Uncertainty in Predicting Pesticide Surface
Runoff Reduction with Vegetative Filter Strips
Garey A. Fox, Ph.D., P.E. - Oklahoma State University
Rafael Munoz-Carpena, Ph.D. – University of Florida
George Sabbagh, Ph.D. – Bayer CropScience
Organization of Presentations
• Introduction to Vegetative Filter Strips (VFS)
– Predicting flow, sediment, and pesticide mass reduction
• Development of an integrated modeling tool for VFS
(VFSMOD-W)
• Need for understanding parameter importance and
uncertainty
• Global sensitivity and uncertainty analyses applied to
VFSMOD-W
– Uniform flow studies - Sabbagh et al., 2009; Munoz-Carpena et
al., 2010
– Uniform vs. Concentrated Flow - Poletika et al., 2009; Fox et al.,
2010
Vegetative Filter Strips (VFS)
• Also known as riparian buffers
and grassed waterways
• Take home message:
One size does not fit all!
http://tti.tamu.edu/publications/resear
cher/v41n1/images/roadway_grass.gif
VFS Processes
Increase in hydraulic resistance
to flow and soil infiltration
Overland flow (and dissolved
pollutants) reduction
(infiltration) and delay
Decrease in sediment/particles
transport capacity of flow
Sediment/particles deposition
(and pollutants bonded) in filter
VFS - Complex and Dynamic Systems
VFS - Complex and Dynamic Systems
• VFS efficacy is difficult to
predict
• Variability cannot be explained
by buffer width or buffer slope
alone
• Large number of parameters
and uncertainties need to be
taken into account
Liu, X., X. Zhang, and M. Zhang. 2008. Major factors influencing the efficacy of vegetated buffers on sediment trapping: A
review and analysis. J. Environ. Qual. 37:1667–1674.
Fox, G.A.; Sabbagh, G.J. Comment on “Major Factors Influencing the Efficacy of Vegetated Buffers on Sediment Trapping:
A Review and Analysis”. J. Environ. Qual. 2009, 38 (1), 1-3.
VFS - Complex and Dynamic Systems
• Limited prediction equations available for pesticide
reduction (DP):
Predictions with simple empirical equation
(SWAT)
Lack of relationship with Koc
Sabbagh, G.J.; Fox, G.A.; Kamanzi, A.; Roepke, B.; Tang, J.Z. Effectiveness of vegetative filter strips in reducing
pesticide loading: Quantifying pesticide trapping efficiency. J. Environ. Qual. 2009, 38 (2), 762-771.
Pesticide Reduction Equation for VFS
Calibration
Validation
R2=0.86, adjusted R2=0.84
standard error of estimate of 8.43, P-value< 0.001
Sabbagh, G.J.; Fox, G.A.; Kamanzi, A.; Roepke, B.; Tang, J.Z. Effectiveness of vegetative filter strips in reducing
pesticide loading: Quantifying pesticide trapping efficiency. J. Environ. Qual. 2009, 38 (2), 762-771.
Linking Empirical Equation with VFSMOD-W
• Parameters for estimating DP, such as DQ and DE, not
easily predicted
• Uncalibrated VFS model that predicts DQ and DE
– Vegetative Filter Strip Modeling System, VFSMOD
– Finite-element, field-scale, storm-based model
• Routes incoming
hydrograph and sedigraph
• Infiltration - Green-Ampt
• Sediment trapping GRASSF
VFSMOD-W Performance
DQ and DE
DP
Sabbagh, G.J.; Fox, G.A.; Kamanzi, A.; Roepke, B.; Tang, J.Z. Effectiveness of vegetative filter strips in reducing
pesticide loading: Quantifying pesticide trapping efficiency. J. Environ. Qual. 2009, 38 (2), 762-771.
Effect of Concentrated Flow
Poletika, N.N.; Coody, P.N.; Fox, G.A.; Sabbagh, G.J.; Dolder, S.C.; White, J. Chlorpyrifos and atrazine removal from
runoff by vegetated filter strips: Experiments and predictive modeling. J. Environ. Qual. 2009, 38 (3), 1042-1052.
Effect of Concentrated Flow
All
Atrazine
Block means
Chlorpyrifos
Mathematical Model with 18 Input Parameters
Muñoz-Carpena, R., G.A. Fox and G.J. Sabbagh. 2010. Parameter importance and uncertainty in predicting runoff
pesticide reduction with filter strips. J. Environ. Qual. 39(1):1-12
So how to handle this complexity?
• Key Drivers: Hydrologic response
• So what do we really know?
– Mathematical Models Built in Presence of
UNCERTAINTY
– Input factors (uncertainty sources): input variables,
parameters, equations, calibration data, scale, model
structure
Uncertainty Analysis (UA)
100%
80%
300
60%
40%
200
100
20%
0%
UNCERTAINTY ANALYSIS
0.38
0.34
0.31
0.28
0.25
0.22
0.19
0.16
0.13
0.09
0.06
0.03
0.00
0
Bin
CDF
MODEL
Frequency
• Propagates all these uncertainties, using the model, onto
the model output of interest.
Sensitivity Analysis (SA)
• Apportions the uncertainty in the output to different
sources of uncertainty in model input
For model with 2 input factors: A, B. Residual variance C
TOTAL OUTPUT VARIANCE
200
100%
80%
60%
40%
100
20%
0%
SENSITIVITY
ANALISIS
SENSITIVITY
ANALYSIS
0.38
0.34
0.31
0.28
0.25
0.22
0.19
0.16
0.13
0.09
0.06
0.03
0
0.00
C
?
300
Bin
CDF
B
?
Frequency
A
?
UA/SA Methods
• Why is it important?
– Explore model behavior, identify influential
parameters, characterize interactions, simplify
• Local vs. global sensitivity:
– Local techniques inherently assume models are
monotonic, linear and additive
– Parameters are varied over a limited range and about
an assumed central value, one at a time –
interactions of parameters are not accounted for
– Global analysis techniques attempt to measure total
sensitivity to a parameter
Two-Step Global Process
1. Global SA – Screening with limited number of simulations
(Morris Method) - QUALITATIVE RESULTS
2. Global SA and UA - Variance-based method (Extended
Fourier Analysis of Sensitivity Test - Extended FAST) QUANTITATIVE RESULTS
Step 1: Screening w/ Morris Method
0.20
minimum
0.15
s
• Morris Method results
in two sensitivity
measures: μ* and σ
σ- Interactions
• Uses few simulations to map relative sensitivity
• Identifies a subset of more important parameters for
quantitative analysis
• Provides an early indication of the importance of first
order effects vs. interactions
0.10
0.05
0.00
0.00
a
valueSH
0.05
TOPO
detent
0.10
m*
0.15
μ* - Importance
0.20
Step 2: Variance-Based Method
• Quantifies the direct contribution to variance of each
parameter
• Quantifies the total contribution to variance of all the
interactions between parameters
• Variance decomposition requires a large number of
simulations per parameter, hence the need for initial
screening (Morris)
Step 2: Variance-Based Method
V (Y )  V1  V 2  ...  V k  R
V(Y) – variance of output, Vi – variance due input factor
Xi, k – number of uncertain factors, R - residual
R
V3
V1
V2
Quantitative Extended FAST
1. Si - first-order sensitivity index: Si = Vi / V(Y)
2. ST(i) - total sensitivity index
For model with 3 parameters: A, B, and C:
ST(A) = SA + SAB + SAC + SABC
S
T(A)
STi - Si = higher-order effects
SABC
SAC
SAB
SA
Evaluation Framework
Application of Framework to VFS Studies
• Uniform Flow Studies:
– Arora et al. (1996), Patzold et al. (2007) and Poletika
et al. (2009)
– Input PDFs derived for the model’s 18 input variables
– Output variables: DQ, DE, and DP
Uniform Flow Studies – Morris DQ
Poletika and Patzold
Arora
40
30
Q - Poletika et al. (2009)
Q - Arora et al. (1996)
Standard Deviation of
Elementary Effects,
Standard Deviation of
Elementary Effects,
25
30
20
VKS
10
OS
FWIDTH OI
0
0
10
20
15
10
VKS
OS VL
5 FWIDTH
OI
SOA
RNA
0
20
30
Absolute Value of Mean Elementary Effects, *
40
0
5
10
15
20
25
Absolute Value of Mean Elementary Effects, *
30
Uniform Flow Studies – Morris DE
Poletika and Patzold
Arora
5
10
E - Arora et al. (1996)
4
Standard Deviation of
Elementary Effects,
Standard Deviation of
Elementary Effects,
E - Poletika et al. (2009)
3
2
OI
OS
VKS
SAV
1
DP
SS
8
6
4
OI
VKS
SOA
VL FWIDTH
0
1
2
3
4
Absolute Value of Mean Elementary Effects, *
5
0
VN
SS
RNA
0
0
DP
2
2
4
6
8
Absolute Value of Mean Elementary Effects, *
10
Uniform Flow Studies – Morris DP
Poletika and Patzold
Arora
35
15
P - Arora et al. (1996) - Metolachlor
P - Patzold et al. (2007) - Metolachlor
Standard Deviation of
Elementary Effects,
Standard Deviation of
Elementary Effects,
30
25
20
15
10
VKS
OI OS
5
KOC
0
0
5
PCTC
10
12
9
6
FWIDTH
3
VL
OS
OI
DP VN
KOC
VKS
SOA
RNA
PCTC
0
15
20
25
30
Absolute Value of Mean Elementary Effects, *
35
0
3
6
9
12
Absolute Value of Mean Elementary Effects, *
15
Uniform Flow Studies – Extended FAST
• Global SA confirmed Morris results:
– Removal efficiencies were not simple and were dominated by
interactions and non-linear responses
– VKS single most important input factor (DQ and DP)
Total Output
Variance
Explained by an
Input Parameter
= First-Order
Index
Si = Vi / V(Y)
Uniform Flow Studies – Extended FAST
• Global UA provided ranges in expected DQ, DE, and DP:
25%
Poletika et al. (2009)
Q
E
P - Atrazine
P - Chlorpyrifos
Relative Frequency
20%
15%
10%
Towards Q Towards E
5%
0%
0%
20%
40%
60%
80%
100%
Percent Reduction in Runoff ( Q), Erosion ( E) and Pesticide ( P)
Application of Framework to VFS Studies
• Uniform vs. Concentrated Flow:
– Poletika et al. (2009) study included both uniform flow
and concentrated flow treatments
– Input PDFs derived for the model’s 18 input variables
with varying FWIDTH distributions (4.6 m vs. 0.46 m)
– Output variables: DQ, DE, and DP
Uniform vs. Concentrated – Morris DQ
Uniform
Concentrated
40
5
Q - Concentrated Flow
Standard Deviation of
Elementary Effects,
Standard Deviation of
Elementary Effects,
Q - Uniform Flow
30
20
VKS
10
FWIDTH
0
0
OS
OI
10
4
3
2
VKS
1
FWIDTH
0
20
30
Absolute Value of Mean Elementary Effects, *
40
0
OS
OI
1
2
3
4
Absolute Value of Mean Elementary Effects, *
5
Uniform vs. Concentrated – Morris DE
Uniform
Concentrated
5
15
E - Concentrated Flow
4
Standard Deviation of
Elementary Effects,
Standard Deviation of
Elementary Effects,
E - Uniform Flow
3
2
OI OS
VKS
SAV
1
12
9
6
3
DP
SS
0
0
0
1
2
3
4
Absolute Value of Mean Elementary Effects, *
5
DP
VKS VN SS
VL
FWIDTH
VL FWIDTH
0
3
6
9
12
Absolute Value of Mean Elementary Effects, *
15
Uniform vs. Concentrated – Morris DP
Uniform
Concentrated
25
6
P - Atrazine - Concentrated Flow
5
20
Standard Deviation of
Elementary Effects,
Standard Deviation of
Elementary Effects,
P - Atrazine - Uniform Flow
15
10
VKS
5
OI OS
KOCPCTC
0
0
5
4
3
2
FWIDTH
1
OI OS
VL
0
10
15
20
Absolute Value of Mean Elementary Effects, *
25
0
1
VN
VKS
KOC
SS
2
DP
PCTC
3
4
5
Absolute Value of Mean Elementary Effects, *
6
Uniform vs. Concentrated – Extended FAST
• Global SA results:
– Percent of total output variance explained by first-order effects:
• 48-64% for Uniform Flow
• 19-21% for Concentrated Flow
– Uniform flow - DQ controlled model response under uniform flow
with VKS accounting for 46-51% of total output variance
– Concentrated flow – not one input factor explained more than
8% of the total output variance
• Unique processes introduced into VFS during concentrated
flow
Uniform vs. Concentrated – Extended FAST
• Global UA provided ranges in expected DQ, DE, and DP:
30%
PDF - Uniform Flow
Relative Frequency
25%
Q
E
P - Atrazine
P - Chlorpyrifos
20%
15%
10%
5%
0%
0%
20%
40%
60%
80%
100%
Percent Reduction in Runoff ( Q), Erosion ( E) and Pesticide ( P)
Uniform vs. Concentrated – Extended FAST
• Global UA provided ranges in expected DQ, DE, and DP:
30%
PDF - Concentrated Flow
Relative Frequency
25%
Q
E
P - Atrazine
P - Chlorpyrifos
20%
15%
10%
5%
0%
0%
20%
40%
60%
80%
100%
Percent Reduction in Runoff ( Q), Erosion ( E) and Pesticide ( P)
Conclusions
• Global SA and UA helped in the analysis of VFS
– Hydraulic conductivity most important input factor for
flow
– Average particle diameter and conductivity most
important for sedimentation
– Same parameters most important for pesticide
trapping
• Significant interaction effects between variables,
especially for concentrated flow
• Global UA showed commonly observed reduction in
pesticide trapping with concentrated flow
Questions?
E-mail:
garey.fox@okstate.edu
Uniform Flow Studies – Extended FAST
• Global UA provided ranges in expected DQ, DE, and DP:
16%
10%
Arora et al. (1996)
Patzold et al. (2007)
Q
E
P - Atrazine, Cyanazine
P - Metolachlor
12%
10%
Q
E
P - Metolachlor
P - Pentimethalin
P - Terbuthylazine
8%
Relative Frequency
Relative Frequency
14%
8%
6%
4%
6%
4%
2%
2%
0%
0%
0%
20%
40%
60%
80%
100%
Percent Reduction in Runoff ( Q), Erosion ( E) and Pesticide ( P)
0%
20%
40%
60%
80%
100%
Percent Reduction in Runoff ( Q), Erosion ( E) and Pesticide ( P)