Estuarine

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Estuarine Coastal Modelling Course
MODULE IV SIMPLE MODELS
Michael Hartnett, Environmental Change Institute,
NUI Galway
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SIMPLE MODELS Objectives- To review simple
modelling techniques and their applications.
These are useful tools to help understand the
waterbody and to help assess more complex models.
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SIMPLE MODELS CONTENT- I Concepts
definitions II Dilution III Mass
balance IV Salinity analysis V Flushing/residenc
e times
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I CONCEPTS DEFINITIONS
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I CONCEPTS DEFINITIONS MODELS
Tools we use to try to reliably predict
consequences of various actions. Models use
mathematics to represent reality and provide us
with estimates of likely results In particular
here, we develop models to predict impacts of
loads on water quality. e.g. if we increase N
load by 100kg per month what will the
concentration of phytoplankton be?
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I CONCEPTS DEFINITIONS
Concentration C mass per unit volume e.g.
mg/l Note Concentration (M/V) x flow
rate (V/T) mass/rate (M/T) Dilution S
volume of a sample / volume of effluent in
sample p 1/S relative concentration
p 1 gt 0 pure water Flux Material mass
passing a unit area in unit time
Example Sample volume 1000l Effluent volume
50ml S 1000/50 20 i.e. achieved 20 dilutions
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I CONCEPTS DEFINITIONS

• Steady or unsteady
• Steady state implies that the variables within
  the system and the
• boundary conditions do not change with respect
  to time
• eg rivers may be at steady state for periods
• Unsteady implies that variables change with
  respect to time.
• eg estuaries usually not at steady state
  semi-diurnal tide

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I CONCEPTS DEFINITIONS
Assimilative capacity depends on mixing and
dilution Estuary Large volume and
well-mixed - Small volume and poorly
mixed Thus water quality impacts are due to a
combination of the pollutant loads and the
characteristics of the waterbody
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II DILUTION
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II DILUTION

• Near/far field problems different
  rates/expectations
• Diffuser designed to achieve rapid initial
  dilution O(100)
• Within hours further dilution of O(5-10)
• Local currents major influence

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II DILUTION

• Dilution Example
• Consider an effluent with BOD 350mg/l
• Downstream BOD 2mg/l
• Obtained 350/2 175 dilutions
• Often dictates near field designs

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III MASS BALANCE
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III MASS BALANCE

• Most models based on three fundamental laws of
  physics
• Conservation of energy
• Conservation of momentum
• Conservation of mass
• Mass can be neither created nor destroyed, but
  merely transferred or transformed

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III MASS BALANCE
Mass entering a system Change of mass in
system mass leaving Mass in mass out
change in mass in system
M_in
M_out
River system
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III MASS BALANCE
Application of mass balance (steady state) Point
A River Qr 10m3/s Cr
3mg/l BOD Discharge Qd 0.5m3/s Cd
300mg/l Find BOD concentration in river at
B QB x CB Qr x Cr QA x
CA or CB Qr x Cr QA x CA
QB
17.1mg/l
Steady state conditions
Q flow rate C BOD
concentration
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III MASS BALANCE

• Used for preliminary assessment
• Rivers with multiple discharges and tributaries
• Linear simple estuaries
• Initial near field dilution

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III MASS BALANCE

• Zero dimension models
• Assumes all mass is uniformly mixed in the
  entire water volume
• Completely stirred tank reactor (CSTR)
• Simple example
• Cork Harbour Volume (V) 283x106 m3
• Monthly input of Mg (M) 100kg
• Average concentration M/V
• 0.35mg/l

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IV SALINITY ANALYSIS
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IV SALINITY ANALYSIS

• From measurements of salinity distributions about
  an estuary
• Tidal exchange ratios
• Approximate pollutant concentrations
• Initial water quality conditions (initial
  grids)
• Dilutions
• Flushing/assimilative capacity
• Dispersion coefficients
• Stratification

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IV SALINITY ANALYSIS
Tidal exchange ratio (R) ratio of new ocean
water to total water volume
entering during flood tide. Larger R gt
better dilution and mixing
So
Vf
Sf
Vr
Se
R (Sf Se)/(So-Se)
OR R Se/(So-Se)/(Vr/Vf)
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IV SALINITY ANALYSIS
Given a waste discharge - predict
upstream/downstream concentration!

• Use distribution of ambient salinity as a guide
• At outfall assume ocean water is undiluted,
  mixes with effluent and tributary waters and
  returns to sea

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IV SALINITY ANALYSIS
Dilution discharge -

• From salt mass balance
• QoSo (QoQeQf)S
• Qo (QeQf)S/(So-S)
• Total flow for effluent dilution
• Qd QoQeQf
• (QeQf)So/(So-S)
• ? Mean effluent conc. near outfall
• Cd M/Qd

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IV SALINITY ANALYSIS

• Example Dilution discharge (Part A)
• An industrial plant discharges 0.5m3/s of
  effluent containing 5mg/l of a toxic chemical.
  The minimum tributary inflow upstream is 10m3/s.
  
• Salinity measurements at the discharge point and
  in the open coastal waters are 19ppt and 33ppt
  respectively.
• Estimate the average concentration of the toxic
  substance in the vicinity of the discharge.
• Solution
• Compute dilution discharge Qd
  (QeQf)So/(So-S)
• (0.5 10) x 33 / (33 19)
• 24.75m3/s
• Compute mean concentration C M/Qd
• 5 x 0.5 / 24.75
• 0.1mg/l

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IV SALINITY ANALYSIS
Upstream / downstream concentrations (Conservative
material) Upstream pollutant diluted similar
to salinity dilution
SEA
So
SALINITY
Concentration upstream at X Cx Cd(Sx/Sd)
Sd
Sx

Discharge point - d
X
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IV SALINITY ANALYSIS
Upstream / downstream concentrations (Conservative
material) Downstream pollutant diluted
similar to freshwater
Freshness (So Sx)/So 0 -gt 1
SEA
So
SALINITY
Freshness
(So Sx)
(So Sd)

Concentration downstream at X Cx
Cd(So-Sx)/(So-Sd)
Discharge point - d
X
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IV SALINITY ANALYSIS

• Example Dilution discharge (Part B)
• Same conditions as Part A
• Salinity measurements a) point downstream of
  outfall 24ppt
• b) point upstream of outfall 5ppt
• Estimate the average concentrations of the toxic
  substance at these two points
• Solution
• Downstream concentration C 0.1 x
  (33-24)/(33-19)
• 0.064mg/l
• Upstream concentration C 0.1 x 5 /
  9
• 0.056mg/l

SEA
0.1 mg/l
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IV SALINITY ANALYSIS
Initial water quality grids WQ measurements
Orthophosphate
Salinity
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IV SALINITY ANALYSIS
Initial water quality grids as functions of
salinity
Cork Harbour BOD (mg/l) 3.17 - 0.0762 (SAL)
TN(mg/l N) 5.36 - 0.145 (SAL) TAN(mg/l N)
0.335 - 0.00742 (SAL) TON(mg/l N) 4.41 -
0.127 (SAL) DO(mg/l) 10.67 0.202 (SAL)
0.00524 (SAL)2 TP (mg/l P) 0.173 - 0.00375
(SAL) SRP (mg/l P) 0.0992 - 0.00214 (SAL)
CHL (mg/m3) 2.311
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V FLUSHING/RESIDENCE TIMES
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V FLUSHING/RESIDENCE TIMES

• Significance?
• Flushing/residence times are used to gain
  understandings of how quickly, on average,
  estuaries flush or retain material.
• Particularly useful in making intercomparisons
  between estuaries
• Can relate residence times to algal growth very
  useful for WQ
• Need experience in assessing the values
  calculated
• e.g. is a 10day flushing time short or long?

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V FLUSHING/RESIDENCE TIMES
Intercomparisons-
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V FLUSHING/RESIDENCE TIMES

• Flushing Characteristics
• Flushing Time
• Flushing Rate
• Average Residence Time
• Turn-over Time
• Age
• Transit Time
• Estuarine Residence Time and Pulse Residence Time
  
• Exchange Per Tidal Cycle Coefficient and Flushing
  Ratio
• Flushing Efficiency

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V FLUSHING/RESIDENCE TIMES
Existing Methodologies
Tidal Prism Method
Modified Tidal Prism Method Box Models
Pritchards Tidal
Prism Model Officers Box Models
Dyer / Taylors Estuary Segmentation
Robinsons Tidal Prism Model Salt
Budget Methods Fraction of Fresh Water Method
Knudsens Hydrographical Theorem Mixed
and New Water Concept Return Flow
Factor Model Jet Sink Circulation
Conservative Dye Decay Studies
Theory of a Mixing Length
Physical Scale Models
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V FLUSHING/RESIDENCE TIMES

• Different types and definitions
• a) Flushing time
• Time to replace freshwater volume (Vf) within an
  estuary at the rate of the net flow through the
  estuary (R)
• Tf Vf/R
• Requires much observational data to calculate
  Vf
• Tidal prism method easier to compute
• Tf TxV/(Vt Vr)
• Predicts the lower limit of Tf

Definitions T tidal period V estuary vol Vt
flood tide vol Vr river vol
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V FLUSHING/RESIDENCE TIMES

• b) Residence time
• The average age of a given water particle in an
  estuary
• Similar concept to Turnover time
• The time required to remove 63 of water in an
  estuary
• More difficult to calculate than Flushing time
• Requires models to compute accurately

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V FLUSHING/RESIDENCE TIMES

• Flushing efficiency
• Exchange per tidal cycle coefficient (E)
• fraction of water which is removed and
  replaced with ambient
• water during each tidal cycle
• Tidal Prism Ratio

• Flushing efficiency

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V FLUSHING/RESIDENCE TIMES
Consider Dublin Bay well flushed
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V FLUSHING/RESIDENCE TIMES
Ebb tide currents Flood tide currents Flushing
on both stages of tide
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V FLUSHING/RESIDENCE TIMES
Residual currents Net current over a tidal cycle
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V FLUSHING/RESIDENCE TIMES
Decay curves Dublin Bay

• Dublin Bay initially completely
• mixed with dye
• Allow tides/river/wind to mix
• and transport dye
• Dye is flushed out over time
• e.g. Irish Sea A B

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V FLUSHING/RESIDENCE TIMES
Decay curves Killary Harbour

• Similar shape to Dublin Bay
• However curve not as steep
• Flushing much slower
• cf Cn/Co 0.1
• Dublin Bay 5-6 tides
• Killary Harbour 250 tides

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V FLUSHING/RESIDENCE TIMES
Effect of tidal ranges Dublin Bay

• When comparing residence times must compare
  like with like
• e.g. spring tide with spring tide

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V FLUSHING/RESIDENCE TIMES
Galway Bay Residual Currents

• Currents smaller than
• Dublin Bay
• Particularly in inner part
• Poor flushing

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V FLUSHING/RESIDENCE TIMES
Galway Bay Corrib River annual flows

• Major seasonal variations
• Factor of 5
• Significant effect on
• inner bay

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V FLUSHING/RESIDENCE TIMES
Effects of river flows Galway Bay

• Significant variations
• Seasonal residence times
• Improved winter flushing

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V FLUSHING/RESIDENCE TIMES
Estuary classifications - Tidal
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V FLUSHING/RESIDENCE TIMES
Estuary classifications - Flushing mechanism
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V FLUSHING/RESIDENCE TIMES
Estuary classifications - Residence time
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V FLUSHING/RESIDENCE TIMES
Estuary classifications - Flushing efficiency
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V FLUSHING/RESIDENCE TIMES
Calculation of residence times Formula based on
simple physical characteristics
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V FLUSHING/RESIDENCE TIMES

• Nutrients Flushing
• Algae require time to assimilate nutrients
• Rule of thumb
• Tr lt 3days no algal bloom
• Possible to relate critical N/P loadings to Tr

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SIMPLE MODELS CONTENT- I Concepts
definitions II Dilution III Mass
balance IV Salinity analysis V Flushing/residenc
e times
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Estuarine Coastal Modelling Course
MODULE IV SIMPLE MODELS
Michael Hartnett, Environmental Change Institute,
NUI Galway