Using Empirical ModelsTo Set EOS Targets For

Phase 5

Gary Shenk

1/10/07

Modeling Subcommittee

Final TextOutput

River variableWDM

METWDM

ATDEPWDM

PSWDM

River Input File Generator

5

6

4

ProcessParameter

Files • Assume the sensitivity of the simulation to each parameter

• Determine an appropriate adjustment direction for each parameter

• Take a small step in that direction

Rule-Based Optimization

River Calibration

Calibration Information

• Consistent with recommendations of STAC review team

• Observed and simulated CFDs for paired data

10-1

100

101

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TOTAL N, IN MG/L

CU

MU

LAT

IVE

DIS

TR

IBU

TIO

N

EMPIRICAL CUMULATIVE DISTRIBUTION FOR TOTN >> scen: WQT1 >> seg: RU5-6030-0001 >> name: RAPPAHANNOCK R

h = 1p = 7.6549e-055k = 0.53089

SimulatedObserved

Potomac CalibrationChange in transformation vs iteration

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0 5 10 15 20 25 30 35 40 45 50

TNbrbod

TNbodsink

TNbenal

TNtamscr

TNbrtam

TNtamvol

TNnitden

TNrefset

TNphyset

TNdiv

TPbrbod

TPbodsink

TPbenal

TPpo4scr

TPbrpo4

TPrefset

TPphyset

TPdiv

TN: Estimator and P5 WSM

100000

1000000

10000000

100000000

1000000000

PL0

_451

0_00

01

PS

2_67

30_6

660

XU

2_43

30_4

480

YP

3_63

30_6

700

RU

2_59

40_6

200

EM

2_39

80_0

001

YM

4_66

20_0

003

PM

2_28

60_3

040

PU

3_36

80_3

890

YP

4_67

20_6

750

JA5_

7480

_000

1

XU

3_46

50_0

001

PS

3_51

00_5

080

PU

2_30

90_4

050

RU

5_60

30_0

001

PU

3_32

90_3

390

PS

5_52

40_5

200

JL6_

7430

_732

0

PM

4_40

40_0

003

PU

6_40

20_3

870

SL3

_242

0_27

00

JL7_

6800

_707

0

JL7_

7100

_703

0

SJ6

_213

0_00

03

SW

7_16

40_0

003

SU

7_08

50_0

730

SU

8_16

10_1

530

PM

7_48

20_0

001

SL9

_249

0_25

20

SL9

_272

0_00

01

Estimator Load

WSM

TP: Estimator and P5 WSM

1000

10000

100000

1000000

10000000X

U2_

4330

_448

0

EM

2_39

80_0

001

PS

2_67

30_6

660

YP

3_63

30_6

700

PL0

_451

0_00

01

PU

3_36

80_3

890

YM

4_66

20_0

003

PM

2_28

60_3

040

RU

2_59

40_6

200

PU

2_30

90_4

050

XU

3_46

50_0

001

JA5_

7480

_000

1

YP

4_67

20_6

750

PS

3_51

00_5

080

PU

3_32

90_3

390

PM

4_40

40_0

003

PS

5_52

40_5

200

SL3

_242

0_27

00

PU

6_40

20_3

870

SJ6

_213

0_00

03

RU

5_60

30_0

001

JL6_

7430

_732

0

SW

7_16

40_0

003

SU

7_08

50_0

730

JL7_

6800

_707

0

JL7_

7100

_703

0

SU

8_16

10_1

530

SL9

_272

0_00

01

PM

7_48

20_0

001

SL9

_249

0_25

20

Estimator Load

WSM

TSS: Estimator and P5 WSM

100

1000

10000

100000

1000000

10000000

100000000X

U2_

4330

_448

0

EM

2_39

80_0

001

PS

2_67

30_6

660

YM

4_66

20_0

003

YP

3_63

30_6

700

PU

2_30

90_4

050

PM

2_28

60_3

040

PU

3_36

80_3

890

JA5_

7480

_000

1

XU

3_46

50_0

001

PU

3_32

90_3

390

PL0

_451

0_00

01

YP

4_67

20_6

750

PM

4_40

40_0

003

SL3

_242

0_27

00

JL6_

7430

_732

0

RU

2_59

40_6

200

SJ6

_213

0_00

03

PU

6_40

20_3

870

SW

7_16

40_0

003

RU

5_60

30_0

001

JL7_

7100

_703

0

SL9

_272

0_00

01

SU

8_16

10_1

530

SU

7_08

50_0

730

JL7_

6800

_707

0

PS

5_52

40_5

200

PM

7_48

20_0

001

SL9

_249

0_25

20

PS

3_51

00_5

080

Estimator Load

WSM

TN Bias

0

5

10

15

20

25

30

Measure of Concentration Bias

Nu

mb

er o

f S

tati

on

s

TP Bias

0

5

10

15

20

25

30

35

40

45

50

Measure of Concentration Bias

Nu

mb

er o

f S

tati

on

s

TSS Bias

0

5

10

15

20

25

30

35

40

Measure of Concentration Bias

Nu

mb

er o

f S

tati

on

s

TN Average Concentration Bias

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5 6 7 8 9

Basin SIZE

Ave

rag

e B

ias

TN Average Concentration Bias

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Basin

Ave

rag

e B

ias

How to arrive at appropriate EOS loads?

• Start from the outlet

• Add stream attenuation

• Leaves necessary EOS

• Assume watershed with one river and a gauge

Segment Transport Factor = EOS / EOF

What about multiple streams?• Each sub-basin has

preliminary estimate of EOF

• Calculate EOF * product of down stream delivery for each sub-basin

• Determine ratio for all preliminary EOF

1

2

3

ESTIMATOR = TF * ( EOF1 * DF1 * DF3 + EOF2 * DF2 * DF3 + EOF3 * DF3 )

What about nested streams?

• Same as above, but subtract out stations

1

2

3ESTIMATOR(3) = ESTIMATOR(1) * DF3 + TF * ( EOF2 * DF2 * DF3 + EOF3 * DF3 )

Where do we get all of the data?

• EOF = targets

• Loads at Stations = USGS ESTIMATOR

• Stream Attenuation = USGS Sparrow

Estimatorlocations

Assign non-gauged areas based on gauged results

In-stream loss:Sparrow formulation

Streams are grouped into size categories and each stream group has a particular reduction rate

ThetaSc = first-order loss rate for streams of certain sizeT = Travel time

http://pubs.usgs.gov/tm/2006/tm6b3/

Sparrow Attenuation Factors

y = 9.2353x-0.523

R2 = 0.9898

y = 8.7331x-0.5283

R2 = 0.9999

0.01

0.1

1

1 10 100 1000 10000 100000

CFS

per

day

nation

Miss

Ches

All

Power (All)

Power (Ches)Chesapeake Bay

All

Sparrow Phosphorus Attenuation Factors

y = 4.328x-0.8005

R2 = 0.9944

y = 36.809x-0.7436

R2 = 1

0.01

0.1

1

1 10 100 1000 10000

cfs

per

day

1997

2004

Power (2004)

Power (1997)

Big difference:2004 included reservoir settling factor at 14.3 meters per year

New Sparrow Formulations

http://pubs.usgs.gov/tm/2006/tm6b3/

DS = Average DepthThetaMT = mass settling rate

Q = average flowThetaS[1,2] = empirical coefficients

Empirical formulation

‘Settling-velocity’ formulation

http://pubs.usgs.gov/tm/2006/tm6b3/

Piedmont Province (VA, MD, and NC)

y = 1.8543x0.3017

R2 = 0.8447

1

10

100

1 10 100 1,000 10,000

Drainage Area (mi2)

Ban

kfu

ll h

eig

ht

(ft)

River Geomorphology Data

Bankfull Height vs Drainage area in the Piedmont

New Sparrow Formulations

http://pubs.usgs.gov/tm/2006/tm6b3/

Reservoir Attenuation:

qR = outflow / areaThetaR0 = mass settling rate

Conclusions

• Using mass balance and literature to determining EOS targets results in regional biases

• Using ESTIMATOR and Sparrow estimates of river flux and attenuation, we can empirically calculate overall necessary EOS loads.

1

2

3