Institute for Atmospheric Physics – University of Mainz
Name of method:
SAL - Structure, Ampliutde, Location
Investigators:
Marcus Paulat, Heini Wernli – Institute for Atmospheric Physics, University of Mainz
Christoph Frei – Bundesamt für Meteorologie und Klimatologie, MeteoSwiss Zürich
Martin Hagen - Institut für Physik der Atmosphäre, DLR Oberpfaffenhofen
Literature / References: none
- presentations at workshops in Boulder (2006) and ECMWF (2007)
- manuscript in preparation (Wernli et al., MWR)
16. February 2007
What kind of data?
• only gridded data
• fields: so far only precipitation, in principle also applicable to other fields with
well-structures signatures (e.g. wind gusts)
• presently used FC data: ECMWF and COSMO-LM precipitation forecasts
(accumulated over 1 or 24 h) over Germany on rotated lon/lat grid with 7 km
horizontal resolution
• presently used OBS data: gridded rain gauge data set on same grid as models,
based upon ~4000 stations with 24 h values; 1-h disaggregated fields through
combination of rain gauge and radar data
Marcus Paulat
Christoph Frei
Martin Hagen
Heini Wernli
Basic strategy (I): General concept
• consider precipitation in pre-specified area (e.g. river catchment)
• SAL consists of three independent components
• components address quality of structure (S), amplitude (A) and location (L) of
QPF in that area
• according to SAL a forecast is perfect if S = A = L = 0
• S requires the definition of precipitation objects, using a threshold value
• but: no attribution between precipitation objects in forecast and observations!
Marcus Paulat
Christoph Frei
Martin Hagen
Heini Wernli
Basic strategy (II): 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
r(…) denotes the centre of gravity of the precipitation field in the area
normalized location error in considered area
L  [0, …, 1]
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]
Marcus Paulat
Christoph Frei
Martin Hagen
Heini Wernli
Basic strategy (III): The S component
scaling for every object: R* = R / Rmax; R*  [Rthresh/Rmax, …, 1]
R
Rthresh
circular
precipitation
object
Marcus Paulat
R*
Rmax
V(R)
Christoph Frei
x
1
Rthresh/Rmax
Martin Hagen
V(R*)
Heini Wernli
x
Basic strategy (IV): Example 1
R
R*
Rmax
1
OBS
V(R*)
x
R
R*
MOD
x
1
Rmax
x
S=0
A<0
Marcus Paulat
V(R*)
Christoph Frei
Martin Hagen
Heini Wernli
x
Basic strategy (V): Example 2
R
R*
Rmax
1
OBS
V(R*)
x
R
R*
MOD
x
1
Rmax
x
S>0
A=0
Marcus Paulat
V(R*)
Christoph Frei
Martin Hagen
Heini Wernli
x
S A L - statistics: 24h accumulated
summer seasons 2001-2004 for catchment Rhine
aLMo
ECMWF
2
A-component
1
0
-1
-2
-2
-1
0
1
2
-2
S-component
Marcus Paulat
Christoph Frei
-1
0
S-component
Martin Hagen
Heini Wernli
1
2
Kind of verification information / Verification questions
• 3 independent components to quantify quality of structure, amplitude and location
of QPF
• information is valid for a pre-specified area (e.g. river catchment, state, field
campaign area, …)
• questions:
- is the domain averaged precipitation amount correctly forecast? -> A
- is the centre of the precipitation distribution in the domain correctly forecast? -> L
- does the forecast capture the typical structure of the precipitation field
(e.g. large broad vs. small peaked objects)? -> S
Marcus Paulat
Christoph Frei
Martin Hagen
Heini Wernli
Strength
• physically meaningful information about amplitude, location and structure of QPF
• relatively intuitive
• SAL approach is close to “subjective human judgement” (claim)
• no attribution between objects is required (difficult for small objects)
• computationally simple
Marcus Paulat
Christoph Frei
Martin Hagen
Heini Wernli
Weaknesses and limitations
• non-perfect QPFs can yield S = A = L = 0 (slight modification of L component is
underway)
• no consideration of orientation of objects
• currently very simple definition of objects (threshold value)
• S value is sensitive to choice of threshold used for object definition (tests are
underway to quantify sensitivity)
• so far only preliminary results for Germany have been computed
Marcus Paulat
Christoph Frei
Martin Hagen
Heini Wernli