Limnol. Ocectnogr., 42(2), 1997, 299-306
0 1997, by the American Society of Limnology
and Oceanography,
Inc.
Observations of a deep-mixing event in Crater Lake, Oregon
G. B. Crawford and R. W. Collier
College of Oceanic and Atmospheric Sciences, Oregon State University,
Corvallis, Oregon 97331-5503
Abstract
We present observations of the evolution of a deep-mixing event in a deep, temperate lake. The observations
were obtained from thermistors mounted on a long-term mooring in the lake. The event seemsto have originated
near 150-m depth and resulted in a plume or layer of cold water from the upper half of the lake that descendedto
the lake bottom (590 m) over a 3-d period. Net mixing associated with this event resulted in an overall vertical
heat exchange of nearly lOI J and a volume exchange of 0.7-3.2 km? (4-18% of the lake volume) between the
upper and lower portions of the lake. The deep water displaced during the event is estimated to have carried 0.32.5 X lo6 mol of nitrate to the upper lake, which accounts for a significant portion of the average annual nitrate
flux (-2-4 X 10” mol yr-‘) thought to be upwelled in this highly oligotrophic system.
We consider a number of possible generation mechanisms,
including thermobaricity.
The hypolimnion of deep, temperate lakes is usually considered to be largely isolated from the surface waters and
the atmosphere. In recent years, however, some attention has
been focused on hypolimnetic mixing and deep-water formation in such environments. Various measurements in both
Crater Lake, Oregon, and Lake Baikal, Russia, for example,
indicate that partial mixing and ventilation occur every winter and spring in the deep waters (e.g. Shimaraev and Granin
1991; Weiss et al. 1991; McManus et al. 1996). The details
of generation and evolution of this deep mixing are poorly
understood and generally difficult to observe; recently, however, Shimaraev et al. (1993) presented temperature observations from a transect in Lake Baikal where deep convection, owing to the development of a thermal bar in concert
with thermobaric effects, seemed to be ongoing. In contrast,
Imboden et al. (1988) showed observations from Lake Zug,
Switzerland, where hypolimnetic mixing was observed as a
consequence of an internal seiche set up by a very strong
wind storm. In more general terms, Michalski and Lemmin
(1995) discussed the evolution of the hypolimnetic temperature profile in Lake Geneva in summer and concluded that
mixing at depths >90 m is noncontinuous, not associated
with shear produced at the bottom boundary layer, and is
likely three-dimensional.
Here, we report thermistor observations of a deep-mixing
event in Crater Lake, obtained from a fixed mooring. Over
a period of only 3 d, a plume or layer of cold water from
the upper part of the lake descended over 400 m to the lake
bottom, partially mixed with the deep waters, and resulted
in a net vertical exchange of as much as 18% of the entire
lake volume. The available measurements are insufficient to
identify precisely the mechanism responsible for the event.
Background
Acknowledgments
Mark Buktenica provided logistical support and instrument servicing. Gary Larson headed the long-term limnological study at the
lake and contributed in a variety of ways, directly and indirectly,
to the development of this paper. We also benefited greatly from
comments from two anonymous reviewers and from discussions
with Dieter Imboden.
This research was supported by the National Science Foundation
(EAR 92-19953), the U.S. National Park Service Global Change
Research Program, and the College of Oceanic and Atmospheric
Sciences, Oregon State University.
299
Crater Lake was formed by the climactic eruption of the
volcano 6850 B.I? (Bacon and Lanphere 1990). The volcanic
morphology provides a basin for what is now the deepest
lake in the United States (589 m) and the seventh deepest
in the world. Located in the Oregon Cascades at a mean
elevation of 1,882 m asl, the lake is surrounded by steep
caldera walls and occupies 79% of its drainage basin. Most
water enters the lake by direct deposition of snow and leaves
by evaporation and seepage (Redmond 1990; Nathenson
1992). The lake has extremely low nutrient inputs and organic production, and is consequently one of the clearest
lakes in the world (Larson 1972; Smith et al. 1973). The
vertical exchange of water between the epilimnion and hypolimnion dominates the input flux of fixed nitrogen (Dymond et al. 1996), which limits primary production in the
euphotic zone. Variations in this mixing rate could contribute
to interannual variations in productivity and possibly lake
clarity (McManus et al. 1993).
The near-surface temperature typically reaches nearly
18°C in late summer and drops below 3°C in late winter or
early spring, although Crater Lake rarely freezes. Thus, there
is a strong summer thermocline, a late winter period of reverse stratification, and two periods when the upper lake
becomes well mixed (near 4°C). The hypolimnion, which is
nearly isothermal throughout the year (3.5-3.7”C), receives
small fluxes of heat (- 1 W mm2) and solutes (-5 pg m-2
s-l) from hydrothermal inputs. Mixing processes in the hypolimnion lead to a salinity gradient of order 1O-2 mg liter-’
m-l and a hyperadiabatic temperature gradient with depth of
up to 3 X 10-40C m-l that, together, maintain a slightly
stable water column (Neal et al. 1972; Williams and Von
Herzen 1983; McManus et al. 1992).
Methods
As part of a long-term study of mixing in the lake, we
have maintained a meteorological buoy and string of thermistors moored in the deep basin of Crater Lake since 1991
Crawford and Collier
600 +
3.1
50 m contours
PARK HQ
0
’
0
’
1
2’
3’
4’
5’
6’
km
Fig. 1. Bathymetric map of Crater Lake, Oregon, located within
tlhe caldera of Mt. Mazama (Byrne 1965). Two meteorological stations were established in late 1991, one located on a buoy in the
deep north basin (“met buoy”) and one on a tower on the SW
caldera rim (“met tower”). A separate thermistor mooring records
water column temperatures in the deep basin at the site of the met
buoy. “Park HQ” denotes the location of the National Parks Service
headquarters at Crater Lake National Park.
(Fig. 1). Two meteorological stations were established in late
199 1, one located on a buoy in the deep north basin and one
on a tower on the SW caldera rim. The stations include sensors, data-logging computer (Campbell Scientific CRlO),
and radio telemetry. Both stations measure air temperature,
relative humidity (Vaisala HMP35), wind speed, and wind
direction (RM Young 05103). The buoy also includes a
thermistor for surface water temperature (-20 cm below the
water surface mounted on the underside of the buoy) and
the rim station includes a barometer (V&ala PTA427) and
a pyranometer (LiCor Li-200SZ) recording short-wave radiation. A long-wave radiometer (Epply PIR) was deployed
at the rim station for several months to improve our parameterization of the downwelling long-wave heat flux. Water
column temperatures were recorded on a separate mooring
near the met buoy using thermistor chains (Aanderaa) from
September 199 1 through June 1992 and up to 20 individual
thermistors coupled to in situ data recorders (Alpha-Omega,
MDR 9 102) from July 1992 through the present. The water
column temperatures, collected at 10-min intervals, are augmented by periodic profiles made using a recording CTD
(Sea-Bird Electronics, SEACAT model SBE19 modified for
low conductivity environments). Salinity is calculated from
conductivity by using a relationship developed for Crater
Lake (McManus et al. 1992). Density-related properties were
calculated using the limnological equation of state developed
by Chen and Miller0 (1986). All instruments undergo regular
I+
r
3.:3
3.5
3.7 103
105
109
107
Temperature (OC)
Salinity (mg liter -l )
I
I
I
,
0
N-2 (lg7
s-2)4
Fig. 2. Lake hydrographic characteristics. [a.] Mean temperature profile ( -)
before the convective event (averaged over days
32-35) and temperature of maximum density, Tnrd(- - -). Actual
thermistor dlepths are given in the text and displayed in Fig. 3. The
water column is reverse-stratified in the upper 160-200 m during
this period (i.e. colder, lighter water overlying warmer, heavier water). The compensation depth, z, (where the temperature profile
crosses the Tntdprofile), is denoted by an open circle. [b.] Representative winter salinity profiles from CTD profiles taken on 4 April
1989 () and 19 January 1990 (- - -). The salinities have been
averaged and evaluated as described in the text. Uncertainties, plotted as horizontal bars, represent 1 SD. [c.] Two estimates of water
column stability before the mixing event, plotted as buoyancy frequency squared, Nz. NL is calculated using the mean temperature
profile from panel a and the salinity profiles from panel b. Solid
and dashed lines denote use of the 4 April 1989 and 19 January
1990 salinity profiles, respectively. Uncertainties, plotted as horizontal bars, represent 1 SD.
calibration required to support this long-term series of highaccuracy measurements.
Results
The mixing event began in early February 1993 (year-day
36). This was the second and more dramatic of two periods
of deep mixing during the 1992-1993 winter season. During
this period, 19 MDR thermistors were mounted on the mooring at depl:hs of 15, 25, 35, 55, 75, 95, 115, 135, 165, 200,
240, 280, 320, 360, 400, 450, 500, 550, and 590 m. The
mean temperature profile of the lake, T(z), before the mixing
event (Fig. 2a) reveals reverse thermal stratification in the
upper 180 m.
Salinity is usually only measured by CTD during summer
months. No salinity measurements were made during the period discussed here, although a very few profiles have been
obtained in the same season during previous years. In summer, the salinity profile is reasonably well represented by a
nearly uniform layer over the upper 200 m or so (- 104 mg
liter-‘) and a linear gradient down to the lake bottom. In
winter, however, there is more structure in the profile. Fig.
2b shows 1;worepresentative salinity profiles during the latter
stages of the annual lake cooling phase, one just before the
surface temperature, ry,, cools to 4°C (19 January 1990) and
the second near the time of maximum reverse stratification
(6 April 1989; T,, 2.52”C). The salinities, initially recorded
at l-m intervals, have been evaluated at the same depths as
the thermistor depths used for calculating T(z) in Fig. 2a.
Because the conductivity signal is rather noisy for these low
Deep mixing in Crater Luke
salinities (rms salinity error -0.16 mg liter-‘), we determined a weighted average at the thermistor measurement
depths by using a triangular smoothing window with a halfwidth of 10 m. The lines in Fig. 2b represent linear interpolations between these salinity estimates; the associated error bars represent an interval of 1 SD and are based on the
assumption of Gaussian statistics and the effective number
of degrees of freedom.
Although the two salinity profiles in Fig. 2b were taken
in different years, they suggest a complex evolution of the
salinity structure at middepths (150-300 m) during winter.
This evolution must be due at least in part to the details of
vertical mixing at middepth in autumn and winter, which
must partially erode the upper part of the deep salinity gradient. The existence of mixing at these depths is also evident
from the evolution of the mean temperature profile during
autumn and winter 1992-1993 (not shown), which indicates
partial mixing down to 300 m by 15 January 1993 (2 weeks
before the observed deep-mixing event). Thus, there must
be some modification of the mean summertime salinity profile at shallow and middepths as surface cooling and wind
mixing proceed into winter. It is particularly interesting that
for both salinity profiles in Fig. 2b the gradient between
- 160 and 240 m is nearly zero.
The profile of the temperature of maximum density, T,,,d,
calculated from the equation of state (McManus et al. 1992;
Chen and Miller0 1986) by using T(z) from Fig. 2a (dotted
line) and the January salinity profile in Fig. 2b is plotted in
Fig. 2a. T,,rdis relatively insensitive to the magnitude of salinity variations observed in Crater Lake; it is nearly 4°C at
atmospheric pressure (i.e. at the lake surface) and decreases
with increasing pressure (or depth in a profile of the water
column) at --0.0021
“C dbar-I. The depth at which the
temperature profile crosses the Tmdprofile is referred to as
compensation depth, z,; here, z, is - 180 m.
Although we do not know the mean salinity profile just
before the observed deep-mixing event, we choose to use
the two salinity profiles in Fig. 2b as characteristic for this
period. Fig. 2c shows the corresponding profiles for the
square of the buoyancy frequency, Nz [based on T(z) from
Fig. 2a]. We estimate the uncertainty in Nz from the uncertainty in the salinity gradient (which is the dominant error
term in the stability calculation here). The error bounds in
Fig. 2c represent an interval of 1 SD. In both NL profiles,
the water column is slightly stratified in the lower half of
the lake owing to the deep salinity gradient and in the upper
half of the lake owing to the reverse thermal stratification.
However, near the compensation depth, both Nz profiles reduce to nearly zero, suggesting neutral stratification.
A time series of winds and lake isotherms over a period
encompassing the deep-mixing event (day 30 to day 55) is
shown in Fig. 3. Between day 33 and day 37, a storm passes
over the region, with winds blowing roughly northward.
There is some downwelling of the isotherms at the mooring
(which is on the leeward side of the lake), with the 3.3”C
isotherm descending from -50 to 80 m. The winds peak
early on day 36 and then decrease, reaching just a few meters
per second by day 38. In the temperature data, there is a
suggestion of a small, deepening plume or layer on day 34,
as the 3.6”C isotherm penetrates to 250 m, although it re-
301
,
I
I
I
I
I
30
35
40
45
50
55
i-
-- s
-_ 3
I
4
cl
3
._ a
I
35
n,
40
Year-Day
I
45
1993
Fig. 3. Wind velocity and lake temperature during the convection period. Upper panel: Time series of estimates of wind velocity
over the lake (orientation denotes direction in which wind blows).
During this period, the met buoy was inoperative, so winds over
the lake were inferred from the rim station (based on statistics developed during periods when both stations were functioning). Lower
panel: Contours of lake isotherms (contour interval is O.l”C). For
each thermistor, the associated temperature time series was low-pass
filtered by passing the data backward and forward through a firstorder Butterworth filter with a cutoff period of 12 h. The convective
event occurs on day 36 (5 February 1993), as colder water from
the upper half of the lake begins to descend into the deep basin.
The 3.6”C isotherm descends from -150 to 590 m in -3 d. These
data represent the first detailed observation of the onset and evolution of a thermobaric instability.
covers close to its original depth within a day. On day 36,
a more dramatic event occurs, carrying colder, fresher water
from the upper lake down to the lake floor. The 3.6”C isotherm descends from - 150 to 590 m in -3 d, corresponding
to an average vertical velocity of about 1.7 X lop3 m s-l.
This isotherm then shifts back upward to -400 m between
day 40 and day 47. We hypothesize that the observed plume
or downwelling layer was of limited horizontal extent near
the buoy and that the observed isotherm readjustment is a
consequence of horizontal adjustment to this localized event.
Following this interpretation, it would seem that the convective plume was effectively shut off by day 40, if not
beforehand.
By day 45, the “mean” water column appears quasisteady, with a broad thermocline between 150 and 250 m
(dT/dz = -2 X lo-” “C m-l). There is a clear, nearly monochromatic oscillation in the thermocline between day 44 and
day 47, with a period of - 18 h and peak-to-peak amplitude
of -100 m. Another wave, with peak-to-peak amplitude of
-30 m and a period of -7 d, also appears in the main
thermocline between day 40 and day 45 and lasts for another
2 months (not shown). The local inertial frequency, j is - 1
X lop4 s- I (inertial period -17.6 h); the buoyancy frequency, N, of the water column before the mixing event is 3-6
X 1O-4 s-l. We take the mean lake depth, D,,, = 325 m, to
be the characteristic depth, and obtain estimates of the first
mode internal wave speed, c, = NDJv = 3-6 X lop2 m
s-1,
and the associated internal Rossby radius, a, = c,/f =
300-600 m. Because a, is much smaller than the lake radius,
Crawford and Collier
302
column is seen to restratify, whereas below -200 m cold
water seems to descend.
We can approximate the net change in heat content in the
hypolimnion as AH = H(t,) - H(t,):
z= -h
H=
600
0
,
100
E200
5 300
E
m 400
500
/ /
/ /
600 I3
3.2
3.4
Temperature
3.6
(S)
3.8
3
3.2
3.4
Temperature
3.6
PC)
3.8
Fig. 4. Evolution of the temperature profile. Each panel displays
12 consecutive hourly temperature profiles. Periods are: day 35,
1200-2300 hours (a); day 36,0000-l 100 hours (b); day 36, 12002300 hours (c); day 37, 0000-l 100 hours (d). Dashed lines correspond to temperature of maximum density.
r (-3.6 km), inertial effects are very important and a classical internal seiche is not a free-wave solution, The 18-h
wave is most likely a first-mode Poincare wave, with an
angular frequency given by a,, - f( 1 + +a,2/r2)“1 - (1.031.13)JJ or a period of - 18-20 h; the 7-d wave period is most
likely a first-mode internal Kelvin wave, which has an angular frequency of a, = aJ7r = (0.075-0.15)f or, equivalently, a period of -5-10 d (see also Csanady 1982; Imberger and Hamblin 1982).
Figure 4 provides more detail on the evolution of the temperature profile during the early stages of the mixing event.
The four panels represent four consecutive 12-h periods,
starting with the period from 1200 to 2300 hours on day 35
(Fig. 4a). Only temperature profiles measured on the hour
are plotted (i.e. 12 profiles per panel); no temporal filtering
is used. Initially (Fig. 4a), the temperature profile is reverse
stratified, as previously noted; most of the variability is likely due to a broad spectrum of internal waves present (in the
metalimnion, the temperature power spectrum falls off
roughly with op2, where o is angular frequency). The winds
increase during this 12-h period and peak at an estimated
value of 12 m s-l around midnight, then begin to decrease
during the first half of day 36. The mixed layer is seen to
warm up and deepen during this period, probably as a net
result of wind-driven mixing; the thermocline is also seen to
penetrate as deep as 250 m and is likely due to increased
internal wave intensity, net transport of epilimnion waters to
the leeward side of the lake, or both. During the next 36 h
or so, the winds are low and variable, with wind speeds
estimated to be -4 m s-l. In the latter half of day 36 (Fig.
4c) and into day 37 (Fig. 4d), the upper half of the water
I z=
pc,BA dz,
-590m
(1)
where t, and t, are times just before and after the convective
event, p is density, cp is the specific heat capacity at constant
pressure, 8 is the potential temperature (i.e. the temperature
a water parcel would have if lifted adiabatically to the lake
surface), .4(z) is the lake area as a function of depth, and h
is the depth taken as the upper boundary of the hypolimnetic
region. There are various possible choices for h. The wintermixed layer commonly penetrates between 200- and 300-m
depth. Because the lake is nitrate limited, we are also particularly nterested in the vertical exchange of new nitrate
from the hypolimnion (Dymond et al. 1996). As with the
CTD data, nitrate measurements during winter are extremely
scarce. In general, however, the nitrate concentrations in the
upper 250 m are generally below the detection limit (~0.05
PM). Hypolimnetic nitrate concentrations are - 1.O PM, and
a sharp nitracline starts at -280 m. We therefore choose h
= 280 m as the interface separating the upper and lower
lake “boxes.” The net volume of water below 280-m depth
is -6 ktn3; the total volume of the lake is -17 km3.
We use, the temperature profile in Fig. 2a and the January
salinity profile in Fig. 2b to provide our initial conditions
(t,) and calculate the potential temperature profile t3(T,S, p)
following Chen and Miller0 (1986) (note that 8 differs from
T by a maximum of 1 X lop3 “C; if we use the April salinity
profile in Fig. 2b, t9changes at most by -2 X lop7 “C). The
readjustment of the deep isotherms after the mixing event
suggests that the mixing did not take place uniformly over
the lake and that the thermistor string was perhaps coincidentally located within in a downwelling plume. Consequently, we choose for the final conditions a time t2 when
the deep isotherms seem to have fully readjusted to a steady
state (day 70; not shown). The net heat content change, LVY,
over the entire lower lake due to the convective event is then
--8
X lOI J (or, equivalently,
-2.6 X lo7 J rnp2 across
the 31-km2 horizontal surface at 280-m depth). If we take
the duration of the vertical heat exchange to be 3 d, the
effective heat flux is -3.1 X lo9 W (or - 100 W me2).
McManus et al. (1993) estimated a net heating rate due to
hydrothermal of -1 W m-2 over a bottom surface area of
about 22 km2, leading to a net annual hydrothermal input of
heat into the hypolimnion of 7 X lOI J. Therefore, this one
mixing event very nearly compensates for the net hydrothermal h.eating of the hypolimnion over a 1-yr period.
The net volume of water exchanged between the upper
and lower lake, AV, can be approximated from
Av = AHlpc,(B, -
e,3,
(2)
where 0, is the characteristic temperature of the water that
comes down from the upper half of the lake and 0, is a
characteristic temperature of the deep water that must be
displaced into the upper lake. The background temperature
Deep mixing in Crater Lake
in the lower half of the lake is relatively uniform (-3.66”C),
but the value of 0, is less clear because of the temperature
gradient in the upper lake. It seems reasonable, however, to
assume that most of the water carried from the upper lake
to the lower lake originates above the initial z,, where the
temperature is -3.6”C. To put bounds on the volume exchange, we take t?, between 3.4 and 3.6”C, which leads to
estimates of AV between 0.7 and 3.2 km3. These values correspond to -4-18% of the entire lake volume (1 l-53% of
the hypolimnetic volume).
As mentioned previously, the period of deep mixing discussed here was the second of two such periods observed
during winter 1992-1993. The first period occurred between
19 and 29 January 1993 (year-days 19-29) and resulted in
a net heat content change below 280-m depth of --4
X
lOI J, or half as much as the second event. Following the
same line of reasoning as above, we take 8(, = 3.69”C; the
temperatures in the upper half of the lake in late January
were similar to early February, so we take eil to be between
3.4 and 3.6”C again. These values lead to estimates of AV
of 0.3-1.1 km3.
If the net deep-water renewal during winter 1992-1993
may be considered to be typical, then the average residence
time of deep water is between 1 and 6 yr. Although this
range is fairly broad, it is still consistent with estimates of
the average age of deep water by Simpson (1970; l-2 yr,
based on tritium concentrations), McManus et al. (1993; 24 yr, based on oxygen measurements and thermal budgets),
and Weiss (pers. comm.; 3.2 yr for the deepest water, based
on chlorofluorocarbon
concentrations). Internannual variability in deep water renewal will most certainly contribute
to differences among these estimates.
The nitrate inventory of the entire lake is -6 X 10” mol;
surface input (through atmospheric deposition and runoff) is
-3 X lo4 to 6 X lo4 mol yr- I and is roughly balanced with
loss due to seepage of -5 X lo4 mol yr-1 (Dymond et al.
1996). In summer and fall, when nitrate measurements have
been made, essentially all of this nitrate appears in the hypolimnion. To estimate nutrient transport associated with
these mixing events, we take the nitrate concentrations in
the hypolimnion and epilimnion before the January event to
be Nd = 1.0 PM and N, = 0 PM, respectively. We then
calculate that 0.3-l. 1 X lo6 mol of nitrate were displaced
into the upper portion of the lake by the January event (518% of the total lake nitrate). If we assume the nitrate was
then redistributed uniformly within the upper and lower lake
volumes, N,, would then be between 0.03 and 0.12 PM and
Nd between 0.82 and 0.57 PM in the hypolimnion. We can
use these bounds as constraints on the nitrate distribution
just before the February event. For N, = 0.03 ,uM and Nd
= 0.82 PM, we estimate a net nitrate flux of 0.5-2.5 X lo6
mol into the upper lake due to the February event; for N, =
0.12 PM and Nn = 0.57 PM, we obtain 0.3-1.4 X lo6 mol.
The net nitrate flux of nitrate due to these two events is then
estimated to be between 0.8 X lo6 and 3.6 X lo6 mol (-1360% of the total nitrate inventory in the lake). By comparison, Dymond et al. ( 1996) have examined nitrogen cycling
within Crater Lake and estimate an average nitrate flux of
2.0-4.1 X lo6 mol yr-’ upwelled from the hypolimnion into
the epilimnion. Our results suggest that one or two deep-
303
mixing events such as those we have observed can account
for a significant fraction of the average annual flux of nitrogen into the upper lake.
Discussion
The small inputs of heat and salt at the lake bottom lead
to slow increases in temperature and salinity gradients, as
well as stability, in theAlower half of the lake through most
of the year. The deep winter mixing events bring down
colder, fresher water from above, smoothing out those gradients and reducing the stability. Consequently, these events
are clearly important for maintaining near-steady-state conditions (on time scales of several years) for the deep temperature and salinity structure of Crater Lake.
We can learn something about the background mixing processes in the hypolimnion by examining the bottom flux and
gradient estimates. The ratio of the bottom heat flux to salt
flux is -200 J mg-‘. If we assume simple eddy diffusion of
salt and heat up from the bottom, then we can obtain a separate estimate of the flux ratio from the ratio c,(dUdz) : (dS/
dz), where cP is -4.2 X lo6 J me3 K-l. From our earlier
discussion, we take d8/dz = 3 X 10e4 “C m-l and dS/dz =
10M2mg liter-’ m-I, giving a flux ratio of -130 J mg-’ (i.e.
within a factor of two of the actual bottom flux estimates).
This result supports the analysis of McManus (1992) and
McManus et al. (1993) that, to first order, the evolution of
the deep temperature and salinity profiles through most of
the year can be interpreted as a consequence of vertical mixing by turbulent diffusive processes. McManus (1992) and
McManus et al. (1993) have also examined the importance
of double diffusion and found it to play a negligible role in
the mean vertical transport of heat and salt in the hypolimnion.
One of the most important questions that we have yet to
resolve is the process(es) that generated the observed downwelling and mixing. One possible explanation for the initial
deepening of the temperature isotherms is downwelling,
forced by strong, quasi-steady winds, at the leeward side of
the lake. Imboden et al. (1988) observed such a response to
a very strong storm in Lake Zug, Switzerland. This response
set up an internal seiche, which led to temporary ventilation
of the deep waters at the windward end of the lake, broadening of the seasonal thermocline, and significant hypolimnetic mixing.
In the present case, there is some variability in the wind
strength between day 34 and day 36, but the direction is
quite steady and the rms estimated wind speed for day 35 is
8 m s-l. Consequently, it is reasonable to assume some mean
thermocline tilt (roughly north-to-south) occurred in response to those winds. Spigel and Imberger (1980) indicated
that, in response to a suddenly imposed steady wind, the
thermocline in a two-layer fluid should tilt to a new equilibrium position within a time Ti/4, where q = 2L(D,Jg’h, h,)”
is the internal seiche frequency of the basin, L is the characteristic downwind length of the basin, g’ = gdplp, is the
reduced gravity, g is gravitational acceleration, Ap is the
density difference between the upper and lower layer, p. is
the mean density, and h, and h, are the mean depths of the
Crawford and Collier
304
upper and lower layers, respectively. We take L = 2r = 7.2
4 X lo-’ kg rnem3(corresponding to the a, difference between about waters at lOO- and 350-m depth), p =
1,000 kg me3, h, = 180 m, and h, = D,,, - h, = 155 m.
The corresponding internal seiche period is Ti = 2.8 d and
the setup time for the new equilibrium thermocline tilt is
-17 h (for comparison, Imboden et al. 1988 estimated Ti =
30 h for the Lake Zug observations).
The thermocline slope, dydx, for steady-state conditions
(and neglecting friction at the interface and lake bottom) can
be estimated from (Heaps and Ramsbottom 1966)
km,Ap=
d5
-=-dx
7
Poe%
'
where r is the wind stress., We take 7 = CDpJP, where C,
is the drag coefficient (taken to be 1.5 X 10p3), p(, = air
density (taken to be 1 kg rnee3),and U is the wind speed over
the lake. For U = 8 m s-l, then d[/dx = 0.014; for U = 10
m s-l wind, dydx = 0.021. These calculations suggest a
downward thermocline displacement of 50-75 m at the leeward edge of the lake; at the thermistor mooring, which is
-2 km away from the leeward end of the lake, the thermocline should be displaced -22-40 m from the prestorm
equilibrium position. One might argue that there is some
downwelling of the thermocline of some 20-30 m by the
start of day 36 (when the winds slacken) in Fig. 3, but a
thermistor spacing of 30 m around the thermocline depth
and the presence of background internal waves makes it difficult to justify such a claim.
So far our discussions have not addressed why the isotherms at the mooring continue to deepen steadily for 2-3 d
after the end of the storm. Epilimnetic waters would not
continue to pile up on the leeward side of the lake after the
winds stop blowing, so the downwind thermocline slope
would not continue to steepen. In the Lake Zug observations
(Imboden et al. 1988), it is plausible that the observed broadening of the metalimnion and hypolimnetic mixing was due
in part to shear instabilities generated as the internal seiche
began (and enhanced by the narrows in the middle of that
lake.) As we have mentioned, an internal seiche is not a free
wave solution in Crater Lake, although perhaps some shear
was generated as other internal waves developed and propagated.
There has also been considerable focus recently on the
importance of breaking internal waves on slopes in both
lakes (e.g. Wuest et al. 1994) and in the oceans (e.g. Ericksen
1985; Ledwell and Hickey 1995). Shear instabilities may
form near a bottom slope for internal waves with an angular
frequency matching the critical frequency, a,. = N sin A,
where A is the angle defining the bottom slope. Recently, C.
Ericksen (pers. comm.) has measured enhanced energy
around the critical frequency in temperature and velocity
spectra measured close to a sloping ocean bottom. Imberger
(1995) has suggested that large-scale seiching motion due to
Poincare and Kelvin waves can interact with groups of highfrequency nonlinear waves to lead to small-scale, mediumfrequency modes, with frequencies close to critical for typical lake slopes. In Crater Lake, bottom slopes range from
zero at the bottom to -0.5 nearshore. From Fig. 2, the crit-
ical frequencies range from about zero (at the lake bottom)
to -6 X 10m4s-l near the surface. Examination of temperature spectra in the upper half of the lake shows energy at
all measureable frequencies (the spectra generally fall off
roughly as up2 over most of the spectral range). At this stage,
unfortunately, we only have thermistor measurements at the
deep mooring, away from slopes, so we expect to see (and,
in fact, find) no evidence of spectral enhancement near the
lake bottom. Additionally, it remains to be seen why some
winter storms seem to generate significant deep mixing and
other do :not.
McManus (1992) proposed that the deep mixing in Crater
Lake is caused by thermobaric instabilities. Most of the previous work on such instabilities in deep lakes has focused
on their generation by internal waves or seiches (Carmack
and Weiss 1991; Weiss et al. 1991; Walker and Watts 1995).
Farmer and Carmack (198 1) suggested that such thermobaric
instabilities are responsible for partial ventilation and mixing
of lake waters just below the compensation depth during the
entire pressure-sensitive phase of lake cooling (i.e. the period
during which the buoyancy flux changes sign at the depth
of the temperature of maximum density). During this entire
phase, then, convecting plumes of water in Crater Lake must
interact with the deep salt gradient, leading to some evolution of the salinity and temperature gradient. Therefore, the
evolution of the salinity profile during the pressure-sensitive
phase is l.ikely very important in determining whether a deep
mixing event may even form.
The details of the salinity profile, which unfortunately was
not measured at this time, are important for determining the
stability of the water column just below z,. If the salinity
profile was uniform around the compensation depth, as suggested by measurements from other winter periods (Fig. 2b),
then a downward perturbation of the thermocline across z,
(perhaps by downwelling at the leeward side of the lake in
response to the winds of days 34 to 36), in conjunction with
the pressure and temperature effects on the equation of state,
would cause the colder water from above to become more
dense than the water below it, leading to downward convection (Farmer and Carmack 1981; see also Fig. 5). At some
depth, however (within 100 m or so, judging by Fig. 2a),
the convecting water must run into the deep salinity gradient,
leading to mixing and entrainment. We can obtain a measure
of the resistance of the water column to such instabilities by
calculating the difference between the in situ background
density profile and the in situ density profile of a water parcel originating at a depth z, (assumed to be above the compensation depth) as it is moved down through the water column adiabatically. Fig. 6 shows two examples of the resulting densil:y difference profile, one for a parcel originating at
z,, = 160 m with an initial temperature of 3.61”C and one
for a parcel originating at 130-m depth with an initial temperature of 3.45”C. Positive values of the density difference
indicate statically stable conditions; negative values indicate
unstable conditions. As can be seen, the bulk of the hypolimnion in Crater Lake is resistant to thermobaric instabilities. (For comparison, we also show in Fig. 6 the density
difference calculation using a fixed salinity profile of 0.104
mg liter- I. These profiles indicate conditions that are much
more conducive to convection throughout the water column
0
100
305
Deep mixing in Crater Lake
(a)
r
03
100
200
E
5300
2.i
400
_/
I
500
600
-2
I(d)
/
1
3.4
3.8
3.6
3.7
3.5
Temperature (OC)
L
.I
0
3.4
3.5
3.6
3.7
Temperature (S)
3.8
Fig. 5. Temperature structure associated with thermobaric instabilities. Approximate location of the compensation depth, z,, is denoted by circles. [a.] An idealized reverse-stratified temperature profile. The water temperature is uniform at and just below the compensation depth, so the water column is neutrally stable in that region. [b.] The thermocline is displaced downward, possibly by a
seiche (or other internal wave) or by a negatively buoyant plume.
The temperature at the new compensation depth is colder and heavier than the water just below, so the profile becomes unstable and
convection occurs. [c.] The mean temperature profile in Crater Lake
before the observed convection event (from Fig. 2a). Horizontal
bars denote estimates of temperature uncertainty at the measurement
depths. The temperature profile is very nearly uniform below 200
m (the small salinity gradient stabilizes the water column slightly
here). [d.] A selected “instantaneous” temperature profile (day 36,
1550 PST), near the apparent initiation time of the convective event
(see Fig. 4). The temperature at the compensation depth is substantially colder than the water below it, so the midlevel water column
may have been unstable at this point.
due to thermobaric instabilities). We note that, although
these are simple hydrostatic calculations and therefore ignore
the effect of vertical acceleration (which may occur just below the compensation depth if a thermobaric instability is
triggered) and intermediate mixing, the stability of the deep
water column must limit the depth to which convection can
take place. Thermobaric instabilities may certainly play a
role in the lake, but they seem unlikely to generate vertical
mixing down to the bottom of the lake.
Another possible mechanism for the observed mixing is
the generation of a turbidity current. Turbidity currents certainly occur in the lake (Nelson et al. 1986). However, we
do not observe such deep mixing in the lake at other times
of the year. It is generally assumed that the density of turbidity flows is typically at least 5% greater than the back-
-1
0
1
2-2
d~,(lO-~ kg m-3)
/
/
/
/
/
/
/
/
/
I
-1
0
1
Ap, (1O-3 kg m-3)
2
Fig. 6. Profiles of the density difference, Ap,, between the in
situ density and the density of a water parcel displaced downward
adiabatically from a starting depth z,, where z, = 160-m (a) and z,~
= 130-m depth (b). Background temperature profile is taken from
Fig. 2a. For solid lines, salinity profile is taken from the January
1990 profile in Fig. 2b; for dashed lines, a fixed salinity profile of
0.104 mg liter-’ is assumed. Positive values of Ap, indicate hydrostatically stable conditions; negative values indicate hydrostatically
unstable conditions. The results suggest that the deep water column
is resistant to thermobarically driven convection.
ground waters (e.g. Komar 1977), whereas seasonal variations in density associated with heating and cooling generate
variations in the background water density of at most a few
tenths of a percent. It is therefore unlikely that seasonal variations in stratification would affect mixing by turbidity currents significantly. If storms are required to suspend sediments and generate turbidity currents, then one would expect
to have deep-mixing events more frequently than observed.
It is unlikely, we conclude, that turbidity currents are responsible for the observed mixing.
We suspect that interannual variability in surface forcing
must lead to significant variation in the frequency and intensity of these deep-mixing events. The ongoing monitoring
program will ultimately provide a large dataset for quantitative evaluation of the relationship between forcing and
mixing response (indeed, preliminary examination of these
data show more such deep-mixing events in subsequent winters). We also intend to continue to make various supplementary observations in the lake to provide additional insight into the lake dynamics. For example, observations from
two additional thermistor chain moorings, deployed in September 1994, should give us a measure of the horizontal
scales of these mixing processes. We are also investigating
options for monitoring the evolution of the salinity profile
in winter. Finally, it is not yet clear whether these events
dominate the annual vertical recirculation of nutrients between the hypolimnion and epilimnion. We are beginning to
use models of lake physics to try to provide insight into
these questions.
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Received: 5 July 1995
Accepted: 24 January 1996
Amended: 30 September 1996