Developing and Using Surface Weighted Average Concentrations (SWACs) - - PowerPoint PPT Presentation

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Developing and Using Surface Weighted Average Concentrations (SWACs) - - PowerPoint PPT Presentation

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Developing and Using Surface Weighted Average Concentrations (SWACs) John W. Kern Kern Statistical Services, Houghton MI, USA kernstat@gmail.com USEPA ORD Contaminated Sediments Virtual Workshop Series Session 4: Long-term Monitoring

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Developing and Using Surface Weighted Average Concentrations (SWACs)

John W. Kern Kern Statistical Services, Houghton MI, USA kernstat@gmail.com USEPA ORD Contaminated Sediments Virtual Workshop Series – Session 4: Long-term Monitoring November 20th, 2019

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Presentation Overview:

  • SWAC Defined
  • Rationale for Spatial Weighting
  • Application for comparing remedial alternatives (SWAC vs RAL)
  • Uncertainty and need for confidence limits
  • Long term performance monitoring
  • Problems with biased sampling programs
  • Use of probability based sampling to develop unbiased SWAC estimates
  • Recommendations

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What is a SWAC

  • SWAC (Surface Weighted Average Concentration) is a weighted

average of sample data intended to estimate mean contaminant concentration over a specified spatial area.

  • As an exposure point concentration (EPC) confidence limits needed
  • Weights are intended to correct for spatial biases in RI/FS sampling

programs.

  • Weights may be derived in one of several ways.
  • Weights proportional to polygons of influence (Thiessen Polygons).
  • Averaging over a map of interpolated values
  • Natural neighbor
  • Kriging
  • Inverse distance weighting
  • Spatial stratification of site data
  • Equally weighted arithmetic average
  • Geostatistical Simulation

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1993-1994 2001 2003 2008

Why use spatial weighting?

  • Sediment data evolve through many site investigations.
  • Spatial weighting used to correct spatial biases in sampling.

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SWAC vs Remedial Action Limit Relationship

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Two Common Weighting Methods

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Geostatistical simulation to evaluate spatial heterogeneity?

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False Positive False Negative

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Recap

  • SWAC technique evolved out of efforts to de-cluster data generated from

spatially biased sampling plans.

  • Particularly useful at the RI/FS stage of analysis where retrospective

evaluation of the sample data is important for selecting a remedial alternative

  • Choice of weighting method matters
  • SWAC is a retrospective tool for integrating data from mixture of

generally biased sampling programs

  • Spatial weighting does not fully correct for spatially biased sampling.
  • Statistical methods for bounding uncertainty are complicated

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How to make reliable temporal comparisons for monitoring purposes?

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Temporal Change Conflated with Sampling Bias

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Active Remediation Unbiased Spatial Layout 4% Rate 8% Rate For long Term Monitoring probability based sampling and unbiased designs are needed

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A small amount of unbiased data goes a long way!

  • For systematic sampling designs arithmetic

average is the correct weighting

  • Usual Pro-UCL methods for confidence limits
  • Comparison of unbiased estimates for

monitoring

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Stratification To “Bias” Probability Based Sampling

  • Regular triangular grids within

administrative strata

  • Greater sampling density

within areas of greater interests for remediation

  • Overall averages obtained by

area weighting stratum specific arithmetic averages.

  • Confidence limits based on

bootstrap resampling or standard stratified sampling equations

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Systematic Sampling Within Geomorphic Stratification

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A2 A1 A3

3 2 1 3 3 2 2 1 1

A A A x A x A x A SWAC + + + + =

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Stratified Sample with One Sample Per Stratum

  • Unequal probability sampling design and corresponding

unbiased estimator

  • One randomly located sample per cell (i.e. stratum)
  • Cell area weighted average is an unbiased estimator
  • Other weighting schemes are not advised
  • Confidence limits:
  • Student’s T or weighted bootstrap resampling.
  • Balanced Bootstrap with Importance Sampling.

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SWAC Monitoring Recommendations

  • A portion of samples should be collected using a probability based

sampling design.

  • SWAC estimation based solely on probability based data for trend

evaluation

  • Re-occupy sites or not
  • Theoretically higher power obtained by re-occupying locations
  • In practice heterogeneity over small spatial scales may nullify gain in

precision from re-occupying sites

  • Drawing new unbiased sample each time step provides better spatial

coverage as time progresses

  • Complex site conceptual models can be accommodated through careful

stratification of the sampling design

  • Comparisons based on differing sampling designs are valid provided

each estimation procedure is unbiased to the corresponding sampling design

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SWAC Monitoring Recommendations (continued)

  • Estimating trends in sediment concentration is a prospective endeavor
  • Plan for these studies developing unbiased sampling plans early
  • The unbiased data can be used in the RI/FS evaluations,
  • Temporal comparisons based on mixtures of biased and unbiased data

are generally unreliable

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