# Sampling Plans for Water

Quality Monitoring Empirical Modeling Public Meeting Washington, DC, March 20, 2012 John W. Green, Ph.D., Ph.D. Principal Consultant: Biostatistics DuPont Applied Statistics Group 1

# Purpose • Explore various sampling plans for monitoring water quality in streams – For the presence of chemicals of interest – Specifically, compare daily sampling with less frequent sampling plans 

# • Propose simple methodology from which to estimate peak and time-weighted average chemical concentrations from available data • Illustrate with actual data 2

# Data Used • Orestimba Creek at River Road Near Crows Landing, CA – Daily samples May 1, 1996-April 30, 1997 – 1 chemical measured – Chlorpyrifos – Daily discharge rate 

# • Sacramento River at the I Street Bridge – Samples every 1-3 days for 5 years – Numerous chemicals measured 3

# Methodology • Determine family of distributions ( e.g. , lognormal) of complete sample – Compute time-weighted concentrations sums & peaks from complete data 

# • Assuming same distributional family, determine distribution for each subsampling plan – Compute time-weighted concentrations sums & peaks from each subsample – Compare to results from complete data 4

# Calculations • Time-weighted sums of each chemical on – Monthly and yearly basis – Based on Jones (2005) 

# • Monthly mean and maximum (peak) result observed • Estimated monthly time-weighted sums and peaks from alternative sampling plans – Every 1, 2, 3, 4, 7 days 

# • Assessment of the ability to predict the maximum level and existence of spikes in each chemical from the discharge rate of the river 5

# Time-Weighted Concentration Sums

6

# Time-Weighted Sums over 12 Months BEGIN END SAMPLE Delay Chemical WGTSUM SAMPLE_DAYS 5/1/1996 4/30/1997 Daily 0 Chloropyrifos 20.78 364 5/1/1996 4/30/1997 Every 2 Days 0 Chloropyrifos 20.58 182 5/1/1996 4/30/1997 Every 2 Days 1 Chloropyrifos 20.94 182 5/1/1996 4/30/1997 Every 3 Days 0 Chloropyrifos 21.60 121 5/1/1996 4/30/1997 Every 3 Days 1 Chloropyrifos 20.41 122 5/1/1996 4/30/1997 Every 3 Days 2 Chloropyrifos 24.30 121 5/1/1996 4/30/1997 Every 4 Days 0 Chloropyrifos 20.80 91 5/1/1996 4/30/1997 Every 4 Days 1 Chloropyrifos 29.44 91 5/1/1996 4/30/1997 Every 4 Days 2 Chloropyrifos 24.27 91 5/1/1996 4/30/1997 Every 4 Days 3 Chloropyrifos 16.50 91 5/1/1996 4/30/1997 Every 7 Days 0 Chloropyrifos 29.82 52 5/1/1996 4/30/1997 Every 7 Days 1 Chloropyrifos 27.70 52 5/1/1996 4/30/1997 Every 7 Days 2 Chloropyrifos 21.69 52 5/1/1996 4/30/1997 Every 7 Days 3 Chloropyrifos 21.57 52 5/1/1996 4/30/1997 Every 7 Days 4 Chloropyrifos 22.84 52 5/1/1996 4/30/1997 Every 7 Days 5 Chloropyrifos 20.73 52 5/1/1996 4/30/1997 Every 7 Days 6 Chloropyrifos 14.82 52 

# Sample is number of days between samples. Delay is # days from first day of period before sampling begins. Daily samples with delay=0 should be compared to all other plans. Every 4-days: 2 plans over-estimate by 17-41%, 1 plan under-estimates by 21%. Every 7 days: 5 plans over-estimate by 4-43%, 1 plan under-estimates by 29%. 7

# Estimation of Peak Concentration • The estimated peak concentration during a time period is the 99 th 

# percentile from an appropriate distribution fit to the data – U s i n g c o n c s ≥ m d l o n l y 

# • For the two datasets analyzed, log-normal distributions fit the data 8

# Distribution of Log(Conc) Distribution of Log(Concentration)
Orestimba River Chlorpyrifos May, 1996-April, 1997 -6.8 -6.0 -5.2 -4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 0 5 10 15 20 25 30Percent Logconc 

# • Normal distribution fit to log(Conc) for Orestimba River chlorpyrifos concentrations over May, 1996-April, 1997 • Fit adequate for modeling purposes 9

# Estimated Peaks

Star indicates observed peak, dots indicate estimated peaks. Lag indicates # days from beginning of month to first day of sampling plan. Space is # days between samples (space=0 same as space=1). Lag=-1 for observed daily peak. 10 ESTMAX99
0 1 2 3 4 5
month 1 2 3 4 5 6 7 8 9 10 11 12 Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Daily
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6 ESTMAX99
0 1 2 3 4 5
month 1 2 3 4 5 6 7 8 9 10 11 12 Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 2 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6

# Estimated Peaks

Stars are observed peaks, dots are estimated peaks. Delay indicates # daysfrom beginning of month to first day of sampling plan. Potential for overestimates up to 10X w/weekly samples. 11 ESTMAX99
0 1 2 3 4 5
month 1 2 3 4 5 6 7 8 9 10 11 12 Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 4 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6 ESTMAX99
0 1 2 3 4 5
month 1 2 3 4 5 6 7 8 9 10 11 12 Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 7 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6

# Daily Discharge Rate • Mean daily discharge rate was 53.9 CFS in 1996 and 94.1 CFS in 1997 – 2 nd 

# and 3 rd 

# highest daily discharge rates in the 15 year period 1993-2008 

# • Regression of daily chlorpyrifos conc vs. discharge rate and inverse of discharge rate (raw or log-transformed, w/ lag=0, 1, 2, 3, 4, 5, 10, 20 and 30 days prior to sample) – Only 7-10% of variation in conc could be explained collectively by these functions of discharge rate 

# • Following figure illustrates the lack of findings 12

# Chlorpyrifos vs. Discharge dailys

0 10 20 30

Date 01MAY1996 01JUL1996 01SEP1996 01NOV1996 01JAN1997 01MAR1997 01MAY1997 Orestimba Chlorpyrifos & Discharge Data
PLOT dailys qcfss 

# Discharge rate (qcfss) and chlorpyrifos conc (dailys) standardized by dividing each by its mean so both can be plotted on same scale. Red = discharge, Black = conc 13

# Conclusion for Orestimba Data • A sampling plan of every 2, 3 or 4 days – Would generally over-estimate both peak and time-weighted average concentrations • Peaks over-estimated by 2-4X 

# – Under-estimates that occur are modest 

# • Weekly sampling likely to – Over-estimate some peaks by up to 10X – Modestly under-estimate some low peaks 14

# Sacramento River at I Street Bridge • Numerous chemicals were measured May 1, 1991 – April 30, 1994 • Days between samples varied, with 20-30% 1 day apart, 40-50% 2 days apart, and 20-30% 3 or more days apart • Many measurements were below detection limits • Log-normal distributions gave adequate fits to the data for each chemical for which there were sufficient data after non-detects were omitted 15

# Simazine Concentrations I Street Chemicals chemical=simazine

-3.1 -2.9 -2.7 -2.5 -2.3 -2.1 -1.9 -1.7 -1.5 -1.3 -1.1 -0.9 -0.7 -0.5 0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0Percent logconc 

## 16

# Sacramento River at I Street: Simazine

Star indicates observed peak, dots indicate estimated peaks. Delay indicates # days from beginning of month to first day of sampling plan. Lag=-1 for observed daily peak. 17 ESTMAX99
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
month 0 10 20 30 40

Simazine Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Daily
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6 ESTMAX99
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
month 0 10 20 30 40

Simazine Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 2 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6

# Sacramento River at I Street: Simazine

Star indicates observed peak, dots indicate estimated peaks. Delay indicates # days from beginning of month to first day of sampling plan. Lag=-1 for observed daily peak. Increased potential for over-estimates up to 6X w/weekly samples. 18 ESTMAX99
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
month 0 10 20 30 40

Simazine Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 4 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6 ESTMAX99
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
month 0 10 20 30 40

Simazine Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 7 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6

# Molinate Concentrations I Street Chemicals chemical=molinate

-3.6 -3.0 -2.4 -1.8 -1.2 -0.6 0 0.6 0 5 10 15 20 25 30Percent logconc 

## 19

# Sacramento River at I Street: Molinate

Star indicates observed peak, dots indicate estimated peaks. Delay indicates # days from beginning of month to first day of sampling plan. Delay=-1 for observed daily peak. 20 ESTMAX99
0 1 2 3 4 5 6 7 8 9
month 0 10 20 30

Molinate Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Daily
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6 ESTMAX99
0 1 2 3 4 5 6 7 8 9
month 0 10 20 30

Molinate Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 2 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6

# Sacramento River at I Street: Molinate

There were only 67 molinate concentrations above zero. Even with so few observations, the estimated peaks rarely under-estimate the observed peak and only by small amounts when doing so. 21 ESTMAX99
0 1 2 3 4 5 6 7 8 9
month 0 10 20 30

Molinate Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 4 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6 ESTMAX99
0 1 2 3 4 5 6 7 8 9
month 0 10 20 30

Molinate Concentrations in Sacramento River at I Street Bridge Observed and Estimated Max Conc by Sample Spacing and Starting Day Maximum Estimated as 99-th Percentile of Fitted Distribution

Sample=Every 7 Days
Delay Indicates # Days After 1st of Month to Begin Subsample Monthly Max Estimated from Fitted Distribution indicated by Dot Observed Monthly Max indicated by Star (and Delay=-1) Delay -1 0 1 2 3 4 5 6

# Additional Chemicals • Similar results were obtained for two other chemicals measured in the Sacramento River at the I Street bridge during the same period. • The results suggest that a close fit of a lognormal distribution to the data is not critical – Serious deviation from log-normality would indicate the use of an alternative distribution. – There is little technical difficulty in using, e.g., the gamma or beta distributions. 22

# Additional Observations • Weekly sampling plans can exaggerate the peak concentrations by up to 10X • Estimates based on upper confidence bounds of the 90 th 

# , 95 th 

# , or 99 th 

# percentiles over-estimate • As much as 100X observed for Orestimba and Sacramento River data 

# – Other percentiles investigated • 90 th 

# and 95 th 

# under-estimate with greater likelihood • 99.5 th 

# , 99.7 th 

# , 99.9 th 

# percentiles greatly over-estimate – Do not eliminate mild, unusual under-estimates 23

# Conclusions • Sampling every 4 days is adequate to obtain reasonable estimates of peak concentrations and time-weighted mean concentrations on a monthly or yearly basis • Weekly samples increase chance of 8-10X over-estimates but may still be useful 

# • Peak concentrations can be estimated as the 99 th 

# percentile from fitted distributions – Log-normal works well for the data considered 

# • Such sampling plans rarely under-estimate the truevalues and these data suggest only moderate underestimates are likely 24