Journal of Hydrology

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1 Journal of Hydrology xxx (2010) xxx xxx Contents lists available at ScienceDirect Journal of Hydrology journal homepage: Performance evaluation of high-resolution rainfall estimation by X-band dual-polarization radar for flash flood applications in mountainous basins Marios N. Anagnostou a, *, John Kalogiros b, Emmanouil N. Anagnostou a,c, Michele Tarolli d, Anastasios Papadopoulos a, Marco Borga d a Institute of Inland Waters, Hellenic Centre for Marine Research, Anavissos, Greece b Institute for Environmental Research and Sustainable Development, National Observatory of Athens, Athens, Greece c Civil and Environmental Engineering, University of Connecticut, CT, USA d Department of Land and Agroforest Environment, University of Padova, Padova, Italy article info summary Article history: Available online xxxx Keywords: Rainfall estimation High-resolution X-band Dual-polarization Flash flood Mountainous basins Bright band Vertical profile of reflectivity (VPR) Different relations between surface rainfall rate, R, and high-resolution polarimetric X-band radar observations were evaluated using a dense network of rain gauge measurements over complex terrain in Central Italian Alps. The specific differential phase shift, K DP, rainfall algorithm (R KDP ) although associated with low systematic error it exhibits low sensitivity to the spatial variability of rainfall as compared to the standard algorithm (R STD ) that is based on the reflectivity-to-rainfall (Z R) relationship. On the other hand, the dependence of the reflectivity measurement on the absolute radar calibration and the rain-path radar signal attenuation introduces significant systematic error on the R STD rainfall estimates. The study shows that adjusting the Z R relationship for mean-field bias determined using the R KDP estimates as reference is the best technique for acquiring unbiased radar-rainfall estimates at fine space time scales. Overall, the bias of the R KDP -adjusted Z R estimator is shown to be lower than 10% for both storm cases, while the relative root-mean-square error is shown to range from 0.6 (convective storm) to 0.9 (stratiform storm). A vertical rainfall profile correction (VPR) technique is tested in this study for the stratiform storm case. The method is based on a newly developed VPR algorithm that uses the X-band polarimetric information to identify the properties of the melting layer and devices a precipitation profile that varies for each radar volume scan to correct the radar-rainfall estimates. Overall, when accounting for the VPR effect there is up to 70% reduction in the systematic error of the 3 elevation estimates, while the reduction in terms of relative root-mean-square error is limited to within 10%. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Flooding is still the most damaging of all natural disasters; onethird of the annual natural disasters and economic losses and more than half of all victims are flood related (Douben, 2006). In Europe, we count an average of 130 fatalities due to floods per year (Barredo, 2007); of these, 40% are due to flash floods. Flash floods are associated with heavy precipitation events induced often by rough orography as is the case for most of the storms in the Mediterranean coastal area or in the Alpine region in Europe (Gaume et al., 2009). Most flash flood generating storms are associated with Mesoscale weather systems that is, systems with horizontal scales of km (Borga et al., 2008). Generally, complex topography can exaggerate the spatial variability of rainfall, since synoptically forced flows toward and over a topographic barrier may interact with and enhance storm dynamics (Smith, 1979). This * Corresponding author. Tel.: address: managnostou@ath.hcmr.gr (M.N. Anagnostou). may lead to slow-moving or quasi-stationary storms that due to local terrain-morphology can produce heavy rainfall associated with both increased rain durations and intensities over small areas (Rotunno and Ferretti, 2001; Medina and Houze, 2003). Oftentimes, storms developing in mountainous regions are affected by a boundary layer jet (influenced by a stalled frontal boundary) that feeds near-saturated air, thereby creating well-organized formations of precipitation through warm rain processes at relatively low levels in the storm (Petersen et al., 1999; Smith et al., 2000; Kelsch, 2001). This low level enhancement effect of rainfall intensity creates a real challenge for remote sensing (both ground radar and satellites) detection. For ground radars in particular monitoring long ranges, issues with partial beam blockage of the lower beam elevations or with the overshooting of low-level convection signatures by the upper elevation beams may lead to significant range dependent errors in precipitation estimation (White et al., 2003; Smith et al., 2005). In addition, melting snow in widespread storm systems resulting in intense and persistent surface rainfall may substantially increase the threat of flooding in complex /$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi: /j.jhydrol

2 2 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx terrain basins (Barros and Kuligowski, 1998; Smith et al., 2005). Therefore, advancing the quantitative precipitation estimation from remote sensing in mountainous regions is of great importance and practical use in improving the predictability of hydrological impacts such as flash floods and hydrogeological risks and facilitating efficient water management practices. Current operational rainfall monitoring systems based on national weather radar networks operating on the basis of long-range coverage do not provide sufficient measurements to support accurate estimations of precipitation variability in complex terrain. Studies have shown that precipitation estimation from conventional long-range weather radar observations is affected by significant systematic and random error associated with a host of sources ranging from the variability in the relationship for reflectivity-to-rainfall inversion to beam geometry and elevation issues including the rain-path attenuation of signal power, the vertical precipitation structure affecting higher elevation angles and longer ranges and the partial or total beam occlusion affecting lower elevation beams (e.g., Zawadzki, 1984; Austin, 1987; Joss and Waldvogel, 1990; Kitchen and Jackson, 1993; Joss and Lee, 1995). In the past two decades studies have shown that polarization diversity in weather radar can improve the accuracy of rainfall estimation in different ways (Seliga and Bringi, 1976, 1978; Testud et al., 2000; Bringi and Chandrasekar, 2001; Bringi et al., 2002, 2004). Polarimetric information introduces along with the horizontal polarization (Z H in dbz) reflectivity measurement additional parameters such as the differential reflectivity (Z DR in db the ratio of the horizontal to vertical polarization reflectivity) and the differential propagation phase shift (U DP in ). The U DP is a powerful radar parameter for use in quantitative precipitation estimation (QPE) because it is immune to signal power issues, i.e., the attenuation from rainfall or other atmospheric sources and the absolute radar calibration (Ryzhkov and Zrnic, 1996; Testud et al., 2000; Gorgucci et al., 2001, 2002; Bringi and Chandrasekar, 2001; Bringi et al., 2002; Brandes et al., 2003; Anagnostou et al., 2006a,b; Matrosov et al., 2002, 2005). Furthermore, the availability of multiple partially-independent parameters available for any single radar sampling volume can now facilitate precipitation classification and rainfall drop size distribution estimation, which in turn can further improve the rainfall estimation accuracy (Gorgucci et al., 2000, 2001; Brandes et al., 2004; Bringi et al., 2002, 2004; Matrosov et al., 2005). Polarization diversity has a significant impact on attenuating frequency (X-band) radars advancing their potential for use in heavy precipitation estimation. Even though, the typical range of an X- band radar can be short ( km) compared to the long-range operational weather radars (consisting primarily of S-band, e.g., WSR-88D network in US, and C-band radars, e.g., radar networks in Europe), these are low-power and cost effective systems that can be used to fill up critical gaps of the long-range national radar networks. Deployment of local X-band radars can be particularly important for monitoring small-scale basins in mountainous regions and urban areas that are prone to flash floods but are not adequately covered by existing long-range radar networks. The primary disadvantage of X-band frequency is the enhanced rain-path attenuation in power related (Z H and Z DR ) measurements as compared to the S-band (and to the moderate attenuation at C- band) frequency, including the potential for complete signal loss in cases of signal propagation through large paths (>10 km) of heavy rainfall (or mixed phase precipitation). Current research on X-band rainfall measurements shows that the fundamental issue of rainpath signal attenuation at X-band can be reliably resolved using the differential phase shift (U DP ) measurement (Anagnostou et al., 2004, 2006a,b; Matrosov et al., 2005; Park et al., 2005). Furthermore, due to the local deployment and the increased sensitivity of U DP change to precipitation intensity (about three times that of S-band frequency), radar measurements at X-band may achieve higher resolution rain rate estimations than the lower frequency (C-band and S-band) operational radar systems, which is one of the critical issues for local flood applications. However, there are several features of the X-band radar-rainfall measurement that need to be researched to understand the full potential of this radar frequency in flash flood applications. These include issues with respect to: (1) the effect of mixed phase precipitation along the radar ray on the accuracy of polarimetric based rain-path attenuation correction; (2) the consequential effect of attenuation correction uncertainty and Mie resonance effect on precipitation estimation in intense rain storms; and (3) the scale and range dependence of X-band rainfall estimation accuracy and the consequential impact on flood prediction accuracy in small-scale basins. In this work we devise an experimental study to evaluate the use of locally-deployed X-band dual-polarization radar for estimation of rainfall at high spatial and temporal scale over complex terrain. We present a comprehensive error analysis evaluating different rainfall algorithms and the use of a vertical rainfall profile correction technique in high-resolution quantitative precipitation estimation. The study is based on two precipitation systems representing different rainfall intensities as well as spatial and vertical structures. The novelty of this work is the use of a dense mountainous network of rain gauges providing ground truth rainfall observation at different ranges from an X-band dual-polarization radar (from 5 up to 60 km). In the following section we present the study area and experimental data, while in Section 3 we present the rainfall algorithms and the vertical profile of rainfall structure correction technique investigated in this study. In Sections 4 and 5 we present the evaluation results and discuss our conclusions and recommendations for future research in Section Experimental area and data The study is based on radar data collected with the National Observatory of Athens (NOA) dual-polarization X-band radar (hereafter named XPOL) deployed in an experimental area of the Northeast Italian Alps over a period of three months (August October, 2007). The area is part of a Hydro-meteorological Observatory (HO) that provides data on flash floods for a project named HY- DRATE (Hydro-meteorological data resources and technologies for effective flash flood forecasting) funded by the European Commission. In Fig. 1 we show the location and measurement range of the XPOL radar and the in situ rain gauge network (50 tipping bucket gauges) providing half hourly rainfall measurements within the XPOL radar range. As shown in the figure, the XPOL observations cover an experimental basin of 1200 km 2 (named Bacchiglione) and its sub-basin Posina (125 km 2 ). The altitude range of the experimental area is from 100 to 2500 m above sea level (a.s.l). The area frequently receives very intensive rainstorms, resulting in severe erosion and flash floods (particularly in the Posina basin). This steep environmental gradient from North to South is associated with climatic differences (Dinku et al., 2002), e.g., annual precipitation ranges from 2000 to 1000 mm per year and mean annual temperatures from 5 to 14 C. Below we provide description of the XPOL and rain gauge data. The XPOL radar was placed 4 km south of the city of Folgaria, in the Italian Alps (see Fig. 1) at 1650 m a.s.l. The radar was operated remotely only when there was a forecast for rain event in the nearby area. The radar was operated first in a range height indicator (RHI) mode taking two RHI measurements from 0 to 45 elevations and then in a planar position indicator (PPI) mode taking measurements in a 360 sector scan, at 2 and 3 elevation sweeps with its optimum highest range resolution (120 m) for the total range of 50 km. Antenna rotation rate was 10 s 1 for PPI and

3 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx 3 Fig. 1. Map of the experimental area showing the radar coverage, rain gauge network and the two basins: Bacchiglione (light gray shading) and its sub-basin Posina (red shading). The solid line indicates the maximum XPOL range of 50 km. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3 s 1 for RHI mode. The time period for a full volume scan was less than 3 min. The 2 lowest elevation sweep was selected to moderate ground clutter and beam blockage in the south-to-south west and northern section of the sector. For the objective of this study we selected XPOL data from two distinct rainstorm events that created moderate flooding in the Posina basin. The first was a convective storm that persisted for 36 h between August 7 and 8 (2007) creating rain bands within the XPOL area particularly over the Posina basin. The second storm was a widespread system with short duration (8 h) that took place on the 6th of October (2007) with distinct bright band signatures on all radar parameters (Z H, Z DR and co-polar correlation coefficient, q hv ). In Fig. 2 we show the frequency plots of the retrieved rainfall rates (using the standard Z R technique) for the two rain events from XPOL Z H data from the 2 to 3 elevation angle. The reflectivity data are corrected for the percentage (%) of beam blockage due to ground clutter, which is presented in Fig. 3 for the two elevation angles. The beam occlusion was calculated using high resolution (40 m) terrain data of the area and a three dimensional model of the radar beam propagation assuming beam refraction of standard atmospheric conditions and accounting for the Earth curvature effect (Anagnostou and Krajewski, 1997). A point to note from Fig. 2 is a shift in the rainfall distribution to high rain accumulations when it comes to the convective storm case. Another point to note is the significant shift to smaller values in the mode of the distribution of the convective storm rain rates from the 2 (mode at around 35 mm) to 3 (mode at around 15 mm) XPOL estimates. On the other hand, we note a slight shift to larger values for the tails of the distribution of the stratiform rain rates from the 2 to 3 XPOL estimates. Both are related to the effect of the vertical precipitation structure (melting layer) on the XPOL estimates. For the qualitative and quantitative validation of radar-rainfall estimation algorithms this study uses the dense in situ network of the Italian HO. A total number of 50 calibrated tipping-bucket rain gauges were deployed in the area within the XPOL radar coverage. The gauges to be used in the error analysis were selected based on the clearance of their respective location relative to the radar (i.e., beam occlusion below 5%). Fig. 3 shows the total number of gauges associated with 2 (32) and 3 (all 50 gauges) beam occlusions less than 5%. 3. Rainfall estimation algorithms Rainfall varies both in space and time thus making its accurate estimation an extremely difficult task. Since radar does not mea-

4 4 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx Fig. 2. Histograms of the storm-total rainfall accumulations derived from R STD rainfall rates for the two storm cases. Panels (a) and (b) represent data from 2 to 3 beam elevations. Fig. 3. Beam occlusion maps of XPOL for 2 (left panel) and 3 (right panel) beam elevation measurements. sure rainfall directly but rather we relate the measured variable (e.g., radar reflectivity) with rainfall properties, accurate estimation of rainfall requires a model that would best describe the physical properties of rain formation. For decades rainfall estimates were derived from the single polarization radar measurement, i.e., the radar reflectivity factor (Z) (e.g., Atlas and Ulbrich, 1990; and Joss and Waldvogel, 1990). Dual-polarization offers more than one parameters (Z H, Z DR, U DP ) that can facilitate the use of multiparameter rainfall estimation algorithms. The relationships described in this section were derived from T-matrix scattering simulations (Barber and Yeh, 1975; Ishimari, 1991) based on a normalized Gamma distribution (Bringi and Chandrasekar, 2001) for the rainfall drop size distribution (DSD), a linear drop axis ratio model (Pruppacher and Beard, 1970; Matrosov et al., 2002) with a Gaussian distribution model with zero mean and 7.5 standard deviation for the droplets canting angle (Bringi et al., 2003) and a broad range of rainfall DSD parameters derived from high-resolution (1-min averages) spectral data. The dielectric constant of the water was evaluated for an average atmospheric temperature of 10 C). The raindrop spectra were based on longterm (1 year) DSD measurements from a 2D-video (2DVD) disdrometer in the urban area of Athens, Greece in and rain periods Radar-rainfall estimation algorithms Following the normalized Gamma rainfall DSD distribution model the rainfall rate (mm h 1 ) is calculated from the following integral: R ¼ 0:6p10 3 X i t i ðd i ÞD 3 i N iðd i Þ where the t i (D i ) (in m s 1 ) is the drop terminal velocity (at sea level; Gunn and Kinzer, 1949; Atlas and Ulbrich, 1977), D i in mm and N i (D i ) the number of drops (m 3 ) in the interval D i D i+1 (Bringi and Chandrasekar, 2001). The radar algorithms described below are based on power law relationships determined on the basis of least squares fitting of the radar parameters Z H and K DP to rain rate, ð1þ

5 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx 5 R, derived from the measured DSD spectra. Below we discuss the three rainfall algorithms used in this study Differential phase shift-rainfall relationship Differential phase shift is one of the most significant polarimetric radar variables because its first derivative, called specific differential phase shift (K DP, in km 1 ), for X-band radars is nearly linearly related to the rainfall rate. The power-law fit relationship derived from the T-matrix simulations using the above mentioned DSD observations is the following: R KDP ¼ 19:26K 0:85 DP A point to note is that the K DP -based rainfall estimator is immune to power related issues such as the rain-path attenuation and radar calibration. However, a critical weakness is the noise of the K DP parameter, which is the derivative of the differential phase shift. Consequently, the K DP -based rainfall estimates are representative of range averages over several radar gates (i.e., typically of a few kilometers). The X-band frequency has an advantage over lower frequencies on this issue because the differential phase signals are approximately proportional to the reciprocal of the wavelength (in the Rayleigh scattering regime); as a result the differential phase at X-band is about three times more sensitive to rainfall variations than S-band. This results in higher sensitivities to low rainfall intensities (Matrosov et al., 2006; Matrosov, 2009); for example, the X-band R KDP estimates are useful for rainfall rates greater than 1 mm h 1, while the corresponding threshold for S-band frequency is in the range of 5 8 mm h Standard reflectivity-to-rainfall relationship This is the most widely used method in radar-rainfall estimation (hereafter called R STD ) as it relates directly to the radar reflectivity measured by any conventional weather radar. The powerlaw fit of this relationship derived from the T-matrix simulations using the above mentioned DSD observations is the following: R STD ¼ 3: Z 0:58 Hmm where Z Hmm denotes the horizontal polarization reflectivity (in mm 6 m 3 ). This radar retrieval is susceptible to radar calibration errors and to the variability of the rainfall DSD (Doviak and Zrnić, 1993). One approach to limit the effect from these issues is to make this relation immune to radar calibration uncertainties and make the relationship to rainfall more robust with respect to DSD variation using polarimetric parameters (e.g., Ryzhkov et al., 2005) Differential phase-based bias adjusted Z R relationship As discussed above, the K DP rainfall estimator is immune to the radar absolute power calibration and is moderately affected by the natural variability of DSD. On the other hand the R STD technique that uses reflectivity information (Z H ) alone although more suitable to provide high-resolution information on rainfall variability since it is power related it is susceptible to radar calibration, attenuation correction and DSD variability uncertainties (Hogan, 2007). Typically, Z R relationships are used in conjunction with in situ rain gauge rainfall measurements to track variations of the Z R systematic error related to corresponding variations in the rainfall DSD. For a polarimetric radar there is no need to use in situ gauge measurements as one can evaluate the systematic error of R STD through mean-field comparisons against the R KDP estimates (Gorgucci et al., 1992). The mean-field bias ratio of R KDP to R STD was determined in this study for every half hour time intervals using estimates from the 2 elevation scan (i.e., the lowest bean elevation), for cells associated with R KDP values greater than 0.1 mm h 1 and beam occlusion less that 5%. The bias ratio estimated every half hour is then applied on the R STD estimates to produce adjusted R STD rainfall ð2þ ð3þ fields. The intention of this method is not to apply a temporarily or spatially varying calibration factor but to estimate a mean calibration factor for each event or each type of event (stratiform or convective rain) because R KDP is expected to be unbiased on average but not for each measurement (i.e., at each time it is not an accurate rainfall estimator) Vertical precipitation profile effect on rainfall estimation Conditions of freezing levels affecting radar observations is typical when the radar is deployed in complex terrain and for low to moderate precipitation events associated with weak vertical motion (i.e., stratiform rain type). The effect of melting layer on radar reflectivity is called bright band, because of the enhancement apparent at the reflectivity factor, which can significantly bias rainfall estimates (Fabry and Zawadzki, 1995). In the case of X-band measurements the effect of mixed phase precipitation on dualpolarization measurements complicates the attenuation correction and polarimetric rainfall algorithms. Due to the quick rise of radar beam with distance at high elevation angles, it is necessary to develop an approach to identify the rain, melting layer and snow regions in each radar ray and quantify the surface rainfall for the range gates falling in those regions. The method examined in this study is based on a modified vertical profile correction (VPR) algorithm (Kalogiros et al., submitted for publication) that uses the polarimetric information (i.e., q hv and Z H ) to identify the properties of the melting layer in a way similar to Matrosov et al. (2007). The boundaries of the melting layer were detected using q hv similar with Matrosov et al. (2007). For the XPOL radar the q hv in rain is generally greater than and in snow regions. The melting layer boundaries are identified in each ray as the lowest altitude where q hv first decreases below 0.96 (base h b ) or first increases again above 0.95 (top h t ). Also, the minimum value of q hv in the melting layer should be below 0.93 for acceptable detection. An average shape for the precipitation profile in each PPI versus normalized height is used to correct each ray for the melting layer effect and it is estimated as described below. The normalization of height h in the melting layer h n =(h h b )d av /d uses the base h b and the depth d = h t h b of the melting layer in each ray, where d av is the average depth of the melting layer in the PPI. Above the melting layer a simple additive height adjustment is used in order to have continuity of normalized height at h t. This height normalization removes the differences in melting layer base and depth between the rays of the PPI. The precipitation profile is also normalize with the precipitation value at the base of the melting layer in order to remove changes in estimated rainfall at that altitude from ray to ray. The averaging of height normalized precipitation profiles in each PPI assumes that the shape and intensity of the precipitation peak in the melting layer as well as the decrease of estimated precipitation above the melting layer (snow region) is constant (a profile bias with variation within the PPI) but may vary from PPI to PPI. We do not use a predefined intensity of the precipitation peak in the melting layer and, thus, there is problem like its reduction with distance by the volume (beam width) effect. In fact we observed this significant reduction at ranges greater than 5 km. This VPR correction method can be applied to any estimator of rainfall rate as well as to Z H. Therefore, the precipitation profile used to project the XPOL rainfall estimates from every beam elevation at ground level is not a static average profile, but it varies for each PPI observation based on conditions of that storm stage. This algorithm does not require RHI observations and it exhibits improvements in the rainfall estimation under melting layer conditions compared to the mean-field VPR techniques. In the next section we present qualitative and quantitative (based on comparisons against rain gauge measurements) evaluations of the different rain estimation techniques and the VPR cor-

6 6 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx rection discussed above. Before conducting any evaluation on the rainfall estimates the XPOL power related measurements (Z H and Z DR ) were corrected for a number of issues: (1) ground clutter using a Doppler wind velocity (<0.1 m/s), the standard deviation of Doppler spectrum (<1 m/s) and horizontal to vertical polarization reflectivity filter, (2) partial beam occlusion using the theoretical beam occlusion maps presented in Fig. 3, and (3) rain-path attenuation using the differential phase shift attenuation-correction technique described in Anagnostou et al. (2006b). 4. Qualitative comparison of the rainfall estimation techniques In this section we discuss comparisons of storm total accumulation maps (shown in Fig. 4) derived from the different rainfall estimation techniques for the two rain storm events (07/08-August and 06-October-2007). We note distinct rainfall structure differences between the two storms with the convective storm in August exhibiting rainfall accumulations exceeding 200 mm over a significant portion of the mountainous terrain centered on Posina basin. On the other hand, the stratiform storm in October exhibits moderate accumulations and a distinct mixed phase layer signature that is particularly apparent in the K DP -derived (R KDP ) rainfall product. Comparing the three radar-rainfall maps, a point to note from Fig. 4 is the higher rainfall accumulations derived from the R KDP algorithm relative to the standard reflectivity-to-rainfall (Z R) relationship (R STD ). As expected, the rainfall accumulation map of the R KDP -based adjusted Z R algorithm (R STD1 ) shows a close agreement with the R KDP rainfall accumulation map. In Fig. 5 we show the effect of the vertical precipitation profile on the R STD1 rainfall accumulations for the October stratiform rain event, and the impact of the VPR adjustment technique proposed in the previous section. We particularly note a ring of enhanced rainfall due to bright-band enhancement on the 3 beam elevation PPI product. Although bright-band enhancement is not apparent on the 2 beam elevation PPI rainfall accumulation map, the estimates at this beam elevation have several sectors affected by beam blockage due to ground clutter. These areas, however, become visible at the 3 beam elevation rainfall map. Application of the VPR adjustment technique at the 3 elevation PPI removes significantly the bright-band enhancement and the snow underestimation (at further ranges) as noted comparing the three panels. Qualitative comparison of the VPR-adjusted R STD1 to the 2 elevation R STD1 over sectors where there is no beam blockage (65%) at 2 elevation shows a good agreement in terms of rainfall distribution, indicating an efficient correction by the VPR technique. This is evident from the cumulative distributions of the storm-total rainfall accumulations (Fig. 6) for R STD1 presented from XPOL estimates at 2 and 3 beam elevation with and without VPR adjustment. The cumulative distribution plot for the 3 VPR-adjusted estimates has similar shape to the cumulative distribution from the 2 elevation estimates. However, we note an underestimation in the low to medium values of rainfall accumulations relative to the 2 elevation estimates. This is explained by the fact that even the 2 eleva- Fig. 4. XPOL (3 beam elevation) estimated rainfall accumulation maps from the standard Z R technique (left column panels), the R KDP -based adjusted standard Z R technique (middle column panels) and the polarimetric R KDP estimator (right column panels). The top and bottom panels correspond to the August 2007 and 06 October 2007 storms, respectively.

7 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx 7 Fig. 5. XPOL estimated rainfall accumulation maps from the R KDP -adjusted standard Z R technique at 2 beam elevation (left panel), 3 beam elevation (middle panel) and VPR-adjusted 3 elevation measurements (right panels) for the 06 October 2007 storm. Fig. 6. Cumulative probability plots of the storm-total rainfall accumulations of R STD1 at 2 and 3 beam elevations, with and without adjusting for VPR. The radar cells contributing to these cumulative probabilities are associated with beam occlusion less than 5% and radar ranges >10 km. tion is partly within the melting layer. So, we should also adjust the 2 estimates for VPR effect as it is expected to overestimate due to the bright-band enhancement effect. As shown in Fig. 6 the cumulative distributions of the storm-total rain accumulations from the VPR-adjusted 3 and 2 beam elevation estimates are almost identical. In this study we did not have near-surface (0.5 1 ) radar observations to compare against the VPR-adjusted 2 and 3 estimates, so the results can only be viewed as qualitative. In the next section we use the 1/2 hourly rain gauge measurements to provide a quantitative evaluation of the proposed rain estimation techniques for the two storm cases. 5. Quantitative evaluation against rain gauge measurements As stated earlier the selection criterion for the rain gauges to be included in this evaluation exercise is that the 2 radar beam at the gauge location is not occluded by more than 5%. This criterion identified 32 gauges to be used in this analysis. The rain gauges perform measurements at a point, while the radar measurements are volume averages. The volume size and the average measurement altitude above ground increases with distance and are about 120 m 500 m (volume length and diameter) and 1500 m, respectively, at 30 km range and 3 elevation. This spatial separation and difference in measurement volume introduces significant scatter in the comparison of radar and rain gauge rainfall measurements. We start the evaluation showing for the two storm cases (Figs. 7 and 8) scatter plots of the estimated radar rainfall versus the rain gauge rainfall at half hourly temporal resolution. The scatter plots are grouped in two radar-gauge ranges: short (630 km) and long (>30 km) range, and in two beam elevations: 2 and 3. A point to note from these figures is the improved radar-to-gauge rainfall scatter exhibited by the R STD and R STD1 techniques compared to the R KDP. A second point to note is the improvement in the scatter of R STD when it is adjusted by the R KDP (i.e., the R STD1 technique). This is apparent in both rain events, i.e., the convective (particularly in the 2 elevation) and the stratiform (particularly in the 3 elevation) storm cases. The exception is with the VPR-adjusted fields where R STD and R STD1 seem to have similar scatter. A last point to note from the scatter plots of Fig. 8 is the improvement in the scatter of all three techniques due to VPR correction. The above arguments are also supported from Tables 1 2 presenting the total bulk statistics of the scatter plots. The important points we should note from these are the consistent improvement in all the statistical parameters (correlation, ratio and rrmse) for both rain events and for the different ranges and elevations of the R STD1 compared to the R STD and R KDP. In addition, we note an improvement in all statistical fields of the R STD1 compared to the other two methods when we adjust for the VPR effect (see Table 2c). Quantitative error statistics derived for different rainfall rate threshold based on the above radar-gauge pairs are described next. The statistical metrics for the error statistics include: (1) the bias defined as the ratio of the total storm accumulated reference (gauge rainfall) to the radar estimate, (2) the correlation coefficient between the half hourly rainfall values derived by the radar estimates to the half hourly rainfall measured by the rain gauges, and (3) the relative root-mean-square error (rrmse) of the half hourly radar rainfall estimate versus the rain gauge rainfall measurement (normalized by the storm average rain gauge rainfall). The error statistics were evaluated for different rainfall rate thresholds defined by the reference (i.e., the half hourly rain gauge rainfall) and grouped by beam elevation (2 and 3 ) and radar-gauge range (>30 km and 630 km). The number of couples used for the different rain thresholds is above 50 and it increases as the rain threshold decreases up to a number of 230 couples. Figs. 9 and 10 show the correlation, bias ratio and rrmse error statistics of the convective storm case XPOL estimates at the 2 and 3 beam elevations, respectively. A first point to note is that R STD1 (R KDP - based adjusted R STD ) exhibits the highest correlation at both radar

8 8 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx Fig. 7. Scatter plots of storm-total rainfall accumulations (mm) measured by the rain gauges versus the three radar estimates (R STD, R STD1 and R KDP ) for the 2 and 3 beam elevation measurements of the August 2007 storm. range categories and beam elevations. The impact of R KDP adjustment is more pronounced on the longer range and the higher beam elevation data where the correlation is significantly improved over both techniques. Improvement in correlation indicates significant temporal variability in the Z R mean-field bias identified by the R KDP estimates. Another point to note on the aspect of correlation is that the R KDP correlation is only better than the standard Z R in the convective storm case, and only for the shorter ranges (630 km), which is an indication of the weakness of K DP base rain estimation techniques to capture the small-scale variability of rainfall in moderate to low rainfall intensities due to the 3 km filter used along each beam to estimate K DP from U DP. In terms of bias, the R KDP estimator exhibits very low underestimation (<5% and <10% for range categories less than and great than 30 km, respectively) for the 2 elevation estimates. At the 3 elevation the R KDP underestimation slightly higher than 20% in the short-range category, while at the long-range category although estimator exhibits unbiased estimates it cannot be considered reliable due to the significant effect of mixed phase precipitation. The standard Z R technique (R STD ), on the other hand, exhibits significant underestimation at both short (70%) and long (100%) radar-gauge range categories for the 2 beam elevation estimates. This underestimation is further enhanced (up to 200%) for the 3 elevation estimates. Monitoring the R STD mean-field bias using the R KDP estimates is shown to be an effective way of reducing the systematic error. Specifically, for the 2 beam elevation XPOL estimates, the R STD1 underestimation is found to be even slightly less than the underestimation of the R KDP estimator, while for the 3 beam elevation estimates the systematic errors of the R STD1 and R KDP estimators are nearly equal at radar ranges below 30 km. This aspect along with the fact that R STD1 exhibits the highest correlation with gauges at half hourly temporal resolutions indicates that this estimator provides the best accuracy in representing the fine scale variability of rainfall. This is further supported by the rrmse error statistics. As shown in Figs. 9 and 10, although at close ranges (630 km) the reduction of R STD1 is moderate exhibiting values at similar levels as those of the R KDP estimator, at further ranges (>30 km) the reduction is significant (100%) from either R STD or R KDP rrmse error statistics. The above observations are also valid for the stratiform case, for which the error statistics are presented in Figs. 11 and 12. Higher correlations of R STD1 are shown for radar ranges 630 km and the ratio and rrmse are comparable to the R KDP estimates. The R KDP estimator is nearly unbiased, while the R KDP -based bias adjustment applied on the R STD algorithm reduces significantly the underestimation of the R STD technique. These two aspects combined leads to a reduction of the rrmse. The additional aspect investigated by Fig. 12 is the effect on the bulk statistics when correcting the XPOL estimates for VPR. The three panels on the left (radar ranges 630 km) show that the power-related estimates give higher correlation when adjusted for VPR (compare to Fig. 11). The results on the bias ratio indicate that at short ranges (630 km) the

9 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx 9 Fig. 8. Same as in Fig. 7 but for the 06 October 2007 storm and for VPR correction. Table 1a Bulk statistics of August 2007 for 2 elevation. el = 2 ( ) 630 km >30 km Corr Ratio rrmse Corr Ratio rrmse R STD R STD R KDP Table 2b Similar to Table 2a but for 3 elevation. el = km >30 km Corr Ratio rrmse Corr Ratio rrmse R STD R STD R KDP Table 1b Similar to Table 1a but for 3 elevation. el = km >30 km Corr Ratio rrmse Corr Ratio rrmse R STD R STD R KDP Table 2c Similar to Table 2b but accounting for VPR. el = km >30 km Corr Ratio rrmse Corr Ratio rrmse R STD R STD R KDP Table 2a Bulk statistics of 06 October 2007 for 2 elevation. el = km >30 km Corr Ratio rrmse Corr Ratio rrmse R STD R STD R KDP R STD is improved while the R STD1 and R KDP are less affected by the VPR correction. Similarly, there is an improvement on the rrmse of R STD and R STD1, but more moderate on the R KDP. At further ranges (>30 km), the improvement on the bias ratio and rrmse statistics of R STD is more than 70% while for the R STD1 is around 30%. 6. Conclusions In this paper we investigated the performance of high resolution X-band polarimetric (XPOL) radar measurements of rainfall

10 10 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx Fig. 9. Error statistics (correlation, ratio, and rrmse) evaluated for three radar rainfall techniques (R STD : standard Z R, R STD1 : differential phase based bias adjusted standard Z R; and R KDP : polarimetric algorithm) for different rain gauge rainfall (mm h 1 ) thresholds and radar-gauge ranges: (a) 630 km and (b) >30 km. The XPOL rainfall estimates are from 2 beam elevation measurements of the storm event of August Fig. 10. Same as in Fig. 9 but XPOL rainfall estimates are from 3 beam elevation measurements of the storm event of August 2007.

11 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx 11 Fig. 11. Similar to Fig. 10 (XPOL measurements at 3 elevation) but for the storm event of 06 October Fig. 12. Similar to Fig. 11 (XPOL measurements at 3 elevation for the storm event of 06 October 2007) but now accounting for VPR correction.

12 12 M.N. Anagnostou et al. / Journal of Hydrology xxx (2010) xxx xxx in complex terrain. The XPOL data were corrected for effects due to rain-path attenuation and the complex terrain (beam blockage, VPR correction). For beam blockage estimation high resolution terrain information and a three dimensional model of the radar beam was applied. For the rain-path attenuation correction we used an iterative self-consistent algorithm based on U DP measurement in rain cells defined in each radar ray by the horizontal to vertical polarization correlation (q hv ) parameter. The algorithms used to retrieve rainfall rate from the XPOL parameters include a K DP R relationship, the standard Z R relationship and a K DP -adjusted Z R relationship. High quality drop size distribution measurements from a video disdrometer located in the urban region of Athens and T-matrix simulations were used to estimate the parameters of the above rainfall algorithms. Radar-rainfall estimates from the different techniques were compared against high-resolution measurements from a dense rain gauge network located within a 60-km radar range. An overview from the bulk statistics described in this study is that for both convective and stratiform rain storm events investigated in this study power-related rainfall estimates give higher correlations compared to the K DP -rainfall algorithm, therefore the Z R relationship can better represent the high-resolution variability of rainfall. However, even though the reflectivity measurements can capture better the spatial structure of the storm, it is associated with a time-varying systematic error due to a number of issues (radar calibration, rain-path attenuation, and partial beam occlusion). Correcting for the systematic error is critical in modeling accurately flash floods. The non power-related R KDP estimator is less susceptible to the main sources (e.g., radar calibration, rain-path attenuation, DSD variations) causing the systematic error. On the other hand, K DP -based rainfall estimates cannot capture adequately the small-scale variability of rainfall (particularly in low to moderate intensity rainfall) due to the smoothness introduced in the derivation of K DP (i.e., 3-km filter) from the differential phase shift measurements. Results from this study show that a R KDP -based mean-field bias adjusted Z R technique is the way to provide unbiased rainfall estimates at fine space time scales, which can be of great value in predicting flash floods induced by orographic precipitation. We also showed improvements in accounting for the VPR effect when using high beam elevation (3 ) radar measurements, which is another typical issue in radar applications over complex terrain. The findings from this study demonstrate the importance of using locally-deployed X-band radar units in quantifying precipitation at high spatio-temporal resolution over complex terrain basins. It remains to be demonstrated as to how significant is this improvement in terms of rainfall product resolution and accuracy on the simulation of floods for a range of basin scales and watershed characteristics. Another limitation of this study is the number of storm cases. Although the sample size associated with the two storms and used to determine the error statistics is large (mainly due to the number of gauges), we lack comprehensive evaluation in terms of different storm types and precipitation microphysics. Field experiments are planned for the same region in the Spring-Fall 2010 to enrich the database to further support the error analysis presented in this study. Finally, the data collected in this study can be used to quantify the improvement in terms of flood prediction achieved by locally-deployed low-power X-band radar relative to measurements from a standard long-range operational (C-band) radar. Acknowledgments This work was part of the HYDRATE project (STREP category GOGE ) funded by the European Commission 6th Framework Program. References Anagnostou, E.N., Krajewski, W.F., Simulation of radar reflectivity fields: algorithm formulation and evaluation. Water Resour. Res. 33, Anagnostou, E.N., Anagnostou, M.N., Krajewski, W.F., Kruger, A., Miriovsky, B.J., High-resolution rainfall estimation from X-band polarimetric radar measurements. J. Hydrometeorol. 5, Anagnostou, E.N., Grecu, M., Anagnostou, M.N., 2006a. X-band polarimetric radar rainfall measurements in keys area microphysics project. J. Atmos. Sci. 63, Anagnostou, M.N., Anagnostou, E.N., Vivekananda, J., 2006b. 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