Roma, 5 September 2011 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 Outline Introduction Data and methods of data analysis Results Conclusions

Roma, 5 September 2011 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.

Roma, 5 September 2011 Data sourceData TypeResolution 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

Roma, 5 September 2011 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

Roma, 5 September 2011 Type of event # Days# Hourly maps (RADAR/COSMO) # Instant maps (RADAR) Stratiform12240/ Mixed stratiform- convective 20357/ Convective340/38145 Classification of data depending on type of event

Roma, 5 September ) 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

Roma, 5 September 2011 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 log

Roma, 5 September 2011 ANGULAR AVERAGING (a) original field (b) 2D power (c) 1D power Original field 2D power spectrum 1D power spectrum (isotropic) Scaling:

Roma, 5 September 2011 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 StratiformConvectiveMixed Stratiform-convective

Roma, 5 September 2011 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 RADAR rateCOSMO I2RADAR 1h

Roma, 5 September 2011 Property of invariant Pk spectra 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. log k Pk Red-noise Changing from K

Roma, 5 September 2011 Results: Invariant Pk spectra Clearer strong differences between precipitation rate and 1h precipitation data. Differences between RADAR and COSMO data. log StratiformConvectiveMixed Stratiform-convective

Roma, 5 September 2011 Examples of time series of maximum of instant Pk spectra for two mixed stratiform-convective events Results: Invariant Pk spectra

Roma, 5 September 2011 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). StratiformConvectiveMixed Stratiform-convective freq scale freq scale freq scale

Roma, 5 September 2011 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

Roma, 5 September 2011 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………….

Roma, 5 September 2011 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.

Roma, 5 September 2011 Properties of Pk spectra But β is piece-wise constant