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Geom and Fake Case Verification with SAL Contribution from U Mainz

This study presents the concept of the SAL 3-component quality measure for verifying GEOM and FAKE cases, considering QPF in a specified region. The study includes the definition, examples, and findings of the SAL measure.

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Geom and Fake Case Verification with SAL Contribution from U Mainz

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  1. Verification of GEOM and FAKE cases with SAL Contribution from U Mainz Christiane Hofmann, Matthias Zimmer, Heini Wernli Kindly presented by Christian Keil (DLR) April 2008

  2. The concept of SAL 3-component quality measure that considers QPF in pre-specified region (e.g. river catchment): S structure -2 … 0 … +2 objects too perfect objects too small/peaked large/flat A amplitude -2 … 0 … +2 averaged precip perfect averaged precip underestimated overestimated L location0 … +2 perfect wrong location of total center of mass (TCM) and/or of objects rel. to TCM Exact definition, examples etc: Wernli et al. 2008 (MWR, in press, see AMS early online webpage)

  3. GEOM cases OBS GEOM 0 S A L MOD GEOM 0 0 0 0 perfect forecast GEOM 1 -0.01 -0.01 0.11 small displacement GEOM 2 -0.03 -0.03 0.42 large displacement

  4. GEOM cases OBS GEOM 0 S A L MOD GEOM 0 0 0 0 perfect forecast GEOM 1 -0.01 -0.01 0.11 small displacement GEOM 2 -0.03 -0.03 0.42 large displacement “noise” induced by construction of cases (interpolation leads to small changes in total precipitation amount)

  5. GEOM cases OBS GEOM 0 S A L MOD GEOM 0 0 0 0 perfect forecast GEOM 1 -0.01 -0.01 0.11 small displacement GEOM 2 -0.03 -0.03 0.42 large displacement GEOM 3 1.19 1.19 0.27 large overestimation of amount and size, intermediate displacem. GEOM 4 -0.02 -0.02 0.27 intermediate displacem. - no information about orientation of object! GEOM 51.55 1.55 0.28 very large overestimation amount and size, intermediate displacem.

  6. FAKE cases OBS FAKE 0 S A L MOD FAKE 0 0 0 0 perfect forecast FAKE 3 -0.02 0 0.03 small displacement due to interpolation -> slightly different choice of threshold for object identification -> weak spurious signal in S

  7. FAKE cases OBS FAKE 0 S A L MOD FAKE 0 0 0 0 perfect forecast FAKE 3 -0.02 0 0.03 small displacement FAKE 5 0.02 -0.16 0.15 large displacement

  8. FAKE cases OBS FAKE 0 S A L MOD FAKE 0 0 0 0 perfect forecast FAKE 3 -0.02 0 0.03 small displacement FAKE 5 0.02 -0.16 0.15 large displacement part of precipitation is shifted out of domain -> correctly identified as underestimation of amount

  9. FAKE cases OBS FAKE 0 S A L MOD FAKE 3 -0.02 0 0.03 small displacement FAKE 5 0.02 -0.16 0.15 large displacement FAKE 6 -0.03 0.38 0.03 overestimation of amount, small displacem. FAKE 7 -0.54 -0.300.04 underestimation of amount, small displacem.

  10. FAKE cases OBS FAKE 0 S A L MOD FAKE 3 -0.02 0 0.03 small displacement FAKE 5 0.02 -0.16 0.15 large displacement FAKE 6 -0.03 0.38 0.03 overestimation of amount, small displacem. FAKE 7 -0.54 -0.300.04 underestimation of amount, small displacem. S is sensitive to uniform reduction of precip values (in contrast to uniform scaling, cf. FAKE 6)!

  11. FAKE cases 3 vs. 7 Threshold contour for identification of objects: max. value in domain/15. FAKE 3/6: larger max. value -> larger threshold -> 1 large object FAKE 7: smaller max. value -> smaller threshold -> several objects -> S < 0

  12. R R threshold for object identification threshold for object identification • Summary • GEOM cases: • SAL results are OK • weak point: SAL does not provide information about orientation of objects (GEOM 4) • FAKE cases: • SAL results are also OK • interesting difference FAKE 6 vs. FAKE 7: uniform scaling (FAKE 6) does not lead to error in S, but uniform reduction (FAKE 7) does! Explanation: uniform reduction can lead to identification of more and smaller objects: • all except FAKE 7: 1 large object FAKE 7: two small objects

  13. S A L - Definition of the components A = (D(Rmod) - D(Robs)) / 0.5*(D(Rmod) + D(Robs)) D(…) denotes the area-mean value (e.g. catchment) normalized amplitude error in considered area A  [-2, …, 0, …, +2] L = |r(Rmod) - r(Robs)| / distmax+measure of distance of objects to r(…) r(…) denotes the centre of mass of the precipitation field in the area normalized location error in considered area L  [0, …, 2] S = (V(Rmod*) - V(Robs*)) / 0.5*(V(Rmod*) + V(Robs*)) V(…) denotes the weighted volume average of all scaled precipitation objects in considered area normalized structure error in considered area S  [-2, …, 0, …, +2]

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