Limnol. Oceanogr., 54(6), 2009, 2041–2057
2009, by the American Society of Limnology and Oceanography, Inc.
E
Flow paths and spatial heterogeneity of stream inflows in a small multibasin lake
Francisco J. Rueda,a,* and Sally MacIntyreb
a Instituto
del Agua and Departamento de Ingenierı́a Civil, Universidad de Granada, Granada, Spain
of Ecology, Evolution, and Marine Biology, and Marine Science Institute, University of California, Santa Barbara,
California
b Department
Abstract
We describe the flow paths of negatively buoyant river inflows in a small lake with multiple basins separated by
sills (Toolik Lake, Alaska) using field data and three-dimensional simulations. Comparisons of field observations,
analytical computations, and simulations show that in small basins in which the timescale for filling (tf) is less
than the timescale of an event (t0), overflow is the dominant mechanism of interbasin exchange. Exchange is
mediated by internal wave displacements if upwelling reaches the height of the sills, zs. This criterion is met if the
Lake number, the inverse of which is proportional to the degree of metalimnetic tilting, is less than zi /(zi 2 zs),
where zi is the vertical displacement of the intrusion. Entrainment followed by horizontal dispersion is the
dominant mechanism of interbasin transport and can account for ,65% of the exchange between large subbasins.
Entrainment is enhanced when submerged sills force river water to flow close to the surface layer. Depths of
intrusions depend upon discharge. They occurred in the lower metalimnion for the coldest events analyzed but
were near the top of the metalimnion during low-discharge events, such as during brief cold fronts. Persistence of
intrusions depends upon the time interval between cold fronts; they ranged from a few days to three weeks.
Timescales of horizontal mixing vary with meteorological forcing; they ranged from on the order of 1 d for wind
events with speeds of up to 6–8 m s21 to on the order of 10 d for light winds.
Storm-inflow events are one of the major disturbances
affecting the seasonal and long-term behavior of lacustrine
ecosystems (Robarts 1987; Elber and Schanz 1990;
Barbiero et al. 1999). These events provide a large fraction
of the annual nutrient loading. For example, Inamdar et al.
(2006) found that the largest storms contributed 15% of
the annual discharge but one-third of the annual inputs
of ammonium, dissolved organic nitrogen, and dissolved
organic carbon in glaciated lakes in New York. MacIntyre
et al. (2006) estimated that loading of inorganic nitrogen
from one storm event in an oligotrophic arctic lake was
,34% of the loading that occurs in more typical years. The
response of aquatic ecosystems to such storm-runoff events
largely depends on the fate of the incoming storm water
and the associated dissolved and particulate constituents. It
is important to know whether storm water forms intrusions
and, if so, the depth and persistence of the intrusions. If the
intrusions are enriched with nutrients or labile organic
matter and are introduced into the surface layer, they will
immediately be available for phytoplankton or bacterial
growth. Alternatively, if they are introduced into the
metalimnion, they may fuel growth within a chlorophyll
maximum or be below the euphotic zone. Then, they may
be available to phytoplankton if mixed vertically at another
time, or they may be sequestered via adsorption to
particulates or consumption by bacteria. Further, if
nutrients, dissolved organic carbon, particulates, or organisms are introduced in discrete intrusions that persist,
layered communities may result. Hence, an understanding
of the flow paths of stream inflows is essential assess their
importance to lake ecosystem function.
* Corresponding
author: fjrueda@ugr.es
The pathways of storm river water depend on a lake’s
geometry, stream density relative to lake water, stream
hydraulics, the hydrodynamics and mixing away from river
inlets, and the ambient stratification (Fischer and Smith
1983; Akiyama and Stephan 1987; Johnson et al. 1987),
which can vary both as a consequence of meteorological
forcing and the stream flow itself. In long and narrow lakes
and reservoirs with simple geometries in which lateral
motions are not restricted, the pathways of distribution of
stream water and their relevant timescales and spatial scales
have been well described in the literature. Our understanding of the fate of river plumes in these cases is based on an
extensive body of literature that includes laboratory
experiments (Ellison and Turner 1959; Britter and Linden
1980; Hallworth et al. 1996), analytical work (Savage and
Brimberg 1975; Jain 1981; Hauenstein and Dracos 1984),
numerical simulations (Chung and Gu 1998; Bournet et al.
1999; Kassem et al. 2003), and field data (Hebbert et al.
1979; Fischer and Smith 1983; Dallimore et al. 2001). For
negatively buoyant inflows (i.e., river water that is denser
than lake water), the stream water initially pushes the
stagnant lake water ahead of itself until it is arrested by
buoyancy forces due to the difference in density between
lake and stream water. At this point, the colder stream
water will plunge beneath the surface. Once submerged, it
will flow downward along the bottom as a gravity-driven
density current, gradually entraining water until it reaches
the level of neutral buoyancy, where the densities of the
flowing current and the ambient fluid are equal (Stevens et
al. 1995; Ahlfeld et al. 2003), or the bottom of the basin
(Hebbert et al. 1979; Finger et al. 2006). In the first case,
the density current separates, forming intrusions that
spread horizontally. Once the intrusions have formed, their
fate is tightly linked to vertical mixing in the water column.
2041
2042
Rueda and MacIntyre
Fig. 1. Interbasin exchange mechanisms along a longitudinal
section of Toolik Lake: (a) overflow, (b) internal displacement,
and (c) entrainment due to wind mixing and heat loss.
That is, if vertical mixing is weak or infrequent, intrusions
may remain at depth for extended periods of time. If winds
or cooling intensify mixing and deepening of the upper
mixed layer, the intrusions could be entrained into the
surface mixed layer.
Lakes with multiple basins occur frequently in the
landscape. The sills found at depth within them will modify
the flow path of incoming water. In order to develop
generalities about the movement of incoming water, the
resulting intrusions, and the persistence of spatial heterogeneity in the vertical and horizontal directions, the
dominant mechanisms of cross-basin exchange within
multibasin lakes must be determined and put into the
context of plume dynamics, within-lake stratification, and
meteorological forcing. With negatively buoyant plumes,
exchange between basins could occur as the incoming water
fills basins sequentially along a flow path (Fig. 1a) due to
mechanisms similar to seiche-pumping (Van Senden and
Imboden 1989), in which the up and down motions of
internal waves facilitate exchanges (Fig. 1b), or via
entrainment of intruding water and its subsequent lateral
transport (Fig. 1c). The presence of topographic features
may further moderate exchange because these features will
force deep intrusions closer to the surface, where they may
be entrained into the surface layer. The importance of these
processes to cross-basin exchange in small multibasin lakes
is currently unknown and likely depends upon discharge,
the intensity of mixing as the incoming water first enters a
lake, the size of subbasins relative to the volume of
incoming water, and the ambient physical forcing.
Due to the differences in composition between lake and
storm water, the occurrence of storm-inflow events will
likely induce spatially variable concentration fields in the
lake. The persistence of heterogeneous fields in the lake will
depend upon the incidence of vertical and horizontal
mixing. Horizontal heterogeneity at depth will develop
when the lateral spreading of intrusions is restricted or due
to changes in inflow characteristics during events (Fernández and Imberger 2008). Horizontal heterogeneity in the
surface layer, in turn, can be created as a result of wind
forcing inducing preferential flow paths of incoming water.
It is also created after entrainment of deep intrusions that
have not spread horizontally due to restricted interbasin
transport. The efficacy of vertical mixing entraining the
intrusions into the surface layer will depend upon the
magnitude of cooling coupled with storm-related factors
that determine the depth of the intrusions. Persistence of
horizontal patchiness in the surface layer depends on
turbulent diffusion in the horizontal direction caused by
fluctuations in the velocity field smaller than the cloud or
patch size of entrained solutes; horizontal velocity gradients at scales larger than patch size, which, together with
small-scale horizontal fluctuations, cause horizontal shear
dispersion; and vertical shear dispersion from vertical
gradients in the flow field associated with small-scale
vertical velocity fluctuations (Fischer et al. 1979; Stocker
and Imberger 2003). Stocker and Imberger (2003) argued
that dispersion from horizontal shear should be the
dominant mechanism of dispersion in small- to mediumsize lakes. The presence of submerged features could make
aspects of the larger flow field more important.
In the following, we use simulations conducted with a
three-dimensional (3-D) hydrodynamic model supported
by experimental data collected in situ to describe and
understand the behavior of storm river inflows and the
spatial variability they induce and to develop generalities.
Our goals include describing mechanisms that cause
interbasin transport, assessing the conditions under which
each process is dominant, and characterizing the depth and
persistence of the resulting intrusions as a function of
stream hydraulics, thermal stratification, and changing
meteorological forcing. Secondly, we quantify the timescales of the physical processes involved in the transport
and mixing of storm river and lake water to enable
predictions for multibasin lakes of different sizes. Our
effort is based on the analysis of field data and modeling
results from a multibasin lake, Toolik Lake, Alaska
(Fig. 2).
Study site
Toolik Lake, Alaska (68u389N, 149u389W), lies in the
northern foothills of the Brooks Range. It is an oligotrophic kettle lake with a surface area of 1.5 km2, mean depth
of 7.1 m, and maximum depth of 25 m (Fig. 2). Shifts
between warm and cold air masses occur frequently; cold
air masses typically come from the north (Miller et al. 1986;
MacIntyre et al. in press) and may lead to increased rainfall
and high discharge events (MacIntyre et al. 2006). The
diffuse attenuation coefficient ranges from 0.5 to 0.9 m21
Pathways of stream inflows in lakes
2043
periods of time (which we will refer to as the study period):
one from day 190 to day 210 (1999), and the second from
day 188 to day 225 (2004). The model was forced using
hydrological and meteorological information collected in
the field, and its results were validated by comparing
temperature simulations against the field data. The model
velocity fields were used to drive the simulations of tracer
releases during four inflow events that occurred during the
study period. One of the events occurred in 1999, and the
other three occurred in 2004 (events 2004-1, 2004-2, and
2004-3). All simulations started at least 4 d before the
inflow events. Hence, the effects of the artificial initial
conditions on model results were deemed negligible during
the storm events. Experimental and numerical results from
1999 were used to analyze pathways of riverborne
substances across moraines and to the surface layers and
to quantify the importance of different mechanisms of
transport. The 2004 data and simulations extend our
understanding of the effects of varying forcing conditions
on the pathways of storm river water in Toolik Lake.
Fig. 2. Bathymetric map of Toolik Lake, with isobaths
shown every 2 m. Gray areas mark shallow zones, or moraines,
which separate the Toolik basin into subbasins: inlet, main, and
west basins. The symbols mark the approximate locations where
microstructure profiles (MacIntyre et al. 2006) and/or thermistor
chains were deployed and sites where model results were checked
(IB 5 inlet bay; TM 5 Toolik main; CN 5 Central; WB 5 west
basins; SWB 5 southwest basin). In 1999, thermistor arrays were
located at TM and CN. In 2004, arrays were located at each
symbol. Also shown in the figure is the M-axis, a line that
originates at the inlet basin and is perpendicular to the moraine
that separates the main from the west basins.
(Miller et al. 1986). The basic limnology of the lake is
reviewed in O’Brien et al. (1997). Its geometry is
characterized by the presence of several subbasins that
are separated by shallow, ,3-m-deep moraines. The
smallest subbasin to the southeast of the lake is the Inlet
Bay, and it is also the one that receives the largest inflow.
The next basin, in the direction of the flow from inlet to
outlet, is the main basin. Its long axis runs from northeast
to southwest. Its deepest point, ,25 m, is toward the south;
its eastern portion is nearly flat and shallow (,4–6 m) with
some small depressions. The west basin is adjacent to the
main basin and is separated from it by shallow moraines
arranged from SW to NE. The southwest basin is further
separated from the west basin by a small promontory. The
lake’s outlet is to the northeast.
Methods
Approach—We studied the space–time distribution of
storm river water as it flows into Toolik Lake through the
analysis of field observations and a series of simulated
tracer experiments conducted with a 3-D hydrodynamic
model. Data and simulations correspond to two different
Meteorological and temperature methods—Meteorological instrumentation for both years and temperature sensors
used in 1999 are described in MacIntyre et al. (2006). In
2004, Brancker TR-1050 self-contained temperature loggers with accuracy of 0.002uC, resolution of 0.0001uC, and
time constant of 3 s were deployed at three stations: inlet
bay (IB), Toolik main (TM), and Central (CN) (see Fig. 2).
Onset Stowaways, with accuracy of 0.2uC and time
constant of 1 min were deployed in the west basin (WB),
southwest basin (SWB), and an additional station between
CN and the outlet. Analysis of the meteorological and
water temperature data followed MacIntyre et al. (2002, in
press).
Model description—Numerical simulations of circulation
and transport in Toolik Lake were conducted with a threedimensional (3-D) free-surface hydrodynamic model
(Smith 2006), which has been extensively validated with
both analytical solutions and field data (Rueda and Cowen
2005). The model is based on the continuity equation for
incompressible fluids, the Reynolds-averaged form of the
Navier-Stokes equations for momentum, the transport
equation for scalars, and an equation of state relating the
concentration of active scalars to fluid density. The
governing equations are solved in layer-averaged form
using a semi-implicit, three-level, iterative leapfrog-trapezoidal finite-difference scheme on a staggered Cartesian
grid. Turbulent mixing is represented in the 3-D model
using diffusion-like terms. A Laplacian operator with
constant mixing coefficients (horizontal eddy viscosity Ah
or diffusivity Kh) is used in the model to represent
horizontal mixing of momentum and scalars (see below).
Vertical eddy coefficients of mixing Kz are calculated using
a two-equation turbulence model (Kantha and Clayson
1994). Nonactive (i.e., tracers) scalar transport equations
are solved using a two-level semi-implicit scheme, in which
only vertical diffusion is discretized implicitly. The advection terms in the transport equation for nonactive scalars
are discretized with flux-limiter methods (Durran 1999).
2044
Rueda and MacIntyre
Fig. 3. (a) Lake numbers with times when wind was from the northwest identified with gray histograms; dashed line indicates LN 5
3. (b) Short-wave radiation, (c) air and surface-water temperatures (thick black line), (d) relative humidity, (e) wind speed, (f) wind
direction, (g) heat fluxes (LW 5 long-wave radiation; L 5 latent heat flux; S 5 sensible heat flux), (h) stream discharge Q and rainfall
(note the rain is inverted), (i) stream temperature and specific conductance SC (conductivity normalized to 25uC), and (j) water
temperatures. The thick white line in (j) indicates the theoretical depth of neutral buoyancy as if it were only a function of stream
temperature for Toolik Lake during the study periods (1999 and 2004). The dashed line marks the level of the moraines separating the
different basins.
Model setup and validation—The computational model
was set up to simulate the processes of transport and
mixing in Toolik Lake during the two study periods. The
lake was discretized using 20 3 20 3 0.5 m grid cells, and,
for stability purposes, the time step was set to 20 s. The
model was forced using observed inflow rates and
temperature in Toolik inlet, and surface heat and momentum fluxes estimated as in MacIntyre et al. (2002) from
local atmospheric variables (Fig. 3). Heat-flux estimates
were corrected for atmospheric stability. Mass-balance
equations were used to estimate outflow rates from
observed water-level fluctuations in the lake, rainfall, and
inflow rates. The time series of estimated outflow rates was
used as boundary condition at the outflow section. With
the grid resolution adopted in the model, the advective
terms should be able to resolve transport features on the
order of (O) 102 m, which, according to Knauer et al.
(2000), is the scale of the eddies that will contribute most to
the horizontal mixing in lakes with horizontal length scales
of O(103) m. The horizontal eddy viscosity, Ah, and
diffusivity, Kh, in the model were set to 2 3 1022 m2 s21.
This value corresponds to the lowest limit of the range of
values encountered by Peeters et al. (1996) during tracer
studies in the metalimnion of lakes with dimensions similar
Pathways of stream inflows in lakes
2045
Table 1. Characterization of the four inflow events. Those events were identified as times when the inflow rate exceeded 2 m3 s21.
The symbol Qave is the average inflow rate during the event, Qmax is the maximum inflow rate, F0 is the inflow densimetric Froude
number, xp is distance to plunge point, and C is dilution rate. Columns 10 and 11 show the length of time that river water took to reach
the main and west basins. These values were estimated from model simulations. The final column represents the time to horizontal
mixing, th, which was estimated from tracer simulations in which storm river water was traced. The variance of tracer concentration S2(t) in
the layer just below the surface was initially zero before the storm; it increased to a maximum value S 2max during the inflow event, and
decreased thereafter. Horizontal mixing is presumed to occur by the time S2(t) first drops to 0.05 of S 2max .
(1)
Start
date
(2)
(3)
Duration Qave
(h) (m3 s21)
1999
2004-1
198.69
191.88
63
80
7.5
5.6
2004-2
2004-3
200.92
213.46
69
116
3.1
3.6
(4)
(5)
Qmax
(m3 s21)
Date of
Qmax
16.2
7.7
11.3
5.0
6.2
5.0
199.00
192.25
(193.10)
201.23
213.90
(216.75)
(6)
Volume
discharged at
Qmax (m3)
(7)
(8)
(9)
(10)
(11)
(12)
F0
xp
(m)
C
216,950
123,077
5.59
6.07
183
195
2.14
2.21
2
6
11
40
3.19
7.09
66,960
117,850
2.80
3.67
111
133
1.66
1.83
5
5
33
24
4.74
5.59
DtreachMB* DtreachWB*
(h)
(h)
th (d)
* The arrival time was defined as the time when the tracer loading to any subbasin reached an arbitrary threshold set to 105 mmol d21.
to Toolik’s, but it is the result of applying the empirical law
proposed by Lawrence et al. (1995) for a length scale (,) of
40 m (52 3 Dx), which represents the horizontal scale of
the smallest flow features that can be resolved by the
numerical model. The diffusion terms with Ah and Kh set to
2 3 1022 m2 s21 should therefore represent the effects on
mixing due to nonresolved subgrid-scale transport processes. In the model, we presumed that temperature is the only
active scalar. We ignore the influence of sediments in
suspension and salinity in the density of the water, given
the low conductivity values (ranging from 40 to 80 mS
cm21; MacIntyre et al. 2006) and total suspended sediment
(TSS) concentrations (ranging from 0.4 to 35 mg L21;
Kriet et al. 1992) reported for stream water in the nearby
but larger Kuparuk River. For a change in TSS of
35 mg L21, the relative change in density Dr/r, estimated
as in Finger et al. (2006), is O(1025), which is one order of
magnitude smaller than the change in density (Dr/r) that
results from changing the river-water temperature by 1uC
from a reference value of 10uC (see values of thermal
expansion coefficient in Fischer et al. 1979).
Our model of Toolik Lake was validated by comparing
simulations and observations collected during 1999 and
2004 at station TM (Fig. 2). The mean root mean squared
error (RMSE), a measure of the discrepancy between
observations and simulations, calculated from daily temperature profiles was 0.25uC in 1999 and 0.15uC in 2004.
This level of accuracy is consistent with other 3-D modeling
studies in lakes (Hodges et al. 2000; Jin et al. 2000; Rueda
and Cowen 2005). Later herein, we illustrate the comparison of the measurements and simulations from four of the
temperature arrays deployed in 2004. Comparisons of
modeled and computed vertical eddy diffusivities (Kz)
indicated that they were similar in the mixed layer and at
the depths of intrusions. Further, a comparison of
measured and simulated profiles of specific conductance
indicates that both gave similar estimates of the vertical
dimensions of the intrusions at TM, CN, and WB (Rueda
and MacIntyre, in press).
Tracer experiments—The fate of river water during the
four inflow events that occurred during the study period
was analyzed by simulating a series of tracer-release
experiments. In this analysis, Toolik Lake was subdivided
into three subbasins (referred to in Fig. 2 and throughout
this work as inlet bay, the main basin, and the western
basins [including both the west and southwest basins]). The
amount of simulated tracer existing within each subbasin
was monitored during the whole period simulated. The
tracer was released in the simulations continuously at all
times whenever the river inflow Q was larger than 2 m3 s21
(i.e., Qevent 5 2 m3 s21; see Table 1). The river water was
presumed to have a constant tracer concentration C, which
was set to 1 mmol m23. These values for inflow threshold
(Qevent) and tracer constant concentrations (C), although
arbitrary, allowed us to define quantitatively when an
inflow event started and finished and to directly quantify
the space–time changes in the fraction of river water within
the lake. Simulated tracer-release experiments conducted
during the inflow event that occurred in 1999, together with
field data collected during and after that event and
presented in MacIntyre et al. (2006), were first used to
study the dominant mechanisms of interbasin exchange and
the timescales relevant for river intrusion transport and
dispersion. We then analyzed and compared the tracerrelease simulations conducted during the inflow events in
1999 and 2004 to establish the dominant processes involved
in dispersing intrusions and to relate the variability in
dispersion timescales with differences in hydraulic or freesurface forcing. Throughout, we assessed the consequences
of morphometry on the physical pathways of distribution
of the river intrusions.
Dimensionless indices and mixing rates—Here we introduce definitions and define procedures used throughout the
text to estimate the scales of transport and mixing processes
affecting storm river water in lakes. Lake–river mixing near
the inflow can be parameterized in terms of the densimetric
Froude number F0 (Stevens et al. 1995) calculated as F0 5
2046
Rueda and MacIntyre
U0/(g9h0)1/2, where U0 is the inflow velocity, h0 is the depth
of the river channel, and g9 is the reduced gravitational
acceleration. Inflow velocity was obtained by dividing the
inflow rate Q by the area of the inflow channel, which was
assumed to be 10 m wide and 1.5 m deep. Reduced gravity
is calculated as g|r0 2 r|/r0, where g is gravity, and r and r0
are densities of the river and the lake surface water,
respectively. The dilution rate C at the plunge point is the
ratio between the inflow discharge at the plunge point
(after mixing) and the discharge at the inflow section, and it
quantifies the initial mixing. An alternative means of
defining the rate of river–lake mixing is through the mixing
ratio c, which is defined as the fraction of river water in a
mixture. Note that the dilution rate C is related to the
fraction of river water c in the intrusion as C 5 c21. The
initial dilution rate C was estimated from average inflow
densimetric Froude numbers and using empirical equations
taken from the literature. We first followed Hauenstein and
Dracos (1984) to estimate the distance to the plunge point
xp in terms of F0 and river channel geometry, as
"
xp ~
S{1
0
0:774F0 h0
S0
h0 =b0
Rates of horizontal dispersion at the center of Toolik
Lake were determined from a series of tracer-release
experiments. In these experiments, a Gaussian tracer cloud
with standard deviations (sx, sy, sz) set equal to (100, 100,
1) m was released at intervals of 6 h, where the center of
mass was located ,1 m below the free surface and near the
geometric center of the lake. The original size of the cloud
was such that the most energetic eddies, which should be of
O(100) m for lakes of the size of Toolik Lake (Knauer et al.
2000), would be effective in modifying the shape of the
cloud. The evolution of the tracer concentration field was
followed for 6 h after the releases. We defined the time
varying horizontal extension of the vertically integrated
concentration distribution, s2(t), as twice the product of
sma and smi, where s 2ma and s 2mi are the variances of the
vertically integrated tracer concentration in the direction of
the major and minor principal axis, respectively. The
apparent dispersion coefficient was then estimated, from
the initial and final size of the cloud after 6 h of
simulations, as (Peeters et al. 1996)
#
1=4
z 1:16
Kapp ~
ð1Þ
ð3Þ
Results
where S0 is the bottom slope, and h0 and b0 represent the
depth and width of the river upstream from the lake,
respectively. This equation applies for large divergence
angles, as found in many lakes, where inflows initially
behave as jets and entrain water along their margins until
they plunge, and for large densimetric inflow Froude
numbers (F0 . 1). We then used Eq. 4 in Johnson et al.
(1989) to estimate C in terms of the ratio xp /b0, as C <
0.5(xp /b0)1/2. The fraction of river water in the intrusions (c)
was estimated from changes in the observed conductivities
following McNamara et al. (1997).
Entrainment rates into the surface-mixed layer due to
heat losses at the free surface were computed using the onedimensional mixed-layer model of Fischer et al. (1979). In
that model, the rate at which the depth of the mixed-layer h
increases with time t is determined as
h
i dh
CTf w2 z gaDTh
~ q3 CKf
dt
CTf ~ 0:50,CKf ~ 0:13
1 Ds2
4 Dt
ð2Þ
where w is a velocity scale of thermals generated by
*
cooling, DT is the temperature change at the bottom of the
mixed layer, and q is a velocity scale defined in terms of w
*
and the wind friction velocity u , as q 5 (w 3 + 1.23u 3)1/3.
*
*
*
The thermal coefficient of expansion, a, was taken as 1.51
3 1024 uC21, which corresponds to water at 10uC (Fischer
et al. 1979). Shear-induced mixing was not included, so our
calculations of entrainment are conservative.
The Lake number was calculated as in MacIntyre et al.
(1999). This dimensionless index is an integral form of the
Wedderburn number (Imberger and Patterson 1990), which
provides an estimate of the degree of thermocline tilting in
response to the wind (Stevens and Imberger 1996; Stevens
and Lawrence 1997; Horn et al. 2001).
The variations in discharge in the four storm events
investigated are illustrated in Fig. 3, and additional details
are given in Table 1. The volume of water discharged was
similar in the event in 1999 and in the first and third events
in 2004, whereas the volume discharged in the second event
of 2004 was ,50% of the other three. The durations of the
events varied considerably: the shortest lasted 63 h, and the
longest lasted 116 h. Consequently, average discharge
varied by a factor of two. In addition, the rate of increase
in discharge at the onset of the storms varied, and
volumetric flow rates increased most rapidly in 1999
(Fig. 3). Together, these factors affected maximum discharge, which varied from 5 to 16 m3 s21. The four discharge events all occurred during cold fronts, accompanied
by concomitant increased cloudiness and higher relative
humidity (Fig. 3b,d). Importantly, the degree of cooling
varied between events. Heat losses during 1999-1, 2004-1,
and 2004-3 events exceeded 250 W m22, whereas the heat
loss in 2004-2 was ,100 W m 22. Related to these
differences, stream temperatures determining inflow density dropped below 10uC in the colder events but not in the
warmer 2004-2 event. The average densimetric Froude
number (F0) during the inflow events, which parameterizes
the mixing associated with the inflow (Johnson et al. 1989;
Stevens et al. 1995), was F0 .1, which suggests that inflow
mixing was vigorous in all events. It was ,3 during 2004-2
and 2004-3, and 6 during 2004-1 and 1999 (Table 1).
Estimated dilution rates (C) before the plunge point were
,2 (Table 1). C was larger for events with the largest inflow
rates. Wind speeds were higher in the three colder events,
and prolonged periods with winds over 6 m s21 were
observed before and sometimes during the event. The upper
mixed layer at Toolik main was 4–5 m deep at the onset of
all events, and the metalimnion was strongly stratified.
Despite the stratification, wind forcing was sufficient to
Pathways of stream inflows in lakes
2047
Fig. 4. Observed and simulated thermal structure in (a, e) IB, (b, f) TM, (c, g) CN, and (d, h)
WB from day 190 to day 223 (2004). The right frames represent simulated results, while the
frames to the left are drawn from observations. Isotherms are shown every 1uC. The 6uC is
marked on frame (b).
drive the Lake number to values O(1) for several hours in
all events but 2004-2 (Fig. 3), which is indicative of upand downwelling of the thermocline and intensified mixing in the metalimnion (Boegman et al. 2005; MacIntyre et al. 2006, in press). As a consequence of heat loss
and increased wind forcing at the start of the events, the
mixed layer deepened by at least 1 m.
The temperature time series at IB, TM, CN, and WB
provide insight into the flow paths of the storm water in
2004, as well as model validation (Fig. 4). During the two
colder events with higher discharge, overall temperature of
the inlet basin became much colder. In 2004-1, the
isotherms spread vertically above and below 6-m depth,
suggesting that the river inflow intruded initially at that
depth. The upward deflections of the isotherms in 2004-3
occurred above 8 m depth, which suggests that incoming
water flowed deeper at that time. The abrupt vertical
deflections of isotherms in both events indicate that
incoming water quickly filled the inlet basin. The temper-
ature gradients at the depths of the intrusion indicate
partial mixing of incoming water with ambient water. In
2004-2, isotherm spreading occurred near 4 m and was
restricted to about 1.5 m. The thermocline thickened in
2004-1 at TM and CN such that the upper mixed layer was
only 2 m deep at those stations but was 4 m deep at WB.
From these differences, we infer that much more storm
water intruded into the main basin than into the west basin.
The magnitude of the changes in isotherm depths was so
small in 2004-2 that we cannot assess the flow path of the
intrusion from temperature data alone. The 2004-3 inflow
event was accompanied by intense cooling at its onset,
which would have entrained storm water into the mixed
layer. However, the subsequent spreading of the isotherms
between 3- and 8-m depth suggests that storm water
intruded at those depths. These observations suggest that
storm river water may form large intrusions in the main
basin, but the dispersion of storm water into the west basin
is limited by the presence of shallow sills.
2048
Rueda and MacIntyre
Comparison of model and observations at multiple sites—
A comparison of the temperature records collected in
summer 2004 at multiple locations with the results of our
simulations shows that the temperatures, temperature
gradients in the metalimnion, and, in general, the longterm evolution of stratification in the water column are all
well-captured by the model (Fig. 4). The model captured
the temporal patterns of heating and cooling with respect
to the storms, the cooling in IB due to the large stream
inflows, and the separation of the isotherms in the main
basin that occurred in response to storm inflows. Discrepancies included lower temperatures in the epilimnion and
more pronounced diurnal heating and cooling. The model
predicted water temperatures about a degree colder than
values measured in IB near the depth of the sill. The overall
successful comparison of field observations and modeled
temperature structure indicates that the model can be used
to assess the mechanisms enabling interbasin exchange and
to quantify how the exchange flow varies in response to
different forcing.
Fig. 5. (a) Conductivity profiles collected with a temperature-gradient microstructure profiler at TM at different times in
1999. (b) Conductivity profiles collected in different locations
along the M-axis in Toolik Lake on day 200 (2004). The locations
of the profiles are shown in Fig. 1. (c–d) Fraction of storm river
water derived from the conductivity profiles shown in frames (a)
and (b), respectively. The fractions were calculated using a mixing
model (see Methods) in which it was presumed that the
conductivity of lake (CL) and storm river water (CR) were
constant. Different fractions are obtained depending on the values
assumed; the range of values obtained taking into account the
variability in CL and CR is indicated by the shadowed areas. CL
was varied from 62 to 66 mS cm21, which corresponds to the
minimum and maximum values of specific conductance measured
in TM on day 190 prior to the storm event. CR was, in turn, varied
between 38 and 45 mS cm21, the minimum and the maximum
values of stream conductivity during the inflow event.
Profiles of specific conductance (SC) taken in 1999
illustrate the flow paths during the early part of the storm
in that year (Fig. 5a,b). From those profiles and using a
mixing model (McNamara et al. 1997), we computed the
fraction of river water at each depth. Specific conductance
in the inlet basin 13 h after peak discharge was depressed
below 3-m depth and was 80% river water (Fig. 5b,d). At
TM and near the far moraine in the main basin, SC was
depressed between 2 and 6 m, and the intrusion was 40% to
60% storm water (Fig. 5a,c). In contrast, on the other side
of the moraine at FJ, SC was low, between 3 and 5 m
(Fig. 5b), and the intrusion was less than 20% storm water
(Fig. 5d). Interestingly, a SC profile at station FI on the far
side of the west basin (Fig. 2) showed an intrusion at the
same depth as at FJ, as well as one centered at 2 m. The
higher concentrations of storm water at FI provide
evidence for an additional pathway of storm-water inflow.
Hydraulically forced exchange: Overflow mechanism—
The length of time until water spills into adjacent basins
by overflow is determined by the particular bathymetry of
the subbasin, the inflow rate, the depth of the intrusion,
and the rate that inflow water mixes with ambient water.
For the average inflow rate during the 1999 event, the
inlet basin would fill in ,3 h at depths between the top of
the sill and the bottom of the intrusion (see Tables 1, 2).
After that time, river water would start overflowing over
the moraines to adjacent basins. Similar computations for
the 3–8-m depth range in the main basin, and assuming no
vertical mixing, indicate that the layer would fill in 2–3 d
(Tables 1, 2). Our simulations, however, indicate that
spillage over the moraine to the west basins occurred only
after 6 h. The shorter time may be due to dilution and
enlargement of intrusions as inflow and lake water mixed
(Fig. 5). The fraction of river water (c) in the intrusions
formed in TM, estimated from the observed conductivities, was approximately 0.44. This estimate agrees, first,
with the simulations (Rueda and MacIntyre, in press)
and, second, with our estimates of lake–river mixing rates
obtained from the average values of inflow densimetric
Froude numbers F0 (Table 1). The filling timescale,
including the effects of the initial lake–river mixing, can
be estimated as
tf ~
V
c
Q
ð4Þ
where Q is the average inflow rate, and V is the volume of
the basin between the theoretical intrusion depth and the
top of the sills. Assuming that c is constant, tf is ,20 h.
These results indicate that initial mixing may significantly
reduce the transit time between basins. The estimates of
transit time, however, are larger than the observed and
simulated values (Table 3) and indicate that overflow may
not be important for large basins during the first stages of
a storm, and other mechanisms of horizontal exchange, as
described in Fig. 1, could be operative.
Pathways of stream inflows in lakes
Table 2. Estimates of the time to fill the volume between two
depths (receiving layer) with and without mixing with ambient
water in the main and inlet basins (Fig. 2) during the 1999 event.
The estimates were constructed by first dividing the volume of the
receiving layer by the average inflow rates during the 24-h period
from 12:00 h on day 198 to 12:00 h on day 199 and multiplying
the result by a mixing ratio c. The mixing ratio defines the fraction
of river water in the intrusion mixture (c 5 1 if no mixing occurs; c
5 0.44 when mixing is taken into account). After this filling time,
river water would start to flow over the moraines separating the
main and the west basins.
Depth ranges
for receiving
layer (m)
Vlake (m3)
tf (h)
no mixing
tf (h)
mixing
IB 3–8
MB 3–8
MB 3–7
MB 3–6
MB 3–5
MB 3–4
71,320
2,396,200
2,046,400
1,659,800
1,205,000
625,600
2.7
56
48
39
28
15
25
21
17
12
6
Internal displacements driving inter-basin exchange—
Winds during the inflow events analyzed tended to be
from the NW and perpendicular to the moraines separating
the main and west basins (Fig. 3). The tilting of the
metalimnetic intrusion in the model (Fig. 6a,b,c) and the
increases in simulated concentrations of tracer at 8-m depth
in the west basin (Fig. 6d,e,f) after such an event provide
evidence for this mechanism.
With a two-layered model of the lake and the
assumption that rotational effects and variability in wind
stress are negligible, the amplitude of internal waves
required for overflow into the next basin can be computed
following Monismith (1987) and Horn et al. (2001). The
magnitude of the thermocline displacement zmax is zmax 5
2L/Ri*, where L is the fetch length of the lake, and Ri* is
the bulk Richardson number, given by
Ri ~
agDTh
u2
ð5Þ
Here h is the depth of the water column above the
intrusion, DT is the temperature difference between the
2049
intrusion and the surface layer, and u is the water friction
*
velocity due to wind stress. For h < 5 m, DT < 5uC, as
observed on day 199 (1999) in Toolik main, and letting L <
1000 m, the minimum wind speed to induce the 2-m
isotherm displacements large enough to bring river
intrusions over the 3-m-deep moraines and into the west
basin is 6–7 m s21. From 00:00 h to 12:00 h on day 199
(1999) (Fig. 3), winds exceeded this threshold. During that
time, the tracer loads into the west basins reached a
maximum (Fig. 7f), and intrusions appeared in WB
(Fig. 6c). A threshold for exchange by internal displacement can be similarly defined in terms of the Lake number
LN. If we assume that the metaliminion is centered at 5 m,
the threshold value for a displacement to reach the depth of
the sill and then overflow is LN < 3. Lake numbers dropped
to values of 2 for several hours prior to peak discharge in
1999 (Fig. 3), confirming that this dimensionless index can
be used to infer when interbasin transport occurred via the
displacement mechanism. As a further test of the importance of wind-induced upwelling for interbasin exchange,
we ran simulations in which the surface shear stress was
reduced to 1% of its measured value. With this reduction,
the tracer was primarily confined to the metalimnion in the
main basin, and concentrations in the west basin were only
14% of those computed with the actual wind forcing
(Fig. 6g,h,i). Thus, internal wave displacements, as opposed to overflow, mediated transport across submerged
features between larger basins for at least the initial stages
of storm events.
Entrainment of shallow intrusions—When river water
intrudes just below the mixed layer, as occurs when it fills
the inlet basin and starts flowing over the moraines into the
main basin (Fig. 4), it can be entrained into the surface
mixed layer. The likelihood of entrainment can be analyzed
using the mixed-layer model of Fischer et al. (1979). During
the first part of day 199 (1999) and shortly after the peak
discharge, the lake was subject to ,6 m s21 winds and lost
energy at a rate of < 200 W m22. Subject to that forcing,
the model in Eq. 2 predicts that a 2-m-deep surface mixed
layer (Fig. 3) overlying inflow water 5uC colder would
deepen and entrain river water at a rate dh/dt of ,7.5 3
Table 3. Persistence (tintr) of intrusions; averaged depth for the top of the intrusion (zintr-min), averaged depth of their bottom
(zintr-max), and averaged location where maximum concentration is achieved (zintr-avg). Note, because of the averaging, these data do not
show the full depth range of the intrusions. Intrusions were identified from inspection of one-dimensional vertical projection of the tracer
concentrations fields C1D(z). An intrusion was deemed to exist if the following conditions were met: C1D(z) has a maximum at a given
depth below the surface, zintr, and the value of maximum aerial averaged concentration C1Dmax is at least 10% larger than the
concentration calculated by averaging C1D(z) from zintr to the surface C1Davg. The intrusion layers were identified as the layers where the
tracer concentration was at least 0.80 times the maximum value of C1D at each time.
Basin
IB
WB
MB
MB
MB
MB
Scale
1999
2004-1
2004-2
2004-3
tintr (d)
tintr (d)
tintr (d)
zintr-max (m)
zintr-min (m)
zintr-avg (m)
11.2{
22.2*
13.2*
1.4
3.4
6.89
4.39
6.03
10.6
20.5
8.6
4.2
7.23
1.0
3.7
5.32
2.88
4.66
11.5{
0.5
4.7
7.94
4.70
6.67
* Washed out during third event in 2004.
{ Limited by the extent of simulation.
2050
Rueda and MacIntyre
Fig. 6. Tracer concentration field predicted by the model at 03:00 h on day 199 along three longitudinal sections parallel to the
M-axis (see Fig. 1): (a) a section 200 m north of the M-axis, (b) a section along the M-axis, (c) a section 200 m south of the M-axis.
(d–f) Same as (a–c) but at 13:00 h on day 199 (1999). (g–i) Tracer field predicted by the model at 13:00 h on day 199 (1999) for a synthetic
wind field, in which wind speeds were reduced to 10% of their measured values on days 198 and 199 (1999). Note that the shear stress,
being proportional to the square of the velocity, is only 1% the value of the ‘‘measured shear stress’’ when the velocities are multiplied by
the factor 0.1. In all simulations, the heat fluxes were set to the measured values.
1026 m s 21. During the 12–14-h period when these
conditions prevailed, ,37% of the river water just below
the mixed layer could have been entrained and rapidly
mixed into the surface layers. If the shallow incoming layers
had a tracer concentration of 1 mmol m23, the concentration of the tracer in the 2-m-thick surface layers of IB after
mixing vertically would be ,0.2 mmol m23. This value is
similar to our modeled results, 0.25 mmol m23, and implies
that 20% of the water in the surface layer in IB would be
river water. These values are consistent with the observations, which suggest that a non-negligible fraction of lowconductance river water might have reached the surface
layers in the inlet (Fig. 5d). As a consequence of entrainment and subsequent surface overflow, nearly 30% of the
total mass of tracer in the main basin at 12:00 h on day 199
(1999) was within the upper 3 m of the water column. The
remaining 70% was between 3 and 8 m (see also Fig. 5a,b).
After 12:00 h on day 199 (1999), the wind ceased, and the
cooling rate decreased. As a result of the reduced
entrainment, the river water flowed mainly as an intrusion
between 3 and 8 m, and the percentage of tracer mass
between 3 and 8 m by 00:00 h on day 200 increased to
reach ,80%. These results indicate that the percentage of
inflowing water in the surface layer versus metalimnion
strongly depends on the extent of heat loss and wind mixing
throughout the storm period.
Entrainment of deep intrusions—Once river water has
reached its depth of neutral buoyancy zintr, the resulting
intrusions will persist (see Table 3) until the upper mixed
layer deepens to reach zintr. The intrusion will then be
rapidly incorporated in the surface layers, where it can be
freely transported to reach other basins. The depth of the
surface mixing layer was defined, from modeled values of
eddy diffusivity Kz, as layers in which Kz . 1025 m2 s21.
In the field data, it was defined as the depth to which
temperatures were within 0.02uC of the surface temperature. These two methods gave comparable estimates of
mixed-layer depth. In 1999, the average diffusivity Kz in
the surface mixing layer was O(1022) m2 s21. With an
estimated mixing time of h2/Kz, an 8-m-thick layer with
that diffusivity will mix in ,2 h. Hence, once the bottom
of the mixed-layer reaches the intrusion, it will be
dispersed rapidly. During the event in 1999, the mixedlayer depth was shallower than the depth of the intrusion
in the main basin until day 201 (Fig. 7b), and, consequently, tracer remained confined in a layer between 3 m
to 8 m. On day 201, maximum heat fluxes into the lake
were at most 100 W m22, fluxes out of the lake exceeded
200 W m22, and NW winds averaged ,6 m s21 (Fig. 3).
Toward the end of day 201, the surface mixing layer
reached 6.5 m. As a result, tracer concentrations decreased in the upper 7 m of inlet bay and the main basin
and increased rapidly in the west basins (Fig. 7). Sixtyfour percent of the total mass of tracer in the WB at the
end of the simulations entered during the 2-d period from
day 201 to 203. The two deep-water exchange mechanisms
that occurred on days 199–201 only transported 32% of
the total mass that reached WB (Fig. 7f). Thus, deep
vertical mixing combined with lateral wind-driven transport and horizontal mixing effectively transfers inflow
water across moraines and can be responsible for most of
Pathways of stream inflows in lakes
2051
the exchange to basins away from those that receive the
initial inflows.
Fig. 7. (a–c) Area-averaged tracer concentration in (a) inlet
bay, (b) Toolik main basin, and (c) west basins for the tracerrelease experiments in 1999. The time is represented on the x-axis,
the depth is on the y-axis, and the color represents the areaaveraged tracer concentration (note, scale of color bar changes for
each panel). Frame (b) also shows the evolution of a mixing-layer
depth (white line). Black lines in (a–c) show the evolution of the
top, bottom (discontinuous), and center (continuous) of the
intrusion structure. The vertical extent of the intrusion layer was
identified from an analysis of a one-dimensional vertical
projection of the tracer concentration fields C1D(z). The intrusion
layers were identified as the layers where the tracer concentration
was at least 0.80 times the maximum value of C1D at each time.
(d–f) Time series of tracer loads into (d) inlet bay, (e) Toolik main
basin, and (f) west basin. Tracer mass loadings were estimated on
a 6-h basis by subtracting the mass existing at any given time and
Influence of discharge and surface forcing on the fate of
storm river water—The variations in meteorological and
hydrological forcing among the four events allow us to
assess the effects of different forcing on the interbasin
transport rate (Table 1) and depth and persistence of
intrusions (Table 3). The sequence of events in 2004,
furthermore, allows us to analyze the influence of
subsequent storms on the fate and dispersion of previously
formed intrusions. The depth of the intrusion is largely set
by the stream temperature, the volume of introduced storm
water, and the mixing of the introduced water with that in
the inlet bay. As a result, intrusion depths in the main basin
centered between 6 and 7 m for the three larger storms and
at 4.7 m for the smallest one (2004-2). Note that attempts
to predict mean intrusion depth based on stream temperatures alone (Fig. 3) would be at least 1 m too deep. This
discrepancy attests to the importance of mixing dynamics
in the inlet bay and modification of the temperature, and
thus density, of the storm water as water flows over the sills
between basins.
Travel times in 1999 were two to four times faster than
during the events in 2004 (Table 1). These faster times were
driven by the greater discharge. However, for discharges
between 5 and 11 m3 s21, travel times from TM to WB
were independent of discharge and varied between 24 and
40 h. Due to lower discharge, wind forcing, and heat losses
in the first two events in 2004, the overflow, internal
displacement, and entrainment mechanisms were all slower
than in 1999 and 2004-3. Consequently, travel times were
longer (Table 1), and tracer persisted longer within
intrusions in TM (Table 3). Wind forcing and rate of
cooling in 2004 were greatest during the third event (event
2004-3). Winds were from the northwest and Lake numbers
were near 1 for the first 24 h of the event. The net heat flux
during the first hours of day 214 was 2400 W m22, and it
remained negative almost until 08:00 h on day 215. Hence,
not only internal displacement, but also entrainment led to
faster rates of transport from TM to WB relative to the first
two events in 2004 (Table 1).
The persistence of intrusions of stream water in the lake
varied with the proximity of each basin to the incoming
stream, with the physical forcing during and after the time
stream water flowed into the lake, and with the proximity
in time of storm events that could flush stream water out of
a basin (Table 3). For instance, intrusions tended to persist
longer in the inlet basin than at the main basin. The
intrusion in the inlet basin from 2004-1 persisted for 22 d.
r
at any given subbasin from the mass existing in that same
subbasin 6 h later. (g) Evolution of the apparent or effective
dispersion coefficient calculated from pulsed tracer-release experiments. Finally, frame (h) represents the evolution of areaaveraged vorticity (dashed line) and the area-averaged absolute
vorticity (solid line), estimated from the simulated velocity field
for the 1999 runs calculated in the uppermost layer.
2052
Rueda and MacIntyre
Vertical mixing was insufficient to entrain it into the
surface layer; also, the next event was warmer, and much of
the inflow water flowed in on top of it. Intrusions from
both 2004-1 and 2004-2 in the inlet basin were flushed
during the third event.
In the main basin, the persistence of intrusions varied
from 3.4 to 20.5 d. The intrusion in 1999 was dispersed
after 3.4 d, in part by internal displacements, but mainly by
entrainment into the mixed layer (Fig. 7b). The intrusion in
2004-1, in turn, lasted 20.5 d because the mixed layer
shoaled due to warming shortly after inflow, resulting in a
reduction in the potential for entrainment. Mean Kz values
were O(1026) m2 s21 in the center of the intrusion and
O(1025) m2 s21 near its upper boundary. The timescales
for mixing across the 4-m-thick intrusion, estimated as d2/
Kz (with d 5 4 m), were on the order of one to several
months. Exchanges over the 0.5-m upper boundary,
though, would have occurred daily. The 2004-2 intrusion
came in on top of the first and did not contribute toward its
dispersion. The intrusion from the 2004-1 event was finally
entrained into the surface mixed layer during the 2004-3
event, mainly due to strong cooling and wind mixing.
In the west basin, the intrusions were short-lived and
occurred discontinuously (e.g., Fig. 7c). They generally
formed during strong NW wind forcing, which suggests
that they were fed by upwelling from intrusions in the main
basin. The largest exchanges between the west and the main
basins occurred after the intrusions in the main basin had
been entrained and were mixed horizontally.
Horizontal heterogeneity—The tracer concentration
fields simulated by the model were highly variable, both
horizontally and vertically within events and between
events (Figs. 8, 9). The fact that the model is based on
physical laws, and that the simulations agree with the
available field observations (see Model setup and validation
in the Methods section; Fig. 5; Rueda and MacIntyre, in
press), allows us to place confidence in the simulated
horizontal fields. The model shows detailed patterns of river
inflows at time and space intervals that cannot be duplicated
by field sampling. For example, the patterns 36 h after the
start of the event varied between storms (Fig. 8). During
event 1999, concentrations in surface waters extended
throughout much of the main basin, whereas, in the three
events with lower discharge, there was a tendency for
incoming water either to flow along the lake margins, where
they bathed the benthic algal communities, or to form gyrelike structures. Concentrations remained heterogeneous 72 h
after the start of the event. The moraine separating the main
and the west basins contributed to the heterogeneity, even at
depths above the moraine (Fig. 9), as did prevailing winds
(Fig. 9, surface layer TM). Considerable dispersion results
from frequent shifts in wind direction (2004-3). Overall, the
persistence of horizontal heterogeneity depended upon the
time from the onset of the discharge event until the next event
with strong winds. For instance, the surface layer in the main
basin became homogeneous shortly after the wind events at
the end of day 201 (1999) (Fig. 10). It took several more days
until tracer concentrations were uniform in the main basin
and the west basin.
Discussion
In multibasin lakes, the introduction of negatively
buoyant water during storm inflow events induces significant spatial–temporal variability in the composition of
water. These changes occur in the vertical direction as a
consequence of the formation of intrusions. They occur in
the horizontal direction because of the presence of shallow
sills that restrict the lateral spreading of intrusions and
beacuse of variations in surface currents caused in part by
these same features. We identified three mechanisms that
induce cross-basin exchange across sills, and we showed a
variety of factors that influence the depth of intrusions and
their persistence. In the following, we compare the
timescales and dimensionless indices which determine the
importance of these different mechanisms, so that our
results can be generalized to other storm events in other
locations and in the context of changing weather patterns.
Role of different mechanisms for interbasin exchange—
The inflow rate, Q, the size of the basins, V, and the rate at
which the incoming water mixes with ambient water prior
to the formation of the intrusion will determine the rate at
which sequential basins are filled and, hence, the rate of
lateral transport by overflow. The ratio of the filling
timescale (tf), as given by Eq. 4, to the length of the inflow
event (t0) provides an indication of the importance of
overflow as an exchange mechanism between basins during
any given inflow event. If an event ceases before a basin has
filled or before an intrusion has thickened enough to allow
overflow (i.e., tf /t0 & 1), this mechanism will not be
important. The inlet basin was, for example, characterized
by ratios tf /t0 % 1, whereas the main basin was
characterized by tf /t0 & 1 during the four events analyzed.
Consequently, overflow was the dominant form of exchange out of the inlet basin (Fig. 7d) and into the main
basin (Fig. 7e), but it did not contribute significantly to the
exchange between the main and west basins (Fig. 7f). Large
values of F0 (&1) and consequently large initial mixing
rates (C 5 c21 &1) are also expected for large inflow rates
(Q), as reported by Johnson et al. (1989), which should
further decrease the ratio tf /t0 and further contribute to the
importance of overflow.
Internal wave–mediated exchanges have been observed
previously in a number of lakes (Lawrence et al. 1997;
Umlauf and Lemmin 2005; Laval et al. 2008), and the
process has been called seiche pumping (Van Senden and
Imboden 1989). In most of these cases, the ratio of the
depth of the thermocline to the depth of the sill was ,1
(Laval et al. 2008). The internal waves drove bidirectional
exchange of hypolimnetic water through sills, and the
magnitude of exchange was dependent on the amplitude
and duration of the internal waves (Laval et al. 2008). In
contrast, in Toolik Lake, and as expected in many kettle
lakes, the sills are shallow, and the intrusions tend to occur
within the metalimnion. Thus, the ratio of the depth of the
thermocline to that of the sill is .1, and intruded water can
only be transported between basins when winds are large
enough that isotherm excursions are larger than the
difference in depth between the top of the intrusion (zi)
Pathways of stream inflows in lakes
2053
Fig. 8. Tracer concentrations 36 h after the beginning of each event as a function of depth
for the four events simulated: (a) 05:00 h on day 200 (1999); (b) 09:00 h on day 193 (2004); (c)
09:00 h on day 202 (2004); and (d) 23:00 h on day 214 (2004). The color scale is the same for
all plots.
and the sill (zs) and in a direction that induces upwelling
perpendicular to the sill. Our calculations showed that
the Lake number can be used to predict when
interbasin exchange will occur by isotherm displacement.
Given that the magnitude of the displacement depends on
LN, the criterion for exchange is LN , zi /|zi 2 zs|. In arctic
lakes, such events occur frequently due to the relatively
weak stratification and frequent windy periods (MacIntyre and Melack 2009; MacIntyre et al. in press). In
lakes with stronger stratification or greater sheltering
from wind, this mechanism would likely occur less
frequently.
2054
Rueda and MacIntyre
Fig. 9. As in Fig. 8, but 36 h later (i.e., 72 h after the beginning of the event): (a) 17:00 h on
day 201 (1999); (b) 21:00 h on day 194 (2004); (c) 23:00 h on day 203 (2004); and (d) 11:00 h on
day 216 (2004).
Entrainment occurs as wind and cooling deepen the
surface mixed layer to the depth of intrusions. Entrainment
distributes storm water throughout the surface mixed layer
in a timescale te 5 h2/Kz, which is typically of O(1) h
(Imboden and Wüest 1995; MacIntyre et al. 2002), i.e.,
much shorter than the wind or inflow events. Once in the
surface layer, the entrained water will rapidly be dispersed
to other basins on timescales that depend on horizontal
dispersion rates. Our simulations suggest that entrainment
probably accounts for most of the transport between large
basins downstream of inlet basins. For instance, almost
65% of the water exchanged between TM and WB in 1999
occurred during a 2-d period when the intrusion in TM was
entrained into the surface mixed layer. In addition, a
Pathways of stream inflows in lakes
Fig. 10. Evolution of the tracer concentration near the
surface and at four different sites in Toolik Lake for the simulated
tracer-release experiment in 1999.
significant fraction of the storm river water is entrained
into the surface layers before reaching the theoretical depth
of neutral buoyancy. These fluxes mainly occur as water
flows through the small inlet basin and through and over
the sills. We estimated that almost 30% of riverborne
substances entering during the initial stages of the storm in
1999 could have been entrained into the surface layers while
flowing near the surface in the inlet bay and adjacent
shallow regions. In consequence, small inlet basins are not
mere conveyors of storm river water from the inlet to the
deep intrusions in the largest basins. Instead, the smallest
inlet basins behave as mixers, facilitating the incorporation
of river water into the surface layers from where they can
be freely transported to other subbasins over the sills. In
basins with complex morphometry, this mechanism might
significantly increase fluxes to the surface layer relative to
lakes in which inflows occur directly into a large basin and
sink quickly to their depth of neutral buoyancy. Thus,
entrainment and interbasin transport are facilitated in
basins with shallow shelving areas or sills that force
incoming water to depths where vertical mixing is induced
by surface forcing.
Timescales of horizontal heterogeneity—Horizontal dispersion depends upon wind, depth of the mixed layer and,
thus, vertical shear, and bottom topography and basin
morphometry, which affect the magnitude of velocity
gradients. Our simulations with tracer clouds gave values
of Kapp of O(1021) m2 s21 during calm periods and
,1.4 m2 s21 during the strong wind events on days 199
and 202 (Fig. 7g). These values are comparable with those
in Lawrence et al. (1995) for length scales , 5 3s of O(102)
m and , 5 O(103) m, the latter being the horizontal scale of
Toolik Lake, and they are consistent with those in
Kootenay Lake (,3 km wide) (Stevens et al. 1995). Stocker
and Imberger (2003) and Stevens et al. (1995) argued that
2055
the irreversible spreading of solutes and particulates in the
surface layer in small- to medium-size lakes is largely the
result of dispersion driven by horizontal shear. Our
simulations suggest that large horizontal velocity gradients
develop in response to strong and persistent wind events
(see Figs. 2, 7g), and our time series figures of tracer
distribution suggest that these may be accentuated by basin
morphometry (Figs. 8, 9). Area-averaged vorticity, f,
which indicates the magnitude of the velocity gradients,
was two to three times higher during storm events and
cooling periods (<2.5 3 1025 s21) than during calm
periods (1 3 1025 s21). If we assume that the lateral
dispersion rate is proportional to the square of the
magnitude of the velocity gradients, as dimensional
analysis suggests (Smagorinsky 1963; see also Fischer et
al. 1979), then the rate of dispersion during strong winds
should be nearly one order of magnitude larger than under
calm conditions. The order-of-magnitude difference during
calm and windy periods in both f and Kapp supports this
hypothesis and indicates that large velocity gradients
induced by strong wind events contribute substantially to
rapid horizontal mixing.
The timescale for a tracer to become uniformly distributed
over the whole lake, th, is computed from the rate of
spreading of a tracer cloud, where the initial and final
variances are set to s 20 5 A0 /p and s2 5 A/p, respectively.
For example, A0 can be taken as the surface area of the main
basin, and A is the area of the whole lake. The time th for a
cloud to grow from s 20 < 3.2 3 105 m2 to s2 < 4.7 3 105 m2
when Kapp 5 O(1) m2 s21, as on windy days and using Eq. 3,
is O(1) d. During calm periods, with Kapp , O(1021) m2 s21,
mixing time is O(10) d. Thus, spatial heterogeneity can
rapidly be reduced when winds are moderate to high, such as
during the passage of fronts, but this reduction persists with
the low to moderate winds that are prevalent at other times
(Fig. 3). The implications of the temporal heterogeneity
depend upon the rates of the biological and chemical
reactions induced when the intruding water mixes with
ambient water (Knauer et al. 2000). For instance, whether
benthic algae or pelagic phytoplankton preferentially
acquire nutrients will depend upon the amount of time the
stream inflows hug the nearshore regions (Fig. 8), the timing
of nutrient loading relative to changes in the storm
hydrograph, and uptake rates.
Hydraulic and meteorological forcing—The ecological
response of lakes as weather patterns vary under different
climate regimes will depend upon the pathways of inflow
events as they vary with stratification and surface forcing.
All the discharge events described here were initiated
during cold fronts, but other conditions varied. The depth
of penetration of the incoming water was linked to the
degree of cooling associated with the event, since decreased
air temperatures and increased evaporation rates affected
both the stream temperatures and the average temperature
of the inlet basin. The discharge rate and related volume of
incoming water determined the amount of the incoming
water that mixed with water in the inlet basin. Given these
combined factors, intrusion depths were deeper during cold
fronts, which were accompanied by the largest heat losses
2056
Rueda and MacIntyre
and largest incoming volumes of water. The volume of
water at peak discharge contributed strongly to the rate
that water moved between basins. The frequency of shifts
between warm and cold air masses and the associated
increases in wind speed affected the frequency of events
having Lake numbers low enough to cause upwelling and
overflow into adjacent basins, persistence of intrusions, and
the timescale for horizontal uniformity in the surface layer.
Thus, the effect of incoming waters and the associated
nutrients, microbes, and phytoplankton, whether they will
become well mixed on timescales of days or weeks, is highly
dependent upon climate-related factors that influence the
frequency and intensity of storm events (Serreze and
Barrett 2008; MacIntyre et al. in press).
The combined modeling and field studies presented here
illustrate the space–time scales of pathways of stream
inflows in small lakes with complex bathymetry. Results
indicate that synoptic sampling is required even in small
lakes to quantify the biological consequences of increased
stream discharge. Variations in dominant patterns and in
mixing rates depend on atmospheric forcing in predictable
ways. With an understanding of these patterns, we are
poised to predict the implications for benthic and pelagic
communities as climate changes. Of major importance,
modeling allows confirmation and extension of the
intuition gained from field studies. The synoptic view
allows questions to be raised and strategies to be developed
to more fully address the implications of physical processes
on ecosystem function.
Acknowledgments
We thank James King, Neil Bettez, Chris Wallace, Chris
Crockett, Mary Anne Evans, and Jim Laundre for help with field
measurements. We thank Brice Loose, Chad Helmle, Lorenz
Moosmann, and Chris Wallace for assistance with processing and
analysis of physical data. The Arctic Long-term Ecological
Research (LTER) provided meteorological and stream discharge
data. We particularly thank George Kling for his assistance with
this data. Logistic support was provided by the University of
Alaska Toolik Lake Field Station. Financial support was
provided by National Science Foundation (NSF) Division of
Environmental Biology grants DEB-0508570, DEB-0423385, and
DEB-9810222, and Office of Polar Programs (OPP) grants OPP9911278 to the Arctic LTER, and DEB-9726932, -0108572,
-0640953, OCE-9906924, and ARC-0714085 to Sally MacIntyre.
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Associate editor: Chris Rehmann
Received: 28 August 2008
Accepted: 11 May 2009
Amended: 24 June 2009