Hydrodynamic and Water Quality Modeling Basics

Jim Bowen, UNC Charlotte

LCFRP Advisory Board/Tech. Comm. Meeting, November 27, 2007

Wilmington, NC

Objectives of Presentation

•  Introduction to Numerical Water Quality Models

•  Introduction to Model Used - Environmental Fluid Dynamics Code (EFDC)

• Description of LCFR Application

A Numerical Model Example - The “Monty Hall Problem”

Letter to Marilyn vos Savant (Sept. 9, 1990)

"Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you: 'Do you want to pick door #2?' Is it to your advantage to switch your choice of doors?"—Craig F. Whitaker, Columbia, Maryland

Marilyn’s Response “You should switch because door #2 has

a 2/3 chance of winning whereas door #1 has only a 1/3 chance of winning.”

Marilyn’s Response “You should switch because door #2 has

a 2/3 chance of winning whereas door #1 has only a 1/3 chance of winning.”

Thousands responded, (including many College Math professors)

• Marilyn is wrong •  the doors are equally likely to win

The Debate Rages at Work

“Yes, Marilyn is right, your odds are better if you switch”

“No, Marilyn is wrong, 2 doors, 1 car, each door has a 50% chance of winning”

The Debate Rages at Work

“Yes, Marilyn is right, your odds are better if you switch”

“No, Marilyn is wrong, 2 doors, 1 car, each door has a 50% chance of winning”

My response - “I’m not sure, but I could easily write a computer program to simulate this problem”

The Monty Hall Simulator, p1

The Monty Hall Simulator, p2

The Monty Hall Simulator, p2

• About 50 lines of computer code •  Took about 45 minutes to write

The Monty Hall Simulator, The Results, Don’t Switch >> lmad How many trials? (1-9,999): 999 What is your strategy? k = keep your door s = switch your door f = flip a coin, since the choices are equally

likely Choose a letter: k You won the prize 34% of the time

The Monty Hall Simulator, The Results, Switch >> lmad How many trials? (1-9,999): 999 What is your strategy? k = keep your door s = switch your door f = flip a coin, since the choices are equally

likely Choose a letter: s You won the prize 68% of the time

A Numerical SimulationModel

•  Computer program that simulates the behavior of the system being studied

•  Based on a conceptual model of how the system operates

•  Computer code written to implement the conceptual model description

•  Scenario testing used to answer questions of interest about system

What is a Water Quality Model? Models are Numerical Calculations Used to Estimate Anthropogenic Impact

Given: 1. Amount of Point and Nonpoint Source Inputs 2. Water Body Characteristics Find: 1. Water Quality of the Receiving Body

A Typical Modeling Problem

What is a Model? (continued) Given: 1. Amount of Point and Nonpoint Source Inputs 2. Water Body Characteristics Find: 1. Water Quality of the Receiving Body

What is a Model? (continued)

Empirical Models

Given: 1. Amount of Point and Nonpoint Source Inputs 2. Water Body Characteristics Find: 1. Water Quality of the Receiving Body

What is a Model? (continued)

Empirical Models

Mechanistic Models

Given: 1. Amount of Point and Nonpoint Source Inputs 2. Water Body Characteristics Find: 1. Water Quality of the Receiving Body

What is a Model? (continued)

Mechanistic Models

Neuse, LCFR models

Given: 1. Amount of Point and Nonpoint Source Inputs 2. Water Body Characteristics Find: 1. Water Quality of the Receiving Body

Steps in Creating a Mechanistic Model Code

1.  Decide on What to Model 2.  Create Conceptual Model(s) 3.  Make Necessary Simplifying

Assumptions 4.  Write Governing Equations 5.  Devise Numerical Solution Schemes 6.  Implement Above in Computer Program

Steps in Applying a Mechanistic Model 1.  Decide on What to Model 2.  Decide on Questions to be Answered 3.  Choose Model 4.  Collect Data for Inputs, Calibration 5.  Create Input Files 6.  Create Initial Test Application 7.  Perform Qualitative “Reality Check”

Calibration & Debugging

Steps in Applying a Mechanistic Model, continued

8.  Perform quantitative calibration & model verification

9.  Design model scenario testing procedure (endpoints, scenarios, etc.)

10. Perform scenario tests 11. Assess model reliability 12. Document results

Mechanistic Model Basis: Conservation Equations

Outflow

Water Volume Sources Sinks

State Variable

Inflow

Mechanistic Model Basis: Conservation Equations

Outflow

Water Volume Sources Sinks

State Variable

Inflow

•  Momentum Conservation (for Water Velocities) •  Energy Conservation (for Temperature) •  Mass Conservation (for WQ Constituents)

Mechanistic Model Basis: Conservation Equations

Outflow

Water Volume Sources Sinks

State Variable

Inflow

•  Momentum Conservation (for Water Velocities) •  Energy Conservation (for Temperature) •  Mass Conservation (for WQ Constituents)

4. Governing Equations Based on Conservation Equations

Outflow

Water Volume Sources Sinks

State Variable

Inflow

•  Momentum Conservation (for Water Velocities) •  Energy Conservation (for Temperature) •  Mass Conservation (for WQ Constituents)

Mechanistic Model Basis: Conservation Equations

Outflow

Water Volume Sources Sinks

State Variable

Inflow

Change in Variable/Time = Inflow Rate - Outflow Rate +/- Sources & Sinks

Atmosphere

Water Column

Governing Equation 1. Momentum Balance

Wind Mixing

Inflow/Outflow

Turbulent Diffusion

Sediment

Convection

Gravity

Bottom Friction

Atmosphere

Water Column

Governing Equation 2. Heat Balance

Conduction

Conduction

Solar Radiation

Inflow/Outflow Evaporation

Sediment

Turbulent Transport

Example of Mass Conservation: Dissolved Oxygen

Single Segment

DO Inflow

DO Outflow

DO & BOD Consumption

Reaeration

SOD

Example of Mass Conservation : Dissolved Oxygen

Single Segment

DO Inflow

DO Outflow

DO & BOD Consumption

Reaeration

SOD

Inflow

Example of Mass Conservation: Dissolved Oxygen

Single Segment

DO Inflow

DO Outflow

DO & BOD Consumption

Reaeration

SOD

Inflow

Outflow

Example of Mass Conservation: Dissolved Oxygen

Single Segment

DO Inflow

DO Outflow

DO & BOD Consumption

Reaeration

SOD

Inflow

Outflow

Source

Example of Mass Conservation: Dissolved Oxygen

Single Segment

DO Inflow

DO Outflow

DO & BOD Consumption

Reaeration

SOD

Inflow

Outflow

Source

Sinks

Governing Eq. 3: DO Conceptual Model BOD Sources

Sediment

Cape Fear BOD Load

NECF & Black R. BOD Load

Muni & Ind. BOD Load

decaying phytopl.

BOD Consumption

Governing Eq. 3: DO Conceptual Model BOD Sources, DO Sources & Sinks

Sediment Sediment O2 Demand

Cape Fear BOD Load

NECF & Black R. BOD Load

Ocean Inflows

Surface Reaeration

Input of NECF & Black R. Low DO Water

Phytoplank. Productivity Muni & Ind.

BOD Load

decaying phytopl.

MCFR Inflows

BOD Consumption

Governing Eq. 3: DO Conceptual Model BOD Sources, DO Sources & Sinks

Sediment Sediment O2 Demand

Cape Fear BOD Load

NECF & Black R. BOD Load

Ocean Inflows

Surface Reaeration

Input of NECF & Black R. Low DO Water

Phytoplank. Productivity Muni & Ind.

BOD Load

decaying phytopl.

MCFR Inflows

EFDC, the big picture

Estuary Physical Characteristics: e.g. length, width, depth, roughness

EFDC Software Adjustable Parameters: (e.g. BOD decay, SOD, reaeration)

Hydrologic Conditions

River Flows, Temp’s, Conc’s Tides Time

“Met” Data Air temps, precip, wind, cloudiness

Time

State Variables

nutrients DO, organic C

Time

Next Part of Presentation: More Info on EFDC

Go to Very Short Intro to EFDC.ppt

Description of Model Application

•  Flow boundary condition upstream •  Elevation boundary condition downstream •  17 lateral point sources •  Extra lateral point sources add water from

marshes

Description of Model Application

Open Boundary Elevation Cond.

Lower Cape Fear River Estuary Schematic

Black River Flow Boundary Cond.

Cape Fear R. Flow Boundary Cond.

NE Cape Fear Flow Boundary Cond.

LCFR Grid • Channel

Cells in Blue • Wetland

Cells in White

• Marsh and Swamp Forest in Green, Purple

Data Source for Wetland Information

LCFR Grid Characteristics

• Off-channel storage locations based on wetland delineations

•  46 additional marsh cells added to original grid (1050 total cells, 8 vertical layers)

• Additional off-channel storage added to each basin (Cape Fear, Black, NECF)

•  Significant amount of marsh area added to middle and lower estuary

LCFR EFDC Application: Other Input Files • Meteorological forcings (from NWS) • Freshwater inflows (from USGS) • Elevations at Estuary mouth (from

NOAA) • Quality, temperature of freshwater

inflows, at estuary mouth (from LCFRP)

• Other discharges (from DWQ)

LCFR EFDC Application: Data Collected

• Data Collected from 8 sources – COE, DWQ, IP, LCFRP, NOAA, NWS, USGS,

Wilmington WWTP • Over 800 MB of original data collected so

far • Original data archived and saved as read

only files

LCFR Model - What Does it Simulate?

•  Water Properties – Temperature, salinities

•  Circulation – Flows, velocities, water surface elevations

•  Nutrients – Organic and Inorganic nitrogen, phosphorus

•  Organic Matter – BOD (dissolved, particulate), chlorophyll

•  Other – Dissolved Oxygen

Cape fear rivercheck point

1: NC112: LC

3: ACME4: B210

5: DP6: IC

7: NAV8: HB

9: NC_710: NCF6

11: BR12: M61

13: M5414: M42

15: M3516: M23

17: M18

April - November 2004 Salinity, New

April - November 2004 Temp., New

LCFR Model Application - What Can You Do With It?

• Model simulates behavior of estuary •  Pose scenarios - use model to estimate

impacts – e.g. climate impacts (how does WQ change w/

reduced inflows) – e.g. management scenarios (how does WQ

change w/ reduced wastewater inputs)

LCFR Model - What are we Working on Now?

• Hydrodynamic model calibrated • Plan to finish WQ model calibration in

December • Run scenarios in January • More in next talk

Information Available Online •  See LCFR website for more info

www.coe.uncc.edu/~jdbowen/LCFR •  This presentation is available • Google Earth files available for download

– Grid and wetland data from presentation – Monitoring stations, point sources – Final EFDC grid information – NOAA bathymetry – Hydrodynamic model animations