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Spatial Forecast Verification Methods Intercomparison Project: Forecast Quality Index
Sukanta BasuTexas Tech University
&Efi Foufoula-Georgiou
University of Minnesota
NCAR – Feb 20th, 2007
Forecast Quality Index (FQI)
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Ingredients:
(a) Partial Hausdorff distance (PHD) → Displacement Error
(b) (Modified) Universal Image Quality Index (UIQI) → Amplitude Error(c) Surrogates
References:
(1)Basu, S., Dodov, B., and Foufoula-Georgiou, E. (2003). A novel measure for QPF verification and its usefulness in multimodel ensemble forecasting, Geophys. Res. Abstracts, 5, 04323, European Geophysical Society.
(2) Venugopal, V., Basu, S., and Foufoula-Georgiou, E. (2005). A new metric for comparing precipitation patterns with an application to ensemble forecasts, J. Geophys. Res., 110, D08111, doi:10.1029/2004JD005395.
Forecast Quality Index: Framework
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Fcs
Surr # M
Fcs(Fcs>Th)
Fcs>Th
Obs
Obs(Obs>Th)
Surr # 1
Obs>Th
Compute UIQI
Compute PHD
Compute PHD
Compute PHD
Surr # M>ThSurr # 1>Th
1,..., pA a a 1,..., qB b b
, max , , ,H A B h A B h B A
, max minb Ba A
h A B a b
where,
Finite Point Sets: and
then every point A of must be within a distance d of some point of B and vice versa.
,H A B dIf
√ √
√ ,h A B
Hausdorff Distance (for Sets)
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
where,
1 2 1 2 2 1, max , , ,H I I h I I h I I
2 21 1
2 21 1
1 2 1 2,,
,,
, max min , ,
max min
I l m NII i j NI
I l m NII i j NI
h I I I i j I l m
i l j m
2 21 1
2 21 1
1 2 1 2,,
,,
, min , ,
min
th
I l m NII i j NI
th
I l m NII i j NI
h I I k I i j I l m
k i l j m
Effects of Outliers: Partial Hausdorff Distance (PHD)
Hausdorff Distance (for Binary Images)
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
May 13th, 2005 Case Study
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Surrogates (Stochastic Realizations) of the Observed Field
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Results (May 13th Case): Forecast Quality Index (FQI)
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Forecast Quality Index: Sensitivity to Percentile Distance
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Forecast Quality Index: Sensitivity to # Surrogates
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Results (May 13th Case): Universal Image Quality Index
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Results (May 13th Case): Partial Hausdorff Distance (PHD)
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
June 1st, 2005 Case Study
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Results (June 1st Case): Forecast Quality Index (FQI)
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Results (June 1st Case): Universal Image Quality Index
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Results (June 1st Case): Partial Hausdorff Distance (PHD)
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Results: May 13th vs. June 1st Case
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
← May 13th
June 1st →
What’s Next?
NCAR – Feb 20th, 2007 Basu & Foufoula-Georgiou
Transportation (Kantorovich) Distance-based Metric