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The Cumulative Frequency Diagram (CFD) as a Criteria Assessment Tool

The Cumulative Frequency Diagram (CFD) as a Criteria Assessment Tool. Chlorophyll Criteria Workshop 05/19/05 Elgin Perry. “CRITERIA ASSESSMENT USING LIMITED DATA”. “10% RULE”. Motivation for New Assessment tool.

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The Cumulative Frequency Diagram (CFD) as a Criteria Assessment Tool

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  1. The Cumulative Frequency Diagram (CFD)as a Criteria Assessment Tool Chlorophyll Criteria Workshop 05/19/05 Elgin Perry

  2. “CRITERIA ASSESSMENT USING LIMITED DATA” “10% RULE”

  3. Motivation for New Assessment tool • Accommodate temporal and spatial variance in addition to sampling variance • Allow spatially broad but ephemeral events. • Allow spatially small but persistent events.

  4. Overview of CFD Assessment Process • Determine a Compliance criteria, C (C may be a collection of points) • Collect samples over segment for m dates in 3 year period. • For each date interpolate (Krig) to n cells over segment.

  5. Overview of CFD Assessment Process • For each date estimate proportion of segment that does not comply with C.

  6. Overview of CFD Assessment Process • Estimate Cumulative Frequency Distribution (CFD) of Area out of compliance for all dates. • Inverse of the Empirical Distribution Function of the psj. Plot step ptj versus psj.

  7. CFD assessment of impairment

  8. 100 100 Percent of Time Percent of Time 90 90 CFD Curve CFD Curve 80 80 70 70 Area of Criteria Exceedence Area of Criteria Exceedence 60 60 50 50 Area of Allowable Criteria Exceedence Area of Allowable Criteria Exceedence 40 40 30 30 20 20 10 10 0 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Percent of Space Percent of Space Definition of Attainment

  9. Wrinkles • How to define the reference curve.

  10. Proposed ModelXij = m + ai + bij i = 1, 2, . . . M and j = 1, 2, . . . N.a is temporal variance termb is spatial variance term

  11. Plot Parameters

  12. DecreasingMean

  13. Increasing Temporal Variance

  14. Increasing Spatial Variance

  15. Wrinkles • How to define the reference curve. • The shape of the CFD is influenced by level of sampling.

  16. Simulation • Assume segment has 1000 cells. • Simulate values for the 1000 cells each day for 3 years. • Sample 10 cells once a month. • Interpolate from the 10 to the 1000. • Compare the CFD from sampling to the true CFD.

  17. Wrinkles • How to define the reference curve. • The shape of the CFD is influenced by level of sampling. • A confidence envelope for the CFD is proving analytically complex.

  18. 100 100 Percent of Time Percent of Time Reference Curve C.I. 90 90 Reference Curve C.I. 80 80 70 70 60 60 Assessment Curve C.I. Assessment Curve C.I. 50 50 40 40 30 30 20 20 10 10 0 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Percent of Space Percent of Space Criteria Assessment Incorporating Error Well Characterized Reference Curve Well Characterized Assessment Curve

  19. Needs Work

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