## Abstract

A new method for mitigation of partial beam blockage that uses the consistency between reflectivity factor *Z* and specific differential phase *K*_{DP} and their radial integrals in rain is presented. The immunity of differential phase Φ_{DP} to partial beam blockage is utilized to estimate the bias of reflectivity factor caused by beam blockage. The algorithm is tested on dual-polarization radar data collected by the NCAR S-band polarimetric Dopper radar system (S-Pol) during the Southwest Monsoon Experiment/Terrain-Influenced Monsoon Rainfall Experiment (SoWMEX/TiMREX) in June 2008 in Taiwan. Corrected reflectivity factors in the blocked sectors are compared with corresponding values deduced from a digital elevation model (DEM) to show the advantage of the suggested method in areas where obstacles such as high-rise buildings cause additional blockage that is not accounted for by DEM. The accuracy and robustness of the method is quantitatively evaluated using a series of radar volume scans obtained in three rainfall events.

## 1. Introduction

Beam blockage caused by terrain and other obstacles such as buildings and trees limits radar coverage and introduces biases in radar measurements. Many radars in the national network of S-band operational Weather Surveillance Radar-1988 Doppler (WSR-88D) radars, especially in the mountainous areas of the western United States, are severely affected by beam blockage. As a result, the accuracy of the weather radar products such as quantitative precipitation estimates (QPEs) (Westrick et al. 1999; Young et al. 1999; Testud et al. 2000; Pellarin et al. 2002) and vertically integrated liquid (VIL) estimates is compromised. Polarimetrically upgraded WSR-88D radars have the potential to mitigate this problem, as indicated in the series of previous studies (e.g., Zrnic and Ryzhkov 1996; Vivekanandan et al. 1999; Giangrande and Ryzhkov 2005; Friedrich et al. 2007; Lang et al. 2009).

Digital elevation models (DEMs) can be used to correct reduced reflectivity caused by radar beam blockage. Two ways of making the correction have been proposed. One implies using DEM and partitioning the radar volume scan region into blocked and unblocked parts. Then, a vertical profile of reflectivity (VPR) in the unblocked region is constructed and used to estimate the reflectivity in the blocked region (Andrieu et al. 1997; Creutin et al. 1997; Kucera et al. 2004). The other way is to estimate beam blockage fraction from the DEM (Kabeche et al. 2011) and radar beam geometry (Bech et al. 2003); these authors have studied the impact of variability of surrounding vertical refractivity gradient on the sensitivity of their beam blockage correction and found the correction to be fairly robust.

It is well known that radar reflectivity *Z*, differential reflectivity *Z*_{DR}, and specific differential phase *K*_{DP} are interdependent in rain and that their consistency has been used for absolute calibration of *Z* (Gorgucci et al. 1992; Goddard et al. 1994; Scarchilli et al. 1996; Gorgucci et al. 1999; Ryzhkov et al. 2005; Marks et al. 2011). Because *K*_{DP} is immune to blockage, the idea of self-consistency can be utilized to mitigate the bias of *Z* caused by partial beam blockage (PBB) provided that *Z*_{DR} is not affected by PBB (Carey et al. 2000; Giangrande and Ryzhkov 2005; Lang et al. 2009) Direct utilization of specific differential phase *K*_{DP} for estimating rainfall in the areas affected by PBB has also been explored. It has been found that the rainfall accumulation estimated using the *R*(*K*_{DP}) relation is more close to the rain gauge measurements than using the *R*(*Z*) relation in the region where the radar beam is partially blocked (Vivekanandan et al. 1999). Friedrich et al. (2007) confirmed that *K*_{DP} measurements are not biased by beam blockage on the operational, polarimetric C-band weather in France. However, a well-known impediment to *R*(*K*_{DP}) is the uncertainty caused by fluctuations in the *K*_{DP} estimates, particularly in lower rain-rate regions (Zrnic and Ryzhkov 1996; Blackman and Illingworth 1997; Vivekanandan et al. 1999). The *K*_{DP} estimate at S band becomes noisy at rain rates less than 10 mm h^{−1}. The noisiness of *K*_{DP} might be further exacerbated because of lower signal-to-noise ratio (SNR) caused by blockage and generally lower magnitude of the cross-correlation coefficient ρ_{hv} due to reflection by the occultation object (e.g., mountains).

We propose a new method that capitalizes on the total span of the differential phase Φ_{DP} along the beam. It uses integration of the self-consistency relations over each radar beam to estimate the beam blockage fraction (BBF) dynamically and then correct the measured reflectivity factor in the blocked area. Instead of applying the self-consistency relation at each range location, the integration mitigates the uncertainty of the *K*_{DP} estimates and improves the accuracy and stability of the BBF estimations. The methodology is described in section 2. In section 3, the new method is applied to radar observations in a mountainous area and the results are evaluated. The method and results are discussed and summarized in section 4. Future work is discussed in the last section.

## 2. Methodology

According to the consistency concept, *Z*, *Z*_{DR}, and *K*_{DP} are interdependent in pure rain, so that

where *Z* and *Z*_{DR} are expressed in linear units (*Z* is in mm^{6} m^{−3} and *K*_{DP} is in deg km^{−1}). The coefficients in (1) are relatively insensitive to the variability of drop size distributions. Left-hand and right-hand parts of (1) are equal if both *Z* and *Z*_{DR} are perfectly calibrated and are not biased by attenuation/differential attenuation. Checking the consistency locally (i.e., from gate to gate) is limited to the areas of moderate-to-heavy rain (at S and C bands), where the estimates of *K*_{DP} are less noisy. To avoid such a limitation and to make the consistency check reliable in any rain regardless of its intensity, Ryzhkov et al. (2005) suggested to compare the integrals of the left and right sides of (1) over sufficiently large temporal/spatial domain:

If the integration is performed along radial direction, then the integral on the left side of (2) is proportional to the total differential phase Φ_{DP}, which is a very robust radar measurement, so that

Using Φ_{DP} is convenient to sort out unblocked and blocked azimuthal directions and to select the radials that are suitable for consistency check, that is, those where attenuation is not significant. The problem in the utilization of (3) for absolute calibration of *Z* in the areas affected by PBB is that differential reflectivity *Z*_{DR} is commonly affected by PBB as well (Giangrande and Ryzhkov 2005). The related *Z*_{DR} bias for each partially blocked azimuthal direction has to be eliminated first.

Therefore, we resort to a relatively simple but robust algorithm for PBB correction that capitalizes on the ideas from previous studies and is easy to implement in operations. In a nutshell, the method is based on the use of the power-law *K*_{DP}*–Z* relation (Ryzhkov et al. 1997):

where the variable *a* is determined at each scan using data in the unblocked azimuthal directions. Constancy of *a* in a scan hinges on the assumption that the drop size distribution and the temperature within the scan are homogeneous. The parameter *b* is assumed to be constant for the whole event or climate region. For example, its value at S band is set to 0.72 as determined from simulations using disdrometer data collected in Oklahoma (Ryzhkov et al. 1997). If *Z* is well calibrated and not biased by attenuation, then the parameter *a* can be estimated by integrating (4) (i.e., obtaining Φ_{DP}) along radials as follows:

where (*r*_{0}, *r _{m}*) is the range interval containing rain. In the blocked area, the measured reflectivity factor

*Z*becomes smaller and can be written as the product of (1-BBF) and unblocked (or restored) reflectivity factor

*Z*. BBF is the fractional loss of power caused by the blockage; thus, BBF = 1 (100%) indicates total loss. The parameter

*a*along blocked beams is labeled

*a*and for each blocked radial it is estimated as

_{B}where *r*_{0}* _{B}* represents the starting range of beam blockage for the blocked radials. Note that multiple blockages with increasing blockage faction with a range along a radial are not considered here. It is evident that

*a*>

_{B}*a*because Φ

_{DP}measurements are not affected by blockage, while the integral in the denominator of (6) decreases because of beam blockage.

It follows from (1) and (4) that the parameter *a* depends on *Z*_{DR} and may vary from storm to storm and, strictly speaking, between successive scans and individual radials due to the impact of the variability in drop size distributions. So, in our method the mean or median value of the parameter *a* is determined in real time based on (5) in the azimuths where blockage is absent. Then, the BBF can be obtained for each blocked radial as

The bias Δ*Z* caused by blockage can be estimated as

If the type of precipitation is similar in blocked and unblocked sectors, then the ratio *a _{B}*/

*a*is expected to be more stable than parameters

*a*and

*a*themselves.

_{B}## 3. Case test

During the Southwest Monsoon Experiment/Terrain-Influenced Monsoon Rainfall Experiment (SoWMEX/TiMREX) in June 2008, the National Center for Atmospheric Research (NCAR) S-band polarimetric Doppler radar system (S-Pol) observed several precipitation events in the western plain and mountainous regions of southern Taiwan. S-Pol radar was deployed on the western side of the Central Mountain Range. The radial resolution of the data was 150 m and the azimuthal resolution was 0.91°. The east side of the radar coverage area was partially or totally blocked by the mountains at several of the lowest elevation angles. A DEM of the area around the S-Pol radar in a polar coordinate system has been generated from the geographical information system (GIS) with a spatial resolution of about 270 m. By using the DEM and radar beam height with standard atmosphere (Doviak and Zrnić 2006), the BBF for each radar beam of S-Pol with an elevation and azimuth resolution of 0.1° and a range resolution of 1 km is calculated from the two-way beam pattern, whereby the blocked fraction is normalized by the 3-dB beam cross section. Figure 1 illustrates the BBF of the S-Pol radar at the elevation angles of 0.5° and 1.1°. Attenuation caused by rain was insignificant for the S-Pol radar for the selected cases and is neglected in this study. It can be seen in Fig. 1 that at an elevation angle of 0.5°, the radar beam is partially or totally blocked in about two-thirds of the radar coverage area.

To illustrate the performance of our method, we examined the data collected by S-Pol at 1200 UTC 14 June 2008. Following the methodology introduced in the previous section, the parameter *a* was calculated along clear azimuths and *a _{B}* in partially blocked areas of precipitation. The estimated parameters

*a*and

*a*are shown at each azimuth for the entire radar scan at 0.5° in Fig. 2a. Note that the DEM data are used here to identify partially blocked beams and to determine the starting range [

_{B}*r*

_{0}

*in (6)] of blockage for the beams. The median value of the parameter*

_{B}*a*estimated in the unblocked area is 4.21 × 10

^{−4}for this radar scan. Comparing the BBF estimated using our method in the partially blocked sector with the estimates from DEM, we found that the azimuthal dependence of estimated BBF is consistent with the one obtained from DEM (Fig. 2b) except in the azimuthal interval between 262° and 315°.

To highlight the difference of BBFs derived by the suggested method and DEM, the values of BBF at azimuths between 250° and 340° are shown in more detail in Fig. 3. It is obvious that most of BBFs estimated using our method (open squares) are higher than the BBFs derived from DEM (solid dots). To understand the reason for such a discrepancy, we resort to 3D representation of the S-Pol radar beams using the Google Earth tools (Fig. 4a). The geometry of the radar beam is calculated assuming standard atmospheric refraction and the equations described by Doviak and Zrnić (2006). Examining the geographic information provided by the Google Earth in the azimuthal sector between 280° and 330°, we found many high-rise buildings in the downtown of Kaohsiung City, which are not accounted for in DEM but cause additional blockage of the radar beams in this sector. These buildings are also observed by the S-Pol radar and can be identified as strong echoes in the unfiltered reflectivity factor field (not shown). This suggests that our dynamically adaptive BBF estimates are likely more accurate than the estimates from the DEM.

Figure 4a illustrates the geometry of the S-Pol radar beam in the azimuth of 305° and elevation 0.5° on the Google Earth display. It is evident that in addition to the mountains marked by red ellipse, there are two high-rise buildings (highlighted by the red box) that intercept the beam. The spacing between the two blue rays corresponds to the radar beamwidth of 0.91°. Yellow lines divide the propagation path into 150-m range increments. Without removing the clutter, the polarimetric feature of the mountains and building observed as ground clutter marked by eclipses and squares in Figs. 4b and 4c is very distinct in the reflectivity and differential reflectivity fields. The average reflectivity exceeds 50 dB and the average *Z*_{DR} is about −2.0 dB. Scrutinizing Fig. 4b further, several strong echoes with similar features are found on the northeast side of the square mark—that is the location of downtown Kaohsiung City with other high-rise buildings.

Using (8), Δ*Z* is estimated for the elevation 0.5° at 1200 UTC 14 June 2008 (Fig. 4e). The measured and blockage-corrected reflectivity fields are also displayed in Figs. 4d and 4f for comparison. Obviously, negatively biased reflectivity in the sector encompassing the azimuth of 270° is successfully restored and corrected reflectivity in the blocked sector is consistent with reflectivity in the neighboring clear areas. Reflectivity along few azimuths is not recovered because the measured total ΔΦ_{DP} is below the prescribed threshold of 1°. The quantitative evaluation of the method is discussed in the next section.

## 4. Evaluation of correction

### a. Artificial case test

To quantify the performance of our method, an artificial beam blockage test is designed. The received power is artificially reduced by 90% and 99% in the sector from an azimuth of 200° to 205° at 0.5° elevation angle starting at 30 km from the radar where the radar beams are not blocked originally. The 90% and 99% reductions in the received power are equivalent to a 10- and 20-dB loss in reflectivity factor. Figure 5b displays the 20-dB loss in the specified sector. These beams are intentionally selected in the area with relatively strong radar echoes (~30 dB). Thus, the Φ_{DP} difference and integral term of (5) or (6) are large enough not only to satisfy the thresholds in the algorithm but also to reduce the errors in the estimates. The coefficient *a* is estimated *outside of the* “artificially blocked” sector just as it is done in the case of real blockage. Thus, the only difference between this emulation and a real blockage situation is that the standard errors of Φ_{DP} would be larger in the latter case. But this would affect the result only if SNRs are relatively modest (~20 dB or less) because at higher values other factors (spectrum width, correlation between H and V samples, pulse repetition time, and dwell time) are dominant contributors to errors.

Then our method is applied to correct the reflectivity factor at the artificially blocked radar beams. Comparing Fig. 5a with Fig. 5c, it can be seen that the reduced reflectivity is restored. To quantitatively assess the accuracy of our correction, the reflectivity biases for each blocked beam are listed in Table 1. The compensations are not exactly 10 or 20 dB at these radar beams, and they vary beam by beam within about 1.5 dB as functions of azimuth. Nonetheless, the average bias of corrected reflectivity is 0.06 dB, which is small (within the specification for the WSR-88D). We expect similar uncertainty in case of real blockage. The uncertainty in the assumptions such as the constant parameter *a* made in section 2 and errors in the radar measurements may cause the difference between original and corrected reflectivity.

### b. Comparison between upper and lower scans

Comparison of corrected reflectivities at partially blocked elevation (0.5°) with measured reflectivities at elevation of 1.1° (not affected by blockage) was utilized to test the performance of the suggested method. The uniformity of the vertical profile of *Z* should be assessed in the areas where beams at both elevations are not blocked before such a comparison is made. For this purpose, the radar coverage area is partitioned into the following three regions; 1) both elevations are not blocked (area 1), 2) only the upper elevation is not blocked (area 2), and 3) both elevations are blocked. Comparing the reflectivity factors at the same horizontal locations for lower and upper scans in the areas 1 and 2, statistical relations between the two reflectivities are found and vertical gradients of reflectivity are estimated. To avoid contamination from ground clutter, the melting layer, and nonmeteorological scatterers, only the reflectivity factor measurements with the corresponding correlation coefficient (between horizontally and vertically polarized returns) *ρ*_{hv} larger than 0.9 in the range interval between 50 and 100 km are considered.

To quantify the correction efficiency, the median difference *Z*_{upper }*− Z*_{lower} between reflectivity observed at the upper elevation (1.1°) and lower elevation (0.5°) at the same horizontal locations is examined as a function of *Z*_{upper}. The median difference is estimated for every 2-dB step of Z_{upper}. Figure 6 displays the median values of these differences in a wide range of reflectivity obtained from the data collected by the S-Pol radar at 1200 UTC 14 June 2008. In area 1 where radar beams are not blocked at both upper and lower tilts, the reflectivity differences (marked by crosses in Fig. 6) vary from −1.0 to 3.0 dB for different values of *Z*_{upper}. Such variability is related to the diversity of intrinsic vertical profiles of *Z* in lighter and heavier precipitation. The average of the reflectivity difference is 1.10 dB. In contrast, in area 2 where radar beams at lower tilt are partially blocked, the reflectivity differences (marked by solid boxes in Fig. 6) are consistently higher by 2–5 dB (at least for *Z*_{upper} > 20 dB) and the average value is about 3.9 dB. After the beam blockage correction, the reflectivity differences (marked by open boxes in Fig. 6) in area 2 become very close to the ones in the clear area 1. The accuracy of the beam blockage correction can be quantified as the average difference between values denoted by open boxes and crosses. In the example shown in Fig. 6, it is equal to 0.17 dB.

### c. Verification with rain gauges

Another way to evaluate the performance of the suggested method is to compare measured and corrected reflectivity-derived QPE with rain gauge measurements. To quantify the improvement of radar QPE after beam blockage correction, the following four different measures of the quality of radar rainfall estimates are applied.

Bias ratio is defined as

correlation coefficient between the radar storm total *T _{R}* and gauge storm total

*T*is

_{G}fractional root-mean-square error (FRMSE) is defined as

and median fractional RMS error (MFRMSE) is determined as

where *T _{R}*(

*i*) and

*T*(

_{G}*i*) are the radar and gauge estimates of rain totals for the

*i*th gauge, and 〈

*T*〉 and 〈

_{R}*T*〉 are average rain totals from radar and gauges, respectively.

_{G}There are numerous relations between rain rate and dual-polarimetric radar measurements. To isolate the impact of reflectivity correction on rainfall estimation in the blocked region, an *R*(*Z*) relation is utilized. In this study, the tropical *R*(*Z*) relation

used by the U.S. National Weather Service is selected to estimate rain rate *R* for the moderate rainfall event observed between 1000 and 1300 UTC 14 June 2008 in Taiwan.

Using reflectivity observed at the elevation angle of 0.5°, a 3-h rainfall amount is estimated. In the partially blocked region where 0 < BBF < 1 (gray sectors in Fig. 1a), rainfall is estimated using measured and corrected reflectivity separately. It is worth mentioning that the median value of parameter *a* in (5) is dynamically estimated in the clear region of each scan, and then used in (8) to calculate the bias Δ*Z* and correct reflectivity along each blocked beam during the rainfall accumulation period. Considering the difference of raindrop size distributions in the precipitation over ocean and land, only the unblocked sector over land (between azimuths 320° and 345°) are adopted for the estimation of *a* because all the gauges except one used in the comparison are on the Taiwan island. Rainfall in the fully blocked region where BFF = 1 (black sectors in Fig. 1) is not estimated because of a lack of reflectivity measurements. In addition, the QPE and gauge measurements in the region with multiple blockages are not considered.

The statistic measures of radar QPE relative to gauge measurements are listed in Table 2. Only radar and rain gauge pairs having valid (nonzero) values of rain total are utilized in (9)–(12) to calculate the statistical measures. In the unblocked region (BBF = 0 in Table 2) including 19 valid rain gauges, the bias ratio is equal to 1.08, which indicates a slight overestimation of radar QPE using the selected *R*(*Z*) relation (13). The correlation coefficient, FRMSE, and MFRMSE in this region are 0.88, 0.39, and 0.26, respectively. These values are considered as references in evaluating the performance of the correction in the following analysis.

In the blocked region, there are 37 valid gauges. Without blockage correction of reflectivity, not surprisingly, the bias ratio of 0.61 means that the radar significantly underestimates the rainfall amount. The radar QPE is less correlated to gauge measurements, and the errors become larger relative to those in the unblocked region. After the correction, the bias ratio increases and reaches 0.96. Clearly, the correction recovered the QPE reduction caused by beam blockage. The improvements in QPE after the correction can be observed in the other statistical measures as well. The correlation coefficient increases from 0.69 to 0.79, and FRMSE and MFRMSE decrease from 0.62 to 0.45 and from 0.33 to 0.24, respectively (see Dual-Pol row in Table 2). But these statistical measures are still inferior to the ones in the clear region. The errors may come from the variability of the coefficients in the self-consistency (4) and the *R*(*Z*) (13) relations due to terrain-driven microphysical variation in precipitation that may differ in clear and blocked regions. Note that most of the rain gauges in the blocked region are either on the mountain slopes or in the valleys, and rain gauges in the unblocked region are located along the coast of the Taiwan island.

Since DEM information is available, geometric correction (GEOC) is a straightforward choice to recover the deficit of reflectivity caused by blockage. The corrected *Z* can be computed from the formula

where *Z _{m}* is the measured reflectivity in the blocked region. BBF obtained from the DEM is the same as the one mentioned in section 3. Applying the same

*R*(

*Z*) relation (13) with GEOC, the radar QPE and statistical measures are calculated and listed on Table 2. The radar QPE is improved by the compensation (14) of

*Z*. The enhancements of QPE can be clearly observed in the bias ratio that increases from 0.61 to 0.77, but it is still underestimated by 23% relative to gauge measurements. Although the other statistical measures indicate improvements compared to the no-correction category, these are not as good as dual-polarization correction. Because the factors such as high-rise buildings, trees, and anomalous propagations that could cause additional beam blockage are not considered, the DEM-derived BBF is smaller than the BBF that the radar beam experienced in the observation. The fact that the bias ratio obtained from GEOC is smaller than the one from Dual-Pol correction is consistent with the results that BBF derived from the proposed method is larger than BBF calculated based on DEM (Figs. 2 and 3). The results demonstrate the advantages of the proposed method over the GEOC method in the complicated blockage environment where natural and human-made obstacles coexist in the radar scan.

## 5. Stability of the method

To examine the robustness of the beam blockage correction method, the average of reflectivity difference is calculated for each volume scan over the duration of three rainfall events observed by S-Pol radar in June 2008 during the SoWMEX/TiMREX field experiment. Figure 7 shows the time series of the reflectivity difference *Z*_{upper }*− Z*_{lower} in area 1 and area 2 before and after beam blockage correction for 44 radar volume scans. This difference after blockage correction in area 2 is consistently close to the corresponding estimate in the unshielded area 1, which attests to the stability and robustness of the algorithm. The corresponding averages over 44 scans are 0.2 and 0.5 dB, respectively. The average difference *Z*_{upper }*− Z*_{lower} over these 44 scans before the correction in area 2 is 3.6 dB. Hence, the estimated average areal bias in *Z* at elevation 0.5° is 3.4 dB. In the consistency examination, the parameter *a* in (5) is assumed to be constant for each individual scan and obtained in the clear area. The assumption of constant parameter *a* implies that the variations of the parameter *a* due to raindrop size distribution (DSD) diversity are smaller than the ones caused by PBB. In other words, it is assumed that parameter *a* is relatively robust with respect to DSD variability. Simulations based on DSDs measured in central Oklahoma indicate that parameter *a* strongly depends on differential reflectivity *Z*_{DR}, which characterizes the type of DSD and to a lesser degree the temperature of raindrops.

Nonetheless, what really matters is the ratio of *a _{B}*/

*a*. According to (8), the reflectivity bias caused by PBB is less affected by the uncertainty of parameter

*a*because its effect is compensated to a certain degree in the ratio. Also the total differential phase and integration along radar beams include the contributions from a wide range of DSDs and this reduces the uncertainty in parameter

*a*.

Another way to check the robustness of our proposed method is to examine the stability of estimated reflectivity bias at a specified beam location for a period of time. If there are no significant changes in weather, terrain, and radar condition, then the estimated bias should be relatively stable. Also, two types of parameter *a* are utilized: one is dynamically obtained at each scan, whereas another is the climatological value of 4.26 × 10^{−4}. This climatological value has been obtained via simulations for *T* = 20°C using 25 920 drop size distributions measured in central Oklahoma. Radar beam at the azimuth of 300° is selected to estimate the reflectivity biases over 44 radar scans. By scrutinizing the results, it has been found that the estimated reflectivity biases vary quite intensively if the total span of differential phase ΔΦ_{DP}(*r _{o}*,

*r*) along the beam is smaller than 10°. This indicates that the cumulative rainfall along the radial is small, leading to large fractional errors in the estimates of ΔΦ

_{m}_{DP}. Thus, the threshold ΔΦ

_{DP}(

*r*,

_{o}*r*) > 10° is adopted and in 32 of the 44 scans it was exceeded at the examined azimuth. The time series of the reflectivity biases estimated using our method with the dynamic and the climatological parameter

_{m}*a*in the azimuth of 300° and the elevation of 0.5° from the 32 scans are displayed in Fig. 8. The reflectivity biases averaged over 32 scans are practically the same (7.0 dB) if dynamically adjusted or climatological values of the parameter

*a*are utilized. This suggests that the climatological value of

*a*might be well suited for the correction. The corresponding rms errors of the bias estimates are 1.0 and 1.3 dB, respectively.

The temporal fluctuations of estimated biases (Fig. 8) might reflect the temporal changes of atmospheric conditions (i.e., vertical profile of refractive index) along the propagation path. Thus, the scan-by-scan bias estimate using either climatological or dynamic parameter *a* may provide more accurate correction of reflectivity, especially in regions where unexpected objects severely block the radar beam. A more general benefit of this dynamic bias estimation is under conditions of anomalous propagation. In such cases the reflectivity bias derived from DEM with standard atmospheric condition can severely drift away from the actual bias.

Our dynamic method is not suitable for radials with low cumulative rainfall. To overcome this, a bias correction map can be built by taking the average value of biases obtained for each radar beam in the presence of sufficiently intense rainfall over an appropriate time period. Then corrections can be applied along the blocked beam if echoes are not strong enough to produce a ΔΦ_{DP}(*r _{o}*,

*r*) measurement larger than the threshold needed for accurate bias estimation.

_{m}Comparing to 1.25 dB estimated using DEM (dashed line in Fig. 8), the average bias estimated using our method is about 4.7 dB higher. The extra bias is most likely caused by high-rise buildings in the downtown of Kaohsiung City that are not accounted for in DEM; the details are discussed in the next section.

## 6. Discussion

### a. Data quality

Data quality is extremely important for the performance of this method. Several data quality control steps are embedded in the algorithm. First, ground clutter is filtered out in the dataset by the NCAR data quality control processor. Second, observed Φ_{DP} is smoothed along the radial and the gaps (in Φ_{DP}) due to weak signal are filled by linear interpolation (Ryzhkov and Zrnic 1996). Third, only the reflectivity factors associated with high *ρ*_{hv} and high signal-to-noise ratio are selected for estimation of parameters *a* and *a _{B}*. The entire quality control process helps avoid contamination by ground clutter and nonmeteorological scatterers and reduces the uncertainty of radar measurements in the weak signal regions.

### b. Differences in biases

It is noticeable that there are some disagreements in biases derived from DEM data and our method (Fig. 2b). These differences may be due to the following reasons:

Parameter

*b*in (1)–(8) is not constant for all different types of rain and can be affected by variability of raindrop size distributions.The spatial resolution of DEM is not high enough to describe the terrain profile of the actual blockage.

The biases derived from DEM data are calculated from the two-way beam pattern, whereby the blocked fraction is normalized by the 3-dB beam cross section. The reflectivity biases estimated by our method are not sensitive to the vertical profile of the blockage.

There are radar measurement errors, such as radar antenna positioning and contributions from sidelobes.

Trees, buildings, and other human-made objects, which are not accounted for in DEM, may cause extra blockage.

Multiple blockages along the beam (such as two or more mountain ranges) are not considered at this time.

Attenuation caused by rain has not been considered.

### c. Future work

The results presented in this paper have demonstrated successful retrieval of the reflectivity bias caused by beam blockage using the consistency between *K*_{DP} and *Z*. Still, several issues that should be addressed remain.

The method can be applied to individual scans for each blocked radial. However, if there are no radials free of partial beam blockage to obtain parameter

*a*, or if precipitation is not present along the blocked radial to obtain parameter*a*, then the correction cannot be made. To resolve this we suggest a global approach. For a relatively long-lasting precipitation event over radar, a mean bias for each azimuth/elevation could be obtained over several sequential radar scans. Then, these mean biases can be stored in a correction table for each beam position in a volume scan. These would provide a reasonable correction along beams with small total Φ_{B}_{DP}and/or weak radar echoes. Further, by gathering enough bias data over a period of time, a climatological bias table for each azimuth/elevation can be made.The impact of DSD variability and temperature on the performance of the suggested method should be quantified using theoretical simulations and radar measurements for different types of rain.

Combining with ground clutter detection algorithm, this algorithm can dynamically estimate reflectivity bias beyond the range location where ground clutter is detected. The idea is to exploit the fact that at these locations, the clutter often partially blocks the beam.

Extension of the method to the cases with significant attenuation in rain (and/or shorter radar wavelengths) is in order.

## 7. Conclusions

We have proposed a novel method to estimate reflectivity bias caused by beam blockage. It implies integrating the self-consistency relation between *K*_{DP} and *Z* along radar beam and capitalizes on the immunity of total differential phase Φ_{DP} to partial beam blockage (PBB).

Instead of using the self-consistency relation to restore reduced *Z* at an individual radar gate, the total span of differential phase ΔΦ_{DP} and integration of measured reflectivity are utilized to estimate blockage-related bias of *Z* for each radar beam in the blocked area. This allows avoiding statistical uncertainties inherent to point measurements of Φ_{DP} and estimates of *K*_{DP}. For the sake of simplicity and robustness, differential reflectivity *Z*_{DR} (which is prone to PBB-related biases, miscalibration, and statistical errors) is not utilized as opposed to the traditional self-consistency approach. Instead, the proposed technique assumes that rain type, which is characterized by the parameters in the power-law *Z*–*K*_{DP} relation, is the same in the blocked and unblocked radar coverage areas. The dynamical nature of the recommended procedure helps to mitigate the variability of beam blockage fraction caused by changes in atmospheric refractive conditions.

The results of applications of the proposed method on the S-Pol observations in the SoWMEX/TiMREX and the comparison with DEM-based methodology show its capability to estimate the bias in the beam blockage area and the advantage over DEM if unaccounted high-rise buildings (or other man-made obstacles or trees) produce additional blockage.

The algorithm was validated using comparisons of corrected *Z* at blocked elevations and higher unblocked elevations and assessing the relative performance of the *R*(*Z*) relation in the blocked and unblocked areas utilizing rain gauge data. The robustness of the technique was verified via examining the temporal variability of the retrieved Z bias. The standard deviation of the bias estimate is within 1.5 dB.

Eventually, the method opens up a potentially promising avenue for operational application, as the WSR-88D operational radar network is being upgraded with dual-polarimetric capability. The application of the method could make improvements in the accuracy of radar QPE as well as vertically integrated liquid (VIL) estimation in the mountainous regions where radar beams are significantly blocked.

## Acknowledgments

The authors extend their thanks to Carrie Langston and Ami Arthur, who helped us to generate the DEM for S-Pol in Taiwan. We also want to thank Pin-Fang Lin, a scientist from the Central Weather Bureau of Taiwan, who provided the S-Pol observation data in the SoWMEX; and Scott Ellis, a scientist from NCAR, who provided the S-Pol radar calibration information. This work was partially supported by MIT Lincoln Laboratory under the MOUs of Implementation of NEXRAD Dual Polarization Products FA8721-05-C-0002 and Design Weather Radar Products for use in FAA Weather Systems 700013024. Funding for the CIMMS authors came from the NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA17RJ1227, U.S. Department of Commerce.

_{DP}rainrate estimation including a case study at S-band. Preprints, 28th Conf. on Radar Meteorology, Austin, TX, Amer. Meteor. Soc., 117–118