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AN ABSTRACT OF THE THESIS OF
John W.P. Metta for the degree of Master of Science in Biological and EcologicalEngineering and Geography presented on December 3, 2007.
Title: Sensitivity Analysis of the Catchment Modeling Framework (CMF) and Usein 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 e�ects 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 e�ectiveness 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 bene�t 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
bene�t 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. MettaDecember 3, 2007All 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 ful�llment 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 OregonState University libraries. My signature below authorizes release of my thesis to anyreader 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�
McDonnell, 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 di�culties 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 CONTENTSPage
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 . . . . . . . . . . . . . . . . . . 6
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
2.5.1 Evaluative Criteria . . . . . . . . . . . . . . . . . . . . . . . 30
2.5.2 Screening-level Sensitivity Estimation . . . . . . . . . . . . 32
2.5.3 Global Sensitivity Analysis . . . . . . . . . . . . . . . . . . 33
2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6.1 Local Sensitivity Results . . . . . . . . . . . . . . . . . . . . 34
2.6.2 Extended FAST Results . . . . . . . . . . . . . . . . . . . . 46
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3 Sensitivity Analysis of CMF � Pesticide Model . . . . . . . . . . . . . . 55
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Pesticide Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1 Upslope Model . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.2 Instream Model . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3.1 Evaluative Criteria . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4.1 Management implications . . . . . . . . . . . . . . . . . . . 64
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
TABLE OF CONTENTS (Continued)
Page
4 Comparison of Two Pesticide Mitigation Strategies using CMF . . . . . 67
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1.1 CMF Sensitivity, Revisited . . . . . . . . . . . . . . . . . . 68
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.2 Variable Parameters . . . . . . . . . . . . . . . . . . . . . . 72
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Management Implications . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.1 Application Method . . . . . . . . . . . . . . . . . . . . . . 76
4.4.2 Crop Density . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.3 Intercropping . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.4 Dose Modi�cation . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.5 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
A Ghost Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
LIST OF FIGURESFigure 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 di�erent transformation functions (a), (c) and (e) and their
respective empirical distributions (b), (d) and (f) (from: Saltelli et al.,
1999). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Scatterplots of sampling points in a two-factor case, based on the trans-
formations given in Equation 2.21 (a), Equation 2.22 (b) and Equa-
tion 2.23 with one (c) and two (d) resamplings of the random phase-shift
modi�er ϕ (from: Saltelli et al., 1999). . . . . . . . . . . . . . . . . . . . 25
2.5 Initial saturation values vs. Nash-Sutcli�e e�ciencies for 500 model runs. 36
2.6 kdepth values vs. Nash-Sutcli�e e�ciencies for 500 model runs. . . . . . 37
2.7 Saturated hydraulic conductivity values vs. Nash-Sutcli�e e�ciencies for
500 model runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.8 phi values vs. Nash-Sutcli�e e�ciencies for 500 model runs. . . . . . . . 40
2.9 Power law exponent values vs. Nash-Sutcli�e e�ciencies for 500 model
runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.10 Pore size distribution values vs. Nash-Sutcli�e e�ciencies for 500 model
runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.11 Residual water content values vs. Nash-Sutcli�e e�ciencies for 500 model
runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.12 Wilting point values vs. Nash-Sutcli�e e�ciencies for 500 model runs. . 45
2.13 First-order FAST results for the Hydrology model. . . . . . . . . . . . . 49
2.14 Total-order FAST results for the Hydrology model. . . . . . . . . . . . . 50
2.15 First- and Total-order results for the Hydrology model using r2 as the
evaluation criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.1 First-order FAST results for the pesticide model. . . . . . . . . . . . . . 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. . . . . . . . . . . 9
2.2 Parameters used in the sensitivity analysis, their mathematical symbols,
equations in which they are found, and the ranges used in this study. . . 29
2.3 First Order results of FAST test of Nash-Suttcli�e and Root Mean Squared
Error, and R2 for all hydrology variables. . . . . . . . . . . . . . . . . . . 47
2.4 Total Order results of FAST test of Nash-Suttcli�e, Root Mean Squared
Error, and R2 for all hydrology variables. . . . . . . . . . . . . . . . . . . 48
3.1 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 (w) and maximum (wm) limits (in terms of mass frac-
tions mg/kg) for initial pesticide residues on crop groups following appli-
cations of kg/ha. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
DEDICATION
For Jessica.
1 �Introduction
These and other developments in the �eld of agriculture contain themakings of a new revolution. It is not a violent Red Revolution like that ofthe Soviets, nor is it a White Revolution like that of the Shah of Iran. I callit the Green Revolution. (Gaud , 1968)
During his speech to the Society for International Development, William Gaud called
pesticides one of �the physical requirements of the new agriculture (Gaud , 1968).� Used
ubiquitously in the agricultural industry to maintain production �gures while minimiz-
ing losses, their development and use was indeed a blessing. Like so many blessings,
however, we are �nding increasingly that pesticide use comes with some signi�cant costs,
not the least of which are the negative human health e�ects 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)
and the Federal Food, Drug and Cosmetic Act (FFDCA).1 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, reg-
ulators 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
1Most, if not all, regulations are in place speci�cally to protect human health, as opposed to ecosys-tem health or another concern.
2
e�ects had been achieved.
Governmental and non-governmental scientists alike believe that modeling can be
an e�ective tool in estimating pesticide contamination (Larson et al., 1999; Gilliom,
2001). Many also propose that the use of regionally applicable models that link land-
use/economics and pesticide use are bene�cial (Bernardo et al., 1993). The most re-
cent watershed-scale models can e�ectively estimate hydrologic response based on land-
use (Vaché, 2003). These systems have been used successfully to study various aspects of
water quality in relation to fertilizer contamination (Vaché et al., 2002; Srinivasan et al.,
1998; 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 man-
agement 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 e�ects 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 (Steinitz
and McDowell , 2001; Steinitz et al., 1994), agricultural management analysis (Berger
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
hydrology and pesticide contamination given land-use/land cover data (Vaché, 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 manage-
ment implications of the pesticide model's sensitivity. Chapter 4 is a comparison of two
possible pesticide mitigation strategies, �eld-size reduction and pesticide application
modi�cation, 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 com-
plex 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 di�erently by various technical com-
munities and problem settings (Saltelli et al., 2004, p. 42), however, it can generally
be de�ned 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
simply, it is the assessment of the impacts of input changes on output values (Frey
et al., 2004). The motivations one uses in performing sensitivity analysis are varied
and include the identi�cation of variability and uncertainty sources, veri�cation and
validation, data requirement prioritization, parameter prioritization and overall model
re�nement (Frey et al., 2004; Ascough et al., 2005; Fraedrich and Goldberg , 2000; Klei-
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 ro-
bustness (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. gov-
ernments are increasingly demanding that SA be published on models used in policy
decisions (Saltelli et al., 2004, p. 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 Vaché
and McDonnell , 2006). CMF is a watershed-scale (1-999 km2) hydrology model with
fate/transport componants for sediment, conservative tracers and pesticides. While the
model has been used e�ectively in studies (Vaché and McDonnell , 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, speci�cally 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
Put simply, there are two types of sensitivity analyses, local and global1. Local sen-
sitivity 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 e�ect 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 considera-
tions one must make when chosing a sensitivity analysis method, we will consider the
mathematical foundations of sensitivity. Consider the function
y = f (θ) (2.1)
where θ is an n-length vector of model parameters: θ = {x1, x2, . . . , xn}. The change in
y resulting from a change in any single parameter xi can be expressed in mathematical
form by a Taylor series expansion of the function:
f(xi + ∆xi, xj|j 6=i
)= f (θ) +
δy
δxi∆xi +
12!δ2y
δx2i
∆x2i + . . . (2.2)
where the expansion proceeds until all higher order terms in f (θ) are accounted for. If
higher order terms are non-existent, or are suitably small in comparison to the �rst-order
1Saltelli et al. (2000) suggest that there are actually 3 types of analysis, the third being a screeninganalysis. This, they suggest, is a relatively rapid, often qualitative, assessment of model response whichcan guide model evaluators to possible issues before a more detailed analysis is undertaken.
7
terms, the expansion can be reduced to
f(xi + ∆xi, xj|j 6=i
)= f (θ) +
δy
δxi∆xi (2.3)
thus:
∆f (θ) = f(xi + ∆xi, xj|j 6=i
)− f (θ)
=(δy
δxi
)∆xi (2.4)
Equation 2.4 has been called the linearized sensitivity equation (McCuen, 1973) and
measures the change in model output (∆y) due to a change in the ith parameter (∆xi).
The general de�nition for sensitivity is given as:
S =
[f(xi + ∆xi, xj|j 6=i
)− f (θ)
]∆xi
(2.5)
Equation 2.5 de�nes the absolute sensitivity of a linear model to a change in the ith
element of the input parameter θ. 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 be-
cause the computed values are not invariant to the magnitude of y or xi (McCuen,
1973). Comparison between model parameters can be done by dividing both terms by
8
the nominal value:
Sr =
([f(xi+∆xi,xj|j 6=i)−f(θ)]
f(θ)
)(
∆xixi
) (2.6)
thereby yielding a value which provides an estimate of the relative change in y due to
the relative change in xi. This is the relative sensitivity, and provides an estimate of
comparison between model factors that is invariant to the magnitudes of y and xi.
2.2.1.1 Local SA and Non-Linear Models
SA using Equations 2.5 or 2.6 is an e�ective analysis technique only for �rst-order models
with few parameters. More appropriately, it is e�ective for models with parameters that
do not a�ect 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 ine�ective where more than one parameter controls the model
output because each parameter can a�ect other parameters, as well as the model output.
Thus, each parameter can have both direct e�ects (i.e. a�ecting model output, called
�rst-order) and indirect e�ects (i.e. a�ecting other parameters, called second-order).
The simplest illustration of this situation can be seen by evaluating the two equations
f(θ) =x+ a (2.7)
g(θ) =xa + a (2.8)
where θ is a parameter vector θ = {x, a}. Equation 2.7 is a linear, �rst-order equation
9
x\a 2 3 4
2 6 11 20
5 27 128 629
10 102 1003 10004
x\a 2 3 4
2 1 1.75 3
5 2 7.75 31.2
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). In other
words, as x increases across its range, the di�erence between f(θ) and f(x + ∆x, a)
remains constant. While parameter a does a�ect the output of f , we note that model
sensitivity to parameter x is stable across the entire model domain, regardless of the
value of parameter a (Figure 2.1b). In other words, parameter a does not actually e�ect
the model's sensitivity to parameter x; 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 x increases across the model domain, the magnitude of di�erence between g(θ)
and g(x+ ∆x, a) increases. The model response shows that the sensitivity of the model
to x is lower for lower values of x than for higher values. Furthermore, the parameter
a has a signi�cant e�ect on the model response, and higher values of a directly e�ect
the magnitude of di�erence between g(θ) and g(x+ ∆x, a) (Figure 2.2b).
For all values of a, we see that for low values of x, g yields results such that the
di�erence between g (θ) and g (x+ ∆x, a) are quite close regardless of the value of a.
However, as x increases, g increases such that for high values of x, g increases an order
of magnitude for a unit increase in a (Table 2.1). 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 g, the simple mathematical techniques derived from Equation 2.4 are
invalid methods.
10
(a) Model response
(b) Sensitivity to parameter x
Figure 2.1: Model response (a) and sensitivity results (b) for Equation 2.7. Sensitivitywas calculated using Equation 2.6. For a given value for parameter a, the sensitivity ofthe model to parameter x is unchanging.
11
(a) Model response
(b) Sensitivity to parameter x
Figure 2.2: Model response (a) and sensitivity results (b) for Equation 2.8. Sensitivitywas calculated using Equation 2.6. In contrast to Figure 2.1, the slope of the sensitivitycurve reacts di�erently 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 pa-
rameter 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-
els (Ho et al., 2005; Ravalico et al., 2005). The Soil Water Assessment Toolkit (SWAT,
Arnold et al., 1998) has also been the subject of numerous local and OAT sensitivity
analyses (Francos et al., 2001; van Griensven et al., 2002; Lenhart et al., 2002), despite
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 unjusti�ed, unless the model under analysis is proved to
be linear.�
While some state that the use of OAT methods are justi�ed because of the compu-
tational expense of other methods, such as FAST (van Griensven et al., 2006), Saltelli
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
end-user programs such as SimLab (Saltelli et al., 2004, Chap. 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 e�ects 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:
f (θ) = f(θ)
+n∑i=1
δf
δxi(x− xi) (2.9)
where θ = {x1, . . . , xn}. The mean and standard deviation can then be calculated as:
f =f(θ)
(2.10)
σ2f =
n∑i=1
(δf
δxiσθ
)2
(2.11)
14
where σθ ={σx1 , . . . , σxp
}.
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 mean-
value 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:
M (θ) = M(θ)
+n∑i=1
δf
δxi(xi − xi) +
12×
n∑i=1
n∑j=1
δf
δxixj(xi − xi) (xj − xj) (2.12)
thus creating a matrix of second-order derivatives A, containing elements of the form:
Ai,j =σiσj
2
(δ2f
δxiδxj
)(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 (Mailhot and Villeneuve, 2003).
2.2.2.2 Morris Methods
Morris (1991) proposed the possibility of integrating local sensitivity e�ects into a (semi-
)global analysis. The elementary e�ects of the model parameters are found by evaluating
the model with independent sample vectors θ, each the size of the number of con�gurable
model parameters, n. An n-dimensional sample vector θ contains the components xi
such that each component can contain p possible values in the set{
0, 1(p−1) ,
2(p−1) , . . . , 1
}
15
where xi is scaled to(0, 1). The model domain Θ is then an n-dimensional, p-level grid.
If ∆ is a pre-determined multiple of 1(p−1) , then the elementary e�ect of the ith factor
at a given point in the space is (Alam et al., 2004):
fi (θ) =[M (x1, . . . , xi−1, xi + ∆, xi+1, . . . , xk)−M(θ)]
∆(2.14)
where θ is any value in Θ such that θ + ∆ remains in Θ. The process of selecting a
new sample vector is completed until a collection of samples θ1, θ2, . . . , θn−1 is produced
de�ning an orientation matrix B∗ Alam et al. (2004) which can then be used to assess
the elementary e�ect 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 e�ective 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
multi-parameter modeling techniques that hydrologic modeling relied upon (McCuen,
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 param-
eters 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 to-
tal parameter space. Global sensitivity methods allow assessment of the shape of the
model response for all parameters individually (�rst-order) and collectively (higher-
order) 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 Ascough et al., 2005), Response Surface Method (RSM,Myers and Mont-
gomery , 1995), the method developed by Sobol' (Sobol' , 1990, in Saltelli and Bolado,
1998; 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
functions approach (Pierce and Cukier , 1981).
Sensitivity methods based on correlation or regression coe�cients such as the stan-
dardised regression coe�cient (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 Fourier amplitude sensitivity test (FAST)
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
FAST technique, as given in (Saltelli et al., 1999), follows.
For a given model y = f (θ), the model domain Θwill contain k parameter vectors
θ, where k is the total number of individual vectors required to characterize the full
parameter space:
Θ =
θ1
θ2
· · ·
θk
=
x11 x1
2 · · · x1n
x21 x2
2 · · · x2n
· · · · · · · · · · · ·
xk1 xk2 · · · xkn
(2.15)
This parameter matrix will yield a hypercube for the parameter domain expressed
as
Kn = (θ | 0 ≤ xi ≤; i = 1, . . . , n) (2.16)
If we assume that θ is a random vector with a pdf P (θ) = P (x1, x2, . . . , xn), then
18
a summary statistic for the rth moment of the model is
⟨y(r)⟩
=∫kn
f r (θ)P (θ) dx (2.17)
It was suggested by Cukier et al. (1978) that it would be possible to compute an
ANOVA-like decomposition of y as a function of θ using a multi-dimensional Fourier
transformation of f , 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 de�ned as
xi (s) = Gi (sinωis) , ∀i = 1, 2, . . . , n (2.18)
where s varies in [−∞,∞], and {ωi} ,∀i = 1, 2, . . . , n, is a set of angular frequencies
associated with each factor2. Gi is a transformation function which de�nes the search
curve, further described in Section 2.2.3.3.
The curve searches the entire hypercube Kn such that as the scalar quantity s
changes, all model parameters change simultaneously. Regardless of the model f or the
transformation function Gi, each xi oscillates at the corresponding frequency ωi while
y shows di�erent periodicities with di�erent frequencies ωi. For any ith input factor,
the amplitude of oscillation of y at frequency ωi will be high if the factor has a strong
in�uence on the model output. Thus, the sensitivity measure of any factor xi is based
2Saltelli et al. (1999) note that the the exploration curve is only e�ective if it can explore arbitrarilyclose to any point of the input domain, and that this is possible if and only if the chosen set offrequencies is incommensurate. To ensure this, they state, no frequency must be obtainable as a linearcombination of the others. Thus, it must be true that
Pni=1riωi 6= 0, −∞ < ri <∞.
19
on the coe�cients 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' , 1993)3
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 e�ects and parameter interaction e�ects shown as
s (y) =∑i
si +∑i<j
sij +∑i<j<k
sijk + s12...n (2.19)
where si is the sensitivity of the model output y to the ith component of the input
parameter vector θ, sij is the variance of y due to interactions of xi and xj , and n is
3Following the conventional transliteration found in the literature, I include a trailing apostrophein the name.
20
the size of the input parameter vector θ. The sensitivity indices are then calculated as:
Si =sis
Sij =sijs
ST i =1−(s∼i
s
)
where Si is the �rst-order sensitivity resulting from parameter xi and Sij is the second-
order sensitivity resulting from the interaction of parameters xi and xj . s∼i is the
average variance resulting from all parameters except for xi, thus allowing for a cal-
culation of total-order sensitivity ST i as the main e�ect of xi up to the nth-order of
interaction.
The individual parameter variance required in Equation 2.19 is evaluated using
Monte Carlo approximations given as (Tang et al., 2006):
f0 =1n
n∑i=1
f (xi)
s =1n
n∑i=1
f2 (xi)− f0
si =1n
n∑i=1
f (xαi ) f(xβ∼i, x
αi
)− f0
2
sijc =
1n
n∑i=1
f (xαi ) f(xβ∼i,∼j , x
αi,j
)− f0
2
sij =sijc − si − sj
s∼i =1n
n∑i=1
f (xαi ) f(xα∼i, x
βi
)− f0
2
where n is the sample size, xi is the ith parameter of the parameter vector θ and α
21
and β are two di�erent samples of xi. As stated above, ∼ i denotes all but the ith
parameter, thus xα∼i denotes all values from the parameter vector θ except xi, where
those values are samples from the α sample vector.
One note that should be made here regarding the Sobol' method is the computational
expense. Sobol's original method required n × (2m+ 1) model runs to calculate the
�rst- and total-order sensitivity, where n is the number of sample vectors required
to characterize the entire unit hypercube, and m is the number of parameters. An
improved method of Saltelli (2002) requires n × (2m+ 2) model runs. Tang et al.
(2006), noted that the sample size necessary to fully sample Kn of their 18 parameter
snowpack energy balance model was 213. Thus, the number of model runs necessary
was 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 �rst-
order 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 Saltelli et al. (1999), who note that the
selection of a di�erent transformation function Gi can yield results that more completely
22
sample Kn. They note that the original transformation function proposed by Cukier
et al. (1973) is insu�cient. The function is expressed as
xi = xie(vi sinωis), ∀i = 1, 2, . . . , n (2.20)
where xi is the nominal value of the ith input factor, vi de�nes the uncertainty range
endpoints of xi and s varies in(−π
2 ,π2
).
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 distri-
bution, 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 + vi sinωis) (2.21)
with vi = 1, xi = 12 and 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 =12
+1π
arcsin (sinωis) (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 di�erent transformation functions (a), (c) and (e) and theirrespective 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 Kn as s varies in(−π
2 ,π2
). Thus, they propose a random phase-shift
modi�er, ϕ, be chosen uniformly in [0, 2π) yielding a transformation function expressed
as
xi =12
+1π
arcsin (sin [ωis+ ϕi]) (2.23)
thus yielding a search-curve that can have a start point at an arbitrary point in Kn,
thus tracing an arbitrary curve through Kn.
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 Kn (Figures 2.4(a,b)),
while Equation 2.23 can be resampled4 to provide non-predictable paths and full sam-
pling of Kn (Figures 2.4(c,d)).
2.2.4 Entropy
One �nal approach to sensitivity is that summarized by Krzykacz-Hausmann (2001).
Entropy is a scalar measure of uncertainty maximized by the uniform distribution (Ka-
pur , 1989, in Krzykacz-Hausmann, 2001). For a discrete distribution of Y , given a
probability function pi = (p1, . . . , pn), it is de�ned as
H (Y ) = −∑
pi · ln pi (2.24)
4Truthfully, it must be resampled over (−π, π) to satisfy the assumption of symmetry in f (s). SeeSaltelli et al. (1999) Appendix C, for a detailed analysis of this issue.
25
Figure 2.4: Scatterplots of sampling points in a two-factor case, based on the trans-formations 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 modi�er ϕ (from: Saltelli et al.,1999).
26
while for a continuous distribution of Y with a probability density de�ned as f (y), it
is de�ned as
H (Y ) = −∫f (y) · ln f (y) · dy (2.25)
The result of this output is interpreted somewhat di�erently 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 indeterminacy
of Y represented by its distribution.�
One argument for entropy as a measure of sensitivity over variance is explained by
Saltelli et al. (2004, pp.53-57). Their explanation centers on the model Y = X1X22 ,
where X1 ∼ U (−0.5, 0.5) and X2 ∼ U (0.5, 1.5). The �rst-order partial variance of X2
is zero, despite it being obvious that changing that parameter will change the model
signi�cantly. 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 e�ect of
X2 at the second order (Saltelli et al., 2004, p. 54).�
Saltelli et al. (2004, p. 57) suggest that alternatives to variance such as entropy
�[seem] to be associated with speci�c 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 McDonnell (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 de�ning spatially explicit reservoirs, generally generated from
a DEM where each reservoir is a 3-dimensional unit with a de�ned depth, z, and a
surface area A, which is given by the DEM grid-cell size.5 The total volume of water,
Vt, within this reservoir is calculated as the sum of the saturated zone volume, Vs, and
the unsaturated zone volume, Vu, as follows:
Vt =Vs + Vu (2.26)
dVsdt
=k (θ) + SSin + SSout − SOFout − kd + EXw (2.27)
dVudt
=I − k (θ)− EXw (2.28)
where the change in volume is calculated in time, t, of days. k (θ) is the recharge rate,
de�ned in Equation 2.29, SSin and SSout are the rate of subsurface in�ow and out�ow,
respectively, from adjacent reservoirs, SOFout is the output rate of saturated excess
overland �ow. kd is the rate of loss to groundwater, and EXwrepresents the exchange
of water between the saturated and unsaturated zones as a function of water table depth
adjustment, de�ned in Equation 2.30.
The recharge rate is calculated as a Brooks-Corey relationship:
5This de�nition of the reservoir introduces one of the important assumptions of the model, thatbeing that there is a de�ned soil depth. The model assumes that this depth is bounded by an aquatard.Thus, testing the sensitivity of the model to parameter z is a good assement of the importance of thisassumption.
28
k (θ) = ks
(θ − θsθs − θr
)λ(2.29)
where ks is the saturated hydraulic conductivity, θ is the volumetric water content, θs
is the residual water content, θr is the wilting point, and λ is the pore size distribution.
Due to hysteresis, EXw is calculated di�erently depending on the direction of water
table change,
EXw = ∆l · x
x = Vu
A·zu; ∆l > 0
x = 0 ; ∆l = 0
x = φ ; ∆l < 0
(2.30)
where ∆l, the change in water table height, can be positive (rising), zero (stable) or
negative (falling). zu is the depth of the unsaturated zone.
Subsurface in�ow and out�ow are calculated independently for each reservoir at
each timestep as:
SSi,j =k<9∑k=0
Ti,j,k · S
S = Slopei,j,k ;Slopei,j,k > 0
S = |Slopei,j,k| ;Slopei,j,k < 0
where i and j 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 di�erence 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 de�ned by the power law
29
Parameter Symbol Equation Range
Power Law Exponent ε 2.31 8-15
Residual Water Content θr 2.29 0.01-0.1
Pore Size Index λ 2.29 0.08-0.5
Soil Depth z 2.31 0.8-1.4
Saturated Conductivity ks 2.29,2.31 10-250
Groundwater Loss Rate kd 2.27 10−6 − 10−5
Trace Water Content θt 2.31 0.25-0.5
Initial Saturation θi Boundary Condition 0.4-0.8
Field Capacity θFC Soil Parameter 0.02-0.1
Table 2.2: Parameters used in the sensitivity analysis, their mathematical symbols,equations in which they are found, and the ranges used in this study. Initial saturationand �eld capacity are used elsewhere in the model to evaluate initial conditions and inthe evapotranspiration calculations.
exponent, ε. It is calculated as (Iorgulescu and Musy , 1997):
T =ks · zε
(1− zwt
z
)ε(2.31)
where zwt 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 'Practica-
ble 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 con-
centrations 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
e�ectiveness 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 screening-
level 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 ∆y where y is a single value. Thus, in cases of
time series modeling, the output 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 di�erent 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
functions are the Nash-Sutcli�e e�ciency criterion (Nash and Sutcli�e, 1970):
Reff =
1n
n∑t=0
(dt − ot (θ))2
1n
n∑t=0
(dt − d
)2 (2.32)
the root mean squared error:
RMSE =
√√√√ 1n
n∑t=0
(dt − ot (θ))2 (2.33)
and the coe�cient of determination:
r2 =
n∑t=0
(dt − d
) (ot (θ)− ot (θ)
)[
n∑t=0
(dt − d
)]0.5 [ n∑t=0
(ot (θ)− ot (θ)
)]0.5
2
(2.34)
where 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-Sutcli�e criterion, Reff , since this
is the value most commonly used in hydrologic response assessment (Leavesley et al.,
2002; Legates and McCabe Jr. G. J., 1999; Loague and Freeze, 1985).6 Values for Reff
lie in the range (1.0,−∞) where 1.0 indicates that the model is a perfect predictor,
6Campbell et al. (2005) provide further discussion on performing sensitivity analysis when modeoutput 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 e�ciency across basins and response
regimes because it is a normalized measurement. Root mean squared error, RMSE,
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 coe�cient of determination, r2, while presented in the global SA, is less than
e�ective 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 Reff
and RMSE.
2.5.2 Screening-level Sensitivity Estimation
Although it has been suggested that a purely local SA is e�ective in determining model
sensitivity to highly complex watershed-scale hydrologic models (Lenhart et al., 2002),
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
7E�ciencies below zero indicate that the model is an increasingly poor predictor of measured values.
33
10-day spinup period to stabilize and decrease the e�ects of initial conditions. I chose
the parameter vector from Θ which yielded the highest value of Reff 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 Reff 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
local and integrated methods for the analysis of hydrologic models (Francos et al., 2001;
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
methods are unequivically superior to local methods (Chan et al., 1997) and FAST
and other variance-based methods have been shown to be good methods for use with
hydrologic and environmental models (Ascough et al., 2005; Ratto et al., 2006; Ravalico
et al., 2005; Tang et al., 2006).
Despite the arguments that FAST methods are far too computationally expensive
and/or di�cult 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. Ascough
et al., 2005; Saltelli , 2002; Saltelli and Bolado, 1998; Saltelli et al., 2000, 2006, 1999;
Tang et al., 2006), computational numerics have been presented (McRae et al., 1982) and
34
there are tools available as both end-user programs and programming libraries for C++
and MatLab that allow for easy model integration (Saltelli et al., 2000). Furthermore,
e�ciency 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 satis�ed. Thus,
for a model with an input parameter vector with size n = 10, the number of model runs
necessary for e�cient E-FAST evaluation is as small as 1,641 (Saltelli et al., 1999;
Saltelli and Bolado, 1998). 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 Results
2.6.1 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 repre-
sentation 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 pa-
rameter. 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 e�ect on model e�ciency
during the screening. While each parameter varied fully within the uniform distribution
bounds, the results of the NSeff and RMSE did not vary. While it is possible that two
distinct discharge curves could be produced, each yielding the same NSeff or RMSE
value, it is highly unlikely that 200 would do so for both of the metrics. 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 e�-
ciencies above zero for initial saturation values between 63% and 73%. The e�ciency
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 e�ciency
Figure 2.5: Initial saturation values vs. Nash-Sutcli�e e�ciencies for 500 model runs.Sub�gure (a) shows the full parameter domain while sub�gure (b) focuses on thosee�ciencies above zero.
37
(a) Domain above zero e�ciency
Figure 2.6: kdepth values vs. Nash-Sutcli�e e�ciencies 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 e�ciencies above
0.71, despite a downward trend as loss-rates increase. This suggested that, with the
bounds of the variable, the model's e�ciency might be insensitive to this parameter.
2.6.1.4 Saturated Hydraulic Conductivity
Results for ks are shown in Figure 2.7. The domain chosen spanned from 10 to 250
mmd . The conductivities that yielded e�ciencies above zero spanned a wide domain
38
with the resulting trajectory roughly bell-shaped. Maximum e�ciency 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
e�ciencies above 0.49 and stabilization at 73% above 0.56. Because of the steep drop-o�
of e�ciencies 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 ε 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 e�ciencies for values below 0.15. While the majority of the model
domain was below zero e�ciency, 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 e�ciency
Figure 2.7: Saturated hydraulic conductivity values vs. Nash-Sutcli�e e�ciencies for500 model runs.
40
(a) Full measurement domain
(b) Domain above zero e�ciency
Figure 2.8: phi values vs. Nash-Sutcli�e e�ciencies for 500 model runs.
41
(a) Full measurement domain
(b) Domain above zero e�ciency
Figure 2.9: Power law exponent values vs. Nash-Sutcli�e e�ciencies for 500 model runs.
42
(a) Full measurement domain
(b) Domain above zero e�ciency
Figure 2.10: Pore size distribution values vs. Nash-Sutcli�e e�ciencies for 500 modelruns.
43
2.6.1.8 Residual Water Content
Results for θr are shown in Figure 2.11. The model domain was from 0.01 to 0.1 and
the model yielded e�ciencies 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 Wilting Point
Results for 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 de�ned 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 e�ects 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-a�ecting parameters turned out to be wrong, although soil
depth was later shown to have only a small e�ect 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 e�ciency
Figure 2.11: Residual water content values vs. Nash-Sutcli�e e�ciencies for 500 modelruns.
45
(a) Full measurement domain
(b) Domain above zero e�ciency
Figure 2.12: Wilting point values vs. Nash-Sutcli�e e�ciencies 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� NSeff , RMSE 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 di�erent, and less reliable than NSeff and RMSE,
graphical representations for r2 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 insen-
sitive (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 NSeff and RMSE, respectively. The model
47
Parameter NSeff RMSE r2
ε 0.0577 0.0521 0.0035
θr 0.0370 0.0405 0.0021
λ 0.0351 0.0282 0.0218
zsoil 0.0293 0.0188 0.0004
φ 0.1620 0.2053 0.3196
ks 0.0171 0.0088 0.0026
kd 0.0025 0.0012 0.0005
θt 0.0264 0.0189 0.0005
θi 0.1893 0.2174 0.2553
θFC 0.0374 0.0289 0.0001
Table 2.3: First Order results of FAST test of Nash-Suttcli�e and Root Mean SquaredError, and R2 for all hydrology variables.
was insensitive to all other parameters except porosity, φ, and initial saturation, θi.
Using all objective functions, the model showed sensitivity to φ and θi with values of
NSeff = {0.162, 0.1893}, RMSE = {0.2053, 0.2174} and r2 = {0.3196, 0.2553} for
{φ, θi}, respectively. 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 kd, for which results
were 0.0716 and 0.0418 for NSeff and RMSE, respectively (Table 2.1). The results for
second-order sensitivity using r2 as an objective function mirror those of the �rst-order,
possibily indicating that this is not an appropriate evaluative function for estimating
second-order e�ects.
48
Parameter NSeff RMSE r2
ε 0.6992 0.5376 0.1168
θr 0.7833 0.6842 0.0148
λ 0.7718 0.6261 0.0710
zsoil 0.6782 0.4453 0.0445
φ 0.8934 0.8993 0.6658
ks 0.4588 0.2310 0.0757
kd 0.0716 0.0418 0.0143
θt 0.6122 0.4265 0.0298
θi 0.3492 0.3585 0.6599
θFC 0.7852 0.5539 0.0068
Table 2.4: Total Order results of FAST test of Nash-Suttcli�e, Root Mean SquaredError, and R2 for all hydrology variables.
2.6.2.3 Discussion
While NS and RMSE yielded similiar sensitivity results, they di�ered slightly in their
assessment of the dominance of the parameters φ and θi in �rst order results. As shown
in Figure 2.13, {φ, θ} comprised {27%, 32%} of �rst order sensitivity using NSeff as
the objective function, while they comprised {33%, 35%} using RMSE. The RMSE
results show that the �rst-order a�ects of the remaining parameters are likewise similiar
to NSeff 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 RMSE
may make the sensitivity analysis itself more sensitive to dominant parameters than
using the NSeff . One possible reason for this is the fact that RMSE tends to weigh
the more extreme cases of a series, while NSeff normalizes these. 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 NSeff and RMSE
(Figure 2.14) again with some less pronounced di�erences, mainly in the assessment of
φ and ks.
49
Figure 2.13: First-order FAST results for the Hydrology model. Wedges indicate per-centages of total-order sensitivity with exploded wedges for parameters greater than10% of the total. Values for kd are not shown here because they account for less than0.5% of the total variability in both cases.
50
Figure 2.14: Total-order FAST results for the Hydrology model. Wedges indicate per-centages of total-order sensitivity. Values for kd (exploded) account for less than 2% ofthe total second-order variability in both cases.
51
Both orders show that analyses using r2 as the measurement metric yielded dras-
tically di�erent results than NSeff and RMSE (See Figure 2.15). Both �rst- and
second-order analyses are heavily dominated by φ and θi 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 con�ning 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 e�ect of an
individual parameter to the model's sensitivity of all other parameters. Thus, it can
be seen as the parameter's e�ect 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 e�ect 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 di�erent 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 theevaluation criteria. All parameters with �rst-order values less than 1.0% account foronly 1.6% of total �rst-order variability. Parameters with total-order values less than1.0% have been exploded.
53
same equations in some cases, it is quite likely that the total-order results of this sensi-
tivity analysis would be similiar for a model such as SWAT, in as much as there would
likely be a number of parameters with signi�cant total-order e�ects 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 ap-
pear to be justi�ed when examining the literature. Saltelli (1999) found that the vast
majority of studies written in the literature involved local or OAT methods. Further-
more, there seems to be a number of papers stating that variance-based methods are too
di�cult, expensive or unnecessary (e.g. Francos et al., 2001; van Griensven et al., 2002,
2006). Thus, many researchers might feel justi�ed in their reliance on local methods
because they can fall back on these arguments.8
2.7 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. Furthermore, the SA analysis showed that all factors except kd have a strong
8I have found what seems to be a fear of the mathematics and di�culty of global methods in my ownexperience working as a water quality hydrologist for the Oregon State Department of EnvironmentalQuality. When I recently suggested to my team that it would be appropriate to perform a globalSA on our stream temperature model, the response was negative with the argument that it would betoo complicated to perform. This was in spite of the fact that we are mandated to perform such ananalysis. Our individual use of situation-speci�c, local methods is �good enough� for current purposes.
54
total-order e�ect 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 e�ective 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 Model-
ing 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 hydro-
logic, 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 de�ned
by a set of mass balance equations that are distributed in space and solved in time. The
equations are essentially those de�ned 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
de�ned 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
mixed reactor (Jenkins et al., 2004).
A complete mathematical description of the pesticide model is provided in Carsel
et al. (1985). A concise version, provided in Jenkins et al. (2004), is given here.
3.2.1 Upslope Model
As stated above, pesticide mass is de�ned by di�erentially 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 speci�c 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 de�ned by the equation:
dMplantpest
dt= Rapp −Rfoliar −Rtrans (3.1)
where Rapp is the rate of application (that portion of the total application that is applied
to the plants), Rfoliar is the foliar runo� rate, and Rtrans is the rate of transformation.
The foliar runo� rate is de�ned by the equation:
57
Rfoliar = ε · P ·Mpest (3.2)
where ε is the extraction coe�cient (set to 0.1 in accordance with PRZM), P is the
precipitation rate, and Mpest is the mass of pesticide. The rate of transformation is
de�ned as the mass of the pesticide times the �rst-order foliar degradation constant:
Rtrans = Kf ·Mpest (3.3)
3.2.1.2 Surface Compartment
M surfacepest = Rfoliar +Rapp −Radv −Rtrans −Rro −Rup −Rerosion (3.4)
where the inputs are the runo� from the plants Rfoliar 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, Rerosion.
The advection rate is de�ned as the concentration of pesticides Cpest = mpest
vwatertimes
the velocity of water �owing into the unsaturated zone. The transformation rate is
de�ned as:
Rtrans = (Ks ·Mpest) + (Cpest ·Kd ·Ks · ρb) (3.5)
where Ks is the degradation constant, Kd is the adsorption partition coe�cient 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 e�ciency times the current rate of evapotranspiration:
58
Rup = Mpest · e · ET (3.6)
where uptake e�ciency, e, is de�ned as:
e = 0.784[log(Koc)−1.78]2
2.44 (3.7)
and Koc is a parameter describing sorption of pesticides to soil particles (further de�ned
in Section 3.3.2).
The erosion rate is:
Rerosion = Msed−out ·Rom ·Kd · Cpest (3.8)
where the mass of sediment eroding, Msed−out, is multiplied by the organic matter
enrichment ratio, Rom, times the adsorption partition coe�cient,Kd, times the pesticide
concentration, Cpest.
3.2.1.3 Vadose and saturated compartments
Pesticide concentration in the vadose and saturated zones are de�ned similarly to the
surface zone as:
M[unsat|sat]pest = I −Radv −Rtrans −Rup (3.9)
where I is the input from surface or vadose zone for vadose and saturated mass, respec-
tively.
59
3.2.2 Instream Model
The model treats instream pesticides as conservative substances. There are two inde-
pendent routing models implemented, however, only one was used for this study. Input
concentration to each reach is de�ned 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 di�erence is in the choice
of an evaluative criteria and the addition of pesticide speci�c 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.
1This increase in model runtimes was due to increased memory usage internally as the number ofruns 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-
propriate to the question that the model will be used to answer (Saltelli et al., 2000).
There are many ways to characterize a pollutant plume with a single number. Total
mass at catchment out�ow 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 di�erence 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-speci�c parameters.
61
The �rst is the fraction of pesticide that is applied to the ground, Fgnd. Fgnd is
mainly a re�ection 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% re�ects 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% re�ects 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, kf , and is varied from 0.001 to 2.0. The
third parameter the partitioning coe�cient, koc 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 =
(CsCw
)% soil organic carbon
(3.10)
where CsCw
is the ratio of the concentrations of chemical in solid and liquid phases at
equilibrium. This value is pesticide speci�c, and was varied from 0 to 9000.
Ranges for kf 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 pre-
emergent application or application during periods of plowing, where coverages can be
as low as 0% (Breuer et al., 2003).
62
First-order First-order Total-order Total-orderParameter Mass Peak Mass Peak
Field Cap. θFC 0.0368 0.0462 0.7066 0.7619
Init. Sat. θi 0.1749 0.1670 0.6017 0.6172
Trace Water Content θt 0.0581 0.0589 0.8587 0.8602
GW Loss Rate kd 0.0584 0.0597 0.8675 0.8708
Sat. Hyd. Cond. ks 0.2142 0.2420 0.6561 0.7285
Porosity, φ 0.1481 0.1179 0.8817 0.8806
Soil Depth dsoil 0.0118 0.0320 0.4470 0.5967
Pore Size Dist. λ 0.0521 0.0369 0.5058 0.4811
Res. Water Content θr 0.0484 0.0484 0.7825 0.7780
Power Law Exp. ε 0.0386 0.0511 0.6510 0.7747
Part. Coe�., koc 0.0406 0.0322 0.6230 0.5431
Foliar Deg. Rate, kf 0.0381 0.0260 0.6952 0.6161
Frac. on Ground, Fgnd 0.0413 0.0432 0.8152 0.8278
Table 3.1: FAST sensitivity values for all model parameters using Mass and Peakconcentration 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, θi, saturated hydraulic conductivity, ks, and porosity,
φ� dominate the total �rst-order sensitivity pro�le, 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-speci�c 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 in�uence the model's response to
63
Figure 3.1: First-order FAST results for the pesticide model. Wedges indicate percent-ages of �rst-order sensitivity with exploded wedges for parameters greater than 10% ofthe 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 prop-
erties, the knowledge that hydraulic conductivity and soil porosity are strong determi-
nants 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 consider-
ation 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 fol-
lowing 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 con-
siderations, crop type and planting strategies, and soil properties are all important
when weighing application options. 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 percent-ages of total-order sensitivity with exploded wedges for parameters greater than 9% ofthe 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 de�ning 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 e�ect 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 de�ned values for pesticide application
method (fraction reaching ground) or soil organic carbon are unlikely to have a large
e�ect on model results.
It is important to remember, however, that this analysis does not account for what
e�ects 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%
is in agricultural use (Lubowski et al., 2006). The total land area in use for cropland
alone is 179 million hectares (442 million acres), or nearly 20% (Lubowski et al., 2006).
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 1992�2001, 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 e�ect
of modifying one pesticide-speci�c 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-speci�c parameters that can be most
easily changed by management practices alone, those are the partitioning coe�cient
(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 coe�ent 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-speci�c 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 in�uenced. 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 e�ect of modifying the most important,
pesticide-speci�c 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-speci�c parameter, total �eld-size under
cultivation will be varied simultaneously in an e�ort to assess the relative merits of
reducing application to the ground versus reducing total application area.
A Note on Bu�er Strips and the Partitioning Coe�cient
Bu�er 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. Bu�er
strips or similar strategies, by allowing natural plant stages, would increase soil organic
carbon, thus modifying the partitioning coe�cient favorably for reduced pesticide trans-
port. Reichenberger et al. (2007) note that there is disagreement in the literature on
the e�ect of edge-of-�eld vs. riparian bu�er strip e�ciency; however, their extensive
literature review found that �eld-edge bu�ers are generally more e�ective than ripar-
ian bu�ers in pesticide mitigation. This e�ectiveness is not dependent on soil organic
carbon so much as on �ow characteristics.
This study does not evaluate bu�er strips with increased soil organic carbon. Rather,
by reducing the size of the �elds, it is more closely a study of the e�ect of non-carbon
bene�tted bu�ers. As such, a more systematic approach can later be performed by
evaluating carbon bene�tted vs. non-carbon bene�tted bu�er 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 speci�c 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 justi�ed 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 speci�ed 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 Nash-
Sutcli�e 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 di�erence in e�ectiveness of in-�eld, after-�eld
71
and edge-of-�eld bu�ers 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 bu�er 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 speci�c,
desirable, Nash-Sutcli�e 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 pa-
rameters 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 bu�ers are
equivalent. While there is evidence that combining in-�eld, edge-of-�eld and other
bu�ers is a bene�cial management strategy (Dabney et al., 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 applica-
tion 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 modi�ed simply by changing the fraction of the total catchment to
which pesticides are applied. In both cases, the values are fractional and thus scale
from 0 to 1.1
1While 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 di-
rectly 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 corre-
lation 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 e�ective pesticide mitigation
were included in the Monte Carlo sample generation to ensure complete coverage of the parameterranges.
74
(a)
(b)
Figu
re4.1:
Plots
show
inginstream
pesticid
emass
plotted
againststu
dyparam
eters.Plot
(a)show
sinstream
mass
vs.
fractionof
totalcatch
mentarea
cultivated
.Theam
ountof
pesticid
eapplied
directly
onthegrou
ndisnoted
bytheshadeanddiam
eterof
thedatap
oints.
Plot
(b)show
sinstream
mass
vs.fraction
ofpesticid
emass
applied
directly
tothegrou
nd.Thefraction
alsize
ofthe�eld
isthen
noted
bythecolor
andsize
ofthedatap
oints.
Both
plots
share
thesam
elog-scale
y-ax
is.Each
datap
ointexists
inboth
plots,
asisillu
stratedbythenoted
datap
oint
ineach
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 in�uence pesticide movement). Given
the choice, it seems as though it would be more bene�cial 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 bene�t 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 bene�t of reducing total pesticide usage. Such
reduction may prove a �nancial bene�t 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, rel-
atively simple. The salient result is that reducing the amount of pesticides that land
directly on the ground surface is generally more bene�cial than reducing the amount of
�eld under cultivation, even in the extreme cases.
Agriculture is, by its nature, very situation speci�c. The climatic, cultural, ecologi-
cal, economic and other characteristics that a farmer works within in Western Oregon
can be very di�erent 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 di�erent manage-
76
ment strategies, each which can be combined with others to yield a practical mitigation
approach in a situation speci�c manner.
4.4.1 Application Method
Probably the most obvious method for reducing ground application is by merely ap-
plying 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 signi�cant health hazard to the laborer.
Machine application may be the most cost-e�ective 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 e�ciency was im-
proved by a factor of 3 or greater. (Tian et al., 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
varied cropping systems (Paice et al., 1995).
Precision application of pesticides can reduce total application masses, lower on-
ground percentages and lower costs to the farmer, but the application technique has to
be cost-e�ective itself. For instance, saving on pesticide costs by applying with precision
methods would hardly be seen as an economic bene�t if the savings, and possibly more,
is spent by having laborers hand-spray, or by purchasing machinery.
77
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
Table 4.1: Fraction of pesticide landing on soil (Fgnd) for various crops. Fractionassumes a default loss to air of 0.1. Remaining fraction is considered a default valuethat is intercepted by the plant. The term a.e. signi�es after emergence (Adapted fromRIVM, 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 speci�c 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 Pes-
ticide Root Zone Model (PRZM)) and evaluating pesticides (Urban and Cook , 1986).
The EPA numbers, originally developed by Hoerger and Kenaga (1972) in what be-
came known as the 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 speci�c
crops in various important growth phases. This proposal includes interception values
78
Plant Category w † (est.) w±S.D. ‡ (meas.) wm† (est.) wm
‡(est.)
Short-range grass 112 76 ± 54 214 214
Long grass 82 32 ± 36 98 98
Leaves, leafy crops 31 31 ± 40 112 112
Forage legumes 30 40 ± 51 52 121
Pods and seeds 3 4 ± 5 11 11
Fruits 1 5 ± 9 6 13
Table 4.2: Estimated mean (w) and maximum (wm) limits (in terms of mass fractionsmg/kg) for initial pesticide residues on crop groups following applications of kg/ha. Valuesinitially reported in lb/a were converted by 1 lb/a = 1.12 kg/ha . Note the high standarddeviations in the measured data of Fletcher ref. (from Linders et al., 2000)† (Hoerger and Kenaga, 1972)
‡ (Fletcher et al., 1994)
for 28 di�erent 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 e�ect 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, in-
creasing crop density can result in lower pesticide needs. Baker and Dunning (1975)
found that crop densities of sugar-beet plants could, in themselves, a�ect 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 di�erent, mutually bene�cial 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
viable approach even in modern, industrial agriculture (Horwith, 1985). Intercropping
is seen to enhance biodiversity and thus provide bene�ts 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 bene�ts of intercropping are not limited to productivity increases,
however. Since di�erent 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 speci�c '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 e�ect,� and is less e�ective 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 e�ective 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 Modi�cation
Another strategy that could e�ectively 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 (1966). Much of this early concern began with
the publication of Silent Spring (Carson, 1962) which detailed the e�ects 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 e�ective
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 sigi�cantly 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 certi�ed their �elds
to use pesticide-free production methods. One year after certi�cation, 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
billion in 2000 and has seen 20% or more growth annually since 1990 (Dimitri and
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 con-
ditions can be very bene�cial 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. Mada�glio et al. (2000) found that
increasing temperatures can increase pesticide e�ciency. Thus, if farmers are able
to time applications with respect to local climate, they may be able to increase the
e�ciency 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 strate-
gies and should be seen as ways to reduce the amount of pesticide that reaches the
ground surface. Each method, of course, has its bene�ts and its drawbacks; however,
each method can be combined with others in a situation-speci�c 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 Catch-
ment 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 e�ects 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-e�ective 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
speci�c manner to yield an integrated pesticide management strategy. The literature
would bene�t from a more speci�c study where a given �eld with known crop type
and density and known pesticide usage would be evaluated. Such a speci�c 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 speci�c
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 con�ning layer constrains soil depth,
will likely not a�ect 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 re-
spect 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 pes-
ticide 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 speci�c parameters tested; these were the par-
titioning coe�cient, foliar degradation rate, and fractional application directly to the
ground surface.
Chapter 4 provided a comparison of two di�erent 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
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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-Sutcli�e and RMSE values, even though it is impossible for the parameter
to have a�ected the values.
There may be the possibility of using this ghost e�ect 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 e�ects.
Because it may add unwanted e�ects to the analysis, the full mathematical impli-
cations 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.
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