AN ABSTRACT OF THE THESIS OF
John W.P. Metta for the degree of Master of Science in Biological and Ecological
Engineering and Geography presented on December 3, 2007.
Title: Sensitivity Analysis of the Catchment Modeling Framework (CMF) and Use
in Evaluating Two Agricultural Management Scenarios
Abstract approved:
John P. Bolte
Gordon Matzke
Watershed-scale fate/transport modeling of contaminants is a tool that scientists and
land managers can use to assess pesticide contamination to stream systems. The
Catchment Modeling Framework (CMF) is a catchment-scale fate/transport modeling
tool. It was developed to help scientists and land managers assess the eects of
possible land-use decisions on water quality. This study performed a sensitivity
analysis on the CMF using Extended Fourier Amplitude Sensitivity Testing (FAST)
methods. The hydrology model and the pesticide model were analysed separately.
Additionally, results of a local sensitivity analysis are compared to a global analysis.
Finally, the model is used to assess the eectiveness of two possible land-use strategies.
The sensitivity analysis showed that initial soil moisture and porosity were the
dominant rst-order parameters for the hydrology model. Combined, they yielded
greater than 50% of the total rst-order sensitivity. Results from the local sensitivity
analysis compared less than favorably with the global analysis.
The sensitivity analysis of the pesticide model showed that initial soil moisture,
porosity and saturated hydraulic conductivity are the dominant rst-order parameters,
again combining to yield greater than 50% of the total rst order sensitivity.
The model was then used to assess the relative benet of reducing the cultivated
area of an agricultural catchment (eld size) vs. reducing the amount of pesticides
that land directly on the soil. Results show that reduction in eld size yields little
benet when compared to reducing the amount of pesticides landing on the soil.
Management implications of this nding are explored.
c
Copyright by John W.P. Metta
December 3, 2007
All Rights Reserved
Sensitivity Analysis of the Catchment Modeling Framework (CMF) and Use in
Evaluating Two Agricultural Management Scenarios
by
John W.P. Metta
A THESIS
submitted to
Oregon State University
in partial fulllment of
the requirements for the
degree of
Master of Science
Presented December 3, 2007
Commencement June 2008
Master of Science thesis of John W.P. Metta presented on December 3, 2007.
APPROVED:
Co-Major Professor, representing Biological and Ecological Engineering
Co-Major Professor, representing Geography
Head of the Department of Biological and Ecological Engineering
Chair of the Department of Geosciences
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of Oregon
State University libraries. My signature below authorizes release of my thesis to any
reader upon request.
John W.P. Metta, Author
ACKNOWLEDGEMENTS
To John Bolte. After turning down his project for the wrong reason, I returned to him
a year and a half later nearly ready to leave the masters program. With the wave of a
wand, he found a project that was great for me, funding for what I needed, and
numerous counseling sessions during which he said little in words and depths in
meaning. I would likely not have a masters degree were it not for his help. To Je
c
M Donnell, Gordon Grant and Julia Jones for their incredible understanding in my
time of crisis. To Stephen Lancaster for his help in bringing me to Oregon State
University, to the wonders and diculties of complex mathematics, and eventually to
my switch to the Geography program. To Kellie Vaché, for his incredible help and
kindness, and wonderful family, and let's not forget two trips to Germany. To Lutz
Breuer and Herr Frede and the rest of the wonderful people at the University of
Gieÿen, Germany for making me feel so welcome. I dearly hope I can return. To
Brent, Chris, Kristel, Rob, Colin, Biniam, Sam, Brian and a host of other Geography
students who struggled for nearly two years to convince me that I just didn't t in on
the Geology side because I laughed way too much. To Gordon Matzke who likes
interesting cases. I'm glad mine was interesting because it means alot to be advised by
one so famous and uncompromising. To Amiee, David, Alan, Kevin, Kelly, Colin and
the rest of the musicians with whom I've played, and to Barbara, Sarah, Danielle,
Laura and all other hosts where I've been allowed to play music. To John Selker, for
making me realize that I shouldn't already know it, but that I can learn it.
But mostly to my second skin, for not pulling away from my body during my time
in the re.
TABLE OF CONTENTS
Page
1
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
Sensitivity Analysis of CMF Hydrologic Model . . . . . . . . . . . . .
4
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2.2
Review of Sensitivity Analysis Methods
6
2.2.1
Mathematical Foundations
2.2.2
Advancements to Simple Sensitivity
. . . . . . . . . . . . .
13
2.2.3
Variance-Based Methods . . . . . . . . . . . . . . . . . . . .
15
2.2.4
Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.3
Hydrology Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.4
Site Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.5
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.6
2.7
3
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
6
2.5.1
Evaluative Criteria . . . . . . . . . . . . . . . . . . . . . . .
30
2.5.2
Screening-level Sensitivity Estimation
. . . . . . . . . . . .
32
2.5.3
Global Sensitivity Analysis
. . . . . . . . . . . . . . . . . .
33
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.6.1
Local Sensitivity Results . . . . . . . . . . . . . . . . . . . .
34
2.6.2
Extended FAST Results . . . . . . . . . . . . . . . . . . . .
46
Conclusions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
Sensitivity Analysis of CMF Pesticide Model . . . . . . . . . . . . . .
55
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.2
Pesticide Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.3
3.4
3.2.1
Upslope Model
. . . . . . . . . . . . . . . . . . . . . . . . .
56
3.2.2
Instream Model . . . . . . . . . . . . . . . . . . . . . . . . .
59
Method
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.3.1
Evaluative Criteria . . . . . . . . . . . . . . . . . . . . . . .
60
3.3.2
Parameters
. . . . . . . . . . . . . . . . . . . . . . . . . . .
60
Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
62
3.4.1
3.5
Management implications
Conclusions
. . . . . . . . . . . . . . . . . . .
64
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
TABLE OF CONTENTS (Continued)
Page
4
Comparison of Two Pesticide Mitigation Strategies using CMF
4.1
. . . . .
67
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
4.1.1
4.2
CMF Sensitivity, Revisited
. . . . . . . . . . . . . . . . . .
68
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
4.2.1
Assumptions
. . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2
Variable Parameters
70
. . . . . . . . . . . . . . . . . . . . . .
72
4.3
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4.4
Management Implications
75
4.5
. . . . . . . . . . . . . . . . . . . . . . .
4.4.1
Application Method
. . . . . . . . . . . . . . . . . . . . . .
76
4.4.2
Crop Density . . . . . . . . . . . . . . . . . . . . . . . . . .
77
4.4.3
Intercropping . . . . . . . . . . . . . . . . . . . . . . . . . .
79
4.4.4
Dose Modication
. . . . . . . . . . . . . . . . . . . . . . .
80
4.4.5
Timing
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
Conclusions
4.5.1
. . . . . . . . . . . . . . . . . . . . . . . . . .
83
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
5
Conclusion
Future Work
A Ghost Parameter
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
LIST OF FIGURES
Figure
Page
2.1
Model response (a) and sensitivity results (b) for Equation 2.7.
. . . . .
10
2.2
Model response (a) and sensitivity results (b) for Equation 2.8.
. . . . .
11
2.3
Plot of three dierent transformation functions (a), (c) and (e) and their
respective empirical distributions (b), (d) and (f ) (from:
1999).
2.4
Saltelli et al.,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
Scatterplots of sampling points in a two-factor case, based on the transformations given in Equation 2.21 (a), Equation 2.22 (b) and Equation 2.23 with one (c) and two (d) resamplings of the random phase-shift
modier
ϕ
(from:
Saltelli et al., 1999).
. . . . . . . . . . . . . . . . . . .
25
2.5
Initial saturation values vs. Nash-Sutclie eciencies for 500 model runs.
36
2.6
kdepth values vs. Nash-Sutclie eciencies for 500 model runs.
37
2.7
Saturated hydraulic conductivity values vs. Nash-Sutclie eciencies for
. . . . .
500 model runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
2.8
phi values vs. Nash-Sutclie eciencies for 500 model runs.
40
2.9
Power law exponent values vs. Nash-Sutclie eciencies for 500 model
. . . . . . .
runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.10 Pore size distribution values vs. Nash-Sutclie eciencies for 500 model
runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
2.11 Residual water content values vs. Nash-Sutclie eciencies for 500 model
runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.12 Wilting point values vs. Nash-Sutclie eciencies for 500 model runs.
44
.
45
. . . . . . . . . . . .
49
2.14 Total-order FAST results for the Hydrology model. . . . . . . . . . . . .
50
2.13 First-order FAST results for the Hydrology model.
2.15 First- and Total-order results for the Hydrology model using
evaluation criteria.
3.1
r2
as the
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
First-order FAST results for the pesticide model.
. . . . . . . . . . . . .
52
63
LIST OF FIGURES (Continued)
Figure
Page
3.2
Total-order FAST results for the pesticide model. . . . . . . . . . . . . .
65
4.1
Plots showing instream pesticide mass plotted against study parameters.
74
LIST OF TABLES
Table
Page
2.1
Model results (a) and sensitivity (b) for Equation 2.8.
. . . . . . . . . .
2.2
Parameters used in the sensitivity analysis, their mathematical symbols,
equations in which they are found, and the ranges used in this study. . .
2.3
2 for all hydrology variables. . . . . . . . . . . . . . . . . . .
47
Total Order results of FAST test of Nash-Suttclie, Root Mean Squared
Error, and R
3.1
29
First Order results of FAST test of Nash-Suttclie and Root Mean Squared
Error, and R
2.4
9
2 for all hydrology variables. . . . . . . . . . . . . . . . . . .
48
FAST sensitivity values for all model parameters using Mass and Peak
concentration as measurement indicators.
. . . . . . . . . . . . . . . . .
62
4.1
Fraction of pesticide landing on soil (Fgnd ) for various crops. . . . . . . .
77
4.2
Estimated mean (w̄ ) and maximum (wm ) limits (in terms of mass fractions mg/kg ) for initial pesticide residues on crop groups following applications of kg/ha. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
DEDICATION
For Jessica.
1 Introduction
These and other developments in the eld of agriculture contain the
makings of a new revolution. It is not a violent Red Revolution like that of
the Soviets, nor is it a White Revolution like that of the Shah of Iran. I call
it the Green Revolution. (
Gaud , 1968)
During his speech to the Society for International Development, William Gaud called
Gaud , 1968).
pesticides one of the physical requirements of the new agriculture (
Used
ubiquitously in the agricultural industry to maintain production gures while minimizing losses, their development and use was indeed a blessing. Like so many blessings,
however, we are nding increasingly that pesticide use comes with some signicant costs,
not the least of which are the negative human health eects associated with their use.
Agricultural pesticides are probably some of the most regulated chemical products used
in the U.S. with upwards of 14 separate federal regulations governing their use, the two
most notable being the Federal Insecticide, Fungicide and Rodenticide Act (FIFRA)
1
and the Federal Food, Drug and Cosmetic Act (FFDCA).
Despite this regulation, pes-
ticide residues both from currently applied and previously banned pesticides are
still found both in the environment and food supply at potentially dangerous levels (e.g.
Carpenter , 2004; Bonn , 1999; Brasher and Anthony , 2000; Larson et al., 1999).
In order to mitigate the hazards involved with pesticide contamination, farmers, regulators and land managers need to evaluate management practices to determine which
ones will be both economically and logistically viable.
Historically, such evaluations
have involved developing a plan, implementing it, and then testing whether the desired
1
Most, if not all, regulations are in place specically to protect human health, as opposed to ecosys-
tem health or another concern.
2
eects had been achieved.
Governmental and non-governmental scientists alike believe that modeling can be
Larson et al.,
an eective tool in estimating pesticide contamination (
1999;
Gilliom ,
2001). Many also propose that the use of regionally applicable models that link landuse/economics and pesticide use are benecial (
Bernardo et al.,
1993). The most re-
cent watershed-scale models can eectively estimate hydrologic response based on landuse (
Vaché , 2003).
These systems have been used successfully to study various aspects of
water quality in relation to fertilizer contamination (
1998;
Vaché et al., 2002; Srinivasan et al.,
Santelmann et al., 2001; Arnold et al., 1998), and are currently being developed
for use in modeling pesticide contamination.
Linking GIS, watershed-scale modeling
and alternative futures development can serve the purpose of analyzing possible management scenarios without the cost of implementing large scale land-use planning or
regulatory changes.
Alternative Futures are hypothetical scenarios (e.g.
land-use estimations) which
can be used to evaluate possible management decisions.
Using alternative futures,
scientists and managers can generate hypothetical conditions and then analyze the
possible eects of those conditions.
For example, desired conditions of a watershed
can be developed in GIS by changing land-use/land cover (LULC) attributes, then GIS
based environmental models can be run on those alternative conditions to model various
management scenarios. Such studies have already been used in county planning (
and McDowell ,
2001;
Steinitz et al.,
Steinitz
Berger
1994), agricultural management analysis (
and Bolte , 2004; Vaché et al., 2002) and riparian restoration (Hulse and Gregory , 2001).
This thesis provides an analysis of the Catchment Modeling Framework (CMF),
a hydrologic and pesticide fate/transport model linked to GIS, for use in evaluating
3
Vaché ,
hydrology and pesticide contamination given land-use/land cover data (
2003).
Chapter 2 provides a full sensitivity analysis (SA) of the hydrologic model within CMF,
including a background on SA fundamentals and methodology. Chapter 3 provides a
sensitivity analysis of the pesticide model within CMF and touches on possible management implications of the pesticide model's sensitivity. Chapter 4 is a comparison of two
possible pesticide mitigation strategies, eld-size reduction and pesticide application
modication, in a hypothetical agricultural basin.
4
2 Sensitivity Analysis of CMF Hydrologic Model
2.1
Introduction
Watershed-scale hydrology and fate/transport models have become increasingly complex with the advancement of computing resources and hydrological and enviro-chemical
knowledge. Coincident with the increasing complexity of the models and with increases
in the numbers of model parameters is an increase in the importance of assessing the
model's performance both as a way to determine its utility and as a way to evaluate
possible improvements (
Kelton , 1997).
One way to accomplish this model performance
assessment is to perform a sensitivity analysis.
Sensitivity analysis (SA) has been interpreted dierently by various technical communities and problem settings (
Saltelli et al.,
2004, p. 42), however, it can generally
be dened as the assessment of the model output by the apportioning of the variation
of that output, either qualitatively or quantitatively, among the model inputs. More
Frey
simply, it is the assessment of the impacts of input changes on output values (
et al.,
2004).
The motivations one uses in performing sensitivity analysis are varied
and include the identication of variability and uncertainty sources, verication and
validation, data requirement prioritization, parameter prioritization and overall model
Frey et al., 2004; Ascough et al., 2005; Fraedrich and Goldberg , 2000; Klei-
renement (
jnen and Sargent ,
2000).
Saltelli et al.
(2004, p. 61) also made the argument that a
well-designed sensitivity analysis can inform model users and designers about the robustness (or, alternatively, fragility) of the model itself because it often uncovers model
5
errors. In addition to these motivations, both the European Union and the U.S. governments are increasingly demanding that SA be published on models used in policy
Saltelli et al., 2004, p.
decisions (
61).
The purpose of this study is to perform a sensitivity analysis of the hydrologic
model within the Catchment Modeling Framework (CMF, hydrology presented in
and Mc Donnell ,
Vaché
2
2006). CMF is a watershed-scale (1-999 km ) hydrology model with
fate/transport componants for sediment, conservative tracers and pesticides. While the
model has been used eectively in studies (
Vaché and Mc Donnell , 2006), a sensitivity
analysis has never been performed on the main hydrologic model, either as an assessment
of importance of model parameters, or to estimate the importance of the main model
assumptions of hydrology. This study attempts to ll this gap.
Section 2.2 provides a summary review of sensitivity analysis, including some of the
most important local and global analysis methods. Section 2.3 reviews the hydrology
model component of CMF, specically in relation to the parameters that are studied
in the analysis. Section 2.4 introduces the study site and archival dataset used to run
the model for both this analysis, and the pesticide validation in the following chapter.
Section 2.5 explains the methodology chosen for both the local and global SA, while
Section 2.6 provides the results and summary discussions. Finally, Section 2.7 provides
conclusionary remarks.
6
2.2
Review of Sensitivity Analysis Methods
1
Put simply, there are two types of sensitivity analyses, local and global . Local sensitivity analysis allow assessment of model response in a very small area of the model
domain by focusing on small perturbations in model input. Global methods attempt to
analyse the eect of the entire parameter space and focus on model sensitivity to either
individual (rst order), paired (second order) or grouped (higher order) parameters.
2.2.1
Mathematical Foundations
To fully understand the concepts of sensitivity as a whole, as well as some considerations one must make when chosing a sensitivity analysis method, we will consider the
mathematical foundations of sensitivity. Consider the function
y = f (θ)
where
y
θ
is an
(2.1)
n-length vector of model parameters: θ = {x1 , x2 , . . . , xn }.
resulting from a change in any single parameter
xi
The change in
can be expressed in mathematical
form by a Taylor series expansion of the function:
1 δ2y
δy
∆xi +
∆x2i + . . .
f xi + ∆xi , xj|j6=i = f (θ) +
δxi
2! δx2i
where the expansion proceeds until all higher order terms in
f (θ)
(2.2)
are accounted for. If
higher order terms are non-existent, or are suitably small in comparison to the rst-order
1
Saltelli et al. (2000) suggest that there are actually 3 types of analysis, the third being a screening
analysis. This, they suggest, is a relatively rapid, often qualitative, assessment of model response which
can guide model evaluators to possible issues before a more detailed analysis is undertaken.
7
terms, the expansion can be reduced to
δy
∆xi
f xi + ∆xi , xj|j6=i = f (θ) +
δxi
(2.3)
thus:
∆f (θ) = f xi + ∆xi , xj|j6=i − f (θ)
δy
=
∆xi
δxi
(2.4)
Mc Cuen , 1973) and
Equation 2.4 has been called the linearized sensitivity equation (
measures the change in model output
(∆y) due to a change in the ith
parameter
(∆xi ).
The general denition for sensitivity is given as:
f xi + ∆xi , xj|j6=i − f (θ)
S=
∆xi
Equation 2.5 denes the
absolute sensitivity
element of the input parameter
θ.
(2.5)
of a linear model to a change in the
ith
The sensitivity value is only valid in the local region
of the parameter space.
It is important to remember that Equation 2.5 was derived from Equation 2.4,
which ignores all but the rst order terms of Equation 2.2. As such it represents a very
important assumption of linearity. Equation 2.5 and derivations of it, can only be used
to assess rst order models if it is known that the higher order terms of the model are
non-existent or not important.
Absolute sensitivity is not appropriate for comparison between model factors because the computed values are not invariant to the magnitude of
y
or
xi
Mc Cuen ,
(
1973). Comparison between model parameters can be done by dividing both terms by
8
the nominal value:
[f (xi +∆xi ,xj|j6=i )−f (θ)]
f (θ)
Sr =
∆xi
xi
(2.6)
thereby yielding a value which provides an estimate of the relative change in
the relative change in
xi .
This is the
relative sensitivity,
due to
and provides an estimate of
comparison between model factors that is invariant to the magnitudes of
2.2.1.1
y
y
and
xi .
Local SA and Non-Linear Models
SA using Equations 2.5 or 2.6 is an eective analysis technique only for rst-order models
with few parameters. More appropriately, it is eective for models with parameters that
do not aect other parameters at second-order or higher levels. The main issue with
this method is that it assesses model sensitivity to a single parameter only at a single
point in the model domain.
Local analysis can be ineective where more than one parameter controls the model
output because each parameter can aect other parameters, as well as the model output.
Thus, each parameter can have both direct eects (i.e. aecting model output, called
rst-order) and indirect eects (i.e.
aecting other parameters, called second-order).
The simplest illustration of this situation can be seen by evaluating the two equations
where
θ
is a parameter vector
f (θ) =x + a
(2.7)
g(θ) =xa + a
(2.8)
θ = {x, a}.
Equation 2.7 is a linear, rst-order equation
9
x\a
2
3
4
x\a
2
3
4
2
6
11
20
2
1
1.75
3
5
27
128
629
5
2
7.75
31.2
10
102
1003
10004
10
3.67
27.75
222.2
Table 2.1: Model results (a) and sensitivity (b) for Equation 2.8.
while Equation 2.8 is non-linear and second-order.
The model response of Equation 2.7 is, of course, linear (Figure 2.1a).
words, as
x
increases across its range, the dierence between
remains constant. While parameter
sensitivity to parameter
value of parameter
x
a
does
aect the output of
f (θ)
f,
In other
f (x + ∆x, a)
and
we note that model
is stable across the entire model domain, regardless of the
a (Figure 2.1b).
In other words, parameter
the model's sensitivity to parameter
x;
a does not actually eect
thus the assumptions of Equation 2.4 are valid.
Contrasting with this is the results of runs for Equation 2.8 (Figure 2.2a). We see
that as
and
to
a
x
x
increases across the model domain, the magnitude of dierence between
g(x + ∆x, a) increases.
The model response shows that the sensitivity of the model
is lower for lower values of
x
than for higher values. Furthermore, the parameter
has a signicant eect on the model response, and higher values of
the magnitude of dierence between
For all values of
dierence between
However, as
x
a,
g(θ)
and
g(x + ∆x, a)
we see that for low values of
g (θ)
increases,
and
g
g(θ)
g (x + ∆x, a)
x, g
directly eect
(Figure 2.2b).
yields results such that the
are quite close regardless of the value of
increases such that for high values of
of magnitude for a unit increase in
a
a (Table 2.1).
x, g
a.
increases an order
Thus, the assumptions of Equation 2.4
are not valid because the higher-order terms of the Taylor expansion are important. In
the case of model
invalid methods.
g,
the simple mathematical techniques derived from Equation 2.4 are
10
(a) Model response
(b) Sensitivity to parameter x
Figure 2.1: Model response (a) and sensitivity results (b) for Equation 2.7. Sensitivity
was calculated using Equation 2.6. For a given value for parameter
the model to parameter
x
is unchanging.
a,
the sensitivity of
11
(a) Model response
(b) Sensitivity to parameter x
Figure 2.2: Model response (a) and sensitivity results (b) for Equation 2.8. Sensitivity
was calculated using Equation 2.6. In contrast to Figure 2.1, the slope of the sensitivity
curve reacts dierently depending on the value of
a.
12
Despite the knowledge that the mathematical assumptions made in Equation 2.4
require a linear model, many researchers try to rely on these techniques to assess model
sensitivity in large, multi-parameter models. It is often believed that by varying one parameter at a time (a technique called the OAT, or one-at-a-time, approach) a researcher
can achieve a genuine understanding of model response.
Such approaches have been used to try to assess environmental and hydrologic mod-
Ho et al., 2005; Ravalico et al., 2005).
els (
Arnold et al.,
The Soil Water Assessment Toolkit (SWAT,
1998) has also been the subject of numerous local and OAT sensitivity
Francos et al., 2001; van Griensven et al., 2002; Lenhart et al., 2002), despite
analyses (
the obvious problems with applying these techniques to complex, non-linear models (See
also:
Saltelli , 1999).
Enhancements of OAT techniques have even been suggested (e.g.
van Griensven et al.,
2006), often by improving the sampling strategy, or exploring
distributed derivative strategies such as that developed by
Morris
(1991).
In a recent review of the usage of various sensitivity analysis techniques throughout
the literature,
Saltelli et al. (2006) found that the almost totality of sensitivity analyses
met in the literature, not only in
Science's
ones. . . , are of an OAT type. They argue
strongly that these techniques are, by today's standards, quite primitive. Providing
both mathematical and logical reasoning, they state that they nd unwarranted any
use of OAT approaches with models other than strictly linear, and that the use of
OAT methods are illicit and unjustied, unless the model under analysis is proved to
be linear.
are
While some state that the use of OAT methods
justied because of the compu-
van Griensven et al., 2006), Saltelli
tational expense of other methods, such as FAST (
et al.
(2006) argue convincingly that the complexity of truely global techniques such
as FAST is not overwhelming. Furthermore, the availability programming libraries and
13
Saltelli et al., 2004, Chap.
end-user programs such as SimLab (
7) make the exploration
of global, variance-based techniques worth the avoidance of the consequences of relying
on local or OAT techniques.
2.2.2
Advancements to Simple Sensitivity
Various ways have been proposed to further enhance the information provided by local
sensitivity. Most of these methods involve enhancing the assumptions of Equation 2.4
to include higher-order terms, or by integrating many local eects into a semi-global
analysis.
Though there are a great many approaches, only two are presented here
because they have direct applicability to environmental modeling.
2.2.2.1
Second-Order Reliability Method
Yen et al. (1986) describe a way to measure the mean (rst moment) and the variance
(second moment) of the model output. They do this by evaluating the derivative of the
output to model input at a single point, and call this the First-Order, Second Moment
(FOSM) method. The method involves approximating the model output solution as a
Taylor series:
n
X
δf
(x − x̄i )
f (θ) = f θ̄ +
δxi
(2.9)
i=1
where
θ̄ = {x̄1 , . . . , x̄n }.
The mean and standard deviation can then be calculated as:
f¯ =f θ̄
σf2 =
n X
i=1
(2.10)
δf
σθ
δxi
2
(2.11)
14
where
σ θ = σ x1 , . . . , σ xp .
Special forms of the FOSM method have also been developed.
One such special
form is based on the second-order expansion of the Taylor series evaluated at the meanvalue point in the model parameter space (
Saltelli et al., 2000, in van Griensven et al.,
2006). The form, called the Mean-Value Second Order Reliability Method (SORM), is
expressed as:
n
n
n
X
1 X X δf
δf
(xi − x̄i ) + ×
(xi − x̄i ) (xj − x¯j )
M (θ) = M θ̄ +
δxi
2
δxi xj
(2.12)
i=1 j=1
i=1
thus creating a matrix of second-order derivatives
Ai,j =
σi σj
2
A,
δ2f
δxi δxj
containing elements of the form:
(2.13)
Eigenvalues are obtained by diagonalization of the resulting matrix and sensitivity
values are then represented by a quadratic surface.
SORM can yield good results when the parameters are correlated, and has been
used in analysis of water quality models (
2.2.2.2
Mailhot and Villeneuve , 2003).
Morris Methods
Morris (1991) proposed the possibility of integrating local sensitivity eects into a (semi)global analysis. The elementary eects of the model parameters are found by evaluating
the model with independent sample vectors
xi
o
n
2
1
,
,
.
.
.
,
1
such that each component can contain p possible values in the set 0,
(p−1) (p−1)
model parameters,
n.
An
n-dimensional
θ, each the size of the number of congurable
sample vector
θ
contains the components
15
where
If
∆
xi
is scaled to(0, 1). The model domain
is a pre-determined multiple of
Θ
is then an
n-dimensional, p-level
grid.
1
th
factor
(p−1) , then the elementary eect of the i
Alam et al., 2004):
at a given point in the space is (
fi (θ) =
where
θ
is any value in
[M (x1 , . . . , xi−1 , xi + ∆, xi+1, . . . , xk ) − M (θ)]
∆
Θ
such that
θ+∆
remains in
Θ.
new sample vector is completed until a collection of samples
dening an orientation matrix
B∗
(2.14)
The process of selecting a
θ1 , θ2 , . . . , θn−1
is produced
Alam et al. (2004) which can then be used to assess
the elementary eect of each parameter.
Saltelli et al. (2004, Chap.
4) fully describe the
Morris method as well as detail its usefulness. They note that its primary utility comes
in its use as a factor screening method as an inexpensive way to rank sensitivity to a
few parameters in a large parameter set. However, they state explicitly that it provides
only a
qualitative
assessment- as a rank- of parameter importance
Saltelli et al. (2004,
p. 108), rather than a quantitative analysis of each parameter, as is assumed in
van
Griensven et al. (2006).
2.2.3
Variance-Based Methods
Local and integrated techniques are eective when model dimensionality is very small,
and for many linear, static and/or deterministic models such a local analysis may be
an appropriate choice.
As early as 1973, reasearchers realized that SA was vital to
hydrologic modeling, but that these simple methods were just not appropriate to the
Mc Cuen ,
multi-parameter modeling techniques that hydrologic modeling relied upon (
1973;
Gardner et al.,
1981;
Beck ,
1987;
Yeh and Tung ,
1993) as many higher-scale
16
hydrology models are neither linear, static nor deterministic. The number of parameters for many complex models can reach into the hundreds, and even models with
relatively few parameters (1-10) require the creation of a multi-dimensional response
surface upon which many local maxima may exist.
This surface has been likened to
a block of Swiss cheese (for a two-parameter model) where the response surface has
a great many holes representing local minima, with the size of the holes representing
uncertainty (
Abbaspour ,
2005). While local methods may be valid in a at portion of
this parameter-cheese-block, or even within one of the local minima, it is not valid for
the entire block's surface.
Whereas local methods are based on the individual evaluation of a derivative of
each given parameter
xi
in the sample vector
θ,
global SA techniques are those that
simultaneously assess the sensitivity of the model to all input parameters in the total parameter space. Global sensitivity methods allow assessment of the shape of the
model response for all parameters individually (rst-order) and collectively (higherorder) while all parameters vary simultaneously (
Saltelli et al.,
2000).
There are a
number of robust global sensitivity analysis methods including the Mutual Information
Index (MII, in
gomery ,
1998;
Ascough et al., 2005), Response Surface Method (RSM, Myers and MontSobol' ,
1995), the method developed by Sobol' (
1990, in
Saltelli and Bolado ,
Sobol' , 1993, in Ascough et al., 2005), as well as techniques using Fourier analysis
such as the Fourier amplitude sensitivity test (FAST) (
Cukier et al., 1973) and Walsh
Pierce and Cukier , 1981).
functions approach (
Sensitivity methods based on correlation or regression coecients such as the standardised regression coecient (SRC,
Draper and Smith ,
1981, in
Saltelli and Bolado ,
1998) have been shown to be less than useful for SA because the analysis is dependent
on the goodness of t of the underlying regression model.
17
Following is a description of the lineage of the FAST technique as is applied to this
study.
2.2.3.1
FAST (
Fourier amplitude sensitivity test (FAST)
Cukier et al., 1973) is a global, varianced-based technique for evaluating the To-
tal Sensitivity Indices (TSIs) of a model's parameters. Although FAST has been around
for over 30 years, it remains possibly one of the most elegant solutions to sensitivity
analysis (
Saltelli et al.,
1999).
FAST computes sensitivity by reducing the multidi-
mensional parameter space of a model's input factors to one dimension. It does this
by exploring the parameter space along a particular search-curve. A summary of the
Saltelli et al., 1999), follows.
FAST technique, as given in (
For a given model
θ,
where
k
y = f (θ),
the model domain
Θwill
contain
k
parameter vectors
is the total number of individual vectors required to characterize the full
parameter space:

θ1


x11

 

 
 θ2   x2

  1
Θ=
=

 
·
·
·

  ···

 
k
θ
xk1
x12
···
x22
···
···
···
xk2
···
x1n







··· 

k
xn
x2n
(2.15)
This parameter matrix will yield a hypercube for the parameter domain expressed
as
K n = (θ | 0 ≤ xi ≤; i = 1, . . . , n)
If we assume that
θ
is a random vector with a pdf
(2.16)
P (θ) = P (x1 , x2 , . . . , xn ),
then
18
a summary statistic for the
rth
moment of the model is
D
E Z
(r)
y
=
f r (θ) P (θ) dx
(2.17)
kn
It was suggested by
Cukier et al.
ANOVA-like decomposition of
transformation of
f,
y
(1978) that it would be possible to compute an
as a function of
θ
using a multi-dimensional Fourier
but that the computational complexity was daunting. Thus, the
authors suggested that by exploring the parameters space hypercube along a suitable
search curve, a monodimensional Fourier transformation can be accomplished at much
less computational complexity. This search curve suggested by
Cukier et al. (1978) is a
set of parametric equations dened as
∀i = 1, 2, . . . , n
xi (s) = Gi (sin ωi s) ,
where
s
varies in
[−∞, ∞],
2
{ωi } , ∀i = 1, 2, . . . , n,
and
associated with each factor .
Gi
(2.18)
is a set of angular frequencies
is a transformation function which denes the search
curve, further described in Section 2.2.3.3.
The curve searches the entire hypercube
Kn
such that as the scalar quantity
changes, all model parameters change simultaneously. Regardless of the model
transformation function
y
Gi ,
each
xi
oscillates at the corresponding frequency
shows dierent periodicities with dierent frequencies
the amplitude of oscillation of
y
at frequency
ωi
ωi .
For any
ith
f
or the
ωi
while
input factor,
will be high if the factor has a strong
inuence on the model output. Thus, the sensitivity measure of any factor
2
s
xi
is based
Saltelli et al. (1999) note that the the exploration curve is only eective if it can explore arbitrarily
close to any point of the input domain, and that this is possible if and only if the chosen set of
frequencies is incommensurate. To ensure this, they state, no frequency must be obtainable as a linear
Pn
combination of the others. Thus, it must be true that
i=1 ri ωi 6= 0, −∞ < ri < ∞.
19
on the coecients of the corresponding frequency
ωi ,
and its harmonics.
Various improvements and variations have been made to the FAST technique. For
instance,
Fang et al. (2004) suggest that using the cumulative probability rather than the
probability density for distribution transformation can increase accuracy and improve
performance.
Pierce and Cukier
(1981) suggested that the use of Walsh functions can
provide a method where variation of each factor is strictly two-valued, thus reducing
the overall computational complexity in cases where such an assumption is valid.
2.2.3.2
The Sobol' method
The Russian mathematician Ilya Sobol' (in
Sobol' ,
1990, translated in:
Sobol' ,
3
1993)
proposed another truely global technique that he suggested as an improvement over
all existing techniques. As with other techniques it decomposes the model output into
individual parameter eects and parameter interaction eects shown as
s (y) =
X
i
where
si
X
sij +
i<j
X
θ, sij
is the variance of
sijk + s12...n
(2.19)
i<j<k
is the sensitivity of the model output
parameter vector
3
si +
y
y
to the
ith
component of the input
due to interactions of
xi
and
xj ,
and
n
is
Following the conventional transliteration found in the literature, I include a trailing apostrophe
in the name.
20
the size of the input parameter vector
θ.
The sensitivity indices are then calculated as:
si
s
sij
Sij =
s
Si =
ST i =1 −
where
Si
s
∼i
s
is the rst-order sensitivity resulting from parameter
xi
order sensitivity resulting from the interaction of parameters
average variance resulting from all parameters except for
culation of total-order sensitivity
ST i
xi ,
as the main eect of
xi
and
xi
Sij
and
is the second-
xj . s∼i
is the
thus allowing for a calup to the
nth -order
of
interaction.
The individual parameter variance required in Equation 2.19 is evaluated using
Tang et al., 2006):
Monte Carlo approximations given as (
1
fb0 =
n
b
s=
sbi =
c
sc
ij =
1
n
1
n
1
n
n
X
i=1
n
X
i=1
n
X
i=1
n
X
f (xi )
f 2 (xi ) − fb0
2
f (xαi ) f xβ∼i , xαi − fb0
2
f (xαi ) f xβ∼i,∼j , xαi,j − fb0
i=1
sc
sij c − sbi − sbj
ij =c
n
2
1X
sc
f (xαi ) f xα∼i , xβi − fb0
∼i =
n
i=1
where
n
is the sample size,
xi
is the
ith
parameter of the parameter vector
θ
and
α
21
and
β
are two dierent samples of
parameter, thus
xα∼i
xi .
As stated above,
∼ i
denotes all but the
denotes all values from the parameter vector
those values are samples from the
α
θ
except
xi ,
ith
where
sample vector.
One note that should be made here regarding the Sobol' method is the computational
expense.
Sobol's original method required
rst- and total-order sensitivity, where
n
n × (2m + 1)
is the number of sample vectors required
to characterize the entire unit hypercube, and
improved method of
Saltelli
model runs to calculate the
m
is the number of parameters.
n × (2m + 2)
(2002) requires
(2006), noted that the sample size necessary to fully sample
snowpack energy balance model was
was
213 .
model runs.
Kn
An
Tang et al.
of their 18 parameter
Thus, the number of model runs necessary
8192 × (2 (18) + 2) = 311, 296.
Another note regarding Sobol's method is that Equation 2.19 requires that the input
parameter vector
θ
contain only parameters such that
xi 6= k · xj
for any
xi
and
xj .
Because of this requirement for parameter independance, the method is invalid for many
hydrologic models where parameters are quite often correlated.
2.2.3.3
Extended-FAST
Saltelli and Bolado (1998) note that the standard FAST analysis provides excellent rstorder sensitivity results, but when compared to methods such as Sobol's the higher-order
sensitivity results are less than adequate.
They argue that, as introduced by
Cukier
et al. (1978), the FAST technique can only be used to truly estimate global rst-order
sensitivity.
This situation has been improved upon by
selection of a dierent transformation function
Saltelli et al. (1999), who note that the
Gi can yield results that more completely
22
sample
K n.
They note that the original transformation function proposed by
et al. (1973) is insucient.
The function is expressed as
xi = xi e(vi sin ωi s) ,
where
xi
is the nominal value of the
endpoints of
xi
and
s
Cukier
varies in
− π2 ,
ith
π
∀i = 1, 2, . . . , n
input factor,
vi
(2.20)
denes the uncertainty range
2 .
Saltelli et al. (1999) plotted Equation 2.20 using vi = 5, xi = e−5 and ωi = 11. The
result is shown in Figure 2.3(a) with a histogram of the empirical distribution of the
parameter
xi
in Figure 2.3(b). They note that the histogram is strongly asymmetrical
because the majority of sampling points for the curve lie in the lower end of the distribution, making this transformation function appropriate only for an input parameter
whose pdf is long-tailed and positively skewed.
They then plotted an equation suggested by
Koda et al. (1979), expressed as
xi = xi (1 + v i sin ωi s)
with
v i = 1, xi =
1
2 and
(2.21)
ωi = 11. The results for this transformation function are shown
in Figure 2.3(c) with the resulting histogram in Figure 2.3(d).
This transformation
fails to yield a true uniform distribution as well, with highly sampled tails and a poorly
sampled middle region.
The solution, they suggest, is to use the following transformation function:
xi =
1 1
+ arcsin (sin ωi s)
2 π
(2.22)
which is a set of straight lines oscillating between 0 and 1 (Figure 2.3(e)), yielding a
23
Figure 2.3: Plot of three dierent transformation functions (a), (c) and (e) and their
respective empirical distributions (b), (d) and (f ) (from:
Saltelli et al., 1999).
24
distribution that is very close to uniform (Figure 2.3(f )). They note that a drawback of
all proposed transformation functions is that they always return the same points in the
unit hypercube
modier,
Kn
as
s
varies in
− π2 , π2
. Thus, they propose a random phase-shift
ϕ, be chosen uniformly in [0, 2π) yielding a transformation function expressed
as
xi =
1 1
+ arcsin (sin [ωi s + ϕi ])
2 π
(2.23)
thus yielding a search-curve that can have a start point at an arbitrary point in
thus tracing an arbitrary curve through
K n,
K n.
Figure 2.4 shows the scatterplots of Equations 2.21-2.23 for a two-factor model. Note
that Equations 2.21 and 2.22 yield a predictable path through
while Equation 2.23 can be resampled
pling of
2.2.4
Kn
4
Kn
(Figures 2.4(a,b)),
to provide non-predictable paths and full sam-
(Figures 2.4(c,d)).
Entropy
One nal approach to sensitivity is that summarized by
Krzykacz-Hausmann
(2001).
Ka-
Entropy is a scalar measure of uncertainty maximized by the uniform distribution (
pur ,
1989, in
Krzykacz-Hausmann ,
probability function
2001).
pi = (p1 , . . . , pn ),
Truthfully, it must be resampled over
Y,
given a
it is dened as
H (Y ) = −
4
For a discrete distribution of
(−π, π)
X
pi · ln pi
to satisfy the assumption of symmetry in
Saltelli et al. (1999) Appendix C, for a detailed analysis of this issue.
(2.24)
f (s).
See
25
Figure 2.4: Scatterplots of sampling points in a two-factor case, based on the transformations given in Equation 2.21 (a), Equation 2.22 (b) and Equation 2.23 with one
(c) and two (d) resamplings of the random phase-shift modier
1999).
ϕ
(from:
Saltelli et al.,
26
while for a continuous distribution of
Y
with a probability density dened as
f (y),
it
is dened as
Z
H (Y ) = −
f (y) · ln f (y) · dy
(2.25)
The result of this output is interpreted somewhat dierently than for sensitivity.
Krzykacz-Hausmann
(2001) states that
it may be interpreted as 'a measure of the extent to which the distribution of
Y
is concentrated over a small range of values, or dispersed over a wide range
of values', or, in other words, as a measure of the degree of
of
Y
indeterminacy
represented by its distribution.
One argument for entropy as a measure of sensitivity over variance is explained by
Saltelli et al.
where
(2004, pp.53-57).
X1 ∼ U (−0.5, 0.5)
and
Their explanation centers on the model
X2 ∼ U (0.5, 1.5).
Y = X1 X22 ,
The rst-order partial variance of
X2
is zero, despite it being obvious that changing that parameter will change the model
signicantly. This incongruity is not found using entropy as a measure. The authors do
note, however, that this does not mean that variance based measures should be ruled
out, because in this example it is clear that a practitioner would recover the eect of
X2
at the second order (
Saltelli et al.
Saltelli et al., 2004, p.
(2004, p.
54).
57) suggest that alternatives to variance such as entropy
[seem] to be associated with specic problems and are less convincing as a general
method for framing a sensitivity analysis.
Because of the increased mathematical
complexity and framework development that would be involved, as well as availability
of variance-based tools such as SimLab (
Saltelli et al., 2004, Chap.
7), I have decided
to ignore entropy-based methods in this study in favor of sensitivity.
27
2.3
Hydrology Model
The hydrologic model used in CMF is presented in full by
Vaché and Mc Donnell
(2006).
A shorter description of the model is presented here in order to introduce some of the
parameters used in the sensitivity analysis.
The model works by dening spatially explicit reservoirs, generally generated from
a DEM where each reservoir is a 3-dimensional unit with a dened depth,
surface area
Vt ,
A,
which is given by the DEM grid-cell size.
5
z,
The total volume of water,
within this reservoir is calculated as the sum of the saturated zone volume,
the unsaturated zone volume,
Vu ,
where the change in volume is calculated in time,
and
SSout
respectively, from adjacent reservoirs,
overland ow.
kd
and
(2.26)
dVs
=k (θ) + SSin + SSout − SOFout − kd + EXw
dt
dVu
=I − k (θ) − EXw
dt
SSin
Vs ,
as follows:
Vt =Vs + Vu
dened in Equation 2.29,
and a
t,
of days.
k (θ)
(2.27)
(2.28)
is the recharge rate,
are the rate of subsurface inow and outow,
SOFout
is the output rate of saturated excess
is the rate of loss to groundwater, and
EXw represents
the exchange
of water between the saturated and unsaturated zones as a function of water table depth
adjustment, dened in Equation 2.30.
The recharge rate is calculated as a Brooks-Corey relationship:
5
This denition of the reservoir introduces one of the important assumptions of the model, that
being that there is a dened soil depth. The model assumes that this depth is bounded by an aquatard.
Thus, testing the sensitivity of the model to parameter
assumption.
z
is a good assement of the importance of this
28
k (θ) = ks
where
ks
θ − θs
θs − θ r
is the saturated hydraulic conductivity,
is the residual water content,
Due to hysteresis,
EXw
θr
θ
λ
(2.29)
is the volumetric water content,
is the wilting point, and
θs
λ is the pore size distribution.
is calculated dierently depending on the direction of water
table change,
EXw = ∆l · x
where
∆l,




x=




Vu
A·zu
x = 0





x = φ
; ∆l > 0
(2.30)
; ∆l = 0
; ∆l < 0
the change in water table height, can be positive (rising), zero (stable) or
negative (falling).
zu
is the depth of the unsaturated zone.
Subsurface inow and outow are calculated independently for each reservoir at
each timestep as:
SSi,j =
k<9
X
Ti,j,k · S
k=0
where
i
and
j



S = Slopei,j,k
; Slopei,j,k > 0


S = |Slopei,j,k | ; Slopei,j,k < 0
are individual grid cells and each grid cell can have a maximum of 8
neighbors, each in a single direction
k.
Slope is calculated using the dierence between
the grid cell water table elevation and the neighboring grid cell's watertable elevation
and is negative in the case of a downslope neighbor. Transmissivity,
T,
is assumed to
decrease with depth as a power law, the degree of decline dened by the power law
29
Parameter
Symbol
Equation
Range
Power Law Exponent
θr
λ
z
ks
kd
θt
θi
θF C
2.31
8-15
2.29
0.01-0.1
2.29
0.08-0.5
2.31
0.8-1.4
Residual Water Content
Pore Size Index
Soil Depth
Saturated Conductivity
Groundwater Loss Rate
Trace Water Content
Initial Saturation
Field Capacity
Table 2.2:
2.29,2.31
2.27
2.31
10-250
10−6
− 10−5
0.25-0.5
Boundary Condition
0.4-0.8
Soil Parameter
0.02-0.1
Parameters used in the sensitivity analysis, their mathematical symbols,
equations in which they are found, and the ranges used in this study. Initial saturation
and eld capacity are used elsewhere in the model to evaluate initial conditions and in
the evapotranspiration calculations.
exponent,
.
It is calculated as (
Iorgulescu and Musy , 1997):
T =
where
zwt
ks · z zwt 1−
z
(2.31)
is the depth to the water table.
Table 2.2 shows the parameters for which the sensitivity of the model was analysed,
as well as the equations in which the parameters are used and the domain for each
parameter.
2.4
Site Description
This study follows results of a 4 year study of residual pesticides in agricultural surface
waters commissioned by the German Federal Ministry of Agriculture entitled 'Practicable ways and methods to avoid entry of pesticides in surface waters by run-o or drift.'
(Presented at the XI Symposium on Pesticide Chemistry in Cremona 1999). The study
30
data consisted of roughly 250 water samples spanning the years 1998-2002. The concentrations of most contemporary plant protection substances (included 12 herbicides,
13 fungicides and 2 insecticides).
The study catchment was an agricultural eld at
Lamspringe, Lower Saxony, Germany. The catchment comprises roughly 110 ha within
which are grown winter wheat, winter barley, winter rape and sugar beets. The model
simulated a period of roughly 6 months from October 1, 1998 to April 15, 1999.
2.5
Methods
In addition to a FAST analysis, I performed a type of local, screening-level sensitivity
analysis mainly as a means to further understand the model, but also to evaluate the
eectiveness of performing such an analysis.
The following sections provide details on the objective functions used in the analysis
as the evaluative criteria (Section 2.5.1), on the methods used in a preliminary screeninglevel SA (Section 2.5.2), and on the full FAST analysis (Section 2.5.3).
2.5.1
Evaluative Criteria
While the main function of CMF is the generation of rainfall/runo time series response,
both local and global SA methods measure
time series modeling, the output of
∆y where y is a single value.
Thus, in cases of
f (θ) cannot be directly used because it is evaluated
at each timestep, and would yield sensitivity results for each individual timestep. In
such cases, an objective function must be used, which will yield a single result upon
which the sensitivity can be analysed.
Three dierent objective values were chosen for this study, each providing a single
31
value for the goodness-of-t of the entire modeled timeseries.
The three objective
Nash and Sutclie , 1970):
functions are the Nash-Sutclie eciency criterion (
1
n
Ref f =
n
X
(dt − ot (θ))2
t=0
n
X
1
n
t=0
(2.32)
2
dt − d
the root mean squared error:
v
u n
u1X
RM SE = t
(dt − ot (θ))2
n
(2.33)
t=0
and the coecient of determination:

n
X



r = "
n
 X

2
t=0
where
2
dt − d ot (θ) − ot (θ)
t=0
dt − d
#0.5 " n
X
ot (θ) − ot (θ)



# 
0.5 

(2.34)
t=0
n is the number of observations, t is time, d is the observed discharge and ot (θ)is
the modeled value of discharge using the parameter vector
θ. d and ot (θ) are the means
for observed and modeled discharge, respectively.
The main statistic used in this study is the Nash-Sutclie criterion,
is the value most commonly used in hydrologic response assessment (
2002;
Legates and Mc Cabe Jr. G. J., 1999; Loague and Freeze , 1985).6
lie in the range
6
(1.0, −∞)
Ref f ,
since this
Leavesley et al.,
Values for
Ref f
where 1.0 indicates that the model is a perfect predictor,
Campbell et al. (2005) provide further discussion on performing sensitivity analysis when mode
output is a function.
32
and zero indicates that the model predicts just as good as the average
d.7
Because the
statistic relies on the least squares, it tends to weigh peak ows more heavily than low
ows, though it is still commonly used to assess eciency across basins and response
regimes because it is a normalized measurement. Root mean squared error,
RM SE ,
was also included in the global analysis as an alternative objective function because it
was found by
Tang et al. (2006) to be useful in SA, despite it being similarly dominated
by peak ows.
The coecient of determination,
r2 ,
while presented in the global SA, is less than
eective as a test statistic because it measures only colinearity. Thus, a high
r2
value
indicates only a similar pattern in the modeled vs. measured data, while it does not
guarantee any similarity in the magnitude of the response. Its inclusion in this study
is purely to document the relative utility of the measurement when compared to
and
Ref f
RM SE .
2.5.2
Screening-level Sensitivity Estimation
Although it has been suggested that a purely local SA is eective in determining model
Lenhart et al., 2002),
sensitivity to highly complex watershed-scale hydrologic models (
I disagree with this assessment given the arguments against local sensitivity analysis for
complex models (See Section 2.2). However, I wanted to both document the utility of
performing such a local analysis in the context of the arguments of
Saltelli et al. (2006).
I performed this local, screening-level analysis by running the model in a Monte
Carlo framework using a uniform distribution with wide, but realistic, bounds for all
parameters. The model ran for 2000 iterations over a 10-day simulation period with a
7
Eciencies below zero indicate that the model is an increasingly poor predictor of measured values.
33
10-day spinup period to stabilize and decrease the eects of initial conditions. I chose
the parameter vector from
Θ
which yielded the highest value of
Ref f
and used that as
my focus locality in the model domain.
Using this focus locality, I ran the model for 200-400 iterations in 10 Monte Carlo
tests, allowing each parameter
xi to vary in turn over a range that was chosen arbitrarily
based on the value of the parameter in the parameter vector where
Ref f
was highest.
This gave me 10 result domains where a single parameter varied in the focus locality.
2.5.3
Global Sensitivity Analysis
In order to fully guage the sensitivity of the model, I chose the Extended FAST method
of
Saltelli et al. (1999).
The main reason for chosing FAST is that, despite the use of
Francos et al., 2001;
local and integrated methods for the analysis of hydrologic models (
Ho et al., 2005; Lenhart et al., 2002; van Griensven et al., 2002, 2006), I considered the
strong and well articulated arguments of
Saltelli et al.
(2006) against the use of such
technique where the model cannot be proven to be linear. Furthermore, variance-based
Chan et al.,
methods are unequivically superior to local methods (
1997) and FAST
and other variance-based methods have been shown to be good methods for use with
Ascough et al., 2005; Ratto et al., 2006; Ravalico
hydrologic and environmental models (
et al., 2005; Tang et al., 2006).
Despite the arguments that FAST methods are far too computationally expensive
and/or dicult to use (e.g.
Francos et al.,
2001;
van Griensven et al.,
2002, 2006), I
found this to be untrue. FAST is very well documented in the literature (e.g.
et al.,
2005;
Saltelli ,
2002;
Saltelli and Bolado ,
1998;
Saltelli et al.,
Ascough
2000, 2006, 1999;
Tang et al., 2006), computational numerics have been presented (Mc Rae et al., 1982) and
34
there are tools available as both end-user programs and programming libraries for C++
Saltelli et al., 2000).
and MatLab that allow for easy model integration (
Furthermore,
eciency of the technique has been shown to be adequate so long as the Nyquist criteria
(See
Saltelli and Bolado , 1998, and Saltelli et al., 1999, Appendix A) are satised.
for a model with an input parameter vector with size
n = 10, the number of model runs
Saltelli et al.,
necessary for ecient E-FAST evaluation is as small as 1,641 (
Saltelli and Bolado ,
1998).
Thus,
1999;
At the chosen spatial and temporal scale, the simulation
time for CMF was 5 minutes 8 seconds, requiring just under one week (6.7 days) for an
evaluation using 1930 sample vectors.
2.6
2.6.1
Results
Local Sensitivity Results
As mentioned above, the local sensitivity analysis, especially when performed in this
manner, would not be appropriate to truely estimate the sensitivity of the model to
parameters. I did nd it useful, however, because the results yielded a graphical representation of the trajectory of the model results within each parameter distribution in
the model domain. Furthermore, while some of the results do not necessarily coincide
completely with the global analysis, many show at least enough similarity to support
the suggestion of
Saltelli et al. (2000) that screening-level analysis can be an important
rst step in understanding the model's behavior in the domain.
Following are descriptions of the model's response to variation in each model parameter. Because of the inability to generate meaningful quantitative analysis of this
inherently awed method, only a qualitative assessment is given here. No direct dis-
35
cussion regarding the relationship of results from this section to those of Section 2.6.2
is provided here. Rather, relation of the local to global sensitivity results is given in
Section 2.6.2.3.
2.6.1.1
Non-sensitive parameters
Two parameters, eld capacity and
z , were found to have zero eect on model eciency
during the screening. While each parameter varied fully within the uniform distribution
bounds, the results of the
N Sef f
and
RM SE
did not vary. While it is possible that two
distinct discharge curves could be produced, each yielding the same
value, it is highly unlikely that 200 would do so for
both
N Sef f
of the metrics.
or
RM SE
This left
me with the initial conclusion that either the model was completely insensitive to the
parameters, or more likely there was a locality of zero slope with relation to the
parameters in the multidimensional parameter space.
2.6.1.2
Initial Saturation
Results for model runs with varying
θi
are shown in Figure 2.5. The domain of values
chosen was 40-80% saturation at model inception. The model yielded consistent eciencies above zero for initial saturation values between 63% and 73%. The eciency
stablized at roughly -1.3 at lower values, and dropped asymptotically at higher values.
From this analysis, I felt that the model was likely quite sensitive to this parameter.
36
(a) Full measurement domain
(b) Domain above zero eciency
Figure 2.5: Initial saturation values vs. Nash-Sutclie eciencies for 500 model runs.
Subgure (a) shows the full parameter domain while subgure (b) focuses on those
eciencies above zero.
37
(a) Domain above zero eciency
Figure 2.6: kdepth values vs. Nash-Sutclie eciencies for 500 model runs.
2.6.1.3
Groundwater Loss Rate
Results for
kd
are shown in Figure 2.6. As can be seen, all values yield eciencies above
0.71, despite a downward trend as loss-rates increase.
This suggested that, with the
bounds of the variable, the model's eciency might be insensitive to this parameter.
2.6.1.4
Results for
mm
d .
Saturated Hydraulic Conductivity
ks
are shown in Figure 2.7.
The domain chosen spanned from 10 to 250
The conductivities that yielded eciencies above zero spanned a wide domain
38
with the resulting trajectory roughly bell-shaped.
Maximum eciency of 75% was
achieved. From this analysis, I estimated that the model was only mildly sensitive to
this parameter.
2.6.1.5
Porosity
Results for
φ are shown in Figure 2.8.
The domain ranged from 0.4 to 0.6 with positive
eciencies above 0.49 and stabilization at 73% above 0.56. Because of the steep drop-o
of eciencies below 0.5, I deemed the model to be quite sensitive to this parameter.
2.6.1.6
Power Law Exponent
Results for the value of the
are shown in Figure 2.9. Interestingly, the results show
a near mirror image of those for initial saturation, with an asymptotic drop below 10
and a stabilization above roughly 14. My estimate of model sensitivy to this parameter
similiarly mirrored that of initial saturation.
2.6.1.7
Pore Size Distribution
Results for the
λ
value are shown in Figure 2.10. The domain ranged from 0.05 to 0.5
and yielded positive eciencies for values below 0.15. While the majority of the model
domain was below zero eciency, the slope of the trajectory was gradual, causing me
to evaluate the model as only fairly, not drastically, sensitive to this parameter.
39
(a) Full measurement domain
(b) Domain above zero eciency
Figure 2.7: Saturated hydraulic conductivity values vs. Nash-Sutclie eciencies for
500 model runs.
40
(a) Full measurement domain
(b) Domain above zero eciency
Figure 2.8: phi values vs. Nash-Sutclie eciencies for 500 model runs.
41
(a) Full measurement domain
(b) Domain above zero eciency
Figure 2.9: Power law exponent values vs. Nash-Sutclie eciencies for 500 model runs.
42
(a) Full measurement domain
(b) Domain above zero eciency
Figure 2.10: Pore size distribution values vs. Nash-Sutclie eciencies for 500 model
runs.
43
2.6.1.8
Results for
Residual Water Content
θr
are shown in Figure 2.11. The model domain was from 0.01 to 0.1 and
the model yielded eciencies above 0.6 for the entire domain. Because of the near zero
slope to this trajectory, I evaluated the model as almost completely insensitive to this
parameter.
2.6.1.9
Results for
Wilting Point
θt
(also called trace water content) are shown in Figure 2.12. The model
domain spanned from 0.25 to 0.5 and yielded all positive results between 0.55 and 0.65.
Interestingly, this is the only plot which did not yield a dened result surface. Rather,
the plot points were scattered heavily throughout the domain.
2.6.1.10
Discussion
The screening-level analysis provided an opportunity to work with the model and to
see the eects of changes of individual parameters in a single locality of the input
domain. While it could not provide quantitative assessment of model sensitivity, I was
able to notice that the model had a fair amount of sensitivity to most parameters. The
assessment of the three non-aecting parameters turned out to be wrong, although soil
depth was later shown to have only a small eect on model variance.
The problem with the local analysis, however, is that a great deal of time was spent
setting up the model and obtaining a large number of model runs. The amount of time
spent on the analysis, because of the lack of quantitative results, suggests to me that it
44
(a) Full measurement domain
(b) Domain above zero eciency
Figure 2.11: Residual water content values vs. Nash-Sutclie eciencies for 500 model
runs.
45
(a) Full measurement domain
(b) Domain above zero eciency
Figure 2.12: Wilting point values vs. Nash-Sutclie eciencies for 500 model runs.
46
was not time well spent. This is further borne out by the fact that the time spent on
the local analysis was greater than four times that spent on the global. Thus, without
a far easier method for local analysis, I would not choose to do it again.
Rather, a
relatively short time could be spent using tools such as SimLab to perform a robust
global analysis from the start.
2.6.2
Extended FAST Results
Tables 2.3 and 2.4 show the results of the Extended FAST analysis for the three separate
metrics
N Sef f , RM SE
and
r2 .
Sensitivity is depicted graphically in Figures 2.14
and 2.13 as percentages of total sensitivity for rst- and total-order results, respectively.
Because they are fundamentally dierent, and less reliable than
graphical representations for
r2
N Sef f
and
RM SE ,
are given separately in Figure 2.15.
A set of initial magnitude thresholds was arbitrarily set at {0.1, 0.01, 0,001} for
sensitivities of high, medium and low, respectively. After an initial SA using a ghost
parameter that yielded results in the medium sensitivity range (See Appendix 5), we
re-evaluated these thresholds to include two ranges: sensitive (above 0.1) and insensitive (0.01) parameters. Some parameters yielded model sensitivities below the 0.01
threshold. These parameters are considered to yield trace sensitivities.
2.6.2.1
First-order results
The rst order sensitivity results in Table 2.3 show that
kd
was the only parameter to
which the model had only trace sensitivity in all objective function evaluations. The
sensitivity was 0.0025 and 0.0012 for
N Sef f
and
RM SE ,
respectively.
The model
47
Parameter
N Sef f
RM SE
r2
θr
λ
zsoil
φ
ks
kd
θt
θi
θF C
0.0577
0.0521
0.0035
0.0370
0.0405
0.0021
0.0351
0.0282
0.0218
0.0293
0.0188
0.0004
0.1620
0.2053
0.3196
0.0171
0.0088
0.0026
0.0025
0.0012
0.0005
0.0264
0.0189
0.0005
0.1893
0.2174
0.2553
0.0374
0.0289
0.0001
Table 2.3: First Order results of FAST test of Nash-Suttclie and Root Mean Squared
Error, and R
2 for all hydrology variables.
was insensitive to all other parameters except porosity,
φ,
and initial saturation,
Using all objective functions, the model showed sensitivity to
N Sef f = {0.162, 0.1893}, RM SE = {0.2053, 0.2174}
{φ, θi },
respectively.
and
φ
and
θi
θi .
with values of
r2 = {0.3196, 0.2553}
for
Figure 2.14 shows relative sensitivities as percentages of total
sensitivity. It is quickly evident that the parameters
φ
and
θi
dominate the sensitivity
using all objective functions.
2.6.2.2
Total-order results
The model shows second-order sensitivity to all parameters except
were 0.0716 and 0.0418 for
N Sef f
second-order sensitivity using
r2
and
kd ,
for which results
RM SE , respectively (Table 2.1).
The results for
as an objective function mirror those of the rst-order,
possibily indicating that this is not an appropriate evaluative function for estimating
second-order eects.
48
Parameter
N Sef f
RM SE
r2
θr
λ
zsoil
φ
ks
kd
θt
θi
θF C
0.6992
0.5376
0.1168
0.7833
0.6842
0.0148
0.7718
0.6261
0.0710
0.6782
0.4453
0.0445
0.8934
0.8993
0.6658
0.4588
0.2310
0.0757
0.0716
0.0418
0.0143
0.6122
0.4265
0.0298
0.3492
0.3585
0.6599
0.7852
0.5539
0.0068
Table 2.4: Total Order results of FAST test of Nash-Suttclie, Root Mean Squared
Error, and R
2.6.2.3
2 for all hydrology variables.
Discussion
While NS and RMSE yielded similiar sensitivity results, they diered slightly in their
assessment of the dominance of the parameters
in Figure 2.13,
{φ, θ}
comprised
{27%, 32%}
the objective function, while they comprised
φ and θi
in rst order results. As shown
of rst order sensitivity using
{33%, 35%}
using
RM SE .
N Sef f
The
as
RM SE
results show that the rst-order aects of the remaining parameters are likewise similiar
to
N Sef f
results in relation to themselves, yet their magnitude is often reduced in
relation to the dominant parameters. It appears from this result that using the
RM SE
may make the sensitivity analysis itself more sensitive to dominant parameters than
using the
N Sef f .
One possible reason for this is the fact that
the more extreme cases of a series, while
N Sef f
RM SE
normalizes these.
tends to weigh
Of course, more
study would be necessary to determine which of these two is a more appropriate metric.
Total-order results were also similiar between analyses using
N Sef f
and
RM SE
(Figure 2.14) again with some less pronounced dierences, mainly in the assessment of
φ
and
ks .
49
Figure 2.13: First-order FAST results for the Hydrology model. Wedges indicate percentages of total-order sensitivity with exploded wedges for parameters greater than
10% of the total. Values for
kd
are not shown here because they account for less than
0.5% of the total variability in both cases.
50
Figure 2.14: Total-order FAST results for the Hydrology model. Wedges indicate percentages of total-order sensitivity. Values for
kd
the total second-order variability in both cases.
(exploded) account for less than 2% of
51
Both orders show that analyses using
tically dierent results than
N Sef f
and
r2
as the measurement metric yielded dras-
RM SE
second-order analyses are heavily dominated by
φ
(See Figure 2.15).
and
θi
Both rst- and
provide 53% and 42% of the
total sensitivity, respectively. 1.6% of rst-order sensitivity is accounted for in all but
three parameters, and
λ,
one of those parameters, comprises only 3.6% (Figure 2.15).
The total-order results are similiarly dominated by these parameters, which yield 39%
each, of the total sensitivity.
Such results suggest that
r2
may be a useful objective
function if the desired goal is only to identify the few parameters with high rst-order
sensitivity, but that using the function to fully assess relational rst-order sensitivity,
or analyse total-order sensitivity, is inappropriate.
The SA shows us that the model is all but insensitive to the assumption that the
soil is bounded on the bottom by a conning layer, since the sensitivity to the depth of
this layer is so low in both rst- and total-order analyses.
The high total-order sensitivities further provide an understanding about the limited
utility of performing a local analysis similiar to that performed by
Lenhart et al. (2002).
Recalling Section 2.2.1.1, this total-order sensitivity is an expression of the eect of an
individual parameter to the model's sensitivity of
all other
parameters. Thus, it can
be seen as the parameter's eect on the variability, or smoothness, of the parameter
surface. The number of parameters with high total-order sensitivity indicates that the
parameter surface is not smooth, but that any small change in any given parameter will
likely eect the model's sensitivity to other parameters quite drastically. Furthermore,
it should be understood that a change in the entire parameter vector, or a portion of the
parameter vector, will likely result in relocation of the model to an area of parameter
space that is very dierent from that surrounding the initial vector.
Since many hydrological models use similiar equations and principles, if not the
52
Figure 2.15: First- and Total-order results for the Hydrology model using
r2
as the
evaluation criteria. All parameters with rst-order values less than 1.0% account for
only 1.6% of total rst-order variability. Parameters with total-order values less than
1.0% have been exploded.
53
same equations in some cases, it is quite likely that the total-order results of this sensitivity analysis would be similiar for a model such as SWAT, in as much as there would
likely be a number of parameters with signicant total-order eects on the model. As
such, the studies of
Lenhart et al. (2002) and others who rely on techniques that carry
a fundamental assumption of Equation 2.4 are, as suggested by
Saltelli et al.
(2006),
questionable, if not invalid. Unfortunately, local analyses of complex models might appear to be justied when examining the literature.
Saltelli
(1999) found that the vast
majority of studies written in the literature involved local or OAT methods. Furthermore, there seems to be a number of papers stating that variance-based methods are too
dicult, expensive or unnecessary (e.g.
Francos et al., 2001; van Griensven et al., 2002,
2006). Thus, many researchers might feel justied in their reliance on local methods
because they can fall back on these arguments.
2.7
8
Conclusions
Sensitivity analysis is an important step in model evaluation as it provides information
on the variance of model output that is attributable to each model input parameter, thus
informing us as to the importance of accuracy of each parameter. A SA of CMF showed
that the parameters
φ and θi were the most important input factors with regards to rst-
order sensitivity, with all other factors being somewhat important with the exception
of
kd .
8
Furthermore, the SA analysis showed that all factors except
kd
have a strong
I have found what seems to be a fear of the mathematics and diculty of global methods in my own
experience working as a water quality hydrologist for the Oregon State Department of Environmental
Quality.
When I recently suggested to my team that it would be appropriate to perform a global
SA on our stream temperature model, the response was negative with the argument that it would be
too complicated to perform. This was in spite of the fact that we are mandated to perform such an
analysis. Our individual use of situation-specic, local methods is good enough for current purposes.
54
total-order eect on the variance of the model, meaning that a change in any given
factor will likely change the response of the model strongly. This means that any local
analysis will be less than eective and that the multidimensional parameter surface is
not smooth.
55
3 Sensitivity Analysis of CMF Pesticide Model
3.1
Introduction
This paper introduces the pesticide fate/transport model within the Catchment Modeling Framework (CMF) and the results of a global sensitivity analysis. The paper builds
on the work of Chapter 2 and simultaneously evaluates model sensitivity to the hydrologic, and additional pesticide, parameters. Section 3.2 introduces the pesticide model
in CMF. Section 3.3 provides the methodology behind the sensitivity analysis of the
pesticide model and Section 3.4 provides the results and discussion. Finally, Section 3.5
provides a chapter conclusion.
3.2
Pesticide Model
The pesticide model in CMF is similiar to the hydrological model in that it is dened
by a set of mass balance equations that are distributed in space and solved in time. The
equations are essentially those dened in the one-dimensional, plot-scale EPA Pesticide
Root Zone Model (PRZM) (
Carsel et al., 1985).
At its most basic, the model consists
of 4 state variables for pesticide mass on the plant, on the surface, and in the vadose
and saturated groundwater zones. The input and output rates from each model unit are
dened using the PRZM-like rate equations. This solution procedure is supported by
two fundamental assumptions, the rst being that dispersive processes are not dominant
within each model unit, allowing for a simple plug-ow model of water and pesticide
56
transport. The second assumption is that the process of mixing within each model unit
is not important, and that each can be described by a homogeneous and completely
Jenkins et al., 2004).
mixed reactor (
A complete mathematical description of the pesticide model is provided in
et al. (1985).
3.2.1
A concise version, provided in
Carsel
Jenkins et al. (2004), is given here.
Upslope Model
As stated above, pesticide mass is dened by dierentially calculating mass balances
in the plant, surface, vadose and saturated portions of each model unit in time. The
generalized equation for mass per timestep provided in
Jenkins et al. (2004) has been
broken out here by compartment to isolate the specic components responsible for
mass within each compartment. Following PRZM, it is assumed that adsorption equals
desorption and that dispersion is zero.
3.2.1.1
Plant Compartment
Pesticide mass on the plant surface is dened by the equation:
dM plant
pest
= Rapp − Rf oliar − Rtrans
dt
where
(3.1)
Rapp is the rate of application (that portion of the total application that is applied
to the plants),
Rf oliar
is the foliar runo rate, and
The foliar runo rate is dened by the equation:
Rtrans
is the rate of transformation.
57
Rf oliar = · P · Mpest
where
(3.2)
is the extraction coecient (set to 0.1 in accordance with PRZM),
precipitation rate, and
Mpest
is the mass of pesticide.
P
is the
The rate of transformation is
dened as the mass of the pesticide times the rst-order foliar degradation constant:
Rtrans = Kf · Mpest
3.2.1.2
(3.3)
Surface Compartment
surf ace
Mpest
= Rf oliar + Rapp − Radv − Rtrans − Rro − Rup − Rerosion
where the inputs are the runo from the plants
Rf oliar
(3.4)
and the portion of the total
application that was applied directy to the soil. The outputs are the rates of advection,
Radv ,
transformation,
Rtrans ,
runo,
Rro ,
uptake,
Rup ,
and erosion,
The advection rate is dened as the concentration of pesticides
the velocity of water owing into the unsaturated zone.
Rerosion .
Cpest =
mpest
vwater times
The transformation rate is
dened as:
Rtrans = (Ks · Mpest ) + (Cpest · Kd · Ks · ρb )
where
Ks
is the degradation constant,
Kd
(3.5)
is the adsorption partition coecient and
ρb
is the bulk density. The runo rate is the concentration of pesticides times the volume
of water owing out on the surface. The uptake rate is the pesticide mass times the
uptake eciency times the current rate of evapotranspiration:
58
Rup = Mpest · e · ET
where uptake eciency,
e,
is dened as:
e = 0.784
and
Koc
(3.6)
[log(Koc )−1.78]2
2.44
(3.7)
is a parameter describing sorption of pesticides to soil particles (further dened
in Section 3.3.2).
The erosion rate is:
Rerosion = Msed−out · Rom · Kd · Cpest
where the mass of sediment eroding,
enrichment ratio,
concentration,
3.2.1.3
Msed−out ,
(3.8)
is multiplied by the organic matter
Rom , times the adsorption partition coecient, Kd , times the pesticide
Cpest .
Vadose and saturated compartments
Pesticide concentration in the vadose and saturated zones are dened similarly to the
surface zone as:
[unsat|sat]
Mpest
where
tively.
I
= I − Radv − Rtrans − Rup
(3.9)
is the input from surface or vadose zone for vadose and saturated mass, respec-
59
3.2.2
Instream Model
The model treats instream pesticides as conservative substances. There are two independent routing models implemented, however, only one was used for this study. Input
concentration to each reach is dened as the sum concentration of all contributing
upslope units and the upstream reach(s).
3.3
Method
The method used for this analysis is essentially identical to that used for the analysis
of the hydrology component in Chapter 2. The fundamental dierence is in the choice
of an evaluative criteria and the addition of pesticide specic parameters.
With the
increase of parameters to 13, the number of sample parameter sets was increased to
8,957 model runs to ensure coverage of the full parameter space was as complete as
possible. This was problematic because the model runtime was roughly 12 minutes at
the beginning of the simulation, increasing to roughly 16 minutes by the end.
1
This
translated to roughly 3 months of model runtime for the analysis. The simulation period
was identical to that in Chapter 2 with the exception of it being limited to 4 months to
try to reduce the simulation time as much as possible while simultaneously capturing
the full pesticide plume in the outlying cases.
1
This increase in model runtimes was due to increased memory usage internally as the number of
runs increased.
60
3.3.1
Evaluative Criteria
In Chapter 2, error functions were used as the evaluative criteria because there was
enough measured data against which to weigh the modeled results. Given that there is
not enough measured data available to calculate error for the pesticide model, we must
rely on another appropriately chosen though perhaps more arbitrary metric.
Generally, the metric chosen for the sensitivity analysis of a model should be ap-
Saltelli et al., 2000).
propriate to the question that the model will be used to answer (
There are many ways to characterize a pollutant plume with a single number. Total
mass at catchment outow will give us an indication of how much of the pesticide either
degraded or remained sorbed to the soil. Time to breakthrough and time to centroid
(center of mass) can give an indication of reactivity of the catchment with regards to the
pollutant. We could also combine measurements, for example, the dierence between
time to peak and time to centroid. If the peak time is well before centroid, then the
system likely has a rapid initial response but a long tail.
For the purposes of this analysis, we have arbitrarily chosen two metrics to support
the study that the model is used for in Chapter 4. The rst metric is the total pesticide
mass calculated at the catchment output and the second is the peak concentration seen
at the output.
3.3.2
Parameters
Because the fate and transport of pesticides in a catchment are dependent on the
hydrology, the parameters are identical to those analysed in Chapter 2 with the addition
of three pesticide-specic parameters.
61
The rst is the fraction of pesticide that is applied to the ground,
Fgnd . Fgnd
is
mainly a reection of application type and leaf area index. For instance, given areal
spraying of pesticides on row crops where the area of the land surface is 30% covered
by the plants themselves, we can make an assumption (ignoring drift) that 30% of the
applied pesticides will land on the plants, while 70% lands directly on the soil.
For this analysis, the low value of 20% reects precision application methods or high
leaf-area-index plants where most of the pesticide is applied directly to the plant. The
high value of 80% reects aerial spray techniques or croping with lots of un-vegetated
soil where the majority of the pesticide will fall directly onto the soil.
The second parameter is foliar degradation,
third parameter the partitioning coecient,
kf , and is varied from 0.001 to 2.0.
koc
The
is the main parameter responsible for
characterizing sorption of the pesticide to soil particles, and is related to the carbon
content of the soil by the following equation:
koc =
where
Cs
Cw
% soil organic carbon
(3.10)
Cs
Cw is the ratio of the concentrations of chemical in solid and liquid phases at
equilibrium. This value is pesticide specic, and was varied from 0 to 9000.
kf
Ranges for
and
koc were chosen to span the ranges for the majority of active pesti-
cides in use. The range for crops was taken to account for the majority of crop rotations
where crops would have pesticides applied. This range does not take into account preemergent application or application during periods of plowing, where coverages can be
Breuer et al., 2003).
as low as 0% (
62
First-order
First-order
Total-order
Total-order
Mass
Peak
Mass
Peak
0.0368
0.0462
0.7066
0.7619
0.1749
0.1670
0.6017
0.6172
Trace Water Content
0.0581
0.0589
0.8587
0.8602
GW Loss Rate
0.0584
0.0597
0.8675
0.8708
0.2142
0.2420
0.6561
0.7285
0.1481
0.1179
0.8817
0.8806
0.0118
0.0320
0.4470
0.5967
0.0521
0.0369
0.5058
0.4811
0.0484
0.0484
0.7825
0.7780
0.0386
0.0511
0.6510
0.7747
0.0406
0.0322
0.6230
0.5431
0.0381
0.0260
0.6952
0.6161
0.0413
0.0432
0.8152
0.8278
Parameter
Field Cap.
Init. Sat.
θF C
θi
θt
kd
Sat. Hyd. Cond. ks
Porosity, φ
Soil Depth dsoil
Pore Size Dist. λ
Res. Water Content θr
Power Law Exp. Part. Coe., koc
Foliar Deg. Rate, kf
Frac. on Ground, Fgnd
Table 3.1:
FAST sensitivity values for all model parameters using Mass and Peak
concentration as measurement indicators.
3.4
Results & Discussion
Results of the rst- and total-order FAST analysis are presented in Table 3.1 for both
evaluative criteria. First-order sensitivity for both evaluative criteria indicate three main
parameters initial saturation,
φ
θi ,
saturated hydraulic conductivity,
ks ,
and porosity,
dominate the total rst-order sensitivity prole, accounting for greater than 50%
of rst-order sensitivity in both cases (Figure 3.1). We can note that both cases track
each other very well. Pesticide-specic parameters account for a small fraction (<5%
each) of rst-order sensitivity.
The story told by the total-order sensitivities is similar to that for the hydrology
component (Figure 3.2).
All values are relatively high, with no single value having
true dominance. This indicates that the sensitivity surface is very dynamic and that a
change in any single parameter would be expected to inuence the model's response to
63
Figure 3.1: First-order FAST results for the pesticide model. Wedges indicate percentages of rst-order sensitivity with exploded wedges for parameters greater than 10% of
the total.
64
all other parameters.
3.4.1
Management implications
Given that managers and land users often do not have the ability to change soil properties, the knowledge that hydraulic conductivity and soil porosity are strong determinants of pesticide movement to streams is of little practical use. However, these things
being constant, management can take advantage of the fact that initial saturation is a
primary determinant. Applying pesticides during wet periods allows them to be routed
quickly through the dominant owpaths to the stream.
Application during periods where the soil moisture is relatively low may be a useful
practice in limiting pesticide pollution in streams; however, there should be consideration of the overall climatic period, rather than relying solely on antecedent wetness.
The situation could arise when pesticides are applied to a eld with low soil moisture
and very dry antecedent conditions, but which will experience rain showers in the following hours or days. The positive results gained by application to a dry eld could be
eliminated in this case.
One example of this would be application to a low soil moisture, clay-rich soil which
has become hydrophobic. The dominant owpath for water at this point may be surface
runo, with much of the ground-applied pesticide running directly into the stream.
For reasons such as this, pesticide type and dose, application timing, climatic considerations, crop type and planting strategies, and soil properties are
when weighing application options.
all
important
To say that application to a dry eld will solve
most problems would be missing quite a bit of the picture.
65
Figure 3.2: Total-order FAST results for the pesticide model. Wedges indicate percentages of total-order sensitivity with exploded wedges for parameters greater than 9% of
the total.
66
3.5
Conclusions
Using total mass and peak concentration, the rst-order sensitivity of the pesticide
model within CMF to changes in input parameters is relatively low for all parameters
except initial soil moisture, porosity and saturated hydraulic conductivity. These three
parameters account for greater than 50% of the total rst-order sensitivity, thus, greater
care should be taken when dening these three parameters.
Total sensitivities were fairly high and evenly distributed among parameters with
the exception of soil depth, which is quite low.
This indicates that caution must be
used when changing any one parameter because its change is likely to eect the model's
response to all remaining parameters.
CMF is relatively insensitive to the three main parameters added to the model for
pesticide fate/transport. This seems to indicate that hydrology is the main driver of
pesticide transport, and that changes in the dened values for pesticide application
method (fraction reaching ground) or soil organic carbon are unlikely to have a large
eect on model results.
It is important to remember, however, that this analysis does not account for what
eects actual changes in these parameters will have on measured water quality, but only
that changes in the values of these parameters are likely to cause only small changes in
the model output.
67
4 Comparison of Two Pesticide Mitigation Strategies using CMF
4.1
Introduction
Of the nearly 2.3 billion acres of land area in the continental United States, over 50%
Lubowski et al.,
is in agricultural use (
2006). The total land area in use for cropland
Lubowski et al., 2006).
alone is 179 million hectares (442 million acres), or nearly 20% (
Pesticides are an important part of our agricultural industry's success, but are also a
serious problem in water quality, resulting in risks to both human and environmental
health(
Larson et al., 1999; Gilliom , 2001).
In the period from 19922001,
Gilliom et al.
(2006) found that agricultural pesticides were present in 97% of surface water samples
and 61% of shallow ground water samples taken throughout the United States. They
also found that concentrations exceeded human health standards in 10% of stream
samples and aquatic health standards in nearly 60% of stream samples and 31% of
bed-sediment samples (
Gilliom et al., 2006).
This paper builds on the results of Chapters 2 and 3 by examining in detail the eect
of modifying one pesticide-specic parameter (fraction of pesticide on the ground) using
two possible best management practice (BMP) alternatives for pesticide mitigation
in agricultural elds.
Section 4.2 discusses the methods used in this paper to assess
the merits/detriments of each strategy.
Section 4.3 provides the results of the study
followed by Section 4.4 which details the management implications of the study. Finally,
section 4.5 concludes the paper.
68
4.1.1
CMF Sensitivity, Revisited
Chapters 2 and 3 detailed a global sensitivity analysis of CMF with the result that three
commonly unchangeable soil parameters (saturated hydraulic conductivity, porosity and
initial saturation) are the most important rst-order parameters when in comes to both
peak pesticide concentration and total pesticide mass at the stream output.
Similarly, many of the total-order parameters are unchangable (loss rate to deep
groundwater and trace saturation) for both mass and peak. Additionally, the fraction
of pesticide on the ground is important for the total-order sensitivity of total instream
mass.
Looking further, there are two main pesticide-specic parameters that can be most
easily changed by management practices alone, those are the partitioning coecient
(changed by modifying the amount of organic carbon in the soil) and the fraction of
pesticide landing on the ground. Section 3.4 shows that CMF is more sensitive to the
fraction of pesticides on the ground than to the partitioning coeent for both total
mass and peak concentration in both the rst- and total-order sensitivities.
4.2
Methods
As noted in Section 3.4.1, farmers and managers do not often have the luxury of changing
the hydrologic characteristics of the soil under cultivation. Likewise, they do not always
have the ability to change pesticide-specic parameters because these parameters are
often tied to the crops that are cultivated.
Thus, best management practices (BMPs) often involve working to modify those
parameters which
can
be inuenced. Section 3.4.1 indicates one way that this can be
69
achieved, given knowledge that soil moisture conditions can often be chosen through
application timing.
The method in this chapter is to assess the eect of modifying the most important,
pesticide-specic parameter by changing the fraction of total pesticide that is applied
directly to the ground. This can be seen as a surrogate for various BMPs as detailed
in Section 4.4.
In addition to the pesticide-specic parameter, total eld-size under
cultivation will be varied simultaneously in an eort to assess the relative merits of
reducing application to the ground versus reducing total application area.
A Note on Buer Strips and the Partitioning Coecient
Buer strips, uncultivated areas adjacent to streams or other important features, are a
common BMP and one that can, in the future, be analyzed with this method. Buer
strips or similar strategies, by allowing natural plant stages, would increase soil organic
carbon, thus modifying the partitioning coecient favorably for reduced pesticide transport.
Reichenberger et al.
(2007) note that there is disagreement in the literature on
the eect of edge-of-eld vs.
riparian buer strip eciency; however, their extensive
literature review found that eld-edge buers are generally more eective than riparian buers in pesticide mitigation. This eectiveness is not dependent on soil organic
carbon so much as on ow characteristics.
This study does not evaluate buer strips with increased soil organic carbon. Rather,
by reducing the size of the elds, it is more closely a study of the eect of
benetted buers.
non-carbon
As such, a more systematic approach can later be performed by
evaluating carbon benetted vs. non-carbon benetted buer regions.
70
4.2.1
Assumptions
Both to simplify the study and reduce the total number of model parameters (and thus
the model runtime), we make a number of assumptions in this study. These assumptions
do not prevent the study from being applicable in the general case, but do ensure that
a full description of another case will require analysis with the parameters specic to
that case.
The rst assumption is that we can examine a limited case of one hypothetical
catchment where the hydrologic parameters and the applied pesticide are xed. This
assumption is made to support the case where a farmer is cultivating the entire area of a
small catchment, and is not able to change the crop (and hence the pesticide). We also
make this assumption because of the importance of total-order parameter sensitivity and
the fact that increasing variable parameters increases model run needs in a non-linear
fashion.
The assumption of xed parameters is justied in the single catchment, single crop
case for all parameters except initial soil moisture, which can be easily changed by
modifying the application date. Thus, we also make an assumption that an average soil
moisture value of 0.46 can be used for all model runs.
The mathematical method specied in Section 4.2.2 is dependant on the ground
coverage of the crop. Thus, another assumption we make is that the coverage of this
crop is xed for all application types and times at 30%.
All xed hydrologic parameters were based on a parameter set yielding a NashSutclie value of 0.6 for the model catchment. Pesticide parameters for
kf
and
koc
were
taken from acceptable values for Isoproturon (0.0816 and 2.8, respectively).
The nal assumption is that the dierence in eectiveness of in-eld, after-eld
71
and edge-of-eld buers can be considered essentially equivalent with regards to this
study.
Reduction of total eld size was achieved by reducing sub-catchments within
the total catchment by the appropriate amount. The programming algorithm resulted
in each catchment being reduced in a linear fashion starting at its north-western most
model unit and continuing to the south-eastern most unit. The result of this is that
the resulting buer areas are at the upslope eld boundaries for those elds north of
the stream, and at the downslope eld boundaries for those catchments south of the
stream.
4.2.1.1
Implications
There are a number of implications of our assumptions that should, in good faith, be
presented outright. The rst is that our assumption of single catchment, single crop
ignores the assessment of intercropping. For instance, a farmer can achieve good results
by planting a eld where rows of corn (nitrogen utilizers) are mixed with rows of beans
(nitrogen xers). Such strategies can themselves mitigate the crop coverage, pesticide
usage and timing, water usage, etc.
The second implication is that the use of a single crop coverage value may limit the
assessment of close cropping, where farmers increase the density of their crops. It might
be argued that increasing the crop coverage variable might, in inself, be an assessment
of close cropping; but this has not been fully investigated.
The third implication is that of choosing a parameter vector based on a specic,
desirable, Nash-Sutclie variable.
There are a host of problems with using this as a
method, not the least of which is the underlying assumption that tting our model parameters to data may result in multiple parameter vectors, each one possibly containing
72
parameters that are wildly out of the realistic value range. The parameter vector chosen
was not completely arbitrary, however, and was the result of consultation with faculty
of the University of Gieÿen, where the data was collected.
The nal important implication is that of assuming the eld-reduction buers are
equivalent.
While there is evidence that combining in-eld, edge-of-eld and other
Dabney et al.,
buers is a benecial management strategy (
2006), it may have been
better to ensure that this study focused on one type of eld reduction (e.g. downslope,
edge-of-eld) rather than mixing them.
4.2.2
Variable Parameters
Percentage of pesticide on the ground was used as a proxy to assess the range of application procedures from precision application to areal spraying. This is assessed indirectly
by, in the case of precision application, reducing the total mass of the pesticides and
decreasing the fraction of that mass applied directly to the ground. Areal application
involves the application of more mass and an increased percentage on the ground. Our
main assumption here is that a constant mass of pesticide will be on the leaf for all
model runs. Thus, if 40 kg of mass is on leaf, and we are practicing precision agriculture
with 80% leaf application, we have a total application mass of 50 kg. By contrast, with
an areal application method resulting in 30% on leaf fraction, we have 133 kg of total
mass applied.
Field-size is modied simply by changing the fraction of the total catchment to
which pesticides are applied.
from 0 to 1.
1
In both cases, the values are fractional and thus scale
1
While there is basically no actual case where the end member fractions would be possible, they
73
1000 simulations were run, each covering a 6 month period, and samples for the
variable parameters were generated using the Monte Carlo generation capability of the
SimLab software to ensure complete coverage of the sample space.
4.3
Results
Results, on semi-log (y-axis) plots, for both parameters are given in Figure 4.1. The
left plot shows a graph of instream pesticide concentration vs. fractional eld size. The
size and color of each datapoint is proportional to the fraction of the pesticide applied
directly to the ground (See color scale at right).
The left plot shows the corollary graph with the fraction of the pesticide applied directly to the ground along the X-axis, and the fractional eld-size given by the datapoint
size and color.
It is immediately apparent that the fraction of pesticides applied to the ground are
highly correlated to pesticide transport to the stream, while there is very little correlation between the amount of the catchment under cultivation and instream pesticide
mass. Looking at the right plot, we see that eld-sizes as small as 30% can yield some
of the highest instream masses when much of the pesticides are applied to the ground.
By contrast, there is low instream mass with precision application, and high instream
mass with areal spraying. This relationship is strong in all cases but those closest to
the end member parameter values.
These results would seem to indicate that all other parameters being equal
reduction of the eld-size under cultivation is not a very eective pesticide mitigation
were included in the Monte Carlo sample generation to ensure complete coverage of the parameter
ranges.
74
(a)
(b)
Figure 4.1: Plots showing instream pesticide mass plotted against study parameters. Plot (a) shows instream mass
vs. fraction of total catchment area cultivated. The amount of pesticide applied directly on the ground is noted
by the shade and diameter of the datapoints. Plot (b) shows instream mass vs. fraction of pesticide mass applied
directly to the ground. The fractional size of the eld is then noted by the color and size of the datapoints. Both
plots share the same log-scale y-axis. Each datapoint exists in both plots, as is illustrated by the noted datapoint
in each plot.
75
strategy when taken alone (i.e. when the eld-size reduction is not co-incident with an
increase in soil organic carbon that would further inuence pesticide movement). Given
the choice, it seems as though it would be more benecial for a farmer to increase the
precision with which pesticides are applied than to leave a portion of a eld fallow.
Consulting the main plot of Figure 4.1, we see that areal application of pesticides (70%
ground application) on as little as 30% or less of the total catchment provides little
to no greater benet than would more precise application methods where 20% of the
pesticides were applied directly to the ground of an entire catchment.
Precision application as opposed to eld-size reduction can not only result in greater
mitigation reward, it has the ancillary benet of reducing total pesticide usage. Such
reduction may prove a nancial benet to the farmer if precision application does not
cost more than the savings gained elsewhere. It also prevents the farmer from having to
reduce eld-size, and thus yield, allowing for continued production at the same levels.
4.4
Management Implications
The results shown in Figure 4.1 and discussed in Section 4.3 are, on the surface, relatively simple. The salient result is that reducing the amount of pesticides that land
directly on the ground surface is generally more benecial than reducing the amount of
eld under cultivation, even in the extreme cases.
Agriculture is, by its nature, very situation specic. The climatic, cultural, ecological, economic and other characteristics that a farmer works within in Western Oregon
can be very dierent than those a farmer in the Ohio Valley would experience. Thus,
merely stating that reducing the number of pesticides applied to the ground surface is,
of itself, little practical use. However, this lends itself to a number of dierent manage-
76
ment strategies, each which can be combined with others to yield a practical mitigation
approach in a situation specic manner.
4.4.1
Application Method
Probably the most obvious method for reducing ground application is by merely applying pesticides in a more precise manner. This can be achieved by hiring laborers to
apply pesticides directly to individual plants, though this technique is both expensive
and a signicant health hazard to the laborer.
Machine application may be the most cost-eective and safe method for precision
application. (
Giles and Slaughter , 1997) evaluated a precision band application system
for small row crops.
The system included machine-guided vision and nozzles which
could adjust their yaw and resulted in not-target deposition reductions from 72-90%.
Application rates were reduced from 66-80% and overall application eciency was im-
Tian et al.,
proved by a factor of 3 or greater. (
1999) evaluated a similar system for
tall crops (corn and soybeans) and noted herbicide reductions of 48%. Machines such
as this can also be made to adjust their application settings on the y to account for
Paice et al., 1995).
varied cropping systems (
Precision application of pesticides can reduce total application masses, lower onground percentages and lower costs to the farmer, but the application technique has to
be cost-eective itself. For instance, saving on pesticide costs by applying with precision
methods would hardly be seen as an economic benet if the savings, and possibly more,
is spent by having laborers hand-spray, or by purchasing machinery.
77
Table 4.1:
Crop
Growth Phase
Fgnd
Potatoes
2-4 weeks a.e.
0.7
Potatoes
Full Growth
0.1
Beets
2-4 weeks a.e.
0.7
Beets
Full Growth
0.1
Peas
Shortly a.e.
0.8
Peas
During bloom
0.2
Cereals
1 month a.e.
0.8
Cereals
Full growth
0.1
Sprouts
Full growth
0.4
Onion
Full growth
0.4
Fraction of pesticide landing on soil (Fgnd ) for various crops.
Fraction
assumes a default loss to air of 0.1. Remaining fraction is considered a default value
that is intercepted by the plant. The term a.e. signies after emergence (Adapted from
RIVM, VROM, and VWS , 1998, in Linders et al., 2000).
4.4.2
Crop Density
Crop density is a well studied parameter in farming, with many crops having accepted,
standardized densities at various life stages (
Linders et al., 2000).
These densities result
in specic fractions of pesticide being intercepted by the plant, lost to drift, and landing
directly on the soil. Table 4.1 shows 6 crops and their accepted soil fraction in use in
The Netherlands.
The U.S. EPA uses similar standarized values when modeling (e.g. with the Pesticide Root Zone Model (PRZM)) and evaluating pesticides (
The EPA numbers, originally developed by
came known as the
Urban and Cook ,
Hoerger and Kenaga
1986).
(1972) in what be-
Kenega Monogram, were later restudied by (Fletcher et al., 1994).
Table 4.2 shows the original numbers and the re-evaluation.
Linders et al. (2000) provide a proposal for universal interception factors for specic
crops in various important growth phases. This proposal includes interception values
78
w̄ †
Plant Category
(est.)
Short-range grass
112
Long grass
82
Leaves, leafy crops
31
Forage legumes
30
Pods and seeds
3
Fruits
1
w¯±S.D. ‡
76 ±
32 ±
31 ±
40 ±
4 ±
5 ±
(meas.)
54
wm †
(est.)
wm ‡ (est.)
214
214
36
98
98
40
112
112
51
52
121
5
11
11
9
6
13
Table 4.2: Estimated mean (w̄ ) and maximum (wm ) limits (in terms of mass fractions
mg/kg ) for initial pesticide residues on crop groups following applications of kg/ha. Values
initially reported in lb/a were converted by 1 lb/a = 1.12 kg/ha . Note the high standard
deviations in the measured data of Fletcher ref. (from
Linders et al., 2000)
† (Hoerger and Kenaga , 1972)
‡ (Fletcher
et al.,
1994)
for 28 dierent crop types (e.g. vines, stone fruit, cereals). While this proposal is useful
for quickly evaluating a possible case, it does not allow for modifying crop density,
timing, etc. on a case by case basis.
In the simple case, increasing crop densities can decrease pesticides reaching the
ground merely by providing more plant interception. There is evidence that increasing
crop densities can have a second-order eect on pesticide mitigation in some cases.
Lindquist et al. (1995) note that competition from crops themselves can, in certain
cases, inhibit weed seed return, thus providing the argument that, in some cases, increasing crop density can result in lower pesticide needs.
Baker and Dunning
(1975)
found that crop densities of sugar-beet plants could, in themselves, aect insect activity
and
van Emdeen et al.
(1988) note that some species of aphids respond negatively to
increased crop densities. Still, increasing crop densities is no panacea, as
van Emdeen
et al. (1988) also note that there are aphid species that prefer denser stands.
79
4.4.3
Intercropping
Intercropping the planting of alternating rows of dierent, mutually benecial crops
in a single eld is another way to reduce the amount of pesticides necessary in a
eld.
Since at least the mid 1980s, there has been evidence that intercropping is a
Horwith , 1985).
viable approach even in modern, industrial agriculture (
Intercropping
is seen to enhance biodiversity and thus provide benets that can aid coincident plant
species, enhancing their productivity. For instance,
Li et al. (2001) noted 40-70% pro-
ductivity increase in wheat intercropped with maize and 28-30% wheat intercropped
with soybeans. The benets of intercropping are not limited to productivity increases,
however. Since dierent crops can 'steal' resources from weeds, and provide habitat for
pest predators, the practice of intercropping can be used as part of a coordinated pest
management strategy.
Baumann et al.
(2000) found that intercropping celery within a leek eld (Leeks
are a week weed competitor) reduced weed density by 41%.
Khan et al. (1997) found
that intercropping wild grasses with cereals in Africa decreased the number of pests
while simultaneously increasing pest parasitism.
Liebman and Dyck
(1993) noted that
intercropping with specic 'smother' crops reduced weed biomasses in 47 of 51 cases.
Without smother crops, weed biomass was reduced in 9 of 12 cases with the remaining
3 being equivalent.
Intercropping should not be limited to using viable crops.
Ucar and Hall
(2001)
found that windbreaks have been useful in cutting spray drift losses. They note that
a single wall of tall windbreak plants creates a wall eect, and is less eective than
interspersing tall plants througout the eld to reduce windspeed.
Crop rotation is another strategy similar to intercropping and can be used both
80
with and without intercropping.
Liebman and Dyck
(1993) found that crop rotation
was eective in lowering weed densities in 21 of 27 cases, with 5 of the remaining 6 cases
yielding equivalent, not greater, weed biomass.
4.4.4
Dose Modication
Another strategy that could eectively reduce ground application is dose reduction. The
cost of precision application or the management changes with intercropping might be
less attractive alternatives than simply allowing a percentage of crop loss before applying
pesticides, or applying the pesticides in a lower dosage. This practice has led to, most
notably, organic agriculture, which is performed without the use of environmentally
hazardous chemicals.
Since the late 1960s, there has been good evidence that people would prefer higher
food costs and food imperfections (e.g. spots on apples) to the long-term consequences
of ecological pesticide damage
Mitchel
the publication of Silent Spring (
(1966). Much of this early concern began with
Carson , 1962) which detailed the eects of the pesticide
DDT on the environment, particularly bird populations. Since then, there has been a
growing movement in organic farming and Pesticide Free Production.
While uncontrolled weeds can increase their numbers in the weed seed bank by up
to 14 times (
Leguizamon and Roberts , 1982) thus threatening economically viable pro-
duction, integrated organic pest management strategies have been increasingly eective
at overcoming this barrier.
Pimentel et al. (1991) noted in the early 1990s that strate-
gies for reducing pesticide use by 35-50% were already in place and that substantial
reductions in pesticide use would not lead to sigicantly higher food costs. Thus, the
economic argument for pesticide use has been questioned for some time.
81
Nazarko et al.
(2003) performed a pilot project where farmers certied their elds
to use pesticide-free production methods. One year after certication, they found that
farmers rated 72% of the study elds as having no or slightly higher weed pressure than
they would expect following herbicide treatment. This indicates that the argument of
reduced productivity is also not necessarily supported.
There is strong, and growing, demand for organic agriculture in the United States.
Dimitri and Greene (2002) note that this demand reached a threshold in 2000.
Whereas
previously, organic produce was limited to venues such as farmers markets, specialty
stores and community supported agricultural programs, in 2000 more organic food was
purchased in conventional supermarkets than in any other venue.
Sales totaled 7.8
Dimitri and
billion in 2000 and has seen 20% or more growth annually since 1990 (
Greene , 2002).
4.4.5
Timing
One nal method of reducing pesticide losses involves timing. As noted in Section 3.4.1,
modifying application timing so that pesticides are applied at low soil moisture conditions can be very benecial in reducing losses. The corallary is an understanding of
local climatic patterns to ensure that pesticides are not applied directly before rainfall
when soils may be hydrophobic or when soil moisture will immediately be raised.
Another technique is timing for temperature.
Madaglio et al.
increasing temperatures can increase pesticide eciency.
(2000) found that
Thus, if farmers are able
to time applications with respect to local climate, they may be able to increase the
eciency and therefore decrease the dose necessary to accomplish the same goals.
Farmers can also integrate economic analysis into their application strategy by de-
82
termining the cost of application vs. the cost of loss.
Using such a method, they
can apply pesticides only after a certain amount of crop has been lost.
This could,
then, be integrated with temperature sensitivity and soil moisture knowledge to create
an integrated timing strategy.
All of the previous concepts can be used in integrated pest management strategies and should be seen as ways to reduce the amount of pesticide that reaches the
ground surface. Each method, of course, has its benets and its drawbacks; however,
each method can be combined with others in a situation-specic manner to aid farmer
productivity. This makes the question of how to reduce the ground application more
complex, but it also gives farmers more options, some which might be more feasible or
successful than others.
4.5
Conclusions
Pesticides are often necessary in our current, mainstream agricultural system; however,
they are a hazard to both human and environmental health.
Mitigation strategies,
often through BMPs and integrated pest management are increasingly seen as a way
to ensure continued crop yields while improving the health of the environment. One
important way to reduce pesticide losses to streams is by the reduction of the pesticides
that land directly on the ground. Modeling a hypothetical catchment using the Catchment Modeling Framework indicates a strong correlation between application type and
instream pesticide mass, where eld-size holds little correlation.
83
4.5.1
Future Work
This result is limited to the hypothetical case, because the full total-order eects of all
hydrologic and pesticide parameters were not evaluated. Still, limited applicability of
this result can be made to a general case, indicating that it is possible that application
type may be the most cost-eective pesticide mitigation strategy of the two, in most
cases.
There are a number of ways to achieve reduced pesticide application to the
ground, many are detailed herein, and all ways can be combined and used in a situation
specic manner to yield an integrated pesticide management strategy. The literature
would benet from a more specic study where a given eld with known crop type
and density and known pesticide usage would be evaluated. Such a specic case would
provide a baseline from which deviations (e.g. density, timing or application technique)
could be modeled. In this way, the model could be used to develop and evaluate specic
strategies for a given situation.
84
5 Conclusion
Pesticide contamination in stream systems is a known problem. Scientists, farmers and
land managers need to investigate management and mitigation strategies to protect
both human and environmental health. One type of tool in this investigation involves
linking watershed-scale modeling with alternative futures through GIS. The Catchment
Modeling Framework (CMF) is one watershed-scale model that can be used to evaluate
possible management practices prior to implementation.
Chapter 2 provided a sensitivity analysis of the hydrologic componant of CMF. The
model is directly sensitive to the parameters porosity and initial soil moisture.
The
combined rst-order sensitivity of these two parameters is greater than 50%. Soil depth
is the parameter to which the model is least sensitive in the rst-order, and the model is
sensitive in higher-orders to all parameters
except
soil depth. These results shows that
one of the primary assumptions of CMF, that a conning layer constrains soil depth,
will likely not aect the accuracy of the model. The results also show that changing any
given model parameter other than soil depth is likely to drastically change the model's
sensitivity to all other parameters.
This is an example of why local sensitivity in a
complex, higher-order model, is not a valid approach.
Chapter 3 provided a sensitivity analysis of the pesticide model of CMF. With respect to pesticide instream mass and peak concentration, the model is directly sensitive
to the parameters porosity, initial soil moisture and saturated hydraulic conductivity.
Similar to the hydraulic model, soil depth is not an important parameter for the pesticide model at the rst- or higher-orders. Likewise, the model is sensitive to all other
85
parameters at the higher-orders. In comparison to the hydrologic parameters, the model
was not very sensitive to the pesticide specic parameters tested; these were the partitioning coecient, foliar degradation rate, and fractional application directly to the
ground surface.
Chapter 4 provided a comparison of two dierent mitigation strategies, eld-size
reduction and precision application. The model results indicate that eld-size reduction
is only very loosely correlated with instream pesticide mass, while application method
is very highly correlated. This shows that farmers and managers would be better o
exploring ways to apply less total pesticide directly to the plants, rather than reducing
the size of the eld they cultivate, and therefore their overall productivity.
86
Bibliography
Abbaspour, K. (2005), Calibration of hydrologic models: When is a model calibrated?,
in
MODSIM 2005 International Congress on Modelling and Simulation,
pp. 2449
2456, Modelling and Simulation Society of Australia and New Zealand.
Alam, F. M., K. R. McNaught, and T. J. Ringrose (2004), Using Morris' randomized
OAT design as a factor screening method for developing simulation metamodels, in
WSC '04: Proceedings of the 2004 Winter Simulation Conference,
edited by R. G.
Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters, WGS Winter Simulation Series,
pp. 949957.
Arnold, J. G., R. Srinivasan, R. S. Muttiah, and J. R. Williams (1998), Large area hydrologic modeling and assessment part I: model development,
Water Resources Association, 34 (1), 7390.
Journal of the American
Ascough, I., J. C., T. R. Green, L. Ma, and L. R. Ahjua (2005), Key criteria and selec-
MODSIM
2005 International Congress on Modelling and Simulation, pp. 26432649, Modelling
tion of sensitivity analysis methods applied to natural resource models, in
and Simulation Society of Australia and New Zealand.
Baker, A. N., and R. A. Dunning (1975), Some eects of soil type and crop density on
the activity and abundance of the epigenic fauna, particulary
elds,
Journal of Applied Ecology, 12 (3), 809818.
Carabidae in sugar-beet
Baumann, D. T., M. J. Krop, and L. Bastiaans (2000), Intercropping leeks to suppress
weeds,
Weed Research, 40, 359374.
Beck, M. B. (1987), Water quality modeling: A review of the analysis of uncertainty,
Water Resources Research, 23 (5), 13931441.
Berger, P. A., and J. P. Bolte (2004), Evaluating the impact of policy options on agricultural landscapes: An alternative-futures approach,
Ecological Applications, 14 (2),
342354.
Bernardo, D. J., H. P. Mapp, G. J. Sabbagh, S. Geleta, K. B. Watkins, R. L. Elliott, and
J. F. Stone (1993), Economic and environmental impacts of water quality protection
policies: 1. framework for regional analysis,
3079.
Water Resources Research, 29 (9), 3069
87
Bonn, B. A. (1999), Selected elements and organic chemicals in bed sediment and sh
tissue of the Tualatin River Basin, Oregon, 1992-96,
Water-Resources Investigations
Report 99-4107, U.S. Geological Survey, Portland, Oregon.
Brasher, A. M., and S. S. Anthony (2000), Occurence of organochlorine pesticides in
stream bed sediment and sh from selected streams on the island of Oahu, Hawaii,
1998,
Fact Sheet 140-00, U.S. Geological Survey, Honolulu.
Breuer, L., K. Eckhardt, and H.-G. Frede (2003), Plant parameter values for models in
temperate climates,
Ecological Modeling, 169, 237293.
c
Campbell, K., M. D. M Kay, and B. J. Williams (2005), Sensitivity analysis when
model outputs are functions, in
Sensitivity Analysis of Model Output, edited by K. M.
Hanson and F. M. Hemez, pp. 8189, Los Alamos National Laboratory, Los Alamos.
Carpenter, K. D. (2004), Pesticides in the Lower Clackamas River Basin, Oregon, 200001,
Water-Resources Investigations Report 03-4145, U.S. Geological Survey, Portland.
Carsel, R. F., L. A. Mulkey, M. N. Lorber, and L. B. Baskin (1985), The Pesticide
Root Zone Model (PRZM): a procedure for evaluating pesticide leaching threats to
groundwater,
Ecological Modeling, 30, 4969.
Carson, R. (1962),
Silent Spring, Houghton Miin, Boston, Ma.
Chan, K., A. Saltelli, and S. Tarantola (1997), Sensitivity analysis of model output:
WSC '97: Proceedings of the 29th
conference on Winter simulation, edited by S. Andraóttir, K. J. Healy, D. H. Withers,
variance-based methods make the dierence, in
and B. L. Nelson, pp. 261268.
Cukier, R. I., C. M. Fortuin, K. E. Shuler, A. G. Petschek, and J. K. Schaibly (1973),
Study of the sensitivity of coupled reaction systems to uncertainties in rate coecients. I: Theory,
Journal of Chemical Physics, 59 (8), 38733878.
Cukier, R. I., H. B. Levine, and K. E. Shuler (1978), Nonlinear sensitivity analysis of
multiparameter model systems,
Journal of Computational Physics, 26, 142.
Dabney, S. M., M. T. Moore, and M. A. Locke (2006), Integrated management of ineld, edge-of-eld and after-eld buers,
Association, 42 (1), 1524.
Journal of the American Water Resources
Dimitri, C., and C. Greene (2002), Recent growth patters in the U.S. organic foods market,
Agricultural Information Bulletin 777,
ington, DC.
U. S. Department of Agriculture, Wash-
88
Draper, N. R., and H. Smith (1981),
Applied Regression Analysis, Wiley and Sons, Ltd.,
New York, N.Y.
Fang, S., G. Z. Gertner, S. Shinkareva, G. Wang, and A. Anderson (2004), Improved
generalized Fourier amplitude sensitivity test (FAST) for model assessment,
and Computing, 13 (3), 221226.
Statistics
Fletcher, J. S., J. E. Nellesson, and T. G. Peeger (1994), Literature review and evaluation of the EPA food-chain (Kenaga) nomogram, an instrument for estimating
pesticide residues on plants.,
Environmental Toxicology and Chemistry, 13 (9), 1383
1391.
Fraedrich, D., and A. Goldberg (2000), A methodological framework for the validation
of predictive simulations,
European Journal of Operational Research, 124 (1), 5562.
Francos, A., F. J. Elorza, F. Bouraoui, L. Galbiati, and G. Bidoglio (2001), Sensitivity analysis of hydrological models at the catchment scale: A two-step procedure,
Reliability Engineering and System Safety, 79, 205218.
Frey, H. C., A. Mokhtari, and J. Zheng (2004), Recommended practice regarding selection, application, and interpretation of sensitivity analysis methods applied to food
safety process risk models,
Tech. rep., Prepared by North Carolina State University
for U.S. Department of Agriculture, Washington, D.C.
Gardner, R. H., R. V. O'Neill, J. B. Mankin, and J. H. Carney (1981), A comparison of
sensitivity and error analysis based on a stream ecosystem model,
12, 173190.
Gaud, W. S. (1968), The Green Revolution:
Ecological Modeling,
Accomplishments and Apprehensions,
Former Adminstrator, Agency of International Development, U.S. Department of
State. Speech before The Society for International Development, Shorehan Hotel,
Washington, D.C.
Giles, D. K., and D. C. Slaughter (1997), Precision band spraying with machine-vision
guidance and adjustable yaw nozzles,
Transactions of the ASAE, 40 (1), 2936, small
row crops. Non-target deposition reduced 72-902.5-3.7 times greater than broadcast.
Airborne displacement reduced by 62-93
Gilliom, R. J. (2001), Pesticides in the hydrologic system- what do we know and what's
next? (invited commentary),
Hydrological Processes, 15, 31973201.
Gilliom, R. J., J. E. Barbash, C. G. Crawford, P. A. Hamilton, J. D. Martin, N. Nakagaki, L. H. Nowell, J. C. Scott, P. E. Stackelberg, G. P. Thelin, and D. M. Wolock
89
(2006), The quality of our Nation's waters pesticides in the Nation's streams and
ground water,
USGS Circular 1291, U.S. Geological Survey.
Ho, C. M., R. A. Cropp, and R. D. Braddock (2005), On the sensitivity analysis of
two hydrologic models, in MODSIM 2005 International Congress on Modelling and
Simulation, pp. 24912497, Modelling and Simulation Society of Australia and New
Zealand.
Hoerger, F., and E. E. Kenaga (1972), Pesticide residues on plants:
correlation of
representative data as a basis for estimation of their magnitude in the environment,
in
Environmental Quality and Safety: Chemistry, Toxicology and Technology, vol. 1,
edited by F. Coulston, F. Corte, pp. 928, Georg Theime.
Horwith, B. (1985), A role for intercropping in modern agriculture,
BioScience, 35 (5),
286291.
Hulse, D. W., and S. V. Gregory (2001), Alternative futures as an integrative frame-
Applying Ecological Principles to Land
Management, edited by V. H. Dale and R. A. Haeuber, chap. 9, pp. 194212, Springerwork for riparian restoration of large rivers, in
Verlag, New York.
Iorgulescu, I. K., and A. Musy (1997), Generalization of TOPMODEL for a power law
transmissivity prole,
Hydrological Processes, 119, 13531355.
Jenkins, J., P. Jepson, J. Bolte, and K. Vaché (2004), Watershed-based ecological risk
assessment of pesticide use in Western Oregon: A conceptual framework,
Tech. rep.,
Unpublished report given at SETAC workshop.
Kapur, J. (1989),
Maximum entropy models in science and engineering, John Wiley and
Sons.
Kelton, W. D. (1997), Statistical analysis of simulation output, in
of the 29th conference on winter simulation,
WSC '97: Proceedings
edited by S. Andraóttir, K. J. Healy,
D. H. Withers, and B. L. Nelson, pp. 2330.
Khan, Z. R., K. Ampong-Nyarko, P. Chiliswa, A. Hassanali, S. Kimani, W. Lwande,
W. A. Overholt, J. A. Picket, L. E. Smart, L. J. Wadhams, and C. M. Woodcock (1997), Intercropping increases parasitism of pests,
Nature, 388 (6643),
631
632, mixed cropping of wild and cultivated grasses for cereal production in Africa
and found that intercropping reduced numbers of pests and increased pest parasites
simultaneously.
Kleijnen, J. P. C., and R. G. Sargent (2000), A methodology for tting and validating
metamodels in simulations,
European Journal of Operational Research, 120 (1), 1429.
90
Koda, M., G. J. McRae, and J. H. Seinfeld (1979), Automatic sensitivity analysis of
kinetic mechanisms,
International Journal of Chemical Kinetics, 11, 427444.
Krzykacz-Hausmann, B. (2001), Epistemic sensitivity analysis based on the concept of
entropy, in
Proccedings of "Sensitivity Analysis of Model Output", edited by P. Prado
and R. Bolado, pp. 3135, CIEMAT, Madrid, Spain.
Larson, S. J., R. J. Gilliom, and P. D. Capel (1999), Pesticides in streams of the
United States- initial results from the National Water-Quality Assessment Program,
Water-Resources Investigations Report 98-4222, U.S. Geological Survey, Sacramento,
California.
Leavesley, G., H. S. L. Markstrom, P. J. Restrepo, and R. J. Viger (2002), A modular approach to addressing model design, scale and parameter estimation issues in
distributed hydrological modeling,
Hydrological Processes, 16, 173187.
c
Legates, D. R., and M Cabe Jr. G. J. (1999), Evaluating the use of "goodness-oft" measures in hydrologic and hydroclimate model validation,
search, 35, 233241.
Water Resources Re-
Leguizamon, E. S., and H. A. Roberts (1982), Seed production by an arable weed
community,
Weed Research, 22, 3539.
Lenhart, T., K. Eckhardt, N. Fohrer, and H. G. Frede (2002), Comparison of two
dierent approaches of sensitivity analysis,
Physics and Chemistry of the Earth, 27,
645654.
Li, L., J. Sun, F. Zhang, X. Li, S. Yang, and Z. Rengel (2001), Wheat/maize or
wheat/soybean strip intercropping 1. yield advantage and interspecic interactions
on nutrients,
Field Crops Research, 71 (2), 123137, 40-70intercropped with soybean.
Liebman, M., and E. Dyck (1993), Crop rotation and intercropping strategies for weed
management,
Ecological Applications, 3 (1), 92122, in crop rotation, weed densities
were lower in 21 cases, higher in 1 case and equivalent in 5 cases. In intercropping of
12 cases, 9 were lower in weed seed density and 3 were equivalent. intersowing with
a 'smother' crop produced weed biomasses lower in 47 cases and higher in 4 cases.
Dierent intercrops steal resources from weeds to dierent extents.
Linders, J., H. Mensink, G. Stephenson, D. Wauchope, and K. Racke (2000), Foliar
interception and retention values after pesticide application. A proposal for standardized values for environmental risk assessment,
21992218.
Pure and Applied Chemistry, 72 (11),
91
Lindquist, J. L., B. D. Maxwell, D. D. Buhler, and J. L. Gunsolus (1995), Velvetleaf
Abutilon theophrasti ) recruitment, survival, seed production, and interference in soybean (Glycine max ), Weed Science, 43, 226232.
(
Loague, K. M., and R. A. Freeze (1985), A comparison of rainfall-runo modeling
techniques on small upland catchmentes,
Water Resources Research, 21, 229248.
Lubowski, R. N., M. Vesterby, S. Bucholtz, Baez Alba, and M. J. Roberts (2006), Major
uses of land in the {U}nited {S}tates, 2002,
Economic Information Bulletin EIB-14,
United States Department of Agriculture.
Madaglio, G. P., R. W. Medd, P. S. Cornish, and R. van de Ven (2000), Temperaturemediated responses of umetsulam and metosulam on
Research, 40, 387395.
Raphanus raphanistrum, Weed
Mailhot, A., and J. P. Villeneuve (2003), Mean-value second-order uncertainty analysis
method: Application to water quality modeling,
Advances in Water Resources, 26,
401499.
c
M Cuen, R. H. (1973), The role of sensitivity analysis in hydrologic modeling,
of Hydrology, 18, 3753.
Journal
c
M Rae, G. J., J. W. Tilden, and J. H. Seinfeld (1982), Global sensitivity analysis
A computational implementation of the Fourier amplitude sensitivity test (FAST),
Computers and Chemical Engineering, 6 (1), 1525.
Mitchel, J. (1966), Big Yellow Taxi,
Lyrics, Siquomb Publishing Co. BMI.
Morris, M. D. (1991), Factorial sampling plans for Preliminary Computational Experiments,
Technometrics, 33 (2), 161174.
Response surface methodology: Process
and product optimization using designed experiments, Wiley & Sons, Ltd., New York,
Myers, R. H., and D. C. Montgomery (1995),
N. Y.
Nash, J. E., and J. P. Sutclie (1970), River ow forcasting through conceptual models,
I: A discussion of principles,
Journal of Hydrology, 10, 282290.
Nazarko, O. M., R. C. van Acker, M. H. Entz, A. Schoofs, and G. Martens (2003),
Pesticide free production of eld crops: Results of an on-farm pilot project,
Journal, 95, 12621273.
Agronomy
Paice, M. E. R., P. C. H. Miller, and J. D. Bodle (1995), An experimental sprayer for
the spatially selective application of herbicides,
Journal of agricultural engineering
92
research, 60 (2), 107116, spatially variant pesticide application that can be changed
"on the y.".
Pierce, T. H., and R. I. Cukier (1981), Global nonlinear sensitivity analysis using walsh
functions,
Journal of Computationaly Physics, 41, 427443.
c
Pimentel, D., L. M Laughlin, A. Zepp, B. Lakitan, T. Kraus, P. Kleinman, F. Vancini,
W. J. Roach, E. Graap, S. Keeton, William, and G. Selig (1991), Environmental and
economic eects of reducing pesticide use,
BioScience, 41 (6), 402409.
Ratto, M., P. C. Young, R. Romanowicz, F. Pappenberge, A. Saltelli, and A. Pagano
(2006), Uncertainty, sensitivity analysis and the role of data-based mechanistic modeling in hydrology,
Hydrology and Earth System Sciences Discussions, 3, 30993146.
Ravalico, J. K., H. R. Maier, G. C. Dandy, J. P. Norton, and B. F. W. Croke (2005),
A comparison of sensitivity analysis techniques for complex models of environmental
management, in
MODSIM 2005 International Congress on Modelling and Simulation,
pp. 25332539, Modelling and Simulation Society of Australia and New Zealand.
Reichenberger, S., M. Bach, A. Skitschak, and H.-G. Frede (2007), Mitigation strategies
to reduce pesticide inputs into ground- and surface water and the eectiveness; a
review,
Science of the Total Environment, 384, 135.
RIVM, VROM, and VWS (1998), Uniform system for the evaluation of substances 2.0,
RIVM report 679102044,
National Institute of Public Health and the Environment
(RIVM), Ministry of Housing, Spatial Planning and the Environment (VROM), Ministry of Health, Welfare and Sport (VWS), The Netherlands.
Saltelli, A. (1999), Sensitivity analysis. Could better methods be used,
physical Research, 104 (D3), 37893793.
Journal of Geo-
Saltelli, A. (2002), Making best use of model evaluations to compute sensitivity indices,
Computer Physics Communications, 145, 280297.
Saltelli, A., and R. Bolado (1998), An alternative way to compute fourier amplitude
sensitivity test (FAST),
Computational Statistics and Data Analysis, 26 (4), 445460.
Saltelli, A., S. Tarantola, and K. Chan (1999), A quantitative, model independent
method for global sensitivity analysis of model output,
Saltelli, A., K. Chan, and M. Scott (Eds.) (2000),
Technometrics, 41, 3956.
Sensitivity Analysis, Probability and
Statistics Series, John Wiley and Sons, New York, N.Y.
93
Saltelli, A., S. Tarantola, F. Campolongo, and M. Ratto (2004),
practice: A guide to assessing scientic models,
Sensitivity analysis in
John Wiley and Sons, Chichester,
England.
Saltelli, A., M. Ratto, S. Tarantola, and F. Campolongo (2006), Sensitivity analysis
practices:
Strategies for model-based inference,
Safety, 91 (10-11), 11091125.
Reliability Engineering & System
Santelmann, M., K. Freemark, D. White, J. Nassauer, M. Clark, B. Danielson, J. Eilers,
R. M. Cruse, S. Galatowitsch, S. Polasky, K. Vache, and J. Wu (2001), Applying eco-
Applying
Ecological Principles to Land Management, edited by V. H. Dale and R. A. Haeuber,
logical principals to land-use decision making in agricultural watersheds, in
chap. 11, pp. 226254, Springer-Verlag, New York.
Sobol', I. M. (1990), Sensitivity estimates for nonlinear mathematical models,
Matem-
Sobol', I. M. (1993), Sensitivity estimates for nonlinear mathematical models,
Mathe-
aticheskoe Modelironvanie, 2, 112118, in Russian.
matical Modeling and Computation, 1 (4), 407414.
Srinivasan, R., T. S. Ramanarayanan, J. G. Arnold, and S. T. Bednarz (1998), Large
area hydrologic modeling and assessment part II: model application,
American Water Resources Association, 34 (1), 91102.
Journal of the
Steinitz, C., and S. McDowell (2001), Alternative futures for Monro County, Pennsylvania: A case study in applying ecological principles, in
Applying Ecological Principles
to Land Management, edited by V. H. Dale and R. A. Haeuber, chap. 8, pp. 163193,
Springer-Verlag, New York.
Steinitz, C., E. Bilda, J. Ellis, T. Johnson, Y. Hung, E. Katz, P. Meijerink, D. Olson, A. Shearer, H. Smith, and A. Sternberg (1994), Alternative futures for Monroe
County, Pennsylvania,
Tech. rep.,
Harvard University Graduate School of Design,
Cambridge, Massachusetts.
Tang, Y., P. Reed, T. Wagener, and K. van Werkhoven (2006), Comparing sensitivity
analysis methods to advance lumped watershed model identication and evaluation,
Hydrology and Earth System Sciences Discussions, 3, 33333395.
Tian, L., J. F. Reid, and J. W. Hummel (1999), Development of a precision sprayer for
site-specic weed management,
Transactions of the ASAE, 42 (4), 893900, machine-
vision-system-guided precision application for corn and soybeans. 48
Ucar, T., and F. R. Hall (2001), Windbreaks as a pesticide drift mitigation strategy: a
review,
Pest Management Science, 57 (8), 663675.
94
Urban, D. J., and N. J. Cook (1986), Hazard evaluation division, standard evaluation
procedure, ecological risk assessment,
EPA Report 540/9-85-001, U.S. Environmental
Protection Agency, Washington, DC.
Vaché, K. (2003), Model assessment of the eects of land use change on hydrologic
response, Phd dissertation, Oregon State University, Corvallis, Oregon.
Vaché, K., J. M. Eilers, and M. V. Santelmann (2002), Water quality modeling of
alternative agricultural scenarios in the U.S. corn belt,
Resources Association, 38 (3), 773787.
Journal of the American Water
c
Vaché, K. B., and J. J. M Donnell (2006), A process-based rejectionist framework for
evaluating catchment runo model structure,
Water Resources Research, 42.
van Emdeen, H. F., M. J. Way, T. Lewis, K. D. Sunderland, J. K. Waage, and R. J.
Cook (1988), The potential for managing indigenous natural enemies of aphids on eld
Philosophical Transactions of the Royal Society of London, Series B, Biological
Sciences, 318 (1189), 183201.
crops,
van Griensven, A., A. Francos, and W. Bauwens (2002), Sensitivity analysis and autocalibration of an integral dynamic model for river water quality,
Technology, 45 (5), 321328.
Water Science and
van Griensven, A., T. Meixner, S. Grunwald, T. Bishop, M. Diluzio, and R. Srinivasan (2006), A global sensitivity analysis tool for the parameters of multi-variable
catchment models,
Journal of Hydrology, 324, 1023.
Yeh, K. C., and Y. K. Tung (1993), Uncertainty and sensitivity analysis of pit-migration
model,
Journal of Hydraulic Engineering, 119 (2), 262283.
Yen, B. C., S. T. Cheng, and C. S. Melching (1986), First order reliability analysis, in
Stochastic and risk analysis in hydraulic engineering, edited by B. C. Yen, pp. 136,
Water Resources Publications, Littleton, Co.
95
Appendix
A Ghost Parameter
Because of a misunderstanding, an entire hydrologic sensitivity analysis was run initially
using a parameter set of size
n = 11
with one parameter that was not actually used
in any calculations within the model.
The parameter, which I am calling a ghost
parameter yielded sensitivity results similiar to many other parameters (Those with
the lowest sensitivity).
The most likely reason that the ghost parameter yielded a
value greater than one is that the sensitivity of any parameter is calculated based on
the relationship of the oscillation of each parameter's value with the oscillation of the
evaluative criteria. Thus, it is probable that the parameter's value had some
correlation
with the Nash-Sutclie and RMSE values, even though it is impossible for the parameter
to have
aected
the values.
There may be the possibility of using this ghost eect in other analyses. For instance,
it may be possible to purposfully introduce a ghost parameter into a sensitivity analysis,
and then assume that the model is completely insensitive to parameters with values very
close to the value of the ghost parameter. This is only a possibility and should not be
attempted until one is sure there are no unwanted eects.
Because it may add unwanted eects to the analysis, the full mathematical implications of actually
using
a ghost parameter have not yet been fully evaluated. Doing
so would make my head explode and my wife is not prepared to clean my brains o of
the walls of her new house.