qual2k you’ve heard of qual2e -...

Developed by Steve Chapra for 2004 QUAL2K Workshop (Some slides have been updated)

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You’ve heard of QUAL2E

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THE TMDL TERMINATOR

Coming soon to your Watershed

QUAL2K


QUAL2K WORKSHOP: INTRODUCTION*

Steve Chapra Tufts University

!   Rationale and Overview !   Segmentation and Hydraulics

* Abbreviated for Region 6 Modeling Workshop, November 2013, by Robert Ambrose


QUAL2K •  Fast C (BOD), Slow C (BOD), organic N,

NH3, NO3, organic P, SRP, oxygen, phytoplankton, FIXED PLANTS, suspended solids, conservative/color

•  Heat budget

•  Point and distributed loads and abstractions

•  Steady-state, 1-D Mainstem River


  Shuts down oxidation at low DO

  SOD and sediment nutrient fluxes calculated

  Denitrification

  Speciates carbon

  Fixed plants

  Anoxia

QUAL2K


QUAL2K !   Software environment and interface !   Model segmentation !   Carbon speciation !   Anoxia and denitrification !   Sediment-water interactions !   Bottom plants !   Light extinction !   pH !   Pathogens


QUAL2K Documentation

1

2

3

4 5

6

8

7

Non - point abstraction

Non - point source

Point source

Point source

Point abstraction

Point abstraction

Headwater boundary

Downstream boundary

Point source

SEGMENTATION

i i + 1 i - 1 Qi-1 Qi

Qin,i Qab,i

FLOW BALANCE

Qi = Qi-1 + Qin,i – Qab,i

Q npt

25% Q npt 25% Q npt 50% Q npt

start end

DISTRIBUTED (NON-POINT) LOADS


B

D

E

F C

G

QA QC QF QE QD QB QG

A

Upstream Lake

STEADY-STATE FLOW BALANCE


WHAT HAPPENS WHEN YOU ADD FLOW TO A SLOPING CHANNEL?

The water velocity and depth increase

Given Qoutflow, compute depth (H) and velocity (U): •  Continuity and Manning equation •  Rating Curves


RATING CURVES

1

10

100 500 Q (m 3 /s)

H (m)

0.1

1

100 500 Q (m 3 /s)

U (m/s)

H = 1.6487 Q 0.1622 U = 0.0279 Q 0.5652


Ac = Q/U B = Ac /H As = Δx B

V = B H Δx τw = Δx / U = V/Q

Q

Manning Rating Curves

U, H

RIVER HYDROGEOMETRY (STEADY)


B

D

E

F C

G

QA QC QF QE QD QB QG

A

Upstream Lake

STEADY-STATE FLOW BALANCE

Rating Curve

Rating Curve

Manning Manning


LONGITUDINAL DISPERSION

U gHS * =

E U B

HU = 0 011

2 2

. *


QUAL2K WORKSHOP: TEMPERATURE MODELING

!   Heat Balance

!   Meteorological Data !   Surface Heat Flux

!   Sediment Heat Flux !   Air-Water Converter


Q2K

i inflow outflow

dispersion dispersion

heat load heat abstraction

atmospheric transfer

sediment-water transfer

sediment


SURFACE HEAT BALANCE

air-water interface

solar shortwave radiation

atmospheric longwave radiation

water longwave radiation

conduction and

convection

evaporation and

condensation

water-dependent terms net absorbed radiation

non-radiation terms radiation terms


ANNUAL SOLAR RADIATION

Summer Solstice

Winter Solstice

Lat = 24O

Havana/Sao Paolo

Lat = 64O

Reykjavik, Iceland

0

200

400

600

800

1-Jan 1-Mar 1-May 1-Jul 31-Aug 31-Oct 31-Dec

cal cm2 d


DAILY SOLAR RADIATION

0

500

1000

1500

2000

0 6 12 18 24

Winter solstice

Summer solstice

Equinox


WHAT YOU NEED??? (METEOROLOGICAL DATA)

( )

) )( ( ) )( ( 15 273 (

) 1 ( 031 . 0 15 273 (

air air 1 4

4 air

e e U f T T U f c ) . T

R e A ) . T J J

s w s w s

L air sn

- - - - + -

- + + + =

εσ

σ

Solar (Cloud Cover)

Air Temperature

Dew Point Temperature

Wind Speed


SEDIMENT HEAT BUDGET

Ts,i

( ) si i s

s i s T T

H J - =

α

,

si p

i s i s

H C

J

dt

dT =

ρ

, ,

Ti


Q2K WATER QUALITY Variable Symbol Units* Conductivity s µmhos Inorganic suspended solids mi mgD/L Dissolved oxygen o mgO2/L Slowly reacting CBOD cs mgO2/L Fast reacting CBOD cf mgO2/L Organic nitrogen no µgN/L Ammonia nitrogen na µgN/L Nitrate nitrogen nn µgN/L Organic phosphorus po µgP/L Inorganic phosphorus pi µgP/L Phytoplankton ap µgA/L Phytoplankton nitrogen INp µgN/L Phytoplankton phosphorus IPp µgP/L Detritus mo mgD/L Pathogen X cfu/100 mL Alkalinity Alk mgCaCO3/L Total inorganic carbon cT mole/L Bottom algae biomass ab mgA/m2 Bottom algae nitrogen INb mgN/m2 Bottom algae phosphorus IPb mgP/m2 Constituent i Constituent ii Constituent iii


i inflow outflow

dispersion dispersion

mass load mass abstraction

atmospheric transfer

bottom algae sediments

i i

i S V

W + + ( ) ( ) i i i

i i i

i

i c c V

E c c V

E - + - + + - -

1

'

1

' 1

i i

i ab i

i

i i

i

i i c V

Q c

V

Q c V

Q

dt dc - - = -

- , 1

1

i i

i S V

W + + ( ) ( ) i i i

i i i

i

i c c V

E c c V

E - + - + + - -

1

'

1

' 1

i i

i S V

W + + ( ) ( ) i i i

i i i

i

i c c V

E c c V

E - + - + + - -

1

'

1

' 1 ( ) ( ) i i

i

i i i

i

i c c V

E c c V

E - + - + + - -

1

'

1

' 1

i i

i ab i

i

i i

i

i i c V

Q c

V

Q c V

Q

dt dc - - = -

- , 1

1 i

i

i ab i

i

i i

i

i i c V

Q c

V

Q c V

Q

dt dc - - = -

- , 1

1

i b i b S

dt da

, , = i b i b S

dt da

, , =

MASS BALANCE


PHYTOPLANKTON AND DETRITUS STOICHIOMETRY:

The “Redfield Ratio”

100% : 40% : 7.2% : 1% : 0.5-2.0%

D : C : N : P : A


TEMPERATURE EFFECT ON THE REACTION RATE

k ( T )

k (20)

0

1

2

3

4

0 T ( o C)

10 20 30

θ = 1 θ = 1.024

θ = 1.047

θ = 1.08

θ = 1.1

θ = 1.07

biotic

gas transfer

k T k T ( ) ( ) = - 20 20 θ


Q2K CHEMISTRY AND pH MODELING

!   Mass Balance versus Chemical Equilibria Models

!   Ammonia-Ammonium Acid Base !   pH Modeling

!   Chemistry 101


THE CHEMISTRY PERSPECTIVE: AMMONIA ACID-BASE EQUILIBRIUM

H NH NH 3 4

+ + + H NH NH 3 4

+ + +

] = ] H ][ NH [ 3 +

b k ] H ][ NH [ 3 +

b k NH [ 4 +

f k NH [ 4 +

f k

NH3 NH4+

kf

kb

H+


FAST REACTIONS

FOOD CHAIN

P R

SLOW REACTIONS

V

inorganic carbon CO 3 2- HCO 3 - H 2 CO 3 *

pH MODELING


Q2K PLANTS

!   Phytoplankton

!   Stationary or Attached Plants


da

dt k a g =

a a t

a a e o k t g

=

=

if at = 0 0

t , d 0 1 10 100

a , mg m -3 1 7.8 4.85x10 8 7.2x10 86

da dt

k T N I a k a g d = - ( , , )

k T N I k g g T N L = ( , , ) , φ φ

temperature nutrients light

Incorporating Limits to Growth


TEMPERATURE DEPENDENCY

k g , T (d -1 )

T ( o C) T min T opt T max

k g ,opt k g ,20

0

2

4

6

8

0 20 40

Theta model θ = 1.066

linear

optimal


0

0.5

1

0 N k s

φ N

φ N s

N k N

= +

NUTRIENT LIMITATION MICHAELIS-MENTEN KINETICS

Half-saturation Constant


Light Response Models for Plant Growth

0

0.5

1

0 200 400 600 800 Light ( langley /d)

Mich - Ment Photinhib Smith

: Model Menten ) - ( Michaelis Saturation

si I k I +

= φ

: Model Menten ) - ( Michaelis Saturation

si I k I +

= φ

1

: Model ition Photoinhib

I I

s e

I I s =

- φ

1

: Model ition Photoinhib

I I

s e

I I s =

- φ

2 2

: Model Smith

k I I

I

+ = φ 2 2

: Model Smith

k I I + = φ


( c ) Dependence of growth rate

on light

I

z

( b ) Light attenuation with depth

mixed layer

( a ) Diurnal variation of

light t

I

midnight noon midnight

I

k g

IMPACT OF LIGHT ON

PHOTOSYNTHESIS


STATIONARY OR “ATTACHED” PLANTS

!   Overview

!   Macrophytes !   Simple Periphyton Modeling


Differences between fixed and floating plants

Types Diatoms Greens Blue Greens

Periphyton Filamentous Algae

Rooted Macrophytes Units mgchl a/m3 gD/m2 or mgA/m2

Light Average Water Column Bottom Light

Transport Yes No

Predation Zooplankton Insect Larvae, Snails, etc.

Floating Attached

Substrate Not an issue Rock vs. Mud


Functional Groups

  Macrophytes: Vascular, Rooted Plants   Myriophyllum, Elodea, Potamogeton

  Periphyton: algae attached to and living upon submerged solid surfaces   Diatoms, Greens, Blue Greens

  Filamentous Algae   Cladophora


Phytoplankton:

+ transport - settling

p d p r p n l g p a k a k a T k

dt

da - - = φ φ ) (

Based on integral light

f d f r n l max f a k a k T G

dt

da - - = φ φ ) (

Periphyton: Based on bottom light

PERIPHYTON MODELS


EFFECT OF LIGHT ON PERIPHYTON

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( a ) floating plants

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( b ) periphyton


Macrophytes

  Can get nutrients from roots

  Can extend up into water column

  Lakes/Slow-moving streams/shallow rivers

  Myriophyllum, Elodea, Potamogeton (Water milfoil) (Waterweed) (Pondweed Oxygen weed)

  Vascular, Rooted Plants


Q2K SEDIMENT/WATER

INTERACTIONS

!   Sediment Oxygen Demand

!   Diffusion/Reaction Competition

!   Methane Bubble Formation

!   Numerical Methods


sediments

water

air

SEDIMENT-WATER PROCESSES “THE MISSING LINK OF WATER-QUALITY MODELLING”

Organic Matter

Organic Matter

Oxygen Nutrients

SOD N, P

Fluxes

SEWAGE, RUNOFF PHOTOSYNTHESIS

?


1.5 Estuarine mud 4

1.5 Municipal sewage sludge outfall vicinity downstream of outfall, "aged"

2-10 1-2 1-2

0.5 0.07

Sandy bottom Mineral soils Areal hypolimnetic oxygen demand

(AHOD) -- lakes

0.2-1 0.05-1 0.06-2

TYPICAL SOD VALUES S B , '

20 (g m -2 d -1 ) Average value Bottom type and location Range

2 7 Sphaerolitus (10 g dry wt/m ) - 5 Zebra Mussels (6000 individuals/m2) -


SOD (g/m 2 /d)

0

4

8

0 100 200

COD (mgO/L)

THE “SQUARE-ROOT” RELATIONSHIP OF SEDIMENT OXYGEN DEMAND

AND OVERENRICHMENT

SOD = α COD0.5


WHY NONLINEARITIES MATTER

/d) 60

SOD (gO/m 2 /d)

Downward Flux of Organic Carbon (gO/m 2

0

2

4

6

0 20 40

Zero-order fiction The “Environmentalist’s Dream”

Nonlinear reality


WHERE DOES NONLINEARITY COME FROM?

!   Loss of carbon as methane gas in anaerobic sediments

!   Competition between reaction and diffusion in aerobic surface sediment


!   Seems like a lot of parameters

!   For steady state, really only three

CALIBRATION

!   Mass transfer, vd01 !   Reaction rates, kn1 + kc1

Modified for Region 6 Modeling Workshop, November 2013, by Robert Ambrose


Boulder Creek Example

!   Create a folder: C:/Q2K

!   Files Q2KMaster*.xls and q2kfortran*.exe should be in this folder

!   Create a folder: C:/Q2K/DataFiles

!   Unzip Q2K*.zip in this folder



!   Change Saved File Name to Boulder Creek

!   Change Directory where file stored to C:/Q2K/DataFiles

!   Click Run Fortran button


Boulder Creek Example

!   Launch Q2KMaster.xls

qual2k you’ve heard of qual2e -...

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