lake mead water management numerical model

Modeling water ages and thermal structure of Lake Mead under changing water levels

Yiping Lip g(liyiping@hhu.edu.cn)

Co author: Kumud AcharyaCo-author: Kumud Acharya

Hohai UniversityHohai University

Outline

1 Introduction ( Problem Statement, Purpose, Study Area etc )Study Area, etc.) 2 Methods (EFDC 3D)3 Model Calibration4 Application of the modelpp5 Discussion6 C l i6 Conclusions

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 concludes there will be a 10–30%

Lake Mead

run off reduction over this region during the next 50 years.

What will be the status of Lake Mead?

1 Introduction

Lake Mead is the largest man-made reservoir by

l (35 5 k 3 ) i USvolume (35.5 km3 ) in US, formed by the construction of Hoover Dam in the 1930s.

Approximately 96% of the inflow into Lake Meadinflow into Lake Mead comes from the Colorado River. Outflow remains unchanged (NASA 2003).

Hoover Dam & Lake Mead

365

370

375

350

355

360

365

SE (m

)1 Introduction

335

340

345

350W

The water level has dropped about 35 m since 2000.

330Dec-99 Apr-01 Sep-02 Jan-04 May-05 Oct-06 Feb-08 Jul-09

Date

It has been hypothesized that there is 50% chance that it will become functionally dry by 2017 (Barnett and Pierce 2008).

2000( )

Significant declines in water level would have substantial socio-

35 m

2009

economic and environmental impacts.p

1 Introduction

Objectives

Investigate impacts of lake’s water level onInvestigate impacts of lake s water level on it’s hydrodynamic processes (e.g. circulation, water ages, temperature).

Develop a publicly-available 3D p p yhydrodynamic model of Lake Mead to support future management decisions.

Study Area

From: http://nevada.usgs.gov/lmqw

Outline

1 Introduction ( Problem Statement, Purpose, Study Area etc )Study Area, etc.) 2 Methods (EFDC 3D)3 Model Calibration4 Application of the modelpp5 Discussion6 C l i6 Conclusions

Methods

Model descriptionThe 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

Methods

Model Description--Hydrodynamics

Hydrodynamics

Dynamics(E, u, v, w, mixing) Dye Temperature Salinity Near Field

Plume Drifter

Three-Dimensional with 2-D and 1-D OptionsSigma Vertical Grid and GVC coordinateSigma Vertical Grid and GVC coordinateDrying and Wetting of Shallow Regions H d li C t l St tHydraulic Control StructuresWave Boundary Layers and Wave Induced Currents

EFDC website: http://ds-international.biz

Methods

Model Description—Water Quality

Water Quality

HydrodynamicModel Dynamics

Algae OrganicCarbon Phosphorus Nitrogen Silica DO COD

TAM FCB SedimentDiagenesis

Greens

DiatomsPredicted Flux

Specified FluxOther Specified Flux

Directly Coupled to HydrodynamicsBased on CE-QUAL-IC water quality modelBased on CE QUAL IC water quality model21 Water Quality Parameters Including Algae and Organic Carbon, Nitrogen and PhosphorousCarbon, Nitrogen and Phosphorous

EFDC website: http://ds-international.biz

Methods

Model Description—Water ages

Water age is defined as “the time that has elapsed since the particle under consideration left the region in which its age is p g gprescribed as being zero” (Delhez et al. 1999)

0)())((),(=∇−∇+

∂ xtcKxtucxtc rrr

0),()),(( =∇−∇+∂

xtcKxtuct

),(),()),((),( xtcxtKxtuxt rrrr

=∇−∇+∂

∂ ααα ),(),()),((t∂

),(/),(),( xtcxtxt rrr αα =

where c is the tracer concentration, is the age concentration, u is the velocity field in space and time domains, K is the diffusivity tensor, t is time. is the average water age.

α

α

Similar to Water residence time or Water retention time in unit scale

Methods

Model Description— Interface

Preprocessing software for grid generation and input file creationp

Postprocessing software for analysis graphic andfor analysis, graphic and visualization

EFDC website: http://ds-international.biz

Methods

Mesh Generation

3,512 cells in the horizontal plane with ahorizontal plane with a uniform grid size of 216 m.

Uniformly stratified (30 layers) Cartesianlayers) Cartesian computational mesh.

Methods

Boundary and initial conditions

1. Flow1 1 L C l d Ri

3. Atmospheric3 1 At h i1.1 Lower Colorado River

1.2 Las Vegas Wash

3.1 Atmospheric pressure

3.2 Air temperature

1.3 Hoover Dam

1.4 Drinking water intake

3.3 Wet bulb temperature

3.4 Rainfall rate

2. Wind2.1 Wind Speed

3.5 Evaporation rate

3.6 Solar short wave radiation f2.2 Wind Direction at water surface

Initial conditions water surface elevations water column and bed temperatures andInitial conditions- water surface elevations, water column and bed temperatures, and water ages. The water age is ”zero” at inflow inlets.

Outline

1 Introduction ( Problem Statement, Purpose, Study Area etc )Study Area, etc.) 2 Methods (EFDC 3D)3 Model Calibration4 Application of the modelpp5 Discussion6 C l i6 Conclusions

3 Model Calibration—Water levelLake 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 MeanMean Error (AME) and Mean Absolute Relative Error (MARE) for water level was 0 084 d 0 02%0.084 m and 0.02%,respectively, which suggests that the calibration results are accurate enough to set up model parameters.

Water level calibration

3 Model Calibration—Water temperature

The AMEs for surface, iddl d b tt tmiddle and bottom water

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

3 Model Calibration—Parameters selection

Outline

1 Introduction ( Problem Statement, Purpose, Study Area etc )Study Area, etc.) 2 Methods (EFDC 3D)3 Model Calibration4 Application of the modelpp5 Discussion6 C l i6 Conclusions

4 Application of the model

Two tested scenariosTh lib d d l li d l l d h lThe calibrated model was applied to calculate water ages and thermal structures under two scenarios:

1) A hi h t it ti i th 2000 ith i iti l t1) A high-stage situation in the year 2000 with an initial water level of 370.0 m (LMWD 2009)

2) A j d d d i i h 2017 i h2) A projected drawdown scenario in the year 2017 with an initial water level 320.0 m, which is the minimum power pool level for Lake Mead (Barnett and Pierce 2008)pool level for Lake Mead (Barnett and Pierce 2008).

370 m -320 m =50 m (water level drop)( p)

4 Application of the model

Two tested scenarios 2000

50m

2017

.5 150Depth (m)[Time 1.000]

Year: 2000 2017Year: 2000 2017Water level: 370.0 m 320.0 mVolume: 30.8 km3 12.3 km3

4 Application of the model

Circulation Pattern

Horizontal distribution of Velocity2000

Winds and inflow tributaries play an important role in lake’s circulation.

2000

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 processesprocesses.

Horizontal distribution of temperature

Vertical distribution of temperature

4 Application of the model

Water ages distributionsites A: shallow region

205

255

255

305 (b)(a) sites A sites Bsites A: shallow regionsites B: deep region230d

270d

155

205

Age

(day

)

155

205

Age

(day

)

55

105

Wat

er

Surface WAMiddle WABottom WA 55

105Wat

er

Surface WAMiddle WABottom WA

50 100 200 300 400

Julian Date (day)

50 100 200 300 400

Julian Date (day)

Calculated time series of water age at sites A (a) and B (b) in 2000

( y) ( y)

4 Application of the model

Impact of water level drawdown on temperature stratification

24

26A-2017

A-2000

18

20

22

ratu

re (C

)

A-2000

14

16

18

Tem

per

Station A 2000Station A 2017Station B 2000

B-2017

10

12

0 100 200 300 400Julian Date (day)

Station B 2017B-2000

Julian Date (day)

The extent and duration of thermal stratification were strongly influenced by declining water levels influenced by declining water levels.

4 Application of the model

Impact of water level drawdown on temperature stratification

10 10

2

4

7

2

4

7

Surface ∆T0

2

0

2

Depth averaged ∆T

Surface ∆T

7

10

The depth-averaged water temperature increased by 4 7

p g

2

4temperature increased by 4–7 ºC for shallow regions versus2–4 ºC for deep regions.

Bottom ∆T

0p g

ΔT means temperature at Day 219 in 2000 subtracted from that of 2017.

4 Application of the model

Impact of water level drawdown on water ages

100

80

100

60

80

40

6040

Depth averaged ΔWASurface ΔWA

100

p g

ΔWA(day)

Surface Layer (%)

Bottom Layer (%)

Depth Average

(%)<70 3 1 18 3 1 2

60

80

Bottom ΔWA

<70 3.1 18.3 1.270-80 18.0 22.3 32.180-90 55.2 20.4 39.390-100 20.5 11.2 13.6

40

ΔWA represents water age at Day 365 of 2000 subtracted from that of 2017.

100-150 2.6 21.1 13.0>150 0.7 6.8 0.8

Outline

1 Introduction ( Problem Statement, Purpose, Study Area etc )Study Area, etc.) 2 Methods (EFDC 3D)3 Model Calibration4 Application of the modelpp5 Discussion6 C l i6 Conclusions

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) d th di l d t ti(1) depress the dissolved oxygen concentration(2) degrade water quality(3) promote the growth of harmful algae species(3) promote the growth of harmful algae species(4) force fish to move away from their existing habitat and seek out refuge areas elsewhereThe 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 theWater 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 pollutantspollutants.

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 th PG t t blthe PG errors to acceptable levels(1) increase vertical(1) increase vertical

resolution(2) apply large horizontal i i b i l C

Modeled Value

Observed Valueviscosity by using a large CMvalue.

5 Discussion

5.2 Pressure gradient error– Changing vertical resolution

Time series of bottom temperature at site BAs expected, higher the vertical resolution, lower the PG errors Howeverthe PG errors. However, higher vertical resolution requires a longer CPU time.

For example, the case with 30 layers: 120 CPU hrs(Dell Intel Core 4-CPU(Dell, Intel Core 4 CPU processor, 2.6 GHz)

14 layers: only 40 CPU hrs.y y

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

2/1222 1⎥⎤

⎢⎡

⎟⎟⎞

⎜⎜⎛ ∂

⎟⎟⎞

⎜⎜⎛ ∂∂

⎟⎞

⎜⎛ ∂ΔΔ

VUVUCA2 ⎥

⎥⎦⎢

⎢⎣

⎟⎟⎠

⎜⎜⎝ ∂

+⎟⎟⎠

⎜⎜⎝ ∂

+∂

+⎟⎠⎞

⎜⎝⎛∂

ΔΔ=yyxx

yxCA MM

where AM is horizontal viscosity, CM is a nondimensionless viscosity parameter. Usually recommended value is 0.2.

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 M ,model was unstable under larger adjustments to CMadjustments to CM.

Time series of bottom temperature at site B (Deep region)

Outline

1 Introduction ( Problem Statement, Purpose, Study Area etc )Study Area, etc.) 2 Methods (EFDC 3D)3 Model Calibration4 Application of the Lake Mead modelpp5 Discussion6 C l i6 Conclusions

6 ConclusionsAtmospheric 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 forApplication of EFDC model requires special attention to account for pressure gradient errors especially at places where bottom slopes are steep. I l th t d id d f l i f ti f d t diIn general, the study provided useful information for understanding 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.