ArticlePDF Available

Flow and Temperature Models for the Fraser and Thompson Rivers

Authors:

Abstract and Figures

High river temperatures have been linked to pre‐spawning mortalities in salmon returning to their natal streams. As a first step in predicting these temperatures, flow and temperature models were developed for the Fraser and Thompson Rivers in British Columbia. The flow model is essentially pre‐calibrated while the temperature model was calibrated against data collected in 1993 and then verified against data from 1994. Root mean square differences between measured and calculated temperatures were found to be 0.70° C at thirteen stations in 1993 and 0.60°C at fifteen stations in 1994. As a purely speculative exercise, the models were then used to investigate the feasibility of using cooler waters from lakes to reduce the warm temperatures recorded in 1994.
Content may be subject to copyright.
Flow and Temperature Models for the Fraser and
Thompson Rivers
M.G.G. Foreman
Institue of Ocean Sciences,
Sidney3
B.C.
C.B. James
Triton Environmental Consultants Ltd., Richmond,
B.C,
M.C. Quick
Department of Civil Engineering
University of British Columbia, Vancouver, B.C.
and
P. Hollemans and E. Wiebe
Department of Physics
University of Victoria, Victoria, B.C.
[Original manuscript submitted 6 October 1995; in revised form 2 August
19961
ABSTRACT
High river temperatures have been linked to pre-spawning mortalities in salmon
returning to their natal streams. As
a
first
step in predicting these
temperatures,
flow
and tem-
perature models were developed
for
the Fraser and Thompson Rivers in British Columbia.
The flow model is essentially pre-calibrated while the temperature model was calibrated
against data collected in 1993 and then verified against data from 1994. Root mean square
dtflerences behveen measured and calculated temperatures were found to be
0.7O”C
at thir-
teen stations in 1993 and
0.6O”C
at
fifteen
stations in 1994. As a purely speculative exercise,
the models were then used to investigate the feasibility of using cooler waters from lakes to
reduce the warm temperatures recorded in 1994.
RCSUMC
La temperature
@levee
des rivikres a
et&
associee
a
la mortalite davant fraie des
sau-
mons retournant h leurs tours deau
natals.
Comme premier pas en vue de la prevision de
cette temperature on a elabore des
modeles
du courant et de la temperature
duJleuve Fraser
et de la
riviere
Thompson en Colornbie-Britanique.
L.e
modele du courant est essentiellement
calibre davance alors que celui de la temperature a
he
calibre en fonction de
don&es
obtenues en 1993 et verifie en fonction de celles de 1994.
Les
diflerences quadratiques
moy-
ennes entre
les
temperatures mesurees et culculees
etaient
de 0,7o”C
a
13 stations en 1993 et
de 0,6o”C
-
15 stations en 1994. En pure speculation,
les
modeles ont
PtP
employ&s
pour
estimer
la
possibilite dutiliser de leau plus froide des
lacs
pour reduire
les
temperatures
elevees de 1994.
ATMOSPHERE-OCEAN35
(I) 1997, 109-134
0705-5900/97/~00-0109S1.25/0
0
Canadian Meteorological and Oceanographic Society
110
/
M.G.G. Foreman et al.
1 Introduction
Elevated water temperatures have been linked to pre-spawning mortalities for many
salmon stocks (Gilhousen, 1990) returning to their natal streams in the Fraser River
watershed (Fig. 1). During the migration period of 1994, Fraser River water temper-
atures were periodically at, or near, historic maximum levels and it was concluded
that approximately 466,000 fish which entered the Fraser River died before reaching
their spawning grounds (Fraser River Sockeye Public Review Board, 1995). There
is no information in the scientific literature regarding the laboratory or natural deter-
mination of optimal temperatures for adult sockeye salmon. However, it is known
that when the water is too cold, their metabolic rate slows, and when it is too hot,
their rate increases and their
energy reserves can he rapidly depleted. As migrating
salmon do not eat after they enter freshwater, energy conservation is a critical factor
in determining their survival. Exposure of adult sockeye salmon to temperatures
above 24°C causes acute thermal shock that leads to death within a few hours
(Bouck
et al., 1975). Sustained exposure to temperatures between 22and 24°C is
also lethal but the time to death may be as long as four days and the cause of death
includes acute infection as well as acute thermal shock (Servizi and Jensen, 1977).
In addition, other stress-related agents such as very high or low water levels, high
sediment events, higher incidence of infections and high fisheries pressure can exac-
erbate the effects of warm water. (Low water levels can make the passage through
certain sections of the river more difficult by narrowing the channel, while high
water levels are associated with high discharges and thus require more energy
expenditure for the salmon to advance.)
Historically, the inability to estimate in-river mortality has been a major defi-
ciency in managing the salmon fishery in British Columbia.
Were
such mortality
estimates available, management could better regulate the commercial fisheries in
order to
ensure
that the desired number of spawners would still arrive at their natal
streams. Given the linkage between high water temperatures and pre-spawn mortal-
ity in some sockeye stocks, the Fraser River Sockeye Public Review Board (Fraser
River Sockeye Public Review Board, 1995) recently recommended both the devel-
opment of a predictive water temperature model for the Fraser River and its major
sockeye tributaries, and further research on means by which to mitigate adverse
water temperature and flow fluctuations. This paper describes the preliminary devel-
opment and verification of such a model and some simple tests to investigate the
feasibility of using cool lake water to decrease the warm temperatures recorded in
1994.
The Fraser (see Fig. 1) is the largest Canadian river that empties into the Pacific
Ocean. With its intricate network of tributaries, the Fraser watershed drains approx-
imately 230,000
km2,
or one quarter of British Columbia. The river originates in the
Rocky Mountains near Jasper Alberta, descends rapidly until it reaches Hope, and
then spreads to a flat alluvial valley for the final 160 km of its 1370 km journey to
the Strait of Georgia. Typical discharges at Hope peak in May and June
at
about
7000
m3/s
(Thomson, 1981) and diminish to about 1000
m3/s
in the winter months.
Flow and Temperature Models for the Fraser and Thompson Rivers
/
111
Fig.
I
The Fraser River watershed
The 1994 Hope water temperatures during
the
summer and autumn period are
shown in Fig. 2. Although they rise to about
2O”C,
temperatures in tributaries such
as the Quesnel,
Westroad
and Nechako Rivers (also Fig.
2).
whose flows are slower
and depths are shallower than those in the Fraser, can be warmer.
This paper is organized as follows. Sections 2 and 3 provide a brief description of
the flow and temperature models. Section 4 presents both model results and obser-
vations for 1993 and 1994. Section 5 provides a summary of hypothetical mitigation
112 / M.G.G. Foreman et al.
12
10
....:
88-I_
\
i
:
:.
:
;I
'.
_-!I
Jun28/1994 Ju123/1994
Aug1?/1994 sep11/1994
Ott
6/1994
oct31/1994
Da:.?
Fig. 2
1994 temperatures for the Fraser River at Hope (solid) and the Ncchako River at Prince George
(dotted).
exercises conducted to determine the effectiveness of taking cooler water from lakes
in order to lower river temperatures during the 1994 salmon migration period.
Finally conclusions are presented in Section
6.
2
The flow model
The one-dimensional flow model used in this study was previously described in
Quick and Pipes (1975). In order to overcome the difficulties associated with a river
system where there existed large ungauged lateral inflows and limited data, Quick
and Pipes developed a technique based on routing coefftcients and parameters that
were calculated from existing river stage-discharge and stage-velocity measure-
ments taken by Water Survey of Canada (henceforth WSC). In essence this meant
that regardless of ungauged lateral input, the model was precalibrated before the
routing commenced.
The Quick and Pipes (1975) computations consist of two procedures. The first is
the calculation of a travel time for each
subreach
that is dependent on the river stage.
With this travel time, the inflow for each reach is then translated to give an outflow
downstream. The second procedure takes the translated outflow and routes it
through a simple linear reservoir which represents the storage characteristics of the
reach. This routing involves a further delay to the outflow, but in practice this delay
Flow and Temperature Models for the Fraser and Thompson Rivers
/
113
T
ABLE
1.
Headwater and tributary flow locations for the Fraser and
Thompson Rivers.
River
Tributary Location WSC Stn
#
Fraser
Fraser
Fraser
Fraser
Fraser
Fraser
Fraser
Fraser
FGISIX
Fraser
Fraser
Fraser
Fraser
Fraser
Thompson
Thompson
Thompson
Thompson
Thompson
Thompson
Ncchako
West Road
Cottonwood
Quesnel
ungauged
Williams Lake
Chilcotin
Ungauged
Seton
Thompson
Nahatlatch
ungauged
Coquihalla
South Thompson
North Thompson
Deadman
Bonaparte
Nicola
ungauged
Shelby
Isle
Pierre
Cinema
Cinema
Quesnel
Marguerite
Williams Lake
Big Creek
Texas Creek
Lillonet
Spences Bridge
Tachewana Creek
Hope
Alexander Creek
Chase
McLure
Criss Creek
Cache Creek
Spcnces Bridge
Spences Bridge
OXKBOO
I
08JCOO2
08KGOO
1
08KEOO9
08KH006
-
08MCOO5
OSMBOOS
08ME003
08LFOS
1
08MF065
-
08MF062
08LE03
1
08LBO64
08LFO27
08LFOO2
08LGOO6
time is small compared with the travel time calculated in the first part of the routing
procedure. Additional tributary inflows can also be included at this point in the pro-
cedure. Further details on the model can be found in Mountain Hydrology Group
(1994) and Quick and Pipes (1975, 1976). and a good reference for the underlying
kinematic wave theory is Lighthill and Whitham (1955).
The present application of the flow model consists of sixty-six
IO
km reaches
from Shelley to Hope on the Fraser River, and eighteen 10 km reaches on the
Thompson River from Chase to its confluence with the Fraser at Lytton. The time
step was chosen to be one hour, a value that yields travel times (variable 7T in Quick
and Pipes (1975)) close to unity.
Headwater and tributary inflows for the 1993 and 1994 hindcast runs were
obtained from WSC. The specific sites and station numbers are listed in Table 1.
The four ungauged lateral inflows were calculated as the difference between WSC
measurements at stations on the mainstem Fraser or Thompson Rivers, and model
values in the corresponding reach using only upstream gauged headwater and tribu-
tary inflows. This is the recommended procedure (Quick and Pipes, 1975) for deal-
ing with ungauged inflows.
In addition to this inflow data, the model also requires relationships between the
river discharge and velocity, and the river discharge and cross-sectional flow area.
These are available from area-discharge and velocity-discharge curves that were
computed from measurements taken by WSC at five gauging stations located on the
Fraser at Shelley, near Marguerite, and above Texas Creek; on the South Thompson
114 /
M.G.G.
Foreman et al.
TABLE
2. Coefficients in the Eq. (14) regression between river width and
flow, and model reach assignments.
h
is nondimensional and
o
has units
s
mm2
Site
n
b River
reaches
Shelley
I
18.0265
Marguerite
103.4000
Texas Creek
90.6495
Chase
36.765 1
Spenccs Bridge
53.2537
0.092
I
0.0920
0.1098
0.2461
0.1040
Fraser: 2-20
Fraser: 2 l-37
Fraser: 3867
Thompson:
24
Thompson: 8-l 9
at Chase; and on the Thompson near
Spences
Bridge. See Figs 4 and 5 in Quick and
Pipes
(1975)
for typical examples of these curves.
Though the Quick
and
Pipes (1975) model is over twenty years old, it should be
emphasized that the development of a more advanced two- or three-dimensional
flow model that would permit the study of horizontal and vertical channel varia-
tions, is limited by the lack of river survey data. The Fraser and Thompson Rivers
^_^
_^I
_^..:--LI_
^L...._
11_-_
..-?I
I_...._
_^.
l-0--
-L--r-J
^^
.L..
P.
V
^...-^-^^
L
l?..
Luc.
l,UL
rla”Lga”Ie
avove
1
It-G
all
1111G
I,,
E;GLI
CLL(IILc;
aa
LLIC;
3,.
LdWLG;IILG
,163,
,,
example. Only at the previously-mentioned five gauging stations along the two riv-
ers has WSC performed the necessary measurements to establish the flow versus
width relationships listed in Table 2 and required by a routing model.
3
The temperature model
a
Suflace Heat Exchange Calculation
The river temperature calculation is a simple combination of heating from both the
surface, and either upstream and/or tributary input. We first deal with the surface
calculation.
There are a number of different processes that transfer heat between a natural
body of water and its surroundings. Back-radiation, evaporation and conduction are
responsible for heat dissipation into the atmosphere while shortwave solar radiation
and longwave atmospheric radiation are primarily responsible for heat absorbtion by
the water body (Edinger et al., 1974). The net rate of heat transfer from the sur-
roundings into the body can be expressed as:
%,I
=
(Hs
-
H,,) + (H,
-
H,,)
-
Ho
-
H,
-
H,
= Hs,,, +
Haner
-
Hh
-
H,
-
H,
(1)
where
H,y
is the short-wave solar radiation rate,
H,
is the long-wave atmospheric
radiation rate,
Hb
is the long-wave back radiation rate,
H,
is the rate of evaporation
heat loss,
H,
is the rate of conduction heat loss,
H,y,
is the reflected solar radiation
rate,
H,,
is the rate of reflected atmospheric radiation, and
H,,,,,
and
Hanet
are
net
rates. All these heat exchange rates are expressed in W
rne2.
Briefly,
shortwave solar radiation
is that radiation received directly from the
sun through the earths atmosphere. Its magnitude at any given point depends on
Flow and Temperature Models for the Fraser and Thompson Rivers
/
115
the suns inclination with respect to the horizon and the cloud cover (Edinger et
al., 1974).
Longwave
atmospheric radiation
results from the absorbtion and
re-
radiation of solar radiation, primarily by water droplets and vapour in the atmo-
sphere. Its magnitude is related to cloud cover and cloud altitude (Edinger et al.,
1974). Both shortwave solar and longwave atmospheric radiation are independent
of water temperature and are subject to reflection and scattering at the air-water
interface (Edinger et al., 1974). In contrast, the
hack-radiation
emitted by a water
body is
dependent
on the water temperature following
Stefans
Law.
Conduction
and
evupporutionkondensution
also depend largely on the water temperature,. or
more accurately, the difference between the air and water temperatures (Edinger
et al., 1974).
The precise formulation of these heat exchange components follow those given in
Edinger et al.
(I
974) and Wunderlich
(1972),
and are summarized in the following
set of equations:
HslltV
=
0.94H,Y
(2)
H
ane,
=
(0.937
X
lO_)a(7;,
+
X)6(
I
+
0.17@)(
1
-
0.03)
(3)
Hb
=
(0.96)~(7;.
+
7-J4
(4)
H,
=Aw)(e,
-
e,)
(5)
AW)
= 9.2
+
0.46W2
(6)
e
(1
=
e2.3026[a7jl(Td+
h)+
(.I
(7)
e,
=
e2.3026[uT,l(TX
+
6)
+
cl
(8)
H, =
(0.47)flw)(7;.
-
T,).
(9)
T,,
q.
and
Td
are the air, water surface and dewpoint temperatures respectively (“C),
T:
is the absolute temperature corresponding to zero
“C
(=273.
I5
K),
u
is the
Ste-
fan-Boltzmann constant
(=5.67
x
1
O-
W
m-*
K$,
C is the fractional cloud cover,
W
is the wind speed in m
s-l,
and the evaporation constants a,
h
and
c
are given as:
u
= 7.5,
b =
237.3, c = 0.6609.
H,,
T,,
Td,
C
and
W
are assumed to be available
from a meteorological service.
b
Heat Budget Equation
The governing equation for the temperature model takes into account the heat
exchanged at the surface of the water as described in Section
3a,
as well as
the
heat
advected from upstream and from tributaries. It is equally applicable to rivers and
lakes and has been previously used in the time varying analysis of a cooling pond in
(Edinger et al., 1968) and of the Nechako River in (Envirocon, 1984). Specifically,
the heat budget equation is
aW.7)
a(QTs>
Kw,
aQ,rTs,,
-+------_---+
at
aA
PC,,
aA
(10)
116
/
M.G.G. Foreman et al.
where
A(x,t)
is the cumulative surface area
(m2),
h(x,t)
is the hydraulic mean depth
(m),
T,(x,t)
and
7;.,,.(x,t)
are the mainstem river and tributary temperatures respec-
tively
(“C),
Q(.x,rj
and
Q,k~,t)
are the mainstem river and cumulative tributary flow
rates respectively
(m3
s-l),
H,,,l(x,t)
is from Eq.
(1).
p
is the density of water
(=
1000
kg
mm3),
and c,, is the specific heat capacity of water at constant pressure (=4186 J
kg- C-I). The first term on the left of Eq. (10) represents the change in heat stor-
age with time, while the second term represents the net heat flow into or out of a
fixed position along the river (Triton Environmental Consultants, 1995). The right
side contains the surface heat exchange term as described in Section
3a,
and a tribu-
tary inflow term that must be averaged over an area in order to maintain consistency
in the units.
The costs associated with an extensive river survey preclude the likelihood that
there will soon (or ever) be sufficient bathymetric data to develop reliable two- or
three-dimensional flow and temperature models for the entire Fraser and Thompson
Rivers. The present one-dimensional models obviously do not permit the representa-
tion of transverse mixing that in some rivers can persist for long distances below the
confluence with tributaries. However, most sections of the Fraser and Thompson
Rivers
are
lasi
muvillg
ad
IlliAillg
iiiK;S
UCCUi
SiiKiuXiilji
~-dp;Gj;
CLG
hi-
iiiSiXL&
neous mixing assumption implicit in Eq. (10) is reasonably valid. Summer aerial
photographs (obtained from Maps B.C., Ministry of Environment, Lands and Parks,
B.C. Provincial Government) showing the confluences of the Nechako, Quesnel,
Chilcotin and Thompson Rivers with the Fraser River, and the confluence of the
North and South Thompson Rivers, demonstrate that only in the case of the
Nechako do the different water colours persist longer than one grid cell (10 km)
downstream. (Due to heavy sediment content, the Frasers brown colour is easily
distinguishable from that of its tributaries.) In the other cases, rapids or turns in
the river cause relatively quick mixing.
1
DISCRETIZATION
In order to maintain consistency, the same IO-km grids that are used for both the
Fraser and Thompson flow models are also used for the temperature models. In par-
ticular, the flow rates and velocities from these models are associated with the
downstream cross-sections of particular subreaches in the temperature model.
Equation 10 is discretized with the following forward Euler finite difference
scheme
h(n,,)Ts(n,,)
-
h(n,r-~)Tss(n,r-~)
+
Q(n,r,?vcn,r,
-
Qcn-I$.wI,~)
At
WW)
H
Qrr(n,t)7-srr(n.r)
IV?,
=-+
PCP
4l.r)
7
01)
where
n
is the
subreach
number,
t
is the time step, AA,,, is the surface area of the
Flow and Temperature Models for the Fraser and Thompson Rivers
/
117
reach, and
Q,,.,,,,,
is the flow increment due to a tributary (or tributaries) entering
subreach
n.
Rearranging for
T,,,,,,
then yields
T
s(n,,)
=
c Supplementary Calculations
1
RIVERSUBREACHES
As Eq. (12) shows, the solution for jr.,,,,,
depends on a number of variables. Of
these, only the depth,
/I(,,,,,
and surface area, AA,,,,,, are not given as model input or
calculated in the previous iteration. Steeper rivers are frictionally controlled (Quick
and Pipes, 1975) and their flows are governed by kinematic, rather than dynamic,
wave theory. In particular this means that the flow is quasi-steady at any point and
can be expressed as being proportional to either the river surface width,
w,
or the
stage,
-rt,
which is defined as the height of the free surface with respect to a fixed ref-
erence (Lighthill and Whitham, 1955; Seddon, 1900). Here we assume that the river
bed is independent of time and
/I
= q +
H,
where
H is
the river depth below the
same fixed reference. The calculation of depth via
h(
n,
,)
=
(Qd+v))
(13)
W(V)
then follows by equating two expressions for the time-varying cross-channel area.
The flow rate,
Q(,,,,,
and the cross-sectional velocity,
v,,,,,,,
are output from the flow
model, while
w,,,,,
is obtained from the following relationship between flow rate and
river surface width
w(,.,)
=
%Q,",l,,.
(14)
The constants
a,
and b,, are site specific and depend on the geometric characteristics
of the river cross-section. They are determined using a linear regression algorithm
together with data collected by WSC. Table 2 gives the
a,,
and
6,
values for the five
WSC river gauging stations and their assignments to model subreaches.
The river surface area over which the heat exchange occurs is given by
4n.t)
=
2tw(.,t)
+
w(,-I,,)W
where
w,,,,,
is from Eq. (14) and Ax =
10
km.
(1%
2
LAKESUBREACH
In the Thompson River system, Kamloops Lake is designated as model
subreach
7.
For the purposes of the heat exchange computation, the lake depth is assumed to be
the surface layer thickness with initial values being taken from Fig. 4 in Killworth
118
/
M.G.G. Foreman et al.
and
Carmack
(1979). Computation of the surface area over which the heat exchange
occurs is more complicated for a lake
subreach
than for a river subreach, as it
requires the two constants
and
dV
C&v
=
-&-
(17)
where
z
is the lake elevation (m) and
V
is the volume
(ms).
Given that
AM?,)
= A; +
aA,
where
Ah,,,
and
Ai
are the current and initial areas of the lake respectively and
dA
is
the change in area since the start of the simulation, then
(18)
where
aV
is the change in volume since the start of the simulation. Its calculation
follows.
The volume of each subreach is calculated during the course of the simulation as
a check to make sure that the flow data is correct and to provide an input for the lake
surface area calculation mentioned above. If the volume in one of the subreaches
drops to zero or swells to an unreasonable amount, the temperature calculation will
be adversely affected. Thus, by keeping track of subreach volume, the model can
provide a diagnostic for the temperature calculations. The volume of a
subreach
is
calculated as:
V(W)
=
v,,,,,
-
I)
+
av
=
Vcn.,
-
1)
+
(Qcn
-
1.0
+
Qrtw,
-
Q,n,,,)Af~
(19)
and assumes knowledge of the initial volume. For a lake, this is obtained from an
available volume versus elevation relationship or is calculated from the lakes initial
depth,
h,
and initial surface area,
A,
as
For a non-lake subreach, the calculation is similar,
V(,*,O)
=
1
4J)
$h(,,O,
+ &-LO,).
(21)
Flow and Temperature Models for the Fraser and Thompson Rivers
/
119
Needless to say Kamloops Lake is much more complicated than the simple repre-
sentation assigned to it in this model. Numerous studies have been performed on the
lake and have identified a variety of interesting phenomena such as cabbeling and
convective overturning (Carmack,
1979),
inflow waters that plunge below the sur-
face layer (Killworth and Carmack,
1979),
and wind generated seiches (Hamblin,
1978). Nevertheless, we feel that our simple treatment can be justified. For the pur-
pose of salmon migration, the most important temperature in the lake is that at the
outflow, as it determines the temperatures further downstream. (When delayed by
six hours, the 1994 river temperatures measured at Savona had a 0.94 correlation
with those at
Spences
Bridge.) We assume that salmon entering the lake can swim to
a depth where the temperatures are sufficiently cool that they may avoid any addi-
tional thermal stress. So from a biological perspective, it is not important that we
accurately represent the entire three-dimensional thermal patterns in the lake. Our
computational efforts are therefore focused on calculating heat transfers to the sur-
face mixed layer as its temperature will determine that of the outflow.
Cam-rack
(1979) describes the lake circulation in the spring before the late June through Sep-
tember time period when the salmon are migrating. During the summer, there is no
cabbeling or convective overturning (both of which typically occur in April and
early May (Fig. 4, Carmack
(1979))),
the lake is thermally stratified, and, as seen in
Fig. 8 of Hamblin and Carmack
(1978),
the transverse sections of temperature are
close to horizontal. During this time, inflow from the Thompson River is colder than
the surface water in Kamloops Lake and plunges to a depth of about 20 m (Fig. 4,
Killworth and Carmack (1979)). So apart from wind effects, the heat transfer is sim-
ply confined to the surface mixed layer.
However wind-generated upwelling, seiches (Hamblin, 1978) and mixing are not
considered in the present model and their effect on the outflow temperatures at
Savona admittedly requires further study. The predominant orientation of Kamloops
Lake is east-west and, as seen in Fig. 3, there are several instances
(e.g.,
1 October
and 30 August) when strong persistent winds from the west (east) are associated
with cooler (warmer) outflow temperatures. The correlation coefficient between
Savona outflow temperatures and the cast-west component of the wind at Kamloops
is -0.40 over the period July through October 1994. For comparison, the correlation
coefficient between Savona temperatures and those from the eastern end of the lake
(just downstream from Kamloops) is 0.87, while the correlation between the Savona
temperatures and the Kamloops air temperatures is 0.25. Were wind-driven
upwelling (and downwelling) significant we would expect a much smaller (perhaps
even negative) correlation between the two ends of the lake.
Seiche effects are more difficult to quantify. A spectral
(FFT)
analysis of the
I994
temperatures at Savona does not reveal any significant peaks in the
33-
to 69-hour
period band. This is the range suggested by Hamblins (1978) theoretical calcula-
tions that used water temperature observations between June and October 1974. The
largest 1994 signals are near the diurnal and semi-diurnal frequencies, reflecting the
strong diurnal variations in air temperature. Nevertheless, both wind and seiche
120
I
M.G.G. Foreman et al.
lo-L_
Jcl
2/1994
J&6/1994
I
Aug19/1994 Sepl2/1994
Ott
6/1994
oct30/1994
Date
Fig. 3
1994 water temperatures
(“C)
at the eastern (dashed) and western (dotted) ends of Kamloops
Lake, and the cast-west component of the Kamloops airport wind (m/s) shifted up by 15 m/s
(solid).
effects will be studied further and attempts will be made to represent them in a
future, improved version of the model.
4 Model results for 1993 and 1994
An extensive electronic temperature monitoring network (see Fig. 4) that was
installed and maintained in the Fraser Watershed during the summers of 1993 and
1994 (Lauzier et al., 1995) provided considerable data with which the temperature
model could be tested and verified. The data loggers were programmed to store the
average temperature over hourly periods and were located at positions that were
deemed to be sufficiently well-mixed that the observations would be representative
of that reach. This assumption was verified by taking cross-stream profiles at loca-
tions FR245, FR262, FR610, FR763, NR3, TR24, TR 113 and
TRI
63 (Lauzier et al.,
1995).
Meteorological data required for the temperature model were supplied by the
Atmospheric Environment Service, while headwater and tributary flow data
required by the flow model were obtained from WSC. Although the meteorological
time-series were complete, the river flow and temperature time-series had occa-
sional gaps that were filled by either linear interpolation or correlations with nearby
stations. Unknown temperatures for the ungauged tributaries were estimated based
Flow and Temperature Models for the Fraser and Thompson Rivers
/
121
FRASER
RIVER TEMFEFLATURE STATIONS
Fig. 4
Location of the temperature data-loggers in
1993
and 1994. Tables 3 and 4 list those sites used in
comparisons with the model data.
122
/
M.G.G. Foreman et al.
on records for nearby streams or by setting them equal to modelled temperatures for
the nearest upstream mainstem segment. The latter approach meant that they would
have no effect on the temperatures further downstream.
Calibration of the temperature model was conducted using available hourly data
for the period of 1 May to 30 September 1993. Results of the calibration revealed
that no adjustments were required to the input data or parameters in order to obtain a
pre-determined accuracy threshhold of 1 .O to 15°C. The initial depth of the surface
layer for Kamloops Lake was assumed to be 10 m, and Kamloops meteorological
data were used for the entire model domain. Further studies and a discussion on the
suitability of this data will be given in the context of the 1994 simulations.
Figure 5 shows the observed and modelled temperatures at Hells Gate
(5a)
on the
Fraser River and near Spences Bridge
(5b)
on the Thompson River. In both cases,
the data loggers were not installed until July so a full comparison with the model
temperatures beginning 1 May was not possible.
Table 3 shows the average and root mean square (rrns) difference between
observed and computed mean daily temperatures at thirteen sites on the mainstem
Fraser and Thompson Rivers. (See Fig. 4 for the precise locations.) Times when the
observed temperatures were missing were not included in the calculation. The aver-
age rms difference for the thirteen sites is
0.7O”C
and on average, the computed tem-
peratures were
0.23”C
lower than the observed values.
For 1994, limited headwater temperature data meant that the Fraser and Thomp-
son River models could only be run for the periods of 10 July to 13 September and
10 July to 27 October respectively. Figure 6 shows observed and computed mean
daily flows near Spences Bridge in the Thompson River, and in the Fraser River
above Texas Creek for these simulation periods. Consistent differences between the
observed and computed mean daily flows are due to the ungauged tributaries. How-
ever, adjustments for these ungauged flows were made and incorporated into the
flow and velocity output required by the temperature model.
The Thompson River model was run with only Kamloops meteorological data
while the Fraser River model was run with both Kamloops and Prince George mete-
orological data. Figure 7 shows the observed and computed mean daily water tem-
peratures in the Fraser River at Hells Gate (7a) and in the Thompson River near
Spences Bridge (7b) for the respective simulation periods. Table 4 shows the aver-
age and root mean square (rms) differences between observed and modelled temper-
atures at fifteen measurement sites in the model domain. Clearly the Kamloops
meteorological data produces more accurate model results than the Prince George
data for most of the Fraser watershed. In fact the local meteorological data produced
more accurate model temperatures for only those sites within 76 km of Prince
George. This suggests that the Prince George (airport) data is only representative of
a small region.
Notice that the 22 July through 12 August and 5 October through 26 October seg-
ments of the observations shown in Fig. 7b appear to have a four-day signal super-
imposed on the longer term trend. Spectral analyses of the TR24 time-series reveal
Flow and Temperature Models for the Fraser and Thompson Rivers
/
123
12
1
I
I I
I
1
JuI24/1993 Aug
L/l993 nug15/1993
Aug26/1993
Sop
6/1993
Sep17/1993 Sep26/1993
Date
22
I
I
I
I
I
b
-
zo-
14
I
I
I I
I
1
JuIl3/1993
JuI25/1993 Aug
6/1993
n"gls/1993
Aug30/1993
sep11/1993 ssp23/1993
Dote
Fig.
5
1993 observed (solid) and modelled (dotted)
temperacures
at a) Hells Gate on the Fraser River,
and b) Gold Pan near Spences Bridge on the Thompson River.
124
I
M.G.G. Foreman et al.
T
ABLE
3. Average and root mean square differences between 1993
observed and modelled temperatures using Kamloops meteoro-
logical data. (Difference
=
observed-modelled)
Observation Site
Code River Reach Average RMS
Gold Pan Park
TR24
Thompson
Weyerhauser Mill
TR163
Thompson
Hells Gate
FR200
Fraser
Siska Creek
FR245
Fraser
Upstream of Lytton
FR262
Fraser
Saulus
Creek
FR337
Fraser
Big Bar Ferry
FR390
Fraser
Upstream from Chilcotin
FR500
Fraser
Marguerite Ferry
FRSSO
Fraser
Upstream from Quesnel
FR617
Fraser
Whites Landing
FR687
Fraser
Stoner
FR730
Fraser
Prince George
FR763
Fraser
17
6
59
54
53
45
40
29
24
17
10
6
0.14 0.70
0.42
0.83
0.15 0.65
0.51 1.05
0.20 0.78
0.42
0.7 1
0.33 0.69
0.35 0.68
0.44 0.75
0.02 0.84
0.17 0.57
0.08 0.52
-0.17
0.30
energy at periods of about 4.4 days in the first interval, and of about 3.6 days in the
,.,,,%...,I
:nrw..ro1
,..
+I.,_
4-G_.,
;..,.,,..nn
*I.,.
TD?
l
:...,.
,.,.A,...
..,.-,.I..+--
. .
..*I.
“,.,.4x
O~C”,,”
*,,,c1
t&u.
II.
L11b
lll.Y.
IIIJLUIIbti,
L1.b
11.L-r
L*III~-.>cL*cIJ
b”IIL1ULcIJ
w
Llll
L”L.11
cients
between 0.5 and 0.7 (depending on the lag) with the TRI 13 time-series and in
the second instance with coefftcients greater than 0.95. This suggests that a signifi-
cant portion of the four-day oscillation arises further upstream, perhaps from
Kam-
loops Lake. Spectral analyses of both components of the Kamloops wind display
broad energy peaks around these same periods, and correlate weakly (-0.22 for the
east-west component and 0.33 for the north-south component) with the TR24 tem-
peratures. The former correlation suggests that the TR24 temperature oscillations
may be related to upwelling and/or mixing in the lake while the latter suggests that
there may be direct wind effects in the section of the Thompson River above TR24
that flows predominantly southward. These phenomena will be studied further and
the findings will be incorporated into an improved version of the model.
The average rms difference between the observed and modelled (with Kamloops
meteorological data) river temperatures for 1994 was
0.6O”C
and on average, the
model temperatures were now
O.OYC
lower than the observed values. The fact that
the model results were on average 0.57lower than the observations at the Weyer-
hauser Mill site downstream of the contluence of the North and South Thompson
Rivers suggests a problem with either the model or observations. As this systematic
bias does not persist further downstream, we suspect that the data-logger is in a loca-
tion that is preferentially sampling more of the warmer South Thompson waters,
rather than the well-mixed waters from both rivers.
Figure 8 contours modelled Thompson temperatures for the 1994 simulation.
Time, from 10 July to 27 October, extends along the x-axis while the river extent,
from the headwater downstream, is along the y-axis. The most notable features of
Fig. 8a are the cooling influence of the North Thompson River and the warming
influence of Kamloops Lake. Over the modelling period, the North Thompson flows
Flow and Temperature Models for the Fraser and Thompson Rivers
/
125
1
0
.I
I
I
1
JuIlO/1994
JuI21/1994
Aug
l/1994 Aug12/1994 Aug23/1994
Sep
3/1994 Sep14/1994
DotI?
0.01..__._
I
JuIlO/1994
Aug
l/1994
Aug23/1994
ssp14/1994
Ott
6/1994
Oct26/1994
Dote
Fig.
fj
1994 observed (solid) and modelled (dotted) flows at a) Texas Creek on the Fraser River, and b)
Spences Bridge on the Thompson River.
126
/
M.G.G. Foreman et al.
141..
I
1 1
I 1
J"l1
O/l
994
Jul21/1994
Auq
l/1994
Auql2/1994
Auq23/1994
ssp
3/1994
sep14/
Date
18
E
1
;
:'
u
z.,,
:.'
::
..:'
&
:'
14
12
:;
:.
.
.
. .
--:i
..,
._
..
::
Jd10/1994 Auq l/1994
Auq23/1994 sep14/1994
act
6/1994
Oc128/1994
Dote
Fig.
7
1994 observed (solid) and modelled (dotted) temperatures at a) Hells Gate on the Fraser River,
and
b)
Gold Pan near Spences Bridge on the Thompson River.
Flow and Temperature Models for the Fraser and Thompson Rivers
/
127
T
ABLE
4. Average and root mean square differences between 1994 observed and modelled temperatures
using Kamloops and Prince George meteorological data. (Difference = observed-modelled)
Observation Site
Code River
Kamloops
Reach Average RMS
Prince George
Average
RMS
Gold Pan Park
TR24
Thompson
17
0.24
0.67
-
-
Savona TRl13
Thompson
8
0.11
0.75
-
Weyerhauser Mill
TR163
Thompson
6 0.57
0.77
-
-
Hope
FR149
Fraser
64
-0.16
0.50 0.73 0.89
Hells Gate
FR200
Fraser
59
-0.29
0.64 0.57 0.80
Siska
Creek
l-3245
Fraser
54
0.23
0.69
1.41
1.57
Upstream of Lytton
FR262
Fraser
53
-0.03
0.69 0.97
1.17
Saulus
Creek
FR337
Fraser
45
-0.04
0.62 0.96
1.06
Big Bar Ferry
PR390
Fraser
40 0.10
0.52
1.01
1.08
Upstream from Chilcotin
FR500
Fraser
29
0.03
0.54 0.79 0.87
Marguerite Ferry
FR550
Fraser
24
0.02
0.57 0.68 0.77
Upstream from Quesnel
FR610
Fraser
18
0.01
0.63 0.67 0.73
Whites Landing
FR687
Fraser
10
-0.06
0.50 0.28 0.38
Stoner
FR730
Fraser
6
0.15
0.48 0.35 0.40
Prince George
FR763
Fraser
3
-0.12
0.44 0.02
0.2 1
at Kamloops (the junction of the two rivers) were, on average, 32% larger than the
South Thompson flows while its temperatures were, on average,
2.9”C
cooler. This
produced a net cooling of
1.7”C
downstream of the junction and for some periods,
such as around 14 August, an even larger effect. However, as the average river tem-
peratures after leaving Kamloops Lake were
1.2”C
warmer than those entering the
lake, this net cooling is short-lived. The other tributaries had much smaller flows
and are seen to have virtually no influence on the Thompson temperatures down-
stream of Kamloops Lake.
Figure
8b
is equally revealing for the Fraser River. The Nechako River is seen to
have a consistent warming influence on the upper reaches of the Fraser. Over the
modelling period (10 July to 13 September, 1994) its average temperatures at Prince
George were
3.6”C
higher than those of the Fraser River upstream of Prince George.
However, as its flows (as measured upstream from Prince George) during this
mod-
elling period were, on average, only about 43% of the Frasers, the net warming of
the Fraser just downstream of the confluence was only 1 .l”C. The Quesnel and
Chilcotin River were, on average, cooler than the Fraser by
0.3”C
and
1.8”C,
but at
their respective junctions with the Fraser, their respective flow rates were only 24%
and 13% as large. So their net effect was not significant. On the other hand, the
Thompson did have a net warming effect of
0.4”C
on the Fraser temperatures down-
stream of Lytton between 10 July and 13 September 1994. Its temperatures were, on
average, l.2”C warmer and its flows were about 44% as large as the Frasers.
5
Possible
temperature control scenarios for
1994
Figure B
in Fraser River Sockeye Public Review Board 1994 (1995) gives the
fol-
Flow and Temperature Models for the Fraser and Thompson Rivers
I
129
lowing estimates of the
1994
up-river migration to the major spawning grounds:
Thompson River, 1.6 million; Chilcotin River, 1.56 million; Quesnel River, 0.66
million; Stuart River, 0.11 million; Nechako River, 0.14 million. Although these
numbers vary considerably from year to year depending on each stocks cycle (dom-
inant or subdominant) and numerous physical conditions, they do provide some
indication of the relative size of runs. (It should be mentioned that 1994 was a sub-
dominant year for the Stuart River run. Over the years 1983-1992, Nechako/Stuart
returns comprised roughly one sixth of the Fraser River sockeye resource. However,
in 1993 the estimated wholesale value of Nechako basin sockeye was $77 million,
about three times larger than the 1981-92 average of $26 million (Kemano Comple-
tion Project Review,
1994).)
Given the temperatures shown in Fig. 8, it is clear that,
due to their relatively high flows and warm temperatures, the Nechako and South
Thompson Rivers are two of the largest sources of warming for the Fraser and
Thompson Rivers, respectively. Although other tributaries can be as warm or
warmer (depending on the spring or summer period considered), flows in these other
tributaries are much lower and consequently their effect on the Fraser and Thomp-
son Rivers is much less.
Although there is no direct evidence indicating that warm temperatures in the
Nechako and South Thompson Rivers have caused problems for migrating sockeye,
in this section we investigate two possible scenarios for moderating the tempera-
tures in these rivers and their effects further downstream in the Fraser and Thomp-
son Rivers. The scenarios considered include the discharge of hypolimnetic water
from Stuart Lake into Stuart River for the upper portion of the Fraser River water-
shed, and from Shuswap Lake in the lower portion of the Fraser River watershed
(Fig.
I).
Stuart Lake has deep water at temperatures less than 10°C (E. C. Carmack,
personal communication) that could be added to the natural drainage into the Stuart
River and thus provide the potential for enhancement of the Stuart River salmon
stocks. However, Stuart Lake currently has no means of providing thermally
con-
trolled
discharges and doing so, in fact, could be physically difficult. The Stuart
River enters the Nechako River just downstream of Finmoore and the Nechako then
flows east to its confluence with the Fraser River at Prince George (Fig. 1). Flows
and temperatures in the Nechako River upstream of the Stuart River confluence are
currently being managed under contract to the Nechako Fisheries Conservation Pro-
gram in order to meet fisheries conservation objectives defined in the 1987 Settle-
ment Agreement (Nechako Fisheries Conservation Program, 1988) between
Alcan
Aluminium Limited, the Canadian Federal Government and the British Columbia
Provincial Government. As the present water temperature and flow models do not
explicitly include
the
Stuart/Nechako system,
the
effects of introducing the cooler
Stuart River waters on temperatures in the Nechako River at Prince George, and fur-
ther downstream in the Fraser, can only be estimated.
The first temperature control scenario considered assumes that the flows in the
Nechako River at Prince George remain unchanged from the flows recorded in
1994,
but the 1994 temperatures at the same location are reduced through thermally
130
/
M.G.G. Foreman et al.
controlled releases from Stuart Lake. The new time-series of Nechako River temper-
atures (at Prince George) were simply calculated by replacing all temperatures
greater than 18°C with
18C.
As seen in Fig. 2, this reduces the recorded tempera-
tures by as much as 3S”C in the 13 July to 23 August period, and by as much as
0.7”C
in the 30 August to 1 September period. The results of rerunning the 1994
simulation with this new Nechako time-series are shown in Fig. 9. (It should be
mentioned that for this run, the ungauged lateral temperatures remained the same as
for the 1994 simulation.) Comparison with the original 1994 simulation reveals that
the high temperatures in the Fraser River at Prince George for 26 July, 15 August
and 1 September were reduced by
0.8”C,
0.9”C
and
0.2”C,
respectively, while
downstream at Hope, they were only reduced by
0.2”C,
0.
1°C and
O.OlC,
respec-
tively. Thus, due to the relative magnitudes of the Nechako and Fraser River flows
at their confluence, and the large tributary inflow entering downstream of Prince
George, significantly cooler Nechako temperatures may not have a large effect on
Fraser River temperatures. Consequently, the major effect of thermally controlling
Stuart River temperatures would be to reduce temperatures in the Stuart River and in
the Nechako River between the Stuart River confluence and Prince George, and
pos-
-:I..,.,
..,,..:A,
l,-..
rrr,rnt-..l
,.,...,4;r:,.,,-
c,..,
,.,.I
-_.._
-:,.-,.r:-..
:..
rL_r
-^-r:-..l
^_
r-L..
0V.J
~...Uti
.tiJi)
LI.Iti.JJI.
C”IL”.l.“llJ
I”.
a-nti~c
Wlg.*rl”rr
L11
ulal
rJalU~“lal
u*uu-
tary system of the Fraser River.
Although further study is required to confirm any potential benefits to fish, the
preceding temperature control scenario may have helped sockeye returning to the
Stuart, Nechako, Quesnel (Horsefly) and Chilcotin Rivers in 1994. Providing cooler
temperatures for salmon migrating up the Thompson River to, for example, the
Adams River, would require a different strategy. Moderating the Thompson River
temperatures might be accomplished, in a manner similar to that for the Stuart sys-
tem, by accessing cooler waters from the depths of lakes in the system. Kamloops
Lake is an obvious candidate but since it is located downstream from the confluence
with the cooler North Thompson, it cannot affect the South Thompson temperatures.
An alternative is Shuswap Lake, located just upstream of the present model
headwa-
ters at Chase. Previous studies (Ross, 1984) in Shuswap Lake indicate that water
colder than 10°C does exist below the thermocline in summer. However, as these
studies were not conducted near Chase, if this temperature control scenario were to
be pursued, field work would be necessary to ascertain the precise temperature of
available deep water. For the purpose of this discussion, it was assumed that such
cold water is available. The second temperature control scenario then simply consid-
ers the addition of thermally controlled waters to the 1994 flows recorded at Chase.
Figure 10 shows the effect of adding 100
m3/s
of 10°C water to 1994 tempera-
tures recorded at Chase. The new time-series of Chase temperatures were calculated
using a simple blending equation, namely
T,
=
KQ,
+
T,QaY(Qo
+ QJ.
(22)
T,,
is
the
new temperature, and the o, a subscripts denote the 1994 values and the
additional values respectively. Comparison with Fig.
8a
shows that significant
cool-
Flow and Temperature Models for the Fraser and Thompson Rivers
/
133
up to
WC), the
Fraser River temperatures immediately downstream of Prince
George for 26 July,
I5
August and 1 September were reduced by
O.SC,
0.9”C
and
0.2"C,
respectively, while further downstream at Hope, they were reduced by
0.2”C,
O.l”C
and
O.Ol”C,
respectively. These results demonstrated that the use of cool
water from Stuart Lake would be most beneficial in the Stuart River and in the
Nechako River downstream from the Stuart River confluence, and would provide
only a limited benefit to Fraser River temperatures due to the relative magnitude of
the Fraser and Nechako River flows and the effect of additional tributary inflow
downstream. It was also shown that an additional 100
m3/s
of 10°C water from
Shuswap Lake would have been sufficient to lower the South Thompson peak tem-
peratures by
1.7”C
and
2.4”C
for the same July and August time periods.
Aside from cooling, no other implications of accessing deep water from Stuart
Lake or Shuswap Lake were considered. For sockeye, possible detrimental factors
that would require further investigation include lower oxygen levels, elevated levels
of total gas pressure, higher sediment levels and stronger river velocities. Although
the infusion of these additional cool
waters
could admittedly affect all aspects of the
riverine system, a discussion of other biological effects is beyond the scope of this
paper. However we do wish to emphasize that our scenarios are not intended to
cause long term changes to the river. They would only be temporary infusions of
cooler water comparable to those that could occur naturally from, for example, a
heavy rainfall in the mountains (as was experienced in 1995).
Obviously, the direct and indirect costs associated with accessing cool water
would also have to be included in a complete cost-benefit analysis. The purpose of
the foregoing exercise was only to examine the effects of cooler headwater or tribu-
tary inputs on mainstem temperatures further downstream. The results presented
indicate that the use of cool water from the identified sources could be beneficial in
reducing temperatures and providing assistance to migratory sockeye salmon.
Future work will include the development of new models for the Stuart/Nechako
and
QucsncUHorscfly
River systems, a more thorough investigation of temperature
control scenarios, and use of the present model to provide ten-day forecasts of river
temperatures in order to estimate in-river mortality and assist fisheries managers in
their regulation of commercial and sport fishing. The results of this work will
be presented in future publications.
Acknowledgements
We wish to thank Ian Williams, Tom Brown and Ray Lauzier for helpful comments
and for providing both the temperature observations and Fig. 4.
References
RO,,CK,
G.R.;
G.A. CHAPMAN. P.W.
SCHNEIDER,JR.
Annual Northwest Fish Culture Conference, 3-5
and
D.G.
Sl'EVENS.
1975. Effects of holding
tem-
December 1975, Otter Rock, Oregon, pp.
24-40.
perdture
on
reproduclive
development in adult
CHARMACK
, E.C.
1979. Combined influence of
sockeye
salmon
(0ncorhyrrchu.s
wrka). In:
inflow and lake temperatures on spring circula-
134 / M.G.G. Foreman et al.
tion in a riverine lake.
J.
Phys.
Oceanogr.
9(Z):
422-434.
EDINGER,J.E.;D.K.BRADY
and
w.L.GRAVES.
1968.
The
variation of water temperatures
due to
steam electric cooling operations. J.
Wafer
Pol-
lur.
Corm
Fed.
40(9):
1632-1639.
-;
_
and
J.C.
GEYER.
1974.
Heat
Exchange and Transport in the Environment.
Electric Power Research Institute, Palo Alto,
California, U.S.A. 124 pp.
ENVIROCON
.
1984. Kemano Completion Hydro-
electric Development Environmental Studies.
Vol. 2. Physical and Hydrological Studies:
Baseline Information. Section E. Prepared for
the Aluminum Company of Canada, Ltd. Van-
couver, B.C., 105 pp.
FRASER RIVER SOCKEYE PUBLIC REVIEW BOARD.
1995.
Problems
&
Discrepancies. Public Works
and Government Services Canada, 1995. Can-
ada Communications Group
-
Publishing,
Ottawa.
I3
I
pp.
GILHOUSEN,
P
.
1990. Prespawning Mortalities of
Sockeye Salmon in the Fraser River System and
Possible Causal Factors. Bulletin XXVI,
Intcr-
national Pacific Salmon Fisheries Commission.
Vancouver, B.C., 53 pp.
HAMBLIIV.
P.F.
1978. Internal Kelvin waves in a
fjord lake. J.
Ger~phys.
Res.
83(CS):
2409-
2418.
-
and
E.C. C
ARMACK
.
1978. River-induced
currents in a fiord lake.
J.
Gec@rys.
Res.
83(C2):
885-899.
KEMANO COMPLETION PROJECT REVIEW.
1994.
Report and Recommendations to the Lieutenant
Governor in Council. Chair of the Review:
Loma
Barr. British Columbia Utilities Commis-
sion, December 1994.260
pp.
KILLWOR?H,P.D.
and
E.C.CARMACK.
1979. A fill-
ing-box model of river-dominated lakes.
Lim-
nology
Oceanogr.
24(2):
201-2
17.
LAUZIER,
R.; T.J. BROWN,
I.V.
WILLIAMS
and
L.C.
WALTHERS. 19%.
Water temperatures at
selected sites in the Fraser River Basin during
the summers of 1993 and 1994. Canadian Data
Report of Fisheries and Aquatic Sciences No.
956, Department of Fisheries and Oceans,
Nan-
aimo, B.C., 86
pp.
LIGHTHILL, M.J.
and
G.B. WHITHAM.
1955.
Dtl
kinematic waves: I
-
Flood Movement in long
rivers.
Proc.
R.
Sot.
London,
Vol. 229, No.
1178: 281-316.
MOUNTAIN HYDROLOGY
GROuP.
1994. U.B.C.
Flow Model Manual Version 2.0. Department of
Civil Engineering, University of British Colum-
bia, Canada. September 1994,
62pp.
NECHAKO
FISHERIFS
CONSEKVATION PROGRAM.
1988. Annual Report. Appendix A.
QUICK
, M.C.
and
A
.
P
IPES.
1975. Nonlinear Chan-
nel Routing by Computer, J.
Hydraul.
Div.
ASCE,
Vol.
101,
No.
HY6:
651664.
-
and
-.
1976. A combined snowmclt
and rainfall model.
Cdn. J. Civil
Engin.
3: 449-
460.
ROSS, M.
1984. The Trophic Status of Shuswap
Lake. Regional Program Report 84-20, Envi-
ronmenull
Protection
Servictt:
Acptic
Program
and Contaminants Control, Pacific and Yukon
Region,
114
pp.
SEDDON,
J
.
A
.
1900. River Hydraulics,
Trans.
ASCE,
Vol. 43 No. 871: 179-229.
SERVIZI,
J
.
A
.
and
J
.
O
.
T
.
JENSEN
.
1977. Resistance
of adult sockeye salmon to acute thermal shock.
International Pacific Salmon Fisheries Commis-
sion Progress Report No. 34,
I1
pp.
TIIOMSON,
R.E.
198
I.
Oceanography
of
rhe British
Columbia
Cousf,
Canadian Special Publication
of Fisheries and Aquatic Sciences
56,291
pp.
TRITON
ENVIRONMENTAL CONSULTANTS LTD.
1995.
Temperature Prediction Model for the
Mainstem of the Fraser and Thompson Rivers.
Report prepared for Department of Fisheries
and Oceans, Institute of Ocean Sciences, Sidney
B.C. March, 1995.31 pp.
WUNDERLICH,
W
.
1972. Heat and Mass Transport
Between a Water Surface and the Atmosphere.
Tennessee Valley Authority, Division of Water
Control Planning Engineering Laboratory.
Water Resources Research Laboratory Report
No. 14 (Report No. O-6803) Norris, Tennessee,
April 1972,
I64
pp.
@
Printed on Recycled Stock
... Surface heat fluxes are estimated by applying the method in Cole and Wells (2017) suggested by Edinger et al. (1974). Consequently, the net surface heat flux (H t ) in Watt/m 2 and as follows (Foreman et al., 1997) : ...
... Atmospheric long-wave radiation is the radiation that results from the absorption and re-radiation of solar short-wave radiation, mainly by water drops and vapor in the atmosphere. It depends on cloud cover and cloud altitude (Foreman et al., 1997;Wang & Dickinson, 2013). Both short-wave solar and long-wave atmospheric radiations are not a fashion of water temperature and are submitted to be scattered and reflected at the interface of air and water (Foreman et al., 1997). ...
... It depends on cloud cover and cloud altitude (Foreman et al., 1997;Wang & Dickinson, 2013). Both short-wave solar and long-wave atmospheric radiations are not a fashion of water temperature and are submitted to be scattered and reflected at the interface of air and water (Foreman et al., 1997). While the solar radiation measurements are comparatively available from numerous meteorological stations, the long-wave radiation measurements are computed. ...
Thesis
Full-text available
Accurate estimation of surface heat exchange and its components is the basis for simulating surface water quality, especially in lakes and reservoirs, because the direct heat transfer between water and air affects thermal stratification. In this work and based on high time resolution data of water surface temperature and meteorological parameters from Lawrence Lake (OR, US), the term-by-term method was used to model surface heat fluxes (solar and atmospheric radiation, back radiation, evaporation, and conduction) by using the MATLAB environment to develop the code and simulate the results. The developed model is considered as a stand-alone model and can be used by other authors to simulate temperature in surface waterbodies. The ability to highlight the contribution of each flux is the main feature of the model, providing evidence of the strong interaction between the water surface and the atmosphere. This interaction cannot be neglected in surface water quality modelling. During the study period (487-670) Julian day, the results showed that summer solar energy was the highest intensity with a peak record of 842.05 Watt/m2 at 540.91 Julian day. And because of the natural event of sunrise and sunset, solar energy has its daily fluctuation. It fluctuates between 0 Watt/m2 at night and reaches its daily peak at approximately noon. Although the maximum value of evaporation heat flux was recorded at 578.44 Julian day (359.77 Watt/m2), the minimum conduction value at 655.54 Julian day was (126.039 Watt/m2). Back radiation fluctuates less than other fluxes. This returns to its dependence on one variable factor, which is water temperature. The maximum value, recorded to the back radiation, was (410.06 Watt/m2) related to the maximum water temperature (21.5 oC). The simulation of the model highlighted the influence of the solar radiation bell-shaped curve on the total heat flux curve. In addition, the model implementation of Edinger's suggestion for wind speed coefficients (b1 = 9.4, b2= 0 and b3 =0.46) was used as a feature in the model to calibrate the total heat flux. It was found that the resulted curves of this calibration simulated the fluxes but in different ranges. For more flexibility, other suggestions from several wind functions were applied in the model. It was found that (Ahsan & Blumberg, 1999; Arifin et al., 2016; Ji, 2017) models were the closest to the Edinger's model. Furthermore, a wind sheltering coefficient (WSC) was proposed and taken into account as a multiplication factor of wind speed. In order to link the developed model with the advection-dispersion equation, a case study was performed based on field data from an aeration basin located in Al-Muamirah wastewater treatment plant. Based on available data from the Al-Muamirah wastewater treatment plant, the model was run for 24 hours to estimate the temperature along the aeration tank. Some data has been enforced due to a lack of data related to the research location. After multiple trials, the hypothesis was validated. The predicted temperatures were very close to the real data. The MAE and RMSE were relatively low. It's also worth noting that the arrival of waste water heralds the start of a new heat wave, which steadily intensifies until it reaches the basin outlet, when it reaches its peak. With each entry, the process is repeated. The low errors values demonstrate the model was able to simulate the aeration basin temperatures efficiently. At 10 a.m. on 28/6/2021, the measured wastewater temperature at the middle of the tank was 30 oC and the estimated wastewater temperature at the middle of the tank was 29.81 oC. Moreover, several plots presented the estimated temperatures for the aeration basin for 24 hr were displayed.
... The study area in the present study is the Lower Fraser River (LFR). The Fraser River is the largest river in Canada flowing into the Pacific and a key pathway for the migration of Pacific salmon (Foreman et al., 1997(Foreman et al., , 2001Cooke et al., 2004;Rand et al., 2006;Rennie and Church, 2010;Halverson and Pawlowicz, 2011;Pawlowicz et al., 2017). The LFR drains into the Strait of Georgia through an estuarine network mainly composed of two branches separated by the city of Richmond (Fig. 1). ...
Article
We investigated the tidal propagation in the Lower Fraser River (LFR) in British Columbia, Canada using observed water elevations, river discharge, and a hydrodynamic model. The observed water elevations and discharge are analyzed using a tidal analysis package called NS_Tide. The results indicate that the amplitudes of the two principal tides (lunar semidiurnal, M2, and luni-solar diurnal, K1) decrease from the river mouth to the upstream. The amplitudes in the high flow season (spring and summer) are lower than those in the low flow season (fall and winter). The amplitudes of the overtides and compound tides amplify from the downstream to the upstream in the low flow season; however, in the high flow season, the amplitudes only amplify in the lower part (0–35 km from the river mouth) and then decrease in the upper part (60–78 km from the river mouth). The temporal variation of tidal amplitudes are strongly correlated to the river discharge. Using the model results in 2013, we analyzed the momentum balance in the river channel and examined the significance of the Pitt River and Pitt Lake system. The momentum balance in the river channel is dominated by the balance between the pressure gradient and the bottom friction. The river-tide interaction plays an important role in the friction term in the lower part of the river channel, while the river flow explains most of the variability moving upstream. The system of the Pitt River and Pitt Lake is important for the tidal propagation in the river channel. Modelling tides without including this system systematically leads to significant inaccuracies of the tides in the river channel of the LFR.
... Many biological situations are related to water thermal regime [27,7,20]. For instance, Foreman et al. [19] linked the pre-spawning mortalities in salmon returning to their natal streams with high river temperature. Where the exposure of adult sockeye salmon to water temperature higher than 24°C leads to acute thermal shock and death within hours later. ...
Article
Surface heat exchange is essential in water quality modelling. It is necessary to provide water surface temperature data for determining the air-water heat fluxes. In this paper, air-water temperature relationship was developed statistically by using the non-linear logistic regression. The model outcome made water temperature easy to calculate depending on air temperature data, which is available from the close by weather stations. The regression development and analysis were performed based on meteorological and water temperature data measured at Laurance Lake, Oregon US. The air-water relationship impact on surface heat fluxes (short and long radiation, back radiation, evaporation, conduction) was used to evaluate the regression function goodness in conjugate with error statistics. Results showed that the regression can reproduce the total heat flux wave without curve shifting. For one-day computational time, MAE, RMSE, and NSE recorded 0.552, 6.936, and 0.902 Watt/m2, respectively using the logistic regression. The regression kept the same behaviour when running over longer period of time, matching the real total flux (When a maximum value of 774.21 Watt/m2 was estimated based on measured water temperature, the logistic modelling gave a value of 752.52 Watt/m2 corresponding to water temperature of 15.642 °C and 15.637 °C, respectively).
... (1) physically based models (rooted in the solution of fluid flow and heat transport equations), e.g., SNTEMP (Theurer et al. 1984), HEATSOURCE (Boyd and Kasper 2003), QUAL2K (Chapra et al. 2008), MASS1 (Richmond et al. 2000), FJQHW97 (Foreman et al. 1997), CE-QUAL-W2 (Cole and Wells 2002), RPSTM (Cheng and Wiley 2016), and RBM (Yearsley 2009), and (2) empirical models, which rely on the correlation strength between meteorology and stream temperature, e.g., generalized linear models (McCullagh and Nelder, 1989), ARMA, non-parametric models (k-Nearest Neighbours (Caldwell et al. 2013), etc.), and hierarchical models (Letcher et al. 2016). Although physical models can be adapted for different temporal and spatial domains, they are typically restricted in terms of performance in data sparse situations. ...
Article
Full-text available
Stream temperature is an important control of many in-stream processes. There is rising concern about increases in stream temperature with projected climate changes and human-related water activities. Here, we investigate the responses to climate change and water diversions in Eel River basin. The increase in stream temperatures is considered to be the result of changes in air temperature, the proportion of base flow and the amount of stream flow derived from historical and future simulations using the integrated VIC hydrologic model and ANN stream temperature model. The results show that stream temperature will increase throughout the basin in the future under two climate change representative concentration pathways (RCPs 4.5 and 8.5) and will also be influenced by the water diversion activities schedules. Specifically, the stream temperature increases, in the late twenty-first century under RCP8.5 scenarios, from 1.20 to 2.40 °C in summer and from 0.58–3.46 °C in winter respectively; Water diversion activities in Eel River Basin can increase nearly 1 °C in stream temperature. Therefore, both climate change and water diversion activities can substantially cause the rise of more than 2 °C in stream temperature. In conclusion, stream temperature is mainly sensitive to the proportion of base flow in summer, but also the change of the amount of stream flow in winter in our case study area. In addition, it should be noted that the low intensity irrigation schedule has lower impacts on increasing stream temperature, whereas the high intensity irrigation schedule will further exacerbate the rise of stream temperature. Understanding the different impacts of climate change scenarios and irrigation schedules on stream temperature can help identify climate-sensitive regions, climate-sensitive seasons and water diversion schedules as well as assist in planning for climate change and social adaptive management.
... Because river temperatures are critical to the survival of spawners migrating upstream (cf. Royal, 1966), the Canadian Department of Fisheries and Oceans (DFO) now monitors and forecasts temperatures in the Fraser River system (Foreman et al, 1997). Summer temperatures in the Quesnel River, which flows from Quesnel Lake into the Fraser River, have been observed to fluctuate by as much as 7°C in a single day (unpublished data), causing stress to migrating spawners and making temperature forecasts much less reliable. ...
Conference Paper
Full-text available
Quesnel Lake, a deep fjord-type lake in the interior plateau of British Columbia, is a cornerstone of the province's salmon fishery. Fluctuating temperatures in the outflowing Quesnel River prompted the installation of thermistor chains in the lake and its West Basin, which are connected by a shallow (35 m) sill. The heat content of the West Basin changes rapidly (>100 GJs-1). Surface fluxes (<18 GJs-1) and hydraulic throughflow (<8 GJs-1) are too small to account for these fluctuations and wind-forced, two-way advection across the sill is assumed to be the mechanism responsible for the observed heat change in the West Basin. The magnitude of two-way flow is estimated using conservation equations, and found to be comparable to hydraulic control limits.
... A number of studies from the literature were chosen for purposes of comparison. The studies represent a variety of methods, including deterministic process models [Foreman et al., 1997;Sinokrot and Stefan, 1993;Sullivan and Rounds, 2004], multiple regression models Pilgrim et al., 1998;van Vliet et al., 2010], time series models [Caissie et al., 1998], and neural network models [Risley et al., 2002]. The number and type of metrics used to assess model performance vary from study to study, but all report some measure of the second moment of the difference between simulated (predicted) and observed, similar to the RMSD of (14). ...
Article
Full-text available
[1] Applications of grid-based systems are widespread in many areas of environmental analysis. In this study, the concept is adapted to the modeling of water temperature by integrating a macroscale hydrologic model, variable infiltration capacity (VIC), with a computationally efficient and accurate water temperature model. The hydrologic model has been applied to many river basins at scales from 0.0625° to 1.0°. The water temperature model, which uses a semi-Lagrangian numerical scheme to solve the one-dimensional, time-dependent equations for thermal energy balance in advective river systems, has been applied and tested on segmented river systems in the Pacific Northwest. The state-space structure of the water temperature model described in previous work is extended to include propagation of uncertainty. Model results focus on proof of concept by comparing statistics from a study of a test basin with results from other studies that have used either process models or statistical models to estimate water temperature. The results from this study compared favorably with those of selected case studies using data-driven statistical models. The results for deterministic process models of water temperature were generally better than the grid-based method, particularly for those models developed from site-specific, data-intensive studies. Biases in the results from the grid-based system are attributed to heterogeneity in hydraulic characteristics and the method of estimating headwater temperatures.
... Al respecto en un estudio hecho por Justic et al. (1996), indicaron que la contaminación térmica incrementa la solubilidad de ciertos compuestos químicos, y en general disminuye la solubilidad de gases, especialmente la del oxígeno disuelto, reportando también que a mayor temperatura, mayor evaporación del agua. En otro trabajo Foreman et al. (1997), registraron que el agua caliente puede afectar la vida en el agua, lo cual resulta en un cambio de la composición fisiológica de las especies acuáticas; el calentamiento puede acelerar los procesos biológicos en plantas y animales por disminución del oxígeno en el agua. En otro reporte, Sawidis (1997), comenta que la vulnerabilidad para el incremento de enfermedades y cambios en la producción de algas e invasión de organismos destructivos es expectante; cada pequeño cambio de temperatura en un cuerpo de agua puede conducir a lo largo del tiempo al fin de una especie y a el origen de otra vida silvestre, que originalmente estuvo presente cerca de la descarga de la fuente y atraer otra especie en su lugar. ...
Article
Full-text available
This paper presents an integral study on the quality of the superficial waters in ponds and streams of the watershed of Amajac river. The problems associated to specific pollutants are identified and alternative solutions are detailed to be used in public policies of water resources. Four ponds, one lake and five streams were considered in the study and runoff volume, water speed, and maximum depth were measured. Also, the main physical, chemical and biological parameters were determined: dissolved oxygen, fecal coli forms, nitrogen, phosphorus, sulphate, carbonate, bicarbonate, chloride, and manganese. According to the results, it is concluded that water of the river in Tulancingo city is strongly contaminated.
... Waters in the Fraser River during anomalously warm years surpass the thermal limits for in migrating salmon resulting in large-scale pre-spawn mortality (Foreman et al. 1997, Macdonald et al. 2010. Exposure of temperatures above 22°C for several days can result in acute infection or acute thermal shock and death (Servizi and Jensen 1977). ...
Thesis
Full-text available
The prevalence of large-scale anthropogenic and natural disturbance has increased in recent decades around the world. For example, over 50% of the world’s large rivers are currently dammed and the frequency of large wildfires has nearly quadrupled in western North America since the mid-1980s. Disturbances such as these are principal drivers of change in lotic ecosystems and we seek to improve our understanding of how they affect recipient ecosystems in the context of fisheries management and conservation. My thesis research combines empirical studies and modeling to improve our ability to predict and measure the effects of several major types of natural and anthropogenic disturbance in lotic ecosystems. In Chapter 1 I improved the accuracy of hydrodynamic habitat models for juvenile salmon by up to 10% by applying Akaike information criterion and model averaging. In Chapters 2 and 3 I applied multiple regression and bioenergetic models to illustrate how wildfire, by burning riparian vegetation, can elevate stream temperatures by up to 0.6°C adding ~5 kJ of metabolic costs to salmonids. As well, I found concentrations of food web resources such as nitrate and fine particulate organic matter increased in burned compared to unburned regions by 244% and 44%, respectively, and I found significantly greater seasonal changes in terrestrial and aquatic invertebrate abundance than changes attributable to wildfire. Despite similar regional invertebrate prey abundance, Bayesian stable isotope mixing models revealed seasonal and regional differences in salmonid diets, with higher trophic level prey contributing more to diets in the burned compared to a reference region. Lastly, in Chapter 4 I found that forest harvest and rising air temperatures are warming waters in the Fraser River basin at 0.07°C per decade on average by applying Spatial Stream Network models. In total, my thesis research builds on previous work and illuminates how disturbance can affect abiotic and biotic responses in lotic ecosystems at spatial scales ranging from less than 10 m2 to over 200,000 km2. Thus, results from my thesis research will aid fisheries management and conservation by improving our understanding of how natural and anthropogenic disturbance may alter streams and rivers in our future.
Technical Report
Full-text available
For many generations in western Canada, five species of Pacific salmon have provided a defining role to native and non-native peoples. As a reflection of this cultural importance, there has been a long-standing tradition of communities and governments taking action to help salmon cope with both natural and human pressures on their survival. Recognizing that Pacific salmon will face significant hurdles in the face of climate change and that society can take action to help them survive, this report presents an approach and research around key elements to help government decision makers and local communities decide upon appropriate actions moving forward. This approach involves four steps. The first step involves clarifying the local setting within which governments or communities are pursuing actions to help salmon. What is the region, watershed, or stream of interest? Are there competing resource uses—among salmon, freshwater supplies, and hydropower generation, for instance? Who are the decision makers? Although the general issues of interest discussed in this report relate to changes in freshwater flows and water temperatures, we recognize that local issues of concern may be more varied. A companion report, “Helping Pacific salmon survive the impacts of climate change on freshwater habitats: Case study perspectives from the Okanagan, Nicola, Quesnel, Cowichan, Nass, and Englishman River watersheds”, presents a sample of issues in a local context of geography, people, and salmon at three interior and three coastal basins in British Columbia. The second step requires describing the sensitivity of Pacific salmon to expected changes in their freshwater habitats. Across the globe, the effects of a warming climate are consistently predicted to change freshwater flows, especially in snow-dominated regions. In British Columbia, a variety of measurable changes in air temperatures, precipitation, snow pack, streamflows, and water temperatures are expected. For instance, in the Okanagan Basin, predictions suggest noticeable increases in winter air temperatures (from 1.5 to 4.0°C) and precipitation (5–20%) by the 2050s, as well as decreases in summer precipitation (by 20%). By the 2050s in the Georgia Basin, climate models predict general warming (1.5–2.0°C), a reduction in snowpack (by 50%), and a possible increase in December runoff (by 60%). On the coast, these predictions mean little change in the total amount of water flowing through our watersheds, though increases in the number and size of floods are likely. For Pacific salmon, the effect of such changes in freshwater flows and temperatures are fundamentally linked to their survival. Warming of Fraser River water temperatures can delay sockeye salmon migration and reduce enroute survival. Low water flows in the late summer can block access to spawning grounds. Winter flooding can wash eggs out of the gravels. Parts of B.C. are also uniquely vulnerable. Although incomplete, this report identifies thirty-two areas that have warm water temperatures or low / high freshwater flows that currently affect salmon survival. These areas are centered in the Southwestern, Southern Interior, and Central Interior of the province. Management agencies and local communities have a wealth of knowledge about salmon watersheds and experience working with local partners. This knowledge and experience is an asset because it can be used to help plan and implement feasible actions most likely to be successful in the future. Hence, the third step of the approach requires accounting for existing assets. Several planning efforts are currently being developed that could help identify freshwater streams and lakes most vulnerable to climate change. These efforts include identifying the status of salmon populations under Fisheries and Oceans Canada’s Wild Salmon Policy, designating “Fisheries Sensitive Watersheds” and “Temperature Sensitive Streams” by the BC Ministry of Environment, as well as developing tools to help governmental and non-governmental agencies prioritize areas for conservation and restoration. There is also a long history of taking action to help a variety of fish species and their habitats, including salmon. The final step describes strategies or actions that could be implemented in the short or long-term to help reduce Pacific salmon’s vulnerability to climate change. A first group of actions includes “hard infrastructure” strategies; engineering or technology-focused innovations that can be implemented on-the-ground to either help salmon adapt to climatic changes, mitigate the effect of changes in habitats, compensate for climate-induced losses to salmon, or restore habitats affected by past deterioration in habitats. Strategies can be aligned with four types of actions: (i) flow-focused, (ii) temperature-focused, (iii) fish-focused, and (iv) fish habitat-focused. A second group of actions to help salmon are termed “soft infrastructure” strategies—those changes in local governance, regulations, policy, or agency management approaches that might encourage innovation and more efficient / effective use of society’s hard infrastructure. The intention of using such levers would be to encourage positive human behaviour, innovation, and technological changes to help mitigate the effect of human and climate-induced disturbances on salmon and their freshwater habitats. As highlighted by the presented list of adaptation strategies in this report, governments and local communities are not limited by creative approaches for helping Pacific salmon in freshwater habitats. Barriers to helping salmon may be centred on a lack of political will at a regional level or a lack of appropriate planning and implementation at a local level. Helping salmon survive the impacts of climate change on freshwater habitats will require smart assessment, design, implementation, and evaluation of alternative strategies to identify successes in the short and long-term.
Article
Full-text available
Kamloops Lake is a long (25 km), deep (maximum depth, 145 m) intermontane lake in central British Columbia fed at its eastern end by the Thompson River (mean annual flow, 720 mSUB2 sSUB-SUB1). Spring overturn and the onset of stratification is described, on the basis of three conceptual models distinguishing between river-induced, surface-induced and edge-induced circulations. The lake during winter is characterized by weak reverse stratification; the incoming river waters are less dense than ambient lake water and thus tend to remain at the lake surface. During spring, the shallow river water warms more rapidly than the deep water of the lake; as inflow water warms tow rds the temperature of maximum density (4SUPC), it becomes denser than lake water and thus tends to sink on entry into the lake. Further warming of the inflow water above 4SUPC decreases its density causing it to again enter the lake as a surface overflow. Although the inflow itself it less dense than lake water, some mixtures of the two will necessarily have temperatures near 4SUPC, and thus be denser than either parent water mass; this process is called cabbeling. The dense mixtures than sink along a narrow frontal zone, filling the lake basin with 4SUPC water from the bottom upward, while new unmixed inflow water is held as an arrested wedge near the point of entry. When the whole lake is warmed above 4SUPC, the cabbeling instability disappears and the wedge of warm water is released to spread down the lake. Transport of warm water across the lake subsequently froms the spring thermocline. Budget considerations show that although surface heating of the open lake contributes the major portion of the spring heat income, the riverine flow dominates lakewide circulation patterns, and thus determines the distribution of material properties during and subsequent to spring overturn. (A)
Article
A dynamical model of river-lake interaction is used to quantitatively examine the physical behavior of the Kamloops Lake-Thompson River system in British Columbia. Analysis is based on the so-called filling-box method which predicts the thermal stratification of the lake relative to hydrological conditions; specifically the river's effect on thermocline formation and decay, convective overturn, heat exchange, and particle residence time are examined. The model can be used to simulate the effects of hypothetical developments in the watershed and to examine physical processes relevant to the release of pollutants upstream.
Article
In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k. In view of this, these waves are described as 'kinematic', as distinct from the classical wave motions, which depend also on Newton's second law of motion and are therefore called 'dynamic'. Kinematic waves travel with the velocity partial q/partial k, and the flow q remains constant on each kinematic wave. Since the velocity of propagation of each wave depends upon the value of q carried by it, successive waves may coalesce to form 'kinematic shock waves'. From the point of view of kinematic wave theory, there is a discontinuous increase in q at a shock, but in reality a shock wave is a relatively narrow region in which (owing to the rapid increase of q) terms neglected by the flow-concentration relation become important. The general properties of kinematic waves and shock waves are discussed in detail in section 1. One example included in section 1 is the interpretation of the group-velocity phenomenon in a dispersive medium as a particular case of the kinematic wave phenomenon. The remainder of part I is devoted to a detailed treatment of flood movement in long rivers, a problem in which kinematic waves play the leading role although dynamic waves (in this case, the long gravity waves) also appear. First (section 2), we consider the variety of factors which can influence the approximate flow-concentration relation, and survey the various formulae which have been used in attempts to describe it. Then follows a more mathematical section (section 3) in which the role of the dynamic waves is clarified. From the full equations of motion for an idealized problem it is shown that at the 'Froude numbers' appropriate to flood waves, the dynamic waves are rapidly attenuated and the main disturbance is carried downstream by the kinematic waves; some account is then given of the behaviour of the flow at higher Froude numbers. Also in section 3, the full equations of motion are used to investigate the structure of the kinematic shock; for this problem, the shock is the 'monoclinal flood wave' which is well known in the literature of this subject. The final sections (section section 4 and 5) contain the application of the theory of kinematic waves to the determination of flood movement. In section 4 it is shown how the waves (including shock waves) travelling downstream from an observation point may be deduced from a knowledge of the variation with time of the flow at the observation point; this section then concludes with a brief account of the effect on the waves of tributaries and run-off. In section 5, the modifications (similar to diffusion effects) which arise due to the slight dependence of the flow-concentration curve on the rate of change of flow or concentration, are described and methods for their inclusion in the theory are given.
Article
wind records. The unusual characteristics of the thermal structure in the lake are shown to exert a stabilizing influence on large-amplitude wave disturbances. Long-period internal waves are generated primarily by suddenly imposed and vigorous wind forcing along the axis of the lake. During the years 1974-1975, temperatures were observed at an array of three moored profilers in an elongated or fjord lake located in the interior plateau of British Columbia (Figure 1). The vertical displacements of the isotherms observed in Kamloops Lake may be broadly classified into motions having periods of 1 hour or less and amplitudes of 0.5 m and into waves having periods from 40 to 100 hours and amplitudes of 10 m. The well-defined separation between these two classes of internal motion was first shown by Hamblin [1977], who related the high-frequency motions to the river-induced shear in the eastern end of the lake. It is the goal of this paper to develop a simple dynamical model of the second class of longperiod internal motions and to compare the model results with field data as a means of gaining understanding of these waves. Attention is focused on the three-dimensional aspects of the
Article
An outline description is given of the University of British Columbia watershed and flow models, which are a set of computer programs for the calculation of hydrologic behavior of watershed and river systems. The U. B. C. watershed model calculates snowmelt and rain runoff from meteorological data for mountainous watersheds. A revised temperature index for the calculation of snowmelt is presented and illustrated. The enhanced watershed response resulting from high intensity rainfall is examined and it is shown that this enhanced watershed response can be described by one additional parameter which modifies the normal watershed calibration. Application of the watershed and flow models for streamflow forecasting and planning studies are described.
Report and Recommendations to the Lieutenant Governor in Council. Chair of the Review
  • Kemano Completion
KEMANO COMPLETION PROJECT REVIEW. 1994. Report and Recommendations to the Lieutenant Governor in Council. Chair of the Review: Loma Barr. British Columbia Utilities Commission, December 1994.260 pp.
Physical and Hydrological Studies: Baseline Information. Section E. Prepared for the Aluminum Company of Canada, Ltd
ENVIROCON. 1984. Kemano Completion Hydroelectric Development Environmental Studies. Vol. 2. Physical and Hydrological Studies: Baseline Information. Section E. Prepared for the Aluminum Company of Canada, Ltd. Vancouver, B.C., 105 pp.
Effects of holding tem
  • D G Sl 'evens
and D.G. Sl'EVENS. 1975. Effects of holding tem- December 1975, Otter Rock, Oregon, pp. 24-40.