Historic low stand of Great Salt Lake, Utah: I: Mass balance model and origin of the deep brine layer

Abstract

Great Salt Lake of Utah is among the largest and most ecologically important water bodies in North America. Since the late 1950s, the lake has been divided into two hydrologically distinct water bodies by a rock-fill railroad causeway. Flux through the causeway is driven by two forces: differential surface elevation and differential density between the north and south arms. The south arm features episodic vertical stratification due to the influx of deep, dense brine from the north arm. The source of this brine (a breach, two culverts, or subsurface flow) has been investigated over the past 50 years. Quantification of subsurface water flux through the causeway has been problematic due to the heterogeneous and slowly compacting nature of the causeway fill over time. Between 2008 and 2015, enhanced gauging of various surface inflows and outflows and density measurements made throughout the lake permitted detailed water volume calculations of both lake arms. Results show that during high precipitation years, density-driven, north-to-south flow through the causeway predominates due to freshening of water in the south arm. At other times, south-to-north head gradient driven flow and north-to-south density-driven flow are approximately equal. The model suggests subsurface flux through the causeway is one important driver of the ecologically important deep brine layer in the south arm of the lake over the past 20 years.

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Research Article
Historic low stand ofGreat Salt Lake, Utah: I
Mass balance model and origin of the deep brine layer
PaulW.Jewell1
Received: 29 March 2021 / Accepted: 7 June 2021
© The Author(s) 2021 OPEN
Abstract
Great Salt Lake of Utah is among the largest and most ecologically important water bodies in North America. Since
the late 1950s, the lake has been divided into two hydrologically distinct water bodies by a rock-ll railroad causeway.
Flux through the causeway is driven by two forces: dierential surface elevation and dierential density between the
north and south arms. The south arm features episodic vertical stratication due to the inux of deep, dense brine from
the north arm. The source of this brine (a breach, two culverts, or subsurface ow) has been investigated over the past
50years. Quantication of subsurface water ux through the causeway has been problematic due to the heterogene-
ous and slowly compacting nature of the causeway ll over time. Between 2008 and 2015, enhanced gauging of various
surface inows and outows and density measurements made throughout the lake permitted detailed water volume
calculations of both lake arms. Results show that during high precipitation years, density-driven, north-to-south ow
through the causeway predominates due to freshening of water in the south arm. At other times, south-to-north head
gradient driven ow and north-to-south density-driven ow are approximately equal. The model suggests subsurface
ux through the causeway is one important driver of the ecologically important deep brine layer in the south arm of
the lake over the past 20years.
Keyword limnology· Great Salt Lake· Mass balance model
1 Introduction
Saline lakes have long been recognized for their cultural
and scientic importance. A common feature of these
lakes is distinctive water masses separated by sharp verti-
cal density gradients. Natural examples include the Dead
Sea (e.g., [23] and Canadian prairie lakes [21, 22]. Exam-
ples of human-caused stratication include Big Soda Lake
in the western Great Basin of the U.S. [19, 38], Salton Sea
[20] and Mono Lake [15] in California, and the southern
arm of Great Salt Lake of the eastern Great Basin [13]. Ver-
tical stratication often leads to anoxic bottom waters
with anomalously high metal concentrations (e.g., [32].
Understanding the controls by which these water masses
form and disappear is thus a critical question in the eld
of physical limnology and lacustrine geochemical cycles.
Great Salt Lake in the eastern Great Basin of Utah is the
largest closed-basin lake in North America. The lake and
surrounding wetlands are important resting places and
food resources for migratory water fowl (e.g., [2], as an eco-
nomic driver for a variety of extractive industries [9], and as
a record of climate and paleoclimate [12, 29, 47].
During the mid-1950s, a rock-ll railroad causeway was
constructed across Great Salt Lake separating the lake into
* Paul W. Jewell, paul.jewell@utah.edu | 1Department ofGeology andGeophysics, University ofUtah, SaltLakeCity, UT84112, USA.
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two hydrologically distinct water bodies: the north and
south arms (Fig.1). The only signicant water inputs to
the north arm of the lake are from precipitation and ux
through the causeway. The south arm receives water from
precipitation, three major river systems (Bear, Weber, and
Jordan), and small secondary streams principally along
the eastern edge of the lake. The Jordan River has been
extensively engineered into a series of canals, the larg-
est of which (the Goggin) discharges into the southern
end of the lake. Lesser components of the Jordan River
discharge into the southern end of Farmington Bay. These
dierences produce signicant salinity contrasts between
the two lake arms. The south arm is also characterized by a
bathymetric high (sill) south of the causeway (Fig.1).
Mechanisms to mitigate salinity dierences between
the two arms of the lake have evolved over time. Two,
4.6-m wide culverts were initially installed to allow boat
trac between the two arms while also permitting signi-
cant two-way exchange of water between the arms (Fig.1).
The two culverts often became clogged with debris [49]
Fig. 1 Location and lake
bathymetry (1m contours)
of the Great Salt Lake as of
2008 with river inlets, breach
and culvert locations, and U.S.
Geological Survey sampling
localities (squares) and Utah
Geological Survey localities
(circles). Inputs for the mass
balance model are shown in
italics. The Jordan River primar-
ily enters the Great Salt Lake
through Farmington Bay and
the Goggin Drain
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and by 1998 had subsided 2.4–3.3m below their original
elevation [24]. By 2014, the railroad abandoned eorts to
keep the culverts open and they were subsequently com-
pletely lled in.
Following the historic mid-1980s lake hightstand, a
47m breach was constructed and opened in 1984 on the
western side of the causeway to facilitate better water
exchange between the two lake arms (Fig.1). However, a
drought and historically low lake levels during the 2000s
left the breach with minimal water transmission. A wider
55m and deeper breach was completed and opened in
late 2016 to replace the decommissioned culverts. Quan-
tifying water ux through the breach has proved problem-
atic due to lateral and bottom shear stresses that create
complex ow patterns not captured by the acoustic Dop-
pler proler in the oor of the breach (R. Rowland, pers.
comm., 2019).
Subsurface ow through the rock-ll causeway is con-
sidered signicant yet very dicult to quantify [24, 46, 49].
Subsidence of the causeway into soft lake sediments has
necessitated continual additions and upgrades of cause-
way materials (e.g., [36]) changing the subsurface hydro-
logic characteristics of the causeway as well as reducing
the eectiveness of the original culverts over time.
It has long been recognized that less dense south arm
water has owed from south-to-north and denser north
arm water has owed north-to-south through the culverts,
breach, and in the subsurface through the causeway [13].
South-to-north ow is favored by dierential elevation
head between the two arms of the lake, north-to-south
ow is favored by density dierences between the two
arms. The existence of a distinct layer of saline deep, north
arm water in the southern arm (the deep brine layer or
DBL) was rst recognized in 1966 [42] (Fig.2) and has been
an irregular and poorly understood feature of the lake ever
since. The signicantly higher density of the DBL inhibits
mixing with less saline, overlying south arm brines. The
result is highly anoxic water with elevated concentrations
of dissolved suldes and metals [8, 30]. In general, the DBL
has been more pronounced and long-lasting north of the
bathymetric sill that bisects the south arm of Great Salt
Lake (Fig.1).
Understanding the cycling of nutrients and mercury in
Great Salt Lake has been a longstanding research focus
[8, 18, 30, 33, 43]. In 2007, human consumption advisories
were issued for three species of ducks found in marshlands
adjacent to Great Salt Lake due to high levels of mercury
in the bird tissue [40]. Subsequent geochemical studies
revealed very high concentrations of methylmercury in
the deep brine layer [17, 30, 32] suggesting the DBL may
have been the source for the mercury observed in the
water fowl [1, 44]. However, exact sources and pathways
of mercury in Great Salt Lake ecosystem have yet to be
denitively worked out [32, 51].
Given the possible importance of subsurface cause-
way ux to deep brine layer formation as well as the over-
all water balance of the lake, quantitative models have
attempted to characterize the subsurface hydrologic
regime of the causeway. A model based on the subsur-
face nite dierence code of Pinder and Cooper [34] was
originally developed by Wadell and Bloke [46]. Wold etal.
[49] and Loving etal. [24] then used the more rened
model of Sanford and Konikow [39] to simulate subsurface
causeway ow. Calibration and validation of this subsur-
face model was done largely with dye studies. The two
drivers of ux through the causeway were clearly identi-
ed: (1) a head gradient between the higher south arm
driving south-to-north ow in the upper portion of the
causeway and (2) north-to-south ow in the lower portion
of the causeway, culverts, and breach driven by horizontal
density gradients (Fig.2). Validation of the USGS model
was undertaken during the 1990s, a period of relatively
high lake levels.
During the past decade, two studies using mass balance
techniques have shed additional light on the behavior of
Great Salt Lake. Mohammed and Tarboton [28] examined
the sensitivity of lake elevations and volume to lake inputs
between 1950 and 2010 as well as sensitivity to future cli-
mate change. White etal. [48] used a similar approach to
examine scenarios for opening of the breach in 2016.
As a closed-basin lake, Great Salt Lake is very responsive
to regional climate changes in the Great Basin. For much
of the past decade, an extended drought has brought lake
elevation to historic (north arm) and near historic (south
arm) lows. Several features of the 2008–2015 period of
low lake level present an opportunity to construct a mass
model of Great Salt Lake that is simpler but more tem-
porally detailed than those of Mohammed and Tarbon-
ton [28]and White etal. [48]. The most important inows
to the lake have relatively complete records during this
Fig. 2 Cartoon of Great Salt Lake rock-causeway cross section
showing bidirectional ow leading formation of the Deep Brine
Layer (DBL) ( adapted from [24], Fig.3)
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period. In particular, gauging of the causeway breach,
Bear River Bay discharge, and Farmington Bay discharge
during this period of time provide a rich data set some of
which was unavailable to earlier Great Salt Lake research-
ers (Fig.1) (Table1). Furthermore, minor ows and ulti-
mate collapse of the culverts during this time period allow
their contribution to the water balance and their role in
formation of the deep brine layer in the southern arm to
be quantitatively assessed.
With these simplifications in place, key questions
regarding Great Salt Lake can be addressed with this sim-
ple mass balance model. (1) What is the relative impor-
tance of density-driven vs. head-driven ow through the
causeway (Fig.2)? (2) What are the relative roles of the
culverts, breach, and subsurface ow in maintaining the
deep brine layer? 3) How does a mass balance model com-
pare to published numerical models regarding subsurface
causeway ux [24, 49]?
2 Methodology
2.1 Data sources
Data for the mass balance model were largely derived
from publically available resources. The temporally vary-
ing surface area of the lake was calculated from the bathy-
metric data set of Baskin [5, 6] in conjunction with USGS
lake elevation data (Table1). Surface area of Farmington
and Bear River bays (Fig.1) was not included in this study
although they have been a part of previous mass balance
studies [28, 48].
Since construction of the causeway, the U. S. Geologi-
cal Survey (USGS) has been responsible for installing and
maintaining water elevation gauges in the north arm (just
north of the causeway) and south arm (at the marina at the
south end of the lake) (Fig.1). Additional sampling stations
subsequently have been established throughout the lake
(https:// maps. water data. usgs. gov/ mapper/).
Although stream discharge data for the period of this
paper (2008–2015) are relatively complete there are some
gaps. The USGS stream gauge at the Bear River Bay bridge
(Fig.1) was discontinued in 2013 and is missing for the rst
part of 2008. A polynomial t between the Bear River Bay
bridge and the gauge upstream at Corrine was developed
with the 2009–2013 data and used to approximate ow at
the Bear River Bay bridge for early 2008 and 2013–2015.
Shorter gaps in the data were the result of equipment
failure. Due to these gaps and the variable nature of
the daily discharge data, monthly averages were calcu-
lated and reported all for discharge as well as elevation
measurements.
A particularly important and useful, relatively recent
(2003) gauging station is located at the causeway between
Farmington Bay and the main body of Great Salt Lake
(Fig.1). Discharge measurements at this location integrate
water input from a part of the Jordan River and numerous
smaller streams discharging directly into Farmington Bay
plus or minus Farmington Bay evaporation and precipita-
tion thus simplifying previous mass balance models which
had to account for these diverse, smaller, and highly varia-
ble water inputs. Weber River and Goggin Canal discharge
data are considered accurate and relatively complete.
Table 1 Data sources for mass balance model
Parentheses represent variable in the mass balance model
Variable Data availability (interval) Source
Weber River near Plain City (Kr) 1907 to present (daily) USGS site 10,141,000
Goggin Drain discharge (Kr) 1963 to present (daily) USGS site 10,172,630
Causeway breach discharge (Kbr) 2008 to present (daily) USGS site 10,010,020
Bear River Bay discharge (data) (Kr) 2008 to 2013 (daily) USGS site 10,010,060
Bear River Bay discharge (interpolation
from Corrine station) (Kr)Early 2008 and 2013 to present (daily) USGS site 10,126,000
Farmington Bay discharge (Kr) 2003 to 2016 (daily) USGS site 410,401,112,134,801
East and west culvert discharge 1997, 2011 to present (irregular) USGS sites 411,325,112,400,701 and 411,318,112,334,001
South arm lake level (ΔVS) 1847 to present (15min) USGS site 10,010,000
North arm lake level (ΔVN) 1966 to present (15min) USGS site 10,010,100
Water density (USGS sites 2565 and 3510) 2010 to present (irregular) USGS sites 410,644,112,382,601 and 405,356,112,205,601
Water density (Utah Geological Survey) 2008 to present (irregular) UGS sites (FB2, AC3, AS2)
Precipitation (KpS,KpN) 2008 to 2016 (daily) National Climate Data Center (https:// www. ncdc. noaa.
gov/ cdo- web/)
Great Salt Lake hypsometry Baskin [5, 6]
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Discharge measurements through the two causeway
culverts, both north-to-south and south-to-north, were
made at irregular intervals by the USGS. These data are not
reported on the public web site (https:// maps. water data.
usgs. gov/ mapper/) but were made available as a spread-
sheet to the author.
Since World War II, the Utah Geological Survey (UGS)
has collected water quality data that includes density
measurements at a variety of stations within the lake
(Table2). Additional density data have been collected
by the USGS at Great Salt Lake marina and in the north
arm as well as at various stations in the southern arm over
the past couple of decades (Fig.1). The only water quality
data reported at these two stations are density. The UGS
measurements were made at irregular intervals (typically
4–8 times per year) but the record contains gaps as long
as multiple years. UGS density measurements were typi-
cally made for the entire water column at 1.5m intervals
and rarely 0.3m intervals. USGS measurements are usually
only for the top and bottom of the water column (Fig.3).
Both UGS and USGS bottom density measurements were
made ~ 0.5m above the bottom to avoid interaction with
the bottom sediments. Density data are reported in this
paper as quarterly averages from both UGS and USGS
stations. Where only salinity and temperature data are
reported, density was calculated using the equation of
state of Naftz etal. [31].
Daily precipitation values were downloaded from pub-
lically available data of the National Climate Data Center
(NCDC) (https:// www. ncdc. noaa. gov/ cdo- web/) at 10
stations surrounding the lake (Fig.4). This approach dif-
fers from Mohummad and Tarboton (2012) who used the
interpolation-based output from the Parameter-elevations
on Independent Slopes Model (PRISM) [10]. The NCDC data
were spatially interpolated with Matlab routines by inverse
distance weighting and used as input for the mass balance
model. For stations in which some daily data were missing,
the weighing factors were recalculated as appropriate.
2.2 Mass balances
A simple mass balance model of the entire Great Salt Lake
consists of river inputs, precipitation, groundwater inows,
and precipitation minus evaporation;
All units are expressed as m3/s. ΔVT represents total
net volume change in the lake as determined from gauge
height changes of the lake and lake hypsometry [5, 6],Kr is
total river input; KpT is total precipitation of the combined
south and north arms, KeT is total evaporation; and Kgw is
groundwater input (Fig.5) (Table1). A time step of one
day was used for all variables. Monthly averages were then
calculated for presentation of model results. The volume
ux of both precipitation and evaporation was adjusted
for changing lake level with time.
The amount of groundwater inow to the lake is not
precisely known and has been quantied over spatially
limited areas (e.g., [3]). Previous studies at higher lake
(1)
ΔVT=Kr+KpT−KeT +Kgw
Table 2 Summary of Great Salt Lake sampling stations for density
* Beginning of record for 2008–2015
Station Easting Northing Bottom
elevation (m) Sampling interval Period of record Periods of top–bottom strati-
cation 2008 -2015 (> 5kg/
m3)
AS2 (UGS) 394,123 4,521,193 1271.6 Full column, 1.5m interval 4/1969 to present 7/2008 to 5/2014 (irregular)
AC3 (UGS) 378,337 4,539,758 1272.0 Full column,1.5m interval 6/1966 to present 7/2009 to 10/2013
FB2 (UGS) 377,394 4,554,765 1272.0 Full column,1.5m interval 6/1966 to present 7/2008 to 5/2014 (irregular)
RT4 (UGS) 355,600 4,558,105 1273.8 Full column,1.5m interval 7/1984 to present None
2565 (USGS) 362,258 4,552,512 1272.0 Top, bottom 8/1985 to present 6/2010* to 7/2014
3510 (USGS) 386,382 4,528,409 1272.0 Top, bottom 8/1985 to present 6/2011 to 4/2014
Fig. 3 Typical density proles for Utah Geological Survey locations
AC3 (south arm) and LGV4 (north arm) for a period of widespread
dense brine layer (DBL) (mid-2012) and lack of the DBL (mid-2014)
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levels suggest the groundwater component is minor
(approximately 3% of total lake input) [28, 45]. That
value is adopted in this study although it must be con-
sidered a potential source of error in the model results.
Total lake volume change (ΔVT), total river input (KR), and
total precipitation (KpT) can be derived from existing data
bases (Table1) leaving total lake evaporation as the only
unknown in Eq.(1).
Fig. 4 a Location of mete-
orological stations used to
calculate monthly precipita-
tion. RO, Rossette; TA, Thatcher;
GA, Garland; BC, Brigham City
waste treatment plant; WW,
West Weber; WH, West Haven;
OG, Odgen Hinkley Airport;
SL, Salt Lake International
Airport; UT, Utah Test Range;
MG, Magna; GV,Grantsville; AR,
Aragonite. Stations WW, WH,
and DG were averaged into a
single value. Squares represent
stations used to calculate both
north and south arm precipita-
tion; circles represent stations
only used to calculate north
arm precipitation; triangles
represent station only used to
calculate south arm precipita-
tion. b Summary of precipita-
tion near the Great Salt Lake,
2009–2015. Triangles represent
south arm precipitation, x’s
represent north arm precipita-
tion
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South arm mass balances consist of river inows, pre-
cipitation minus evaporation, and net ux through the
causeway breach, culverts, and subsurface ow through
the rock-ll causeway. With no river inows, the mass bal-
ance for the northern arm is simpler (Fig.5). The water
mass balance equations are as follows:
ΔVS and ΔVN represent net volume change in the south
and north arms of the lake as determined from gauge
height changes of the lake and lake hypsometry; Kr is river
inputs; Kbr is causeway breach ux; Kcu,N is north-to-south
culvert ux; Kcu,S is south-to-north culvert ux; KpS and KpN
is precipitation to the south and north arms, respectively;
Kca is net subsurface ux through the causeway; Kgw is
groundwater ow; KeT is total evaporation as calculated
in Eq.(1); and z is the fraction of evaporation in the north
arm divided by total lake evaporation (Table1).
The net result is two equations and two unknowns (Kca
and z). Unfortunately, the two equations are not inde-
pendent since the two unknowns have opposite signs in
each equation. Furthermore, while most components of
Eqs.(2) and (3) have solid, publicly reported time series
data (Table1), culvert ux data (Kcu,N and Kcu,S) were col-
lected over irregular time periods. Sensitivity analyses of
these three components (z, Kcu, N and Kcu,S) are discussed
below.
(2)
ΔVS=Kr+Kcu,N−Kcu,S +KpS −(1−z)KeT −Kbr−Kca +Kgw
(3)
ΔVN=Kbr +Kca +KpN +Kcu,S−Kcu,N −zKeT +Kgw
3 Results
3.1 Total lake mass balances
Lake volume increases in the spring before declining sig-
nicantly in the late summer with seasonal changes as
much as 30% (Fig.6a). Both lake volume and river ux were
anomalously high in 2011 (Fig.6a, b) reecting very high
precipitation that year (Fig.6c). Precipitation was also high
in the spring of 2015 although lack of associated higher
river ow and lake volume may reect upstream reservoir
storage after a period of prolonged regional drought.
Calculated evaporation (Fig.6d) follows a pattern simi-
lar to that of total lake volume with maximum water loss
in the hottest part of summer. Mass balance calculations
of yearly evaporation rates (m/yr) are reasonably close to
those reported by Mohammed and Tarboton [28] (Table3).
The mass balance calculations produce small negative
evaporation in the winter months of 2008–2012 suggest-
ing small errors in the inputs to Eq.(1).
Mohammed and Tarboton [28] calculated evaporation
by two methods: (1) a modied Penman method incor-
porating a number of atmospheric variables (the “climate”
method) and (2) a mass balance approach similar to the
one in this study. Their climate method produced evapora-
tion rates 5–15% higher than the mass balance method.
Mohammed and Tarboton [28] suggest that some inputs
to the mass balance model may be missing or poorly
defined (e.g., groundwater inputs). Similar issues may
account for the negative evaporation rates calculated for
small time intervals calculated in this study (Fig.6d).
3.2 Mass balances ofthenorth andsouth arms
The seasonal nature of lake elevation in both the north
and south arms of the lake has long been recognized (e.g.,
Arnow and Stephens [4]). Maximum elevation for both
arms is typically reached in May soon after peak spring
runoff (Fig.7a, b). South-to-north elevation gradients
which are believed to be a primary driver of south-to-
north ux through the causeway likewise show seasonal
peaks although the signal of the elevation dierence is
smaller than the seasonal north and south arm elevation
changes (Fig.7). Closure of the culverts in 2014 resulted in
signicantly higher elevation dierences in the two lake
arms (Fig.7c).
3.3 Sensitivity analyses
One of the key goals of the mass balance model is insight
into the magnitude of subsurface flux through the
Fig. 5 Diagrammatic representation of Great Salt Lake mass bal-
ance model (W. Wurtsburgh, pers. comm.)
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causeway (Kca in Eqs.1 and 2). However, since ow through
the culverts (Kcu,N, Kcu,S) and the relative proportion of
evaporation in the north and south arms (z) in Eqs.2 and 3,
are dicult to precisely quantify, their relative importance
must be evaluated with sensitivity analyses.
3.3.1 Culvert flows
Because flow measurements of the east and west cul-
verts were made at irregular intervals, monthly culvert
discharge was estimated by two dierent approaches.
Culvert ow of dense north arm water to the south took
place in the deeper portions of the culvert and thus prob-
ably did not have a signicant seasonal signal. Third-order
polynomial ts of these data show relatively good correla-
tion (Fig.8a, b). Flow of less dense south arm water to the
north, however, may have been inuenced by relatively
high south-to-north elevation gradients and therefore had
a seasonal signal (Fig.8c, d). These data were interpolated
with two methods: 1) cubic splines and 2) tting with a
-300
-200
-100
0
100
200
300
400
2008 2009 2010 2011 2012 2013 2014 2015 2016
m(egnahcemulovlatot 3/s)
Year
0
50
100
150
200
250
300
350
2008 2009 2010 2011 2012 2013 2014 2015 2016
total river input (m3/s)
Year
0
25
50
75
100
125
150
2008 2009 2010 2011 2012 2013 2014 2015 2016
m(noitatipicerp 3/s)
Year
-50
0
50
100
150
200
250
300
2008 2009 2010 2011 2012 2013 2014 2015 2016
evaporaon (m3/s)
Year
AB
CD
Fig. 6 Results of whole Great Salt Lake mass balance model. a Total volume change calculated using USGS lake elevation (Table1) and
hyposometric data [4, 5]. b Total river input. c Precipitation. d Computed evaporation
Table 3 Yearly summary
of mass balance model
calculations (km3 unless
otherwise specied)
2008 2009 2010 2011 2012 2013 2014 2015
River input 1.74 1.60 1.57 4.42 1.11 1.08 2.45 2.21
Total lake evaporation 3.38 2.19 2.59 2.51 3.34 3.52 4.33 4.41
Total lake evaporation (m/yr) 1.19 0.77 0.92 0.78 1.04 1.18 1.54 1.60
Total lake precipitation 0.62 0.61 0.99 1.22 0.90 0.70 0.95 1.16
South-to-north breach ux 0.63 0.51 0.34 2.09 1.51 0.52 0.30 0.07
North-to-south breach ux n.a .0021 .0002 .0044 .0035 .0127 .0065 .0028
North-to-south culvert ux (poly.) 0.17 0.23 0.41 0.54 0.14 0.25 – –
South-to-north culvert ux (poly.) 0.25 0.50 0.73 0.58 0.39 0.01 – –
South-to-north culvert ux (spline) 0.27 0.68 0.48 0.35 0.07 0.06 – –
Net south-to-north causeway ux −0.06 −0.27 0.21 −0.03 −0.92 −0.05 0.54 0.64
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third-order polynomial. Correlation of the polynomial was
poor (R2 = 0.3624 and 0.3664). Final collapse and closure of
the west culvert occurred in late 2012 and the east culvert
closed in late 2013 and for subsequent years, culvert ow
does not enter into the mass balances (Eq.2 and 3). Note
that calculated south-to-north ow after 2012 in the east
culvert is very close to zero in both methods (Fig.8c).
3.3.2 Relative evaporation rates
Since salinity of the north arm of Great Salt Lake is
40–100% higher than that of the south arm, north arm
evaporation would presumably be lower than south arm
evaporation [28], their Fig.10). A baseline simulation of
net subsurface ux (Kca) in this study was calculated using
spline calculations for south-to-north culvert flux and
evaporation assuming dierential salinity of the north
and south arms has no eect on evaporation rates (Fig.9a).
Mass balance model calculations with evaporative ux in
the north arm 20% lower than that of the south arm pro-
duce only minor changes in calculated subsurface cause-
way ux (Fig.9b). Likewise, the method for calculating the
ow through culverts (spline or polynomial interpolation
does not signicantly change either the magnitude or pat-
terns of net subsurface causeway ux (Fig.9c).
3.4 Controls ofdeep brine layer formation
For this study, the existence of the deep brine layer (DBL)
is defined as a significant density contrast (> 5kg/m3)
between the bottom sampling point and the sampling
point immediately above (typically 2.3m in the UGS data).
Density contrasts in the water column above the bottom
two sampling points are typically < 5kg/m3 and can be
attributed at least partially to spring runo, seasonal tem-
perature contrasts, or analysis error. Because USGS data are
only reported at the surface and bottom, the UGS data are
reported in a similar fashion.
Starting around 1970, stratification was a continu-
ous feature for nearly 25years as a result of signicant
north-to-south flow through the breach, culverts, and
porous causeway. Shorter DBL events are documented in
1997–2004, 2006–2009, and 2011–2014 (Fig.10). In addi-
tion to the three possible sources of deep brine water,
water depth may play a role in maintaining the deep brine
layer over extended periods of time. None of these factors
are exclusive to each other and all will be examined here.
3.4.1 Pre‑2008
The prolonged DBL period from ~ 1970 to 1990 can be
attributed to eective ow through the culverts, the rela-
tively new, relatively porous rock causeway, and the high
level and relatively deep water in the lake during that time
period. The ooding and historically high lake levels of
the early 1980s necessitated constructing the 47-m wide
breach on the eastern side of the causeway at an elevation
of 1280m [13]. Two-way ow through this breach and a
much deeper lake (which mitigates wind-induced mixing)
no doubt enhanced post-1984 stratication (Fig.10).
Disappearance of the DBL at the stations reported in
1993 can be attributed to clogging of the culverts, pro-
gressive compaction of causeway materials, and shallower
lake levels [13]. In 2000, the causeway breach was deep-
ened from 1280 to 1278m [14] thus allowing two-way
A
B
C
1277.5
1278.0
1278.5
1279.0
1279.5
1280.0
1280.5
2008 2009 2010 2011 2012 2013 2014 2015 2016
North arm elevaon (m)
Year
1277.5
1278.0
1278.5
1279.0
1279.5
1280.0
1280.5
2008 2009 2010 2011 2012 2013 2014 2015 2016
South arm elevaon (m)
Year
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2008 2009 2010 2011 2012 2013 2014 2015 2016
South -North elevaon (m)
Year
Fig. 7 Great Salt Lake hydrograph (2009–2015). a South arm eleva-
tion (m). b North arm elevation (m). c (South–north) elevation dif-
ference
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exchange of water between the two lake arms to resume
with subsequent strengthening of the DBL (Fig.10).
3.4.2 2008–2015: breach andculvert flows
The DBL is strongest close to the causeway where it has
been identied 1.8km south of the causeway in August,
2010 [18]. The DBL reappeared north of the south arm sill
at USGS station 2565 at an unknown date before 2010 and
then expanded throughout the south arm by 2011 (Figs.1,
12). A distinct DBL had disappeared by early to mid-2014
through most of the south arm although it persisted close
to the causeway at least until May, 2015 [25].
As declining lake elevation in the southern arm
approached the1278 m mark, ow through the breach
was minimal from 2008 to 2011 and 2013–2015 as well as
being completely south-to-north (Fig.12a, Table3). As a
result, the breach is not considered a viable candidate for
source of DBL water for the 2011–2014 time frame. Total
north-to-south ux through culverts (~ 15 m3/s increasing
to ~ 30 m3/s) (Fig.8) suggest modest contribution to the
DBL at the onset of stratication (Fig.12b). As stratication
in the south arm increased and achieved its maximum in
2013, culvert ow decreased and then ended.
3.4.3 2008–2015: water depth
The persistence of the deep brine layer (DBL) depends
critically on the degree of wind-induced mixing in the
lower part of the water column. Obviously, transmission
of wave energy to the sediment–water interface is favored
by relatively low lake levels. The longest and strongest
DBL episode occurred during a period of high lake level
(~ 1283m during the 1980s and early 1990s) (Fig.10).
During the period ofthis study lake level was as low as
1278.5m (Fig.7).
The amount of bottom water mixing as function of lake
depth can be examined with simple linear wave relation-
ships. The dispersion equation relates radian wave fre-
quency (ω), radian wave number (k), gravity (g) and water
depth (H) (e.g., [35]:
While general wave parameters for Great Salt Lake have
not been published, constraints can be derived from stud-
ies of other large lakes. For instance, peak wave periods
are 4–12s in Lake Ontario [26], 3–4s [37] in Lake Tahoe,
and 1.5–2.5s in Lake Constance of Switzerland [41]. The
(4)
𝜔2=gk tanh (kH)
AB
CD
R² = 0.8245
0
5
10
15
20
2008 2009 2010 2011 2012 2013 2014
discharge (m3/s)
East culvert north-to-south flux
R² = 0.8075
0
5
10
15
20
2008 2009 2010 2011 2012 2013 2014
discharge (m3/s)
West culvert north-to-south flux
0
5
10
15
20
25
30
2008 2009 2010 2011 2012 2013 2014
discharge (m3/s)
East culvert south-to-north flux
data spline 3rd order polynomial
0
2
4
6
8
10
12
2008 2009 2010 2011 2012 2013 2014
discharge (m3/s)
West culvert south-to-north flux
data spline 3rd order polynomial
Fig. 8 Summary of east and west culvert measurements and
approximations. a East culvert north-to-south ux. b West culvert
north-to-south ux. c East culvert south-to-north ux. Blue line
is a cubit spline t of the data; red line is a 3rd order polynomial
t (R2 = 0.3624). d West culvert south-to-north ux. Blue line is
a cubit spline t of the data; red line is a 3rd order polynomial t
(R2 = 0.3664)
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development of surface wind waves is related to maximum
lake fetch which for Great Salt Lake is between that of Lake
Ontario (maximum fetch ~ 250km) and Lake Tahoe (maxi-
mum fetch ~ 25km). Maximum Great Salt Lake wave period
would thus be ~ 7–8s. Applying Eq.(4) yields a radian wave
frequency (ω) of 3–4 s−1 and a radian wave length (k) of
0.3–0.4 m−1.
The absolute bottom velocity (Vo) which would be the
primary factor in mixing the deep brine layer and can be
expressed as [16]:
A is wave amplitude or one half of signicant wave
height (SWH). Reported SWHs are ~ 3 m for Lake
Ontario, ~ 0.8m for Lake Tahoe and ~ 0.5m for Lake Con-
stance. Equation(5) produces Vo for maximum Great Salt
Lake typical depths during the 2011–2014 DBL episode
(8.5–9.5m) and the 1970–1990 DBL episode (10.5–11.5m)
(Fig.13). Absolute maximum bottom velocity varies by
approximately 50% (0.6 – 0.9m/s) over the depth range
for 2011–2014. This is considerably higher than typical bot-
tom velocity (~ 0.3m/s) of the historically high lake levels
and extensive1970-1990 DBL period. While these calcu-
lations must be regarded as approximate, they suggest
that lake depth was important in maintaining the DBL at
high lake levels relative to lower lake levels of 2011–2014.
A ~ 1m change in lake level (Figs.7, 13) during 2011–2014
produces relatively high and consistent bottom water
mixing.
3.4.4 2008–2015: causeway flow
Unlike open water exchange via the culverts and breach,
pressure on the causeway face is the driving force for water
ux through the rock-ll causeway. South-to-north ow is
the result of head gradient driven pressure expressed as:
ρ is density, g is gravity, and Δh is the south-to-north head
gradient.
North-to-south ow is driven by the pressure of north-
to-south density differences in the overlying water
column:
(5)
Vo
=A
2
𝜋𝜔
sinh(kH)
(6)
p=𝜌gΔh
A
B
C
-80
-60
-40
-20
0
20
40
60
2008 2009 2010 2011 2012 2013 2014 2015 2016
m( xulf yawesuac 3/s)
Year
-100
-80
-60
-40
-20
0
20
40
60
2008 2009 2010 2011 2012 2013 2014 2015 2016
3m( xulf yawesuac/s)
Year
baseline (spline)3rd order polynomial
-100
-80
-60
-40
-20
0
20
40
60
2008 2009 2010 2011 2012 2013 2014 2015 2016
m( xulf yawesuac 3/s)
Year
baseline (spline)80% north arm evaporaon
Fig. 9 Calculated net causeway ux. a Baseline calculation of sub-
surface causeway ux (spline interpolation of culvert ux, evapora-
tion of north and south arms proportional to lake area). b Baseline
calculation and north arm evaporation depressed by 20%. C. Base-
line calculation and polynomial interpolation of culvert ux
Fig. 10 Average vertical density (ρ–1000, kg/m3) dierences in
south arm of the Great Salt Lake at Utah Geological Survey stations
with the most continuous density records (FB2, AC3, AS2) (Fig.1)
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(7)
Δ
p=g
(
𝜌
N
H
N
−𝜌
s
H
s)
, where HN, ρN and HS, ρS are water depths and density
in the north and south arms, respectively. Obviously, the
pressure dierence of Eq.(7) is maximum at the base of the
Fig. 11 Surface density (solid line) and bottom density (dashed line) for UGS station AS2, UGS station AC3, UGS station FB2, USGS station
2565, USGS sation 3510 (station locations shown in Fig.1)
Fig. 12 a Breach ow for 2010–2015. b Combined ow of east and west culverts (Fig.8). Medium-dashed line represents end of the west
culvert; heavy dashed line represents end of the east culvert
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causeway and the dominance of Eq.6 or Eq.7 at any given
depth is unknown (Fig.14). Furthermore, the force mov-
ing water through the causeway is the pressure of Eqs.6
and 7 applied over the causeway surface area exposed to
the water.
Calculation of both types of pressure shows a sharp
increase in bottom pressure difference in the summer
of 2011 (Fig.15a), precisely the time of the widespread
appearance of the deep brine layer (Fig.11) and the maxi-
mum computed north-to-south causeway ux (Fig.15b)
as well as increased density dierence between the north
and south arms (Fig.15c). It should be re-emphasized that
the mass balance model only computes net subsurface
ow through the causeway (Eqs.2, 3). For much of the
2008–2015 period, the two-way subsurface ows were in
approximate balance. However from mid-2011 to 2013,
dense north-to-south ow dominated (Fig.9, 15a). North-
to-south subsurface ow through the rock causeway was
signicant (at least 60 m3/s) during the time that strati-
cation became pronounced (Fig.11). Interestingly, strati-
cation persisted until 2014 despite decreases in both
Fig. 13 Absolute orbital velocity for typical surface waves of Great
Salt Lake as a function of depth
Fig. 14 Diagrammatic representation of two-way ow through the
rock-ll causeway and resulting pressure prisms
Fig. 15 a Net north-minus-south bottom pressure and head pres-
sure gradient calculated from bottom density at UGS station VG4
and USGS station 2565 (Fig.1) b Net causeway ux for 2010–2015. c
Surface density calculated from the averages of south arm stations
AC3, AS2, FB2, 2565 and 3510 (Fig.1) (squares) and north arm den-
sity from the Salina station (Fig.1) (circles). Arrows represent the
periods of widespread deep brine layer
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net culvert and subsurface causeway ux suggesting that
residence time for the DBL may be signicant even after
the input of dense source water has ceased.
4 Discussion
As discussed above, north arm water conveyed to the
south arm by the breach was minor during 2008–2015.
Minor flow reversals through the breach (north-to-south
rather than the dominant south-to-north) as a result of
strong northerly wind events have been documented
[11, 32] and suggested as a significant contributor to for-
mation of the DBL in 2012 [32]. However, total north-to-
south flow through the breach constituted a very small
percentage of total flow during the 2008–2015 period
of low lake elevation (Fig.12a, Table3). Furthermore,
the ~ 1-m-thick DBL discussed by Naftz etal. [32] has a
volume of approximately 0.12 km3 (1.2 × 108 m3) as cal-
culated from the hypsometric data of Baskin [5, 6]. If flow
reversal through the breach were the sole source of the
deep brine layer, DBL residence times (volume divided
by flux rates) would need to be on the order of years or
decades. Interestingly, Jones and Wurtsbaugh [18] sug-
gest a DBL residence time of 2.5years.
It is important to recall that net subsurface cause-
way fluxes in this study (Fig.14a, Table3) are the sum of
south-to-north and north-to-south flow. While the mass
balance model does not compute absolute flux values,
the net north-to-south flux during the first four months
of 2012 (Fig.15b; 0.40 km3) (Table3) is more than ade-
quate to replenish the DBL volume (0.12 km3) described
for that year [32].
Comparing results of this mass balance model with
the numerical model of Wold etal. [49] and Loving etal.
[24] shows broad agreement but with considerable
scatter at relatively low causeway fluxes (Fig.16). At the
higher south-to-north elevation gradients (0.3–0.6m)
during 2008–2015 net causeway flux of this mass bal-
ance model differs from that of Wold etal. [49] and Lov-
ing etal. [24]. While not encompassing the full range of
causeway elevation gradients, the mass balance model
suggests considerable lower subsurface causeway flux
than the Wold/Loving model. Given the continued com-
paction and consolidation of the causeway material over
the past 20years, this is not necessarily surprising but
it does suggest the numerical model needs updating.
It should be emphasized that the subsurface struc-
ture and permeability of the causeway have never been
precisely characterized. Does the flow come through a
small number of flow paths produced by piping in the
60-plus year-old causeway or is flow more widely dis-
persed? A detailed geophysical survey could address this
issue and point the way toward a better understanding
of the hydrologic regime of the lake as a whole.
The mass balance model might be used to evaluate
a number of scenarios. A logical next step would be
to analyze the effect of the new (2016) breach on lake
fluxes. Doing so will require a viable model of net flux
through the breach which is considerable larger than the
breach used in this study. However, the lack of a gauge at
the Bear River bridge could be a hindrance to application
of the model of this study. Furthermore, the model might
be used to forecast issues related to water diversions
such as the proposed Bear River dam and climate change
[7, 27] with attendant lowering levels of the Great Salt
Lake and those throughout the world (e.g., [50].
5 Conclusions
(1) A mass balance model for an historic low stand of
Great Salt Lake (2008–2015) demonstrates subsurface
ux through the causeway was equal to or greater
than culvert uxes between the north and south arms
of the lake.
(2) Subsurface ux through the causeway as a result of
density differences between the north and south
arms is a viable source for the Deep Brine Layer period
over the entire south arm of the lake from late 2011
to early 2012 although causeway ux may or may not
have been the driver for similar DBL episodes from
the late 1990s to 2008.
-80
-60
-40
-20
0
20
40
60
80
100
120
140
160
0.00.2 0.40.6 0.81.0 1.2
)s/3m(xulfssam
north-south elevaon gradient (m)
Loving et al. (2002)
this study (2008-2011,
2012-2016)
this study (2011-2012)
Fig. 16 Causeway elevation gradient versus net mass ux through
the causeway. Solid line is taken from Table C-4 and C-5 of Loving
etal. [24] assuming a north–south density gradient of 100kg/m3
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(3) Compaction of the rock causeway ll necessitates
revision of earlier models of subsurface ow through
the causeway.
Acknowledgements This work was supported by a FY 2015 grant
from the Division of Forestry, Fire, and State Lands, State of Utah.
Andrew Rupke (Utah Geological Survey) and Cory Angeroth (U.S.
Geological Survey) kindly provided some of the data used in this
research. Comments from Dr. Wayne Wurtsbaugh and two anony-
mous reviewers improved the manuscript.
Declarations
Conflict of interest The author states that there is no conict of inter-
est.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adap-
tation, distribution and reproduction in any medium or format, as
long as you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons licence, and indicate
if changes were made. The images or other third party material in this
article are included in the article’s Creative Commons licence, unless
indicated otherwise in a credit line to the material. If material is not
included in the article’s Creative Commons licence and your intended
use is not permitted by statutory regulation or exceeds the permitted
use, you will need to obtain permission directly from the copyright
holder. To view a copy of this licence, visit http:// creat iveco mmons.
org/ licen ses/ by/4. 0/.
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