results are all preliminary andresults are all preliminary

Andrew Fangg

Jim Patek, Monica Suarez

Nutrient TMDL Workshop, New Orleans, LAFebruary 15-17 2011February 15-17, 2011

Results are all preliminary andResults are all preliminary and not to be quoted.

1. Project backgroundj g2. Project area3. SWAT watershed model3. SWAT watershed model4. BATHTUB lake model5 Sensitivity analysis5. Sensitivity analysis6. Monte Carlo uncertainty analysis

and MOSand MOS7. Preliminary TMDL

SWS Lakes in Oklahoma

Sources of public or private water supplySources of public or private water supply

Many of them are small municipal reservoirs with a watershed < 100 mi2watershed < 100 mi2

81 SWS lakes in Oklahoma

Long term average Chl-a standard of 10 µg/L

22 SWS lakes on 2008 303(d) list due to high Chl-a

Limited data availabilityLimited data availability◦ In most cases, state’s Beneficial Use Monitoring

Program (BUMP) is the only water quality data sourcek l l◦ BUMP takes 4 quarterly samples every 2-3 years

(P it ) Chl N t i t(Per site per year) Chl-a NutrientsRocky 1.5 1.1Tom Steed 1.9 1.8

We needed an acceptable method to developWe needed an acceptable method to develop Chl-a TMDLs for the lakes

Data availability does not support complex hydrodynamic/water quality models such as EFDC

Si l d l lib t d i t l tSimpler models calibrated against long-term average values of monitoring data are best fit

North Fork of the Red

Annual ClimatologyPrecipitation 29.7”Temperature 60 oFWind speed 11 mphThunderstorms 44Tornados 1

Drainage(mi2)

Volume(m3)

Surface Area (km2)

Mean Depth (m)

Tom Steed 119 120,176,000 25.9 4.64

Rocky 55 3,784,000 1.376 2.75

Rocky SteedWheat 66% 42%

Shrub 16 36Grass 6 7Forest 2 4

No stream monitoring stations within either gof the two lake watersheds

Stations in the larger 8-digit HUC watershed: North Fork of the Red River

A SWAT model was set up for the larger watershedwatershed

Watershed Monitoring

2 USGS gage stations:1998/2000-2008

6 TSS stations: 18-22 samples in 2 years

2 nutrients stations:2 nutrients stations: 38 samples in 4 years

Flows and loadings

70 subwatersheds and 1,970 HRUs,

Local pasture, wheat, and cotton operations

County level soil test P levels

80

USGS Gage 07307028 (Subbasin 63)

Observed

d l dValidationCalibration

50

60

70

w (m

3 /s)

Modeled

30

40

50

nthly Average

Flow

10

20Mo

0

Jan‐98 Jan‐99 Jan‐00 Dec‐00 Dec‐01 Dec‐02 Dec‐03 Dec‐04 Dec‐05 Dec‐06 Dec‐07 Dec‐08Date

Calibration ValidationCalibration ValidationModel error (annual) -12% 3%r2 (monthly) 0.86 0.87NSE (monthly) 0.85 0.87

Results are all preliminary and not to be quoted.

250ValidationCalibration

150

200

ation (mg/L)

Error=‐10%

Error=9%

100

150

ge TSS Concentra

Observed

ModeledError=15%

Error=0%

Error=13%

0

50Averag o 5%

Error=‐5%

0

20 26 51 53 24 34

Subbasin

TSS average at the 6 monitoring stations


1 6

1.8

2.0

/L)

Subbasin 26 ‐ Elk Creek near Hobart

0.8

1.0

1.2

1.4

1.6

Concen

tration (m

g/

Observed

Modeled

0.0

0.2

0.4

0.6

OrgP PO4 TP OrgN NH4 NOx TN

Average C

Parameter

1.4

Subbasin 51 ‐ North Fork Red River near Headrick Nutrients

0 6

0.8

1.0

1.2

centratio

n (m

g/L)

Observed

0.0

0.2

0.4

0.6

Average

Con Modeled

OrgP PO4 TP OrgN NH4 NOx TN

Parameter


Summary of Model Performance for Water Quality

Average AverageParameter Subbasin

Average observed

(mg/L)

Average modeled (mg/L)

Error NSE r2

20 67.14 77.5 15% 0.643 0.694

24 87 42 98 8 13% 0 778 0 985

TSS

24 87.42 98.8 13% 0.778 0.985

26 121.55 121.8 0% 0.869 0.921

34 180.15 197.2 9% 0.861 0.895

51 172.23 155.1 -10% 0.840 0.84651 172.23 155.1 10% 0.840 0.846

53 55.10 52.3 -5% 0.647 0.709

Total Phosphorus 26 0.226 0.186 -17% 0.744 0.803

51 0.138 0.126 -8% 0.661 0.665

Total Nitrogen 26 1.794 1.568 -13% 0.579 0.665

51 1.148 1.114 -3% 0.796 0.821


Average Daily Flows and Nutrient Loads to the Lakes(SWAT model output)

Parameter Rocky Tom Steed

Flow (m3/s) 0.46 1.39

Organic Phosphorus (kg/day) 40 40g p ( g y)

Mineral Phosphorus (kg/day) 64 148

Total Phosphorus (kg/day) 104 189

Organic Nitrogen (kg/day) 67 137

NH4 (kg/day) 28 91

NO3 (kg/day) 73 77

NO2 (kg/day) 2 14

Total Nitrogen (kg/day) 170 319


Calibration

Average Morphometric Characteristics

Volume(m3)

Surface Area (km2) Mean Depth (m)

Tom Steed 120,176,000 25.9 4.64

Rocky 3,784,000 1.376 2.75

BATHTUB and Field Obser ations

Water Quality Parameter

Modeled Mean Concentration

Field Mean Concentrations Water Quality

Parameter

Modeled Mean Concentration

Field Mean Concentrations

BATHTUB and Field Observations

Parameter for Steed for Steed

Total P (µg/L) 70.4 73.0Total N (µg/L) 739.8 759Chl ( /L) 16 6 16 6

Parameter for Rocky for Rocky

Total P (µg/L) 130.2 133.0Total N (µg/L) 1452 1519Chl ( /L) 44 9 44 9Chl-a (µg/L) 16.6 16.6

Secchi (meter) 0.4 0.38Chl-a (µg/L) 44.9 44.9Secchi (meter) 0.3 0.29


How can we quantify the uncertainty associated with the limited water quality data and a non-mechanistic model?

(how confident are we when we set a load reduction goal to achieve an in-lake Chl-areduction goal to achieve an in lake Chl alevel?)

Monte Carlo Uncertainty Analysis for BATHTUB

Calibrate Model

Choose most sensitive parameters

Determine parameter distributions

Given a TP load reduction, run BATHTUB many times with parameter values randomly sampled from the distributions

Probability distribution of BATHTUB results

Input to TMDL

Narrow down the parameters

Sensitivity Matrix for BATHTUB Parameters for Tom Steed

16.0

18.0

20.0

TS e of

Con

cern

total nitrogen calibration factor

total phosphoruscalibration factor

10.0

12.0

14.0

VIT

Y O

F R

ES

ULT

n O

utpu

t Var

iabl

e total phosphorus calibration factor

annual evaporation

annual precipitation

chlorophyll-a temporal CV

inflow

hl h ll fl hi

4.0

6.0

8.0

SE

NS

ITIV

mum

Cha

nge

in chlorophyll-a flushing term

chlorophyll-a/ secchi depth slope factor

dispersion calibration factor

mixed layer depth

non-algal turbidity

0.0

2.0

0% 50% 100% 150% 200%

Max

im

Average Change in Parameter (%)

chlorophyll-a calibration factor

organic nitrogen calibration factor

Secchi depth calibration factor

VARIABILITY IN STUDY ASSUMPTIONS AND INPUTS

• non-algal turbidity• annual average evaporationannual average evaporation• chlorophyll-a calibration factor• inflow rate• mixed layer depthResults are all preliminary and not to be quoted.

Sensitivity Matrix for BATHTUB Parameters for Rocky

34 036.038.040.042.044.046.0

TS

of C

once

rn

total nitrogen calibration factor

20 022.024.026.028.030.032.034.0

TY O

F R

ESU

LT

Out

put V

aria

ble total phosphorus calibration factor

annual evaporation

annual precipitation

chlorophyll-a temporal CV

inflow

6 08.0

10.012.014.016.018.020.0

SE

NS

ITIV

I

um C

hang

e in

O chlorophyll-a f lushing term

chlorophyll-a/ secchi depth slope factor

dispersion calibration factor

mixed layer depth

non-algal turbidity

0.02.04.06.0

0% 50% 100% 150% 200%

Average Change in Parameter (%)

Max

imu

chlorophyll-a calibration factor

organic nitrogen calibration factor

Secchi depth calibration factor

• non-algal turbidity• chlorophyll-a calibration factor

g g ( )

VARIABILITY IN STUDY ASSUMPTIONS AND INPUTS

• chl-a/Secchi depth slope factor• TP calculation factor• TN calculation factorResults are all preliminary and not to be quoted.

Selected Distribution of Parameters for BATHTUB Uncertainty Analysis

Parameter Definition Distribution

a Non-algal turbidity (1/m) Normal (Steed: mean = 2.21, std.dev. = 1.348; Rocky: mean = 2.33, std.dev. = 0.65)

CB Calibration factor for chlorophyll-a Normal (Steed: mean = 1.5, std.dev. = 0.25; Rocky: mean = 2.0, std.dev. = 0.25)

evp Annual Evaporation (m/yr) Normal (Steed: mean = 2.07, std.dev. = 0.621)

b Chl-a/Secchi depth slope factor (m2/mg) Normal (Rocky: mean = 0.025, std.dev. = 0.015)

Q Inflow (hm3/yr) Normal (Steed: mean = 45.44, std.dev. = 33.6)

Mi d L D th N l (St d 4 0 td d 1 5)zmx Mixed Layer Depth Normal (Steed: mean = 4.0, std.dev. = 1.5)

CP Total P calibration factor Normal (Rocky: mean = 0.35, std.dev. = 0.2)

CN Total N calibration factor Normal (Rocky: mean = 0.8, std.dev. = 0.5)


Monte Carlo Simulations

Lake Tom Steed Probability Plot of Chlorophyll-aConcentrations Obtained from 20,000 MC Samples

6.00%

4.00%

5.00%

ity

2.00%

3.00%

% P

roba

bil

Target 9 ug/l Chl-a; TP = 35 ug/lTarget 10 ug// Chl-a; TP = 41 ug/l

1.00%

Note: Chl-a is the target to achieve and TP value is tributary incoming concentration and

0.00%0 5 10 15 20 25

Chl-a (ug/l)

not in-lake concentration.

Cumulative probability :42% for <10 µg/L and 50%, if we target 9 µg/LResults are all preliminary and not to be quoted.

Rocky Lake Probability Plot of Chlorophyll-aConcentrations Obtained from 20,000 MC Samples

12.00%

8.00%

10.00%

ity

4.00%

6.00%

% P

roba

bil

Target 9 ug/l Chl-a; TP = 18.5 ug/lTarget 10 ug/l Chl-a; TP = 20.5 ug/l

2.00%

Note: Chl-a is the target to achieve and TP value is tributary incoming concentration and

0.00%0 5 10 15 20 25

Chl-a (ug/l)

not in-lake concentration.

Cumulative probability :57% for <10 µg/L and 75% if we target 9 µg/LResults are all preliminary and not to be quoted.

1. Explicit: lower target Chl-a level in the lake p gby a percentage (MOS) until achieving a certain target probability level (e.g., 51 or 67%)67%)

Implicit (1) probabilit red ction table2. Implicit (1): probability-reduction table

3 Implicit (2): reduction for both TP and TN3. Implicit (2): reduction for both TP and TN

10 µg/L (WQS) 45

MOS: 0%Prob: 42%9 µg/L30

35

40

Tom Steed Lake 10

9 µg/L MOS: 10%Prob: 50%

20

25

Chl

-a (u

g/l)

8

9

8 µg/LMOS: 20%5

10

15

Prob: 70%00.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00%

Cumulative Probability


Probability to Nonpoint Sources Point Sources yachieve

Standard (%)

pReduction

(%)Reduction

(%)0 0 0

30 20 042 65 050 70 050 70 065 80 080 90 099 100 099 100 0


Rocky Tom Steed

Load Reduction Goals

Maximum Allowable Load of TP (kg/year) 5,000 24,000

Maximum Allowable Load of TN (kg/year) 8,000 41,000

% Reduction 87% 65%


What is the MOS?

Waterbody Name Nutrient TMDL (kg/day)

WLA (kg/day)

LA (kg/day)

MOS (kg/day)

Rocky LakeTP 12 0 12 ?

TN 22 0 22 ?

Tom Steed LakeTP 48 0 48 ?

TN 98 0 98 ?

(MDL = LTA x e zσ-0.5σ2)


Model a larger watershed to include monitoring sites and multiple target lakes

N h i i d l f l k i h li i dNon-mechanistic model for lakes with limited monitoring data

Monte Carlo uncertainty analysis

Multiple options for MOS


results are all preliminary andresults are all preliminary

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