Connecting The Dynamics of the Great Connecting The Dynamics of the Great Salt Lake Volumes to the Volume - Area Salt Lake Volumes to the Volume - Area

RelationshipRelationship

IBRAHIM N. MOHAMMEDIBRAHIM N. MOHAMMEDDAVID G. TARBOTONDAVID G. TARBOTON

nourein@cc.usu.edunourein@cc.usu.edu

Utah Water Research Laboratory, Utah State University, Utah Water Research Laboratory, Utah State University, Logan, UtahLogan, Utahhttp://www.engineering.usu.edu/dtarbhttp://www.engineering.usu.edu/dtarb

GSA presentation, Salt Lake City, Utah, USA, Oct. 18, 2005

Great Salt LakeGreat Salt Lake The Great Salt Lake (latitude 40°

to 42° N, longitude 112° to 113° W) is a closed lake in the lowest part of the Great basin, located in semiarid northwestern Utah, United States.

Historic variation in level of the Great Salt Lake. (Implications for airport, SLC, Industries, Transportation Infrastructure …)

1850 1900 1950 2000

41

90

41

95

42

00

42

05

42

10

12

77

.11

27

8.4

12

79

.71

28

0.9

12

82

.21

28

3.5

Lake Level

South Arm Level

North Arm Level Source: (USGS)Source: (USGS)

feet

met

ers

1850 1900 1950

1.0

e+07

2.0

e+07

3.0

e+07

What is the role of topography/bathymetry in the What is the role of topography/bathymetry in the lake dynamics and the occurrence of modes in the lake dynamics and the occurrence of modes in the volume distribution?volume distribution?

GSL Biweekly total Volume (1847-1992) Multimodality observed in biweekly lake volumes 1847-1992, Lall et al., 1996

Acr

e-fe

et

Frequency

GSL Total Volume Probability GSL Total Volume Probability Density Function for record to dateDensity Function for record to date

Gaussian kernels with 7.886e+05 bandwidth (LSCV; Silverman, 1986)

Den

sity

Cubic Km

1.0 e+07 1.5 e+07 2.0 e+07 2.5 e+07 3.0 e+07

0

e+

00

2

e-0

84

e

-08

6

e-0

88

e

-08

9.6 19.2 28.8 38.4

Biweekly total volume density (1847-2004)

Biweekly total volume density (1847-1992)

Annual average volume

Acre-feet

GSL Bathymetry Relations…GSL Bathymetry Relations…

(LovingLoving et al., 2000)et al., 2000)

0 e+00 1 e+07 2 e+07 3 e+07 4 e+07

4170

4180

4190

4200

4210

4220

North Arm

South Arm

Lake Total

(a)

4170

4180

4190

4200

4210

4220

(b)

0 0.5e+06 1.0e+06 1.5e+06 2.0e+06

North Arm

South Arm

Lake Total

0 e+00 1 e+07 2 e+07 3 e+07

(c)

00.

5e+0

61.

0e+0

61.

5e+0

62.

0e+0

6

North Arm

South Arm

Lake Total

Volume (acre-feet) Area (acre) Volume (acre-feet)

Le

vel (

fee

t)

Le

vel (

fee

t)

Are

a (

acre

)

TheoryTheory

EAQPdtdV Mass Balance:

Steady State:

I

EIA /

I,E A

Bathymetry: )(AV

V

f(I) f(A) f(V)f(E)

A

E

V

Bathymetry

I = Inflow (Precipitation + Streamflow) [L3/T]

E = Evaporation [L/T]

A = Area [L2]

V = Volume [L3]

Derived distributionsDerived distributions

fI(i) fA(a) fV(v)

)()( dVdAafvf AV

A

E

V

Mass Balance

Bathymetry

0 e+00 1 e+07 2 e+07 3 e+07

0.0

50

.10

0.1

50

.0 e

+0

05

.0 e

-07

1.0

e-0

61

.5 e

-06

2.0

e-0

62

.5 e

-06

0.5 0.72 0.94 1.16 1.38 1.6

(acre × 10^6)

PDF AreaApplicationApplicationObserved Area density function

Bathymetry

)()( dVdAafvf AV

Volume (ac-ft)

dA

/dV

Area

Den

sity

1.0 e+07 1.5 e+07 2.0 e+07 2.5 e+07 3.0 e+07

0 e

+00

2 e

-08

4 e

-08

6 e

-08

8 e

-08

1847-2004

9.6 19.2 28.8 38.4

PDF Volume

Den

sity

Volume (acre-feet)

Cubic Km

Area’s PDF has modes already ?Area’s PDF has modes already ?

1. Observed fA(a) with Constant dA/dV

2. fA(a) a normal distribution with observed dA/dV

3. Observed fA(a) with observed dA/dV

How sensitive is fHow sensitive is fVV(v) to (v) to

bathymetry described by bathymetry described by dA/dV?dA/dV?

Area Density Function(1847-2004)

0.0

e+00

5.0

e-07

1.0

e-06

1.5

e-06

2.0

e-06

2.5

e-06

0.5 0.72 0.94 1.16 1.38 1.6

(acre × 10^6)

PDF Area

Area

Den

sity

Observed fObserved fAA(a) with constant dA/dV (a) with constant dA/dV

GSL total Volume Modes

Volume (acre-feet)

De

nsi

ty

1.0 e+07 1.5 e+07 2.0 e+07 2.5 e+07 3.0 e+07

0.0

e+

00

4.0

e-0

88

.0 e

-08

1.2

e-0

7

Observed

Constant dA/dV

ffAA(a) a normal distribution with (a) a normal distribution with

observed dA/dVobserved dA/dV

GSL total Volume Modes

Volume (acre-feet)

De

nsi

ty

1.0 e+07 1.5 e+07 2.0 e+07 2.5 e+07 3.0 e+07

0.0

e+

00

4.0

e-0

88

.0 e

-08

1.2

e-0

7

Observed

Normal dist.

Observed fObserved fAA(a) with observed (a) with observed

dA/dVdA/dV

GSL total Volume Modes

De

nsi

ty

Volume (acre-feet)1.0 e+07 1.5 e+07 2.0 e+07 2.5 e+07 3.0 e+07

0.0

e+

00

4.0

e-0

88

.0 e

-08

1.2

e-0

7

Observed

Observed dA/dV

5.0 e+06 1.0 e+07 1.5 e+07 2.0 e+07 2.5 e+07 3.0 e+07

0.0

e+

00

4.0

e-0

88

.0 e

-08

1.2

e-0

7

All together,,,All together,,,GSLGSL total Volume Modestotal Volume Modes

Volume (acre-feet)

De

nsi

ty

Obs. fA(a(V)) Obs. dA/dV

Nrm. fA(a(V)) Obs. dA/dV

Obs. fA(a(V)) Const. dA/dV

Obs. fV(v)

ConclusionsConclusions

Multimodality in the area pdf suggests preferred states in driving inputs.

Bathymetry through dA/dV modulates to the pdf of the lake volumes.

Multimodality in the lake volume is due to both inputs (as inferred from area) and bathymetry through dA/dV.

FutureFuture Work…Work…

Role of Salinity ?Role of Salinity ?

GSL Causeway (2 Lakes concept) GSL Causeway (2 Lakes concept)

Role of Evaporation?Role of Evaporation?

Thank you!