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 99th percentile from an

appropriate distribution fit to the data

– Using concs ≥ mdl only

• 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

30

P e r c e n t

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 # days

from 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 3rd 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

20.0

Percent

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

30

Percent

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 90th, 95th, or 99th percentiles over-estimate

• As much as 100X observed for Orestimba and Sacramento

River data

– Other percentiles investigated

• 90th and 95th under-estimate with greater likelihood

• 99.5th , 99.7th , 99.9th 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 99th

percentile from fitted distributions

– Log-normal works well for the data considered

• Such sampling plans rarely under-estimate the true

values and these data suggest only moderate underestimates are likely

24