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): Sstructure-2…0…+2 objects tooperfectobjects too small/peakedlarge/flat Aamplitude-2…0…+2 averaged precipperfectaveraged precip underestimatedoverestimated Llocation0…+2 perfectwrong 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 OBSGEOM0 SAL MODGEOM 0000perfect forecast GEOM 1-0.01-0.010.11small displacement GEOM 2-0.03-0.030.42large displacement

4. GEOM cases OBSGEOM0 SAL MODGEOM 0000perfect forecast GEOM 1-0.01-0.010.11small displacement GEOM 2-0.03-0.030.42large displacement “noise” induced by construction of cases (interpolation leads to small changes in total precipitation amount)

5. GEOM cases OBSGEOM0 SAL MODGEOM 0000perfect forecast GEOM 1-0.01-0.010.11small displacement GEOM 2-0.03-0.030.42large displacement GEOM 31.191.190.27large overestimation of amount and size, intermediate displacem. GEOM 4-0.02-0.020.27intermediate displacem. - no information about orientation of object! GEOM 51.551.550.28very large overestimation amount and size, intermediate displacem.

6. FAKE cases OBSFAKE0 SAL MODFAKE 0000perfect forecast FAKE 3-0.0200.03small displacement due to interpolation -> slightly different choice of threshold for object identification -> weak spurious signal in S

7. FAKE cases OBSFAKE0 SAL MODFAKE 0000perfect forecast FAKE 3-0.0200.03small displacement FAKE 50.02-0.160.15large displacement

8. FAKE cases OBSFAKE0 SAL MODFAKE 0000perfect forecast FAKE 3-0.0200.03small displacement FAKE 50.02-0.160.15large displacement part of precipitation is shifted out of domain -> correctly identified as underestimation of amount

9. FAKE cases OBSFAKE0 SAL MODFAKE 3-0.0200.03small displacement FAKE 50.02-0.160.15large displacement FAKE 6-0.030.380.03overestimation of amount, small displacem. FAKE 7-0.54-0.300.04underestimation of amount, small displacem.

10. FAKE cases OBSFAKE0 SAL MODFAKE 3-0.0200.03small displacement FAKE 50.02-0.160.15large displacement FAKE 6-0.030.380.03overestimation of amount, small displacem. FAKE 7-0.54-0.300.04underestimation 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. 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 R threshold for object identification R

14. S A L - Definition of the components A = (D(R mod ) - D(R obs )) / 0.5*(D(R mod ) + D(R obs )) D(…) denotes the area-mean value (e.g. catchment) normalized amplitude error in considered area A  [-2, …, 0, …, +2] L = |r(R mod ) - r(R obs )| / dist max + 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(R mod *) - V(R obs *)) / 0.5*(V(R mod *) + V(R obs *)) V(…) denotes the weighted volume average of all scaled precipitation objects in considered area normalized structure error in considered area S  [-2, …, 0, …, +2]