Articles : Special Edition on Years of the Maritime Continent (YMC)
Cバンド二重偏波レーダーで降雨中に観測された偏波間位相差におけるスプリアス信号の検出・除去アルゴリズム
2020 年 98 巻 3 号 p. 585-613
詳細
2020 年 98 巻 3 号 p. 585-613
In this study, an algorithm was developed to detect the spurious differential phase ΦDP and specific differential phase KDP in the rain for application after the removal of gate-to-gate ΦDP fluctuations. The algorithm is a threshold filter designed based on the empirical relationship between the KDP and radar reflectivity factor at horizontal polarization ZH for raindrops. The construction and validation of the algorithm were performed using the data observed by the C-band polarimetric radar on board the research vessel Mirai near Sumatra from 23 November to 17 December 2015, when a pilot field campaign of the Years of the Maritime Continent (YMC) project was conducted. Perturbations exist in the ΦDP and associated spurious values of KDP on a 10-km scale in the range direction, which are mainly induced by second-trip echoes and nonuniform beam filling. This new algorithm can efficiently detect these perturbed ΦDP values and the positively and negatively biased KDP values. The standard deviation of the KDP in areas with relatively low ZH is also significantly reduced by the application of the algorithm. Simultaneously, the estimation of the rain rate from the filtered KDP has been greatly improved. The results indicate that the algorithm developed in this study can efficiently manage the quality of the data observed not only in the open ocean but also in coastal areas of the Maritime Continent.
Differential phase ΦDP is a parameter observed by polarimetric weather radar, and this parameter is the difference between the propagation phase shift of horizontally and vertically polarized waves as the waves propagate through precipitation (Bringi and Chandrasekar 2001). Because ΦDP is insensitive to radar calibration errors and precipitation attenuation, it plays a significant role in meteorological applications. ΦDP is a very useful parameter when correcting propagation effects at shorter radar wavelengths, because the propagation effects induce attenuation and differential attenuation throughout the radar echo volume (Bringi et al. 1990; Aydin and Giridhar 1992; May et al. 1999; Carey et al. 2000). The specific differential phase KDP derived from the range derivative of ΦDP along a radial is closely related to rain intensity and has largely been applied to more accurate estimations of rainfall and raindrop size distribution (Balakrishnan and Zrnić 1990; May et al. 1999; Brandes et al. 2001; Maki et al. 2005; Bringi et al. 2006; Silvestro et al. 2009; Matrosov et al. 2013; Adachi et al. 2015; Boodoo et al. 2015).
Since raindrops are oblate and have a minor axis oriented vertically in the mean, ΦDP in the rain generally exhibits a monotonically increasing trend within a particular range. However, ΦDP, which is measured by polarimetric weather radar, is easily contaminated, resulting in both positively and negatively biased KDP values and greatly degrading the usefulness of ΦDP and KDP. Previous studies showed that the contamination of ΦDP and biases in KDP are commonly manifested as both gate-to-gate fluctuations and perturbations within a distance much greater than a range gate (or on a 10-km scale) along the radial direction. In this study, the former will be referred to as high-frequency range fluctuations and the latter as low-frequency range perturbations. The identification and removal of these high-frequency range fluctuations and low-frequency range perturbations in ΦDP and KDP remain challenging issues.
High-frequency range fluctuations in ΦDP originate from the statistical variance of the ΦDP measurement and are commonly induced by both nonmeteorological echoes and differential backscatter phase δ. Nonmeteorological echoes stem from targets, such as ground clutter, sea clutter, chaff, biological scatter, clear air echoes, and so on. These targets produce highly variable ΦDP values. Ryzhkov and Zrnić (1998b) found that the combined use of thresholds of the copolar cross-correlation coefficient ρHV and the standard deviation of ΦDP can notably remove nonmeteorological noises. Their method for removing nonmeteorological echoes has largely been applied to the quality control of polarimetric radar measurements. Algorithms based on fuzzy logic can also be successfully applied to distinguish between meteorological and nonmeteorological radar echoes (Gourley et al. 2007; Moisseev and Chandrasekar 2009; Chandrasekar et al. 2013; Krause 2016).
On the other hand, δ is attributed to non-Rayleigh scatter and becomes more significant at shorter radar wavelengths (Bringi and Chandrasekar 2001), which can often induce high-frequency range fluctuations in ΦDP and greatly affect the accuracies of ΦDP and KDP. An effective method for removing the undesirable effect of δ was proposed by Hubbert and Bringi (1995), where an iterative filtering technique was employed along the range direction. Recently, Maesaka et al. (2012) and Giangrande et al. (2013) proposed methods with a monotonicity constraint on ΦDP to remove high-frequency range fluctuations from phase measurements. As indicated by Hubbert and Bringi (1995), δ can also extend over many range gates, resulting in perturbed ΦDP and biased KDP within longer distances along the radial direction.
Low-frequency range perturbations in ΦDP and the effects of these perturbations were described in detail by Ryzhkov and Zrnić (1998a). They revealed evidence from both the modeling and observational investigations that negatively biased KDP can appear on both sides of a rain cell in the range direction if the ΦDP profile used to estimate the KDP is perturbed by nonuniform beam filling (NBF). Negatively biased KDP on both sides of a rain cell may be accompanied by a positively biased KDP near the center of the cell. The perturbation of ΦDP induced by NBF was also found by Ryzhkov and Zrnić (1998a) in regions with large cross-beam gradients around strong reflectivity. The perturbed ΦDP exhibited a spurious oscillatory behavior with a wavelength of approximately 14 km in the range direction. Such a low-frequency range perturbation in ΦDP resulted in a biased KDP with similar oscillatory behavior, leading to biases in the KDP-based rain rate estimates. As indicated by Ryzhkov (2007), enhanced attenuation can also increase the gradient of reflectivity and induce the NBF-related perturbation in ΦDP. Some studies have also investigated the detailed impacts of NBF on the qualities of polarimetric variables, both theoretically and experimentally (Gorgucci et al. 1999; Gosset 2004; Ryzhkov 2007). Gorgucci et al. (1999) revealed that the KDP bias induced by NBF can be both positive and negative, and this bias increases with increased reflectivity variation along the range direction. Simple formulas have been developed to theoretically estimate ΔΦDP, which is the perturbation of ΦDP induced by NBF due to large cross-beam gradients of reflectivity (Ryzhkov 2007; Ryzhkov and Zrnić 2019). The correlation between the radial profiles of ΦDP and ΔΦDP is high when ΦDP is perturbed by NBF. As will be presented in Sections 3 and 5 of this study, ΦDP and KDP contaminated by second-trip echoes also show significant low-frequency range perturbations along the radial direction. Specifically, second-trip echoes can induce spurious ΦDP and KDP with considerably greater magnitudes than those induced by NBF.
Although several methods have been developed to detect and remove spurious ΦDP and KDP with high-frequency range fluctuations, few studies have addressed the identification and removal of low-frequency range perturbations in ΦDP and KDP. Particularly, as will be presented in Sections 3 and 5 of this study, the methods developed to handle high-frequency range fluctuations in ΦDP and KDP may not be suitable for the detection and removal of the spurious KDP resulting from the low-frequency range perturbations of ΦDP.
The purpose of this study was to develop an algorithm to detect low-frequency range perturbations in the range profiles of ΦDP and KDP measured in the rain by C-band polarimetric radar. The algorithm, which is applied after the removal of high-frequency range fluctuations in ΦDP, is a threshold filter based on an empirical relationship between KDP and the radar reflectivity factor at horizontal polarization ZH for raindrops. In Section 2, the data used to construct and validate the algorithm and data preprocessing are described. In Section 3, the features of the spurious low-frequency range perturbations in ΦDP and KDP are illustrated. Details of the algorithm development are presented in Section 4. In Section 5, the algorithm's performance is investigated, and finally, a summary and discussion are presented in Section 6.
In this study, the data measured by the polarimetric radar on board the research vessel Mirai were used to illustrate the characteristics of spurious ΦDP and KDP with low-frequency range perturbations. These data were also utilized to develop and validate the algorithm to detect the spurious ΦDP and KDP.
The Mirai polarimetric radar is a C-band weather radar that has been under operation since the summer of 2014 (Katsumata 2014). This radar uses a solid-state transmitter and has been developed by employing advanced semiconductor and pulse compression techniques (Wada et al. 2009; Anraku et al. 2013). The major specifications of the Mirai polarimetric radar are presented in Table 1.
The data used in this study were observed by the Mirai polarimetric radar around 4.067°S, 101.9°E at an elevation of 0.5° from 23 November to 17 December 2015, when a pilot field campaign of the Years of the Maritime Continent (YMC) project was conducted in the Indian Ocean (Yokoi et al. 2017). As presented in Fig. 1, the observational area is part of a tropical rainy region near Sumatra in Indonesia. The time interval, azimuthal resolution, range resolution, and maximum range of the data used to develop the algorithm were 6 min, 0.7°, 150 m, and 150 km, respectively. The data were obtained by using a pulse of 1-µs width before and 64-µs width after the range of 12 km. At the same time, a dual-pulse repetition frequency (PRF) (667/833 Hz) mode was employed to extend the range of the Nyquist velocity interval. Low-level plan position indicator (PPI) scans were also performed with a low PRF (400 Hz) every 30 min. Data from these low-PRF scans have an unambiguous range greater than 300 km and were used as the supplemental material for the identification of second-trip echoes.
Geographic map of the observational site. The circle radius is 150 km from the Mirai, which is the range of the radar data used in this study.
Before analyzing the spurious ΦDP and KDP with low-frequency range perturbations and developing the algorithm to detect the perturbations, the observed parameters were processed as follows. The initial ΦDP measurements were performed to remove the system offsets and correct aliased data using the method of Wang and Chandrasekar (2009). Similar to previous studies (e.g., Ryzhkov and Zrnić 1998b), nonmeteorological echoes, such as ground and sea clutter, were detected and removed based on thresholds of ρHV and the areal standard deviation of ΦDP, and these thresholds were set to 0.65° and 40°, respectively. These values were determined experimentally by analyzing the observed data for various precipitation events. The standard deviation of ΦDP was computed in a box consisting of three pixels in the azimuthal direction and nine pixels in the range direction. Similar to previous studies (e.g., Katsumata et al. 2008; Boodoo et al. 2015), echoes with low values of the signal quality index (SQI) have also been removed. The SQI threshold used in this study was set to 0.3. Some second-trip echoes can be removed by applying the thresholds of ρHV and SQI. However, as will be shown in Sections 3 and 5 of this study, considerable second-trip echoes still remained undetected. The dual-PRF technique used to reduce second-trip echoes (e.g., Katsumata et al. 2005) has not been employed in this study.
Occasionally, radar observables were contaminated with the presence of other ships. Those ship-contaminated data have been identified and removed manually. The contribution of δ within ΦDP was then removed by applying the iterative finite impulse response (FIR) filtering technique of Hubbert and Bringi (1995). The FIR filtering process was repeated 10 times by using the same coefficients of the FIR as those of Hubbert and Bringi (1995).
After removing the high-frequency range fluctuations induced by nonmeteorological echoes and δ from ΦDP, KDP was calculated based on the slope of a least-squares fit of the filtered profile of ΦDP over a range interval of 1.5 km. The range interval utilized here corresponds to a light filter for the estimation of KDP (Ryzhkov and Zrnić 1996; Wang and Chandrasekar 2009). Notably, although the light filter for the KDP estimation is useful for high spatial resolution, the light filter may induce larger standard errors in KDP if there are errors in the estimation of ΦDP.
The high-frequency range fluctuations in ρHV and ZH were then removed using the same filter as that of Hubbert and Bringi (1995). Next, ρHV was corrected for noise using the signal-to-noise ratio (Schuur et al. 2003). The attenuation of ZH was corrected using ΦDP. The linear ΦDP method was applied owing to its simplicity (e.g., Bringi et al. 1990). An attenuation correction coefficient of 0.072 dB per degree was utilized, which was experimentally determined by applying the correcting method of Carey et al. (2000) to the observed data. To reduce the undesirable effect of the contaminated ΦDP, the attenuation correction of ZH was repeated three times with the detection and removal of spurious ΦDP. The impact of attenuation on the algorithm developed in this study has been examined. Before the application of attenuation correction, some relatively high KDP values may be misjudged as spurious data in areas where enhanced attenuation of ZH occurred. Such a defect has been resolved by performing the above attenuation correction process (not shown). The range derivatives of KDP and ZH, which have been used in the algorithm developed in this study, were also calculated based on the slope of the least-squares fit of their profiles over a range interval of 1.5 km.
The ΔΦDP value was calculated based on Eq. (6.73) of Ryzhkov and Zrnić (2019):
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Although the Mirai radar antenna is operated by compensating for the attitude angles of the ship so that data can be obtained at a ground-relative elevation and azimuth of designation, the effects of ship movement on the polarization plane remained uncorrected. However, Thurai et al. (2014) found that the effects of ship movement are tolerable if the canting angle of the drop's symmetry axis relative to the polarization plane is less than 10–15°. In fact, the sea was calm when the data used in this study were obtained, with the maximum and mean canting angles of the data being 3.43° and 0.37°, respectively. More than 99 % of the total data have canting angles below 1.5°, which is much smaller than the tolerable canting angle revealed by Thurai et al. (2014). Therefore, the polarization plane remained as observed, and the correction method of Thurai et al. (2014) for ship movement has not been applied in this study.
An analysis of the observed data revealed that the low-frequency range perturbations of ΦDP and KDP exhibit distinct signatures. These signatures will be illustrated in this section based on a low-elevation scan from the Mirai polarimetric radar.
As an example, Fig. 2 presents the horizontal distributions of ZH and KDP observed at a 0.5° elevation angle for 1930 UTC 25 November 2015. The precipitation system presented in Fig. 2 was generally of intermediate intensity. In some regions, a ZH value greater than 44 dBZ and a KDP value greater than 1° km−1 were observed. As indicated by the light purple color in Fig. 2b, prominent features in the KDP field were the dozen pockets of large negative KDP values recognized on the west and northwest sides of the radar.
Distributions of (a) ZH and (b) KDP at an elevation of 0.5° for 1930 UTC 25 November 2015. In (c), the distribution of ZH at an elevation of 0.5° from the low-PRF scan for 1929 UTC is presented. The solid lines of A1–A3 indicate the locations of the range profiles presented in Fig. 3. Hatching indicates the sectors suffering from beam blockage caused by Mirai structures. The coastline is indicated by a dashed curve.
The characteristics of spurious ΦDP and KDP can be seen more clearly in Fig. 3, which presents the range profiles of the radar observables in three directions, along lines A1, A2, and A3, as depicted in Fig. 2. Notably, for the data used in Fig. 3, the high-frequency range fluctuations in ΦDP have already been removed, and then, the KDP has been derived. Most of the low-frequency range perturbations in ΦDP can be attributed to the effect of second-trip echoes or NBF. The arrows in the top panels of Fig. 3 indicate some of these perturbations in ΦDP.
Range profiles (from left to right) along lines (a) A1, (b) A2, and (c) A3, as presented in Figs. 2a and 2b, for ΦDP (top panels, black curves), ΔΦDP (upper middle panels), KDP (middle panels), ZH (lower middle panels, black curves), ρHV (black curves), and SQI (green curves) (bottom panels). In the top and lower middle panels, the range profiles of ΦDP and ZH (chartreuse curves) from the low-PRF scan presented in Fig. 2c are supplemented. The arrows in the top panels designate some regions where spurious perturbations of ΦDP were observed.
Figure 3a presents the range profiles along line A1. A 20° jump in ΦDP is evident in the range of approximately 50 km to 55 km. Then, ΦDP returns to nearly the value before the jump and begins a generally monotonic increase from a range of 60 km. Corresponding to the jump and resumption of ΦDP, KDP exhibited a maximum (greater than 2° km−1) and a minimum (less than −3° km−1) before a range of 60 km. The values of the maximum and minimum KDP appear to be unrealistic and inconsistent with the intensity of the ZH (below 22 dBZ) observed in the same segment. Consequently, the ΦDP jump is spurious and results in an unrealistic KDP.
The ΦDP jump from its local mean trend occurred where relatively weak echoes below 22 dBZ were observed (Fig. 3a). There was no such jump in the ΦDP profile obtained from the low-PRF scan during the nearest time. These facts suggest that the jump and resumption of ΦDP could be attributed to the contamination of second-trip echoes from rain located beyond the maximum range of 150 km (Fig. 2c). Because the ΦDP measured by the polarimetric radar is cumulated along the range direction, the jump of ΦDP as shown above could be attributed to the fact that second-trip echoes originate from rain outside the unambiguous range, which possesses higher ΦDP than that related to rain within the unambiguous range.
A sharp drop and restoration in the SQI and ρHV were observed in the segment contaminated by the second-trip echoes (Fig. 3a). The values of the SQI and ρHV dropped as low as 0.3 and 0.86, respectively, near the range of 55 km, where second-trip contaminated ΦDP reached its maximum value. However, it is evident that the spurious ΦDP and KDP induced by the second-trip echoes in the range of approximately 50 to 60 km could also be accompanied by relatively high SQI and ρHV values. Second-trip echoes with high SQI and ρHV values were also observed in other studies (e.g., Park et al. 2016). Thus, using only SQI and ρHV thresholds may not be effective for the elimination of the second-trip contamination from ΦDP and KDP.
In addition, the second-trip contamination induced an inconsistent variation between KDP and ZH along the range direction. The change in KDP measured in the rain is positively correlated with that of ZH. However, Figure 3a shows that overall, the rapid increase in KDP in ranges from approximately 45 to 53 km occurred with a decrease in ZH, whereas the sharp decrease in KDP in ranges from approximately 53 to 58 km was associated with an increase in ZH. Notably, values of spurious KDP were close to 0° km−1 near the range of 55 km, where relatively weak echoes below 20 dBZ were observed.
Another perturbation in the ΦDP profile along line A1 was found at distances over 135 km (Fig. 3a). The perturbation of ΦDP resulted in negatively biased KDP in ranges from approximately 135 to 145 km. KDP exhibited a minimum (less than −1° km−1) near the range of 140 km, where ZH was close to 35 dBZ. As seen from Fig. 2, line A1 passed through the periphery of a reflectivity core stretching approximately along the radar beam at far distances from the radar. Consequently, relatively large cross-beam gradients of reflectivity could exist along line A1. Figure 3a shows that the magnitude of ΔΦDP increased from approximately 120 km. An increase or a decrease in ΦDP was generally in agreement with that in ΔΦDP at far distances from the radar. As seen from Fig. 3a, a noticeable decrease in ρHV occurred from the range of 120 km. These facts suggest that the perturbation in ΦDP and unrealistic KDP at distances over 135 km could be attributed to NBF due to large cross-beam gradients of reflectivity (e.g., Ryzhkov 2007).
The range profiles along line A2 are presented in Fig. 3b. Line A2 passed through a reflectivity core centered at a distance of 110 km. In ranges from approximately 100 km to 116 km, perturbations in ΦDP induced KDP to have a negative minimum in front of and behind the reflectivity core, respectively, which is consistent with the results of Ryzhkov and Zrnić (1998a) and could be attributed to the NBF effects. Figure 3b shows that NBF can also induce an inconsistent variation between KDP and ZH along the range direction. In fact, the decrease in KDP in ranges from approximately 100 to 102 km occurred with the increase in ZH. In contrast, the increase in KDP in ranges from approximately 116 km to 120 km occurred with the decrease in ZH.
The perturbation of ΦDP along line A2 also occurred in ranges from approximately 120 km to 130 km, which induced both positive (as high as 1.5° km−1) and negative (as low as −1.5° km−1) biased KDP in areas of ZH at approximately 30 dBZ. Notably, line A2 passed through the periphery of another reflectivity core, and the magnitude of ΔΦDP increased in ranges between 120 and 130 km (Figs. 2a, 3b), which indicates that the ΦDP perturbation and the associated spurious KDP along line A2 at far distances from the radar could also be attributed to NBF (e.g., Ryzhkov 2007).
Figure 3c presents the range profiles along line A3. Perturbations in ΦDP occurred before the range of 75 km. Such perturbations were not found in the ΦDP profile obtained from the low-PRF scan during the nearest time, which suggests that the ΦDP perturbations before the range of 75 km could be attributed to the contamination of second-trip echoes from rain located beyond the maximum range of 150 km (Fig. 2c). Similar to the second-trip contamination presented in Fig. 3a, spurious jumps of ΦDP from the local mean trend and pairs of unrealistically positive and negative KDP are evident in Fig. 3c before the range of 75 km. In the segment contaminated by the second-trip echoes, KDP showed spurious maximum values of more than 3° km−1 and spurious minimum values of less than −1.5° km−1 in areas with a ZH intensity of below 15 dBZ. The spurious ΦDP and KDP induced by the second-trip echoes were also associated with a sharp drop in but relatively high values of SQI and ρHV.
The KDP biases were further statistically investigated. Figure 4 presents the scatterplot of KDP versus ZH from the low-level scan, as presented in Figs. 2a and 2b. The dashed curve in Fig. 4 is generated by a best fit to log (KDP) and ZH based on a linear regression analysis. Figure 4 reveals that KDP and ZH were clustered around the best fitting curve. In areas with ZH values below 40 dBZ, some data significantly deviated and were outside the major cluster, which could be attributed to the KDP biases of both signs, as seen from Fig. 3. In contrast, Fig. 4 also reveals that in areas with ZH values above 40 dBZ, the KDP and ZH were clustered more tightly around the best fitting curve, with a much smaller deviation from the major cluster. This fact suggests that KDP is less noisy in the high-ZH areas. The observational results in Fig. 4 are consistent with the conclusion of Ryzhkov and Zrnić (1996), indicating that deviations due to processing noise prevail in the low-ZH areas, whereas meteorological variability, such as the variability of drop size distribution (DSD), dominates scatter in the high-ZH areas.
(a) Scatterplot of KDP versus ZH at an elevation of 0.5° for 1930 UTC 25 November 2015. The dashed curve was obtained by a least-squares fit to log (KDP) and ZH. The detection of the spurious KDP, which is shown in red, was tested by setting D2, D3, and RK to 0 and the threshold of F to 8. (b) Same as (a), but for setting D2, D3, and RK to 0 and the threshold of F to 1. (c) Same as (a), but for setting RK to 0 and the threshold of F to 8. (d) Same as (a), but for setting the threshold of F to 8 and using RK, as expressed by Eq. (10).
In summary, the analyses presented above reveal that after the removal of high-frequency range fluctuations in ΦDP, the low-frequency range perturbations of ΦDP can remain. Second-trip echoes and NBF could be two sources of low-frequency range perturbations in ΦDP. The low-frequency range perturbations in ΦDP can induce spurious KDP that may show significantly positive and negative biases on the best fitting curve between log (KDP) and ZH. Moreover, the spurious KDP may also have a range variation inconsistent with that of ZH. These signatures facilitate the development of an algorithm to identify both spurious ΦDP and unrealistic KDP.
As presented in Fig. 4, KDP may increase logarithmically with ZH, as measured in the rain by the Mirai C-band polarimetric radar. Such an empirical relationship between the KDP and ZH has also been previously noted via observational studies and scattering simulations for C-band polarimetric radar (Aydin and Giridhar 1992; Carey et al. 2000; Bringi et al. 2001). According to Aydin and Giridhar (1992), the empirical relationship between KDP and ZH in the rain can be expressed as follows:
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Ryzhkov and Zrnić (1996) have suggested that the spurious values of KDP can be recognized by examining the scattergrams of KDP versus ZH. They noted that “bad” data points are outside “good” data points in the scattergrams of KDP versus ZH, which was also observed in this study (Fig. 4). Based on their suggestion, an objective function is used to identify spurious ΦDP and KDP.
The algorithm developed in this study processes radar observables on an individual radial basis. To obtain the objective function, Eq. (2) is changed into an exponential form:
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The member on the right-hand side of Eq. (3) can be considered as the empirical KDP estimated from ZH. In addition, the range derivative of Eq. (2) is obtained, which results in the following:
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The objective function, F, is determined to contain three variables, which can be expressed as follows:
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In Eq. (5), the variable RA is used to regulate the magnitude of F for all measured data. The variable RK is designed to further regulate the magnitude of F in a distinct KDP area, where spurious KDP cannot be sufficiently detected by RA. The values of RA and RK are set to 0 if the measured KDP and ZH are positioned along both empirical curves defined by Eqs. (3) and (4). The values of RA and RK are augmented for possibly spurious KDP deviating significantly from either of the empirical curves defined by Eqs. (3) and (4). N represents a normalization factor with respect to ZH. F is designed as a dimensionless quality. The dimensionless F is obtained simply by dividing each of the variables used in F by 1 with an identical unit, which will not be shown explicitly in this study.
F has been determined experimentally according to the signatures of the spurious ΦDP and KDP revealed in Section 3. A threshold of F is then used to detect spurious KDP. As shown in Fig. 3, the correlation between the low-frequency perturbations of ΦDP and the spurious values of KDP was high. As a result, spurious ΦDP can be detected simultaneously with the detection of spurious KDP.
4.2 Objective function design a. Definition of RARA is used to evaluate deviations for all measured data and is defined as follows:
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RA has utilized the multiplication of D1–D3. As shown below, D1–D3 are the measured KDP and ZH deviations from the empirical curve defined by Eq. (3) or Eq. (4). The magnitude of RA is also inversely correlated with that of the squared ρHV, based on the observation that the values of ρHV often decrease in the region associated with spurious ΦDP and KDP (Fig. 3).
1) D1D1 is calculated according to the formula
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D1 is the measured KDP and ZH deviation from the empirical curve defined by Eq. (3), which facilitates the identification of the spurious KDP deviating from the empirical KDP as estimated from ZH. The effectiveness and limitation of D1 in detecting spurious KDP have been examined. As presented in Figs. 4a and 4b, a lower threshold of F is required for using only D1 to detect spurious KDP values in low-ZH areas. On the other hand, the lower threshold of F results in overdetection of spurious data in the high-ZH areas. Therefore, D2 is designed to facilitate in the identification of spurious KDP values in the low-ZH areas while retaining quality measures of KDP in the high-ZH areas.
2) D2D2 is calculated according to the formula
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D2 utilizes the ratio of D1 to the empirical KDP estimated from ZH, which allows the magnitude of D2 to increase with a decrease in ZH. This ratio also varies in accordance with a and b, with the ratio value tending to be larger with smaller a and larger b for the KDP measured at the same ZH. Such variation can be compensated for by using an exponent a/b in Eq. (8). Figure 4c shows that after the supplement of D2, the spurious values of KDP in low-ZH areas can be detected effectively. However, some spuriously small or negative KDP values in the high-ZH areas still remained undetected.
3) D3Figure 3a shows that spurious ΦDP around the range of 55 km can induce spurious KDP close to 0° km−1 in regions with relatively weak echoes. Such spuriously small KDP associated with weak echoes can hardly be identified using only D1 and D2 (Fig. 5a), because it is located near the empirical curve defined by Eq. (3), with values of D1 and D2 close to 0.
(a) A segment of range profiles along line A1 presented in Figs. 2a and 2b for ΦDP (top panels) and KDP (bottom panels). The detection of the spurious ΦDP and KDP, which are shown in red, was tested by setting D3 and RK to 0 and the threshold of F to 8. The arrows indicate the region where the spurious ΦDP and KDP remained undetected. (b) Same as (a), but for setting RK to 0 and the threshold of F to 8 and using D3, as expressed by Eq. (9). (c) Scatterplot of KDP versus ZH at an elevation of 0.5° for 1624 UTC 28 November 2015. The dashed curve was obtained by a least-squares fit to log (KDP) and ZH. The identification of the spurious KDP, which is shown in red, was tested by setting N to 1 and the threshold of F to 8. Horizontal distributions of ZH and KDP are presented in Figs. 7b and 8b, respectively. (d) Same as (c), but for setting the threshold of F to 8 and using N, as expressed by Eq. (11).
D3 is designed to overcome the above restriction, which is calculated according to the formula
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The design of D3 has utilized the observational fact seen from Fig. 3, which shows that spurious KDP may have a range variation inconsistent with that of ZH. On the right-hand side of Eq. (9), the absolute value represents the deviation of the measured range derivatives of KDP and ZH from the empirical curve defined by Eq. (4). As indicated by the numerator within the parentheses on the right-hand side of Eq. (9), D3 is designed to be proportional to the magnitude of the range derivative of KDP. Such a design is based on the observational fact seen from Fig. 5a, which shows that the spurious KDP remaining undetected by applying only D1 and D2 may vary rapidly in the range direction.
Since D3 is used to further facilitate the identification of spuriously small KDP values located close to the empirical curve defined by Eq. (3), it is designed to be inversely proportional to the magnitudes of D1, D2, and KDP, as expressed by the denominators within the parentheses on the right-hand side of Eq. (9). As a result, the magnitude of D3 decreases when the magnitudes of D1, D2, and KDP increase, allowing D3 to have a smaller effect on the realistic, large KDP values deviating from the empirical curve defined by Eq. (3). Figures 5a and 5b indicate that with the supplement of D3, the remaining spurious ΦDP and KDP after applying only D1 and D2 can be detected effectively.
b. Definition of RKAs presented in Fig. 4c, if only RA, which utilized the multiplication of D1–D3, is applied to the detection of spurious KDP, some spuriously small or negative KDP values in the high-ZH areas remain undetected. RK is designed to overcome this restriction, and RK is defined as follows:
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As seen from Eq. (10), RK is applied only to those KDP values that are less than the empirical KDP estimated from ZH. RK has utilized the ratio of D1 to 1 + D2 based on the fact that the magnitude of D2 increases with a decrease in ZH. As a result, RK can effectively identify the spurious KDP in the high-ZH areas that cannot be detected using only RA, whereas RK has a smaller effect in the low-ZH areas (Figs. 4c, d). Since RK is used to further facilitate in the identification of spuriously small and negative KDP, the exponential expression of Eq. (10) is designed to allow the magnitude of RK to decrease with an increase in KDP above 1.0° km−1. As a result, RK has a smaller effect on the realistic, large KDP in the high-ZH areas. The effectiveness of the supplement of RK in detecting spurious KDP can be seen by comparing Fig. 4c with Fig. 4d.
The algorithm designed in this study is intended for retaining the negative KDP that may be statistically significant. Ryzhkov and Zrnić (1996) noted that after the removal of high-frequency fluctuations in ΦDP, negative KDP can stem from statistical noise at low rain rates or from low-frequency perturbations of ΦDP. They emphasized that these negative KDP values need to be treated differently. Negative KDP associated with spurious ΦDP should be removed. However, to avoid bias at low rain rates, a statistically significant negative KDP is necessary for KDP-based rainfall estimates. The magnitudes of statistically significant negative KDP values are small. Ryzhkov and Zrnić (1998a) suggested the removal of negative KDP values if the values are below −1° km−1. As presented in Fig. 4d, the algorithm developed in this study can effectively identify and remove negative KDP values below −1° km−1.
c. Definition of NN normalizes F with respect to ZH and is defined as follows:
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Figure 4 shows that KDP becomes less noisy with increases in ZH. As noted by Ryzhkov and Zrnić (1996), meteorological variability, such as the variability in drop size distribution, dominates scatter in the high-ZH areas. Figure 5c shows that if F is not normalized with respect to ZH (i.e., N = 1), it means that there were large amounts of quality measures of KDP misjudged as spurious data in the high-ZH areas. The normalization factor N is experimentally designed to allow for KDP and ZH scatter due to meteorological variability in the high-ZH areas remaining unaffected as much as possible. As expressed on the right-hand side of Eq. (11), the magnitude of N is designed to vary in accordance with the second power of the empirical KDP estimated from ZH. The effectiveness of N in retaining variations and quality measures of KDP in the high-ZH area can be seen by comparing Fig. 5c with Fig. 5d.
4.3 Procedures for applying the algorithmCoefficients a and b, as presented in Eq. (2), are first obtained via a linear least-squares fit to log (KDP) and ZH. Data from a PPI scan are used for the above statistical process. Notably, both a and b contain implicit information on the microphysics of rain, which varies with time. To reflect such variations, a and b are statistically calculated from each PPI scan.
An adequate number of radar observables in the high-ZH areas are necessary for a and b to be properly retrieved. The minimum number of data points required for the statistical calculation of a and b in the high-ZH areas has been tested by utilizing the observed data. Coefficients a and b can be properly retrieved if the number of data with ZH values greater than 45 dBZ is greater than 5000. For a PPI scan with fewer data points in the high-ZH areas, pseudo-data were added between 45 and 65 dBZ, utilizing the a and b that were retrieved from the latest PPI scan with a sufficient number of data points in the high-ZH areas. As will be presented in Section 5, by using such a pseudodata approach, the algorithm can efficiently detect and remove spurious ΦDP and KDP values observed from weak precipitation.
After the coefficients a and b have been determined, F is calculated according to Eq. (5), and spurious ΦDP and KDP values are then identified using a threshold of F. However, unlike a and b, the threshold of F appears to be independent of precipitation system types. In this study, the threshold of F is set as 8.0. By using such a threshold of F, spurious data can be detected, whereas quality data, especially those with high ZH values, remain unaffected as far as possible (Fig. 6a). A detailed validation of the algorithm's performance will be presented in Section 5.
(a–b) Scatterplots of KDP versus ZH (left panel) and SD (KDP) versus ZH (right panel) at an elevation of 0.5° for 1930 UTC 25 November 2015. The dashed curve was obtained by a least-squares fit to log (KDP) and ZH. The spurious KDP, which is shown in red, was detected by the algorithm presented in this study by setting the threshold of F to 8. (c–d) Same as (a–b), but for setting the threshold of F to 3. (e–f) Same as (a–b), but for setting the threshold of F to 20.
The threshold of F used in this study was determined by comparing the scatterplots and range profiles of the polarimetric radar variables before and after the applications of the algorithm. At first, the threshold of F was determined approximately by examining the scatterplots of KDP versus ZH (Fig. 6). One of the decisive factors in determining the threshold of F is that quality measures of KDP need to be less affected by applying the algorithm. Figure 6c indicates that a lower threshold of F results in overdetection of spurious data. As stated previously, KDP is less noisy in the high-ZH areas, where meteorological variability dominates (Ryzhkov and Zrnić 1996). Quality measures of KDP prevail in areas with ZH values above 40 dBZ, and the selected threshold of F ought to retain these quality data as much as possible. Another decisive factor in determining the threshold of F is that an acceptable accuracy for KDP observed in light rain or low-ZH areas, where meteorological variability is less dominant and KDP becomes very noisy (Ryzhkov and Zrnić 1996), needs to be obtained after the application of the algorithm.
The statistical accuracy of KDP can be evaluated using the standard deviation of KDP, which has been calculated based on the expression of Balakrishnan and Zrnić (1990) and Carey et al. (2000)
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As discussed by Bringi and Chandrasekar (2001), the acceptable value of SD (ΦDP) for accurate KDP estimation is around 2°, or lower. Based on Eq. (12), if SD (ΦDP) = 2°, then SD (KDP) = 0.73° km−1. Accordingly, it is determined that the selected threshold of F ought to reduce the values of SD (KDP) to less than 0.73° km−1 for light rain with ZH values below 30 dBZ. As presented in Figs. 6e and 6f, a higher threshold of F results in both underdetection of spurious KDP and an increase in SD (KDP) in the low-ZH areas. By using the selected threshold of F, the values of SD (KDP) in the low-ZH areas have been improved (Fig. 6b). An improvement of SD (KDP) for all the observed data can be seen from Fig. 19b.
A final decision on the threshold of F was made with the supplementary examination of range profiles of the polarimetric radar variables. As presented in Figs. 3, 5a, and 5b, the range variation of spurious ΦDP often deviates from the mean trend of genuine ΦDP, whereas spurious KDP may have a range variation inconsistent with that of ZH. These signatures make it easier to discriminate between spurious and genuine ΦDP and KDP. Therefore, the performance of the selected threshold of F can be evaluated more precisely through the examination of range profiles of the observed data.
In this section, the algorithm's performance will be investigated through the application of the algorithm to the observed data used in this study, and the observed data contain information for a variety of precipitation systems (Yokoi et al. 2017). Detailed examinations were conducted for three selected precipitation events, which cover the major modes of convective organization in the observational area. These events were observed on 28 November, 11 December and 15 December 2015. A validation using all the observed data was also conducted.
5.1 The 28 November 2015 eventFigure 7 presents the horizontal distributions of ZH observed at a 0.5° elevation angle on 28 November 2015. On this day, synoptic-scale disturbances were not observed. Precipitation had been initiated over land in the afternoon (LST = UTC + 7 h) and propagated westward away from the coast. At 1154 UTC (Fig. 7a), a rainband nearly parallel to the coast was observed by the Mirai radar over the offshore regions. The rainband propagated further westward and evolved by 1624 UTC into a loosely organized precipitation system over the ocean (Fig. 7b).
Distributions of ZH at an elevation of 0.5° for (a) 1154 UTC and (b) 1624 UTC 28 November 2015. In (c) and (d), the distributions of ZH at an elevation of 0.5° from the low-PRF scans for 1159 UTC and 1629 UTC are presented, respectively. The solid lines of B1–B3 indicate the locations of the range profiles presented in Fig. 9. Hatching indicates the sectors suffering from beam blockage caused by Mirai structures. The coastline is indicated by a dashed curve.
The horizontal distributions of KDP measured at a 0.5° elevation angle simultaneously with ZH are presented in Fig. 8. Before the application of the algorithm (Figs. 8a, b), large negative values of KDP, which are indicated by the light purple color, can be recognized on the west and northwest sides of the radar. The horizontal distributions of KDP after the application of the algorithm are presented in Figs. 8c and 8d, which indicate that the spurious KDP seen from Figs. 8a and 8b can be identified and removed, whereas the genuine KDP is less affected.
(a–b) Distributions of KDP at an elevation of 0.5° for (a) 1154 UTC and (b) 1624 UTC 28 November 2015. The solid lines of B1–B3 indicate the locations of the range profiles presented in Fig. 9. Hatching indicates the sectors suffering from beam blockages caused by Mirai structures. The coastline is indicated by a dashed curve. (c–d) Same as (a–b), but after the removal of the spurious KDP detected by the algorithm presented in this study.
The ability and accuracy of the algorithm can be verified in detail in Fig. 9, which shows the range profiles along lines B1–B3, as illustrated in Figs. 7 and 8. In Fig. 9, the spurious ΦDP and KDP values detected by the algorithm are shown in red.
Range profiles (from left to right) along lines (a) B1, (b) B2, and (c) B3, as presented in Figs. 7a, 7b and 8, for ΦDP (top panels, black and red curves), ΔΦDP (upper middle panels), KDP (middle panels, black and red curves), ZH (black curves), and F (gray curves) (lower middle panels), ρHV (black curves), and SQI (green curves) (bottom panels). The spurious ΦDP and KDP detected by the algorithm presented in this study are shown in red. The gray horizontal line in the lower middle panels indicates the threshold of F (= 8) used in this study. In the top and lower middle panels, the range profiles of ΦDP and ZH (chartreuse curves) from the low-PRF scans presented in Figs. 7c and 7d, respectively, are supplemented.
The profiles of ΦDP and KDP along line B1 are presented in Fig. 9a. By comparing the ΦDP profile with that from the low-PRF scan during the nearest time, the ΦDP profile could have been contaminated by second-trip echoes before the range of 95 km. The second-trip echoes originated from precipitation in the far northwest, as presented in Fig. 7c. The jumps and resumptions of ΦDP due to the second-trip echoes were much more apparent in ranges from approximately 20 km to 35 km and from approximately 45 km to 65 km, respectively. Each jump in ΦDP was accompanied by a sharp drop in SQI and ρHV. The second-trip echoes induced both positively and negatively biased KDP, reaching as high as 4.5° km−1 and as low as −4.5° km−1, respectively. Clearly, these spurious ΦDP and KDP values have been successfully identified by the algorithm.
As presented in Fig. 9a, the algorithm also detected the ΦDP perturbation and positively and negatively biased KDP along line B1 from the range of 120 km, where line B1 passed between two reflectivity cores (Fig. 7a). These spurious ΦDP and KDP values could be associated with NBF (e.g., Ryzhkov 2007), as ΔΦDP increased in magnitude and exhibited a range variation consistent with the ΦDP perturbation in the same segment (Fig. 9a).
Figure 9b presents the range profiles along line B2. A contamination of second-trip echoes appears to have occurred close to the radar. The second-trip contamination near the radar can be identified by a comparison between the ΦDP profiles, which were obtained by using different PRFs. The second-trip echoes resulted from precipitation beyond the range of 150 km (Fig. 7d). The algorithm has identified a positively biased KDP occurring from a range of 12 km. The biased KDP was apparently induced by the spurious jump in ΦDP, which was also identified by the algorithm. The spurious ΦDP and KDP values near the range of 12 km occurred in the regions where ZH was close to 45 dBZ, SQI was close to 0.85, and ρHV was close to 0.97. This fact implies that the contamination of ΦDP and KDP by second-trip echoes may occur despite the ZH, SQI, and ρHV showing negligible influences of the second-trip echoes.
Figure 9b shows that in addition to the second-trip contamination, the algorithm has also successfully identified spurious ΦDP and KDP values beyond the range of 110 km, where relatively large cross-beam gradients of reflectivity could exist along line B2 (Fig. 7b). These spurious ΦDP and KDP values could have been induced by NBF, as evidenced by the fact that ΔΦDP increased in magnitude and exhibited a range variation generally consistent with that of ΦDP beyond the range of 110 km (e.g., Ryzhkov 2007).
The range profiles along line B3 are presented in Fig. 9c. The algorithm detected the spurious perturbations of ΦDP and the associated negative values of KDP before the range of 90 km. Notably, these spurious ΦDP and KDP values occurred in front of or behind reflectivity cores, which suggests that these values could have been induced by NBF (e.g., Ryzhkov and Zrnić 1998a). Figure 9c shows that ΔΦDP increased in magnitude and had a range variation consistent with that of ΦDP beyond the range of 90 km, indicating that the spurious ΦDP and biased KDP values of both signs detected by the algorithm at far distances from the radar could have also been induced by NBF. Notably, the increase in ΔΦDP occurred behind intense reflectivity cores and in regions with relatively weak echoes. This fact suggests that the NBF-related perturbation in ΦDP could have been enhanced by the attenuation of radar reflectivity (e.g., Ryzhkov 2007).
The ability of the algorithm can be further supported by Figs. 10a and 10b, which shows the scatterplots of the KDP versus ZH observed on 28 November. In Figs. 10a and 10b, the spurious KDP detected by the algorithm has also been shown in red. Evidently, the algorithm can efficiently detect not only the negatively biased KDP but also the positively biased KDP. Although the biased KDP prevailed in areas with relatively low ZH, there were also small amounts of biased KDP in regions with ZH values above 45 dBZ.
(a–b) Scatterplots of KDP versus ZH at an elevation of 0.5° for (a) 1154 UTC and (b) 1624 UTC 28 November 2015. The dashed curve was obtained by a least-squares fit to log (KDP) and ZH. The spurious KDP detected by the algorithm presented in this study is shown in red. (c–d) Same as (a–b), but for scatterplots of SD (KDP) versus ZH.
In addition to the qualitative verification shown above, a quantitative statistical evaluation was further conducted using SD (KDP). The scatterplots of the SD (KDP) versus ZH observed on 28 November 2015, are presented in Figs. 10c and 10d. In areas with ZH values below 40 dBZ, the magnitude of SD (KDP) was substantially reduced after the application of the algorithm. Specifically, the maximum values of SD (KDP) have been reduced to less than 0.5° km−1 for ZH values below 30 dBZ and less than 0.25° km−1 for ZH values below 20 dBZ. This result indicates that the application of the algorithm has led to the improvement of the KDP estimation.
5.2 The 11 December 2015 eventOn 11 December 2015, precipitation was initiated over land in the afternoon and moved offshore (Fig. 11), as was the case in the 28 November event. Radar echoes were also organized into a rainband parallel to the coast and propagated westward. However, in contrast to the 28 November event, precipitation on this day was enhanced by a synoptic-scale, west-ward-moving disturbance (not shown). The rainband developed strongly and lasted for a long time.
Figure 12 presents the horizontal distributions of the KDP at a 0.5° elevation angle before and after applications of the algorithm. Relatively high KDP values were observed in the intensified precipitation region. Before the application of the algorithm, artifacts, such as large negative KDP values, were found along the rainband (Figs. 12a, b). These artifacts have been successfully detected and removed using the algorithm (Figs. 12c, d). Similar to the previous event, the distribution of genuine KDP values was less affected by the application of the algorithm.
The range profiles of ΦDP and KDP along line C1 are presented in Fig. 13a. Perturbations in ΦDP and positively and negatively biased KDP values were observed before the range of 75 km. A jump and resumption of ΦDP were much more apparent in ranges from approximately 60 to 75 km, which were not found in the ΦDP profile obtained from the low-PRF scan during the nearest time. Relatively steep decreases in SQI and ρHV were associated with the ΦDP perturbations. These facts indicate that the ΦDP profile before the range of 75 km could have been contaminated by second-trip echoes from the rain located beyond the maximum range of 150 km, as found in the low-PRF scan (Fig. 11c). From the range of 75 km, line C1 passed through strong echoes. Three reflectivity cores with ZH values above 40 dBZ were found around the ranges of 90, 120, and 145 km, respectively. Negatively biased KDP values were observed in front of and behind these reflectivity cores. These results indicate that the ΦDP perturbations and associated spurious KDP values beyond the range of 75 km could be attributed to the NBF effects (e.g., Ryzhkov and Zrnić 1998a).
Same as Fig. 9, but for the range profiles (from left to right) along lines (a) C1, (b) C2, and (c) C3, as presented in Figs. 11a, 11b and 12. In the top and lower middle panels, the range profiles of ΦDP and ZH (chartreuse curves) from the low-PRF scans presented in Figs. 11c and 11d, respectively, are supplemented.
Line C2 passed through strong echoes before the range of 100 km (Fig. 13b). Four reflectivity cores with ZH values above 45 dBZ were found around the ranges of 25, 45, 70, and 85 km, respectively. The NBF effects (e.g., Ryzhkov and Zrnić 1998a) could account for the negatively biased KDP values observed in front of and behind these reflectivity cores. Line C2 was also located near the edge of the strong reflectivity beyond the range of 100 km (Fig. 11b), and both positively and negatively biased KDP values were observed along line C2 at far distances from the radar (Fig. 13b). These facts indicate that the perturbations of ΦDP and associated spurious KDP along line C2 beyond the range of 100 km could also be attributed to the NBF effects (e.g., Ryzhkov 2007).
Along line C3 (Fig. 13c), the ΦDP profile exhibited repeated jumps and resumptions beyond the range of 29 km, which were not observed in the ΦDP profile obtained from the low-PRF scan during the nearest time. Therefore, the ΦDP perturbations and associated positively and negatively biased KDP values along line C3 could be attributed to second-trip echoes (Fig. 11d).
As clearly seen from Fig. 13, NBF and second-trip contaminated ΦDP and KDP values have been successfully detected by the algorithm. Figure 13 further supports the ability of the algorithm to detect and remove spurious ΦDP and KDP.
Figures 14a and 14b present the scatterplots of the KDP versus ZH observed on 11 December. Similar to the previous event, the algorithm detected a number of positively and negatively biased KDP values. This event was associated with an intense rainband. Strong attenuation of radar reflectivity occurred over a larger area (not shown). The validation results of this event indicate that the algorithm can detect and remove spurious ΦDP and KDP for intense precipitation. An improvement in data quality with the application of the algorithm can be seen from the scatterplots of the SD (KDP) versus ZH observed on 11 December (Figs. 14c, d). Similar to the previous event, larger SD (KDP) values in the low-ZH areas were removed after the application of the algorithm.
Same as Fig. 10, but for (a, c) 1300 UTC and (b, d) 1500 UTC 11 December 2015.
Unlike the previous events, precipitation on 15 December was not triggered over the land. Instead, the precipitation accompanying the convectively active phase of the Madden–Julian Oscillation (MJO, Madden and Julian 1972) was observed over a wide area of the ocean (Yokoi et al. 2017). On this day, a precipitation system associated with the MJO was observed by the Mirai radar over the ocean (Fig. 15). Notably, the precipitation system propagated eastward toward land, which is the opposite of the propagation direction in the previously shown cases. The precipitation system associated with the MJO was organized with leading convective echoes and wide trailing stratiform echoes.
The horizontal distributions of the KDP measured on 15 December are presented in Fig. 16. Compared with the previous events (Figs. 8, 12), relatively low values of KDP were observed. Artifactitious KDP values, manifested as large negative KDP values, were concentrated around the leading convective regions (Figs. 16a, b). Once again, the algorithm correctly detected the artifactitious KDP and showed little influence on the distribution of the genuine KDP (Figs. 16c, d). Additionally, as seen from Fig. 16, the algorithm is capable of identifying spurious KDP observed in both convective and stratiform precipitation.
The range profiles presented in Fig. 17 were analyzed to validate the ability and accuracy of the algorithm. The algorithm correctly detected the spurious ΦDP and KDP before the range of 60 km along line D1 (Fig. 17a) and before the range of 45 km along line D3 (Fig. 17c), respectively. These spurious data were associated with the jumps and resumptions of ΦDP, which were not observed in the ΦDP profiles obtained from the low-PRF scan during the nearest time (Figs. 15c, d). Accordingly, the ΦDP perturbations in these regions could have been induced by the second-trip echoes originating from the wide trailing stratiform precipitation.
Same as Fig. 9, but for the range profiles (from left to right) along lines (a) D1, (b) D2, and (c) D3, as presented in Figs. 15a, 15b and 16. In the top and lower middle panels, the range profiles of ΦDP and ZH (chartreuse curves) from the low-PRF scans presented in Figs. 15c and 15d, respectively, are supplemented.
Simultaneously, the algorithm has also successfully identified both the positively and negatively biased values of KDP along line D1 beyond the range of 100 km (Fig. 17a) and along line D2 beyond the range of 90 km (Fig. 17b). In these regions, lines D1 and D2 passed through either reflectivity cores or the edges of intense reflectivity with strong horizontal gradients of reflectivity (Figs. 15a, b). These results indicate that the ΦDP perturbations and associated biased KDP along lines D1 and D2 at far distances from the radar could have been induced by NBF (e.g., Ryzhkov and Zrnić 1998a; Ryzhkov 2007).
The scatterplots of KDP versus ZH and SD (KDP) versus ZH observed on 15 December are presented in Fig. 18. Figure 18 reveals that the algorithm can identify and remove the biased KDP values of both signs very well. In this event, data with ZH values above 45 dBZ were very few. The validation results of this event reveal that the algorithm is also able to detect and remove spurious ΦDP and KDP for weak precipitation.
Same as Fig. 10, but for (a, c) 0630 UTC and (b, d) 1100 UTC 15 December 2015.
In total, data from 5998 low-level PPI scans were available during the observational period from 23 November to 17 December 2015, in the tropical rainy regions near Sumatra (Fig. 1). These data covered a variety of precipitation systems, which were initiated either over land or over ocean and evolved under a variety of larger-scale environmental conditions, such as MJO and synoptic-scale disturbances.
The improved quality of KDP for all the observed data is presented in Fig. 19a in the scatterplot of KDP versus ZH. Figure 19a reveals that the algorithm can detect both positively and negatively biased KDP values observed from various precipitation systems. The improvement of the KDP statistical accuracy after the application of the algorithm for all the observed data is also achieved, as seen from the scatterplot of SD (KDP) versus ZH (Fig. 19b). It is evident that after the application of the algorithm, the magnitude of SD (KDP) was reduced. The reduction in the magnitude of SD (KDP) was much more significant in the low-ZH areas, with a maximum SD (KDP) as low as 0.73° km−1 for all the observed data with ZH values below 30 dBZ.
Scatterplots of (a) KDP versus ZH, (b) SD (KDP) versus ZH, (c) the rain rate estimated from KDP versus that from ZH, and (d) coefficient a versus coefficient b at an elevation of 0.5° for all 5998 scans from 23 November to 17 December 2015. The data associated with the spurious KDP detected by the algorithm presented in this study are shown in red. The vertical dashed line in (b) indicates the location where SD (KDP) = 0.73° km−1.
As indicated by Ryzhkov and Zrnić (1996) and Wang and Chandrasekar (2009), the estimation of rainfall by using KDP is highly susceptible to a large variance in the KDP measured in light and moderate rain. To reduce the variation in KDP and facilitate the rainfall estimation, the researchers applied a longer averaging interval (greater than 3 km) to estimate the KDP observed in the low-ZH areas. In this study, KDP was estimated over a range interval of 1.5 km. The result presented in Fig. 19b reveals that even with a shorter averaging interval, the algorithm presented in this study enables suppression of the KDP variation in the low-ZH areas. Therefore, the algorithm facilitates to improve the statistical accuracy of KDP without sacrificing its spatial resolution.
As stated previously, spurious KDP has a considerable influence on the accuracy of KDP-based rainfall estimations. To verify the impact of the algorithm on the improvement of KDP-based rainfall estimation, Fig. 19c presents the scatterplot of the rain rate derived from KDP [R (KDP)] versus that from ZH [R (ZH)]. The relations given by Keenan et al. (2000) were used to estimate the radar rainfalls, which can be expressed as follows:
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Two changes were made to use the formulas of Keenan et al. (2000) (see their Eqs. 2, 3). First, the unit of ZH in R (ZH) was changed to dBZ. Second, the R (KDP) formula was changed to be able to handle negative KDP values.
It should be noted that the scales of the abscissa and ordinate of Fig. 19c were different: the abscissa ranged from −380 to 380 mm h−1, whereas the ordinate ranged from 0 to 380 mm h−1. Figure 19c indicates that before the application of the algorithm, the scatters of R (KDP) and R (ZH) were large, especially in areas below a ZH-based rain rate of 60 mm h−1. Consistent with the existence of both positive and negative biases in KDP (Fig. 19a), R (KDP) could also be positively and negatively biased against R (ZH). After the detection and removal of the biased KDP via the algorithm, both the positively and negatively biased R (KDP) values were significantly reduced, and the scatters of R (KDP) and R (ZH) were much tighter than before. As a result, the variation in R (KDP) became more comparable with that of R (ZH) at both the low and high rain rates. These results imply that the physical consistency of R (KDP) and R (ZH) can be improved with the application of the algorithm.
The performance of the algorithm depends on the retrieval of coefficients a and b on the right-hand side of Eq. (2). Figure 19d presents the scatterplot of a versus b derived from the observed data. There is a pronounced variation in both a and b. The values of a and b varied from approximately 9.0 to 16.5 and 35.2 to 45.4, respectively. In general, the variation in a was inversely correlated with that in b. The variation in a and b would be associated with that in precipitation systems. It is evident from Figs. 19a and 19b that by incorporating the variation of a and b, the algorithm developed in this study is suitable for the identification of spurious ΦDP and KDP observed from various types of precipitation systems.
Figure 20 presents the time series of the number of data points observed from a PPI scan for positive and negative KDP, respectively, in areas with ZH above 10 dBZ. There were a considerable number of data attended with negative KDP values. On average, the number of the negative KDP data accounted for approximately 40 % of the total number of the observed data. As presented in Fig. 20 and Table 2, the number of the spurious data identified by the algorithm and its fraction to the total number of the observed data have been examined. The average fractions of the spurious data detected by the algorithm were 6.39 % and 9.86 % for positive and negative KDP, respectively. Table 2 shows that relatively large fractions of the spurious data occurred where weak echoes below 20 dBZ were observed. This result can be attributed to the fact that there were large amounts of noisy KDP and second-trip echoes in areas with weaker reflectivity. The faction of the spurious data decreased with the increase in ZH. The spurious data detected by the algorithm accounted for just a few percent of the observed data in areas with ZH above 30 dBZ, consistent with the fact that KDP became less noisy in the high-ZH areas. It is evident from Fig. 19 that the removal of these spurious data has led to the improvement of the KDP estimation.
(a) Time series of the number of the observed data at an elevation of 0.5° for positive KDP with ZH values above 10 dBZ. The number of the spurious KDP detected by the algorithm presented in this study is shown in red. (b) Same as (a), but for negative KDP.
The differential phase ΦDP is easily contaminated, manifesting as both gate-to-gate fluctuations (i.e., high-frequency range fluctuations) and perturbations within a distance much greater than a range gate along the radial direction (i.e., low-frequency range perturbations). Several previous studies have addressed the removal of high-frequency range fluctuations in ΦDP, which is typically induced by nonmeteorological echoes and differential backscatter phases. However, low-frequency range perturbations in ΦDP often remain, inducing considerably biased specific differential phase KDP values of both signs. Second-trip echoes and nonuniform beam filling (NBF) could be two significant sources of the low-frequency range perturbations in ΦDP and the associated biased values of KDP.
In this study, an algorithm was developed to detect low-frequency range perturbations in ΦDP and associated spurious KDP in the rain, as observed by the C-band polarimetric radar on board the research vessel Mirai. The algorithm is designed to be applied after the removal of the high-frequency range fluctuations in ΦDP. An objective function is formed based on a combination of several formulas developed via the empirical relationship between KDP and the radar reflectivity factor at horizontal polarization ZH in the rain. A threshold of the objective function is then used to simultaneously detect spurious ΦDP and KDP.
The development and validation of the algorithm were conducted using the observed data during a pilot field campaign of the Years of the Maritime Continent (YMC) project in the tropical rainy regions around Sumatra in Indonesia from 23 November to 17 December 2015. These data included a variety of precipitation systems, which were organized with distinct environmental conditions and evolved either over land or over ocean.
The ability and accuracy of the algorithm were examined in detail by comparing the horizontal distributions, range profiles, and scatterplots of the polarimetric radar variables before and after the applications of the algorithm. Low-frequency range perturbations of ΦDP and associated spurious values of KDP can be efficiently detected by the algorithm, whereas realistic ΦDP and KDP values are less affected after the application of the algorithm. Both positively and negatively biased KDP can be ascertained by the algorithm. After the removal of positively and negatively biased KDP in both the low-ZH and high-ZH areas, the rain rate estimated from the KDP was greatly improved. The performance of the algorithm was further evaluated by using statistics from KDP. The standard deviation of KDP is significantly reduced in the low-ZH areas after the spurious ΦDP identified by the algorithm was removed, which implies that the quality of ΦDP and KDP can be improved by applying the algorithm.
The data from the YMC project were observed not only in the open ocean but also in coastal areas of the Maritime Continent. Precipitation systems in these regions are usually tall and huge due to both largescale and orographic lift forces. Second-trip echoes from these precipitation systems are complicated and severely reduce the quality of radar data. The results shown in previous sections indicate that the algorithm developed in this study has good performances in the identification and removal of second-trip echoes not only in the open ocean but also in coastal areas of the Maritime Continent. Therefore, the algorithm can efficiently manage the quality of the data observed during the YMC project.
The empirical relationship between the KDP and ZH, as expressed by Eq. (2), is essential to the algorithm. Notably, such an empirical relationship is also reported for S-band (Balakrishnan and Zrnić 1990; Bringi et al. 1991; Ryzhkov and Zrnić 1996) and X-band (Anagnostou et al. 2004; Park et al. 2005; Schneebeli and Berne 2012) polarimetric radars. The application of the algorithm developed in this study with S-band and X-band polarimetric radars will be investigated in detail in the future.
Notably, the algorithm developed in this study is based on the empirical relationship between the KDP and ZH, which is valid primarily for liquid precipitation. As indicated by Balakrishnan and Zrnić (1990) and Aydin and Giridhar (1992), hydrometeors other than raindrops can significantly deviate from the empirical relationship, as expressed by Eq. (2). Therefore, caution should be exercised in applying the algorithm for mixed-phase or ice-phase precipitation. Modifying the algorithm so that hydrometeors other than raindrops can also be treated by the algorithm is a challenging issue.
The KDP and ZH scatter about the empirical curve of Eq. (2) due to meteorological variability is not currently clear and can only be determined experimentally, rather than quantitatively, in the algorithm developed in this study. In the future, the intention is to investigate the characteristics and processes of the spreads of KDP and ZH about the empirical curve due to meteorological variation alone for various precipitation types. Such work is essential to distinguish between meteorological variability-induced and contaminator-induced scatters about the empirical curve, thus facilitating the establishment of a more robust and quantitative algorithm for quality control of ΦDP and KDP.
The authors would like to express their sincere thanks to the entire crew of the research vessel Mirai and the technical staff of Global Ocean Development Inc. for their great support in conducting radar observations and data archiving. The authors also want to thank two anonymous reviewers for their thorough reviews and constructive suggestions that were of great help in the improvement of the manuscript. This study was supported partly by the Japanese Aerospace Exploration Agency (JAXA) Precipitation Measuring Mission (PMM) project.
