Andrew Fang Jim Patek , Monica Suarez Nutrient TMDL Workshop, New Orleans, LA February 15-17 2011 February 15-17, 2011 Results are all preliminary and Results are all preliminary and not to be quoted.
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
Results are all preliminary and not to be quoted.
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
Results are all preliminary and not to be quoted.
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
Results are all preliminary and not to be quoted.
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
Results are all preliminary and not to be quoted.
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
Results are all preliminary and not to be quoted.
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)
Results are all preliminary and not to be quoted.
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
Results are all preliminary and not to be quoted.
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
Results are all preliminary and not to be quoted.
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%
Results are all preliminary and not to be quoted.
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)
Results are all preliminary and not to be quoted.
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 and not to be quoted.