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 and Blackwell (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 to microwave link measurements.

Variability ranges of the factor α (dB deg−1) in rain at S, C, and X bands.
The optimization of α 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 ΔΦDP.
DSD variability is the second major source of uncertainty in radar-based QPE with both single- and dual-polarization 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 α = 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 ΔΦDP) 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 α.
Stability of the R(A) estimate and the parameter α at different microwave frequency bands. FSE denotes the fractional standard deviation (i.e., the standard deviation divided by the mean value).
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 α 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 shift ΦDP and the received signal level (RSL) of microwave links. Results of the determination of α 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
(a) Histogram of log(Nw) and (b) mean DSDs for tropical rain with log(Nw) > 4.2 and for continental rain with log(Nw) < 2.7 retrieved from the large DSD dataset in Oklahoma. Normalized concentration Nw is expressed (m−3 mm−1).
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
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 (Σg and Σr, respectively); the ratio Σr/Σg 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.
Average bias ratios for different rainfall estimators and the very tropical and very continental rain types at S, C, and X bands at 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 the R(A) relation at S band requires the smallest adjustment related to the DSD variability. This is not the case for the R(A) algorithm at 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,
3. Variability of α = A/KDP at S, C, and X bands


Scatterplotts of α = Ah/KDP vs ZDR at C band based on disdrometer measurements in (left) Bonn and (right) Oklahoma at 0° (black dots) and 30°C (gray dots).
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
Ryzhkov et al. (2014) suggest that at least at X band, the ratio α = A/KDP can be roughly estimated from the ratio β = ADP/KDP, where ADP is specific differential attenuation. Parameter β is easier to evaluate from the data than the parameter α if differential attenuation is sufficiently strong. In this case, β = |ΔZDR|/ΔΦDP, where ΔZDR is the negative bias of ZDR caused by differential attenuation. The coefficient of proportionality γ between α and β (β = γα) 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 α exploits the measurements of path-integrated attenuation provided by microwave links and is introduced in this paper. The microwave links provide new opportunity for α 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 fl using the Ar = f(Al) relation and compare it with αΔφDP. Subsequently, the factor α 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 1007 m above sea level). The plan position indicator (PPI) scan at 0.5° elevation is available every 10 min. Our analyses are restricted to PPI scans at 0.5° 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 (680 m above sea level) and operated at 15 GHz and vertical polarization. The 10.2-km microwave link north of the radar is directed toward Weilheim (550 m above sea level) and operated at 18.7 GHz 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 shift measurements, 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 2° phase shift along the link have been included in the study, even though a higher threshold of about 4° appeared more appropriate for the Murnau link showing higher fluctuations compared to the Weilheim 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 shift ΦDP, which may 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
Location of the microwave links to Weilheim (top red line) and Murnau (bottom red line) together with the polarimetric C-band radar (blue dot) on top of Mt. Hohenpeissenberg in southern Germany.
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
5. Method
a. Polarimetric radar data processing


b. Processing of the microwave link measurements
c. Comparison of path-integrated attenuation from microwave link and radar
1) Radially oriented microwave links





Scatterplots of Aυ (18.7 GHz) vs Ah (C). Both quantities are derived from (left) the Bonn disdrometer dataset at T = 20°C and (right) the Oklahoma disdrometer dataset at T = 20°C.
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
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 Aυ (15 GHz) versus Ah(C), derived from the Bonn disdrometer dataset (left) and the Oklahoma disdrometer dataset (right) at T = 20°C. 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%.
Scatterplots of Aυ (15 GHz) vs Ah (C). Both quantities are derived from (left) the Bonn disdrometer dataset at T = 20°C and (right) the Oklahoma disdrometer dataset at T = 20°C.
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
2) Arbitrarily oriented microwave links
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 129°. The scatterplot of path-integrated attenuation directly measured by the Murnau link operating at 15 GHz versus the differential phase shift along the link path measured by the C-band dual-polarization radar shows good consistency between ΔφDP and PIA1(Ku), particularly for ΔφDP > 6° (Fig. 6). The apparent lack of correlation for lower values of ΔφDP can be attributed to uncertainties in differential phase and PIA1 estimates for lighter rain. The slope of the ΔφDP − PIA1(Ku) dependence agrees quite well with what is expected from (26) for α = 0.08 dB deg−1. As already mentioned in section 4, choosing a higher ΔφDP threshold of about 4° would be more appropriate in order to obtain more reliable phase shifts for which better correlation is anticipated between ΔφDP and PIA1(Ku).
Scatterplot of path-integrated attenuation measured by the Murnau link operating at 15 GHz vs differential phase shift ΔϕDP along the link path at azimuth 129° estimated by the C-band dual-polarization radar. The straight line indicates the expected relationship according to (26).
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
A similar ΔφDP − PIA1(Ku) comparison for the Weilheim link operating at 18.7 GHz 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 α estimation, but the results in Fig. 6 show that the optimal α and the default α = 0.08 dB deg−1 do not differ by more than 20% for ΔφDP exceeding 6°, which is within the accuracy limits claimed for the method. In other words, the measurements with ΔφDP > 6° show that the default value of α can be used for rain events on 14, 19, and 26 May (at least in the area containing the Murnau link).
Scatterplot of path-integrated attenuation measured by the Weilheim link operating at 18.7 GHz vs differential phase shift ΔϕDP along the link path at azimuth 67° estimated by the C-band dual-polarization radar. The straight line indicates the expected average slope of 1.34 according to (22) and (23).
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
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 α 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.
Scatterplot of one-way path-integrated attenuation measured by the Weilheim link vs the one-way path-integrated attenuation measured by the C-band radar.
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
Scatterplot of one-way path-integrated attenuation measured by the Murnau link vs the one-way path-integrated attenuation measured by the C-band radar.
Citation: Journal of Atmospheric and Oceanic Technology 31, 8; 10.1175/JTECH-D-14-00016.1
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 α = 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 α = 0.09 dB deg−1 and b = 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 shift along the propagation path ΔφDP. 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 α = 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 ΔϕDP along the radial and used to estimate α. Simulations based on disdrometer measurements around Bonn, Germany, and Oklahoma show that α 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 α 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 attenuation measured by the links and its estimate from the polarimetric radar. Although the analyzed dataset is relatively small, it is found that the optimal α and the default α = 0.08 dB deg−1 at C band differ by not more than 20% for ΔφDP exceeding 6°, 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 the Hans-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 for Hohenpeissenberg. 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). We also acknowledge partial support by the SFB TR32 (Transregional Collaborative Research Centre 32), funded by the DFG (German Research Foundation) for Michael Ziegert and cooperation with NOAA’s NSSL. The microwave link data were collected within the project “Regional Precipitation Observation by Cellular Network Microwave Attenuation and Application to Water Resources Management” (PROCEMA), funded by the Helmholtz Association of German Research Centers under Grant VH-VI-314.
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