Transcript Diapositiva 1

Comparison of spectral characteristics of
hourly precipitation between
RADAR and COSMO Model data
over Emilia-Romagna
M. Willeit, R. Amorati and V. Pavan
ARPA-SIMC Emilia-Romagna
Roma, 5 September 2011
[email protected]
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Outline
•Introduction
•Data and methods of data analysis
•Results
•Conclusions
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Goals of the study
• Investigate the statistical properties of spatial distribution of
precipitation fields by comparing RADAR retrieved (observed) and
COSMO-I2 modelled data for different meteorological events.
• Analyze :
 differences between modelled and observed fields;
 differences between 1h-cumulated and instantaneous rain-rate
fields;
 sensitivity of results to the type of precipitation events: stratiform,
convective and mixed stratiform-convective.
• Particular attention will be paid to scaling properties.
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Data sources
Data source
Data Type
Resolution
RADAR
(@ San
Pietro
Capofiume)
Precipitation rate and
1h-cumulated
precipitation
1km
COSMO-I2
operational
nonhydrostatic,
limited area
model
1h-cumulated total
precipitation
2.8 km
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Examples of data
RADAR prec rate
Used only fields with a
sufficient number of grid
points with precipitation
exceeding 0.5mm/h
RADAR 1h prec
COSMO 1h prec
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Classification of data depending on type of event
Type of
event
# Days
# Hourly
maps
# Instant
maps
(RADAR/COSMO)
(RADAR)
Stratiform
12
240/404
997
Mixed
stratiformconvective
20
357/462
1439
Convective
3
40/38
145
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Assumptions
1) Spatial stationarity (strong!): by averaging fields at each
instant over all horizontal directions
F = F(r,t)
2) Time stationarity: by pooling together all fields, disregarding
their time
F = F(r)
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Scaling & power laws
A power-law statistics is defined as
Φ(r ) ∝ r b , α∈R
A statistics is invariant under a change
of scale when
r → λr
( r )   (r )
Scale invariance suggests that the
same physical processes dominate
over the scaling range.
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log

log
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(a) original field
(b) 2D power
| FFT |2
Original field
2D power ANGULAR
spectrum AVERAGING
(c) 1D power
1D power
spectrum
(isotropic)
Scaling:
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E(k )  k b
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Results: Power spectra (1)
log
• Generally
Convective
log
Mixed Stratiform-convective
log
log
Stratiform
log
log
good agreement between RADAR-COSMO 1h data.
• Greater power density in precipitation rate with respect 1h
precipitation at high resolution due to time integration.
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Results: Power spectra (2)
RADAR 1h
log
COSMO I2
log
log
log
RADAR rate
log
log
• RADAR precipitation spectra present different scale laws depending
on type of events;
• COSMO precipitation spectra present only small differences
depending on type of events.
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Property of invariant Pk spectra
Pk
At the ‘knee’ of classical power spectra (break in scale
invariance) β changes from values >1 to values <1. Possible
maxima in invariant Pk spectra occur for same values of β.
y  Pk  k  b k  k1b
Changing from K
x (1 b )
y  10
x  logk
k  10x
log k
Red-noise
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Results: Invariant Pk spectra
Stratiform
log
Mixed Stratiform-convective
log
Convective
log
• Clearer strong differences between precipitation rate and 1h
precipitation data.
• Differences between RADAR and COSMO data.
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Results: Invariant Pk spectra
Examples of time series of maximum of instant Pk spectra for two
mixed stratiform-convective events
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Results: Histograms of position of max
scale
Convective
freq
Mixed Stratiform-convective
freq
freq
Stratiform
scale
scale
• Greater noise in convective RADAR rate histograms due to small
number of maps used.
• Differences between results due to type of events.
• Differences between results due to different types of data (uniform
probability of change of scale invariance in COSMO data between 50
and 120 Km).
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Power spectra invariance coefficient b
Examples of time series of scale coefficient
for two mixed stratiform convective events
b
of power spectra
(RADAR precipitation rate data)
Close to
5/3
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Conclusions (1)
Comparison and analysis of characteristics of precipitation
fields power spectra from RADAR and COSMO data
have shown that:
1. there is a general agreement between horizontal 1D
spectra of COSMO and RADAR 1h precipitation data;
2. it is possible to identify the presence of different
physical processes working at different spatial scale
looking at scale invariance of precipitation spatial 1D
power spectra (large scale and convective processes);
3. differences in scale invariance law depending on the
horizontal scale considered are more evident in
precipitation rate RADAR data;
……….continued………….
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Conclusions (2)
4. there are some differences between scale invariance
characteristics of RADAR and COSMO 1h precipitation data
spectra suggesting that the representation of convection in the
COSMO model is still not completely similar to that observed. In
particular
• COSMO presents a general tendency to underestimate
intensity of convective processes;
• COSMO presents smaller differences than RADAR in 1h
precipitation spectra depending on type of events;
• COSMO presents uniform probability to shift from large-scale
to convective processes at a horizontal scale from 50 to 120
Km while RADAR data present probability of shift proportional
to the scale of the process over 70 Km.
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Properties of Pk spectra
dy
db 
x (1 b ( x )) 
 ln 1010
(
1

b
(
x
))

x

dx
dx 
But β is piece-wise constant
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