Rainfall estimation in mountainous regions using X-band polarimetric weather radar

Transcription

1 Rainfall estimation in mountainous regions using X-band polarimetric weather radar Shakti P.C. 1,2, M. Maki 1,2, S. Shimizu 2, T. Maesaka 2, D.-S. Kim 2, D.-I. Lee 3 and H. Iida 4 1 Graduate School of Life and Environmental Science, University of Tsukuba, Japan 2 National Research Institute for Earth Science and Disaster Prevention(NIED), Japan, shakti.pc@gmail.com 3 Pukyong National University, South Korea 4 Japan Weather Association(JWA),Japan Shakti P.C. 1. Introduction (Dated: 30 May 2012) The application of X-band radar to hydrometeorological problems has been described by many researchers (Anagnostou et al. 2004, Maki et al. 2005a, Matrosov et al., 2005), and this research has shown that rain rates derived from X-band polarimetric radar observations compare well with rain gauge data, especially in flat areas (Park et al. 2005b, Maki et al. 2005a). However, while high-resolution spatial and temporal rainfall estimates can be derived from X-band radar, there are several uncertainties inherent within the radar parameters that must be considered during the observation period. A common problem associated with weather radar is errors caused by signal attenuation (Ryzhkov and Zrnic 1995, Park et al. 2005a, Germann et al. 2006, Maki et al. 2005a, Kim et al. 2010). Other problems include beam blockage (mainly over mountainous regions), ground clutter, and anomalous propagation. In general, beam blockage and ground clutter over flat terrain are not significant when compared with their impact over more complex terrain. Many studies have shown that an effective beam blockage correction scheme is essential to ensure that quantitative precipitation estimations (QPE) in mountainous regions are accurate (Bech et al. 2003, Maki et al. 2005a). Various direct and indirect methods have been applied to different types of radar to correct errors caused by partial beam blockage (PBB) (Kucera et al. 2004, Krajewski et al. 2006, Germann et al. 2006, Friedrich et al. 2007, Lang et al. 2009), but there is still no agreement regarding the most appropriate solution, and there a c b have been few studies using X-band dual polarization radar. Therefore, in this study we focus on the correction of reflectivity in the presence of beam blockage over a mountainous region (see Fig. 1) using a research X-band dual polarization radar (MP-X) at the National Research Institute for Erath Science and Disaster Prevention (NIED). 2. Method 2.1 Attenuation correction The basic formula used to correct attenuation of radar reflectivity (Z H_att ) is expressed by (1) Fig.1. Maps of the study area. (a) General location of the MP-X (Ebina) radar in Japan. (b) Coverage range of radar observation in the Kanto region. (c) Detailed view of the Hakone region (area of red rectangle in Fig. b). Red circles indicate raingauge stations; triangle and star are sites with JW and 2DVD disdrometers (as well as raingauges), respectively. where Z H_raw is the observed reflectivity in mm6 mm 3, A H is the attenuation coefficient of reflectivity, and s is the distance between range gates. The logarithmic form of Eq. (1) is To determine A H, the self-consistent method proposed by Bringi et al. (2001), who extended the ZPHI rain profiling algorithm of Testud et al. (2000), and the method of Smyth and Illingworth (1998), was modified for use with X-band dual polarization radar. (Details can be found in Park at el. 2005a). (2)

2 2.2. DEM method The DEM method is based on power loss due to beam shielding in a standard atmosphere, and is widely used to correct bias reflectivity over the PBB zone. The general equation of the DEM method in a logarithmic form is where 10logZ H_dem is the corrected reflectivity using the DEM method, and BBR is the fractional beam blockage rate Modified DEM method The filtering process, ground clutter, etc. are additional problems that frequently occur in the presence of PBB in mountainous regions, and which should be addressed. In such cases, Eq. (3) can be modified as follows Equation (4) is the modified DEM method. F represents the power loss caused by unknown errors over the mountainous area, and is considered to be zero in the case of no PBB. Eq. (4) expressed in terms of the elevation angle (θ) is Two unknown factors appear in Eq. (5). Although, it is difficult to estimate the factor F, a straightforward relationship can be used to solve the unknown terms by considering the reflectivity at several elevation angles. A true reflectivity equal to attenuation corrected reflectivity in the presence of no PBB at any elevation angle. However, if there is a PBB at any one elevation angle, the reflectivity of the nearest elevation angle (no PBB) is considered to be the true reflectivity for that blocked elevation angle (Fig. 2). A true reflectivity may vary from one elevation angle to another depending upon the height of the mountain, as well as distance from the radar location. We believe that there is no significant change in vertical profile up to the specified elevation angles in the case of X-band radar. The present method is of no use if there is a marked change in the vertical profile of reflectivity. Mathematically, we can write the assumption required to solve the Eq. (5) as where θ is the antenna elevation angle affected by the PBB, and θ* is a minimum elevation angle at which no PBB occurs. Based upon this assumption, we can rewrite Eq. (5) as It is clear that ΔZ H in Eq. (7) depends on the BBR, and an empirical relationship can be derived by statistical analysis of the last term of Eq. (7) using observed radar data. It should be noted that the radar data should be collected from a set of special PPI scans in which θ* is set as low as possible. To satisfy this condition, PPI scanning elevation angles should be altered in small steps; e.g., from 0.2 to 0.5, depending on the location of the radar and the topography. The scan strategy used in the present study will be described later. Having established the relationship between ΔZ H and BBR, reflectivity in the PBB zone can be corrected using Eq. (5). 3. Observation Our study area on Hakone Mountain was selected to examine the effect of PBB on rain rates derived from radar observations, and is 35 km from the radar station. Data were collected from three sources (radar, raingauge, and disdrometer observations) during the summer seasons of 2010 and To obtain the polarimetric parameters affected by PBB, specific observations were completed using the MP-X radar with the lowest elevation angle set at 1.4, and then increased to 1.7, 1.9, 2.1, and 2.7. The total scanning time for all elevation angles was almost 2.5 minutes, with 20 seconds for each elevation angle. We focused our research between 230 and 255, as this covers almost Z(θ ) H_mod_dem = Z(θ* ) H_att Mountain the entire Hakone mountain region (Fig. 1). The five raingauges were deployed around the Hakone mountain region, provided continuous rainfall data at 1-minute intervals. Disdrometer observations (JWD and 2DVD disdrometer) were deployed at Kowakien and Prince Station in the summer season of Due to internal problems with the 2DVD, it was only possible to record a complete data set from one event, while surface gauge measurements were carried out over both seasons. We collected data during eight precipitation events, which covered a range of durations. (3) (4) (5) θ* θ θ =θ* Mountain FIG. 2. Schematic diagram showing the determination of true reflectivity at a PBB elevation angle θ. FIG. 3. Comparison of time series of Z H_raw and Z H_att over the Kowakien station disdrometer site at an elevation angle of 1.9, from 20:00 to 24:00 UTC on 19 July Error bars indicate the standard deviation of the radar data (6) (7)

3 3. Results 3.1 Validation of attenuation correction The JWD was set up around 36 km from the radar station (Fig. 1). There is a small amount of BBR at Kowakien station for the elevation angles of 1.4 and 1.7. Therefore, to validate the attenuation term, reflectivity at an elevation angle of 1.9 (no PBB) was selected. To compare the two data sets, the radar data were averaged over four ranges (i.e., a range sector of 0.1 km) and two consecutive azimuth rays (about 1 ) centered over the disdrometer site, on the PPI surface at each elevation angle. Figure 3 compares the time series of Z H_raw and Z H_att with Z H_dsd over 4 hours on 19 July Z H_dsd is shown at 1-minute intervals, while Z H_att is shown at an interval of about 2.5 minutes. A clear underestimation occurs between Z H_raw and Z H_dsd, but good agreement is observed between Z H_att and Z H_dsd during the whole monitoring period. To clarify the relationship, statistical analysis was carried out, where 2-minute averages of Z H_dsd were considered against the radar data collected every 2.5 minutes. Overall, Correlation coefficient (COR) was about 80%, except for one case (Case_4). The mean absolute error (MAE) and root mean square error (RMSE) are below 5 db, and the difference between them has a small gap, which indicates that there is no systematic difference in the case of higher reflectivity values. Normalized error (NE) is below 16% and Normalized biases (NB) varies between 15% and 0%, which indicates a good match between Z H_att and Z H_dsd. We repeated this analysis for elevation angles of 2.1 and 2.7, and comparable results were obtained. A maximum bias (NB 12%) was found in Case_4, with a poor COR value. Z H_att at Kowakien for that case was around 35 dbz during the selected time period. Note that attenuation correction in very light rainfall is almost negligible. Another possibility could be the adjustment of radar bias. 3.2 Partial beam blockage correction The BBR is different at each azimuth angle, and in the range profiles at all elevation angles, except at an elevation angle of 2.7 when there is no PBB for all azimuth angles. Having obtained the BBR, the DEM method simply corrects reflectivity based on the BBR. In the case of the modified DEM method, the simple linear relationship between Δ Z H and BBR was carried out for all events and comparable trends were observed in all cases (Fig. 4). The averaged relationship is ΔZ H =21.83 BBR (8) with a maximum standard deviation of 1.4 db. Figure 5 illustrates a single range profile of Z H_raw, Z H_att, Z H_dem, and Z H_mod_dem and corresponding BBR at angles between 1.4 and 2.7. Maximum BBR is found at an elevation angle of 1.4. BBR decreases with increasing elevation angle, and no BBR occurs over the mountains at an elevation angle of 2.7 (Fig 5e). The two black dots indicate the Z H_dsd calculated by a disdrometer located very close to the 241 azimuth FIG. 4. Relationship between ΔZ H and BBR for the eight rainfall events. The black solid line is the average of all events. FIG. 5. Range profiles of reflectivity and corresponding BBR: (a) Z H_raw, (b)z H_att, (c) Z H_dem, (d) Z H_mod_dem and (e) BBR at elevation angles between 1.4 and 2.7 on 19 July Two black dots indicate Z H_dsd, derived from disdrometer observations located close to an azimuth angle of 241 angle. The Z H_att from all elevation angles are fairly similar up to about 31 km from the radar station, where the BBR at all elevation angles is zero. However, some discrepancies exist between Z H_att at the various elevation angles, which may be due to a time lag, moving of the echo etc. In contrast, a systematic discrepancy at each elevation angle can be seen in the BBR over the mountain (Fig 5 a&b). The BBR at each angle is different, which causes the differing reflectivity patterns. Some data near the top of the mountain are missing, and this is due to the effect of ground clutter. A decrease in HV is the result of

4 a decrease in the signal-to-noise ratio (SNR) caused by ground clutter, especially near the top of the mountain. If the value of HV becomes too low, the filtering process is used. Z H_dem of all PBB elevation angles are clearly an underestimation when compared with Z H_att at an elevation angle of 2.7 (Fig. 5c), while Z H_mod_dem of all PBB angles are very close to Z H_att at the same angle(fig 5d). It should be mentioned that Z H_mod_dem is close to Z H_dsd (black dots), which confirms the accuracy of the modified DEM method. It was found that reflectivity corrected using the modified DEM method at all elevation angles in the PBB zones generated a similar pattern to Z H_att in the no PBB zone (Fig. 5). This suggests that only the DEM method is unable to solve beam blockage problems over the mountainous regions. It has already been noted that missing reflectivity data, and the fluctuation of ΔZ H, increase at higher BBR, so that the correction of reflectivity at higher BBR may contain some uncertainties. Harrold et al. (1974) and Bech et al. (2003) suggested a simple correction scheme for reflectivity-based rainfall measurements when beam blockage is less than 60%, or slightly higher in the absence of ground clutter. Vivekanandan et al. (1999) focused on a BBR of less than 70%, Lang et al. (2009) extended up to a 90% BBR. There is no limit to the maximum BBR in the reflectivity correction. However, we did not limit our method in this study, but based on the missing data and larger fluctuation rate of ΔZ H at higher BBRs, the probability of uncertainties would increase above a BBR of 70%. 3.3 Validation of modified DEM method To validate the modified DEM method, we used observational data from the 2DVD at Prince station (see Fig. 1). BBR at Prince station for the elevation angles of 1.4, 1.7, 1.9, and 2.1 was about 80%, 47%, 25%, and 8%, respectively. To compare the two data sets, we applied the same procedure used to validate the attenuation correction to selected grid points within the radar data. An average Z H_mod_dem from all elevation angles was then compared with the derived Z H_dsd from the scattering simulation based on the 2DVD data (as explained previously, 2DVD data were only available from one event). A comparison of the time series of Z H_mod_dem, Z H_dem, and Z H_dsd for the elevation angles of 1.7 between 20:00 and 24:00 UTC on 19 July 2011 is shown in Fig. 6. More radar reflectivity data is missing at the elevation angle of 1.4 than at 1.7. Note that the PPI scan of the MP-X radar was repeated every 2.5 minutes. Neither method was able to correct reflectivity at an elevation angle of 1.4, where the proportion of missing radar data was high, and this is one of the limitations of this approach; i.e., we cannot generate the true reflectivity pattern in the absence of radar data. Z H_mod_dem and Z H_dsd are in good agreement across the whole time series profile at all PBB elevation angles, but Z H_dem systematically underestimates Z H_dsd. To examine in more detail the relationship between Z H_mod_dem and Z H_dsd, the same statistical procedure (Validation of attenuation correction) was applied to all the elevation angles. All angles COR were greater than 80%. As the elevation angle of 2.7 has no PBB, the statistical comparison of the results obtained from Z H_att and Z H_dsd at this angle should be closer to the results of Z H_mod_dem and Z H_dsd at the other, lower elevation angles. Similar values of MAE and RMSE indicate that there is little error in the case of higher values of Z H_mod_dem and Z H_dsd. NE and NB vary from 5% to less than 12%, and from 1% to less than 10%, respectively, at all elevation angles. Such variations are reasonable when comparing variables from different environments. 3.4 Rainfall estimation To estimate and validate the rain rate calculated from Z H_mod_dem over the mountain region, we derived an appropriate Z-R relationship based on a scatter simulation using all disdrometer data from Kowakien (located close to the mountain). We used the criteria and methodology of Park et al. (2005b) to fit the Z-R relationship as follows FIG. 6. Comparison of time series of Z H_dsd, Z H_dem, and Z H_mod_dem over the Prince station disdrometer site at elevation angle of 1.7 between 20:00 and 24:00 UTC, 19 July Error bars indicate the standard deviation of the radar data. (9) FIG. 7. Scatter plot of R(Z H_mod_dem ) and R(Gauge) 10-minute average rain rates from four rainfall 4 events at an elevation angle of 1.7.

5 The derived Z-R relationship was quite close to that of Park et al. (2005b) for reflectivity (Z H ) 35 dbz, but we obtained a slightly higher value of the exponential coefficient than Park et al. (2005b) for Z H > 35 dbz. We first calculated the rain rate using the differential phase (K DP ) and fitted the relationship of R(K DP ) and Z H_att in the no PBB zone. Using this approach, two forms of the Z-R relationship were obtained. The first was a constant Z-R relationship in which the coefficient and the exponent were calculated by fitting a least squares line to the scatter plot of R(K DP ) and Z H_att for all observed events. The second was a dynamic Z-R relationship in which the coefficient and the exponent were estimated every 15 minutes from R(K DP ) vs. Z H_att. Next, we estimated the rain rate using the three methods and compared the results with gauge data. The best result was obtained from the Z-R relationship derived from the scattering simulation of disdrometer DSD data. Therefore, we only use the Z-R relationship derived from DSD data for further analysis here. Figure 7 shows the scatter plot of the combined 10-minute averages of R(Z H_mod_dem ) and R(gauge) data from 4 events at Prince station for an elevation angle of 1.7 where BBR is 47%. A comparison of the statistical summaries of the 10-minute averages of R(Z H_mod_dem ) and R(gauge) from all stations at different elevation angles, together with the associated BBR, is shown in Table 1. The BBR at each station varies with the elevation angle. The NB at all stations, for all elevation angles, varies between 22% and 29%, while NE varies from 15% to 10%. A slight underestimation is evident at all elevation angles, except the lowest, based on NE. Some data are missing at lower elevation angles; therefore, the statistical result is sometimes less significant when compared with results from higher elevation angles. In general, good agreement was found at all elevation angles and at all stations using R(Z H_mod_dem ). Taking all of our results into account, we believe that the rainfall rates derived in the presence of PBB over the mountain region were very close to the actual values. Finally, the spatial distributions of one-hour accumulated rainfall were examined using different reflectivity parameters to determine how the accumulation rate varied over the PBB zones. Figure 8 shows the accumulated rainfall estimated from Z H_att, Z H_dem, and Z H_mod_dem for one hour (22:00 23:00 UTC) on 19 July Different accumulation rates estimated from R(Z H_att ), R(Z H_dem ), and R(Z H_mod_dem ) are found at the elevation angles of 1.9, especially over the mountain region. A sudden decrease in the R(Z H_att ) accumulated rainfall is found around the Prince Station (star symbol in Fig. 8). R(Z H_dem ) shows some improvement in terms of this sudden decreasing trend, but not enough compared with nearby accumulated rainfall. However, R(Z H_mod_dem ) removes most of the sudden decrease in accumulated rainfall. Other small pockets (* symbol in Fig. 8) showing a sudden decrease in accumulated rainfall occur over the mountain peaks, and this is due to missing data at higher elevations (see Fig. 5), probably caused by the filtering process of the radar. Further research is needed to address this problem. 3. Conlcusion The two methods of correcting the radar reflectivity produced clearly different results. Corrected reflectivity using the modified DEM method showed good agreement with reflectivity derived from disdrometer observations, which indicates that this modified DEM method may be an effective approach to overcoming the effect of beam shielding in mountainous areas. Previous research has shown that the DEM method is not applicable at higher BBRs (e.g., Vivekanandan et al. 1999, Germann et al. 2006, Lang et al. 2009). In the present study, the amount of missing reflectivity data was greatest TABLE 1. BBR, together with NE and NB of 10-minute average rain rates obtained from reflectivity corrected by the modified DEM method [R(Z H_mod_dem )] for different elevation angles at the five raingauge stations. Station name FIG. 8. One-hour accumulated rainfall between 22:00 and 23:00 UTC, 19 July 2011 based on R(Z H_att ) (top), R(Z H_dem ) (middle), and R(Z H_mod_dem ) (bottom) for elevation angles of 1.9. at higher BBRs, and the probability of uncertainty in ΔZ H increases at a higher BBR. Therefore, we suggest that the modified DEM method is applicable up to a BBR of 70% when calculating QPE. BBR (%) Elevation angle NE NB BBR NE NB BBR NE NB BBR NE NB BBR NE (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) Kowakuken < Yunohana Prince Panorama Fuji View < * * * NB (%)

6 We conclude that the DEM method is not appropriate for correcting PBB, even though it has been widely used for this purpose due to its simplicity. Many studies have shown that its accuracy could be increased by using a higher-resolution DEM (e.g., Vivekanandan et al. 1999, Kucera et al. 2004, Lang et al. 2009). In this study, we used a 50-m resolution DEM map to recreate BBR over the mountain region, which provided improved BBR data when compared with previous studies. However, our results indicate that the increased detail of the BBR data seems to make only a limited contribution to improving the accuracy of the PBB correction. Based on this research, the modified DEM method was able to successfully solve the problem of PBB over a mountain region. While the modified DEM method may be used with other radar systems, the obtained empirical formula of the modified DEM is applicable only to the NIED X-band dual polarization radar located at Ebina city, Kanagawa Prefecture, Japan. Agreement between the radar and raingauge measurements was reasonable; however, some overestimation was observed, especially at higher rain rates. An interesting area for further study is the development of a more appropriate Z-R relationship that will help to improve the accuracy of rain rate estimates based on radar observations. In mountainous regions the distribution of accumulated rainfall amounts varies greatly, even within a small area. The limited coverage of surface raingauge stations in mountainous areas, combined with coarse-resolution data from radar observations, cannot provide precise spatial data regarding the distribution of rainfall. This can lead to significant spatial errors in hydrometeorological forecasting or operational water resource management systems in areas of complex topography. From a hydrometeorological viewpoint, the use of X-band weather radar to estimate rainfall rates may offer an appropriate solution to the problem of obtaining high-resolution spatial rainfall data, and this will be considered in a future paper. References Anagnostou, E. N., M.N. Anagnostou, W. F. Krajewski, A. Kruger, and B. J. Miriovsky, 2004: High-resolution rainfall estimation from X-band polarimetric radar measurements. J. Hydrometeor., 5, Bech, J., B. Codina, J. Lorente, and D. Bebbington, 2003: Thesensitivity of single polarization weather radar beam blockagecorrection to variability in the vertical refractivity gradient. J. Atmos. Oceanic Technol., 20, Bringi, V. N., T. D. Keenan, and V. Chandrasekar, 2001: Correcting C-band radar reflectivity and differential reflectivity data for rain attenuation: A self-consistent method with constraints. IEEE Trans. Geosci. Remote Sens., 39, Friedrich, K., U. Germann, J. J. Gourley, and P. 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