Comparison Between Radar and Rain Gauges Data at Different Distances

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icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Hydrol. Earth Syst. Sci. Discuss., 7, 5171–5212, 2010 Hydrology and www.hydrol-earth-syst-sci-discuss.net/7/5171/2010/ Earth System HESSD doi:10.5194/hessd-7-5171-2010 Sciences 7, 5171–5212, 2010 © Author(s) 2010. CC Attribution 3.0 License. Discussions

Comparison between This discussion paper is/has been under review for the journal Hydrology and Earth radar and rain System Sciences (HESS). Please refer to the corresponding final paper in HESS gauges data at if available. different distances Comparison between radar and rain S. Sebastianelli et al. gauges data at different distances from Title Page radar and correlation existing between Abstract Introduction the rainfall values in the adjacent pixels Conclusions References Tables Figures S. Sebastianelli1, F. Russo1, F. Napolitano1, and L. Baldini2

1Department of Hydraulic, Transportations and Roads, “Sapienza” Univ. of Rome, Rome, Italy J I 2National Research Council, Institute of Atmospheric Sciences and Climate, Rome, Italy J I

Received: 30 June 2010 – Accepted: 2 July 2010 – Published: 30 July 2010 Back Close Correspondence to: S. Sebastianelli ([email protected]) Full Screen / Esc Published by Copernicus Publications on behalf of the European Geosciences Union.

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5171 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Abstract HESSD Rainfall intensity data in pixels very far from radar are less correlated than values in pixels near the radar, because at far distances the width of a range-bin is comparable 7, 5171–5212, 2010 or bigger than the pixel width, so in a pixel there are one or just a few rainfall intensity 5 values. Vice versa, near the radar, there are many radar resolution bins which belong Comparison between to a single pixel, so great correlation between rainfall intensity values for contiguous radar and rain pixels is expected. gauges data at Moreover, the signal returned from precipitation at far distance from radar antenna different distances can be due to a radar sample volume partially or completely filled with mixed phase or 10 ice particles, or can be quite close to the minimum detectable signal. S. Sebastianelli et al. All these phenomena can influence the goodness of rainfall estimates, introducing errors which increase as the distance from radar increases. The objective of this work is to characterize these errors as a function of the distance. Title Page

For this aim is possible to compare the rainfall data obtained by rain gauges at dif- Abstract Introduction 15 ferent distances from radar with rainfall radar data at the same distances, verifying the correlation existing between the rainfall values in the adjacent pixels and how the Conclusions References diﬀerence between radar and rain gauges data changes. Tables Figures The radar data utilized in this work have been collected from the CNR–ISAC (Institute of Atmospheric Sciences and Climate of the National Research Council) Polar 55C J I 20 radar in Rome Tor Vergata during 2008.

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1 Introduction Back Close

Precipitation measurements are the starting point to study hydrological processes. Full Screen / Esc They are utilized both for a better understanding of these processes and as input in hydrological simulation models indispensable to a correct territorial planning and to an Printer-friendly Version 25 adequate management of hydraulic system. Interactive Discussion

5172 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Radar and rain gauge are very different precipitation measuring devices. Radar samples precipitation in a volume aloft, estimating measurements related to scattering HESSD or propagation that are subsequently converted into rainfall intensity; the extension 7, 5171–5212, 2010 and height of this volume depending on the distance from radar and from the elevation ◦ 5 (usually small, but greater than 0 ). Rain gauge makes a point measurement (if we compare its dimensions with the extension of precipitation) at ground, sampling with a Comparison between delay the precipitation sampled aloft by the radar. radar and rain The radar is an electronic device that transmits an electromagnetic wave, which in- gauges data at teracts with the objects in the atmosphere (typically raindrops, snowflakes, hailstones different distances 10 or graupel), which reflect some of the intercepted power toward the radar (backscattering). The radar analyses the received echo, allowing to estimate important information S. Sebastianelli et al. with regard to scatterers, like position (azimuth and distance with respect to the radar) and properties of the backscattered echo (intensity, phase, polarization). Title Page Rain gauges measurements are a major input of hydrological models. The accuracy 15 of flood estimates depends essentially on the rain gauges network density configura- Abstract Introduction tion and on the instrument precision (Maheepala et al., 2001). In fact the low spatial resolution of input of hydrological models is an important limit of hydrological prediction Conclusions References

(Vaes et al., 2001). Therefore, to estimate the rainfall fields over an entire basin, rain Tables Figures gauges pointwise measurements need to be interpolated. However, different interpola- 20 tion methods can to give significative differences in rainfall field estimates (Dirks et al., J I 1998). Conversely, the weather radar is able to give, in real time and over a wide region, high J I spatial and temporal resolution rainfall intensity estimates, thus playing a significant Back Close role in the rainfall fields estimation and consequentially in the improvement of hydro- 25 graphs simulation (Lopez et al., 2005); this fact allows obtaining an improvement of Full Screen / Esc the hydrological models input data reliability, for correct simulations of run-off, which is necessary to flood forecasting and forewarning, with safety margin, and for drainage Printer-friendly Version systems design (Clothier and Pegram, 2002). Interactive Discussion

5173 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion However, the spatial sampling of precipitation performed by radar is not uniform. As a consequence, the spatial structure of a rain field derived from weather radar HESSD measurements will be affected the way it sample precipitation and will be dependent 7, 5171–5212, 2010 on the distance from the radar and that influence the rainfall estimates, introducing an 5 error which increase as the distance from radar increases. The objective of this work is to quantifying this error. For this aim is possible to com- Comparison between pare the rainfall data obtained by rain gauges to different distances from radar with radar and rain rainfall radar data to the same distances, verifying the correlation existing between the gauges data at rainfall values in the adjacent pixels and analyzing the trend of the correlation between different distances 10 rain gauges and radar measures when increasing the distance from radar (Sebas- tianelli et al., 2010). S. Sebastianelli et al. Since rainfall data estimated by weather radar are smoothed in space, while rainfall data measured by rain gauges are both referred to a point and measured with a time Title Page delay as regards the radar, there are differences between radar data and rain gauges 15 data. Usually radar estimates of rainfall are compared with rain gauges measures of Abstract Introduction precipitation and it is possible to give the mean square error of the radar-rain gauge comparison, the correlation coefficient and the biases of the comparison as statistical Conclusions References

parameters of rainfall intensity (Zawadzki, 1975). The factors which produce discrepan- Tables Figures cies between radar and rain gauges data can be sources of random errors, as the error 20 associated with the transformation from reflectivity to rain rate due to the variability of J I drop size distribution, or of systematic errors, as attenuation, or of range dependent errors too, associated with beam broadening and the increase in height with range of J I the sample volume. Back Close Berenguer and Zawadzki (2008, 2009) have characterized the error structure con- 25 sidering the contributions of the range dependent errors, the effect of the error due to Full Screen / Esc the Z-R transformation and their interaction at nonattenuating wavelengths limiting to stratiform precipitation. Printer-friendly Version The single polarization radar-based estimates of rainfall are affected by source of uncertainty including radar miscalibration, attenuation, ground clutter, anomalous Interactive Discussion

5174 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion propagation, beam-blocking, variability of Z-R relation, range degradation, vertical variability of the precipitation system, vertical air motion, precipitation drift and temporal HESSD sampling error (Villarini and Krajewski, 2010). 7, 5171–5212, 2010 Therefore there is significatives uncertainty in rainfall amounts estimations, because 5 of sampling differences of the two devices, especially when short time intervals are considered: the correlation between radar and rain gauges data increases when the Comparison between rainfall amounts are integrated over longer periods (Krajewski, 1995; Steiner et al., radar and rain 1999; Russo et al., 2005; Sebastianelli et al., 2010). gauges data at In order to characterize errors between radar and raingauge correlation, correlation different distances 10 coefficient, which is a measure of linear dependency between a pair of random vari- ables, is used. The population correlation coefficient can be defined by choosing a pair S. Sebastianelli et al. of rainfall processes observed at two rain gauge locations. By considering pairs of rain gauges, it can be examinated the spatial dependence of rainfall through the analysis Title Page of the behaviour of Pearson’s correlation coefficient in dependence on the distance 15 between the two devices (Montesarchio et al., 2010). Abstract Introduction To characterize rainfall fields by Pearson’s correlation coefficient, Yoo and Ha (2007) and Ha and Yoo (2007) investigated the influence of zero values; in fact, because of Conclusions References

the intermittent nature of precipitation, the estimates of Pearson’s correlation coefficient Tables Figures are affected by the presence of zero rainfall values. If (X,Y ) denote a pair of rainfall 20 processes observed at two rain gauges locations, to analyse the three different kinds J I of possible pairs, which are: all pairs (X ≥ 0, Y ≥ 0), all pairs except those with both values equal to zero (X > 0, Y = 0) and (X = 0, Y > 0) and (X > 0, Y > 0), positive J I values at both rain gauges (X > 0, Y > 0). The authors have found that the Pearson Back Close coefficient estimate is useful for the characterization of rainfall fields only considering 25 positive values at both rain gauges. Full Screen / Esc Montesarchio et al. (2010) have examined the time and space correlation between time series for different time scales separately for the rain gauge data set (considering Printer-friendly Version the correlation between pairs of rain gauges) and the weather radar data set (considering the correlation between pixels). Then they are also evaluated the Pearson Interactive Discussion

5175 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion coefficient against absolute distances both for radar data and rain gauge found the same trend in the two cases; the Pearson coefficient decreases when increasing the HESSD absolute distances and, higher is the time scale, higher is the correlation. As shown by 7, 5171–5212, 2010 Yoo and Ha (2007), they are concluded that consider zero measurement in case of rain 5 gauge produce a high variability of inter-station correlation coefficients and somehow estimates not coherent with time scale aggregation. Comparison between In this work, to analyze the trend of the correlation between rain gauges and radar radar and rain estimates as a function of the distance from radar, we eliminate the numerous couples gauges data at of homologues components equal to zero of the rain gauges and radar vectors between different distances 10 we are calculated the Pearson correlation coefficient, while, to verify the correlation existing between the rainfall values estimated by the radar in the adjacent pixels, we S. Sebastianelli et al. have not considered pixels with zero rainfall intensities values, because the numerous couples of adjacent pixels with rainfall intensities values equal to zero increase very Title Page much the correlation coefficient value, on the other hand the presence of a pixel with a 15 zero rainfall intensity value in many couples of adjacent pixels decreases the correlation Abstract Introduction coefficient value. For this work, we have utilized rainfall intensity maps derived from radar reflectivity Conclusions References

maps collected with the Polar 55C weather radar in the year 2008. Tables Figures The paper is organized as follows. In the next section we explain the differences 20 between radar and rain gauges quantitative measurements of precipitation. In Sect. 3, J I characteristics of the weather radar are described. In Sect. 4, we explain the assumed methodologies for the comparison between radar and rain gauges data process and for J I the correlation between the rainfall values in the adjacent pixels. In Sect. 5, we make Back Close the comparison between the rainfall values in the adjacent pixels and, finally, in Sect. 6 25 we make the comparison between radar and rain gauges data at different distances Full Screen / Esc from radar. Printer-friendly Version

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5176 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2 Different radar and rain gauges quantitative measurements of precipitation HESSD A typical weather radar uses a pencil-beam antenna and the volume sampled increases with the distance, so the power intercepted by a meteorological target at a 7, 5171–5212, 2010 distance from antenna radar is only a part of the transmitted power because of the 5 radar beam tends to widen. Moreover, due to the earth curvature and to the fact that Comparison between elevation angles greater than zero must be used to avoid beam interceptions by obsta- radar and rain cles or relieves, the signal returned from precipitation at far distance from radar antenna gauges data at can be due to a radar sample volume partially or completely filled with mixed phase or different distances ice particles, or can be quite close to the minimum detectable signal, in fact, also at 10 low elevations, the radar beam may sample above the clouds and does not intercept S. Sebastianelli et al. precipitation. On the other hand, being equal their reflectivity, only a part of the energy is scattered in the radar direction and the amount of energy collected by radar antenna, decreases as distance from radar increases. Therefore, the spatial sampling of precip- Title Page

itation performed by radar is not uniform and the same precipitation produces a return Abstract Introduction 15 characterized by a signal to noise ration that decreases with increasing distance. Besides, the minimum size of raindrops which radar can detect is smaller with de- Conclusions References creasing wavelength but, on the other hand, the portion of signal absorbed by precipi- Tables Figures tation is larger for smaller wavelengths and, in the presence of precipitation, increases on average as the distance from radar increases. Considering typical weather radar J I 20 wavelengths, it is known that S-band can be considered fairly immune from attenuation

problems, whereas X-band is severely aﬀected by attenuation. C-band, which is the J I typical choice of European operational weather radar, is aﬀected by attenuation, but not as X-band. When the radar beam passes through an intense storm cell it weaken and Back Close

therefore the rainfall intensity due to the cell is underestimated (Pegram and Clothier, Full Screen / Esc 25 1999). A further cause of attenuation is due to mountains or other obstacles that intercept the radar beam (Bringi and Chandrasekar, 2001). In case of total beam-blocking, Printer-friendly Version rainfall intensity due to a rain cell beyond the obstacle cannot be estimates. Interactive Discussion

5177 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion As a consequence, the spatial structure of a rain field derived from weather radar measurements will be affected the way it sample precipitation and will be dependent HESSD on the distance from the radar. All these effects can influence the goodness of rainfall 7, 5171–5212, 2010 estimates, introducing errors which increase as the distance from radar increases. 5 In radar hydrology, radar rainfall intensity maps are obtained by remapping radar polar pixels onto a Cartesian grid. It is expected that rainfall intensity data in pixels very Comparison between far from radar are less correlated than rainfall intensity data in pixels near the radar, radar and rain because of several reasons. At a long distance from radar the width of a range-bin is gauges data at comparable or bigger than the pixel width, so in a pixel there are one or a few rain- different distances 10 fall intensity values. In consequence the rainfall intensity values in a pixel is relative to range-bins very distant from the pixel contiguous, so there is not much correlation S. Sebastianelli et al. between the rainfall intensity values of contiguous pixels. Vice versa, near the radar, a single pixel is determined by many radar resolution volumes, so higher correlation Title Page between rainfall intensity values for contiguous range-bins of two adjacent pixels is ex- 15 pected; consequently, also rainfall intensity data of two adjacent pixels are correlated, Abstract Introduction because the rainfall in a considered pixel is the mean of the rainfall intensity values of the range-bins which belong to the considered pixel. Conclusions References

An objective of this work is to verify the correlation existing between the rainfall values Tables Figures in the adjacent pixels. 20 In the presence of wind or in the presence of trees or buildings, the rain gauge mea- J I sures can be distorted, so the precipitation which is intercepted by the rain gauge can be appreciably different from the effective precipitation. The rain gauge observations J I are affected by errors due to different causes, like internal frictions and occasional im- Back Close perfections of the rain gauge, reading errors, wind action which deflect the precipitation. 25 Since radar measures precipitation at a given height, rainfall is registered by the rain Full Screen / Esc gauge below the radar sample volume with a delay with respect to the radar; the delay depends on the time needed to raindrops to precipitate. However the updraught can Printer-friendly Version retard or block the precipitation, while the wind can transport the raindrops at a distance from the rain gauge. In some cases the rain gauge cannot measure any precipitation, Interactive Discussion

5178 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion at the contrary the radar can detect the presence of the raindrops in the atmosphere. In addition, if the precipitation is formed by small diameter raindrops, they can evaporate HESSD in atmosphere before reaching the ground, and therefore they can be intercepted only 7, 5171–5212, 2010 by the radar but not by the rain gauge. Vice versa larger raindrops can drag along the 5 moisture present in the air, that cannot be detect by the radar and become larger during fall. In this condition the precipitation measured by the rain gauge can be greater than Comparison between the precipitation measured by the radar. radar and rain The amount of water intercepted by the radar beam depends on sampling volume gauges data at size. Therefore large sampling volumes determine decorrelation between rain rate de- diﬀerent distances 10 rived from radar data and rain rate measured by rain gauges. Moreover, higher is the radar beam, greater is the sampling volumes and the number of raindrops intercepted. S. Sebastianelli et al. As a consequence, since the radar samples all the raindrops into the sampling volume instantaneously, while the rain gauge collects a part of them with a delay, a decorrela- Title Page tion between rain rate measured by the rain gauge and rain rate estimated by the radar 15 is expected. Besides, for higher radar beam, during the falling, it is very probable both Abstract Introduction that the wind action distort the trajectory of the raindrops and that, because of coales- cence, the raindrops combine or divide, so that the distribution of size at the gauge is Conclusions References

diﬀerent from that sampled by radar. These facts give further decorrelation between Tables Figures radar estimates and rain gauges measures of rainfall rate. 20 There is also a contribution to decorrelation between rain rate derived from radar data J I and rain rate measured by rain gauge due to the fact that the radar beam intercepts the freezing level. By observing the Figs. 8, 9, 10, 11 and 12, at distance of about J I 60 km from radar, the height of radar beam is over 2000 m above the sea level, at Back Close the elevation of 1.5◦, therefore, especially in winter, the radar beam likely intercepts 25 the freezing level. In case of stratiform precipitation, the air vertical motion velocity Full Screen / Esc is lower than that of snow particles, so, in the most height layer of the clouds, the ice particles fall as soon as they are formed and they aggregate during the falling. Printer-friendly Version Above the freezing level there are only ice particles, but under the freezing level there is a melting layer where there are both raindrops and ice particles which acquire a Interactive Discussion

5179 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion thin coat of water because they are melting. In this case radar overestimates the reflectivity factor and, consequently, the rainfall. In fact the ice particles width is greater HESSD than the raindrop width and the water layer on their surface reflects the radar signal. 7, 5171–5212, 2010 Therefore these particles reflect the radar signal as if the power was back-scattered 5 by very large raindrops with the same width of the ice particles. Since back-scattered power depends on the raindrop diameter sixth power, a few wet great ice particles are Comparison between sufficient to overestimate the reflectivity factor, so a little number of great raindrops radar and rain gives most of back-scattered power. The region where there are big wet snowflakes gauges data at is frequently detected by weather radar through a very intense echo bright band in a different distances 10 horizontal layer for about 0.5 km under the freezing level (Battan, 1970). Moreover, some wet ice particles persist over the melting layer, so the region characterized by the S. Sebastianelli et al. bright band extends as far as the temperature of 4–5 ◦C under the melting layer (see Fig. 1). Title Page Even if in convective events the bright band is not well defined, also in case of wet ◦ 15 hailstone, frequent at mid latitudes, at the elevation of 1.5 (considered in this study) the Abstract Introduction radar overestimate the reflectivity. In fact the wet hailstone is formed both by raindrops and by hailstones covered by a water melting layer, like in the precedent case. Conclusions References

For the reasons mentioned above, radar and rain gauge can provide diﬀerent quan- Tables Figures titative measurements of precipitation and this work aims to analyses the trend of the 20 correlation between rain gauge and radar measures when increasing the distance from J I radar. J I

3 The Polar 55C weather radar Back Close

3.1 Features of Polar 55C weather radar Full Screen / Esc

The Polar 55C is a C-band (5.6 GHz) Doppler dual polarized coherent weather radar Printer-friendly Version 25 with polarization agility managed by the Institute of Atmospheric Sciences and Cli- mate of the National Research Council, Italy. The radar is located 15 km South-East of Interactive Discussion 5180 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Rome, in the CNR (National Research Council) Tor Vergata area (lat. 41◦5002400 N, lon. 12◦3805000 E, 102 m a. s. l.). The radar employs a single offset antenna with 0.92◦ az- HESSD imuth beamwidth and 1.02◦ elevation beamwidth. With its current configuration, Polar 7, 5171–5212, 2010 55C can provide the commonly used polarimetric measurements, namely horizontally 5 reflectivity factor (Z), differential reflectivity (ZDR) and differential phase shift (ΦDP). Radar measurements are obtained by averaging 64 pulses transmitted with a 1200-Hz Comparison between pulse repetition frequency in range-bin spaced apart of 75 m, up to 120 km away from radar and rain the radar location (Gorgucci et al., 2002). gauges data at For the cases in point the scanning strategy adopted by Polar 55C prefigured the different distances 10 cyclical repetition of eight sweeps all directions with constant elevation (Plan Position S. Sebastianelli et al. Indicators). Each 5 min 8 Plan Position Indicators (PPI) are acquired, each one with a different elevation angle, ranging from 0.5 to 7.5◦. This work considers measurements collected at 1.5◦ elevation. This elevation angle is selected considering two contrasting Title Page needs: on the one hand the need to increase the elevation value to minimize the 15 ground-clutter problem, on the other hand the need to avoid that, at great distance Abstract Introduction from radar, the scanning beam would measure the water content into the clouds rather than water content into the precipitation (Gorgucci et al., 1995; Russo et al., 2005; Conclusions References Lombardo et al., 2006; Russo et al., 2006). Tables Figures

3.2 From reﬂectivity data to rainfall intensity J I

20 In this study rainfall estimates are obtained using radar reﬂectivity factor measure- J I ments. The reﬂectivity data of Polar 55C are corrected for calibration bias by adding a cor- Back Close rection factor to each recorded Z value. This value is obtained during periodical main- Full Screen / Esc tenance by a static calibration procedure of radar receiver, which consists in direct- 25 ing towards the radar a pulse in C-band of known power, and then in verifying the Printer-friendly Version power measured by the receiver (Bringi and Chandrasekar, 2001) and measurements of losses in passive microwave components. Interactive Discussion

5181 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion To use radar data for rain estimation two fundamental steps must be performed: distinction between meteorological signal and noise and between meteorological signal HESSD and ground clutter. 7, 5171–5212, 2010 The weather radar transmits a power which is absorbed and then beamed isotrop- 5 ically in every direction by the raindrops. The back-scattered power by the raindrops is: Comparison between CZ radar and rain Pr = . (1) gauges data at r2 different distances where r is the distance of the raindrops from radar, C is the radar constant and Z is the reflectivity factor (mm6 m−3). S. Sebastianelli et al. 10 The noise level is determinated in every radar reflectivity map supposing that at great distance, the radar, also with relatively low elevations like that we have utilized in this work, samples with a good chance in an atmospheric region above precipitation or Title Page clouds. Therefore the reflectivity factor measured at that distance derives from noise Abstract Introduction only. In this way the modal value in the last two range-bins can be chosen like a 15 reference to determine the noise level at the receiver. The noise estimated as above- Conclusions References mentioned is a constant power but, to distinguish between meteorological signal and noise, the noise is converted in reflectivity. The noise level at a distance r from radar Tables Figures can be expressed by the Eq. (2) in the following way: J I r Z (r) = Z +20log . (2) s f 10 J I rend Back Close 20 where in the left-hand rend is the maximum distance from radar, Zf is the modal value of Z in the last two range-bins and the other addend is a corrective term due to the h Full Screen / Esc fact that the signal power decrease depending on the second power of the distance from radar (in linear scale). It is now possible to distinguish between meteorological Printer-friendly Version signal and noise comparing along each record the values of Zh at the distance r with 25 the relative values of Zs(r) and considering affected by noise the range-bins whose Interactive Discussion reflectivity does not exceed noise level by a threshold of 4 dBZ introduced to esteem in 5182 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion regard the noise fluctuations about median value. It should be noted that this method allows monitoring the noise level of the system. HESSD Finally the reflectivity maps were purged from bins affected by ground clutter. The 7, 5171–5212, 2010 modality developed for the ground clutter removal is based on the existence of typi- 5 cal values for the standard deviations of the differential reflectivity σ(ZDR) and of the differential phase σ(ΦDP) when the radar return is due to precipitation. In fact with Comparison between meteorological echoes these standard deviations can be expressed by the width of the radar and rain Doppler spectrum and the co-polar correlation coefficient about which is well-known gauges data at the variation range characteristic of rainfall (Bringi and Chandrasekar, 2001; Lombardo different distances 10 et al., 2006). Another method to eliminate the effects of ground clutter is based on the use of S. Sebastianelli et al. Constant Altitude Plan Position Indicators (Pegram and Clothier, 1999). A CAPPI at the altitude of, say, 2 km above the ground level assures that there is almost not ground Title Page clutter and, besides, the bright band is usually above or at the 2 km level because of 15 the high summer temperatures they are experienced in wet season in South Africa. Abstract Introduction Since the range at which the radar beam passes through the level situated 2 km above the ground is 67 km, they are used data received beyond this range only for qualitative Conclusions References

analysis; in fact these data are referred to a region within or above the melting layer. Tables Figures In Fig. 2 the reﬂectivity map and the corresponding rainfall intensity map concern- 20 ing the same instant of data acquisition are shown. By a parametric algorithm, radar J I reﬂectivity is converted into rainfall intensity as (Gorgucci and Baldini, 2009):

Z J I 0.5358 h R = 0.19055×10 10 . (3) Back Close where Z is the reflectivity factor (at horizontal polarization) and R is the rainfall in- h Full Screen / Esc tensity (in mm h−1). Coefficients of this algorithm are determined through simulations 25 assuming theoretical derived distribution of the Drop Size Distribution (DSD) param- Printer-friendly Version eters, a drop shape model, a fixed temperature and the distribution of canting angle. In this study, algorithms were derived choosing a normalized gamma DSD defined by Interactive Discussion its parameters varying in the range: 0.5 < Do < 3.5 mm; 3 < log10 Nw < 5; −1 < µ < 5. 5183 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Further assumptions are: a) Pruppacher and Beard drop shape model (1970); b) canting angle distributed with mean 0◦ and standard deviation 10◦; c) temperature of 20 ◦C HESSD (Bringi and Chandrasekar, 2001). 7, 5171–5212, 2010 Finally, radar rainfall values are remapped onto a 1 km2 Cartesian grid, by assigning 5 to each pixel the mean of rainfall intensity estimated in the radar range-bins belonging to the pixel. Comparison between radar and rain gauges data at 4 Methodologies different distances

In this section, we describe the methodologies adopted to compare radar and rain S. Sebastianelli et al. gauge measurements and to estimate correlation between the rainfall values in the 10 adjacent pixels. The database of rainfall intensity was collected during the 2008 year utilizing the Polar 55C weather radar. Title Page

4.1 Methodologies for correlation between the rainfall values in the Abstract Introduction adjacent pixels Conclusions References

To estimate the trend of the correlation between rainfall values in the adjacent pixels Tables Figures 15 depending on distance from radar we have employed three different methods. Considering a PPI collected by the radar during a rainfall event in the year 2008 and J I fixing a circumference centred on the radar site, we select the pixels which have the barycentre on this circumference and therefore are at the same distance from radar. J I For each of them we have considered the rainfall intensity observed and the rainfall Back Close 20 intensity of one of the adjacent pixels. We then calculate the Pearson correlation coefficient of these data, which is relative to the distance considered. We have repeated Full Screen / Esc the same procedure for every distance from radar until the edge of the scanning circle (120 km). For a single PPI, a Pearson correlation coefficient values vector, each Printer-friendly Version of them relative to a particular distance, is obtained. Finally, after having obtained a Interactive Discussion 25 vector of coefficient values for each PPI, we have calculated the arithmetic mean of the

5184 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion corresponding coefficients of each vector relative to the same distance and the result is a value relative to the whole of the rainfall event. For each rainfall event in the year HESSD 2008 a coefficient values vector was obtained. The single element of this vector is 7, 5171–5212, 2010 relative to a fixed distance and it is the arithmetic mean of the coefficients relative to 5 each PPI and to the same distance. This vector represents the trend of the correlation between the adjacent pixels when increasing the distance from radar. Comparison between A second method considers for each pixel at the same distance from radar, four ad- radar and rain jacent pixels and computes the corresponding four correlation coefficients. Finally the gauges data at arithmetic mean of the four coefficients was computed, obtaining a correlation coeffi- different distances 10 cient relative to the distance considered and to the fixed PPI. After which we proceeded like in the first case, obtaining a correlation coefficient values vector for each PPI into S. Sebastianelli et al. the same event and then for each event of the year 2008. In a third method, for a fixed PPI and at a distance from radar, the arithmetic mean Title Page of the rainfall intensity of the four pixels adjacent each pixel placed at the distance 15 from radar fixed is calculated. Therefore we have made two rainfall intensities values Abstract Introduction vectors. The Pearson correlation coefficient was calculated between these arithmetic means and the values of the pixels, relative to the distance specified and to the fixed Conclusions References

PPI. Then we proceed like in the other two cases, calculating the correlation coefficient Tables Figures for each distance, obtaining a correlation coefficients vector relative to a single PPI. 20 Finally we calculate the arithmetic mean of the homologue components of each vector J I obtained for a single PPI, calculating i.e. the correlation coefficients vector relative to the whole of the rainfall event. This vector represents the trend of the correlation J I between the rainfall intensities in the adjacent pixels when increasing the distance from Back Close radar. Full Screen / Esc 25 4.2 Methodologies for comparison between radar and rain gauges data

The rain gauges we have considered are 38; whereof 22 located in the roman area: Printer-friendly Version Acilia, Acqua Acetosa, Capannacce, Casilino, Cassiodoro, Eleniano, Eur, Falcognana, Interactive Discussion Flaminio, Fregene, Isola Sacra, La Storta, Monte Mario, Ostia, Ostiense, Ottavia, Ponte 5185 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Galeria, Regillo, Roma Est, Roma Nord, Roma Sud and Via Marchi. We have considered also rain gauges located in the Marta river basin and in the Mignone river basin: HESSD Allumiere, Civitavecchia, Mignone, Rocca Respampani and Tarquinia. The other rain 7, 5171–5212, 2010 gauges utilized in this work are: Alatri, Borgo s. Maria, Bracciano, Castello Vici, Cervet- 5 eri, Poggio Mirteto, Ponte Felice, Posticciola, Rieti, Rocca Sinibalda and S. Martino. Figure 3 shows the case-study region, the rain gauges utilized in this work and their Comparison between positions in relation to the Polar 55C location (in the centre of the scanning circle), the radar and rain Rome ring road, the coast-line and the hydrographical network of the river Tiber. The gauges data at rain gauges we are considered are reported in Table 1, with their distances (in km) different distances 10 from radar and the Cartesian coordinates (in km) of the barycentre of the pixel where the single rain gauge belongs. S. Sebastianelli et al. At first we have identified the pixels where are located the rain gauges considered, by calculating the Cartesian coordinates of the pixels barycentres and by knowing the Title Page Cartesian coordinates of the rain gauges, both respect Polar 55C. Then, for each rain- 15 fall event and for each rain gauge, we have selected the periods when the radar and Abstract Introduction the rain gauge have measured contemporaneously. Therefore, having fixed a rainfall event and considered a single rain gauge, we have made a radar vector and a rain Conclusions References

gauge vector. A radar vector component is the rainfall (in mm) measured by the radar Tables Figures above the pixel where is located the rain gauge considered, while a rain gauge vector 20 component is the rainfall (in mm) which was measured by the rain gauge specified. J I The homologous components of the vectors are the rainfall which was measured by the radar and by the rain gauge at the same time. We have effectuated three analysis. J I In the first analysis, for the rain gauges which are located in Rome, the generic com- Back Close ponent of the two vectors is the rainfall which was precipitated in a period of 10 min, 25 while, for the other rain gauges, the component represents the rainfall which was pre- Full Screen / Esc cipitated in a period of 15 min. In the second analysis, for all the rain gauges, the generic component of the two vectors is the rainfall which was precipitated in a period Printer-friendly Version of 30 min. Instead, in the last analysis, for all the rain gauges, the single component of the two vectors is the rainfall which was precipitated in a period of 1 h. We have applied Interactive Discussion

5186 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion the same methodology for all the analysis. Selected a rainfall event, it was calculated the Pearson correlation coefficient between the radar vector and the rain gauge vec- HESSD tor and that was performed for all the rain gauges. The same procedure was applied 7, 5171–5212, 2010 for the following rainfall events of the year 2008: 15 April 2008, 4–5 November 2008, 5 12–13 November 2008, 24 November 2008, 25–26 November 2008, 5 December 2008, 11–12 December 2008. As each rain gauge is situated at a different distance from the Comparison between radar, for every rainfall event it was calculated a Pearson correlation coefficient for each radar and rain distance. At last, for each rain gauge, we have made a rain gauge vector by linking to- gauges data at gether the rain gauge vectors we have made for every rainfall event. The resulting different distances 10 vector components represent the rainfall values registered by the specified rain gauge in the whole of the year 2008. In the same way we have made a radar vector by con- S. Sebastianelli et al. catenating the radar vectors we have made for every rainfall event. Finally we have calculated the Pearson correlation coefficient between the resulting radar vector and Title Page the resultant rain gauge vector, for each rain gauge, by obtaining the trend of the Pear- 15 son correlation coefficient when increasing the distance from radar related to the whole Abstract Introduction of the year 2008. It must be noted that the rainfall values lower than 0.2 mm measured by the radar Conclusions References

were considered equal to zero, because the rain gauges utilized in this work cannot Tables Figures measures a rainfall value lower than 0.2 mm. Besides, if both the homologues com- 20 ponents of the radar and the rain gauge vectors are equal to zero, they have been J I removed and they are not considered in the analysis, to avoid, if both the radar esteem a rainfall equal to zero and the rain gauge do not measures precipitation in the J I same temporal instant, the numerous couples of homologue components equal to zero Back Close increasing very much the Pearson correlation coeﬃcient values, because of the inter- 25 mittent nature of rainfall. Full Screen / Esc

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5187 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 5 Comparison between rainfall values in the adjacent pixels HESSD Figure 4 shows the trend of the correlation between adjacent pixels estimated with the three methods above-mentioned for the rainfall event of 12–13 November 2008. Each 7, 5171–5212, 2010 dot of the plots represents the mean of the values in a range of 2.5 km. 5 A rain value in a generic pixel is similar to those in adjacent pixels, especially for Comparison between stratiform rain events. However, if the considered pixel belong to a small convective rain radar and rain cell, rain values in the adjacent pixels can be very bigger or smaller as to the selected gauges data at value. Therefore, to estimate the trend of the correlation between adjacent pixels when different distances increasing the distance from radar, is necessary to consider, for each selected pixel, 10 a greater number of contiguous pixels. Besides, it can happen that the contiguous S. Sebastianelli et al. pixel can be affected by ground clutter that was not identified by the used algorithms. To mitigate the effect due to clutter contamination, it is convenient, before to estimate the Pearson correlation coefficients, to calculate the average of the rain values in all Title Page the adjacent pixels, for each considered pixel at the same distance from radar. For Abstract Introduction 15 these reasons we are chosen the third method to estimate the trend of the correlation between adjacent pixels when increasing the distance from radar. Figure 4 shows that Conclusions References the third method gives the highest values of the Pearson correlation coefficient and this fact is true for all of the rainfall events we have considered. Tables Figures In the analysis we have not considered pixels with rainfall intensity values equal to 20 zero. In fact the numerous couples of adjacent pixels with rainfall intensity values equal J I to zero increase very much the correlation coefficient value. On the other hand the J I presence of a pixel with a rainfall intensity value equal to zero in many couples of adjacent pixels decreases the correlation coefficient value (Yoo and Ha, 2007; Ha and Back Close Yoo, 2007). Full Screen / Esc 25 The correlation between adjacent pixels as a function of distance was studied also in terms of differences between the seasons and relatively to the whole set of the year 2008. We have calculated the average of the corresponding elements of each Printer-friendly Version correlation coefficients vector for each rainfall event of the same season, achieving the Interactive Discussion results showed in the Fig. 5. 5188 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion By observing the Fig. 4 we can note that the Pearson coefficient tends to decrease as the distance from radar increases and, also, that its smallest values are in the neigh- HESSD bourhood of the radar. In fact, near the radar, at the elevations we have considered, 7, 5171–5212, 2010 reflectivity values are affected by clutter due to terrain, buildings and other human- 5 made artefacts collected from antenna side lobes. Therefore near the radar there are many range-bins affected by ground clutter and probably not removed by the proce- Comparison between dure based on standard deviation of polarimetric measurements. Since often ground radar and rain clutter exhibits high decorrelation in space, for small distances from radar, the resulting gauges data at Pearson correlation coefficient has the small values in Fig. 5. As explained in the intro- different distances 10 duction, at a great distance from radar, the signal received by the radar from scatterers is so little because of geometric effect, attenuation due to precipitation, beam-blocking S. Sebastianelli et al. (in some areas), or sampling at layer above precipitation. As a consequence, the received signal is greatly influenced by noise which decorrelates the signal received by Title Page the radar. 15 That it was also performed for all the rainfall events in the year 2008, as showed in Abstract Introduction Fig. 6. The curves we have obtained, which show the trend of the correlation between ad- Conclusions References

jacent pixels, have many peaks, dues to the natural effects which occur when very Tables Figures intense rain cells in a mesoscale area decorrelate locally the meteorological signal. 20 In Fig. 5 each plot, representing the trend of the correlation between adjacent pixels J I and relatives to a specified season, is coupled with another plot which represents a typical PPI of that season. Always in Fig. 5 we can see that the Pearson correlation J I coefficient assumes lowest values in summer because of the natural effect due to iso- Back Close lated precipitation cells like those showed in the last plot in Fig. 5, whereas the other 25 two plots on the right represent the typical PPI in autumn season and in the spring sea- Full Screen / Esc son, when the great rainfall intensity regions are most extensive and regular, therefore there is more correlation between adjacent pixels (Sebastianelli et al., 2010). Printer-friendly Version

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5189 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 6 Comparison between radar and rain gauge data at different distances from radar HESSD Figure 7 shows the trend of the Pearson correlation coefficient when increasing the 7, 5171–5212, 2010 distance from radar estimated, for the rainfall events of 11–12 December 2008 and 5 of 5 December 2008, with the methodology specified in Sect. 3.2. The plots rela- Comparison between tives to the same rainfall event in Fig. 7 are referred to different time intervals. Each radar and rain point in Fig. 7 represents Pearson correlation coefficient value relatives to a single rain gauges data at gauge, calculated between the vector of radar measurements and the corresponding different distances rain gauge vector. Each rain gauge is located at a different distance from radar so every 10 point corresponds only to a distance. The dots in green, black, blue and red represent S. Sebastianelli et al. values of the Pearson correlation coefficient calculated between two vectors whose components are the rainfall amounts measured (by the radar and the rain gauges) in a time interval of 10 min, 15 min, 30 min and 1 h, respectively. Black dots refer to rain Title Page gauges which have rainfall amounts available each 15 min, as those in the Marta river Abstract Introduction 15 basin and in the Mignone river basin (except for Rocca Respampani rain gauge which provides rainfall amounts available each 5 min), while green dots refer to rain gauges Conclusions References which have rainfall amounts available each 10 min, as those located in the roman area. Blue and red dots are referred to the whole of the rain gauges considered in this study. Tables Figures By observing the Fig. 7 we can note that the Pearson correlation coefficient de- 20 creases when increasing the distance from radar, as showed by the black regression J I lines in the first four plots given for time intervals of 1 h and 30 min; in fact, at great J I distance from radar, the radar measures and the rain gauges measures are very less correlated because of a several factors about which we have discuss in the introduc- Back Close tion. For example the radar can samples above the clouds when the signal emit is very Full Screen / Esc 25 far from it otherwise, always at great distances, the raindrops maybe intercepted by the signal emit are some kilometres above the ground, therefore they precipitates in a long time, being collected by the rain gauge after a time. In this case the radar measures Printer-friendly Version and the rain gauge measures are very decorrelate. Interactive Discussion

5190 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion By comparing the plots in Fig. 7, we can also to note that, fixed a distance from radar, the Pearson correlation coefficient values increase as the time interval over which rain- HESSD fall amounts are computed increases (Krajewski, 1995; Steiner et al., 1999; Russo et 7, 5171–5212, 2010 al., 2005; Montesarchio et al., 2010; Sebastianelli et al., 2010). In fact, in a large time 5 interval a rain gauge can collect raindrops that the radar have detected before a time above it, because in this time interval the raindrops are likely precipitated. Therefore, Comparison between as discussed in the introduction, in relation to a large time interval, the radar measures radar and rain and the rain gauge measures are more correlated than the same measures relative to gauges data at a small time interval. different distances 10 By observing the Fig. 7 we can see that the Pearson correlation coefficient assumes some low values for rain gauges located within 20 km from the radar, in the roman S. Sebastianelli et al. area, even for time intervals of 30 min or 1 h. This effect is ascribed to the urban clutter, due to backscattering from buildings and other constructions which the radar main Title Page beam or its side lobes intercept in the neighbourhood of the radar. As a consequence, 15 urban clutter decorrelates radar and rain gauges measurements decreasing Pearson Abstract Introduction correlation coefficient. Besides, Figs. 7 and 10 show that, fixed a rain gauge, the correlation between rain Conclusions References

gauge measurements and radar estimates can also depend on the rainfall event con- Tables Figures sidered. For example, considering rain gauges located in roman area, their measure- 20 ments are usually correlate with radar estimates (in the absence of urban clutter), but, J I during some events, it is not true in the presence of temporary obstacles which produce ◦ ground clutter, or because the elevation angle is not always exactly equal to 1.5 , but J I it can changes (for example because of the wind action) and, since near the radar the Back Close radar beam is not so high, small variations of the elevation angle are suﬃcient so that 25 the radar beam intercepts some obstacle, which produces a not meteorological signal Full Screen / Esc at the receiver. Figure 8 shows that, considering a rainfall event made by linking together all the Printer-friendly Version events utilized in this work, Interactive Discussion

5191 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion we can give the same comments given about the trend of the Pearson correlation coefficient showed in Fig. 7 for a single rainfall event. HESSD Further to the comments done for the Figs. 7 and 8, Fig. 9 shows also the trend, 7, 5171–5212, 2010 when increasing the distance from radar, of the differences between Pearson correla- 5 tion coefficient values relative to different time aggregations, for the rainfall events of 12–13 November 2008, of 5 December 2008 and for the whole of the events utilized in Comparison between this work; the plots in Fig. 9 show that by increasing the time interval utilized to calcu- radar and rain late the rainfall values (in mm) from 10 min up to 1 h or from 15 min up to 1 h (depending gauges data at on the considered rain gauges), the corresponding increase of the Pearson correlation different distances 10 coefficient, indicated in Fig. 9 by the differences r60−r10 represented by green dots and S. Sebastianelli et al. r60−r15 represented by black dots respectively, is greater close to the radar because of the lowest radar beam with respect to the rain gauges as explained in the introduction (Sebastianelli et al., 2010). Title Page The single plots in Fig. 10 show the trend of the Pearson correlation coefficient with 15 increasing the distance from radar estimated for rainfall cumulated in different time Abstract Introduction intervals. The first plot concerns the rainfall event of 5 December 2008, the second plot is relative to the rainfall event of 11–12 December 2008, the third plot was made Conclusions References

considering the rainfall event of 25–26 November 2008 and the fourth plot is referred Tables Figures to the whole of the rainfall events utilized in this work. 20 The violet arrows in Fig. 10 shown that the Pearson correlation coefficient values J I relative to rain gauges localized in Fig. 15, for each time interval, are generally lower than Pearson coefficient values concerned rain gauges at comparable distances from J I radar because off the beam-blockage. But, in some rainfall events, rainfall measure- Back Close ments performed by a rain gauge situated in a cone of shade (due to beam-blocking) 25 are correlated with radar estimates. That occurs if there are, between the two devices, Full Screen / Esc some range-bins affected by ground clutter not removed by the removal algorithm, and if there is a very intense precipitation on the pixel where belong the rain gauge. In Printer-friendly Version fact the reflectivity factor due to ground clutter is comparable with those due to an intense storm. Nevertheless, as showed in the last plot in Fig. 10 (down on the right), Interactive Discussion

5192 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion considering a rainfall event made by linking together all the events utilized in this work, measurements of rain gauges located into a cone of shade (showed by Fig. 15) are not HESSD much correlated with radar estimates. 7, 5171–5212, 2010 Finally, we have compared the trend of the radar beam with the altimetrical profile 5 when increasing the distance from radar, to investigate the visibility of the radar beam for all the pixels where belong the range-bins utilized in this study. Comparison between The Digital Elevation Model (DEM) we have utilized is the Italy.bin file, with a pixel radar and rain resolution of 800×600 m, which is product by Servizio Geologico Nazionale. gauges data at Each plot in Figs. 11, 12, 13 and 14 shows that there is not beam-blocking, because different distances 10 the radar beam do not intercepts the altimetrical profile along the course from radar to rain gauge (unless anomalous propagations), therefore the radar can samples in the S. Sebastianelli et al. volume aloft above the rain gauge specified by the plot. In the plots in Fig. 15 we can observe a total or partial radar beam-blocking caused Title Page by relieves located between the radar and the pixels where the rain gauges considered 15 by the plots belong. In cases of partial beam-blocking the radar data and the rain Abstract Introduction gauges data are very decorrelate or not correlate, in fact the radar underestimates the rainfall rate because only a part of the radar beam intercepts the raindrops, while in Conclusions References

case of total beam-blocking the radar cannot measures in a sampling volume above Tables Figures the rain gauge.

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For several reasons radar and rain gauge quantitative measurements of precipitation Back Close can be different. Rain gauge and radar are very different precipitation measuring devices: rain gauge makes a point measurements integrated in time at ground, while Full Screen / Esc radar instantaneously samples precipitation in a volume aloft. Besides, since radar 25 measures precipitation at a given height, rainfall is registered by the rain gauge below Printer-friendly Version the rain cell with a delay with respect to the radar which depends on the time needed Interactive Discussion to raindrops to precipitate. The rain gauge observations are affected by errors due to 5193 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion different causes, like internal frictions and occasional imperfections of the rain gauge, reading errors, presence of wind, trees or buildings that distorts the rain gauge mea- HESSD sures. Radar measurements are affected by several sources of error, some of which 7, 5171–5212, 2010 determine errors that can be considered as depending on the distance from radar. In 5 this work we have showed that both the correlation between rain gauge and radar measures and the correlation between rainfall values in the adjacent pixels decreases when Comparison between increasing the distance from radar. As shown by the results in Sect. 6, it is not possible radar and rain to characterize discrepancies between measurements of the two instruments only as gauges data at a function of distance from radar site. Other sources of error should be considered. different distances 10 Nevertheless, the correlation coefficient exhibits a trend with the distance that must be accounted for when radar rainfall data are interpreted to study the spatial correlation of S. Sebastianelli et al. rainfall events.

Acknowledgements. The authors thank Eugenio Gorgucci of the Institute of Atmospheric Title Page Sciences and Climate of the National Research Council for interesting discussions and Abstract Introduction 15 suggestions.

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References Tables Figures Bringi, V. N. and Chandrasekar, V.: Polarimetric Doppler Weather Radar: Principles and Appli- cations, Cambridge University Press, New York, USA, 648 pp., 2001. J I Battan, L. J.: Radarmeteorologia, Zanichelli editore, Bologna, Italy, 1970. J I 20 Berenguer, M. and Zawadzki, I.: A Study af the Error Covariance Matrix of Radar Rainfall Estimates in Stratiform Rain, Weather Forecast., 23, 1085–1101, 2008. Back Close Berenguer, M. and Zawadzki, I. A.: Study af the Error Covariance Matrix of Radar Rainfall Estimates in Stratiform Rain. Part II: Scale Dependence, Weather Forecast., 24, 800–811, Full Screen / Esc 2009. 25 Clothier, A. and Pegram, G.: Space-time modelling of rainfall using the String of beads model: Printer-friendly Version integration of radar and raingauge data, Water Research Commission, WRC Report No. 1010/1/02, Durban, South Africa, 166 pp., 2002. Interactive Discussion

5194 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Dirks, K. N., Hay, J. E., Stow, C. D., and Harris, D.: High-resolution studies of rainfall on Norfolk Island. Part II: Interpolation of rainfall data, J. Hydrol., 208, 187–193, 1998. HESSD Gorgucci, E. and Baldini, L.: An Examination of the Validity of the Mean Raindrop-Shape Model for Dual-Polarization Radar Rainfall Retrievals, Geoscience and Remote Sensing, 7, 5171–5212, 2010 5 IEEE Transactions on, vol. 47, 8, 2752-2761, doi: 10.1109/TGRS.2009.2017936, 2009. Gorgucci, E., Baldini, L., and Volpi, A.: Polar 55C: an upgraded instrument for polarimetric radar research, Proc. of the 2nd European Conf. of Radar Meteorology ERAD, Delft, The Comparison between Netherlands, 18–23 November 2002, 394–399, 2002. radar and rain Gorgucci, E., Scarchilli, G., and Chandrasekar, V.: Radar and surface measurements of rainfall gauges data at 10 during CaPE, J. Appl. Meteorol., 34, 1570–1577, 1995. different distances Ha, E. and Yoo, C.: Use of mixed bivariate distributions for deriving inter-station correlation coefficients of rainfall, Hydrol. Process., 21(22), 3078–3086, 2007. S. Sebastianelli et al. Krajewski, W. F.: Rainfall estimation using weather radar and ground stations, in: Proceedings of the III Intemational Symposium on Weather Radars, San Paulo, Brazil, 1995. 15 Lombardo, F., Napolitano, F., and Russo, F.: On the use of radar reflectivity for estimation of the Title Page areal reduction factor, Nat. Hazards Earth Syst. Sci., 6, 377–386, doi:10.5194/nhess-6-377- 2006, 2006. Abstract Introduction Lombardo, F., Napolitano, F., Russo, F., Scialanga, G., Baldini, L., and Gorgucci, E.: Rainfall estimation and ground clutter rejection with dual polarization weather radar, Adv. Geosci., 7, Conclusions References 20 127–130, doi:10.5194/adgeo-7-127-2006, 2006. Lopez, V., Napolitano, F., and Russo, F.: Calibration of a rainfall-runoff model using radar and Tables Figures raingauge data, Adv. Geosci., 2, 41–46, doi:10.5194/adgeo-2-41-2005, 2005. Maheepala, U. K., Takyi, A. K., and Perera, B. J. C.: Hydrological data monitoring for urban J I stormwater drainage systems, J. Hydrol., 245, 32–47, 2001. 25 Montesarchio, V., Russo, F., Napolitano, F., Lombardo, F., and Baldini, L.: Study on the rainfall J I dependence structure using radar and rain gauge data, in: Proceedings of the International Workshop Advances in statistical hydrology, Taormina, ltaly, 23–25 May 2010, 24, 2010. Back Close Pegram, G. and Clothier, A.: High resolution space-time modelling of rainfall: the “String Full Screen / Esc of beads” model, Water Research Commission, Durban, South Africa, WRC Report No. 30 752/1/99, 115 pp., 1999. Pruppacher, R. and Beard, K. V.: A wind tunnel investigation of the internal circulation and Printer-friendly Version shape of water drops falling at terminal velocity in air, Q. J. Roy. Meteor. Soc., 96, 247–256, 1970. Interactive Discussion 5195 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Russo, F., Lombardo, F., Napolitano, F., and Gorgucci, E.: Rainfall stochastic modelling for runoff forecasting, Phys. Chem. Earth, 31(18), 1252–1261, 2006. HESSD Russo, F., Napolitano, F., and Gorgucci, E.: Rainfall monitoring systems over an urban area: the city of Rome, Hydrol. Process., 19(5), 1007–1019, 2005. 7, 5171–5212, 2010 5 Sebastianelli, S., Russo, F., Napolitano, F., and Baldini, L.: Comparison between radar and rain gauges data at different distances from radar and correlation existing between the rainfall values in the adjacent pixels, in: Proceedings of the International Workshop Advances in Comparison between statistical hydrology, Taormina, Italy, 23–25 May 2010, 31, 2010. radar and rain Steiner, M., Smith, J. A., Burges, S. J., Alonso, C. V., and Darden, R. W.: Effect of bias adjust- gauges data at 10 ment and rain gauge data quality control on radar rainfall estimation, Water Resour. Res., different distances 35(8), 2487–2503, 1999. Vaes, G., Wt1lems, P., and Berlamont, J.: Rainfall input requirements for hydrological calcula- S. Sebastianelli et al. tions, Urban Water J., 3, 107–112, 2001. Villarini, G. and Krajewski, W. F.: Review of the different sources of uncertainty in single polar- 15 ization radar-based estimates of rainfall, Surv. Geophys., 31(1), 107–129, 2010. Title Page Yoo, C. and Ha, E.: Effect of zero measurements on the spatial correlation structure of rainfall, Stoch. Env. Res. Risk. A., 21(3), 287–297, 2007. Abstract Introduction Zawadzki, I.: On radar-rain gauge comparison, J. Appl. Meteorol., 14, 1430–1436, 1975. Conclusions References

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Table 1. Rain gauges considered in the analysis, their distances (in km) from radar and Carte- HESSD sian coordinates (in km) of the barycentre of the pixels where belong the rain gauges. 7, 5171–5212, 2010 Rain gauge Distance from radar Abscissa Ordinate Acilia 23.269 −22.5 −7.5 Acqua Acetosa 16.647 −12.5 11.5 Comparison between Alatri 60.631 58.5 −14.5 Allumiere 70.719 −60.5 37.5 radar and rain Borgo s. Maria 43.972 12.5 −42.5 gauges data at Bracciano 48.854 −38.5 30.5 Capannacce 11.139 −0.5 11.5 diﬀerent distances Casilino 8.944 −8.5 3.5 Cassiodoro 16.712 −14.5 7.5 Castello Vici 41.780 −29.5 29.5 S. Sebastianelli et al. Cerveteri 48.218 −44.5 19.5 Civitavecchia 76.965 −70.5 30.5 Eleniano 12.343 −10.5 5.5 Eur 12.621 −12.5 −1.5 Title Page Falcognana 11.237 −7.5 −8.5 Flaminio 24.578 −15.5 19.5 Fregene 38.092 −37.5 4.5 Abstract Introduction Isola Sacra 35.347 −34.5 −7.5 La Storta 28.889 −21.5 18.5 Conclusions References Mignone 81.554 −70.5 41.5 Monte Mario 19.785 −16.5 10.5 Tables Figures Ostia 32.184 −30.5 −11.5 Ostiense 14.139 −13.5 4.5 Ottavia 23.371 −19.5 13.5 Poggio Mirteto 46.374 2.5 46.5 J I Ponte Felice 58.861 −13.5 57.5 Ponte Galeria 24.584 −24.5 −0.5 Posticciola 50.070 25.5 43.5 J I Regillo 8.593 7.5 3.5 Rieti 65.209 20.5 61.5 Back Close Rocca Respampani 84.830 −57.5 62.5 Rocca Sinibalda 55.413 23.5 50.5 Full Screen / Esc Roma est 10.804 −5.5 9.5 Roma nord 18.564 −12.5 13.5 Roma sud 18.377 −18.5 −1.5 S. Martino 61.201 29.5 53.5 Printer-friendly Version Tarquinia 88.131 −73.5 48.5 Via Marchi 13.892 −10.5 9.5 Interactive Discussion

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Fig.3 8. Trend of the Pearson correlation coeﬃcient when increasing the distance from radar Full Screen / Esc estimated for all the rainfall events considered in this study, by utilizing time intervals of 1 h (in red),4 Figure 30 min (in8. Trend blue), 10of the min Pearson (in green) correlation and 15 min coe (infficient black). when increasing the distance from radar Printer-friendly Version 5 estimated for all the rainfall events considered in this study, by utilizing time intervals of 1 Interactive Discussion 6 hour (in red), 30 minutes (in blue), 10 minutes (in green) and 15 minutes (in black). 7 5205

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Capannacce: azimuth(°) = 359.5011; elevation(°) = 1.5 Casilino: azimuth(°) = 295.2615; elevation(°) = 1.5 Eleniano: azimuth(°) = 298.9468; elevation(°) = 1.5 3000 3000 3000

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Eur: azimuth(°) = 263.2612; elevation(°) = 1.5 Ostiense: azimuth(°) = 288.3452; elevation(°) = 1.5 Falcognana: azimuth(°) = 222.5693; elevation(°) = 1.5 3000 3000 3000 diﬀerent distances

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Via Marchi: azimuth(°) = 311.6325; elevation(°) = 1.5 Regillo: azimuth(°) = 66.1106; elevation(°) = 1.5 Roma Est: azimuth(°) = 329.8585; elevation(°) = 1.5 3000 3000 3000 Conclusions References

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Acilia: azimuth(°) = 252.255; elevation(°) = 1.5 Acqua Acetosa: azimuth(°) = 311.9662; elevation(°) = 1.5 Cassiodoro: azimuth(°) = 298.1245; elevation(°) = 1.5 3000 3000 3000

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0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120 2 Distance from radar (km) Distance from radar (km) Distance from radar (km) Title Page Ottavia: azimuth(°) = 304.7257; elevation(°) = 1.5 Roma Nord: azimuth(°) = 318.8701; elevation(°) = 1.5 Ponte Galeria: azimuth(°) = 268.1749; elevation(°) = 1.5 3000 3000 3000

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Bracciano: azimuth(°) = 308.4818; elevation(°) = 1.5 Castello Vici: azimuth(°) = 314.7644; elevation(°) = 1.5 Cerveteri: azimuth(°) = 293.3164; elevation(°) = 1.5 3000 3000 3000 HESSD 2500 2500 2500

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Fregene: azimuth(°) = 276.459; elevation(°) = 1.5 Isola Sacra: azimuth(°) = 258.5133; elevation(°) = 1.5 Ostia: azimuth(°) = 249.1616; elevation(°) = 1.5 3000 3000 3000 diﬀerent distances

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Allumiere: azimuth(°) = 301.7345; elevation(°) = 1.5 Civitavecchia: azimuth(°) = 293.6764; elevation(°) = 1.5 Rieti: azimuth(°) = 18.0557; elevazione(°) = 1.5 3000 3000 3000

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Mignone: azimuth(°) = 300.8234; elevation(°) = 1.5 Rocca Respampani: azimuth(°) = 317.3332; elevation(°) = 1.5 Tarquinia: azimuth(°) = 303.6399; elevation(°) = 1.5 Title Page 3000 3000 3000

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Alatri: azimuth(°) = 103.4463; elevation(°) = 1.5 Borgo s. Maria: azimuth(°) = 163.1962; elevation(°) = 1.5 Posticciola: azimuth(°) = 30.6949; elevation(°) = 1.5 Comparison between 3000 3000 3000 radar and rain 2500 2500 2500 gauges data at 2000 2000 2000 diﬀerent distances 1500 1500 1500 Altitude (m s. l. s.m.) l. (m Altitude Altitude (m s. l. s.m.) l. (m Altitude Altitude (m s. l. m.) s. l. (m Altitude 1000 1000 1000 S. Sebastianelli et al.

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