International Workshop Advances in Statistical hydrology, May 23-25 2010, Taormina, Italy Study on the rainfall dependence structure using radar and rain gauge data V. Montesarchio, F. Russo, F. Napolitano Dipartimento di Idraulica, Trasporti e Strade, Sapienza Università di Roma, Italy F. Lombardo Dipartimento di Scienze dell Ingegneria Civile, Università degli Studi Roma Tre, Italy L. Baldini Istituto di Scienze dell Atmosfera e del Clima, Consiglio Nazionale delle Ricerche, Italy May 25, 2010 Analysis and modelling of hydrological processes
Motivation The identification of the spatial structure of rainfall is widely recognized as a key issue in the hydrological applications. Integrating information coming from different sources, such as rain gauge networks and weather radars, can be useful to better understand the rainfall behaviour in the space-time domain. Rain gauges can directly provide quantitative rainfall measurements for fine time scales, but the information is only punctual. Weather radars provide high space-time resolution data, but the rainfall amounts are indirectly estimated. The aim of this preliminary study is to highlight correlation structure in order to improve rainfall field stochastic simulation. 2
Radar-raingauge differences Spatial differences: Raingauge makes point measurements at ground while radar samples precipitation in a volume aloft, whose size and height strongly depend on the distance from the radar site and on the radar elevation angle (Ground Truth Problem) (Rinehart, 2004). Temporal differences: Raingauges usually have a temporal resolution of 1 min or longer while radar makes instantaneous rainfall estimates. Consequently, directly comparing radar QPE with raingauge measurements could lead to miscalibration. 3
Remote sensing The weather radar transmits a power which is absorbed and then beamed isotropically in every direction by the raindrops. The back-scattered power by the raindrops is: where r is the distance of the raindrops from radar, C is the radar constant and Z is the reflectivity factor (mm 6 m -3 ). 4
raingauge network data available from 1992 to 2009 Study area: A Cartesian grid (82 km 104 km) is built in the northwestern part of the radar field. The finest resolution is 1 km 2. 5
Radar data The radar data come from the Polar 55C polarimetric C-band Doppler weather radar located in Rome, Italy. Radar measurements have a range-bin resolution of 75 m up to 120 km from the radar site. The temporal resolution is 5 minutes. Data were collected during 2008. The reflectivity maps were purged from bins affected by ground clutter. The ground clutter removal is based on the analysis of the standard deviations of some polarimetric radar measurables for rainfall (Lombardo et al., 2006). By a parametric algorithm, radar reflectivity is converted into rainfall intensity as (Gorgucci and Baldini, 2009): where Z h is the reflectivity factor (at horizontal polarization) and R is the rainfall intensity (in mm h -1 ). 6
Radar data set DATE DATE DATE 8-9 APRIL 2008 30 JULY 2008 13-14 NOVEMBER 2008 11 APRIL 2008 31 JULY 2008 21 NOVEMBER 2008 Spring 15 APRIL 2008 1 AUGUST 2008 24 NOVEMBER 2008 24 APRIL 2008 12 SEPTEMBER 2008 25-26 NOVEMBER 2008 29 APRIL 2008 15 SEPTEMBER 2008 28-29 NOVEMBER 2008 12-13 MAY 2008 19 SEPTEMBER 2008 29-30 NOVEMBER 2008 5 JUNE 2008 3 OCTOBER 2008 1-2 DECEMBER 2008 Autumn 17 JUNE 2008 17 OCTOBER 2008 5 DECEMBER 2008 18 JULY 2008 28-29 OCTOBER 2008 9-10 DECEMBER 2008 Summer 21 JULY 2008 4-5 NOVEMBER 2008 11-12 DECEMBER 2008 22 JULY 2008 6 NOVEMBER 2008 14-15 DECEMBER 2008 28 JULY 2008 12-13 NOVEMBER 2008 15-16 DECEMBER 2008 29 JULY 2008 7
Radar data Uncertainty sources (Villarini and Krajewski, 2010): Radar miscalibration. Attenuation. Ground clutter and anomalous propagation. Beam blockage. Variability of the Z R relation. Range degradation: radar beam broadening and beam overshooting of the low clouds. Vertical variability of the precipitation system. Vertical air motion and precipitation drift. Temporal sampling errors. 8
Radar data Many of the uncertainty sources are strongly dependent on the distance from the radar site: In radar derived rainfall intensity maps, radar polar pixels are usually remapped into a Cartesian grid. It is expected that rainfall intensity data in pixels far from radar are less correlated than rainfall intensity data in pixels near the radar. An analysis of correlation between the rainfall values in the adjacent pixels is performed in the study area. 9
Radar data 10
Since often ground clutter exhibits high decorrelation in space, for small distances from radar, the resulting Pearson correlation coefficient has the small values in figures. Lowest values in summer due to isolated precipitation cells. 11
Radar-Raingauges comparison Identified the pixels where the raingauges considered are located, for each rainfall event and for each rain gauge, we have selected the periods when the radar and the raingauge have contemporaneous rainfall measurements. 12
Raingauge cross-correlation analysis Pearson correlation coefficient (X,Y) denote a pair of rainfall processes observed at two locations Evaluated for both rain gauges and weather radar dataset. Kendall τ k, measure of concordance c n and d n denote respectively the number of concordant and discordant pairs If (X, Y) denote a pair of rainfall processes observed at two locations, the pairs (x 1,y 1 ) and (x 2,y 2 ) of observations are said concordant if (x 1 -x 2 )(y 1 -y 2 )>0 and discordant if (x 1 -x 2 )(y 1 -y 2 )<0. Evaluated only for rain gauges dataset. 13
Rain gauges data set Given the intermittent nature of rainfall and therefore the presence of zero values, the estimate of correlation coefficient can be affected. It is possible to distinguish three cases: Case A: only positive values at both rain gauges: A={X>0, Y>0} Case B: all pairs except those with both values equal to zero: B={(X+, 0) apple (0, Y+)} Case C: all pairs C={X 0, Y 0} Rain gauges data are analysed in the three case A, B and C, for both Pearson and Kendall coefficients. The results presented are related to the month of November 2008, to allows the comparison with the correspondent radar data analysis. 14
Rain gauges data set: Case A May 25, 2010 Analysis and modelling of hydrological processes 15
Rain gauges data set: Case B May 25, 2010 Analysis and modelling of hydrological processes 16
Rain gauges data set: Case C 17
Comparison of rain gauges data analysis An anisotropic behaviour of the rainfall amount over the study area is observed when the zero values are neglected. The zero values strongly influence the observed behaviour in terms of the main direction of the rainfall correlation structure. 18
Radar data set: Case C May 25, 2010 Analysis and modelling of hydrological processes 19
Radar data set: Case A May 25, 2010 Analysis and modelling of hydrological processes 20
Discussion and perspectives 1. The rain gauge network and weather radar data are useful to determine and validate spatial and temporal correlation structure of rainfall fields in order to develop: nowcasting radar models; stochastic simulation of rainfall fields. 2. To these aims the correlation structure obtained by radar needs to be merged with raingauge data in order to take into account the influence of the distance from radar site. 3. A wide campaign of calibration of Italian weather radar network is needed in order to extend to other sites the proposed analysis. 21
References Gorgucci, E. and Baldini, L. (2009). An Examination of the Validity of the Mean Raindrop-Shape Model for Dual-Polarization Radar Rainfall Retrievals, Geoscience and Remote Sensing, IEEE Transactions, 47(8), 2752 2761, doi: 10.1109/TGRS.2009.2017936. Lombardo, F., Napolitano, F., Russo, F., Scialanga, G., Baldini, L. and Gorgucci, E. (2006). Rainfall estimation and ground clutter rejection with dual polarization weather radar, Adv. Geosci., 7, 127 130. Rinehart, R.E. (2004). Radar for meteorologists. Rinehart Publications, Grand Forks. Villarini, G. and Krajewski, W.F. (2010). Review of the Different Sources of Uncertainty in Single Polarization Radar-Based Estimates of Rainfall, Surv. Geophys., 31, 107 129, doi: 10.1007/s10712-009-9079-x. 22