Water Quality Modeling and TMDL Development: The WASP Model

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Transcript Water Quality Modeling and TMDL Development: The WASP Model

Water Quality Modeling and TMDL Development: The WASP Model US EPA Region IV Water Quality Assessment Section

The Instructors • Tim Wool – US EPA Region 4 Technical Staff • Bob Ambrose – US EPA, NERL @ Athens

Course Objectives

Basic Concepts • What is a Model and Why Model ?

• What are Mechanistic Versus Empirical Models ?

• What are the Basic Principals of Mechanistic Models ?

What is a Model and Why Model?

A model is a “conceived image of reality”, or a theoretical construct, relating some stimulus to a response

What Can Models Do?

• Describe – Present water quality in detail – Interpolate observed data – Identify important processes impacting water quality

What Can Models Do?

• Predict (generic) Types of water bodies at risk Chemicals that may provide risk

What Can Models Do?

• Predict (site specific) – Likely result of remedial actions or allocations • Ultimate levels • Time frame (dynamic models) – Reasonable allocation of waste loads to protect standards – Cost-effective monitoring plans

C C=W/¶ W

Empirical approach

: assume that ¶ is known or related to some external variable and will not be affected by allocation (will not change). Example: determine empirical relationship between DO and waste load based upon measurements

Mechanistic approach

: attempt to determine underlying mechanisms affecting ¶ and include those in predictions Example: include processes such as BOD decay, reaeration, etc. in equations relating W and C.

Basic Principal of Mechanistic Models • Laws of Conservation – Conservative properties are those that are not gained or lost through ordinary reactions. Therefore we can account for any change by simply keeping track of all those processes that can cause change

Basic Principal of Mechanistic Models – Examples of conservative properties • Mass (water mass, constituent mass) • Momentum • Heat

Characteristics of Models • Variables and processes • Time and space scales • Solution technique and operation • Descriptive or predictive

• Water movement • Salinity • Bacteria • BOD-DO • Nutrients • Eutrophication • Toxics Variables

• Empirical • Lumped process • Mechanistic Process

Time

Steady-state Steady-input Quasi-dynamic Dynamic

Space

One-dimensional (x or z) Two-dimensional (x-y or x-z) Three-dimensional

Numerical Analytical

Solution Operations:

Computer platform (PC, mainframe) Input style and support software

Box Model Approach • Numerical solution allows greater flexibility as to processes considered (i.e. eutrophication, toxics, etc.) • Allows greater flexibility as to segmentation • Flows and mixing coefficients obtained from – Field data – Predicted by hydrodynamic models (which produce output that is read by WASP)

Control Volume z y x 



  



x x C

  

x E x



 



y y C

  

 

E y



   



z z C

  

z E z





Sources and Sinks

Three Dimensional Transport Equation

Three-Dimensional Equation • Has no known analytical solution – Analytical solutions are available only for simplified forms • Assuming steady state • Assuming one-dimension

Three-Dimensional Equation – Numerical solutions are generally required • Box modeling approach (applicable to 1,2 or 3 dimensions) • Other numerical approaches (specific to 1,2 or 3-d models)

Box Modeling Approach To obtain a 1-D model, integrate over y,z to obtain

A dC dt

 

A dUC dx



d dx EA dC dx



Sources and Sinks

And obtain difference approximation j-1 j j+1 



  

i Q i

j C i

i=1  

i E i

j A i



C i

, i=2



Sources



X i

j and Sinks

Box Modeling Approach • The flows and dispersion can be – Across the boundary between the “box” and the outside world (an external boundary) – Across the interfaces between boxes (an internal boundary), so the “load “ due to advection and dispersion is based on the computed concentration of the other boxes

Box Modeling Approach – The changes in volume can be computed from continuity

Box Modeling Approach • Boxes – The boxes have no defined shape, so can be fit to any morphometry – The boxes can be “stacked” so the approach can be applied to 0 dimensions (1 box) or 1, 2 or three dimensional systems

Box Models • Examples – Water Analysis Simulation Program (WASP) (US EPA, Ambrose, Wool and Martin 1993) – CE-QUAL-ICM (US COE WES, Cerco and Cole 1997)

Introduction to Hydrodynamics

Three Dimensions • Why?

• Why Not?

• Available Models – EFDC – CH3D

R N iv eu er se Swift Creek Bachelor Creek N 0 W E S Scale 5 km 10 km Trent River Upper Broad Creek Goose Beard Creek Dawson Creek Greens Creek Broad Creek Slocum Creek Hancock Creek Clubfoot Creek Adams Creek South River Pamlico Sound

Neuse Bathymetry depth (m) 6 5.5

5 4.5

4 3.5

3 2.5

2 1.5

1 0.5

What Does th e 3-D Hydrodynamic Model Get You?

How Does this Translate to WASP ?

Introduction to WASP • Model History • Design Concept Generalized Framework Model • Dynamic Water Quality Model

Basic WASP System • WASP Version 6.0

– Data Preprocessor – Project Manager – Data Server – Import/Export Functions • Old WASP Files • MOVEM – Graphical Post Processor – Basic Statistics

Basic WASP System • Model DLL’s – EUTRO.DLL -- Eutrophication Model – TOXI.DLL -- Organic Chemical Model – HEAT.DLL – Full/Equilibrium Heat Balance + Pathogens – MERCURY.DLL – Specialized version of TOXI to handle Mercury

WASP Structure WASP Transport Bookkeeping

EUTRO or TOXI

Kinetics

WASP Terminology

• Advantages – Flexibility • Almost any Waterbody – Most Water Quality Problems • EUTRO/TOXI • Others – Separation of Processes • Transport • Kinetics – Two Solution Techniques • Simple/Quick – Euler • Complex/Flux Limiting - COSMIC WASP • Disadvantages – Does not Handle • Mixing Zone • Floatables/Sinkables

WASP Linkages • Direct Linkages – Hydrodynamic – Non-Point Source Loads • In-Direct Linkages – Spreadsheets – Windows Clipboard

Loading Models •SWMM •HSPF •LSPC •NPSM •PRZM WASP Linkages WASP Hydrodynamic Models •EFDC •DYNHYD •RIVMOD •CE-QUAL-RIV1 •SWMM Transport/Extran Bioaccumulation •FGETS •FCM-2 External •Spreadsheets •ASCII Files •Windows Clipboard

WASP Data Requirements Component Volume Flow Velocity Depth Settling Minimum   Simulated     Described     

Dataset Development • Parameterization • Timestep/Print Interval • Segmentation • Flow • Dispersion • Boundaries • Loads

Dataset Development • Environmental Time Series • Segment Parameters • Constants/Kinetics

WASP is a Variable Complexity Model • Adjust Complexity to Match the Problem – More Complex Aquatic Systems – More Complex Chemical or Interaction – Management Question?

Processes that Control Complexity • Network Spatial Variability • Time Variability • Transport Patterns • Loading Patterns • Chemical Interactions

• WASP Time Scales • Steady • Seasonal • Monthly • Daily/Hourly Time Scale

Input EUTRO TOXI

Overview of WASP6

WASP BMD MOVEM Stored Data

Introduction to WASP Input Data • Control Parameters – Model Type • Eutrophication • Organic Chemicals – Non Point Source Option – Simulation Start/End Date & Time – Hydrodynamic Linkage – Time Step Option – Restart Option

Model Segmentation General Rules

Considerations for Segmentation • Spatial Scale of the Problem – Segment of a River – Whole River – Embayment of Lake/Estuary • Model Limitation – Maximum # of Segments 3000 – Maximum # of Time Pairs 4000

Considerations for Segmentation

Considerations for Segmentation • Temporal Variability of the Inputs – How Often?

– How Much?

Considerations for Segmentation • How Much Averaging?

– Model Assumption:

Considerations for Segmentation • Averaging – Degree to which you want to Reproduce Observed Gradients?

Considerations for Segmentation • Data Availability – How much data is available to define the transport system

General Rules for Segmentation

Segmentation for Advective Systems

Sampling Stations

WASP State Variables System By-Pass Options

System Information • EUTRO – Ammonia – Nitrate – Orthophosphate – Chlorophyll-a – BOD – Organic Nitrogen – Organic Phosphorus • TOXI – Chemical 1 – Chemical 2 – Chemical 3 – Solids 1 – Solids 2 – Solids 3

System By-Pass Options • Three System By-Pass Options – Simulates – Constant – By-Passed

Simulated • WASP recalculates state variable concentration every timestep.

Constant • State Variable is not Re-calculated by concentration is set at Initial Conditions – Model Impacts of Chlorophyll-a without Dynamic Simulation

By-Passed • State Variable is not Re-calculated – No Initial Conditions are Required

Boundary Conditions & Pollutant Loads

What is a Boundary?

Pollutant Loads

Loads

Loading Pathways • Point Source Discharges • Non-Point Source – ASCII File – Created LWWM – Created HSPF – Combine Sewer Overflow – Groundwater

Loading Time Functions

Flows

Surface Flow Options • Type 1 - Water Column Flows Carries both dissolved and particulate material • Type 2 - Pore Water Flow Carries dissolved material only • Type 3,4,5 - Solids Settling/Resuspension • Type 6 - Evaporation/Precipitation Water Only

Surface Flow Options

WASP Transport Scheme • Six Different Flow Fields – Surface Water – Porewater – 3 Solids Transport Fields – Evaporation/Precipition

WASP Transport Scheme • Each Flow field can have multiple flow patterns and time functions.

• WASP sums the individual flows for each segment to determine overall transport

WASP Transport Scheme • Flows in WASP can be – Specified in the input dataset – Read from a hydrodynamic interface file created by another model or program

Examples of Specifying Flows

Simple 1 Segment Pond 0 1

From 0 1 To 1 0 Cont 1 1

5 0 4 5 4 0 3 5 3 0 2 5 2 0 15 10 5 0 0 5 10 15 F lo w

2 Layer Pond

From 0 1 From 0 2

Surface

To 1 0 Cont 1 1

Pore Water

To 2 1 Cont 1 1 From 1

Surface

To 0 Cont 1

0 0 2 1 0

60 40 20 0 0 10 20 Flow 1 Flow 2 Flow 3

Variable Flow

From 0 1 From 0 1

Surface

To 1 0 Cont 1 1

Pore Water

To 1 0 Cont 1 1 From 1

Surface

To 0 Cont 1

0 2 1 0 0

60 40 20 0 0 10 20 Flow 1 Flow 2 Flow 3

From 1 To 2 SA 5000

Solids Deposition 1 2

0.12

0.1

0.08

0.06

0.04

0.02

0 0 5 10 15 Vel

Simple Flow Through River 0 1 2 3 4 5 6 0

From 0 1 2 3 4 5 6 To 1 2 3 4 5 6 0 Cont 1 1 1 1 1 1 1 200 150 100 50 0 0 10 20 Flow

Tributary River 0 1

From 0 1 2 3 4 5 6 From 0 7 4 5 6 To 1 2 3 4 5 6 0 To 7 4 5 6 0 Cont 1 1 1 1 1 1 1 Cont 1 1 1 1 1

2 3 7 4 5 6

200 150 100 50 0 0 10 20

Flow Flow

From 0 1 2 3 4 3 5 6 7 To 1 2 3 4 6 5 6 7 0 Cont 1 1 1 0.4

0.4

0.6

1 1

1 Branched Flow 4 2 3 6 7 5

200 150 100 50 0 0 10 20

Flow

From 0 1 2 3 4 5 To 1 2 3 4 5 0 Cont 1 1 1 1 1 1

Netflow through Estuary 1 2 3 4 5

150 100 50 0 0 10 20 Flow

Stratified Flow 0

From 0 1 2 3 4 5 To 1 2 3 4 5 0 Cont 1 1 1 1 1 1 From 0 8 7 6 3 4 5 7 8 To 8 7 6 3 4 5 0 4 5 Cont 1 0.8

0.4

0.8

1 0.4

0.2

1 2 3 6

150 100 50 0 0

4 7 5 8

10 20

Flow Flow

Hydrodynamic Linkage to WASP DYNHYD Example

Hydrodynamic Linkage • Provides detailed flow, depth, volume and velocities to WASP at every timestep for every segment.

Linkage DYNHYD Junctions overlay WASP segments. The DYNHYD channels provide the flows entering and leaving WASP segments.

DYNHYD Junctions that have boundaries can not be linked to WASP. The channels leaving these Junctions are boundaries for WASP.

Correspondence of Network

Partial Linkage

When to use Hydrodynamic Model • High Gradient Systems • Preserve Travel Time • Where Depth & Velocity calculations are important for reaeration

Other Methods for Altering Velocity and Depth

Altering Depth & Velocity as a function of Flow WASP allows the user to enter exponents and coefficient that will allow for the recalculation of depth and velocity as a function of flow.

depth



a

Q b

Dispersion

Transport

Mixing Processes

Random Walk

Computational Form

Mixing Processes

Diffusion Coefficients

Dispersion in Rivers

Tidally Averaged Dispersion

Determining Dispersion • Streams & Rivers – Generally Neglect Dispersion – Determine by Calibration or Dye Study • Estuaries – Calibration to Salinity data using observed downstream boundary concentration as the forcing function

Determining Dispersion • Lakes – Calibration to Temperature Data – Calibration to Chloride Data

Dye Studies

Dye Study References

Dispersion from Dye Studies

Environmental Time Functions & Segment Parameters

Environmental Time Functions • Vary Conditions over Simulation Period • Multiple Time Functions – Temperature – Light Extinction • Time Functions can have their own intervals

Eutrophication Time Functions • Temperature (4) • Water Velocity (4) • Light • Fraction of Daylight • Wind • Light Extinction (5) • Ammonia & Phosphorus Benthic Flux • Zooplankton • Salinity • Air Temperature • Rearation

TOXI’s Time Functions • Temperature (4) • Water Velocity (4) • pH Water Column & Benthic • Fraction of Daylight • Wind • Air Temperature • Bacteria Population (Water & Benthos) • Air Temperature • Rearation • Chlorophyll-a

Segment Parameters • Varies Environmental Conditions Spatially • Scale Environmental Conditions for Individual Segments.

EUTRO Segment Parameters • Velocity • Temperature • Salinity • Light Extinction • Ammonia & Phosphorus Flux • SOD • Zooplankton

TOXI Segment Parameters • Velocity • Temperature • Rearation • Dissolved Organic Carbon • Fraction Organic Carbon • pH • Bacteria Population

Time Functions & Parameters How They Work Together

Working Together • Segment Parameters can Point to Individual Time Functions – User can specify up to 4 temperature functions.

– User can specify segment temperature by point to 1 of the 4

30 25 20 15 10 5 0 0 5 10 Temp 1 Temp 2

Seg 1 Temperature Function 1 Temperature Scale 1 Temperature Time Series used is 1 Seg 2 Temperature Function 2 Temperature Scale 1 Temperature Time Series used is 21

Introduction to Eutrophication

WASP State Variables • Ammonia • Nitrate • Orthophosphate • Chlorophyll-a • BOD • DO • Organic Nitrogen • Organic Phosphorus

Eutrophication Diagram

Processes Considered • Phytoplankton Kinetics • Phosphorus Cycling • Nitrogen Cycling • Dissolved Oxygen Balance

Levels of Complexity

Dissolved Oxygen -- BOD Interactions

Sources & Sinks

CBOD

Model Parameters for BOD

Sediment Oxygen Demand

Reaeration

Reaeration Coefficients

Modified Streeter-Phelps

Nitrogenous BOD

Modified Streeter-Phelps Input

Temperature Dependency

Linear DO Balance

Linear DO Balance Input

Photosynthesis & Respiration

Measuring Photosynthesis & Respiration

Eutrophication Processes

Phytoplankton Kinetics

Phytoplankton Growth

Light Effects

Light

Light Effect on Phytoplankton

Nutrient Effect Phytoplankton

Nutrient Limitation on Growth

Phytoplankton Death

Ammonia

Ammonia Preference

Nitrogen Cycle

Nitrate

Nitrogen Cycle

Nitrogen Reaction Terms

Phosphorus Cycle

Phosphorus Reaction Terms

DO Balance

DO/BOD Reaction Terms

Sediment Transport

Transport Processes

Implementation in WASP

Solids Flow

Solids Flow Data

Settling & Deposition Velocities

Stokes Settling Velocities

Sediment Initial Conditions

Bed Volume Option 1

Bed Volume Option 2

Organic Chemical Model

Sorption And Equilibrium Partitioning

Sorption • Definition – Movement of chemical between the dissolved phase and particulate or solid phase – The chemical may be physically associated or chemically bound through attachment to functional groups on the surface of the solid.

Important Factors • Characteristics of the Chemical – for neutral organics sorption is related to the hydrophobicity of the solid.

• Characteristics of the Solid – Size (sand, silt, clay) • specific surface area • cation exchange capacity – Organic Carbon Content

Important Factors • Characteristics of the Aqueous Solution – Presence of dissolved & colloidal organics such-as humic acid – pH – Temperature

Implications of Sorption • Microbial degradation rates can be altered • Volatilization is diminished • Direct photolysis is inhibited • Transport is altered

Sorption Assumption • The available models assume the rate of adsorption is much more rapid than any other transport or kinetic process affecting the chemical, so that on the time scale of all other processes sorption appears to be at equilibrium.

• Therefore, kinetics are not considered. Sorption is instantaneously

Adsorption Isotherms

Basic Relationship

Sorption Input Data

Volatilization

Volatilization Options

Volatilization Input

Two Resistance Model

Covar’s Method

Rate Constant Calculation

Biodegradation

Types of Biodegradation • Growth Metabolism – Organic compound serves as a food source – Microbial adaptation time -- 2-50 days • faster for chronic exposure • faster for high microbial population • slower in presence of easily degradable carbon source – Fast first-order rates after adaptation

Types of Biodegradation • Cometabolism – Organic compound not a food source – No adaptation time (often) – Slow degradation rates • “B” unaffected by “C” or • measure “B” on environment using same method (e.g. plate counts) as in lab

Biolysis Transformation Rate

Environmental Influence

Second Order Rate Constant • Specify using time functions – Water Column Bacteria concentration (ml/cell/hr) – Benthic Bacteria concentration (ml/cell/hr)

Input Data for Biodegradation

Representative Population Sizes

Hydrolysis

Hydrolytic Reactions

pH Dependency

Hydrolysis Rate Constant

WASP Hydrolysis Equation

Data for Hydrolysis

Ionization

Weak Acid

Weak Base

Photolysis

Solar Radiation

Photolysis Reaction Basic Equation:

d C d t

 

k pG



C d

Rate constant:

k ai

where: 

k ai



 



I Gk k pG



ki d k

 

 2303 

sunlight absorption rate

quantum yield

m ole



(

)

k ai

86400 / 

m ole

) 

f ij

6 .

022  10 23 

day



I k k

 

irradience by wavelength

decadic m olar absorptivi ty

photons

2  sec

m ole



 ln 10

Light Attenuation

Photolysis

Photolysis Reaction

Photolysis Options

Data for Option 1

Data for Option 2

Introduction to Modeling Rivers and Streams using WASP General Characteristics of Rivers

Characteristics of Rivers and Streams Rivers and streams vary widely in their size, flows and ecological characteristics - They are strongly influenced by the characteristics of their watersheds.

- They range from small ephemeral or intermittent streams, which flow only in response to rainfall, to rivers such as the Mississippi-Missouri system - The running nature of rivers and streams which generally distinguishes them from all other water bodies.

- Rivers and streams are

lotic

(from lotus, meaning washed) systems which are characterized by running water, as opposed to standing water or

lentic

(from lenis, meaning calm) water bodies - Rivers and streams generally flow in a particular direction within a definite channel (the

thalweg

) and ultimately discharge into some other water body.

Characteristics of Rivers and Streams -Current is a major controlling or limiting factor in rivers and streams - The flow often determines the expected variations in water quality -

Cross-sectional mixing is usually rapid in comparison with other waterbodies, so that rivers and streams are often assumed for modeling purposes to be one-dimensional (longitudinal) systems. That is, velocities are assumed to be adequately represented by a mean value.

Factors Distinguishing Modeling Approaches • Flow model complexity – Spatial resolution – Temporal resolution • Water quality model complexity – State variables – Kinetic resolution

Factors Distinguishing Modeling Approaches • Model complexity – Spatial resolution • Usually assume rivers are one-dimensional • Length of river, location and number of segments will vary with application – Temporal resolution

Factors Distinguishing Modeling Approaches • Model complexity – WASP Temporal resolution Condition Flows Water Quality Steady- State Quasi-Steady State Quasi-Steady Sate Dynamic Constant Constant Constant (WASP run in dynamic with constant forcings model until predictions do not vary) Dynamic Time-variable inflows but uniform flows through study area Time Variable Constant or dynamic Time Variable Examples of WASP applications Like traditional WLA analysis (DOSAG, QUAL2) Like QUAL2 analysis with diurnal variations Like running QUAL2 with varying flows Continuous simulations required where have variable inflows, loadings, etc.

Dynamic Analysis • Quasi-steady approach – Run a dynamic model (such as WASP) using steady flows (descriptive flows) • Dynamic Approach – Run a dynamic model with descriptive flows – Predict time-varying flows and quality • Requires coupled hydrodynamic and quality model • Typical approach is to run hydrodynamic model and save output (flows, volumes, depths, velocities) for use by quality model

Dynamic Analysis • Application conditions – When and for how long to apply ?

– Typical applications require continuous simulation (wet and dry weather periods)

Dynamic Analysis • When to run a dynamic analysis?

– When flows are highly variable • Below peaking hydropower facilities • When considering the impact of transient inflows, such as from storm events – When quality is variable over time • Predicting seasonal variations • Predicting impact of storm events or a sequence of dry weather and storm events • When critical conditions are not known (dry before wet, and 1 yr vs a 2 yr storm)

Factors Distinguishing Modeling Approaches • Water Quality Model Complexity – State variables • Simple dissolved oxygen (e.g. Streeter Phelps) • Intermediate eutrophication • Eutrophication • Organic chemicals • Metals – Kinetic resolution • Number and kind of processes included

WASP Data Requirements for Transport • Channel Segmentation • Flows • Channel hydraulic characteristics – Depths – Velocities • Mixing coefficients

WASP Channel Segmentation • How valid is one dimensional assumption – Is there stratification?

– Are their lateral variations?

• ex. a considerable distance may be required for complete lateral mixing downstream of a discharge

WASP Channel Segmentation • How long a reach of river must be simulated?

• Example if a material decays at a first order rate of 0.2/day, then the time for 90 percent of the material to decompose is 11.5 days. If the river has a mean velocity of 1 ft/s, then a parcel of water could travel 188 miles in that time.

WASP Channel Segmentation – Are their lateral variations ?

• Example, for a discharge into the side of a channel, the distance to downstream complete mixing can be estimated from:

L m = 0.4

u W D t 2 D t = c Y u * u * 2 = gY S o

example: if u = 0.5 m/s, Y = 2.5 m, W = 90 m, and S o 12.6 km = 0.0003, then L m = u = channel velocity u* = shear velocity W = top width D t = transverse mixing coefficient g = gravitational acceleration, Y = depth S o = channel slope c = coefficient (approximately 0.6)

WASP Channel Segmentation • How much resolution (how many segments) are required ?

– Consequences of too little resolution • Gradients not adequately characterized • Increased numerical dilution (assumption that a segment is completely mixed) – Consequences of too much resolution • Simulation times increased (controlled in part by travel time through smallest segment)

Specification of Flows to WASP • Descriptive Approach – Based upon measured data – examples include flow measurements and time of travel estimates • Predictive Approach – Simple Hydrologic Stream Routing – Steady, Uniform Flow Methods – Hydraulic methods for steady, non-uniform flow – Hydraulic methods for unsteady flows

Measurement of Velocities and Flow • Float methods • Current meters – Mechanical – Acoustic – Electromagnetic • Control structures • Dyes and tracers • Remote sensing

Flow, Depth, Velocity Correlations • In addition to flow, WASP requires estimates of depth and velocity • These hydraulic characteristics affect processes such as reaeration and light penetration • May be specified (descriptive approach) or obtained from hydrodynamic model predictions

Empirical Relationships (descriptive approach only)

Y = a Q b u = c Q d W = e Q f

where Q is flow, velocity u, depth Y, width W and a-f are empirical coefficients

So that Empirical Relationships

a c e = 1 b + d + f = 1

Empirical Relationships Channel Cross-Section Rectangular Exponent for Velocity (b) .40 Average of 158 USGS Gaging Stations Average of 10 Gaging Stations on Rhine River Ephemeral Streams in Semiarid US .43 .43 .34 Exponent for Depth (d) .60 .45 .41 .36 Exponent for Width (f) 0.00 .12 .13 .29 Source: WASP Manual (Ambrose, Wool and Martin 1993)

Time of Travel and Dye studies • Purpose of dye studies • Time of travel • Dispersion and mixing • Lagrangian Sampling • Dilution in reaeration measurements • Circulation and stratification • Determining discharge in streams • Groundwater movement • Mass balance studies • Source (discharge) investigations

Slug Dye Release Source: Martin and McCutcheon 1998

Continuous Release Source: EPA EWLA Workshop

C Dye Studies: Flow measurements



W dye C



Q dye C dye C stream

Continuous (steady-state) conditions Centroid of Dye Cloud Distance Length Velocity=Length/Travel Time

Introduction to Modeling Lakes and Reservoirs using WASP General Characteristics of Lakes and Reservoirs

General Characteristics • Lakes and reservoirs are

lentic

(from lenis, meaning calm) systems, characterized by standing water.

• The impacts of the standing nature of lakes and reservoirs include : – Velocities are much lower than in rivers and streams so that water quality constituents and contaminants are moved slowly.

– Wind mixing and solar heating dominant gravity-driven flow. – Water is stored for relatively long periods of time – The increased storage or residence time allows for internal cycling and matter originating within the lake or reservoir (

autochthonous

materials) to have an increased importance relative to materials originating outside and carried in to the lake or reservoir (

allochthonous

materials).

General Characteristics • Lakes and reservoirs are generally much deeper than streams and rivers – Light does not penetrate to the bottom of many lakes and reservoirs so that heat exchange and productivity is limited to surface layers.

– Stratification retards vertical mixing during periods of the year and large vertical gradients in temperature, density, and water quality often result.

Factors Distinguishing Lakes and Reservoirs • Reservoirs much more common in the south than natural lakes • Reservoirs are mainly formed by damming a steep sided valley with a concrete structure, like Hoover Dam, or an earthen embankment.

• Reservoirs differ primarily from lakes in that their out-flows and volumes are regulated to achieve a beneficial use. The degree of regulation, and the manner in which the reservoirs are operated has a large influence on transport and mixing patterns within the reservoir and, consequently, the water quality within the reservoir and of its releases

Hydropower Facilities • Hydropower releases – Many dams built for hydropower are constructed in areas where steep slopes allow sufficient head drop to generate electricity.

» Base load hydropower: constant or unregulated flows » Peaking operations, where the reservoir stores water for release when electrical power demands are greatest, such as in the morning or evening.

Reservoirs: Storage Areas • Useful storage: reservoirs authorized for a variety of uses. Some uses often result in conflict, particular for what were considered secondary uses (recreation, fisheries management, water quality enhancement).

Reservoirs: Storage Areas • The storage may be used for: – Flood control and mitigation – Water supply – Hydropower – Navigation – Recreation – Water quality enhancement – Fisheries management

Processes Impacting Water Quality Physical Processes: • Lake Morphometry • Stratification • Inflow and Outflow Mixing

Lake Morphometry • Shapes: – Artificial impoundments almost always made by damming a river and tend to be dendritic and elongated – Lakes tend to be less elongated and more round • Size – Important factors are volumes (affecting residence time), depth, and interfacial areas

Heat and DO Exchange Water Surface wind

Epilimnion

•Warm, complete mixing •Abundant DO •Productive

Metalimnion Hypolimnion

•Cold, complete mixing •DO low or absent •increased reduced materials (Fe, Mn, metals) Sediments: region of sorption and release

Source: EPA Workshop notes

Mixing Processes • Mixing may be due to – The mixing energy that results from inflows, – The mixing energy from outflows or withdrawals, and – The transfer of energy across the air-water interface due to wind and other meteorological conditions • The relative importance of the mixing processes may vary widely along the length of a reservoir as well as with depth

Source: Martin and McCutcheon 1998

Lacustrine Zone of Transition Riverine

Outflow mixing processes • Outflow mixing affected by – Location, size and characteristics of outflow port – Magnitude of withdrawal – Stratification Source: Martin and McCutcheon 1998

Water Balance for a Lake or Reservoir Computed from a mass balance for water where S is storage

Components of the Water Balance • Storage – The actual volume of water in the lake or reservoir at any given time – Not measured directly but is inferred from lake stage and bathymetry measurements, reduced to a relationship between lake stage and storage – Sources of error • Errors in measurements of stage • Month to month temperature changes increase or decrease the density of water • Measurements of bathymetry are inexact or may be out of date

Components of the Water Balance • Inflows – Usually obtained from USGS or other gaging stations – Sources of error • Error in gage measurements • Ungaged areas below station • Ungaged tributaries • Non-point source (distributed inflows)

Components of the Water Balance • Outflows – usually measured at control structure – Sources of error • Seepage or leakage flows through turbines may be large • Some flows may be ungaged

Components of the Water Balance • Direct precipitation onto lakes surface – Measured using standard rain gage and converted to flow by surface area – Sources of error • Localized nature of rain

Components of the Water Balance • Evaporation – Usually measured using the standard Class A pan or computed from energy balance – Sources of error • Errors in pan measurement • Transpiration

Components of the Water Balance • Ground water seepage and infiltration – Usually estimated by difference in the water balance but may be estimated from ground water models or seepage meters – Sources of error • Difficult to measure • Cumulative errors in other terms of water balance if estimated by difference

Components of the Water Balance • Methodology for typical application – Obtain records of outflows and estimates of seepage losses – Obtain records of water surface elevations – Obtain storage capacity curve for reservoir – Estimate all inflows and losses (gaged and ungaged inflows, precipitation, evaporation, groundwater infiltration/seepage)

Components of Water Balance • Methodology (continued) – Estimate total inflows from stage, discharge, and storage capacity curve • From stage and storage capacity curve, estimate storage • From mass balance equation, compute inflows

Components of Water Balance • Methodology (cont) – Example for storage induction method (using averages of values at time 1 and time 2 (time 1 +  t) – Since S (storage) and O (outflow) are known, can solve for inflow (I)

2  

t S

1   

( I 2 + I 1 ) 2



+ O

2 )

 

Components of Water Balance • Methodology (continued) – Once the total inflow is known, it can be compared to the inflow computed from all sources – Errors can be corrected by additional studies or field measurement

Components of Water Balance • For water quality modeling, concentrations for all constituents modeled must be determined for each inflow source

Example of a Whole Lake Model

 

Q in

 

Q out dt

water balance

dVC

 

Q in C in

 

Q out C

 

k i VC

constituent mass balance

Whole Lake Models • Have been widely used in modeling eutrophication and toxics • Example: Lake Ontario has been modeled using this approach – Overall average assumption is that it is completely mixed

Example of a Two-layer Lake Model water balance

dV e dt

 

Q in

 

Q out

constituent mass balance epilimnion hypolimnion

dV e C e dt

 

Q in C in

 

Q out C e

 

k i V e C e



E z A



C h L



C e



dV h C h dt

  

k i V h C h



E z A L



C e



C h

 epilimnion hypolimnion

Two Layer Model (or Greater Segmentation) • Have to determine – Volumes and shapes for individual layers – Where the inflows go – Where the outflows come from • Note in the previous slide we assumed all the inflows and outflows were confined to the epilimnion (not necessarily a good assumption, see inflow mixing) – Vertical exchange coefficient

Inflow Placement • Often estimated from density alone • Plume methods available to compute whether an overflow, underflow, or interflow (see Martin and McCutcheon 1998)

Outflow Envelope • Estimated from density pattern • Estimated using models such as SELECT (from USACOE WES) – SELECT is incorporated into WES’s reservoir models (CE-QUAL R1 and CE-QUAL-W2) – Can also be run as stand alone program • Requires structure of port • Outflow rates and thermal profile (and constituent profile) • Estimates withdrawal locations, temperatures and concentrations of other materials in outflows

Estimation of Vertical Exchange Rate • May be estimated from seasonal changes in temperatures of the hypolimnion • May be estimated by model calibration

Estimation of Vertical Exchange Rate • May be estimated from empirical equations

E z E z,0 = E f(S) z,0 = c u * f(S) = (1 +

 where

MA R i )



MA u * = C d

 

a u 2 w R i = g

   



z 2



   



z 2

Estimation of Vertical Exchange Rate • Or, in other words – There is a normal rate of vertical exchange (E z,o ) that occurs in the absence of stratification – That rate is reduced by stratification or the stability of the stratification [f(s)] – The stability can be estimated from the ratio of the buoyancy of the system (density differences) that oppose the mixing to the force (due to wind) that would cause mixing (the R i or Richardson number)

Lakes: Modeling Approaches • Steady-state models (rarely used) • Dynamic analysis (usually required) – Whole lake models – Segmentation using box modeling approach – One-dimensional (vertical) models – Two-dimensional (longitudinal-vertical) models – Three dimensional models

Examples of Available Models • Box type models – WASP (US EPA) – BETTER (TVA) – CE-QUAL-ICM (US COE WES) • One-dimensional (vertical) models – CE-QUAL-R1 (US COE WES) • Two-dimensional (longitudinal-vertical) – -CE-QUAL-W2 (US COE WES) • Three dimensional (???)

Introduction to Modeling Estuaries using WASP General Characteristics of Estuaries

Source: EPA 1987 EWLA Workshop

Processes Impacting Transport • Tides – Often dominate mixing in estuaries – Produced principally by interaction of the gravitational fields of the earth, moon, sun and, to a lesser degree, other solar system bodies.

Processes Impacting Transport • The movement of the moon causes the principal effects to occur with a roughly 12.4-hour period. That is due to the time of the rotation of the moon with respect to the earth being, on average, 24.8 solar hours long (or 1.035 times as long as the mean solar day).

Processes Impacting Transport • Tides – Tides are expressed in terms of •

Amplitude:

level, and the variation of water level about some datum •

Tidal current:

the ebb and flood velocity fields

Processes Impacting Transport – Tidal amplitudes and currents are usually out of phase so the time of high water is not the same as the time of high water slack. Such differences in phase and interaction between main and side channels can lead to tidal trapping of parcels of water in side channels or embayments.

Processes Impacting Transport • Tidal amplitude – Tidal curve: plot of height of the water surface of a system that is subject to tidal action • Generally, two high and two low tides on the tidal curve per

tidal day

(or

lunar day

, about 24.84 hours).

Processes Impacting Transport – Period corresponds to the time between successive passes of the moon over any point on the earth.

» Tidal period: time between low and high tides is known as the

tidal period

Processes Impacting Transport • Tidal amplitude • Semidurnal tides: tides that occur twice during a tidal day are called

semidiurnal

tides • Daily tides: have only one high and one low per day, such as in some area such as estuaries in the Gulf of Mexico

Processes Impacting Transport • Mixed tides: magnitude of high and low tides are quite different (e.g. Pacific estuaries)

Processes Impacting Transport • Tidal amplitude – Solar effects occur at 12 hours rather than 12.4 hour periods (the mean

solar day

is 24 hours).

– Because all the bodies in the solar system are in motion relative to one another, the effects of their gravitational fields vary in time. Therefore, tides may vary over longer periods such as days, weeks or years.

Processes Impacting Transport • •

Spring tides

occur approximately every two weeks, usually within a few days of the times that the moon is full or new and the tidal range is larger than the mean tidal variations. During this period the sun and the moon act together, causing greater tidal variations.

Neap Tides

moon.

: occur during the first and third quarters of the

Tidal Amplitudes: San Francisco Harbor 150 100 50 0 -50 -100 -150 0 200 400 600 Time (hours) 800 1000 1200

150 100 50 Seattle, WA Pensacola, FL 0 0 -50 100 200 300 400 500 600 700 800 -100 -150

Time (hrs)

Processes Impacting Transport • Tidal Amplitude – Sources of information • NOAA • Stage recorders

Processes Impacting Transport • Tidal currents – Horizontal water movements associated with the rising and falling tides • Typically weak in the open sea, with velocities on the order of 5-10 cm s -1 • Highly variable in estuaries

Processes Impacting Transport – Progressive wave • Flood current: occurs as the wave crest moves into an estuary, culminating in high tide • Ebb current: occurs when the wave crest moves out of the estuary, culminating in low water or low tide • Slack water: occurs Each time the water changes directions where there is a period of no net current

Processes Impacting Transport • Tidal currents – Standing wave: occurs in many estuaries when the tidal wave reaches the upper part of the estuary and is reflected back • Progressive wave: maximum tidal amplitude and velocities occur at the same time

Processes Impacting Transport • Standing wave: tidal amplitude and velocities are out of phase • Most estuaries have characteristics in between the standing and progressive waves

Source: Martin and McCutcheon 1998

Source: EPA 1987 EWLA Workshop

Processes Impacting Transport • Tidal currents – Tidal excursion: distance along the main axis of the estuary that the particle will transverse over the course of the tidal cycle • Important in selecting size of system to be modeled (has to at least include tidal excursion) • Important in selecting boundaries

Processes Impacting Transport – May be estimated from (for the principal M 2 Thomann and Mueller (1987) tidal component,

Processes Impacting Transport • Tidal currents – Tidal excursion distance may be estimated from (for the principal M 2 tidal component, Thomann and Mueller (1987)

x te =



2 u

max

T 2 m2

where x te is the length of the tidal excursion, u max maximum tidal velocity, and T m2 the average the period of the M 2 tide (12.42 hours).

Processes Impacting Transport • Coriolis force: • Apparent force due to the earth’s rotation. In the Northern Hemisphere, the impact is to deflect the flow to the right side, looking seaward, of the estuary

Processes Impacting Transport • Inflows – Determine characteristic chemical gradients in estuaries; affect mixing; affect duration of flood and slack currents • Meteorological effects – Wind: effects wave formation, mixing,and may cause surface currents.

Source: Martin and McCutcheon 1998

Processes Impacting Transport • Estuarine Morphometry – Affects circulation patterns • May cause residual circulation, such as tidal pumping (in analogy to using pipes and pumps to move water around and estuary) • May also cause tidal trapping (like the trapping of particles in embayments during one phase of the tidal cycle)

Water Quality Processes • Toxicity – e.g. ammonia toxicity affected by salinity • Solids – Fall velocities, flocculation, etc. impacted by salinity and salinity gradients • Nutrients and eutrophication – Although different organisms, etc., the methods used for predicting eutrophication are similar to those used for lakes and reservoirs

Factors Affecting Water Quality • Salinity – Affects water density – Affects concentration of dissolved gases

Comparison of Water Density vs. Salinity

1018 1013 1008 1003 998 993 0 5 10 15 20

Temperature (degrees C)

25 30 35 0 ppt 5 ppt 10 ppt 15 ppt 20 ppt 25 ppt

Source: EPA 1987 EWLA Workshop

Modeling Approaches Using WASP • Tidally-averaged model – Flows and tidal mixing affects described (rather than predicted) – Based on averaged effect of tides over multiple tidal cycles

Modeling Approaches Using WASP • Inter-tidal model – Predictions required within tidal cycles – Requires use of hydrodynamic model used to predict variations in flows, volumes, depths, and velocities which are then specified to WASP

Estuaries: Modeling Approaches using WASP • Tidally averaged models – Assumption: the volume of the estuary, on average, remains constant • River flow coming into the estuary travels out over averaging period (can be steady or time varying)

Estuaries: Modeling Approaches using WASP • The tidally flow coming in to the estuary during the flood tide goes back out (steady-tidal mixing)

Tidally Averaged Estuary Modeling • Vertically well mixed estuaries – Since the tidal flow in equals the tidal flow out, the impact of the tidal flow can be described using a dispersion or tidal mixing coefficient Q R C R +Q T C o -Q T C= Q R C Q T (C o -C)=EA/L(C o -C)

Tidally Averaged Model • Freshwater flow: – Obtain from gaged flows – Estimate ungaged flows – Include other water (and loading source such as point and non-point) sources – Route through estuary

Tidally Averaged Model • Tidal Dispersion coefficient – Estimate from similar estuaries or literature – Estimate from concentrations of • Dye • Salinity

Estimating Tidal Dispersion Coefficient Example: analytical equation for a conservative material



0 exp

Ux E

which can be solved for E between two points, given, for example, measured salinities



ln  (

2 / 

1  )

3.5

3 2.5

2 1.5

1 U=3.28 mi/day 0.5

0 -14 -12 -10 -8

 3 .

28 ln    1 .

10 8 /  (  2 ) 18 .

1 

x coordinate

  11 .

4 -6 -4

2 /

day

-2 0

Dispersion Coefficients from Dye Tracers Estimate using analytic solution to time variable spread of dye



A M

2  2

exp     1 2  

Ut Et

  2    time =1 time =2 Distance

Tidally Averaged Estuary Modeling • Stratified estuaries – Steady flows • Use simplified methods such as Pritchard’s method to back compute flows from salinity distribution (see Martin and McCutcheon 1998) • Requires average salinity for each “box” in model

Tidally Averaged Estuary Modeling – Unsteady flows • Typically requires inter-tidal model for hydrodynamics • Tidally average inter-tidal predictions (as in Chesapeake Bay study)

Sampling for Tidally Averaged Predictions • Question, when do you sample to determine the “average” condition since you are trying to “hit a moving target” • One alternative is to – Sample over the tidal cycle – Average results

Sampling for Tidally Averaged Predictions • A second alternative is sampling a particular point in the tidal cycle – Commonly take sample at slack-tide – Slack-tide is when the flow goes to zero at the point when the tide reverses direction • This point moves up or down the estuary

Sampling for Tidally Averaged Predictions • Should be measured synoptically, requiring – A fast boat (typically moves at about 20 m/hr), or – Multiple boats, equipment, etc.

Modeling Approaches Tidal Models of Estuaries

Intertidal Models • Used to predict variations within as well as between tidal cycles • Typically requires application of – Hydrodynamic model – Water quality model such as WASP

Example of Available Models • Examples of One-Dimensional Hydrodynamic Models • DYNHYD (USEPA) • RIVMOD (USEPA) • UNET (USACE HEC) • RIV1 (USACE WES)

Example of Available Models • Examples of Two-Dimensional Hydrodynamic Models (XY) • TABS-MD and RMA2 (USACE WES) • WIFM (USACE WES) • FESWMS (USGS)

Example of Available Models • Example of a Two-Dimensional Hydrodynamic and Quality Model (XZ) • CE-QUAL-W2 (USACE WES)

Example of Available Models • Examples of Three Dimensional Hydrodynamic Models • CH3D (USACE WES) • EFDC (Tetra Tech) • BFHYDRO (ASA) • GLVHHT (Edinger and Associates) • TIDE3D (USGS)

Introduction to Modeling Toxicity and Pathogens

Ammonia and toxicity • Sources: – About three-fourths of the ammonia produced in the United States is used in fertilizers either as the compound itself or as ammonium salts such as sulfate and nitrate.

– Large quantities of ammonia are used in the production of nitric acid, urea and nitrogen compounds. – It is used in the production of ice and in refrigerating plants.

– "Household ammonia" is an aqueous solution of ammonia. It is used to remove carbonate from hard water.

– Since ammonia is a decomposition product from urea and protein, it is found in domestic wastewater.

– Aquatic life and fish also contribute to ammonia levels in a stream.

Ammonia and toxicity • Impacts – NH3 is the principal form of toxic ammonia.

– It has been reported toxic to fresh water organisms at concentrations ranging from 0.53 to 22.8 mg/L.

• Toxic levels are both pH and temperature dependent. Toxicity increases as pH increases and as temperature increases.

• Plants are more tolerant of ammonia than animals, and invertebrates are more tolerant than fish. Hatching and growth rates of fishes may be affected. In the structural development, changes in tissues of gills, liver, and kidneys may also occur.

• Toxic concentrations of ammonia in humans may cause loss of equilibrium, convulsions, coma, and death.

Toxicity Reduction Procedures for State of Mississippi • 1) A detailed review of the permit application and any historical bioassay data and the use of specific screening procedures.

– To identify the universe of those facilities which have discharges which are potentially toxic instream. – To determine whether the data in an application has been submitted in strict adherence with EPA accepted analytical procedures with all of the appropriate parameters reported.

Toxicity Reduction Procedures for State of Mississippi • 2) The development of permit limits in accordance with accepted state and national water quality criteria for those facilities exhibiting potential toxicity. Permit limits may take the form of chemical specific and/or whole effluent toxicity based limits.

• 3) Additional testing and actual toxicity reduction for those facilities which fail any whole effluent toxicity requirements included in their permits. Permits addressing whole effluent toxicity have specific language requiring the permittee to perform a Toxicity Reduction Evaluation (TRE) upon non compliance with the whole effluent toxicity limitations contained in the permit.

Ammonia Equilibrium Reaction



 4 

3 

 - The toxicity of aqueous ammonia to aquatic organisms is primarily attributable to the unionized form - The percent unionized ammonia can be calculated from %

UIA

 100    1   [

1  ] /

K a

    Where K a is a function of pH and temperature

K a

 Ammonia 

 4    and

pK a



0 .

09018



2729 .

92

T a

Where T a is the absolute temperature ( o K)

100 10 1 0.1

0.01

0.001

0 5 10 15 20 25

Temperature (oC)

30 35 40 45 pH = 6 pH = 7 pH = 8 pH = 9

Ammonia Toxicity • Ammonia nitrogen toxicity criterion (ANTC) shall be applied as follows: – (1) Minor Municipal and Minor Industrial Dischargers • (a) If application of the ANTC indicates a limit greater than 1 mg/l but less than 2 mg/l, the permit limit will be 2 mg/l and no effluent biomonitoring will be required.

Ammonia Toxicity • Ammonia nitrogen toxicity criterion (ANTC) shall be applied as follows: – (1) Minor Municipal and Minor Industrial Dischargers • (b) If application of the ANTC indicates a limit less than 1 mg/l, the permit limit will be 2 mg/l, with a requirement for effluent biomonitoring. If existing effluent biomonitoring indicate no effluent toxicity, the permit will not require effluent biomonitoring.

Ammonia Toxicity • (2) Major Municipal and Major Industrial Dischargers – (a) If application of the ANTC indicates a limit less than 2 mg/l, the permit limit will be 2 mg/l, with a requirement for effluent biomonitoring. Effluent biomonitoring will not be required if existing data indicate that the discharge is not toxic.

– (b) If any biomonitoring data indicate adverse impact due to ammonia toxicity, a permit will contain a limit for ammonia nitrogen protective of water quality.

Bacteria and Pathogens • Indicator organisms – Total coliform (TC): exist in polluted and unpolluted solids and occur in feces of warm-blooded animals (E. coli is a common member of this group) – Fecal coliform (FC): a subset of TC that come from intestines of warm blooded animals – Fecal streptococci (FS): include several varieties of streptococci that come from humans and domesticated animals

Modeling Approaches • Factors affecting – temperature – salinity – settling – solar radiation – base mortality

Estimation of loss rates Mortality Light Settling

K b

K bi K bS

   ( 0 .

8  0 .

006

P S



k e F P I o H v S H

( 1 



k e H

) 1 .

 20 ) where P S k e is the fraction sea water, T temperature, the light extinction coefficient, I o  a proportionality constant, the surface light intensity, H depth, F p the fraction attached, and v S a settling velocity. Note that the first equation assumes a fresh water mortality rate of 0.8/day at 20 o C.

Water Quality Modeling and TMDL Development: The WASP Model

Transcript Water Quality Modeling and TMDL Development: The WASP Model

depth

a

0 .

09018

2729 .

92

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