Post on 30-Jan-2016
description
The Cumulative Frequency Diagram (CFD)
as a Criteria Assessment ToolChlorophyll Criteria Workshop
05/19/05
Elgin Perry
““CRITERIA ASSESSMENT USING LIMITED DATA”CRITERIA ASSESSMENT USING LIMITED DATA”““CRITERIA ASSESSMENT USING LIMITED DATA”CRITERIA ASSESSMENT USING LIMITED DATA”
““10% RULE”10% RULE”““10% RULE”10% RULE”
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.
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.
Overview of CFD Assessment Process
• For each date estimate proportion of segment that does not comply with C.
)cI(xn
1ps ijij
n
1ij
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.
)rank(ps m1pt j j
CFD assessment of impairment
Definition of Attainment
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Percent of Space
Per
cent
of
Tim
e
CFD Curve
Area of Criteria Exceedence
Area of AllowableCriteria
Exceedence
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Percent of Space
Per
cent
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CFD Curve
Area of Criteria Exceedence
Area of AllowableCriteria
Exceedence
Wrinkles
• How to define the reference curve.
Proposed Model
Xij = m + ai + bij
i = 1, 2, . . . M and j = 1, 2, . . . N.
a is temporal variance termb is spatial variance term
U a b c
5 1 1 5 Red
4 1 1 5 Orange
3 1 1 5 Yellow
2 1 1 5 Green
1 1 1 5 Blue
Plot Parameters
Decreasing Mean
Increasing Temporal Variance
Increasing Spatial Variance
Wrinkles
• How to define the reference curve.
• The shape of the CFD is influenced by level of sampling.
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.
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.
ReferenceCurve
C.I.
Criteria Assessment Incorporating Error
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Percent of Space
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cent
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e
Well CharacterizedReference Curve
Well CharacterizedAssessment Curve
AssessmentCurve
C.I.
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Percent of Space
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cent
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ReferenceCurve
C.I.
AssessmentCurve
C.I.
Needs Work