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)

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.Theam

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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.