**Wenlin Chen, Sy ngenta Crop Protection,**  **LLC**

**Paul Mosquin, RTI International Jeremy**  **Aldw orth,**  **RTI International Clint Truman, Sy**  **ngenta 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) = 95 th 

### 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 non**   ** daily** **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 maxConcentration

Sampling dates6 

# 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:

t t t 

### Z S   

, , t t t 

### Z Data 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 regression coefficients 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) non daily residuals to predict daily residuals of signal (filter out noise at sampled points). Universal kriging predictor = Regression estimate + Ordinary kriging predictor of residual10 

## 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 C 0 

### estimates **noise** variance12 

## Estimation of Noise

• Direct estimate of nugget (C 0 

### ) 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., C 0 is approximately = 0)


### • Indirect estimate: by approximating C 0 

### 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)

− STF A: Log(short term flow anomaly)

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

− SWMI – Surface Wa ter Mobility Index model predictions

− Seawave and SeawaveQ

− AT RN – Log(complete - data atrazine concentration at nearest hydrologically similar site)

− PRZM hybrid + Flow; SWMI + Flow; Seawave + Flow; AT RN + Flow 

### • Restricted analyses to:

− 59 Eco site -years & 2 CWS in Dataset 3 which had PRZM Hybrid 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

**An nual**  **Rolling Av** **erage 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 Interv al**  **7 -**  **d 14**  **- d**  **28 -**  **d 7**  **- d**  **14 -**  **d 28**  **- d**  **7 -**  **d 14**  **- d**  **28 -**  **d Daily**  **m ax**  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. • **Av erage**  **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 s** **t i** **m a** **t e** 

**Measured (T rue)**  **An nual**  **Daily M**  **ax (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 s** **t i** **m a** **t e** 

**Measured (T rue)**  **An nual**  **Daily M**  **ax (ppb)** CWS Source (or Raw) Water Samples (201 1 - 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 C 0

### /C (i.e., noise to signal variance ratio) is approximately = 0

• Only 3 (5%) of 59 Eco site -years indicate C 0

### /C > 0.5

• Where C 0

### /C not close to 0, C 0 

### 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)19 

# 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 sampling20 

# Covariate Evaluation

**Cov ariate**  **Min. 1st Qu.**  **Median Mean**  **3rd Qu. Max.**  **n NA Flow**  - 0.55 0.20 0.37 0.34 0.47 0.88 0 **STF A**  - 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 **Seaw av** **e 7day**  0.24 0.69 0.77 0.74 0.82 0.91 2 **Seaw av** **e 14day**  0.24 0.68 0.75 0.72 0.80 0.91 4 **AT RN**  0.44 0.75 0.83 0.79 0.88 0.95 0 **Seaw av** **eQ 7day**  0.18 0.73 0.80 0.76 0.83 0.93 2 **Seaw av** **eQ 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 **Seaw av** **e7 x**  **Flow** 0.23 0.67 0.72 0.71 0.78 0.90 2 **Seaw av** **e14 x**  **Flow** 0.23 0.67 0.72 0.71 0.78 0.90 2 **AT RN**  **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**K riging (with no covariate)** 

Upper and lower 90% prediction limits 7 - day sampling interval

201 122 

## Ordinary**K riging (with no covariate)** 

Upper and lower 90% prediction limits 14 - day sampling interval

201 123 

## Universal Kriging with covariate: SeawaveQ Wa tershed MO - 02; 7 - day sub - samplingLog10(ppb)24 

## Universal Kriging with covariate: PRZM **- Hy**  **brid** Wa tershed NE - 05; 7 - day sub - sampling25 

# Model performance: Site **- Year RMSEs**  Covariates can be grouped into two general categories based on performance 1) Covariates w ith more day-to - day variability (Flow, STF

A, SeawaveQ , AT RN) 2) Covariates w hich ty pically provide smoother predictions of overall atrazine concentration: ( Seawave , PRZM - Hybrid) Performance of the first group showed susceptibility to extreme over- prediction

Flow: Ye arly Maximum 7 - day sampling SeawaveQ: max 7 - day RA 7 - day sampling26 

# Model performance: Site **- Year RMSEs**  Performance of the second group of covariates showed overall improved prediction for certain maxRAs and sampling frequencies Seawave, 14 - day sampling PRZM - Hybrid, 7 - day sampling Three ef fects: 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 e cological 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 m onitoring 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!