This document describes modeling the impacts of declining water levels on the hydrodynamics, thermal structure, and water ages of Lake Mead under changing climate conditions. The authors developed a 3D hydrodynamic model of Lake Mead calibrated for water level and temperature. The model was applied to simulate current (2000) and potential future (2017) water levels. Results showed declining water levels would increase water temperatures by 2-7°C, accelerate water movement, and impact habitat and water quality. Modeling challenges with pressure gradients were addressed by increasing vertical resolution and horizontal viscosity parameters.

1. Modeling water ages and thermal structure
of Lake Mead under changing water levels
Yiping Li
p g
(liyiping@hhu.edu.cn)
Co-author:
Co author: Kumud Acharya
Hohai University

3. Outline
1 Introduction ( Problem Statement, Purpose,
Study Area, etc.)
Area etc )
2 Methods (EFDC 3D)
3 Model Calibration
4 Application of the model
pp
5 Discussion
6C l i
Conclusions

4. 1 Introduction
There may be a decrease in
runoff over the Southwestern
United States because of sustained
drought owing to global warming.
The IPCC Working Group II Lake Mead
concludes there will be a 10–30%
run off reduction over this region
during the next 50 years.
What will be the status
of Lake Mead?

5. 1 Introduction
Lake Mead is the largest
man-made reservoir by
volume (35.5 km3 ) in US,
l (35 5 k i US
formed by the construction of
Hoover Dam in the 1930s.
Approximately 96% of the
inflow into Lake Mead
comes from the Colorado
River. Outflow remains
unchanged (NASA 2003).

6. Hoover Dam & Lake Mead

7. 375
370
365
1 Introduction 360
W S E (m )
355
350
The water level has dropped 345
340
about 35 m since 2000. 335
It has been hypothesized that 330
Dec-99 Apr-01 Sep-02 Jan-04 May-05 Oct-06 Feb-08 Jul-09
there is 50% chance that it will Date
become functionally dry by 2017
2000
(
(Barnett and Pierce 2008).
)
35 m
Significant declines in water level
would have substantial socio- 2009
economic and environmental
p
impacts.

8. 1 Introduction
Objectives
Investigate impacts of lake s water level on
lake’s
it’s hydrodynamic processes (e.g. circulation,
water ages, temperature).
Develop a publicly-available 3D
p p y
hydrodynamic model of Lake Mead to
support future management decisions.

9. Study Area
From: http://nevada.usgs.gov/lmqw

10. Outline
1 Introduction ( Problem Statement, Purpose,
Study Area, etc.)
Area etc )
2 Methods (EFDC 3D)
3 Model Calibration
4 Application of the model
pp
5 Discussion
6C l i
Conclusions

11. Methods
Model description
The model is based upon 3D Environmental Fluid Dynamic Code
p y
(EFDC) model, originally developed by Hamrick (1992) for USEPA.
This is a well tested and commonly used model for such studies.
The EFDC model is a public domain surface water modeling System
incorporating fully integrated hydrodynamic, water quality and sediment-
transport simulation capabilities.
The model can be used for 1, 2, or 3-D simulation of rivers, lakes,
estuaries, coastal regions and wetlands.
, g
EFDC website: http://ds-international.biz

12. Methods
Model Description--Hydrodynamics
Hydrodynamics
Dynamics Near Field
Dye Temperature Salinity Drifter
(E, u, v, w, mixing) Plume
Three-Dimensional with 2-D and 1-D Options
Sigma Vertical Grid and GVC coordinate
Drying and Wetting of Shallow Regions
Hydraulic C t l St t
H d li Control Structures
Wave Boundary Layers and Wave Induced Currents
EFDC website: http://ds-international.biz

13. Methods
Model Description—Water Quality
Hydrodynamic
Model Dynam
ics
Water Quality
Organic COD Sediment
Algae Phosphorus Nitrogen Silica DO FCB
Carbon TAM Diagenesis
Greens
Predicted Flux
Diatoms
Other Specified Flux
Directly Coupled to Hydrodynamics
Based on CE QUAL IC water quality model
CE-QUAL-IC
21 Water Quality Parameters Including Algae and Organic
Carbon, Nitrogen and Phosphorous
EFDC website: http://ds-international.biz

14. Methods
Model Description—Water ages
Water age is defined as “the time that has elapsed since the
p
particle under consideration left the region in which its age is
g g
prescribed as being zero” (Delhez et al. 1999)
r
∂c (t , x ) r r
+ ∇ (uc (t , x )) − K ∇ c (t , x ) = 0
∂t
r
∂α ( t , x ) r r r
+ ∇ (uα (t , x )) − K∇α (t , x ) = c (t , x )
∂t
r r r
α ( t , x ) = α ( t , x ) / c (t , x )
where c is the tracer concentration,α is the age concentration, u is the velocity field in
space and time domains, K is the diffusivity tensor, t is time. α is the average water age.
Similar to Water residence time or Water retention time in unit scale

15. Methods
Model Description— Interface
Preprocessing software
for grid generation and
input file creation
p
Postprocessing software
for analysis, graphic and
analysis
visualization
EFDC website: http://ds-international.biz

16. Methods
Mesh Generation
3,512 cells in the
horizontal plane with a
uniform grid size of 216
m.
Uniformly stratified (30
layers) Cartesian
computational mesh.

17. Methods
Boundary and initial conditions
1. Flow 3. Atmospheric
1.1 L
1 1 Lower Colorado River
C l d Ri 3.1 Atmospheric pressure
3 1 At h i
1.2 Las Vegas Wash 3.2 Air temperature
1.3 Hoover Dam 3.3 Wet bulb temperature
1.4 Drinking water intake 3.4 Rainfall rate
2. Wind 3.5 Evaporation rate
2.1 Wind Speed 3.6 Solar short wave radiation
f
at water surface
2.2 Wind Direction
Initial conditions- water surface elevations, water column and bed temperatures, and
conditions elevations temperatures
water ages. The water age is ”zero” at inflow inlets.

18. Outline
1 Introduction ( Problem Statement, Purpose,
Study Area, etc.)
Area etc )
2 Methods (EFDC 3D)
3 Model Calibration
4 Application of the model
pp
5 Discussion
6C l i
Conclusions

19. 3 Model Calibration—Water level
Lake stage and temperature profiles at Sentinel Island
between 3/1-10/31, 2005 were used to calibrate the model.
The calculated Absolute
Mean Error (AME) and Mean
Absolute Relative Error
(MARE) for water level was
0.084
0 084 m and 0 02%
d 0.02%,
respectively, which suggests
that the calibration results are
accurate enough to set up
model parameters.
Water level calibration

20. 3 Model Calibration—Water temperature
The AMEs for surface,
middle and b tt
iddl d bottom water
t
temperatures were 1.51 ºC,
1.04 ºC and 1.42 ºC,
respectively.
Corresponding MAREs
were 7.3%, 6.9% and
10.9%.
Water temperature calibration

21. 3 Model Calibration—Parameters selection

22. Outline
1 Introduction ( Problem Statement, Purpose,
Study Area, etc.)
Area etc )
2 Methods (EFDC 3D)
3 Model Calibration
4 Application of the model
pp
5 Discussion
6C l i
Conclusions

23. 4 Application of the model
Two tested scenarios
The lib d
Th calibrated model was applied to calculate water ages and thermal
d l li d l l d h l
structures under two scenarios:
1) A hi h t
high-stage situation in the year 2000 with an initial water
it ti i th ith i iti l t
level of 370.0 m (LMWD 2009)
2) A projected d
j d drawdown scenario in the year 2017 with an
d i i h ih
initial water level 320.0 m, which is the minimum power
pool level for Lake Mead (Barnett and Pierce 2008).
2008)
370 m -320 m =50 m (water level drop)
( p)

24. 4 Application of the model
Two tested scenarios 2000
50m
2017
Depth (m)
.5 [Time 1.000] 150
Year: 2000 2017
Water level: 370.0 m 320.0 m
Volume: 30.8 km3 12.3 km3

25. 4 Application of the model
Circulation Pattern
Horizontal distribution of Velocity
2000
Winds and inflow tributaries play an important role in lake’s circulation.

26. 4 Application of the model
Temperature distribution
Water age and temperature were selected to study the impact of water level
drawdown as indicative parameters of thermal regime and hydrodynamic
processes.
processes
Horizontal distribution of Vertical distribution of
temperature temperature

27. 4 Application of the model
Water ages distribution
sites A: shallow region
255 (a) sites A 230d 305 (b) sites B sites B: deep region
205
255 270d
W a te r A g e (d a y )
W a te r A g e (d a y )
205
155
155
105
Surface WA 105 Surface WA
Middle WA Middle WA
55 Bottom WA Bottom WA
55
5 5
0 100 200 300 400 0 100 200 300 400
Julian Date (day)
( y) Julian Date (day)
( y)
Calculated time series of water age at sites A (a) and B (b) in 2000

28. 4 Application of the model
Impact of water level drawdown on temperature stratification
26
A-2017
24
A-2000
22
rature (C)
20
18
Temper
16
Station A 2000
14 Station A 2017 B-2017
Station B 2000
12 Station B 2017
B-2000
10
0 100 200 300 400
Julian Date (day)
The extent and duration of thermal stratification were strongly
influenced by declining water levels
levels.

29. 4 Application of the model
Impact of water level drawdown on temperature stratification
10
10
7
7
4
4
2 Surface ∆T 2
0
0
Depth averaged ∆T
p g
10
The depth-averaged water 7
temperature increased by 4 7
4–7 4
ºC for shallow regions versus Bottom ∆T 2
2–4 ºC for deep regions.
p g
0
ΔT means temperature at Day 219 in 2000 subtracted from that of 2017.

30. 4 Application of the model
Impact of water level drawdown on water ages
100
100
80
80
60
60
Surface ΔWA 40
Depth averaged ΔWA
p g
40
ΔWA Surface Bottom Depth
(day) Layer (%) Layer (%) Average
(%) 100
<70 3.1
31 18.3
18 3 1.2
12
70-80 18.0 22.3 32.1 80
80-90 55.2 20.4 39.3
90-100 20.5 11.2 13.6 Bottom ΔWA
60
100-150 2.6 21.1 13.0
40
>150 0.7 6.8 0.8
ΔWA represents water age at Day 365 of 2000 subtracted from that of 2017.

31. Outline
1 Introduction ( Problem Statement, Purpose,
Study Area, etc.)
Area etc )
2 Methods (EFDC 3D)
3 Model Calibration
4 Application of the model
pp
5 Discussion
6C l i
Conclusions

32. 5 Discussion
5.1 Impact of water level drawdown
Temperature changes (2-7 ºC) would likely have a notable impact
on the lake’s aquatic habitat and food web
(1) depress the dissolved oxygen concentration
d th di l d t ti
(2) degrade water quality
(3) promote the growth of harmful algae species
(4) force fish to move away from their existing habitat and seek out
refuge areas elsewhere
The decline of water volume would result in the reduction of
habitat and increase in competition for resources.
Water age changed faster for the bottom water than it did for the
surface, suggesting that water level drawdown could accelerate the
bottom water’s movement, and affect the transfer and transport of
pollutants.
pollutants

33. 5 Discussion
5.2 Pressure gradient error
Due to the rapid change of bottom topography in the lake, the
model has issues with pressure gradients (PG) error.
For this study, two methods
were investigated to reduce
the
th PG errors to acceptable
t t bl
levels
(1) increase vertical
resolution
(2) apply large horizontal
viscosity by using a large CM
i i b i l
Observed Value
value.
Modeled Value

34. 5 Discussion
5.2 Pressure gradient error– Changing vertical resolution
As expected, higher the Time series of bottom temperature at site B
vertical resolution, lower
the PG errors However
errors. However,
higher vertical resolution
requires a longer CPU time.
For example, the case with
30 layers: 120 CPU hrs
(Dell,
(Dell Intel Core 4 CPU
4-CPU
processor, 2.6 GHz)
14 layers: only 40 CPU hrs.
y y

35. 5 Discussion
5.2 Pressure gradient error – Changing CM values
The formulation of Smagorinsky method (Smagorinsky, 1963)
for calculating horizontal viscosity is shown as below:
g y
2 1/ 2
⎡⎛ ∂U ⎞ 1 ⎛ ∂V ∂U ⎞ ⎛ ∂V ⎞ ⎤
2 2
AM = C M ΔxΔy ⎢⎜ ⎟ + ⎜
⎜ ∂x + ∂y ⎟ + ⎜ ∂y ⎟ ⎥
⎟ ⎜ ⎟
⎢
⎣⎝ ∂x ⎠ 2 ⎝ ⎠ ⎝ ⎥
⎠ ⎦
where AM is horizontal viscosity, CM is a nondimensionless viscosity
parameter. Usually recommended value is 0.2.

36. 5 Discussion
5.2 Pressure gradient error – Changing CM values
The results indicated
that the model is not
highly sensitive to
moderate changes to
CM. However, the
,
model was unstable
under larger
adjustments to CM.
Time series of bottom temperature at site B (Deep region)

37. Outline
1 Introduction ( Problem Statement, Purpose,
Study Area, etc.)
Area etc )
2 Methods (EFDC 3D)
3 Model Calibration
4 Application of the Lake Mead model
pp
5 Discussion
6C l i
Conclusions

38. 6 Conclusions
Atmospheric boundary plays a more important role than inflow
temperature on thermal stratification of the lake.
The drop in water levels impact shallow regions of the lake on the
thermal stratification regime and flow circulation pattern.
Application of EFDC model requires special attention to account for
pressure gradient errors especially at places where bottom slopes are
steep.
In
I general, the study provided useful i f
l th t d id d f l information for understanding
ti f d t di
the thermal and hydrological processes in Lake Mead under extreme
water level drawdown scenarios.
The future work should concentrate on the contaminant and nutrient
dynamics and ecosystem of the lake.