Diapositiva 1

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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
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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 (_at_ 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
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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 (RADAR/COSMO) Instant maps (RADAR)
Stratiform 12 240/404 997
Mixed stratiform-convective 20 357/462 1439
Convective 3 40/38 145
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Assumptions

• Spatial stationarity (strong!) by averaging
  fields at each instant over all horizontal
  directions
• F F(r,t)
• 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
F(r ) ? r b , a?R A statistics is invariant
under a change of scale when r
? ?r Scale invariance suggests that the
same physical processes dominate over the scaling
range.
log
log
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(a) original field (b)
2D power (c) 1D
power
ANGULAR AVERAGING
2D power spectrum
1D power spectrum (isotropic)
Original field
Scaling
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Results Power spectra (1)
Stratiform
Convective
Mixed Stratiform-convective
log
log
log
log
log
log

• 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.

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Results Power spectra (2)
RADAR rate
COSMO I2
RADAR 1h
log
log
log
log
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
At the knee of classical power spectra (break
in scale invariance) ß changes from values gt1 to
values lt1. Possible maxima in invariant Pk
spectra occur for same values of ß.
Pk
Changing from K
log k
Red-noise
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Results Invariant Pk spectra
Stratiform
Convective
Mixed Stratiform-convective
log
log
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
Stratiform
Convective
Mixed Stratiform-convective
freq
freq
freq
scale
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
Examples of time series of scale coefficient
of power spectra for two mixed stratiform
convective events (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
• there is a general agreement between horizontal
  1D spectra of COSMO and RADAR 1h precipitation
  data
• 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)
• 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)

• 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
But ß is piece-wise constant