Conventional weather radars transmit signals in the microwave frequency range that are backscattered towards the radar antenna when precipitation particles (also known as hydrometeors, including raindrops, snow, melting snow, hail, graupel) lie along the path of the radar beam. The signal backscattered by hydrometeors is related to the radar reflectivity Z that can be converted to an estimation of rainfall rate R using a power-law equation Z=aRb. Dual-polarisation weather radars measure the radar reflectivity at horizontal ZH and vertical ZV polarisations, and the ratio between both of them is known as the differential reflectivity ZDR. ZDR was proposed to improve radar rainfall estimation because raindrops are distorted into oblate spheroids as they fall to the ground . Small raindrops give ZDR values close to zero, whereas larger raindrops give ZDR>0. The differential reflectivity (ZDR) plays a crucial role in quantitative precipitation estimation (QPE) algorithms using polarimetric weather radars. Its relation with the orientation, shape and size of the hydrometeors improves not only the accuracy of radar QPE algorithms but also the classification of hydrometeors .

However, to incorporate ZDR as a valid input for radar QPE, it is necessary to ensure that it is properly calibrated. showed that an accuracy of 0.2 dB in the differential reflectivity calibration is desirable for practical applications of polarimetric weather radar data, as this value generates uncertainty in the rain estimates close to 18 %. However, several factors introduce a bias into ZDR, e.g. (a) the presence of cross-polar radiation ; (b) errors in the transmitter and the receiver chain (or both) , or (c) an overall system bias due to the ratio of power transmitted to the horizontal and vertical polarisations .

Several calibration procedures have been proposed to correct the overall system bias (or offset) in ZDR depending on the radar scanning strategy. For radars capable of performing measurements at a 90∘ elevation angle (herein referred to as birdbath scans), the most accepted calibration procedure is based on radar observations of raindrops as the antenna rotates about the vertical; non-zero values of ZDR present under these conditions can be set as the ZDR offset. This method was introduced by and has been further explored and validated on several radar campaigns; e.g.  used vertical profiles (VPs) generated from data collected by a weather radar located in Italy to estimate both the ZDR offset and the error in the radar reflectivity (ZH). They analysed the standard deviation of ZDR taken at vertical incident and concluded that the accuracy of this method is close to 0.1 dB. Similarly, estimated the ZDR offset using birdbath scans collected by a C-band radar, and their results demonstrated its impact on the absolute calibration of ZH; used polarimetric birdbath scans measured by a C-band radar located in Australia to validate a new approach for calibrating and monitoring ZH using ground clutter and satellite data. used data collected from the radar network operated by the German Meteorological Service to monitor the ZDR calibration. Their method relies on range-averaged values of ZDR collected in light rain and detected using thresholds on polarimetric variables like the co-polar correlation coefficient or the coherent power to target an accuracy of ZDR of around ±0.1 dB. More recently, expanded the birdbath method by estimating the offset based on interpolated ZDR values taken from rain, snow or ice regions, the main advantage of this method being its applicability when rain regions are not available to estimate the ZDR offset.

However, some weather radar networks are unable to perform birdbath scans due to mechanical constraints. So several procedures have been proposed to overcome this restriction and correct the ZDR offset. presented a method based on the ZDR values of dry snow collected at elevation angles between 40 and 60∘. They linked these values to the ZDR offset, achieving an accuracy of 0.2 dB. expanded this method for scans affected by the presence of partial beam blockage and explored its relation with the ZDR offset, stating that this method achieves an accuracy of 0.3 dB when applied to large data sets. proposed a method to quantify the ZDR offset by probing the differential reflectivity while increasing the elevation angle but remaining below the melting layer (ML). Then these data are compared with theoretical profiles of ZDR to estimate the ZDR offset. Although it is possible to achieve high accuracy by applying this method (∼0.1 dB), thousands of profiles are needed to generate profiles suitable for the comparison process.

Another well-known technique to calibrate ZDR relies on sun measurements. It is based on the detection of solar spike echoes as this type of radiation has equal power at both horizontal and vertical polarisations , hence generating measurements of ZDR close to 0 dB. The sun-radiation detection method has been further investigated in several works; e.g.  compared both the birdbath scans and sun-radiation detection methods using C-band polarimetric data, determining that higher accuracy is achieved when using the former. An online variation of the solar-radiation detection method that does not require the operational scanning strategy to be stopped was introduced by . It is based on other works conceived to monitor the absolute radar calibration, like the methods introduced by and . This online method enables monitoring the calibration of ZDR and also the analysis of the correlation between horizontal and vertical channels. Later, expanded this method based on data collected from the Finnish radar network, adding quality control to the solar signals and achieving accuracy of ZDR below 0.05 dB. also used the sun-radiation detection method and concluded that an accurate calibration depends on the availability of radar data taken at sunrise/sunset, among other considerations. It is worth noting that the offset detected by the solar method must be taken with care as it is related to the receiver chain only, whereas the offset computed from birdbath scans includes both the transmitter and the receiver chain .

Some other alternative techniques have been proposed to complement the operational calibration and monitoring of ZDR. estimated the ZDR offset using range–height–indicator (RHI) scans collected by a C-band polarimetric radar located in Japan. They probed ZDR in ice regions (i.e. at high altitudes) where values of 0 dB are expected and set the mean values of the observed data as the ZDR offset. proposed the use of turbulent eddies to monitor the differential reflectivity as the nature of such scatters results in values of ZDR close to 0 dB. Additionally, proposed the application of the quasi-vertical profile (QVP) approach to monitor the calibration of ZDR using a similar rationale to that in . This approach is explored by and , in which previously offset-corrected QVPs of ZDR are used to describe processes like the ML and ice aggregation/riming. Although the QVPs are a valuable tool for monitoring the temporal evolution of precipitation and the microphysics of precipitation, there is little research using QVPs in rain to estimate the ZDR offset. Most of the ZDR calibration methods described above (except for the method that relies on sun measurements) rely on higher-elevation scans. There is a need to develop alternative methods that can be used when only lower-elevation scans are available.

This study presents an operational method to correct the ZDR offset that can be implemented using QVPs of polarimetric variables. The method is based on QVPs generated from scans with elevation angles of 9∘ and collected during light rain. These scans are usually available in operational radar scanning strategies deployed in radar networks worldwide, thus becoming an excellent option for radar networks not capable of collecting measurements at vertical incidence. The C-band polarimetric weather radars developed by the UK Met Office (UKMO) can perform measurements at vertical incidence, allowing a thorough comparison of the performance of both methods. Additionally, we explore the temporal variation in the ZDR offset using long-term observations collected by two operational weather radars. The calibrated ZDR measurements are further compared with measurements from independent disdrometer observations located near the radar sites. The paper is organised as follows. In Sect. , we define the radar and disdrometer data sets used in this work. The two different methods used to calibrate the radar ZDR are described in Sect. . In Sect. , we examine the performance of the proposed method using long-term data sets collected by two weather radars and several disdrometers. We discuss the methods and results in Sect. . Finally, we summarise the findings of this work in Sect. .

We processed the radar data sets collected by two operational weather radars throughout 1 year of precipitation events to generate VPs and QVPs of polarimetric variables as described in Sect. . Then we applied both ZDR offset-correction methods to the generated VPs and QVPs to compare the results of the ZDR calibration.

We present a rain event recorded in southern England by the Chenies radar to exemplify the above-mentioned processes. In Fig. a, the left panel shows VPs (each one representing the mean value of 360 rays) of ZDR in a height-versus-time (HTI) plot related to a rain event. In contrast, the right panel shows a single VP taken from the same event. Note that the first kilometre of the VPs is contaminated with spurious echoes; hence all bins below this height were discarded from the analysis. The HTI plot shows that the values of ZDR deviate from 0 dB in the rain medium, i.e. below the bottom of the bright band (BBbottom); thus ZDR needs to be calibrated. The single VP plot enables an in-depth analysis of the profile characteristics. For example, it can be seen that ZDR values within the rain region (below 1.5 km in height) are close to -0.35 dB and also that its standard deviation (SD) remains relatively steady. But this changes in the ML, where the VP turns noisy and produces a higher standard deviation. However, dry aggregated snow signatures are visible above 2 km in height (at the top of the melting layer), where the ZDR values are similar to those observed for liquid precipitation (∼0.37 dB), confirming the reliability of dry snow in detecting the ZDR offset. These characteristics are consistent throughout the entire event.

On the other hand, Fig. b shows QVPs of ZDR values generated from data related to the event described above. It can be seen that there are clear signatures of the melting layer within the QVPs that are useful to classify the hydrometeors' phase. The single QVP plot shows that the standard deviation of the averaged values used to generate the QVP is smaller in the rain region (below 1.35 km) compared to the standard deviation observed within and above the ML. Moreover, the signatures of dry snow are not clearly visible, and the values observed for rain particles differ from those seen at the top of the ML, thus hampering using dry snow as the calibration target for our data sets. After applying the proposed method, the averaged value of ZDR in the rain region is -0.26 dB, which, along with the computed intrinsic value of ZDR (0.18 dB), results in an offset of -0.44 dB, which is close to the offset calculated using the VP method (-0.35 dB).

Figure c shows the temporal variation in the ZDR offset for both VP (ZDROVP) and QVP (ZDROQVP) methods. For this precipitation event, the differences between methods are around 0.1 dB. Still, it is worth mentioning that ZDROVP exhibits values that remain relatively constant during this event, whereas the values of ZDROQVP show greater variation and are not altogether far from ZDROVP. It is also important for this event that the number of valid VPs is larger than the number of QVPs classified as valid according to the proposed constraints described in the method. A discussion on the selection of the natural targets to detect the ZDR offset and the performance of the proposed method is provided in Sect. .

This work reviews the use of QVPs of polarimetric radar measurements to estimate and monitor the overall system bias (or offset) in the differential reflectivity. Although several sources of error affect this variable, we focused on detecting and correcting the overall system bias. It is important to calibrate ZDR measurements as this variable is a crucial input to hydrometeor classification methods , attenuation correction schemes or QPE algorithms . demonstrated that keeping the bias below ±0.2 dB generates accurate and reliable radar products.

Previous works have developed methods to compute the ZDR offset using different targets, like light rain , dry snow , ice , sun spikes or turbulent eddies . Most of these methods are based on measurements taken at high elevation angles that reduce the intrinsic variability in ZDR. However, mechanical restrictions may prevent some radars from scanning at such high elevation angles; therefore, we evaluate a new approach to compute and correct the offset in radar ZDR measurements based on QVPs of polarimetric variables built from PPI scans taken at lower elevation angles of around 9∘. The proposed method is an alternative method to calibrate ZDR measurements, but the traditional method based on VPs should be used instead if these vertical scans are available. As described in Sect. , we set light rain as the target to compute the ZDR offset, using QVPs mainly to reduce the variability in ZDR. Regarding the selection of this natural target, it is worth saying that we also explored the use of dry snow to derive the ZDR offset. Dry aggregated snow can be found 1 or 2 km above the melting layer in stratiform clouds . explored high-elevation-angle scans (∼ 40–60∘) and observed that dry aggregated snow yields distinctive polarimetric signatures, i.e. values of ZDR close to 0 dB, demonstrating that this target can be used to detect the ZDR offset. Consequently, we analysed hundreds of polarimetric profiles (both VPs and QVPs data sets) and found that such a signature of dry snow is only observable on the VPs in our data set. This effect can be seen in Fig. a, where similar values of ZDR can be seen on both light rain (below the melting layer bottom) and dry snow (above the melting layer top). Conversely, in the QVP data set (obtained at lower elevation angles of 9∘), we observed that values of ZDR in the rain medium were not consistent with those observed aloft, as shown in Fig. b. This lack of clear signatures of dry snow on QVPs is probably related to the beam broadening and non-uniform beam-filling effects, expected when the QVPs intercept the ML and regions above 9∘ elevations. As shown in the right panel of Fig. b, the standard deviation (blue area) increases within and above the ML due to the presence of mixed-phase particles, hence complicating the estimation of the ZDR offset using such meteorological targets. This is the reason why we could not use QVPs built from relatively low elevation angle scans (<10∘) and set dry snow as the target to derive the ZDR offset.

But using QVPs in light-rain events for detecting the ZDR offset also presents several risks. First, it is important that there is an inherent variability in ZDR in light rain. This is shown in Fig. a, where it can be seen that the variability in ZDR increases with larger values of ZH. Thus, we propose a constraint to reduce the variability in ZDR; i.e. 0<ZH<20. This range is a compromise to avoid having significant variations on ZDR but still keep enough QVPs related to light rain in the analysis and enable the reliable detection of the ZDR offset. In addition, the inherent averaging process in the QVP construction may wash out some key microphysical processes within the precipitation events. Thus, we proposed several constraints to minimise these effects. For example, we imposed a limit of 3 km in height within the QVPs to apply our method: as shown in Fig. b, the coverage of the PPI scans at a 9∘ elevation angle captures a mostly uniform volume in the rain region (below 2.5 km). For this elevation angle and a height of 3 km, the base diameter of the cone is around 37 km. Hence we consider that the azimuthal averaging procedure to generate the QVPs below this height reduces deviations in ZDR and enables proper monitoring of the calibration of this variable. Additionally, we define thresholds to discard values within QVPs not related to light rain; e.g. Fig. b shows a collection of QVPs related to a rain event. Most of the QVPs show a constant value of ZDR below the ML, whilst outlier values can be discarded by checking their corresponding values on the QVPs of ZH and ρHV (plots not shown). This figure also shows that the values of ZDR above the rain region are loosely correlated to the ZDR offset, hence hampering the use of meteorological targets like snow or ice. It is clear that dry snow has lower natural ZDR variability compared to light rain when using high tilts (40–60∘). However, this variability increases at lower elevations, and the QVPs are affected by this issue. This is why we restricted the height within the QVPs along with thresholds in ρHV in an effort to keep the variability at a minimum.

It is worth mentioning that setting the boundaries of the melting layer correctly within the QVPs is a critical step towards detecting reliable values of the ZDR offset, as this enables the identification of echoes related to liquid precipitation. , , and demonstrated that heights of the ML top and bottom could be accurately estimated using QVPs. We consider that QVPs without ML signatures are filtered by this requirement, thus reducing the uncertainty of using QVPs of polarimetric variables that do not depict light stratiform rain.

To validate the proposed approach, we implemented an operational procedure to detect the ZDR offset using light-rain measurements taken at vertical incidence. This method was proposed initially by , and it is a boilerplate practice that has been tested on several radar campaigns and has confirmed its reliability by keeping the ZDR offset below 0.2 dB . Figures  and show the good agreement between both methods: the proposed method based on QVPs shows maximum differences of 0.1 dB compared to the method based on VPs. A few data points exhibit larger variation, but this is mainly caused by vague polarimetric signatures of the ML (no peaks within the polarimetric profiles, especially on those generated from ρHV measurements), misleading the ML detection algorithm and, thus, the classification of the particles in the liquid phase. The good performance of the method based on QVPs is also confirmed in Fig. , where we evaluated data classified by the disdrometers as related to light to moderate rain rates, and the differences between both ZDR calibration methods remain around 0.1 dB.

Figures – show a comparison between radar and disdrometer data. It is important to keep in mind that there is some uncertainty in the interpretation of these results, such as (i) the spatial distribution of radar measurements and the well-known discrepancy when comparing it to a fixed-point location, (ii) the impact of the signal attenuation in ZH and ZDR, (iii) the distance between the radars and the disdrometers, (iv) the use of PPI scans collected at higher elevation containing issues related to beam blockage or clutter contamination, and (v) the different temporal resolution of each device. However, the errors (MAE and RMSE) between ZDR measured by the radar and ZDR derived from disdrometers are below 0.4 dB in all cases, which is acceptable considering the factors mentioned above but also that this analysis includes 1 year of data related to precipitation events. Furthermore, we compared the disdrometer-derived ZDR measurements with radar ZDR measurements but without applying the offset correction procedure, and we observed bigger discrepancies between data sets, reaching differences of the order of 1 dB (plots not shown).

Finally, the case studies shown in Figs.  and confirm the good performance of the proposed method to correct the ZDR offset. These events, related to moderate to intense rain events, exhibit differences below ±0.2 dB. These results are in good agreement with the required accuracy established by to generate reliable quantitative precipitation estimates using polarimetric weather radar data.

In this work, we have evaluated different methods for monitoring the calibration of the radar differential reflectivity (ZDR). We explored the use of vertical profiles to calibrate the radar differential reflectivity. Light rain or dry snow are excellent targets to detect the ZDR offset, and we consider that these methods must be used when possible. However, some radar systems cannot perform scans at such high elevation angles. Thus, we proposed a novel, operational method to calibrate ZDR using QVPs of polarimetric variables built from low-elevation scans. This method has the main advantage of not depending on scans taken at vertical incidence or high elevation angles. However, it relies on detecting QVPs depicting stratiform light-rain events (common in the UK), but it may not be suitable for places where heavy-rain events are recurrent. Moreover, we are not suggesting that our approach should replace the well-known ZDR calibration method based on birdbath scans.

In addition, we carried out several trials using other meteorological targets like dry snow, but the results were inconclusive. Targeting areas above the melting layer exacerbate the beam broadening and non-uniform beam-filling problems as the range increases. These circumstances complicate using dry snow or other solid-phase targets to detect the ZDR offset on QVPs built from relatively low elevation scans. Thus, we selected the use of light rain, but we proposed several constraints to minimise the variability in ZDR in this media. Future work may implement a previous hydrometeor classification on the QVPs to improve this method. The proposed method is based on a reference ZDR value expected at ground level derived from a wide range of DSDs using a range of parameters expected in real storm events. This value (0.18 dB) was computed using constraints related to light rain using ZH. Additionally, we compared this theoretical ZDR value to real data derived from disdrometer observations, observing consistency between data.

We applied both methods to precipitation events collected by two C-band weather radars for the whole year of 2018. The proposed method to detect the offset in ZDR using QVPs was compared against the true offset computed from VPs. We observed a good agreement between both methods, as the MAE and the RMSE are within ±0.1 dB. However, we are aware that this is a relative evaluation; thus, we also implemented evaluation methods using disdrometer measurements. We compared radar ZDR measurements with ZDR measurements derived from disdrometer observations, obtaining a good agreement between the various data sets. This long-term evaluation of our method includes different types of precipitation events, ranging from light to heavy rain. We consider that this evaluation process demonstrates the efficacy of the proposed constraints to filter unsuitable QVPs. The proposed method using QVPs generated from PPIs proved to be effective for calibrating and monitoring the radar differential reflectivity as our results are close to those produced by the traditional method that uses birdbath scans.