Wenlin Chen, Syngenta Crop Protection, LLC

Paul Mosquin, RTI International 

Jeremy Aldworth, RTI International 

Clint Truman, Syngenta Crop Protection, LLC

Chris Harbourt, Waterborne Environmental, Inc. 

Methods for predicting atrazine peak 

concentrations of non-daily surface water 

monitoring
2

INTRODUCTION

● Abundant pesticide aquatic monitoring data with variable sampling 

frequency and fewer daily samples. 

● Challenges to estimate potential exposure maxima (peak, rolling 

average concentrations) based on non-daily data.

● Objective: Present two approaches for predicting potential maximum 

concentrations and daily chemographs.

- Bias Factor (BF): Derived from available daily/near daily datasets 

to estimate potential “missed peaks” in non-daily samples.

- Universal Kriging: Combine sample data and model predictions 

(e.g. PRZM-Hybrid, Seawave, etc.), and/or other covariates. 
3

DATA SETS

Bias Factor determination:

Dataset 1: CDPR (CA); Chlorpyrifos (1996-1997) in 

Orestimba Crk. Simazine & Molinate (1991-1994) in 

Sacramento R.

Dataset 2: NCWQR (OH); Atrazine 62 site-years monitoring 

(1993-2008) in watersheds of Maumee, Sandusky, Honey, 

and Rock.

BF validation, and Universal Kriging development:

Dataset 3: Syngenta 90 site-years atrazine eco monitoring 

(non drinking water Midwest headwater watersheds; 2008-

12), and 17 site-years CWS daily sampling (2011-12).
4

METHOD 1: BIAS FACTOR

Bias Factor (BF) = 95th centile of the Multiplicative 

Factor (MF) distribution.

Endpoint of interest (e.g., 

peak or max rolling 

averages) from daily or 

near daily data

Endpoint of interest (peak 

or max rolling averages) 

from sampling of nondaily intervals
5

Use of Bias Factor

● If , same as true value.

● The closer is to 1, the more accurate in predicted 

maxima.

● Synthetic peak may be constructed using BF: 

Measured max

BF-adjusted max

C

o

n

c

e

n

t

r

a

tio

n

Sampling dates
6

METHOD 2: UNIVERSAL KRIGING
7

Kriging – Signal and Noise

• A simple modeling approach for predicting daily

time series from non-daily sampled data – based 

on temporal (time-lagged) correlation structure. 

• Can seamlessly predict signal time series, when 

observed time series is decomposed into 

additive signal and noise components:

Z S t t t   

, , Z D t t t  ata S Signal   Noise
8

Universal Kriging – Includes Regression Model

• Allows prediction of signal in model that can 

include regression covariates:

t t t

S   xβ 

 , , t

t

covariates regressioncoefficients

 residual time series

 



x β

2

;

cov( , )

( , ); t u

t u

t u t u



 



 

 

 

• Ordinary kriging: covariate = intercept only 

(regression slope = zero)
9

Universal Kriging – 2 Steps

1. Run regression on observed (noisy) data at 

non-daily sampled points.

2. Apply ordinary kriging to observed (noisy) nondaily residuals to predict daily residuals of signal

(filter out noise at sampled points).

Universal kriging predictor =

Regression estimate + 

Ordinary kriging predictor of residual
10

Kriging – Semivariogram of Residuals

• Kriging requires semivariogram (SVG) of 

observed (noisy) non-daily residuals:

1. SVG estimated at all time lags supported by data

2. SVG model is fitted to SVG estimates

• Ex 1: if non-daily samples taken every 7 days, 

then time lags include {7, 14, 21, 28,...}

• Ex 2: for daily data, time lags include {1,2,3,...}
11

Kriging – Illustration of Semivariogram

http://theses.ulaval.ca/archimede/fichiers/23419/apb.html

• Sill C estimates signal variance

• Nugget C0 estimates noise variance
12

Estimation of Noise

• Direct estimate of nugget (C0) requires replicates in 

time series (i.e., multiple measurements at same site 

on same day – usually not available)

− But replicated analytical determinations of atrazine 

concentrations in labs indicate little measurement error (i.e., 

C0is approximately = 0)

• Indirect estimate: by approximating C0 by 

extrapolating SVG model to lag 0

− Need site-years with daily data (this provides time lags = 

{1,2,3,...}; then extrapolate model to lag 0)
13

Model and covariate evaluation

• Covariates & combinations considered:

− Flow: Log(flow)

− STFA: Log(short term flow anomaly)

− PRZM-Hybrid: Log(linearly interpolated PRZM hybrid output)

− SWMI – Surface Water Mobility Index model predictions

− Seawave and SeawaveQ 

− ATRN – Log(complete-data atrazine concentration at nearest 

hydrologically similar site)

− PRZM hybrid + Flow; SWMI + Flow; Seawave + Flow; ATRN + 

Flow

• Restricted analyses to:

− 59 Eco site-years & 2 CWS in Dataset 3 which had PRZMHybrid runs

− Every 7-day and every 14-day sampling

− Maximum 1-day, 7-day, 14-day, and 30-day rolling averages

• Evaluation by Mean Squared Prediction Error (MSPE)
14

RESULTS: BIAS FACTOR
15

Bias factor values from Datasets 1 & 2

Annual 

Rolling 

Average 

Maxima

Dataset 1: 1996-97

(Chlorpyrifos; 1 site-year)

Dataset 1: 1991-94

(Simazine & Molinate; 6 

chemical-years) 

Dataset 2: 1993-2008

(Atrazine; 62 site-years) 

Sampling Interval

7-d 14-d 28-d 7-d 14-d 28-d 7-d 14-d 28-d

Daily max 4.1 8.2 30.3 1.0-2.8 1.0-4.2 1.1-7.5 1.1-6.3 1.1-15.3 1.6-54.3

4-day 2.0 3.7 13.3 1.0-1.9 1.0-2.6 1.1-4.9 1.0-3.5 1.1-9.1 1.6-51.2

7-day 1.8 3.1 11.0 1.0-1.5 1.0-2.6 1.1-3.6 1.0-2.8 1.1-8.4 1.6-45.6

14-day 1.4 2.0 6.9 1.0-1.6 1.0-2.2 1.1-3.7 Not calculated

30-day 1.3 1.4 4.0 1.0-1.6 1.0-2.0 1.0-3.1 1.1-2.2 1.2-4.6 1.5-18.3

60-day 1.4 1.9 4.2 1.0-1.4 1.0-1.7 1.0-2.4 1.0-2.0 1.2-3.8 1.3-14.2

90-day 1.4 1.9 3.8 1.0-1.3 1.0-1.6 1.0-2.0 1.0-2.1 1.2-3.5 1.3-11.5

• BF increases as sampling interval increases or as endpoint duration decreases.

• Average BF=2.4 (1.0 to 6.3) for 7-d sampling to estimate the daily max/year.

• Highest BF may be driven by peak shape (not necessarily peak magnitude)
16

BF-predicted (7-d sampling) vs. measured 

annual maximum concentrations in Dataset 3 

1:1 Line

y = 1.25x + 3.07

R2 = 0.85

N=90

y = 3.3x + 8.0

R2 = 0.85

N=90

0.0

200.0

400.0

600.0

800.0

1,000.0

0.0 50.0 100.0 150.0 200.0 250.0

B

F

E

stim

ate

Measured (True) Annual Daily Max (ppb)

BF = 2.4

BF = 6.3

Ecological Midwest streams (non 

drinking water) (2008-12).

y = 1.45x + 1.34

R2 = 0.91

N=17

y = 3.80x + 3.51

R2 = 0.91

N=17

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0

B

F

E

stim

ate

Measured (True) Annual Daily Max (ppb)

CWS Source (or Raw) Water 

Samples (2011-12).
17

RESULTS: UNIVERSAL KRIGING
18

Estimation of Noise

• For SVGs from residuals of PRZM-Hybrid 

regression model, 39 (66%) of 59 site-years indicate 

C0/C (i.e., noise to signal variance ratio) is 

approximately = 0 

• Only 3 (5%) of 59 Eco site-years indicate C0/C > 0.5 

• Where C0/C not close to 0, C0 may be overestimated 

by large SVG estimates at lags close to 0 (e.g., 

“sawtooth” time series will generate large SVG 

estimate at lag 1)
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Kriging – Examples of Observed SVG 

Assumption about Noise

• Evidence from: 

1. Lab determinations of 

atrazine concentration 

2. Extrapolated SVGs at lag 0

• Suggest it is reasonable to 

assume nugget = 0 in 

predictions for 7-day and 14-

day sampling
20

Covariate Evaluation 

Covariate Min. 1st Qu. Median Mean 3rd Qu. Max. n NA

Flow -0.55 0.20 0.37 0.34 0.47 0.88 0

STFA -0.28 0.15 0.27 0.28 0.42 0.67 0

PRZM-Hybrid 0.06 0.34 0.46 0.46 0.55 0.87 0

SWMI 0.26 0.51 0.61 0.58 0.67 0.75 50

Seawave 7day 0.24 0.69 0.77 0.74 0.82 0.91 2

Seawave 14day 0.24 0.68 0.75 0.72 0.80 0.91 4

ATRN 0.44 0.75 0.83 0.79 0.88 0.95 0

SeawaveQ 7day 0.18 0.73 0.80 0.76 0.83 0.93 2

SeawaveQ 14day 0.18 0.72 0.77 0.74 0.82 0.92 2

PRZM-H x Flow 0.18 0.46 0.56 0.55 0.67 0.88 0

SWMI x Flow 0.21 0.49 0.61 0.58 0.71 0.91 50

Seawave7 x Flow 0.23 0.67 0.72 0.71 0.78 0.90 2

Seawave14 x Flow 0.23 0.67 0.72 0.71 0.78 0.90 2

ATRN x Flow 0.37 0.70 0.79 0.76 0.85 0.93 0

Pearson correlation summary: site-year covariate and log(ppb)
21

Ordinary Kriging (with no covariate)

Upper and lower 90% prediction limits

7-day sampling interval

2011
22

Ordinary Kriging (with no covariate)

Upper and lower 90% prediction limits

14 - day sampling interval

2011
23

Universal Kriging with covariate: SeawaveQ

Watershed MO-02; 7-day sub-sampling

L

o

g

1

0 (p

p

b)
24

Universal Kriging with covariate: PRZM-Hybrid 

Watershed NE-05; 7-day sub-sampling 
25

Model performance: Site-Year RMSEs

Covariates can be grouped into two general categories based on performance

1) Covariates with more day-to-day variability

(Flow, STFA, SeawaveQ, ATRN)

2) Covariates which typically provide smoother predictions of overall

atrazine concentration: (Seawave, PRZM-Hybrid)

Performance of the first group showed susceptibility to extreme over-prediction

Flow: Yearly Maximum

7-day sampling

SeawaveQ: max 7-day RA

7-day sampling
26

Model performance: Site-Year RMSEs

Performance of the second group of 

covariates showed overall improved 

prediction for certain maxRAs and 

sampling frequencies

PRZM-Hybrid, 7-day sampling Seawave, 14-day sampling

Three effects:

1) Overall decrease in RMSE

2) Overall decrease in 

(RMSE/true value)

3) Overall decrease in variation 

of (RMSE/true value) 
27

SUMMARY – Bias Factor

● BF = f (duration of endpoint, sampling interval/frequency).

- Avg. BF=2.4 (range=1.0-6.3 in 69 site-yr.-chemical data) for 7-d 

sampling predicts annual daily max independently measured in 90 

site-yr ecological Midwest watersheds and 17 CWS-yrs with 

reasonable conservatism. 

- BF dependency on watershed characteristics (e.g., CWS & large 

vs. small ecological Midwest streams; reservoirs vs. streams, etc.)

● Further work & recommendation: 

- Complete analysis of correlating BF with watershed characteristics. 

- BF approach is good for

- Potential peak estimates.

- Optimizing monitoring study design (e.g., sampling frequency 

based on different watershed characteristics).

- Guide deterministic modeling (screening for higher tier model 

refinement).
28

SUMMARY – Universal Kriging

● All covariates examined were positively correlated with atrazine 

concentrations and could be used for kriging prediction.

● Daily Atrazine data indicate nugget (noise) variance approx. = 0.

● Kriging with covariates using PRZM-Hybrid and 

Seawave/SeawaveQ generally performed well for 7- and 14-d 

sampling to estimate daily concentrations. 

● Kriging without covariates provides good coverage of potential 

peak values using upper prediction limits.

● Further work & recommendation:

- Complete analysis for all CWS sites.

- Method provides reasonable though conservative daily 

concentration refinement (taking advantage of both modeling 

and available sample data).
29

Thank you!