Overview of Statistical Methods to 

Quantify Uncertainty of Pesticide 

Concentrations in Surface Water 

Monitoring Data

James Hetrick, Charles Peck, Frank Farruggia, R. 

David Jones, James Wolf, and Nelson Thurman 

Environmental Fate and Effects Division

USEPA Office of Pesticide Programs

1
Nature of Pesticide Occurrence in 

Water

• Complex spatial patterns

• Related to pesticide use, rainfall patterns, soil/hydrologic 

vulnerabilities

• Complex temporal patterns

• Often low or non-detectable levels 

• Infrequent sampling

• Year-to-year variation related to cropping patterns, 

pesticide usage, rainfall patterns, climate change

• Temporal autocorrelation

2
Statistical Methods

• Probabilistic Bootstrap Sampling

• Bias Factor

• FIFRA Scientific Advisory Panel Reviews in 

2010, 2011, and 2012 

• Kriging and Gaussian Sequential Stochastic 

Simulation

• GEOEAS (Englund, Sparks, and Robinson, 1989) 

• GSLIB (Deutsch and Journel, 1998)

• Regression Modeling

• SEAWAVEQ 

• USGS Model (Ryberg and Vecchia, 2013)

3
Intensively Sampled Data Sets Used in 

Evaluating Methods

Heidelberg U. NCWQR 

data for OH: Maumee 

River, sampled in 17,000 

km2 catchment area

0

2

4

6

8

10

12

14

16

91 98 105 112 119 126 133 140 147 154 161 168 175 182 189

Atra

zin

e

C

o

n

c

e

ntratio

n, u

g/L

Maumee River, 1995

Syngenta atrazine 

ecological exposure 

monitoring: MO-01, 

30 km2 catchment area

0

10

20

30

40

50

60

70

80

90

100

91 98 105 112 119 126 133 140 147 154 161 168 175 182 189

Atra

zin

e

C

o

n

c

e

ntratio

n, u

g/L

MO-01, 2007

4
Monitoring Data 

Monitoring Data Dates Site-Years

Watershed

Size

(acres)

Streamflow

(m3/sec)

Atrazine Ecological

Exposure Monitoring 

(AEEMP) 

(MO-01 site 2007)

2004-2012 279 5,786-63,182 0.013-5.86

Heidelberg U. NCWQR 

(Maumee River 1995) 1983-1999 16 4,024,019 0-2,578

5
Statistical Properties of Monitoring 

Data 

Monitoring

Data

Statistical Properties

Minimum Median Average Maximum

_______________μg/L________________

MO-01

(2007)

Grab Sample

0.05 1.17 4.00 33.29

MO-01

(2007)

Auto and Grab 

Samples Combined

0.05 0.78 5.02 91.06

Maumee

River (1995)

0 (ND) 0.40 1.89 14.06

6
Bias Factor Estimation

7

Julian Day

100 120 140 160 180 200 220 240 260

Atrazine Conc (ug/L)

0

2

4

6

8

10

12

14

16

18

Julian D ay

100 120 140 160 180 200 220 240 260

Atrazine Conc (ug/L)

0

2

4

6

8

10

12

14

16

18

True max 60-day mean 

5

th percentile max 60 -day mean 

4,7,14, 28 

Day 

Sampling

Intervals

Random Sampling 

Distribution of 

Maximum 60-day 

Mean 

Concentration

Julian Day

90 100 110 120 130 140

Atrazine Concentration (ug/L)

0

2

4

6

8

10

12

14

16

18
Bias Factors for Peak 

Concentration

Sample 

Interval Statistic AEEMP MaumeeRiver

4-day Min 1 1.1

Max 20.6 1.78

Median 2.4 1.4

7-day Min 1 1.1

Max 43.8 2.4

Median 4.0 1.6

14-day Min 1 1.3

Max 72.9 4.1

Median 9.8 1.9

28-day Min 1 1.7

Max 303 10.6

Median 21 2.9

8

 AEEMP Monitoring Data

Bias Factor for Peak Concentration

Sample Interval (Days)

0 5 10 15 20 25 30

Bias Factor

0

20

40

60

80

100

120

140

160

180

200
Impact of Average Daily Flow and 

Watershed Area on Bias Factor

9

Stream Flow (m3/s)

0 1 2 3 4 5 6 7

Bia

s

F

a

ctor

0

20

40

60

80

100

120

140

160

180

200

4 day Sample Interval

7 day Sample Interval

14 day Sample Interval

28 day Sample Interval

Watershed Area (acres)

0 10000 20000 30000 40000 50000 60000 70000

Bia

s

F

a

ctor

0

20

40

60

80

100

120

140

160

180

200

4 day Sample Interval

7 day Sample Interval

14 day Sample Interval

28 day Sample Interval
Kriging and Gaussian Sequential 

Stochastic Simulation

10

• Select section of time series 

with runoff dominated flow

• Stationarity is required; 

assumed equal probability 

of occurrence regardless of 

time

• Describe autocorrelation of 

pesticide concentration in time 

series using a variogram 

model. 

• Define variance of 

pesticide concentration at 

different time lags. 

• Probabilistic interpretation of 

concentrations is derived from 

realization of time series

Julian Day

0 100 200 300 400

Atra

zine

C

onc

entration (ug/L)

0

2

4

6

8

10

12

14

16

Base-flow Base-flow

Runoff 
Variograms: 1995 Maumee River 

Atrazine

(a) 4-day sampling intervals (b) 7-day sampling intervals

Va

ria

n

c

e (μ

g

/

L)

2

Va

ria

n

c

e (μ

g

/

L)

2

11
Realizations of Atrazine Time Series for 

1995 Maumee Data

Julian Day

100 120 140 160 180 200 220

Atrazine Conc (ug/L)

0

2

4

6

8

10

12

14

16

Estimate Mean (SD) 

 Actual Data 

Julian Day

100 120 140 160 180 200 220

Atrazine Conc (ug/L)

0

2

4

6

8

10

12

14

16

Estimate Mean (SD) 

 Actual Data 

Julian Day

100 120 140 160 180 200 220

Atrazine Conc (ug/L)

0

2

4

6

8

10

12

14

16

Estimate Mean (SD) 

 Actual Data 

(a) 4-day intervals

(c) 14-day intervals (d) 28-day intervals

Julian Day

100 120 140 160 180 200 220

Atrazine Conc (ug/L)

0

2

4

6

8

10

12

14

16

Estimate Mean (SD) 

 Actual Data 

(b) 7-day intervals

12
Variograms: 2007 MO-01

(a) 4-day sampling intervals (b) 7-day sampling intervals

Va

ria

n

c

e (μ

g

/

L)

2

Va

ria

n

c

e (μ

g

/

L)

2

13
Julian Day

100 120 140 160 180

Atrazine Concentration (ug/L)

0

20

40

60

80

100

Estimated Mean (SD) 

Actual Data

Julian Day

100 120 140 160 180

Atrazine Concentration (ug/L)

0

20

40

60

80

100

Estimated Mean (SD) 

Actual Data 

Julian Day

100 120 140 160 180

Atrazine Concentration (ug/L)

0

20

40

60

80

100

Estimated Mean (SD) 

Actual Data

Realizations of Atrazine Time Series for 

2007 MO-01 Data

Realizations of Atrazine Time Series for 

2007 MO-01 Data

(a) 4-day intervals

(c) 14-day intervals

Julian Day

100 120 140 160 180

Atrazine Concentration (ug/L)

0

20

40

60

80

100

Estimated Mean (SD)

Actual Data 

(b) 7-day intervals

14

(d) 28-day intervals
SEAWAVEQ Regression Modeling

• Assemble consecutive years of pesticide monitoring 

data 

• Assemble a complete daily time series of average 

stream flow to correspond to the pesticide monitoring 

data

• Determine short-, medium-, and long-term flow 

variability using WaterData program

• Use SEAWAVEQ to estimate regression equation:

• Log (Pesticide Concentration) = f(seasonal wave of intraannual variability in pesticide concentration and flow 

anomalies)

• Ability to conduct trend analysis 

15
SEAWAVEQ Regression: Maumee River

16

L

o

g

C

o

n

c

e

n

t

r

a

tio

n (μ

g

/

L)

Measured concentrations

Non-detections

Fitted concentrations (SEAWAVE)

Trend

Year
17

SEAWAVEQ Regression: Maumee River

C

o

n

c

e

n

t

r

a

tio

n (μ

g

/

L)

Year
SEAWAVEQ Regression: MO-01 

18

L

o

g

C

o

n

c

e

n

t

r

a

tio

n (μ

g

/

L)

Year

Measured concentrations

Non-detections

Fitted concentrations (SEAWAVE)

Trend
Comparison of Methods for Prediction of 95th

Percentile Concentration

Comparison of Methods for Prediction of 95th

Percentile Concentration

Method Monitoring

Peak

Bias 

Factor1

Kriging 

and 

Sequential

Stochastic

Simulation

SEAWAVEQ

Regression

Modeling

_____________μg/L______________

Maumee

River (1995) 14.1 16-25(19) 11 112

MO-01(2007)

Grab and Auto 

Samples 91.1 91-1876

(219)

572

314

MO-01 

(2007)

Grab

33.3 33 - 685

(80) 186

19

1. Bias factor based on 4-day sampling interval. Values in parenthesis are median values.

2. 7 day sampling interval
Key Findings

• Bias Factor

• Bias factor generally decreases with an increase in watershed area 

and flow

• Larger bias factors are found with wider sample intervals

• Prediction capability is dependent on the monitoring data

• Kriging and Gaussian Sequential Stochastic Simulation 

• Temporal correlation is dependent on sampling interval 

• Use of variogram model leads to data smoothing; underestimation 

of predicted values

• SEAWAVEQ Regression Models

• Dependent on availability and statistical relationship of 

covariate data 

• Provide capability for estimation of concentrations higher than 

observed in monitoring data

20
Method Comparison

21

Method Advantages Disadvantages

Bias Factor  Easy to use  Requires high frequency 

monitoring data

Kriging and 

Gaussian 

Sequential

Stochastic 

Simulation 

 Autocorrelation is considered

 Standard software available

 Requires stationarity in time 

series

 Subjectivity in selection / fit of 

variogram models

 Pesticide with low or sporadic 

detection frequencies are 

difficult to analyze

 Data smoothing

SEAWAVE-Q  Standard software available

 Rigorous probabilistic 

estimation provided 

 Minimal data requirements 

(daily flow, pesticide 

concentration)

 Trend analysis can be 

conducted

 Requires multiple years of 

monitoring data
Questions?

22
Literature Cited

• Deutsch Clayton V. and Andre G. Journel. 1998. GSLIB: Geostatistical 

Software Library and User’s Guide. Oxford University Press, New York.

• Englund, E.J., A. Sparks, and M.D. Robinson. 1989. Geo-EAS 

(Geostatistical Environmental Assessment Software). Environ. 

Software:4(2). pp 70-75.

• FIFRA Scientific Advisory Panel. 2010. Re-Evaluation of Human Health 

Effects of Atrazine; Review of Experimental In Vitro Studies and Drinking 

Water Monitoring Frequency.

• FIFRA Scientific Advisory Panel. 2011. Re-Evaluation of Human Health 

Effects of Atrazine; Review of Non-Cancer Effects; Drinking Water 

Monitoring Frequency, and Cancer Epidemiology. 

• FIFRA Scientific Advisory Panel. 2011. Problem Formulation of the 

Reassessment of Ecological Effects from the Use of Atrazine.

• Ryberg Karen and Aldo V. Vecchia. 2013. SEAWAVEQ-An R Package 

Providing a Model and Utilities for Analyzing Trends in Chemical 

Concentrations In Streams with a Seasonal Wave (seawave) and 

Adjustment for Streamflow(Q) and Other Ancillary Variables. USGS. OpenFile Report 2013-1255

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