lc tmdl modeling strategy w. walker walk thru july 2011 progress report data strengths &...
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LC TMDL Modeling StrategyW. Walker
• Walk Thru July 2011 Progress Report• Data Strengths & Weaknesses• Preliminary Testing Results• Dynamic vs. Steady State Models• Sensitivity & Uncertainty Analysis• Software Demonstrations
– BATHTUB– Load Calculation
• Ideas for Workplan
Tune Up
• Add TMDL Goal to TP Test Slide• Hyperlinks• Path Forward - Live
Path Forward
• Task..
Model Testing Results
0
20
40
60
80
100
01 South B01 South B02 South A02 South A03 Pt H
enry
04 Ott
er Ck04 O
tter Ck
05 Main L
05 Main L
06 Shelb B
07 Burl B
08 Cumb B
09 Mallett
s
10 NE Arm
11 St Alb
12 Missisq
13 IsleLam
Tota
l P p
pb
Observed & Predicted TP vs. Standard
Observed
Predicted
Standard
8
80
01 South B01 South B02 South A02 South A03 Pt H
enry
04 Ott
er Ck04 O
tter Ck
05 Main L
05 Main L
06 Shelb B
07 Burl B
08 Cumb B
09 Mallett
s
10 NE Arm
11 St Alb
12 Missisq
13 IsleLam
Tota
l P p
pb
Observed & Predicted TP vs. Standard
Observed
Predicted
Standard
0
10
20
30
40
50
01 South B01 South B02 South A02 South A03 Pt H
enry
04 Ott
er Ck04 O
tter Ck
05 Main L
05 Main L
06 Shelb B
07 Burl B
08 Cumb B
09 Mallett
s
10 NE Arm
11 St Alb
12 Missisq
13 IsleLam
Tota
l P p
pb
Observed & Predicted TP vs. Standard
Observed
Predicted
Standard
Data Limitations 1992-2010 vs 1990-1991
• Lower Sampling Frequency: weekly/biweekly - monthly + high flow• Less Winter Sampling• No Minor Tributaries• Tributary data limited in lake segments the deviate most from model
predictions– Mississquoi Bay (missing Rock 1992-2006)– St Albans Bay (no inflow data 1992-2007)– South Lake (~46% of inflows gauged)
• Complexifying model will not improve forecasts if the inflows are not accurately specified
• General Ranking– 1990-1991: high– 1992-1999: low– 2001-2008: OK – 2009-2010: high
Precision of Measured TP Loads & Lake Concentrations
01South
A
02South
B
03 PtHenry
04Otter
Ck
05Main
L
06Shelb
B
07Burl B
08Cumb
B
09Malle
tts
10 NEArm
11 StAlb
12Missis
q
13IsleLa
mLake South Main NE
1991 60.3 36.4 12.5 13.2 10.5 15.9 12.4 13.9 8.7 12.5 25.3 35.0 11.6 14.4 39.2 11.1 15.501-10 53.9 38.6 16.9 17.5 12.6 13.9 13.8 13.9 11.5 17.9 30.3 48.1 15.5 18.5 40.4 13.6 21.3Orig 91 58.0 34.0 15.0 15.0 12.0 15.0 13.0 14.0 9.0 14.0 24.0 35.0 12.0 15.5 36.8 12.7 16.2Standard 25.0 25.0 14.0 14.0 10.0 14.0 14.0 14.0 10.0 14.0 17.0 25.0 14.0 13.7 25.0 11.0 15.3
0
10
20
30
40
50
60
70
TP p
pb
Long-Term Means (2010-2010) vs. 1991 & Lake Standard
1991
01-10
Orig 91
Standard
Mean 54 39 17 17 13 14 14 14 12 18 30 48 15 19 40 14 21Min 39 30 12 12 10 12 11 12 9 16 26 39 13 16 32 11 18Max 71 46 23 25 16 18 17 16 14 21 42 57 19 21 48 16 24SE 3.0 1.6 1.0 1.5 0.6 0.6 0.5 0.5 0.4 0.4 1.5 1.6 0.6 0.5 1.6 0.6 0.5
Standard 25 25 14 14 10 14 14 14 10 14 17 25 14 14 25 11 15F>Std 100 100 90 90 90 40 50 40 80 100 100 100 80 100 100 90 100
0
10
20
30
40
50
60
70
80
01 South A
02 South B
03 Pt Henry
04 Ott
er Ck
05 Main L
06 Shelb B
07 Burl B
08 Cumb B
09 Mallett
s
10 NE Arm
11 St Alb
12 Missisq
13 IsleLam
Lake
South
Main
NE
TP p
pb
Mean & Range of Annual TP Values in 2001-2010 vs. Lake Standard
Max-Mean
Mean-Min
Standard
Original values used in TMDL Model Calibration. Recomputed values derived from historical database (mean +/1 Std Error)
0
10
20
30
40
50
60
70
80
01 South A
02 South B
03 Pt Henry
04 Ott
er Ck
05 Main L
06 Shelb B
07 Burl B
08 Cumb B
09 Mallett
s
10 NE Arm
11 St Alb
12 Missisq
13 IsleLam
TP p
pb
Recomputed vs. Original TP Means for 1991
Recomp
Orig
Standard
0
0.05
0.1
0.15
0.2
0.25
Std
Erro
r / M
ean
Relative precision of Mean Annual TP Values by Segment & Year
01 South A
02 South B
03 Pt Henry
04 Otter Ck
05 Main L
06 Shelb B
07 Burl B
08 Cumb B
09 Malletts
10 NE Arm
11 St Alb
12 Missisq
13 IsleLam
Number of TP Samples vs. Tributary & Water Year
Precision of Yearly TP Load EstimatesRelative Standard Error = Std Error / Mean
Variability & Uncertainty
Model Categories
• Steady Steady-State• Dynamic• “Quasi-Dynamic”
Algorithm for Estimating LoadsLN CONC (T ) = PREDICTED (T) + RESID (T)PREDICTED (T) = LN ( Concentration Predicted by Regression Model on Day T )RESID ( T ) = Residual for Day T Interpolated between Sampling DatesResidual = LN ( Observed / Predicted Concentration on Sampling Dates )
Variance of Load Estimates for Period T1 Thru T2, NDAYS = T2 - T1 + 1LOADVAR (T1-T2) = ( LOAD x RSD) ^2 / NSAMPLESNSAMPLES = number of sampling dates in period (Minimum = 1)RSD = Residual Standard Error of Regression Model (natural log units), from calibrationLOAD = Total Estimated Load for Period T1 - T2SE= LOADVAR^0.5 = Standard Error of LOADRSE = Relative Standard Error of Load Estimate = SE / LOAD = standard error as fraction of LOAD
The regression is design to capture seasonality, flow dependence (mean and time derivative), and long-term trend.The interpolation captures drift in the model residuals over time; i.e. serial correlation of errors, etc.The interpolation forces the observed and predicted concentrations to be equal on each sampling date.The regression intercept is adjusted to account for the bias introduced by log-transform (smear coefficient).
Regression Model Coefficients are listed in the LoadCalcSummary sheetTerm DescriptionReg_Q Deriv Natural Log ( Q (day) / Q ( Day-1) ), = 0 if either flow = 0Reg_Year^2 year = year + fraction of year = Year + julian Day / 365.25Reg_Year "Reg_Cos(2t) t = 2 x Pi x Julian / 365.25 seasonalityReg_Sin(2t) " "Reg_Cos(t) " "Reg_Sin(t) " "Reg_Log q3 Natural Log (Q = flow) flow-dependenceReg_Log q2 " "Reg_Log q " "Reg_Intercept Regression Intercept, Predict Natural Log of Daily ConcRegression R2 Coefficient of DeterminationRegression SE Residual Standard Error (natural Log Units)
Alternative Algorithms are also applied for comparisionResults are listed in the LoadCalcSummary sheet and shown in the time series graphs
Method 1 Constant flow-weighted-mean concentration (FLUX Method 2, without stratifying)Method 2 Constant flow-weighted-mean conc within low and high-flow strata (above and below mean flow for entire period)Method 3 Simple Linear Interpolation of concentrations between sampling datesMethod 4 Regression without residual interpolationMethod 5 Regression with residual interpolation (default)
