Roma, 5 September 2011 [email protected]@arpa.emr.it Comparison of spectral characteristics of hourly precipitation between RADAR and COSMO Model

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


Outline

•Introduction

•Data and methods of data analysis

•Results

•Conclusions


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.


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


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


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


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


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


ANGULAR

AVERAGING

(a) original field (b) 2D power (c) 1D power

Original field

2||FFT 2D power spectrum

1D power spectrum

(isotropic)

Scaling: kkE )(


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


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


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


Results: Invariant Pk spectra

• Clearer strong differences between precipitation rate and 1h precipitation data.

• Differences between RADAR and COSMO data.

log log log



Examples of time series of maximum of instant Pk spectra for two mixed stratiform-convective events

Results: Invariant Pk spectra


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).


freq

scale

freq

scale

freq

scale


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


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………….


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.


Properties of Pk spectra

dx

dxx

dx

dy xx ))(1(1010ln ))(1(

But β is piece-wise constant

Documents

Roma, 5 September 2011 [email protected]@arpa.emr.it Comparison of spectral characteristics of hourly precipitation between RADAR and COSMO Model