1.._

<(

E
::s
E

·c:
~

5

.llJil

0

-5

~

Jul1

~

Jul8

Jul15

Jul22

Jul29

Aug 12
Aug 26
Sep 9
Sep 23
Aug 5
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-5 ---Box plots of the daily minimum air temperature at Horsefly Lake / Gruhs Lake for
each day between July 1 and September 30. Displayed are the medians (bars), inter-quartile ranges
(boxes), either the 1.5 times the inter-quartile ranges or the data minimums / maximums (whiskers)
and outliers (points).

14

35

30

()

25

0

Q)

C)

r:::

t\l

a-::

20

~

::J

~
Q)

15

II

Q_

E
Q)

1..._

<(

10

5

Jul1

Jul8

Jul 15

Jul22

Jul 29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-6 ---Box plots of the daily air temperature range at Horsefly Lake / Grohs Lake for each
day between July 1 and September 30. Displayed are the medians (bars), inter-quartile ranges
(boxes), either the 1.5 times the inter-quartile ranges or the data minimums/ maximums (whiskers)
and outliers (points).

15

45
40
35

E
E
c::

0

30
25

~

:g_
"(3

20

~

a..

15
10
5 -

Jul 1

Jul8

Jul 15

Jul22

Jul 29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-7 ---Box plots of the total daily precipitation at Horsefly Lake/ Grohs Lake for each day
between July 1 and September 30. Displayed are the medians (bars), inter-quartile ranges (boxes),
either the 1.5 times the inter-quartile ranges or the data minimums/maximums (whiskers) and
outliers (points).

16

150 --------------------------------------------------------.

125

~ 100
E

M

Q)

~
~
0

75 -

<I)

i:5

E

m so

Ci5

! ! I.Iii!! I!!!Ill

25

!!!!! !!! !!!! !!!
Jul 1

Jul8

Jul15

Jul22

Jul29

Aug 5

!!

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-8 ---Box plots of the daily average stream discharge at Horsefly River above McKinley
Creek for each day between July 1 and September 30. Displayed are the medians (bars), interquartile ranges (boxes), either the 1.5 times the inter-quartile ranges or the data minimums/
maximums (whiskers) and outliers (points).

17

30 --------------------------------------------------------.

25
(.)

0

~

::l

~
Q)

20

a.

E
Q)

1-

E
co

15

~

U5

E
::l
E
·x
co

10 -

~

5

Jul 1

Jul8

Jul 15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-9 ---Box plots of the daily maximum stream temperature at Horsefly River near Horsefly
Townsite for each day between July 1 and September 30. Displayed are the medians (bars), interquartile ranges (boxes), either the 1.5 times the inter-quartile ranges or the data minimums/
maximums (whiskers) and outliers (points).

18

30 --------------------------------------------------------,

25 ()

0

:;
Q)

20

iii

Q;
a.
E
Q)

I-

15

I.i!jl !

E
Ill

~

U5

E
:::J
E

10

1

·c:

~

5

Jul 1

Jul8

Jul 15

Jul22

Jul 29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-10 --- Box plots of the daily minimum stream temperature at Horsefly River near Horsefly
Townsite for each day between July 1 and September 30. Displayed are the medians (bars), interquartile ranges (boxes), either the 1.5 times the inter-quartile ranges or the data minimums/
maximums (whiskers) and outliers (points).

19

15 .-------------------------------------------------------,

0

0

:g,
c::

10

Ill

0:::
~

:I

"§
(I)

a.

E

(I)

I-

E

Ill

~

5

li)

Jul 1

Jul8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Date

Figure 1-11 --- Box plots of the daily stream temperature range at Horsefly River near Horsefly
Townsite for each day between July 1 and September 30. Displayed are the medians (bars), interquartile ranges (boxes), either the 1.5 times the inter-quartile ranges or the data minimums/
maximums (whiskers) and outliers (points).

20

1.2.1.2

Historical Disturbances within the Horsefly Watershed

Recorded disturbances to the Horsefly Watershed include mads, agriculture, mining, fire, and forestry.
Roads have been constructed throughout the watershed; agriculture and mining were contained in the
lower and middle reaches; fire and forestry were mostly contained in the middle and upper reaches
(Figure 1-12). Agriculture and mining were well established prior to 1938 (Jackson, 1938) and the
recorded industrial forestry activities started after a large wild fire in 1961. This major fire disturbed
just over 5 percent of the watershed. Following this fire, forestry activities remained fairly constant
with an annual disturbance of approximately 0.4 percent of the forested area pet: year. Agricultural
lands adjacent to the Horsefly Rivet: are in the process of being planted with woody vegetation.

21

10

0

10

........

~~~~

20 Kilometers

Figure 1-12--- Recorded forested area that has been used for forestry activities and/or has been
disturbed by fire in the Horsefly Watershed. These data were extracted from the 1999 Ministry of
Forests (MOF) forest cover database.

22

2

METHODS

The following methodology was employed to assess the Horsefly River's temperature patterns near the
Horsefly Townsite:
1) Define the Horsefly Watershed and extract land-based data.

Determine when and where

landscape disturbances have occurred (Section 2.1 ).
2) Compile the existing stream/ air temperature, stream discharge and snow accumulation data for the
Horsefly area. (Sections 2.2, 2.3, 2.4, 2.5)
3) Collect and describe high spatial and temporal resolution meteorological and stream temperature
data to account for short-term variation within the Horsefly Watershed (Sections 2.6, 3.1).
4) Perform linear regression analysis on snow accumulation and yearly averaged air temperature to
account for possible long-term variation in the quantity and quality of cold-water sources (Section 3).
5) Perform multiple linear regression analysis on the historic data to account for long-term variation
in the Horsefly River's temperature (Section 3.2).
2.1

Defining the Horsefly Watershed

The historical Horsefly River temperature sampling location was used as a reference point for all the
spatial analysis and as such defined the Horsefly Watershed (Figure 2-1). Ibe Horsefly Watershed was
defined as all locations for which water could flow from that location to this stream temperature
sampling location. This delineation was performed using the Digital Elevation Model and the existing
surface water locations (Band, 1986; Fairfield and Leymarie, 1991; Desmit and Glover, 1996; ESRI,
1996).
23

The Horsefly Watershed boundary was used to subset the MOF forest cover data. Descriptions of the
MOF forest cover data are found at http: //www.for.ggv.bc.ca/ resinv/reports/rdd/rdd.htnl. These
data were acquired through the Williams Lake District office for the MOF and were used to describe
the landscape conditions in the Horsefly Watershed (Section 1.2.1). It was assumed that the Horsefly
Watershed was defined as the area for which landscape changes could have an effect on historic
stream temperature near the Horsefly Townsite.

2

Date last accessed: July, 2001
24

10

0

10

20 Kilometers

~~~~

Figure 2-1 --- Horsefly Watershed boundary indicated by the dark solid line.

2.2

Historic Stream Temperature Data

The historical Horsefly River temperature data were collected for most years in the summer (July 1 to
September 30) near the Horsefly Townsite (Figure 1-2) and summarized as daily maximums and daily
minimums ('C). These data were collected in 1946, 1953-90 and 1995-1999. The International Pacific
Salmon Commission collected the years from 1946 to 1990 and MOELP collected the years 19951999. These data were acquired through the Williams Lake District office of the MEOLP and defined
the minimum temporal scale (a day) and the season (July 1 to September 30) that could be used in the
analysis as well as the spatial scale (all area that drains into this location).

25

The daily maximum and daily minimum stream temperature where extracted direcdy from the data
records. The average of the daily stream temperature extremes (maximum and minimum) and the
daily stream temperature range were computed from the extracted data.

The four daily stream

temperature statistics were then summarized as weekly running averages where consecutive weeks
have six days in common. For example, week 1 is July 1 to July 7; week 2 is July 2 to July 8 and so on
until week 86 is September 23 to September 30. Each week was denoted by its centre date (week 1 is
Jul 4, week 2 is Jul 5, ... , week 86 is Sep 27). A weekly average was computed only if all seven daily
values were available. The weekly stream temperature statistics used to analyse the historic stream
temperature signal using multiple linear regression analysis were:
1) Weekly averaged daily maximum stream temperature.
2) Weekly averaged daily minimum stream temperature.
3) Weekly averaged average of the daily stream temperature extremes (weekly averaged stream
temperature).
4) Weekly averaged daily stream temperature range.
These weekly stream temperature statistics were used to describe long-term changes in the Horsefly
River's temperature near the Horsefly Townsite.
2.3

Meteorological and Hydrological Data

Environment Canada collects and compiles air temperature, precipitation and stream discharge data
for Canada and a subset was used for this study. More informacion about the Environment Canada
monitoring stations can be found at http://scitech.pyr.ec.gc.ca/climhydro/main frames bc.htm3 and
the data were acquired through the regional BC Climate Services office of Environment Canada. The
3

Date last accessed: July, 2001

26

four climate stations used in this study were: Horsefly BCFS, Horsefly Lake Gruhs Lake, Moffat Creek
and Quesnel Allport (Table 2-1, Figure 2-2). Quesnel Allport is located near Quesnel (Figure 1-1).
Station 1093598 (Horsefly) was not used in this study since it only recorded one month of data
(September, 1961) within the period of interest.

Quesnel Allport was used as the single climate

indicator since it was the closest station that had recorded data during the entire period stream
temperature was recorded at Horsefly Townsite.
The daily maxtmum and daily tn1Illffium air temperatures where extracted directly from the data
records. The average of the daily air temperature extremes (maximum and minimum) and the daily air
temperature range were computed from the extracted data. The four air temperature statistics were
then summarized as weekly running averages for the period July 1 to September 30. This procedure is
detailed in Section 2.2.

The weekly averaged air temperature and the weekly average daily air

temperature range from Quesnel Allport were used in the multiple linear regression analyses.
The final air temperature statistic computed was yearly averaged average of the daily air temperature
e}..'tremes (yearly average air temperature). This statistic was used to indicate long-term climate changes
with implications to possible changes in ground and ground water temperatures for the Horsefly
Watershed. The trend in the yearly average air temperature was considered the hypothesised trend in
ground and ground water temperatures.

Trends in weekly averaged daily maximum/average

/minimum stream temperature determined from the multiple linear regression analyses were
compared with this hypothesised trend.
Since Quesnel Airport is approximately 107 km northwest from the Horsefly Townsite, its weekly and
yearly air temperature statistics were correlated with the three climate stations near the Horsefly
Townsite to demonstrate the appropriateness of using Quesnel Airport climate data as indicators of
climate at Horsefly Townsite.

27

Table 2-1 --- Environment Canada Climate Stations in the vicinity of the Horsefly Townsite
providing data for this study. Each station had records for daily maximum/minimum air
temperature ('C) and total precipitation (mm). This table displays the station ID, station name, Lat.
and Long. coordinates, elevation, approximate distance from the Horsefly Townsite, and years of
operation.

Elevation
(m)

Approximate
Distance (km)

Years of
Operation

121°25'

788

2

1961-62

52°20'

121°25'

785

2

1970-83

Horsefly Lake
Grohs Lake

52°22'

121°22'

777

8

1950-61,83,
84,87-99

1095195

Moffat Creek

52°14'

121°29'

945

9

1975-86

1096630

Quesnel Airport

53°2 1

122°31'

545

107

1946-99

Station ID

Station Name

1093598

Horsefly

52°20'

1093599

Horsefly BCFS

1093600

Latitude Longitude

28

10

0

10

~~~~

20 Kilometers

Figure 2-2 --- Map of the Environment Canada climate stations within 10 km of the Horsefly
'T'

.

J.0W11Stte.

The two stream discharge stations used in this study are: Horsefly River at Horsefly, Horsefly River
above McKinley Creek (Table 2-2, Figure 2-3). Horsefly River above McKinley Creek was used in the
multiple linear regression analyses. It was chosen as the reference location since it was located on the
mainstem of the Horsefly River and had recorded data for most of the years in which stre-am
temperature data were recorded near Horsefly Townsite. Horsefly River at Horsefly was at the same
location as the historical Horsefly River temperature monitoring location and was approximately 35

km downstream from Horsefly River above McKinley Creek.

29

The daily average stream discharge for the period July 1 to September 30 were extracted dit:ecdy from
the data records and summarized as running weekly averages (refer to Section 2.2).

The weekly

averaged stream discharge from Horsefly River above McKinley Creek was used as the hydrologic
indicator in the multiple linear regression analyses and correlated with weekly averaged stream
discharge &om Horsefly River at Horsefly to demonstrate that this site represented conditions near the
Horsefly Townsite.
Table 2-2 ---Environment Canada Hydrologic Stations that provided data for this study. Each
station had records for daily average stream discharge (m3 / s). This table displays the station ID,
station name, Lat. and Long. coordinates, basin area and years of operation.

Station ID
08KH007
08KH010

Station Name
Horsefly River
at Horsefly
Horsefly River above
McKinley Creek

Latitude Longitude

Basin
?

Area (km)

Years

52°20'

121°25'

2310

1945-59

52°18'

121 °03'

785

1955-58,
64-99

30

10

0

10

20 Kilometers

Figure 2-3 --- Map of the Environment Canada stream discharge monitoring locations within the
Horsefly River Watershed.

2.4

Snow Pack Data

MOELP collects and compiles snow pack data for British Columbia. These snow pack data were
available from http:/ / ,vww.elp.goY.bc.ca./ rib / wat / rfc / archive / historic.html 4 • The three snow survey
sites that were used in this study are: Horsefly Mountain, Black Mountain, and Boss Mountain Mine
(Table 2-3, Figure 2-4). Each station is contained in the Horsefly Watershed. The amount of snow
accumulation was the indicator for the quantity of available cold water for the Horsefly River. The
data are generally collected near the beginning of each month for January to June and also mid-month

31

for May and June. Water equivalent depth for the beginning of April and May were analysed using
linear regression analysis with a yearly trend variable as the predictor to assess possible changes in the
quantity of available cold water for the Horsefly Watershed.
Table 2-3 --- MOELP snow survey locations providing data for this study. Each station has records
for snow depth (em) and water equivalent (rom). This table displays the station ID, station name,
Lat. and Long. coordinates, elevation and years of operation.

Station ID
1C13A
1C13
1C20

4

Station Name
Horsefly
Mountain
Black
Mountain
Boss Mountain
Mine

Latitude Longitude

Elevation
(m)

Years of
Operation

52°20'

121°03'

1550

1969-99

52°20'

121°07'

1570

1961-82

52°06'

120°52'

1500

1968-98

Date last accessed: July, 2001
32

10

0

10

20 Kilometers

~~~~~

Figw:e 2-4 --- Map of MOELP snow /water equivalent monitoring locations within the Horsefly
Watershed.

2.5

MOELP Air/Stream Temperature Data

The seven air/ stream temperature survey sites used in this study are: Horsefly River at Bosk, Upper
Horsefly River, Horsefly River at Woodjam, Horsefly River at Townsite, Mackay River, McKusky
River and McKinley Creek (fable 2-4, Figure 2-5). These data were acquired through the Williams
Lake District office of the MEOLP. Horsefly River at Townsite (INS) is at the same location as the
historic stream temperature location and was used to update the historic temperature record. 1bese
sites were used in the summer 2000 survey (Section 2.6) to assess the spatial and short-term temporal
variability of stream temperature throughout the watershed.

33

Table 2-4--- MOELP air/stream temperature monitoring locations within the Horsefly Watershed.
Each station has records for daily maximum/average/minimum air/stream temperature ('C). This
table displays the station id, station name, Lat. /Long. coordinates, and years of operation.

Station ID
BSK
UHF

WDJ
TNS

Station Name
Horsefly River
atBosk
Upper Horsefly
River
Horsefly River
atWoodjam
Horsefly River
at Townsite

Latitude

Longitude

Years of
Operation

52°18'

121°02'

1994-99

52°26'

120°39'

1994-99

52°17'

121°17'

1994-99

52°20'

121°25'

1995-99

KAY

MacKay River

52°20'

120°38'

1994-99

KUS

McKusky River

52°21'

120°50'

1994-99

KIN

McKinley Creek

52°17'

121°02'

1994-2000

34

10

0

10

20 Kilometers

Figure 2-5 --- Map of MOELP air/ stream temperature monitoring locations within the Horsefly
Watershed.

2.6

Summer 2000 Survey

The two main focuses of this survey were to describe the Horsefly River's temperature signature and
to assess the influence of the two major lake-fed tributaries, McKinley Creek and McKusky River, on
this signature.

The main logistical constraint was that all data must be collected in the 2000 field

season (July 1 to September 30).

The variables measured were: air and stream temperature, solar

radiation, precipitation, and wind speed.

Due to the expense and time requirements for data

collection, ground and ground water temperatures; and stream characteristics were not measured. As
well it was anticipated that stream discharge would be accounted for at the existing stream discharge
data monitoring location, Horsefly River above McKinley Creek (fable 2-2, Figure 2-3).
35

All data were collected using low maintenance electronic automatic sampling equipment Most of the
equipment was borrowed from faculty at the University of Northern British Columbia. Equipment
was placed in the watershed and periodically checked throughout the summer season.

Riverside

Forest Products supplied a field assistant and covered all transportation requirements within the
watershed. Locations of the automatic sampling equipment were determined by considering access,
exposure, spatial resolution and incorporating the existing MOELP's air/stream temperature
monitoring locations (fable 2-4, Figure 2-5).

Table 2-5 ---Summer 2000 stream temperature survey locations. The table displays the station ID,
station name, an approximate distance upstream from the Horsefly Townsite, elevation and drainage
area.

Station ID
1
2a
2b
3
4
5
6a
6b
7
8

Station Name
Horsefly River
at Townsite
Horsefly River
above Moffat
Moffat Creek
at Mouth
Horsefly River
below Sucker
Horsefly River
atWoodjam
Horsefly River
in Agriculture
Horsefly River
atBosk
McKinley Creek
at Mouth
Horsefly River
below Prairie
Horsefly River
below Doreen

Distance Elevation
(km)
(m)

Drainage
Area( km 2 )

0

776

2182

1

778

1619

1

778

559

9

807

1578

15

828

1526

23

830

1398

34

842

792

34

842

449

42

895

769

51

899

712

36

Table 2-5 (continued)

Station ID
9a
9b
10
11a
11b
12a
12b
13a
13b
14a
14b

Station Name
Horsefly River
above McKusky
McKusky River
at Mouth
Horesfly River
below Wiskey Bridges
Upper Horsefly
River at Mouth
MacKay River
at Mouth
Upper Horsefly
River
MacKay
River
Upper Horsefly
River above Falls
Upper MacKay
River
Upper Horsefly
River Headwaters
MacKay River
Headwaters

Distance
(km)

Elevation
(m_l

Drainage
2
Area ( km j

61

920

352

61

920

314

67

983

317

72

1032

143

72

1032

144

79

1062

107

80

1183

120

89

1191

69

87

1254

55

98

1432

14

93

1382

12

37

10

0

10

20 Kilometers

Figure 2-6 ---Summer 2000 environmental survey locations. Refer to Table 2-5 for location detail.

Air/stream temperature were recorded approximately every 8 km along the Horsefly River (1, 2a, 3, 4,
5, 6a, 7, 8, 9a, 10), into the Upper Horsefly (11 a, 12a, 13a, 14a) and MacKay (11 b, 12b, 13b, 14b)
Rivers and at the major tributary junctions: Moffat Creek (2b), McKinley Creek (6b), and McKusky
River (9b) (Table 2-5, Figure 2-6).

Locations 1, 5, 6a, 9b, 12a and 12b employed Smart Reader

temperature data loggers (ACR Systems Incorporated, Surrey, Bq and the other stations employed
Hobo Optic Stowaways (Onset Instruments, Bourne, MA).

Solar radiation and precipitation were

recorded near locations 1, 6a/ 6b, and 11 a/ 11 b; and wind speed was recorded near location 6a/ 6b.
Solar radiation was measured with pyranometers (LI-COR, Lincoln, NE), precipitation was measured
with tipping buckets (Texas Electronics, Dallas, TX) and wind speed was measured with a wind
monitor (R.. M Young Company, Traverse Gty, Michigan). Campbell Scientific, Edmonton, AB, CR10

38

data loggers recorded the data from these measuring devices. Temperature was recorded as halfhourly values in degrees Celsius rq; solar radiation was recorded as half-hourly maximums in watts
per square metre ry.l /mJ; precipitation was recorded as half-hourly totals in millimetres (mm); and
wind speed was recorded as half-hourly averages in metres per second (m/s).
Stream temperature was used to describe the temperature signature of the Horsefly River and the
influences of the major lake-fed tributaries. Air temperature, solar radiation, precipitation, and wind
speed were used to assess the spatial variation in stream temperature. A few mistakes were made
during data collection, such as data logger malfuctions. The final dataset was viewed using a variety of
plotting techniques together with animations for describing the spatial patterns of the Horsefly River's
temperature above the Horsefly Townsite.
2. 7

Multiple Linear Regression Analysis

Multiple linear regression analysis decomposed the historic stream temperature signal at the Horsefly
Townsite into three components (Equation 1).
Equation 1 ---Multiple Linear Regression Model

Where;

y

was the stream temperature statistic rq

xj was the air temperature statistic rq

x2 was the stream discharge statistic (m / s)
3

X 3 was the yearly trend variable (year)

bo was the regression constant rq
39

b1

was the association between stream temperature and air temperature (C/ oq

b2 was the association between stream temperature and stream discharge (C / ( m 3 / s))

b3

was the association between stream temperature and the yearly trend variable (C/ year)

&

was random error (q

Each of these components is assumed to be linearly independent of each other. Air temperature
represented meteorological variability, stream discharge represented hydrological variability and the
yearly trend variable was used to define any trends in stream temperature. Since analysis required that
data be available for all the variables (stream temperature, July 1-September 30, 1946, 55-90, 95-99; air
temperature, 1946-99; stream discharge, 1955-58, 64-99), only July 1 to September 30 for the years
1955-58, 64-90, 95-99 could be considered.

Weekly averages of the daily values were chosen as the summary statistics used in the multiple linear
regression analysis.

Weekly averaged daily maximum/ minimum/ average stream temperature (Y 's)

were linearly regressed against:

1) Weekly averaged air temperature (X 1 )

2) Weekly averaged stream discharge (X 2 )

3) The yearly trend variable (X 3 )

Linearly regressing three stream temperature statistics against the same predictor variables allowed for
direct comparisons among the results. Similarly, weekly averaged daily stream temperature range was
linearly regressed against:

1) Weekly averaged air temperature range (X 1 )

40

2) Weekly averaged stream discharge (X 2 )

3) The yearly trend variable (X 3 )

The first step in this analysis was to verify the assumptions that data collected at Quesnel Airport (air
temperatt.Ire) and Horsefly River above McKinley Creek (stream discharge) represented conditions
near the Horsefly Townsite at a weekly time scale. The next step was to demonstrate that weekly
averaged air temperature and weekly averaged daily air temperatt.Ire range are the appropriate air
temperatt.Ire statistics as indicators of climate. These initial steps employed correlation analysis. The
multiple linear regression models were then estimated and the modelling assumptions tested using a
variety of techniques. The amount of variance in the stream temperatt.Ire statistics explained by each
of the models was then partitioned into the amount of variance each of the three components
explained. Finally, the measured associations the stream temperatt.Ire statistic had with air temperatt.Ire
statistic ( b1 ), stream discharge statistic (b2 ) and the yearly trend variable ( b3 ) were assessed for how
they change across the season (July 1 to September 30). The associations that stream temperatt.Ire had
with the yearly trend variable were also compared with a zero trend (0 oC/ year) and the hypothesised
trend in ground and ground water temperatt.Ires.
Correlation analysis consisted of computing the simple correlation coefficient and the correlation
indices for two variables.

The simple correlation coefficient measures the intensity of a linear

association between two variables. Values of this coefficient are between -1 and 1 where -1 and 1
indicate perfect linear associations, negative and positive respectively; zero indicates no linear
association; and other values indicate a degree of linear association, positive or negative.

The

correlation index describes the amount (proportion) of variability that two variables have in common
through a linear relationship (Zar, 1984). A1r temperatt.Ire recorded at Quesnel Airport and stream
discharge recorded at Horsefly River above McKinley Creek were, respectively, the air temperatt.Ire
41

and stream discharge indicators for the area near the Horsefly Townsite. Data from these sites were
correlated with the air temperature recording sites that were within 10 km of the Horsefly Townsite
(fable 2-1, Figure 2-2) and the stream discharge monitoring location, Horsefly River at Horsefly, to
demonstrate the appropriateness of using these sites as the air temperature and stream discharge
indicators for the area near the Horsefly Townsite.
Determining which air temperature statistic to associate with each of the stream temperature statistics
used correlation analysis. Each of the fow: weekly stream temperature statistics was correlated with
the four weekly air temperature statistics and a choice was made based on maximizing the correlation
index between a particular stream temperature statistic and the air temperature statistics as well as
retaining the ability to compare the multiple linear regression models for each of the stream
temperature statistics. To allow for direct comparisons between results from separate multiple linear
regression analyses, it is necessary that all variables be the same except the variable for which
comparisons are being made. Direct comparisons were made between the multiple linear regression
models for weekly averaged daily maximum/ average/ minimum stream temperature and as such a
single meteorological indicator was chosen for all three of these stream temperature statistics. The
weekly averaged daily stream temperature range was considered separately.
A multiple linear regress1on model has other assumptions besides the linear independence of the
predictor variables. Firstly, the model is assumed to be 'correct'. An implication of correctness is that
the residual error terms are independent, have an average of zero, have constant variance and are
normally distributed (Neter et al., 1990). The first assumption, the model is correct, is validated by the
other assumptions together with the idea that the model gives useful answers. If any of these implied
assumptions are violated then the model is deemed 'incorrect' and should be revised.

An iterative loop ensues when a model is chosen to predict a particular natural event, for example,

stream temperature. If the model violates an assumption then the model is revised and the process
42

starts again. If the model does not violate any assumption, the predictive capabilities of the model are
tested. If the model's predictions are not satisfactory, the model is revised and the process starts again.
Finally, if all the assumptions are met and the model performs satisfactorily, the loop ceases and the
model is accepted as 'correct'.
The assumption, the residual errors are independendy distributed, has been discussed by other stream
temperature researchers (Brown and Krygier, 1970; Hostetler, 1991).

Daily statistics of stream

temperature are highly autocorrelated with the previous days values (Brown and Krygier, 1970;
Hostetler, 1991 ). As a result, consecutive daily values of stream temperature can only be considered if
an autoregressive term is used as a predictor variable. Otherwise, the residual error terms will not be
independent.

The intention of this analysis was not to explain stream temperature using stream

temperature. The analysis was therefore performed using a series (running weeks) of multiple linear
regressions where each regression was intetpreted separately.

This methodology removes inter-

seasonal autocorrelation by considering a single value (weekly average) of stream temperature for each
season in each regression and then performing regression analysis for each week within the season.

The four sets of multiple linear regression analysis were performed and standard assumptions were
tested.

If any of the assumptions are violated, the model was deemed 'revisable'; otherwise, it was

'correct'.

The first assumption, linear independence of the predictor variables was tested using

tolerance values.

The next assumption, the residual errors are independent, was tested using the

Durban-Watson statistic. The next two assumptions, the residuals have an average of zero and have
constant variance, were assessed by visually inspecting residual plots for non-linear bias. The final
assumption, the residuals are normally distributed was tested using the Kolmogorov-Smimov
goodness of fit test. Whenever the model violated an assumption a possible solution was hypothesised
that could adjust the modeL It was expected that a simple model such as multiple linear regression

43

could not possibly capture the complexity of stream temperature dynamics at the watershed scale, yet
general results were attained with such a model.
In multiple linear regression analysis, if any combination of the predictor variables is intercorrelated,

not independent, the regression coefficients may not be assumed to reflect the association each
variable has with predicted the variable (Zar, 1984). The intercorrelation of the predictor variable is
often called multicollinearity or 'ill conditioning'.

Determining whether multicollinearity may be a

problem can be accomplished using the tolerance values (Neter et al., 1990; Wtlkinson et al., 1996).
Tolerance values are one minus the squared multiple correlation of a particular predictor variable with
the other predictor variables.

For each of the predictor variables in the multiple linear regression

analyses, the tolerance values were computed.

If the tolerance was less than 0.1, there was an

indication that multicollinearity may be a problem when interpreting the regression coefficients.
Serial autocorrelation is generally a problem when the process being modeled is a time sequence
(Draper and Smith, 1981).

By considering single weeks across years, the within year serial

autocorrelation was removed, but there might still be serial autocorrelation across years. To assess
serial autocorrelation across years, the data were entered into the analysis as a yearly sequence and the
Durban-Watson statistic was considered as a measure of serial autocorrelation. The Durban-Watson
was computed and compared with tabular values compiled by Draper and Smith (1981, page 164).
Statistically significant serial autocorrelation indicates that the linear yearly trend variable might not
fully account for the association that a particular stream temperature statistic has with the yearly trend
variable.

Non-linear bias was determined by visually examining plots of the residuals versus the predictor
variables and plots of the predicted versus the actual values. Curvature in these data plots indicates
non-linear bias (Draper and Smith, 1981). In total, 1032 plots were examined for non-linear bias. For
each of the four weekly stream temperature statistics, 86 plots of the residuals versus the weekly air
44

temperature statistic, 86 plots of the residuals versus the weekly average stream discharge and 86 plots
of the estimated versus the actual weekly stream temperature values were examined. Each of the 12
sets of 86 plots was examined as a sequence across the season and blocks of dates were formed that
exhibited non-linear bias. Detecting non-linear bias indicates the linear model does not fully account
for the relationships among the variables.
The assumption that the residuals are normal is required to assess the statistical validity of a multiple
linear regression model (Draper and Smith, 1981).

This assumption was tested using the

Kolmogorov-Smimov Goodness of Fit test (Zar, 1984).

The standardized residuals were tested

against the hypothesis that they were distributed normally with a mean of zero and a variance of one.
The multiple R squared represents the amount of variance explained by a multiple linear regression
model. This multiple R squared can then be partitioned into the amount of variance that each of the
predictor variables is explaining using Pratt's Measure (Thomas et al, 1998). Pratt's Measure for each
predictor variable is the product of its standardized regression coefficient and its simple correlation
with the predicted variable. For each stream temperature statistic, 86 multiple R squared values were
partitioned into the amount of variance explained by the air temperature statistic, weekly averaged
stream discharge and the yearly trend variable. This partition was used to assess the importance of
each predictor variable for describing stream temperature
For each of the sets of measured associations that the stream temperature statistics have with their
corresponding predictor variables, 86 regression coefficients were computed along with 95%
confidence intervals. The associations the stream temperature statistics have with the air temperature
statistics, stream discharge and the yearly trend variable for the four regression models across the
season Q"uly 1 to September 30) were used to describe the temporal patterns of the Horsefly River's
temperature near the Horsefly Townsite.

The associations these stream temperature statistics have

45

with the yearly trend variable were compared to a zero trend and the hypothesised trend in ground and
ground water temperatures.

46

3

RESULTS

For all results in this study, statistical significance was determined using a. = 0.05 and the general null
hypothesis is that there were no associations between the environmental variables and that these
variables exhibited no annual trends. The computational algorithms used to calculate the results were
executed using SYSTAT (v.8.0, SPSS Ltd., 1998). Graphical and animation display of these results
employed S-Plus (v.2000, MathSoft Inc., 1999) and Tecplot (v.8, Amtec, 1998) respectively.
For each of the three snow survey sites (fable 2-3, Figure 2-4), the yearly trend variable was not a
statistically significant predictor of the water equivalent depth for the beginning of April and May.
Yearly averaged air temperature at Quesnel Airport was found to have a moderate association with
yearly averaged air temperature at Horsefly Lake I Grohs Lake. The correlation coefficient and index
were 0.79 and 0.62 respectively (n=22). Moffat Creek (n=7) and Horsefly BCFS (n=13) had too few
years in common with Quesnel Airport for meaningful correlation analysis on an annual scale. Linear
regression of yearly averaged air temperature at Quesnel Airport against the yearly trend variable
yielded an association of 0.033 ± 0.009 oCiyear (n=SS) (Figure 3-1).

Based on the Kolmogorov-

Smimov goodness of fit test, the residuals were very close to normal (p-value = 0.91) and the DurbanWatson statistic (1.62) suggests that a linearly increasing function across years removes serial
autocorrelation. This association was statistically significant (p-value = 0.001) and the linear regression
model accounted for 21 % of the variation in the yearly averaged air temperature.
Linear regression of yearly averaged air temperature at Horsefly Lake I Grohs Lake against the yearly
trend variable yielded a non-significant association of 0.036 ± 0.019 ocl year (p-value = 0.08) (Figure 32).

Although this association was not statistically significant, presumably due to the small dataset

(n=22) and missing data from 1961 to 1987, the estimate was consistent with the trend at Quesnel
47

Airport. Examination of the trends in stream temperature considered the estimated trend in yearly
averaged air temperature (0.033 ± 0.009 oC/ year) to be the hypothesised trend in ground and ground
water temperatures (Section 3.2.4).

48

8
7
6
5
()

0

4

~

:::J

iii

3

E

2

Q;
c..
Cl)

I-

0
-1
~

1945

~

1950

1955

1960

1965

1970 1975
Year

1980

1985

1990

1995

2000

Figure 3-1 --- Yearly averaged air temperature at Quesnel Airport against year with a linear trend
line. The slope of the line is 0.033 oC/year. The years included are 1946 to 1999.

49

8
7

6
5
0

0

4

~

.3
~

3

E
Q)

2

Q)

c..

1-

0
-1
~

1945

~

1950

~

1955

1960

~

~

1965

1970

~

1975

1980

~

1985

1990

~

1995

2000

Year

Figure 3-2 --- Yearly averaged air temperature at Horsefly Lake / Grohs Lake against year with a
linear trend line. The slope of the line is 0.036 oC/year. The years included are 1951 to 1960 and
1988 to 1999.

3.1

Descriptive Analysis of the Summer 2000 Spatial Variability

The most striking result was the general linear increase in stream temperature as the water travelled
downstream (Figure 3-3).

This linear increase was observed for the half-hourly values, the daily

ma:cimum/ minimum/ average and the weekly averages of the daily statistics. The rate of increase was
variable throughout the season with an average of 0.075 oC/km, yet maintained a strong linear
relationship. As well, the rate of increase in the daily minimum was greater than the rate of increase in
the daily marimum and consequendy there was a decrease in the daily range in the downstream
direction.

so

This linear increase in stream temperature was disrupted by the tributary inflows at sites 6b (McKinley
Creek at Mouth) and 9b (McKusky River at Mouth).
generally 6 oc higher than the Horsefly River.

These two tributaries are lake-fed and were

Their influence was clearly perceivable at the

downstream sites 5 (Horsefly River in Agriculture), 7 (Horsefly River below Prairie) and 8 (Horsefly
River below Doreen). At sites 4 (Horsefly River at Woodjam) and 6a (Horsefly River at Bosk) the
influence of these lake-fed tributaries was unperceivable. The implications of these observations were
that the influence of McKinley Creek and McKusk-y River on the Horsefly River's temperature decay
downstream to a point where their influence was near zero.

51

25 .------------------------------------------------------.

20

w}b

()

w}b

0

~

~ 15
C»

a.
E
Q)

1-

10
a

5

-10

0

10

20

30

40

50

60

70

80

90

100

110

Distance Upstream from the Horsefly Townsite ( km)

Figure 3-3 ---Average stream temperature for the week centred on July 24 plotted against the
distance upstream from the Horsefly Townsite. The bars represent the average range and the line
indicates the linear change in stream temperature.

3.2

Multiple Linear Regression Analysis of the Historic Stream Temperature

Weekly averages of the daily air temperature statistics from Quesnel Airport were good correlates for
generalizing air temperature at the Horsefly Townsite (Table 3-1). Also, weekly averages of the daily
maximum and average have higher correlation indices than the daily minimum and range.

52

Table 3-1 --- Simple correlation coefficients and the correlation indexes, in brackets, for the weekly
averaged daily air temperature statistics from Quesnel Airport associated with the climate stations
within 10 km of the Horsefly Townsite. Only data from July 1 to September 30 data were used.

Simple Correlation Coefficient (Correlation Index)
Daily Air
Horsefly Lake
Moffat Creek
Horsefly BCFS
Temperature Statistics
Grubs Lake
Maximum
0.97(0.94)
0.98(0.96)
0.98(0.96)
Minimum
0.93(0.86)
0.93(0.86)
0.92(0.85)
Average
0.98(0.96)
0.97(0.94)
0.98(0.96)
Range
0.91(0.83)
0.92(0.85)
0.95(0.90)

The correlation coefficient and index between weekly averaged stream discharge recorded at Horsefly
River above McKinley Creek and Horsefly River at Horsefly were 0. 94 and 0. 96, respectively. This
demonstrated that data from Horsefly River above McKinley Creek were good indicators of weekly
average stream discharge for the mainstem of the Horsefly River near the Horsefly Townsite.

From the results of the correlation analysis between weekly stream temperature statistics and weekly
air temperature statistics (fable 3-2), it was evident that no single air temperature statistic was best for

all the stream temperature statistics. Oearly, weekly averaged daily stream temperature range should
be associated with weekly averaged daily air temperature range. The other three stream temperature
statistics were more complicated. Firstly, weekly averaged daily minimum air temperature could not be
used to predict any of the stream temperature statistics. It had the lowest correlation index for each of
the remaining stream temperature statistics. Weekly averaged air temperature was chosen as the single
air temperature statistic for the predictor variable in the multiple linear regressions that accounted for

variation in weekly averaged maximum/ minimum/ average stream temperature. It was chosen since it
had a higher average correlation index (0. 72) for the three stream temperature statistics than did weekly
averaged daily maximum air temperature (0.69).

53

Table 3-2 ---Simple correlation coefficients and the correlation indexes, in brackets, for weekly
averaged daily stream temperature statistics from Horsefly Townsite associated with weekly averaged
daily air temperature statistics from Quesnel Airport. Only data from July 1 to September 30 were
used in the analysis.

Simple Correlation Coefficient (Correlation Index)
Daily Air
Daily Water Temperature Statistics
Minimum
Average
Range
Temperature Statistics
Maximum
0.84(0.71)
0.48(0.23)
0.81(0.66)
Maximum
0.83(0.69)
-0.09(0.01)
0.76(0.58)
Minimum
0.66(0.44)
0.55(0.30)
0.86(0.74)
0.29(0.08)
Average
0.80(0.64)
0.89(0.79)
0.59(0.35)
0.40(0.16)
0.52(0.27)
0.66(0.44)
Range

Non-linear bias was detected in the multiple linear regression analysis for the prediction of weekly
averaged daily maximum stream temperature and weekly averaged daily stream temperature range
(fable 3-3). The observed non-linear bias associated with the predictor variable weekly average stream
discharge (Figure 3-4, Figure 3-5) suggested a non-linear function of weekly averaged stream discharge,
such as an inverse relationship, might be more appropriate in the model. For the purposes of this
study, the association the particular stream temperature statistic had with weekly average stream
discharge was interpreted with caution for the days where non-linear bias was observed. The nonlinear bias that was observed when the predicted values of the weekly averaged daily stream
temperature range were plotted against the actual values (Figure 3-6) suggested that a non-linear
function of weekly average daily stream temperature range, such as a logarithmic relationship, might be
more appropriate as a predicted variable. This latter type of bias, when observed, suggested that all
results from these multiple linear regression analyses should be interpreted with caution.

54

Table 3-3 ---Dates where non-linear bias was observed in the multiple linear regression analyses
along with the type of bias.

Daily Stream
Temperature
Statistic
Range

Range

Maximum

Plot

Dates

Patterned
Bias

residuals
versus
discharge
estimate
versus
actual
residuals
versus
discharge

Jul.17
to
Aug.24

Underestimating the range for
low and high values of discharge
and overestimating for medium values
Underestimating the range for
high values of range
and overestimating for medium values
Underestimating the range for
low and high values of discharge
and overestimating for medium values

Jul.12
to
Aug.19
Jul.lO
to
Jul.23

55

1.5

•
•

1.0

•

0.5

••

(J

0

t;j

:::J
"C

·u;

•

0.0

Q)

•

•
•

•
•

•

0:::

•

•

• • •
• •

-0.5

•
-1 .0

•

•

•

•

•

•
•

•

••

-1 .5

~

0

10

20

30

40

50

60

Weekly Averaged Stream Discharge ( m3 /s)

Figure 3-4 --- Residuals from the multiple linear regression analysis of weekly averaged daily stream
temperature range for week centred on August 3 plotted against weekly averaged stream discharge.

56

3

•

2

•

•
•

u

0

(ij

:::l

"C

·u;

•

0

Q)

•

• •
•

0:::

-1

••

-2

-3

•

•

•

•

•

.

•
•
•

•
• •
•

•

•

••

• •

.

•

•
0

20

40

60

80

100

Weekly Averaged Stream Discharge ( m3/s )

Figure 3-5 --- Residuals from the multiple linear regression analysis of weekly averaged daily
maximum stream temperature for week centred on July 15 plotted against weekly averaged stream
discharge.

57

5

4
()

0

Cl.l

iii

E

3

~

w
2

0

2

4

5

6

Figure 3-6 --- Estimates from the multiple linear regression analysis of weekly averaged stream
temperature range for week centred on August 3 plotted against weekly averaged daily stream
temperature range (actual).

Serial autocorrelation was detected for some of the multiple linear regression analyses (fable 3-4).
Plots of the residuals versus the yearly trend variable were examined and it was found that the serial
autocorrelation was most likely due to random perturbations of the data (Figure 3-7). The oscillatory
behaviour of the data from 1971 to 1986 for the week centred on July 31 produced statistically
significant serial autocorrelation.

Plots of other dates where serial autocorrelation was indicated

exhibited similar patterns that were less pronounced and not necessarily for the same set of years. It is
safe to assume that serial autocorrelation was not a problem in the multiple regression analysis.

58

Table 3-4--- Dates where the Dw:ban-Watson statistic indicated that there was significant serial
autocorrelation in the multiple linear regression model.

Weekly Averaged Daily
Stream Tern eratw:e Statistic
Minimum
Maximum
ul.19
u1.18
ul.20
ul.21
ul.21
ul.22
ul.22
ul.23
ul.23
ul.25
u1.25
Jul.26
ul.29
ul.27
ul.29
Jul.30
u1.31
u1.30
ul.31
Aug.l
Aug.2
Aug.3
Aug.12
Aug.18
Aug.19
Aug.20
Aug.21
Sep.7
Sep.17
Sep.23
Sep.24
Se .25

Aug.l
Aug.2
Aug.3
Aug.4
Aug.25
Aug.26
Aug.27
Aug.28
Aug.29
Sep.18
Sep.19
Sep.27

Aug.2
Aug.3
Sep.l
Sep.2
Sep.19
Sep.27

Aug.l
Aug.31
Sep.8
Sep.9
Sep.16
Sep.21
Sep.27

59

1.0

0.5
()

0

m 0.0

:::J
"C

.iii

Cll

a:::

-0.5

-1 .0

-1 .5 + - - - , - - - - - - . - - - , - - , - -- , - - - , - - - - , - - - - , - - - - , - - - - i
1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Year

Figure 3-7 --- Residuals from the multiple linear regression analysis of weekly averaged daily
minimum stream temperature for week centred on July 31 plotted against the yearly trend variable.

For all the multiple linear regression analyses, tolerance values were greater than 0.5 and therefore
multicollinearity was not a problem in these analyses. Predictor variables can be assumed independent
of one another. In all cases, the p-values for Kolmogorov-Smirnov goodness of fit test were much
greater than 0.05, with an average value of 0.76, and as a result the assumptions that the residuals were
normally distributed were not rejected.

3.2.1

Partitioning the Variance of Stream Temperature

Since the assumptions of linear independence of the predictor variables and normality of the residuals
were satisfied, then the variance partitions using Pratt's Measure could be interpreted The variance
partitions were plotted against the centre date of a given week to display the changing contributions of
60

each of the predictor variables through the season (Figure 3-8; Figure 3-9; Figure 3-10; Figure 3-11).
Immediately apparent from these plots were that the air temperature statistics and the weekly averaged
stream discharge account for a large amount of the variance in the four stream temperature statistics,
approximately 80%. The yearly trend variable explained less of the variance, but it was a contributing
factor for each of the stream temperature statistics, especially the weekly averaged daily minimum.
In all four sets of multiple linear regression analyses, contributions of the predictor variables change

through the season.

At the beginning of the season, weekly averaged air temperature and weekly

average stream discharge equally explained variance in weekly averaged maximum/ minimum/ average
stream temperature. As the season progressed, the contribution of weekly averaged air temperature
increased, whereas the contribution of weekly averaged stream discharge decreased. There also were
apparent oscillations in the contribution of weekly averaged air temperature that had a period of
approximately two weeks. For the weekly averaged stream temperature range, the weekly averaged
stream discharge started out contributing little and rapidly became a dominant factor and the weekly
averaged air temperature range had an erratic contribution with no consistent trend through the
season.
The importance of the yearly trend variable accounting for variance varied through the season as well
as among stream temperature statistics. It contributed most to explaining the weekly averaged daily
minimum stream temperature with prominence during the mid season. A similar pattern was apparent
for the weekly average stream temperature with the exception that the magnitude of the explained
variance was considerably less. The variances in weekly averaged daily maximum stream temperature
and weekly averaged daily stream temperature range had the least association with the yearly trend
variable. At times, this association was neat: zero. The variance in weekly averaged daily maximum
stream temperature started the season with a small component attributable to the yearly trend variable,
then around mid season this component nearly disappeared and weekly averaged air temperature and
61

stream discharge dominated the relationship. The opposite pattern emerged for the variance in weekly
averaged stream temperatru:e range, where the yearly trend component started the season near zero
and then contributed in the latter half of the season.

62

air
1.0 - . - - - - - - - - - - - - - - - - - - - - - - - - - 1 c:::::J
c:::::J discharge
-year
0.9
0.8
Q)

0.7

0

c
aJ
·c:::

aJ

>
0

c

w

....

0.6
0.5

0

'E

0
0.

e
a.

0.4
0.3
0.2
0.1
~~

Jul1

Jul8

~~~~

Jul 15

Jul22

~~~~~~~

Jul 29

Aug 5

~~~

~~~~~

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30

Centre Date

Figure 3-8 --- Partitioned variance in weekly averaged daily maximum stream temperature as a result
of the multiple linear regression models. White, grey and black represent the proportion of variance
attributed to weekly averaged air temperature, weekly average stream discharge and the yearly trend
variable respectively. Variance that was not accounted for by the model was considered random
error.

63

-

c::::::J air
c:::::J discharge

1.0
0.9
0.8

Q)

0.7

0

c::

cu

~

>
0

c::

0.6
0.5

0

:e0
a. 0.4
e
a..

0.3
0.2
0.1
~~~

~~~

~~~~~~~

~~~~

~

~

Aug 12
Aug 26
Sep 9
Sep 23
Jul15
Jul29
Jul1
Aug 5
Aug 19
Sep 2
Sep 16
Sep 30
Jul22
Jul8
Centre Date

Figure 3-9 ---Partitioned variance in weekly averaged daily minimum stream temperature as a result
of the multiple linear regression models. White, grey and black represent the proportion of variance
attributed to weekly averaged air temperature, weekly average stream discharge and the yearly trend
variable respectively. Variance that was not accounted for by the model was considered random
error.

64

1.0
0.9
0.8
Q)

0.7

0

c:

til
~

0.6

0

0.5

>

c:
0

.llrllrtW
~
.

' ' .

' ~

,

..

-

r:::::::::J air
c:::J discharge
year

~

'

,

:e0

c. 0.4

e
a.

0.3
0.2
0.1
0.0
Jul 1

Jul8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30

Centre Date

Figure 3-10 ---Partitioned variance in weekly averaged stream temperature as a result of the multiple
linear regression models. White, grey and black represent the proportion of variance attributed to
weekly average air temperature, weekly average stream discharge and the yearly trend variable
respectively. Variance that was not accounted for by the model was considered random error.

65

c:::::::J air
1.0 - - . - - - - - - - - - - - - - - - - - - - - - - - - - - - i c:::::::::J discharge

-year

0.9

~

0.8

Q)

0.7

0

c:

<U

"iij

-

0.6

0

0.5

0

0.4

>

c:
0

'2

a.

e
0..

0.3

'

'

.. .

0.2
0.1
~

Jul1

~~~

Jul 8

Jul15

~~~

Jul22

Jul29

~

~~

~~~

~~~~~

~~~

Aug 12
Aug 26
Sep 9
Sep 23
Aug 5
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-11 --- Partitioned variance in weekly averaged daily stream temperature range as a result of
the multiple linear regression models. White, grey and black represent the proportion of variance
attributed to weekly averaged daily air temperature range, weekly average stream discharge and the
yearly trend variable respectively. Variance that was not accounted for by the model was considered
random error.

3.2.2

Stream Temperature's Associations with Air Temperature

The magnitudes of the estimated regression coefficients for the air temperature statistics, with 95%
confidence intervals, were plotted against the centre date of a given week to display the changing
associations through the season (Figure 3-12; Figure 3-13; Figure 3-14; Figure 3-15).

Each of the

stream temperature statistics had a positive association with the corresponding air temperature statistic.
This implied that an increase in the air temperature statistics directly corresponded to an increase in the

66

stream

temperature

statistics.

Weekly

averaged

daily

maximum/minimum/average

stream

temperatures had similar seasonal patterns of association with weekly averaged air temperature. Each
of the patterns had oscillations, yet remained fairly constant across the season.

Average associations

across the season for weekly averaged maximum/ minimum/ average stream temperatures were 0.67,

0.50, and 0.59 ac;oc respectively.

Oscillations for the weekly averaged daily minimum stream

temperature were the most pronounced and exhibited periodicity of approximately two weeks. Even
though the residuals from the multiple linear regressions exhibited non-linear bias, the weekly averaged
daily stream temperature range had a definite non-constant association with the weekly average daily

air temperature range. This pattern started and ended the season with an approximate association of
0.1 ac;ac and had a peak of 0.27 ac;oc around August 20th. In addition to this pattern, there were
oscillations similar to the other stream temperature statistics.

67

1.2

1.0

-()

1

0

() 0.8

0

"E
Q)
·o

If:
Q) 0.6
0

()

c::

0

·u;

:g.... 0.4

Cl
Q)

lr

0.2

~

Jul1

Jul 8

Jul15

Jul 22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-12 --- Associations weekly averaged daily maximum stream temperature had with weekly
averaged air temperature as a result of the multiple linear regression analyses with 95% confidence
bounds.

68

1.2 , - - - - - - - - - - - - - - - - - - - - ,

1.0

---u

0

.._

u 0.8

0

~

'E
Q)

·o

li:
Q) 0.6
0

u

c::

0
·;n
~ 0.4
Cl

Q)

~

0.2

Jul1

Jul8

Jul15

Jul22

Ju129

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-13 --- Associations weekly averaged daily minimum stream temperature had with weekly
averaged air temperature as a result of the multiple linear regression analyses with 95% confidence
bounds.

69

1.2 . . - - - - - - - - - - ,

1.0
~

()

0

-..
() 0.8

0

~

"E
Q)

·u

It=
Q) 0.6
0

()

r::
0

·;;;

~ 0.4

Ol
Q)

0::

0.2

Jul 1

Jul8

Jul 15

Jul22

Jul 29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-14 --- Associations weekly averaged stream temperature had with weekly averaged air
temperature as a result of the multiple linear regression analyses with 95% confidence bounds.

70

0.4 .---------------------------------------------------------,

0 o.3

0

()

0

"E
Q)

·c::;

IE
Q) 0.2

~

0

()

c:

0

·u;
Ul

~

01
Q)

0::: 0.1 -

j!lj

Jul 1

Jul8

Jul 15

Jul22

Jul 29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-15 --- Associations weekly averaged daily stream temperature range had with weekly
averaged daily air temperature range as a result of the multiple linear regression analyses with 95%
confidence bounds. Grey indicates that there was non-linear bias in the analyses; whereas, black
indicates no violation of the assumptions.

3.2.3

Stream Temperature's Associations with Stream Discharge

The magnitude of the estimated regression coefficients for weekly averaged stream discharge, with
95% confidence intervals, was plotted against the centre date of a given week to display the changing
associations through the season (Figure 3-16; Figure 3-17; Figure 3-18; Figure 3-19). For each stream
temperature statistic, there was a definite seasonal pattern of association with weekly averaged stream
discharge. In general, these patterns exhibited a negative association. This implies that an increase in
weekly average stream discharge was related to a decrease in all weekly stream temperature statistics
71

through the season. During September, weekly averaged daily minimum stream temperature was an
exception to this. The associations at this time were near zero and generally positive. Each of these
patterns also contained periods where the general patterns were subject to oscillations. The most
pronounced oscillations occurred in August and had a period of approximately two weeks.
Weekly averaged daily maximum/minimum/average stream temperatures each started the season with
similar associations

(-o.os oc ; (m3I s)) with weekly stream discharge and then diverged.

The

associations with weekly average stream temperature were essentially the average associations of the
other two stream temperature statistics. The associations between weekly averaged daily maximum
stream temperature and weekly averaged stream discharge reached a peak of -0.17 oC/(m3/s) on
August 7d' then tended towards -0.07 oc ; (m3 I s) at the end of September. The associations between
weekly averaged daily minimum stream temperature and weekly average stream discharge peaked at -

0.09 oc; (m3I s) on July 24, and approached zero near the end of September.

Although the

interpretations were made with caution, the associations weekly averaged daily stream temperature
range had with stream discharge started around -0.01 oc; (m3 I s) then progressed to -0.07 oc; (m31s)
around the beginning of August and remained fairly constant afterwards.

72

0.10

0.05
~

--E 0.00
--

~

tJ)

(<)

~

0

0

-0.05
"E
Q)
~

·u
!E
Q)
0

0

ffilli

-0.10

c
0

·u;
tJ)

~

Ol

-0.15

Q)

0::

-0.20

Jul 1

Jul8

Jul 15

Jul22

Jul 29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-16 --- Associations weekly averaged daily maximum stream temperature had with weekly
averaged stream discharge as a result of the multiple linear regression analyses with 95% confidence
bounds. Grey indicates that there was non-linear bias in the analyses; whereas, black indicates no
violation of the assumptions.

73

0.05
U)

-.

"'e o.oo -l --------------++++.---::-+++.+---::Tt+-tt-...T"H-'ft+t-+++tffir++++Tt+-()

E" -o.o5

0

Q)

·u

~

8 -0.10
Q)

c:
0

"iii
U)

~ -0.15

C)
Q)

a::

-0.20

Jul 1

Jul 8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-17 --- Associations weekly averaged daily minimum stream temperature had with weekly
averaged stream discharge as a result of the multiple linear regression analyses with 95% confidence
bounds.

74

o.1 o . - - - - - - - - 0.05
~

-- o.oo
"'e
~

<J)

--

........

...j- - - - - - - t t h - T - - f t t t t t - - 1

()

E' -o.o5

0

Q)

·c::;
!i:
Q)

8 -0.10

c
0
·u;
<J)

~ -0.15

C)

Q)

0:::

-0.20

Jul1

Jul 8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-18 --- Associations weekly averaged stream temperature had with weekly averaged stream
discharge as a result of the multiple linear regression analyses with 95% confidence bounds.

75

0.10

--

0.05

~

tJ)

"'E
0

0.00

0

~

"E
Cll

~ -0.05
Cll

0

0

c
0

"gj -0.10
~

Ol

Cll

0:::

-0.15

Jul 1

Jul8

Jul 15

Jul22

Jul 29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-19 --- Associations weekly averaged daily stream temperature range had with weekly
averaged stream discharge as a result of the multiple linear regression analyses with 95% confidence
bounds. Grey indicates that there was non-linear bias in the analyses; whereas, black indicates no
violation of the assumptions.

3.2.4

Stream Temperature's Associations with the Yearly Trend Variable

The magnitude of the estimated regression coefficients for the yearly trend variable, with 95%
confidence intervals, was plotted against the centre date of a given week to display the changing
associations through the season (Figure 3-20; Figure 3-21; Figure 3-22; Figure 3-23).

Initially apparent from the multiple linear regress10n analyses were that trends in the four stream
temperature statistics were statistically different from zero and trends changed across the season. The
most consistent trends were that of the weekly averaged daily minimum stream temperature, which

76

remained essentially constant t:lu:ough the season. Trends followed the hypothesised trend in ground
and ground water temperatures with slight deviations in mid-August and late September. For most of
the season, trends were statistically different from the zero trend and for all of the season they were
not statistically different from the hypothesised trend in ground and ground water temperatures.
The trends in the weekly averaged daily maximum stream temperature had a pronounced change
around mid-August.

These trends followed a path similar to the trends in weekly averaged daily

stream temperature up until mid-August. The high variability in the estimated trends along made it
difficult to assess whether this section of the trends were statistically different from the zero trend, but
it was clear, they are not statistically different from the hypothesised trend in ground and ground water
temperatures. The trends then progressed sharply to the zero trend line. During this progression, the
trends in weekly averaged daily maximum stream temperature became statistically different from the
hypothesised trend in ground and ground water temperatures. The trends then deviated from the zero
trend in mid-September and became not statistically different from either the zero trend or the
hypothesised trend in ground and ground water temperatures.
The trends in weekly averaged stream temperature and weekly averaged daily stream temperature range
were implied from the trends in the weekly averaged daily maximum/minimum stream temperature.
This result was expected since these two stream temperature statistics were dit:ecdy calculated from the

other two stream temperature statistics. During July and the beginning of August the trends in weekly
averaged daily maximum/ minimum stream temperature closely resembled the hypothesised trend in
ground and ground water temperatures. As a consequence, trends in the weekly averaged daily stream
temperature range were near zero.

After mid-August the trends in these two stream temperature

statistics diverged, while trends in weekly averaged daily minimum stream temperature remained
essentially constant following the hypothesised trend in ground and ground water temperatures.
Trends in weekly averaged daily maximum stream temperature diminished. In late September, the

77

trends in these two stream temperature statistics converged and were not statistically different from
either the zero trend or the hypothesised trend in ground and ground water temperatures.

lbis

divergence in the trends in weekly averaged daily maximum/ minimum stream temperature was also
apparent in the decreasing trend in the weekly averaged daily stream temperature range.

78

0.10

tv 0.05
~

--- ----- .............

--·

()

0

c:

lf.

.!!1

lj

0

!i: 0.00
CD

0

()

c::

0

·u;

..

- --

~~
Q<;

Jll

!II

~

Cl

~

-0.10
Jul1

Jul8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-20 --- Associations weekly averaged daily maximum stream temperature had with the yearly
trend variable as a result of the multiple linear regression analyses with 95% confidence bounds.
The dashed line indicates the hypothesised trend in ground and ground water temperatures (0.033
oC/ year) and the bold line indicates the zero trend (0 oC/ year).

79

iii 0.05
Q)

>-

()

0

Jul1

Jul 8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-21 --- Associations weekly averaged daily minimum stream temperature had with the yearly
trend variable as a result of the multiple linear regression analyses with 95% confidence bounds.
The dashed line indicates the hypothesised trend in ground and ground water temperatures (0.033
oC/year) and the bold line indicates the zero trend (0 oC/year).

80

0.10 . , . . . . . . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - ,

ro·
~

~ ~ ~~~~~ ~ ~ - - if!: ~~
-f.*ffij.

---1

1

o.oo

~

1' u*IHtti
lllH----'+tt+t-t+t+-i

(.)

c:
0
"iii
<I)

~

01

~

-0.10 -'r--..--..---.--...,--..,....-.---.---,---,---.---.-----,.-----T
Jul1

Jul 8

Jul15

Jul22

Jul29

Aug 5

Aug 12
Aug 26
Sep 9
Sep 23
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-22 --- Associations weekly averaged stream temperature had with the yearly trend variable
as a result of the multiple linear regression analyses with 95% confidence bounds. The dashed line
indicates the hypothesised trend in ground water temperature (0.033 oC/year) and the bold line
indicates the zero trend (0 oC/year).

81

0.10 . . . . - - - - -- - - - - - - - - - - - - -- - - - - - - - - - - - - ,

,....._

ro o.os
~

()

0

c

Q)

·u

lt:
0.00
Q)

- - -- -

- - - - - --+t-1--TT- - ----rt-''1-rt+tt-

~

0
()

c:
0
"iii

<n

~

Ol

~

'H·+----l

JW

&-0.05

-0.10 ---',.-----,-------,---,---,.-----,-----,-------,,-Jul 1

Jul8

Jul 15

Jul22

Jul 29

-,---,.-----,--

- - - , - - - . - - --r

Aug 12
Aug 26
Sep 9
Sep 23
Aug 5
Aug 19
Sep 2
Sep 16
Sep 30
Centre Date

Figure 3-23 --- Associations weekly averaged daily stream temperature range had with the yearly
trend variable as a result of the multiple linear regression analyses. Grey indicates that a non-linear
function of the predicted variable is appropriate in the analyses; whereas, black indicates nonsignificant serial autocorrelation or that a linear function was appropriate.

82

4

DISCUSSION

The concepts of stream temperature signatures (Zwieniecki and Newton, 1999) and annual trends in
air temperature being indicators for trends in ground and ground water temperatures (Pollack and

Chapman, 1993) were important factors in this study. Other researchers may not have considered
spatial characteristics of stream temperature and trends in ground and ground water temperatures
within their study areas when analysing long-term trends in stream temperature. This makes the
approach novel to this study.
The results from the multiple linear regression analyses were related to conditions within the Horsefly
Watershed using a high spatial and temporal resolution environmental survey. Certainly one season of
data collection cannot fully describe spatial patterns of stream temperature throughout the Horsefly
Watershed for all time. However it was a step towards a description. The main findings from the
summer 2000 survey were the description of Horsefly River's temperature signature and determining
the influence lake-fed tributaries have on the signature. The sections of the Horsefly River that are
affected by the lake-fed tributaries are referred to as thermal transition reaches (Sinokrot and Stefan,
1993; Zwieniecki and New-ton, 1999). The implications of these observations are that disturbances to
the Horsefly River's temperature signature decay downstream to a point where their influence is near
zero (Burton and Likens, 1973; Zwieniecki and Newton, 1999). In essence, temperature fluxes within
the Horsefly River are not cumulative downstream, which is contrary to the conclusions of a smaller
scale watershed study (325 km~ expressed by Beschta and Taylor (1988).

The summer 2000 survey found that the effect of the lake-fed tributaries on the Horsefly River's
temperature signature could only be detected within 25 km. This implies that landscape disturbances
more than 25 km upstream from the Horsefly Townsite should not affect the Horsefly River's
83

temperature near the Horsefly Townsite. Approximately 95% of the recorded landscape disturbances
that have occurred since 1955 (-20% of the forest area within the Horsefly Watershed) are more than
25 km upstream from the Horsefly Townsite. 1bis leaves about one percent of forest area within the
Horsefly watershed that has been disturbed since 1955 and could possibly have affected the Horsefly
River's temperature near the Horsefly Townsite.

If a measured change in the Horsefly River's

temperature near townsite could be attributed to landscape disturbances, then the landscape effect on
stream temperature within this one percent of disturbed forest would have to many times greater in
magnitude as a result of mixing disturbed water with undisturbed water.

1bis certainly is an

understatement since factors such as vegetative regrowth O"ohnson and Jones, 2000) and streamside
adjacency (Rashin and Graber, 1992) have been shown to limit the local effect of landscape
disturbances on stream temperature. These variables were not assessed during this study. Based on the
summer 2000 survey, the independence of the Horsefly River's temperature near the Horsefly
Townsite from landscape disturbances since 1955 was inferred.
The ground and ground water temperatures have well known effects on stream temperature (Ibeurer
et al., 1984; Sinokrot and Stefan, 1993) and trends in yearly averaged air temperature have been
assumed to or shown to correspond with trends in ground and ground water temperatures (ffeath and
Trainer, 1968; Rohsenow et al., 1985; Pollack and Chapman, 1993; Taniguchi et al., 1999a). Theurer et
al. (1984) expressed the relationship that ground temperature has with stream temperature using onedimensional conductive heat transfer between the streambed surface, which was assumed to be the
temperature of the stream, and a point where ground temperature is at equilibrium. Using Theurer et
al.'s (1984) formulae, changes in the equilibrium ground temperature would directly correspond to
changes in streambed surface temperature. As a result stream temperature would change. In stream
temperature simulations performed by Sinokrot and Stefan (1993), they assumed ground temperature
was at equilibrium beyond a depth of 6 metres. Using routines expressed by Heath and Trainer (1968)
for damp soil approximately 7, 43, and 76 percent of the annual, decadal, and centennial surface
84

temperature range can, respectively, be translated to a depth of 6 metres using only conductive heat
transfer. It is clear that climate warming should increase stream temperatures and a route that would
transfer heat from the air into the streams will pass through the ground. It is not yet clear how the
magnitudes of air, ground and stream temperature fluctuations functionally relate to each other.
Further research is necessary for a complete description of how the ground acts as a conduit between

air temperatures and stream temperatures. Linear regression of the yearly averaged air temperature at
Quesnel Airport yielded a significant association of 0.033 ± 0.009 oC/ year. It is hypothesized a similat:
trend occurred during this period to the ground and ground water temperatures within the Horsefly
Watershed and in the Horsefly River's temperature near the Horsefly Townsite.
Multiple regress10n models where all the terms are linear are considered simplistic and yet easily
generalized.

As such, these models are considered a first approach to predicting an event using

multiple predictor variables.

For most of the multiple linear regress10n analyses, the modelling

assumptions were not violated and the models were assumed 'correct'. Non-linear bias was detected
in the multiple linear regression analyses for the prediction of the weekly averaged daily ma.ximum
stream temperature and the weekly averaged daily stream temperature range.

Future work should

include revisions to the multiple linear regression models with non-linear adjustments to weekly
averaged stream temperature range and weekly averaged stream discharge. An inverse relationship for
weekly averaged stream discharge should be considered since other researchers have considered this
relationship (Goodman, 1966; Brown, 1969; Hockey et al, 1982; Barton et al, 1985).
Oscillations were observed in the variance partitions and associations that the air temperature statistics
and weekly averaged stream discharge had with the stream temperature statistics.

The oscillations

imply unaccounted factors might be driving the relationship between stream temperature and the
combination of stream discharge and air temperature. Oscillations were also apparent, although not as
prominent, in the daily total precipitation records at Horsefly Lake/ Grubs Lake (Figw:e 1-7). Direct
85

comparisons could not be made between these oscillatory patterns since they were constructed using
different sets of years (regression: 1955-58, 64-90 and 1995-99 versus precipitation: 1950-61, 83, 84,
and 1987-1999). However there certainly was an indication that precipitation events may have changed
the associations air temperature and stream discharge had with stream temperature.

Incorporating

weekly averaged daily total precipitation from Quesnel Airport as a linear term in the multiple linear
regress10n analysis of weekly averaged daily minimum stream temperature produced statistically
significant associations but there were multicollinearity problems.

This implies that precipitation

events were highly associated with stream discharge and air temperature. Further, if precipitation is
incorporated into the regression models, it is not as simple as just adding another linear term.
Precipitation data are available for analysis but incorporating terms that are functions of daily total
precipitation requires techniques that are different from those used in this study.
Nevertheless, the multiple linear regression analyses produced some intriguing results. Immediately
apparent from the partitioned multiple R squared was that the weekly air temperature statistics and the
weekly averaged stream discharge accounted for a large amount of the variance in the four weekly
stream temperature statistics, approximately 80%. The decreasing importance of stream discharge and
increasing importance of air temperature for weekly averaged daily maximum, average, and minimum
stream temperature across the season may be due to the seasonal decrease in stream discharge (Figure
1-8). Stefan and Preud'homme (1993) suggested that larger river systems are less responsive to air
temperature because they have larger thermal inertia. This would imply that as the stream discharge in
the Horsefly River decreases, it's thermal inertia decreases. As a result, the river is more responsive to

air temperature.

Using just air temperature to predict the Horsefly River's temperature near the

Horsefly Townsite may be appropriate during September, but the importance of stream discharge
cannot be neglected during July and August Both air temperature range and stream discharge should
be used as predictors throughout the season for the weekly averaged daily stream temperature range.

86

Each of the weekly stream temperature statistics had a consistendy positive association with the
corresponding weekly air temperature statistic. This implies that an increase in the weekly au:
temperature statistics direcdy corresponded to an increase in the weekly stream temperature statistic.
Such associations have been used to predict the effect of climate warming on stream temperatures
(Pilgrim

et

al.,

Pilgrim

1998).

et

al.

(1998)

linearly

regressed weekly

averaged

daily

maximum/ minimum/ average stream temperature from 39 streams in Minnesota against weekly
averaged air temperature from the nearest climate station. They then used projected average increases
in air temperature to predict increases in weekly stream temperatures. Pilgrim et al. (1998) assumed
that the direct associations between stream temperatures and air temperatures accounted for the
relationship stream temperatures may have with climate. If this assumption is valid for the Horsefly
River, including air temperature in the regression models should have accounted for the relationship
stream temperatures have with climate. As indicated by Hostetler (1991), by also including stream
discharge with air temperature in the regression model the yearly trend variable should be related to
landscape disturbances.

The reasoning put forth by Pilgrim et al. (1998) together with that of

Hosteder (1991) does not seem appropriate for the Horsefly River's temperature near the Horsefly
Townsite since the summer 2000 survey suggested that the yearly trend variable was not associated
with landscape disturbances.
Weekly averaged stream discharge had a definite seasonal pattern of association with each of the
stream temperature statistics. In general, these patterns exhibited a negative association, implying that
an increase in weekly average stream discharge resulted in a decrease in all the weekly stream
temperature statistics. These results are comparable to other studies (Goodman, 1966; Theurer et al.,
1984; Holtby, 1988; Mackey and Berries, 1991) and verified that linear functions of stream discharge
can account for some of the variation in stream temperature.

87

The yearly trend variable was a contributing factor for explaining each of the stream temperature
statistics, especially the weekly averaged daily minimum.

There were yearly trends in the stream

temperature statistics that were statistically different from zero and the magnitude of these trends
changed across the season. The strongest and most consistent trends were of weekly averaged daily
minimum stream temperature. It essentially remained constant through the season. The trends in the
weekly averaged daily maximum stream temperature followed a path similar to the trends in weekly
averaged daily minimum stream temperature up untiL mid-August and then diverged. The divergence
of trends after mid-August in weekly averaged daily maximum/minimum stream temperature were
also apparent in the decreasing trends in the weekly averaged daily stream temperature range. Changes
in monthly stream temperature statistics in response to global warming have been suggested to exhibit
a similar pattern. Arnell (1996) suggested there should be a greater increase in the monthly minimum
stream temperature than the monthly maximum with a consequent reduction in the monthly range in
response to climate warming.
The trends in the Horsefly River's temperature near the Horsefly Townsite compared favourably with
the hypothesised trend in ground and ground water temperatures. A review of the literature did not
determine whether other researchers have used trends in ground and ground water temperature to
explain trends in stream temperature. However it certainly provides a good explanation for the trends
in Horsefly River's temperature. If the determined stream temperature trends were responding directly
to the hypothesised trend in ground and ground water temperatures from July 1 to mid-August, the
weekly averaged daily maximum/ average/ minimum stream temperatures were receiving the full effect
of the ground and ground water temperatures. For the rest of the season, ground and ground water
temperatures were still affecting the weekly averaged daily minimum stream temperature but their
effect on weekly averaged daily maximum/ average stream temperatures may have been masked by
other environmental factors, such as air temperature, solar radiation and wind speed.

It is quite

plausible that climate warming was inducing trends in the weekly Horsefly River's temperature near the

88

Horsefly Townsite, that could not be accounted for by the associations with weekly air temperature
and stream discharge. The effect of climate warming may be a result of the relationship stream
temperature has with ground and ground water temperatures.
Relating results from other stream temperature studies to this study was problematic because of the
wide variety of temporal and spatial scales used to analyse stream temperature as well as the summary
statistics. For example, it was not clear how changes in monthly minimum stream temperature (Amell,
1996) related to changes in weekly averaged daily minimum stream temperature for a particular spatial
scale and it becomes less clear for diffe1:ent spatial scales. Weekly ave1:ages of daily stream tempe1:ature
statistics were chosen for this study but similar analysis could have been conducted on daily values,
weekly extremes, monthly ave1:ages, etc. Ful:the1: analysis of the Hmsefly Rivers temperature near the
Horsefly Townsite could include varying the time scale within the season; this would produce a more
complete description of the trends in stream temperature and assist in relating trends in the Horsefly
Rivers temperature with temperature trends in other rivers.
A recent study by Fmeman et al. (2001) linearly 1:egressed the ave1:age stream temperature for the
Fraser River at Hell's Gate from July 1 to September 15 against a yearly trend variable. The years
included in their analysis we1:e 1953 to 1998. They found that this stream temperature statistic had a
significant trend of 0.022 ± 0.009 oC/year (p-value < 0.05). This procedure was reproduced for the
Hmsefly Rivers tempe1:ature near the Horsefly Townsite with the exceptions that (1) 1991 to 1994
could not be included due to missing data and (2) averaged average of the daily stream temperature
extremes from July 1 to Septembe1: 15 we1:e the stream tempe1:ature statistic. The 1:esults produced a
non-significant trend of 0.032 ± 0.017 oC/year (p-value = 0.062). It is uncertain whether these two
trends are consistent with one anothe1:, due possibly to the missing data (1991-1994) and/ or highe1:
variability of the Horsefly Rivers temperature. The hypothesis put fol:th by Forman et al. (2001) was
that most of the F1:ase1: Rivers warming could be attributed to climatic effects. This is consistent with
89

the hypotheses presented in this thesis. Forman et aL (2001) did not consider possible changes in
ground and ground water temperatures in their hypothesis. It seems plausible to suggest the reswts
and hypotheses presented in this thesis are not localized within the Horsefly area and in fact may apply
to other river systems within the Fraser River Watershed
All the results presented in this study suggest that increases in the Horsefly River's temperature near
the Horsefly Townsite could possible be attributable to landscape disturbances were actually responses
to long-term climate changes. This statement is based on some unverified assumptions.
The first assumption was that the results from the summer survey were indicative of the previous 45
years. The main result from the summer survey was the stable temperature signature for the Horsefly
River that was only locally affected by the major lake-fed tributaries. How the temperature signature
has changed since 1955 and whether the effects of the major lake-fed tributaries have changed since
then cannot be verified. Thus it was assumed that for each season a strong temperature signature
existed and that the effects of these lake-fed tributaries on the temperature signature were localized
events (< 25 km).

The assumption seems appropriate but an effort should be made to verify its

validity.
The next two assumptions were necessary for concluding that trends in ground and ground water
temperatures may have affected the Horsefly River's temperature near the Horsefly Townsite. The
first being that yearly averaged average of the daily air temperature extremes was highly correlated with
yearly averaged air temperature. The relationship between long-term trends in ground and ground
water temperatures and air temperature are described using the yearly average air temperature (Heath
and Trainer, 1968; Rohsenow et al., 1985; Pollack and Chapman, 1993; Taniguchi et al., 1999a). This
seemed to be a reasonable assumption, but it was not verified. The second assumption was that the
hypothesised trend in ground and ground water termperatures had the same magnitude as the longterm trend in yearly average air temperature. This assumption was very important when assessing the
90

trends in the stream temperature statistics.

Although this assumption seemed realistic based on a

review of the literature, its importance for explaining trends in stream temperature warrants further
research before the results from this study can be interpreted completely.
Tills study of stream temperature is preliminary to addressing the issue of the effect of landscape
disturbances on stream temperature on large watersheds. The Horsefly Watershed was a good study
area for this issue since it had a detailed database of an environmental history. The methodology used
for this study was quite simple and easily interpreted, yet there were parts of this methodology that
could have been refined. As well, the conclusions are based on some unverified assumptions, which
should be addressed Although there were some unanswered questions, it was very likely that the
increasing trends in the Horsefly River's temperature near the Horsefly Townsite that could have been
attributed to landscape disturbances were more likely a result of a general heating of the Horsefly
Watershed induced by climate warming.

91

5

CONCLUSION

All the results presented in this research are consistent with the hypothesis: annual changes in the
Horsefly River's temperature near the Horsefly Townsite from 1955 to 1999 are a direct consequence
of climate warming and not related to landscape disturbances within the Horsefly Watershed. This
hypothesis does not imply that landscape disturbances have not changed stream temperature within
the Horsefly Watershed.

Local effects of landscape disturbances on stream temperature may have

occurred but their effects were most likely unperceivable near the Horsefly Townsite. Management of
aquatic ecosystems in the Horsefly River should consider long-term trends in climate as an indicator
for changes in aquatic habitat quality.

92

6

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