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Using Microwave Backhaul Links to Optimize the Performance of Algorithms for Rainfall Estimation and Attenuation Correction [Journal of Atmospheric and Oceanic Technology](Journal of Atmospheric and Oceanic Technology Via Acquire Media NewsEdge) ABSTRACT The variability in raindrop size distributions and attenuation effects are the two major sources of uncertainty in radar-based quantitative precipitation estimation (QPE) even when dual-polarization radars are used. New methods are introduced to exploit the measurements by commercial microwave radio links to reduce the uncertainties in both attenuation correction and rainfall estimation. The ratio a of specific attenuation A and specific differential phase KDP is the key parameter used in attenuation correction schemes and the recently introduced R(A) algorithm. It is demonstrated that the factor a can be optimized using microwave links at Ku band oriented along radar radials with an accuracy of about 20%-30%. The microwave links with arbitrary orientation can be utilized to optimize the intercepts in the R(KDP) and R(A) relations with an accuracy of about 25%. The performance of the suggested methods is tested using the polarimetric C-band radar operated by the German Weather Service on Mount Hohenpeissenberg in southern Germany and two radially oriented Ku-band microwave links from Ericsson GmbH. (ProQuest: ... denotes formulae omitted.) 1. Introduction High-quality quantitative precipitation estimation (QPE) is of the highest importance for applications in meteorology, hydrology, and agriculture-just to name a few. Long-term, large-scale precipitation records guide decisions related to water resource management; short-term, finescale measurements are mandatory for accurate predictions of flash floods. Accurate QPE may also lead to improved precipitation forecasts by means of data assimilation in numerical weather prediction (NWP) models (e.g., Milan et al. 2008, 2014), for the verification of weather forecast and climate models (e.g., Bachner et al. 2008; Lindau and Simmer 2013), and development of statistical forecasting tools, such as model output statistics (MOS). Precipitation radars have the potential to provide the fields of precipitation rate with high temporal and spatial resolution. Rain gauges are traditionally used for validation of QPE and their optimization. Gauges provide, however, point measurements of precipitation, which have a vastly different spatial resolution compared to radar observations, which yield rainfall estimates over larger areas. Kitchen andBlackwell (1992) and Ciach and Krajewski (1999) examined in detail gauge representativeness errors and showed that discrepancies between radar and gauge measurements may not be entirely attributed to the radar-only estimates. Microwave links represent an alternative source for validating and optimizing the radar-based QPE. The path-integrated attenuation (PIA) along the link can be related to line-averaged precipitation estimates (e.g., Leijnse et al. 2008; Chwala et al. 2012), which are more compatible with radar observations than point measurements by gauges. Microwave link networks exhibit a high spatial density in many countries (e.g., more than 100 000 links in Germany). Combining rainfall estimates from polarimetric radars, rain gauges, and microwave links appears promising (Grum et al. 2005; Krämer et al. 2005; Rahimi et al. 2006; Cummings et al. 2009; Bianchi et al. 2013), though its implementation is partially hampered by limited access tomicrowave link measurements. Attenuation of the radar signal by hydrometeors and the variability of the drop size distribution (DSD) of rainfall are major sources of uncertainty in radar-based QPE. At shorter radar wavelengths in the X-band and C-band ranges, radar reflectivity factor Z and differential reflectivity ZDR can be strongly biased by attenuation (Matrosov et al. 2002; Anagnostou et al. 2004; Park et al. 2005; Matrosov 2010). Polarimetry offers the potential to correct for attenuation by relating specific attenuation and specific differential attenuation to specific differential phase KDP (Bringi et al. 1990). This paper focuses on specific attenuation Ah, which affects reflectivity Zh. Under the assumption of a quasi-linear relationship between Ah and KDP (degkm-1), ... (1) with c close to unity and a constant a along the radial, the attenuation-related bias ?Z at distance r can be expressed via propagation differential phase uDP as ... (2) The two-way path-integrated attenuation PIA2 is proportional to the total span of the propagation differential phase: ... (3) The fact that the attenuation bias of Zh (and ZDR) is directly proportional to differential phase is one of the greatest advantages of using polarimetric radars, which allows for a quite accurate quantification of precipitation even in the presence of strong attenuation, for example, at shorter radar wavelengths (C and X bands). The factor a, however, is sensitive to the variability of raindrop size distribution and temperature, and its uncertainty has an impact on the accuracy of attenuation correction and eventually on the quality of QPE. Analysis of numerous literature sources shows that the range of variability of the factor a is quite broad, as indicated in Table 1. Although the use of the ''default'' or globally averaged factors a listed in the right column of Table 1 guarantees substantial improvement in Zh compared to the absence of attenuation correction, further optimization of a is necessary. The optimization of a is a key to rainfall estimation based on specific attenuation Ah. The R(A) algorithm for rainfall estimation has been introduced by Ryzhkov et al. (2014), who used specific attenuation estimation via the ZPHI method by Testud et al. (2000). The ZPHI method and consequently the R(A) algorithm use a ''net'' value of the ratio A/KDP along the propagation path, which is equal to the ratio between the two-way path-integrated attenuation PIA2 [(3)] and the total span of differential phase DFDP. DSD variability is the second major source of uncertainty in radar-based QPE with both single- and dualpolarization radars, although its impact is generally smaller for polarimetric rainfall algorithms. There is growing evidence that the parameters of the QPE algorithms should be tuned to precipitation type and prevalent DSD. According to Ryzhkov et al. (2014), the R(A) algorithm exhibits low sensitivity to DSD variations and is immune to radar miscalibration, attenuation, partial beam blockage, and wet radome effects. Nevertheless, even the most sophisticated rainfall algorithms are sensitive to DSD variability, although with different extent depending on radar frequency. The performance of the R(A) method is more robust at frequencies where its parameters and the net ratio a = A/KDP are least sensitive to DSD and temperature variations. The comparison of such variabilities at S, C, X, Ku, and Ka bands using the large DSD dataset from Oklahoma shows that best performance should be expected at S and Ku bands (Table 2). Indeed, the relation between A and KDP (or PIA and DFDP) is most stable at Ku band. The R(A) relation at Ka band is least sensitive to the DSD variability, followed by S band, but there is practically no correlation between A and KDP at Ka band because KDP is poorly correlated with rain rate. Commercial microwave radio links that form cellular communication networks often operate at Ku band, which makes attenuation estimates by these networks most valuable for estimation of the factor a. This study will demonstrate the great potential of current microwave backhaul links operated at Ku band for optimizing the performance of attenuation correction algorithms and eventually QPE. Section 2 elaborates on the variability of radar rainfall relations, while section 3 introduces the reader to the variability of a and existing methods to address the issue. Section 4 describes the study region and the database. Section 5 explains the method applied to compare attenuation measurements of radar and microwave links, including the processing of radar-based differential phase shiftFDP and the received signal level (RSL) of microwave links. Results of the determination of a by means of radially oriented microwave links as well as the optimization of radar rainfall relations using arbitrary oriented links are presented in section 6, followed by a summary and conclusions in section 7. 2. Variability of radar rainfall relations at S, C, and X bands The range of QPE bias caused by DSD variability for various algorithms is estimated from simulations based on a large dataset of 47 144 DSDs obtained with a 2D video disdrometer during 7 years of continuous observations in central Oklahoma. In this dataset two extreme DSD categories associated with ''very continental'' and ''very tropical'' rain can be identified using the histogram of normalized raindrop concentrations Nw and mean DSDs (Fig. 1). The normalized raindrop concentration is determined as (Testud et al. 2001; Illingworth and Blackman 2002) ... (4) where LWC is the liquid water content and Dm is the mean volume diameter. Based on the histogram of log(Nw) for the whole Oklahoma DSD dataset (Fig. 1a, leftpanel), we classify the DSDs with log(Nw) < 2.7 (Nw is in m-3mm-1) as ''very continental'' rain, which is heavily affected by melting of graupel/hail, while DSDs with log(Nw) > 4.2 are conditionally attributed to ''very tropical'' rain formed via ''warm rain'' processes with little impact of graupel/hail. The 2.7 and 4.2 thresholds were visually determined from Fig. 1a to characterize the ''wings'' of the Nw distribution, so that the very tropical category represents 8.9% of the highest Nw and the very continental category represents 6.1% of the lowest Nw. Mean DSDs associated with both extreme classes are quite different (Fig. 1, right panel). It is not surprising that the DSDs for ''continental rain'' have much smaller slopes and intercepts than the DSDs for ''tropical'' rain (Fig. 1b, right panel), indicating the predominance of smaller drops in the latter case going along with a smaller amount of large drops compared to continental rain. This fundamental difference has very important implications for radar rainfall estimation. The sensitivity range of radar rainfall estimates to DSD variations can be estimated by comparing the resulting mean biases when applying them to the cases of very tropical and very continental rain. All rain rates and corresponding radar estimates for both categories are summed up individually (Sg and Sr, respectively); the ratio Sr/Sg is then used as a bias measure for all listed rainfall estimators separately for both categories. These ratios are shown in Table 3 for simulations at S, C, and X bands and temperature T = 20°C. Two R(Z) relations are included in the list of algorithms: the ''thunderstorm'' relation Z = 300R1.4 widely used for S-band Weather Surveillance Radar-1988 Doppler (WSR-88D) radars in the United States and the Marshall-Palmer relation Z = 200R1.6. The R(KDP) and R(A) relations have been optimized for the whole DSD dataset and are taken from Ryzhkov et al. (2014). All of these ''standard'' relations usually underestimate tropical and overestimate continental rain intensity. Overall, the R(Z) relations are-as expected-most sensitive to DSD variations (largest difference between the values in the two columns), while theR(A) relation at S band requires the smallest adjustment related to the DSD variability. This is not the case for the R(A) algorithmat C band, where it can overestimate very continental rain [even more than the R(KDP) algorithm]. We note, however, that the R(A) method yields less noisy estimates of light and moderate rain than the R(KDP) estimate, and does not involve degradation of radial resolution typical for R(KDP) (Ryzhkov et al. 2014). The gist of this section is that even the best polarimeric power-law radar relations require parameter adjustments- primarily the intercepts-to account for DSD variability related to precipitation type. Such adjustments might be possible by matching path-integrated attenuation estimated from the radar and from microwave links. Optimization could be implemented as follows: First, rain rate is estimated along the microwave link line of sight using the radar rainfall relation with a fixed (standard) intercept, for example, R(KDP)5a0Kb DP. Second, this rain rate is converted to specific attenuation at the frequency of the microwave link using an appropriate A(R) relation and integrated over the microwave link to obtain the estimate of path-integrated attenuation PIA(e) along the link line. Finally, the ratio between the measured [PIA(m)] and the estimated PIAs yields the ratio of the ''true'' intercept a and the standard intercept a0 [see section 5c(2)]. This assumes that the exponents in the rainfall relations are much less sensitive to DSD variability compared to the intercept. 3. Variability of a = A/KDP at S, C, and X bands As discussed in the introduction, the ratio a is required for the R(A) algorithms and even more for the attenuation correction of Z, especially at shorter wavelengths (C and X bands). Local disdrometer measurements may be used to estimate average climatological values. But this may not be sufficient in regions with a strong diversity of precipitation regimes; moreover, actual values may change dramatically even in a single storm. The dependencies of a on ZDR and temperature at C band are illustrated in Fig. 2 using simulations from the Oklahoma disdrometer dataset already introduced in section 2 and simulations from a large dataset of 65 556 DSDs collected in Bonn, Germany, for temperatures 0° and 30°C. The simulations for 0° and 30°C should indicate expected changes between winter and summertime, respectively, while the dependencies on ZDR should also represent the variability among different regimes like continental and tropical rain regimes). The DSDs of Bonn are collected with a Parsivel disdrometer in the time period August 2007-January 2010. For very tropical rain characterized by a very high concentration of small raindrops and a deficit of large raindrops (small ZDR andKDP, largeA), high values of a can be expected. Typical ranges of a at different radar wavelengths are shown in Table 1 and were discussed in section 1. Attenuation correction in the first approximation can be made using default or average values in the right column in Table 1. The averaged value (a) = 0.08 dB deg-1 at C band will also be used in later sections. There are three different approaches to address the variability of the factor a. One way to account for the variability of a is the self-consistent method with constraints (Bringi et al. 2001). The method aims at estimating optimal a valid for a whole ray. Once A(r) at each range is calculated according to the ZPHI algorithm, a ''calculated'' radial profile of differential propagation phase fcalDP can be determined as ... (5) where the parameter b is the exponent in the power-law relationship between specific attenuation A and reflectivity Z: A = aZb. The self-consistent method of Bringi et al. (2001) searches for optimal a by minimizing the difference ? between the calculated &cal DP and the measured FDP: ... (6) Gu et al. (2011) separates relative contributions of ''hot spots'' (HS; i.e., strong convective cells) and the rest of the storm to the path-integrated total and differential attenuation. The HS algorithm implies that ... (7) in the HS, whereas the ''background'' values a0 and b0 are constant outside hot spots for a given radar sweep. According to the hot-spot method, the radial profile of Ah is estimated by means of the ZPHI method but with PIA determined as ... (8) This means that two measured differential phase parameters, ?FDP(r0, rm) and ?FDP(HS), are used instead of one. Ryzhkov et al. (2014) suggest that at least at X band, the ratio a = A/KDP can be roughly estimated from the ratio ß = ADP/KDP, where ADP is specific differential attenuation. Parameter ß is easier to evaluate from the data than the parameter a if differential attenuation is sufficiently strong. In this case, ß=|?ZDR|/?FDP, where DZDR is the negative bias of ZDR caused by differential attenuation. The coefficient of proportionality ? between a and ß (ß = ?a) may vary with the DSD, but this dependence appears not be too strong at X band. An alternative approach to dealing with the variability of a exploits the measurements of path-integrated attenuation provided by microwave links and is introduced in this paper. The microwave links provide new opportunity for a optimization. If the link is radially (or nearly radially) oriented with respect to the radar, then one can estimate PIAr at the radar frequency fr from the PIAl measured by the microwave link at the microwave frequency flusing the Ar5f(Al) relation and compare it with a?fDP. Subsequently, the factor a can be calculated from the ratio of these two estimates of PIA [see section 5c(1)]. 4. Database and study region The access to simultaneous polarimetric radar and microlink observations is still restricted. Currently, the microwave link data are accessible only in the area of the Hohenpeissenberg research C-band German Weather Service radar. Thus, the study area (Fig. 3) is confined in proximity to Mount Hohenpeissenberg (968 m) in southern Germany, where the German Weather Service [Deutscher Wetterdienst (DWD)] operates a meteorological observatory and polarimetric C-band radar (antenna is at 1007m above sea level). The plan position indicator (PPI) scan at 0.58 elevation is available every 10 min. Our analyses are restricted to PPI scans at 0.58 elevation in order to exclude brightband contamination, which is more common at higher elevation angles. In the vicinity of the radar, two microwave links operated by Ericsson GmbH as part of a German cell phone network are accessible by Karlsruhe Institute of Technology (KIT) Campus Alpine. The link paths are nearly oriented along the radar beam. The 17.4-km microwave link south of the radar is oriented toward Murnau (680m above sea level) and operated at 15GHz and vertical polarization. The 10.2-km microwave link north of the radar is directed toward Weilheim (550m above sea level) and operated at 18.7GHz and vertical polarization. Both links measure the RSL every 3 s, and average values are recorded every minute with small dataloggers at the towers. For the comparison with the radar data, 10-min averages are used. However, for our case study the 1-min averages, and the 3- and 5-min averages, do not show significant differences in terms of correlation with the radar data. Because of the inherent noisiness of the propagation differential phase shiftmeasurements, it is recommended to exclude cases with small phase shifts along the link path. On the other hand, the dataset gets smaller if only intense rain events crossing two links of 10.2- and 17.4-km length on single days are considered. Therefore, only the observations with a 28 phase shiftalong the link have been included in the study, even though a higher threshold of about 48 appeared more appropriate for the Murnau link showing higher fluctuations compared to theWeilheim link (cf. Figs. 8 and 9). Rain cells crossing the link paths on 14, 19, 26, and 27 May 2011 were selected for analysis. The melting layer during these events was at an altitude of 3 km or higher according to the closest radiosounding in Munich- Oberschleissheim. However, nonmonotonic behavior has been occasionally observed in the radials of total differential phase shiftFDP, whichmay be explained by residual brightband contaminations or backscatter differential phase in rain, which is likely in strong convective cells. The use of the ZPHI method for estimating the propagation differential phase uDP mostly avoids these effects. Because of the observational scarcity, the focus of the paper is on the general principles of joint utilization of dual-polarization radars and microwave links and the theoretical analysis of uncertainties involved, whereas the observational data simply illustrate the viability of the idea, the correlation between radar and microwave link measurements, and its potential for QPE. 5. Method a. Polarimetric radar data processing Testud et al. (2000) suggested using PIA2 [see (3)] to derive the radial profile of specific attenuation at horizontal polarization Ah: ... (9) where ... (10) ... (11) ... (12) Term Za is the measured and possibly attenuated reflectivity at horizontal polarization, and b is the exponent of the power-law relation between specific attenuation and the unattenuated reflectivity: ... (13) The estimate of specific attenuation A in (9) depends on the value of a, since (3) is used as an external constraint. Once the radial profile A(r) for each azimuth is derived from the total differential phase shiftalong the entire ray, a calculated radial profile of differential propagation phase (fcal DP) can be determined as ... (14) The use of the ZPHI method is expected to be superior to conventional processing of applying a running average filter to the measured total differential phase FDP, especially if a significant component of the backscatter differential phase d in rain or brightband contaminations are present (e.g., Trömel et al. 2013). b. Processing of the microwave link measurements Minute averages of the RSL are recorded at the link receiver stations with a power resolution < 0.05 dB. The transmission power is constant; hence, a decreased RSL indicates attenuation along the path. If brightband contamination and snow can be excluded from this attenuation-in our cases, at vertical polarization-then Ay (dB) can be in principle related to a path-averaged rain rate R (mmh-1) via ... (15) where a and b are parameters, depending on frequency, DSD, and temperature; and Leffis the effective link length. In addition to hydrometeors, gaseous components (water vapor andmolecular oxygen) and fog (David et al. 2013) cause an offset with significant fluctuations of RSL depending on humidity and temperature (Ulaby et al. 1981). Furthermore, the accumulation of water or water drops on the microwave link antennas can cause additional wet antenna attenuation that may lead to an overestimation of the attenuation caused by the precipitation along the link path (e.g., Overeem et al. 2011; Schleiss et al. 2013). The fluctuation of atmospheric gases, especially water vapor, together with other known parameters (temperature, pressure) and unknown parameters (ducting, microwave link hardware drifts, etc.), complicates the identification of rain events in microwave link RSL data. Thus, the baseline level (the zero attenuation RSL) has to be adjusted for every rain event when calculating the rain-induced attenuation component. An identification of wet (rain) and dry (no rain) periods is hence necessary. This is accomplished in two ways, by using the short-term Fourier transform wet/dry classification approach from Chwala et al. (2012), who used the same microwave link data as this work; and by using the radar as a wet/dry classifier. Following Chwala et al. (2012), a sliding Fourier transform window of length 256 is used to identify wet periods on the basis of increased amplitudes in the low-frequency regime of the resulting spectra. For the estimation of attenuation caused by precipitation, the baseline level is kept constant during a rain event, at the RSL of the last dry minute before the event. The Fourier-based approach is especially useful when no other information is available, as is the case, for example, in mountain areas or in developing countries. In our case we could, however, use the radar as a wet/dry indicator. If a threshold of 0.1mmh-1 is exceeded in at least one radar pixel along the link, then a wet period is assumed. In general, the latter procedure should yield more accurate onset and end times for the rain events. In our case study, however, the resulting differences are small and reach 0.32 dB maximum. Consequently, only results using the radar as a wet/dry classifier are presented in section 6. The effect of wet antenna on the microwave links is also not considered here. Visual inspection of the RSL time series (not shown) suggests a wet antenna attenuation <1 dB, with varying magnitude for different rain events. However, the uncertainties introduced by the radar data because of brightband contaminations encountered at the mountain station exceed 1 dB. In the scope of this work, the uncertainty introduced by estimating and removing the wet antenna attenuation is hence not worth the expected gain in performance. c. Comparison of path-integrated attenuation from microwave link and radar 1) RADIALLY ORIENTED MICROWAVE LINKS The one-way path-integrated attenuation of the C-band signal along the link with radial orientation with respect to the radar is equal to (3): ... (16) where Ah (C) is specific attenuation at horizontal polarization, a is the net ratio Ah/KDP over the interval (r1, r2), and ?fDP is the total differential phase shiftalong the link path. The one-way path-integrated attenuation measured by the Weilheim link operated at 18.7GHz and vertical polarization is ... (17) The values of Ah (C) and Ay (18.7 GHz) can be expressed as functions of rain rate with coefficients depending on temperature. For C band at T = 20°C, the simulations based on the Oklahoma disdrometer measurements yield ... (18) For Ku band at 18.7 GHz, the simulations provide ... (19) Note that the International Telecommunication Union Radiocommunication Assembly (ITU 2003) recommends the relation Ay(18.7 GHz)=0.0591R1.0777. To compare (16) and (17), one has to include a conversion factor f : ... (20) where ... (21) according to (18) and (19). Since our analyses cover path-integrated 10-min rain-rate averages ranging from 3.1 to 34mmh-1, f ranges between 34.74 and 32.02. For C band with default value <a>=0.08 dB deg-1, we expect ... (22) and ... (23) If we neglect the weak dependence of f on rain rate, the factor a can be estimated using (20) as ... (24) where <f18.7GHz> = 32.13. The relation between specific attenuation at 15GHz (Murnau link) and R according to simulations is ... (25) Again, this is close to the relation recommended by ITU: Ay(15 GHz)=0.0335R1.128. Because the exponents of the A(R) relations (18) and (25) are almost equal, the ratio <f15GHz> = Ay(15GHz)/ Ah (C) is approximately equal to 18.7. Therefore, we can write ... (26) using again <a> = 0.08 dB deg-1. Similar to (24) a can be estimated via ... (27) The accuracy of the ... estimates from (24) or (27) is determined by the uncertainty in <f>. To determine the accuracy achievable for ... estimated via microwave links, large disdrometer datasets have been investigated. Fig. 4 illustrates the scatterplot of Ay(18.7 GHz) versus Ah(C), both derived from the Bonn disdrometer dataset (left) and the Oklahoma disdrometer dataset (right) at T = 20°C. The simulations show that the mean ratios f are very similar in both climate regions. It can be concluded from both scatterplots in Fig. 4 that the fractional standard deviation of f is about 30%. Figure 5 shows similar scatterplots of Ay (15 GHz) versus Ah(C), derived from the Bonn disdrometer dataset (left) and the Oklahoma disdrometer dataset (right) at T = 208C. Again, the slopes of the A(Ku) - A(C) dependencies are very similar, and the fractional standard deviation of the ratio A(Ku)/A(C) varies between 20% and 30%. 2) ARBITRARILY ORIENTED MICROWAVE LINKS Arbitrary link orientations cannot be used for a estimation, which requires radially oriented links, but they can be exploited to optimize rainfall relations. According to this methodology, the radar-based rain rates along the link are first estimated using existing rainfall relations R(Z), R(KDP), or R(A). In this study we will focus on the R(A) relation. Ryzhkov et al. (2014) found that the relation ... (28) is optimal for the large DSD dataset in Oklahoma. Specific attenuation Ah is estimated with the ZPHI method (section 5a). In a second step, these first-guess rain rates along the link path are transformed to the values of specific attenuation at the microlink frequencies A(18.7GHzequiv) or A(15GHzequiv), using (19) and (25). In a third step, specific attenuation is integrated along the link path to obtain PIA1 (e)(18.7GHZ) and PIA1 (e)(15GHz), respectively. The estimated PIA1 (e) values at Ku band are then compared to PIA1 (m)(18.7GHz) or PIA1 (m)(15GHz) directly measured by the microwave link. Finally, the optimal intercept b in the radar rainfall power-law relation is determined as ... (29) The underlying assumption is that the exponents in the rainfall relations [R(KDP), R(A), or others] are much less sensitive to the variability of DSD than the intercepts. The accuracy of b estimated from (29) is determined by the accuracy of the A(R) estimate at Ku band, which is about 25% (see Table 2). 6. Results We start with the comparisons of the radar and microwave link data for the Murnau link, which is very well aligned with the radar azimuthal direction 1298. The scatterplot of path-integrated attenuation directly measured by the Murnau link operating at 15GHz versus the differential phase shiftalong the link path measured by the C-band dual-polarization radar shows good consistency between ?fDP and PIA1(Ku), particularly for ?fDP . 68 (Fig. 6). The apparent lack of correlation for lower values of ?fDP can be attributed to uncertainties in differential phase and PIA1 estimates for lighter rain. The slope of the ?fDP - PIA1(Ku) dependence agrees quite well with what is expected from (26) for a = 0.08 dB deg-1. As already mentioned in section 4, choosing a higher ?fDP threshold of about 48 would be more appropriate in order to obtain more reliable phase shifts for which better correlation is anticipated between ?fDP and PIA1(Ku). A similar ?fDP - PIA1(Ku) comparison for the Weilheim link operating at 18.7GHz shows less correspondence between both measurements, which is not surprising because the Weilheim link is not very well aligned with the radar radials (Fig. 7). The size of the dataset containing simultaneous radar and microwave link measurements in our study is not large enough to thoroughly assess the accuracy of the factor a estimation, but the results in Fig. 6 show that the optimal a and the default a=0.08 dB deg-1 do not differ by more than 20% for ?fDP exceeding 68, which is within the accuracy limits claimed for the method. In other words, the measurements with ?fDP . 68 show that the default value of a can be used for rain events on 14, 19, and 26 May (at least in the area containing the Murnau link). According to the concept explained in section 5c(2), microwave links with arbitrary orientation can be utilized for optimizing the intercept in the R(A) relation, provided that the factor a is already optimized using measurements at radar radial-oriented links. Both, the Murnau and Weilheim links were used for comparing the directly measured path-integrated attenuation PIA1 (m) and its estimate from the polarimetric radar PIA1 (e), assuming the default intercept value b0 = 294 in the R(A) relation. The optimal intercept in the R(A) relation can then be estimated using the ratio of the two PIAs. The scatterplot of PIA1 (m) versus its estimate from the radar PIA1 (e) for the Weilheim link is displayed in Fig. 8. The overall correlation between the two is quite good. However, for the majority of points, PIA1 (e) . PIA1 (m) and according to (29) b < b0. The average value of b for all available measurements is 259, which is 12% lower than the default intercept. Note that this is still within the accuracy limit of the suggested method (25%). The scatterplot of PIA1 (m) versus PIA1 (e) for the Murnau link shown in Fig. 9 also indicates that PIA1 (e) . PIA1 (m) and b < b0, which is consistent with the results from the Weilheim link. Summarizing we can conclude that the comparison of the observations performed by the C-band polarimetric radar and the two microwave links demonstrates that the default version of the R(A) method with the factor a = 0.08 dB deg-1 and the intercept 294 suggested by Ryzhkov et al. (2014) can be utilized for rainfall estimation in southern Germany in the proximity of the radar for the selected rain events. Note that in the recent study of Wang et al. (2014), the performance of the default version of the R(A) algorithm at C band was examined for tropical rain observed in Taiwan including two typhoon events. It was shown that the R(A) algorithm with a = 0.09 dB deg-1 and ß = 359 works best in Taiwan according to comparison with gauges. The difference between the optimal intercepts in the Taiwan study and the current study (although very limited) is about 40%, which calls for an optimization of the parameters of the R(A) algorithm, and the use of microwave links is one possibility to do this. 7. Conclusions For the first time, attenuation measurements from commercial microwave links are directly compared to polarimetric radar observations with the goal to evaluate the potential of the microwave links for the improvement of radar-based QPE and attenuation correction of radar signals. Methods for polarimetric attenuation correction and a recently introduced algorithm for rainfall estimation based on specific attenuation require the knowledge of the ratio of two-way path-integrated attenuation and total differential phase shiftalong the propagation path ?fDP. Because the microwave links directly measure PIA (although at a different wavelength), they can be used to estimate PIA at the radar wavelength and to optimize the net ratio a = A/KDP, provided that the specific attenuations at the two wavelengths are closely correlated. For close-to-radar radial alignments of the microlink path, the one-way path-integrated attenuation PIA1 from the link can be directly compared with DfDP along the radial and used to estimate a. Simulations based on disdrometer measurements around Bonn, Germany, and Oklahoma show that a can be estimated with an accuracy of 20%-30% depending on microwave link frequency and the climatic regime. For less fortuitous orientations of the microlinks, the radar rainfall relations can still be improved, while a better estimate of a cannot be obtained. The basic idea is to first transform the rain rate along the microwave link path estimated with the radar to the microwave link equivalent attenuation PIA(e) and to determine the optimal intercept in the radar rainfall relation from the ratio of directly measured microwave link attenuation PIA(m) and PIA(e). Simulations based on disdrometer measurements show that the intercept of any rainfall relation can be optimized with an accuracy of about 25%. The performance of both methodologies has been tested with the polarimetric C-band radar mounted on Mount Hohenpeissenberg in southern Germany, and two microwave links from Ericsson GmbH operated at Ku band and vertical polarization. The observations of four rain events show a good overall correlation between path-integrated attenuationmeasured by the links and its estimate from the polarimetric radar. Although the analyzed dataset is relatively small, it is found that the optimal a and the default a = 0.08 dB deg21 at C band differ by not more than 20% for ?fDP exceeding 68, which is within the accuracy limits claimed for the method. The estimated intercept in the R(A) relation is somewhat smaller than its default value recommended by Ryzhkov et al. (2014) for rain of the continental type in the United States. The results of this study show good promise that microwave links are useful for the optimization of the performance of precipitation radars. The developed methods can also be applied to other data from commercial microwave links if they provide sufficient resolution of the RSL. An RSL quantization of 0.3 dB, which is, for example, provided by the widely used Ericsson MINI-LINK TN, would suffice. The complete benefit can be investigated and exploited with the ongoing expansion of polarimetric radars and access to a larger number of line-integrated attenuation measurements from commercial microwave link networks. Acknowledgments. The research of S. Trömel was carried out in the framework of theHans-Ertel-Centre for Weather Research (http://www.herz-tb1.uni-bonn.de/). This research network of universities, research institutes, and Deutscher Wetterdienst (DWD) is funded by the BMVBS (Federal Ministry of Transport, Building and Urban Development). We gratefully acknowledge the support of the German Weather Service, which provided the radar data forHohenpeissenberg.Alexander Ryzhkov was supported via funding from NOAA-University of Oklahoma Cooperative Agreement NA11OAR4320072 under the U.S. Department of Commerce and from the National Science Foundation (Grant AGS-1143948). 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Diederich, 2013: Backscatter differential phase-Estimation and variability. J. Appl. Meteor. Climatol., 52, 2529-2548, doi:10.1175/JAMC-D-13-0124.1. Ulaby, F. T., R. K. Moore, and A. K. Fung, 1981: Microwave Remote Sensing Fundamentals and Radiometry. Remote Sensing Series, Vol. 1, Artech House, 456 pp. Wang, Y., P. Zhang, A. Ryzhkov, J. Zhang, and P.-L. Chang, 2014: Utilization of specific attenuation for tropical rainfall estimation in complex terrain. J. Hydrometeor., doi:10.1175/ JHM-D-14-0003.1, in press. SILKE TRÖMEL Atmospheric Dynamics and Predictability Branch, Hans-Ertel-Centre for Weather Research, University of Bonn, Bonn, Germany MICHAEL ZIEGERT Meteorological Institute, University of Bonn, Bonn, Germany ALEXANDER V. RYZHKOV Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma CHRISTIAN CHWALA Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, Garmisch-Partenkirchen, Germany CLEMENS SIMMER Meteorological Institute, University of Bonn, Bonn, Germany (Manuscript received 14 January 2014, in final form 24 April 2014) Corresponding author address: Dr. Silke Trömel, University of Bonn, Auf dem Hügel 20, D-53121 Bonn, Germany. E-mail: [email protected] (c) 2014 American Meteorological Society |