The Great Salt Lake Water Budget - Great Salt Lake Advisory Council

The Great Salt Lake Water Budget
David Tarboton
Utah State University
dtarb@usu.edu
435‐797‐3172

Outline
• General overview
• Historic lake levels
• Streamflow
• Water Budget
• Future Simulations
• Details if you want on
– Bathymetry, Streamflow, Precipitation, Climate,
Salinity, Evaporation

How a closed basin (e.g. GSL works)
Inflows I
I
Evaporation depth E
Evaporation volume E x A
E x A
Area, A
E x A
Area, A
Volume, V
Salt Load L
Salt Concentration C=L/V
Level
Level
If I > E x A level rises
If I < E x A level falls
Level adjusts to
fluctuating inputs so that
on average
I = E x A
I includes inflows from
streams and precipitation
on the lake
I = Q + P x A
Subject to climate
variability.
E is less variable, but also
depends on climate and
salinity, C.

GSL Level Record
Level (ft)
4195 4200 4205 4210
16% 4195.6
50% 4200.5
South Arm USGS 10010000 Great Salt Lake at Saltair boat harbour, UT
North Arm USGS 10010100 Great Salt Lake near Saline, UT
South Arm water year mean
84% 4205.6
84% 4202.5
50% 4198.9
16% 4194.8
Minimum level on Record 4191.4
10/14/2010
S 4193.7
N 4193.2
1900 1950 2000
10/1/1949‐9/30/2010 period with complete
climate and streamflow input data

Streamflow Inflows
•Bear (10126000)
•Weber (10141000)
•Jordan
− 10172550
− 10170800 (Surplus
Canal)
− 10172630 (Goggin)
•Davis
− 10143500
(Centerville)
− 10141500 (Holmes)
− 10142000
(Farmington)
− 10142500 (Ricks)
− 10143000 (Parish)
− 10144000 (Stone)
− 10145000 (Mill)
•Other
− 10141040 (Hooper)
− 10141400 (Howard)
− 10172640 (Lee)
− 10172650
(Kennecott)

Water Budget
V
Q
P
A
E
A
• Q, Streamflow+Groundwater‐Withdrawals
– Groundwater 75000 acre ft/yr (Waddell and Barton,
1980)
– Withdrawals (West desert pumping, Evaporation
ponds)
• A, V Area and Volume
– From bathymetry and level
• P, Precipitation
– From PRISM (Oregon State University)

Water Budget Summary
(thousand Acre ft/yr)
1949/10‐2008/9 2003/10‐2008/9
Bear 1347 986
Jordan 495 425
Weber 338 242
Davis 31 30
Other 105 95
All Streamflow 2316 1778
Direct Precipitation 876 781
Groundwater 75 75
Evaporation (‐3666 3 ) ‐3264 2 (2961 3 ) ‐2834 2
Adjustments ‐39 1 0
Ave Vol Change ‐32 ‐212
Notes:
Closure ‐4 12
1. Net west desert pumping loss averaged over 59 years
2. Mass balance evaporation
3. Calculated evaporation

Future simulations
• Water budget model with inputs P, Q
• Inputs resampled from historic years
retaining each year as a block
• Resampling used k‐nearest neighbors
(based on total streamflow) to sample
similar years together and maintain
statistical dependence
• Evaporation used either the historic
value from mass balance, or was
calculated from salinity as a function of
volume (C=L/V)
• Level differences between arms not
modeled
• Pumping limits level to 4208 ft
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
Annual streamflow autocorrelation from knn
0 2 4 6 8 10 12 14 16
Lag years

100 resampled input simulations
10 year simulations
Distribution of 10 year ahead
Levels
4185 4190 4195 4200 4205
Frequency
0 5 10 15 20
2010 2012 2014 2016 2018 2020
4190 4195 4200 4205
Level (ft)

Simulated Water Budget Sensitivity over
2003/10‐
2008/9
next 10 years
(thousand Acre ft/yr)
16%
(‐1 std dev)
50%
(median)
84%
(+1 std dev)
All Streamflow 1778 1801 2067 2857
Direct
Precipitation
781 818 891 1252
Groundwater 75 75 75 75
Evaporation (ft) 3.58 3.48 3.31 3.47
End Level 4194.1 4191.6 4195.6 4199.5
Conclusions
•8 ft range possible over next 10 years ahead due to natural variability
•Human or natural reduction in streamflow of 260 000 acre ft/yr below
median could drive level down to near 4191 ft in next 10 yr
•Without change lake most likely to stay near current levels
•About 13% chance lake may even rise above 4200 ft in next 10 years

Bathymetry
South Arm
North Arm
Level (ft)
4170 4180 4190 4200 4210
Baskin 2005
Loving 2000
Baskin 2005 + Farmington Bay
+MagCorp ponds
Level (ft)
4170 4180 4190 4200 4210
Baskin 2006
Loving 2000
0 200000 600000 1000000
0e+00 2e+05 4e+05 6e+05 8e+05 1e+06
Area (acre)
Area (acre)
the lake bed topography that relates area
to level and volume

Using “steady state” to evaluate potential
impact of pond withdrawals and
bathymetry on lake level
• Inputs
– Evaporation, E (from climate)
– Area, A (from low, median,
high percentile levels)
• Net inflows estimated from
“steady state”
– I=A x E
• Withdrawal subtracted
from net inflow and
modified area determined
– A'= (I‐W)/E
1,055,576
979,500
Area (acre)
• Level determined from
bathymetry (modified)
4194 4196 4198 4200 4202 4204 4206
4199.9
600000 800000 1000000 1200000 1400000
Current
Modified
1,055,576
979,500
4199.9
4200.6
level (ft)
the sensitivity is greater when the arealevel
function is flatter

GSL streamflow inputs
Ac ft
2e+05 4e+05 6e+05 8e+05 1e+06
Total
Bear
Weber
Jordan
Davis
Other
Monthly streamflow from USGS
gauges with regression to fill
missing values
1950 1960 1970 1980 1990 2000 2010
Annual average GSL Streamflow inputs (Acre ft)
Bear Weber Jordan Davis Other Total
1347346 338385 494874 30783 104832 2316220
58% 15% 21% 1% 5% 100%
Loving, et al., (2000), USGS 00‐4221. Calculated inflows for the period 1987‐1998. These
methods with minor adjustments were applied to obtain streamflow from 1949 to 2008

Precipitation
inches/month
0 1 2 3 4 5
South
North
Monthly
1950 1960 1970 1980 1990 2000 2010
inches
0 5 10 15 20
South
North
Annual
1950 1960 1970 1980 1990 2000 2010
Monthly PRISM climate data for the U.S. from Oregon State University from
http://www.prism.oregonstate.edu/

Other climate variables
Degrees C
-10 0 10 20 30 40
South Max North Max South Min North Min
1950 1960 1970 1980 1990 2000 2010
• Monthly averages of daily maximum and minimum
temperatures from PRISM (shown)
• Monthly average of daily dewpoint from PRISM (not shown)
• Monthly average of daily wind speed from University of
Washington (not shown)

Great Salt Lake Inputs
acre ft
0e+00 4e+06 8e+06
Total
Streamflow
Precip
Groundwater
W Desert Pumping
W Desert return
1950 1960 1970 1980 1990 2000 2010
Adjustments to GSL inputs
•West Desert pumping. 2.5 MAF removed 4/87 to 6/89. 27
months
• 200000 AF return from West Desert. 1/90 to 6/92. 30 months
Wyr

Total Salt Load
Billion tons
0 1 2 3 4
LVG4 [north]
RD2 [north]
FB2 [south]
AS2 [south]
3.89 billion tons
Total
North
South
4/87‐6/89
West desert
pumping
1/90‐6/92
West desert
return flow
3.64 billion tons
1970 1980 1990 2000
Calculated from volume and depth average
measurements. Data from Wally Gwynn (UGS)

Salt concentrations
C g/L
0 50 100 200 300
LVG4 [north]
RD2 [north]
FB2 [south]
AS2 [south]
Causeway closure
1950 1960 1970 1980 1990 2000 2010
Salinity computed from C=L/V for each arm
(lines) and compared to observations

Salinity dependent evaporation
Penman evaporation equation modified for salinity
(Mohammed, 2008)
E
'
R
n
'
Where:-
R n Net Radiation,
λ v latent heat of vaporization,
β water activity coefficient,
ν a wind speed ,
e
( T,
S)
∆' gradient of saturated vapor content of air corrected
for salinity,
γ psychrometric constant,
s
e
T
K E bulk transfer coefficient.
v
w
s
s
'
e
s
e
( T ) ( T,
S)
s
K
T
s
E
a
( e
s
( T
a
) (
T
Ebrine/Efresh
a
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
, S)
e
a
)
0 100 200 300 400
TDS (g/L)

Annual GSL Evaporation
meters
0.4 0.6 0.8 1.0 1.2 1.4
Mass balance
N brine
N fresh
S brine
S fresh
10 20 30 40 50 60
inches
1950 1960 1970 1980 1990 2000 2010
Mass Balance
E
P
N
A
N
PS
A
A
S
N
Q
A
S
W
V

Predictive Mass Balance Model
• Inputs
– Precipitation (N and S)
– Evaporation (Historic or Calculated)
– Streamflow
– Initial Level
• Output
V
Q P A
– Levels and volumes
E A

Verification with historic inputs
Level
4190 4195 4200 4205 4210
North Obs
South Obs
Mass Bal. E
Climate E
1960 1970 1980 1990 2000 2010