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

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 (MWR, in press, see AMS early online webpage)

GEOM cases OBSGEOM0 SAL MODGEOM 0000perfect forecast GEOM small displacement GEOM large displacement

GEOM cases OBSGEOM0 SAL MODGEOM 0000perfect forecast GEOM small displacement GEOM large displacement “noise” induced by construction of cases (interpolation leads to small changes in total precipitation amount)

GEOM cases OBSGEOM0 SAL MODGEOM 0000perfect forecast GEOM small displacement GEOM large displacement GEOM large overestimation of amount and size, intermediate displacem. GEOM intermediate displacem. - no information about orientation of object! GEOM very large overestimation amount and size, intermediate displacem.

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

FAKE cases OBSFAKE0 SAL MODFAKE 0000perfect forecast FAKE small displacement FAKE large displacement

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

FAKE cases OBSFAKE0 SAL MODFAKE small displacement FAKE large displacement FAKE overestimation of amount, small displacem. FAKE underestimation of amount, small displacem.

FAKE cases OBSFAKE0 SAL MODFAKE small displacement FAKE large displacement FAKE overestimation of amount, small displacem. FAKE underestimation of amount, small displacem. S is sensitive to uniform reduction of precip values (in contrast to uniform scaling, cf. FAKE 6)!

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

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

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]