# 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 km 2 

# 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**A t** **r a** **z i** **n e** **C o** **n c** **e n** **t r** **a t** **i o** **n ,** **u g** **/ L**  

## Maumee **River , 1995**  

# Syngenta atrazine

ecological exposure monitoring: MO

- 01, 30 km 2 

# 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**A t** **r a** **z i** **n e** **C o** **n c** **e n** **t r** **a t** **i o** **n ,** **u g** **/ L**  

## MO
**- 01,**  **2007**



# 4

# Monitoring Data

**Monitoring Data**  **Dates Site** 
**- Ye**  **ars Wa**  **tershed Size**  **(acres) Stream**  **flow**

**(m 3**  

# /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 Av erage 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 260AtrazineConc(ug/L)

0 2 4 6 8 10 12 14 16 18

Jul ia n D a y 100 120 140 160 180 200 220 240 260AtrazineConc(ug/L)

0 2 4 6 8 10 12 14 16 18



# Tr **ue max 60**
**- day**  **m ean** 
**5 th**  

## percentile **max 60**
**- day**  **m ean**  

# 4,7,14, 28 Day Sampling Intervals



# Random Sampling Distribution of Maximum 60

- day Mean Concentration

Julian Day 90 100 110 120 130 140AtrazineConcentration(ug/L)

0 2 4 6 8 10 12 14 16 18

# Bias Factors for Peak

**Concentration**

**Sample Interv**  **al Statistic**  **AE EMP**  **Maumee Riv**  **er** 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** A EEM P Mo nito ring D ata Bi as F ac to r f or

P ea k C on cen tratio n

Sa mpl e Int erv

al (D ay s) 0 5 10 15 20 25 30BiasFactor

0 20 40 60 80 100 120 140 160 180 200

# Impact of Average **Daily Flow and Watershed Area on Bias Factor** 

**9** St re am F lo w (m3 /s ) 0 1 2 3 4 5 6 7BiasFactor

0 20 40 60 80 100 120 140 160 180 200

4 day Sa mple Int erv al 7 day Sa mple Int erv

al 14 day Sa mp le Int erv

al 28 day Sa mp le Int erv

al



### Wat er sh ed Ar ea (a cres) 0 10000 20000 30000 40000 50000 60000 70000BiasFactor

0 20 40 60 80 100 120 140 160 180 200

4 day Sa mp le I nt erv al 7 day Sa mp le I nt erv

al 14 day Sa mple

I nt erv al 28 day Sa mple

I nt erv al

# 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 400AtrazineConcentration(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 intervalsVariance(μg/L)2Variance(μg/L)2



# 11

# Realizations **of Atrazine Time Series for** 

**1995 Maumee Data**

Julian Day 100 120 140 160 180 200 220AtrazineConc(ug/L)

0 2 4 6 8 10 12 14 16 Estimate Mean (SD) Actual Data

Julian Day 100 120 140 160 180 200 220AtrazineConc(ug/L)

0 2 4 6 8 10 12 14 16 Estimate Mean (SD) Actual Data

Julian Day 100 120 140 160 180 200 220AtrazineConc(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 220AtrazineConc(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 intervalsVariance(μg/L)2Variance(μg/L)2



# 13Julian Day 100 120 140 160 180AtrazineConcentration(ug/L)

0 20 40 60 80 100 Estimated Mean (SD)

Actual Data Julian Day 100 120 140 160 180AtrazineConcentration(ug/L)

0 20 40 60 80 100

Estimated Mean (SD)

Actual Data

Julian Day 100 120 140 160 180AtrazineConcentration(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 180AtrazineConcentration(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 progra m

• Use SEAWAVEQ to estimate regression equation:

• Log (Pesticide Concentration) = f(seasonal wave of intra

annual variability in pesticide concentration and flow anomalies)

• Ability to conduct trend analysis

**15**

# SEAWAVEQ Regression: **Maumee River**

**16**LogConcentration(μg/L) 

# Measur ed concentr ations Non

- detections Fitted concentr ations (SEA WAV E) Tr end



# Ye ar

# 17 

# SEAWAVEQ Regression: **Maumee River**Concentration(μg/L)



# Ye ar

# SEAWAVEQ Regression: **MO**
**- 01** 

**18**LogConcentration(μg/L)



# Ye ar Measur ed concentr ations Non

- detections Fitted concentr ations (SEA WAV E) Tr end

# Comparison **of M ethods**  **for Prediction of 95 th** 



# Percentile Concentration **Comparison of M**  **ethods for Prediction of 95**  **th**



# Percentile Concentration

**Method Monitoring** 

**Peak Bias** 

**Factor 1**  

# Kriging

**and Sequential**  **Stochastic Simulation**  **SEA**

**WA VEQ**  **Regression Modeling** 

_____________μg/L______________ **Maumee Riv**  **er (1995)**  14.1 16

- 25 (19) 11 11 2
**MO**
**- 01(2007)**  **Grab and Au**  **to Samples**  

# 91.1 91

- 1876 (219) 57 2 

# 314

**MO**
**- 01**  **(2007) Grab**  

# 33.3 33

- 685 (80) 186

**19** 1. Bias factor based on 4

- day sampling interval. Va lues in parenthesis are median values. 2. 7 day sampling interval

# Key Findings

• Bias Factor

• Bias factor generally decreases w ith an increase in w atershed area and flow

• Larger bias factors are found w ith wi der 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 Ad**  **vantages Disadv**  **antages**
**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 dif ficult to analyze

 Data smoothing **SEA WA**  **VE**
**- Q**   Standard software available

 Rigorous probabilistic estimation provided

 Minimal data requirements (daily flow , pesticide concentration)

 Tr end analysis can be conducted  Requires multiple years of monitoring data

# Questions?

**22**

# Literature Cited

• Deutsch Clay ton 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.

• Ry berg Karen and Aldo V. Vecchia. 2013. SEAWAVEQ

- An R Package Providing a Model and Utilities for Analy zing Trends in Chemical Concentrations In Streams with a Seasonal Wave (seawave) and Adjustment for Streamflow(Q) and Other Ancillary Variables. USGS. Open

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