roma, 5 september 2011 [email protected]@arpa.emr.it comparison of spectral characteristics...
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Roma, 5 September 2011 [email protected] 1
Comparison of spectral characteristics of hourly precipitation between RADAR and COSMO Model dataover Emilia-Romagna
M. Willeit, R. Amorati and V. Pavan
ARPA-SIMC Emilia-Romagna
Roma, 5 September 2011 [email protected] 2
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 source Data Type Resolution
RADAR
(@ San Pietro Capofiume)
Precipitation rate and 1h-cumulated precipitation
1km
COSMO-I2
operational
non-hydrostatic,
limited area model
1h-cumulated total precipitation
2.8 km
Data sources
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Examples of data
COSMO 1h prec
RADAR 1h prec
RADAR prec rate
Used only fields with a sufficient number of grid points with precipitation exceeding 0.5mm/h
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Type of event
# Days # Hourly maps
(RADAR/COSMO)
# Instant maps(RADAR)
Stratiform 12 240/404 997
Mixed stratiform-convective
20 357/462 1439
Convective 3 40/38 145
Classification of data depending on type of event
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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)
Assumptions
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A power-law statistics is defined as
Φ(r ) r∝ , α R∈
A statistics is invariant under a change of scale when r → λr
Scale invariance suggests that the same physical processes dominate over the scaling range.
Scaling & power laws
)()( rr
log
log
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ANGULAR
AVERAGING
(a) original field (b) 2D power (c) 1D power
Original field
2||FFT 2D power spectrum
1D power spectrum
(isotropic)
Scaling: kkE )(
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Results: Power spectra (1)
• Generally good agreement between RADAR-COSMO 1h data.
• Greater power density in precipitation rate with respect 1h precipitation at high resolution due to time integration.
log
log
log
log
log
log
Stratiform ConvectiveMixed Stratiform-convective
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Results: Power spectra (2)
• RADAR precipitation spectra present different scale laws depending on type of events;
• COSMO precipitation spectra present only small differences depending on type of events.
log
log
log
log
log
log
RADAR rate COSMO I2RADAR 1h
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Property of invariant Pk spectraAt 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.
1kkkPky
xk 10)1(10 xy
log k
Pk
Red-noise
kx logChanging from K
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Results: Invariant Pk spectra
• Clearer strong differences between precipitation rate and 1h precipitation data.
• Differences between RADAR and COSMO data.
log log log
Stratiform ConvectiveMixed Stratiform-convective
Roma, 5 September 2011 [email protected] 14
Examples of time series of maximum of instant Pk spectra for two mixed stratiform-convective events
Results: Invariant Pk spectra
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Results: Histograms of position of max
• 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).
Stratiform ConvectiveMixed Stratiform-convective
freq
scale
freq
scale
freq
scale
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Examples of time series of scale coefficient of power spectra for two mixed stratiform convective events
(RADAR precipitation rate data)
Close to 5/3
Power spectra invariance coefficient
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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
dx
dxx
dx
dy xx ))(1(1010ln ))(1(
But β is piece-wise constant